id	sid	tid	token	lemma	pos
ejpam-4971	1	1	european	european	PROPN
ejpam-4971	1	2	journal	journal	PROPN
ejpam-4971	1	3	of	of	ADP
ejpam-4971	1	4	pure	pure	ADJ
ejpam-4971	1	5	and	and	CCONJ
ejpam-4971	1	6	applied	apply	VERB
ejpam-4971	1	7	mathematics	mathematic	NOUN
ejpam-4971	1	8	vol	vol	NOUN
ejpam-4971	1	9	.	.	PUNCT
ejpam-4971	2	1	16	16	NUM
ejpam-4971	2	2	,	,	PUNCT
ejpam-4971	2	3	no	no	INTJ
ejpam-4971	2	4	.	.	NOUN
ejpam-4971	2	5	4	4	NUM
ejpam-4971	2	6	,	,	PUNCT
ejpam-4971	2	7	2023	2023	NUM
ejpam-4971	2	8	,	,	PUNCT
ejpam-4971	2	9	2643	2643	NUM
ejpam-4971	2	10	-	-	SYM
ejpam-4971	2	11	2661	2661	NUM
ejpam-4971	2	12	issn	issn	PROPN
ejpam-4971	2	13	1307	1307	NUM
ejpam-4971	2	14	-	-	SYM
ejpam-4971	2	15	5543	5543	NUM
ejpam-4971	2	16	–	–	PUNCT
ejpam-4971	2	17	ejpam.com	ejpam.com	X
ejpam-4971	2	18	published	publish	VERB
ejpam-4971	2	19	by	by	ADP
ejpam-4971	2	20	new	new	PROPN
ejpam-4971	2	21	york	york	PROPN
ejpam-4971	2	22	business	business	PROPN
ejpam-4971	2	23	global	global	ADJ
ejpam-4971	2	24	bifurcation	bifurcation	NOUN
ejpam-4971	2	25	and	and	CCONJ
ejpam-4971	2	26	exact	exact	ADJ
ejpam-4971	2	27	traveling	traveling	ADJ
ejpam-4971	2	28	wave	wave	NOUN
ejpam-4971	2	29	solutions	solution	NOUN
ejpam-4971	2	30	for	for	ADP
ejpam-4971	2	31	the	the	DET
ejpam-4971	2	32	nonlinear	nonlinear	PROPN
ejpam-4971	2	33	klein	klein	PROPN
ejpam-4971	2	34	–	–	PUNCT
ejpam-4971	2	35	gordon	gordon	PROPN
ejpam-4971	2	36	equation	equation	NOUN
ejpam-4971	2	37	meraa	meraa	NOUN
ejpam-4971	2	38	arab	arab	PROPN
ejpam-4971	2	39	department	department	PROPN
ejpam-4971	2	40	of	of	ADP
ejpam-4971	2	41	mathematics	mathematics	PROPN
ejpam-4971	2	42	and	and	CCONJ
ejpam-4971	2	43	statistics	statistic	NOUN
ejpam-4971	2	44	,	,	PUNCT
ejpam-4971	2	45	college	college	NOUN
ejpam-4971	2	46	of	of	ADP
ejpam-4971	2	47	science	science	NOUN
ejpam-4971	2	48	,	,	PUNCT
ejpam-4971	2	49	king	king	NOUN
ejpam-4971	2	50	faisal	faisal	PROPN
ejpam-4971	2	51	university	university	PROPN
ejpam-4971	2	52	,	,	PUNCT
ejpam-4971	2	53	po	po	PROPN
ejpam-4971	2	54	box	box	PROPN
ejpam-4971	2	55	400	400	NUM
ejpam-4971	2	56	,	,	PUNCT
ejpam-4971	2	57	al	al	PROPN
ejpam-4971	2	58	-	-	PUNCT
ejpam-4971	2	59	ahsa	ahsa	NOUN
ejpam-4971	2	60	31982	31982	NUM
ejpam-4971	2	61	,	,	PUNCT
ejpam-4971	2	62	saudi	saudi	PROPN
ejpam-4971	2	63	arabia	arabia	PROPN
ejpam-4971	2	64	abstract	abstract	NOUN
ejpam-4971	2	65	.	.	PUNCT
ejpam-4971	3	1	this	this	DET
