id	sid	tid	token	lemma	pos
ejde-887	1	1	third	third	ADJ
ejde-887	1	2	international	international	ADJ
ejde-887	1	3	conference	conference	NOUN
ejde-887	1	4	on	on	ADP
ejde-887	1	5	applications	application	NOUN
ejde-887	1	6	of	of	ADP
ejde-887	1	7	mathematics	mathematic	NOUN
ejde-887	1	8	to	to	ADP
ejde-887	1	9	nonlinear	nonlinear	ADJ
ejde-887	1	10	sciences	science	NOUN
ejde-887	1	11	,	,	PUNCT
ejde-887	1	12	electronic	electronic	ADJ
ejde-887	1	13	journal	journal	NOUN
ejde-887	1	14	of	of	ADP
ejde-887	1	15	differential	differential	ADJ
ejde-887	1	16	equations	equation	NOUN
ejde-887	1	17	,	,	PUNCT
ejde-887	1	18	conference	conference	NOUN
ejde-887	1	19	27	27	NUM
ejde-887	1	20	(	(	PUNCT
ejde-887	1	21	2024	2024	NUM
ejde-887	1	22	)	)	PUNCT
ejde-887	1	23	,	,	PUNCT
ejde-887	1	24	pp	pp	ADJ
ejde-887	1	25	.	.	PUNCT
ejde-887	2	1	27–47	27–47	NUM
ejde-887	2	2	.	.	PUNCT
ejde-887	3	1	issn	issn	PROPN
ejde-887	3	2	:	:	PUNCT
ejde-887	3	3	1072	1072	NUM
ejde-887	3	4	-	-	SYM
ejde-887	3	5	6691	6691	NUM
ejde-887	3	6	.	.	PUNCT
ejde-887	4	1	url	url	PROPN
ejde-887	4	2	:	:	PUNCT
ejde-887	4	3	https://ejde.math.txstate.edu	https://ejde.math.txstate.edu	PROPN
ejde-887	4	4	,	,	PUNCT
ejde-887	4	5	https://ejde.math.unt.edu	https://ejde.math.unt.edu	PROPN
ejde-887	4	6	doi	doi	PROPN
ejde-887	4	7	:	:	PUNCT
ejde-887	4	8	10.58997	10.58997	NUM
ejde-887	4	9	/	/	SYM
ejde-887	4	10	ejde.conf.27.l1	ejde.conf.27.l1	PROPN
ejde-887	4	11	nonlinear	nonlinear	ADJ
ejde-887	4	12	non	non	ADJ
ejde-887	4	13	-	-	ADJ
ejde-887	4	14	autonomous	autonomous	ADJ
ejde-887	4	15	boussinesq	boussinesq	ADJ
ejde-887	4	16	equations	equation	NOUN
ejde-887	4	17	andrei	andrei	PROPN
ejde-887	4	18	ludu	ludu	PROPN
ejde-887	4	19	,	,	PUNCT
ejde-887	4	20	harihar	harihar	ADJ
ejde-887	4	21	khanal	khanal	NOUN
ejde-887	4	22	,	,	PUNCT
ejde-887	4	23	adrian	adrian	PROPN
ejde-887	4	24	stefan	stefan	PROPN
ejde-887	4	25	carstea	carstea	PROPN
ejde-887	4	26	abstract	abstract	PROPN
ejde-887	4	27	.	.	PUNCT
ejde-887	5	1	we	we	PRON
ejde-887	5	2	study	study	VERB
ejde-887	5	3	solitary	solitary	ADJ
ejde-887	5	4	wave	wave	NOUN
ejde-887	5	5	solutions	solution	NOUN
ejde-887	5	6	for	for	ADP
ejde-887	5	7	a	a	DET
ejde-887	5	8	nonlinear	nonlinear	ADJ
ejde-887	5	9	and	and	CCONJ
ejde-887	5	10	non	non	ADJ
ejde-887	5	11	-	-	ADJ
ejde-887	5	12	autonomous	autonomous	ADJ
ejde-887	5	13	boussinesq	boussinesq	ADJ
ejde-887	5	14	system	system	NOUN
ejde-887	5	15	with	with	ADP
ejde-887	5	16	initial	initial	ADJ
ejde-887	5	17	conditions	condition	NOUN
ejde-887	5	18	.	.	PUNCT
ejde-887	6	1	since	since	SCONJ
ejde-887	6	2	the	the	DET
ejde-887	6	3	variable	variable	ADJ
ejde-887	6	4	coefficients	coefficient	NOUN
ejde-887	6	5	introduce	introduce	VERB
ejde-887	6	6	distortions	distortion	NOUN
ejde-887	6	7	and	and	CCONJ
ejde-887	6	8	modulations	modulation	NOUN
ejde-887	6	9	of	of	ADP
ejde-887	6	10	the	the	DET
ejde-887	6	11	solution	solution	NOUN
ejde-887	6	12	amplitudes	amplitude	NOUN
ejde-887	6	13	,	,	PUNCT
ejde-887	6	14	we	we	PRON
ejde-887	6	15	implement	implement	VERB
ejde-887	6	16	a	a	DET
ejde-887	6	17	multiple	multiple	ADJ
ejde-887	6	18	-	-	PUNCT
ejde-887	6	19	scale	scale	NOUN
ejde-887	6	20	approach	approach	NOUN
ejde-887	6	21	combining	combine	VERB
ejde-887	6	22	various	various	ADJ
ejde-887	6	23	modes	mode	NOUN
ejde-887	6	24	in	in	ADP
ejde-887	6	25	order	order	NOUN
ejde-887	6	26	to	to	PART
ejde-887	6	27	capture	capture	VERB
ejde-887	6	28	the	the	DET
ejde-887	6	29	coupling	coupling	NOUN
ejde-887	6	30	between	between	ADP
ejde-887	6	31	the	the	DET
ejde-887	6	32	nonlinear	nonlinear	ADJ
ejde-887	6	33	evolution	evolution	NOUN
ejde-887	6	34	and	and	CCONJ
ejde-887	6	35	the	the	DET
ejde-887	6	36	effect	effect	NOUN
ejde-887	6	37	of	of	ADP
ejde-887	6	38	the	the	DET
ejde-887	6	39	variable	variable	ADJ
ejde-887	6	40	coefficient	coefficient	NOUN
ejde-887	6	41	.	.	PUNCT
ejde-887	7	1	the	the	DET
ejde-887	7	2	differential	differential	ADJ
ejde-887	7	3	system	system	NOUN
ejde-887	7	4	is	be	AUX
ejde-887	7	5	mapped	map	VERB
ejde-887	7	6	into	into	ADP
ejde-887	7	7	a	a	DET
ejde-887	7	8	solvable	solvable	ADJ
ejde-887	7	9	system	system	NOUN
ejde-887	7	10	of	of	ADP
ejde-887	7	11	nonlinear	nonlinear	ADJ
ejde-887	7	12	and	and	CCONJ
ejde-887	7	13	nonautonomous	nonautonomous	ADJ
ejde-887	7	14	ode	ode	PROPN
ejde-887	7	15	which	which	PRON
ejde-887	7	16	is	be	AUX
ejde-887	7	17	integrable	integrable	ADJ
ejde-887	7	18	by	by	ADP
ejde-887	7	19	recursion	recursion	NOUN
ejde-887	7	20	procedures	procedure	NOUN
ejde-887	7	21	.	.	PUNCT
ejde-887	8	1	we	we	PRON
ejde-887	8	2	show	show	VERB
ejde-887	8	3	that	that	SCONJ
ejde-887	8	4	even	even	ADV
ejde-887	8	5	in	in	ADP
ejde-887	8	6	the	the	DET
ejde-887	8	7	limiting	limit	VERB
ejde-887	8	8	autonomous	autonomous	ADJ
ejde-887	8	9	case	case	NOUN
ejde-887	8	10	,	,	PUNCT
ejde-887	8	11	the	the	DET
ejde-887	8	12	multiple	multiple	ADJ
ejde-887	8	13	-	-	PUNCT
ejde-887	8	14	scale	scale	NOUN
ejde-887	8	15	approach	approach	NOUN
ejde-887	8	16	gives	give	VERB
ejde-887	8	17	a	a	DET
ejde-887	8	18	new	new	ADJ
ejde-887	8	19	possibly	possibly	ADV
ejde-887	8	20	integrable	integrable	ADJ
ejde-887	8	21	dispersionless	dispersionless	NOUN
ejde-887	8	22	coupled	couple	VERB
ejde-887	8	23	envelope	envelope	NOUN
ejde-887	8	24	system	system	NOUN
ejde-887	8	25	,	,	PUNCT
ejde-887	8	26	which	which	PRON
ejde-887	8	27	deserves	deserve	VERB
ejde-887	8	28	further	further	ADJ
ejde-887	8	29	study	study	NOUN
ejde-887	8	30	.	.	PUNCT
ejde-887	9	1	we	we	PRON
ejde-887	9	2	validate	validate	VERB
ejde-887	9	3	our	our	PRON
ejde-887	9	4	theoretical	theoretical	ADJ
ejde-887	9	5	results	result	NOUN
ejde-887	9	6	with	with	ADP
ejde-887	9	7	numerical	numerical	ADJ
ejde-887	9	8	simulations	simulation	NOUN
ejde-887	9	9	,	,	PUNCT
ejde-887	9	10	and	and	CCONJ
ejde-887	9	11	we	we	PRON
ejde-887	9	12	study	study	VERB
ejde-887	9	13	their	their	PRON
ejde-887	9	14	stability	stability	NOUN
ejde-887	9	15	.	.	PUNCT
ejde-887	10	1	1	1	X
ejde-887	10	2	.	.	X
ejde-887	10	3	introduction	introduction	NOUN
ejde-887	10	4	there	there	PRON
ejde-887	10	5	is	be	VERB
ejde-887	10	6	a	a	DET
ejde-887	10	7	high	high	ADJ
ejde-887	10	8	and	and	CCONJ
ejde-887	10	9	sustained	sustained	ADJ
ejde-887	10	10	interest	interest	NOUN
ejde-887	10	11	for	for	ADP
ejde-887	10	12	the	the	DET
ejde-887	10	13	scientists	scientist	NOUN
ejde-887	10	14	and	and	CCONJ
ejde-887	10	15	engineers	engineer	NOUN
ejde-887	10	16	to	to	PART
ejde-887	10	17	study	study	VERB
ejde-887	10	18	and	and	CCONJ
ejde-887	10	19	understand	understand	VERB
ejde-887	10	20	the	the	DET
ejde-887	10	21	nonlinear	nonlinear	ADJ
ejde-887	10	22	waves	wave	NOUN
ejde-887	10	23	and	and	CCONJ
ejde-887	10	24	soliton	soliton	NOUN
ejde-887	10	25	propagation	propagation	NOUN
ejde-887	10	26	under	under	ADP
ejde-887	10	27	variable	variable	ADJ
ejde-887	10	28	conditions	condition	NOUN
ejde-887	10	29	which	which	PRON
ejde-887	10	30	occur	occur	VERB
ejde-887	10	31	in	in	ADP
ejde-887	10	32	real	real	ADJ
ejde-887	10	33	coastal	coastal	ADJ
ejde-887	10	34	and	and	CCONJ
ejde-887	10	35	oceanographic	oceanographic	ADJ
ejde-887	10	36	applications	application	NOUN
ejde-887	10	37	[	[	X
ejde-887	10	38	9	9	NUM
ejde-887	10	39	,	,	PUNCT
ejde-887	10	40	13	13	NUM
ejde-887	10	41	,	,	PUNCT
ejde-887	10	42	18	18	NUM
ejde-887	10	43	,	,	PUNCT
ejde-887	10	44	34	34	NUM
ejde-887	10	45	]	]	PUNCT
ejde-887	10	46	.	.	PUNCT
ejde-887	11	1	the	the	DET
ejde-887	11	2	mathematical	mathematical	ADJ
ejde-887	11	3	modeling	modeling	NOUN
ejde-887	11	4	of	of	ADP
ejde-887	11	5	such	such	ADJ
ejde-887	11	6	systems	system	NOUN
ejde-887	11	7	,	,	PUNCT
ejde-887	11	8	even	even	ADV
ejde-887	11	9	in	in	ADP
ejde-887	11	10	the	the	DET
ejde-887	11	11	two	two	NUM
ejde-887	11	12	-	-	PUNCT
ejde-887	11	13	dimensional	dimensional	ADJ
ejde-887	11	14	case	case	NOUN
ejde-887	11	15	,	,	PUNCT
ejde-887	11	16	is	be	AUX
ejde-887	11	17	inherently	inherently	ADV
ejde-887	11	18	difficult	difficult	ADJ
ejde-887	11	19	because	because	SCONJ
ejde-887	11	20	it	it	PRON
ejde-887	11	21	combines	combine	VERB
ejde-887	11	22	the	the	DET
ejde-887	11	23	complexity	complexity	NOUN
ejde-887	11	24	of	of	ADP
ejde-887	11	25	solving	solve	VERB
ejde-887	11	26	nonlinear	nonlinear	ADJ
ejde-887	11	27	and	and	CCONJ
ejde-887	11	28	non	non	ADJ
ejde-887	11	29	-	-	ADJ
ejde-887	11	30	autonomous	autonomous	ADJ
ejde-887	11	31	equations	equation	NOUN
ejde-887	11	32	.	.	PUNCT
ejde-887	12	1	to	to	ADP
ejde-887	12	2	our	our	PRON
ejde-887	12	3	knowledge	knowledge	NOUN
ejde-887	12	4	there	there	PRON
ejde-887	12	5	are	be	VERB
ejde-887	12	6	no	no	DET
ejde-887	12	7	exact	exact	ADJ
ejde-887	12	8	results	result	NOUN
ejde-887	12	9	providing	provide	VERB
ejde-887	12	10	integrability	integrability	NOUN
ejde-887	12	11	and	and	CCONJ
ejde-887	12	12	constructing	construct	VERB
ejde-887	12	13	solitons	soliton	NOUN
ejde-887	12	14	or	or	CCONJ
ejde-887	12	15	other	other	ADJ
ejde-887	12	16	nonlinear	nonlinear	ADJ
ejde-887	12	17	waves	wave	NOUN
ejde-887	12	18	for	for	ADP
ejde-887	12	19	such	such	ADJ
ejde-887	12	20	equations	equation	NOUN
ejde-887	12	21	with	with	ADP
ejde-887	12	22	coefficients	coefficient	NOUN
ejde-887	12	23	depending	depend	VERB
ejde-887	12	24	on	on	ADP
ejde-887	12	25	space	space	NOUN
ejde-887	12	26	.	.	PUNCT
ejde-887	13	1	in	in	ADP
ejde-887	13	2	consequence	consequence	NOUN
ejde-887	13	3	,	,	PUNCT
ejde-887	13	4	there	there	PRON
ejde-887	13	5	is	be	VERB
ejde-887	13	6	a	a	DET
ejde-887	13	7	large	large	ADJ
ejde-887	13	8	amount	amount	NOUN
ejde-887	13	9	of	of	ADP
ejde-887	13	10	approximate	approximate	ADJ
ejde-887	13	11	theories	theory	NOUN
ejde-887	13	12	developed	develop	VERB
ejde-887	13	13	by	by	ADP
ejde-887	13	14	using	use	VERB
ejde-887	13	15	various	various	ADJ
ejde-887	13	16	techniques	technique	NOUN
ejde-887	13	17	and	and	CCONJ
ejde-887	13	18	making	make	VERB
ejde-887	13	19	various	various	ADJ
ejde-887	13	20	hypotheses	hypothesis	NOUN
ejde-887	13	21	,	,	PUNCT
ejde-887	13	22	such	such	ADJ
ejde-887	13	23	as	as	ADP
ejde-887	13	24	linearization	linearization	NOUN
ejde-887	13	25	,	,	PUNCT
ejde-887	13	26	slowly	slowly	ADV
ejde-887	13	27	varying	vary	VERB
ejde-887	13	28	waves	wave	NOUN
ejde-887	13	29	,	,	PUNCT
ejde-887	13	30	as	as	ADV
ejde-887	13	31	well	well	ADV
ejde-887	13	32	as	as	ADP
ejde-887	13	33	numerical	numerical	ADJ
ejde-887	13	34	,	,	PUNCT
ejde-887	13	35	or	or	CCONJ
ejde-887	13	36	semi	semi	ADJ
ejde-887	13	37	-	-	ADJ
ejde-887	13	38	numerical	numerical	ADJ
ejde-887	13	39	,	,	PUNCT
ejde-887	13	40	methods	method	NOUN
ejde-887	13	41	that	that	PRON
ejde-887	13	42	have	have	AUX
ejde-887	13	43	generated	generate	VERB
ejde-887	13	44	a	a	DET
ejde-887	13	45	large	large	ADJ
ejde-887	13	46	amount	amount	NOUN
ejde-887	13	47	of	of	ADP
ejde-887	13	48	data	datum	NOUN
ejde-887	13	49	.	.	PUNCT
ejde-887	14	1	over	over	ADP
ejde-887	14	2	the	the	DET
ejde-887	14	3	last	last	ADJ
ejde-887	14	4	decade	decade	NOUN
ejde-887	14	5	,	,	PUNCT
ejde-887	14	6	a	a	DET
ejde-887	14	7	large	large	ADJ
ejde-887	14	8	body	body	NOUN
ejde-887	14	9	of	of	ADP
ejde-887	14	10	literature	literature	NOUN
ejde-887	14	11	has	have	AUX
ejde-887	14	12	evolved	evolve	VERB
ejde-887	14	13	attempting	attempt	VERB
ejde-887	14	14	to	to	PART
ejde-887	14	15	determine	determine	VERB
ejde-887	14	16	the	the	DET
ejde-887	14	17	most	most	ADV
ejde-887	14	18	appropriate	appropriate	ADJ
ejde-887	14	19	analytical	analytical	ADJ
ejde-887	14	20	or	or	CCONJ
ejde-887	14	21	numerical	numerical	ADJ
ejde-887	14	22	approach	approach	NOUN
ejde-887	14	23	to	to	PART
ejde-887	14	24	understand	understand	VERB
ejde-887	14	25	the	the	DET
ejde-887	14	26	dynamics	dynamic	NOUN
ejde-887	14	27	of	of	ADP
ejde-887	14	28	nonlinear	nonlinear	ADJ
ejde-887	14	29	waves	wave	NOUN
ejde-887	14	30	governed	govern	VERB
ejde-887	14	31	by	by	ADP
ejde-887	14	32	non	non	ADJ
ejde-887	14	33	-	-	ADJ
ejde-887	14	34	autonomous	autonomous	ADJ
ejde-887	14	35	equations	equation	NOUN
ejde-887	14	36	.	.	PUNCT
ejde-887	15	1	among	among	ADP
ejde-887	15	2	such	such	ADJ
ejde-887	15	3	approaches	approach	NOUN
ejde-887	15	4	we	we	PRON
ejde-887	15	5	mention	mention	VERB
ejde-887	15	6	,	,	PUNCT
ejde-887	15	7	for	for	ADP
ejde-887	15	8	example	example	NOUN
ejde-887	15	9	,	,	PUNCT
ejde-887	15	10	the	the	DET
ejde-887	15	11	use	use	NOUN
ejde-887	15	12	of	of	ADP
ejde-887	15	13	conformal	conformal	ADJ
ejde-887	15	14	-	-	PUNCT
ejde-887	15	15	mapping	map	VERB
ejde-887	15	16	spectral	spectral	ADJ
ejde-887	15	17	method	method	NOUN
ejde-887	15	18	in	in	ADP
ejde-887	15	19	the	the	DET
ejde-887	15	20	study	study	NOUN
ejde-887	15	21	of	of	ADP
ejde-887	15	22	run	run	NOUN
ejde-887	15	23	-	-	PUNCT
ejde-887	15	24	up	up	NOUN
ejde-887	15	25	of	of	ADP
ejde-887	15	26	waves	wave	NOUN
ejde-887	15	27	over	over	ADP
ejde-887	15	28	vertical	vertical	ADJ
ejde-887	15	29	walls	wall	NOUN
ejde-887	15	30	and	and	CCONJ
ejde-887	15	31	breakers	breaker	NOUN
ejde-887	15	32	[	[	X
ejde-887	15	33	20	20	NUM
ejde-887	15	34	]	]	PUNCT
ejde-887	15	35	,	,	PUNCT
ejde-887	15	36	the	the	DET
ejde-887	15	37	(	(	PUNCT
ejde-887	15	38	saint	saint	NOUN
ejde-887	15	39	-	-	PUNCT
ejde-887	15	40	venant	venant	NOUN
ejde-887	15	41	)	)	PUNCT
ejde-887	15	42	nonlinear	nonlinear	ADJ
ejde-887	15	43	shallow	shallow	ADJ
ejde-887	15	44	water	water	NOUN
ejde-887	15	45	model	model	NOUN
ejde-887	15	46	for	for	ADP
ejde-887	15	47	waves	wave	NOUN
ejde-887	15	48	over	over	ADP
ejde-887	15	49	significantly	significantly	ADV
ejde-887	15	50	varying	vary	VERB
ejde-887	15	51	seabeds	seabed	NOUN
ejde-887	15	52	[	[	X
ejde-887	15	53	14	14	NUM
ejde-887	15	54	]	]	PUNCT
ejde-887	15	55	,	,	PUNCT
ejde-887	15	56	benjamin	benjamin	NOUN
ejde-887	15	57	-	-	PUNCT
ejde-887	15	58	bona	bona	ADJ
ejde-887	15	59	-	-	PUNCT
ejde-887	15	60	mahony	mahony	NOUN
ejde-887	15	61	model	model	NOUN
ejde-887	15	62	and	and	CCONJ
ejde-887	15	63	smoothed	smooth	VERB
ejde-887	15	64	particle	particle	NOUN
ejde-887	15	65	hydrodynamics	hydrodynamic	NOUN
ejde-887	15	66	method	method	NOUN
ejde-887	15	67	for	for	ADP
ejde-887	15	68	understanding	understand	VERB
ejde-887	15	69	tsunami	tsunami	NOUN
ejde-887	15	70	generation	generation	NOUN
ejde-887	15	71	[	[	X
ejde-887	15	72	13	13	NUM
ejde-887	15	73	,	,	PUNCT
ejde-887	15	74	31	31	NUM
ejde-887	15	75	]	]	PUNCT
ejde-887	15	76	,	,	PUNCT
ejde-887	15	77	pseudo	pseudo	NOUN
ejde-887	15	78	-	-	ADJ
ejde-887	15	79	spectral	spectral	ADJ
ejde-887	15	80	method	method	NOUN
ejde-887	15	81	for	for	ADP
ejde-887	15	82	the	the	DET
ejde-887	15	83	babenko	babenko	ADJ
ejde-887	15	84	equation	equation	NOUN
ejde-887	15	85	and	and	CCONJ
ejde-887	15	86	petviashvili	petviashvili	NOUN
ejde-887	15	87	iterations	iteration	NOUN
ejde-887	15	88	for	for	ADP
ejde-887	15	89	the	the	DET
ejde-887	15	90	study	study	NOUN
ejde-887	15	91	of	of	ADP
ejde-887	15	92	waves	wave	NOUN
ejde-887	15	93	over	over	ADP
ejde-887	15	94	arbitrary	arbitrary	ADJ
ejde-887	15	95	depth	depth	NOUN
ejde-887	15	96	[	[	X
ejde-887	15	97	8	8	NUM
ejde-887	15	98	]	]	PUNCT
ejde-887	15	99	,	,	PUNCT
ejde-887	15	100	the	the	DET
ejde-887	15	101	dirichlet	dirichlet	PROPN
ejde-887	15	102	-	-	PUNCT
ejde-887	15	103	to	to	ADP
ejde-887	15	104	-	-	PUNCT
ejde-887	15	105	neumann	neumann	NOUN
ejde-887	15	106	operator	operator	NOUN
ejde-887	15	107	for	for	ADP
ejde-887	15	108	the	the	DET
ejde-887	15	109	dissipative	dissipative	ADJ
ejde-887	15	110	boussinesq	boussinesq	ADJ
ejde-887	15	111	problem	problem	NOUN
ejde-887	15	112	[	[	X
ejde-887	15	113	15	15	NUM
ejde-887	15	114	]	]	PUNCT
ejde-887	15	115	,	,	PUNCT
ejde-887	15	116	or	or	CCONJ
ejde-887	15	117	2010	2010	NUM
ejde-887	15	118	mathematics	mathematic	NOUN
ejde-887	15	119	subject	subject	NOUN
ejde-887	15	120	classification	classification	NOUN
ejde-887	15	121	.	.	PUNCT
ejde-887	16	1	35q51	35q51	NUM
ejde-887	16	2	,	,	PUNCT
ejde-887	16	3	35q53	35q53	NUM
ejde-887	16	4	,	,	PUNCT
ejde-887	16	5	35g50	35g50	NUM
ejde-887	16	6	,	,	PUNCT
ejde-887	16	7	34e13	34e13	NUM
ejde-887	16	8	,	,	PUNCT
ejde-887	16	9	93c70	93c70	NUM
ejde-887	16	10	.	.	PUNCT
ejde-887	17	1	key	key	ADJ
ejde-887	17	2	words	word	NOUN
ejde-887	17	3	and	and	CCONJ
ejde-887	17	4	phrases	phrase	NOUN
ejde-887	17	5	.	.	PUNCT
ejde-887	18	1	boussinesq	boussinesq	ADJ
ejde-887	18	2	;	;	PUNCT
ejde-887	18	3	non	non	ADJ
ejde-887	18	4	-	-	ADJ
ejde-887	18	5	autonomou	autonomou	ADJ
ejde-887	18	6	;	;	PUNCT
ejde-887	18	7	nonlinear	nonlinear	ADJ
ejde-887	18	8	;	;	PUNCT
ejde-887	18	9	multiple	multiple	ADJ
ejde-887	18	10	-	-	PUNCT
ejde-887	18	11	scale	scale	NOUN
ejde-887	18	12	;	;	PUNCT
ejde-887	18	13	soliton	soliton	NOUN
ejde-887	18	14	.	.	PUNCT
ejde-887	19	1	©	©	ADP
ejde-887	19	2	2024	2024	NUM
ejde-887	19	3	this	this	DET
ejde-887	19	4	work	work	NOUN
ejde-887	19	5	is	be	AUX
ejde-887	19	6	licensed	license	VERB
ejde-887	19	7	under	under	ADP
ejde-887	19	8	a	a	DET
ejde-887	19	9	cc	cc	NOUN
ejde-887	19	10	by	by	ADP
ejde-887	19	11	4.0	4.0	NUM
ejde-887	19	12	license	license	NOUN
ejde-887	19	13	.	.	PUNCT
ejde-887	20	1	published	publish	VERB
ejde-887	20	2	august	august	PROPN
ejde-887	20	3	20	20	NUM
ejde-887	20	4	,	,	PUNCT
ejde-887	20	5	2024	2024	NUM
ejde-887	20	6	.	.	PUNCT
ejde-887	21	1	27	27	NUM
ejde-887	21	2	28	28	NUM
ejde-887	21	3	a.	a.	NOUN
ejde-887	21	4	ludu	ludu	NOUN
ejde-887	21	5	,	,	PUNCT
ejde-887	21	6	h.	h.	PROPN
ejde-887	21	7	khanal	khanal	NOUN
ejde-887	21	8	,	,	PUNCT
ejde-887	21	9	a.	a.	PROPN
ejde-887	21	10	s.	s.	PROPN
ejde-887	21	11	carstea	carstea	PROPN
ejde-887	21	12	ejde-2022	ejde-2022	PROPN
ejde-887	21	13	/	/	SYM
ejde-887	21	14	conf/27	conf/27	NOUN
ejde-887	21	15	non	non	ADJ
ejde-887	21	16	-	-	ADJ
ejde-887	21	17	hydrostatic	hydrostatic	ADJ
ejde-887	21	18	σ−model	σ−model	NOUN
ejde-887	21	19	for	for	ADP
ejde-887	21	20	waves	wave	NOUN
ejde-887	21	21	over	over	ADP
ejde-887	21	22	rapidly	rapidly	ADV
ejde-887	21	23	varying	vary	VERB
ejde-887	21	24	topography	topography	NOUN
ejde-887	21	25	[	[	X
ejde-887	21	26	13	13	NUM
ejde-887	21	27	]	]	PUNCT
ejde-887	21	28	.	.	PUNCT
ejde-887	22	1	nonautonomous	nonautonomous	ADJ
ejde-887	22	2	equations	equation	NOUN
ejde-887	22	3	related	relate	VERB
ejde-887	22	4	to	to	ADP
ejde-887	22	5	fluid	fluid	ADJ
ejde-887	22	6	dynamics	dynamic	NOUN
ejde-887	22	7	models	model	NOUN
ejde-887	22	8	are	be	AUX
ejde-887	22	9	analyzed	analyze	VERB
ejde-887	22	10	for	for	ADP
ejde-887	22	11	the	the	DET
ejde-887	22	12	burgers	burger	NOUN
ejde-887	22	13	equation	equation	NOUN
ejde-887	22	14	[	[	X
ejde-887	22	15	6	6	NUM
ejde-887	22	16	]	]	PUNCT
ejde-887	22	17	,	,	PUNCT
ejde-887	22	18	and	and	CCONJ
ejde-887	22	19	for	for	ADP
ejde-887	22	20	the	the	DET
ejde-887	22	21	mkdv	mkdv	NOUN
ejde-887	22	22	equation	equation	NOUN
ejde-887	22	23	[	[	X
ejde-887	22	24	12	12	NUM
ejde-887	22	25	]	]	PUNCT
ejde-887	22	26	.	.	PUNCT
ejde-887	23	1	other	other	ADJ
ejde-887	23	2	approaches	approach	NOUN
ejde-887	23	3	for	for	ADP
ejde-887	23	4	nonlinear	nonlinear	ADJ
ejde-887	23	5	waves	wave	NOUN
ejde-887	23	6	over	over	ADP
ejde-887	23	7	a	a	DET
ejde-887	23	8	variable	variable	ADJ
ejde-887	23	9	bottom	bottom	NOUN
ejde-887	23	10	include	include	VERB
ejde-887	23	11	studies	study	NOUN
ejde-887	23	12	of	of	ADP
ejde-887	23	13	integrability	integrability	NOUN
ejde-887	23	14	using	use	VERB
ejde-887	23	15	the	the	DET
ejde-887	23	16	four	four	NUM
ejde-887	23	17	-	-	PUNCT
ejde-887	23	18	wave	wave	NOUN
ejde-887	23	19	formalism	formalism	NOUN
ejde-887	23	20	[	[	X
ejde-887	23	21	36	36	NUM
ejde-887	23	22	,	,	PUNCT
ejde-887	23	23	22	22	NUM
ejde-887	23	24	]	]	PUNCT
ejde-887	23	25	,	,	PUNCT
ejde-887	23	26	and	and	CCONJ
ejde-887	23	27	special	special	ADJ
ejde-887	23	28	types	type	NOUN
ejde-887	23	29	of	of	ADP
ejde-887	23	30	variable	variable	NOUN
ejde-887	23	31	re	re	NOUN
ejde-887	23	32	-	-	NOUN
ejde-887	23	33	scaling	scaling	NOUN
ejde-887	23	34	of	of	ADP
ejde-887	23	35	coordinates	coordinate	NOUN
ejde-887	23	36	[	[	X
ejde-887	23	37	23	23	NUM
ejde-887	23	38	]	]	PUNCT
ejde-887	23	39	.	.	PUNCT
ejde-887	24	1	another	another	DET
ejde-887	24	2	traditional	traditional	ADJ
ejde-887	24	3	approach	approach	NOUN
ejde-887	24	4	is	be	AUX
ejde-887	24	5	to	to	PART
ejde-887	24	6	deal	deal	VERB
ejde-887	24	7	with	with	ADP
ejde-887	24	8	variable	variable	ADJ
ejde-887	24	9	boundary	boundary	ADJ
ejde-887	24	10	conditions	condition	NOUN
ejde-887	24	11	using	use	VERB
ejde-887	24	12	the	the	DET
ejde-887	24	13	nonlocal	nonlocal	ADJ
ejde-887	24	14	dirichlet	dirichlet	PROPN
ejde-887	24	15	-	-	PUNCT
ejde-887	24	16	neumann	neumann	PROPN
ejde-887	24	17	operator	operator	NOUN
ejde-887	24	18	[	[	X
ejde-887	24	19	41	41	NUM
ejde-887	24	20	]	]	PUNCT
ejde-887	24	21	,	,	PUNCT
ejde-887	24	22	and	and	CCONJ
ejde-887	24	23	the	the	DET
ejde-887	24	24	studies	study	NOUN
ejde-887	24	25	using	use	VERB
ejde-887	24	26	this	this	DET
ejde-887	24	27	operator	operator	NOUN
ejde-887	24	28	while	while	SCONJ
ejde-887	24	29	performing	perform	VERB
ejde-887	24	30	a	a	DET
ejde-887	24	31	conformal	conformal	ADJ
ejde-887	24	32	transform	transform	NOUN
ejde-887	24	33	[	[	X
ejde-887	24	34	17	17	NUM
ejde-887	24	35	]	]	PUNCT
ejde-887	24	36	.	.	PUNCT
ejde-887	25	1	a	a	DET
ejde-887	25	2	very	very	ADV
ejde-887	25	3	important	important	ADJ
ejde-887	25	4	model	model	NOUN
ejde-887	25	5	equation	equation	NOUN
ejde-887	25	6	for	for	ADP
ejde-887	25	7	such	such	ADJ
ejde-887	25	8	problems	problem	NOUN
ejde-887	25	9	is	be	AUX
ejde-887	25	10	provided	provide	VERB
ejde-887	25	11	by	by	ADP
ejde-887	25	12	various	various	ADJ
ejde-887	25	13	types	type	NOUN
ejde-887	25	14	of	of	ADP
ejde-887	25	15	boussinesq	boussinesq	ADJ
ejde-887	25	16	systems	system	NOUN
ejde-887	25	17	[	[	X
ejde-887	25	18	17	17	NUM
ejde-887	25	19	,	,	PUNCT
ejde-887	25	20	46	46	NUM
ejde-887	25	21	]	]	PUNCT
ejde-887	25	22	.	.	PUNCT
ejde-887	26	1	such	such	ADJ
ejde-887	26	2	models	model	NOUN
ejde-887	26	3	are	be	AUX
ejde-887	26	4	used	use	VERB
ejde-887	26	5	in	in	ADP
ejde-887	26	6	engineering	engineering	NOUN
ejde-887	26	7	in	in	ADP
ejde-887	26	8	the	the	DET
ejde-887	26	9	study	study	NOUN
ejde-887	26	10	of	of	ADP
ejde-887	26	11	the	the	DET
ejde-887	26	12	importance	importance	NOUN
ejde-887	26	13	of	of	ADP
ejde-887	26	14	specific	specific	ADJ
ejde-887	26	15	water	water	NOUN
ejde-887	26	16	waves	wave	NOUN
ejde-887	26	17	in	in	ADP
ejde-887	26	18	the	the	DET
ejde-887	26	19	coastal	coastal	ADJ
ejde-887	26	20	and	and	CCONJ
ejde-887	26	21	harbor	harbor	NOUN
ejde-887	26	22	design	design	NOUN
ejde-887	26	23	.	.	PUNCT
ejde-887	27	1	for	for	ADP
ejde-887	27	2	these	these	DET
ejde-887	27	3	purposes	purpose	NOUN
ejde-887	27	4	,	,	PUNCT
ejde-887	27	5	the	the	DET
ejde-887	27	6	mathematical	mathematical	ADJ
ejde-887	27	7	properties	property	NOUN
ejde-887	27	8	of	of	ADP
ejde-887	27	9	the	the	DET
ejde-887	27	10	wave	wave	NOUN
ejde-887	27	11	solutions	solution	NOUN
ejde-887	27	12	,	,	PUNCT
ejde-887	27	13	such	such	ADJ
ejde-887	27	14	as	as	ADP
ejde-887	27	15	integrability	integrability	NOUN
ejde-887	27	16	and	and	CCONJ
ejde-887	27	17	stability	stability	NOUN
ejde-887	27	18	of	of	ADP
ejde-887	27	19	solitary	solitary	ADJ
ejde-887	27	20	waves	wave	NOUN
ejde-887	27	21	,	,	PUNCT
ejde-887	27	22	are	be	AUX
ejde-887	27	23	crucial	crucial	ADJ
ejde-887	27	24	.	.	PUNCT
ejde-887	28	1	the	the	DET
ejde-887	28	2	goal	goal	NOUN
ejde-887	28	3	of	of	ADP
ejde-887	28	4	this	this	DET
ejde-887	28	5	article	article	NOUN
ejde-887	28	6	is	be	AUX
ejde-887	28	7	to	to	PART
ejde-887	28	8	build	build	VERB
ejde-887	28	9	an	an	DET
ejde-887	28	10	integrable	integrable	ADJ
ejde-887	28	11	procedure	procedure	NOUN
ejde-887	28	12	for	for	ADP
ejde-887	28	13	the	the	DET
ejde-887	28	14	nonlinear	nonlinear	ADJ
ejde-887	28	15	nonautonomous	nonautonomous	ADJ
ejde-887	28	16	boussinesq	boussinesq	NOUN
ejde-887	28	17	system	system	NOUN
ejde-887	28	18	of	of	ADP
ejde-887	28	19	equations	equation	NOUN
ejde-887	28	20	.	.	PUNCT
ejde-887	29	1	to	to	PART
ejde-887	29	2	accomplish	accomplish	VERB
ejde-887	29	3	this	this	DET
ejde-887	29	4	goal	goal	NOUN
ejde-887	29	5	we	we	PRON
ejde-887	29	6	combine	combine	VERB
ejde-887	29	7	the	the	DET
ejde-887	29	8	results	result	NOUN
ejde-887	29	9	from	from	ADP
ejde-887	29	10	two	two	NUM
ejde-887	29	11	limiting	limit	VERB
ejde-887	29	12	theories	theory	NOUN
ejde-887	29	13	:	:	PUNCT
ejde-887	29	14	on	on	ADP
ejde-887	29	15	the	the	DET
ejde-887	29	16	one	one	NUM
ejde-887	29	17	hand	hand	NOUN
ejde-887	29	18	the	the	DET
ejde-887	29	19	linear	linear	ADJ
ejde-887	29	20	approximation	approximation	NOUN
ejde-887	29	21	for	for	ADP
ejde-887	29	22	non	non	ADJ
ejde-887	29	23	-	-	ADJ
ejde-887	29	24	autonomous	autonomous	ADJ
ejde-887	29	25	equations	equation	NOUN
ejde-887	29	26	[	[	X
ejde-887	29	27	6	6	NUM
ejde-887	29	28	,	,	PUNCT
ejde-887	29	29	8	8	NUM
ejde-887	29	30	,	,	PUNCT
ejde-887	29	31	12	12	NUM
ejde-887	29	32	,	,	PUNCT
ejde-887	29	33	14	14	NUM
ejde-887	29	34	,	,	PUNCT
ejde-887	29	35	23	23	NUM
ejde-887	29	36	,	,	PUNCT
ejde-887	29	37	35	35	NUM
ejde-887	29	38	,	,	PUNCT
ejde-887	29	39	41	41	NUM
ejde-887	29	40	]	]	PUNCT
ejde-887	29	41	,	,	PUNCT
ejde-887	29	42	and	and	CCONJ
ejde-887	29	43	on	on	ADP
ejde-887	29	44	the	the	DET
ejde-887	29	45	other	other	ADJ
ejde-887	29	46	hand	hand	NOUN
ejde-887	29	47	,	,	PUNCT
ejde-887	29	48	the	the	DET
ejde-887	29	49	theory	theory	NOUN
ejde-887	29	50	of	of	ADP
ejde-887	29	51	integrable	integrable	ADJ
ejde-887	29	52	boussinesq	boussinesq	NOUN
ejde-887	29	53	and	and	CCONJ
ejde-887	29	54	broer	broer	NOUN
ejde-887	29	55	-	-	PUNCT
ejde-887	29	56	kaup	kaup	PROPN
ejde-887	29	57	(	(	PUNCT
ejde-887	29	58	bk	bk	NOUN
ejde-887	29	59	)	)	PUNCT
ejde-887	29	60	systems	system	NOUN
ejde-887	29	61	with	with	ADP
ejde-887	29	62	the	the	DET
ejde-887	29	63	corresponding	corresponding	ADJ
ejde-887	29	64	soliton	soliton	NOUN
ejde-887	29	65	solutions	solution	NOUN
ejde-887	29	66	,	,	PUNCT
ejde-887	29	67	where	where	SCONJ
ejde-887	29	68	the	the	DET
ejde-887	29	69	nonlinearity	nonlinearity	NOUN
ejde-887	29	70	is	be	AUX
ejde-887	29	71	considered	consider	VERB
ejde-887	29	72	,	,	PUNCT
ejde-887	29	73	but	but	CCONJ
ejde-887	29	74	the	the	DET
ejde-887	29	75	system	system	NOUN
ejde-887	29	76	is	be	AUX
ejde-887	29	77	autonomous	autonomous	ADJ
ejde-887	29	78	[	[	X
ejde-887	29	79	21	21	NUM
ejde-887	29	80	,	,	PUNCT
ejde-887	29	81	22	22	NUM
ejde-887	29	82	,	,	PUNCT
ejde-887	29	83	24	24	NUM
ejde-887	29	84	,	,	PUNCT
ejde-887	29	85	26	26	NUM
ejde-887	29	86	,	,	PUNCT
ejde-887	29	87	28	28	NUM
ejde-887	29	88	,	,	PUNCT
ejde-887	29	89	29	29	NUM
ejde-887	29	90	,	,	PUNCT
ejde-887	29	91	36	36	NUM
ejde-887	29	92	,	,	PUNCT
ejde-887	29	93	45	45	NUM
ejde-887	29	94	,	,	PUNCT
ejde-887	29	95	47	47	NUM
ejde-887	29	96	]	]	PUNCT
ejde-887	29	97	.	.	PUNCT
ejde-887	30	1	the	the	DET
ejde-887	30	2	solitary	solitary	ADJ
ejde-887	30	3	wave	wave	NOUN
ejde-887	30	4	solutions	solution	NOUN
ejde-887	30	5	to	to	ADP
ejde-887	30	6	the	the	DET
ejde-887	30	7	classical	classical	ADJ
ejde-887	30	8	boussinesq	boussinesq	ADJ
ejde-887	30	9	equation	equation	NOUN
ejde-887	30	10	(	(	PUNCT
ejde-887	30	11	with	with	ADP
ejde-887	30	12	and	and	CCONJ
ejde-887	30	13	without	without	ADP
ejde-887	30	14	a	a	DET
ejde-887	30	15	restoring	restore	VERB
ejde-887	30	16	force	force	NOUN
ejde-887	30	17	)	)	PUNCT
ejde-887	30	18	have	have	AUX
ejde-887	30	19	also	also	ADV
ejde-887	30	20	been	be	AUX
ejde-887	30	21	obtained	obtain	VERB
ejde-887	30	22	in	in	ADP
ejde-887	30	23	[	[	X
ejde-887	30	24	27	27	NUM
ejde-887	30	25	,	,	PUNCT
ejde-887	30	26	42	42	NUM
ejde-887	30	27	]	]	PUNCT
ejde-887	30	28	.	.	PUNCT
ejde-887	31	1	this	this	DET
ejde-887	31	2	article	article	NOUN
ejde-887	31	3	is	be	AUX
ejde-887	31	4	organized	organize	VERB
ejde-887	31	5	as	as	SCONJ
ejde-887	31	6	follows	follow	VERB
ejde-887	31	7	.	.	PUNCT
ejde-887	32	1	in	in	ADP
ejde-887	32	2	section	section	NOUN
ejde-887	32	3	2	2	NUM
ejde-887	32	4	we	we	PRON
ejde-887	32	5	present	present	VERB
ejde-887	32	6	the	the	DET
ejde-887	32	7	nonlinear	nonlinear	ADJ
ejde-887	32	8	nonautonomous	nonautonomous	ADJ
ejde-887	32	9	boussinesq	boussinesq	NOUN
ejde-887	32	10	system	system	NOUN
ejde-887	32	11	and	and	CCONJ
ejde-887	32	12	the	the	DET
ejde-887	32	13	associated	associated	ADJ
ejde-887	32	14	initial	initial	ADJ
ejde-887	32	15	conditions	condition	NOUN
ejde-887	32	16	.	.	PUNCT
ejde-887	33	1	in	in	ADP
ejde-887	33	2	subsection	subsection	NOUN
ejde-887	33	3	2.1	2.1	NUM
ejde-887	33	4	we	we	PRON
ejde-887	33	5	review	review	VERB
ejde-887	33	6	and	and	CCONJ
ejde-887	33	7	elaborate	elaborate	VERB
ejde-887	33	8	on	on	ADP
ejde-887	33	9	the	the	DET
ejde-887	33	10	extent	extent	NOUN
ejde-887	33	11	to	to	PART
ejde-887	33	12	which	which	PRON
ejde-887	33	13	the	the	DET
ejde-887	33	14	non	non	ADJ
ejde-887	33	15	-	-	ADJ
ejde-887	33	16	autonomous	autonomous	ADJ
ejde-887	33	17	boussinesq	boussinesq	ADJ
ejde-887	33	18	system	system	NOUN
ejde-887	33	19	under	under	ADP
ejde-887	33	20	study	study	NOUN
ejde-887	33	21	is	be	AUX
ejde-887	33	22	a	a	DET
ejde-887	33	23	well	well	ADV
ejde-887	33	24	posed	pose	VERB
ejde-887	33	25	problem	problem	NOUN
ejde-887	33	26	.	.	PUNCT
ejde-887	34	1	section	section	NOUN
ejde-887	34	2	3	3	NUM
ejde-887	34	3	presents	present	VERB
ejde-887	34	4	some	some	DET
ejde-887	34	5	qualitative	qualitative	ADJ
ejde-887	34	6	asymptotic	asymptotic	ADJ
ejde-887	34	7	analysis	analysis	NOUN
ejde-887	34	8	of	of	ADP
ejde-887	34	9	this	this	DET
ejde-887	34	10	boussinesq	boussinesq	ADJ
ejde-887	34	11	system	system	NOUN
ejde-887	34	12	.	.	PUNCT
ejde-887	35	1	in	in	ADP
ejde-887	35	2	section	section	NOUN
ejde-887	35	3	3.1	3.1	NUM
ejde-887	35	4	we	we	PRON
ejde-887	35	5	study	study	VERB
ejde-887	35	6	the	the	DET
ejde-887	35	7	autonomous	autonomous	ADJ
ejde-887	35	8	nonlinear	nonlinear	ADJ
ejde-887	35	9	limit	limit	NOUN
ejde-887	35	10	,	,	PUNCT
ejde-887	35	11	and	and	CCONJ
ejde-887	35	12	introduce	introduce	VERB
ejde-887	35	13	exact	exact	ADJ
ejde-887	35	14	one	one	NUM
ejde-887	35	15	-	-	PUNCT
ejde-887	35	16	soliton	soliton	NOUN
ejde-887	35	17	solutions	solution	NOUN
ejde-887	35	18	which	which	PRON
ejde-887	35	19	will	will	AUX
ejde-887	35	20	be	be	AUX
ejde-887	35	21	used	use	VERB
ejde-887	35	22	further	far	ADV
ejde-887	35	23	as	as	ADP
ejde-887	35	24	initial	initial	ADJ
ejde-887	35	25	conditions	condition	NOUN
ejde-887	35	26	for	for	ADP
ejde-887	35	27	the	the	DET
ejde-887	35	28	non	non	ADJ
ejde-887	35	29	-	-	ADJ
ejde-887	35	30	autonomous	autonomous	ADJ
ejde-887	35	31	system	system	NOUN
ejde-887	35	32	.	.	PUNCT
ejde-887	36	1	in	in	ADP
ejde-887	36	2	subsection	subsection	NOUN
ejde-887	36	3	3.2	3.2	NUM
ejde-887	36	4	we	we	PRON
ejde-887	36	5	study	study	VERB
ejde-887	36	6	the	the	DET
ejde-887	36	7	other	other	ADJ
ejde-887	36	8	asymptotic	asymptotic	ADJ
ejde-887	36	9	limit	limit	NOUN
ejde-887	36	10	,	,	PUNCT
ejde-887	36	11	the	the	DET
ejde-887	36	12	non	non	ADJ
ejde-887	36	13	-	-	ADJ
ejde-887	36	14	autonomous	autonomous	ADJ
ejde-887	36	15	linear	linear	ADJ
ejde-887	36	16	case	case	NOUN
ejde-887	36	17	.	.	PUNCT
ejde-887	37	1	section	section	NOUN
ejde-887	37	2	4	4	NUM
ejde-887	37	3	is	be	AUX
ejde-887	37	4	part	part	NOUN
ejde-887	37	5	of	of	ADP
ejde-887	37	6	the	the	DET
ejde-887	37	7	main	main	ADJ
ejde-887	37	8	core	core	NOUN
ejde-887	37	9	of	of	ADP
ejde-887	37	10	results	result	NOUN
ejde-887	37	11	of	of	ADP
ejde-887	37	12	this	this	DET
ejde-887	37	13	work	work	NOUN
ejde-887	37	14	.	.	PUNCT
ejde-887	38	1	in	in	ADP
ejde-887	38	2	subsection	subsection	NOUN
ejde-887	38	3	4.1	4.1	NUM
ejde-887	38	4	we	we	PRON
ejde-887	38	5	apply	apply	VERB
ejde-887	38	6	the	the	DET
ejde-887	38	7	procedure	procedure	NOUN
ejde-887	38	8	of	of	ADP
ejde-887	38	9	amplitude	amplitude	NOUN
ejde-887	38	10	modulation	modulation	NOUN
ejde-887	38	11	for	for	ADP
ejde-887	38	12	the	the	DET
ejde-887	38	13	autonomous	autonomous	ADJ
ejde-887	38	14	case	case	NOUN
ejde-887	38	15	of	of	ADP
ejde-887	38	16	the	the	DET
ejde-887	38	17	boussinesq	boussinesq	ADJ
ejde-887	38	18	system	system	NOUN
ejde-887	38	19	,	,	PUNCT
ejde-887	38	20	which	which	PRON
ejde-887	38	21	results	result	VERB
ejde-887	38	22	in	in	ADP
ejde-887	38	23	a	a	DET
ejde-887	38	24	non	non	ADJ
ejde-887	38	25	-	-	ADJ
ejde-887	38	26	dispersive	dispersive	ADJ
ejde-887	38	27	type	type	NOUN
ejde-887	38	28	of	of	ADP
ejde-887	38	29	differential	differential	ADJ
ejde-887	38	30	system	system	NOUN
ejde-887	38	31	.	.	PUNCT
ejde-887	39	1	we	we	PRON
ejde-887	39	2	describe	describe	VERB
ejde-887	39	3	the	the	DET
ejde-887	39	4	property	property	NOUN
ejde-887	39	5	of	of	ADP
ejde-887	39	6	integrability	integrability	NOUN
ejde-887	39	7	of	of	ADP
ejde-887	39	8	the	the	DET
ejde-887	39	9	nonlinear	nonlinear	ADJ
ejde-887	39	10	system	system	NOUN
ejde-887	39	11	,	,	PUNCT
ejde-887	39	12	beginning	begin	VERB
ejde-887	39	13	with	with	ADP
ejde-887	39	14	the	the	DET
ejde-887	39	15	inverse	inverse	NOUN
ejde-887	39	16	scattering	scattering	NOUN
ejde-887	39	17	theory	theory	NOUN
ejde-887	39	18	integrability	integrability	NOUN
ejde-887	39	19	problem	problem	NOUN
ejde-887	39	20	for	for	ADP
ejde-887	39	21	the	the	DET
ejde-887	39	22	autonomous	autonomous	ADJ
ejde-887	39	23	limiting	limit	VERB
ejde-887	39	24	case	case	NOUN
ejde-887	39	25	(	(	PUNCT
ejde-887	39	26	the	the	DET
ejde-887	39	27	traditional	traditional	ADJ
ejde-887	39	28	boussinesq	boussinesq	ADJ
ejde-887	39	29	system	system	NOUN
ejde-887	39	30	)	)	PUNCT
ejde-887	39	31	.	.	PUNCT
ejde-887	40	1	in	in	ADP
ejde-887	40	2	addition	addition	NOUN
ejde-887	40	3	,	,	PUNCT
ejde-887	40	4	in	in	ADP
ejde-887	40	5	this	this	DET
ejde-887	40	6	section	section	NOUN
ejde-887	40	7	we	we	PRON
ejde-887	40	8	investigate	investigate	VERB
ejde-887	40	9	the	the	DET
ejde-887	40	10	integrability	integrability	NOUN
ejde-887	40	11	of	of	ADP
ejde-887	40	12	the	the	DET
ejde-887	40	13	nonlinear	nonlinear	ADJ
ejde-887	40	14	problem	problem	NOUN
ejde-887	40	15	with	with	ADP
ejde-887	40	16	the	the	DET
ejde-887	40	17	zakharov	zakharov	ADJ
ejde-887	40	18	-	-	PUNCT
ejde-887	40	19	kuznetsov	kuznetsov	NOUN
ejde-887	40	20	multiple	multiple	ADJ
ejde-887	40	21	-	-	PUNCT
ejde-887	40	22	scale	scale	NOUN
ejde-887	40	23	theory	theory	NOUN
ejde-887	40	24	for	for	ADP
ejde-887	40	25	wave	wave	NOUN
ejde-887	40	26	amplitude	amplitude	NOUN
ejde-887	40	27	modulation	modulation	NOUN
ejde-887	40	28	of	of	ADP
ejde-887	40	29	boussinesq	boussinesq	ADJ
ejde-887	40	30	system	system	NOUN
ejde-887	40	31	(	(	PUNCT
ejde-887	40	32	which	which	PRON
ejde-887	40	33	can	can	AUX
ejde-887	40	34	be	be	AUX
ejde-887	40	35	mapped	map	VERB
ejde-887	40	36	into	into	ADP
ejde-887	40	37	the	the	DET
ejde-887	40	38	integrable	integrable	ADJ
ejde-887	40	39	broer	broer	NOUN
ejde-887	40	40	-	-	PUNCT
ejde-887	40	41	kaup	kaup	PROPN
ejde-887	40	42	system	system	NOUN
ejde-887	40	43	)	)	PUNCT
ejde-887	40	44	and	and	CCONJ
ejde-887	40	45	we	we	PRON
ejde-887	40	46	obtain	obtain	VERB
ejde-887	40	47	a	a	DET
ejde-887	40	48	dispersionless	dispersionless	NOUN
ejde-887	40	49	envelope	envelope	NOUN
ejde-887	40	50	system	system	NOUN
ejde-887	40	51	which	which	PRON
ejde-887	40	52	is	be	AUX
ejde-887	40	53	likely	likely	ADJ
ejde-887	40	54	to	to	PART
ejde-887	40	55	be	be	AUX
ejde-887	40	56	integrable	integrable	ADJ
ejde-887	40	57	.	.	PUNCT
ejde-887	41	1	the	the	DET
ejde-887	41	2	fully	fully	ADV
ejde-887	41	3	nonlinear	nonlinear	ADJ
ejde-887	41	4	and	and	CCONJ
ejde-887	41	5	non	non	ADJ
ejde-887	41	6	-	-	ADJ
ejde-887	41	7	autonomous	autonomous	ADJ
ejde-887	41	8	case	case	NOUN
ejde-887	41	9	is	be	AUX
ejde-887	41	10	studied	study	VERB
ejde-887	41	11	by	by	ADP
ejde-887	41	12	using	use	VERB
ejde-887	41	13	the	the	DET
ejde-887	41	14	zakharov	zakharov	ADJ
ejde-887	41	15	-	-	PUNCT
ejde-887	41	16	kuznetsov	kuznetsov	NOUN
ejde-887	41	17	multiple	multiple	ADJ
ejde-887	41	18	-	-	PUNCT
ejde-887	41	19	scale	scale	NOUN
ejde-887	41	20	procedure	procedure	NOUN
ejde-887	41	21	in	in	ADP
ejde-887	41	22	subsection	subsection	NOUN
ejde-887	41	23	4.2	4.2	NUM
ejde-887	41	24	.	.	PUNCT
ejde-887	42	1	to	to	PART
ejde-887	42	2	obtain	obtain	VERB
ejde-887	42	3	explicit	explicit	ADJ
ejde-887	42	4	analytic	analytic	ADJ
ejde-887	42	5	solutions	solution	NOUN
ejde-887	42	6	we	we	PRON
ejde-887	42	7	use	use	VERB
ejde-887	42	8	a	a	DET
ejde-887	42	9	generalization	generalization	NOUN
ejde-887	42	10	of	of	ADP
ejde-887	42	11	the	the	DET
ejde-887	42	12	multiple	multiple	ADJ
ejde-887	42	13	-	-	PUNCT
ejde-887	42	14	scale	scale	NOUN
ejde-887	42	15	method	method	NOUN
ejde-887	42	16	of	of	ADP
ejde-887	42	17	integration	integration	NOUN
ejde-887	42	18	by	by	ADP
ejde-887	42	19	using	use	VERB
ejde-887	42	20	n	n	PRON
ejde-887	42	21	-waves	-wave	NOUN
ejde-887	42	22	mixing	mix	VERB
ejde-887	42	23	procedure	procedure	NOUN
ejde-887	42	24	where	where	SCONJ
ejde-887	42	25	we	we	PRON
ejde-887	42	26	combine	combine	VERB
ejde-887	42	27	the	the	DET
ejde-887	42	28	phases	phase	NOUN
ejde-887	42	29	of	of	ADP
ejde-887	42	30	the	the	DET
ejde-887	42	31	autonomous	autonomous	ADJ
ejde-887	42	32	solutions	solution	NOUN
ejde-887	42	33	.	.	PUNCT
ejde-887	43	1	these	these	DET
ejde-887	43	2	calculations	calculation	NOUN
ejde-887	43	3	result	result	VERB
ejde-887	43	4	in	in	ADP
ejde-887	43	5	a	a	DET
ejde-887	43	6	recursive	recursive	ADJ
ejde-887	43	7	hierarchy	hierarchy	NOUN
ejde-887	43	8	of	of	ADP
ejde-887	43	9	differential	differential	ADJ
ejde-887	43	10	equations	equation	NOUN
ejde-887	43	11	.	.	PUNCT
ejde-887	44	1	we	we	PRON
ejde-887	44	2	noticed	notice	VERB
ejde-887	44	3	that	that	SCONJ
ejde-887	44	4	even	even	ADV
ejde-887	44	5	the	the	DET
ejde-887	44	6	autonomous	autonomous	ADJ
ejde-887	44	7	case	case	NOUN
ejde-887	44	8	can	can	AUX
ejde-887	44	9	produce	produce	VERB
ejde-887	44	10	modulations	modulation	NOUN
ejde-887	44	11	of	of	ADP
ejde-887	44	12	solution	solution	NOUN
ejde-887	44	13	amplitudes	amplitude	NOUN
ejde-887	44	14	,	,	PUNCT
ejde-887	44	15	so	so	SCONJ
ejde-887	44	16	this	this	DET
ejde-887	44	17	limiting	limit	VERB
ejde-887	44	18	case	case	NOUN
ejde-887	44	19	is	be	AUX
ejde-887	44	20	instructive	instructive	ADJ
ejde-887	44	21	.	.	PUNCT
ejde-887	45	1	using	use	VERB
ejde-887	45	2	this	this	DET
ejde-887	45	3	multiple	multiple	ADJ
ejde-887	45	4	-	-	PUNCT
ejde-887	45	5	scale	scale	NOUN
ejde-887	45	6	generalized	generalized	ADJ
ejde-887	45	7	approach	approach	NOUN
ejde-887	45	8	we	we	PRON
ejde-887	45	9	obtain	obtain	VERB
ejde-887	45	10	a	a	DET
ejde-887	45	11	hierarchy	hierarchy	NOUN
ejde-887	45	12	of	of	ADP
ejde-887	45	13	dispersionless	dispersionless	NOUN
ejde-887	45	14	systems	system	NOUN
ejde-887	45	15	of	of	ADP
ejde-887	45	16	equations	equation	NOUN
ejde-887	45	17	for	for	ADP
ejde-887	45	18	the	the	DET
ejde-887	45	19	amplitudes	amplitude	NOUN
ejde-887	45	20	of	of	ADP
ejde-887	45	21	the	the	DET
ejde-887	45	22	waves	wave	NOUN
ejde-887	45	23	.	.	PUNCT
ejde-887	46	1	this	this	DET
ejde-887	46	2	systems	system	NOUN
ejde-887	46	3	are	be	AUX
ejde-887	46	4	integrable	integrable	ADJ
ejde-887	46	5	since	since	SCONJ
ejde-887	46	6	they	they	PRON
ejde-887	46	7	ejde-202x	ejde-202x	PROPN
ejde-887	46	8	/	/	SYM
ejde-887	46	9	conf/27	conf/27	NOUN
ejde-887	46	10	boussinesq	boussinesq	ADJ
ejde-887	46	11	equations	equation	NOUN
ejde-887	46	12	29	29	NUM
ejde-887	46	13	are	be	AUX
ejde-887	46	14	derived	derive	VERB
ejde-887	46	15	from	from	ADP
ejde-887	46	16	a	a	DET
ejde-887	46	17	completely	completely	ADV
ejde-887	46	18	integrable	integrable	ADJ
ejde-887	46	19	boussinesq	boussinesq	ADJ
ejde-887	46	20	system	system	NOUN
ejde-887	46	21	by	by	ADP
ejde-887	46	22	a	a	DET
ejde-887	46	23	limiting	limit	VERB
ejde-887	46	24	procedure	procedure	NOUN
ejde-887	46	25	.	.	PUNCT
ejde-887	47	1	in	in	ADP
ejde-887	47	2	section	section	NOUN
ejde-887	47	3	5	5	NUM
ejde-887	47	4	we	we	PRON
ejde-887	47	5	present	present	VERB
ejde-887	47	6	numerical	numerical	ADJ
ejde-887	47	7	results	result	NOUN
ejde-887	47	8	for	for	ADP
ejde-887	47	9	the	the	DET
ejde-887	47	10	non	non	ADJ
ejde-887	47	11	-	-	ADJ
ejde-887	47	12	autonomous	autonomous	ADJ
ejde-887	47	13	nonlinear	nonlinear	ADJ
ejde-887	47	14	boussinesq	boussinesq	ADJ
ejde-887	47	15	system	system	NOUN
ejde-887	47	16	under	under	ADP
ejde-887	47	17	consideration	consideration	NOUN
ejde-887	47	18	.	.	PUNCT
ejde-887	48	1	in	in	ADP
ejde-887	48	2	subsection	subsection	NOUN
ejde-887	48	3	5.1	5.1	NUM
ejde-887	48	4	we	we	PRON
ejde-887	48	5	describe	describe	VERB
ejde-887	48	6	the	the	DET
ejde-887	48	7	numerical	numerical	ADJ
ejde-887	48	8	algorithms	algorithm	NOUN
ejde-887	48	9	.	.	PUNCT
ejde-887	49	1	in	in	ADP
ejde-887	49	2	section	section	NOUN
ejde-887	49	3	5.2	5.2	NUM
ejde-887	49	4	we	we	PRON
ejde-887	49	5	present	present	VERB
ejde-887	49	6	relevant	relevant	ADJ
ejde-887	49	7	examples	example	NOUN
ejde-887	49	8	of	of	ADP
ejde-887	49	9	numerical	numerical	ADJ
ejde-887	49	10	solutions	solution	NOUN
ejde-887	49	11	,	,	PUNCT
ejde-887	49	12	for	for	ADP
ejde-887	49	13	various	various	ADJ
ejde-887	49	14	combinations	combination	NOUN
ejde-887	49	15	of	of	ADP
ejde-887	49	16	parameters	parameter	NOUN
ejde-887	49	17	and	and	CCONJ
ejde-887	49	18	initial	initial	ADJ
ejde-887	49	19	conditions	condition	NOUN
ejde-887	49	20	,	,	PUNCT
ejde-887	49	21	and	and	CCONJ
ejde-887	49	22	we	we	PRON
ejde-887	49	23	analyze	analyze	VERB
ejde-887	49	24	how	how	SCONJ
ejde-887	49	25	the	the	DET
ejde-887	49	26	predictions	prediction	NOUN
ejde-887	49	27	of	of	ADP
ejde-887	49	28	the	the	DET
ejde-887	49	29	theoretical	theoretical	ADJ
ejde-887	49	30	results	result	NOUN
ejde-887	49	31	presented	present	VERB
ejde-887	49	32	in	in	ADP
ejde-887	49	33	section	section	NOUN
ejde-887	49	34	4	4	NUM
ejde-887	49	35	can	can	AUX
ejde-887	49	36	apply	apply	VERB
ejde-887	49	37	or	or	CCONJ
ejde-887	49	38	justify	justify	VERB
ejde-887	49	39	these	these	DET
ejde-887	49	40	numerical	numerical	ADJ
ejde-887	49	41	solutions	solution	NOUN
ejde-887	49	42	.	.	PUNCT
ejde-887	50	1	in	in	ADP
ejde-887	50	2	subsection	subsection	NOUN
ejde-887	50	3	5.3	5.3	NUM
ejde-887	50	4	we	we	PRON
ejde-887	50	5	discuss	discuss	VERB
ejde-887	50	6	the	the	DET
ejde-887	50	7	stability	stability	NOUN
ejde-887	50	8	of	of	ADP
ejde-887	50	9	the	the	DET
ejde-887	50	10	solitary	solitary	ADJ
ejde-887	50	11	waves	wave	NOUN
ejde-887	50	12	obtained	obtain	VERB
ejde-887	50	13	numerically	numerically	ADV
ejde-887	50	14	.	.	PUNCT
ejde-887	51	1	2	2	X
ejde-887	51	2	.	.	X
ejde-887	51	3	boussinesq	boussinesq	ADJ
ejde-887	51	4	non	non	ADJ
ejde-887	51	5	-	-	ADJ
ejde-887	51	6	autonomous	autonomous	ADJ
ejde-887	51	7	nonlinear	nonlinear	ADJ
ejde-887	51	8	system	system	NOUN
ejde-887	51	9	we	we	PRON
ejde-887	51	10	consider	consider	VERB
ejde-887	51	11	a	a	DET
ejde-887	51	12	non	non	ADJ
ejde-887	51	13	-	-	ADJ
ejde-887	51	14	autonomous	autonomous	ADJ
ejde-887	51	15	and	and	CCONJ
ejde-887	51	16	nonlinear	nonlinear	ADJ
ejde-887	51	17	boussinesq	boussinesq	NOUN
ejde-887	51	18	-	-	PUNCT
ejde-887	51	19	type	type	NOUN
ejde-887	51	20	of	of	ADP
ejde-887	51	21	differential	differential	ADJ
ejde-887	51	22	system	system	NOUN
ejde-887	51	23	in	in	ADP
ejde-887	51	24	the	the	DET
ejde-887	51	25	form	form	NOUN
ejde-887	51	26	qzt	qzt	NOUN
ejde-887	51	27	+	+	CCONJ
ejde-887	51	28	(	(	PUNCT
ejde-887	51	29	qu+	qu+	ADJ
ejde-887	51	30	αzu)x	αzu)x	PROPN
ejde-887	51	31	+	+	CCONJ
ejde-887	51	32	β	β	X
ejde-887	51	33	3	3	NUM
ejde-887	51	34	(	(	PUNCT
ejde-887	51	35	qu)xxx	qu)xxx	ADV
ejde-887	51	36	=	=	SYM
ejde-887	51	37	0	0	NUM
ejde-887	51	38	,	,	PUNCT
ejde-887	51	39	qut	qut	PROPN
ejde-887	51	40	+	+	CCONJ
ejde-887	51	41	zx	zx	PROPN
ejde-887	51	42	+	+	CCONJ
ejde-887	51	43	αuux	αuux	NOUN
ejde-887	51	44	=	=	SYM
ejde-887	51	45	0	0	NUM
ejde-887	51	46	,	,	PUNCT
ejde-887	51	47	(	(	PUNCT
ejde-887	51	48	2.1	2.1	NUM
ejde-887	51	49	)	)	PUNCT
ejde-887	51	50	for	for	ADP
ejde-887	51	51	the	the	DET
ejde-887	51	52	solutions	solution	NOUN
ejde-887	51	53	z(x	z(x	NUM
ejde-887	51	54	,	,	PUNCT
ejde-887	51	55	t	t	PROPN
ejde-887	51	56	)	)	PUNCT
ejde-887	51	57	,	,	PUNCT
ejde-887	51	58	u(x	u(x	PROPN
ejde-887	51	59	,	,	PUNCT
ejde-887	51	60	t	t	PROPN
ejde-887	51	61	)	)	PUNCT
ejde-887	51	62	where	where	SCONJ
ejde-887	51	63	(	(	PUNCT
ejde-887	51	64	x	x	NOUN
ejde-887	51	65	,	,	PUNCT
ejde-887	51	66	t	t	PROPN
ejde-887	51	67	)	)	PUNCT
ejde-887	51	68	∈	∈	PROPN
ejde-887	51	69	(	(	PUNCT
ejde-887	51	70	−l	−l	NOUN
ejde-887	51	71	,	,	PUNCT
ejde-887	51	72	l)×[0,∞	l)×[0,∞	PUNCT
ejde-887	51	73	)	)	PUNCT
ejde-887	51	74	and	and	CCONJ
ejde-887	51	75	the	the	DET
ejde-887	51	76	space	space	NOUN
ejde-887	51	77	domain	domain	NOUN
ejde-887	51	78	can	can	AUX
ejde-887	51	79	be	be	AUX
ejde-887	51	80	arbitrary	arbitrary	ADJ
ejde-887	51	81	extended	extended	ADJ
ejde-887	51	82	l	l	NOUN
ejde-887	51	83	to∞.	to∞.	PROPN
ejde-887	51	84	subscripts	subscript	NOUN
ejde-887	51	85	x	x	X
ejde-887	51	86	,	,	PUNCT
ejde-887	51	87	t	t	PROPN
ejde-887	51	88	represent	represent	VERB
ejde-887	51	89	differentiation	differentiation	NOUN
ejde-887	51	90	.	.	PUNCT
ejde-887	52	1	the	the	DET
ejde-887	52	2	two	two	NUM
ejde-887	52	3	parameters	parameter	NOUN
ejde-887	52	4	α	α	PRON
ejde-887	52	5	,	,	PUNCT
ejde-887	52	6	β	β	X
ejde-887	52	7	∈	∈	PROPN
ejde-887	53	1	[	[	X
ejde-887	53	2	0	0	NUM
ejde-887	53	3	,	,	PUNCT
ejde-887	53	4	1	1	NUM
ejde-887	53	5	]	]	PUNCT
ejde-887	53	6	control	control	VERB
ejde-887	53	7	the	the	DET
ejde-887	53	8	nonlinearity	nonlinearity	NOUN
ejde-887	53	9	and	and	CCONJ
ejde-887	53	10	dispersion	dispersion	NOUN
ejde-887	53	11	,	,	PUNCT
ejde-887	53	12	respectively	respectively	ADV
ejde-887	53	13	,	,	PUNCT
ejde-887	53	14	and	and	CCONJ
ejde-887	53	15	the	the	DET
ejde-887	53	16	variable	variable	ADJ
ejde-887	53	17	coefficient	coefficient	NOUN
ejde-887	53	18	q(x	q(x	NOUN
ejde-887	53	19	)	)	PUNCT
ejde-887	53	20	is	be	AUX
ejde-887	53	21	a	a	DET
ejde-887	53	22	time	time	NOUN
ejde-887	53	23	-	-	PUNCT
ejde-887	53	24	independent	independent	ADJ
ejde-887	53	25	conveniently	conveniently	ADV
ejde-887	53	26	smooth	smooth	ADJ
ejde-887	53	27	and	and	CCONJ
ejde-887	53	28	ls(r	ls(r	NUM
ejde-887	53	29	)	)	PUNCT
ejde-887	53	30	bounded	bound	VERB
ejde-887	53	31	function	function	NOUN
ejde-887	53	32	.	.	PUNCT
ejde-887	54	1	system	system	NOUN
ejde-887	54	2	(	(	PUNCT
ejde-887	54	3	2.1	2.1	NUM
ejde-887	54	4	)	)	PUNCT
ejde-887	54	5	represents	represent	VERB
ejde-887	54	6	the	the	DET
ejde-887	54	7	(	(	PUNCT
ejde-887	54	8	1	1	NUM
ejde-887	54	9	+	+	NOUN
ejde-887	54	10	1	1	NUM
ejde-887	54	11	)	)	PUNCT
ejde-887	54	12	conservative	conservative	ADJ
ejde-887	54	13	(	(	PUNCT
ejde-887	54	14	evolutionary	evolutionary	ADJ
ejde-887	54	15	)	)	PUNCT
ejde-887	54	16	version	version	NOUN
ejde-887	54	17	of	of	ADP
ejde-887	54	18	the	the	DET
ejde-887	54	19	surface	surface	NOUN
ejde-887	54	20	-	-	PUNCT
ejde-887	54	21	variable	variable	ADJ
ejde-887	54	22	boussinesq	boussinesq	ADJ
ejde-887	54	23	system	system	NOUN
ejde-887	54	24	for	for	ADP
ejde-887	54	25	surface	surface	NOUN
ejde-887	54	26	waves	wave	NOUN
ejde-887	54	27	[	[	X
ejde-887	54	28	46	46	NUM
ejde-887	54	29	]	]	PUNCT
ejde-887	54	30	.	.	PUNCT
ejde-887	55	1	while	while	SCONJ
ejde-887	55	2	the	the	DET
ejde-887	55	3	β	β	PROPN
ejde-887	55	4	dispersion	dispersion	NOUN
ejde-887	55	5	parameter	parameter	NOUN
ejde-887	55	6	is	be	AUX
ejde-887	55	7	not	not	PART
ejde-887	55	8	qualitatively	qualitatively	ADV
ejde-887	55	9	relevant	relevant	ADJ
ejde-887	55	10	for	for	ADP
ejde-887	55	11	this	this	DET
ejde-887	55	12	system	system	NOUN
ejde-887	55	13	because	because	SCONJ
ejde-887	55	14	it	it	PRON
ejde-887	55	15	can	can	AUX
ejde-887	55	16	be	be	AUX
ejde-887	55	17	absorbed	absorb	VERB
ejde-887	55	18	in	in	ADP
ejde-887	55	19	a	a	DET
ejde-887	55	20	scaling	scale	VERB
ejde-887	55	21	transformation	transformation	NOUN
ejde-887	55	22	,	,	PUNCT
ejde-887	55	23	handling	handle	VERB
ejde-887	55	24	the	the	DET
ejde-887	55	25	other	other	ADJ
ejde-887	55	26	two	two	NUM
ejde-887	55	27	parameters	parameter	NOUN
ejde-887	55	28	α	α	PRON
ejde-887	55	29	,	,	PUNCT
ejde-887	55	30	q(x	q(x	NOUN
ejde-887	55	31	)	)	PUNCT
ejde-887	55	32	can	can	AUX
ejde-887	55	33	help	help	VERB
ejde-887	55	34	analyzing	analyze	VERB
ejde-887	55	35	asymptotic	asymptotic	ADJ
ejde-887	55	36	limiting	limiting	NOUN
ejde-887	55	37	situations	situation	NOUN
ejde-887	55	38	of	of	ADP