ejpam-4971	3	2	paper	paper	NOUN
ejpam-4971	3	3	focuses	focus	VERB
ejpam-4971	3	4	on	on	ADP
ejpam-4971	3	5	the	the	DET
ejpam-4971	3	6	construction	construction	NOUN
ejpam-4971	3	7	of	of	ADP
ejpam-4971	3	8	traveling	travel	VERB
ejpam-4971	3	9	wave	wave	NOUN
ejpam-4971	3	10	solutions	solution	NOUN
ejpam-4971	3	11	to	to	ADP
ejpam-4971	3	12	the	the	DET
ejpam-4971	3	13	nonlinear	nonlinear	PROPN
ejpam-4971	3	14	klein	klein	PROPN
ejpam-4971	3	15	–	–	PUNCT
ejpam-4971	3	16	gordon	gordon	PROPN
ejpam-4971	3	17	equation	equation	NOUN
ejpam-4971	3	18	by	by	ADP
ejpam-4971	3	19	employing	employ	VERB
ejpam-4971	3	20	the	the	DET
ejpam-4971	3	21	qualitative	qualitative	ADJ
ejpam-4971	3	22	theory	theory	NOUN
ejpam-4971	3	23	of	of	ADP
ejpam-4971	3	24	planar	planar	ADJ
ejpam-4971	3	25	dynamical	dynamical	ADJ
ejpam-4971	3	26	systems	system	NOUN
ejpam-4971	3	27	.	.	PUNCT
ejpam-4971	4	1	based	base	VERB
ejpam-4971	4	2	on	on	ADP
ejpam-4971	4	3	this	this	DET
ejpam-4971	4	4	theory	theory	NOUN
ejpam-4971	4	5	,	,	PUNCT
ejpam-4971	4	6	we	we	PRON
ejpam-4971	4	7	analytically	analytically	ADV
ejpam-4971	4	8	study	study	VERB
ejpam-4971	4	9	the	the	DET
ejpam-4971	4	10	existence	existence	NOUN
ejpam-4971	4	11	of	of	ADP
ejpam-4971	4	12	periodic	periodic	ADJ
ejpam-4971	4	13	,	,	PUNCT
ejpam-4971	4	14	kink	kink	PROPN
ejpam-4971	4	15	(	(	PUNCT
ejpam-4971	4	16	anti	anti	ADJ
ejpam-4971	4	17	-	-	ADJ
ejpam-4971	4	18	kink	kink	ADJ
ejpam-4971	4	19	)	)	PUNCT
ejpam-4971	4	20	,	,	PUNCT
ejpam-4971	4	21	and	and	CCONJ
ejpam-4971	4	22	solitary	solitary	ADJ
ejpam-4971	4	23	wave	wave	NOUN
ejpam-4971	4	24	solutions	solution	NOUN
ejpam-4971	4	25	.	.	PUNCT
ejpam-4971	5	1	we	we	PRON
ejpam-4971	5	2	then	then	ADV
ejpam-4971	5	3	attempt	attempt	VERB
ejpam-4971	5	4	to	to	PART
ejpam-4971	5	5	construct	construct	VERB
ejpam-4971	5	6	such	such	ADJ
ejpam-4971	5	7	solutions	solution	NOUN
ejpam-4971	5	8	.	.	PUNCT
ejpam-4971	6	1	for	for	ADP
ejpam-4971	6	2	this	this	DET
ejpam-4971	6	3	purpose	purpose	NOUN
ejpam-4971	6	4	,	,	PUNCT
ejpam-4971	6	5	we	we	PRON
ejpam-4971	6	6	apply	apply	VERB
ejpam-4971	6	7	a	a	DET
ejpam-4971	6	8	well	well	ADV
ejpam-4971	6	9	-	-	PUNCT
ejpam-4971	6	10	known	know	VERB
ejpam-4971	6	11	traveling	travel	VERB
ejpam-4971	6	12	wave	wave	NOUN
ejpam-4971	6	13	solution	solution	NOUN
ejpam-4971	6	14	to	to	PART
ejpam-4971	6	15	convert	convert	VERB
ejpam-4971	6	16	the	the	DET
ejpam-4971	6	17	nonlinear	nonlinear	PROPN