ejde-887	55	39	this	this	DET
ejde-887	55	40	boussinesq	boussinesq	ADJ
ejde-887	55	41	system	system	NOUN
ejde-887	55	42	:	:	PUNCT
ejde-887	55	43	the	the	DET
ejde-887	55	44	nonlinear	nonlinear	ADJ
ejde-887	55	45	autonomous	autonomous	ADJ
ejde-887	55	46	limit	limit	NOUN
ejde-887	55	47	,	,	PUNCT
ejde-887	55	48	and	and	CCONJ
ejde-887	55	49	the	the	DET
ejde-887	55	50	linear	linear	ADJ
ejde-887	55	51	non	non	ADJ
ejde-887	55	52	-	-	ADJ
ejde-887	55	53	autonomous	autonomous	ADJ
ejde-887	55	54	limit	limit	NOUN
ejde-887	55	55	.	.	PUNCT
ejde-887	56	1	with	with	ADP
ejde-887	56	2	this	this	DET
ejde-887	56	3	system	system	NOUN
ejde-887	56	4	we	we	PRON
ejde-887	56	5	associate	associate	VERB
ejde-887	56	6	regular	regular	ADJ
ejde-887	56	7	initial	initial	ADJ
ejde-887	56	8	cauchy	cauchy	ADJ
ejde-887	56	9	conditions	condition	NOUN
ejde-887	56	10	,	,	PUNCT
ejde-887	56	11	z(x	z(x	NUM
ejde-887	56	12	,	,	PUNCT
ejde-887	56	13	0	0	NUM
ejde-887	56	14	)	)	PUNCT
ejde-887	56	15	=	=	SYM
ejde-887	57	1	z0(x	z0(x	NUM
ejde-887	57	2	)	)	PUNCT
ejde-887	57	3	,	,	PUNCT
ejde-887	57	4	u(x	u(x	NOUN
ejde-887	57	5	,	,	PUNCT
ejde-887	57	6	0	0	NUM
ejde-887	57	7	)	)	PUNCT
ejde-887	57	8	=	=	SYM
ejde-887	58	1	u0(x	u0(x	NOUN
ejde-887	58	2	)	)	PUNCT
ejde-887	58	3	,	,	PUNCT
ejde-887	58	4	z0	z0	PROPN
ejde-887	58	5	,	,	PUNCT
ejde-887	58	6	u0	u0	PROPN
ejde-887	58	7	∈	∈	PROPN
ejde-887	58	8	hs(r	hs(r	PUNCT
ejde-887	58	9	)	)	PUNCT
ejde-887	58	10	,	,	PUNCT
ejde-887	58	11	(	(	PUNCT
ejde-887	58	12	2.2	2.2	NUM
ejde-887	58	13	)	)	PUNCT
ejde-887	59	1	where	where	SCONJ
ejde-887	59	2	hs(r	hs(r	PUNCT
ejde-887	59	3	)	)	PUNCT
ejde-887	59	4	is	be	AUX
ejde-887	59	5	the	the	DET
ejde-887	59	6	sobolev	sobolev	PROPN
ejde-887	59	7	spacew	spacew	NOUN
ejde-887	59	8	s,2(r	s,2(r	PROPN
ejde-887	59	9	)	)	PUNCT
ejde-887	59	10	for	for	ADP
ejde-887	59	11	some	some	PRON
ejde-887	59	12	s	s	PART
ejde-887	59	13	>	>	X
ejde-887	59	14	1	1	NUM
ejde-887	59	15	.	.	PUNCT
ejde-887	60	1	in	in	ADP
ejde-887	60	2	fact	fact	NOUN
ejde-887	60	3	,	,	PUNCT
ejde-887	60	4	in	in	ADP
ejde-887	60	5	this	this	DET
ejde-887	60	6	paper	paper	NOUN
ejde-887	60	7	we	we	PRON
ejde-887	60	8	will	will	AUX
ejde-887	60	9	use	use	VERB
ejde-887	60	10	for	for	ADP
ejde-887	60	11	the	the	DET
ejde-887	60	12	initial	initial	ADJ
ejde-887	60	13	conditions	condition	NOUN
ejde-887	60	14	only	only	ADV
ejde-887	60	15	one	one	NUM
ejde-887	60	16	-	-	PUNCT
ejde-887	60	17	soliton	soliton	NOUN
ejde-887	60	18	solutions	solution	NOUN
ejde-887	60	19	of	of	ADP
ejde-887	60	20	the	the	DET
ejde-887	60	21	autonomous	autonomous	ADJ
ejde-887	60	22	limit	limit	NOUN
ejde-887	60	23	of	of	ADP
ejde-887	60	24	(	(	PUNCT
ejde-887	60	25	2.1	2.1	NUM
ejde-887	60	26	)	)	PUNCT
ejde-887	60	27	which	which	PRON
ejde-887	60	28	obey	obey	VERB
ejde-887	60	29	the	the	DET
ejde-887	60	30	requested	request	VERB
ejde-887	60	31	constraints	constraint	NOUN
ejde-887	60	32	being	be	AUX
ejde-887	60	33	rapidly	rapidly	ADV
ejde-887	60	34	decreasing	decrease	VERB
ejde-887	60	35	functions	function	NOUN
ejde-887	60	36	in	in	ADP
ejde-887	60	37	lp(r	lp(r	NOUN
ejde-887	60	38	)	)	PUNCT
ejde-887	60	39	of	of	ADP
ejde-887	60	40	sech	sech	PROPN
ejde-887	60	41	types	type	NOUN
ejde-887	60	42	,	,	PUNCT
ejde-887	60	43	p	p	NOUN
ejde-887	60	44	≥	≥	NUM
ejde-887	60	45	1	1	NUM
ejde-887	60	46	,	,	PUNCT
ejde-887	60	47	in	in	ADP
ejde-887	60	48	(	(	PUNCT
ejde-887	60	49	3.8	3.8	NUM
ejde-887	60	50	)	)	PUNCT
ejde-887	60	51	.	.	PUNCT
ejde-887	61	1	2.1	2.1	NUM
ejde-887	61	2	.	.	PUNCT
ejde-887	62	1	well	well	INTJ
ejde-887	62	2	posed	pose	VERB
ejde-887	62	3	problem	problem	NOUN
ejde-887	62	4	for	for	ADP
ejde-887	62	5	the	the	DET
ejde-887	62	6	nonlinear	nonlinear	ADJ
ejde-887	62	7	and	and	CCONJ
ejde-887	62	8	non	non	ADJ
ejde-887	62	9	-	-	ADJ
ejde-887	62	10	autonomous	autonomous	ADJ
ejde-887	62	11	boussinesq	boussinesq	ADJ
ejde-887	62	12	system	system	NOUN
ejde-887	62	13	.	.	PUNCT
ejde-887	63	1	the	the	DET
ejde-887	63	2	autonomous	autonomous	ADJ
ejde-887	63	3	(	(	PUNCT
ejde-887	63	4	q	q	NOUN
ejde-887	63	5	=	=	SYM
ejde-887	63	6	1	1	NUM
ejde-887	63	7	)	)	PUNCT
ejde-887	63	8	version	version	NOUN
ejde-887	63	9	of	of	ADP
ejde-887	63	10	the	the	DET
ejde-887	63	11	boussinesq	boussinesq	ADJ
ejde-887	63	12	system	system	NOUN
ejde-887	63	13	(	(	PUNCT
ejde-887	63	14	2.1	2.1	NUM
ejde-887	63	15	)	)	PUNCT
ejde-887	63	16	together	together	ADV
ejde-887	63	17	with	with	ADP
ejde-887	63	18	the	the	DET
ejde-887	63	19	initial	initial	ADJ
ejde-887	63	20	conditions	condition	NOUN
ejde-887	63	21	(	(	PUNCT
ejde-887	63	22	2.2	2.2	NUM
ejde-887	63	23	)	)	PUNCT
ejde-887	63	24	was	be	AUX
ejde-887	63	25	shown	show	VERB
ejde-887	63	26	to	to	PART
ejde-887	63	27	be	be	AUX
ejde-887	63	28	a	a	DET
ejde-887	63	29	linearly	linearly	ADV
ejde-887	63	30	well	well	ADV
ejde-887	63	31	posed	pose	VERB
ejde-887	63	32	problem	problem	NOUN
ejde-887	63	33	[	[	X
ejde-887	63	34	1	1	NUM
ejde-887	63	35	]	]	PUNCT
ejde-887	63	36	,	,	PUNCT
ejde-887	63	37	and	and	CCONJ
ejde-887	63	38	actually	actually	ADV
ejde-887	63	39	locally	locally	ADV
ejde-887	63	40	nonlinearly	nonlinearly	ADV
ejde-887	63	41	well	well	ADV
ejde-887	63	42	posed	pose	VERB
ejde-887	63	43	for	for	ADP
ejde-887	63	44	the	the	DET
ejde-887	63	45	case	case	NOUN
ejde-887	63	46	when	when	SCONJ
ejde-887	63	47	β	β	X
ejde-887	63	48	>	>	X
ejde-887	63	49	0	0	PUNCT
ejde-887	64	1	[	[	X
ejde-887	64	2	2	2	X
ejde-887	64	3	]	]	PUNCT
ejde-887	64	4	if	if	SCONJ
ejde-887	64	5	the	the	DET
ejde-887	64	6	initial	initial	ADJ
ejde-887	64	7	conditions	condition	NOUN
ejde-887	64	8	functions	function	NOUN
ejde-887	64	9	z0	z0	PROPN
ejde-887	64	10	,	,	PUNCT
ejde-887	64	11	u0	u0	PROPN
ejde-887	64	12	belong	belong	VERB
ejde-887	64	13	to	to	ADP
ejde-887	64	14	a	a	DET
ejde-887	64	15	sobolev	sobolev	NOUN
ejde-887	64	16	space	space	NOUN
ejde-887	64	17	hs	hs	PROPN
ejde-887	64	18	with	with	ADP
ejde-887	64	19	s	s	PRON
ejde-887	64	20	>	>	X
ejde-887	64	21	1	1	NUM
ejde-887	64	22	.	.	PUNCT
ejde-887	65	1	for	for	ADP
ejde-887	65	2	some	some	DET
ejde-887	65	3	generalized	generalized	ADJ
ejde-887	65	4	boussinesq	boussinesq	ADJ
ejde-887	65	5	systems	system	NOUN
ejde-887	65	6	,	,	PUNCT
ejde-887	65	7	which	which	PRON
ejde-887	65	8	include	include	VERB
ejde-887	65	9	our	our	PRON
ejde-887	65	10	case	case	NOUN
ejde-887	65	11	,	,	PUNCT
ejde-887	65	12	if	if	SCONJ
ejde-887	65	13	the	the	DET
ejde-887	65	14	system	system	NOUN
ejde-887	65	15	has	have	VERB
ejde-887	65	16	hamiltonian	hamiltonian	ADJ
ejde-887	65	17	form	form	NOUN
ejde-887	65	18	,	,	PUNCT
ejde-887	65	19	the	the	DET
ejde-887	65	20	problem	problem	NOUN
ejde-887	65	21	becomes	become	VERB
ejde-887	65	22	even	even	ADV
ejde-887	65	23	globally	globally	ADV
ejde-887	65	24	well	well	ADV
ejde-887	65	25	posed	pose	VERB
ejde-887	65	26	in	in	ADP
ejde-887	65	27	the	the	DET
ejde-887	65	28	physically	physically	ADV
ejde-887	65	29	relevant	relevant	ADJ
ejde-887	65	30	realm	realm	NOUN
ejde-887	65	31	of	of	ADP
ejde-887	65	32	small	small	ADJ
ejde-887	65	33	-	-	PUNCT
ejde-887	65	34	amplitude	amplitude	NOUN
ejde-887	65	35	,	,	PUNCT
ejde-887	65	36	long	long	ADJ
ejde-887	65	37	-	-	PUNCT
ejde-887	65	38	wavelength	wavelength	NOUN
ejde-887	65	39	disturbances	disturbance	NOUN
ejde-887	65	40	.	.	PUNCT
ejde-887	66	1	consequently	consequently	ADV
ejde-887	66	2	,	,	PUNCT
ejde-887	66	3	these	these	DET
ejde-887	66	4	types	type	NOUN
ejde-887	66	5	of	of	ADP
ejde-887	66	6	autonomous	autonomous	ADJ
ejde-887	66	7	boussinesq	boussinesq	NOUN
ejde-887	66	8	systems	system	NOUN
ejde-887	66	9	represent	represent	VERB
ejde-887	66	10	a	a	DET
ejde-887	66	11	good	good	ADJ
ejde-887	66	12	set	set	NOUN
ejde-887	66	13	of	of	ADP
ejde-887	66	14	models	model	NOUN
ejde-887	66	15	for	for	ADP
ejde-887	66	16	the	the	DET
ejde-887	66	17	propagation	propagation	NOUN
ejde-887	66	18	of	of	ADP
ejde-887	66	19	long	long	ADV
ejde-887	66	20	-	-	PUNCT
ejde-887	66	21	crested	crest	VERB
ejde-887	66	22	waves	wave	NOUN
ejde-887	66	23	in	in	ADP
ejde-887	66	24	the	the	DET
ejde-887	66	25	small	small	ADJ
ejde-887	66	26	amplitude	amplitude	NOUN
ejde-887	66	27	,	,	PUNCT
ejde-887	66	28	long	long	ADJ
ejde-887	66	29	waves	wave	NOUN
ejde-887	66	30	with	with	ADP
ejde-887	66	31	stokes	stoke	NOUN
ejde-887	66	32	number	number	NOUN
ejde-887	66	33	of	of	ADP
ejde-887	66	34	order	order	NOUN
ejde-887	66	35	o(1	o(1	NOUN
ejde-887	66	36	)	)	PUNCT
ejde-887	66	37	regime	regime	NOUN
ejde-887	66	38	(	(	PUNCT
ejde-887	66	39	boussinesq	boussinesq	ADJ
ejde-887	66	40	regime	regime	NOUN
ejde-887	66	41	)	)	PUNCT
ejde-887	66	42	with	with	ADP
ejde-887	66	43	satisfactory	satisfactory	ADJ
ejde-887	66	44	mathematical	mathematical	ADJ
ejde-887	66	45	theories	theory	NOUN
ejde-887	66	46	,	,	PUNCT
ejde-887	66	47	at	at	ADP
ejde-887	66	48	least	least	ADJ
ejde-887	66	49	as	as	SCONJ
ejde-887	66	50	regards	regard	VERB
ejde-887	66	51	the	the	DET
ejde-887	66	52	pure	pure	ADJ
ejde-887	66	53	initial	initial	ADJ
ejde-887	66	54	-	-	PUNCT
ejde-887	66	55	value	value	NOUN
ejde-887	66	56	problems	problem	NOUN
ejde-887	66	57	(	(	PUNCT
ejde-887	66	58	2.2	2.2	NUM
ejde-887	66	59	)	)	PUNCT
ejde-887	66	60	.	.	PUNCT
ejde-887	67	1	our	our	PRON
ejde-887	67	2	system	system	NOUN
ejde-887	67	3	(	(	PUNCT
ejde-887	67	4	2.1	2.1	NUM
ejde-887	67	5	)	)	PUNCT
ejde-887	67	6	falls	fall	VERB
ejde-887	67	7	into	into	ADP
ejde-887	67	8	the	the	DET
ejde-887	67	9	so	so	ADV
ejde-887	67	10	-	-	PUNCT
ejde-887	67	11	called	call	VERB
ejde-887	67	12	c-1	c-1	NOUN
ejde-887	67	13	category	category	NOUN
ejde-887	67	14	of	of	ADP
ejde-887	67	15	well	well	ADV
ejde-887	67	16	posed	pose	VERB
ejde-887	67	17	problems	problem	NOUN
ejde-887	67	18	from	from	ADP
ejde-887	67	19	[	[	X
ejde-887	67	20	1	1	NUM
ejde-887	67	21	,	,	PUNCT
ejde-887	67	22	2	2	NUM
ejde-887	67	23	]	]	PUNCT
ejde-887	67	24	because	because	SCONJ
ejde-887	67	25	the	the	DET
ejde-887	67	26	conditions	condition	NOUN
ejde-887	67	27	for	for	ADP
ejde-887	67	28	the	the	DET
ejde-887	67	29	coefficients	coefficient	NOUN
ejde-887	67	30	of	of	ADP
ejde-887	67	31	the	the	DET
ejde-887	67	32	equations	equation	NOUN
ejde-887	67	33	in	in	ADP
ejde-887	67	34	these	these	DET
ejde-887	67	35	works	work	VERB
ejde-887	67	36	a	a	DET
ejde-887	67	37	≤	≤	NUM
ejde-887	67	38	0	0	NUM
ejde-887	67	39	,	,	PUNCT
ejde-887	67	40	c	c	NOUN
ejde-887	67	41	≤	≤	ADV
ejde-887	67	42	0	0	NUM
ejde-887	67	43	,	,	PUNCT
ejde-887	67	44	d	d	X
ejde-887	67	45	≥	≥	NUM
ejde-887	67	46	0	0	NUM
ejde-887	67	47	,	,	PUNCT
ejde-887	67	48	b	b	PRON
ejde-887	67	49	≥	≥	X
ejde-887	67	50	0	0	NUM
ejde-887	67	51	are	be	AUX
ejde-887	67	52	fulfilled	fulfil	VERB
ejde-887	67	53	in	in	ADP
ejde-887	67	54	our	our	PRON
ejde-887	67	55	case	case	NOUN
ejde-887	67	56	,	,	PUNCT
ejde-887	68	1	namely	namely	ADV
ejde-887	68	2	a	a	DET
ejde-887	68	3	=	=	SYM
ejde-887	68	4	c	c	NOUN
ejde-887	68	5	=	=	SYM
ejde-887	68	6	d	d	NOUN
ejde-887	68	7	=	=	SYM
ejde-887	68	8	0	0	NUM
ejde-887	68	9	,	,	PUNCT
ejde-887	68	10	b	b	X
ejde-887	68	11	=	=	PUNCT
ejde-887	68	12	βh3/3	βh3/3	X
ejde-887	68	13	>	>	X
ejde-887	68	14	0	0	NUM
ejde-887	68	15	.	.	PROPN
ejde-887	68	16	30	30	NUM
ejde-887	68	17	a.	a.	NOUN
ejde-887	68	18	ludu	ludu	PROPN
ejde-887	68	19	,	,	PUNCT
ejde-887	68	20	h.	h.	PROPN
ejde-887	68	21	khanal	khanal	NOUN
ejde-887	68	22	,	,	PUNCT
ejde-887	68	23	a.	a.	PROPN
ejde-887	68	24	s.	s.	PROPN
ejde-887	68	25	carstea	carstea	PROPN
ejde-887	68	26	ejde-2022	ejde-2022	PROPN
ejde-887	68	27	/	/	SYM
ejde-887	68	28	conf/27	conf/27	NOUN
ejde-887	68	29	this	this	PRON
ejde-887	68	30	can	can	AUX
ejde-887	68	31	be	be	AUX
ejde-887	68	32	proved	prove	VERB
ejde-887	68	33	by	by	ADP
ejde-887	68	34	a	a	DET
ejde-887	68	35	simple	simple	ADJ
ejde-887	68	36	substitution	substitution	NOUN
ejde-887	68	37	in	in	ADP
ejde-887	68	38	the	the	DET
ejde-887	68	39	first	first	ADJ
ejde-887	68	40	equation	equation	NOUN
ejde-887	68	41	in	in	ADP
ejde-887	68	42	(	(	PUNCT
ejde-887	68	43	2.1	2.1	NUM
ejde-887	68	44	)	)	PUNCT
ejde-887	68	45	which	which	PRON
ejde-887	68	46	turns	turn	VERB
ejde-887	68	47	the	the	DET
ejde-887	68	48	term	term	NOUN
ejde-887	68	49	βh3(u)xxx	βh3(u)xxx	NOUN
ejde-887	68	50	into	into	ADP
ejde-887	68	51	−βh3(u)xxt	−βh3(u)xxt	NOUN
ejde-887	68	52	.	.	PUNCT
ejde-887	69	1	for	for	ADP
ejde-887	69	2	the	the	DET
ejde-887	69	3	nonlinear	nonlinear	ADJ
ejde-887	69	4	non	non	ADJ
ejde-887	69	5	-	-	ADJ
ejde-887	69	6	autonomous	autonomous	ADJ
ejde-887	69	7	boussinesq	boussinesq	NOUN
ejde-887	69	8	case	case	NOUN
ejde-887	69	9	,	,	PUNCT
ejde-887	69	10	in	in	ADP
ejde-887	69	11	[	[	PUNCT
ejde-887	69	12	2	2	NUM
ejde-887	69	13	,	,	PUNCT
ejde-887	69	14	30	30	NUM
ejde-887	69	15	]	]	PUNCT
ejde-887	69	16	it	it	PRON
ejde-887	69	17	is	be	AUX
ejde-887	69	18	shown	show	VERB
ejde-887	69	19	that	that	SCONJ
ejde-887	69	20	for	for	ADP
ejde-887	69	21	the	the	DET
ejde-887	69	22	initial	initial	ADJ
ejde-887	69	23	-	-	PUNCT
ejde-887	69	24	value	value	NOUN
ejde-887	69	25	problem	problem	NOUN
ejde-887	69	26	(	(	PUNCT
ejde-887	69	27	2.2	2.2	NUM
ejde-887	69	28	)	)	PUNCT
ejde-887	69	29	under	under	ADP
ejde-887	69	30	the	the	DET
ejde-887	69	31	restriction	restriction	NOUN
ejde-887	69	32	c-1	c-1	NOUN
ejde-887	69	33	(	(	PUNCT
ejde-887	69	34	meaning	meaning	NOUN
ejde-887	69	35	for	for	ADP
ejde-887	69	36	physically	physically	ADV
ejde-887	69	37	relevant	relevant	ADJ
ejde-887	69	38	initial	initial	ADJ
ejde-887	69	39	disturbances	disturbance	NOUN
ejde-887	69	40	)	)	PUNCT
ejde-887	69	41	the	the	DET
ejde-887	69	42	problem	problem	NOUN
ejde-887	69	43	is	be	AUX
ejde-887	69	44	globally	globally	ADV
ejde-887	69	45	well	well	ADV
ejde-887	69	46	posed	pose	VERB
ejde-887	69	47	in	in	ADP
ejde-887	69	48	time	time	NOUN
ejde-887	69	49	.	.	PUNCT
ejde-887	70	1	on	on	ADP
ejde-887	70	2	the	the	DET
ejde-887	70	3	other	other	ADJ
ejde-887	70	4	hand	hand	NOUN
ejde-887	70	5	,	,	PUNCT
ejde-887	70	6	numerical	numerical	ADJ
ejde-887	70	7	simulations	simulation	NOUN
ejde-887	70	8	for	for	ADP
ejde-887	70	9	this	this	DET
ejde-887	70	10	case	case	NOUN
ejde-887	70	11	[	[	X
ejde-887	70	12	2	2	X
ejde-887	70	13	]	]	PUNCT
ejde-887	70	14	indicate	indicate	VERB
ejde-887	70	15	that	that	SCONJ
ejde-887	70	16	the	the	DET
ejde-887	70	17	equations	equation	NOUN
ejde-887	70	18	do	do	AUX
ejde-887	70	19	feature	feature	VERB
ejde-887	70	20	singularity	singularity	NOUN
ejde-887	70	21	formation	formation	NOUN
ejde-887	70	22	in	in	ADP
ejde-887	70	23	finite	finite	ADJ
ejde-887	70	24	time	time	NOUN
ejde-887	70	25	for	for	ADP
ejde-887	70	26	large	large	ADJ
ejde-887	70	27	initial	initial	ADJ
ejde-887	70	28	data	datum	NOUN
ejde-887	70	29	,	,	PUNCT
ejde-887	70	30	just	just	ADV
ejde-887	70	31	as	as	SCONJ
ejde-887	70	32	happens	happen	VERB
ejde-887	70	33	for	for	ADP
ejde-887	70	34	kdv	kdv	NOUN
ejde-887	70	35	-	-	PUNCT
ejde-887	70	36	type	type	NOUN
ejde-887	70	37	unidirectional	unidirectional	ADJ
ejde-887	70	38	models	model	NOUN
ejde-887	70	39	in	in	ADP
ejde-887	70	40	the	the	DET
ejde-887	70	41	same	same	ADJ
ejde-887	70	42	long	long	ADJ
ejde-887	70	43	-	-	PUNCT
ejde-887	70	44	wave	wave	NOUN
ejde-887	70	45	regime	regime	NOUN
ejde-887	70	46	.	.	PUNCT
ejde-887	71	1	moreover	moreover	ADV
ejde-887	71	2	,	,	PUNCT
ejde-887	71	3	they	they	PRON
ejde-887	71	4	found	find	VERB
ejde-887	71	5	that	that	SCONJ
ejde-887	71	6	non	non	ADJ
ejde-887	71	7	-	-	ADJ
ejde-887	71	8	homogeneous	homogeneous	ADJ
ejde-887	71	9	boundary	boundary	ADJ
ejde-887	71	10	conditions	condition	NOUN
ejde-887	71	11	imposed	impose	VERB
ejde-887	71	12	at	at	ADP
ejde-887	71	13	finite	finite	PROPN
ejde-887	71	14	spatial	spatial	ADJ
ejde-887	71	15	positions	position	NOUN
ejde-887	71	16	often	often	ADV
ejde-887	71	17	intrude	intrude	VERB
ejde-887	71	18	just	just	ADV
ejde-887	71	19	as	as	SCONJ
ejde-887	71	20	they	they	PRON
ejde-887	71	21	do	do	VERB
ejde-887	71	22	for	for	ADP
ejde-887	71	23	unidirectional	unidirectional	ADJ
ejde-887	71	24	kdv	kdv	NOUN
ejde-887	71	25	models	model	NOUN
ejde-887	71	26	[	[	X
ejde-887	71	27	1	1	NUM
ejde-887	71	28	]	]	PUNCT
ejde-887	71	29	.	.	PUNCT
ejde-887	72	1	to	to	PART
ejde-887	72	2	apply	apply	VERB
ejde-887	72	3	these	these	DET
ejde-887	72	4	results	result	NOUN
ejde-887	72	5	to	to	ADP
ejde-887	72	6	our	our	PRON
ejde-887	72	7	non	non	ADJ
ejde-887	72	8	-	-	ADJ
ejde-887	72	9	autonomous	autonomous	ADJ
ejde-887	72	10	case	case	NOUN
ejde-887	72	11	,	,	PUNCT
ejde-887	72	12	we	we	PRON
ejde-887	72	13	need	need	VERB
ejde-887	72	14	to	to	PART
ejde-887	72	15	generalize	generalize	VERB
ejde-887	72	16	the	the	DET
ejde-887	72	17	boundness	boundness	NOUN
ejde-887	72	18	criteria	criterion	NOUN
ejde-887	72	19	to	to	ADP
ejde-887	72	20	a	a	DET
ejde-887	72	21	weighted	weight	VERB
ejde-887	72	22	sobolev	sobolev	ADJ
ejde-887	72	23	space	space	NOUN
ejde-887	72	24	,	,	PUNCT
ejde-887	72	25	in	in	ADP
ejde-887	72	26	order	order	NOUN
ejde-887	72	27	to	to	PART
ejde-887	72	28	include	include	VERB
ejde-887	72	29	the	the	DET
ejde-887	72	30	variable	variable	ADJ
ejde-887	72	31	coefficient	coefficient	NOUN
ejde-887	72	32	q(x	q(x	NOUN
ejde-887	72	33	)	)	PUNCT
ejde-887	72	34	.	.	PUNCT
ejde-887	73	1	the	the	DET
ejde-887	73	2	norm	norm	NOUN
ejde-887	73	3	of	of	ADP
ejde-887	73	4	a	a	DET
ejde-887	73	5	function	function	NOUN
ejde-887	73	6	f	f	PROPN
ejde-887	73	7	∈	∈	PROPN
ejde-887	73	8	ck(r	ck(r	NOUN
ejde-887	73	9	)	)	PUNCT
ejde-887	73	10	in	in	ADP
ejde-887	73	11	a	a	DET
ejde-887	73	12	weighted	weight	VERB
ejde-887	73	13	sobolev	sobolev	NOUN
ejde-887	73	14	space	space	NOUN
ejde-887	73	15	w	w	PROPN
ejde-887	73	16	p	p	X
ejde-887	73	17	,	,	PUNCT
ejde-887	73	18	k	k	PROPN
ejde-887	73	19	w	w	PROPN
ejde-887	73	20	is	be	AUX
ejde-887	73	21	given	give	VERB
ejde-887	73	22	by	by	ADP
ejde-887	73	23	the	the	DET
ejde-887	73	24	sum	sum	NOUN
ejde-887	73	25	of	of	ADP
ejde-887	73	26	the	the	DET
ejde-887	73	27	lebesgue	lebesgue	NOUN
ejde-887	73	28	integrals	integral	NOUN
ejde-887	73	29	over	over	ADP
ejde-887	73	30	r	r	NOUN
ejde-887	73	31	of	of	ADP
ejde-887	73	32	the	the	DET
ejde-887	73	33	pth	pth	NOUN
ejde-887	73	34	power	power	NOUN
ejde-887	73	35	of	of	ADP
ejde-887	73	36	the	the	DET
ejde-887	73	37	absolute	absolute	ADJ
ejde-887	73	38	values	value	NOUN
ejde-887	73	39	of	of	ADP
ejde-887	73	40	products	product	NOUN
ejde-887	73	41	between	between	ADP
ejde-887	73	42	a	a	DET
ejde-887	73	43	weight	weight	NOUN
ejde-887	73	44	function	function	NOUN
ejde-887	73	45	w(x	w(x	NOUN
ejde-887	73	46	)	)	PUNCT
ejde-887	73	47	and	and	CCONJ
ejde-887	73	48	partial	partial	ADJ
ejde-887	73	49	derivatives	derivative	NOUN
ejde-887	73	50	f	f	NOUN
ejde-887	73	51	,	,	PUNCT
ejde-887	73	52	fx	fx	PROPN
ejde-887	73	53	,	,	PUNCT
ejde-887	73	54	.	.	PUNCT
ejde-887	73	55	.	.	PUNCT
ejde-887	74	1	.	.	PUNCT
ejde-887	75	1	,	,	PUNCT
ejde-887	75	2	fxx	fxx	PROPN
ejde-887	75	3	...	...	PUNCT
ejde-887	75	4	x	x	X
ejde-887	75	5	up	up	ADP
ejde-887	75	6	to	to	PART
ejde-887	75	7	order	order	VERB
ejde-887	75	8	k	k	NOUN
ejde-887	75	9	,	,	PUNCT
ejde-887	75	10	denoted	denote	VERB
ejde-887	75	11	∥f∥lp	∥f∥lp	PROPN
ejde-887	75	12	w	w	PROPN
ejde-887	75	13	.	.	PUNCT
ejde-887	76	1	the	the	DET
ejde-887	76	2	weight	weight	NOUN
ejde-887	76	3	function	function	NOUN
ejde-887	76	4	must	must	AUX
ejde-887	76	5	be	be	AUX
ejde-887	76	6	a	a	DET
ejde-887	76	7	strictly	strictly	ADV
ejde-887	76	8	positive	positive	ADJ
ejde-887	76	9	locally	locally	ADV
ejde-887	76	10	integrable	integrable	ADJ
ejde-887	76	11	function	function	NOUN
ejde-887	76	12	on	on	ADP
ejde-887	76	13	r	r	NOUN
ejde-887	76	14	[	[	X
ejde-887	76	15	40	40	NUM
ejde-887	76	16	]	]	PUNCT
ejde-887	76	17	.	.	PUNCT
ejde-887	77	1	by	by	ADP
ejde-887	77	2	hölder	hölder	PROPN
ejde-887	77	3	’s	’s	PART
ejde-887	77	4	inequality	inequality	NOUN
ejde-887	77	5	,	,	PUNCT
ejde-887	77	6	if	if	SCONJ
ejde-887	77	7	a	a	DET
ejde-887	77	8	ck(r	ck(r	NOUN
ejde-887	77	9	)	)	PUNCT
ejde-887	77	10	function	function	NOUN
ejde-887	77	11	f	f	PROPN
ejde-887	77	12	is	be	AUX
ejde-887	77	13	sobolev	sobolev	NOUN
ejde-887	77	14	weighted	weight	VERB
ejde-887	77	15	,	,	PUNCT
ejde-887	77	16	and	and	CCONJ
ejde-887	77	17	the	the	DET
ejde-887	77	18	weight	weight	NOUN
ejde-887	77	19	function	function	NOUN
ejde-887	77	20	is	be	AUX
ejde-887	77	21	lp(r	lp(r	NOUN
ejde-887	77	22	)	)	PUNCT
ejde-887	77	23	,	,	PUNCT
ejde-887	77	24	then	then	ADV
ejde-887	77	25	f	f	PROPN
ejde-887	77	26	is	be	AUX
ejde-887	77	27	also	also	ADV
ejde-887	77	28	in	in	ADP
ejde-887	77	29	w	w	PROPN
ejde-887	77	30	p	p	X
ejde-887	77	31	,	,	PUNCT
ejde-887	77	32	k	k	PROPN
ejde-887	77	33	w	w	PROPN
ejde-887	78	1	[	[	X
ejde-887	78	2	40	40	NUM
ejde-887	78	3	,	,	PUNCT
ejde-887	78	4	7	7	NUM
ejde-887	78	5	]	]	PUNCT
ejde-887	78	6	.	.	PUNCT
ejde-887	79	1	it	it	PRON
ejde-887	79	2	results	result	VERB
ejde-887	79	3	that	that	SCONJ
ejde-887	79	4	the	the	DET
ejde-887	79	5	well	well	ADV
ejde-887	79	6	posed	pose	VERB
ejde-887	79	7	criteria	criterion	NOUN
ejde-887	79	8	in	in	ADP
ejde-887	79	9	[	[	X
ejde-887	79	10	1	1	NUM
ejde-887	79	11	,	,	PUNCT
ejde-887	79	12	2	2	NUM
ejde-887	79	13	,	,	PUNCT
ejde-887	79	14	30	30	NUM
ejde-887	79	15	]	]	PUNCT
ejde-887	79	16	can	can	AUX
ejde-887	79	17	be	be	AUX
ejde-887	79	18	applied	apply	VERB
ejde-887	79	19	to	to	ADP
ejde-887	79	20	the	the	DET
ejde-887	79	21	non	non	ADJ
ejde-887	79	22	-	-	ADJ
ejde-887	79	23	autonomous	autonomous	ADJ
ejde-887	79	24	boussinesq	boussinesq	ADJ
ejde-887	79	25	system	system	NOUN
ejde-887	79	26	if	if	SCONJ
ejde-887	79	27	the	the	DET
ejde-887	79	28	variable	variable	ADJ
ejde-887	79	29	coefficient	coefficient	NOUN
ejde-887	79	30	fulfills	fulfill	VERB
ejde-887	79	31	the	the	DET
ejde-887	79	32	condition	condition	NOUN
ejde-887	79	33	to	to	PART
ejde-887	79	34	be	be	AUX
ejde-887	79	35	a	a	DET
ejde-887	79	36	weight	weight	NOUN
ejde-887	79	37	functions	function	NOUN
ejde-887	79	38	.	.	PUNCT
ejde-887	80	1	it	it	PRON
ejde-887	80	2	results	result	VERB
ejde-887	80	3	that	that	SCONJ
ejde-887	80	4	for	for	ADP
ejde-887	80	5	smooth	smooth	ADJ
ejde-887	80	6	and	and	CCONJ
ejde-887	80	7	locally	locally	ADV
ejde-887	80	8	integrable	integrable	ADJ
ejde-887	80	9	coefficient	coefficient	NOUN
ejde-887	80	10	functions	function	NOUN
ejde-887	80	11	q(x	q(x	NOUN
ejde-887	80	12	)	)	PUNCT
ejde-887	80	13	with	with	ADP
ejde-887	80	14	values	value	NOUN
ejde-887	80	15	close	close	ADJ
ejde-887	80	16	to	to	ADP
ejde-887	80	17	1	1	NUM
ejde-887	80	18	our	our	PRON
ejde-887	80	19	boussinesq	boussinesq	ADJ
ejde-887	80	20	system	system	NOUN
ejde-887	80	21	represents	represent	VERB
ejde-887	80	22	a	a	DET
ejde-887	80	23	well	well	ADV
ejde-887	80	24	posed	pose	VERB
ejde-887	80	25	problem	problem	NOUN
ejde-887	80	26	,	,	PUNCT
ejde-887	80	27	at	at	ADP
ejde-887	80	28	least	least	ADJ
ejde-887	80	29	for	for	ADP
ejde-887	80	30	certain	certain	ADJ
ejde-887	80	31	finite	finite	ADJ
ejde-887	80	32	time	time	NOUN
ejde-887	80	33	interval	interval	NOUN
ejde-887	80	34	following	follow	VERB
ejde-887	80	35	the	the	DET
ejde-887	80	36	initial	initial	ADJ
ejde-887	80	37	moment	moment	NOUN
ejde-887	80	38	.	.	PUNCT
ejde-887	81	1	since	since	SCONJ
ejde-887	81	2	numerical	numerical	ADJ
ejde-887	81	3	simulations	simulation	NOUN
ejde-887	81	4	used	use	VERB
ejde-887	81	5	for	for	ADP
ejde-887	81	6	the	the	DET
ejde-887	81	7	validations	validation	NOUN
ejde-887	81	8	of	of	ADP
ejde-887	81	9	the	the	DET
ejde-887	81	10	analytical	analytical	ADJ
ejde-887	81	11	results	result	NOUN
ejde-887	81	12	(	(	PUNCT
ejde-887	81	13	see	see	VERB
ejde-887	81	14	section	section	NOUN
ejde-887	81	15	5	5	NUM
ejde-887	81	16	)	)	PUNCT
ejde-887	81	17	are	be	AUX
ejde-887	81	18	invariably	invariably	ADV
ejde-887	81	19	performed	perform	VERB
ejde-887	81	20	on	on	ADP
ejde-887	81	21	bounded	bounded	ADJ
ejde-887	81	22	domains	domain	NOUN
ejde-887	81	23	,	,	PUNCT
ejde-887	81	24	if	if	SCONJ
ejde-887	81	25	we	we	PRON
ejde-887	81	26	use	use	VERB
ejde-887	81	27	homogeneous	homogeneous	ADJ
ejde-887	81	28	boundary	boundary	ADJ
ejde-887	81	29	conditions	condition	NOUN
ejde-887	81	30	placed	place	VERB
ejde-887	81	31	relatively	relatively	ADV
ejde-887	81	32	far	far	ADV
ejde-887	81	33	away	away	ADV
ejde-887	81	34	from	from	ADP
ejde-887	81	35	the	the	DET
ejde-887	81	36	support	support	NOUN
ejde-887	81	37	of	of	ADP
ejde-887	81	38	the	the	DET
ejde-887	81	39	initial	initial	ADJ
ejde-887	81	40	condition	condition	NOUN
ejde-887	81	41	functions	function	NOUN
ejde-887	81	42	,	,	PUNCT
ejde-887	81	43	we	we	PRON
ejde-887	81	44	conclude	conclude	VERB
ejde-887	81	45	that	that	SCONJ
ejde-887	81	46	the	the	DET
ejde-887	81	47	system	system	NOUN
ejde-887	81	48	(	(	PUNCT
ejde-887	81	49	2.1)-(2.2	2.1)-(2.2	NUM
ejde-887	81	50	)	)	PUNCT
ejde-887	81	51	represents	represent	VERB
ejde-887	81	52	at	at	ADP
ejde-887	81	53	least	least	ADJ
ejde-887	81	54	a	a	DET
ejde-887	81	55	locally	locally	ADV
ejde-887	81	56	well	well	ADV
ejde-887	81	57	posed	pose	VERB
ejde-887	81	58	problem	problem	NOUN
ejde-887	81	59	.	.	PUNCT
ejde-887	82	1	3	3	X
ejde-887	82	2	.	.	X
ejde-887	82	3	asymptotic	asymptotic	ADJ
ejde-887	82	4	approach	approach	NOUN
ejde-887	82	5	3.1	3.1	NUM
ejde-887	82	6	.	.	PUNCT
ejde-887	82	7	autonomous	autonomous	ADJ
ejde-887	82	8	nonlinear	nonlinear	ADJ
ejde-887	82	9	limit	limit	NOUN
ejde-887	82	10	.	.	PUNCT
ejde-887	83	1	if	if	SCONJ
ejde-887	83	2	we	we	PRON
ejde-887	83	3	take	take	VERB
ejde-887	83	4	q(x	q(x	NOUN
ejde-887	83	5	)	)	PUNCT
ejde-887	83	6	→	→	SYM
ejde-887	83	7	1	1	NUM
ejde-887	83	8	,	,	PUNCT
ejde-887	83	9	equations	equation	NOUN
ejde-887	83	10	(	(	PUNCT
ejde-887	83	11	2.1	2.1	NUM
ejde-887	83	12	)	)	PUNCT
ejde-887	83	13	become	become	VERB
ejde-887	83	14	autonomous	autonomous	ADJ
ejde-887	83	15	,	,	PUNCT
ejde-887	83	16	and	and	CCONJ
ejde-887	83	17	we	we	PRON
ejde-887	83	18	obtain	obtain	VERB
ejde-887	83	19	the	the	DET
ejde-887	83	20	traditional	traditional	ADJ
ejde-887	83	21	boussinesq	boussinesq	ADJ
ejde-887	83	22	nonlinear	nonlinear	ADJ
ejde-887	83	23	system	system	NOUN
ejde-887	83	24	zt	zt	PROPN
ejde-887	83	25	+	+	PROPN
ejde-887	83	26	ux	ux	PROPN
ejde-887	84	1	+	+	CCONJ
ejde-887	84	2	α(zu)x	α(zu)x	NOUN
ejde-887	84	3	+	+	CCONJ
ejde-887	84	4	β	β	X
ejde-887	84	5	3	3	NUM
ejde-887	84	6	uxxx	uxxx	NOUN
ejde-887	84	7	=	=	SYM
ejde-887	84	8	0	0	NUM
ejde-887	84	9	,	,	PUNCT
ejde-887	84	10	ut	ut	PROPN
ejde-887	85	1	+	+	PROPN
ejde-887	85	2	zx	zx	PROPN
ejde-887	85	3	+	+	CCONJ
ejde-887	85	4	αuux	αuux	NOUN
ejde-887	85	5	=	=	SYM
ejde-887	85	6	0	0	NUM
ejde-887	85	7	,	,	PUNCT
ejde-887	85	8	(	(	PUNCT
ejde-887	85	9	3.1	3.1	NUM
ejde-887	85	10	)	)	PUNCT
ejde-887	85	11	in	in	ADP
ejde-887	85	12	this	this	DET
ejde-887	85	13	limit	limit	NOUN
ejde-887	85	14	(	(	PUNCT
ejde-887	85	15	2.1	2.1	NUM
ejde-887	85	16	)	)	PUNCT
ejde-887	85	17	reduce	reduce	VERB
ejde-887	85	18	to	to	ADP
ejde-887	85	19	the	the	DET
ejde-887	85	20	broer	broer	NOUN
ejde-887	85	21	-	-	PUNCT
ejde-887	85	22	kaup	kaup	PROPN
ejde-887	85	23	(	(	PUNCT
ejde-887	85	24	bk	bk	NOUN
ejde-887	85	25	)	)	PUNCT
ejde-887	85	26	nonlinear	nonlinear	ADJ
ejde-887	85	27	system	system	NOUN
ejde-887	85	28	which	which	PRON
ejde-887	85	29	is	be	AUX
ejde-887	85	30	integrable	integrable	ADJ
ejde-887	85	31	,	,	PUNCT
ejde-887	85	32	and	and	CCONJ
ejde-887	85	33	has	have	VERB
ejde-887	85	34	three	three	NUM
ejde-887	85	35	independent	independent	ADJ
ejde-887	85	36	hamiltonian	hamiltonian	ADJ
ejde-887	85	37	structures	structure	NOUN
ejde-887	85	38	[	[	X
ejde-887	85	39	24	24	NUM
ejde-887	85	40	,	,	PUNCT
ejde-887	85	41	46	46	NUM
ejde-887	85	42	]	]	PUNCT
ejde-887	85	43	.	.	PUNCT
ejde-887	86	1	integrability	integrability	NOUN
ejde-887	86	2	for	for	ADP
ejde-887	86	3	the	the	DET
ejde-887	86	4	bk	bk	PROPN
ejde-887	86	5	system	system	NOUN
ejde-887	86	6	was	be	AUX
ejde-887	86	7	proved	prove	VERB
ejde-887	86	8	using	use	VERB
ejde-887	86	9	the	the	DET
ejde-887	86	10	inverse	inverse	NOUN
ejde-887	86	11	scattering	scatter	VERB
ejde-887	86	12	transformation	transformation	NOUN
ejde-887	86	13	(	(	PUNCT
ejde-887	86	14	ist	ist	NOUN
ejde-887	86	15	)	)	PUNCT
ejde-887	86	16	,	,	PUNCT
ejde-887	86	17	but	but	CCONJ
ejde-887	86	18	there	there	PRON
ejde-887	86	19	are	be	VERB
ejde-887	86	20	also	also	ADV
ejde-887	86	21	integrability	integrability	NOUN
ejde-887	86	22	proofs	proof	NOUN
ejde-887	86	23	using	use	VERB
ejde-887	86	24	the	the	DET
ejde-887	86	25	bäcklund	bäcklund	NOUN
ejde-887	86	26	transformation	transformation	NOUN
ejde-887	86	27	[	[	X
ejde-887	86	28	21	21	NUM
ejde-887	86	29	,	,	PUNCT
ejde-887	86	30	23	23	NUM
ejde-887	86	31	]	]	PUNCT
ejde-887	86	32	,	,	PUNCT
ejde-887	86	33	or	or	CCONJ
ejde-887	86	34	the	the	DET
ejde-887	86	35	darboux	darboux	ADJ
ejde-887	86	36	transformation	transformation	NOUN
ejde-887	86	37	[	[	X
ejde-887	86	38	28	28	NUM
ejde-887	86	39	]	]	PUNCT
ejde-887	86	40	.	.	PUNCT
ejde-887	87	1	the	the	DET
ejde-887	87	2	flat	flat	ADJ
ejde-887	87	3	-	-	PUNCT
ejde-887	87	4	bottom	bottom	NOUN
ejde-887	87	5	boussinesq	boussinesq	NOUN
ejde-887	87	6	system	system	NOUN
ejde-887	87	7	is	be	AUX
ejde-887	87	8	also	also	ADV
ejde-887	87	9	a	a	DET
ejde-887	87	10	member	member	NOUN
ejde-887	87	11	of	of	ADP
ejde-887	87	12	the	the	DET
ejde-887	87	13	ablowitz	ablowitz	NOUN
ejde-887	87	14	-	-	PUNCT
ejde-887	87	15	kaup	kaup	PROPN
ejde-887	87	16	-	-	PUNCT
ejde-887	87	17	newell	newell	PROPN
ejde-887	87	18	-	-	PUNCT
ejde-887	87	19	segur	segur	NOUN
ejde-887	87	20	hierarchy	hierarchy	NOUN
ejde-887	87	21	(	(	PUNCT
ejde-887	87	22	akns	akns	NOUN
ejde-887	87	23	)	)	PUNCT
ejde-887	87	24	,	,	PUNCT
ejde-887	88	1	[	[	X
ejde-887	88	2	24	24	NUM
ejde-887	88	3	]	]	PUNCT
ejde-887	88	4	,	,	PUNCT
ejde-887	88	5	having	have	VERB
ejde-887	88	6	exact	exact	ADJ
ejde-887	88	7	rational	rational	ADJ
ejde-887	88	8	solutions	solution	NOUN
ejde-887	88	9	relevant	relevant	ADJ
ejde-887	88	10	to	to	ADP
ejde-887	88	11	the	the	DET
ejde-887	88	12	occurrence	occurrence	NOUN
ejde-887	88	13	of	of	ADP
ejde-887	88	14	rogue	rogue	ADJ
ejde-887	88	15	waves	wave	NOUN
ejde-887	88	16	,	,	PUNCT
ejde-887	88	17	[	[	X
ejde-887	88	18	9	9	NUM
ejde-887	88	19	]	]	PUNCT
ejde-887	88	20	,	,	PUNCT
ejde-887	88	21	a	a	DET
ejde-887	88	22	multi	multi	ADJ
ejde-887	88	23	-	-	ADJ
ejde-887	88	24	soliton	soliton	ADJ
ejde-887	88	25	solution	solution	NOUN
ejde-887	88	26	that	that	PRON
ejde-887	88	27	is	be	AUX
ejde-887	88	28	expressed	express	VERB
ejde-887	88	29	in	in	ADP
ejde-887	88	30	a	a	DET
ejde-887	88	31	closed	closed	ADJ
ejde-887	88	32	implicit	implicit	ADJ
ejde-887	88	33	form	form	NOUN
ejde-887	88	34	,	,	PUNCT
ejde-887	88	35	[	[	X
ejde-887	88	36	46	46	NUM
ejde-887	88	37	,	,	PUNCT
ejde-887	88	38	13	13	NUM
ejde-887	88	39	,	,	PUNCT
ejde-887	88	40	18	18	NUM
ejde-887	88	41	]	]	PUNCT
ejde-887	88	42	,	,	PUNCT
ejde-887	88	43	as	as	ADV
ejde-887	88	44	well	well	ADV
ejde-887	88	45	as	as	ADP
ejde-887	88	46	exact	exact	ADJ
ejde-887	88	47	solutions	solution	NOUN
ejde-887	88	48	obtained	obtain	VERB
ejde-887	88	49	by	by	ADP
ejde-887	88	50	the	the	DET
ejde-887	88	51	painlevé	painlevé	NOUN
ejde-887	88	52	method	method	NOUN
ejde-887	88	53	[	[	X
ejde-887	88	54	5	5	NUM
ejde-887	88	55	]	]	PUNCT
ejde-887	88	56	.	.	PUNCT
ejde-887	89	1	our	our	PRON
ejde-887	89	2	first	first	ADJ
ejde-887	89	3	step	step	NOUN
ejde-887	89	4	is	be	AUX
ejde-887	89	5	to	to	PART
ejde-887	89	6	obtain	obtain	VERB
ejde-887	89	7	oneor	oneor	PROPN
ejde-887	89	8	multi	multi	ADJ
ejde-887	89	9	-	-	ADJ
ejde-887	89	10	soliton	soliton	ADJ
ejde-887	89	11	solutions	solution	NOUN
ejde-887	89	12	for	for	ADP
ejde-887	89	13	the	the	DET
ejde-887	89	14	autonomous	autonomous	ADJ
ejde-887	89	15	system	system	NOUN
ejde-887	89	16	(	(	PUNCT
ejde-887	89	17	3.1	3.1	NUM
ejde-887	89	18	)	)	PUNCT
ejde-887	89	19	,	,	PUNCT
ejde-887	89	20	in	in	ADP
ejde-887	89	21	order	order	NOUN
ejde-887	89	22	to	to	PART
ejde-887	89	23	build	build	VERB
ejde-887	89	24	the	the	DET
ejde-887	89	25	perturbative	perturbative	ADJ
ejde-887	89	26	solutions	solution	NOUN
ejde-887	89	27	for	for	ADP
ejde-887	89	28	the	the	DET
ejde-887	89	29	non	non	ADJ
ejde-887	89	30	-	-	ADJ
ejde-887	89	31	autonomous	autonomous	ADJ
ejde-887	89	32	ejde-202x	ejde-202x	PROPN
ejde-887	89	33	/	/	SYM
ejde-887	89	34	conf/27	conf/27	NOUN
ejde-887	89	35	boussinesq	boussinesq	ADJ
ejde-887	89	36	equations	equation	NOUN
ejde-887	89	37	31	31	NUM
ejde-887	89	38	system	system	NOUN
ejde-887	89	39	(	(	PUNCT
ejde-887	89	40	2.1	2.1	NUM
ejde-887	89	41	)	)	PUNCT
ejde-887	89	42	.	.	PUNCT
ejde-887	90	1	by	by	ADP
ejde-887	90	2	applying	apply	VERB
ejde-887	90	3	a	a	DET
ejde-887	90	4	bäcklund	bäcklund	NOUN
ejde-887	90	5	transformation	transformation	NOUN
ejde-887	90	6	to	to	ADP
ejde-887	90	7	(	(	PUNCT
ejde-887	90	8	2.1	2.1	NUM
ejde-887	90	9	)	)	PUNCT
ejde-887	90	10	x→	x→	X
ejde-887	91	1	x	x	PUNCT
ejde-887	91	2	=	=	PUNCT
ejde-887	91	3	x	x	SYM
ejde-887	91	4	2	2	NUM
ejde-887	91	5	√	√	NUM
ejde-887	91	6	3	3	NUM
ejde-887	91	7	β	β	X
ejde-887	91	8	,	,	PUNCT
ejde-887	91	9	v(x	v(x	PROPN
ejde-887	91	10	,	,	PUNCT
ejde-887	91	11	t	t	PROPN
ejde-887	91	12	)	)	PUNCT
ejde-887	91	13	=	=	SYM
ejde-887	91	14	−αu	−αu	PROPN
ejde-887	91	15	,	,	PUNCT
ejde-887	91	16	w(x	w(x	PROPN
ejde-887	91	17	,	,	PUNCT
ejde-887	91	18	t	t	PROPN
ejde-887	91	19	)	)	PUNCT
ejde-887	91	20	=	=	SYM
ejde-887	92	1	1	1	NUM
ejde-887	92	2	+	+	CCONJ
ejde-887	92	3	αz	αz	NOUN
ejde-887	93	1	−	−	NOUN
ejde-887	93	2	2α	2α	NOUN
ejde-887	93	3	√	√	PROPN
ejde-887	93	4	β√	β√	SYM
ejde-887	93	5	3	3	NUM
ejde-887	93	6	ux	ux	NOUN
ejde-887	93	7	,	,	PUNCT
ejde-887	93	8	when	when	SCONJ
ejde-887	93	9	q	q	NOUN
ejde-887	93	10	=	=	SYM
ejde-887	93	11	1	1	NUM
ejde-887	93	12	,	,	PUNCT
ejde-887	93	13	equation	equation	NOUN
ejde-887	93	14	(	(	PUNCT
ejde-887	93	15	2.1	2.1	NUM
ejde-887	93	16	)	)	PUNCT
ejde-887	93	17	become	become	VERB
ejde-887	93	18	(	(	PUNCT
ejde-887	93	19	3.1	3.1	NUM
ejde-887	93	20	)	)	PUNCT
ejde-887	93	21	which	which	PRON
ejde-887	93	22	are	be	AUX
ejde-887	93	23	a	a	DET
ejde-887	93	24	bk	bk	NOUN
ejde-887	93	25	ist	ist	NOUN
ejde-887	93	26	-	-	PUNCT
ejde-887	93	27	integrable	integrable	ADJ
ejde-887	93	28	system	system	NOUN
ejde-887	93	29	[	[	X
ejde-887	93	30	24	24	NUM
ejde-887	93	31	,	,	PUNCT
ejde-887	93	32	28	28	NUM
ejde-887	93	33	]	]	PUNCT
ejde-887	93	34	vt	vt	NOUN
ejde-887	93	35	=	=	NOUN
ejde-887	93	36	1	1	NUM
ejde-887	93	37	2	2	NUM
ejde-887	93	38	(	(	PUNCT
ejde-887	93	39	2w	2w	NUM
ejde-887	93	40	−	−	PROPN
ejde-887	93	41	vx	vx	PROPN
ejde-887	93	42	+	+	CCONJ
ejde-887	93	43	v2)x	v2)x	ADJ
ejde-887	93	44	,	,	PUNCT
ejde-887	93	45	wt	wt	NOUN
ejde-887	93	46	=	=	SYM
ejde-887	93	47	(	(	PUNCT
ejde-887	93	48	vw	vw	X
ejde-887	93	49	+	+	CCONJ
ejde-887	93	50	1	1	NUM
ejde-887	93	51	2	2	NUM
ejde-887	93	52	wx	wx	NOUN
ejde-887	93	53	)	)	PUNCT
ejde-887	93	54	x	x	X
ejde-887	93	55	,	,	PUNCT
ejde-887	93	56	(	(	PUNCT
ejde-887	93	57	3.2	3.2	NUM
ejde-887	93	58	)	)	PUNCT
ejde-887	93	59	as	as	ADP
ejde-887	93	60	a	a	DET
ejde-887	93	61	consequence	consequence	NOUN
ejde-887	93	62	of	of	ADP
ejde-887	93	63	the	the	DET
ejde-887	93	64	compatibility	compatibility	NOUN
ejde-887	93	65	condition	condition	NOUN
ejde-887	93	66	(	(	PUNCT
ejde-887	93	67	zero	zero	NUM
ejde-887	93	68	-	-	PUNCT
ejde-887	93	69	curvature	curvature	NOUN
ejde-887	93	70	equation	equation	NOUN
ejde-887	93	71	)	)	PUNCT
ejde-887	93	72	for	for	ADP
ejde-887	93	73	the	the	DET
ejde-887	93	74	associated	associated	ADJ
ejde-887	93	75	linear	linear	PROPN
ejde-887	93	76	spectral	spectral	ADJ
ejde-887	93	77	problem	problem	NOUN
ejde-887	93	78	.	.	PUNCT
ejde-887	94	1	in	in	ADP
ejde-887	94	2	order	order	NOUN
ejde-887	94	3	to	to	PART
ejde-887	94	4	demonstrate	demonstrate	VERB
ejde-887	94	5	the	the	DET
ejde-887	94	6	integrability	integrability	NOUN
ejde-887	94	7	of	of	ADP
ejde-887	94	8	this	this	DET
ejde-887	94	9	bk	bk	NOUN
ejde-887	94	10	system	system	NOUN
ejde-887	94	11	(	(	PUNCT
ejde-887	94	12	3.2	3.2	NUM
ejde-887	94	13	)	)	PUNCT
ejde-887	94	14	we	we	PRON
ejde-887	94	15	consider	consider	VERB
ejde-887	94	16	the	the	DET
ejde-887	94	17	linear	linear	ADJ
ejde-887	94	18	spectral	spectral	ADJ
ejde-887	94	19	problem	problem	NOUN
ejde-887	94	20	for	for	ADP
ejde-887	94	21	the	the	DET
ejde-887	94	22	vector	vector	PROPN
ejde-887	94	23	ψ(x	ψ(x	PROPN
ejde-887	94	24	,	,	PUNCT
ejde-887	94	25	t	t	PROPN
ejde-887	94	26	)	)	PUNCT
ejde-887	94	27	ψx	ψx	PART
ejde-887	94	28	=	=	PUNCT
ejde-887	94	29	p̂ψ	p̂ψ	X
ejde-887	94	30	,	,	PUNCT
ejde-887	94	31	ψt	ψt	NOUN
ejde-887	94	32	=	=	SYM
ejde-887	94	33	n̂ψ	n̂ψ	NUM
ejde-887	94	34	,	,	PUNCT
ejde-887	94	35	ψ	ψ	X
ejde-887	94	36	=	=	SYM
ejde-887	94	37	(	(	PUNCT
ejde-887	94	38	ψ1,ψ2	ψ1,ψ2	PROPN
ejde-887	94	39	)	)	PUNCT
ejde-887	94	40	t	t	PROPN
ejde-887	94	41	,	,	PUNCT
ejde-887	94	42	(	(	PUNCT
ejde-887	94	43	3.3	3.3	NUM
ejde-887	94	44	)	)	PUNCT
ejde-887	94	45	where	where	SCONJ
ejde-887	94	46	p̂	p̂	X
ejde-887	94	47	=	=	PUNCT
ejde-887	95	1	(	(	PUNCT
ejde-887	95	2	−λ+	−λ+	NOUN
ejde-887	95	3	v	v	ADP
ejde-887	95	4	2	2	NUM
ejde-887	95	5	1	1	NUM
ejde-887	95	6	−w	−w	ADV
ejde-887	95	7	λ−	λ−	PROPN
ejde-887	95	8	v	v	ADV
ejde-887	95	9	2	2	NUM
ejde-887	95	10	)	)	PUNCT
ejde-887	95	11	(	(	PUNCT
ejde-887	95	12	3.4	3.4	NUM
ejde-887	95	13	)	)	PUNCT
ejde-887	95	14	n̂	n̂	NUM
ejde-887	95	15	=	=	PUNCT
ejde-887	95	16	(	(	PUNCT
ejde-887	95	17	−λ2	−λ2	NOUN
ejde-887	95	18	−	−	PROPN
ejde-887	95	19	1	1	NUM
ejde-887	95	20	4	4	NUM
ejde-887	95	21	(	(	PUNCT
ejde-887	95	22	vx	vx	PROPN
ejde-887	95	23	−	−	PROPN
ejde-887	95	24	v2	v2	PROPN
ejde-887	95	25	)	)	PUNCT
ejde-887	95	26	λ+	λ+	PUNCT
ejde-887	95	27	v	v	NUM
ejde-887	95	28	2	2	NUM
ejde-887	95	29	−λw	−λw	NOUN
ejde-887	95	30	−	−	NOUN
ejde-887	95	31	1	1	NUM
ejde-887	95	32	2	2	NUM
ejde-887	95	33	(	(	PUNCT
ejde-887	95	34	wx	wx	PROPN
ejde-887	95	35	+	+	X
ejde-887	95	36	vw	vw	PROPN
ejde-887	95	37	)	)	PUNCT
ejde-887	95	38	λ2	λ2	NOUN
ejde-887	95	39	+	+	CCONJ
ejde-887	95	40	1	1	NUM
ejde-887	95	41	4	4	NUM
ejde-887	95	42	(	(	PUNCT
ejde-887	95	43	vx	vx	PROPN
ejde-887	95	44	−	−	PROPN
ejde-887	95	45	v2	v2	PROPN
ejde-887	95	46	)	)	PUNCT
ejde-887	95	47	)	)	PUNCT
ejde-887	95	48	(	(	PUNCT
ejde-887	95	49	3.5	3.5	NUM
ejde-887	95	50	)	)	PUNCT
ejde-887	95	51	from	from	ADP
ejde-887	95	52	the	the	DET
ejde-887	95	53	compatibility	compatibility	NOUN
ejde-887	95	54	condition	condition	NOUN
ejde-887	95	55	ψx	ψx	PROPN
ejde-887	95	56	,	,	PUNCT
ejde-887	95	57	t	t	PROPN
ejde-887	95	58	=	=	PUNCT
ejde-887	95	59	ψt	ψt	NOUN
ejde-887	95	60	,	,	PUNCT
ejde-887	95	61	x	x	VERB
ejde-887	95	62	we	we	PRON
ejde-887	95	63	obtain	obtain	VERB
ejde-887	95	64	the	the	DET
ejde-887	95	65	zero	zero	NUM
ejde-887	95	66	-	-	PUNCT
ejde-887	95	67	curvature	curvature	NOUN
ejde-887	95	68	equation	equation	NOUN
ejde-887	95	69	p̂t	p̂t	PRON
ejde-887	95	70	−	−	PROPN
ejde-887	95	71	n̂x	n̂x	PROPN
ejde-887	95	72	+	+	CCONJ
ejde-887	96	1	[	[	X
ejde-887	96	2	n̂	n̂	NUM
ejde-887	96	3	,	,	PUNCT
ejde-887	96	4	p̂	p̂	X
ejde-887	96	5	]	]	PUNCT
ejde-887	96	6	=	=	PUNCT
ejde-887	96	7	0	0	NUM
ejde-887	96	8	,	,	PUNCT
ejde-887	96	9	(	(	PUNCT
ejde-887	96	10	3.6	3.6	NUM
ejde-887	96	11	)	)	PUNCT
ejde-887	96	12	which	which	PRON
ejde-887	96	13	generates	generate	VERB
ejde-887	96	14	the	the	DET
ejde-887	96	15	bk	bk	NOUN
ejde-887	96	16	system	system	NOUN
ejde-887	96	17	(	(	PUNCT
ejde-887	96	18	3.2	3.2	NUM
ejde-887	96	19	)	)	PUNCT
ejde-887	96	20	and	and	CCONJ
ejde-887	96	21	proves	prove	VERB
ejde-887	96	22	its	its	PRON
ejde-887	96	23	ist	ist	NOUN
ejde-887	96	24	integrability	integrability	NOUN
ejde-887	96	25	.	.	PUNCT
ejde-887	97	1	technically	technically	ADV
ejde-887	97	2	,	,	PUNCT
ejde-887	97	3	to	to	PART
ejde-887	97	4	construct	construct	VERB
ejde-887	97	5	the	the	DET
ejde-887	97	6	explicit	explicit	ADJ
ejde-887	97	7	solutions	solution	NOUN
ejde-887	97	8	we	we	PRON
ejde-887	97	9	can	can	AUX
ejde-887	97	10	follow	follow	VERB
ejde-887	97	11	[	[	X
ejde-887	97	12	46	46	NUM
ejde-887	97	13	]	]	PUNCT
ejde-887	97	14	and	and	CCONJ
ejde-887	97	15	perform	perform	VERB
ejde-887	97	16	a	a	DET
ejde-887	97	17	miura	miura	PROPN
ejde-887	97	18	transform	transform	NOUN
ejde-887	97	19	[	[	X
ejde-887	97	20	46	46	NUM
ejde-887	97	21	]	]	X
ejde-887	97	22	q	q	X
ejde-887	97	23	=	=	PUNCT
ejde-887	97	24	e	e	PROPN
ejde-887	97	25	∫	∫	PROPN
ejde-887	97	26	udx	udx	PROPN
ejde-887	97	27	,	,	PUNCT
ejde-887	97	28	r	r	NOUN
ejde-887	97	29	=	=	SYM
ejde-887	97	30	−	−	PROPN
ejde-887	97	31	(	(	PUNCT
ejde-887	97	32	1	1	NUM
ejde-887	97	33	+	+	CCONJ
ejde-887	97	34	z	z	NOUN
ejde-887	97	35	−	−	NOUN
ejde-887	97	36	1	1	NUM
ejde-887	97	37	2	2	NUM
ejde-887	97	38	ux	ux	NOUN
ejde-887	97	39	)	)	PUNCT
ejde-887	98	1	e−	e−	PROPN
ejde-887	98	2	∫	∫	PROPN
ejde-887	98	3	udx	udx	NOUN
ejde-887	98	4	,	,	PUNCT
ejde-887	98	5	(	(	PUNCT
ejde-887	98	6	3.7	3.7	NUM
ejde-887	98	7	)	)	PUNCT
ejde-887	98	8	which	which	PRON
ejde-887	98	9	maps	map	VERB
ejde-887	98	10	(	(	PUNCT
ejde-887	98	11	3.2	3.2	NUM
ejde-887	98	12	)	)	PUNCT
ejde-887	98	13	into	into	ADP
ejde-887	98	14	the	the	DET
ejde-887	98	15	first	first	ADJ
ejde-887	98	16	member	member	NOUN
ejde-887	98	17	of	of	ADP
ejde-887	98	18	akns	akns	PROPN
ejde-887	98	19	hierarchy	hierarchy	NOUN
ejde-887	98	20	system	system	NOUN
ejde-887	98	21	.	.	PUNCT
ejde-887	99	1	for	for	ADP
ejde-887	99	2	example	example	NOUN
ejde-887	99	3	,	,	PUNCT
ejde-887	99	4	a	a	DET
ejde-887	99	5	right	right	ADV
ejde-887	99	6	-	-	PUNCT
ejde-887	99	7	moving	move	VERB
ejde-887	99	8	one	one	NUM
ejde-887	99	9	-	-	PUNCT
ejde-887	99	10	soliton	soliton	NOUN
ejde-887	99	11	solution	solution	NOUN
ejde-887	99	12	of	of	ADP
ejde-887	99	13	the	the	DET
ejde-887	99	14	autonomous	autonomous	ADJ
ejde-887	99	15	version	version	NOUN
ejde-887	99	16	(	(	PUNCT
ejde-887	99	17	3.1	3.1	NUM
ejde-887	99	18	)	)	PUNCT
ejde-887	99	19	has	have	VERB
ejde-887	99	20	the	the	DET
ejde-887	99	21	form	form	NOUN
ejde-887	99	22	[	[	X
ejde-887	99	23	46	46	NUM
ejde-887	99	24	]	]	PUNCT
ejde-887	99	25	zsol	zsol	NOUN
ejde-887	99	26	=	=	SYM
ejde-887	99	27	α(4	α(4	PROPN
ejde-887	99	28	+	+	NUM
ejde-887	99	29	α2	α2	ADJ
ejde-887	99	30	)	)	PUNCT
ejde-887	99	31	[	[	PUNCT
ejde-887	99	32	2	2	NUM
ejde-887	99	33	+	+	CCONJ
ejde-887	99	34	(	(	PUNCT
ejde-887	99	35	2	2	NUM
ejde-887	99	36	+	+	CCONJ
ejde-887	99	37	α2	α2	ADJ
ejde-887	99	38	)	)	PUNCT
ejde-887	99	39	cosh	cosh	NOUN
ejde-887	99	40	(	(	PUNCT
ejde-887	99	41	α	α	NOUN
ejde-887	99	42	√	√	PROPN
ejde-887	99	43	3(4+α2)(2x−t(2+α2	3(4+α2)(2x−t(2+α2	NUM
ejde-887	99	44	)	)	PUNCT
ejde-887	99	45	)	)	PUNCT
ejde-887	99	46	4	4	NUM
ejde-887	99	47	√	√	NUM
ejde-887	99	48	β	β	X
ejde-887	99	49	)	)	PUNCT
ejde-887	99	50	]	]	PUNCT
ejde-887	100	1	[	[	PUNCT
ejde-887	100	2	2	2	NUM
ejde-887	100	3	+	+	CCONJ
ejde-887	100	4	α2	α2	ADJ
ejde-887	100	5	+	+	CCONJ
ejde-887	100	6	2	2	NUM
ejde-887	100	7	cosh	cosh	NOUN
ejde-887	100	8	(	(	PUNCT
ejde-887	100	9	α√3(4+α2)(2x−t(2+α2	α√3(4+α2)(2x−t(2+α2	NOUN
ejde-887	100	10	)	)	PUNCT
ejde-887	100	11	)	)	PUNCT
ejde-887	100	12	4	4	NUM
ejde-887	100	13	√	√	NUM
ejde-887	100	14	β	β	X
ejde-887	100	15	)	)	PUNCT
ejde-887	100	16	]	]	SYM
ejde-887	100	17	2	2	X
ejde-887	100	18	=	=	SYM
ejde-887	100	19	4α	4α	NOUN
ejde-887	100	20	1	1	NUM
ejde-887	100	21	+	+	CCONJ
ejde-887	100	22	cosh	cosh	PROPN
ejde-887	100	23	α	α	NOUN
ejde-887	100	24	√	√	ADP
ejde-887	100	25	3(x−t)√	3(x−t)√	NUM
ejde-887	100	26	β	β	X
ejde-887	100	27	+	+	NOUN
ejde-887	100	28	o(α2	o(α2	NOUN
ejde-887	100	29	)	)	PUNCT
ejde-887	100	30	usol	usol	NOUN
ejde-887	100	31	=	=	PUNCT
ejde-887	100	32	α(4	α(4	PROPN
ejde-887	100	33	+	+	CCONJ
ejde-887	100	34	α2	α2	ADJ
ejde-887	100	35	)	)	PUNCT
ejde-887	100	36	2	2	NUM
ejde-887	101	1	+	+	CCONJ
ejde-887	101	2	α2	α2	ADJ
ejde-887	101	3	+	+	CCONJ
ejde-887	101	4	2	2	NUM
ejde-887	101	5	cosh	cosh	NOUN
ejde-887	101	6	(	(	PUNCT
ejde-887	101	7	α√3(4+α2)(2x−t(2+α2	α√3(4+α2)(2x−t(2+α2	NOUN
ejde-887	101	8	)	)	PUNCT
ejde-887	101	9	)	)	PUNCT
ejde-887	102	1	4	4	NUM
ejde-887	102	2	√	√	NUM
ejde-887	102	3	β	β	NOUN
ejde-887	102	4	)	)	PUNCT
ejde-887	102	5	(	(	PUNCT
ejde-887	102	6	3.8	3.8	NUM
ejde-887	102	7	)	)	PUNCT
ejde-887	102	8	with	with	ADP
ejde-887	102	9	usol	usol	NOUN
ejde-887	102	10	,	,	PUNCT
ejde-887	102	11	zsol	zsol	NOUN
ejde-887	102	12	≤	≤	NUM
ejde-887	102	13	α	α	X
ejde-887	102	14	,	,	PUNCT
ejde-887	102	15	vsol	vsol	NOUN
ejde-887	102	16	=	=	SYM
ejde-887	102	17	1	1	NUM
ejde-887	102	18	+	+	CCONJ
ejde-887	102	19	α2	α2	ADJ
ejde-887	102	20	2	2	NUM
ejde-887	102	21	,	,	PUNCT
ejde-887	102	22	lsol	lsol	NOUN
ejde-887	102	23	=	=	SYM
ejde-887	102	24	2	2	NUM
ejde-887	102	25	√	√	NUM
ejde-887	102	26	β	β	VERB
ejde-887	102	27	α	α	NOUN
ejde-887	102	28	√	√	PROPN
ejde-887	102	29	3(4	3(4	NUM
ejde-887	102	30	+	+	CCONJ
ejde-887	102	31	α2	α2	ADJ
ejde-887	102	32	)	)	PUNCT
ejde-887	102	33	,	,	PUNCT
ejde-887	102	34	where	where	SCONJ
ejde-887	102	35	the	the	DET
ejde-887	102	36	last	last	ADJ
ejde-887	102	37	two	two	NUM
ejde-887	102	38	expressions	expression	NOUN
ejde-887	102	39	are	be	AUX
ejde-887	102	40	the	the	DET
ejde-887	102	41	traveling	travel	VERB
ejde-887	102	42	velocity	velocity	NOUN
ejde-887	102	43	v	v	NOUN
ejde-887	102	44	of	of	ADP
ejde-887	102	45	this	this	DET
ejde-887	102	46	one	one	NUM
ejde-887	102	47	-	-	PUNCT
ejde-887	102	48	soliton	soliton	NOUN
ejde-887	102	49	,	,	PUNCT
ejde-887	102	50	and	and	CCONJ
ejde-887	102	51	its	its	PRON
ejde-887	102	52	half	half	ADJ
ejde-887	102	53	-	-	PUNCT
ejde-887	102	54	width	width	NOUN
ejde-887	102	55	l.	l.	NOUN
ejde-887	102	56	by	by	ADP
ejde-887	102	57	applying	apply	VERB
ejde-887	102	58	other	other	ADJ
ejde-887	102	59	types	type	NOUN
ejde-887	102	60	of	of	ADP
ejde-887	102	61	darboux	darboux	NOUN
ejde-887	102	62	transforms	transform	NOUN
ejde-887	102	63	we	we	PRON
ejde-887	102	64	can	can	AUX
ejde-887	102	65	obtain	obtain	VERB
ejde-887	102	66	other	other	ADJ
ejde-887	102	67	multi	multi	ADJ
ejde-887	102	68	-	-	ADJ
ejde-887	102	69	soliton	soliton	ADJ
ejde-887	102	70	solutions	solution	NOUN
ejde-887	102	71	.	.	PUNCT
ejde-887	103	1	this	this	DET
ejde-887	103	2	soliton	soliton	NOUN
ejde-887	103	3	solution	solution	NOUN
ejde-887	103	4	has	have	VERB
ejde-887	103	5	the	the	DET
ejde-887	103	6	property	property	NOUN
ejde-887	103	7	that	that	PRON
ejde-887	103	8	its	its	PRON
ejde-887	103	9	group	group	NOUN
ejde-887	103	10	velocity	velocity	NOUN
ejde-887	103	11	increases	increase	VERB
ejde-887	103	12	with	with	ADP
ejde-887	103	13	the	the	DET
ejde-887	103	14	amplitude	amplitude	NOUN
ejde-887	103	15	of	of	ADP
ejde-887	103	16	the	the	DET
ejde-887	103	17	soliton	soliton	NOUN
ejde-887	103	18	,	,	PUNCT
ejde-887	103	19	and	and	CCONJ
ejde-887	103	20	decreases	decrease	VERB
ejde-887	103	21	with	with	ADP
ejde-887	103	22	the	the	DET
ejde-887	103	23	increasing	increasing	NOUN
ejde-887	103	24	of	of	ADP
ejde-887	103	25	the	the	DET
ejde-887	103	26	half	half	ADJ
ejde-887	103	27	-	-	PUNCT
ejde-887	103	28	width	width	NOUN
ejde-887	103	29	.	.	PUNCT
ejde-887	104	1	the	the	PRON
ejde-887	104	2	stronger	strong	ADJ
ejde-887	104	3	the	the	DET
ejde-887	104	4	coefficient	coefficient	NOUN
ejde-887	104	5	of	of	ADP
ejde-887	104	6	nonlinearity	nonlinearity	NOUN
ejde-887	104	7	α	α	NOUN
ejde-887	104	8	,	,	PUNCT
ejde-887	104	9	the	the	DET
ejde-887	104	10	narrower	narrow	ADJ
ejde-887	104	11	becomes	become	VERB
ejde-887	104	12	the	the	DET
ejde-887	104	13	soliton	soliton	NOUN
ejde-887	104	14	.	.	PUNCT
ejde-887	105	1	this	this	DET
ejde-887	105	2	one	one	NUM
ejde-887	105	3	-	-	PUNCT
ejde-887	105	4	soliton	soliton	NOUN
ejde-887	105	5	has	have	VERB
ejde-887	105	6	a	a	DET
ejde-887	105	7	single	single	ADJ
ejde-887	105	8	peak	peak	NOUN
ejde-887	105	9	when	when	SCONJ
ejde-887	105	10	its	its	PRON
ejde-887	105	11	amplitude	amplitude	NOUN
ejde-887	105	12	is	be	AUX
ejde-887	105	13	less	less	ADJ
ejde-887	105	14	than	than	ADP
ejde-887	105	15	2	2	NUM
ejde-887	105	16	/	/	SYM
ejde-887	105	17	α	α	PROPN
ejde-887	105	18	32	32	NUM
ejde-887	105	19	a.	a.	NOUN
ejde-887	105	20	ludu	ludu	NOUN
ejde-887	105	21	,	,	PUNCT
ejde-887	105	22	h.	h.	PROPN
ejde-887	105	23	khanal	khanal	NOUN
ejde-887	105	24	,	,	PUNCT
ejde-887	105	25	a.	a.	PROPN
ejde-887	105	26	s.	s.	PROPN
ejde-887	105	27	carstea	carstea	PROPN
ejde-887	105	28	ejde-2022	ejde-2022	PROPN
ejde-887	105	29	/	/	SYM
ejde-887	105	30	conf/27	conf/27	NOUN
ejde-887	105	31	and	and	CCONJ
ejde-887	105	32	double	double	ADJ
ejde-887	105	33	-	-	PUNCT
ejde-887	105	34	peak	peak	NOUN
ejde-887	105	35	when	when	SCONJ
ejde-887	105	36	the	the	DET
ejde-887	105	37	wave	wave	NOUN