ejpam-4971	6	18	klein	klein	PROPN
ejpam-4971	6	19	–	–	PUNCT
ejpam-4971	6	20	gordon	gordon	PROPN
ejpam-4971	6	21	equation	equation	NOUN
ejpam-4971	6	22	into	into	ADP
ejpam-4971	6	23	an	an	DET
ejpam-4971	6	24	ordinary	ordinary	ADJ
ejpam-4971	6	25	differential	differential	ADJ
ejpam-4971	6	26	equation	equation	NOUN
ejpam-4971	6	27	that	that	PRON
ejpam-4971	6	28	can	can	AUX
ejpam-4971	6	29	be	be	AUX
ejpam-4971	6	30	written	write	VERB
ejpam-4971	6	31	as	as	ADP
ejpam-4971	6	32	a	a	DET
ejpam-4971	6	33	one	one	NUM
ejpam-4971	6	34	-	-	PUNCT
ejpam-4971	6	35	dimensional	dimensional	ADJ
ejpam-4971	6	36	hamiltonian	hamiltonian	ADJ
ejpam-4971	6	37	system	system	NOUN
ejpam-4971	6	38	.	.	PUNCT
ejpam-4971	7	1	the	the	DET
ejpam-4971	7	2	qualitative	qualitative	ADJ
ejpam-4971	7	3	theory	theory	NOUN
ejpam-4971	7	4	is	be	AUX
ejpam-4971	7	5	applied	apply	VERB
ejpam-4971	7	6	to	to	PART
ejpam-4971	7	7	investigate	investigate	VERB
ejpam-4971	7	8	and	and	CCONJ
ejpam-4971	7	9	describe	describe	VERB
ejpam-4971	7	10	phase	phase	NOUN
ejpam-4971	7	11	portraits	portrait	NOUN
ejpam-4971	7	12	of	of	ADP
ejpam-4971	7	13	the	the	DET
ejpam-4971	7	14	hamiltonian	hamiltonian	ADJ
ejpam-4971	7	15	system	system	NOUN
ejpam-4971	7	16	.	.	PUNCT
ejpam-4971	8	1	based	base	VERB
ejpam-4971	8	2	on	on	ADP
ejpam-4971	8	3	the	the	DET
ejpam-4971	8	4	bifurcation	bifurcation	NOUN
ejpam-4971	8	5	constraints	constraint	NOUN
ejpam-4971	8	6	on	on	ADP
ejpam-4971	8	7	the	the	DET
ejpam-4971	8	8	system	system	NOUN
ejpam-4971	8	9	parameters	parameter	NOUN
ejpam-4971	8	10	,	,	PUNCT
ejpam-4971	8	11	we	we	PRON
ejpam-4971	8	12	integrate	integrate	VERB
ejpam-4971	8	13	the	the	DET
ejpam-4971	8	14	conserved	conserve	VERB
ejpam-4971	8	15	quantities	quantity	NOUN
ejpam-4971	8	16	to	to	PART
ejpam-4971	8	17	build	build	VERB
ejpam-4971	8	18	new	new	ADJ
ejpam-4971	8	19	wave	wave	NOUN
ejpam-4971	8	20	solutions	solution	NOUN
ejpam-4971	8	21	that	that	PRON
ejpam-4971	8	22	can	can	AUX
ejpam-4971	8	23	be	be	AUX
ejpam-4971	8	24	classified	classify	VERB
ejpam-4971	8	25	into	into	ADP
ejpam-4971	8	26	periodic	periodic	ADJ
ejpam-4971	8	27	,	,	PUNCT
ejpam-4971	8	28	kink	kink	PROPN
ejpam-4971	8	29	(	(	PUNCT
ejpam-4971	8	30	anti	anti	ADJ
ejpam-4971	8	31	-	-	ADJ
ejpam-4971	8	32	kink	kink	ADJ
ejpam-4971	8	33	)	)	PUNCT
ejpam-4971	8	34	,	,	PUNCT
ejpam-4971	8	35	and	and	CCONJ
ejpam-4971	8	36	solitary	solitary	ADJ
ejpam-4971	8	37	wave	wave	NOUN
ejpam-4971	8	38	solutions	solution	NOUN
ejpam-4971	8	39	.	.	PUNCT
ejpam-4971	9	1	some	some	PRON
ejpam-4971	9	2	of	of	ADP
ejpam-4971	9	3	the	the	DET
ejpam-4971	9	4	obtained	obtain	VERB
ejpam-4971	9	5	solutions	solution	NOUN
ejpam-4971	9	6	are	be	AUX
ejpam-4971	9	7	clarified	clarify	VERB
ejpam-4971	9	8	graphically	graphically	ADV
ejpam-4971	9	9	and	and	CCONJ
ejpam-4971	9	10	their	their	PRON
ejpam-4971	9	11	connection	connection	NOUN
ejpam-4971	9	12	with	with	ADP
ejpam-4971	9	13	the	the	DET
ejpam-4971	9	14	phase	phase	NOUN
ejpam-4971	9	15	orbits	orbit	NOUN
ejpam-4971	9	16	is	be	AUX
ejpam-4971	9	17	derived	derive	VERB
ejpam-4971	9	18	.	.	PUNCT
ejpam-4971	10	1	2020	2020	NUM
ejpam-4971	10	2	mathematics	mathematic	NOUN
ejpam-4971	10	3	subject	subject	NOUN
ejpam-4971	10	4	classifications	classification	NOUN
ejpam-4971	10	5	:	:	PUNCT
ejpam-4971	10	6	35c07	35c07	NUM
ejpam-4971	10	7	,	,	PUNCT
ejpam-4971	10	8	34c23	34c23	NUM
ejpam-4971	10	9	,	,	PUNCT
ejpam-4971	10	10	35q51	35q51	NUM
ejpam-4971	10	11	,	,	PUNCT
ejpam-4971	10	12	35b10	35b10	NUM
ejpam-4971	10	13	key	key	ADJ
ejpam-4971	10	14	words	word	NOUN
ejpam-4971	10	15	and	and	CCONJ
ejpam-4971	10	16	phrases	phrase	NOUN
ejpam-4971	10	17	:	:	PUNCT
ejpam-4971	10	18	travel	travel	NOUN
ejpam-4971	10	19	wave	wave	NOUN
ejpam-4971	10	20	solution	solution	NOUN
ejpam-4971	10	21	,	,	PUNCT
ejpam-4971	10	22	bifurcation	bifurcation	NOUN
ejpam-4971	10	23	,	,	PUNCT
ejpam-4971	10	24	phase	phase	NOUN
ejpam-4971	10	25	portrait	portrait	NOUN
ejpam-4971	10	26	,	,	PUNCT
ejpam-4971	10	27	nonlinear	nonlinear	ADJ
ejpam-4971	10	28	kleingordon	kleingordon	NOUN
ejpam-4971	10	29	equation	equation	NOUN
ejpam-4971	10	30	1	1	NUM
ejpam-4971	10	31	.	.	PUNCT
ejpam-4971	10	32	introduction	introduction	NOUN
ejpam-4971	10	33	a	a	DET
ejpam-4971	10	34	wave	wave	NOUN
ejpam-4971	10	35	that	that	PRON
ejpam-4971	10	36	moves	move	VERB
ejpam-4971	10	37	in	in	ADP
ejpam-4971	10	38	a	a	DET
ejpam-4971	10	39	certain	certain	ADJ
ejpam-4971	10	40	direction	direction	NOUN
ejpam-4971	10	41	while	while	SCONJ
ejpam-4971	10	42	maintaining	maintain	VERB
ejpam-4971	10	43	a	a	DET
ejpam-4971	10	44	solid	solid	ADJ
ejpam-4971	10	45	shape	shape	NOUN
ejpam-4971	10	46	is	be	AUX
ejpam-4971	10	47	called	call	VERB
ejpam-4971	10	48	a	a	DET
ejpam-4971	10	49	traveling	travel	VERB
ejpam-4971	10	50	wave	wave	NOUN
ejpam-4971	10	51	.	.	PUNCT
ejpam-4971	11	1	traveling	travel	VERB