ejde-887	105	38	amplitude	amplitude	NOUN
ejde-887	105	39	is	be	AUX
ejde-887	105	40	larger	large	ADJ
ejde-887	105	41	than	than	ADP
ejde-887	105	42	2	2	NUM
ejde-887	105	43	/	/	SYM
ejde-887	105	44	α	α	NOUN
ejde-887	105	45	,	,	PUNCT
ejde-887	105	46	thus	thus	ADV
ejde-887	105	47	having	have	VERB
ejde-887	105	48	some	some	DET
ejde-887	105	49	remarkable	remarkable	ADJ
ejde-887	105	50	features	feature	NOUN
ejde-887	105	51	.	.	PUNCT
ejde-887	106	1	3.2	3.2	NUM
ejde-887	106	2	.	.	PUNCT
ejde-887	107	1	non	non	ADJ
ejde-887	107	2	-	-	ADJ
ejde-887	107	3	autonomous	autonomous	ADJ
ejde-887	107	4	linear	linear	ADJ
ejde-887	107	5	limit	limit	NOUN
ejde-887	107	6	.	.	PUNCT
ejde-887	108	1	in	in	ADP
ejde-887	108	2	the	the	DET
ejde-887	108	3	linear	linear	ADJ
ejde-887	108	4	limit	limit	NOUN
ejde-887	108	5	α	α	X
ejde-887	108	6	→	→	SYM
ejde-887	108	7	0	0	NUM
ejde-887	108	8	of	of	ADP
ejde-887	108	9	the	the	DET
ejde-887	108	10	nonautonomous	nonautonomous	ADJ
ejde-887	108	11	case	case	NOUN
ejde-887	108	12	,	,	PUNCT
ejde-887	108	13	(	(	PUNCT
ejde-887	108	14	2.1	2.1	NUM
ejde-887	108	15	)	)	PUNCT
ejde-887	108	16	become	become	VERB
ejde-887	108	17	the	the	DET
ejde-887	108	18	differential	differential	ADJ
ejde-887	108	19	system	system	NOUN
ejde-887	108	20	qzlint	qzlint	NOUN
ejde-887	109	1	+	+	CCONJ
ejde-887	109	2	(	(	PUNCT
ejde-887	109	3	qulin)x	qulin)x	PROPN
ejde-887	109	4	+	+	CCONJ
ejde-887	109	5	β	β	X
ejde-887	109	6	3	3	NUM
ejde-887	109	7	(	(	PUNCT
ejde-887	109	8	qulin)xxx	qulin)xxx	NOUN
ejde-887	109	9	=	=	SYM
ejde-887	109	10	0	0	NUM
ejde-887	109	11	,	,	PUNCT
ejde-887	109	12	qulint	qulint	NOUN
ejde-887	109	13	+	+	CCONJ
ejde-887	109	14	zlinx	zlinx	NOUN
ejde-887	109	15	=	=	SYM
ejde-887	109	16	0	0	PROPN
ejde-887	109	17	,	,	PUNCT
ejde-887	109	18	(	(	PUNCT
ejde-887	109	19	3.9	3.9	NUM
ejde-887	109	20	)	)	PUNCT
ejde-887	109	21	where	where	SCONJ
ejde-887	109	22	we	we	PRON
ejde-887	109	23	denote	denote	VERB
ejde-887	109	24	by	by	ADP
ejde-887	109	25	zlin	zlin	PROPN
ejde-887	109	26	,	,	PUNCT
ejde-887	109	27	ulin	ulin	PROPN
ejde-887	109	28	the	the	DET
ejde-887	109	29	solutions	solution	NOUN
ejde-887	109	30	of	of	ADP
ejde-887	109	31	this	this	DET
ejde-887	109	32	linear	linear	ADJ
ejde-887	109	33	approximation	approximation	NOUN
ejde-887	109	34	,	,	PUNCT
ejde-887	109	35	to	to	PART
ejde-887	109	36	discern	discern	VERB
ejde-887	109	37	them	they	PRON
ejde-887	109	38	from	from	ADP
ejde-887	109	39	the	the	DET
ejde-887	109	40	solutions	solution	NOUN
ejde-887	109	41	z	z	PROPN
ejde-887	109	42	,	,	PUNCT
ejde-887	109	43	u	u	NOUN
ejde-887	109	44	of	of	ADP
ejde-887	109	45	the	the	DET
ejde-887	109	46	full	full	ADJ
ejde-887	109	47	nonlinear	nonlinear	ADJ
ejde-887	109	48	system	system	NOUN
ejde-887	109	49	.	.	PUNCT
ejde-887	110	1	while	while	SCONJ
ejde-887	110	2	there	there	PRON
ejde-887	110	3	is	be	VERB
ejde-887	110	4	no	no	DET
ejde-887	110	5	general	general	ADJ
ejde-887	110	6	analytic	analytic	ADJ
ejde-887	110	7	solution	solution	NOUN
ejde-887	110	8	for	for	ADP
ejde-887	110	9	the	the	DET
ejde-887	110	10	system	system	NOUN
ejde-887	110	11	(	(	PUNCT
ejde-887	110	12	3.9	3.9	NUM
ejde-887	110	13	)	)	PUNCT
ejde-887	110	14	for	for	ADP
ejde-887	110	15	an	an	DET
ejde-887	110	16	arbitrary	arbitrary	ADJ
ejde-887	110	17	coefficient	coefficient	NOUN
ejde-887	110	18	function	function	NOUN
ejde-887	110	19	q(x	q(x	NOUN
ejde-887	110	20	)	)	PUNCT
ejde-887	110	21	we	we	PRON
ejde-887	110	22	can	can	AUX
ejde-887	110	23	always	always	ADV
ejde-887	110	24	write	write	VERB
ejde-887	110	25	the	the	DET
ejde-887	110	26	solutions	solution	NOUN
ejde-887	110	27	in	in	ADP
ejde-887	110	28	terms	term	NOUN
ejde-887	110	29	of	of	ADP
ejde-887	110	30	a	a	DET
ejde-887	110	31	fourier	fourier	NOUN
ejde-887	110	32	integral	integral	ADJ
ejde-887	110	33	with	with	ADP
ejde-887	110	34	respect	respect	NOUN
ejde-887	110	35	to	to	ADP
ejde-887	110	36	time	time	NOUN
ejde-887	110	37	,	,	PUNCT
ejde-887	110	38	and	and	CCONJ
ejde-887	110	39	a	a	DET
ejde-887	110	40	fourier	fourier	NOUN
ejde-887	110	41	series	series	NOUN
ejde-887	110	42	with	with	ADP
ejde-887	110	43	respect	respect	NOUN
ejde-887	110	44	to	to	ADP
ejde-887	110	45	the	the	DET
ejde-887	110	46	bounded	bounded	ADJ
ejde-887	110	47	variable	variable	NOUN
ejde-887	110	48	x	x	X
ejde-887	110	49	(	(	PUNCT
ejde-887	110	50	which	which	PRON
ejde-887	110	51	approaches	approach	VERB
ejde-887	110	52	a	a	DET
ejde-887	110	53	fourier	fourier	NOUN
ejde-887	110	54	integral	integral	ADJ
ejde-887	110	55	in	in	ADP
ejde-887	110	56	the	the	DET
ejde-887	110	57	limit	limit	NOUN
ejde-887	110	58	l→	l→	VERB
ejde-887	110	59	∞	∞	PROPN
ejde-887	110	60	)	)	PUNCT
ejde-887	110	61	.	.	PUNCT
ejde-887	111	1	this	this	DET
ejde-887	111	2	linear	linear	ADJ
ejde-887	111	3	problem	problem	NOUN
ejde-887	111	4	for	for	ADP
ejde-887	111	5	the	the	DET
ejde-887	111	6	non	non	ADJ
ejde-887	111	7	-	-	ADJ
ejde-887	111	8	autonomous	autonomous	ADJ
ejde-887	111	9	boussinesq	boussinesq	NOUN
ejde-887	111	10	system	system	NOUN
ejde-887	111	11	was	be	AUX
ejde-887	111	12	solved	solve	VERB
ejde-887	111	13	in	in	ADP
ejde-887	111	14	literature	literature	NOUN
ejde-887	111	15	[	[	X
ejde-887	111	16	17	17	NUM
ejde-887	111	17	,	,	PUNCT
ejde-887	111	18	44	44	NUM
ejde-887	111	19	,	,	PUNCT
ejde-887	111	20	43	43	NUM
ejde-887	111	21	]	]	PUNCT
ejde-887	111	22	for	for	ADP
ejde-887	111	23	various	various	ADJ
ejde-887	111	24	type	type	NOUN
ejde-887	111	25	of	of	ADP
ejde-887	111	26	variable	variable	ADJ
ejde-887	111	27	coefficients	coefficient	NOUN
ejde-887	111	28	q(x	q(x	NOUN
ejde-887	111	29	)	)	PUNCT
ejde-887	111	30	.	.	PUNCT
ejde-887	112	1	when	when	SCONJ
ejde-887	112	2	this	this	DET
ejde-887	112	3	coefficient	coefficient	NOUN
ejde-887	112	4	function	function	NOUN
ejde-887	112	5	is	be	AUX
ejde-887	112	6	periodic	periodic	ADJ
ejde-887	112	7	,	,	PUNCT
ejde-887	112	8	the	the	DET
ejde-887	112	9	linearized	linearize	VERB
ejde-887	112	10	solutions	solution	NOUN
ejde-887	112	11	for	for	ADP
ejde-887	112	12	(	(	PUNCT
ejde-887	112	13	3.9	3.9	NUM
ejde-887	112	14	)	)	PUNCT
ejde-887	112	15	can	can	AUX
ejde-887	112	16	be	be	AUX
ejde-887	112	17	expressed	express	VERB
ejde-887	112	18	as	as	ADP
ejde-887	112	19	series	series	NOUN
ejde-887	112	20	in	in	ADP
ejde-887	112	21	terms	term	NOUN
ejde-887	112	22	of	of	ADP
ejde-887	112	23	floquet	floquet	ADJ
ejde-887	112	24	solutions	solution	NOUN
ejde-887	112	25	in	in	ADP
ejde-887	112	26	the	the	DET
ejde-887	112	27	fourier	fourier	NOUN
ejde-887	112	28	time	time	NOUN
ejde-887	112	29	representation	representation	NOUN
ejde-887	112	30	.	.	PUNCT
ejde-887	113	1	for	for	ADP
ejde-887	113	2	all	all	DET
ejde-887	113	3	these	these	DET
ejde-887	113	4	cases	case	NOUN
ejde-887	113	5	,	,	PUNCT
ejde-887	113	6	the	the	DET
ejde-887	113	7	generic	generic	ADJ
ejde-887	113	8	solution	solution	NOUN
ejde-887	113	9	for	for	ADP
ejde-887	113	10	the	the	DET
ejde-887	113	11	system	system	NOUN
ejde-887	113	12	(	(	PUNCT
ejde-887	113	13	3.9	3.9	NUM
ejde-887	113	14	)	)	PUNCT
ejde-887	113	15	can	can	AUX
ejde-887	113	16	be	be	AUX
ejde-887	113	17	written	write	VERB
ejde-887	113	18	in	in	ADP
ejde-887	113	19	the	the	DET
ejde-887	113	20	fourier	fourier	NOUN
ejde-887	113	21	time	time	NOUN
ejde-887	113	22	representation	representation	NOUN
ejde-887	113	23	in	in	ADP
ejde-887	113	24	the	the	DET
ejde-887	113	25	form	form	NOUN
ejde-887	113	26	zlin	zlin	NOUN
ejde-887	113	27	=	=	PUNCT
ejde-887	113	28	eiωt−µx	eiωt−µx	PROPN
ejde-887	113	29	∞∑	∞∑	NUM
ejde-887	113	30	n=−∞	n=−∞	ADJ
ejde-887	113	31	bneinx	bneinx	NOUN
ejde-887	113	32	,	,	PUNCT
ejde-887	113	33	ulin	ulin	PROPN
ejde-887	113	34	=	=	SYM
ejde-887	113	35	eiωt−µx	eiωt−µx	PROPN
ejde-887	114	1	∞∑	∞∑	NUM
ejde-887	114	2	n=−∞	n=−∞	X
ejde-887	114	3	uneinx	uneinx	NOUN
ejde-887	114	4	,	,	PUNCT
ejde-887	114	5	(	(	PUNCT
ejde-887	114	6	3.10	3.10	NUM
ejde-887	114	7	)	)	PUNCT
ejde-887	114	8	where	where	SCONJ
ejde-887	114	9	bn	bn	X
ejde-887	114	10	,	,	PUNCT
ejde-887	114	11	un	un	PROPN
ejde-887	114	12	are	be	AUX
ejde-887	114	13	the	the	DET
ejde-887	114	14	amplitudes	amplitude	NOUN
ejde-887	114	15	to	to	PART
ejde-887	114	16	be	be	AUX
ejde-887	114	17	determined	determine	VERB
ejde-887	114	18	by	by	ADP
ejde-887	114	19	recursion	recursion	NOUN
ejde-887	114	20	relations	relation	NOUN
ejde-887	114	21	and	and	CCONJ
ejde-887	114	22	boundary	boundary	ADJ
ejde-887	114	23	conditions	condition	NOUN
ejde-887	114	24	,	,	PUNCT
ejde-887	114	25	and	and	CCONJ
ejde-887	114	26	the	the	DET
ejde-887	114	27	constants	constant	NOUN
ejde-887	114	28	ω	ω	PROPN
ejde-887	114	29	,	,	PUNCT
ejde-887	114	30	µ	µ	X
ejde-887	114	31	∈	∈	PROPN
ejde-887	114	32	(	(	PUNCT
ejde-887	114	33	0,∞	0,∞	NOUN
ejde-887	114	34	)	)	PUNCT
ejde-887	114	35	parameterize	parameterize	VERB
ejde-887	114	36	the	the	DET
ejde-887	114	37	space	space	NOUN
ejde-887	114	38	of	of	ADP
ejde-887	114	39	the	the	DET
ejde-887	114	40	linear	linear	ADJ
ejde-887	114	41	solutions	solution	NOUN
ejde-887	114	42	with	with	ADP
ejde-887	114	43	respect	respect	NOUN
ejde-887	114	44	to	to	ADP
ejde-887	114	45	the	the	DET
ejde-887	114	46	fourier	fourier	ADJ
ejde-887	114	47	component	component	NOUN
ejde-887	114	48	of	of	ADP
ejde-887	114	49	frequency	frequency	NOUN
ejde-887	114	50	,	,	PUNCT
ejde-887	114	51	and	and	CCONJ
ejde-887	114	52	an	an	DET
ejde-887	114	53	arbitrary	arbitrary	ADJ
ejde-887	114	54	damping	damp	VERB
ejde-887	114	55	coefficient	coefficient	NOUN
ejde-887	114	56	,	,	PUNCT
ejde-887	114	57	respectively	respectively	ADV
ejde-887	114	58	.	.	PUNCT
ejde-887	115	1	actually	actually	ADV
ejde-887	115	2	,	,	PUNCT
ejde-887	115	3	if	if	SCONJ
ejde-887	115	4	the	the	DET
ejde-887	115	5	coefficient	coefficient	NOUN
ejde-887	115	6	function	function	NOUN
ejde-887	115	7	q	q	PUNCT
ejde-887	115	8	is	be	AUX
ejde-887	115	9	periodic	periodic	ADJ
ejde-887	115	10	,	,	PUNCT
ejde-887	115	11	the	the	DET
ejde-887	115	12	parameter	parameter	NOUN
ejde-887	115	13	µ	µ	NOUN
ejde-887	115	14	is	be	AUX
ejde-887	115	15	related	relate	VERB
ejde-887	115	16	to	to	ADP
ejde-887	115	17	the	the	DET
ejde-887	115	18	floquet	floquet	NOUN
ejde-887	115	19	(	(	PUNCT
ejde-887	115	20	lyapunov	lyapunov	NOUN
ejde-887	115	21	)	)	PUNCT
ejde-887	115	22	exponent	exponent	NOUN
ejde-887	115	23	[	[	X
ejde-887	115	24	44	44	NUM
ejde-887	115	25	,	,	PUNCT
ejde-887	115	26	43	43	NUM
ejde-887	115	27	]	]	PUNCT
ejde-887	115	28	.	.	PUNCT
ejde-887	116	1	4	4	X
ejde-887	116	2	.	.	X
ejde-887	116	3	multiple	multiple	ADJ
ejde-887	116	4	-	-	PUNCT
ejde-887	116	5	scales	scale	NOUN
ejde-887	116	6	method	method	NOUN
ejde-887	116	7	for	for	ADP
ejde-887	116	8	the	the	DET
ejde-887	116	9	boussinesq	boussinesq	ADJ
ejde-887	116	10	system	system	NOUN
ejde-887	116	11	4.1	4.1	NUM
ejde-887	116	12	.	.	PUNCT
ejde-887	116	13	amplitude	amplitude	NOUN
ejde-887	116	14	modulation	modulation	NOUN
ejde-887	116	15	in	in	ADP
ejde-887	116	16	the	the	DET
ejde-887	116	17	autonomous	autonomous	ADJ
ejde-887	116	18	case	case	NOUN
ejde-887	116	19	:	:	PUNCT
ejde-887	116	20	a	a	DET
ejde-887	116	21	dispersionless	dispersionless	NOUN
ejde-887	116	22	system	system	NOUN
ejde-887	116	23	.	.	PUNCT
ejde-887	117	1	in	in	ADP
ejde-887	117	2	this	this	DET
ejde-887	117	3	section	section	NOUN
ejde-887	117	4	we	we	PRON
ejde-887	117	5	analyze	analyze	VERB
ejde-887	117	6	the	the	DET
ejde-887	117	7	effect	effect	NOUN
ejde-887	117	8	of	of	ADP
ejde-887	117	9	amplitude	amplitude	NOUN
ejde-887	117	10	modulation	modulation	NOUN
ejde-887	117	11	for	for	ADP
ejde-887	117	12	the	the	DET
ejde-887	117	13	system	system	NOUN
ejde-887	117	14	(	(	PUNCT
ejde-887	117	15	3.1	3.1	NUM
ejde-887	117	16	)	)	PUNCT
ejde-887	117	17	in	in	ADP
ejde-887	117	18	the	the	DET
ejde-887	117	19	autonomous	autonomous	ADJ
ejde-887	117	20	case	case	NOUN
ejde-887	117	21	,	,	PUNCT
ejde-887	117	22	by	by	ADP
ejde-887	117	23	using	use	VERB
ejde-887	117	24	multiple	multiple	ADJ
ejde-887	117	25	-	-	PUNCT
ejde-887	117	26	scales	scale	NOUN
ejde-887	117	27	method	method	NOUN
ejde-887	117	28	[	[	X
ejde-887	117	29	45	45	NUM
ejde-887	117	30	]	]	PUNCT
ejde-887	117	31	.	.	PUNCT
ejde-887	118	1	in	in	ADP
ejde-887	118	2	the	the	DET
ejde-887	118	3	next	next	ADJ
ejde-887	118	4	section	section	NOUN
ejde-887	118	5	we	we	PRON
ejde-887	118	6	will	will	AUX
ejde-887	118	7	extend	extend	VERB
ejde-887	118	8	this	this	DET
ejde-887	118	9	procedure	procedure	NOUN
ejde-887	118	10	for	for	ADP
ejde-887	118	11	the	the	DET
ejde-887	118	12	non	non	ADJ
ejde-887	118	13	-	-	ADJ
ejde-887	118	14	autonomous	autonomous	ADJ
ejde-887	118	15	case	case	NOUN
ejde-887	118	16	.	.	PUNCT
ejde-887	119	1	if	if	SCONJ
ejde-887	119	2	we	we	PRON
ejde-887	119	3	consider	consider	VERB
ejde-887	119	4	u(x	u(x	NOUN
ejde-887	119	5	,	,	PUNCT
ejde-887	119	6	t	t	PROPN
ejde-887	119	7	)	)	PUNCT
ejde-887	119	8	,	,	PUNCT
ejde-887	119	9	z(x	z(x	PROPN
ejde-887	119	10	,	,	PUNCT
ejde-887	119	11	t	t	PROPN
ejde-887	119	12	)	)	PUNCT
ejde-887	119	13	to	to	PART
ejde-887	119	14	be	be	AUX
ejde-887	119	15	small	small	ADJ
ejde-887	119	16	,	,	PUNCT
ejde-887	119	17	then	then	ADV
ejde-887	119	18	we	we	PRON
ejde-887	119	19	can	can	AUX
ejde-887	119	20	neglect	neglect	VERB
ejde-887	119	21	the	the	DET
ejde-887	119	22	nonlinear	nonlinear	ADJ
ejde-887	119	23	terms	term	NOUN
ejde-887	119	24	,	,	PUNCT
ejde-887	119	25	and	and	CCONJ
ejde-887	119	26	from	from	ADP
ejde-887	119	27	the	the	DET
ejde-887	119	28	linear	linear	ADJ
ejde-887	119	29	ones	one	NOUN
ejde-887	119	30	,	,	PUNCT
ejde-887	119	31	when	when	SCONJ
ejde-887	119	32	q	q	NOUN
ejde-887	119	33	=	=	NOUN
ejde-887	119	34	1	1	NUM
ejde-887	119	35	,	,	PUNCT
ejde-887	119	36	we	we	PRON
ejde-887	119	37	obtain	obtain	VERB
ejde-887	119	38	the	the	DET
ejde-887	119	39	dispersion	dispersion	NOUN
ejde-887	119	40	relation	relation	NOUN
ejde-887	119	41	ω(k	ω(k	PROPN
ejde-887	119	42	)	)	PUNCT
ejde-887	120	1	=	=	PUNCT
ejde-887	120	2	±k	±k	NOUN
ejde-887	120	3	√	√	NUM
ejde-887	120	4	βk2	βk2	NOUN
ejde-887	120	5	3	3	NUM
ejde-887	120	6	−	−	NOUN
ejde-887	120	7	1	1	NUM
ejde-887	120	8	,	,	PUNCT
ejde-887	120	9	(	(	PUNCT
ejde-887	120	10	4.1	4.1	NUM
ejde-887	120	11	)	)	PUNCT
ejde-887	120	12	and	and	CCONJ
ejde-887	120	13	accordingly	accordingly	ADV
ejde-887	120	14	,	,	PUNCT
ejde-887	120	15	u(x	u(x	PROPN
ejde-887	120	16	,	,	PUNCT
ejde-887	120	17	t	t	PROPN
ejde-887	120	18	)	)	PUNCT
ejde-887	120	19	,	,	PUNCT
ejde-887	120	20	z(x	z(x	PROPN
ejde-887	120	21	,	,	PUNCT
ejde-887	120	22	t	t	PROPN
ejde-887	120	23	)	)	PUNCT
ejde-887	120	24	will	will	AUX
ejde-887	120	25	be	be	AUX
ejde-887	120	26	small	small	ADJ
ejde-887	120	27	monochromatic	monochromatic	ADJ
ejde-887	120	28	waves	wave	NOUN
ejde-887	120	29	.	.	PUNCT
ejde-887	121	1	starting	start	VERB
ejde-887	121	2	with	with	ADP
ejde-887	121	3	such	such	ADJ
ejde-887	121	4	small	small	ADJ
ejde-887	121	5	monochromatic	monochromatic	ADJ
ejde-887	121	6	solutions	solution	NOUN
ejde-887	121	7	one	one	NOUN
ejde-887	121	8	can	can	AUX
ejde-887	121	9	ask	ask	VERB
ejde-887	121	10	what	what	PRON
ejde-887	121	11	will	will	AUX
ejde-887	121	12	be	be	AUX
ejde-887	121	13	the	the	DET
ejde-887	121	14	effect	effect	NOUN
ejde-887	121	15	of	of	ADP
ejde-887	121	16	nonlinearity	nonlinearity	NOUN
ejde-887	121	17	.	.	PUNCT
ejde-887	122	1	that	that	PRON
ejde-887	122	2	includes	include	VERB
ejde-887	122	3	the	the	DET
ejde-887	122	4	developing	developing	NOUN
ejde-887	122	5	of	of	ADP
ejde-887	122	6	harmonics	harmonic	NOUN
ejde-887	122	7	and	and	CCONJ
ejde-887	122	8	variation	variation	NOUN
ejde-887	122	9	(	(	PUNCT
ejde-887	122	10	modulation	modulation	NOUN
ejde-887	122	11	)	)	PUNCT
ejde-887	122	12	of	of	ADP
ejde-887	122	13	amplitudes	amplitude	NOUN
ejde-887	122	14	on	on	ADP
ejde-887	122	15	long	long	ADJ
ejde-887	122	16	spatial	spatial	ADJ
ejde-887	122	17	scales	scale	NOUN
ejde-887	122	18	.	.	PUNCT
ejde-887	123	1	even	even	ADV
ejde-887	123	2	slow	slow	ADJ
ejde-887	123	3	variations	variation	NOUN
ejde-887	123	4	of	of	ADP
ejde-887	123	5	the	the	DET
ejde-887	123	6	coefficient	coefficient	NOUN
ejde-887	123	7	function	function	NOUN
ejde-887	123	8	q(x	q(x	NOUN
ejde-887	123	9	)	)	PUNCT
ejde-887	123	10	can	can	AUX
ejde-887	123	11	induce	induce	VERB
ejde-887	123	12	such	such	ADJ
ejde-887	123	13	modulations	modulation	NOUN
ejde-887	123	14	,	,	PUNCT
ejde-887	123	15	but	but	CCONJ
ejde-887	123	16	we	we	PRON
ejde-887	123	17	will	will	AUX
ejde-887	123	18	consider	consider	VERB
ejde-887	123	19	this	this	DET
ejde-887	123	20	case	case	NOUN
ejde-887	123	21	in	in	ADP
ejde-887	123	22	the	the	DET
ejde-887	123	23	next	next	ADJ
ejde-887	123	24	section	section	NOUN
ejde-887	123	25	.	.	PUNCT
ejde-887	124	1	the	the	DET
ejde-887	124	2	autonomous	autonomous	ADJ
ejde-887	124	3	solutions	solution	NOUN
ejde-887	124	4	of	of	ADP
ejde-887	124	5	(	(	PUNCT
ejde-887	124	6	3.1	3.1	NUM
ejde-887	124	7	)	)	PUNCT
ejde-887	124	8	expanded	expand	VERB
ejde-887	124	9	in	in	ADP
ejde-887	124	10	harmonics	harmonic	NOUN
ejde-887	124	11	will	will	AUX
ejde-887	124	12	have	have	VERB
ejde-887	124	13	the	the	DET
ejde-887	124	14	form	form	NOUN
ejde-887	124	15	za	za	NOUN
ejde-887	124	16	=	=	SYM
ejde-887	125	1	∞∑	∞∑	NUM
ejde-887	125	2	n=−∞	n=−∞	INTJ
ejde-887	125	3	zne	zne	INTJ
ejde-887	125	4	in[kx+ω(k)t	in[kx+ω(k)t	PROPN
ejde-887	125	5	]	]	PUNCT
ejde-887	125	6	,	,	PUNCT
ejde-887	125	7	ua	ua	PROPN
ejde-887	125	8	=	=	PROPN
ejde-887	126	1	∞∑	∞∑	NUM
ejde-887	126	2	n=−∞	n=−∞	NUM
ejde-887	126	3	une	une	PROPN
ejde-887	126	4	in[kx+ω(k)t	in[kx+ω(k)t	PROPN
ejde-887	126	5	]	]	PUNCT
ejde-887	126	6	,	,	PUNCT
ejde-887	126	7	ejde-202x	ejde-202x	PROPN
ejde-887	126	8	/	/	SYM
ejde-887	126	9	conf/27	conf/27	NOUN
ejde-887	126	10	boussinesq	boussinesq	ADJ
ejde-887	126	11	equations	equation	NOUN
ejde-887	126	12	33	33	NUM
ejde-887	126	13	where	where	SCONJ
ejde-887	126	14	zn	zn	PROPN
ejde-887	126	15	,	,	PUNCT
ejde-887	126	16	un	un	PROPN
ejde-887	126	17	are	be	AUX
ejde-887	126	18	amplitudes	amplitude	NOUN
ejde-887	126	19	,	,	PUNCT
ejde-887	126	20	and	and	CCONJ
ejde-887	126	21	we	we	PRON
ejde-887	126	22	consider	consider	VERB
ejde-887	126	23	the	the	DET
ejde-887	126	24	sum	sum	NOUN
ejde-887	126	25	to	to	PART
ejde-887	126	26	extend	extend	VERB
ejde-887	126	27	over	over	ADP
ejde-887	126	28	the	the	DET
ejde-887	126	29	whole	whole	ADJ
ejde-887	126	30	integer	integer	NOUN
ejde-887	126	31	set	set	VERB
ejde-887	126	32	in	in	ADP
ejde-887	126	33	order	order	NOUN
ejde-887	126	34	to	to	PART
ejde-887	126	35	insure	insure	VERB
ejde-887	126	36	reality	reality	NOUN
ejde-887	126	37	of	of	ADP
ejde-887	126	38	the	the	DET
ejde-887	126	39	solutions	solution	NOUN
ejde-887	126	40	za	za	PROPN
ejde-887	126	41	,	,	PUNCT
ejde-887	126	42	ua	ua	PROPN
ejde-887	126	43	.	.	PUNCT
ejde-887	127	1	in	in	ADP
ejde-887	127	2	order	order	NOUN
ejde-887	127	3	to	to	PART
ejde-887	127	4	include	include	VERB
ejde-887	127	5	the	the	DET
ejde-887	127	6	modulation	modulation	NOUN
ejde-887	127	7	on	on	ADP
ejde-887	127	8	the	the	DET
ejde-887	127	9	spatial	spatial	ADJ
ejde-887	127	10	long	long	ADJ
ejde-887	127	11	scale	scale	NOUN
ejde-887	127	12	,	,	PUNCT
ejde-887	127	13	we	we	PRON
ejde-887	127	14	introduce	introduce	VERB
ejde-887	127	15	the	the	DET
ejde-887	127	16	following	following	NOUN
ejde-887	127	17	stretched	stretch	VERB
ejde-887	127	18	variables	variable	NOUN
ejde-887	127	19	χ	χ	X
ejde-887	128	1	=	=	X
ejde-887	128	2	δ(x+	δ(x+	X
ejde-887	128	3	υt	υt	X
ejde-887	128	4	)	)	PUNCT
ejde-887	128	5	,	,	PUNCT
ejde-887	128	6	θ	θ	X
ejde-887	128	7	=	=	SYM
ejde-887	128	8	δ2	δ2	PROPN
ejde-887	128	9	t	t	PROPN
ejde-887	128	10	,	,	PUNCT
ejde-887	128	11	(	(	PUNCT
ejde-887	128	12	4.2	4.2	NUM
ejde-887	128	13	)	)	PUNCT
ejde-887	128	14	where	where	SCONJ
ejde-887	128	15	the	the	DET
ejde-887	128	16	smallness	smallness	NOUN
ejde-887	128	17	parameter	parameter	PROPN
ejde-887	128	18	δ	δ	PROPN
ejde-887	128	19	and	and	CCONJ
ejde-887	128	20	the	the	DET
ejde-887	128	21	scaling	scale	VERB
ejde-887	128	22	factor	factor	NOUN
ejde-887	128	23	υ	υ	NOUN
ejde-887	128	24	are	be	AUX
ejde-887	128	25	arbitrary	arbitrary	ADJ
ejde-887	128	26	parameters	parameter	NOUN
ejde-887	128	27	at	at	ADP
ejde-887	128	28	this	this	DET
ejde-887	128	29	point	point	NOUN
ejde-887	128	30	.	.	PUNCT
ejde-887	129	1	they	they	PRON
ejde-887	129	2	will	will	AUX
ejde-887	129	3	be	be	AUX
ejde-887	129	4	determined	determine	VERB
ejde-887	129	5	from	from	ADP
ejde-887	129	6	the	the	DET
ejde-887	129	7	balancing	balancing	NOUN
ejde-887	129	8	harmonics	harmonic	NOUN
ejde-887	129	9	,	,	PUNCT
ejde-887	129	10	and	and	CCONJ
ejde-887	129	11	of	of	ADP
ejde-887	129	12	the	the	DET
ejde-887	129	13	powers	power	NOUN
ejde-887	129	14	of	of	ADP
ejde-887	129	15	δ	δ	PROPN
ejde-887	129	16	.	.	PUNCT
ejde-887	130	1	if	if	SCONJ
ejde-887	130	2	we	we	PRON
ejde-887	130	3	consider	consider	VERB
ejde-887	130	4	the	the	DET
ejde-887	130	5	amplitudes	amplitude	NOUN
ejde-887	130	6	depending	depend	VERB
ejde-887	130	7	on	on	ADP
ejde-887	130	8	these	these	DET
ejde-887	130	9	stretched	stretch	VERB
ejde-887	130	10	variables	variable	NOUN
ejde-887	130	11	,	,	PUNCT
ejde-887	130	12	then	then	ADV
ejde-887	130	13	the	the	DET
ejde-887	130	14	amplitudes	amplitude	NOUN
ejde-887	130	15	are	be	AUX
ejde-887	130	16	modulated	modulate	VERB
ejde-887	130	17	according	accord	VERB
ejde-887	130	18	to	to	ADP
ejde-887	130	19	u0	u0	ADJ
ejde-887	130	20	=	=	SYM
ejde-887	130	21	δ2u0(χ	δ2u0(χ	PROPN
ejde-887	130	22	,	,	PUNCT
ejde-887	130	23	θ	θ	NOUN
ejde-887	130	24	)	)	PUNCT
ejde-887	130	25	,	,	PUNCT
ejde-887	130	26	u2	u2	PROPN
ejde-887	130	27	=	=	SYM
ejde-887	130	28	δ2u2(χ	δ2u2(χ	PROPN
ejde-887	130	29	,	,	PUNCT
ejde-887	130	30	θ	θ	NOUN
ejde-887	130	31	)	)	PUNCT
ejde-887	130	32	,	,	PUNCT
ejde-887	130	33	un	un	PROPN
ejde-887	130	34	=	=	PROPN
ejde-887	130	35	δnun(χ	δnun(χ	PROPN
ejde-887	130	36	,	,	PUNCT
ejde-887	130	37	θ	θ	PROPN
ejde-887	130	38	)	)	PUNCT
ejde-887	130	39	,	,	PUNCT
ejde-887	130	40	u−n	u−n	PROPN
ejde-887	130	41	=	=	SYM
ejde-887	130	42	u∗	u∗	PROPN
ejde-887	130	43	n	n	CCONJ
ejde-887	130	44	,	,	PUNCT
ejde-887	130	45	z0	z0	PROPN
ejde-887	130	46	=	=	SYM
ejde-887	130	47	δ2z0(χ	δ2z0(χ	PROPN
ejde-887	130	48	,	,	PUNCT
ejde-887	130	49	θ	θ	NOUN
ejde-887	130	50	)	)	PUNCT
ejde-887	130	51	,	,	PUNCT
ejde-887	130	52	z2	z2	PROPN
ejde-887	130	53	=	=	SYM
ejde-887	130	54	δ2z2(χ	δ2z2(χ	PROPN
ejde-887	130	55	,	,	PUNCT
ejde-887	130	56	θ	θ	PROPN
ejde-887	130	57	)	)	PUNCT
ejde-887	130	58	,	,	PUNCT
ejde-887	130	59	zn	zn	PROPN
ejde-887	130	60	=	=	SYM
ejde-887	130	61	δnzn(χ	δnzn(χ	PROPN
ejde-887	130	62	,	,	PUNCT
ejde-887	130	63	θ	θ	NOUN
ejde-887	130	64	)	)	PUNCT
ejde-887	130	65	,	,	PUNCT
ejde-887	130	66	z−n	z−n	X
ejde-887	130	67	=	=	SYM
ejde-887	130	68	z∗	z∗	PROPN
ejde-887	130	69	n.	n.	NOUN
ejde-887	130	70	equating	equate	VERB
ejde-887	130	71	to	to	ADP
ejde-887	130	72	zero	zero	NUM
ejde-887	130	73	the	the	DET
ejde-887	130	74	coefficients	coefficient	NOUN
ejde-887	130	75	of	of	ADP
ejde-887	130	76	every	every	DET
ejde-887	130	77	order	order	NOUN
ejde-887	130	78	n	n	PRON
ejde-887	130	79	exponential	exponential	VERB
ejde-887	130	80	independently	independently	ADV
ejde-887	130	81	,	,	PUNCT
ejde-887	130	82	we	we	PRON
ejde-887	130	83	obtain	obtain	VERB
ejde-887	130	84	an	an	DET
ejde-887	130	85	infinite	infinite	ADJ
ejde-887	130	86	set	set	NOUN
ejde-887	130	87	of	of	ADP
ejde-887	130	88	equations	equation	NOUN
ejde-887	130	89	for	for	ADP
ejde-887	130	90	un	un	PROPN
ejde-887	130	91	,	,	PUNCT
ejde-887	130	92	(	(	PUNCT
ejde-887	130	93	∂θ	∂θ	X
ejde-887	130	94	+	+	NUM
ejde-887	130	95	inω)zn	inω)zn	NOUN
ejde-887	130	96	+	+	CCONJ
ejde-887	130	97	(	(	PUNCT
ejde-887	130	98	∂χ	∂χ	PROPN
ejde-887	130	99	+	+	CCONJ
ejde-887	130	100	ink)un	ink)un	VERB
ejde-887	130	101	+	+	CCONJ
ejde-887	130	102	α(∂χ	α(∂χ	PROPN
ejde-887	130	103	+	+	CCONJ
ejde-887	130	104	ink	ink	NOUN
ejde-887	130	105	)	)	PUNCT
ejde-887	130	106	∑	∑	PUNCT
ejde-887	130	107	i∈z	i∈z	X
ejde-887	130	108	ziun−i	ziun−i	X
ejde-887	130	109	+	+	CCONJ
ejde-887	130	110	β	β	X
ejde-887	130	111	3	3	NUM
ejde-887	130	112	(	(	PUNCT
ejde-887	130	113	∂χ	∂χ	NOUN
ejde-887	130	114	+	+	CCONJ
ejde-887	130	115	ink)3un	ink)3un	NOUN
ejde-887	130	116	=	=	SYM
ejde-887	130	117	0	0	NUM
ejde-887	130	118	,	,	PUNCT
ejde-887	130	119	(	(	PUNCT
ejde-887	130	120	∂θ	∂θ	PROPN
ejde-887	130	121	+	+	CCONJ
ejde-887	130	122	inω)un	inω)un	VERB
ejde-887	130	123	+	+	CCONJ
ejde-887	130	124	(	(	PUNCT
ejde-887	130	125	∂χ	∂χ	SYM
ejde-887	130	126	+	+	NUM
ejde-887	130	127	ink)zn	ink)zn	NOUN
ejde-887	130	128	+	+	X
ejde-887	130	129	α	α	NOUN
ejde-887	130	130	2	2	NUM
ejde-887	130	131	(	(	PUNCT
ejde-887	130	132	∂χ	∂χ	PROPN
ejde-887	130	133	+	+	NUM
ejde-887	130	134	ink	ink	NOUN
ejde-887	130	135	)	)	PUNCT
ejde-887	130	136	∑	∑	PUNCT
ejde-887	131	1	i∈z	i∈z	PROPN
ejde-887	131	2	uiun−i	uiun−i	NOUN
ejde-887	131	3	=	=	SYM
ejde-887	131	4	0	0	NUM
ejde-887	131	5	.	.	PUNCT
ejde-887	131	6	for	for	ADP
ejde-887	131	7	n	n	NOUN
ejde-887	131	8	=	=	SYM
ejde-887	131	9	0	0	NUM
ejde-887	131	10	and	and	CCONJ
ejde-887	131	11	the	the	DET
ejde-887	131	12	order	order	NOUN
ejde-887	131	13	o(δ	o(δ	NOUN
ejde-887	131	14	)	)	PUNCT
ejde-887	131	15	we	we	PRON
ejde-887	131	16	have	have	VERB
ejde-887	131	17	z0	z0	PROPN
ejde-887	131	18	=	=	SYM
ejde-887	131	19	2αυ(z1u	2αυ(z1u	NUM
ejde-887	131	20	∗	∗	NOUN
ejde-887	131	21	1	1	NUM
ejde-887	131	22	+	+	CCONJ
ejde-887	131	23	z∗	z∗	PROPN
ejde-887	131	24	1u1)−	1u1)−	NOUN
ejde-887	132	1	α|z1|2	α|z1|2	NOUN
ejde-887	132	2	2(1−	2(1−	NUM
ejde-887	132	3	υ2	υ2	NOUN
ejde-887	132	4	)	)	PUNCT
ejde-887	132	5	≡	≡	PROPN
ejde-887	132	6	a1(z1u	a1(z1u	PROPN
ejde-887	132	7	∗	∗	NOUN
ejde-887	132	8	1	1	NUM
ejde-887	132	9	+	+	CCONJ
ejde-887	132	10	z∗	z∗	NOUN
ejde-887	132	11	1u1	1u1	NUM
ejde-887	132	12	)	)	PUNCT
ejde-887	133	1	+	+	ADJ
ejde-887	133	2	a2|z1|2	a2|z1|2	PROPN
ejde-887	133	3	,	,	PUNCT
ejde-887	133	4	u0	u0	ADJ
ejde-887	133	5	:	:	PUNCT
ejde-887	133	6	=	=	SYM
ejde-887	133	7	2α(z1u	2α(z1u	NUM
ejde-887	133	8	∗	∗	NOUN
ejde-887	133	9	1	1	NUM
ejde-887	133	10	+	+	CCONJ
ejde-887	133	11	z∗	z∗	PROPN
ejde-887	133	12	1u1)−	1u1)−	NOUN
ejde-887	134	1	αυ|z1|2	αυ|z1|2	PRON
ejde-887	134	2	2(υ2	2(υ2	NUM
ejde-887	134	3	−	−	NOUN
ejde-887	134	4	1	1	NUM
ejde-887	134	5	)	)	PUNCT
ejde-887	134	6	≡	≡	PROPN
ejde-887	134	7	a3(z1u	a3(z1u	PROPN
ejde-887	134	8	∗	∗	VERB
ejde-887	134	9	1	1	NUM
ejde-887	135	1	+	+	CCONJ
ejde-887	135	2	z∗	z∗	NOUN
ejde-887	135	3	1u1	1u1	NUM
ejde-887	135	4	)	)	PUNCT
ejde-887	136	1	+	+	NOUN
ejde-887	136	2	a4|z1|2	a4|z1|2	PROPN
ejde-887	136	3	.	.	PUNCT
ejde-887	137	1	for	for	ADP
ejde-887	137	2	n	n	NOUN
ejde-887	137	3	=	=	SYM
ejde-887	137	4	2	2	NUM
ejde-887	137	5	and	and	CCONJ
ejde-887	137	6	order	order	NOUN
ejde-887	137	7	o(δ2	o(δ2	ADJ
ejde-887	137	8	)	)	PUNCT
ejde-887	137	9	we	we	PRON
ejde-887	137	10	obtain	obtain	VERB
ejde-887	137	11	u2	u2	NOUN
ejde-887	137	12	=	=	PUNCT
ejde-887	137	13	3(2αk2z1u1	3(2αk2z1u1	PROPN
ejde-887	137	14	−	−	PROPN
ejde-887	137	15	ωαku2	ωαku2	NOUN
ejde-887	137	16	1	1	NUM
ejde-887	137	17	)	)	PUNCT
ejde-887	137	18	2(4βh3k4	2(4βh3k4	NOUN
ejde-887	137	19	−	−	NOUN
ejde-887	137	20	3hk2	3hk2	NUM
ejde-887	137	21	+	+	CCONJ
ejde-887	137	22	3ω2	3ω2	NUM
ejde-887	137	23	)	)	PUNCT
ejde-887	137	24	≡	≡	PROPN
ejde-887	137	25	b1z1u1	b1z1u1	NOUN
ejde-887	138	1	+	+	NOUN
ejde-887	138	2	b2u	b2u	PROPN
ejde-887	138	3	2	2	NUM
ejde-887	138	4	1	1	NUM
ejde-887	138	5	,	,	PUNCT
ejde-887	138	6	z2	z2	NOUN
ejde-887	138	7	=	=	SYM
ejde-887	138	8	(	(	PUNCT
ejde-887	139	1	3αk2h−	3αk2h−	NUM
ejde-887	139	2	4αβh3k4)u2	4αβh3k4)u2	NUM
ejde-887	139	3	1	1	NUM
ejde-887	139	4	−	−	NOUN
ejde-887	139	5	6αkωz1u1	6αkωz1u1	NOUN
ejde-887	139	6	2(4βh3k4	2(4βh3k4	NOUN
ejde-887	139	7	−	−	ADP
ejde-887	139	8	3hk2	3hk2	NUM
ejde-887	139	9	+	+	CCONJ
ejde-887	139	10	3ω2	3ω2	NUM
ejde-887	139	11	)	)	PUNCT
ejde-887	139	12	≡	≡	PROPN
ejde-887	139	13	b3z1u1	b3z1u1	ADP
ejde-887	139	14	+	+	ADJ
ejde-887	139	15	b4z	b4z	ADV
ejde-887	139	16	2	2	NUM
ejde-887	139	17	1	1	NUM
ejde-887	139	18	.	.	PUNCT
ejde-887	140	1	for	for	ADP
ejde-887	140	2	n	n	NOUN
ejde-887	140	3	=	=	SYM
ejde-887	140	4	1	1	NUM
ejde-887	140	5	we	we	PRON
ejde-887	140	6	reproduce	reproduce	VERB
ejde-887	140	7	the	the	DET
ejde-887	140	8	dispersion	dispersion	NOUN
ejde-887	140	9	relation	relation	NOUN
ejde-887	140	10	in	in	ADP
ejde-887	140	11	order	order	NOUN
ejde-887	140	12	o(δ	o(δ	PROPN
ejde-887	140	13	)	)	PUNCT
ejde-887	140	14	.	.	PUNCT
ejde-887	141	1	in	in	ADP
ejde-887	141	2	order	order	NOUN
ejde-887	141	3	o(δ2	o(δ2	NOUN
ejde-887	141	4	)	)	PUNCT
ejde-887	141	5	we	we	PRON
ejde-887	141	6	re	re	VERB
ejde-887	141	7	-	-	VERB
ejde-887	141	8	obtain	obtain	VERB
ejde-887	141	9	the	the	DET
ejde-887	141	10	derivative	derivative	NOUN
ejde-887	141	11	of	of	ADP
ejde-887	141	12	the	the	DET
ejde-887	141	13	dispersion	dispersion	NOUN
ejde-887	141	14	relation	relation	NOUN
ejde-887	141	15	with	with	ADP
ejde-887	141	16	respect	respect	NOUN
ejde-887	141	17	to	to	ADP
ejde-887	141	18	k	k	PROPN
ejde-887	141	19	(	(	PUNCT
ejde-887	141	20	υ	υ	NOUN
ejde-887	141	21	=	=	PUNCT
ejde-887	142	1	dω	dω	PROPN
ejde-887	142	2	/	/	SYM
ejde-887	142	3	dk	dk	X
ejde-887	142	4	the	the	DET
ejde-887	142	5	group	group	NOUN
ejde-887	142	6	velocity	velocity	NOUN
ejde-887	142	7	)	)	PUNCT
ejde-887	142	8	,	,	PUNCT
ejde-887	142	9	and	and	CCONJ
ejde-887	142	10	in	in	ADP
ejde-887	142	11	o(δ3	o(δ3	NOUN
ejde-887	142	12	)	)	PUNCT
ejde-887	142	13	we	we	PRON
ejde-887	142	14	obtain	obtain	VERB
ejde-887	142	15	the	the	DET
ejde-887	142	16	following	following	ADJ
ejde-887	142	17	nonlinear	nonlinear	ADJ
ejde-887	142	18	coupled	couple	VERB
ejde-887	142	19	system	system	NOUN
ejde-887	142	20	u1,θ	u1,θ	PROPN
ejde-887	143	1	+	+	CCONJ
ejde-887	143	2	iαk(u0u1	iαk(u0u1	ADV
ejde-887	143	3	+	+	CCONJ
ejde-887	143	4	u∗	u∗	ADJ
ejde-887	143	5	1u2	1u2	NUM
ejde-887	143	6	)	)	PUNCT
ejde-887	143	7	=	=	SYM
ejde-887	143	8	0	0	NUM
ejde-887	143	9	,	,	PUNCT
ejde-887	143	10	z1,θ	z1,θ	NUM
ejde-887	144	1	+	+	CCONJ
ejde-887	144	2	ikβu1,χχ	ikβu1,χχ	PRON
ejde-887	144	3	+	+	CCONJ
ejde-887	144	4	iαk(z0u1	iαk(z0u1	NOUN
ejde-887	144	5	+	+	CCONJ
ejde-887	144	6	z1u0	z1u0	PROPN
ejde-887	144	7	+	+	SYM
ejde-887	144	8	z2u	z2u	PROPN
ejde-887	144	9	∗	∗	NOUN
ejde-887	144	10	1	1	NUM
ejde-887	144	11	+	+	CCONJ
ejde-887	144	12	z∗	z∗	NOUN
ejde-887	144	13	1u2	1u2	NUM
ejde-887	144	14	)	)	PUNCT
ejde-887	144	15	=	=	SYM
ejde-887	144	16	0	0	X
ejde-887	144	17	.	.	PUNCT
ejde-887	144	18	by	by	ADP
ejde-887	144	19	replacing	replace	VERB
ejde-887	144	20	in	in	ADP
ejde-887	144	21	these	these	DET
ejde-887	144	22	equations	equation	NOUN
ejde-887	144	23	the	the	DET
ejde-887	144	24	expressions	expression	NOUN
ejde-887	144	25	for	for	ADP
ejde-887	144	26	z0	z0	PROPN
ejde-887	144	27	,	,	PUNCT
ejde-887	144	28	u0	u0	ADJ
ejde-887	144	29	,	,	PUNCT
ejde-887	144	30	z2	z2	PROPN
ejde-887	144	31	,	,	PUNCT
ejde-887	144	32	u2	u2	NOUN
ejde-887	144	33	from	from	ADP
ejde-887	144	34	above	above	ADV
ejde-887	144	35	,	,	PUNCT
ejde-887	144	36	we	we	PRON
ejde-887	144	37	obtain	obtain	VERB
ejde-887	144	38	the	the	DET
ejde-887	144	39	equations	equation	NOUN
ejde-887	144	40	describing	describe	VERB
ejde-887	144	41	the	the	DET
ejde-887	144	42	envelope	envelope	NOUN
ejde-887	144	43	nonlinear	nonlinear	ADJ
ejde-887	144	44	waves	wave	NOUN
ejde-887	144	45	over	over	ADP
ejde-887	144	46	flat	flat	ADJ
ejde-887	144	47	bottom	bottom	NOUN
ejde-887	145	1	u1,θ	u1,θ	PROPN
ejde-887	145	2	+	+	CCONJ
ejde-887	145	3	iαk[b2|u1|2u1	iαk[b2|u1|2u1	PROPN
ejde-887	145	4	+	+	CCONJ
ejde-887	145	5	(	(	PUNCT
ejde-887	145	6	a3	a3	VERB
ejde-887	145	7	+	+	CCONJ
ejde-887	145	8	b1)z1|u1|2	b1)z1|u1|2	X
ejde-887	145	9	+	+	SYM
ejde-887	145	10	a4u1|z1|2	a4u1|z1|2	ADJ
ejde-887	145	11	+	+	NOUN
ejde-887	145	12	a3z	a3z	NOUN
ejde-887	145	13	∗	∗	NOUN
ejde-887	145	14	1u	1u	NUM
ejde-887	145	15	2	2	NUM
ejde-887	145	16	1	1	NUM
ejde-887	145	17	]	]	PUNCT
ejde-887	145	18	=	=	SYM
ejde-887	145	19	0	0	NUM
ejde-887	145	20	,	,	PUNCT
ejde-887	145	21	(	(	PUNCT
ejde-887	145	22	4.3	4.3	NUM
ejde-887	145	23	)	)	PUNCT
ejde-887	145	24	z1,θ	z1,θ	NOUN
ejde-887	146	1	+	+	CCONJ
ejde-887	146	2	ikβu1,χχ	ikβu1,χχ	PRON
ejde-887	146	3	+	+	CCONJ
ejde-887	146	4	iαk((a1	iαk((a1	PROPN
ejde-887	146	5	+	+	PROPN
ejde-887	146	6	b2)(z	b2)(z	PROPN
ejde-887	146	7	∗	∗	NOUN
ejde-887	146	8	1u	1u	NUM
ejde-887	146	9	2	2	NUM
ejde-887	146	10	1	1	NUM
ejde-887	146	11	+	+	NUM
ejde-887	146	12	z1|u1|2	z1|u1|2	NUM
ejde-887	146	13	)	)	PUNCT
ejde-887	147	1	+	+	CCONJ
ejde-887	147	2	(	(	PUNCT
ejde-887	147	3	a2	a2	PROPN
ejde-887	147	4	+	+	NOUN
ejde-887	147	5	a3	a3	NOUN
ejde-887	147	6	+	+	NOUN
ejde-887	147	7	b1)|z1|2u1	b1)|z1|2u1	X
ejde-887	147	8	+	+	ADJ
ejde-887	147	9	a3z	a3z	PROPN
ejde-887	147	10	2	2	NUM
ejde-887	147	11	1u	1u	NUM
ejde-887	147	12	∗	∗	NOUN
ejde-887	147	13	1	1	NUM
ejde-887	147	14	+	+	ADJ
ejde-887	147	15	a4|z1|2z1	a4|z1|2z1	ADJ
ejde-887	147	16	+	+	NOUN
ejde-887	147	17	b4|u1|2u1	b4|u1|2u1	NOUN
ejde-887	147	18	)	)	PUNCT
ejde-887	147	19	=	=	SYM
ejde-887	147	20	0	0	X
ejde-887	147	21	.	.	PUNCT
ejde-887	148	1	(	(	PUNCT
ejde-887	148	2	4.4	4.4	NUM
ejde-887	148	3	)	)	PUNCT
ejde-887	148	4	from	from	ADP
ejde-887	148	5	(	(	PUNCT
ejde-887	148	6	4.3)-(4.4	4.3)-(4.4	NOUN
ejde-887	148	7	)	)	PUNCT
ejde-887	148	8	we	we	PRON
ejde-887	148	9	see	see	VERB
ejde-887	148	10	that	that	SCONJ
ejde-887	148	11	the	the	DET
ejde-887	148	12	autonomous	autonomous	ADJ
ejde-887	148	13	multiple	multiple	ADJ
ejde-887	148	14	-	-	PUNCT
ejde-887	148	15	scale	scale	NOUN
ejde-887	148	16	approximation	approximation	NOUN
ejde-887	148	17	(	(	PUNCT
ejde-887	148	18	3.1	3.1	NUM
ejde-887	148	19	)	)	PUNCT
ejde-887	148	20	of	of	ADP
ejde-887	148	21	the	the	DET
ejde-887	148	22	non	non	ADJ
ejde-887	148	23	-	-	ADJ
ejde-887	148	24	autonomous	autonomous	ADJ
ejde-887	148	25	boussinesq	boussinesq	ADJ
ejde-887	148	26	system	system	NOUN
ejde-887	148	27	(	(	PUNCT
ejde-887	148	28	2.1	2.1	NUM
ejde-887	148	29	)	)	PUNCT
ejde-887	148	30	is	be	AUX
ejde-887	148	31	dispersionless	dispersionless	NOUN
ejde-887	148	32	.	.	PUNCT
ejde-887	149	1	the	the	DET
ejde-887	149	2	signature	signature	NOUN
ejde-887	149	3	of	of	ADP
ejde-887	149	4	34	34	NUM
ejde-887	149	5	a.	a.	NOUN
ejde-887	149	6	ludu	ludu	PROPN
ejde-887	149	7	,	,	PUNCT
ejde-887	149	8	h.	h.	PROPN
ejde-887	149	9	khanal	khanal	NOUN
ejde-887	149	10	,	,	PUNCT
ejde-887	149	11	a.	a.	PROPN
ejde-887	149	12	s.	s.	PROPN
ejde-887	149	13	carstea	carstea	PROPN
ejde-887	149	14	ejde-2022	ejde-2022	PROPN
ejde-887	149	15	/	/	SYM
ejde-887	149	16	conf/27	conf/27	NOUN
ejde-887	149	17	this	this	DET
ejde-887	149	18	effect	effect	NOUN
ejde-887	149	19	is	be	AUX
ejde-887	149	20	visible	visible	ADJ
ejde-887	149	21	even	even	ADV
ejde-887	149	22	in	in	ADP
ejde-887	149	23	the	the	DET
ejde-887	149	24	linear	linear	PROPN
ejde-887	149	25	approximation	approximation	NOUN
ejde-887	149	26	,	,	PUNCT
ejde-887	149	27	which	which	DET
ejde-887	149	28	case	case	NOUN
ejde-887	149	29	gives	give	VERB
ejde-887	149	30	a	a	DET
ejde-887	149	31	twisted	twisted	ADJ
ejde-887	149	32	coupling	coupling	NOUN
ejde-887	149	33	of	of	ADP
ejde-887	149	34	equations	equation	NOUN
ejde-887	149	35	containing	contain	VERB
ejde-887	149	36	zn	zn	PROPN
ejde-887	149	37	and	and	CCONJ
ejde-887	149	38	un	un	PROPN
ejde-887	149	39	,	,	PUNCT
ejde-887	149	40	without	without	ADP
ejde-887	149	41	dispersion	dispersion	NOUN
ejde-887	149	42	.	.	PUNCT
ejde-887	150	1	accordingly	accordingly	ADV
ejde-887	150	2	,	,	PUNCT
ejde-887	150	3	we	we	PRON
ejde-887	150	4	may	may	AUX
ejde-887	150	5	expect	expect	VERB
ejde-887	150	6	that	that	SCONJ
ejde-887	150	7	the	the	DET
ejde-887	150	8	weak	weak	ADJ
ejde-887	150	9	modulation	modulation	NOUN
ejde-887	150	10	of	of	ADP
ejde-887	150	11	nonlinear	nonlinear	ADJ
ejde-887	150	12	traveling	travel	VERB
ejde-887	150	13	solutions	solution	NOUN
ejde-887	150	14	will	will	AUX
ejde-887	150	15	drive	drive	VERB
ejde-887	150	16	them	they	PRON
ejde-887	150	17	toward	toward	ADP
ejde-887	150	18	instability	instability	NOUN
ejde-887	150	19	and	and	CCONJ
ejde-887	150	20	breaking	breaking	NOUN
ejde-887	150	21	,	,	PUNCT
ejde-887	150	22	even	even	ADV
ejde-887	150	23	in	in	ADP
ejde-887	150	24	the	the	DET
ejde-887	150	25	autonomous	autonomous	ADJ
ejde-887	150	26	limit	limit	NOUN
ejde-887	150	27	(	(	PUNCT
ejde-887	150	28	of	of	ADP
ejde-887	150	29	course	course	NOUN
ejde-887	150	30	this	this	PRON
ejde-887	150	31	is	be	AUX
ejde-887	150	32	not	not	PART
ejde-887	150	33	mandatory	mandatory	ADJ
ejde-887	150	34	;	;	PUNCT
ejde-887	150	35	there	there	PRON
ejde-887	150	36	are	be	VERB
ejde-887	150	37	dispersionless	dispersionless	ADJ
ejde-887	150	38	systems	system	NOUN
ejde-887	150	39	supporting	support	VERB
ejde-887	150	40	stable	stable	ADJ
ejde-887	150	41	solitons	soliton	NOUN
ejde-887	150	42	)	)	PUNCT
ejde-887	150	43	.	.	PUNCT
ejde-887	151	1	however	however	ADV
ejde-887	151	2	,	,	PUNCT
ejde-887	151	3	since	since	SCONJ
ejde-887	151	4	the	the	DET
ejde-887	151	5	system	system	NOUN
ejde-887	151	6	(	(	PUNCT
ejde-887	151	7	3.1	3.1	NUM
ejde-887	151	8	)	)	PUNCT
ejde-887	151	9	can	can	AUX
ejde-887	151	10	be	be	AUX
ejde-887	151	11	transformed	transform	VERB
ejde-887	151	12	into	into	ADP
ejde-887	151	13	the	the	DET
ejde-887	151	14	integrable	integrable	ADJ
ejde-887	151	15	broer	broer	NOUN
ejde-887	151	16	-	-	PUNCT
ejde-887	151	17	kaup	kaup	PROPN
ejde-887	151	18	(	(	PUNCT
ejde-887	151	19	bk	bk	NOUN
ejde-887	151	20	)	)	PUNCT
ejde-887	151	21	system	system	NOUN
ejde-887	151	22	,	,	PUNCT
ejde-887	151	23	we	we	PRON
ejde-887	151	24	expect	expect	VERB
ejde-887	151	25	that	that	SCONJ
ejde-887	151	26	the	the	DET
ejde-887	151	27	dispersionless	dispersionless	ADJ
ejde-887	151	28	complex	complex	ADJ
ejde-887	151	29	envelope	envelope	NOUN
ejde-887	151	30	system	system	NOUN
ejde-887	151	31	(	(	PUNCT
ejde-887	151	32	4.3)-(4.4	4.3)-(4.4	NOUN
ejde-887	151	33	)	)	PUNCT
ejde-887	151	34	to	to	PART
ejde-887	151	35	be	be	AUX
ejde-887	151	36	completely	completely	ADV
ejde-887	151	37	integrable	integrable	ADJ
ejde-887	151	38	,	,	PUNCT
ejde-887	151	39	and	and	CCONJ
ejde-887	151	40	consequently	consequently	ADV
ejde-887	151	41	deserves	deserve	VERB
ejde-887	151	42	further	further	ADJ
ejde-887	151	43	study	study	NOUN
ejde-887	151	44	.	.	PUNCT
ejde-887	152	1	4.2	4.2	NUM
ejde-887	152	2	.	.	PUNCT
ejde-887	153	1	multi	multi	ADJ
ejde-887	153	2	-	-	ADJ
ejde-887	153	3	scale	scale	ADJ
ejde-887	153	4	analysis	analysis	NOUN
ejde-887	153	5	of	of	ADP
ejde-887	153	6	the	the	DET
ejde-887	153	7	non	non	ADJ
ejde-887	153	8	-	-	ADJ
ejde-887	153	9	autonomous	autonomous	ADJ
ejde-887	153	10	nonlinear	nonlinear	ADJ
ejde-887	153	11	system	system	NOUN
ejde-887	153	12	.	.	PUNCT
ejde-887	154	1	in	in	ADP
ejde-887	154	2	this	this	DET
ejde-887	154	3	section	section	NOUN
ejde-887	154	4	we	we	PRON
ejde-887	154	5	introduce	introduce	VERB
ejde-887	154	6	a	a	DET
ejde-887	154	7	decomposition	decomposition	NOUN
ejde-887	154	8	of	of	ADP
ejde-887	154	9	the	the	DET
ejde-887	154	10	z	z	PROPN
ejde-887	154	11	,	,	PUNCT
ejde-887	154	12	u	u	NOUN
ejde-887	154	13	solutions	solution	NOUN
ejde-887	154	14	in	in	ADP
ejde-887	154	15	a	a	DET
ejde-887	154	16	series	series	NOUN
ejde-887	154	17	of	of	ADP
ejde-887	154	18	amplitudes	amplitude	NOUN
ejde-887	154	19	znj	znj	PROPN
ejde-887	154	20	,	,	PUNCT
ejde-887	154	21	unj	unj	VERB
ejde-887	154	22	which	which	PRON
ejde-887	154	23	obey	obey	VERB
ejde-887	154	24	a	a	DET
ejde-887	154	25	recursive	recursive	ADJ
ejde-887	154	26	system	system	NOUN
ejde-887	154	27	of	of	ADP
ejde-887	154	28	linearized	linearize	VERB
ejde-887	154	29	equations	equation	NOUN
ejde-887	154	30	.	.	PUNCT
ejde-887	155	1	here	here	ADV
ejde-887	155	2	we	we	PRON
ejde-887	155	3	extend	extend	VERB
ejde-887	155	4	the	the	DET
ejde-887	155	5	calculations	calculation	NOUN
ejde-887	155	6	presented	present	VERB
ejde-887	155	7	in	in	ADP
ejde-887	155	8	the	the	DET
ejde-887	155	9	previous	previous	ADJ
ejde-887	155	10	section	section	NOUN
ejde-887	155	11	4.1	4.1	NUM
ejde-887	155	12	from	from	ADP
ejde-887	155	13	one	one	NUM
ejde-887	155	14	sequence	sequence	NOUN
ejde-887	155	15	of	of	ADP
ejde-887	155	16	phases	phase	NOUN
ejde-887	155	17	,	,	PUNCT
ejde-887	155	18	to	to	ADP
ejde-887	155	19	a	a	DET
ejde-887	155	20	set	set	NOUN
ejde-887	155	21	of	of	ADP
ejde-887	155	22	coupled	couple	VERB
ejde-887	155	23	phases	phase	NOUN
ejde-887	155	24	.	.	PUNCT
ejde-887	156	1	to	to	PART
ejde-887	156	2	obtain	obtain	VERB
ejde-887	156	3	the	the	DET
ejde-887	156	4	hierarchy	hierarchy	NOUN
ejde-887	156	5	of	of	ADP
ejde-887	156	6	solutions	solution	NOUN
ejde-887	156	7	for	for	ADP
ejde-887	156	8	the	the	DET
ejde-887	156	9	nonlinear	nonlinear	ADJ
ejde-887	156	10	non	non	ADJ
ejde-887	156	11	-	-	ADJ
ejde-887	156	12	autonomous	autonomous	ADJ
ejde-887	156	13	system	system	NOUN
ejde-887	156	14	(	(	PUNCT
ejde-887	156	15	2.1	2.1	NUM
ejde-887	156	16	)	)	PUNCT
ejde-887	156	17	,	,	PUNCT
ejde-887	156	18	we	we	PRON
ejde-887	156	19	present	present	VERB
ejde-887	156	20	below	below	ADP
ejde-887	156	21	a	a	DET
ejde-887	156	22	generalization	generalization	NOUN
ejde-887	156	23	of	of	ADP
ejde-887	156	24	the	the	DET
ejde-887	156	25	multiplescale	multiplescale	ADJ
ejde-887	156	26	expansion	expansion	NOUN
ejde-887	156	27	method	method	NOUN
ejde-887	156	28	[	[	X
ejde-887	156	29	45	45	NUM
ejde-887	156	30	,	,	PUNCT
ejde-887	156	31	29	29	NUM
ejde-887	156	32	,	,	PUNCT
ejde-887	156	33	22	22	NUM
ejde-887	156	34	]	]	PUNCT
ejde-887	156	35	.	.	PUNCT
ejde-887	157	1	such	such	DET
ejde-887	157	2	a	a	DET
ejde-887	157	3	multiple	multiple	ADJ
ejde-887	157	4	-	-	PUNCT
ejde-887	157	5	scale	scale	NOUN
ejde-887	157	6	approach	approach	NOUN
ejde-887	157	7	should	should	AUX
ejde-887	157	8	be	be	AUX
ejde-887	157	9	able	able	ADJ
ejde-887	157	10	to	to	PART
ejde-887	157	11	circumscribe	circumscribe	VERB
ejde-887	157	12	the	the	DET
ejde-887	157	13	coupling	coupling	NOUN
ejde-887	157	14	between	between	ADP
ejde-887	157	15	nonlinearity	nonlinearity	NOUN
ejde-887	157	16	and	and	CCONJ
ejde-887	157	17	nonautonomous	nonautonomous	ADJ
ejde-887	157	18	coefficient	coefficient	NOUN
ejde-887	157	19	function	function	NOUN
ejde-887	157	20	contributions	contribution	NOUN
ejde-887	157	21	.	.	PUNCT
ejde-887	158	1	the	the	DET
ejde-887	158	2	procedure	procedure	NOUN
ejde-887	158	3	is	be	AUX
ejde-887	158	4	to	to	PART
ejde-887	158	5	build	build	VERB
ejde-887	158	6	a	a	DET
ejde-887	158	7	linear	linear	ADJ
ejde-887	158	8	combination	combination	NOUN
ejde-887	158	9	of	of	ADP
ejde-887	158	10	traveling	travel	VERB
ejde-887	158	11	modes	mode	NOUN
ejde-887	158	12	with	with	ADP
ejde-887	158	13	different	different	ADJ
ejde-887	158	14	phases	phase	NOUN
ejde-887	158	15	.	.	PUNCT
ejde-887	159	1	this	this	DET
ejde-887	159	2	superposition	superposition	NOUN
ejde-887	159	3	should	should	AUX
ejde-887	159	4	be	be	AUX
ejde-887	159	5	realized	realize	VERB
ejde-887	159	6	at	at	ADP
ejde-887	159	7	least	least	ADJ
ejde-887	159	8	through	through	ADP
ejde-887	159	9	a	a	DET
ejde-887	159	10	three	three	NUM
ejde-887	159	11	-	-	PUNCT
ejde-887	159	12	waves	wave	NOUN
ejde-887	159	13	mixing	mixing	NOUN
ejde-887	159	14	(	(	PUNCT
ejde-887	159	15	like	like	INTJ
ejde-887	159	16	k1	k1	NOUN
ejde-887	159	17	+	+	CCONJ
ejde-887	159	18	k2	k2	PROPN
ejde-887	159	19	+	+	CCONJ
ejde-887	159	20	k3	k3	PROPN
ejde-887	159	21	)	)	PUNCT
ejde-887	159	22	where	where	SCONJ
ejde-887	159	23	one	one	NUM
ejde-887	159	24	phase	phase	NOUN
ejde-887	159	25	arises	arise	VERB
ejde-887	159	26	from	from	ADP
ejde-887	159	27	the	the	DET
ejde-887	159	28	linearized	linearize	VERB
ejde-887	159	29	non	non	ADJ
ejde-887	159	30	-	-	ADJ
ejde-887	159	31	autonomous	autonomous	ADJ
ejde-887	159	32	solutions	solution	NOUN
ejde-887	159	33	(	(	PUNCT
ejde-887	159	34	section	section	NOUN
ejde-887	159	35	3.2	3.2	NUM
ejde-887	159	36	)	)	PUNCT
ejde-887	159	37	solution	solution	NOUN
ejde-887	159	38	and	and	CCONJ
ejde-887	159	39	another	another	PRON
ejde-887	159	40	must	must	AUX
ejde-887	159	41	be	be	AUX
ejde-887	159	42	introduced	introduce	VERB
ejde-887	159	43	to	to	PART
ejde-887	159	44	build	build	VERB
ejde-887	159	45	the	the	DET
ejde-887	159	46	multiple	multiple	ADJ
ejde-887	159	47	-	-	PUNCT
ejde-887	159	48	scales	scale	NOUN
ejde-887	159	49	(	(	PUNCT
ejde-887	159	50	section	section	NOUN
ejde-887	159	51	3.1	3.1	NUM
ejde-887	159	52	)	)	PUNCT
ejde-887	159	53	.	.	PUNCT
ejde-887	160	1	however	however	ADV
ejde-887	160	2	,	,	PUNCT
ejde-887	160	3	since	since	SCONJ
ejde-887	160	4	the	the	DET
ejde-887	160	5	contribution	contribution	NOUN
ejde-887	160	6	of	of	ADP
ejde-887	160	7	the	the	DET
ejde-887	160	8	variable	variable	ADJ
ejde-887	160	9	coefficient	coefficient	NOUN
ejde-887	160	10	q(x	q(x	NOUN
ejde-887	160	11	)	)	PUNCT
ejde-887	160	12	is	be	AUX
ejde-887	160	13	time	time	NOUN
ejde-887	160	14	-	-	PUNCT
ejde-887	160	15	independent	independent	ADJ
ejde-887	160	16	(	(	PUNCT
ejde-887	160	17	no	no	DET
ejde-887	160	18	frequency	frequency	NOUN
ejde-887	160	19	parameter	parameter	NOUN
ejde-887	160	20	associated	associate	VERB
ejde-887	160	21	to	to	ADP
ejde-887	160	22	this	this	DET
ejde-887	160	23	interaction	interaction	NOUN
ejde-887	160	24	)	)	PUNCT
ejde-887	160	25	,	,	PUNCT
ejde-887	160	26	it	it	PRON
ejde-887	160	27	becomes	become	VERB
ejde-887	160	28	difficult	difficult	ADJ
ejde-887	160	29	to	to	PART
ejde-887	160	30	balance	balance	VERB
ejde-887	160	31	the	the	DET
ejde-887	160	32	variable	variable	ADJ
ejde-887	160	33	coefficient	coefficient	NOUN
ejde-887	160	34	contribution	contribution	NOUN
ejde-887	160	35	using	use	VERB
ejde-887	160	36	a	a	DET
ejde-887	160	37	classical	classical	ADJ
ejde-887	160	38	multiple	multiple	ADJ
ejde-887	160	39	-	-	PUNCT
ejde-887	160	40	scale	scale	NOUN
ejde-887	160	41	procedure	procedure	NOUN
ejde-887	160	42	.	.	PUNCT
ejde-887	161	1	consequently	consequently	ADV
ejde-887	161	2	,	,	PUNCT
ejde-887	161	3	we	we	PRON
ejde-887	161	4	have	have	VERB
ejde-887	161	5	to	to	PART
ejde-887	161	6	use	use	VERB
ejde-887	161	7	an	an	DET
ejde-887	161	8	n	n	CCONJ
ejde-887	161	9	-waves	-wave	NOUN
ejde-887	161	10	mixing	mix	VERB
ejde-887	161	11	procedure	procedure	NOUN
ejde-887	161	12	[	[	X
ejde-887	161	13	36	36	NUM
ejde-887	161	14	,	,	PUNCT
ejde-887	161	15	22	22	NUM
ejde-887	161	16	]	]	PUNCT
ejde-887	161	17	.	.	PUNCT
ejde-887	162	1	we	we	PRON
ejde-887	162	2	proceed	proceed	VERB
ejde-887	162	3	with	with	ADP
ejde-887	162	4	a	a	DET
ejde-887	162	5	generalized	generalize	VERB
ejde-887	162	6	zakharov	zakharov	ADJ
ejde-887	162	7	-	-	PUNCT
ejde-887	162	8	kuznetsov	kuznetsov	NOUN
ejde-887	162	9	multiple	multiple	ADJ
ejde-887	162	10	-	-	PUNCT
ejde-887	162	11	scale	scale	NOUN
ejde-887	162	12	expansion	expansion	NOUN
ejde-887	162	13	procedure	procedure	NOUN
ejde-887	162	14	[	[	X
ejde-887	162	15	45	45	NUM
ejde-887	162	16	]	]	PUNCT
ejde-887	162	17	.	.	PUNCT
ejde-887	163	1	following	follow	VERB
ejde-887	163	2	(	(	PUNCT
ejde-887	163	3	3.10	3.10	NUM
ejde-887	163	4	)	)	PUNCT
ejde-887	163	5	we	we	PRON
ejde-887	163	6	introduce	introduce	VERB
ejde-887	163	7	a	a	DET
ejde-887	163	8	sequence	sequence	NOUN
ejde-887	163	9	of	of	ADP
ejde-887	163	10	coupling	couple	VERB
ejde-887	163	11	phases	phase	NOUN
ejde-887	163	12	given	give	VERB
ejde-887	163	13	by	by	ADP
ejde-887	163	14	ψj(x	ψj(x	NUM
ejde-887	163	15	,	,	PUNCT
ejde-887	163	16	t	t	PROPN
ejde-887	163	17	)	)	PUNCT
ejde-887	163	18	=	=	PUNCT
ejde-887	164	1	(	(	PUNCT
ejde-887	164	2	j	j	PROPN
ejde-887	164	3	−	−	PROPN
ejde-887	164	4	iµ)x	iµ)x	PROPN
ejde-887	165	1	+	+	CCONJ
ejde-887	165	2	ωt	ωt	PROPN
ejde-887	165	3	,	,	PUNCT
ejde-887	165	4	for	for	ADP
ejde-887	165	5	arbitrary	arbitrary	ADJ
ejde-887	165	6	positive	positive	ADJ
ejde-887	165	7	parameters	parameter	NOUN
ejde-887	165	8	µ	µ	X
ejde-887	165	9	,	,	PUNCT
ejde-887	165	10	ω	ω	NOUN
ejde-887	165	11	.	.	PUNCT
ejde-887	166	1	we	we	PRON
ejde-887	166	2	use	use	VERB
ejde-887	166	3	a	a	DET
ejde-887	166	4	perturbation	perturbation	NOUN
ejde-887	166	5	of	of	ADP
ejde-887	166	6	the	the	DET
ejde-887	166	7	general	general	ADJ
ejde-887	166	8	form	form	NOUN
ejde-887	166	9	of	of	ADP
ejde-887	166	10	the	the	DET
ejde-887	166	11	linear	linear	ADJ
ejde-887	166	12	non	non	ADJ
ejde-887	166	13	-	-	ADJ
ejde-887	166	14	autonomous	autonomous	ADJ
ejde-887	166	15	solutions	solution	NOUN
ejde-887	166	16	from	from	ADP
ejde-887	166	17	(	(	PUNCT
ejde-887	166	18	3.10	3.10	NUM
ejde-887	166	19	)	)	PUNCT
ejde-887	166	20	for	for	ADP
ejde-887	166	21	some	some	DET
ejde-887	166	22	given	give	VERB
ejde-887	166	23	arbitrary	arbitrary	ADJ
ejde-887	166	24	amplitudes	amplitude	NOUN
ejde-887	166	25	bj	bj	VERB
ejde-887	166	26	,	,	PUNCT
ejde-887	166	27	uj	uj	PROPN
ejde-887	166	28	.	.	PUNCT
ejde-887	167	1	based	base	VERB
ejde-887	167	2	on	on	ADP
ejde-887	167	3	these	these	DET
ejde-887	167	4	linear	linear	ADJ
ejde-887	167	5	solutions	solution	NOUN
ejde-887	167	6	we	we	PRON
ejde-887	167	7	build	build	VERB
ejde-887	167	8	the	the	DET
ejde-887	167	9	solution	solution	NOUN
ejde-887	167	10	of	of	ADP
ejde-887	167	11	the	the	DET
ejde-887	167	12	system	system	NOUN
ejde-887	167	13	(	(	PUNCT
ejde-887	167	14	2.1	2.1	NUM
ejde-887	167	15	)	)	PUNCT
ejde-887	167	16	in	in	ADP
ejde-887	167	17	the	the	DET
ejde-887	167	18	form	form	NOUN
ejde-887	167	19	z	z	NOUN
ejde-887	167	20	=	=	SYM
ejde-887	167	21	∞∑	∞∑	NUM
ejde-887	167	22	n	n	CCONJ
ejde-887	167	23	,	,	PUNCT
ejde-887	167	24	j=−∞	j=−∞	NOUN
ejde-887	167	25	δγnzn	δγnzn	NOUN
ejde-887	167	26	,	,	PUNCT
ejde-887	167	27	j(χ	j(χ	PROPN
ejde-887	167	28	,	,	PUNCT
ejde-887	167	29	θ)bjeinψj(χ	θ)bjeinψj(χ	NOUN
ejde-887	167	30	,	,	PUNCT
ejde-887	167	31	θ	θ	PROPN
ejde-887	167	32	)	)	PUNCT
ejde-887	167	33	,	,	PUNCT
ejde-887	167	34	(	(	PUNCT
ejde-887	167	35	4.5	4.5	X
ejde-887	167	36	)	)	PUNCT
ejde-887	167	37	u	u	NOUN
ejde-887	167	38	=	=	NOUN
ejde-887	167	39	∞∑	∞∑	NUM
ejde-887	167	40	n	n	CCONJ
ejde-887	167	41	,	,	PUNCT
ejde-887	167	42	j=−∞	j=−∞	PROPN
ejde-887	167	43	δγnun	δγnun	PROPN
ejde-887	167	44	,	,	PUNCT
ejde-887	167	45	j(χ	j(χ	PROPN
ejde-887	167	46	,	,	PUNCT
ejde-887	167	47	θ)ujeinψj(χ	θ)ujeinψj(χ	NOUN
ejde-887	167	48	,	,	PUNCT
ejde-887	167	49	θ	θ	NOUN
ejde-887	167	50	)	)	PUNCT
ejde-887	167	51	,	,	PUNCT
ejde-887	167	52	(	(	PUNCT
ejde-887	167	53	4.6	4.6	NUM
ejde-887	167	54	)	)	PUNCT
ejde-887	167	55	where	where	SCONJ
ejde-887	167	56	we	we	PRON
ejde-887	167	57	introduced	introduce	VERB
ejde-887	167	58	the	the	DET
ejde-887	167	59	new	new	ADJ
ejde-887	167	60	mixing	mixing	NOUN
ejde-887	167	61	amplitudes	amplitude	NOUN
ejde-887	167	62	z−n	z−n	NOUN
ejde-887	167	63	,	,	PUNCT
ejde-887	167	64	j	j	PROPN
ejde-887	167	65	=	=	SYM
ejde-887	167	66	z∗	z∗	PROPN
ejde-887	167	67	n	n	CCONJ
ejde-887	167	68	,	,	PUNCT
ejde-887	167	69	j	j	PROPN
ejde-887	167	70	and	and	CCONJ
ejde-887	167	71	u−n	u−n	PROPN
ejde-887	167	72	,	,	PUNCT
ejde-887	167	73	j	j	PROPN
ejde-887	167	74	=	=	SYM
ejde-887	168	1	u∗	u∗	PROPN
ejde-887	168	2	n	n	CCONJ
ejde-887	168	3	,	,	PUNCT
ejde-887	168	4	j	j	PROPN
ejde-887	168	5	,	,	PUNCT
ejde-887	168	6	and	and	CCONJ
ejde-887	168	7	we	we	PRON
ejde-887	168	8	are	be	AUX
ejde-887	168	9	using	use	VERB
ejde-887	168	10	the	the	DET
ejde-887	168	11	same	same	ADJ
ejde-887	168	12	smallness	smallness	NOUN
ejde-887	168	13	parameter	parameter	NOUN
ejde-887	168	14	0	0	PUNCT
ejde-887	168	15	<	<	X
ejde-887	168	16	δ	δ	X
ejde-887	168	17	<	<	X
ejde-887	168	18	1	1	NUM
ejde-887	168	19	as	as	ADP
ejde-887	168	20	in	in	ADP
ejde-887	168	21	the	the	DET
ejde-887	168	22	previous	previous	ADJ
ejde-887	168	23	section	section	NOUN
ejde-887	168	24	4.1	4.1	NUM
ejde-887	168	25	,	,	PUNCT
ejde-887	168	26	and	and	CCONJ
ejde-887	168	27	a	a	DET
ejde-887	168	28	similar	similar	ADJ
ejde-887	168	29	re	re	NOUN
ejde-887	168	30	-	-	NOUN
ejde-887	168	31	scaling	scaling	NOUN
ejde-887	168	32	of	of	ADP
ejde-887	168	33	coordinates	coordinate	NOUN
ejde-887	168	34	into	into	ADP
ejde-887	168	35	the	the	DET
ejde-887	168	36	stretched	stretch	VERB
ejde-887	168	37	variables	variable	NOUN
ejde-887	168	38	(	(	PUNCT
ejde-887	168	39	4.2	4.2	NUM
ejde-887	168	40	)	)	PUNCT
ejde-887	168	41	by	by	ADP
ejde-887	168	42	x	x	X
ejde-887	168	43	,	,	PUNCT
ejde-887	168	44	t→	t→	X
ejde-887	168	45	χ	χ	X
ejde-887	168	46	=	=	X
ejde-887	168	47	δ(x+	δ(x+	X
ejde-887	168	48	υt	υt	NOUN
ejde-887	168	49	)	)	PUNCT
ejde-887	168	50	,	,	PUNCT
ejde-887	168	51	θ	θ	X
ejde-887	169	1	=	=	SYM
ejde-887	169	2	−δ2	−δ2	PROPN
ejde-887	169	3	t.	t.	PROPN
ejde-887	169	4	in	in	ADP
ejde-887	169	5	(	(	PUNCT
ejde-887	169	6	4.5	4.5	NUM
ejde-887	169	7	)	)	PUNCT
ejde-887	169	8	,	,	PUNCT
ejde-887	169	9	(	(	PUNCT
ejde-887	169	10	4.6	4.6	X
ejde-887	169	11	)	)	PUNCT
ejde-887	169	12	we	we	PRON
ejde-887	169	13	have	have	VERB
ejde-887	169	14	the	the	DET
ejde-887	169	15	exponent	exponent	NOUN
ejde-887	169	16	γn	γn	NOUN
ejde-887	169	17	=	=	NOUN
ejde-887	169	18	|n|	|n|	PROPN
ejde-887	169	19	if	if	SCONJ
ejde-887	169	20	n	n	PRON
ejde-887	169	21	̸=	̸=	PROPN
ejde-887	169	22	0	0	NUM
ejde-887	169	23	,	,	PUNCT
ejde-887	169	24	and	and	CCONJ
ejde-887	169	25	γ0	γ0	NOUN
ejde-887	169	26	=	=	SYM
ejde-887	169	27	2	2	X
ejde-887	169	28	.	.	PUNCT
ejde-887	170	1	the	the	DET
ejde-887	170	2	stretched	stretch	VERB
ejde-887	170	3	variables	variable	NOUN
ejde-887	170	4	facilitate	facilitate	VERB
ejde-887	170	5	the	the	DET
ejde-887	170	6	coupling	coupling	NOUN
ejde-887	170	7	between	between	ADP
ejde-887	170	8	the	the	DET
ejde-887	170	9	scales	scale	NOUN
ejde-887	170	10	of	of	ADP
ejde-887	170	11	linear	linear	ADJ
ejde-887	170	12	solutions	solution	NOUN
ejde-887	170	13	and	and	CCONJ
ejde-887	170	14	the	the	DET
ejde-887	170	15	scales	scale	NOUN
ejde-887	170	16	of	of	ADP
ejde-887	170	17	modulation	modulation	NOUN
ejde-887	170	18	because	because	SCONJ
ejde-887	170	19	of	of	ADP
ejde-887	170	20	the	the	DET
ejde-887	170	21	nonlinearity	nonlinearity	NOUN
ejde-887	170	22	:	:	PUNCT
ejde-887	170	23	∂t	∂t	PROPN
ejde-887	170	24	→	→	SYM
ejde-887	170	25	δυ∂χ	δυ∂χ	NOUN
ejde-887	170	26	−	−	NOUN
ejde-887	170	27	δ2∂θ	δ2∂θ	NOUN
ejde-887	170	28	+	+	CCONJ
ejde-887	170	29	inω	inω	ADJ
ejde-887	170	30	,	,	PUNCT
ejde-887	170	31	∂x	∂x	PROPN
ejde-887	170	32	→	→	SYM
ejde-887	170	33	δ∂χ	δ∂χ	NOUN
ejde-887	170	34	,	,	PUNCT
ejde-887	170	35	while	while	SCONJ
ejde-887	170	36	the	the	DET
ejde-887	170	37	label	label	NOUN
ejde-887	170	38	n	n	CCONJ
ejde-887	170	39	provides	provide	VERB
ejde-887	170	40	the	the	DET
ejde-887	170	41	mixing	mixing	NOUN
ejde-887	170	42	of	of	ADP
ejde-887	170	43	scales	scale	NOUN
ejde-887	170	44	ψj	ψj	ADV
ejde-887	170	45	→	→	PUNCT
ejde-887	170	46	nψj	nψj	NOUN
ejde-887	170	47	weighted	weight	VERB
ejde-887	170	48	by	by	ADP
ejde-887	170	49	the	the	DET
ejde-887	170	50	unknown	unknown	ADJ
ejde-887	170	51	functions	function	NOUN
ejde-887	170	52	zn	zn	PROPN
ejde-887	170	53	,	,	PUNCT
ejde-887	170	54	j	j	PROPN
ejde-887	170	55	,	,	PUNCT
ejde-887	170	56	un	un	PROPN
ejde-887	170	57	,	,	PUNCT
ejde-887	170	58	j	j	PROPN
ejde-887	170	59	.	.	PUNCT
ejde-887	171	1	we	we	PRON
ejde-887	171	2	plug	plug	VERB
ejde-887	171	3	the	the	DET
ejde-887	171	4	double	double	ADJ
ejde-887	171	5	series	series	NOUN
ejde-887	171	6	in	in	ADP
ejde-887	171	7	the	the	DET
ejde-887	171	8	first	first	ADJ
ejde-887	171	9	equation	equation	NOUN
ejde-887	171	10	in	in	ADP
ejde-887	171	11	(	(	PUNCT
ejde-887	171	12	4.5	4.5	NUM
ejde-887	171	13	)	)	PUNCT
ejde-887	171	14	,	,	PUNCT
ejde-887	171	15	(	(	PUNCT
ejde-887	171	16	4.6	4.6	NUM
ejde-887	171	17	)	)	PUNCT
ejde-887	171	18	into	into	ADP
ejde-887	171	19	(	(	PUNCT
ejde-887	171	20	2.1	2.1	NUM
ejde-887	171	21	)	)	PUNCT
ejde-887	171	22	and	and	CCONJ
ejde-887	171	23	this	this	DET
ejde-887	171	24	system	system	NOUN
ejde-887	171	25	maps	map	VERB
ejde-887	171	26	into	into	ADP
ejde-887	171	27	a	a	DET
ejde-887	171	28	power	power	NOUN
ejde-887	171	29	series	series	NOUN
ejde-887	171	30	with	with	ADP
ejde-887	171	31	respect	respect	NOUN
ejde-887	171	32	to	to	ADP
ejde-887	171	33	δ	δ	PROPN
ejde-887	171	34	,	,	PUNCT
ejde-887	171	35	for	for	ADP
ejde-887	171	36	the	the	DET
ejde-887	171	37	unknown	unknown	ADJ
ejde-887	171	38	amplitudes	amplitude	NOUN
ejde-887	171	39	ejde-202x	ejde-202x	PROPN
ejde-887	171	40	/	/	SYM
ejde-887	171	41	conf/27	conf/27	NOUN
ejde-887	171	42	boussinesq	boussinesq	ADJ
ejde-887	171	43	equations	equation	NOUN
ejde-887	171	44	35	35	NUM
ejde-887	171	45	un	un	PROPN
ejde-887	171	46	,	,	PUNCT
ejde-887	171	47	j	j	PROPN
ejde-887	171	48	,	,	PUNCT
ejde-887	171	49	bn	bn	PROPN
ejde-887	171	50	,	,	PUNCT
ejde-887	171	51	j	j	PROPN
ejde-887	171	52	,	,	PUNCT
ejde-887	171	53	with	with	ADP
ejde-887	171	54	all	all	DET
ejde-887	171	55	other	other	ADJ
ejde-887	171	56	parameters	parameter	NOUN
ejde-887	171	57	known	know	VERB
ejde-887	171	58	(	(	PUNCT
ejde-887	171	59	q	q	NOUN
ejde-887	171	60	,	,	PUNCT
ejde-887	171	61	α	α	PROPN
ejde-887	171	62	,	,	PUNCT
ejde-887	171	63	β	β	X
ejde-887	171	64	,	,	PUNCT
ejde-887	171	65	uj	uj	PROPN
ejde-887	171	66	,	,	PUNCT
ejde-887	171	67	bj	bj	NOUN
ejde-887	171	68	)	)	PUNCT
ejde-887	171	69	.	.	PUNCT
ejde-887	172	1	according	accord	VERB
ejde-887	172	2	to	to	ADP
ejde-887	172	3	the	the	DET
ejde-887	172	4	procedure	procedure	NOUN
ejde-887	172	5	in	in	ADP
ejde-887	172	6	[	[	X
ejde-887	172	7	45	45	NUM
ejde-887	172	8	]	]	PUNCT
ejde-887	172	9	,	,	PUNCT
ejde-887	172	10	we	we	PRON
ejde-887	172	11	approach	approach	VERB
ejde-887	172	12	the	the	DET
ejde-887	172	13	limit	limit	NOUN
ejde-887	172	14	δ	δ	PROPN
ejde-887	172	15	→	→	SYM
ejde-887	172	16	0	0	NUM
ejde-887	172	17	and	and	CCONJ
ejde-887	172	18	we	we	PRON
ejde-887	172	19	cancel	cancel	VERB
ejde-887	172	20	the	the	DET
ejde-887	172	21	terms	term	NOUN
ejde-887	172	22	at	at	ADP
ejde-887	172	23	the	the	DET
ejde-887	172	24	minimal	minimal	ADJ
ejde-887	172	25	(	(	PUNCT
ejde-887	172	26	for	for	ADP
ejde-887	172	27	every	every	DET
ejde-887	172	28	n	n	CCONJ
ejde-887	172	29	)	)	PUNCT
ejde-887	172	30	power	power	NOUN
ejde-887	172	31	of	of	ADP
ejde-887	172	32	δ	δ	PROPN
ejde-887	172	33	.	.	PUNCT
ejde-887	173	1	the	the	DET
ejde-887	173	2	system	system	NOUN
ejde-887	173	3	(	(	PUNCT
ejde-887	173	4	2.1	2.1	NUM
ejde-887	173	5	)	)	PUNCT
ejde-887	173	6	is	be	AUX
ejde-887	173	7	reduced	reduce	VERB
ejde-887	173	8	,	,	PUNCT
ejde-887	173	9	as	as	ADP
ejde-887	173	10	δ	δ	PROPN
ejde-887	173	11	→	→	X
ejde-887	173	12	0	0	NUM
ejde-887	173	13	,	,	PUNCT
ejde-887	173	14	to	to	PART
ejde-887	173	15	explicit	explicit	ADJ
ejde-887	173	16	expressions	expression	NOUN
ejde-887	173	17	for	for	ADP
ejde-887	173	18	the	the	DET
ejde-887	173	19	corresponding	correspond	VERB
ejde-887	173	20	zn	zn	PROPN
ejde-887	173	21	,	,	PUNCT
ejde-887	173	22	j	j	PROPN
ejde-887	173	23	,	,	PUNCT
ejde-887	173	24	un	un	PROPN
ejde-887	173	25	,	,	PUNCT
ejde-887	173	26	j	j	PROPN
ejde-887	173	27	,	,	PUNCT
ejde-887	173	28	except	except	SCONJ
ejde-887	173	29	for	for	ADP
ejde-887	173	30	n	n	NOUN
ejde-887	173	31	=	=	SYM
ejde-887	173	32	1	1	NUM
ejde-887	173	33	at	at	ADP
ejde-887	173	34	the	the	DET
ejde-887	173	35	order	order	NOUN
ejde-887	173	36	o(δ	o(δ	PROPN
ejde-887	173	37	)	)	PUNCT
ejde-887	173	38	.	.	PUNCT
ejde-887	174	1	the	the	DET
ejde-887	174	2	summation	summation	NOUN
ejde-887	174	3	over	over	ADP
ejde-887	174	4	j	j	PROPN
ejde-887	174	5	can	can	AUX
ejde-887	174	6	be	be	AUX
ejde-887	174	7	extended	extend	VERB
ejde-887	174	8	to	to	ADP
ejde-887	174	9	the	the	DET
ejde-887	174	10	highest	high	ADJ
ejde-887	174	11	level	level	NOUN
ejde-887	174	12	of	of	ADP
ejde-887	174	13	accuracy	accuracy	NOUN
ejde-887	174	14	,	,	PUNCT
ejde-887	174	15	as	as	SCONJ
ejde-887	174	16	needed	need	VERB
ejde-887	174	17	for	for	ADP
ejde-887	174	18	the	the	DET
ejde-887	174	19	solution	solution	NOUN
ejde-887	174	20	.	.	PUNCT
ejde-887	175	1	for	for	ADP
ejde-887	175	2	the	the	DET
ejde-887	175	3	order	order	NOUN
ejde-887	175	4	n	n	NOUN
ejde-887	175	5	=	=	SYM
ejde-887	175	6	0	0	PROPN
ejde-887	175	7	the	the	DET
ejde-887	175	8	non	non	ADJ
ejde-887	175	9	-	-	ADJ
ejde-887	175	10	zero	zero	ADJ
ejde-887	175	11	relevant	relevant	ADJ
ejde-887	175	12	terms	term	NOUN
ejde-887	175	13	are	be	AUX
ejde-887	175	14	obtained	obtain	VERB
ejde-887	175	15	for	for	ADP
ejde-887	175	16	o(δ2	o(δ2	ADJ
ejde-887	175	17	)	)	PUNCT
ejde-887	175	18	and	and	CCONJ
ejde-887	175	19	result	result	VERB
ejde-887	175	20	in	in	ADP
ejde-887	175	21	∑	∑	PROPN
ejde-887	175	22	j	j	PROPN
ejde-887	175	23	u0,juj	u0,juj	PROPN
ejde-887	176	1	=	=	SYM
ejde-887	176	2	0	0	X
ejde-887	176	3	.	.	PUNCT
ejde-887	177	1	(	(	PUNCT
ejde-887	177	2	4.7	4.7	NUM
ejde-887	177	3	)	)	PUNCT
ejde-887	177	4	equation	equation	NOUN
ejde-887	177	5	(	(	PUNCT
ejde-887	177	6	4.7	4.7	NUM
ejde-887	177	7	)	)	PUNCT
ejde-887	177	8	for	for	ADP
ejde-887	177	9	the	the	DET
ejde-887	177	10	amplitudes	amplitude	NOUN
ejde-887	177	11	u0,j	u0,j	PROPN
ejde-887	177	12	is	be	AUX
ejde-887	177	13	homogeneous	homogeneous	ADJ
ejde-887	177	14	,	,	PUNCT
ejde-887	177	15	and	and	CCONJ
ejde-887	177	16	the	the	DET
ejde-887	177	17	indeterminacy	indeterminacy	NOUN
ejde-887	177	18	of	of	ADP
ejde-887	177	19	its	its	PRON
ejde-887	177	20	solutions	solution	NOUN
ejde-887	177	21	can	can	AUX
ejde-887	177	22	be	be	AUX
ejde-887	177	23	physically	physically	ADV
ejde-887	177	24	related	relate	VERB
ejde-887	177	25	to	to	ADP
ejde-887	177	26	the	the	DET
ejde-887	177	27	non	non	ADJ
ejde-887	177	28	-	-	NOUN
ejde-887	177	29	conservation	conservation	NOUN
ejde-887	177	30	of	of	ADP
ejde-887	177	31	longitudinal	longitudinal	ADJ
ejde-887	177	32	momentum	momentum	NOUN
ejde-887	177	33	because	because	SCONJ
ejde-887	177	34	of	of	ADP
ejde-887	177	35	the	the	DET
ejde-887	177	36	interaction	interaction	NOUN
ejde-887	177	37	with	with	ADP
ejde-887	177	38	the	the	DET
ejde-887	177	39	variable	variable	ADJ
ejde-887	177	40	coefficient	coefficient	NOUN
ejde-887	177	41	.	.	PUNCT
ejde-887	178	1	the	the	DET
ejde-887	178	2	term	term	NOUN
ejde-887	178	3	with	with	ADP
ejde-887	178	4	n	n	NOUN
ejde-887	178	5	=	=	SYM
ejde-887	178	6	1	1	NUM
ejde-887	178	7	is	be	AUX
ejde-887	178	8	identical	identical	ADJ
ejde-887	178	9	zero	zero	NUM
ejde-887	178	10	in	in	ADP
ejde-887	178	11	o(δ	o(δ	PROPN
ejde-887	178	12	)	)	PUNCT
ejde-887	178	13	.	.	PUNCT
ejde-887	179	1	in	in	ADP
ejde-887	179	2	o(δ2	o(δ2	ADJ
ejde-887	179	3	)	)	PUNCT
ejde-887	179	4	the	the	DET
ejde-887	179	5	equations	equation	NOUN
ejde-887	179	6	of	of	ADP
ejde-887	179	7	interest	interest	NOUN
ejde-887	179	8	for	for	ADP
ejde-887	179	9	this	this	DET
ejde-887	179	10	term	term	NOUN
ejde-887	179	11	is	be	AUX
ejde-887	179	12	q	q	PUNCT
ejde-887	179	13	∑	∑	PROPN
ejde-887	179	14	j	j	PROPN
ejde-887	179	15	u1,j	u1,j	PROPN
ejde-887	179	16	,	,	PUNCT
ejde-887	179	17	χuj	χuj	NOUN
ejde-887	179	18	−	−	PROPN
ejde-887	179	19	2i	2i	NOUN
ejde-887	179	20	3	3	NUM
ejde-887	179	21	βυq′	βυq′	NOUN
ejde-887	179	22	∑	∑	PROPN
ejde-887	179	23	j	j	PROPN
ejde-887	179	24	(	(	PUNCT
ejde-887	179	25	j	j	PROPN
ejde-887	179	26	−	−	PROPN
ejde-887	179	27	iµ)z1,jbj	iµ)z1,jbj	PROPN
ejde-887	180	1	+	+	CCONJ
ejde-887	180	2	∑	∑	PROPN
ejde-887	180	3	j	j	PROPN
ejde-887	180	4	[	[	PUNCT
ejde-887	180	5	υq	υq	ADP
ejde-887	180	6	−	−	PROPN
ejde-887	180	7	2i	2i	NUM
ejde-887	180	8	3	3	NUM
ejde-887	180	9	βq(j	βq(j	PUNCT
ejde-887	180	10	−	−	NOUN
ejde-887	180	11	iµ)−	iµ)−	NOUN
ejde-887	180	12	2i	2i	NOUN
ejde-887	180	13	3	3	NUM
ejde-887	180	14	βq′ω	βq′ω	ADP
ejde-887	180	15	−	−	PROPN
ejde-887	180	16	1	1	NUM
ejde-887	180	17	3	3	NUM
ejde-887	180	18	βυq′′	βυq′′	NOUN
ejde-887	180	19	]	]	X
ejde-887	181	1	z1,j	z1,j	NOUN
ejde-887	181	2	,	,	PUNCT
ejde-887	181	3	χbj	χbj	NOUN
ejde-887	181	4	=	=	SYM
ejde-887	181	5	0	0	NUM
ejde-887	181	6	,	,	PUNCT
ejde-887	181	7	(	(	PUNCT
ejde-887	181	8	4.8	4.8	NUM
ejde-887	181	9	)	)	PUNCT
ejde-887	181	10	where	where	SCONJ
ejde-887	181	11	q′	q′	NOUN
ejde-887	181	12	and	and	CCONJ
ejde-887	181	13	zn	zn	PROPN
ejde-887	181	14	,	,	PUNCT
ejde-887	181	15	j	j	PROPN
ejde-887	181	16	,	,	PUNCT
ejde-887	181	17	χ	χ	PRON
ejde-887	181	18	are	be	AUX
ejde-887	181	19	χ	χ	NOUN
ejde-887	181	20	-	-	PUNCT
ejde-887	181	21	derivatives	derivative	NOUN
ejde-887	181	22	of	of	ADP
ejde-887	181	23	q	q	PROPN
ejde-887	181	24	and	and	CCONJ
ejde-887	181	25	zn	zn	PROPN
ejde-887	181	26	,	,	PUNCT
ejde-887	181	27	j	j	PROPN
ejde-887	181	28	,	,	PUNCT
ejde-887	181	29	respectively	respectively	ADV
ejde-887	181	30	.	.	PUNCT
ejde-887	182	1	the	the	DET
ejde-887	182	2	term	term	NOUN
ejde-887	182	3	for	for	ADP
ejde-887	182	4	n	n	NOUN
ejde-887	182	5	=	=	SYM
ejde-887	182	6	2	2	NUM
ejde-887	182	7	has	have	VERB
ejde-887	182	8	the	the	DET
ejde-887	182	9	first	first	ADJ
ejde-887	182	10	non	non	ADJ
ejde-887	182	11	-	-	ADJ
ejde-887	182	12	zero	zero	NUM
ejde-887	182	13	term	term	NOUN
ejde-887	182	14	in	in	ADP
ejde-887	182	15	o(δ2	o(δ2	ADJ
ejde-887	182	16	)	)	PUNCT
ejde-887	182	17	and	and	CCONJ
ejde-887	182	18	reads∑	reads∑	PROPN
ejde-887	182	19	j	j	PROPN
ejde-887	183	1	[	[	X
ejde-887	183	2	2iq(j	2iq(j	NUM
ejde-887	183	3	−	−	NOUN
ejde-887	183	4	iµ	iµ	NOUN
ejde-887	183	5	)	)	PUNCT
ejde-887	184	1	+	+	CCONJ
ejde-887	185	1	q′]u2,juj	q′]u2,juj	ADJ
ejde-887	186	1	+	+	CCONJ
ejde-887	186	2	∑	∑	PUNCT
ejde-887	186	3	j	j	PROPN
ejde-887	187	1	[	[	X
ejde-887	187	2	4	4	NUM
ejde-887	187	3	3	3	NUM
ejde-887	187	4	βq(j	βq(j	PUNCT
ejde-887	187	5	−	−	PROPN
ejde-887	187	6	iµ)2	iµ)2	PROPN
ejde-887	187	7	+	+	CCONJ
ejde-887	187	8	2iωq	2iωq	NUM
ejde-887	187	9	+	+	CCONJ
ejde-887	187	10	8	8	NUM
ejde-887	187	11	3	3	NUM
ejde-887	187	12	βωq′(j	βωq′(j	ADJ
ejde-887	187	13	−	−	ADP
ejde-887	187	14	iµ)−	iµ)−	NOUN
ejde-887	187	15	2i	2i	NOUN
ejde-887	187	16	3	3	NUM
ejde-887	187	17	βωq′′	βωq′′	NOUN
ejde-887	187	18	]	]	PUNCT
ejde-887	187	19	z2,jbj	z2,jbj	PUNCT
ejde-887	187	20	+	+	CCONJ
ejde-887	187	21	2iα	2iα	ADJ
ejde-887	187	22	∑	∑	PROPN
ejde-887	187	23	j	j	PROPN
ejde-887	187	24	(	(	PUNCT
ejde-887	187	25	j	j	PROPN
ejde-887	187	26	−	−	PROPN
ejde-887	187	27	iµ)e−ijχ	iµ)e−ijχ	PROPN
ejde-887	187	28	[	[	PUNCT
ejde-887	187	29	u1,jz1,−1ujb−1e	u1,jz1,−1ujb−1e	NOUN
ejde-887	187	30	−iχ	−iχ	PROPN
ejde-887	187	31	+	+	CCONJ
ejde-887	187	32	u1,jz1,0ujb0	u1,jz1,0ujb0	PROPN
ejde-887	187	33	+	+	CCONJ
ejde-887	187	34	u1,jz1,1ujb1e	u1,jz1,1ujb1e	PROPN
ejde-887	187	35	iχ	iχ	ADP
ejde-887	187	36	]	]	PUNCT
ejde-887	187	37	=	=	SYM
ejde-887	187	38	0	0	NUM
ejde-887	187	39	(	(	PUNCT
ejde-887	187	40	4.9	4.9	NUM
ejde-887	187	41	)	)	PUNCT
ejde-887	187	42	equations	equation	NOUN
ejde-887	187	43	(	(	PUNCT
ejde-887	187	44	4.8	4.8	NUM
ejde-887	187	45	)	)	PUNCT
ejde-887	187	46	,	,	PUNCT
ejde-887	187	47	(	(	PUNCT
ejde-887	187	48	4.9	4.9	NUM
ejde-887	187	49	)	)	PUNCT
ejde-887	187	50	provide	provide	VERB
ejde-887	187	51	the	the	DET
ejde-887	187	52	coupling	coupling	NOUN
ejde-887	187	53	between	between	ADP
ejde-887	187	54	wave	wave	NOUN
ejde-887	187	55	shape	shape	NOUN
ejde-887	187	56	amplitudes	amplitude	NOUN
ejde-887	187	57	zn	zn	PROPN
ejde-887	187	58	,	,	PUNCT
ejde-887	187	59	j	j	PROPN
ejde-887	187	60	and	and	CCONJ
ejde-887	187	61	velocity	velocity	NOUN
ejde-887	187	62	amplitudes	amplitude	NOUN
ejde-887	187	63	un	un	PROPN
ejde-887	187	64	,	,	PUNCT
ejde-887	187	65	j	j	PROPN
ejde-887	187	66	,	,	PUNCT
ejde-887	187	67	which	which	PRON
ejde-887	187	68	already	already	ADV
ejde-887	187	69	occurs	occur	VERB
ejde-887	187	70	at	at	ADP
ejde-887	187	71	the	the	DET
ejde-887	187	72	lowest	low	ADJ
ejde-887	187	73	order	order	NOUN
ejde-887	187	74	.	.	PUNCT
ejde-887	188	1	at	at	ADP
ejde-887	188	2	o(δ3	o(δ3	NOUN
ejde-887	188	3	)	)	PUNCT
ejde-887	188	4	,	,	PUNCT
ejde-887	188	5	the	the	DET
ejde-887	188	6	equation	equation	NOUN
ejde-887	188	7	for	for	ADP
ejde-887	188	8	n	n	NOUN
ejde-887	188	9	=	=	SYM
ejde-887	188	10	1	1	NUM
ejde-887	188	11	is	be	AUX
ejde-887	188	12	β	β	X
ejde-887	188	13	3	3	NUM
ejde-887	188	14	∑	∑	PART
ejde-887	188	15	j	j	PROPN
ejde-887	189	1	[	[	X
ejde-887	189	2	2iq′(j	2iq′(j	NUM
ejde-887	189	3	−	−	NOUN
ejde-887	189	4	iµ	iµ	NOUN
ejde-887	189	5	)	)	PUNCT
ejde-887	190	1	+	+	CCONJ
ejde-887	191	1	q′′]z1,j	q′′]z1,j	NOUN
ejde-887	191	2	,	,	PUNCT
ejde-887	191	3	θbj	θbj	CCONJ
ejde-887	191	4	−	−	PROPN
ejde-887	191	5	β	β	NOUN
ejde-887	191	6	3	3	NUM
ejde-887	191	7	∑	∑	PROPN
ejde-887	191	8	j	j	PROPN
ejde-887	191	9	(	(	PUNCT
ejde-887	191	10	2υq′	2υq′	NUM
ejde-887	191	11	+	+	CCONJ
ejde-887	191	12	q)z1,j	q)z1,j	ADJ
ejde-887	191	13	,	,	PUNCT
ejde-887	191	14	χχbj	χχbj	ADJ
ejde-887	191	15	+	+	CCONJ
ejde-887	191	16	iα	iα	INTJ
ejde-887	191	17	∑	∑	PROPN
ejde-887	191	18	j	j	PROPN
ejde-887	191	19	,	,	PUNCT
ejde-887	191	20	k	k	PROPN
ejde-887	191	21	,	,	PUNCT
ejde-887	191	22	l	l	PROPN
ejde-887	191	23	(	(	PUNCT
ejde-887	191	24	j	j	PROPN
ejde-887	191	25	−	−	PROPN
ejde-887	191	26	iµ)zk	iµ)zk	PROPN
ejde-887	191	27	,	,	PUNCT
ejde-887	191	28	lu1−k	lu1−k	PROPN
ejde-887	191	29	,	,	PUNCT
ejde-887	191	30	jujbleik(l−j)χ	jujbleik(l−j)χ	NOUN
ejde-887	191	31	=	=	PUNCT
ejde-887	191	32	q	q	X
ejde-887	191	33	∑	∑	PUNCT
ejde-887	191	34	j	j	PROPN
ejde-887	191	35	z1,jbj	z1,jbj	PROPN
ejde-887	191	36	,	,	PUNCT
ejde-887	191	37	(	(	PUNCT
ejde-887	191	38	4.10	4.10	NUM
ejde-887	191	39	)	)	PUNCT
ejde-887	191	40	the	the	DET
ejde-887	191	41	triple	triple	ADJ
ejde-887	191	42	summation	summation	NOUN
ejde-887	191	43	in	in	ADP
ejde-887	191	44	the	the	DET
ejde-887	191	45	last	last	ADJ
ejde-887	191	46	term	term	NOUN
ejde-887	191	47	in	in	ADP
ejde-887	191	48	(	(	PUNCT
ejde-887	191	49	4.10	4.10	NUM
ejde-887	191	50	)	)	PUNCT
ejde-887	191	51	manifests	manifest	VERB
ejde-887	191	52	the	the	DET
ejde-887	191	53	nonlinear	nonlinear	ADJ
ejde-887	191	54	coupling	coupling	NOUN
ejde-887	191	55	between	between	ADP
ejde-887	191	56	various	various	ADJ
ejde-887	191	57	modes	mode	NOUN
ejde-887	191	58	and	and	CCONJ
ejde-887	191	59	scales	scale	NOUN
ejde-887	191	60	of	of	ADP
ejde-887	191	61	the	the	DET
ejde-887	191	62	amplitudes	amplitude	NOUN
ejde-887	191	63	zn	zn	PROPN
ejde-887	191	64	,	,	PUNCT
ejde-887	191	65	j	j	PROPN
ejde-887	191	66	and	and	CCONJ
ejde-887	191	67	un	un	PROPN
ejde-887	191	68	,	,	PUNCT
ejde-887	191	69	j	j	NOUN
ejde-887	191	70	,	,	PUNCT
ejde-887	191	71	and	and	CCONJ
ejde-887	192	1	their	their	PRON
ejde-887	192	2	coupling	coupling	NOUN
ejde-887	192	3	with	with	ADP
ejde-887	192	4	the	the	DET
ejde-887	192	5	modes	mode	NOUN
ejde-887	192	6	generated	generate	VERB
ejde-887	192	7	by	by	ADP
ejde-887	192	8	the	the	DET
ejde-887	192	9	variable	variable	ADJ
ejde-887	192	10	coefficient	coefficient	NOUN
ejde-887	192	11	q.	q.	NOUN
ejde-887	192	12	equation	equation	NOUN
ejde-887	192	13	(	(	PUNCT
ejde-887	192	14	4.10	4.10	NUM
ejde-887	192	15	)	)	PUNCT
ejde-887	192	16	is	be	AUX
ejde-887	192	17	the	the	DET
ejde-887	192	18	first	first	ADJ
ejde-887	192	19	one	one	NUM
ejde-887	192	20	in	in	ADP
ejde-887	192	21	the	the	DET
ejde-887	192	22	hierarchy	hierarchy	NOUN
ejde-887	192	23	to	to	PART
ejde-887	192	24	contain	contain	VERB
ejde-887	192	25	nonlinear	nonlinear	ADJ
ejde-887	192	26	quadratic	quadratic	ADJ
ejde-887	192	27	terms	term	NOUN
ejde-887	192	28	.	.	PUNCT
ejde-887	193	1	this	this	DET
ejde-887	193	2	equation	equation	NOUN
ejde-887	193	3	has	have	VERB
ejde-887	193	4	the	the	DET
ejde-887	193	5	same	same	ADJ
ejde-887	193	6	structure	structure	NOUN
ejde-887	193	7	as	as	ADP
ejde-887	193	8	the	the	DET
ejde-887	193	9	vector	vector	NOUN
ejde-887	193	10	akns	akns	NOUN
ejde-887	193	11	system	system	NOUN
ejde-887	193	12	[	[	X
ejde-887	193	13	29	29	NUM
ejde-887	193	14	]	]	PUNCT
ejde-887	193	15	.	.	PUNCT
ejde-887	194	1	this	this	DET
ejde-887	194	2	result	result	NOUN
ejde-887	194	3	is	be	AUX
ejde-887	194	4	expected	expect	VERB
ejde-887	194	5	,	,	PUNCT
ejde-887	194	6	since	since	SCONJ
ejde-887	194	7	a	a	DET
ejde-887	194	8	similar	similar	ADJ
ejde-887	194	9	model	model	NOUN
ejde-887	194	10	,	,	PUNCT
ejde-887	194	11	the	the	DET
ejde-887	194	12	fokas	fokas	ADJ
ejde-887	194	13	-	-	PUNCT
ejde-887	194	14	lenells	lenell	NOUN
ejde-887	194	15	non	non	ADJ
ejde-887	194	16	-	-	ADJ
ejde-887	194	17	autonomous	autonomous	ADJ
ejde-887	194	18	system	system	NOUN
ejde-887	194	19	was	be	AUX
ejde-887	194	20	also	also	ADV
ejde-887	194	21	proved	prove	VERB
ejde-887	194	22	to	to	PART
ejde-887	194	23	be	be	AUX
ejde-887	194	24	integrable	integrable	ADJ
ejde-887	194	25	towards	towards	ADP
ejde-887	194	26	the	the	DET
ejde-887	194	27	vector	vector	NOUN
ejde-887	194	28	akns	akns	NOUN
ejde-887	194	29	system	system	NOUN
ejde-887	195	1	[	[	X
ejde-887	195	2	47	47	NUM
ejde-887	195	3	]	]	PUNCT
ejde-887	195	4	.	.	PUNCT
ejde-887	196	1	36	36	NUM
ejde-887	196	2	a.	a.	NOUN
ejde-887	196	3	ludu	ludu	PROPN
ejde-887	196	4	,	,	PUNCT
ejde-887	196	5	h.	h.	PROPN
ejde-887	196	6	khanal	khanal	NOUN
ejde-887	196	7	,	,	PUNCT
ejde-887	196	8	a.	a.	PROPN
ejde-887	196	9	s.	s.	PROPN
ejde-887	196	10	carstea	carstea	PROPN
ejde-887	196	11	ejde-2022	ejde-2022	PROPN
ejde-887	196	12	/	/	SYM
ejde-887	196	13	conf/27	conf/27	NOUN
ejde-887	196	14	we	we	PRON
ejde-887	196	15	use	use	VERB
ejde-887	196	16	the	the	DET
ejde-887	196	17	same	same	ADJ
ejde-887	196	18	procedure	procedure	NOUN
ejde-887	196	19	for	for	ADP
ejde-887	196	20	the	the	DET
ejde-887	196	21	second	second	ADJ
ejde-887	196	22	equation	equation	NOUN
ejde-887	196	23	from	from	ADP
ejde-887	196	24	(	(	PUNCT
ejde-887	196	25	2.1	2.1	NUM
ejde-887	196	26	)	)	PUNCT
ejde-887	196	27	.	.	PUNCT
ejde-887	197	1	for	for	ADP
ejde-887	197	2	the	the	DET
ejde-887	197	3	order	order	NOUN
ejde-887	197	4	n	n	NOUN
ejde-887	197	5	=	=	SYM
ejde-887	197	6	0	0	PROPN
ejde-887	197	7	the	the	DET
ejde-887	197	8	first	first	ADJ
ejde-887	197	9	non	non	ADJ
ejde-887	197	10	-	-	ADJ
ejde-887	197	11	trivial	trivial	ADJ
ejde-887	197	12	relation	relation	NOUN
ejde-887	197	13	is	be	AUX
ejde-887	197	14	obtained	obtain	VERB
ejde-887	197	15	at	at	ADP
ejde-887	197	16	o(δ3	o(δ3	NOUN
ejde-887	197	17	)	)	PUNCT
ejde-887	197	18	qυ	qυ	PROPN
ejde-887	198	1	∑	∑	PROPN
ejde-887	198	2	j	j	PROPN
ejde-887	198	3	u0,j	u0,j	PROPN
ejde-887	198	4	,	,	PUNCT
ejde-887	198	5	χuj	χuj	NOUN
ejde-887	198	6	+	+	CCONJ
ejde-887	198	7	∑	∑	PROPN
ejde-887	198	8	j	j	PROPN
ejde-887	198	9	z0,j	z0,j	PROPN
ejde-887	198	10	,	,	PUNCT
ejde-887	198	11	χbj	χbj	NOUN
ejde-887	198	12	+	+	CCONJ
ejde-887	198	13	α	α	PROPN
ejde-887	198	14	2	2	NUM
ejde-887	198	15	∑	∑	PROPN
ejde-887	198	16	j	j	PROPN
ejde-887	198	17	,	,	PUNCT
ejde-887	198	18	k	k	PROPN
ejde-887	198	19	,	,	PUNCT
ejde-887	198	20	l	l	PROPN
ejde-887	199	1	[	[	X
ejde-887	199	2	k(l	k(l	NOUN
ejde-887	199	3	−	−	PROPN
ejde-887	199	4	j)uk	j)uk	PROPN
ejde-887	199	5	,	,	PUNCT
ejde-887	199	6	luk	luk	PROPN
ejde-887	199	7	,	,	PUNCT
ejde-887	199	8	j	j	PROPN
ejde-887	199	9	+	+	PROPN
ejde-887	199	10	uk	uk	PROPN
ejde-887	199	11	,	,	PUNCT
ejde-887	199	12	l	l	NOUN
ejde-887	199	13	,	,	PUNCT
ejde-887	199	14	χu	χu	ADP
ejde-887	199	15	∗	∗	NOUN
ejde-887	199	16	k	k	PROPN
ejde-887	199	17	,	,	PUNCT
ejde-887	199	18	j	j	PROPN
ejde-887	199	19	+	+	PROPN
ejde-887	199	20	uk	uk	PROPN
ejde-887	199	21	,	,	PUNCT
ejde-887	199	22	lu	lu	PROPN
ejde-887	199	23	∗	∗	NOUN
ejde-887	199	24	k	k	PROPN
ejde-887	199	25	,	,	PUNCT
ejde-887	199	26	j	j	PROPN
ejde-887	199	27	,	,	PUNCT
ejde-887	199	28	χ]ulujeik(l−j)χ	χ]ulujeik(l−j)χ	PROPN
ejde-887	199	29	=	=	SYM
ejde-887	199	30	0	0	X
ejde-887	199	31	.	.	PUNCT
ejde-887	199	32	(	(	PUNCT
ejde-887	199	33	4.11	4.11	NUM
ejde-887	199	34	)	)	PUNCT
ejde-887	199	35	for	for	ADP
ejde-887	199	36	n	n	NOUN
ejde-887	199	37	=	=	SYM
ejde-887	199	38	1	1	NUM
ejde-887	199	39	,	,	PUNCT
ejde-887	199	40	the	the	DET
ejde-887	199	41	terms	term	NOUN
ejde-887	199	42	of	of	ADP
ejde-887	199	43	o(δ	o(δ	PROPN
ejde-887	199	44	)	)	PUNCT
ejde-887	199	45	cancel	cancel	VERB
ejde-887	199	46	,	,	PUNCT
ejde-887	199	47	since	since	SCONJ
ejde-887	199	48	they	they	PRON
ejde-887	199	49	satisfy	satisfy	VERB
ejde-887	199	50	the	the	DET
ejde-887	199	51	linearized	linearize	VERB
ejde-887	199	52	equation	equation	NOUN
ejde-887	199	53	.	.	PUNCT
ejde-887	200	1	at	at	ADP
ejde-887	200	2	o(δ2	o(δ2	ADJ
ejde-887	200	3	)	)	PUNCT
ejde-887	200	4	,	,	PUNCT
ejde-887	200	5	we	we	PRON
ejde-887	200	6	obtain	obtain	VERB
ejde-887	200	7	for	for	ADP
ejde-887	200	8	n	n	NOUN
ejde-887	200	9	=	=	SYM
ejde-887	200	10	1	1	NUM
ejde-887	200	11	υq	υq	ADP
ejde-887	200	12	∑	∑	PROPN
ejde-887	200	13	j	j	PROPN
ejde-887	200	14	u1,j	u1,j	PROPN
ejde-887	200	15	,	,	PUNCT
ejde-887	200	16	χuj	χuj	NOUN
ejde-887	201	1	+	+	CCONJ
ejde-887	201	2	∑	∑	PROPN
ejde-887	201	3	j	j	PROPN
ejde-887	201	4	z1,j	z1,j	PROPN
ejde-887	201	5	,	,	PUNCT
ejde-887	201	6	χbj	χbj	NOUN
ejde-887	201	7	=	=	SYM
ejde-887	201	8	0	0	NUM
ejde-887	201	9	,	,	PUNCT
ejde-887	201	10	(	(	PUNCT
ejde-887	201	11	4.12	4.12	NUM
ejde-887	201	12	)	)	PUNCT
ejde-887	201	13	and	and	CCONJ
ejde-887	201	14	for	for	ADP
ejde-887	201	15	n	n	NOUN
ejde-887	201	16	=	=	SYM
ejde-887	201	17	2	2	NUM
ejde-887	201	18	,	,	PUNCT
ejde-887	201	19	2iωq	2iωq	NUM
ejde-887	201	20	∑	∑	SYM
ejde-887	201	21	j	j	PROPN
ejde-887	201	22	u2,juj	u2,juj	PROPN
ejde-887	202	1	+	+	NUM
ejde-887	202	2	2i	2i	NUM
ejde-887	202	3	∑	∑	PROPN
ejde-887	202	4	j	j	PROPN
ejde-887	202	5	(	(	PUNCT
ejde-887	202	6	j	j	PROPN
ejde-887	202	7	−	−	PROPN
ejde-887	202	8	iµ)z2,jbj	iµ)z2,jbj	PROPN
ejde-887	202	9	+	+	CCONJ
ejde-887	202	10	iα	iα	ADP
ejde-887	202	11	∑	∑	PROPN
ejde-887	202	12	j	j	PROPN
ejde-887	202	13	,	,	PUNCT
ejde-887	202	14	k	k	PROPN
ejde-887	202	15	,	,	PUNCT
ejde-887	202	16	l	l	PROPN
ejde-887	202	17	(	(	PUNCT
ejde-887	202	18	j	j	PROPN
ejde-887	202	19	−	−	PROPN
ejde-887	202	20	iµ)uklu2−k	iµ)uklu2−k	PROPN
ejde-887	202	21	,	,	PUNCT
ejde-887	202	22	julujeik(l−j)χ	julujeik(l−j)χ	NOUN
ejde-887	202	23	=	=	SYM
ejde-887	202	24	0	0	X
ejde-887	202	25	.	.	PUNCT
ejde-887	203	1	(	(	PUNCT
ejde-887	203	2	4.13	4.13	NUM
ejde-887	203	3	)	)	PUNCT
ejde-887	203	4	although	although	SCONJ
ejde-887	203	5	this	this	DET
ejde-887	203	6	hierarchy	hierarchy	NOUN
ejde-887	203	7	of	of	ADP
ejde-887	203	8	differential	differential	ADJ
ejde-887	203	9	equations	equation	NOUN
ejde-887	203	10	,	,	PUNCT
ejde-887	203	11	obtained	obtain	VERB
ejde-887	203	12	for	for	ADP
ejde-887	203	13	various	various	ADJ
ejde-887	203	14	n	n	CCONJ
ejde-887	203	15	,	,	PUNCT
ejde-887	203	16	j	j	PROPN
ejde-887	203	17	,	,	PUNCT
ejde-887	203	18	is	be	AUX
ejde-887	203	19	still	still	ADV
ejde-887	203	20	non	non	ADJ
ejde-887	203	21	-	-	ADJ
ejde-887	203	22	autonomous	autonomous	ADJ
ejde-887	203	23	,	,	PUNCT
ejde-887	203	24	the	the	DET
ejde-887	203	25	resulting	result	VERB
ejde-887	203	26	system	system	NOUN
ejde-887	203	27	of	of	ADP
ejde-887	203	28	equations	equation	NOUN
ejde-887	203	29	(	(	PUNCT
ejde-887	203	30	4.7)-(4.13	4.7)-(4.13	NOUN
ejde-887	203	31	)	)	PUNCT
ejde-887	203	32	and	and	CCONJ
ejde-887	203	33	further	far	ADV
ejde-887	203	34	for	for	ADP
ejde-887	203	35	higher	high	ADJ
ejde-887	203	36	n	n	CCONJ
ejde-887	203	37	,	,	PUNCT
ejde-887	203	38	can	can	AUX
ejde-887	203	39	be	be	AUX
ejde-887	203	40	solved	solve	VERB
ejde-887	203	41	by	by	ADP
ejde-887	203	42	a	a	DET
ejde-887	203	43	recursion	recursion	NOUN
ejde-887	203	44	procedure	procedure	NOUN
ejde-887	203	45	,	,	PUNCT
ejde-887	203	46	once	once	ADV
ejde-887	203	47	a	a	DET
ejde-887	203	48	maximum	maximum	ADJ
ejde-887	203	49	value	value	NOUN
ejde-887	203	50	of	of	ADP
ejde-887	203	51	j	j	PROPN
ejde-887	203	52	is	be	AUX
ejde-887	203	53	chosen	choose	VERB
ejde-887	203	54	for	for	ADP
ejde-887	203	55	practical	practical	ADJ
ejde-887	203	56	computation	computation	NOUN
ejde-887	203	57	of	of	ADP
ejde-887	203	58	the	the	DET
ejde-887	203	59	summation	summation	NOUN
ejde-887	203	60	.	.	PUNCT
ejde-887	204	1	this	this	DET
ejde-887	204	2	solvability	solvability	NOUN
ejde-887	204	3	feature	feature	NOUN
ejde-887	204	4	is	be	AUX
ejde-887	204	5	possible	possible	ADJ
ejde-887	204	6	because	because	SCONJ
ejde-887	204	7	at	at	ADP
ejde-887	204	8	each	each	DET
ejde-887	204	9	order	order	NOUN
ejde-887	204	10	n	n	CCONJ
ejde-887	204	11	the	the	DET
ejde-887	204	12	solutions	solution	NOUN
ejde-887	204	13	can	can	AUX
ejde-887	204	14	be	be	AUX
ejde-887	204	15	obtained	obtain	VERB
ejde-887	204	16	from	from	ADP
ejde-887	204	17	the	the	DET
ejde-887	204	18	previous	previous	ADJ
ejde-887	204	19	step	step	NOUN
ejde-887	204	20	of	of	ADP
ejde-887	204	21	order	order	NOUN
ejde-887	204	22	n−	n−	NOUN
ejde-887	204	23	1	1	NUM
ejde-887	204	24	,	,	PUNCT
ejde-887	204	25	by	by	ADP
ejde-887	204	26	either	either	CCONJ
ejde-887	204	27	simple	simple	ADJ
ejde-887	204	28	algebraic	algebraic	ADJ
ejde-887	204	29	relationships	relationship	NOUN
ejde-887	204	30	,	,	PUNCT
ejde-887	204	31	like	like	ADP
ejde-887	204	32	in	in	ADP
ejde-887	204	33	the	the	DET
ejde-887	204	34	case	case	NOUN
ejde-887	204	35	of	of	ADP
ejde-887	204	36	system	system	NOUN
ejde-887	204	37	formed	form	VERB
ejde-887	204	38	by	by	ADP
ejde-887	204	39	(	(	PUNCT
ejde-887	204	40	4.7	4.7	NUM
ejde-887	204	41	)	)	PUNCT
ejde-887	204	42	,	,	PUNCT
ejde-887	204	43	(	(	PUNCT
ejde-887	204	44	4.9	4.9	NUM
ejde-887	204	45	)	)	PUNCT
ejde-887	204	46	,	,	PUNCT
ejde-887	204	47	(	(	PUNCT
ejde-887	204	48	4.11	4.11	NUM
ejde-887	204	49	)	)	PUNCT
ejde-887	204	50	,	,	PUNCT
ejde-887	204	51	4.13	4.13	NUM
ejde-887	204	52	)	)	PUNCT
ejde-887	204	53	,	,	PUNCT
ejde-887	204	54	or	or	CCONJ
ejde-887	204	55	integrating	integrate	VERB
ejde-887	204	56	quadrature	quadrature	NOUN
ejde-887	204	57	,	,	PUNCT
ejde-887	204	58	like	like	ADP
ejde-887	204	59	in	in	ADP
ejde-887	204	60	the	the	DET
ejde-887	204	61	case	case	NOUN
ejde-887	204	62	of	of	ADP
ejde-887	204	63	systems	system	NOUN
ejde-887	204	64	formed	form	VERB
ejde-887	204	65	by	by	ADP
ejde-887	204	66	(	(	PUNCT
ejde-887	204	67	4.8	4.8	NUM
ejde-887	204	68	)	)	PUNCT
ejde-887	204	69	,	,	PUNCT
ejde-887	204	70	(	(	PUNCT
ejde-887	204	71	4.10	4.10	NUM
ejde-887	204	72	)	)	PUNCT
ejde-887	204	73	,	,	PUNCT
ejde-887	204	74	(	(	PUNCT
ejde-887	204	75	4.12	4.12	NUM
ejde-887	204	76	)	)	PUNCT
ejde-887	204	77	,	,	PUNCT
ejde-887	204	78	etc	etc	X
ejde-887	204	79	..	..	X
ejde-887	204	80	to	to	PART
ejde-887	204	81	illustrate	illustrate	VERB
ejde-887	204	82	the	the	DET
ejde-887	204	83	consistency	consistency	NOUN
ejde-887	204	84	of	of	ADP
ejde-887	204	85	this	this	DET
ejde-887	204	86	recursion	recursion	NOUN
ejde-887	204	87	multiple	multiple	ADJ
ejde-887	204	88	-	-	PUNCT
ejde-887	204	89	scale	scale	NOUN
ejde-887	204	90	procedure	procedure	NOUN
ejde-887	204	91	we	we	PRON
ejde-887	204	92	can	can	AUX
ejde-887	204	93	choose	choose	VERB
ejde-887	204	94	for	for	ADP
ejde-887	204	95	example	example	NOUN
ejde-887	204	96	j	j	PROPN
ejde-887	204	97	=	=	SYM
ejde-887	204	98	0	0	PROPN
ejde-887	204	99	.	.	PUNCT
ejde-887	205	1	by	by	ADP
ejde-887	205	2	choosing	choose	VERB
ejde-887	205	3	n	n	PROPN
ejde-887	205	4	=	=	SYM
ejde-887	205	5	0	0	NUM
ejde-887	205	6	in	in	SCONJ
ejde-887	205	7	(	(	PUNCT
ejde-887	205	8	4.7	4.7	NUM
ejde-887	205	9	)	)	PUNCT
ejde-887	205	10	we	we	PRON
ejde-887	205	11	obtain	obtain	VERB
ejde-887	205	12	u0,0	u0,0	NOUN
ejde-887	205	13	=	=	SYM
ejde-887	205	14	0	0	NUM
ejde-887	205	15	.	.	PUNCT
ejde-887	206	1	from	from	ADP
ejde-887	206	2	(	(	PUNCT
ejde-887	206	3	4.8	4.8	NUM
ejde-887	206	4	)	)	PUNCT
ejde-887	206	5	obtained	obtain	VERB
ejde-887	206	6	at	at	ADP
ejde-887	206	7	n	n	NOUN
ejde-887	206	8	=	=	SYM
ejde-887	206	9	1	1	NUM
ejde-887	206	10	,	,	PUNCT
ejde-887	206	11	i.e.	i.e.	X
ejde-887	206	12	o(δ2	o(δ2	ADJ
ejde-887	206	13	)	)	PUNCT
ejde-887	206	14	we	we	PRON
ejde-887	206	15	can	can	AUX
ejde-887	206	16	integrate	integrate	VERB
ejde-887	206	17	the	the	DET
ejde-887	206	18	2×	2×	NUM
ejde-887	206	19	2	2	NUM
ejde-887	206	20	ode	ode	NOUN
ejde-887	206	21	system	system	NOUN
ejde-887	206	22	given	give	VERB
ejde-887	206	23	by	by	ADP
ejde-887	206	24	(	(	PUNCT
ejde-887	206	25	4.8	4.8	NUM
ejde-887	206	26	)	)	PUNCT
ejde-887	206	27	and	and	CCONJ
ejde-887	206	28	(	(	PUNCT
ejde-887	206	29	4.12	4.12	NUM
ejde-887	206	30	)	)	PUNCT
ejde-887	206	31	,	,	PUNCT
ejde-887	206	32	f1(q)z1,0	f1(q)z1,0	VERB
ejde-887	206	33	+	+	CCONJ
ejde-887	206	34	qu1,0,χ	qu1,0,χ	X
ejde-887	206	35	=	=	X
ejde-887	206	36	0	0	NUM
ejde-887	206	37	,	,	PUNCT
ejde-887	206	38	ψ0qu1,0,χ	ψ0qu1,0,χ	X
ejde-887	207	1	+	+	X
ejde-887	207	2	z1,0,χ	z1,0,χ	NOUN
ejde-887	207	3	=	=	SYM
ejde-887	207	4	0	0	NUM
ejde-887	207	5	by	by	ADP
ejde-887	207	6	one	one	NUM
ejde-887	207	7	quadrature	quadrature	NOUN
ejde-887	207	8	,	,	PUNCT
ejde-887	207	9	to	to	PART
ejde-887	207	10	find	find	VERB
ejde-887	207	11	u1,0	u1,0	PROPN
ejde-887	207	12	,	,	PUNCT
ejde-887	207	13	z1,0	z1,0	PROPN
ejde-887	207	14	as	as	ADP
ejde-887	207	15	functions	function	NOUN
ejde-887	207	16	of	of	ADP
ejde-887	207	17	q.	q.	NOUN
ejde-887	207	18	for	for	ADP
ejde-887	207	19	the	the	DET
ejde-887	207	20	term	term	NOUN
ejde-887	207	21	n	n	NOUN
ejde-887	207	22	=	=	SYM
ejde-887	207	23	2	2	NUM
ejde-887	207	24	from	from	ADP
ejde-887	207	25	(	(	PUNCT
ejde-887	207	26	4.9	4.9	NUM
ejde-887	207	27	)	)	PUNCT
ejde-887	207	28	which	which	PRON
ejde-887	207	29	is	be	AUX
ejde-887	207	30	order	order	NOUN
ejde-887	207	31	o(δ2	o(δ2	ADJ
ejde-887	207	32	)	)	PUNCT
ejde-887	207	33	,	,	PUNCT
ejde-887	207	34	we	we	PRON
ejde-887	207	35	have	have	VERB
ejde-887	207	36	to	to	PART
ejde-887	207	37	solve	solve	VERB
ejde-887	207	38	an	an	DET
ejde-887	207	39	algebraic	algebraic	ADJ
ejde-887	207	40	system	system	NOUN
ejde-887	207	41	given	give	VERB
ejde-887	207	42	by	by	ADP
ejde-887	207	43	(	(	PUNCT
ejde-887	207	44	4.9	4.9	NUM
ejde-887	207	45	)	)	PUNCT
ejde-887	207	46	and	and	CCONJ
ejde-887	207	47	(	(	PUNCT
ejde-887	207	48	4.13	4.13	NUM
ejde-887	207	49	)	)	PUNCT
ejde-887	207	50	,	,	PUNCT
ejde-887	207	51	f2(q)u2,0	f2(q)u2,0	VERB
ejde-887	208	1	+	+	CCONJ
ejde-887	208	2	f3(q)z2,0	f3(q)z2,0	NOUN
ejde-887	208	3	+	+	CCONJ
ejde-887	208	4	2αµu1,0z1,0	2αµu1,0z1,0	NUM
ejde-887	208	5	=	=	SYM
ejde-887	208	6	0	0	NUM
ejde-887	208	7	,	,	PUNCT
ejde-887	208	8	2iωu2,0	2iωu2,0	X
ejde-887	209	1	+	+	NOUN
ejde-887	209	2	2µz2,0	2µz2,0	NUM
ejde-887	209	3	=	=	SYM
ejde-887	209	4	0	0	NUM
ejde-887	209	5	,	,	PUNCT
ejde-887	209	6	to	to	PART
ejde-887	209	7	find	find	VERB
ejde-887	209	8	u2,0	u2,0	PROPN
ejde-887	209	9	,	,	PUNCT
ejde-887	209	10	z2,0	z2,0	PROPN
ejde-887	209	11	,	,	PUNCT
ejde-887	209	12	and	and	CCONJ
ejde-887	209	13	so	so	ADV
ejde-887	209	14	on	on	ADV
ejde-887	209	15	.	.	PUNCT
ejde-887	210	1	all	all	DET
ejde-887	210	2	symbols	symbol	NOUN
ejde-887	210	3	fk(q	fk(q	X
ejde-887	210	4	)	)	PUNCT
ejde-887	210	5	are	be	AUX
ejde-887	210	6	known	know	VERB
ejde-887	210	7	functions	function	NOUN
ejde-887	210	8	of	of	ADP
ejde-887	210	9	q(x	q(x	NOUN
ejde-887	210	10	)	)	PUNCT
ejde-887	210	11	=	=	SYM
ejde-887	210	12	q(χ	q(χ	PROPN
ejde-887	210	13	/	/	SYM
ejde-887	210	14	δ	δ	PROPN
ejde-887	210	15	+	+	X
ejde-887	210	16	υθ	υθ	X
ejde-887	210	17	/	/	SYM
ejde-887	210	18	δ2	δ2	VERB
ejde-887	210	19	)	)	PUNCT
ejde-887	210	20	.	.	PUNCT
ejde-887	211	1	the	the	DET
ejde-887	211	2	system	system	NOUN
ejde-887	211	3	becomes	become	VERB
ejde-887	211	4	more	more	ADV
ejde-887	211	5	complicated	complicated	ADJ
ejde-887	211	6	when	when	SCONJ
ejde-887	211	7	j	j	PROPN
ejde-887	211	8	̸=	̸=	PROPN
ejde-887	211	9	0	0	NUM
ejde-887	211	10	yet	yet	CCONJ
ejde-887	211	11	|j|	|j|	PROPN
ejde-887	211	12	≤	≤	ADJ
ejde-887	211	13	jmax	jmax	NOUN
ejde-887	211	14	̸=	̸=	PROPN
ejde-887	211	15	0	0	NUM
ejde-887	211	16	.	.	PUNCT
ejde-887	212	1	it	it	PRON
ejde-887	212	2	is	be	AUX
ejde-887	212	3	easy	easy	ADJ
ejde-887	212	4	to	to	PART
ejde-887	212	5	show	show	VERB
ejde-887	212	6	by	by	ADP
ejde-887	212	7	direct	direct	ADJ
ejde-887	212	8	calculations	calculation	NOUN
ejde-887	212	9	that	that	PRON
ejde-887	212	10	for	for	ADP
ejde-887	212	11	any	any	DET
ejde-887	212	12	jmax	jmax	NOUN
ejde-887	212	13	there	there	PRON
ejde-887	212	14	is	be	VERB
ejde-887	212	15	always	always	ADV
ejde-887	212	16	a	a	DET
ejde-887	212	17	j0	j0	PROPN
ejde-887	212	18	<	<	X
ejde-887	212	19	jmax	jmax	PROPN
ejde-887	212	20	such	such	ADJ
ejde-887	212	21	that	that	SCONJ
ejde-887	212	22	the	the	DET
ejde-887	212	23	components	component	NOUN
ejde-887	212	24	with	with	ADP
ejde-887	212	25	0	0	NUM
ejde-887	212	26	<	<	X
ejde-887	212	27	j	j	PROPN
ejde-887	212	28	≤	≤	PROPN
ejde-887	212	29	j0	j0	PROPN
ejde-887	212	30	of	of	ADP
ejde-887	212	31	the	the	DET
ejde-887	212	32	solutions	solution	NOUN
ejde-887	212	33	are	be	AUX
ejde-887	212	34	arbitrary	arbitrary	ADJ
ejde-887	212	35	,	,	PUNCT
ejde-887	212	36	and	and	CCONJ
ejde-887	212	37	the	the	DET
ejde-887	212	38	terms	term	NOUN
ejde-887	212	39	j	j	PROPN
ejde-887	212	40	>	>	X
ejde-887	212	41	j0	j0	PROPN
ejde-887	212	42	can	can	AUX
ejde-887	212	43	be	be	AUX
ejde-887	212	44	obtained	obtain	VERB
ejde-887	212	45	from	from	ADP
ejde-887	212	46	these	these	DET
ejde-887	212	47	ones	one	NOUN
ejde-887	212	48	by	by	ADP
ejde-887	212	49	quadrature	quadrature	NOUN
ejde-887	212	50	.	.	PUNCT
ejde-887	213	1	in	in	ADP
ejde-887	213	2	the	the	DET
ejde-887	213	3	recursion	recursion	NOUN
ejde-887	213	4	system	system	NOUN
ejde-887	213	5	(	(	PUNCT
ejde-887	213	6	4.8)-(4.13	4.8)-(4.13	NOUN
ejde-887	213	7	)	)	PUNCT
ejde-887	213	8	we	we	PRON
ejde-887	213	9	have	have	VERB
ejde-887	213	10	often	often	ADV
ejde-887	213	11	the	the	DET
ejde-887	213	12	situations	situation	NOUN
ejde-887	213	13	when	when	SCONJ
ejde-887	213	14	in	in	ADP
ejde-887	213	15	the	the	DET
ejde-887	213	16	same	same	ADJ
ejde-887	213	17	equation	equation	NOUN
ejde-887	213	18	there	there	PRON
ejde-887	213	19	are	be	VERB
ejde-887	213	20	either	either	CCONJ
ejde-887	213	21	only	only	ADV
ejde-887	213	22	the	the	DET
ejde-887	213	23	time	time	NOUN
ejde-887	213	24	derivatives	derivative	NOUN
ejde-887	213	25	,	,	PUNCT
ejde-887	213	26	or	or	CCONJ
ejde-887	213	27	only	only	ADV
ejde-887	213	28	the	the	DET
ejde-887	213	29	spatial	spatial	ADJ
ejde-887	213	30	derivatives	derivative	NOUN
ejde-887	213	31	,	,	PUNCT
ejde-887	213	32	but	but	CCONJ
ejde-887	213	33	not	not	PART
ejde-887	213	34	mixed	mixed	ADJ
ejde-887	213	35	derivatives	derivative	NOUN
ejde-887	213	36	,	,	PUNCT
ejde-887	213	37	as	as	ADP
ejde-887	213	38	in	in	ADP
ejde-887	213	39	the	the	DET
ejde-887	213	40	classical	classical	ADJ
ejde-887	213	41	integrable	integrable	ADJ
ejde-887	213	42	systems	system	NOUN
ejde-887	213	43	.	.	PUNCT
ejde-887	214	1	this	this	PRON
ejde-887	214	2	is	be	AUX
ejde-887	214	3	not	not	PART
ejde-887	214	4	an	an	DET
ejde-887	214	5	issue	issue	NOUN
ejde-887	214	6	,	,	PUNCT
ejde-887	214	7	because	because	SCONJ
ejde-887	214	8	in	in	ADP
ejde-887	214	9	the	the	DET
ejde-887	214	10	re	re	ADJ
ejde-887	214	11	-	-	ADJ
ejde-887	214	12	scaled	scaled	ADJ
ejde-887	214	13	variable	variable	NOUN
ejde-887	214	14	χ	χ	X
ejde-887	214	15	we	we	PRON
ejde-887	214	16	have	have	VERB
ejde-887	214	17	both	both	CCONJ
ejde-887	214	18	the	the	DET
ejde-887	214	19	space	space	NOUN
ejde-887	214	20	x	x	NOUN
ejde-887	214	21	and	and	CCONJ
ejde-887	214	22	time	time	NOUN
ejde-887	214	23	t	t	PROPN
ejde-887	214	24	dependence	dependence	NOUN
ejde-887	214	25	.	.	PUNCT
ejde-887	215	1	these	these	DET
ejde-887	215	2	equations	equation	NOUN
ejde-887	215	3	can	can	AUX
ejde-887	215	4	be	be	AUX
ejde-887	215	5	integrated	integrate	VERB
ejde-887	215	6	by	by	ADP
ejde-887	215	7	an	an	DET
ejde-887	215	8	iteration	iteration	NOUN
ejde-887	215	9	procedure	procedure	NOUN
ejde-887	215	10	,	,	PUNCT
ejde-887	215	11	where	where	SCONJ
ejde-887	215	12	the	the	DET
ejde-887	215	13	non	non	ADJ
ejde-887	215	14	-	-	ADJ
ejde-887	215	15	homogeneous	homogeneous	ADJ
ejde-887	215	16	terms	term	NOUN
ejde-887	215	17	at	at	ADP
ejde-887	215	18	one	one	NUM
ejde-887	215	19	step	step	NOUN
ejde-887	215	20	are	be	AUX
ejde-887	215	21	computed	compute	VERB
ejde-887	215	22	using	use	VERB
ejde-887	215	23	the	the	DET
ejde-887	215	24	solutions	solution	NOUN
ejde-887	215	25	from	from	ADP
ejde-887	215	26	the	the	DET
ejde-887	215	27	ejde-202x	ejde-202x	PROPN
ejde-887	215	28	/	/	SYM
ejde-887	215	29	conf/27	conf/27	NOUN
ejde-887	215	30	boussinesq	boussinesq	ADJ
ejde-887	215	31	equations	equation	NOUN
ejde-887	215	32	37	37	NUM
ejde-887	215	33	previous	previous	ADJ
ejde-887	215	34	step	step	NOUN
ejde-887	215	35	.	.	PUNCT
ejde-887	216	1	in	in	ADP
ejde-887	216	2	this	this	DET
ejde-887	216	3	way	way	NOUN
ejde-887	216	4	the	the	DET
ejde-887	216	5	equations	equation	NOUN
ejde-887	216	6	reduce	reduce	VERB
ejde-887	216	7	to	to	ADP
ejde-887	216	8	simple	simple	ADJ
ejde-887	216	9	(	(	PUNCT
ejde-887	216	10	yet	yet	ADV
ejde-887	216	11	tedious	tedious	ADJ
ejde-887	216	12	)	)	PUNCT
ejde-887	216	13	quadratures	quadrature	NOUN
ejde-887	216	14	,	,	PUNCT
ejde-887	216	15	so	so	SCONJ
ejde-887	216	16	they	they	PRON
ejde-887	216	17	can	can	AUX
ejde-887	216	18	be	be	AUX
ejde-887	216	19	integrated	integrate	VERB
ejde-887	216	20	exactly	exactly	ADV
ejde-887	216	21	.	.	PUNCT
ejde-887	217	1	the	the	DET
ejde-887	217	2	absence	absence	NOUN
ejde-887	217	3	of	of	ADP
ejde-887	217	4	a	a	DET
ejde-887	217	5	dispersion	dispersion	NOUN
ejde-887	217	6	relation	relation	NOUN
ejde-887	217	7	(	(	PUNCT
ejde-887	217	8	or	or	CCONJ
ejde-887	217	9	equivalently	equivalently	ADV
ejde-887	217	10	,	,	PUNCT
ejde-887	217	11	zero	zero	NUM
ejde-887	217	12	dispersion	dispersion	NOUN
ejde-887	217	13	)	)	PUNCT
ejde-887	217	14	in	in	ADP
ejde-887	217	15	(	(	PUNCT
ejde-887	217	16	4.8)(4.13	4.8)(4.13	PROPN
ejde-887	217	17	)	)	PUNCT
ejde-887	217	18	is	be	AUX
ejde-887	217	19	only	only	ADV
ejde-887	217	20	apparent	apparent	ADJ
ejde-887	217	21	.	.	PUNCT
ejde-887	218	1	equatio	equatio	NOUN
ejde-887	218	2	.	.	PUNCT
ejde-887	219	1	(	(	PUNCT
ejde-887	219	2	2.1	2.1	NUM
ejde-887	219	3	)	)	PUNCT
ejde-887	219	4	was	be	AUX
ejde-887	219	5	mapped	map	VERB
ejde-887	219	6	into	into	ADP
ejde-887	219	7	the	the	DET
ejde-887	219	8	system	system	NOUN
ejde-887	219	9	(	(	PUNCT
ejde-887	219	10	4.7)-(4.13	4.7)-(4.13	NOUN
ejde-887	219	11	)	)	PUNCT
ejde-887	219	12	and	and	CCONJ
ejde-887	219	13	(	(	PUNCT
ejde-887	219	14	4.7)-(4.13	4.7)-(4.13	NOUN
ejde-887	219	15	)	)	PUNCT
ejde-887	219	16	are	be	AUX
ejde-887	219	17	akns	akns	NOUN
ejde-887	219	18	-	-	PUNCT
ejde-887	219	19	type	type	NOUN
ejde-887	219	20	integrable	integrable	ADJ
ejde-887	219	21	(	(	PUNCT
ejde-887	219	22	a	a	DET
ejde-887	219	23	generalization	generalization	NOUN
ejde-887	219	24	of	of	ADP
ejde-887	219	25	the	the	DET
ejde-887	219	26	nls	nls	ADJ
ejde-887	219	27	classic	classic	ADJ
ejde-887	219	28	system	system	NOUN
ejde-887	219	29	)	)	PUNCT
ejde-887	219	30	and	and	CCONJ
ejde-887	219	31	consequently	consequently	ADV
ejde-887	219	32	one	one	NUM
ejde-887	219	33	can	can	AUX
ejde-887	219	34	obtain	obtain	VERB
ejde-887	219	35	soliton	soliton	NOUN
ejde-887	219	36	solutions	solution	NOUN
ejde-887	219	37	for	for	ADP
ejde-887	219	38	them	they	PRON
ejde-887	219	39	.	.	PUNCT
ejde-887	220	1	this	this	PRON
ejde-887	220	2	means	mean	VERB
ejde-887	220	3	that	that	SCONJ
ejde-887	220	4	a	a	DET
ejde-887	220	5	real	real	ADV
ejde-887	220	6	valued	value	VERB
ejde-887	220	7	dispersion	dispersion	NOUN
ejde-887	220	8	relation	relation	NOUN
ejde-887	220	9	is	be	AUX
ejde-887	220	10	implicitly	implicitly	ADV
ejde-887	220	11	present	present	ADJ
ejde-887	220	12	in	in	ADP
ejde-887	220	13	our	our	PRON
ejde-887	220	14	equations	equation	NOUN
ejde-887	220	15	.	.	PUNCT
ejde-887	221	1	the	the	DET
ejde-887	221	2	difficulty	difficulty	NOUN
ejde-887	221	3	arising	arise	VERB
ejde-887	221	4	from	from	ADP
ejde-887	221	5	the	the	DET
ejde-887	221	6	apparent	apparent	ADJ
ejde-887	221	7	absence	absence	NOUN
ejde-887	221	8	of	of	ADP
ejde-887	221	9	a	a	DET
ejde-887	221	10	dispersion	dispersion	NOUN
ejde-887	221	11	relation	relation	NOUN
ejde-887	221	12	is	be	AUX
ejde-887	221	13	that	that	SCONJ
ejde-887	221	14	it	it	PRON
ejde-887	221	15	may	may	AUX
ejde-887	221	16	be	be	AUX
ejde-887	221	17	difficult	difficult	ADJ
ejde-887	221	18	to	to	PART
ejde-887	221	19	verify	verify	VERB
ejde-887	221	20	the	the	DET
ejde-887	221	21	integrability	integrability	NOUN
ejde-887	221	22	,	,	PUNCT
ejde-887	221	23	or	or	CCONJ
ejde-887	221	24	to	to	PART
ejde-887	221	25	find	find	VERB
ejde-887	221	26	soliton	soliton	NOUN
ejde-887	221	27	solutions	solution	NOUN
ejde-887	221	28	to	to	ADP
ejde-887	221	29	these	these	DET
ejde-887	221	30	equations	equation	NOUN
ejde-887	221	31	using	use	VERB
ejde-887	221	32	the	the	DET
ejde-887	221	33	hirota	hirota	PROPN
ejde-887	221	34	bilinear	bilinear	NOUN
ejde-887	221	35	formalism	formalism	NOUN
ejde-887	221	36	.	.	PUNCT
ejde-887	222	1	in	in	ADP
ejde-887	222	2	our	our	PRON
ejde-887	222	3	case	case	NOUN
ejde-887	222	4	,	,	PUNCT
ejde-887	222	5	the	the	DET
ejde-887	222	6	dispersion	dispersion	NOUN
ejde-887	222	7	must	must	AUX
ejde-887	222	8	be	be	AUX
ejde-887	222	9	real	real	ADV
ejde-887	222	10	valued	value	VERB
ejde-887	222	11	,	,	PUNCT
ejde-887	222	12	and	and	CCONJ
ejde-887	222	13	it	it	PRON
ejde-887	222	14	is	be	AUX
ejde-887	222	15	different	different	ADJ
ejde-887	222	16	from	from	ADP
ejde-887	222	17	the	the	DET
ejde-887	222	18	one	one	NOUN
ejde-887	222	19	for	for	ADP
ejde-887	222	20	the	the	DET
ejde-887	222	21	bk	bk	PROPN
ejde-887	222	22	system	system	NOUN
ejde-887	222	23	which	which	PRON
ejde-887	222	24	has	have	VERB
ejde-887	222	25	imaginary	imaginary	ADJ
ejde-887	222	26	dispersion	dispersion	NOUN
ejde-887	222	27	,	,	PUNCT
ejde-887	222	28	as	as	ADP
ejde-887	222	29	in	in	ADP
ejde-887	222	30	the	the	DET
ejde-887	222	31	case	case	NOUN
ejde-887	222	32	of	of	ADP
ejde-887	222	33	non	non	ADJ
ejde-887	222	34	-	-	ADJ
ejde-887	222	35	conservative	conservative	ADJ
ejde-887	222	36	diffusive	diffusive	ADJ
ejde-887	222	37	systems	system	NOUN
ejde-887	222	38	.	.	PUNCT
ejde-887	223	1	in	in	ADP
ejde-887	223	2	a	a	DET
ejde-887	223	3	forthcoming	forthcoming	ADJ
ejde-887	223	4	paper	paper	NOUN
ejde-887	223	5	we	we	PRON
ejde-887	223	6	will	will	AUX
ejde-887	223	7	present	present	VERB
ejde-887	223	8	a	a	DET
ejde-887	223	9	new	new	ADJ
ejde-887	223	10	bilinear	bilinear	NOUN
ejde-887	223	11	form	form	NOUN
ejde-887	223	12	for	for	ADP
ejde-887	223	13	the	the	DET
ejde-887	223	14	kaup	kaup	NOUN
ejde-887	223	15	-	-	PUNCT
ejde-887	223	16	boussinesq	boussinesq	ADJ
ejde-887	223	17	system	system	NOUN
ejde-887	223	18	(	(	PUNCT
ejde-887	223	19	found	find	VERB
ejde-887	223	20	by	by	ADP
ejde-887	223	21	one	one	NUM
ejde-887	223	22	of	of	ADP
ejde-887	223	23	the	the	DET
ejde-887	223	24	present	present	ADJ
ejde-887	223	25	authors	author	NOUN
ejde-887	223	26	asc	asc	PROPN
ejde-887	223	27	)	)	PUNCT
ejde-887	223	28	,	,	PUNCT
ejde-887	223	29	which	which	PRON
ejde-887	223	30	is	be	AUX
ejde-887	223	31	in	in	ADP
ejde-887	223	32	fact	fact	NOUN
ejde-887	223	33	a	a	DET
ejde-887	223	34	bäcklund	bäcklund	NOUN
ejde-887	223	35	bilinear	bilinear	VERB
ejde-887	223	36	singular	singular	ADJ
ejde-887	223	37	form	form	NOUN
ejde-887	223	38	for	for	ADP
ejde-887	223	39	the	the	DET
ejde-887	223	40	boussinesq	boussinesq	ADJ
ejde-887	223	41	system	system	NOUN
ejde-887	223	42	,	,	PUNCT
ejde-887	223	43	which	which	PRON
ejde-887	223	44	allows	allow	VERB
ejde-887	223	45	a	a	DET
ejde-887	223	46	faster	fast	ADJ
ejde-887	223	47	calculation	calculation	NOUN
ejde-887	223	48	of	of	ADP
ejde-887	223	49	the	the	DET
ejde-887	223	50	solutions	solution	NOUN
ejde-887	223	51	,	,	PUNCT
ejde-887	223	52	including	include	VERB
ejde-887	223	53	multi	multi	NOUN
ejde-887	223	54	-	-	NOUN
ejde-887	223	55	solitons	soliton	NOUN
ejde-887	223	56	.	.	PUNCT
ejde-887	224	1	5	5	NUM
ejde-887	224	2	.	.	X
ejde-887	224	3	numerical	numerical	ADJ
ejde-887	224	4	solutions	solution	NOUN
ejde-887	224	5	5.1	5.1	NUM
ejde-887	224	6	.	.	PUNCT
ejde-887	225	1	numerical	numerical	ADJ
ejde-887	225	2	algorithm	algorithm	PROPN
ejde-887	225	3	.	.	PUNCT
ejde-887	226	1	to	to	PART
ejde-887	226	2	obtain	obtain	VERB
ejde-887	226	3	numerical	numerical	ADJ
ejde-887	226	4	solutions	solution	NOUN
ejde-887	226	5	for	for	ADP
ejde-887	226	6	the	the	DET
ejde-887	226	7	system	system	NOUN
ejde-887	226	8	(	(	PUNCT
ejde-887	226	9	2.1	2.1	NUM
ejde-887	226	10	)	)	PUNCT
ejde-887	226	11	we	we	PRON
ejde-887	226	12	define	define	VERB
ejde-887	226	13	u	u	NOUN
ejde-887	226	14	=	=	NOUN
ejde-887	226	15	[	[	PUNCT
ejde-887	226	16	v	v	X
ejde-887	226	17	v̄	v̄	NOUN
ejde-887	226	18	]	]	PUNCT
ejde-887	226	19	,	,	PUNCT
ejde-887	226	20	f(u	f(u	PROPN
ejde-887	226	21	)	)	PUNCT
ejde-887	226	22	=	=	PUNCT
ejde-887	226	23			X
ejde-887	227	1	v̄	v̄	NOUN
ejde-887	228	1	+	+	CCONJ
ejde-887	228	2	α	α	PROPN
ejde-887	228	3	q2	q2	NOUN
ejde-887	228	4	vv̄	vv̄	VERB
ejde-887	228	5	1	1	NUM
ejde-887	228	6	q	q	NOUN
ejde-887	228	7	v	v	NOUN
ejde-887	228	8	+	+	CCONJ
ejde-887	228	9	α	α	NOUN
ejde-887	228	10	2q2	2q2	NUM
ejde-887	228	11	v̄2	v̄2	ADJ
ejde-887	228	12			NOUN
ejde-887	228	13	,	,	PUNCT
ejde-887	228	14	g(u	g(u	PROPN
ejde-887	228	15	)	)	PUNCT
ejde-887	228	16	=	=	PUNCT
ejde-887	229	1	[	[	PUNCT
ejde-887	229	2	β	β	X
ejde-887	229	3	3	3	NUM
ejde-887	229	4	vxxx	vxxx	NOUN
ejde-887	229	5	0	0	NUM
ejde-887	229	6	]	]	PUNCT
ejde-887	229	7	,	,	PUNCT
ejde-887	229	8	where	where	SCONJ
ejde-887	229	9	v	v	NOUN
ejde-887	229	10	=	=	SYM
ejde-887	229	11	qz	qz	PROPN
ejde-887	229	12	and	and	CCONJ
ejde-887	229	13	v̄	v̄	PROPN
ejde-887	229	14	=	=	SYM
ejde-887	229	15	qu	qu	PROPN
ejde-887	229	16	.	.	PUNCT
ejde-887	230	1	we	we	PRON
ejde-887	230	2	express	express	VERB
ejde-887	230	3	(	(	PUNCT
ejde-887	230	4	2.1	2.1	NUM
ejde-887	230	5	)	)	PUNCT
ejde-887	230	6	in	in	ADP
ejde-887	230	7	the	the	DET
ejde-887	230	8	form	form	NOUN
ejde-887	230	9	∂u	∂u	PROPN
ejde-887	230	10	∂t	∂t	PROPN
ejde-887	230	11	+	+	CCONJ
ejde-887	230	12	∂f(u	∂f(u	PROPN
ejde-887	230	13	)	)	PUNCT
ejde-887	230	14	∂x	∂x	PROPN
ejde-887	230	15	=	=	SYM
ejde-887	230	16	g(u	g(u	PROPN
ejde-887	230	17	)	)	PUNCT
ejde-887	230	18	,	,	PUNCT
ejde-887	230	19	(	(	PUNCT
ejde-887	230	20	5.1	5.1	NUM
ejde-887	230	21	)	)	PUNCT
ejde-887	230	22	with	with	ADP
ejde-887	230	23	a	a	DET
ejde-887	230	24	≤	≤	NUM
ejde-887	230	25	x	x	PUNCT
ejde-887	230	26	≤	≤	NUM
ejde-887	230	27	b	b	NUM
ejde-887	230	28	,	,	PUNCT
ejde-887	230	29	0	0	NUM
ejde-887	230	30	≤	≤	NUM
ejde-887	230	31	t	t	PROPN
ejde-887	230	32	≤	≤	PROPN
ejde-887	230	33	t	t	PROPN
ejde-887	230	34	.	.	PUNCT
ejde-887	231	1	let	let	VERB
ejde-887	231	2	∆x	∆x	PROPN
ejde-887	231	3	=	=	SYM
ejde-887	231	4	(	(	PUNCT
ejde-887	231	5	b	b	NOUN
ejde-887	231	6	−	−	NOUN
ejde-887	231	7	a)/m	a)/m	NOUN
ejde-887	231	8	and	and	CCONJ
ejde-887	231	9	∆t	∆t	PROPN
ejde-887	231	10	=	=	SYM
ejde-887	231	11	t	t	PROPN
ejde-887	231	12	/	/	SYM
ejde-887	231	13	n	n	PROPN
ejde-887	231	14	.	.	PUNCT
ejde-887	232	1	we	we	PRON
ejde-887	232	2	construct	construct	VERB
ejde-887	232	3	a	a	DET
ejde-887	232	4	grid	grid	NOUN
ejde-887	232	5	(	(	PUNCT
ejde-887	232	6	xi	xi	PROPN
ejde-887	232	7	,	,	PUNCT
ejde-887	232	8	tn	tn	PROPN
ejde-887	232	9	)	)	PUNCT
ejde-887	232	10	,	,	PUNCT
ejde-887	232	11	with	with	ADP
ejde-887	232	12	xi	xi	PROPN
ejde-887	232	13	=	=	SYM
ejde-887	232	14	i∆x	i∆x	X
ejde-887	232	15	,	,	PUNCT
ejde-887	232	16	i	i	NOUN
ejde-887	232	17	=	=	NOUN
ejde-887	232	18	0	0	NUM
ejde-887	232	19	,	,	PUNCT
ejde-887	232	20	1	1	NUM
ejde-887	232	21	,	,	PUNCT
ejde-887	232	22	2	2	NUM
ejde-887	232	23	,	,	PUNCT
ejde-887	232	24	.	.	PUNCT
ejde-887	232	25	.	.	PUNCT
ejde-887	232	26	.	.	PUNCT
ejde-887	233	1	,	,	PUNCT
ejde-887	233	2	m	m	VERB
ejde-887	233	3	and	and	CCONJ
ejde-887	233	4	τn	τn	ADP
ejde-887	233	5	=	=	NOUN
ejde-887	233	6	n∆τ	n∆τ	NOUN
ejde-887	233	7	,	,	PUNCT
ejde-887	233	8	n	n	NOUN
ejde-887	233	9	=	=	SYM
ejde-887	233	10	0	0	NUM
ejde-887	233	11	,	,	PUNCT
ejde-887	233	12	1	1	NUM
ejde-887	233	13	,	,	PUNCT
ejde-887	233	14	2	2	NUM
ejde-887	233	15	,	,	PUNCT
ejde-887	233	16	.	.	PUNCT
ejde-887	233	17	.	.	PUNCT
ejde-887	234	1	.	.	PUNCT
ejde-887	235	1	,	,	PUNCT
ejde-887	235	2	n	n	X
ejde-887	235	3	.	.	PUNCT
ejde-887	236	1	let	let	VERB
ejde-887	236	2	vni	vni	VERB
ejde-887	236	3	=	=	SYM
ejde-887	236	4	v(xi	v(xi	PROPN
ejde-887	236	5	,	,	PUNCT
ejde-887	236	6	tn	tn	PROPN
ejde-887	236	7	)	)	PUNCT
ejde-887	236	8	,	,	PUNCT
ejde-887	236	9	v̄	v̄	NOUN
ejde-887	236	10	n	n	NOUN
ejde-887	236	11	i	i	PRON
ejde-887	236	12	=	=	SYM
ejde-887	236	13	v̄(xi	v̄(xi	PROPN
ejde-887	236	14	,	,	PUNCT
ejde-887	236	15	tn	tn	PROPN
ejde-887	236	16	)	)	PUNCT
ejde-887	236	17	,	,	PUNCT
ejde-887	236	18	u	u	NOUN
ejde-887	236	19	n	n	ADV
ejde-887	236	20	i	i	NOUN
ejde-887	236	21	=	=	PRON
ejde-887	237	1	[	[	PUNCT
ejde-887	237	2	vni	vni	NOUN
ejde-887	237	3	v̄ni	v̄ni	PROPN
ejde-887	237	4	]	]	PUNCT
ejde-887	237	5	,	,	PUNCT
ejde-887	237	6	fni	fni	PROPN
ejde-887	237	7	=	=	SYM
ejde-887	237	8	f(un	f(un	PROPN
ejde-887	237	9	i	i	PROPN
ejde-887	237	10	)	)	PUNCT
ejde-887	237	11	and	and	CCONJ
ejde-887	237	12	gn	gn	INTJ
ejde-887	238	1	i	i	NOUN
ejde-887	238	2	=	=	PUNCT
ejde-887	238	3	g(un	g(un	PROPN
ejde-887	238	4	i	i	NOUN
ejde-887	238	5	)	)	PUNCT
ejde-887	238	6	.	.	PUNCT
ejde-887	239	1	we	we	PRON
ejde-887	239	2	solve	solve	VERB
ejde-887	239	3	the	the	DET
ejde-887	239	4	above	above	ADJ
ejde-887	239	5	nonlinear	nonlinear	ADJ
ejde-887	239	6	advection	advection	NOUN
ejde-887	239	7	dispersion	dispersion	NOUN
ejde-887	239	8	system	system	NOUN
ejde-887	239	9	(	(	PUNCT
ejde-887	239	10	5.1	5.1	NUM
ejde-887	239	11	)	)	PUNCT
ejde-887	239	12	numerically	numerically	ADV
ejde-887	239	13	using	use	VERB
ejde-887	239	14	the	the	DET
ejde-887	239	15	following	follow	VERB
ejde-887	239	16	predictor	predictor	NOUN
ejde-887	239	17	-	-	PUNCT
ejde-887	239	18	corrector	corrector	NOUN
ejde-887	239	19	(	(	PUNCT
ejde-887	239	20	mccormack	mccormack	PROPN
ejde-887	239	21	)	)	PUNCT
ejde-887	239	22	scheme	scheme	NOUN
ejde-887	240	1	[	[	X
ejde-887	240	2	16	16	NUM
ejde-887	240	3	]	]	PUNCT
ejde-887	240	4	.	.	PUNCT
ejde-887	241	1	u∗	u∗	INTJ
ejde-887	241	2	i	i	PRON
ejde-887	242	1	=	=	PUNCT
ejde-887	242	2	un	un	PROPN
ejde-887	243	1	i	i	PRON
ejde-887	243	2	−	−	PROPN
ejde-887	243	3	∆t	∆t	PROPN
ejde-887	243	4	∆x	∆x	PROPN
ejde-887	243	5	(	(	PUNCT
ejde-887	243	6	fni+1	fni+1	PROPN
ejde-887	243	7	−	−	PROPN
ejde-887	243	8	fni	fni	NOUN
ejde-887	243	9	)	)	PUNCT
ejde-887	244	1	+	+	PUNCT
ejde-887	244	2	∆tgn	∆tgn	NOUN
ejde-887	244	3	i	i	PRON
ejde-887	244	4	,	,	PUNCT
ejde-887	244	5	(	(	PUNCT
ejde-887	244	6	5.2	5.2	NUM
ejde-887	244	7	)	)	PUNCT
ejde-887	244	8	un+1	un+1	NOUN
ejde-887	245	1	i	i	NOUN
ejde-887	245	2	=	=	NOUN
ejde-887	245	3	1	1	NUM
ejde-887	245	4	2	2	NUM
ejde-887	245	5	(	(	PUNCT
ejde-887	245	6	un	un	PROPN
ejde-887	245	7	i	i	PROPN
ejde-887	245	8	+	+	PROPN
ejde-887	246	1	u∗	u∗	ADJ
ejde-887	246	2	i	i	INTJ
ejde-887	246	3	)	)	PUNCT
ejde-887	246	4	−	−	PROPN
ejde-887	246	5	∆t	∆t	PROPN
ejde-887	246	6	2∆x	2∆x	NUM
ejde-887	246	7	(	(	PUNCT
ejde-887	246	8	f∗	f∗	NOUN
ejde-887	246	9	i	i	NOUN
ejde-887	246	10	−	−	PROPN
ejde-887	246	11	f∗	f∗	VERB
ejde-887	246	12	i−1	i−1	PROPN
ejde-887	246	13	)	)	PUNCT
ejde-887	247	1	+	+	CCONJ
ejde-887	247	2	∆t	∆t	PROPN
ejde-887	247	3	2	2	NUM
ejde-887	247	4	g∗	g∗	NOUN
ejde-887	247	5	i	i	PRON
ejde-887	247	6	(	(	PUNCT
ejde-887	247	7	5.3	5.3	NUM
ejde-887	247	8	)	)	PUNCT
ejde-887	247	9	the	the	DET
ejde-887	247	10	third	third	ADJ
ejde-887	247	11	derivative	derivative	ADJ
ejde-887	247	12	vxxx	vxxx	NOUN
ejde-887	247	13	appearing	appear	VERB
ejde-887	247	14	in	in	ADP
ejde-887	247	15	the	the	DET
ejde-887	247	16	dispersion	dispersion	NOUN
ejde-887	247	17	term	term	NOUN
ejde-887	248	1	gn	gn	INTJ
ejde-887	248	2	i	i	PRON
ejde-887	248	3	=	=	PUNCT
ejde-887	248	4	g(un	g(un	PROPN
ejde-887	248	5	i	i	PROPN
ejde-887	248	6	)	)	PUNCT
ejde-887	248	7	is	be	AUX
ejde-887	248	8	approximated	approximate	VERB
ejde-887	248	9	by	by	ADP
ejde-887	248	10	using	use	VERB
ejde-887	248	11	the	the	DET
ejde-887	248	12	following	follow	VERB
ejde-887	248	13	second	second	ADJ
ejde-887	248	14	order	order	NOUN
ejde-887	248	15	difference	difference	NOUN
ejde-887	248	16	formulas	formula	NOUN
ejde-887	248	17	.	.	PUNCT
ejde-887	249	1	vxxx(xi	vxxx(xi	PROPN
ejde-887	249	2	,	,	PUNCT
ejde-887	249	3	tn	tn	PROPN
ejde-887	249	4	)	)	PUNCT
ejde-887	249	5	=	=	PUNCT
ejde-887	250	1	−5vni	−5vni	NOUN
ejde-887	250	2	+	+	CCONJ
ejde-887	250	3	18vni+1	18vni+1	NUM
ejde-887	251	1	−	−	NOUN
ejde-887	251	2	24vni+2	24vni+2	NUM
ejde-887	251	3	+	+	NUM
ejde-887	251	4	14vni+3	14vni+3	NUM
ejde-887	251	5	−	−	NOUN
ejde-887	251	6	3vni+4	3vni+4	NUM
ejde-887	251	7	2∆x3	2∆x3	NUM
ejde-887	251	8	+	+	CCONJ
ejde-887	251	9	o(∆x2	o(∆x2	NOUN
ejde-887	251	10	)	)	PUNCT
ejde-887	251	11	,	,	PUNCT
ejde-887	251	12	i	i	PRON
ejde-887	251	13	=	=	NOUN
ejde-887	251	14	0	0	NUM
ejde-887	251	15	,	,	PUNCT
ejde-887	251	16	1	1	NUM
ejde-887	251	17	;	;	PUNCT
ejde-887	251	18	vxxx(xi	vxxx(xi	PROPN
ejde-887	251	19	,	,	PUNCT
ejde-887	251	20	tn	tn	PROPN
ejde-887	251	21	)	)	PUNCT
ejde-887	251	22	=	=	PUNCT
ejde-887	251	23	vni+2	vni+2	NOUN
ejde-887	251	24	−	−	NOUN
ejde-887	252	1	2vni+1	2vni+1	NUM
ejde-887	253	1	+	+	CCONJ
ejde-887	253	2	2vni−1	2vni−1	NUM
ejde-887	254	1	−	−	NOUN
ejde-887	254	2	vni−2	vni−2	PROPN
ejde-887	254	3	2∆x3	2∆x3	NUM
ejde-887	255	1	+	+	CCONJ
ejde-887	255	2	o(∆x2	o(∆x2	NOUN
ejde-887	255	3	)	)	PUNCT
ejde-887	256	1	,	,	PUNCT
ejde-887	256	2	i	i	PRON
ejde-887	256	3	=	=	NOUN
ejde-887	256	4	2	2	NUM
ejde-887	256	5	,	,	PUNCT
ejde-887	256	6	3	3	NUM
ejde-887	256	7	,	,	PUNCT
ejde-887	256	8	.	.	PUNCT
ejde-887	256	9	.	.	PUNCT
ejde-887	256	10	.	.	PUNCT
ejde-887	257	1	,	,	PUNCT
ejde-887	257	2	m	m	VERB
ejde-887	257	3	−	−	PROPN
ejde-887	257	4	2	2	NUM
ejde-887	257	5	;	;	PUNCT
ejde-887	257	6	vxxx(xi	vxxx(xi	PROPN
ejde-887	257	7	,	,	PUNCT
ejde-887	257	8	tn	tn	PROPN
ejde-887	257	9	)	)	PUNCT
ejde-887	258	1	=	=	PUNCT
ejde-887	259	1	5vni	5vni	NUM
ejde-887	259	2	−	−	PROPN
ejde-887	259	3	18vni−1	18vni−1	NUM
ejde-887	260	1	+	+	CCONJ
ejde-887	260	2	24vni−2	24vni−2	NUM
ejde-887	260	3	−	−	NUM
ejde-887	260	4	14vni−3	14vni−3	NUM
ejde-887	260	5	+	+	NOUN
ejde-887	260	6	3vni−4	3vni−4	NUM
ejde-887	260	7	2∆x3	2∆x3	NUM
ejde-887	261	1	+	+	CCONJ
ejde-887	261	2	o(∆x2	o(∆x2	NOUN
ejde-887	261	3	)	)	PUNCT
ejde-887	261	4	,	,	PUNCT
ejde-887	261	5	i	i	PRON
ejde-887	261	6	=	=	VERB
ejde-887	261	7	m	m	VERB
ejde-887	261	8	−	−	PROPN
ejde-887	261	9	1,m	1,m	NOUN
ejde-887	261	10	.	.	PUNCT
ejde-887	262	1	38	38	NUM
ejde-887	262	2	a.	a.	NOUN
ejde-887	262	3	ludu	ludu	NOUN
ejde-887	262	4	,	,	PUNCT
ejde-887	262	5	h.	h.	PROPN
ejde-887	262	6	khanal	khanal	NOUN
ejde-887	262	7	,	,	PUNCT
ejde-887	262	8	a.	a.	PROPN
ejde-887	262	9	s.	s.	PROPN
ejde-887	262	10	carstea	carstea	PROPN
ejde-887	262	11	ejde-2022	ejde-2022	PROPN
ejde-887	262	12	/	/	SYM
ejde-887	262	13	conf/27	conf/27	NOUN
ejde-887	262	14	5.2	5.2	NUM
ejde-887	262	15	.	.	PUNCT
ejde-887	263	1	analysis	analysis	NOUN
ejde-887	263	2	of	of	ADP
ejde-887	263	3	numerical	numerical	ADJ
ejde-887	263	4	results	result	NOUN
ejde-887	263	5	.	.	PUNCT
ejde-887	264	1	to	to	PART
ejde-887	264	2	interpret	interpret	VERB
ejde-887	264	3	the	the	DET
ejde-887	264	4	results	result	NOUN
ejde-887	264	5	from	from	ADP
ejde-887	264	6	the	the	DET
ejde-887	264	7	multiplescale	multiplescale	NOUN
ejde-887	264	8	analysis	analysis	NOUN
ejde-887	264	9	presented	present	VERB
ejde-887	264	10	in	in	ADP
ejde-887	264	11	section	section	NOUN
ejde-887	264	12	4	4	NUM
ejde-887	264	13	,	,	PUNCT
ejde-887	264	14	we	we	PRON
ejde-887	264	15	solved	solve	VERB
ejde-887	264	16	numerically	numerically	ADV
ejde-887	264	17	the	the	DET
ejde-887	264	18	system	system	NOUN
ejde-887	264	19	(	(	PUNCT
ejde-887	264	20	2.1)-(2.2	2.1)-(2.2	NUM
ejde-887	264	21	)	)	PUNCT
ejde-887	264	22	for	for	ADP
ejde-887	264	23	several	several	ADJ
ejde-887	264	24	values	value	NOUN
ejde-887	264	25	of	of	ADP
ejde-887	264	26	the	the	DET
ejde-887	264	27	parameters	parameter	NOUN
ejde-887	264	28	.	.	PUNCT
ejde-887	265	1	we	we	PRON
ejde-887	265	2	choose	choose	VERB
ejde-887	265	3	a	a	DET
ejde-887	265	4	region	region	NOUN
ejde-887	265	5	of	of	ADP
ejde-887	265	6	width	width	ADJ
ejde-887	265	7	l	l	NOUN
ejde-887	265	8	=	=	SYM
ejde-887	265	9	150	150	NUM
ejde-887	265	10	and	and	CCONJ
ejde-887	265	11	impose	impose	VERB
ejde-887	265	12	homogeneous	homogeneous	ADJ
ejde-887	265	13	boundary	boundary	ADJ
ejde-887	265	14	conditions	condition	NOUN
ejde-887	265	15	at	at	ADP
ejde-887	265	16	the	the	DET
ejde-887	265	17	ends	end	NOUN
ejde-887	265	18	of	of	ADP
ejde-887	265	19	this	this	DET
ejde-887	265	20	region	region	NOUN
ejde-887	265	21	,	,	PUNCT
ejde-887	265	22	namely	namely	ADV
ejde-887	265	23	z(0	z(0	PROPN
ejde-887	265	24	,	,	PUNCT
ejde-887	265	25	t	t	PROPN
ejde-887	265	26	)	)	PUNCT
ejde-887	265	27	=	=	SYM
ejde-887	265	28	z(150	z(150	PROPN
ejde-887	265	29	,	,	PUNCT
ejde-887	265	30	t	t	PROPN
ejde-887	265	31	)	)	PUNCT
ejde-887	265	32	=	=	SYM
ejde-887	266	1	u(0	u(0	PROPN
ejde-887	266	2	,	,	PUNCT
ejde-887	266	3	t	t	PROPN
ejde-887	266	4	)	)	PUNCT
ejde-887	266	5	=	=	SYM
ejde-887	267	1	u(150	u(150	PROPN
ejde-887	267	2	,	,	PUNCT
ejde-887	267	3	t	t	PROPN
ejde-887	267	4	)	)	PUNCT
ejde-887	267	5	=	=	SYM
ejde-887	268	1	0	0	X
ejde-887	268	2	.	.	PUNCT
ejde-887	269	1	we	we	PRON
ejde-887	269	2	choose	choose	VERB
ejde-887	269	3	these	these	DET
ejde-887	269	4	type	type	NOUN
ejde-887	269	5	of	of	ADP
ejde-887	269	6	boundary	boundary	ADJ
ejde-887	269	7	conditions	condition	NOUN
ejde-887	269	8	because	because	SCONJ
ejde-887	269	9	we	we	PRON
ejde-887	269	10	investigate	investigate	VERB
ejde-887	269	11	the	the	DET
ejde-887	269	12	evolution	evolution	NOUN
ejde-887	269	13	of	of	ADP
ejde-887	269	14	an	an	DET
ejde-887	269	15	initial	initial	ADJ
ejde-887	269	16	one	one	NUM
ejde-887	269	17	-	-	PUNCT
ejde-887	269	18	soliton	soliton	NOUN
ejde-887	269	19	solution	solution	NOUN
ejde-887	269	20	(	(	PUNCT
ejde-887	269	21	3.8	3.8	NUM
ejde-887	269	22	)	)	PUNCT
ejde-887	269	23	under	under	ADP
ejde-887	269	24	the	the	DET
ejde-887	269	25	perturbation	perturbation	NOUN
ejde-887	269	26	caused	cause	VERB
ejde-887	269	27	by	by	ADP
ejde-887	269	28	the	the	DET
ejde-887	269	29	variable	variable	ADJ
ejde-887	269	30	coefficients	coefficient	NOUN
ejde-887	269	31	,	,	PUNCT
ejde-887	269	32	and	and	CCONJ
ejde-887	269	33	this	this	DET
ejde-887	269	34	initial	initial	ADJ
ejde-887	269	35	condition	condition	NOUN
ejde-887	269	36	is	be	AUX
ejde-887	269	37	a	a	DET
ejde-887	269	38	highly	highly	ADV
ejde-887	269	39	localized	localized	ADJ
ejde-887	269	40	function	function	NOUN
ejde-887	269	41	.	.	PUNCT
ejde-887	270	1	we	we	PRON
ejde-887	270	2	also	also	ADV
ejde-887	270	3	investigate	investigate	VERB
ejde-887	270	4	numerically	numerically	ADV
ejde-887	270	5	only	only	ADV
ejde-887	270	6	the	the	DET
ejde-887	270	7	first	first	ADJ
ejde-887	270	8	10	10	NUM
ejde-887	270	9	seconds	second	NOUN
ejde-887	270	10	of	of	ADP
ejde-887	270	11	the	the	DET
ejde-887	270	12	solution	solution	NOUN
ejde-887	270	13	evolution	evolution	NOUN
ejde-887	270	14	,	,	PUNCT
ejde-887	270	15	such	such	ADJ
ejde-887	270	16	that	that	SCONJ
ejde-887	270	17	the	the	DET
ejde-887	270	18	generated	generate	VERB
ejde-887	270	19	solitary	solitary	ADJ
ejde-887	270	20	wave	wave	NOUN
ejde-887	270	21	does	do	AUX
ejde-887	270	22	not	not	PART
ejde-887	270	23	reach	reach	VERB
ejde-887	270	24	the	the	DET
ejde-887	270	25	boundaries	boundary	NOUN
ejde-887	270	26	of	of	ADP
ejde-887	270	27	the	the	DET
ejde-887	270	28	interval	interval	NOUN
ejde-887	270	29	.	.	PUNCT
ejde-887	271	1	in	in	ADP
ejde-887	271	2	order	order	NOUN
ejde-887	271	3	to	to	PART
ejde-887	271	4	validate	validate	VERB
ejde-887	271	5	this	this	DET
ejde-887	271	6	hypothesis	hypothesis	NOUN
ejde-887	271	7	,	,	PUNCT
ejde-887	271	8	we	we	PRON
ejde-887	271	9	substitute	substitute	VERB
ejde-887	271	10	the	the	DET
ejde-887	271	11	homogeneous	homogeneous	ADJ
ejde-887	271	12	boundary	boundary	ADJ
ejde-887	271	13	conditions	condition	NOUN
ejde-887	271	14	with	with	ADP
ejde-887	271	15	periodic	periodic	ADJ
ejde-887	271	16	boundary	boundary	ADJ
ejde-887	271	17	conditions	condition	NOUN
ejde-887	271	18	.	.	PUNCT
ejde-887	272	1	for	for	ADP
ejde-887	272	2	each	each	DET
ejde-887	272	3	set	set	NOUN
ejde-887	272	4	of	of	ADP
ejde-887	272	5	parameters	parameter	NOUN
ejde-887	272	6	,	,	PUNCT
ejde-887	272	7	the	the	DET
ejde-887	272	8	numerical	numerical	ADJ
ejde-887	272	9	solutions	solution	NOUN
ejde-887	272	10	did	do	AUX
ejde-887	272	11	not	not	PART
ejde-887	272	12	change	change	VERB
ejde-887	272	13	with	with	ADP
ejde-887	272	14	these	these	DET
ejde-887	272	15	new	new	ADJ
ejde-887	272	16	boundary	boundary	ADJ
ejde-887	272	17	conditions	condition	NOUN
ejde-887	272	18	.	.	PUNCT
ejde-887	273	1	concerning	concern	VERB
ejde-887	273	2	the	the	DET
ejde-887	273	3	initial	initial	ADJ
ejde-887	273	4	conditions	condition	NOUN
ejde-887	273	5	,	,	PUNCT
ejde-887	273	6	we	we	PRON
ejde-887	273	7	study	study	VERB
ejde-887	273	8	only	only	ADV
ejde-887	273	9	one	one	NUM
ejde-887	273	10	-	-	PUNCT
ejde-887	273	11	soliton	soliton	NOUN
ejde-887	273	12	solution	solution	NOUN
ejde-887	273	13	obtained	obtain	VERB
ejde-887	273	14	from	from	ADP
ejde-887	273	15	the	the	DET
ejde-887	273	16	autonomous	autonomous	ADJ
ejde-887	273	17	boussinesq	boussinesq	ADJ
ejde-887	273	18	system	system	NOUN
ejde-887	273	19	,	,	PUNCT
ejde-887	273	20	zsol(x	zsol(x	PROPN
ejde-887	273	21	)	)	PUNCT
ejde-887	273	22	,	,	PUNCT
ejde-887	273	23	usol(x	usol(x	PROPN
ejde-887	273	24	)	)	PUNCT
ejde-887	273	25	from	from	ADP
ejde-887	273	26	(	(	PUNCT
ejde-887	273	27	3.8	3.8	NUM
ejde-887	273	28	)	)	PUNCT
ejde-887	273	29	,	,	PUNCT
ejde-887	273	30	centered	center	VERB
ejde-887	273	31	at	at	ADP
ejde-887	273	32	the	the	DET
ejde-887	273	33	middle	middle	NOUN
ejde-887	273	34	of	of	ADP
ejde-887	273	35	the	the	DET
ejde-887	273	36	space	space	NOUN
ejde-887	273	37	interval	interval	NOUN
ejde-887	273	38	,	,	PUNCT
ejde-887	273	39	with	with	ADP
ejde-887	273	40	amplitudes	amplitude	NOUN
ejde-887	273	41	controlled	control	VERB
ejde-887	273	42	by	by	ADP
ejde-887	273	43	the	the	DET
ejde-887	273	44	nonlinearity	nonlinearity	NOUN
ejde-887	273	45	parameter	parameter	NOUN
ejde-887	273	46	α	α	PROPN
ejde-887	273	47	and	and	CCONJ
ejde-887	273	48	chosen	choose	VERB
ejde-887	273	49	in	in	ADP
ejde-887	273	50	the	the	DET
ejde-887	273	51	range	range	NOUN
ejde-887	273	52	0.5−0.8	0.5−0.8	ADJ
ejde-887	273	53	and	and	CCONJ
ejde-887	273	54	for	for	ADP
ejde-887	273	55	two	two	NUM
ejde-887	273	56	values	value	NOUN
ejde-887	273	57	of	of	ADP
ejde-887	273	58	the	the	DET
ejde-887	273	59	soliton	soliton	NOUN
ejde-887	273	60	half	half	ADJ
ejde-887	273	61	-	-	PUNCT
ejde-887	273	62	width	width	NOUN
ejde-887	273	63	lsol	lsol	NOUN
ejde-887	273	64	=	=	SYM
ejde-887	273	65	30	30	NUM
ejde-887	273	66	and	and	CCONJ
ejde-887	273	67	5	5	NUM
ejde-887	273	68	.	.	X
ejde-887	274	1	we	we	PRON
ejde-887	274	2	choose	choose	VERB
ejde-887	274	3	a	a	DET
ejde-887	274	4	relatively	relatively	ADV
ejde-887	274	5	large	large	ADJ
ejde-887	274	6	dispersion	dispersion	NOUN
ejde-887	274	7	parameter	parameter	NOUN
ejde-887	274	8	β	β	NOUN
ejde-887	274	9	=	=	NOUN
ejde-887	274	10	0.5	0.5	NUM
ejde-887	274	11	-	-	SYM
ejde-887	274	12	0.7	0.7	NUM
ejde-887	274	13	in	in	ADP
ejde-887	274	14	all	all	DET
ejde-887	274	15	simulations	simulation	NOUN
ejde-887	274	16	.	.	PUNCT
ejde-887	275	1	we	we	PRON
ejde-887	275	2	compare	compare	VERB
ejde-887	275	3	the	the	DET
ejde-887	275	4	evolution	evolution	NOUN
ejde-887	275	5	of	of	ADP
ejde-887	275	6	the	the	DET
ejde-887	275	7	initial	initial	ADJ
ejde-887	275	8	one	one	NUM
ejde-887	275	9	-	-	PUNCT
ejde-887	275	10	soliton	soliton	NOUN
ejde-887	275	11	function	function	NOUN
ejde-887	275	12	governed	govern	VERB
ejde-887	275	13	by	by	ADP
ejde-887	275	14	the	the	DET
ejde-887	275	15	non	non	ADJ
ejde-887	275	16	-	-	ADJ
ejde-887	275	17	autonomous	autonomous	ADJ
ejde-887	275	18	system	system	NOUN
ejde-887	275	19	(	(	PUNCT
ejde-887	275	20	2.1)-(2.2	2.1)-(2.2	NUM
ejde-887	275	21	)	)	PUNCT
ejde-887	275	22	with	with	ADP
ejde-887	275	23	its	its	PRON
ejde-887	275	24	original	original	ADJ
ejde-887	275	25	uniform	uniform	NOUN
ejde-887	275	26	evolution	evolution	NOUN
ejde-887	275	27	in	in	ADP
ejde-887	275	28	shape	shape	NOUN
ejde-887	275	29	and	and	CCONJ
ejde-887	275	30	velocity	velocity	NOUN
ejde-887	275	31	if	if	SCONJ
ejde-887	275	32	its	its	PRON
ejde-887	275	33	dynamics	dynamic	NOUN
ejde-887	275	34	would	would	AUX
ejde-887	275	35	be	be	AUX
ejde-887	275	36	governed	govern	VERB
ejde-887	275	37	by	by	ADP
ejde-887	275	38	autonomous	autonomous	ADJ
ejde-887	275	39	system	system	NOUN
ejde-887	275	40	,	,	PUNCT
ejde-887	275	41	with	with	ADP
ejde-887	275	42	q	q	PROPN
ejde-887	275	43	=	=	SYM
ejde-887	275	44	1	1	X
ejde-887	275	45	.	.	PUNCT
ejde-887	275	46	figure	figure	NOUN
ejde-887	275	47	1	1	NUM
ejde-887	275	48	.	.	PUNCT
ejde-887	275	49	numerical	numerical	ADJ
ejde-887	275	50	solution	solution	NOUN
ejde-887	275	51	z(x	z(x	PROPN
ejde-887	275	52	,	,	PUNCT
ejde-887	275	53	t	t	PROPN
ejde-887	275	54	)	)	PUNCT
ejde-887	275	55	(	(	PUNCT
ejde-887	275	56	red	red	ADJ
ejde-887	275	57	and	and	CCONJ
ejde-887	275	58	blue	blue	ADJ
ejde-887	275	59	)	)	PUNCT
ejde-887	275	60	for	for	ADP
ejde-887	275	61	(	(	PUNCT
ejde-887	275	62	2.1	2.1	NUM
ejde-887	275	63	)	)	PUNCT
ejde-887	275	64	for	for	ADP
ejde-887	275	65	α	α	NOUN
ejde-887	275	66	=	=	SYM
ejde-887	275	67	0.5	0.5	NUM
ejde-887	275	68	,	,	PUNCT
ejde-887	275	69	β	β	X
ejde-887	275	70	=	=	SYM
ejde-887	275	71	0.5	0.5	NUM
ejde-887	275	72	at	at	ADP
ejde-887	275	73	three	three	NUM
ejde-887	275	74	moments	moment	NOUN
ejde-887	275	75	of	of	ADP
ejde-887	275	76	time	time	NOUN
ejde-887	275	77	,	,	PUNCT
ejde-887	275	78	labeled	label	VERB
ejde-887	275	79	in	in	ADP
ejde-887	275	80	the	the	DET
ejde-887	275	81	frames	frame	NOUN
ejde-887	275	82	.	.	PUNCT
ejde-887	276	1	the	the	DET
ejde-887	276	2	initial	initial	ADJ
ejde-887	276	3	condition	condition	NOUN
ejde-887	276	4	(	(	PUNCT
ejde-887	276	5	black	black	NOUN
ejde-887	276	6	)	)	PUNCT
ejde-887	276	7	is	be	AUX
ejde-887	276	8	a	a	DET
ejde-887	276	9	one	one	NUM
ejde-887	276	10	-	-	PUNCT
ejde-887	276	11	soliton	soliton	NOUN
ejde-887	276	12	solution	solution	NOUN
ejde-887	276	13	of	of	ADP
ejde-887	276	14	the	the	DET
ejde-887	276	15	autonomous	autonomous	ADJ
ejde-887	276	16	boussinesq	boussinesq	ADJ
ejde-887	276	17	equation	equation	NOUN
ejde-887	276	18	(	(	PUNCT
ejde-887	276	19	3.8	3.8	NUM
ejde-887	276	20	)	)	PUNCT
ejde-887	276	21	with	with	ADP
ejde-887	276	22	asol	asol	NOUN
ejde-887	276	23	=	=	SYM
ejde-887	276	24	0.01	0.01	NUM
ejde-887	276	25	,	,	PUNCT
ejde-887	276	26	lsol	lsol	NOUN
ejde-887	276	27	=	=	SYM
ejde-887	276	28	30	30	NUM
ejde-887	276	29	.	.	PUNCT
ejde-887	277	1	the	the	DET
ejde-887	277	2	variable	variable	ADJ
ejde-887	277	3	coefficient	coefficient	NOUN
ejde-887	277	4	is	be	AUX
ejde-887	277	5	q	q	NOUN
ejde-887	277	6	=	=	PUNCT
ejde-887	277	7	1	1	NUM
ejde-887	277	8	+	+	NUM
ejde-887	277	9	ϵ	ϵ	DET
ejde-887	277	10	sin(2x	sin(2x	NOUN
ejde-887	277	11	)	)	PUNCT
ejde-887	277	12	with	with	ADP
ejde-887	277	13	amplitude	amplitude	NOUN
ejde-887	277	14	ϵ	ϵ	X
ejde-887	277	15	=	=	SYM
ejde-887	277	16	0.1	0.1	NUM
ejde-887	277	17	.	.	PUNCT
ejde-887	278	1	the	the	DET
ejde-887	278	2	initial	initial	ADJ
ejde-887	278	3	soliton	soliton	NOUN
ejde-887	278	4	breaks	break	NOUN
ejde-887	278	5	into	into	ADP
ejde-887	278	6	smaller	small	ADJ
ejde-887	278	7	multi	multi	ADJ
ejde-887	278	8	-	-	ADJ
ejde-887	278	9	soliton	soliton	ADJ
ejde-887	278	10	solutions	solution	NOUN
ejde-887	278	11	,	,	PUNCT
ejde-887	278	12	but	but	CCONJ
ejde-887	278	13	appears	appear	VERB
ejde-887	278	14	stable	stable	ADJ
ejde-887	278	15	within	within	ADP
ejde-887	278	16	the	the	DET
ejde-887	278	17	time	time	NOUN
ejde-887	278	18	frame	frame	NOUN
ejde-887	278	19	.	.	PUNCT
ejde-887	279	1	when	when	SCONJ
ejde-887	279	2	the	the	DET
ejde-887	279	3	envelope	envelope	NOUN
ejde-887	279	4	is	be	AUX
ejde-887	279	5	modulated	modulate	VERB
ejde-887	279	6	by	by	ADP
ejde-887	279	7	the	the	DET
ejde-887	279	8	secondary	secondary	ADJ
ejde-887	279	9	solitons	soliton	NOUN
ejde-887	279	10	the	the	DET
ejde-887	279	11	height	height	NOUN
ejde-887	279	12	of	of	ADP
ejde-887	279	13	the	the	DET
ejde-887	279	14	wave	wave	NOUN
ejde-887	279	15	slightly	slightly	ADV
ejde-887	279	16	increases	increase	NOUN
ejde-887	279	17	,	,	PUNCT
ejde-887	279	18	which	which	PRON
ejde-887	279	19	shows	show	VERB
ejde-887	279	20	rudiments	rudiment	NOUN
ejde-887	279	21	of	of	ADP
ejde-887	279	22	area	area	NOUN
ejde-887	279	23	conservation	conservation	NOUN
ejde-887	279	24	,	,	PUNCT
ejde-887	279	25	even	even	ADV
ejde-887	279	26	in	in	ADP
ejde-887	279	27	the	the	DET
ejde-887	279	28	non	non	ADJ
ejde-887	279	29	-	-	ADJ
ejde-887	279	30	autonomous	autonomous	ADJ
ejde-887	279	31	case	case	NOUN
ejde-887	279	32	.	.	PUNCT
ejde-887	280	1	once	once	ADV
ejde-887	280	2	the	the	DET
ejde-887	280	3	secondary	secondary	ADJ
ejde-887	280	4	multi	multi	ADJ
ejde-887	280	5	-	-	ADJ
ejde-887	280	6	solitons	soliton	NOUN
ejde-887	280	7	lag	lag	VERB
ejde-887	280	8	the	the	DET
ejde-887	280	9	main	main	ADJ
ejde-887	280	10	one	one	NOUN
ejde-887	280	11	,	,	PUNCT
ejde-887	280	12	the	the	DET
ejde-887	280	13	height	height	NOUN
ejde-887	280	14	of	of	ADP
ejde-887	280	15	solution	solution	NOUN
ejde-887	280	16	returns	return	NOUN
ejde-887	280	17	to	to	ADP
ejde-887	280	18	its	its	PRON
ejde-887	280	19	initial	initial	ADJ
ejde-887	280	20	value	value	NOUN
ejde-887	280	21	.	.	PUNCT
ejde-887	281	1	ejde-202x	ejde-202x	NOUN
ejde-887	281	2	/	/	SYM
ejde-887	281	3	conf/27	conf/27	NOUN
ejde-887	281	4	boussinesq	boussinesq	ADJ
ejde-887	281	5	equations	equation	NOUN
ejde-887	281	6	39	39	NUM
ejde-887	281	7	figure	figure	NOUN
ejde-887	281	8	2	2	NUM
ejde-887	281	9	.	.	PUNCT
ejde-887	281	10	numerical	numerical	ADJ
ejde-887	281	11	solutions	solution	NOUN
ejde-887	281	12	u(x	u(x	PROPN
ejde-887	281	13	,	,	PUNCT
ejde-887	281	14	t	t	PROPN
ejde-887	281	15	)	)	PUNCT
ejde-887	281	16	for	for	ADP
ejde-887	281	17	(	(	PUNCT
ejde-887	281	18	2.1	2.1	NUM
ejde-887	281	19	)	)	PUNCT
ejde-887	281	20	in	in	ADP
ejde-887	281	21	the	the	DET
ejde-887	281	22	same	same	ADJ
ejde-887	281	23	conditions	condition	NOUN
ejde-887	281	24	as	as	ADP
ejde-887	281	25	figure	figure	NOUN
ejde-887	281	26	1	1	NUM
ejde-887	281	27	with	with	ADP
ejde-887	281	28	initial	initial	ADJ
ejde-887	281	29	condition	condition	NOUN
ejde-887	281	30	(	(	PUNCT
ejde-887	281	31	black	black	NOUN
ejde-887	281	32	)	)	PUNCT
ejde-887	281	33	given	give	VERB
ejde-887	281	34	by	by	ADP
ejde-887	281	35	the	the	DET
ejde-887	281	36	usol(x	usol(x	PROPN
ejde-887	281	37	)	)	PUNCT
ejde-887	281	38	autonomous	autonomous	ADJ
ejde-887	281	39	soliton	soliton	NOUN
ejde-887	281	40	,	,	PUNCT
ejde-887	281	41	second	second	ADJ
ejde-887	281	42	(	(	PUNCT
ejde-887	281	43	3.8	3.8	NUM
ejde-887	281	44	)	)	PUNCT
ejde-887	281	45	.	.	PUNCT
ejde-887	282	1	for	for	ADP
ejde-887	282	2	this	this	DET
ejde-887	282	3	component	component	NOUN
ejde-887	282	4	of	of	ADP
ejde-887	282	5	the	the	DET
ejde-887	282	6	solution	solution	NOUN
ejde-887	282	7	,	,	PUNCT
ejde-887	282	8	the	the	DET
ejde-887	282	9	amplitude	amplitude	NOUN
ejde-887	282	10	slightly	slightly	ADV
ejde-887	282	11	increases	increase	VERB
ejde-887	282	12	in	in	ADP
ejde-887	282	13	time	time	NOUN
ejde-887	282	14	because	because	SCONJ
ejde-887	282	15	of	of	ADP
ejde-887	282	16	onset	onset	NOUN
ejde-887	282	17	of	of	ADP
ejde-887	282	18	instability	instability	NOUN
ejde-887	282	19	.	.	PUNCT
ejde-887	283	1	figure	figure	NOUN
ejde-887	283	2	3	3	NUM
ejde-887	283	3	.	.	PUNCT
ejde-887	284	1	numerical	numerical	ADJ
ejde-887	284	2	solutions	solution	NOUN
ejde-887	284	3	z(x	z(x	PROPN
ejde-887	284	4	,	,	PUNCT
ejde-887	284	5	t	t	PROPN
ejde-887	284	6	)	)	PUNCT
ejde-887	284	7	for	for	ADP
ejde-887	284	8	(	(	PUNCT
ejde-887	284	9	2.1	2.1	NUM
ejde-887	284	10	)	)	PUNCT
ejde-887	284	11	.	.	PUNCT
ejde-887	285	1	the	the	DET
ejde-887	285	2	initial	initial	ADJ
ejde-887	285	3	condition	condition	NOUN
ejde-887	285	4	(	(	PUNCT
ejde-887	285	5	black	black	NOUN
ejde-887	285	6	)	)	PUNCT
ejde-887	285	7	is	be	AUX
ejde-887	285	8	the	the	DET
ejde-887	285	9	same	same	ADJ
ejde-887	285	10	one	one	NUM
ejde-887	285	11	-	-	PUNCT
ejde-887	285	12	soliton	soliton	NOUN
ejde-887	285	13	solution	solution	NOUN
ejde-887	285	14	in	in	ADP
ejde-887	285	15	(	(	PUNCT
ejde-887	285	16	3.8	3.8	NUM
ejde-887	285	17	)	)	PUNCT
ejde-887	285	18	with	with	ADP
ejde-887	285	19	asol	asol	NOUN
ejde-887	285	20	=	=	SYM
ejde-887	285	21	0.01	0.01	NUM
ejde-887	285	22	,	,	PUNCT
ejde-887	285	23	lsol	lsol	NOUN
ejde-887	285	24	=	=	SYM
ejde-887	285	25	30	30	NUM
ejde-887	285	26	and	and	CCONJ
ejde-887	285	27	the	the	DET
ejde-887	285	28	equation	equation	NOUN
ejde-887	285	29	parameters	parameter	NOUN
ejde-887	285	30	are	be	AUX
ejde-887	285	31	the	the	DET
ejde-887	285	32	same	same	ADJ
ejde-887	285	33	α	α	NOUN
ejde-887	285	34	=	=	SYM
ejde-887	285	35	0.5	0.5	NUM
ejde-887	285	36	,	,	PUNCT
ejde-887	285	37	β	β	X
ejde-887	285	38	=	=	SYM
ejde-887	285	39	0.5	0.5	NUM
ejde-887	285	40	as	as	ADP
ejde-887	285	41	in	in	ADP
ejde-887	285	42	figures	figure	NOUN
ejde-887	285	43	1	1	NUM
ejde-887	285	44	and	and	CCONJ
ejde-887	285	45	2	2	NUM
ejde-887	285	46	.	.	X
ejde-887	286	1	the	the	DET
ejde-887	286	2	variable	variable	ADJ
ejde-887	286	3	coefficient	coefficient	NOUN
ejde-887	286	4	q	q	NOUN
ejde-887	286	5	=	=	SYM
ejde-887	286	6	1	1	NUM
ejde-887	286	7	+	+	CCONJ
ejde-887	286	8	ϵ	ϵ	DET
ejde-887	286	9	sin(2x	sin(2x	PROPN
ejde-887	286	10	)	)	PUNCT
ejde-887	286	11	has	have	AUX
ejde-887	286	12	increased	increase	VERB
ejde-887	286	13	amplitude	amplitude	NOUN
ejde-887	286	14	ϵ	ϵ	NOUN
ejde-887	286	15	=	=	SYM
ejde-887	286	16	0.2	0.2	NUM
ejde-887	286	17	.	.	PUNCT
ejde-887	287	1	the	the	DET
ejde-887	287	2	larger	large	ADJ
ejde-887	287	3	variation	variation	NOUN
ejde-887	287	4	of	of	ADP
ejde-887	287	5	the	the	DET
ejde-887	287	6	coefficient	coefficient	NOUN
ejde-887	287	7	q	q	NOUN
ejde-887	287	8	induces	induce	VERB
ejde-887	287	9	larger	large	ADJ
ejde-887	287	10	amplitude	amplitude	NOUN
ejde-887	287	11	secondary	secondary	ADJ
ejde-887	287	12	multi	multi	NOUN
ejde-887	287	13	-	-	NOUN
ejde-887	287	14	solitons	soliton	NOUN
ejde-887	287	15	,	,	PUNCT
ejde-887	287	16	and	and	CCONJ
ejde-887	287	17	larger	large	ADJ
ejde-887	287	18	variations	variation	NOUN
ejde-887	287	19	for	for	ADP
ejde-887	287	20	the	the	DET
ejde-887	287	21	maximum	maximum	ADJ
ejde-887	287	22	value	value	NOUN
ejde-887	287	23	of	of	ADP
ejde-887	287	24	the	the	DET
ejde-887	287	25	solution	solution	NOUN
ejde-887	287	26	.	.	PUNCT
ejde-887	288	1	the	the	DET
ejde-887	288	2	soliton	soliton	NOUN
ejde-887	288	3	maintains	maintain	VERB
ejde-887	288	4	stability	stability	NOUN
ejde-887	288	5	after	after	ADP
ejde-887	288	6	10	10	NUM
ejde-887	288	7	seconds	second	NOUN
ejde-887	288	8	.	.	PUNCT
ejde-887	289	1	in	in	ADP
ejde-887	289	2	all	all	DET
ejde-887	289	3	numerical	numerical	ADJ
ejde-887	289	4	simulations	simulation	NOUN
ejde-887	289	5	we	we	PRON
ejde-887	289	6	use	use	VERB
ejde-887	289	7	the	the	DET
ejde-887	289	8	same	same	ADJ
ejde-887	289	9	periodic	periodic	ADJ
ejde-887	289	10	signal	signal	NOUN
ejde-887	289	11	form	form	NOUN
ejde-887	289	12	for	for	ADP
ejde-887	289	13	the	the	DET
ejde-887	289	14	variable	variable	ADJ
ejde-887	289	15	coefficient	coefficient	NOUN
ejde-887	289	16	q(x	q(x	NOUN
ejde-887	289	17	)	)	PUNCT
ejde-887	289	18	=	=	PUNCT
ejde-887	290	1	1	1	NUM
ejde-887	290	2	+	+	CCONJ
ejde-887	290	3	ϵ	ϵ	DET
ejde-887	290	4	sin(2x	sin(2x	PROPN
ejde-887	290	5	)	)	PUNCT
ejde-887	290	6	with	with	ADP
ejde-887	290	7	amplitude	amplitude	NOUN
ejde-887	290	8	in	in	ADP
ejde-887	290	9	the	the	DET
ejde-887	290	10	range	range	NOUN
ejde-887	291	1	ϵ	ϵ	X
ejde-887	291	2	=	=	SYM
ejde-887	291	3	0.1	0.1	NUM
ejde-887	291	4	to	to	ADP
ejde-887	291	5	0.3	0.3	NUM
ejde-887	291	6	,	,	PUNCT
ejde-887	291	7	but	but	CCONJ
ejde-887	291	8	the	the	DET
ejde-887	291	9	same	same	ADJ
ejde-887	291	10	wavelength	wavelength	NOUN
ejde-887	291	11	λ	λ	X
ejde-887	291	12	=	=	SYM
ejde-887	291	13	4π	4π	NUM
ejde-887	291	14	.	.	PUNCT
ejde-887	292	1	from	from	ADP
ejde-887	292	2	the	the	DET
ejde-887	292	3	results	result	NOUN
ejde-887	292	4	of	of	ADP
ejde-887	292	5	the	the	DET
ejde-887	292	6	numerical	numerical	ADJ
ejde-887	292	7	simulations	simulation	NOUN
ejde-887	292	8	presented	present	VERB
ejde-887	292	9	in	in	ADP
ejde-887	292	10	figures	figure	NOUN
ejde-887	292	11	1	1	NUM
ejde-887	292	12	-	-	SYM
ejde-887	292	13	8	8	NUM
ejde-887	292	14	we	we	PRON
ejde-887	292	15	can	can	AUX
ejde-887	292	16	understand	understand	VERB
ejde-887	292	17	the	the	DET
ejde-887	292	18	perturbations	perturbation	NOUN
ejde-887	292	19	induced	induce	VERB
ejde-887	292	20	by	by	ADP
ejde-887	292	21	the	the	DET
ejde-887	292	22	variable	variable	ADJ
ejde-887	292	23	coefficients	coefficient	NOUN
ejde-887	292	24	q(x	q(x	NOUN
ejde-887	292	25	)	)	PUNCT
ejde-887	292	26	of	of	ADP
ejde-887	292	27	the	the	DET
ejde-887	292	28	boussinesq	boussinesq	ADJ
ejde-887	292	29	system	system	NOUN
ejde-887	292	30	on	on	ADP
ejde-887	292	31	the	the	DET
ejde-887	292	32	solitary	solitary	ADJ
ejde-887	292	33	wave	wave	NOUN
ejde-887	292	34	solutions	solution	NOUN
ejde-887	292	35	.	.	PUNCT
ejde-887	293	1	the	the	DET
ejde-887	293	2	perturbation	perturbation	NOUN
ejde-887	293	3	induced	induce	VERB
ejde-887	293	4	in	in	ADP
ejde-887	293	5	the	the	DET
ejde-887	293	6	solitary	solitary	ADJ
ejde-887	293	7	waves	wave	NOUN
ejde-887	293	8	by	by	ADP
ejde-887	293	9	the	the	DET
ejde-887	293	10	periodic	periodic	ADJ
ejde-887	293	11	variable	variable	ADJ
ejde-887	293	12	coefficients	coefficient	NOUN
ejde-887	293	13	are	be	AUX
ejde-887	293	14	controlled	control	VERB
ejde-887	293	15	by	by	ADP
ejde-887	293	16	the	the	DET
ejde-887	293	17	relative	relative	ADJ
ejde-887	293	18	ration	ration	NOUN
ejde-887	293	19	between	between	ADP
ejde-887	293	20	their	their	PRON
ejde-887	293	21	space	space	NOUN
ejde-887	293	22	scales	scale	NOUN
ejde-887	293	23	,	,	PUNCT
ejde-887	293	24	namely	namely	ADV
ejde-887	293	25	between	between	ADP
ejde-887	293	26	the	the	DET
ejde-887	293	27	half	half	ADJ
ejde-887	293	28	-	-	PUNCT
ejde-887	293	29	width	width	NOUN
ejde-887	293	30	of	of	ADP
ejde-887	293	31	the	the	DET
ejde-887	293	32	initial	initial	ADJ
ejde-887	293	33	soliton	soliton	NOUN
ejde-887	293	34	40	40	NUM
ejde-887	293	35	a.	a.	NOUN
ejde-887	293	36	ludu	ludu	NOUN
ejde-887	293	37	,	,	PUNCT
ejde-887	293	38	h.	h.	PROPN
ejde-887	293	39	khanal	khanal	NOUN
ejde-887	293	40	,	,	PUNCT
ejde-887	293	41	a.	a.	PROPN
ejde-887	293	42	s.	s.	PROPN
ejde-887	293	43	carstea	carstea	PROPN
ejde-887	293	44	ejde-2022	ejde-2022	PROPN
ejde-887	293	45	/	/	SYM
ejde-887	293	46	conf/27	conf/27	NOUN
ejde-887	293	47	figure	figure	NOUN
ejde-887	293	48	4	4	NUM
ejde-887	293	49	.	.	PUNCT
ejde-887	293	50	numerical	numerical	ADJ
ejde-887	293	51	solutions	solution	NOUN
ejde-887	293	52	u(x	u(x	PROPN
ejde-887	293	53	,	,	PUNCT
ejde-887	293	54	t	t	PROPN
ejde-887	293	55	)	)	PUNCT
ejde-887	293	56	for	for	ADP
ejde-887	293	57	(	(	PUNCT
ejde-887	293	58	2.1	2.1	NUM
ejde-887	293	59	)	)	PUNCT
ejde-887	293	60	in	in	ADP
ejde-887	293	61	the	the	DET
ejde-887	293	62	same	same	ADJ
ejde-887	293	63	conditions	condition	NOUN
ejde-887	293	64	as	as	ADP
ejde-887	293	65	figure	figure	NOUN
ejde-887	293	66	3	3	NUM
ejde-887	293	67	with	with	ADP
ejde-887	293	68	corresponding	corresponding	ADJ
ejde-887	293	69	usol	usol	ADJ
ejde-887	293	70	initial	initial	ADJ
ejde-887	293	71	condition	condition	NOUN
ejde-887	293	72	(	(	PUNCT
ejde-887	293	73	black	black	NOUN
ejde-887	293	74	)	)	PUNCT
ejde-887	293	75	.	.	PUNCT
ejde-887	294	1	the	the	DET
ejde-887	294	2	shape	shape	NOUN
ejde-887	294	3	of	of	ADP
ejde-887	294	4	the	the	DET
ejde-887	294	5	initial	initial	ADJ
ejde-887	294	6	condition	condition	NOUN
ejde-887	294	7	is	be	AUX
ejde-887	294	8	highly	highly	ADV
ejde-887	294	9	perturbed	perturb	VERB
ejde-887	294	10	and	and	CCONJ
ejde-887	294	11	increases	increase	NOUN
ejde-887	294	12	in	in	ADP
ejde-887	294	13	time	time	NOUN
ejde-887	294	14	.	.	PUNCT
ejde-887	295	1	it	it	PRON
ejde-887	295	2	becomes	become	VERB
ejde-887	295	3	unstable	unstable	ADJ
ejde-887	295	4	after	after	ADP
ejde-887	295	5	10	10	NUM
ejde-887	295	6	seconds	second	NOUN
ejde-887	295	7	,	,	PUNCT
ejde-887	295	8	and	and	CCONJ
ejde-887	295	9	probably	probably	ADV
ejde-887	295	10	approaches	approach	VERB
ejde-887	295	11	a	a	DET
ejde-887	295	12	blow	blow	VERB
ejde-887	295	13	-	-	PUNCT
ejde-887	295	14	out	out	ADP
ejde-887	295	15	singularity	singularity	NOUN
ejde-887	295	16	,	,	PUNCT
ejde-887	295	17	showing	show	VERB
ejde-887	295	18	that	that	SCONJ
ejde-887	295	19	the	the	DET
ejde-887	295	20	u	u	PROPN
ejde-887	295	21	component	component	NOUN
ejde-887	295	22	is	be	AUX
ejde-887	295	23	more	more	ADV
ejde-887	295	24	sensitive	sensitive	ADJ
ejde-887	295	25	to	to	ADP
ejde-887	295	26	the	the	DET
ejde-887	295	27	effect	effect	NOUN
ejde-887	295	28	of	of	ADP
ejde-887	295	29	variable	variable	ADJ
ejde-887	295	30	coefficient	coefficient	NOUN
ejde-887	295	31	.	.	PUNCT
ejde-887	296	1	figure	figure	NOUN
ejde-887	296	2	5	5	NUM
ejde-887	296	3	.	.	PUNCT
ejde-887	297	1	the	the	DET
ejde-887	297	2	same	same	ADJ
ejde-887	297	3	numerical	numerical	ADJ
ejde-887	297	4	solution	solution	NOUN
ejde-887	297	5	z(x	z(x	PROPN
ejde-887	297	6	,	,	PUNCT
ejde-887	297	7	t	t	PROPN
ejde-887	297	8	)	)	PUNCT
ejde-887	297	9	as	as	ADP
ejde-887	297	10	in	in	ADP
ejde-887	297	11	figure	figure	NOUN
ejde-887	297	12	3	3	NUM
ejde-887	297	13	,	,	PUNCT
ejde-887	297	14	obtained	obtain	VERB
ejde-887	297	15	in	in	ADP
ejde-887	297	16	the	the	DET
ejde-887	297	17	same	same	ADJ
ejde-887	297	18	conditions	condition	NOUN
ejde-887	297	19	,	,	PUNCT
ejde-887	297	20	plotted	plot	VERB
ejde-887	297	21	at	at	ADP
ejde-887	297	22	five	five	NUM
ejde-887	297	23	moments	moment	NOUN
ejde-887	297	24	of	of	ADP
ejde-887	297	25	time	time	NOUN
ejde-887	297	26	to	to	PART
ejde-887	297	27	emphasize	emphasize	VERB
ejde-887	297	28	the	the	DET
ejde-887	297	29	oscillations	oscillation	NOUN
ejde-887	297	30	of	of	ADP
ejde-887	297	31	the	the	DET
ejde-887	297	32	maximum	maximum	ADJ
ejde-887	297	33	value	value	NOUN
ejde-887	297	34	of	of	ADP
ejde-887	297	35	the	the	DET
ejde-887	297	36	envelope	envelope	NOUN
ejde-887	297	37	.	.	PUNCT
ejde-887	298	1	lsol	lsol	NOUN
ejde-887	298	2	=	=	NUM
ejde-887	298	3	5	5	NUM
ejde-887	298	4	−	−	NUM
ejde-887	298	5	20	20	NUM
ejde-887	298	6	and	and	CCONJ
ejde-887	298	7	the	the	DET
ejde-887	298	8	wavelength	wavelength	NOUN
ejde-887	298	9	of	of	ADP
ejde-887	298	10	the	the	DET
ejde-887	298	11	perturbation	perturbation	NOUN
ejde-887	298	12	coefficient	coefficient	NOUN
ejde-887	298	13	q(x	q(x	NOUN
ejde-887	298	14	)	)	PUNCT
ejde-887	298	15	.	.	PUNCT
ejde-887	299	1	in	in	ADP
ejde-887	299	2	general	general	ADJ
ejde-887	299	3	,	,	PUNCT
ejde-887	299	4	for	for	ADP
ejde-887	299	5	small	small	ADJ
ejde-887	299	6	variations	variation	NOUN
ejde-887	299	7	of	of	ADP
ejde-887	299	8	the	the	DET
ejde-887	299	9	variable	variable	ADJ
ejde-887	299	10	coefficient	coefficient	NOUN
ejde-887	299	11	around	around	ADP
ejde-887	299	12	1	1	NUM
ejde-887	299	13	,	,	PUNCT
ejde-887	299	14	for	for	ADP
ejde-887	299	15	relatively	relatively	ADV
ejde-887	299	16	small	small	ADJ
ejde-887	299	17	initial	initial	ADJ
ejde-887	299	18	soliton	soliton	NOUN
ejde-887	299	19	amplitudes	amplitude	NOUN
ejde-887	299	20	asol	asol	NOUN
ejde-887	299	21	=	=	PUNCT
ejde-887	299	22	0.010−	0.010−	PROPN
ejde-887	299	23	0.016	0.016	NUM
ejde-887	299	24	representing	represent	VERB
ejde-887	299	25	nonlinearity	nonlinearity	NOUN
ejde-887	299	26	coefficient	coefficient	NOUN
ejde-887	299	27	α	α	NOUN
ejde-887	299	28	=	=	NOUN
ejde-887	299	29	0.1−0.2	0.1−0.2	NOUN
ejde-887	299	30	,	,	PUNCT
ejde-887	299	31	and	and	CCONJ
ejde-887	299	32	for	for	ADP
ejde-887	299	33	relative	relative	ADJ
ejde-887	299	34	small	small	ADJ
ejde-887	299	35	values	value	NOUN
ejde-887	299	36	for	for	ADP
ejde-887	299	37	the	the	DET
ejde-887	299	38	dispersion	dispersion	NOUN
ejde-887	299	39	coefficient	coefficient	NOUN
ejde-887	299	40	β	β	X
ejde-887	299	41	=	=	SYM
ejde-887	299	42	0.5	0.5	NUM
ejde-887	299	43	,	,	PUNCT
ejde-887	299	44	the	the	DET
ejde-887	299	45	initial	initial	ADJ
ejde-887	299	46	soliton	soliton	NOUN
ejde-887	299	47	propagates	propagate	VERB
ejde-887	299	48	with	with	ADP
ejde-887	299	49	uniform	uniform	ADJ
ejde-887	299	50	group	group	NOUN
ejde-887	299	51	velocity	velocity	NOUN
ejde-887	299	52	and	and	CCONJ
ejde-887	299	53	generates	generate	VERB
ejde-887	299	54	small	small	ADJ
ejde-887	299	55	amplitude	amplitude	NOUN
ejde-887	299	56	secondary	secondary	ADJ
ejde-887	299	57	solitons	soliton	NOUN
ejde-887	299	58	in	in	ADP
ejde-887	299	59	its	its	PRON
ejde-887	299	60	trailing	trailing	NOUN
ejde-887	299	61	region	region	NOUN
ejde-887	299	62	.	.	PUNCT
ejde-887	300	1	also	also	ADV
ejde-887	300	2	the	the	DET
ejde-887	300	3	solitary	solitary	ADJ
ejde-887	300	4	wave	wave	NOUN
ejde-887	300	5	amplitude	amplitude	NOUN
ejde-887	300	6	has	have	VERB
ejde-887	300	7	some	some	DET
ejde-887	300	8	oscillations	oscillation	NOUN
ejde-887	300	9	during	during	ADP
ejde-887	300	10	its	its	PRON
ejde-887	300	11	propagation	propagation	NOUN
ejde-887	300	12	,	,	PUNCT
ejde-887	300	13	probably	probably	ADV
ejde-887	300	14	because	because	SCONJ
ejde-887	300	15	of	of	ADP
ejde-887	300	16	a	a	DET
ejde-887	300	17	residual	residual	ADJ
ejde-887	300	18	effect	effect	NOUN
ejde-887	300	19	of	of	ADP
ejde-887	300	20	the	the	DET
ejde-887	300	21	property	property	NOUN
ejde-887	300	22	of	of	ADP
ejde-887	300	23	area	area	NOUN
ejde-887	300	24	conservation	conservation	NOUN
ejde-887	300	25	law	law	NOUN
ejde-887	300	26	for	for	ADP
ejde-887	300	27	the	the	DET
ejde-887	300	28	boussinesq	boussinesq	PROPN
ejde-887	300	29	nonlinear	nonlinear	PROPN
ejde-887	300	30	autonomous	autonomous	ADJ
ejde-887	300	31	equations	equation	NOUN
ejde-887	300	32	.	.	PUNCT
ejde-887	301	1	the	the	DET
ejde-887	301	2	occurrence	occurrence	NOUN
ejde-887	301	3	of	of	ADP
ejde-887	301	4	the	the	DET
ejde-887	301	5	secondary	secondary	ADJ
ejde-887	301	6	multi	multi	NOUN
ejde-887	301	7	-	-	NOUN
ejde-887	301	8	solitons	soliton	NOUN
ejde-887	301	9	becomes	become	VERB
ejde-887	301	10	more	more	ADV
ejde-887	301	11	intense	intense	ADJ
ejde-887	301	12	when	when	SCONJ
ejde-887	301	13	the	the	DET
ejde-887	301	14	amplitude	amplitude	NOUN
ejde-887	301	15	of	of	ADP
ejde-887	301	16	oscillation	oscillation	NOUN
ejde-887	301	17	of	of	ADP
ejde-887	301	18	the	the	DET
ejde-887	301	19	variable	variable	ADJ
ejde-887	301	20	coefficient	coefficient	NOUN
ejde-887	301	21	increases	increase	VERB
ejde-887	301	22	towards	towards	ADP
ejde-887	301	23	ϵ	ϵ	NOUN
ejde-887	301	24	=	=	SYM
ejde-887	301	25	0.3	0.3	NUM
ejde-887	301	26	.	.	PUNCT
ejde-887	302	1	for	for	ADP
ejde-887	302	2	larger	large	ADJ
ejde-887	302	3	soliton	soliton	NOUN
ejde-887	302	4	amplitude	amplitude	NOUN
ejde-887	302	5	asol	asol	NOUN
ejde-887	302	6	>	>	X
ejde-887	302	7	0.015	0.015	NUM
ejde-887	302	8	(	(	PUNCT
ejde-887	302	9	i.e.	i.e.	X
ejde-887	302	10	α	α	X
ejde-887	302	11	>	>	X
ejde-887	302	12	0.55	0.55	NUM
ejde-887	302	13	,	,	PUNCT
ejde-887	302	14	larger	large	ADJ
ejde-887	302	15	dispersion	dispersion	NOUN
ejde-887	302	16	coefficient	coefficient	NOUN
ejde-887	302	17	β	β	VERB
ejde-887	302	18	>	>	X
ejde-887	302	19	0.6	0.6	NUM
ejde-887	302	20	and	and	CCONJ
ejde-887	302	21	for	for	ADP
ejde-887	302	22	larger	large	ADJ
ejde-887	302	23	variation	variation	NOUN
ejde-887	302	24	of	of	ADP
ejde-887	302	25	the	the	DET
ejde-887	302	26	perturbation	perturbation	NOUN
ejde-887	302	27	coefficient	coefficient	NOUN
ejde-887	302	28	ϵ	ϵ	X
ejde-887	302	29	>	>	X
ejde-887	302	30	0.2	0.2	NUM
ejde-887	302	31	,	,	PUNCT
ejde-887	302	32	we	we	PRON
ejde-887	302	33	ejde-202x	ejde-202x	NOUN
ejde-887	302	34	/	/	SYM
ejde-887	302	35	conf/27	conf/27	NOUN
ejde-887	302	36	boussinesq	boussinesq	ADJ
ejde-887	302	37	equations	equation	NOUN
ejde-887	302	38	41	41	NUM
ejde-887	302	39	figure	figure	NOUN
ejde-887	302	40	6	6	NUM
ejde-887	302	41	.	.	PUNCT
ejde-887	302	42	numerical	numerical	ADJ
ejde-887	302	43	solution	solution	NOUN
ejde-887	302	44	z(x	z(x	PROPN
ejde-887	302	45	,	,	PUNCT
ejde-887	302	46	t	t	PROPN
ejde-887	302	47	)	)	PUNCT
ejde-887	302	48	for	for	ADP
ejde-887	302	49	equre	equre	NOUN
ejde-887	302	50	(	(	PUNCT
ejde-887	302	51	2.1	2.1	NUM
ejde-887	302	52	)	)	PUNCT
ejde-887	302	53	for	for	ADP
ejde-887	302	54	α	α	NOUN
ejde-887	302	55	=	=	SYM
ejde-887	302	56	0.65	0.65	NUM
ejde-887	302	57	,	,	PUNCT
ejde-887	302	58	β	β	X
ejde-887	302	59	=	=	NOUN
ejde-887	302	60	0.7	0.7	NUM
ejde-887	302	61	at	at	ADP
ejde-887	302	62	five	five	NUM
ejde-887	302	63	moments	moment	NOUN
ejde-887	302	64	of	of	ADP
ejde-887	302	65	time	time	NOUN
ejde-887	302	66	.	.	PUNCT
ejde-887	303	1	the	the	DET
ejde-887	303	2	initial	initial	ADJ
ejde-887	303	3	condition	condition	NOUN
ejde-887	303	4	is	be	AUX
ejde-887	303	5	the	the	DET
ejde-887	303	6	one	one	NUM
ejde-887	303	7	-	-	PUNCT
ejde-887	303	8	soliton	soliton	NOUN
ejde-887	303	9	solution	solution	NOUN
ejde-887	303	10	with	with	ADP
ejde-887	303	11	asol	asol	NOUN
ejde-887	303	12	=	=	SYM
ejde-887	303	13	0.016	0.016	NUM
ejde-887	303	14	,	,	PUNCT
ejde-887	303	15	lsol	lsol	NOUN
ejde-887	303	16	=	=	SYM
ejde-887	303	17	30	30	NUM
ejde-887	303	18	.	.	PUNCT
ejde-887	304	1	the	the	DET
ejde-887	304	2	variable	variable	ADJ
ejde-887	304	3	coefficient	coefficient	NOUN
ejde-887	304	4	is	be	AUX
ejde-887	304	5	q	q	NOUN
ejde-887	304	6	=	=	SYM
ejde-887	304	7	1	1	NUM
ejde-887	304	8	+	+	CCONJ
ejde-887	304	9	ϵ	ϵ	DET
ejde-887	304	10	sin(2x	sin(2x	PROPN
ejde-887	304	11	)	)	PUNCT
ejde-887	304	12	with	with	ADP
ejde-887	304	13	amplitude	amplitude	NOUN
ejde-887	304	14	ϵ	ϵ	X
ejde-887	304	15	=	=	SYM
ejde-887	304	16	0.2	0.2	NUM
ejde-887	304	17	.	.	PUNCT
ejde-887	305	1	the	the	DET
ejde-887	305	2	larger	large	ADJ
ejde-887	305	3	values	value	NOUN
ejde-887	305	4	for	for	ADP
ejde-887	305	5	the	the	DET
ejde-887	305	6	coefficient	coefficient	NOUN
ejde-887	305	7	of	of	ADP
ejde-887	305	8	nonlinearity	nonlinearity	NOUN
ejde-887	305	9	and	and	CCONJ
ejde-887	305	10	dispersion	dispersion	NOUN
ejde-887	305	11	induce	induce	VERB
ejde-887	305	12	higher	high	ADJ
ejde-887	305	13	frequency	frequency	NOUN
ejde-887	305	14	and	and	CCONJ
ejde-887	305	15	amplitude	amplitude	NOUN
ejde-887	305	16	perturbations	perturbation	NOUN
ejde-887	305	17	in	in	ADP
ejde-887	305	18	the	the	DET
ejde-887	305	19	solution	solution	NOUN
ejde-887	305	20	envelope	envelope	NOUN
ejde-887	305	21	,	,	PUNCT
ejde-887	305	22	while	while	SCONJ
ejde-887	305	23	the	the	DET
ejde-887	305	24	envelope	envelope	NOUN
ejde-887	305	25	keeps	keep	VERB
ejde-887	305	26	traveling	travel	VERB
ejde-887	305	27	with	with	ADP
ejde-887	305	28	the	the	DET
ejde-887	305	29	same	same	ADJ
ejde-887	305	30	group	group	NOUN
ejde-887	305	31	velocity	velocity	NOUN
ejde-887	305	32	and	and	CCONJ
ejde-887	305	33	the	the	DET
ejde-887	305	34	same	same	ADJ
ejde-887	305	35	mean	mean	NOUN
ejde-887	305	36	shape	shape	NOUN
ejde-887	305	37	.	.	PUNCT
ejde-887	306	1	figure	figure	NOUN
ejde-887	306	2	7	7	NUM
ejde-887	306	3	.	.	PUNCT
ejde-887	306	4	numerical	numerical	ADJ
ejde-887	306	5	solution	solution	NOUN
ejde-887	306	6	z(x	z(x	PROPN
ejde-887	306	7	,	,	PUNCT
ejde-887	306	8	t	t	PROPN
ejde-887	306	9	)	)	PUNCT
ejde-887	306	10	starting	start	VERB
ejde-887	306	11	from	from	ADP
ejde-887	306	12	a	a	DET
ejde-887	306	13	larger	large	ADJ
ejde-887	306	14	amplitude	amplitude	NOUN
ejde-887	306	15	one	one	NUM
ejde-887	306	16	-	-	PUNCT
ejde-887	306	17	soliton	soliton	NOUN
ejde-887	306	18	with	with	ADP
ejde-887	306	19	asol	asol	NOUN
ejde-887	306	20	=	=	SYM
ejde-887	306	21	0.055	0.055	NUM
ejde-887	306	22	,	,	PUNCT
ejde-887	306	23	lsol	lsol	NOUN
ejde-887	306	24	=	=	SYM
ejde-887	306	25	30	30	NUM
ejde-887	306	26	with	with	ADP
ejde-887	306	27	higher	high	ADJ
ejde-887	306	28	nonlinearity	nonlinearity	NOUN
ejde-887	306	29	and	and	CCONJ
ejde-887	306	30	dispersion	dispersion	NOUN
ejde-887	306	31	parameters	parameter	NOUN
ejde-887	306	32	α	α	X
ejde-887	306	33	=	=	PUNCT
ejde-887	306	34	0.8	0.8	NUM
ejde-887	306	35	,	,	PUNCT
ejde-887	306	36	β	β	X
ejde-887	306	37	=	=	NOUN
ejde-887	306	38	0.7	0.7	NUM
ejde-887	306	39	.	.	PUNCT
ejde-887	307	1	we	we	PRON
ejde-887	307	2	also	also	ADV
ejde-887	307	3	have	have	VERB
ejde-887	307	4	a	a	DET
ejde-887	307	5	larger	large	ADJ
ejde-887	307	6	amplitude	amplitude	NOUN
ejde-887	307	7	perturbation	perturbation	NOUN
ejde-887	307	8	q(x	q(x	NOUN
ejde-887	307	9	)	)	PUNCT
ejde-887	307	10	=	=	PUNCT
ejde-887	308	1	1	1	NUM
ejde-887	308	2	+	+	CCONJ
ejde-887	308	3	ϵ	ϵ	PRON
ejde-887	308	4	sin(2x	sin(2x	PROPN
ejde-887	308	5	)	)	PUNCT
ejde-887	308	6	with	with	ADP
ejde-887	308	7	ϵ	ϵ	PROPN
ejde-887	308	8	=	=	SYM
ejde-887	308	9	0.3	0.3	NUM
ejde-887	308	10	.	.	PUNCT
ejde-887	309	1	the	the	DET
ejde-887	309	2	envelope	envelope	NOUN
ejde-887	309	3	of	of	ADP
ejde-887	309	4	the	the	DET
ejde-887	309	5	emerging	emerge	VERB
ejde-887	309	6	solution	solution	NOUN
ejde-887	309	7	develops	develop	VERB
ejde-887	309	8	a	a	DET
ejde-887	309	9	very	very	ADV
ejde-887	309	10	dense	dense	ADJ
ejde-887	309	11	modulation	modulation	NOUN
ejde-887	309	12	by	by	ADP
ejde-887	309	13	oscillations	oscillation	NOUN
ejde-887	309	14	of	of	ADP
ejde-887	309	15	higher	high	ADJ
ejde-887	309	16	amplitude	amplitude	NOUN
ejde-887	309	17	.	.	PUNCT
ejde-887	310	1	we	we	PRON
ejde-887	310	2	assume	assume	VERB
ejde-887	310	3	a	a	DET
ejde-887	310	4	part	part	NOUN
ejde-887	310	5	of	of	ADP
ejde-887	310	6	these	these	DET
ejde-887	310	7	larger	large	ADJ
ejde-887	310	8	perturbations	perturbation	NOUN
ejde-887	310	9	in	in	ADP
ejde-887	310	10	the	the	DET
ejde-887	310	11	radiation	radiation	NOUN
ejde-887	310	12	tail	tail	NOUN
ejde-887	310	13	is	be	AUX
ejde-887	310	14	generated	generate	VERB
ejde-887	310	15	by	by	ADP
ejde-887	310	16	numerical	numerical	ADJ
ejde-887	310	17	instability	instability	NOUN
ejde-887	310	18	.	.	PUNCT
ejde-887	311	1	there	there	PRON
ejde-887	311	2	are	be	VERB
ejde-887	311	3	no	no	DET
ejde-887	311	4	secondary	secondary	ADJ
ejde-887	311	5	multi	multi	NOUN
ejde-887	311	6	-	-	NOUN
ejde-887	311	7	solitons	soliton	NOUN
ejde-887	311	8	for	for	ADP
ejde-887	311	9	this	this	DET
ejde-887	311	10	configuration	configuration	NOUN
ejde-887	311	11	,	,	PUNCT
ejde-887	311	12	while	while	SCONJ
ejde-887	311	13	the	the	DET
ejde-887	311	14	envelope	envelope	NOUN
ejde-887	311	15	of	of	ADP
ejde-887	311	16	the	the	DET
ejde-887	311	17	solution	solution	NOUN
ejde-887	311	18	maintains	maintain	VERB
ejde-887	311	19	the	the	DET
ejde-887	311	20	same	same	ADJ
ejde-887	311	21	mean	mean	NOUN
ejde-887	311	22	shape	shape	NOUN
ejde-887	311	23	and	and	CCONJ
ejde-887	311	24	group	group	NOUN
ejde-887	311	25	velocity	velocity	NOUN
ejde-887	311	26	after	after	ADP
ejde-887	311	27	10	10	NUM
ejde-887	311	28	seconds	second	NOUN
ejde-887	311	29	.	.	PUNCT
ejde-887	312	1	obtain	obtain	VERB
ejde-887	312	2	stronger	strong	ADJ
ejde-887	312	3	perturbations	perturbation	NOUN
ejde-887	312	4	of	of	ADP
ejde-887	312	5	the	the	DET
ejde-887	312	6	solitary	solitary	ADJ
ejde-887	312	7	wave	wave	NOUN
ejde-887	312	8	,	,	PUNCT
ejde-887	312	9	as	as	SCONJ
ejde-887	312	10	expected	expect	VERB
ejde-887	312	11	.	.	PUNCT
ejde-887	313	1	in	in	ADP
ejde-887	313	2	these	these	DET
ejde-887	313	3	situations	situation	NOUN
ejde-887	313	4	,	,	PUNCT
ejde-887	313	5	the	the	DET
ejde-887	313	6	secondary	secondary	ADJ
ejde-887	313	7	multi	multi	NOUN
ejde-887	313	8	-	-	NOUN
ejde-887	313	9	solitons	soliton	NOUN
ejde-887	313	10	have	have	VERB
ejde-887	313	11	larger	large	ADJ
ejde-887	313	12	phase	phase	NOUN
ejde-887	313	13	velocity	velocity	NOUN
ejde-887	313	14	and	and	CCONJ
ejde-887	313	15	occur	occur	VERB
ejde-887	313	16	even	even	ADV
ejde-887	313	17	in	in	ADP
ejde-887	313	18	the	the	DET
ejde-887	313	19	front	front	ADJ
ejde-887	313	20	42	42	NUM
ejde-887	313	21	a.	a.	NOUN
ejde-887	313	22	ludu	ludu	NOUN
ejde-887	313	23	,	,	PUNCT
ejde-887	313	24	h.	h.	PROPN
ejde-887	313	25	khanal	khanal	NOUN
ejde-887	313	26	,	,	PUNCT
ejde-887	313	27	a.	a.	PROPN
ejde-887	313	28	s.	s.	PROPN
ejde-887	313	29	carstea	carstea	PROPN
ejde-887	313	30	ejde-2022	ejde-2022	PROPN
ejde-887	313	31	/	/	SYM
ejde-887	313	32	conf/27	conf/27	NOUN
ejde-887	313	33	figure	figure	NOUN
ejde-887	313	34	8	8	NUM
ejde-887	313	35	.	.	PUNCT
ejde-887	314	1	numerical	numerical	ADJ
ejde-887	314	2	solution	solution	NOUN
ejde-887	314	3	z(x	z(x	PROPN
ejde-887	314	4	,	,	PUNCT
ejde-887	314	5	t	t	PROPN
ejde-887	314	6	)	)	PUNCT
ejde-887	314	7	for	for	ADP
ejde-887	314	8	α	α	NOUN
ejde-887	314	9	=	=	SYM
ejde-887	314	10	0.65	0.65	NUM
ejde-887	314	11	,	,	PUNCT
ejde-887	314	12	β	β	X
ejde-887	314	13	=	=	NOUN
ejde-887	314	14	0.7	0.7	NUM
ejde-887	314	15	,	,	PUNCT
ejde-887	314	16	with	with	ADP
ejde-887	314	17	the	the	DET
ejde-887	314	18	same	same	ADJ
ejde-887	314	19	function	function	NOUN
ejde-887	314	20	for	for	ADP
ejde-887	314	21	the	the	DET
ejde-887	314	22	coefficients	coefficient	NOUN
ejde-887	314	23	q(x	q(x	NOUN
ejde-887	314	24	)	)	PUNCT
ejde-887	314	25	=	=	PUNCT
ejde-887	315	1	1	1	NUM
ejde-887	315	2	+	+	NUM
ejde-887	315	3	0.3	0.3	NUM
ejde-887	315	4	sin(2x	sin(2x	VERB
ejde-887	315	5	)	)	PUNCT
ejde-887	315	6	,	,	PUNCT
ejde-887	315	7	this	this	DET
ejde-887	315	8	time	time	NOUN
ejde-887	315	9	the	the	DET
ejde-887	315	10	initial	initial	ADJ
ejde-887	315	11	condition	condition	NOUN
ejde-887	315	12	being	be	AUX
ejde-887	315	13	a	a	DET
ejde-887	315	14	narrower	narrow	ADJ
ejde-887	315	15	soliton	soliton	NOUN
ejde-887	315	16	solution	solution	NOUN
ejde-887	315	17	with	with	ADP
ejde-887	315	18	lsol	lsol	NOUN
ejde-887	315	19	=	=	SYM
ejde-887	315	20	5	5	NUM
ejde-887	315	21	,	,	PUNCT
ejde-887	315	22	and	and	CCONJ
ejde-887	315	23	the	the	DET
ejde-887	315	24	same	same	ADJ
ejde-887	315	25	large	large	ADJ
ejde-887	315	26	amplitude	amplitude	NOUN
ejde-887	315	27	asol	asol	NOUN
ejde-887	315	28	=	=	PUNCT
ejde-887	315	29	0.55	0.55	NUM
ejde-887	315	30	.	.	PUNCT
ejde-887	316	1	this	this	DET
ejde-887	316	2	solution	solution	NOUN
ejde-887	316	3	becomes	become	VERB
ejde-887	316	4	unstable	unstable	ADJ
ejde-887	316	5	very	very	ADV
ejde-887	316	6	fast	fast	ADV
ejde-887	316	7	.	.	PUNCT
ejde-887	317	1	the	the	DET
ejde-887	317	2	initial	initial	ADJ
ejde-887	317	3	soliton	soliton	NOUN
ejde-887	317	4	decays	decay	VERB
ejde-887	317	5	quickly	quickly	ADV
ejde-887	317	6	in	in	ADP
ejde-887	317	7	amplitude	amplitude	NOUN
ejde-887	317	8	,	,	PUNCT
ejde-887	317	9	it	it	PRON
ejde-887	317	10	becomes	become	VERB
ejde-887	317	11	slightly	slightly	ADV
ejde-887	317	12	wider	wide	ADJ
ejde-887	317	13	,	,	PUNCT
ejde-887	317	14	and	and	CCONJ
ejde-887	317	15	generates	generate	VERB
ejde-887	317	16	high	high	ADJ
ejde-887	317	17	frequency	frequency	NOUN
ejde-887	317	18	oscillations	oscillation	NOUN
ejde-887	317	19	in	in	ADP
ejde-887	317	20	the	the	DET
ejde-887	317	21	tail	tail	NOUN
ejde-887	317	22	.	.	PUNCT
ejde-887	318	1	of	of	ADP
ejde-887	318	2	the	the	DET
ejde-887	318	3	original	original	ADJ
ejde-887	318	4	solitary	solitary	ADJ
ejde-887	318	5	wave	wave	NOUN
ejde-887	318	6	,	,	PUNCT
ejde-887	318	7	and	and	CCONJ
ejde-887	318	8	high	high	ADJ
ejde-887	318	9	frequency	frequency	NOUN
ejde-887	318	10	dispersive	dispersive	NOUN
ejde-887	318	11	oscillations	oscillation	NOUN
ejde-887	318	12	grow	grow	VERB
ejde-887	318	13	in	in	ADP
ejde-887	318	14	the	the	DET
ejde-887	318	15	radiation	radiation	NOUN
ejde-887	318	16	tail	tail	NOUN
ejde-887	318	17	.	.	PUNCT
ejde-887	319	1	when	when	SCONJ
ejde-887	319	2	α	α	X
ejde-887	319	3	,	,	PUNCT
ejde-887	319	4	β	β	X
ejde-887	319	5	and	and	CCONJ
ejde-887	319	6	ϵ	ϵ	PROPN
ejde-887	319	7	exceed	exceed	VERB
ejde-887	319	8	some	some	DET
ejde-887	319	9	critical	critical	ADJ
ejde-887	319	10	values	value	NOUN
ejde-887	319	11	,	,	PUNCT
ejde-887	319	12	the	the	DET
ejde-887	319	13	solitary	solitary	ADJ
ejde-887	319	14	wave	wave	NOUN
ejde-887	319	15	becomes	become	VERB
ejde-887	319	16	unstable	unstable	ADJ
ejde-887	319	17	,	,	PUNCT
ejde-887	319	18	breaks	break	VERB
ejde-887	319	19	into	into	ADP
ejde-887	319	20	high	high	ADJ
ejde-887	319	21	frequency	frequency	NOUN
ejde-887	319	22	radiation	radiation	NOUN
ejde-887	319	23	waves	wave	NOUN
ejde-887	319	24	,	,	PUNCT
ejde-887	319	25	and	and	CCONJ
ejde-887	319	26	quickly	quickly	ADV
ejde-887	319	27	decreases	decrease	VERB
ejde-887	319	28	its	its	PRON
ejde-887	319	29	amplitude	amplitude	NOUN
ejde-887	319	30	.	.	PUNCT
ejde-887	320	1	in	in	ADP
ejde-887	320	2	figures	figure	NOUN
ejde-887	320	3	1	1	NUM
ejde-887	320	4	-	-	SYM
ejde-887	320	5	2	2	NUM
ejde-887	320	6	we	we	PRON
ejde-887	320	7	present	present	VERB
ejde-887	320	8	the	the	DET
ejde-887	320	9	time	time	NOUN
ejde-887	320	10	evolution	evolution	NOUN
ejde-887	320	11	of	of	ADP
ejde-887	320	12	the	the	DET
ejde-887	320	13	numerical	numerical	ADJ
ejde-887	320	14	solutions	solution	NOUN
ejde-887	320	15	z(x	z(x	PROPN
ejde-887	320	16	,	,	PUNCT
ejde-887	320	17	t	t	PROPN
ejde-887	320	18	)	)	PUNCT
ejde-887	320	19	and	and	CCONJ
ejde-887	320	20	u(x	u(x	PROPN
ejde-887	320	21	,	,	PUNCT
ejde-887	320	22	t	t	PROPN
ejde-887	320	23	)	)	PUNCT
ejde-887	320	24	,	,	PUNCT
ejde-887	320	25	respectively	respectively	ADV
ejde-887	320	26	for	for	ADP
ejde-887	320	27	coefficient	coefficient	ADJ
ejde-887	320	28	oscillations	oscillation	NOUN
ejde-887	320	29	with	with	ADP
ejde-887	320	30	amplitude	amplitude	NOUN
ejde-887	320	31	ϵ	ϵ	NOUN
ejde-887	320	32	=	=	SYM
ejde-887	320	33	0.1	0.1	NUM
ejde-887	320	34	.	.	PUNCT
ejde-887	321	1	we	we	PRON
ejde-887	321	2	notice	notice	VERB
ejde-887	321	3	that	that	SCONJ
ejde-887	321	4	the	the	DET
ejde-887	321	5	envelope	envelope	NOUN
ejde-887	321	6	of	of	ADP
ejde-887	321	7	the	the	DET
ejde-887	321	8	initial	initial	ADJ
ejde-887	321	9	boussinesq	boussinesq	ADJ
ejde-887	321	10	soliton	soliton	NOUN
ejde-887	321	11	(	(	PUNCT
ejde-887	321	12	black	black	ADJ
ejde-887	321	13	curve	curve	NOUN
ejde-887	321	14	)	)	PUNCT
ejde-887	321	15	travels	travel	VERB
ejde-887	321	16	uniformly	uniformly	ADV
ejde-887	321	17	,	,	PUNCT
ejde-887	321	18	and	and	CCONJ
ejde-887	321	19	its	its	PRON
ejde-887	321	20	trailing	trailing	NOUN
ejde-887	321	21	slope	slope	NOUN
ejde-887	321	22	is	be	AUX
ejde-887	321	23	modulated	modulate	VERB
ejde-887	321	24	by	by	ADP
ejde-887	321	25	the	the	DET
ejde-887	321	26	generation	generation	NOUN
ejde-887	321	27	of	of	ADP
ejde-887	321	28	secondary	secondary	ADJ
ejde-887	321	29	small	small	ADJ
ejde-887	321	30	amplitude	amplitude	NOUN
ejde-887	321	31	multi	multi	ADJ
ejde-887	321	32	-	-	ADJ
ejde-887	321	33	soliton	soliton	ADJ
ejde-887	321	34	solutions	solution	NOUN
ejde-887	321	35	with	with	ADP
ejde-887	321	36	half	half	ADJ
ejde-887	321	37	-	-	PUNCT
ejde-887	321	38	width	width	NOUN
ejde-887	321	39	close	close	ADV
ejde-887	321	40	to	to	ADP
ejde-887	321	41	the	the	DET
ejde-887	321	42	wavelength	wavelength	NOUN
ejde-887	321	43	as	as	ADP
ejde-887	321	44	the	the	DET
ejde-887	321	45	periodic	periodic	ADJ
ejde-887	321	46	coefficient	coefficient	NOUN
ejde-887	321	47	q(x	q(x	NOUN
ejde-887	321	48	)	)	PUNCT
ejde-887	321	49	.	.	PUNCT
ejde-887	322	1	during	during	ADP
ejde-887	322	2	the	the	DET
ejde-887	322	3	evolution	evolution	NOUN
ejde-887	322	4	t	t	PROPN
ejde-887	322	5	>	>	X
ejde-887	322	6	0	0	PUNCT
ejde-887	322	7	the	the	DET
ejde-887	322	8	periodic	periodic	ADJ
ejde-887	322	9	modulation	modulation	NOUN
ejde-887	322	10	decouples	decouple	NOUN
ejde-887	322	11	from	from	ADP
ejde-887	322	12	the	the	DET
ejde-887	322	13	solitary	solitary	ADJ
ejde-887	322	14	wave	wave	NOUN
ejde-887	322	15	and	and	CCONJ
ejde-887	322	16	degenerates	degenerate	NOUN
ejde-887	322	17	into	into	ADP
ejde-887	322	18	a	a	DET
ejde-887	322	19	radiation	radiation	NOUN
ejde-887	322	20	tail	tail	NOUN
ejde-887	322	21	lagging	lag	VERB
ejde-887	322	22	the	the	DET
ejde-887	322	23	solitary	solitary	ADJ
ejde-887	322	24	wave	wave	NOUN
ejde-887	322	25	.	.	PUNCT
ejde-887	323	1	the	the	DET
ejde-887	323	2	modulation	modulation	NOUN
ejde-887	323	3	effect	effect	NOUN
ejde-887	323	4	of	of	ADP
ejde-887	323	5	secondary	secondary	ADJ
ejde-887	323	6	solitons	soliton	NOUN
ejde-887	323	7	is	be	AUX
ejde-887	323	8	more	more	ADV
ejde-887	323	9	pronounced	pronounce	VERB
ejde-887	323	10	in	in	ADP
ejde-887	323	11	the	the	DET
ejde-887	323	12	u(x	u(x	PROPN
ejde-887	323	13	,	,	PUNCT
ejde-887	323	14	t	t	NOUN
ejde-887	323	15	)	)	PUNCT
ejde-887	323	16	solution	solution	NOUN
ejde-887	323	17	.	.	PUNCT
ejde-887	324	1	comparing	compare	VERB
ejde-887	324	2	figures	figure	NOUN
ejde-887	324	3	1	1	NUM
ejde-887	324	4	-	-	SYM
ejde-887	324	5	2	2	NUM
ejde-887	324	6	with	with	ADP
ejde-887	324	7	figures	figure	NOUN
ejde-887	324	8	3	3	NUM
ejde-887	324	9	-	-	SYM
ejde-887	324	10	4	4	NUM
ejde-887	324	11	we	we	PRON
ejde-887	324	12	observe	observe	VERB
ejde-887	324	13	that	that	SCONJ
ejde-887	324	14	the	the	DET
ejde-887	324	15	strength	strength	NOUN
ejde-887	324	16	of	of	ADP
ejde-887	324	17	the	the	DET
ejde-887	324	18	modulation	modulation	NOUN
ejde-887	324	19	is	be	AUX
ejde-887	324	20	proportional	proportional	ADJ
ejde-887	324	21	to	to	ADP
ejde-887	324	22	the	the	DET
ejde-887	324	23	amplitude	amplitude	NOUN
ejde-887	324	24	ϵ	ϵ	X
ejde-887	324	25	of	of	ADP
ejde-887	324	26	the	the	DET
ejde-887	324	27	variable	variable	ADJ
ejde-887	324	28	coefficient	coefficient	NOUN
ejde-887	324	29	:	:	PUNCT
ejde-887	324	30	for	for	SCONJ
ejde-887	324	31	ϵ	ϵ	NOUN
ejde-887	324	32	=	=	SYM
ejde-887	324	33	0.1	0.1	NUM
ejde-887	324	34	the	the	DET
ejde-887	324	35	perturbation	perturbation	NOUN
ejde-887	324	36	effect	effect	NOUN
ejde-887	324	37	is	be	AUX
ejde-887	324	38	weaker	weak	ADJ
ejde-887	324	39	than	than	ADP
ejde-887	324	40	in	in	ADP
ejde-887	324	41	the	the	DET
ejde-887	324	42	case	case	NOUN
ejde-887	324	43	of	of	ADP
ejde-887	324	44	larger	large	ADJ
ejde-887	324	45	coefficient	coefficient	NOUN
ejde-887	324	46	ϵ	ϵ	X
ejde-887	324	47	=	=	NOUN
ejde-887	324	48	0.2	0.2	NUM
ejde-887	324	49	.	.	PUNCT
ejde-887	325	1	the	the	DET
ejde-887	325	2	soliton	soliton	NOUN
ejde-887	325	3	velocity	velocity	NOUN
ejde-887	325	4	,	,	PUNCT
ejde-887	325	5	however	however	ADV
ejde-887	325	6	is	be	AUX
ejde-887	325	7	not	not	PART
ejde-887	325	8	affected	affect	VERB
ejde-887	325	9	by	by	ADP
ejde-887	325	10	the	the	DET
ejde-887	325	11	amplitude	amplitude	NOUN
ejde-887	325	12	of	of	ADP
ejde-887	325	13	the	the	DET
ejde-887	325	14	variable	variable	ADJ
ejde-887	325	15	coefficient	coefficient	NOUN
ejde-887	325	16	.	.	PUNCT
ejde-887	326	1	the	the	DET
ejde-887	326	2	time	time	NOUN
ejde-887	326	3	evolution	evolution	NOUN
ejde-887	326	4	of	of	ADP
ejde-887	326	5	the	the	DET
ejde-887	326	6	amplitude	amplitude	NOUN
ejde-887	326	7	of	of	ADP
ejde-887	326	8	the	the	DET
ejde-887	326	9	soliton	soliton	NOUN
ejde-887	326	10	shows	show	VERB
ejde-887	326	11	the	the	DET
ejde-887	326	12	reminiscence	reminiscence	NOUN
ejde-887	326	13	of	of	ADP
ejde-887	326	14	the	the	DET
ejde-887	326	15	area	area	NOUN
ejde-887	326	16	conservation	conservation	NOUN
ejde-887	326	17	law	law	NOUN
ejde-887	326	18	for	for	ADP
ejde-887	326	19	the	the	DET
ejde-887	326	20	integrable	integrable	ADJ
ejde-887	326	21	autonomous	autonomous	ADJ
ejde-887	326	22	boussinesq	boussinesq	NOUN
ejde-887	326	23	case	case	NOUN
ejde-887	326	24	.	.	PUNCT
ejde-887	327	1	when	when	SCONJ
ejde-887	327	2	the	the	DET
ejde-887	327	3	perturbation	perturbation	NOUN
ejde-887	327	4	affects	affect	VERB
ejde-887	327	5	the	the	DET
ejde-887	327	6	soliton	soliton	NOUN
ejde-887	327	7	envelope	envelope	NOUN
ejde-887	327	8	,	,	PUNCT
ejde-887	327	9	the	the	DET
ejde-887	327	10	soliton	soliton	NOUN
ejde-887	327	11	amplitude	amplitude	NOUN
ejde-887	327	12	has	have	VERB
ejde-887	327	13	a	a	DET
ejde-887	327	14	slight	slight	ADJ
ejde-887	327	15	increase	increase	NOUN
ejde-887	327	16	to	to	PART
ejde-887	327	17	compensate	compensate	VERB
ejde-887	327	18	for	for	ADP
ejde-887	327	19	the	the	DET
ejde-887	327	20	loss	loss	NOUN
ejde-887	327	21	of	of	ADP
ejde-887	327	22	area	area	NOUN
ejde-887	327	23	.	.	PUNCT
ejde-887	328	1	once	once	SCONJ
ejde-887	328	2	the	the	DET
ejde-887	328	3	perturbation	perturbation	NOUN
ejde-887	328	4	is	be	AUX
ejde-887	328	5	decoupled	decouple	VERB
ejde-887	328	6	from	from	ADP
ejde-887	328	7	the	the	DET
ejde-887	328	8	soliton	soliton	NOUN
ejde-887	328	9	,	,	PUNCT
ejde-887	328	10	its	its	PRON
ejde-887	328	11	amplitude	amplitude	NOUN
ejde-887	328	12	returns	return	NOUN
ejde-887	328	13	to	to	ADP
ejde-887	328	14	the	the	DET
ejde-887	328	15	initial	initial	ADJ
ejde-887	328	16	value	value	NOUN
ejde-887	328	17	.	.	PUNCT
ejde-887	329	1	the	the	DET
ejde-887	329	2	theoretical	theoretical	ADJ
ejde-887	329	3	results	result	NOUN
ejde-887	329	4	presented	present	VERB
ejde-887	329	5	in	in	ADP
ejde-887	329	6	sections	section	NOUN
ejde-887	329	7	4.1	4.1	NUM
ejde-887	329	8	-	-	SYM
ejde-887	329	9	4.2	4.2	NUM
ejde-887	329	10	,	,	PUNCT
ejde-887	329	11	concerning	concern	VERB
ejde-887	329	12	the	the	DET
ejde-887	329	13	non	non	ADJ
ejde-887	329	14	-	-	ADJ
ejde-887	329	15	dispersive	dispersive	ADJ
ejde-887	329	16	character	character	NOUN
ejde-887	329	17	of	of	ADP
ejde-887	329	18	the	the	DET
ejde-887	329	19	non	non	ADJ
ejde-887	329	20	-	-	ADJ
ejde-887	329	21	autonomous	autonomous	ADJ
ejde-887	329	22	nonlinear	nonlinear	ADJ
ejde-887	329	23	system	system	NOUN
ejde-887	329	24	are	be	AUX
ejde-887	329	25	validated	validate	VERB
ejde-887	329	26	by	by	ADP
ejde-887	329	27	the	the	DET
ejde-887	329	28	numerical	numerical	ADJ
ejde-887	329	29	results	result	NOUN
ejde-887	329	30	.	.	PUNCT
ejde-887	330	1	for	for	ADP
ejde-887	330	2	relatively	relatively	ADV
ejde-887	330	3	small	small	ADJ
ejde-887	330	4	perturbation	perturbation	NOUN
ejde-887	330	5	compared	compare	VERB
ejde-887	330	6	to	to	ADP
ejde-887	330	7	the	the	DET
ejde-887	330	8	contribution	contribution	NOUN
ejde-887	330	9	of	of	ADP
ejde-887	330	10	the	the	DET
ejde-887	330	11	nonlinear	nonlinear	ADJ
ejde-887	330	12	terms	term	NOUN
ejde-887	330	13	of	of	ADP
ejde-887	330	14	the	the	DET
ejde-887	330	15	system	system	NOUN
ejde-887	330	16	,	,	PUNCT
ejde-887	330	17	|q	|q	NOUN
ejde-887	330	18	−	−	PROPN
ejde-887	330	19	1|	1|	NUM
ejde-887	330	20	≪	≪	VERB
ejde-887	330	21	α	α	X
ejde-887	330	22	,	,	PUNCT
ejde-887	330	23	figures	figure	NOUN
ejde-887	330	24	1	1	NUM
ejde-887	330	25	-	-	SYM
ejde-887	330	26	4	4	NUM
ejde-887	330	27	,	,	PUNCT
ejde-887	330	28	the	the	DET
ejde-887	330	29	envelope	envelope	NOUN
ejde-887	330	30	z(x	z(x	NOUN
ejde-887	330	31	,	,	PUNCT
ejde-887	330	32	t	t	PROPN
ejde-887	330	33	)	)	PUNCT
ejde-887	330	34	of	of	ADP
ejde-887	330	35	initial	initial	ADJ
ejde-887	330	36	soliton	soliton	NOUN
ejde-887	330	37	is	be	AUX
ejde-887	330	38	quasi	quasi	ADJ
ejde-887	330	39	-	-	ADJ
ejde-887	330	40	stable	stable	ADJ
ejde-887	330	41	in	in	ADP
ejde-887	330	42	time	time	NOUN
ejde-887	330	43	,	,	PUNCT
ejde-887	330	44	experiencing	experience	VERB
ejde-887	330	45	small	small	ADJ
ejde-887	330	46	amplitude	amplitude	NOUN
ejde-887	330	47	oscillations	oscillation	NOUN
ejde-887	330	48	around	around	ADP
ejde-887	330	49	its	its	PRON
ejde-887	330	50	initial	initial	ADJ
ejde-887	330	51	shape	shape	NOUN
ejde-887	330	52	,	,	PUNCT
ejde-887	330	53	while	while	SCONJ
ejde-887	330	54	the	the	DET
ejde-887	330	55	secondary	secondary	ADJ
ejde-887	330	56	multi	multi	ADJ
ejde-887	330	57	-	-	ADJ
ejde-887	330	58	soliton	soliton	NOUN
ejde-887	330	59	generated	generate	VERB
ejde-887	330	60	by	by	ADP
ejde-887	330	61	the	the	DET
ejde-887	330	62	perturbation	perturbation	NOUN
ejde-887	330	63	ejde-202x	ejde-202x	NOUN
ejde-887	330	64	/	/	SYM
ejde-887	330	65	conf/27	conf/27	NOUN
ejde-887	330	66	boussinesq	boussinesq	ADJ
ejde-887	330	67	equations	equation	NOUN
ejde-887	330	68	43	43	NUM
ejde-887	330	69	travel	travel	NOUN
ejde-887	330	70	slower	slow	ADJ
ejde-887	330	71	and	and	CCONJ
ejde-887	330	72	decouple	decouple	VERB
ejde-887	330	73	from	from	ADP
ejde-887	330	74	the	the	DET
ejde-887	330	75	solitary	solitary	ADJ
ejde-887	330	76	wave	wave	NOUN
ejde-887	330	77	.	.	PUNCT
ejde-887	331	1	the	the	DET
ejde-887	331	2	evolution	evolution	NOUN
ejde-887	331	3	of	of	ADP
ejde-887	331	4	the	the	DET
ejde-887	331	5	solitary	solitary	ADJ
ejde-887	331	6	wave	wave	NOUN
ejde-887	331	7	velocity	velocity	NOUN
ejde-887	331	8	u(x	u(x	NOUN
ejde-887	331	9	,	,	PUNCT
ejde-887	331	10	t	t	PROPN
ejde-887	331	11	)	)	PUNCT
ejde-887	331	12	is	be	AUX
ejde-887	331	13	affected	affect	VERB
ejde-887	331	14	stroger	stroger	NOUN
ejde-887	331	15	by	by	ADP
ejde-887	331	16	the	the	DET
ejde-887	331	17	perturbation	perturbation	NOUN
ejde-887	331	18	,	,	PUNCT
ejde-887	331	19	and	and	CCONJ
ejde-887	331	20	develops	develop	VERB
ejde-887	331	21	in	in	ADP
ejde-887	331	22	time	time	NOUN
ejde-887	331	23	high	high	ADJ
ejde-887	331	24	amplitude	amplitude	NOUN
ejde-887	331	25	instabilities	instability	NOUN
ejde-887	331	26	.	.	PUNCT
ejde-887	332	1	in	in	ADP
ejde-887	332	2	figures	figure	NOUN
ejde-887	332	3	5	5	NUM
ejde-887	332	4	-	-	SYM
ejde-887	332	5	8	8	NUM
ejde-887	332	6	we	we	PRON
ejde-887	332	7	present	present	VERB
ejde-887	332	8	the	the	DET
ejde-887	332	9	effect	effect	NOUN
ejde-887	332	10	of	of	ADP
ejde-887	332	11	increasing	increase	VERB
ejde-887	332	12	the	the	DET
ejde-887	332	13	intensity	intensity	NOUN
ejde-887	332	14	of	of	ADP
ejde-887	332	15	the	the	DET
ejde-887	332	16	perturbation	perturbation	NOUN
ejde-887	332	17	on	on	ADP
ejde-887	332	18	solution	solution	NOUN
ejde-887	332	19	z(x	z(x	PROPN
ejde-887	332	20	,	,	PUNCT
ejde-887	332	21	t	t	PROPN
ejde-887	332	22	)	)	PUNCT
ejde-887	332	23	for	for	ADP
ejde-887	332	24	several	several	ADJ
ejde-887	332	25	initial	initial	ADJ
ejde-887	332	26	solitons	soliton	NOUN
ejde-887	332	27	(	(	PUNCT
ejde-887	332	28	3.8	3.8	NUM
ejde-887	332	29	)	)	PUNCT
ejde-887	332	30	of	of	ADP
ejde-887	332	31	different	different	ADJ
ejde-887	332	32	amplitudes	amplitude	NOUN
ejde-887	332	33	and	and	CCONJ
ejde-887	332	34	using	use	VERB
ejde-887	332	35	different	different	ADJ
ejde-887	332	36	dispersion	dispersion	NOUN
ejde-887	332	37	coefficient	coefficient	NOUN
ejde-887	332	38	values	value	NOUN
ejde-887	332	39	.	.	PUNCT
ejde-887	333	1	in	in	ADP
ejde-887	333	2	figure	figure	NOUN
ejde-887	333	3	5	5	NUM
ejde-887	333	4	we	we	PRON
ejde-887	333	5	present	present	VERB
ejde-887	333	6	the	the	DET
ejde-887	333	7	numerical	numerical	ADJ
ejde-887	333	8	solution	solution	NOUN
ejde-887	333	9	z(x	z(x	PROPN
ejde-887	333	10	,	,	PUNCT
ejde-887	333	11	t	t	PROPN
ejde-887	333	12	)	)	PUNCT
ejde-887	333	13	obtained	obtain	VERB
ejde-887	333	14	for	for	ADP
ejde-887	333	15	α	α	NOUN
ejde-887	333	16	=	=	SYM
ejde-887	333	17	0.5	0.5	NUM
ejde-887	333	18	,	,	PUNCT
ejde-887	333	19	β	β	X
ejde-887	333	20	=	=	SYM
ejde-887	333	21	0.5	0.5	NUM
ejde-887	333	22	,	,	PUNCT
ejde-887	333	23	ϵ	ϵ	X
ejde-887	333	24	=	=	PUNCT
ejde-887	333	25	0.2	0.2	NUM
ejde-887	333	26	.	.	PUNCT
ejde-887	334	1	the	the	DET
ejde-887	334	2	perturbation	perturbation	NOUN
ejde-887	334	3	induced	induce	VERB
ejde-887	334	4	by	by	ADP
ejde-887	334	5	the	the	DET
ejde-887	334	6	variable	variable	ADJ
ejde-887	334	7	coefficient	coefficient	NOUN
ejde-887	334	8	has	have	VERB
ejde-887	334	9	a	a	DET
ejde-887	334	10	weak	weak	ADJ
ejde-887	334	11	effect	effect	NOUN
ejde-887	334	12	on	on	ADP
ejde-887	334	13	the	the	DET
ejde-887	334	14	propagating	propagate	VERB
ejde-887	334	15	solitary	solitary	ADJ
ejde-887	334	16	wave	wave	NOUN
ejde-887	334	17	in	in	ADP
ejde-887	334	18	this	this	DET
ejde-887	334	19	case	case	NOUN
ejde-887	334	20	,	,	PUNCT
ejde-887	334	21	preserving	preserve	VERB
ejde-887	334	22	the	the	DET
ejde-887	334	23	constant	constant	ADJ
ejde-887	334	24	velocity	velocity	NOUN
ejde-887	334	25	and	and	CCONJ
ejde-887	334	26	shape	shape	NOUN
ejde-887	334	27	,	,	PUNCT
ejde-887	334	28	within	within	ADP
ejde-887	334	29	small	small	ADJ
ejde-887	334	30	amplitude	amplitude	NOUN
ejde-887	334	31	oscillations	oscillation	NOUN
ejde-887	334	32	caused	cause	VERB
ejde-887	334	33	by	by	ADP
ejde-887	334	34	the	the	DET
ejde-887	334	35	emergence	emergence	NOUN
ejde-887	334	36	of	of	ADP
ejde-887	334	37	secondary	secondary	ADJ
ejde-887	334	38	small	small	ADJ
ejde-887	334	39	amplitude	amplitude	NOUN
ejde-887	334	40	solitons	soliton	NOUN
ejde-887	334	41	in	in	ADP
ejde-887	334	42	the	the	DET
ejde-887	334	43	trailing	trail	VERB
ejde-887	334	44	part	part	NOUN
ejde-887	334	45	.	.	PUNCT
ejde-887	335	1	in	in	ADP
ejde-887	335	2	figure	figure	NOUN
ejde-887	335	3	6	6	NUM
ejde-887	335	4	we	we	PRON
ejde-887	335	5	present	present	VERB
ejde-887	335	6	a	a	DET
ejde-887	335	7	case	case	NOUN
ejde-887	335	8	with	with	ADP
ejde-887	335	9	α	α	NOUN
ejde-887	335	10	=	=	SYM
ejde-887	335	11	0.65	0.65	NUM
ejde-887	335	12	,	,	PUNCT
ejde-887	335	13	β	β	X
ejde-887	335	14	=	=	NOUN
ejde-887	335	15	0.7	0.7	NUM
ejde-887	335	16	,	,	PUNCT
ejde-887	335	17	ϵ	ϵ	X
ejde-887	335	18	=	=	PUNCT
ejde-887	335	19	0.2	0.2	NUM
ejde-887	335	20	.	.	PUNCT
ejde-887	336	1	we	we	PRON
ejde-887	336	2	notice	notice	VERB
ejde-887	336	3	an	an	DET
ejde-887	336	4	increase	increase	NOUN
ejde-887	336	5	in	in	ADP
ejde-887	336	6	the	the	DET
ejde-887	336	7	non	non	ADJ
ejde-887	336	8	-	-	ADJ
ejde-887	336	9	autonomous	autonomous	ADJ
ejde-887	336	10	perturbation	perturbation	NOUN
ejde-887	336	11	effect	effect	NOUN
ejde-887	336	12	through	through	ADP
ejde-887	336	13	a	a	DET
ejde-887	336	14	larger	large	ADJ
ejde-887	336	15	amplitude	amplitude	NOUN
ejde-887	336	16	modulation	modulation	NOUN
ejde-887	336	17	of	of	ADP
ejde-887	336	18	the	the	DET
ejde-887	336	19	solitary	solitary	ADJ
ejde-887	336	20	wave	wave	NOUN
ejde-887	336	21	envelope	envelope	NOUN
ejde-887	336	22	.	.	PUNCT
ejde-887	337	1	at	at	ADP
ejde-887	337	2	the	the	DET
ejde-887	337	3	same	same	ADJ
ejde-887	337	4	time	time	NOUN
ejde-887	337	5	,	,	PUNCT
ejde-887	337	6	the	the	DET
ejde-887	337	7	generation	generation	NOUN
ejde-887	337	8	of	of	ADP
ejde-887	337	9	secondary	secondary	ADJ
ejde-887	337	10	solitons	soliton	NOUN
ejde-887	337	11	seem	seem	VERB
ejde-887	337	12	to	to	PART
ejde-887	337	13	be	be	AUX
ejde-887	337	14	overwhelmed	overwhelm	VERB
ejde-887	337	15	by	by	ADP
ejde-887	337	16	occurrence	occurrence	NOUN
ejde-887	337	17	of	of	ADP
ejde-887	337	18	high	high	ADJ
ejde-887	337	19	frequency	frequency	NOUN
ejde-887	337	20	linear	linear	NOUN
ejde-887	337	21	waves	wave	NOUN
ejde-887	337	22	in	in	ADP
ejde-887	337	23	the	the	DET
ejde-887	337	24	trailing	trail	VERB
ejde-887	337	25	part	part	NOUN
ejde-887	337	26	,	,	PUNCT
ejde-887	337	27	while	while	SCONJ
ejde-887	337	28	the	the	DET
ejde-887	337	29	front	front	NOUN
ejde-887	337	30	of	of	ADP
ejde-887	337	31	the	the	DET
ejde-887	337	32	solitary	solitary	ADJ
ejde-887	337	33	wave	wave	NOUN
ejde-887	337	34	begins	begin	VERB
ejde-887	337	35	to	to	PART
ejde-887	337	36	feel	feel	VERB
ejde-887	337	37	a	a	DET
ejde-887	337	38	weakly	weakly	ADJ
ejde-887	337	39	effect	effect	NOUN
ejde-887	337	40	of	of	ADP
ejde-887	337	41	perturbation	perturbation	NOUN
ejde-887	337	42	.	.	PUNCT
ejde-887	338	1	nevertheless	nevertheless	ADV
ejde-887	338	2	,	,	PUNCT
ejde-887	338	3	we	we	PRON
ejde-887	338	4	can	can	AUX
ejde-887	338	5	state	state	VERB
ejde-887	338	6	that	that	SCONJ
ejde-887	338	7	the	the	DET
ejde-887	338	8	solitary	solitary	ADJ
ejde-887	338	9	wave	wave	NOUN
ejde-887	338	10	solution	solution	NOUN
ejde-887	338	11	is	be	AUX
ejde-887	338	12	highly	highly	ADV
ejde-887	338	13	modulated	modulate	VERB
ejde-887	338	14	but	but	CCONJ
ejde-887	338	15	still	still	ADV
ejde-887	338	16	stable	stable	ADJ
ejde-887	338	17	.	.	PUNCT
ejde-887	339	1	in	in	ADP
ejde-887	339	2	figure	figure	NOUN
ejde-887	339	3	7	7	NUM
ejde-887	339	4	we	we	PRON
ejde-887	339	5	present	present	VERB
ejde-887	339	6	a	a	DET
ejde-887	339	7	situation	situation	NOUN
ejde-887	339	8	with	with	ADP
ejde-887	339	9	α	α	PROPN
ejde-887	339	10	=	=	SYM
ejde-887	339	11	0.8	0.8	NUM
ejde-887	339	12	,	,	PUNCT
ejde-887	339	13	β	β	X
ejde-887	339	14	=	=	NOUN
ejde-887	339	15	0.7	0.7	NUM
ejde-887	339	16	,	,	PUNCT
ejde-887	339	17	ϵ	ϵ	X
ejde-887	339	18	=	=	PUNCT
ejde-887	339	19	0.3	0.3	NUM
ejde-887	339	20	.	.	PUNCT
ejde-887	340	1	the	the	DET
ejde-887	340	2	effect	effect	NOUN
ejde-887	340	3	of	of	ADP
ejde-887	340	4	increasing	increase	VERB
ejde-887	340	5	the	the	DET
ejde-887	340	6	amplitude	amplitude	NOUN
ejde-887	340	7	of	of	ADP
ejde-887	340	8	the	the	DET
ejde-887	340	9	perturbative	perturbative	ADJ
ejde-887	340	10	coefficient	coefficient	NOUN
ejde-887	340	11	is	be	AUX
ejde-887	340	12	not	not	PART
ejde-887	340	13	compensated	compensate	VERB
ejde-887	340	14	by	by	ADP
ejde-887	340	15	the	the	DET
ejde-887	340	16	increase	increase	NOUN
ejde-887	340	17	in	in	ADP
ejde-887	340	18	the	the	DET
ejde-887	340	19	soliton	soliton	NOUN
ejde-887	340	20	amplitude	amplitude	NOUN
ejde-887	340	21	(	(	PUNCT
ejde-887	340	22	stronger	strong	ADJ
ejde-887	340	23	value	value	NOUN
ejde-887	340	24	for	for	ADP
ejde-887	340	25	the	the	DET
ejde-887	340	26	perturbation	perturbation	NOUN
ejde-887	340	27	is	be	AUX
ejde-887	340	28	not	not	PART
ejde-887	340	29	compensated	compensate	VERB
ejde-887	340	30	by	by	ADP
ejde-887	340	31	higher	high	ADJ
ejde-887	340	32	order	order	NOUN
ejde-887	340	33	of	of	ADP
ejde-887	340	34	nonlinearity	nonlinearity	NOUN
ejde-887	340	35	,	,	PUNCT
ejde-887	340	36	even	even	ADV
ejde-887	340	37	balanced	balance	VERB
ejde-887	340	38	by	by	ADP
ejde-887	340	39	higher	high	ADJ
ejde-887	340	40	value	value	NOUN
ejde-887	340	41	for	for	ADP
ejde-887	340	42	the	the	DET
ejde-887	340	43	dispersion	dispersion	NOUN
ejde-887	340	44	coefficient	coefficient	NOUN
ejde-887	340	45	)	)	PUNCT
ejde-887	340	46	.	.	PUNCT
ejde-887	341	1	the	the	DET
ejde-887	341	2	solitary	solitary	ADJ
ejde-887	341	3	wave	wave	NOUN
ejde-887	341	4	experience	experience	VERB
ejde-887	341	5	large	large	ADJ
ejde-887	341	6	amplitude	amplitude	NOUN
ejde-887	341	7	and	and	CCONJ
ejde-887	341	8	high	high	ADJ
ejde-887	341	9	frequency	frequency	NOUN
ejde-887	341	10	perturbation	perturbation	NOUN
ejde-887	341	11	modulating	modulate	VERB
ejde-887	341	12	the	the	DET
ejde-887	341	13	whole	whole	ADJ
ejde-887	341	14	envelope	envelope	NOUN
ejde-887	341	15	and	and	CCONJ
ejde-887	341	16	traveling	travel	VERB
ejde-887	341	17	together	together	ADV
ejde-887	341	18	with	with	ADP
ejde-887	341	19	the	the	DET
ejde-887	341	20	solitary	solitary	ADJ
ejde-887	341	21	wave	wave	NOUN
ejde-887	341	22	.	.	PUNCT
ejde-887	342	1	for	for	ADP
ejde-887	342	2	t	t	PROPN
ejde-887	342	3	>	>	X
ejde-887	342	4	10s	10	NOUN
ejde-887	342	5	this	this	DET
ejde-887	342	6	solution	solution	NOUN
ejde-887	342	7	becomes	become	VERB
ejde-887	342	8	unstable	unstable	ADJ
ejde-887	342	9	.	.	PUNCT
ejde-887	343	1	finally	finally	ADV
ejde-887	343	2	,	,	PUNCT
ejde-887	343	3	in	in	ADP
ejde-887	343	4	figure	figure	NOUN
ejde-887	343	5	8	8	NUM
ejde-887	343	6	we	we	PRON
ejde-887	343	7	present	present	VERB
ejde-887	343	8	the	the	DET
ejde-887	343	9	extreme	extreme	ADJ
ejde-887	343	10	case	case	NOUN
ejde-887	343	11	of	of	ADP
ejde-887	343	12	α	α	NOUN
ejde-887	343	13	=	=	SYM
ejde-887	343	14	0.65	0.65	NUM
ejde-887	343	15	,	,	PUNCT
ejde-887	343	16	β	β	X
ejde-887	343	17	=	=	NOUN
ejde-887	343	18	0.7	0.7	NUM
ejde-887	343	19	,	,	PUNCT
ejde-887	343	20	ϵ	ϵ	X
ejde-887	343	21	=	=	PUNCT
ejde-887	343	22	0.3	0.3	NUM
ejde-887	343	23	.	.	PUNCT
ejde-887	344	1	we	we	PRON
ejde-887	344	2	notice	notice	VERB
ejde-887	344	3	that	that	SCONJ
ejde-887	344	4	the	the	DET
ejde-887	344	5	initial	initial	ADJ
ejde-887	344	6	soliton	soliton	NOUN
ejde-887	344	7	becomes	become	VERB
ejde-887	344	8	quickly	quickly	ADV
ejde-887	344	9	unstable	unstable	ADJ
ejde-887	344	10	,	,	PUNCT
ejde-887	344	11	reduces	reduce	VERB
ejde-887	344	12	its	its	PRON
ejde-887	344	13	amplitude	amplitude	NOUN
ejde-887	344	14	and	and	CCONJ
ejde-887	344	15	becomes	becomes	AUX
ejde-887	344	16	modulated	modulate	VERB
ejde-887	344	17	by	by	ADP
ejde-887	344	18	very	very	ADV
ejde-887	344	19	strong	strong	ADJ
ejde-887	344	20	singular	singular	ADJ
ejde-887	344	21	waves	wave	NOUN
ejde-887	344	22	.	.	PUNCT
ejde-887	345	1	the	the	DET
ejde-887	345	2	phenomenon	phenomenon	NOUN
ejde-887	345	3	of	of	ADP
ejde-887	345	4	coupling	coupling	NOUN
ejde-887	345	5	of	of	ADP
ejde-887	345	6	the	the	DET
ejde-887	345	7	horizontal	horizontal	ADJ
ejde-887	345	8	space	space	NOUN
ejde-887	345	9	scales	scale	NOUN
ejde-887	345	10	described	describe	VERB
ejde-887	345	11	in	in	ADP
ejde-887	345	12	(	(	PUNCT
ejde-887	345	13	4.8)(4.13	4.8)(4.13	PROPN
ejde-887	345	14	)	)	PUNCT
ejde-887	345	15	is	be	AUX
ejde-887	345	16	visible	visible	ADJ
ejde-887	345	17	in	in	ADP
ejde-887	345	18	figure	figure	NOUN
ejde-887	345	19	8	8	NUM
ejde-887	345	20	.	.	PUNCT
ejde-887	346	1	when	when	SCONJ
ejde-887	346	2	we	we	PRON
ejde-887	346	3	choose	choose	VERB
ejde-887	346	4	the	the	DET
ejde-887	346	5	half	half	ADJ
ejde-887	346	6	-	-	PUNCT
ejde-887	346	7	width	width	NOUN
ejde-887	346	8	lsol	lsol	NOUN
ejde-887	346	9	=	=	SYM
ejde-887	346	10	5	5	NUM
ejde-887	346	11	of	of	ADP
ejde-887	346	12	the	the	DET
ejde-887	346	13	initial	initial	ADJ
ejde-887	346	14	soliton	soliton	NOUN
ejde-887	346	15	smaller	small	ADJ
ejde-887	346	16	than	than	ADP
ejde-887	346	17	the	the	DET
ejde-887	346	18	wavelength	wavelength	NOUN
ejde-887	346	19	4π	4π	NUM
ejde-887	346	20	of	of	ADP
ejde-887	346	21	the	the	DET
ejde-887	346	22	variable	variable	ADJ
ejde-887	346	23	coefficient	coefficient	NOUN
ejde-887	346	24	q(x	q(x	NOUN
ejde-887	346	25	)	)	PUNCT
ejde-887	346	26	,	,	PUNCT
ejde-887	346	27	the	the	DET
ejde-887	346	28	coupling	coupling	NOUN
ejde-887	346	29	of	of	ADP
ejde-887	346	30	scales	scale	NOUN
ejde-887	346	31	described	describe	VERB
ejde-887	346	32	in	in	ADP
ejde-887	346	33	section	section	NOUN
ejde-887	346	34	4	4	NUM
ejde-887	346	35	by	by	ADP
ejde-887	346	36	(	(	PUNCT
ejde-887	346	37	4.8)-(4.13	4.8)-(4.13	NOUN
ejde-887	346	38	)	)	PUNCT
ejde-887	346	39	generates	generate	VERB
ejde-887	346	40	in	in	ADP
ejde-887	346	41	the	the	DET
ejde-887	346	42	solution	solution	NOUN
ejde-887	346	43	perturbative	perturbative	ADJ
ejde-887	346	44	harmonics	harmonic	NOUN
ejde-887	346	45	of	of	ADP
ejde-887	346	46	frequencies	frequency	NOUN
ejde-887	346	47	higher	high	ADJ
ejde-887	346	48	than	than	ADP
ejde-887	346	49	the	the	DET
ejde-887	346	50	fundamental	fundamental	ADJ
ejde-887	346	51	wavelength	wavelength	NOUN
ejde-887	346	52	of	of	ADP
ejde-887	346	53	the	the	DET
ejde-887	346	54	periodic	periodic	ADJ
ejde-887	346	55	coefficient	coefficient	NOUN
ejde-887	346	56	,	,	PUNCT
ejde-887	346	57	exactly	exactly	ADV
ejde-887	346	58	as	as	SCONJ
ejde-887	346	59	shown	show	VERB
ejde-887	346	60	in	in	ADP
ejde-887	346	61	the	the	DET
ejde-887	346	62	high	high	ADJ
ejde-887	346	63	frequency	frequency	NOUN
ejde-887	346	64	oscillations	oscillation	NOUN
ejde-887	346	65	present	present	ADJ
ejde-887	346	66	in	in	ADP
ejde-887	346	67	the	the	DET
ejde-887	346	68	tail	tail	NOUN
ejde-887	346	69	of	of	ADP
ejde-887	346	70	the	the	DET
ejde-887	346	71	numerical	numerical	ADJ
ejde-887	346	72	solution	solution	NOUN
ejde-887	346	73	.	.	PUNCT
ejde-887	347	1	these	these	DET
ejde-887	347	2	observations	observation	NOUN
ejde-887	347	3	are	be	AUX
ejde-887	347	4	confirmed	confirm	VERB
ejde-887	347	5	in	in	ADP
ejde-887	347	6	literature	literature	NOUN
ejde-887	347	7	.	.	PUNCT
ejde-887	348	1	in	in	ADP
ejde-887	348	2	[	[	X
ejde-887	348	3	11	11	NUM
ejde-887	348	4	]	]	PUNCT
ejde-887	348	5	the	the	DET
ejde-887	348	6	authors	author	NOUN
ejde-887	348	7	derive	derive	VERB
ejde-887	348	8	a	a	DET
ejde-887	348	9	two	two	NUM
ejde-887	348	10	-	-	PUNCT
ejde-887	348	11	dimensional	dimensional	ADJ
ejde-887	348	12	boussinesq	boussinesq	ADJ
ejde-887	348	13	-	-	PUNCT
ejde-887	348	14	type	type	NOUN
ejde-887	348	15	system	system	NOUN
ejde-887	348	16	and	and	CCONJ
ejde-887	348	17	calculate	calculate	VERB
ejde-887	348	18	numerical	numerical	ADJ
ejde-887	348	19	solutions	solution	NOUN
ejde-887	348	20	.	.	PUNCT
ejde-887	349	1	they	they	PRON
ejde-887	349	2	conclude	conclude	VERB
ejde-887	349	3	that	that	SCONJ
ejde-887	349	4	for	for	ADP
ejde-887	349	5	large	large	ADJ
ejde-887	349	6	perturbation	perturbation	NOUN
ejde-887	349	7	in	in	ADP
ejde-887	349	8	the	the	DET
ejde-887	349	9	boussinesq	boussinesq	ADJ
ejde-887	349	10	equation	equation	NOUN
ejde-887	349	11	,	,	PUNCT
ejde-887	349	12	representing	represent	VERB
ejde-887	349	13	in	in	ADP
ejde-887	349	14	their	their	PRON
ejde-887	349	15	case	case	NOUN
ejde-887	349	16	large	large	ADJ
ejde-887	349	17	bottom	bottom	ADJ
ejde-887	349	18	variations	variation	NOUN
ejde-887	349	19	,	,	PUNCT
ejde-887	349	20	nonlinear	nonlinear	ADJ
ejde-887	349	21	effects	effect	NOUN
ejde-887	349	22	dominate	dominate	VERB
ejde-887	349	23	dispersive	dispersive	ADJ
ejde-887	349	24	ones	one	NOUN
ejde-887	349	25	when	when	SCONJ
ejde-887	349	26	the	the	DET
ejde-887	349	27	amplitude	amplitude	NOUN
ejde-887	349	28	of	of	ADP
ejde-887	349	29	bottom	bottom	ADJ
ejde-887	349	30	variations	variation	NOUN
ejde-887	349	31	tends	tend	VERB
ejde-887	349	32	to	to	ADP
ejde-887	349	33	the	the	DET
ejde-887	349	34	shoaling	shoaling	NOUN
ejde-887	349	35	limit	limit	NOUN
ejde-887	349	36	.	.	PUNCT
ejde-887	350	1	in	in	ADP
ejde-887	350	2	[	[	X
ejde-887	350	3	33	33	NUM
ejde-887	350	4	]	]	PUNCT
ejde-887	350	5	the	the	DET
ejde-887	350	6	authors	author	NOUN
ejde-887	350	7	analyze	analyze	VERB
ejde-887	350	8	the	the	DET
ejde-887	350	9	propagation	propagation	NOUN
ejde-887	350	10	of	of	ADP
ejde-887	350	11	long	long	ADJ
ejde-887	350	12	solitary	solitary	ADJ
ejde-887	350	13	wave	wave	NOUN
ejde-887	350	14	pulse	pulse	NOUN
ejde-887	350	15	over	over	ADP
ejde-887	350	16	periodic	periodic	ADJ
ejde-887	350	17	piece	piece	NOUN
ejde-887	350	18	-	-	PUNCT
ejde-887	350	19	wise	wise	ADJ
ejde-887	350	20	constant	constant	ADJ
ejde-887	350	21	topography	topography	NOUN
ejde-887	350	22	,	,	PUNCT
ejde-887	350	23	in	in	ADP
ejde-887	350	24	the	the	DET
ejde-887	350	25	framework	framework	NOUN
ejde-887	350	26	of	of	ADP
ejde-887	350	27	weakly	weakly	ADJ
ejde-887	350	28	nonlinear	nonlinear	ADJ
ejde-887	350	29	-	-	PUNCT
ejde-887	350	30	dispersive	dispersive	ADJ
ejde-887	350	31	theory	theory	NOUN
ejde-887	350	32	.	.	PUNCT
ejde-887	351	1	they	they	PRON
ejde-887	351	2	notice	notice	VERB
ejde-887	351	3	a	a	DET
ejde-887	351	4	similar	similar	ADJ
ejde-887	351	5	behavior	behavior	NOUN
ejde-887	351	6	of	of	ADP
ejde-887	351	7	the	the	DET
ejde-887	351	8	solitary	solitary	ADJ
ejde-887	351	9	waves	wave	NOUN
ejde-887	351	10	with	with	ADP
ejde-887	351	11	what	what	PRON
ejde-887	351	12	we	we	PRON
ejde-887	351	13	present	present	VERB
ejde-887	351	14	in	in	ADP
ejde-887	351	15	figures	figure	NOUN
ejde-887	351	16	1	1	NUM
ejde-887	351	17	-	-	SYM
ejde-887	351	18	6	6	NUM
ejde-887	351	19	.	.	PUNCT
ejde-887	351	20	when	when	SCONJ
ejde-887	351	21	the	the	DET
ejde-887	351	22	obstacle	obstacle	NOUN
ejde-887	351	23	has	have	AUX
ejde-887	351	24	width	width	VERB
ejde-887	351	25	comparable	comparable	ADJ
ejde-887	351	26	or	or	CCONJ
ejde-887	351	27	slightly	slightly	ADV
ejde-887	351	28	larger	large	ADJ
ejde-887	351	29	than	than	ADP
ejde-887	351	30	the	the	DET
ejde-887	351	31	pulse	pulse	NOUN
ejde-887	351	32	width	width	VERB
ejde-887	351	33	the	the	DET
ejde-887	351	34	leading	lead	VERB
ejde-887	351	35	transmitted	transmit	VERB
ejde-887	351	36	wave	wave	NOUN
ejde-887	351	37	keeps	keep	VERB
ejde-887	351	38	its	its	PRON
ejde-887	351	39	solitary	solitary	ADJ
ejde-887	351	40	shape	shape	NOUN
ejde-887	351	41	on	on	ADP
ejde-887	351	42	the	the	DET
ejde-887	351	43	average	average	NOUN
ejde-887	351	44	.	.	PUNCT
ejde-887	352	1	similar	similar	ADJ
ejde-887	352	2	results	result	NOUN
ejde-887	352	3	are	be	AUX
ejde-887	352	4	presented	present	VERB
ejde-887	352	5	on	on	ADP
ejde-887	352	6	the	the	DET
ejde-887	352	7	long	long	ADJ
ejde-887	352	8	-	-	PUNCT
ejde-887	352	9	time	time	NOUN
ejde-887	352	10	asymptotic	asymptotic	ADJ
ejde-887	352	11	effect	effect	NOUN
ejde-887	352	12	of	of	ADP
ejde-887	352	13	varying	vary	VERB
ejde-887	352	14	bottom	bottom	NOUN
ejde-887	352	15	over	over	ADP
ejde-887	352	16	shallow	shallow	ADJ
ejde-887	352	17	water	water	NOUN
ejde-887	352	18	waves	wave	NOUN
ejde-887	352	19	from	from	ADP
ejde-887	352	20	studies	study	NOUN
ejde-887	352	21	on	on	ADP
ejde-887	352	22	non	non	ADJ
ejde-887	352	23	-	-	ADJ
ejde-887	352	24	autonomous	autonomous	ADJ
ejde-887	352	25	euler	euler	NOUN
ejde-887	352	26	equations	equation	NOUN
ejde-887	352	27	with	with	ADP
ejde-887	352	28	44	44	NUM
ejde-887	352	29	a.	a.	NOUN
ejde-887	352	30	ludu	ludu	NOUN
ejde-887	352	31	,	,	PUNCT
ejde-887	352	32	h.	h.	PROPN
ejde-887	352	33	khanal	khanal	NOUN
ejde-887	352	34	,	,	PUNCT
ejde-887	352	35	a.	a.	PROPN
ejde-887	352	36	s.	s.	PROPN
ejde-887	352	37	carstea	carstea	PROPN
ejde-887	352	38	ejde-2022	ejde-2022	PROPN
ejde-887	352	39	/	/	SYM
ejde-887	352	40	conf/27	conf/27	NOUN
ejde-887	352	41	coefficients	coefficient	NOUN
ejde-887	352	42	depending	depend	VERB
ejde-887	352	43	of	of	ADP
ejde-887	352	44	the	the	DET
ejde-887	352	45	bottom	bottom	ADJ
ejde-887	352	46	topography	topography	NOUN
ejde-887	352	47	[	[	X
ejde-887	352	48	3	3	NUM
ejde-887	352	49	]	]	PUNCT
ejde-887	352	50	.	.	PUNCT
ejde-887	353	1	also	also	ADV
ejde-887	353	2	the	the	DET
ejde-887	353	3	green	green	ADJ
ejde-887	353	4	-	-	PUNCT
ejde-887	353	5	naghdi	naghdi	NOUN
ejde-887	353	6	equations	equation	NOUN
ejde-887	353	7	for	for	ADP
ejde-887	353	8	nonlinear	nonlinear	ADJ
ejde-887	353	9	dispersive	dispersive	ADJ
ejde-887	353	10	gravity	gravity	NOUN
ejde-887	353	11	waves	wave	NOUN
ejde-887	353	12	can	can	AUX
ejde-887	353	13	be	be	AUX
ejde-887	353	14	mapped	map	VERB
ejde-887	353	15	into	into	ADP
ejde-887	353	16	generalized	generalized	ADJ
ejde-887	353	17	boussinesq	boussinesq	ADJ
ejde-887	353	18	equations	equation	NOUN
ejde-887	353	19	in	in	ADP
ejde-887	353	20	non	non	ADJ
ejde-887	353	21	-	-	ADJ
ejde-887	353	22	autonomous	autonomous	ADJ
ejde-887	353	23	form	form	NOUN
ejde-887	353	24	,	,	PUNCT
ejde-887	353	25	with	with	ADP
ejde-887	353	26	coefficient	coefficient	NOUN
ejde-887	353	27	depending	depend	VERB
ejde-887	353	28	on	on	ADP
ejde-887	353	29	the	the	DET
ejde-887	353	30	boundary	boundary	ADJ
ejde-887	353	31	conditions	condition	NOUN
ejde-887	353	32	[	[	X
ejde-887	353	33	32	32	NUM
ejde-887	353	34	]	]	PUNCT
ejde-887	353	35	.	.	PUNCT
ejde-887	354	1	different	different	ADJ
ejde-887	354	2	non	non	ADJ
ejde-887	354	3	-	-	ADJ
ejde-887	354	4	autonomous	autonomous	ADJ
ejde-887	354	5	variations	variation	NOUN
ejde-887	354	6	of	of	ADP
ejde-887	354	7	generalized	generalize	VERB
ejde-887	354	8	-	-	PUNCT
ejde-887	354	9	boussinesq	boussinesq	NOUN
ejde-887	354	10	equations	equation	NOUN
ejde-887	354	11	have	have	AUX
ejde-887	354	12	been	be	AUX
ejde-887	354	13	used	use	VERB
ejde-887	354	14	to	to	PART
ejde-887	354	15	study	study	VERB
ejde-887	354	16	soliton	soliton	NOUN
ejde-887	354	17	propagation	propagation	NOUN
ejde-887	354	18	in	in	ADP
ejde-887	354	19	shallow	shallow	ADJ
ejde-887	354	20	fluid	fluid	NOUN
ejde-887	354	21	flow	flow	NOUN
ejde-887	354	22	over	over	ADP
ejde-887	354	23	topography	topography	NOUN
ejde-887	354	24	[	[	X
ejde-887	354	25	3	3	NUM
ejde-887	354	26	,	,	PUNCT
ejde-887	354	27	32	32	NUM
ejde-887	354	28	]	]	PUNCT
ejde-887	354	29	.	.	PUNCT
ejde-887	355	1	their	their	PRON
ejde-887	355	2	numerical	numerical	ADJ
ejde-887	355	3	solutions	solution	NOUN
ejde-887	355	4	predict	predict	VERB
ejde-887	355	5	the	the	DET
ejde-887	355	6	breaking	breaking	NOUN
ejde-887	355	7	of	of	ADP
ejde-887	355	8	the	the	DET
ejde-887	355	9	original	original	ADJ
ejde-887	355	10	soliton	soliton	NOUN
ejde-887	355	11	into	into	ADP
ejde-887	355	12	a	a	DET
ejde-887	355	13	train	train	NOUN
ejde-887	355	14	of	of	ADP
ejde-887	355	15	upstream	upstream	ADJ
ejde-887	355	16	propagating	propagate	VERB
ejde-887	355	17	smaller	small	ADJ
ejde-887	355	18	solitary	solitary	ADJ
ejde-887	355	19	waves	wave	NOUN
ejde-887	355	20	.	.	PUNCT
ejde-887	356	1	however	however	ADV
ejde-887	356	2	,	,	PUNCT
ejde-887	356	3	the	the	DET
ejde-887	356	4	balance	balance	NOUN
ejde-887	356	5	of	of	ADP
ejde-887	356	6	dispersion	dispersion	NOUN
ejde-887	356	7	to	to	ADP
ejde-887	356	8	nonlinearity	nonlinearity	NOUN
ejde-887	356	9	is	be	AUX
ejde-887	356	10	maintained	maintain	VERB
ejde-887	356	11	through	through	ADP
ejde-887	356	12	a	a	DET
ejde-887	356	13	remarkably	remarkably	ADV
ejde-887	356	14	large	large	ADJ
ejde-887	356	15	range	range	NOUN
ejde-887	356	16	,	,	PUNCT
ejde-887	356	17	a	a	DET
ejde-887	356	18	fact	fact	NOUN
ejde-887	356	19	which	which	PRON
ejde-887	356	20	tends	tend	VERB
ejde-887	356	21	to	to	PART
ejde-887	356	22	further	far	ADV
ejde-887	356	23	justify	justify	VERB
ejde-887	356	24	the	the	DET
ejde-887	356	25	use	use	NOUN
ejde-887	356	26	of	of	ADP
ejde-887	356	27	the	the	DET
ejde-887	356	28	boussinesq	boussinesq	ADJ
ejde-887	356	29	and	and	CCONJ
ejde-887	356	30	kdv	kdv	ADJ
ejde-887	356	31	approximations	approximation	NOUN
ejde-887	356	32	in	in	ADP
ejde-887	356	33	the	the	DET
ejde-887	356	34	homogenization	homogenization	NOUN
ejde-887	356	35	limit	limit	NOUN
ejde-887	356	36	[	[	X
ejde-887	356	37	11	11	NUM
ejde-887	356	38	]	]	PUNCT
ejde-887	356	39	.	.	PUNCT
ejde-887	357	1	5.3	5.3	NUM
ejde-887	357	2	.	.	PUNCT
ejde-887	357	3	stability	stability	NOUN
ejde-887	357	4	of	of	ADP
ejde-887	357	5	perturbed	perturb	VERB
ejde-887	357	6	soliton	soliton	NOUN
ejde-887	357	7	solution	solution	NOUN
ejde-887	357	8	.	.	PUNCT
ejde-887	358	1	in	in	ADP
ejde-887	358	2	the	the	DET
ejde-887	358	3	previous	previous	ADJ
ejde-887	358	4	section	section	NOUN
ejde-887	358	5	we	we	PRON
ejde-887	358	6	discussed	discuss	VERB
ejde-887	358	7	how	how	SCONJ
ejde-887	358	8	an	an	DET
ejde-887	358	9	initial	initial	ADJ
ejde-887	358	10	-	-	PUNCT
ejde-887	358	11	value	value	NOUN
ejde-887	358	12	problem	problem	NOUN
ejde-887	358	13	for	for	ADP
ejde-887	358	14	the	the	DET
ejde-887	358	15	system	system	NOUN
ejde-887	358	16	(	(	PUNCT
ejde-887	358	17	2.1)-(2.2	2.1)-(2.2	NUM
ejde-887	358	18	)	)	PUNCT
ejde-887	358	19	is	be	AUX
ejde-887	358	20	always	always	ADV
ejde-887	358	21	locally	locally	ADV
ejde-887	358	22	well	well	ADV
ejde-887	358	23	posed	pose	VERB
ejde-887	358	24	,	,	PUNCT
ejde-887	358	25	for	for	ADP
ejde-887	358	26	initial	initial	ADJ
ejde-887	358	27	conditions	condition	NOUN
ejde-887	358	28	provided	provide	VERB
ejde-887	358	29	by	by	ADP
ejde-887	358	30	smooth	smooth	ADJ
ejde-887	358	31	lp(r	lp(r	NOUN
ejde-887	358	32	functions	function	NOUN
ejde-887	358	33	.	.	PUNCT
ejde-887	359	1	the	the	DET
ejde-887	359	2	numerical	numerical	PROPN
ejde-887	359	3	study	study	PROPN
ejde-887	359	4	above	above	ADP
ejde-887	359	5	uses	use	NOUN
ejde-887	359	6	for	for	ADP
ejde-887	359	7	initial	initial	ADJ
ejde-887	359	8	conditions	condition	NOUN
ejde-887	359	9	the	the	DET
ejde-887	359	10	one	one	NUM
ejde-887	359	11	-	-	PUNCT
ejde-887	359	12	soliton	soliton	NOUN
ejde-887	359	13	solutions	solution	NOUN
ejde-887	359	14	(	(	PUNCT
ejde-887	359	15	3.8	3.8	NUM
ejde-887	359	16	)	)	PUNCT
ejde-887	359	17	of	of	ADP
ejde-887	359	18	the	the	DET
ejde-887	359	19	autonomous	autonomous	ADJ
ejde-887	359	20	boussinesq	boussinesq	ADJ
ejde-887	359	21	system	system	NOUN
ejde-887	359	22	which	which	PRON
ejde-887	359	23	obey	obey	VERB
ejde-887	359	24	these	these	DET
ejde-887	359	25	conditions	condition	NOUN
ejde-887	359	26	.	.	PUNCT
ejde-887	360	1	however	however	ADV
ejde-887	360	2	,	,	PUNCT
ejde-887	360	3	solitary	solitary	ADJ
ejde-887	360	4	-	-	PUNCT
ejde-887	360	5	wave	wave	NOUN
ejde-887	360	6	solutions	solution	NOUN
ejde-887	360	7	for	for	ADP
ejde-887	360	8	the	the	DET
ejde-887	360	9	non	non	ADJ
ejde-887	360	10	-	-	ADJ
ejde-887	360	11	autonomous	autonomous	ADJ
ejde-887	360	12	system	system	NOUN
ejde-887	360	13	(	(	PUNCT
ejde-887	360	14	2.1)-(2.2	2.1)-(2.2	NUM
ejde-887	360	15	)	)	PUNCT
ejde-887	360	16	are	be	AUX
ejde-887	360	17	nonlinearly	nonlinearly	ADV
ejde-887	360	18	stable	stable	ADJ
ejde-887	360	19	only	only	ADV
ejde-887	360	20	for	for	ADP
ejde-887	360	21	specific	specific	ADJ
ejde-887	360	22	range	range	NOUN
ejde-887	360	23	of	of	ADP
ejde-887	360	24	their	their	PRON
ejde-887	360	25	phase	phase	NOUN
ejde-887	360	26	speeds	speed	NOUN
ejde-887	360	27	[	[	X
ejde-887	360	28	1	1	NUM
ejde-887	360	29	,	,	PUNCT
ejde-887	360	30	2	2	NUM
ejde-887	360	31	]	]	PUNCT
ejde-887	360	32	.	.	PUNCT
ejde-887	361	1	the	the	DET
ejde-887	361	2	one	one	NUM
ejde-887	361	3	-	-	PUNCT
ejde-887	361	4	soliton	soliton	NOUN
ejde-887	361	5	initial	initial	ADJ
ejde-887	361	6	data	datum	NOUN
ejde-887	361	7	are	be	AUX
ejde-887	361	8	stable	stable	ADJ
ejde-887	361	9	bidirectional	bidirectional	ADJ
ejde-887	361	10	solitons	soliton	NOUN
ejde-887	361	11	in	in	ADP
ejde-887	361	12	an	an	DET
ejde-887	361	13	autonomous	autonomous	ADJ
ejde-887	361	14	boussinesq	boussinesq	ADJ
ejde-887	361	15	system	system	NOUN
ejde-887	361	16	[	[	X
ejde-887	361	17	46	46	NUM
ejde-887	361	18	]	]	PUNCT
ejde-887	361	19	and	and	CCONJ
ejde-887	361	20	generates	generate	VERB
ejde-887	361	21	solitary	solitary	ADJ
ejde-887	361	22	waves	wave	NOUN
ejde-887	361	23	which	which	PRON
ejde-887	361	24	evolve	evolve	VERB
ejde-887	361	25	into	into	ADP
ejde-887	361	26	global	global	ADJ
ejde-887	361	27	solutions	solution	NOUN
ejde-887	361	28	.	.	PUNCT
ejde-887	362	1	we	we	PRON
ejde-887	362	2	study	study	VERB
ejde-887	362	3	the	the	DET
ejde-887	362	4	stability	stability	NOUN
ejde-887	362	5	of	of	ADP
ejde-887	362	6	these	these	DET
ejde-887	362	7	global	global	ADJ
ejde-887	362	8	solutions	solution	NOUN
ejde-887	362	9	for	for	ADP
ejde-887	362	10	periodic	periodic	ADJ
ejde-887	362	11	coefficients	coefficient	NOUN
ejde-887	362	12	q(x	q(x	NOUN
ejde-887	362	13	)	)	PUNCT
ejde-887	362	14	.	.	PUNCT
ejde-887	363	1	this	this	DET
ejde-887	363	2	perturbation	perturbation	NOUN
ejde-887	363	3	leads	lead	VERB
ejde-887	363	4	to	to	ADP
ejde-887	363	5	the	the	DET
ejde-887	363	6	appearance	appearance	NOUN
ejde-887	363	7	of	of	ADP
ejde-887	363	8	multi	multi	NOUN
ejde-887	363	9	-	-	NOUN
ejde-887	363	10	solitons	soliton	NOUN
ejde-887	363	11	for	for	ADP
ejde-887	363	12	t	t	PROPN
ejde-887	363	13	>	>	X
ejde-887	363	14	0	0	X
ejde-887	363	15	.	.	PUNCT
ejde-887	364	1	in	in	ADP
ejde-887	364	2	figures	figure	NOUN
ejde-887	364	3	1	1	NUM
ejde-887	364	4	and	and	CCONJ
ejde-887	364	5	3	3	NUM
ejde-887	364	6	representing	represent	VERB
ejde-887	364	7	z(x	z(x	PROPN
ejde-887	364	8	,	,	PUNCT
ejde-887	364	9	t	t	PROPN
ejde-887	364	10	)	)	PUNCT
ejde-887	364	11	we	we	PRON
ejde-887	364	12	notice	notice	VERB
ejde-887	364	13	the	the	DET
ejde-887	364	14	emergence	emergence	NOUN
ejde-887	364	15	of	of	ADP
ejde-887	364	16	multi	multi	ADJ
ejde-887	364	17	-	-	ADJ
ejde-887	364	18	soliton	soliton	ADJ
ejde-887	364	19	solution	solution	NOUN
ejde-887	364	20	,	,	PUNCT
ejde-887	364	21	where	where	SCONJ
ejde-887	364	22	the	the	DET
ejde-887	364	23	birth	birth	NOUN
ejde-887	364	24	of	of	ADP
ejde-887	364	25	secondary	secondary	ADJ
ejde-887	364	26	solitons	soliton	NOUN
ejde-887	364	27	of	of	ADP
ejde-887	364	28	a	a	DET
ejde-887	364	29	much	much	ADV
ejde-887	364	30	smaller	small	ADJ
ejde-887	364	31	amplitude	amplitude	NOUN
ejde-887	364	32	is	be	AUX
ejde-887	364	33	visible	visible	ADJ
ejde-887	364	34	in	in	ADP
ejde-887	364	35	the	the	DET
ejde-887	364	36	trail	trail	NOUN
ejde-887	364	37	of	of	ADP
ejde-887	364	38	the	the	DET
ejde-887	364	39	original	original	ADJ
ejde-887	364	40	initial	initial	ADJ
ejde-887	364	41	condition	condition	NOUN
ejde-887	364	42	.	.	PUNCT
ejde-887	365	1	this	this	DET
ejde-887	365	2	effect	effect	NOUN
ejde-887	365	3	become	become	VERB
ejde-887	365	4	stronger	strong	ADJ
ejde-887	365	5	in	in	ADP
ejde-887	365	6	the	the	DET
ejde-887	365	7	case	case	NOUN
ejde-887	365	8	of	of	ADP
ejde-887	365	9	the	the	DET
ejde-887	365	10	component	component	NOUN
ejde-887	365	11	u(x	u(x	NOUN
ejde-887	365	12	,	,	PUNCT
ejde-887	365	13	t	t	PROPN
ejde-887	365	14	)	)	PUNCT
ejde-887	365	15	figures	figure	NOUN
ejde-887	365	16	2	2	NUM
ejde-887	365	17	,	,	PUNCT
ejde-887	365	18	4	4	NUM
ejde-887	365	19	,	,	PUNCT
ejde-887	365	20	where	where	SCONJ
ejde-887	365	21	the	the	DET
ejde-887	365	22	secondary	secondary	ADJ
ejde-887	365	23	solitons	soliton	NOUN
ejde-887	365	24	emerge	emerge	VERB
ejde-887	365	25	also	also	ADV
ejde-887	365	26	in	in	ADP
ejde-887	365	27	the	the	DET
ejde-887	365	28	front	front	NOUN
ejde-887	365	29	of	of	ADP
ejde-887	365	30	the	the	DET
ejde-887	365	31	solitary	solitary	ADJ
ejde-887	365	32	wave	wave	NOUN
ejde-887	365	33	.	.	PUNCT
ejde-887	366	1	when	when	SCONJ
ejde-887	366	2	the	the	DET
ejde-887	366	3	initial	initial	ADJ
ejde-887	366	4	soliton	soliton	NOUN
ejde-887	366	5	travel	travel	NOUN
ejde-887	366	6	under	under	ADP
ejde-887	366	7	the	the	DET
ejde-887	366	8	perturbed	perturb	VERB
ejde-887	366	9	non	non	ADJ
ejde-887	366	10	-	-	ADJ
ejde-887	366	11	autonomous	autonomous	ADJ
ejde-887	366	12	equations	equation	NOUN
ejde-887	366	13	with	with	ADP
ejde-887	366	14	periodic	periodic	ADJ
ejde-887	366	15	coefficients	coefficient	NOUN
ejde-887	366	16	,	,	PUNCT
ejde-887	366	17	a	a	DET
ejde-887	366	18	part	part	NOUN
ejde-887	366	19	of	of	ADP
ejde-887	366	20	the	the	DET
ejde-887	366	21	solution	solution	NOUN
ejde-887	366	22	is	be	AUX
ejde-887	366	23	re	re	VERB
ejde-887	366	24	-	-	VERB
ejde-887	366	25	directed	direct	VERB
ejde-887	366	26	in	in	ADP
ejde-887	366	27	opposite	opposite	ADJ
ejde-887	366	28	direction	direction	NOUN
ejde-887	366	29	while	while	SCONJ
ejde-887	366	30	the	the	DET
ejde-887	366	31	rest	rest	NOUN
ejde-887	366	32	of	of	ADP
ejde-887	366	33	the	the	DET
ejde-887	366	34	solution	solution	NOUN
ejde-887	366	35	continues	continue	VERB
ejde-887	366	36	traveling	travel	VERB
ejde-887	366	37	at	at	ADP
ejde-887	366	38	the	the	DET
ejde-887	366	39	same	same	ADJ
ejde-887	366	40	velocity	velocity	NOUN
ejde-887	366	41	.	.	PUNCT
ejde-887	367	1	we	we	PRON
ejde-887	367	2	notice	notice	VERB
ejde-887	367	3	that	that	SCONJ
ejde-887	367	4	the	the	DET
ejde-887	367	5	solitary	solitary	ADJ
ejde-887	367	6	wave	wave	NOUN
ejde-887	367	7	evolution	evolution	NOUN
ejde-887	367	8	can	can	AUX
ejde-887	367	9	be	be	AUX
ejde-887	367	10	classified	classify	VERB
ejde-887	367	11	into	into	ADP
ejde-887	367	12	four	four	NUM
ejde-887	367	13	type	type	NOUN
ejde-887	367	14	of	of	ADP
ejde-887	367	15	perturbations	perturbation	NOUN
ejde-887	367	16	:	:	PUNCT
ejde-887	367	17	(	(	PUNCT
ejde-887	367	18	1	1	X
ejde-887	367	19	)	)	PUNCT
ejde-887	367	20	propagation	propagation	NOUN
ejde-887	367	21	with	with	ADP
ejde-887	367	22	weak	weak	ADJ
ejde-887	367	23	distortions	distortion	NOUN
ejde-887	367	24	,	,	PUNCT
ejde-887	367	25	(	(	PUNCT
ejde-887	367	26	2	2	X
ejde-887	367	27	)	)	PUNCT
ejde-887	367	28	fission	fission	NOUN
ejde-887	367	29	of	of	ADP
ejde-887	367	30	the	the	DET
ejde-887	367	31	initial	initial	ADJ
ejde-887	367	32	soliton	soliton	NOUN
ejde-887	367	33	in	in	ADP
ejde-887	367	34	smaller	small	ADJ
ejde-887	367	35	multisolitons	multisoliton	NOUN
ejde-887	367	36	,	,	PUNCT
ejde-887	367	37	(	(	PUNCT
ejde-887	367	38	3	3	X
ejde-887	367	39	)	)	PUNCT
ejde-887	367	40	fission	fission	NOUN
ejde-887	367	41	of	of	ADP
ejde-887	367	42	secondary	secondary	ADJ
ejde-887	367	43	solitons	soliton	NOUN
ejde-887	367	44	and	and	CCONJ
ejde-887	367	45	peaking	peaking	NOUN
ejde-887	367	46	of	of	ADP
ejde-887	367	47	the	the	DET
ejde-887	367	48	original	original	ADJ
ejde-887	367	49	soliton	soliton	NOUN
ejde-887	367	50	,	,	PUNCT
ejde-887	367	51	and	and	CCONJ
ejde-887	367	52	(	(	PUNCT
ejde-887	367	53	4	4	X
ejde-887	367	54	)	)	PUNCT
ejde-887	367	55	complete	complete	ADJ
ejde-887	367	56	break	break	NOUN
ejde-887	367	57	-	-	PUNCT
ejde-887	367	58	up	up	NOUN
ejde-887	367	59	of	of	ADP
ejde-887	367	60	the	the	DET
ejde-887	367	61	soliton	soliton	NOUN
ejde-887	367	62	in	in	ADP
ejde-887	367	63	very	very	ADV
ejde-887	367	64	high	high	ADJ
ejde-887	367	65	frequency	frequency	NOUN
ejde-887	367	66	oscillations	oscillation	NOUN
ejde-887	367	67	,	,	PUNCT
ejde-887	367	68	beginning	begin	VERB
ejde-887	367	69	with	with	ADP
ejde-887	367	70	the	the	DET
ejde-887	367	71	tail	tail	NOUN
ejde-887	367	72	.	.	PUNCT
ejde-887	368	1	instabilities	instability	NOUN
ejde-887	368	2	of	of	ADP
ejde-887	368	3	types	type	NOUN
ejde-887	368	4	2	2	NUM
ejde-887	368	5	and	and	CCONJ
ejde-887	368	6	4	4	NUM
ejde-887	368	7	were	be	AUX
ejde-887	368	8	also	also	ADV
ejde-887	368	9	observed	observe	VERB
ejde-887	368	10	in	in	ADP
ejde-887	368	11	[	[	X
ejde-887	368	12	19	19	NUM
ejde-887	368	13	]	]	PUNCT
ejde-887	368	14	where	where	SCONJ
ejde-887	368	15	the	the	DET
ejde-887	368	16	analogous	analogous	ADJ
ejde-887	368	17	wave	wave	NOUN
ejde-887	368	18	patterns	pattern	NOUN
ejde-887	368	19	generate	generate	VERB
ejde-887	368	20	dispersion	dispersion	NOUN
ejde-887	368	21	chains	chain	NOUN
ejde-887	368	22	.	.	PUNCT
ejde-887	369	1	these	these	DET
ejde-887	369	2	type	type	NOUN
ejde-887	369	3	of	of	ADP
ejde-887	369	4	instabilities	instability	NOUN
ejde-887	369	5	were	be	AUX
ejde-887	369	6	also	also	ADV
ejde-887	369	7	identified	identify	VERB
ejde-887	369	8	in	in	ADP
ejde-887	369	9	[	[	X
ejde-887	369	10	10	10	NUM
ejde-887	369	11	]	]	PUNCT
ejde-887	369	12	when	when	SCONJ
ejde-887	369	13	the	the	DET
ejde-887	369	14	authors	author	NOUN
ejde-887	369	15	model	model	VERB
ejde-887	369	16	the	the	DET
ejde-887	369	17	propagation	propagation	NOUN
ejde-887	369	18	of	of	ADP
ejde-887	369	19	a	a	DET
ejde-887	369	20	soliton	soliton	NOUN
ejde-887	369	21	wave	wave	NOUN
ejde-887	369	22	over	over	ADP
ejde-887	369	23	a	a	DET
ejde-887	369	24	bore	bore	NOUN
ejde-887	369	25	in	in	ADP
ejde-887	369	26	the	the	DET
ejde-887	369	27	bottom	bottom	NOUN
ejde-887	369	28	.	.	PUNCT
ejde-887	370	1	namely	namely	ADV
ejde-887	370	2	,	,	PUNCT
ejde-887	370	3	in	in	ADP
ejde-887	370	4	[	[	X
ejde-887	370	5	10	10	NUM
ejde-887	370	6	]	]	X
ejde-887	370	7	the	the	DET
ejde-887	370	8	height	height	NOUN
ejde-887	370	9	of	of	ADP
ejde-887	370	10	the	the	DET
ejde-887	370	11	initial	initial	ADJ
ejde-887	370	12	soliton	soliton	NOUN
ejde-887	370	13	tend	tend	VERB
ejde-887	370	14	to	to	PART
ejde-887	370	15	grow	grow	VERB
ejde-887	370	16	in	in	ADP
ejde-887	370	17	time	time	NOUN
ejde-887	370	18	.	.	PUNCT
ejde-887	371	1	if	if	SCONJ
ejde-887	371	2	the	the	DET
ejde-887	371	3	width	width	NOUN
ejde-887	371	4	of	of	ADP
ejde-887	371	5	the	the	DET
ejde-887	371	6	obstacle	obstacle	NOUN
ejde-887	371	7	is	be	AUX
ejde-887	371	8	much	much	ADV
ejde-887	371	9	narrower	narrow	ADJ
ejde-887	371	10	,	,	PUNCT
ejde-887	371	11	or	or	CCONJ
ejde-887	371	12	much	much	ADV
ejde-887	371	13	larger	large	ADJ
ejde-887	371	14	than	than	ADP
ejde-887	371	15	the	the	DET
ejde-887	371	16	width	width	NOUN
ejde-887	371	17	of	of	ADP
ejde-887	371	18	the	the	DET
ejde-887	371	19	obstacle	obstacle	NOUN
ejde-887	371	20	,	,	PUNCT
ejde-887	371	21	the	the	DET
ejde-887	371	22	initial	initial	ADJ
ejde-887	371	23	soliton	soliton	NOUN
ejde-887	371	24	is	be	AUX
ejde-887	371	25	partially	partially	ADV
ejde-887	371	26	reflected	reflect	VERB
ejde-887	371	27	back	back	ADV
ejde-887	371	28	,	,	PUNCT
ejde-887	371	29	forming	form	VERB
ejde-887	371	30	the	the	DET
ejde-887	371	31	wave	wave	NOUN
ejde-887	371	32	reflection	reflection	NOUN
ejde-887	371	33	,	,	PUNCT
ejde-887	371	34	and	and	CCONJ
ejde-887	371	35	the	the	DET
ejde-887	371	36	rest	rest	NOUN
ejde-887	371	37	passes	pass	VERB
ejde-887	371	38	the	the	DET
ejde-887	371	39	obstacle	obstacle	NOUN
ejde-887	371	40	and	and	CCONJ
ejde-887	371	41	continues	continue	VERB
ejde-887	371	42	to	to	PART
ejde-887	371	43	propagate	propagate	VERB
ejde-887	371	44	forward	forward	ADV
ejde-887	371	45	.	.	PUNCT
ejde-887	372	1	this	this	PRON
ejde-887	372	2	is	be	AUX
ejde-887	372	3	the	the	DET
ejde-887	372	4	case	case	NOUN
ejde-887	372	5	of	of	ADP
ejde-887	372	6	quasi	quasi	ADJ
ejde-887	372	7	-	-	ADJ
ejde-887	372	8	stable	stable	ADJ
ejde-887	372	9	solutions	solution	NOUN
ejde-887	372	10	when	when	SCONJ
ejde-887	372	11	there	there	PRON
ejde-887	372	12	is	be	VERB
ejde-887	372	13	a	a	DET
ejde-887	372	14	weak	weak	ADJ
ejde-887	372	15	interaction	interaction	NOUN
ejde-887	372	16	between	between	ADP
ejde-887	372	17	the	the	DET
ejde-887	372	18	soliton	soliton	NOUN
ejde-887	372	19	and	and	CCONJ
ejde-887	372	20	the	the	DET
ejde-887	372	21	bottom	bottom	ADJ
ejde-887	372	22	deformation	deformation	NOUN
ejde-887	372	23	.	.	PUNCT
ejde-887	373	1	for	for	ADP
ejde-887	373	2	bores	bore	NOUN
ejde-887	373	3	with	with	ADP
ejde-887	373	4	width	width	ADJ
ejde-887	373	5	closer	close	ADV
ejde-887	373	6	to	to	ADP
ejde-887	373	7	that	that	PRON
ejde-887	373	8	of	of	ADP
ejde-887	373	9	the	the	DET
ejde-887	373	10	soliton	soliton	NOUN
ejde-887	373	11	,	,	PUNCT
ejde-887	373	12	the	the	DET
ejde-887	373	13	transmitted	transmit	VERB
ejde-887	373	14	wave	wave	NOUN
ejde-887	373	15	(	(	PUNCT
ejde-887	373	16	belongs	belong	VERB
ejde-887	373	17	to	to	PART
ejde-887	373	18	mode	mode	VERB
ejde-887	373	19	4	4	NUM
ejde-887	373	20	)	)	PUNCT
ejde-887	373	21	splits	split	VERB
ejde-887	373	22	into	into	ADP
ejde-887	373	23	a	a	DET
ejde-887	373	24	large	large	ADJ
ejde-887	373	25	number	number	NOUN
ejde-887	373	26	of	of	ADP
ejde-887	373	27	sub	sub	NOUN
ejde-887	373	28	-	-	NOUN
ejde-887	373	29	harmonics	harmonic	NOUN
ejde-887	373	30	.	.	PUNCT
ejde-887	374	1	the	the	DET
ejde-887	374	2	secondary	secondary	ADJ
ejde-887	374	3	solitons	soliton	NOUN
ejde-887	374	4	break	break	VERB
ejde-887	374	5	up	up	ADP
ejde-887	374	6	in	in	ADP
ejde-887	374	7	dispersive	dispersive	ADJ
ejde-887	374	8	wave	wave	NOUN
ejde-887	374	9	chains	chain	NOUN
ejde-887	374	10	because	because	SCONJ
ejde-887	374	11	of	of	ADP
ejde-887	374	12	the	the	DET
ejde-887	374	13	strong	strong	ADJ
ejde-887	374	14	interaction	interaction	NOUN
ejde-887	374	15	between	between	ADP
ejde-887	374	16	the	the	DET
ejde-887	374	17	nonlinearity	nonlinearity	NOUN
ejde-887	374	18	and	and	CCONJ
ejde-887	374	19	the	the	DET
ejde-887	374	20	variable	variable	ADJ
ejde-887	374	21	boundaries	boundary	NOUN
ejde-887	374	22	.	.	PUNCT
ejde-887	375	1	as	as	SCONJ
ejde-887	375	2	one	one	PRON
ejde-887	375	3	can	can	AUX
ejde-887	375	4	notice	notice	VERB
ejde-887	375	5	in	in	ADP
ejde-887	375	6	figures	figure	NOUN
ejde-887	375	7	6	6	NUM
ejde-887	375	8	-	-	SYM
ejde-887	375	9	8	8	NUM
ejde-887	375	10	the	the	DET
ejde-887	375	11	increase	increase	NOUN
ejde-887	375	12	in	in	ADP
ejde-887	375	13	the	the	DET
ejde-887	375	14	amplitude	amplitude	NOUN
ejde-887	375	15	of	of	ADP
ejde-887	375	16	the	the	DET
ejde-887	375	17	incoming	incoming	ADJ
ejde-887	375	18	soliton	soliton	NOUN
ejde-887	375	19	increases	increase	VERB
ejde-887	375	20	the	the	DET
ejde-887	375	21	reflected	reflect	VERB
ejde-887	375	22	waves	wave	NOUN
ejde-887	375	23	which	which	PRON
ejde-887	375	24	are	be	AUX
ejde-887	375	25	waves	wave	NOUN
ejde-887	375	26	of	of	ADP
ejde-887	375	27	radiation	radiation	NOUN
ejde-887	375	28	.	.	PUNCT
ejde-887	376	1	they	they	PRON
ejde-887	376	2	are	be	AUX
ejde-887	376	3	highly	highly	ADV
ejde-887	376	4	ejde-202x	ejde-202x	NOUN
ejde-887	376	5	/	/	SYM
ejde-887	376	6	conf/27	conf/27	NOUN
ejde-887	376	7	boussinesq	boussinesq	ADJ
ejde-887	376	8	equations	equation	NOUN
ejde-887	376	9	45	45	NUM
ejde-887	376	10	unstable	unstable	ADJ
ejde-887	376	11	and	and	CCONJ
ejde-887	376	12	decay	decay	VERB
ejde-887	376	13	rapidly	rapidly	ADV
ejde-887	376	14	with	with	ADP
ejde-887	376	15	time	time	NOUN
ejde-887	376	16	,	,	PUNCT
ejde-887	376	17	which	which	PRON
ejde-887	376	18	can	can	AUX
ejde-887	376	19	also	also	ADV
ejde-887	376	20	be	be	AUX
ejde-887	376	21	seen	see	VERB
ejde-887	376	22	from	from	ADP
ejde-887	376	23	these	these	DET
ejde-887	376	24	figures	figure	NOUN
ejde-887	376	25	.	.	PUNCT
ejde-887	377	1	the	the	DET
ejde-887	377	2	waves	wave	NOUN
ejde-887	377	3	of	of	ADP
ejde-887	377	4	radiation	radiation	NOUN
ejde-887	377	5	in	in	ADP
ejde-887	377	6	the	the	DET
ejde-887	377	7	soliton	soliton	NOUN
ejde-887	377	8	trail	trail	NOUN
ejde-887	377	9	reduce	reduce	VERB
ejde-887	377	10	the	the	DET
ejde-887	377	11	energy	energy	NOUN
ejde-887	377	12	of	of	ADP
ejde-887	377	13	the	the	DET
ejde-887	377	14	initial	initial	ADJ
ejde-887	377	15	soliton	soliton	NOUN
ejde-887	377	16	.	.	PUNCT
ejde-887	378	1	this	this	PRON
ejde-887	378	2	is	be	AUX
ejde-887	378	3	illustrated	illustrate	VERB
ejde-887	378	4	in	in	ADP
ejde-887	378	5	figure	figure	NOUN
ejde-887	378	6	8	8	NUM
ejde-887	378	7	.	.	PUNCT
ejde-887	379	1	the	the	DET
ejde-887	379	2	dispersive	dispersive	ADJ
ejde-887	379	3	radiation	radiation	NOUN
ejde-887	379	4	waves	wave	NOUN
ejde-887	379	5	of	of	ADP
ejde-887	379	6	small	small	ADJ
ejde-887	379	7	amplitude	amplitude	NOUN
ejde-887	379	8	move	move	NOUN
ejde-887	379	9	to	to	ADP
ejde-887	379	10	the	the	DET
ejde-887	379	11	left	left	NOUN
ejde-887	379	12	because	because	SCONJ
ejde-887	379	13	their	their	PRON
ejde-887	379	14	phase	phase	NOUN
ejde-887	379	15	velocity	velocity	NOUN
ejde-887	379	16	becomes	become	VERB
ejde-887	379	17	significant	significant	ADJ
ejde-887	379	18	for	for	ADP
ejde-887	379	19	the	the	DET
ejde-887	379	20	short	short	ADJ
ejde-887	379	21	waves	wave	NOUN
ejde-887	379	22	where	where	SCONJ
ejde-887	379	23	[	[	X
ejde-887	379	24	10	10	NUM
ejde-887	379	25	]	]	PUNCT
ejde-887	379	26	.	.	PUNCT
ejde-887	380	1	in	in	ADP
ejde-887	380	2	general	general	ADJ
ejde-887	380	3	is	be	AUX
ejde-887	380	4	difficult	difficult	ADJ
ejde-887	380	5	to	to	PART
ejde-887	380	6	find	find	VERB
ejde-887	380	7	analytic	analytic	ADJ
ejde-887	380	8	solutions	solution	NOUN
ejde-887	380	9	when	when	SCONJ
ejde-887	380	10	the	the	DET
ejde-887	380	11	equation	equation	NOUN
ejde-887	380	12	is	be	AUX
ejde-887	380	13	governed	govern	VERB
ejde-887	380	14	by	by	ADP
ejde-887	380	15	the	the	DET
ejde-887	380	16	nonlinear	nonlinear	ADJ
ejde-887	380	17	non	non	ADJ
ejde-887	380	18	-	-	ADJ
ejde-887	380	19	autonomous	autonomous	ADJ
ejde-887	380	20	system	system	NOUN
ejde-887	380	21	of	of	ADP
ejde-887	380	22	equations	equation	NOUN
ejde-887	380	23	.	.	PUNCT
ejde-887	381	1	our	our	PRON
ejde-887	381	2	numerical	numerical	ADJ
ejde-887	381	3	results	result	NOUN
ejde-887	381	4	show	show	VERB
ejde-887	381	5	that	that	SCONJ
ejde-887	381	6	smaller	small	ADJ
ejde-887	381	7	amplitude	amplitude	NOUN
ejde-887	381	8	periodic	periodic	ADJ
ejde-887	381	9	perturbation	perturbation	NOUN
ejde-887	381	10	coefficient	coefficient	NOUN
ejde-887	381	11	q(x	q(x	NOUN
ejde-887	381	12	)	)	PUNCT
ejde-887	381	13	is	be	AUX
ejde-887	381	14	too	too	ADV
ejde-887	381	15	weak	weak	ADJ
ejde-887	381	16	to	to	PART
ejde-887	381	17	affect	affect	VERB
ejde-887	381	18	the	the	DET
ejde-887	381	19	wave	wave	NOUN
ejde-887	381	20	of	of	ADP
ejde-887	381	21	large	large	ADJ
ejde-887	381	22	wavelength	wavelength	NOUN
ejde-887	381	23	like	like	ADP
ejde-887	381	24	a	a	DET
ejde-887	381	25	solitary	solitary	ADJ
ejde-887	381	26	wave	wave	NOUN
ejde-887	381	27	lsol	lsol	NOUN
ejde-887	381	28	=	=	SYM
ejde-887	381	29	20	20	NUM
ejde-887	381	30	compare	compare	VERB
ejde-887	381	31	to	to	ADP
ejde-887	381	32	the	the	DET
ejde-887	381	33	perturbation	perturbation	NOUN
ejde-887	381	34	q	q	NOUN
ejde-887	382	1	=	=	PUNCT
ejde-887	382	2	1	1	NUM
ejde-887	382	3	+	+	NUM
ejde-887	382	4	ϵ	ϵ	DET
ejde-887	382	5	sin(2x	sin(2x	PROPN
ejde-887	382	6	)	)	PUNCT
ejde-887	382	7	with	with	ADP
ejde-887	382	8	wavelength	wavelength	NOUN
ejde-887	382	9	λ	λ	X
ejde-887	382	10	=	=	SYM
ejde-887	382	11	4π	4π	NUM
ejde-887	382	12	.	.	PUNCT
ejde-887	383	1	when	when	SCONJ
ejde-887	383	2	the	the	DET
ejde-887	383	3	initial	initial	ADJ
ejde-887	383	4	soliton	soliton	NOUN
ejde-887	383	5	is	be	AUX
ejde-887	383	6	narrower	narrow	ADJ
ejde-887	383	7	,	,	PUNCT
ejde-887	383	8	like	like	ADP
ejde-887	383	9	in	in	ADP
ejde-887	383	10	figure	figure	NOUN
ejde-887	383	11	8	8	NUM
ejde-887	383	12	perturbation	perturbation	NOUN
ejde-887	383	13	induced	induce	VERB
ejde-887	383	14	by	by	ADP
ejde-887	383	15	the	the	DET
ejde-887	383	16	same	same	ADJ
ejde-887	383	17	form	form	NOUN
ejde-887	383	18	of	of	ADP
ejde-887	383	19	coefficient	coefficient	NOUN
ejde-887	383	20	scatters	scatter	VERB
ejde-887	383	21	both	both	CCONJ
ejde-887	383	22	the	the	DET
ejde-887	383	23	reflected	reflected	ADJ
ejde-887	383	24	tail	tail	NOUN
ejde-887	383	25	waves	wave	NOUN
ejde-887	383	26	and	and	CCONJ
ejde-887	383	27	the	the	DET
ejde-887	383	28	transmitted	transmit	VERB
ejde-887	383	29	front	front	ADJ
ejde-887	383	30	waves	wave	NOUN
ejde-887	383	31	.	.	PUNCT
ejde-887	384	1	when	when	SCONJ
ejde-887	384	2	both	both	PRON
ejde-887	384	3	the	the	DET
ejde-887	384	4	amplitude	amplitude	NOUN
ejde-887	384	5	of	of	ADP
ejde-887	384	6	the	the	DET
ejde-887	384	7	incoming	incoming	ADJ
ejde-887	384	8	soliton	soliton	NOUN
ejde-887	384	9	α	α	NOUN
ejde-887	384	10	and	and	CCONJ
ejde-887	384	11	the	the	DET
ejde-887	384	12	coefficient	coefficient	NOUN
ejde-887	384	13	of	of	ADP
ejde-887	384	14	dispersion	dispersion	NOUN
ejde-887	384	15	β	β	X
ejde-887	384	16	are	be	AUX
ejde-887	384	17	increased	increase	VERB
ejde-887	384	18	,	,	PUNCT
ejde-887	384	19	in	in	ADP
ejde-887	384	20	order	order	NOUN
ejde-887	384	21	to	to	PART
ejde-887	384	22	maintain	maintain	VERB
ejde-887	384	23	the	the	DET
ejde-887	384	24	nonlinear	nonlinear	ADJ
ejde-887	384	25	balance	balance	NOUN
ejde-887	384	26	and	and	CCONJ
ejde-887	384	27	hence	hence	ADV
ejde-887	384	28	the	the	DET
ejde-887	384	29	solitary	solitary	ADJ
ejde-887	384	30	wave	wave	NOUN
ejde-887	384	31	stability	stability	NOUN
ejde-887	384	32	,	,	PUNCT
ejde-887	384	33	the	the	DET
ejde-887	384	34	effect	effect	NOUN
ejde-887	384	35	of	of	ADP
ejde-887	384	36	transmitted	transmit	VERB
ejde-887	384	37	waves	wave	NOUN
ejde-887	384	38	with	with	ADP
ejde-887	384	39	higher	high	ADJ
ejde-887	384	40	phase	phase	NOUN
ejde-887	384	41	velocities	velocity	NOUN
ejde-887	384	42	is	be	AUX
ejde-887	384	43	stronger	strong	ADJ
ejde-887	384	44	,	,	PUNCT
ejde-887	384	45	see	see	VERB
ejde-887	384	46	figures	figure	NOUN
ejde-887	384	47	6	6	NUM
ejde-887	384	48	-	-	SYM
ejde-887	384	49	7	7	NUM
ejde-887	384	50	.	.	PUNCT
ejde-887	384	51	when	when	SCONJ
ejde-887	384	52	this	this	DET
ejde-887	384	53	boussinesq	boussinesq	ADJ
ejde-887	384	54	system	system	NOUN
ejde-887	384	55	is	be	AUX
ejde-887	384	56	used	use	VERB
ejde-887	384	57	to	to	PART
ejde-887	384	58	model	model	VERB
ejde-887	384	59	variable	variable	PROPN
ejde-887	384	60	bathymetry	bathymetry	NOUN
ejde-887	384	61	,	,	PUNCT
ejde-887	384	62	the	the	DET
ejde-887	384	63	wave	wave	NOUN
ejde-887	384	64	dispersion	dispersion	NOUN
ejde-887	384	65	scattered	scatter	VERB
ejde-887	384	66	by	by	ADP
ejde-887	384	67	the	the	DET
ejde-887	384	68	bottom	bottom	NOUN
ejde-887	384	69	not	not	PART
ejde-887	384	70	only	only	ADV
ejde-887	384	71	affects	affect	VERB
ejde-887	384	72	significantly	significantly	ADV
ejde-887	384	73	the	the	DET
ejde-887	384	74	wave	wave	NOUN
ejde-887	384	75	deformation	deformation	NOUN
ejde-887	384	76	,	,	PUNCT
ejde-887	384	77	on	on	SCONJ
ejde-887	384	78	the	the	DET
ejde-887	384	79	primary	primary	ADJ
ejde-887	384	80	wave	wave	NOUN
ejde-887	384	81	height	height	VERB
ejde-887	384	82	together	together	ADV
ejde-887	384	83	with	with	ADP
ejde-887	384	84	the	the	DET
ejde-887	384	85	reflected	reflect	VERB
ejde-887	384	86	and	and	CCONJ
ejde-887	384	87	the	the	DET
ejde-887	384	88	transmitted	transmit	VERB
ejde-887	384	89	trail	trail	NOUN
ejde-887	384	90	waves	wave	NOUN
ejde-887	384	91	,	,	PUNCT
ejde-887	384	92	but	but	CCONJ
ejde-887	384	93	also	also	ADV
ejde-887	384	94	generates	generate	VERB
ejde-887	384	95	the	the	DET
ejde-887	384	96	occurrence	occurrence	NOUN
ejde-887	384	97	of	of	ADP
ejde-887	384	98	local	local	ADJ
ejde-887	384	99	vortical	vortical	ADJ
ejde-887	384	100	flow	flow	NOUN
ejde-887	384	101	pattern	pattern	NOUN
ejde-887	384	102	in	in	ADP
ejde-887	384	103	the	the	DET
ejde-887	384	104	proximity	proximity	NOUN
ejde-887	384	105	of	of	ADP
ejde-887	384	106	the	the	DET
ejde-887	384	107	bottom	bottom	ADJ
ejde-887	384	108	deformations	deformation	NOUN
ejde-887	384	109	[	[	X
ejde-887	384	110	4	4	NUM
ejde-887	384	111	]	]	PUNCT
ejde-887	384	112	.	.	PUNCT
ejde-887	385	1	similar	similar	ADJ
ejde-887	385	2	behavior	behavior	NOUN
ejde-887	385	3	of	of	ADP
ejde-887	385	4	nonlinear	nonlinear	ADJ
ejde-887	385	5	waves	wave	NOUN
ejde-887	385	6	over	over	ADP
ejde-887	385	7	variable	variable	ADJ
ejde-887	385	8	bed	bed	NOUN
ejde-887	385	9	,	,	PUNCT
ejde-887	385	10	in	in	ADP
ejde-887	385	11	the	the	DET
ejde-887	385	12	case	case	NOUN
ejde-887	385	13	of	of	ADP
ejde-887	385	14	weakly	weakly	ADJ
ejde-887	385	15	nonlinear	nonlinear	ADJ
ejde-887	385	16	weakly	weakly	ADJ
ejde-887	385	17	dispersive	dispersive	ADJ
ejde-887	385	18	boussinesq	boussinesq	ADJ
ejde-887	385	19	-	-	PUNCT
ejde-887	385	20	type	type	NOUN
ejde-887	385	21	systems	system	NOUN
ejde-887	385	22	,	,	PUNCT
ejde-887	385	23	were	be	AUX
ejde-887	385	24	obtained	obtain	VERB
ejde-887	385	25	when	when	SCONJ
ejde-887	385	26	the	the	DET
ejde-887	385	27	equations	equation	NOUN
ejde-887	385	28	and	and	CCONJ
ejde-887	385	29	boundary	boundary	ADJ
ejde-887	385	30	conditions	condition	NOUN
ejde-887	385	31	are	be	AUX
ejde-887	385	32	formulated	formulate	VERB
ejde-887	385	33	in	in	ADP
ejde-887	385	34	curvilinear	curvilinear	PROPN
ejde-887	385	35	coordinates	coordinate	NOUN
ejde-887	386	1	[	[	X
ejde-887	386	2	17	17	NUM
ejde-887	386	3	]	]	SYM
ejde-887	386	4	.	.	PUNCT
ejde-887	387	1	6	6	X
ejde-887	387	2	.	.	X
ejde-887	387	3	conclusions	conclusion	NOUN
ejde-887	387	4	in	in	ADP
ejde-887	387	5	this	this	DET
ejde-887	387	6	article	article	NOUN
ejde-887	387	7	we	we	PRON
ejde-887	387	8	investigate	investigate	VERB
ejde-887	387	9	solitary	solitary	ADJ
ejde-887	387	10	wave	wave	NOUN
ejde-887	387	11	solutions	solution	NOUN
ejde-887	387	12	for	for	ADP
ejde-887	387	13	a	a	DET
ejde-887	387	14	nonlinear	nonlinear	ADJ
ejde-887	387	15	non	non	ADJ
ejde-887	387	16	-	-	ADJ
ejde-887	387	17	autonomous	autonomous	ADJ
ejde-887	387	18	boussinesq	boussinesq	ADJ
ejde-887	387	19	system	system	NOUN
ejde-887	387	20	.	.	PUNCT
ejde-887	388	1	we	we	PRON
ejde-887	388	2	study	study	VERB
ejde-887	388	3	the	the	DET
ejde-887	388	4	integrability	integrability	NOUN
ejde-887	388	5	of	of	ADP
ejde-887	388	6	this	this	DET
ejde-887	388	7	nonlinear	nonlinear	ADJ
ejde-887	388	8	system	system	NOUN
ejde-887	388	9	for	for	ADP
ejde-887	388	10	the	the	DET
ejde-887	388	11	corresponding	corresponding	ADJ
ejde-887	388	12	autonomous	autonomous	ADJ
ejde-887	388	13	limit	limit	NOUN
ejde-887	388	14	.	.	PUNCT
ejde-887	389	1	in	in	ADP
ejde-887	389	2	addition	addition	NOUN
ejde-887	389	3	,	,	PUNCT
ejde-887	389	4	we	we	PRON
ejde-887	389	5	investigate	investigate	VERB
ejde-887	389	6	the	the	DET
ejde-887	389	7	integrability	integrability	NOUN
ejde-887	389	8	of	of	ADP
ejde-887	389	9	the	the	DET
ejde-887	389	10	non	non	ADJ
ejde-887	389	11	-	-	ADJ
ejde-887	389	12	autonomous	autonomous	ADJ
ejde-887	389	13	nonlinear	nonlinear	ADJ
ejde-887	389	14	problem	problem	NOUN
ejde-887	389	15	with	with	ADP
ejde-887	389	16	the	the	DET
ejde-887	389	17	zakharov	zakharov	ADJ
ejde-887	389	18	-	-	PUNCT
ejde-887	389	19	kuznetsov	kuznetsov	NOUN
ejde-887	389	20	multiple	multiple	ADJ
ejde-887	389	21	-	-	PUNCT
ejde-887	389	22	scale	scale	NOUN
ejde-887	389	23	theory	theory	NOUN
ejde-887	389	24	for	for	ADP
ejde-887	389	25	amplitude	amplitude	NOUN
ejde-887	389	26	modulation	modulation	NOUN
ejde-887	389	27	of	of	ADP
ejde-887	389	28	boussinesq	boussinesq	ADJ
ejde-887	389	29	system	system	NOUN
ejde-887	389	30	and	and	CCONJ
ejde-887	389	31	we	we	PRON
ejde-887	389	32	obtain	obtain	VERB
ejde-887	389	33	a	a	DET
ejde-887	389	34	dispersionless	dispersionless	NOUN
ejde-887	389	35	envelope	envelope	NOUN
ejde-887	389	36	system	system	NOUN
ejde-887	389	37	which	which	PRON
ejde-887	389	38	is	be	AUX
ejde-887	389	39	likely	likely	ADJ
ejde-887	389	40	to	to	PART
ejde-887	389	41	be	be	AUX
ejde-887	389	42	integrable	integrable	ADJ
ejde-887	389	43	.	.	PUNCT
ejde-887	390	1	we	we	PRON
ejde-887	390	2	use	use	VERB
ejde-887	390	3	an	an	DET
ejde-887	390	4	extension	extension	NOUN
ejde-887	390	5	of	of	ADP
ejde-887	390	6	the	the	DET
ejde-887	390	7	zakharov	zakharov	ADJ
ejde-887	390	8	-	-	PUNCT
ejde-887	390	9	kuznetsov	kuznetsov	NOUN
ejde-887	390	10	multiple	multiple	ADJ
ejde-887	390	11	-	-	PUNCT
ejde-887	390	12	scale	scale	NOUN
ejde-887	390	13	procedure	procedure	NOUN
ejde-887	390	14	by	by	ADP
ejde-887	390	15	combining	combine	VERB
ejde-887	390	16	multiple	multiple	ADJ
ejde-887	390	17	phases	phase	NOUN
ejde-887	390	18	.	.	PUNCT
ejde-887	391	1	we	we	PRON
ejde-887	391	2	generate	generate	VERB
ejde-887	391	3	a	a	DET
ejde-887	391	4	hierarchy	hierarchy	NOUN
ejde-887	391	5	of	of	ADP
ejde-887	391	6	differential	differential	ADJ
ejde-887	391	7	equations	equation	NOUN
ejde-887	391	8	for	for	ADP
ejde-887	391	9	the	the	DET
ejde-887	391	10	solution	solution	NOUN
ejde-887	391	11	wave	wave	NOUN
ejde-887	391	12	mixing	mixing	NOUN
ejde-887	391	13	.	.	PUNCT
ejde-887	392	1	the	the	DET
ejde-887	392	2	resulting	result	VERB
ejde-887	392	3	differential	differential	ADJ
ejde-887	392	4	system	system	NOUN
ejde-887	392	5	of	of	ADP
ejde-887	392	6	order	order	NOUN
ejde-887	392	7	three	three	NUM
ejde-887	392	8	,	,	PUNCT
ejde-887	392	9	represented	represent	VERB
ejde-887	392	10	by	by	ADP
ejde-887	392	11	relatively	relatively	ADV
ejde-887	392	12	complicated	complicated	ADJ
ejde-887	392	13	equations	equation	NOUN
ejde-887	392	14	,	,	PUNCT
ejde-887	392	15	can	can	AUX
ejde-887	392	16	be	be	AUX
ejde-887	392	17	always	always	ADV
ejde-887	392	18	solved	solve	VERB
ejde-887	392	19	by	by	ADP
ejde-887	392	20	iterations	iteration	NOUN
ejde-887	392	21	.	.	PUNCT
ejde-887	393	1	we	we	PRON
ejde-887	393	2	solve	solve	VERB
ejde-887	393	3	numerically	numerically	ADV
ejde-887	393	4	the	the	DET
ejde-887	393	5	nonlinear	nonlinear	ADJ
ejde-887	393	6	non	non	ADJ
ejde-887	393	7	-	-	ADJ
ejde-887	393	8	autonomous	autonomous	ADJ
ejde-887	393	9	system	system	NOUN
ejde-887	393	10	and	and	CCONJ
ejde-887	393	11	present	present	VERB
ejde-887	393	12	several	several	ADJ
ejde-887	393	13	examples	example	NOUN
ejde-887	393	14	of	of	ADP
ejde-887	393	15	solutions	solution	NOUN
ejde-887	393	16	in	in	ADP
ejde-887	393	17	order	order	NOUN
ejde-887	393	18	to	to	PART
ejde-887	393	19	validate	validate	VERB
ejde-887	393	20	our	our	PRON
ejde-887	393	21	theoretical	theoretical	ADJ
ejde-887	393	22	results	result	NOUN
ejde-887	393	23	.	.	PUNCT
ejde-887	394	1	these	these	DET
ejde-887	394	2	results	result	NOUN
ejde-887	394	3	are	be	AUX
ejde-887	394	4	also	also	ADV
ejde-887	394	5	of	of	ADP
ejde-887	394	6	importance	importance	NOUN
ejde-887	394	7	for	for	ADP
ejde-887	394	8	the	the	DET
ejde-887	394	9	field	field	NOUN
ejde-887	394	10	of	of	ADP
ejde-887	394	11	nonlinear	nonlinear	ADJ
ejde-887	394	12	fluid	fluid	ADJ
ejde-887	394	13	mechanics	mechanic	NOUN
ejde-887	394	14	,	,	PUNCT
ejde-887	394	15	because	because	SCONJ
ejde-887	394	16	the	the	DET
ejde-887	394	17	non	non	ADJ
ejde-887	394	18	-	-	ADJ
ejde-887	394	19	autonomous	autonomous	ADJ
ejde-887	394	20	boussinesq	boussinesq	NOUN
ejde-887	394	21	system	system	NOUN
ejde-887	394	22	is	be	AUX
ejde-887	394	23	related	relate	VERB
ejde-887	394	24	to	to	ADP
ejde-887	394	25	models	model	NOUN
ejde-887	394	26	for	for	ADP
ejde-887	394	27	the	the	DET
ejde-887	394	28	dynamics	dynamic	NOUN
ejde-887	394	29	of	of	ADP
ejde-887	394	30	nonlinear	nonlinear	ADJ
ejde-887	394	31	waves	wave	NOUN
ejde-887	394	32	over	over	ADP
ejde-887	394	33	variable	variable	ADJ
ejde-887	394	34	bottom	bottom	NOUN
ejde-887	394	35	in	in	ADP
ejde-887	394	36	the	the	DET
ejde-887	394	37	boussinesq	boussinesq	NOUN
ejde-887	394	38	approximation	approximation	NOUN
ejde-887	394	39	,	,	PUNCT
ejde-887	394	40	which	which	PRON
ejde-887	394	41	represent	represent	VERB
ejde-887	394	42	a	a	DET
ejde-887	394	43	very	very	ADV
ejde-887	394	44	important	important	ADJ
ejde-887	394	45	field	field	NOUN
ejde-887	394	46	of	of	ADP
ejde-887	394	47	applications	application	NOUN
ejde-887	394	48	.	.	PUNCT
ejde-887	395	1	we	we	PRON
ejde-887	395	2	study	study	VERB
ejde-887	395	3	the	the	DET
ejde-887	395	4	stability	stability	NOUN
ejde-887	395	5	of	of	ADP
ejde-887	395	6	these	these	DET
ejde-887	395	7	numerical	numerical	ADJ
ejde-887	395	8	solutions	solution	NOUN
ejde-887	395	9	,	,	PUNCT
ejde-887	395	10	and	and	CCONJ
ejde-887	395	11	compare	compare	VERB
ejde-887	395	12	our	our	PRON
ejde-887	395	13	results	result	NOUN
ejde-887	395	14	with	with	ADP
ejde-887	395	15	the	the	DET
ejde-887	395	16	literature	literature	NOUN
ejde-887	395	17	.	.	PUNCT
ejde-887	396	1	the	the	DET
ejde-887	396	2	presented	present	VERB
ejde-887	396	3	theoretical	theoretical	ADJ
ejde-887	396	4	approach	approach	NOUN
ejde-887	396	5	provides	provide	VERB
ejde-887	396	6	methodical	methodical	ADJ
ejde-887	396	7	value	value	NOUN
ejde-887	396	8	for	for	ADP
ejde-887	396	9	the	the	DET
ejde-887	396	10	general	general	ADJ
ejde-887	396	11	field	field	NOUN
ejde-887	396	12	of	of	ADP
ejde-887	396	13	the	the	DET
ejde-887	396	14	theory	theory	NOUN
ejde-887	396	15	of	of	ADP
ejde-887	396	16	nonlinear	nonlinear	ADJ
ejde-887	396	17	non	non	ADJ
ejde-887	396	18	-	-	ADJ
ejde-887	396	19	autonomous	autonomous	ADJ
ejde-887	396	20	systems	system	NOUN
ejde-887	396	21	,	,	PUNCT
ejde-887	396	22	while	while	SCONJ
ejde-887	396	23	also	also	ADV
ejde-887	396	24	underlying	underlie	VERB
ejde-887	396	25	the	the	DET
ejde-887	396	26	connection	connection	NOUN
ejde-887	396	27	between	between	ADP
ejde-887	396	28	the	the	DET
ejde-887	396	29	variable	variable	ADJ
ejde-887	396	30	bottom	bottom	NOUN
ejde-887	396	31	boussinesq	boussinesq	NOUN
ejde-887	396	32	,	,	PUNCT
ejde-887	396	33	and	and	CCONJ
ejde-887	396	34	the	the	DET
ejde-887	396	35	b	b	PROPN
ejde-887	396	36	-	-	PUNCT
ejde-887	396	37	k	k	NOUN
ejde-887	396	38	and	and	CCONJ
ejde-887	396	39	akns	akns	PROPN
ejde-887	396	40	integrable	integrable	ADJ
ejde-887	396	41	systems	system	NOUN
ejde-887	396	42	.	.	PUNCT
ejde-887	397	1	acknowledgments	acknowledgment	NOUN
ejde-887	397	2	.	.	PUNCT
ejde-887	398	1	a.	a.	PROPN
ejde-887	398	2	ludu	ludu	PROPN
ejde-887	398	3	was	be	AUX
ejde-887	398	4	partial	partial	ADJ
ejde-887	398	5	supported	support	VERB
ejde-887	398	6	by	by	ADP
ejde-887	398	7	the	the	DET
ejde-887	398	8	program	program	NOUN
ejde-887	398	9	onr	onr	ADJ
ejde-887	398	10	-	-	PUNCT
ejde-887	398	11	sfrp2021/2023	sfrp2021/2023	NOUN
ejde-887	398	12	for	for	ADP
ejde-887	398	13	the	the	DET
ejde-887	398	14	discussions	discussion	NOUN
ejde-887	398	15	of	of	ADP
ejde-887	398	16	some	some	PRON
ejde-887	398	17	of	of	ADP
ejde-887	398	18	the	the	DET
ejde-887	398	19	models	model	NOUN
ejde-887	398	20	presented	present	VERB
ejde-887	398	21	in	in	ADP
ejde-887	398	22	this	this	DET
ejde-887	398	23	paper	paper	NOUN
ejde-887	398	24	.	.	PUNCT
ejde-887	399	1	also	also	ADV
ejde-887	399	2	he	he	PRON
ejde-887	399	3	is	be	AUX
ejde-887	399	4	grateful	grateful	ADJ
ejde-887	399	5	for	for	ADP
ejde-887	399	6	enlightening	enlighten	VERB
ejde-887	399	7	discussions	discussion	NOUN
ejde-887	399	8	with	with	ADP
ejde-887	399	9	j.	j.	PROPN
ejde-887	399	10	l.	l.	PROPN
ejde-887	399	11	bona	bona	PROPN
ejde-887	399	12	and	and	CCONJ
ejde-887	399	13	h.	h.	PROPN
ejde-887	399	14	chen	chen	PROPN
ejde-887	399	15	.	.	PUNCT
ejde-887	400	1	46	46	NUM
ejde-887	400	2	a.	a.	NOUN
ejde-887	400	3	ludu	ludu	PROPN
ejde-887	400	4	,	,	PUNCT
ejde-887	400	5	h.	h.	PROPN
ejde-887	400	6	khanal	khanal	NOUN
ejde-887	400	7	,	,	PUNCT
ejde-887	400	8	a.	a.	PROPN
ejde-887	400	9	s.	s.	PROPN
ejde-887	400	10	carstea	carstea	PROPN
ejde-887	400	11	ejde-2022	ejde-2022	PROPN
ejde-887	400	12	/	/	SYM
ejde-887	400	13	conf/27	conf/27	NOUN
ejde-887	400	14	references	reference	NOUN
ejde-887	400	15	[	[	X
ejde-887	400	16	1	1	NUM
ejde-887	400	17	]	]	PUNCT
ejde-887	400	18	j.	j.	PROPN
ejde-887	400	19	l.	l.	PROPN
ejde-887	400	20	bona	bona	PROPN
ejde-887	400	21	,	,	PUNCT
ejde-887	400	22	m.	m.	PROPN
ejde-887	400	23	chen	chen	PROPN
ejde-887	400	24	,	,	PUNCT
ejde-887	400	25	j.	j.	PROPN
ejde-887	400	26	-c	-c	PROPN
ejde-887	400	27	.	.	PROPN
ejde-887	400	28	saut	saut	PROPN
ejde-887	400	29	;	;	PUNCT
ejde-887	400	30	boussinesq	boussinesq	ADJ
ejde-887	400	31	equations	equation	NOUN
ejde-887	400	32	and	and	CCONJ
ejde-887	400	33	other	other	ADJ
ejde-887	400	34	systems	system	NOUN
ejde-887	400	35	for	for	ADP
ejde-887	400	36	small	small	ADJ
ejde-887	400	37	-	-	PUNCT
ejde-887	400	38	amplitude	amplitude	NOUN
ejde-887	400	39	long	long	ADJ
ejde-887	400	40	waves	wave	NOUN
ejde-887	400	41	in	in	ADP
ejde-887	400	42	nonlinear	nonlinear	ADJ
ejde-887	400	43	dispersive	dispersive	ADJ
ejde-887	400	44	media	medium	NOUN
ejde-887	400	45	.	.	PUNCT
ejde-887	401	1	i	i	PRON
ejde-887	401	2	:	:	PUNCT
ejde-887	401	3	derivation	derivation	NOUN
ejde-887	401	4	and	and	CCONJ
ejde-887	401	5	linear	linear	PROPN
ejde-887	401	6	theory	theory	NOUN
ejde-887	401	7	,	,	PUNCT
ejde-887	401	8	j.	j.	PROPN
ejde-887	401	9	nonlin	nonlin	PROPN
ejde-887	401	10	.	.	PUNCT
ejde-887	402	1	sci	sci	PROPN
ejde-887	402	2	.	.	PROPN
ejde-887	402	3	,	,	PUNCT
ejde-887	402	4	12	12	NUM
ejde-887	402	5	(	(	PUNCT
ejde-887	402	6	2002	2002	NUM
ejde-887	402	7	)	)	PUNCT
ejde-887	402	8	283	283	NUM
ejde-887	402	9	-	-	SYM
ejde-887	402	10	318	318	NUM
ejde-887	402	11	.	.	PUNCT
ejde-887	403	1	[	[	X
ejde-887	403	2	2	2	X
ejde-887	403	3	]	]	PUNCT
ejde-887	403	4	j.	j.	PROPN
ejde-887	403	5	l.	l.	PROPN
ejde-887	403	6	bona	bona	PROPN
ejde-887	403	7	,	,	PUNCT
ejde-887	403	8	m.	m.	PROPN
ejde-887	403	9	chen	chen	PROPN
ejde-887	403	10	,	,	PUNCT
ejde-887	403	11	j.	j.	PROPN
ejde-887	403	12	-c	-c	PROPN
ejde-887	403	13	.	.	PROPN
ejde-887	403	14	saut	saut	PROPN
ejde-887	403	15	;	;	PUNCT
ejde-887	403	16	global	global	ADJ
ejde-887	403	17	existence	existence	NOUN
ejde-887	403	18	of	of	ADP
ejde-887	403	19	smooth	smooth	ADJ
ejde-887	403	20	solutions	solution	NOUN
ejde-887	403	21	and	and	CCONJ
ejde-887	403	22	stability	stability	NOUN
ejde-887	403	23	of	of	ADP
ejde-887	403	24	solitary	solitary	ADJ
ejde-887	403	25	waves	wave	NOUN
ejde-887	403	26	for	for	ADP
ejde-887	403	27	a	a	DET
ejde-887	403	28	generalized	generalized	ADJ
ejde-887	403	29	boussinesq	boussinesq	ADJ
ejde-887	403	30	equation	equation	NOUN
ejde-887	403	31	,	,	PUNCT
ejde-887	403	32	comm	comm	NOUN
ejde-887	403	33	.	.	PUNCT
ejde-887	403	34	math	math	NOUN
ejde-887	403	35	.	.	PUNCT
ejde-887	404	1	phys	phy	NOUN
ejde-887	404	2	.	.	PUNCT
ejde-887	404	3	,	,	PUNCT
ejde-887	404	4	118	118	NUM
ejde-887	404	5	(	(	PUNCT
ejde-887	404	6	1988	1988	NUM
ejde-887	404	7	)	)	PUNCT
ejde-887	404	8	15	15	NUM
ejde-887	404	9	-	-	SYM
ejde-887	404	10	29	29	NUM
ejde-887	404	11	.	.	PUNCT
ejde-887	405	1	[	[	X
ejde-887	405	2	3	3	X
ejde-887	405	3	]	]	X
ejde-887	405	4	r.	r.	PROPN
ejde-887	405	5	camassa	camassa	PROPN
ejde-887	405	6	,	,	PUNCT
ejde-887	405	7	d.	d.	PROPN
ejde-887	405	8	d.	d.	PROPN
ejde-887	405	9	holm	holm	PROPN
ejde-887	405	10	,	,	PUNCT
ejde-887	405	11	c.	c.	PROPN
ejde-887	405	12	d.	d.	PROPN
ejde-887	405	13	levermore	levermore	PROPN
ejde-887	405	14	;	;	PUNCT
ejde-887	405	15	long	long	ADJ
ejde-887	405	16	-	-	PUNCT
ejde-887	405	17	time	time	NOUN
ejde-887	405	18	effects	effect	NOUN
ejde-887	405	19	of	of	ADP
ejde-887	405	20	bottom	bottom	ADJ
ejde-887	405	21	topography	topography	NOUN
ejde-887	405	22	in	in	ADP
ejde-887	405	23	shallow	shallow	ADJ
ejde-887	405	24	water	water	NOUN
ejde-887	405	25	,	,	PUNCT
ejde-887	405	26	physica	physica	NOUN
ejde-887	405	27	d	d	PROPN
ejde-887	405	28	98	98	NUM
ejde-887	405	29	(	(	PUNCT
ejde-887	405	30	1996	1996	NUM
ejde-887	405	31	)	)	PUNCT
ejde-887	405	32	258	258	NUM
ejde-887	405	33	-	-	SYM
ejde-887	405	34	286	286	NUM
ejde-887	405	35	.	.	PUNCT
ejde-887	406	1	[	[	X
ejde-887	406	2	4	4	NUM
ejde-887	406	3	]	]	X
ejde-887	406	4	c.-h	c.-h	NOUN
ejde-887	406	5	.	.	PUNCT
ejde-887	407	1	chang	chang	PROPN
ejde-887	407	2	,	,	PUNCT
ejde-887	407	3	c.-j	c.-j	PROPN
ejde-887	407	4	.	.	PUNCT
ejde-887	407	5	tang	tang	PROPN
ejde-887	407	6	,	,	PUNCT
ejde-887	407	7	c.	c.	PROPN
ejde-887	407	8	lin	lin	PROPN
ejde-887	407	9	;	;	PUNCT
ejde-887	407	10	vortex	vortex	NOUN
ejde-887	407	11	generation	generation	NOUN
ejde-887	407	12	and	and	CCONJ
ejde-887	407	13	flow	flow	NOUN
ejde-887	407	14	pattern	pattern	NOUN
ejde-887	407	15	development	development	NOUN
ejde-887	407	16	after	after	ADP
ejde-887	407	17	a	a	DET
ejde-887	407	18	solitary	solitary	ADJ
ejde-887	407	19	wave	wave	NOUN
ejde-887	407	20	passing	pass	VERB
ejde-887	407	21	over	over	ADP
ejde-887	407	22	a	a	DET
ejde-887	407	23	bottom	bottom	ADJ
ejde-887	407	24	cavity	cavity	NOUN
ejde-887	407	25	,	,	PUNCT
ejde-887	407	26	computers	computer	NOUN
ejde-887	407	27	and	and	CCONJ
ejde-887	407	28	fluids	fluid	NOUN
ejde-887	407	29	,	,	PUNCT
ejde-887	407	30	53	53	NUM
ejde-887	407	31	(	(	PUNCT
ejde-887	407	32	2012	2012	NUM
ejde-887	407	33	)	)	PUNCT
ejde-887	407	34	79	79	NUM
ejde-887	407	35	-	-	SYM
ejde-887	407	36	92	92	NUM
ejde-887	407	37	.	.	PUNCT
ejde-887	408	1	[	[	X
ejde-887	408	2	5	5	X
ejde-887	408	3	]	]	X
ejde-887	408	4	c.	c.	PROPN
ejde-887	408	5	-l	-l	PROPN
ejde-887	408	6	.	.	PUNCT
ejde-887	409	1	chen	chen	PROPN
ejde-887	409	2	,	,	PUNCT
ejde-887	409	3	x.	x.	PROPN
ejde-887	409	4	-y	-y	PROPN
ejde-887	409	5	.	.	PROPN
ejde-887	409	6	tang	tang	PROPN
ejde-887	409	7	,	,	PUNCT
ejde-887	409	8	s.	s.	PROPN
ejde-887	409	9	-y	-y	PROPN
ejde-887	409	10	.	.	PUNCT
ejde-887	410	1	lou	lou	PROPN
ejde-887	410	2	;	;	PUNCT
ejde-887	410	3	solutions	solution	NOUN
ejde-887	410	4	of	of	ADP
ejde-887	410	5	a	a	DET
ejde-887	410	6	(	(	PUNCT
ejde-887	410	7	2	2	NUM
ejde-887	410	8	+	+	NOUN
ejde-887	410	9	1)−dimensional	1)−dimensional	ADJ
ejde-887	410	10	dispersive	dispersive	ADJ
ejde-887	410	11	long	long	ADJ
ejde-887	410	12	wave	wave	NOUN
ejde-887	410	13	equation	equation	NOUN
ejde-887	410	14	,	,	PUNCT
ejde-887	410	15	phys	phy	NOUN
ejde-887	410	16	.	.	PUNCT
ejde-887	411	1	rev	rev	PROPN
ejde-887	411	2	.	.	PUNCT
ejde-887	412	1	e	e	PROPN
ejde-887	412	2	66	66	NUM
ejde-887	412	3	,	,	PUNCT
ejde-887	412	4	3	3	NUM
ejde-887	412	5	(	(	PUNCT
ejde-887	412	6	2002	2002	NUM
ejde-887	412	7	)	)	PUNCT
ejde-887	412	8	036605	036605	NUM
ejde-887	412	9	.	.	PUNCT
ejde-887	413	1	[	[	X
ejde-887	413	2	6	6	NUM
ejde-887	413	3	]	]	PUNCT
ejde-887	413	4	s.-j	s.-j	PROPN
ejde-887	413	5	.	.	PUNCT
ejde-887	414	1	chen	chen	PROPN
ejde-887	414	2	,	,	PUNCT
ejde-887	414	3	x.	x.	PROPN
ejde-887	414	4	lüa	lüa	PROPN
ejde-887	414	5	,	,	PUNCT
ejde-887	414	6	x.-f	x.-f	PROPN
ejde-887	414	7	.	.	PUNCT
ejde-887	414	8	tang	tang	PROPN
ejde-887	414	9	;	;	PUNCT
ejde-887	414	10	novel	novel	ADJ
ejde-887	414	11	evolutionary	evolutionary	ADJ
ejde-887	414	12	behaviors	behavior	NOUN
ejde-887	414	13	of	of	ADP
ejde-887	414	14	the	the	DET
ejde-887	414	15	mixed	mixed	ADJ
ejde-887	414	16	solutions	solution	NOUN
ejde-887	414	17	to	to	ADP
ejde-887	414	18	a	a	DET
ejde-887	414	19	generalized	generalize	VERB
ejde-887	414	20	burgers	burger	NOUN
ejde-887	414	21	equation	equation	NOUN
ejde-887	414	22	with	with	ADP
ejde-887	414	23	variable	variable	ADJ
ejde-887	414	24	coefficients	coefficient	NOUN
ejde-887	414	25	,	,	PUNCT
ejde-887	414	26	comm	comm	NOUN
ejde-887	414	27	.	.	PUNCT
ejde-887	415	1	nonlin	nonlin	PROPN
ejde-887	415	2	.	.	PUNCT
ejde-887	416	1	sci	sci	PROPN
ejde-887	416	2	.	.	PUNCT
ejde-887	417	1	numer	numer	PROPN
ejde-887	417	2	simulat	simulat	PROPN
ejde-887	417	3	,	,	PUNCT
ejde-887	417	4	95	95	NUM
ejde-887	417	5	(	(	PUNCT
ejde-887	417	6	2021	2021	NUM
ejde-887	417	7	)	)	PUNCT
ejde-887	417	8	105628	105628	NUM
ejde-887	417	9	.	.	PUNCT
ejde-887	418	1	[	[	X
ejde-887	418	2	7	7	X
ejde-887	418	3	]	]	X
ejde-887	418	4	s.	s.	PROPN
ejde-887	418	5	-k	-k	PROPN
ejde-887	418	6	.	.	PUNCT
ejde-887	418	7	chua	chua	PROPN
ejde-887	418	8	;	;	PUNCT
ejde-887	418	9	on	on	ADP
ejde-887	418	10	weighted	weight	VERB
ejde-887	418	11	sobolev	sobolev	NOUN
ejde-887	418	12	spaces	space	NOUN
ejde-887	418	13	,	,	PUNCT
ejde-887	418	14	can	can	AUX
ejde-887	418	15	.	.	PUNCT
ejde-887	419	1	j.	j.	PROPN
ejde-887	419	2	math	math	PROPN
ejde-887	419	3	.	.	PROPN
ejde-887	419	4	,	,	PUNCT
ejde-887	419	5	48	48	NUM
ejde-887	419	6	,	,	PUNCT
ejde-887	419	7	3	3	NUM
ejde-887	419	8	(	(	PUNCT
ejde-887	419	9	1996	1996	NUM
ejde-887	419	10	)	)	PUNCT
ejde-887	419	11	527	527	NUM
ejde-887	419	12	-	-	SYM
ejde-887	419	13	541	541	NUM
ejde-887	419	14	.	.	PUNCT
ejde-887	420	1	[	[	X
ejde-887	420	2	8	8	NUM
ejde-887	420	3	]	]	X
ejde-887	420	4	d.	d.	PROPN
ejde-887	420	5	clamond	clamond	PROPN
ejde-887	420	6	,	,	PUNCT
ejde-887	420	7	d.	d.	PROPN
ejde-887	420	8	dutykh	dutykh	PROPN
ejde-887	420	9	;	;	PUNCT
ejde-887	420	10	accurate	accurate	ADJ
ejde-887	420	11	fast	fast	ADJ
ejde-887	420	12	computation	computation	NOUN
ejde-887	420	13	of	of	ADP
ejde-887	420	14	steady	steady	ADJ
ejde-887	420	15	two	two	NUM
ejde-887	420	16	-	-	PUNCT
ejde-887	420	17	dimensional	dimensional	ADJ
ejde-887	420	18	surface	surface	NOUN
ejde-887	420	19	gravity	gravity	NOUN
ejde-887	420	20	waves	wave	NOUN
ejde-887	420	21	in	in	ADP
ejde-887	420	22	arbitrary	arbitrary	ADJ
ejde-887	420	23	depth	depth	NOUN
ejde-887	420	24	,	,	PUNCT
ejde-887	420	25	j.	j.	PROPN
ejde-887	420	26	fluid	fluid	PROPN
ejde-887	420	27	mech	mech	NOUN
ejde-887	420	28	.	.	PUNCT
ejde-887	420	29	,	,	PUNCT
ejde-887	420	30	844	844	NUM
ejde-887	420	31	(	(	PUNCT
ejde-887	420	32	2018	2018	NUM
ejde-887	420	33	)	)	PUNCT
ejde-887	420	34	491	491	NUM
ejde-887	420	35	-	-	SYM
ejde-887	420	36	518	518	NUM
ejde-887	420	37	.	.	PUNCT
ejde-887	421	1	[	[	X
ejde-887	421	2	9	9	X
ejde-887	421	3	]	]	PUNCT
ejde-887	421	4	p.	p.	NOUN
ejde-887	421	5	a.	a.	PROPN
ejde-887	421	6	clarkson	clarkson	PROPN
ejde-887	421	7	,	,	PUNCT
ejde-887	421	8	e.	e.	PROPN
ejde-887	421	9	dowie	dowie	PROPN
ejde-887	421	10	;	;	PUNCT
ejde-887	421	11	rational	rational	ADJ
ejde-887	421	12	solutions	solution	NOUN
ejde-887	421	13	of	of	ADP
ejde-887	421	14	the	the	DET
ejde-887	421	15	boussinesq	boussinesq	ADJ
ejde-887	421	16	equation	equation	NOUN
ejde-887	421	17	and	and	CCONJ
ejde-887	421	18	applications	application	NOUN
ejde-887	421	19	to	to	ADP
ejde-887	421	20	rogue	rogue	ADJ
ejde-887	421	21	waves	wave	NOUN
ejde-887	421	22	,	,	PUNCT
ejde-887	421	23	trans	trans	PROPN
ejde-887	421	24	.	.	PROPN
ejde-887	421	25	math	math	PROPN
ejde-887	421	26	.	.	PUNCT
ejde-887	422	1	appl	appl	PROPN
ejde-887	422	2	.	.	PROPN
ejde-887	422	3	,	,	PUNCT
ejde-887	422	4	1	1	NUM
ejde-887	422	5	(	(	PUNCT
ejde-887	422	6	2017	2017	NUM
ejde-887	422	7	)	)	PUNCT
ejde-887	422	8	1	1	NUM
ejde-887	422	9	-	-	SYM
ejde-887	422	10	26	26	NUM
ejde-887	422	11	.	.	PUNCT
ejde-887	423	1	[	[	X
ejde-887	423	2	10	10	NUM
ejde-887	423	3	]	]	PUNCT
ejde-887	423	4	a.	a.	NOUN
ejde-887	423	5	compelli	compelli	PROPN
ejde-887	423	6	,	,	PUNCT
ejde-887	423	7	r.	r.	PROPN
ejde-887	423	8	ivanov	ivanov	PROPN
ejde-887	423	9	,	,	PUNCT
ejde-887	423	10	m.	m.	NOUN
ejde-887	423	11	todorov	todorov	PROPN
ejde-887	423	12	;	;	PUNCT
ejde-887	423	13	hamiltonian	hamiltonian	ADJ
ejde-887	423	14	models	model	NOUN
ejde-887	423	15	for	for	ADP
ejde-887	423	16	the	the	DET
ejde-887	423	17	propagation	propagation	NOUN
ejde-887	423	18	of	of	ADP
ejde-887	423	19	irrotational	irrotational	ADJ
ejde-887	423	20	surface	surface	NOUN
ejde-887	423	21	gravity	gravity	NOUN
ejde-887	423	22	waves	wave	NOUN
ejde-887	423	23	over	over	ADP
ejde-887	423	24	a	a	DET
ejde-887	423	25	variable	variable	ADJ
ejde-887	423	26	bottom	bottom	NOUN
ejde-887	423	27	,	,	PUNCT
ejde-887	423	28	phil	phil	PROPN
ejde-887	423	29	.	.	PUNCT
ejde-887	424	1	trans	trans	PROPN
ejde-887	424	2	.	.	PROPN
ejde-887	425	1	roy	roy	PROPN
ejde-887	425	2	.	.	PROPN
ejde-887	425	3	soc	soc	PROPN
ejde-887	425	4	.	.	PUNCT
ejde-887	426	1	a	a	DET
ejde-887	426	2	376	376	NUM
ejde-887	426	3	,	,	PUNCT
ejde-887	426	4	2111	2111	NUM
ejde-887	426	5	(	(	PUNCT
ejde-887	426	6	2018	2018	NUM
ejde-887	426	7	)	)	PUNCT
ejde-887	426	8	20170091	20170091	NUM
ejde-887	426	9	.	.	PUNCT
ejde-887	427	1	[	[	X
ejde-887	427	2	11	11	NUM
ejde-887	427	3	]	]	PUNCT
ejde-887	427	4	w.	w.	PROPN
ejde-887	427	5	craig	craig	PROPN
ejde-887	427	6	,	,	PUNCT
ejde-887	427	7	p.	p.	PROPN
ejde-887	427	8	guyenne	guyenne	PROPN
ejde-887	427	9	,	,	PUNCT
ejde-887	427	10	d.	d.	PROPN
ejde-887	427	11	p.	p.	PROPN
ejde-887	427	12	nichols	nichols	PROPN
ejde-887	427	13	,	,	PUNCT
ejde-887	427	14	c.	c.	PROPN
ejde-887	427	15	sulem	sulem	PROPN
ejde-887	427	16	;	;	PUNCT
ejde-887	427	17	hamiltonian	hamiltonian	ADJ
ejde-887	427	18	long	long	ADJ
ejde-887	427	19	-	-	PUNCT
ejde-887	427	20	wave	wave	NOUN
ejde-887	427	21	expansions	expansion	NOUN
ejde-887	427	22	for	for	ADP
ejde-887	427	23	water	water	NOUN
ejde-887	427	24	waves	wave	NOUN
ejde-887	427	25	over	over	ADP
ejde-887	427	26	a	a	DET
ejde-887	427	27	rough	rough	ADJ
ejde-887	427	28	bottom	bottom	NOUN
ejde-887	427	29	,	,	PUNCT
ejde-887	427	30	proc	proc	NOUN
ejde-887	427	31	.	.	PUNCT
ejde-887	428	1	roy	roy	PROPN
ejde-887	428	2	.	.	PROPN
ejde-887	428	3	soc	soc	PROPN
ejde-887	428	4	.	.	PUNCT
ejde-887	429	1	a	a	PRON
ejde-887	429	2	,	,	PUNCT
ejde-887	429	3	461	461	NUM
ejde-887	429	4	(	(	PUNCT
ejde-887	429	5	2005	2005	NUM
ejde-887	429	6	)	)	PUNCT
ejde-887	429	7	839	839	NUM
ejde-887	429	8	-	-	NUM
ejde-887	429	9	873	873	NUM
ejde-887	429	10	.	.	PUNCT
ejde-887	430	1	[	[	X
ejde-887	430	2	12	12	NUM
ejde-887	430	3	]	]	X
ejde-887	430	4	c.	c.	PROPN
ejde-887	430	5	dai	dai	PROPN
ejde-887	430	6	,	,	PUNCT
ejde-887	430	7	j.	j.	PROPN
ejde-887	430	8	zhu	zhu	PROPN
ejde-887	430	9	,	,	PUNCT
ejde-887	430	10	j.	j.	PROPN
ejde-887	430	11	zhang	zhang	PROPN
ejde-887	430	12	;	;	PUNCT
ejde-887	430	13	new	new	ADJ
ejde-887	430	14	exact	exact	ADJ
ejde-887	430	15	solutions	solution	NOUN
ejde-887	430	16	to	to	ADP
ejde-887	430	17	the	the	DET
ejde-887	430	18	mkdv	mkdv	NOUN
ejde-887	430	19	equation	equation	NOUN
ejde-887	430	20	with	with	ADP
ejde-887	430	21	variable	variable	ADJ
ejde-887	430	22	coefficients	coefficient	NOUN
ejde-887	430	23	,	,	PUNCT
ejde-887	430	24	chaos	chaos	NOUN
ejde-887	430	25	,	,	PUNCT
ejde-887	430	26	solitons	soliton	NOUN
ejde-887	430	27	and	and	CCONJ
ejde-887	430	28	fractals	fractal	NOUN
ejde-887	430	29	27	27	NUM
ejde-887	430	30	(	(	PUNCT
ejde-887	430	31	2006	2006	NUM
ejde-887	430	32	)	)	PUNCT
ejde-887	430	33	,	,	PUNCT
ejde-887	430	34	881–886	881–886	NUM
ejde-887	430	35	.	.	PUNCT
ejde-887	431	1	[	[	X
ejde-887	431	2	13	13	NUM
ejde-887	431	3	]	]	X
ejde-887	431	4	f.	f.	PROPN
ejde-887	431	5	dias	dias	PROPN
ejde-887	431	6	,	,	PUNCT
ejde-887	431	7	d.	d.	PROPN
ejde-887	431	8	dutykh	dutykh	PROPN
ejde-887	431	9	;	;	PUNCT
ejde-887	431	10	dynamics	dynamic	NOUN
ejde-887	431	11	of	of	ADP
ejde-887	431	12	tsunami	tsunami	NOUN
ejde-887	431	13	waves	wave	NOUN
ejde-887	431	14	in	in	ADP
ejde-887	431	15	extreme	extreme	ADJ
ejde-887	431	16	man	man	NOUN
ejde-887	431	17	-	-	PUNCT
ejde-887	431	18	made	make	VERB
ejde-887	431	19	and	and	CCONJ
ejde-887	431	20	natural	natural	ADJ
ejde-887	431	21	hazards	hazard	NOUN
ejde-887	431	22	in	in	ADP
ejde-887	431	23	dynamics	dynamic	NOUN
ejde-887	431	24	of	of	ADP
ejde-887	431	25	structures	structure	NOUN
ejde-887	431	26	(	(	PUNCT
ejde-887	431	27	springer	springer	NOUN
ejde-887	431	28	,	,	PUNCT
ejde-887	431	29	dordrecht	dordrecht	NOUN
ejde-887	431	30	2007	2007	NUM
ejde-887	431	31	)	)	PUNCT
ejde-887	431	32	,	,	PUNCT
ejde-887	431	33	201	201	NUM
ejde-887	431	34	-	-	SYM
ejde-887	431	35	224	224	NUM
ejde-887	431	36	.	.	PUNCT
ejde-887	432	1	[	[	X
ejde-887	432	2	14	14	NUM
ejde-887	432	3	]	]	X
ejde-887	432	4	d.	d.	PROPN
ejde-887	432	5	dutykh	dutykh	PROPN
ejde-887	432	6	,	,	PUNCT
ejde-887	432	7	d.	d.	PROPN
ejde-887	432	8	clamond	clamond	PROPN
ejde-887	432	9	;	;	PUNCT
ejde-887	432	10	modified	modify	VERB
ejde-887	432	11	shallow	shallow	ADJ
ejde-887	432	12	water	water	NOUN
ejde-887	432	13	equations	equation	NOUN
ejde-887	432	14	for	for	ADP
ejde-887	432	15	significantly	significantly	ADV
ejde-887	432	16	varying	vary	VERB
ejde-887	432	17	seabeds	seabed	NOUN
ejde-887	432	18	,	,	PUNCT
ejde-887	432	19	appl	appl	PROPN
ejde-887	432	20	.	.	PROPN
ejde-887	432	21	math	math	PROPN
ejde-887	432	22	.	.	PUNCT
ejde-887	433	1	modelling	model	VERB
ejde-887	433	2	40	40	NUM
ejde-887	433	3	(	(	PUNCT
ejde-887	433	4	2016	2016	NUM
ejde-887	433	5	)	)	PUNCT
ejde-887	433	6	,	,	PUNCT
ejde-887	433	7	9767–9787	9767–9787	NOUN
ejde-887	433	8	.	.	PUNCT
ejde-887	434	1	[	[	X
ejde-887	434	2	15	15	NUM
ejde-887	434	3	]	]	X
ejde-887	434	4	d.	d.	PROPN
ejde-887	434	5	dutykh	dutykh	PROPN
ejde-887	434	6	,	,	PUNCT
ejde-887	434	7	o.	o.	PROPN
ejde-887	434	8	goubet	goubet	PROPN
ejde-887	434	9	;	;	PUNCT
ejde-887	434	10	derivation	derivation	NOUN
ejde-887	434	11	of	of	ADP
ejde-887	434	12	dissipative	dissipative	ADJ
ejde-887	434	13	boussinesq	boussinesq	ADJ
ejde-887	434	14	equations	equation	NOUN
ejde-887	434	15	using	use	VERB
ejde-887	434	16	the	the	DET
ejde-887	434	17	dirichlet	dirichlet	NOUN
ejde-887	434	18	-	-	PUNCT
ejde-887	434	19	toneumann	toneumann	NOUN
ejde-887	434	20	operator	operator	NOUN
ejde-887	434	21	approach	approach	NOUN
ejde-887	434	22	,	,	PUNCT
ejde-887	434	23	math	math	NOUN
ejde-887	434	24	.	.	PUNCT
ejde-887	435	1	comp	comp	PROPN
ejde-887	435	2	.	.	PUNCT
ejde-887	436	1	sim	sim	PROPN
ejde-887	436	2	.	.	PROPN
ejde-887	437	1	,	,	PUNCT
ejde-887	437	2	127	127	NUM
ejde-887	437	3	(	(	PUNCT
ejde-887	437	4	2016	2016	NUM
ejde-887	437	5	)	)	PUNCT
ejde-887	437	6	,	,	PUNCT
ejde-887	437	7	80–93	80–93	NUM
ejde-887	437	8	.	.	PUNCT
ejde-887	438	1	[	[	X
ejde-887	438	2	16	16	NUM
ejde-887	438	3	]	]	X
ejde-887	438	4	c.	c.	PROPN
ejde-887	438	5	a.	a.	PROPN
ejde-887	438	6	j.	j.	PROPN
ejde-887	438	7	fletcher	fletcher	PROPN
ejde-887	438	8	;	;	PUNCT
ejde-887	438	9	computational	computational	ADJ
ejde-887	438	10	techniques	technique	NOUN
ejde-887	438	11	for	for	ADP
ejde-887	438	12	fluid	fluid	ADJ
ejde-887	438	13	dynamics	dynamic	NOUN
ejde-887	438	14	2	2	NUM
ejde-887	438	15	:	:	PUNCT
ejde-887	438	16	specific	specific	ADJ
ejde-887	438	17	techniques	technique	NOUN
ejde-887	438	18	for	for	ADP
ejde-887	438	19	different	different	ADJ
ejde-887	438	20	flow	flow	NOUN
ejde-887	438	21	categories	category	NOUN
ejde-887	438	22	,	,	PUNCT
ejde-887	438	23	2nd	2nd	ADJ
ejde-887	438	24	ed	ed	NOUN
ejde-887	438	25	,	,	PUNCT
ejde-887	438	26	springer	springer	NOUN
ejde-887	438	27	series	series	NOUN
ejde-887	438	28	in	in	ADP
ejde-887	438	29	computational	computational	ADJ
ejde-887	438	30	physics	physics	NOUN
ejde-887	438	31	,	,	PUNCT
ejde-887	438	32	1991	1991	NUM
ejde-887	438	33	.	.	PUNCT
ejde-887	439	1	[	[	X
ejde-887	439	2	17	17	NUM
ejde-887	439	3	]	]	PUNCT
ejde-887	439	4	a.	a.	NOUN
ejde-887	439	5	s.	s.	PROPN
ejde-887	439	6	fokas	fokas	PROPN
ejde-887	439	7	,	,	PUNCT
ejde-887	439	8	a.	a.	PROPN
ejde-887	439	9	nachbin	nachbin	PROPN
ejde-887	439	10	;	;	PUNCT
ejde-887	439	11	water	water	NOUN
ejde-887	439	12	waves	wave	NOUN
ejde-887	439	13	over	over	ADP
ejde-887	439	14	a	a	DET
ejde-887	439	15	variable	variable	ADJ
ejde-887	439	16	bottom	bottom	NOUN
ejde-887	439	17	:	:	PUNCT
ejde-887	439	18	a	a	DET
ejde-887	439	19	non	non	ADJ
ejde-887	439	20	-	-	ADJ
ejde-887	439	21	local	local	ADJ
ejde-887	439	22	formulation	formulation	NOUN
ejde-887	439	23	and	and	CCONJ
ejde-887	439	24	conformal	conformal	NOUN
ejde-887	439	25	mappings	mapping	NOUN
ejde-887	439	26	,	,	PUNCT
ejde-887	439	27	j.	j.	PROPN
ejde-887	439	28	fluid	fluid	PROPN
ejde-887	439	29	mech	mech	NOUN
ejde-887	439	30	.	.	PUNCT
ejde-887	440	1	695	695	NUM
ejde-887	440	2	(	(	PUNCT
ejde-887	440	3	2012	2012	NUM
ejde-887	440	4	)	)	PUNCT
ejde-887	440	5	,	,	PUNCT
ejde-887	440	6	288	288	NUM
ejde-887	440	7	-	-	SYM
ejde-887	440	8	309	309	NUM
ejde-887	440	9	.	.	PUNCT
ejde-887	441	1	[	[	X
ejde-887	441	2	18	18	NUM
ejde-887	441	3	]	]	PUNCT
ejde-887	441	4	m.	m.	PROPN
ejde-887	441	5	f.	f.	PROPN
ejde-887	441	6	gobbi	gobbi	PROPN
ejde-887	441	7	,	,	PUNCT
ejde-887	441	8	j.	j.	PROPN
ejde-887	441	9	t.	t.	PROPN
ejde-887	441	10	kirby	kirby	PROPN
ejde-887	441	11	,	,	PUNCT
ejde-887	441	12	g.	g.	PROPN
ejde-887	441	13	e.	e.	PROPN
ejde-887	441	14	wei	wei	PROPN
ejde-887	441	15	;	;	PUNCT
ejde-887	441	16	a	a	DET
ejde-887	441	17	fully	fully	ADV
ejde-887	441	18	nonlinear	nonlinear	ADJ
ejde-887	441	19	boussinesq	boussinesq	ADJ
ejde-887	441	20	model	model	NOUN
ejde-887	441	21	for	for	ADP
ejde-887	441	22	surface	surface	NOUN
ejde-887	441	23	waves	wave	NOUN
ejde-887	441	24	.	.	PUNCT
ejde-887	442	1	part	part	NOUN
ejde-887	442	2	2	2	NUM
ejde-887	442	3	.	.	PUNCT
ejde-887	442	4	extension	extension	NOUN
ejde-887	442	5	to	to	ADP
ejde-887	442	6	o(kh)4	o(kh)4	PROPN
ejde-887	442	7	,	,	PUNCT
ejde-887	442	8	j.	j.	PROPN
ejde-887	442	9	fluid	fluid	PROPN
ejde-887	442	10	mech	mech	NOUN
ejde-887	442	11	.	.	PUNCT
ejde-887	443	1	,	,	PUNCT
ejde-887	443	2	405	405	NUM
ejde-887	443	3	(	(	PUNCT
ejde-887	443	4	2000	2000	NUM
ejde-887	443	5	)	)	PUNCT
ejde-887	443	6	,	,	PUNCT
ejde-887	443	7	181	181	NUM
ejde-887	443	8	-	-	SYM
ejde-887	443	9	210	210	NUM
ejde-887	443	10	.	.	PUNCT
ejde-887	444	1	[	[	X
ejde-887	444	2	19	19	NUM
ejde-887	444	3	]	]	X
ejde-887	444	4	i.	i.	PROPN
ejde-887	444	5	m.	m.	PROPN
ejde-887	444	6	gorban	gorban	PROPN
ejde-887	444	7	;	;	PUNCT
ejde-887	444	8	a	a	DET
ejde-887	444	9	numerical	numerical	ADJ
ejde-887	444	10	study	study	NOUN
ejde-887	444	11	of	of	ADP
ejde-887	444	12	solitary	solitary	ADJ
ejde-887	444	13	wave	wave	NOUN
ejde-887	444	14	interactions	interaction	NOUN
ejde-887	444	15	with	with	ADP
ejde-887	444	16	a	a	DET
ejde-887	444	17	bottom	bottom	ADJ
ejde-887	444	18	step	step	NOUN
ejde-887	444	19	,	,	PUNCT
ejde-887	444	20	continuous	continuous	ADJ
ejde-887	444	21	and	and	CCONJ
ejde-887	444	22	distributed	distribute	VERB
ejde-887	444	23	systems	system	NOUN
ejde-887	444	24	ii	ii	PROPN
ejde-887	444	25	:	:	PUNCT
ejde-887	444	26	theory	theory	NOUN
ejde-887	444	27	and	and	CCONJ
ejde-887	444	28	applications	application	NOUN
ejde-887	444	29	(	(	PUNCT
ejde-887	444	30	2015	2015	NUM
ejde-887	444	31	)	)	PUNCT
ejde-887	444	32	,	,	PUNCT
ejde-887	444	33	369	369	NUM
ejde-887	444	34	-	-	SYM
ejde-887	444	35	387	387	NUM
ejde-887	444	36	.	.	PUNCT
ejde-887	445	1	[	[	X
ejde-887	445	2	20	20	NUM
ejde-887	445	3	]	]	PUNCT
ejde-887	445	4	j.	j.	PROPN
ejde-887	445	5	h.	h.	PROPN
ejde-887	445	6	herterich	herterich	PROPN
ejde-887	445	7	,	,	PUNCT
ejde-887	445	8	f.	f.	PROPN
ejde-887	445	9	dias	dias	PROPN
ejde-887	445	10	;	;	PUNCT
ejde-887	445	11	extreme	extreme	ADJ
ejde-887	445	12	long	long	ADJ
ejde-887	445	13	waves	wave	NOUN
ejde-887	445	14	over	over	ADP
ejde-887	445	15	a	a	DET
ejde-887	445	16	varying	vary	VERB
ejde-887	445	17	bathymetry	bathymetry	NOUN
ejde-887	445	18	numerical	numerical	PROPN
ejde-887	445	19	,	,	PUNCT
ejde-887	445	20	j.	j.	PROPN
ejde-887	445	21	fluid	fluid	PROPN
ejde-887	445	22	mech	mech	NOUN
ejde-887	445	23	.	.	PUNCT
ejde-887	445	24	,	,	PUNCT
ejde-887	445	25	878	878	NUM
ejde-887	445	26	(	(	PUNCT
ejde-887	445	27	2019	2019	NUM
ejde-887	445	28	)	)	PUNCT
ejde-887	445	29	,	,	PUNCT
ejde-887	445	30	481	481	NUM
ejde-887	445	31	-	-	SYM
ejde-887	445	32	501	501	NUM
ejde-887	445	33	.	.	PUNCT
ejde-887	446	1	[	[	X
ejde-887	446	2	21	21	NUM
ejde-887	446	3	]	]	X
ejde-887	446	4	r.	r.	PROPN
ejde-887	446	5	hirota	hirota	PROPN
ejde-887	446	6	,	,	PUNCT
ejde-887	446	7	j.	j.	PROPN
ejde-887	446	8	satsuma	satsuma	PROPN
ejde-887	446	9	;	;	PUNCT
ejde-887	446	10	nonlinear	nonlinear	ADJ
ejde-887	446	11	evolution	evolution	NOUN
ejde-887	446	12	equations	equation	NOUN
ejde-887	446	13	generated	generate	VERB
ejde-887	446	14	from	from	ADP
ejde-887	446	15	the	the	DET
ejde-887	446	16	bäcklund	bäcklund	NOUN
ejde-887	446	17	transformation	transformation	NOUN
ejde-887	446	18	for	for	ADP
ejde-887	446	19	the	the	DET
ejde-887	446	20	boussinesq	boussinesq	ADJ
ejde-887	446	21	equation	equation	NOUN
ejde-887	446	22	,	,	PUNCT
ejde-887	446	23	prog	prog	NOUN
ejde-887	446	24	.	.	PUNCT
ejde-887	447	1	th	th	X
ejde-887	447	2	.	.	PUNCT
ejde-887	448	1	phys	phy	NOUN
ejde-887	448	2	.	.	PUNCT
ejde-887	449	1	57	57	NUM
ejde-887	449	2	,	,	PUNCT
ejde-887	449	3	3	3	NUM
ejde-887	449	4	(	(	PUNCT
ejde-887	449	5	1977	1977	NUM
ejde-887	449	6	)	)	PUNCT
ejde-887	449	7	,	,	PUNCT
ejde-887	449	8	797	797	NUM
ejde-887	449	9	-	-	SYM
ejde-887	449	10	807	807	NUM
ejde-887	449	11	.	.	PUNCT
ejde-887	450	1	[	[	X
ejde-887	450	2	22	22	NUM
ejde-887	450	3	]	]	PUNCT
ejde-887	450	4	p.	p.	NOUN
ejde-887	450	5	a.	a.	PROPN
ejde-887	450	6	e.	e.	PROPN
ejde-887	450	7	m.	m.	PROPN
ejde-887	450	8	janssen	janssen	PROPN
ejde-887	450	9	;	;	PUNCT
ejde-887	450	10	nonlinear	nonlinear	ADJ
ejde-887	450	11	four	four	NUM
ejde-887	450	12	-	-	PUNCT
ejde-887	450	13	wave	wave	NOUN
ejde-887	450	14	interactions	interaction	NOUN
ejde-887	450	15	and	and	CCONJ
ejde-887	450	16	freak	freak	NOUN
ejde-887	450	17	waves	wave	NOUN
ejde-887	450	18	,	,	PUNCT
ejde-887	450	19	j.	j.	PROPN
ejde-887	450	20	phys	phys	PROPN
ejde-887	450	21	.	.	PUNCT
ejde-887	451	1	oceanography	oceanography	NOUN
ejde-887	451	2	33	33	NUM
ejde-887	451	3	(	(	PUNCT
ejde-887	451	4	2003	2003	NUM
ejde-887	451	5	)	)	PUNCT
ejde-887	451	6	863	863	NUM
ejde-887	451	7	-	-	SYM
ejde-887	451	8	884	884	NUM
ejde-887	451	9	.	.	PUNCT
ejde-887	452	1	[	[	X
ejde-887	452	2	23	23	NUM
ejde-887	452	3	]	]	X
ejde-887	452	4	o.	o.	PROPN
ejde-887	452	5	v.	v.	PROPN
ejde-887	452	6	kaptsova	kaptsova	PROPN
ejde-887	452	7	,	,	PUNCT
ejde-887	452	8	d.	d.	PROPN
ejde-887	452	9	o.	o.	PROPN
ejde-887	452	10	kaptsov	kaptsov	PROPN
ejde-887	452	11	;	;	PUNCT
ejde-887	452	12	exact	exact	ADJ
ejde-887	452	13	solution	solution	NOUN
ejde-887	452	14	of	of	ADP
ejde-887	452	15	boussinesq	boussinesq	ADJ
ejde-887	452	16	equations	equation	NOUN
ejde-887	452	17	for	for	ADP
ejde-887	452	18	propagation	propagation	NOUN
ejde-887	452	19	of	of	ADP
ejde-887	452	20	nonlinear	nonlinear	ADJ
ejde-887	452	21	waves	wave	NOUN
ejde-887	452	22	,	,	PUNCT
ejde-887	452	23	eur	eur	NOUN
ejde-887	452	24	.	.	PUNCT
ejde-887	453	1	phys	phy	NOUN
ejde-887	453	2	.	.	PUNCT
ejde-887	454	1	j.	j.	PROPN
ejde-887	454	2	plus	plus	CCONJ
ejde-887	454	3	(	(	PUNCT
ejde-887	454	4	2020	2020	NUM
ejde-887	454	5	)	)	PUNCT
ejde-887	454	6	135	135	NUM
ejde-887	454	7	-	-	SYM
ejde-887	454	8	723	723	NUM
ejde-887	454	9	.	.	PUNCT
ejde-887	455	1	[	[	X
ejde-887	455	2	24	24	NUM
ejde-887	455	3	]	]	X
ejde-887	455	4	d.	d.	PROPN
ejde-887	455	5	j.	j.	PROPN
ejde-887	455	6	kaup	kaup	PROPN
ejde-887	455	7	;	;	PUNCT
ejde-887	455	8	a	a	DET
ejde-887	455	9	higher	high	ADJ
ejde-887	455	10	-	-	PUNCT
ejde-887	455	11	order	order	NOUN
ejde-887	455	12	water	water	NOUN
ejde-887	455	13	-	-	PUNCT
ejde-887	455	14	wave	wave	NOUN
ejde-887	455	15	equation	equation	NOUN
ejde-887	455	16	and	and	CCONJ
ejde-887	455	17	the	the	DET
ejde-887	455	18	method	method	NOUN
ejde-887	455	19	for	for	ADP
ejde-887	455	20	solving	solve	VERB
ejde-887	455	21	it	it	PRON
ejde-887	455	22	,	,	PUNCT
ejde-887	455	23	prog	prog	PROPN
ejde-887	455	24	.	.	PUNCT
ejde-887	456	1	theor	theor	PROPN
ejde-887	456	2	.	.	PUNCT
ejde-887	457	1	phys	phy	NOUN
ejde-887	457	2	.	.	PUNCT
ejde-887	457	3	,	,	PUNCT
ejde-887	457	4	54	54	NUM
ejde-887	457	5	,	,	PUNCT
ejde-887	457	6	2	2	NUM
ejde-887	457	7	(	(	PUNCT
ejde-887	457	8	1975	1975	NUM
ejde-887	457	9	)	)	PUNCT
ejde-887	457	10	396	396	NUM
ejde-887	457	11	-	-	SYM
ejde-887	457	12	408	408	NUM
ejde-887	457	13	.	.	PUNCT
ejde-887	458	1	[	[	X
ejde-887	458	2	25	25	NUM
ejde-887	458	3	]	]	PUNCT
ejde-887	458	4	b.	b.	PROPN
ejde-887	458	5	a.	a.	PROPN
ejde-887	458	6	kupershmidt	kupershmidt	PROPN
ejde-887	458	7	;	;	PUNCT
ejde-887	458	8	mathematics	mathematic	NOUN
ejde-887	458	9	of	of	ADP
ejde-887	458	10	dispersive	dispersive	ADJ
ejde-887	458	11	water	water	NOUN
ejde-887	458	12	waves	wave	NOUN
ejde-887	458	13	,	,	PUNCT
ejde-887	458	14	commun	commun	PROPN
ejde-887	458	15	.	.	PUNCT
ejde-887	458	16	math	math	NOUN
ejde-887	458	17	.	.	PUNCT
ejde-887	459	1	phys	phy	NOUN
ejde-887	459	2	.	.	PUNCT
ejde-887	459	3	,	,	PUNCT
ejde-887	459	4	99	99	NUM
ejde-887	459	5	,	,	PUNCT
ejde-887	459	6	1	1	NUM
ejde-887	459	7	(	(	PUNCT
ejde-887	459	8	1985	1985	NUM
ejde-887	459	9	)	)	PUNCT
ejde-887	459	10	51	51	NUM
ejde-887	459	11	-	-	SYM
ejde-887	459	12	73	73	NUM
ejde-887	459	13	.	.	PUNCT
ejde-887	460	1	[	[	X
ejde-887	460	2	26	26	NUM
ejde-887	460	3	]	]	X
ejde-887	460	4	y.	y.	PROPN
ejde-887	460	5	s.	s.	PROPN
ejde-887	460	6	kivshar	kivshar	PROPN
ejde-887	460	7	,	,	PUNCT
ejde-887	460	8	b.	b.	PROPN
ejde-887	460	9	a.	a.	PROPN
ejde-887	460	10	malomed	malomed	PROPN
ejde-887	460	11	;	;	PUNCT
ejde-887	460	12	dynamics	dynamic	NOUN
ejde-887	460	13	of	of	ADP
ejde-887	460	14	solitons	soliton	NOUN
ejde-887	460	15	in	in	ADP
ejde-887	460	16	nearly	nearly	ADV
ejde-887	460	17	integrable	integrable	ADJ
ejde-887	460	18	systems	system	NOUN
ejde-887	460	19	,	,	PUNCT
ejde-887	460	20	rev	rev	PROPN
ejde-887	460	21	.	.	PROPN
ejde-887	460	22	mod	mod	PROPN
ejde-887	460	23	.	.	PUNCT
ejde-887	461	1	phys	phy	NOUN
ejde-887	461	2	.	.	PUNCT
ejde-887	461	3	,	,	PUNCT
ejde-887	461	4	61	61	NUM
ejde-887	461	5	,	,	PUNCT
ejde-887	461	6	4	4	NUM
ejde-887	461	7	(	(	PUNCT
ejde-887	461	8	1989	1989	NUM
ejde-887	461	9	)	)	PUNCT
ejde-887	461	10	763	763	NUM
ejde-887	461	11	.	.	PUNCT
ejde-887	462	1	ejde-202x	ejde-202x	NOUN
ejde-887	462	2	/	/	SYM
ejde-887	462	3	conf/27	conf/27	NOUN
ejde-887	462	4	boussinesq	boussinesq	NOUN
ejde-887	462	5	equations	equation	NOUN
ejde-887	462	6	47	47	NUM
ejde-887	463	1	[	[	SYM
ejde-887	463	2	27	27	NUM
ejde-887	463	3	]	]	X
ejde-887	463	4	n.	n.	NOUN
ejde-887	463	5	kolkovska	kolkovska	PROPN
ejde-887	463	6	,	,	PUNCT
ejde-887	463	7	v.	v.	ADP
ejde-887	463	8	m.	m.	NOUN
ejde-887	463	9	vassilev	vassilev	NOUN
ejde-887	463	10	;	;	PUNCT
ejde-887	463	11	solitary	solitary	ADJ
ejde-887	463	12	waves	wave	NOUN
ejde-887	463	13	to	to	ADP
ejde-887	463	14	boussinesq	boussinesq	ADJ
ejde-887	463	15	equation	equation	NOUN
ejde-887	463	16	with	with	ADP
ejde-887	463	17	linear	linear	ADJ
ejde-887	463	18	restoring	restore	VERB
ejde-887	463	19	force	force	NOUN
ejde-887	463	20	.	.	PUNCT
ejde-887	464	1	aip	aip	PROPN
ejde-887	464	2	conf	conf	PROPN
ejde-887	464	3	.	.	PUNCT
ejde-887	465	1	proc	proc	PROPN
ejde-887	465	2	.	.	PROPN
ejde-887	465	3	,	,	PUNCT
ejde-887	465	4	2164	2164	NUM
ejde-887	465	5	(	(	PUNCT
ejde-887	465	6	2019	2019	NUM
ejde-887	465	7	)	)	PUNCT
ejde-887	465	8	110005	110005	NUM
ejde-887	465	9	.	.	PUNCT
ejde-887	466	1	[	[	X
ejde-887	466	2	28	28	NUM
ejde-887	466	3	]	]	X
ejde-887	466	4	y.	y.	PROPN
ejde-887	466	5	li	li	PROPN
ejde-887	466	6	,	,	PUNCT
ejde-887	466	7	w.	w.	PROPN
ejde-887	466	8	-x	-x	PROPN
ejde-887	466	9	.	.	PROPN
ejde-887	466	10	ma	ma	PROPN
ejde-887	466	11	,	,	PUNCT
ejde-887	466	12	j.	j.	PROPN
ejde-887	466	13	e.	e.	PROPN
ejde-887	466	14	zhang	zhang	PROPN
ejde-887	466	15	;	;	PUNCT
ejde-887	466	16	darboux	darboux	VERB
ejde-887	466	17	transformations	transformation	NOUN
ejde-887	466	18	of	of	ADP
ejde-887	466	19	classical	classical	ADJ
ejde-887	466	20	boussinesq	boussinesq	NOUN
ejde-887	466	21	system	system	NOUN
ejde-887	466	22	and	and	CCONJ
ejde-887	466	23	its	its	PRON
ejde-887	466	24	new	new	ADJ
ejde-887	466	25	solutions	solution	NOUN
ejde-887	466	26	,	,	PUNCT
ejde-887	466	27	phys	phy	NOUN
ejde-887	466	28	.	.	PUNCT
ejde-887	467	1	lett	lett	PROPN
ejde-887	467	2	.	.	PROPN
ejde-887	468	1	,	,	PUNCT
ejde-887	468	2	275	275	NUM
ejde-887	468	3	(	(	PUNCT
ejde-887	468	4	2000	2000	NUM
ejde-887	468	5	)	)	PUNCT
ejde-887	468	6	,	,	PUNCT
ejde-887	468	7	60	60	NUM
ejde-887	468	8	-	-	SYM
ejde-887	468	9	66	66	NUM
ejde-887	468	10	.	.	PUNCT
ejde-887	469	1	[	[	X
ejde-887	469	2	29	29	NUM
ejde-887	469	3	]	]	PUNCT
ejde-887	469	4	w.-x	w.-x	NOUN
ejde-887	469	5	.	.	PUNCT
ejde-887	470	1	ma	ma	PROPN
ejde-887	470	2	;	;	PUNCT
ejde-887	470	3	integrable	integrable	ADJ
ejde-887	470	4	couplings	coupling	NOUN
ejde-887	470	5	of	of	ADP
ejde-887	470	6	vector	vector	NOUN
ejde-887	470	7	akns	akns	NOUN
ejde-887	470	8	soliton	soliton	NOUN
ejde-887	470	9	equations	equation	NOUN
ejde-887	470	10	,	,	PUNCT
ejde-887	470	11	j.	j.	PROPN
ejde-887	470	12	math	math	PROPN
ejde-887	470	13	.	.	PUNCT
ejde-887	471	1	phys	phy	NOUN
ejde-887	471	2	.	.	PUNCT
ejde-887	471	3	,	,	PUNCT
ejde-887	471	4	46	46	NUM
ejde-887	471	5	(	(	PUNCT
ejde-887	471	6	2005	2005	NUM
ejde-887	471	7	)	)	PUNCT
ejde-887	471	8	033507	033507	NUM
ejde-887	471	9	.	.	PUNCT
ejde-887	472	1	[	[	X
ejde-887	472	2	30	30	NUM
ejde-887	472	3	]	]	X
ejde-887	472	4	l.	l.	PROPN
ejde-887	472	5	molinet	molinet	PROPN
ejde-887	472	6	,	,	PUNCT
ejde-887	472	7	t.	t.	NOUN
ejde-887	472	8	raafat	raafat	NOUN
ejde-887	472	9	,	,	PUNCT
ejde-887	472	10	i.	i.	NOUN
ejde-887	472	11	zaiter	zaiter	PROPN
ejde-887	472	12	;	;	PUNCT
ejde-887	472	13	the	the	DET
ejde-887	472	14	classical	classical	ADJ
ejde-887	472	15	boussinesq	boussinesq	NOUN
ejde-887	472	16	system	system	NOUN
ejde-887	472	17	revisited	revisit	VERB
ejde-887	472	18	,	,	PUNCT
ejde-887	472	19	arxiv	arxiv	PROPN
ejde-887	472	20	preprint	preprint	NOUN
ejde-887	472	21	arxiv:2001.11870	arxiv:2001.11870	PROPN
ejde-887	472	22	(	(	PUNCT
ejde-887	472	23	2020	2020	NUM
ejde-887	472	24	)	)	PUNCT
ejde-887	473	1	[	[	X
ejde-887	473	2	31	31	NUM
ejde-887	473	3	]	]	X
ejde-887	473	4	d.	d.	PROPN
ejde-887	473	5	e.	e.	PROPN
ejde-887	473	6	mitsotakis	mitsotakis	PROPN
ejde-887	473	7	;	;	PUNCT
ejde-887	473	8	boussinesq	boussinesq	ADJ
ejde-887	473	9	systems	system	NOUN
ejde-887	473	10	in	in	ADP
ejde-887	473	11	two	two	NUM
ejde-887	473	12	space	space	NOUN
ejde-887	473	13	dimensions	dimension	NOUN
ejde-887	473	14	over	over	ADP
ejde-887	473	15	a	a	DET
ejde-887	473	16	variable	variable	ADJ
ejde-887	473	17	bottom	bottom	NOUN
ejde-887	473	18	for	for	ADP
ejde-887	473	19	the	the	DET
ejde-887	473	20	generation	generation	NOUN
ejde-887	473	21	and	and	CCONJ
ejde-887	473	22	propagation	propagation	NOUN
ejde-887	473	23	of	of	ADP
ejde-887	473	24	tsunami	tsunami	NOUN
ejde-887	473	25	waves	wave	NOUN
ejde-887	473	26	,	,	PUNCT
ejde-887	473	27	math	math	NOUN
ejde-887	473	28	.	.	PUNCT
ejde-887	474	1	comp	comp	PROPN
ejde-887	474	2	.	.	PUNCT
ejde-887	475	1	sim	sim	PROPN
ejde-887	475	2	.	.	PROPN
ejde-887	476	1	,	,	PUNCT
ejde-887	476	2	80	80	NUM
ejde-887	476	3	(	(	PUNCT
ejde-887	476	4	2009	2009	NUM
ejde-887	476	5	)	)	PUNCT
ejde-887	476	6	,	,	PUNCT
ejde-887	476	7	860–873	860–873	NUM
ejde-887	476	8	.	.	PUNCT
ejde-887	477	1	[	[	X
ejde-887	477	2	32	32	NUM
ejde-887	477	3	]	]	PUNCT
ejde-887	477	4	b.	b.	PROPN
ejde-887	477	5	t.	t.	PROPN
ejde-887	477	6	nadiga	nadiga	PROPN
ejde-887	477	7	,	,	PUNCT
ejde-887	477	8	l.	l.	PROPN
ejde-887	477	9	g.	g.	PROPN
ejde-887	477	10	margolin	margolin	PROPN
ejde-887	477	11	,	,	PUNCT
ejde-887	477	12	p.	p.	PROPN
ejde-887	477	13	k.	k.	PROPN
ejde-887	477	14	smolarkiewicz	smolarkiewicz	PROPN
ejde-887	477	15	;	;	PUNCT
ejde-887	477	16	different	different	ADJ
ejde-887	477	17	approximations	approximation	NOUN
ejde-887	477	18	of	of	ADP
ejde-887	477	19	shallow	shallow	ADJ
ejde-887	477	20	fluid	fluid	NOUN
ejde-887	477	21	flow	flow	NOUN
ejde-887	477	22	over	over	ADP
ejde-887	477	23	an	an	DET
ejde-887	477	24	obstacle	obstacle	NOUN
ejde-887	477	25	,	,	PUNCT
ejde-887	477	26	phys	phy	NOUN
ejde-887	477	27	.	.	PUNCT
ejde-887	477	28	fluids	fluid	NOUN
ejde-887	477	29	,	,	PUNCT
ejde-887	477	30	8	8	NUM
ejde-887	477	31	,	,	PUNCT
ejde-887	477	32	8	8	NUM
ejde-887	477	33	(	(	PUNCT
ejde-887	477	34	1996	1996	NUM
ejde-887	477	35	)	)	PUNCT
ejde-887	477	36	,	,	PUNCT
ejde-887	477	37	2066	2066	NUM
ejde-887	477	38	-	-	SYM
ejde-887	477	39	2077	2077	NUM
ejde-887	477	40	.	.	PUNCT
ejde-887	478	1	[	[	X
ejde-887	478	2	33	33	NUM
ejde-887	478	3	]	]	X
ejde-887	478	4	o.	o.	PROPN
ejde-887	478	5	nakoulima	nakoulima	PROPN
ejde-887	478	6	et	et	PROPN
ejde-887	478	7	al	al	PROPN
ejde-887	478	8	;	;	PUNCT
ejde-887	478	9	solitary	solitary	ADJ
ejde-887	478	10	wave	wave	NOUN
ejde-887	478	11	dynamics	dynamic	NOUN
ejde-887	478	12	in	in	ADP
ejde-887	478	13	shallow	shallow	ADJ
ejde-887	478	14	water	water	NOUN
ejde-887	478	15	over	over	ADP
ejde-887	478	16	periodic	periodic	ADJ
ejde-887	478	17	topography	topography	NOUN
ejde-887	478	18	,	,	PUNCT
ejde-887	478	19	chaos	chaos	NOUN
ejde-887	478	20	,	,	PUNCT
ejde-887	478	21	15	15	NUM
ejde-887	478	22	(	(	PUNCT
ejde-887	478	23	2005	2005	NUM
ejde-887	478	24	)	)	PUNCT
ejde-887	478	25	037107	037107	NUM
ejde-887	478	26	.	.	PUNCT
ejde-887	479	1	[	[	X
ejde-887	479	2	34	34	NUM
ejde-887	479	3	]	]	PUNCT
ejde-887	479	4	k.	k.	PROPN
ejde-887	479	5	e.	e.	PROPN
ejde-887	479	6	parnell	parnell	PROPN
ejde-887	479	7	et	et	PROPN
ejde-887	479	8	al	al	PROPN
ejde-887	479	9	.	.	PROPN
ejde-887	479	10	;	;	PUNCT
ejde-887	479	11	ship	ship	NOUN
ejde-887	479	12	-	-	PUNCT
ejde-887	479	13	induced	induce	VERB
ejde-887	479	14	solitary	solitary	ADJ
ejde-887	479	15	riemann	riemann	PROPN
ejde-887	479	16	waves	wave	NOUN
ejde-887	479	17	of	of	ADP
ejde-887	479	18	depression	depression	NOUN
ejde-887	479	19	in	in	ADP
ejde-887	479	20	venice	venice	PROPN
ejde-887	479	21	lagoon	lagoon	NOUN
ejde-887	479	22	,	,	PUNCT
ejde-887	479	23	phys	phy	NOUN
ejde-887	479	24	.	.	PUNCT
ejde-887	480	1	let	let	VERB
ejde-887	480	2	.	.	PUNCT
ejde-887	481	1	a	a	PRON
ejde-887	481	2	,	,	PUNCT
ejde-887	481	3	379	379	NUM
ejde-887	481	4	(	(	PUNCT
ejde-887	481	5	2015	2015	NUM
ejde-887	481	6	)	)	PUNCT
ejde-887	481	7	,	,	PUNCT
ejde-887	481	8	555	555	NUM
ejde-887	481	9	-	-	SYM
ejde-887	481	10	559	559	NUM
ejde-887	481	11	.	.	PUNCT
ejde-887	482	1	[	[	X
ejde-887	482	2	35	35	NUM
ejde-887	482	3	]	]	X
ejde-887	482	4	s.	s.	PROPN
ejde-887	482	5	pierini	pierini	PROPN
ejde-887	482	6	,	,	PUNCT
ejde-887	482	7	m.	m.	NOUN
ejde-887	482	8	ghil	ghil	PROPN
ejde-887	482	9	,	,	PUNCT
ejde-887	482	10	m.	m.	NOUN
ejde-887	482	11	d.	d.	PROPN
ejde-887	482	12	chekroun	chekroun	PROPN
ejde-887	482	13	;	;	PUNCT
ejde-887	482	14	exploring	explore	VERB
ejde-887	482	15	the	the	DET
ejde-887	482	16	pullback	pullback	NOUN
ejde-887	482	17	attractors	attractor	NOUN
ejde-887	482	18	of	of	ADP
ejde-887	482	19	a	a	DET
ejde-887	482	20	low	low	ADJ
ejde-887	482	21	-	-	PUNCT
ejde-887	482	22	order	order	NOUN
ejde-887	482	23	quasigeostrophic	quasigeostrophic	ADJ
ejde-887	482	24	ocean	ocean	NOUN
ejde-887	482	25	model	model	NOUN
ejde-887	482	26	:	:	PUNCT
ejde-887	482	27	the	the	DET
ejde-887	482	28	deterministic	deterministic	ADJ
ejde-887	482	29	case	case	NOUN
ejde-887	482	30	,	,	PUNCT
ejde-887	482	31	j.	j.	PROPN
ejde-887	482	32	climate	climate	PROPN
ejde-887	482	33	29	29	NUM
ejde-887	482	34	,	,	PUNCT
ejde-887	482	35	11	11	NUM
ejde-887	482	36	(	(	PUNCT
ejde-887	482	37	2016	2016	NUM
ejde-887	482	38	)	)	PUNCT
ejde-887	482	39	,	,	PUNCT
ejde-887	482	40	4185	4185	NUM
ejde-887	482	41	-	-	SYM
ejde-887	482	42	4202	4202	NUM
ejde-887	482	43	.	.	PUNCT
ejde-887	483	1	[	[	X
ejde-887	483	2	36	36	NUM
ejde-887	483	3	]	]	PUNCT
ejde-887	483	4	s.	s.	PROPN
ejde-887	483	5	ponce	ponce	PROPN
ejde-887	483	6	de	de	PROPN
ejde-887	483	7	león	león	PROPN
ejde-887	483	8	a.	a.	PROPN
ejde-887	483	9	r.	r.	PROPN
ejde-887	483	10	osborne	osborne	PROPN
ejde-887	483	11	;	;	PUNCT
ejde-887	483	12	role	role	NOUN
ejde-887	483	13	of	of	ADP
ejde-887	483	14	nonlinear	nonlinear	ADJ
ejde-887	483	15	four	four	NUM
ejde-887	483	16	-	-	PUNCT
ejde-887	483	17	wave	wave	NOUN
ejde-887	483	18	interactions	interaction	NOUN
ejde-887	483	19	source	source	NOUN
ejde-887	483	20	term	term	NOUN
ejde-887	483	21	on	on	ADP
ejde-887	483	22	the	the	DET
ejde-887	483	23	spectral	spectral	ADJ
ejde-887	483	24	shape	shape	NOUN
ejde-887	483	25	,	,	PUNCT
ejde-887	483	26	j.	j.	PROPN
ejde-887	483	27	mar	mar	PROPN
ejde-887	483	28	.	.	PUNCT
ejde-887	483	29	sci	sci	PROPN
ejde-887	483	30	.	.	PUNCT
ejde-887	484	1	eng	eng	PROPN
ejde-887	484	2	.	.	PROPN
ejde-887	484	3	,	,	PUNCT
ejde-887	484	4	8	8	NUM
ejde-887	484	5	(	(	PUNCT
ejde-887	484	6	2020	2020	NUM
ejde-887	484	7	)	)	PUNCT
ejde-887	484	8	251	251	NUM
ejde-887	484	9	.	.	PUNCT
ejde-887	485	1	[	[	X
ejde-887	485	2	37	37	NUM
ejde-887	485	3	]	]	PUNCT
ejde-887	485	4	a.	a.	NOUN
ejde-887	485	5	a.	a.	PROPN
ejde-887	485	6	saakyan	saakyan	PROPN
ejde-887	485	7	;	;	PUNCT
ejde-887	485	8	convergence	convergence	NOUN
ejde-887	485	9	of	of	ADP
ejde-887	485	10	double	double	ADJ
ejde-887	485	11	fourier	fourier	NOUN
ejde-887	485	12	series	series	NOUN
ejde-887	485	13	after	after	ADP
ejde-887	485	14	a	a	DET
ejde-887	485	15	change	change	NOUN
ejde-887	485	16	of	of	ADP
ejde-887	485	17	variable	variable	NOUN
ejde-887	485	18	,	,	PUNCT
ejde-887	485	19	math	math	NOUN
ejde-887	485	20	.	.	PUNCT
ejde-887	486	1	notes	note	NOUN
ejde-887	486	2	,	,	PUNCT
ejde-887	486	3	74	74	NUM
ejde-887	486	4	,	,	PUNCT
ejde-887	486	5	2	2	NUM
ejde-887	486	6	(	(	PUNCT
ejde-887	486	7	2003	2003	NUM
ejde-887	486	8	)	)	PUNCT
ejde-887	486	9	255–265	255–265	NUM
ejde-887	486	10	;	;	PUNCT
ejde-887	486	11	for	for	ADP
ejde-887	486	12	basic	basic	ADJ
ejde-887	486	13	reference	reference	NOUN
ejde-887	486	14	to	to	ADP
ejde-887	486	15	the	the	DET
ejde-887	486	16	lipschitz	lipschitz	NOUN
ejde-887	486	17	condition	condition	NOUN
ejde-887	486	18	and	and	CCONJ
ejde-887	486	19	fourier	fourier	NOUN
ejde-887	486	20	series	series	PROPN
ejde-887	486	21	convergence	convergence	PROPN
ejde-887	486	22	see	see	VERB
ejde-887	486	23	:	:	PUNCT
ejde-887	486	24	r.	r.	PROPN
ejde-887	486	25	a.	a.	PROPN
ejde-887	486	26	adams	adams	PROPN
ejde-887	486	27	,	,	PUNCT
ejde-887	486	28	and	and	CCONJ
ejde-887	486	29	j.	j.	PROPN
ejde-887	486	30	j.	j.	PROPN
ejde-887	486	31	f.	f.	PROPN
ejde-887	486	32	fournier	fournier	PROPN
ejde-887	486	33	,	,	PUNCT
ejde-887	486	34	sobolev	sobolev	NOUN
ejde-887	486	35	spaces	space	NOUN
ejde-887	486	36	(	(	PUNCT
ejde-887	486	37	academic	academic	ADJ
ejde-887	486	38	press	press	NOUN
ejde-887	486	39	,	,	PUNCT
ejde-887	486	40	2003	2003	NUM
ejde-887	486	41	)	)	PUNCT
ejde-887	486	42	.	.	PUNCT
ejde-887	487	1	[	[	X
ejde-887	487	2	38	38	NUM
ejde-887	487	3	]	]	PUNCT
ejde-887	487	4	h.	h.	PROPN
ejde-887	487	5	h.	h.	PROPN
ejde-887	487	6	sohrab	sohrab	PROPN
ejde-887	487	7	;	;	PUNCT
ejde-887	487	8	basic	basic	ADJ
ejde-887	487	9	real	real	ADJ
ejde-887	487	10	analysis	analysis	NOUN
ejde-887	487	11	,	,	PUNCT
ejde-887	487	12	vol	vol	NOUN
ejde-887	487	13	.	.	PROPN
ejde-887	487	14	231	231	NUM
ejde-887	487	15	(	(	PUNCT
ejde-887	487	16	birkhäuser	birkhäuser	NOUN
ejde-887	487	17	2003	2003	NUM
ejde-887	487	18	)	)	PUNCT
ejde-887	488	1	p.	p.	NOUN
ejde-887	488	2	142	142	NUM
ejde-887	488	3	.	.	PUNCT
ejde-887	489	1	[	[	X
ejde-887	489	2	39	39	NUM
ejde-887	489	3	]	]	PUNCT
ejde-887	489	4	x.	x.	NOUN
ejde-887	489	5	-y	-y	PROPN
ejde-887	489	6	.	.	PROPN
ejde-887	489	7	tang	tang	PROPN
ejde-887	489	8	,	,	PUNCT
ejde-887	489	9	s.	s.	PROPN
ejde-887	489	10	-y	-y	PROPN
ejde-887	489	11	.	.	PUNCT
ejde-887	490	1	lou	lou	PROPN
ejde-887	490	2	,	,	PUNCT
ejde-887	490	3	y.	y.	PROPN
ejde-887	490	4	zhang	zhang	PROPN
ejde-887	490	5	;	;	PUNCT
ejde-887	490	6	localized	localized	ADJ
ejde-887	490	7	excitations	excitation	NOUN
ejde-887	490	8	in	in	ADP
ejde-887	490	9	(	(	PUNCT
ejde-887	490	10	2	2	NUM
ejde-887	490	11	+	+	CCONJ
ejde-887	490	12	1)−dimensional	1)−dimensional	ADJ
ejde-887	490	13	systems	system	NOUN
ejde-887	490	14	,	,	PUNCT
ejde-887	490	15	phys	phy	NOUN
ejde-887	490	16	.	.	PUNCT
ejde-887	490	17	rev	rev	PROPN
ejde-887	490	18	.	.	PUNCT
ejde-887	491	1	e	e	PROPN
ejde-887	491	2	66	66	NUM
ejde-887	491	3	,	,	PUNCT
ejde-887	491	4	4	4	NUM
ejde-887	491	5	(	(	PUNCT
ejde-887	491	6	2002	2002	NUM
ejde-887	491	7	)	)	PUNCT
ejde-887	491	8	046601	046601	NUM
ejde-887	491	9	.	.	PUNCT
ejde-887	492	1	[	[	X
ejde-887	492	2	40	40	NUM
ejde-887	492	3	]	]	PUNCT
ejde-887	492	4	b.	b.	PROPN
ejde-887	492	5	v.	v.	PROPN
ejde-887	492	6	turesson	turesson	PROPN
ejde-887	492	7	;	;	PUNCT
ejde-887	492	8	nonlinear	nonlinear	ADJ
ejde-887	492	9	potential	potential	ADJ
ejde-887	492	10	theory	theory	NOUN
ejde-887	492	11	and	and	CCONJ
ejde-887	492	12	weighted	weight	VERB
ejde-887	492	13	sobolev	sobolev	NOUN
ejde-887	492	14	spaces	space	NOUN
ejde-887	492	15	(	(	PUNCT
ejde-887	492	16	springer	springer	NOUN
ejde-887	492	17	2000	2000	NUM
ejde-887	492	18	)	)	PUNCT
ejde-887	492	19	section	section	NOUN
ejde-887	492	20	1.2.1	1.2.1	NUM
ejde-887	492	21	.	.	PUNCT
ejde-887	493	1	[	[	X
ejde-887	493	2	41	41	NUM
ejde-887	493	3	]	]	X
ejde-887	493	4	r.	r.	PROPN
ejde-887	493	5	m.	m.	PROPN
ejde-887	493	6	vargas	vargas	PROPN
ejde-887	493	7	-	-	PUNCT
ejde-887	493	8	magaña	magaña	PROPN
ejde-887	493	9	,	,	PUNCT
ejde-887	493	10	p.	p.	PROPN
ejde-887	493	11	panayotaros	panayotaros	PROPN
ejde-887	493	12	;	;	PUNCT
ejde-887	493	13	a	a	DET
ejde-887	493	14	non	non	ADJ
ejde-887	493	15	-	-	ADJ
ejde-887	493	16	local	local	ADJ
ejde-887	493	17	dirichlet	dirichlet	NOUN
ejde-887	493	18	-	-	PUNCT
ejde-887	493	19	to	to	ADP
ejde-887	493	20	-	-	PUNCT
ejde-887	493	21	neumann	neumann	PROPN
ejde-887	493	22	operator	operator	NOUN
ejde-887	493	23	:	:	PUNCT
ejde-887	493	24	a	a	DET
ejde-887	493	25	whitham	whitham	NOUN
ejde-887	493	26	–	–	PUNCT
ejde-887	493	27	boussinesq	boussinesq	ADJ
ejde-887	493	28	long	long	ADJ
ejde-887	493	29	-	-	PUNCT
ejde-887	493	30	wave	wave	NOUN
ejde-887	493	31	model	model	NOUN
ejde-887	493	32	for	for	ADP
ejde-887	493	33	variable	variable	ADJ
ejde-887	493	34	topography	topography	NOUN
ejde-887	493	35	,	,	PUNCT
ejde-887	493	36	wave	wave	NOUN
ejde-887	493	37	motion	motion	NOUN
ejde-887	493	38	65	65	NUM
ejde-887	493	39	(	(	PUNCT
ejde-887	493	40	2016	2016	NUM
ejde-887	493	41	)	)	PUNCT
ejde-887	493	42	156–174	156–174	NUM
ejde-887	493	43	.	.	PUNCT
ejde-887	494	1	[	[	X
ejde-887	494	2	42	42	NUM
ejde-887	494	3	]	]	PUNCT
ejde-887	494	4	v.	v.	ADP
ejde-887	494	5	m.	m.	NOUN
ejde-887	494	6	vassilev	vassilev	NOUN
ejde-887	494	7	,	,	PUNCT
ejde-887	494	8	p.	p.	NOUN
ejde-887	494	9	a.	a.	PROPN
ejde-887	494	10	djondjorov	djondjorov	PROPN
ejde-887	494	11	,	,	PUNCT
ejde-887	494	12	m.	m.	NOUN
ejde-887	494	13	t.	t.	PROPN
ejde-887	494	14	hadzhilazova	hadzhilazova	PROPN
ejde-887	494	15	,	,	PUNCT
ejde-887	494	16	i.	i.	PROPN
ejde-887	494	17	m.	m.	PROPN
ejde-887	494	18	mladenov	mladenov	PROPN
ejde-887	494	19	;	;	PUNCT
ejde-887	494	20	traveling	travel	VERB
ejde-887	494	21	wave	wave	NOUN
ejde-887	494	22	solutions	solution	NOUN
ejde-887	494	23	of	of	ADP
ejde-887	494	24	the	the	DET
ejde-887	494	25	one	one	NUM
ejde-887	494	26	-	-	PUNCT
ejde-887	494	27	dimensional	dimensional	ADJ
ejde-887	494	28	boussinesq	boussinesq	ADJ
ejde-887	494	29	paradigm	paradigm	NOUN
ejde-887	494	30	equation	equation	NOUN
ejde-887	494	31	,	,	PUNCT
ejde-887	494	32	aip	aip	PROPN
ejde-887	494	33	conf	conf	PROPN
ejde-887	494	34	.	.	PUNCT
ejde-887	495	1	proc	proc	PROPN
ejde-887	495	2	.	.	PUNCT
ejde-887	496	1	1561	1561	NUM
ejde-887	496	2	(	(	PUNCT
ejde-887	496	3	2013	2013	NUM
ejde-887	496	4	)	)	PUNCT
ejde-887	496	5	327332	327332	NUM
ejde-887	496	6	.	.	PUNCT
ejde-887	497	1	[	[	X
ejde-887	497	2	43	43	NUM
ejde-887	497	3	]	]	X
ejde-887	497	4	j.	j.	PROPN
ejde-887	497	5	yu	yu	PROPN
ejde-887	497	6	;	;	PUNCT
ejde-887	497	7	revisiting	revisit	VERB
ejde-887	497	8	terrain	terrain	NOUN
ejde-887	497	9	-	-	PUNCT
ejde-887	497	10	following	follow	VERB
ejde-887	497	11	boussinesq	boussinesq	ADJ
ejde-887	497	12	equations	equation	NOUN
ejde-887	497	13	on	on	ADP
ejde-887	497	14	a	a	DET
ejde-887	497	15	highly	highly	ADV
ejde-887	497	16	variable	variable	ADJ
ejde-887	497	17	periodic	periodic	ADJ
ejde-887	497	18	bed	bed	NOUN
ejde-887	497	19	,	,	PUNCT
ejde-887	497	20	j.	j.	PROPN
ejde-887	497	21	ocean	ocean	PROPN
ejde-887	497	22	eng	eng	PROPN
ejde-887	497	23	.	.	PROPN
ejde-887	497	24	marine	marine	PROPN
ejde-887	497	25	eng	eng	PROPN
ejde-887	497	26	.	.	PROPN
ejde-887	497	27	,	,	PUNCT
ejde-887	497	28	5	5	NUM
ejde-887	497	29	(	(	PUNCT
ejde-887	497	30	2019	2019	NUM
ejde-887	497	31	)	)	PUNCT
ejde-887	497	32	403	403	NUM
ejde-887	497	33	-	-	SYM
ejde-887	497	34	412	412	NUM
ejde-887	497	35	.	.	PUNCT
ejde-887	498	1	[	[	X
ejde-887	498	2	44	44	NUM
ejde-887	498	3	]	]	PUNCT
ejde-887	498	4	j.	j.	PROPN
ejde-887	498	5	yu	yu	PROPN
ejde-887	498	6	;	;	PUNCT
ejde-887	498	7	waveform	waveform	NOUN
ejde-887	498	8	of	of	ADP
ejde-887	498	9	gravity	gravity	NOUN
ejde-887	498	10	and	and	CCONJ
ejde-887	498	11	capillary	capillary	ADJ
ejde-887	498	12	-	-	PUNCT
ejde-887	498	13	gravity	gravity	NOUN
ejde-887	498	14	waves	wave	NOUN
ejde-887	498	15	over	over	ADP
ejde-887	498	16	bathymetry	bathymetry	NOUN
ejde-887	498	17	,	,	PUNCT
ejde-887	498	18	phys	phy	NOUN
ejde-887	498	19	.	.	PUNCT
ejde-887	499	1	rev	rev	PROPN
ejde-887	499	2	.	.	PROPN
ejde-887	499	3	fluids	fluid	NOUN
ejde-887	499	4	,	,	PUNCT
ejde-887	499	5	4	4	NUM
ejde-887	499	6	(	(	PUNCT
ejde-887	499	7	2019	2019	NUM
ejde-887	499	8	)	)	PUNCT
ejde-887	499	9	014806	014806	NUM
ejde-887	499	10	.	.	PUNCT
ejde-887	500	1	[	[	X
ejde-887	500	2	45	45	NUM
ejde-887	500	3	]	]	X
ejde-887	500	4	v.	v.	PROPN
ejde-887	500	5	e.	e.	PROPN
ejde-887	500	6	zakharov	zakharov	PROPN
ejde-887	500	7	,	,	PUNCT
ejde-887	500	8	e.	e.	PROPN
ejde-887	500	9	a.	a.	PROPN
ejde-887	500	10	kuznetsov	kuznetsov	PROPN
ejde-887	500	11	;	;	PUNCT
ejde-887	500	12	multi	multi	ADJ
ejde-887	500	13	-	-	ADJ
ejde-887	500	14	scale	scale	ADJ
ejde-887	500	15	expansions	expansion	NOUN
ejde-887	500	16	in	in	ADP
ejde-887	500	17	the	the	DET
ejde-887	500	18	theory	theory	NOUN
ejde-887	500	19	of	of	ADP
ejde-887	500	20	systems	system	NOUN
ejde-887	500	21	integrable	integrable	ADJ
ejde-887	500	22	by	by	ADP
ejde-887	500	23	the	the	DET
ejde-887	500	24	inverse	inverse	NOUN
ejde-887	500	25	scattering	scattering	NOUN
ejde-887	500	26	transform	transform	NOUN
ejde-887	500	27	,	,	PUNCT
ejde-887	500	28	physica	physica	NOUN
ejde-887	500	29	18	18	NUM
ejde-887	500	30	d	d	NOUN
ejde-887	500	31	(	(	PUNCT
ejde-887	500	32	1986	1986	NUM
ejde-887	500	33	)	)	PUNCT
ejde-887	500	34	455	455	NUM
ejde-887	500	35	-	-	SYM
ejde-887	500	36	463	463	NUM
ejde-887	500	37	.	.	PUNCT
ejde-887	501	1	[	[	X
ejde-887	501	2	46	46	NUM
ejde-887	501	3	]	]	X
ejde-887	501	4	j.	j.	PROPN
ejde-887	501	5	e.	e.	PROPN
ejde-887	501	6	zhang	zhang	PROPN
ejde-887	501	7	,	,	PUNCT
ejde-887	501	8	y.	y.	PROPN
ejde-887	501	9	li	li	PROPN
ejde-887	501	10	;	;	PUNCT
ejde-887	501	11	bidirectional	bidirectional	ADJ
ejde-887	501	12	solitons	soliton	NOUN
ejde-887	501	13	on	on	ADP
ejde-887	501	14	water	water	NOUN
ejde-887	501	15	,	,	PUNCT
ejde-887	501	16	phys	phy	NOUN
ejde-887	501	17	.	.	PUNCT
ejde-887	502	1	rev	rev	PROPN
ejde-887	502	2	.	.	PROPN
ejde-887	503	1	e	e	PROPN
ejde-887	503	2	,	,	PUNCT
ejde-887	503	3	67	67	NUM
ejde-887	503	4	(	(	PUNCT
ejde-887	503	5	2003	2003	NUM
ejde-887	503	6	)	)	PUNCT
ejde-887	503	7	016306	016306	NUM
ejde-887	503	8	.	.	PUNCT
ejde-887	504	1	[	[	X
ejde-887	504	2	47	47	NUM
ejde-887	504	3	]	]	X
ejde-887	504	4	d.	d.	PROPN
ejde-887	504	5	zhao	zhao	PROPN
ejde-887	504	6	,	,	PUNCT
ejde-887	504	7	y.-j	y.-j	PROPN
ejde-887	504	8	.	.	PROPN
ejde-887	505	1	zhang	zhang	PROPN
ejde-887	505	2	,	,	PUNCT
ejde-887	505	3	w.-w	w.-w	PROPN
ejde-887	505	4	.	.	PUNCT
ejde-887	506	1	lou	lou	PROPN
ejde-887	506	2	,	,	PUNCT
ejde-887	506	3	h.-g	h.-g	PROPN
ejde-887	506	4	.	.	PUNCT
ejde-887	507	1	luo	luo	PROPN
ejde-887	507	2	;	;	PUNCT
ejde-887	507	3	akns	akns	NOUN
ejde-887	507	4	hierarchy	hierarchy	NOUN
ejde-887	507	5	,	,	PUNCT
ejde-887	507	6	darboux	darboux	VERB
ejde-887	507	7	transformation	transformation	NOUN
ejde-887	507	8	and	and	CCONJ
ejde-887	507	9	conservation	conservation	NOUN
ejde-887	507	10	laws	law	NOUN
ejde-887	507	11	of	of	ADP
ejde-887	507	12	the	the	DET
ejde-887	507	13	1d	1d	NUM
ejde-887	507	14	nonautonomous	nonautonomous	ADJ
ejde-887	507	15	nonlinear	nonlinear	PROPN
ejde-887	507	16	schrödinger	schrödinger	PROPN
ejde-887	507	17	equations	equation	NOUN
ejde-887	507	18	,	,	PUNCT
ejde-887	507	19	j.	j.	PROPN
ejde-887	507	20	math	math	PROPN
ejde-887	507	21	.	.	PUNCT
ejde-887	508	1	phys	phy	NOUN
ejde-887	508	2	.	.	PUNCT
ejde-887	508	3	,	,	PUNCT
ejde-887	508	4	52	52	NUM
ejde-887	508	5	(	(	PUNCT
ejde-887	508	6	2011	2011	NUM
ejde-887	508	7	)	)	PUNCT
ejde-887	508	8	043502	043502	NUM
ejde-887	508	9	.	.	PUNCT
ejde-887	509	1	andrei	andrei	PROPN
ejde-887	509	2	ludu	ludu	PROPN
ejde-887	509	3	embry	embry	PROPN
ejde-887	509	4	-	-	PUNCT
ejde-887	509	5	riddle	riddle	PROPN
ejde-887	509	6	aeronautical	aeronautical	PROPN
ejde-887	509	7	university	university	PROPN
ejde-887	509	8	,	,	PUNCT
ejde-887	509	9	department	department	NOUN
ejde-887	509	10	of	of	ADP
ejde-887	509	11	mathematics	mathematics	PROPN
ejde-887	509	12	&	&	CCONJ
ejde-887	509	13	wave	wave	PROPN
ejde-887	509	14	lab	lab	PROPN
ejde-887	509	15	,	,	PUNCT
ejde-887	509	16	daytona	daytona	PROPN
ejde-887	509	17	beach	beach	PROPN
ejde-887	509	18	,	,	PUNCT
ejde-887	509	19	fl	fl	PROPN
ejde-887	509	20	,	,	PUNCT
ejde-887	509	21	usa	usa	PROPN
ejde-887	509	22	email	email	NOUN
ejde-887	509	23	address	address	NOUN
ejde-887	509	24	:	:	PUNCT
ejde-887	510	1	ludua@erau.edu	ludua@erau.edu	PROPN
ejde-887	510	2	harihar	harihar	PROPN
ejde-887	510	3	khanal	khanal	PROPN
ejde-887	510	4	embry	embry	PROPN
ejde-887	510	5	-	-	PUNCT
ejde-887	510	6	riddle	riddle	PROPN
ejde-887	510	7	aeronautical	aeronautical	PROPN
ejde-887	510	8	university	university	PROPN
ejde-887	510	9	,	,	PUNCT
ejde-887	510	10	department	department	NOUN
ejde-887	510	11	of	of	ADP
ejde-887	510	12	mathematics	mathematics	PROPN
ejde-887	510	13	,	,	PUNCT
ejde-887	510	14	daytona	daytona	PROPN
ejde-887	510	15	beach	beach	PROPN
ejde-887	510	16	,	,	PUNCT
ejde-887	510	17	fl	fl	PROPN
ejde-887	510	18	,	,	PUNCT
ejde-887	510	19	usa	usa	PROPN
ejde-887	510	20	email	email	NOUN
ejde-887	510	21	address	address	NOUN
ejde-887	510	22	:	:	PUNCT
ejde-887	510	23	harihar.khanal@erau.edu	harihar.khanal@erau.edu	PROPN
ejde-887	510	24	adrian	adrian	PROPN
ejde-887	510	25	stefan	stefan	PROPN
ejde-887	510	26	carstea	carstea	PROPN
ejde-887	510	27	department	department	PROPN
ejde-887	510	28	of	of	ADP
ejde-887	510	29	theoretical	theoretical	ADJ
ejde-887	510	30	physics	physics	NOUN
ejde-887	510	31	,	,	PUNCT
ejde-887	510	32	national	national	PROPN
ejde-887	510	33	institute	institute	PROPN
ejde-887	510	34	of	of	ADP
ejde-887	510	35	physics	physics	PROPN
ejde-887	510	36	and	and	CCONJ
ejde-887	510	37	nuclear	nuclear	ADJ
ejde-887	510	38	engineering	engineering	NOUN
ejde-887	510	39	,	,	PUNCT
ejde-887	510	40	bucharest	bucharest	PROPN
ejde-887	510	41	-	-	PUNCT
ejde-887	510	42	măgurele	măgurele	PROPN
ejde-887	510	43	077125	077125	NUM
ejde-887	510	44	,	,	PUNCT
ejde-887	510	45	romania	romania	PROPN
ejde-887	510	46	email	email	NOUN
ejde-887	510	47	address	address	NOUN
ejde-887	510	48	:	:	PUNCT
ejde-887	510	49	acarst@theory.nipne.ro	acarst@theory.nipne.ro	NOUN
ejde-887	510	50	1	1	NUM
ejde-887	510	51	.	.	PUNCT
ejde-887	510	52	introduction	introduction	NOUN
ejde-887	510	53	2	2	NUM
ejde-887	510	54	.	.	PUNCT
ejde-887	510	55	boussinesq	boussinesq	PROPN
ejde-887	510	56	non	non	ADJ
ejde-887	510	57	-	-	ADJ
ejde-887	510	58	autonomous	autonomous	ADJ
ejde-887	510	59	nonlinear	nonlinear	ADJ
ejde-887	510	60	system	system	NOUN
ejde-887	510	61	2.1	2.1	NUM
ejde-887	510	62	.	.	PUNCT
ejde-887	511	1	well	well	INTJ
ejde-887	511	2	posed	pose	VERB
ejde-887	511	3	problem	problem	NOUN
ejde-887	511	4	for	for	ADP
ejde-887	511	5	the	the	DET
ejde-887	511	6	nonlinear	nonlinear	ADJ
ejde-887	511	7	and	and	CCONJ
ejde-887	511	8	non	non	ADJ
ejde-887	511	9	-	-	ADJ
ejde-887	511	10	autonomous	autonomous	ADJ
ejde-887	511	11	boussinesq	boussinesq	ADJ
ejde-887	511	12	system	system	NOUN
ejde-887	511	13	3	3	NUM
ejde-887	511	14	.	.	PUNCT
ejde-887	511	15	asymptotic	asymptotic	ADJ
ejde-887	511	16	approach	approach	NOUN
ejde-887	511	17	3.1	3.1	NUM
ejde-887	511	18	.	.	PUNCT
ejde-887	512	1	autonomous	autonomous	ADJ
ejde-887	512	2	nonlinear	nonlinear	ADJ
ejde-887	512	3	limit	limit	NOUN
ejde-887	512	4	3.2	3.2	NUM
ejde-887	512	5	.	.	PUNCT
ejde-887	513	1	non	non	ADJ
ejde-887	513	2	-	-	ADJ
ejde-887	513	3	autonomous	autonomous	ADJ
ejde-887	513	4	linear	linear	ADJ
ejde-887	513	5	limit	limit	NOUN
ejde-887	513	6	4	4	NUM
ejde-887	513	7	.	.	PUNCT
ejde-887	513	8	multiple	multiple	ADJ
ejde-887	513	9	-	-	PUNCT
ejde-887	513	10	scales	scale	NOUN
ejde-887	513	11	method	method	NOUN
ejde-887	513	12	for	for	ADP
ejde-887	513	13	the	the	DET
ejde-887	513	14	boussinesq	boussinesq	ADJ
ejde-887	513	15	system	system	NOUN
ejde-887	513	16	4.1	4.1	NUM
ejde-887	513	17	.	.	PUNCT
ejde-887	513	18	amplitude	amplitude	NOUN
ejde-887	513	19	modulation	modulation	NOUN
ejde-887	513	20	in	in	ADP
ejde-887	513	21	the	the	DET
ejde-887	513	22	autonomous	autonomous	ADJ
ejde-887	513	23	case	case	NOUN
ejde-887	513	24	:	:	PUNCT
ejde-887	513	25	a	a	DET
ejde-887	513	26	dispersionless	dispersionless	NOUN
ejde-887	513	27	system	system	NOUN
ejde-887	513	28	4.2	4.2	NUM
ejde-887	513	29	.	.	PUNCT
ejde-887	514	1	multi	multi	ADJ
ejde-887	514	2	-	-	ADJ
ejde-887	514	3	scale	scale	ADJ
ejde-887	514	4	analysis	analysis	NOUN
ejde-887	514	5	of	of	ADP
ejde-887	514	6	the	the	DET
ejde-887	514	7	non	non	ADJ
ejde-887	514	8	-	-	ADJ
ejde-887	514	9	autonomous	autonomous	ADJ
ejde-887	514	10	nonlinear	nonlinear	ADJ
ejde-887	514	11	system	system	NOUN
ejde-887	514	12	5	5	NUM
ejde-887	514	13	.	.	PUNCT
ejde-887	514	14	numerical	numerical	ADJ
ejde-887	514	15	solutions	solution	NOUN
ejde-887	514	16	5.1	5.1	NUM
ejde-887	514	17	.	.	PUNCT
ejde-887	515	1	numerical	numerical	ADJ
ejde-887	515	2	algorithm	algorithm	PROPN
ejde-887	515	3	5.2	5.2	NUM
ejde-887	515	4	.	.	PUNCT
ejde-887	516	1	analysis	analysis	NOUN
ejde-887	516	2	of	of	ADP
ejde-887	516	3	numerical	numerical	ADJ
ejde-887	516	4	results	result	NOUN
ejde-887	516	5	5.3	5.3	NUM
ejde-887	516	6	.	.	PUNCT
ejde-887	517	1	stability	stability	NOUN
ejde-887	517	2	of	of	ADP
ejde-887	517	3	perturbed	perturb	VERB
ejde-887	517	4	soliton	soliton	NOUN
ejde-887	517	5	solution	solution	NOUN
ejde-887	517	6	6	6	NUM
ejde-887	517	7	.	.	PUNCT
ejde-887	518	1	conclusions	conclusion	NOUN
ejde-887	518	2	acknowledgments	acknowledgment	NOUN
ejde-887	518	3	references	reference	NOUN