ejpam-4971	11	2	waves	wave	NOUN
ejpam-4971	11	3	typically	typically	ADV
ejpam-4971	11	4	maintain	maintain	VERB
ejpam-4971	11	5	a	a	DET
ejpam-4971	11	6	constant	constant	ADJ
ejpam-4971	11	7	speed	speed	NOUN
ejpam-4971	11	8	throughout	throughout	ADP
ejpam-4971	11	9	their	their	PRON
ejpam-4971	11	10	diffusion	diffusion	NOUN
ejpam-4971	11	11	.	.	PUNCT
ejpam-4971	12	1	these	these	DET
ejpam-4971	12	2	waves	wave	NOUN
ejpam-4971	12	3	are	be	AUX
ejpam-4971	12	4	observed	observe	VERB
ejpam-4971	12	5	in	in	ADP
ejpam-4971	12	6	many	many	ADJ
ejpam-4971	12	7	fields	field	NOUN
ejpam-4971	12	8	of	of	ADP
ejpam-4971	12	9	science	science	NOUN
ejpam-4971	12	10	,	,	PUNCT
ejpam-4971	12	11	such	such	ADJ
ejpam-4971	12	12	as	as	ADP
ejpam-4971	12	13	in	in	ADP
ejpam-4971	12	14	combustion	combustion	NOUN
ejpam-4971	12	15	following	follow	VERB
ejpam-4971	12	16	a	a	DET
ejpam-4971	12	17	chemical	chemical	NOUN
ejpam-4971	12	18	reaction	reaction	NOUN
ejpam-4971	12	19	.	.	PUNCT
ejpam-4971	13	1	recently	recently	ADV
ejpam-4971	13	2	,	,	PUNCT
ejpam-4971	13	3	there	there	PRON
ejpam-4971	13	4	has	have	AUX
ejpam-4971	13	5	been	be	AUX
ejpam-4971	13	6	considerable	considerable	ADJ
ejpam-4971	13	7	interest	interest	NOUN
ejpam-4971	13	8	in	in	ADP
ejpam-4971	13	9	traveling	travel	VERB
ejpam-4971	13	10	wave	wave	NOUN
ejpam-4971	13	11	solutions	solution	NOUN
ejpam-4971	13	12	.	.	PUNCT
ejpam-4971	14	1	in	in	ADP
ejpam-4971	14	2	mathematical	mathematical	ADJ
ejpam-4971	14	3	biology[23	biology[23	NOUN
ejpam-4971	14	4	]	]	PUNCT
ejpam-4971	14	5	,	,	PUNCT
ejpam-4971	14	6	the	the	DET
ejpam-4971	14	7	impulses	impulse	NOUN
ejpam-4971	14	8	that	that	PRON
ejpam-4971	14	9	occur	occur	VERB
ejpam-4971	14	10	in	in	ADP
ejpam-4971	14	11	nerve	nerve	NOUN
ejpam-4971	14	12	fibers	fiber	NOUN
ejpam-4971	14	13	can	can	AUX
ejpam-4971	14	14	be	be	AUX
ejpam-4971	14	15	considered	consider	VERB
ejpam-4971	14	16	as	as	ADP
ejpam-4971	14	17	traveling	travel	VERB
ejpam-4971	14	18	waves	wave	NOUN
ejpam-4971	14	19	,	,	PUNCT
ejpam-4971	14	20	and	and	CCONJ
ejpam-4971	14	21	the	the	DET
ejpam-4971	14	22	conservation	conservation	NOUN
ejpam-4971	14	23	laws	law	NOUN
ejpam-4971	14	24	related	relate	VERB
ejpam-4971	14	25	to	to	ADP
ejpam-4971	14	26	problems	problem	NOUN
ejpam-4971	14	27	in	in	ADP
ejpam-4971	14	28	fluid	fluid	ADJ
ejpam-4971	14	29	dynamics	dynamic	NOUN
ejpam-4971	14	30	describe	describe	VERB
ejpam-4971	14	31	shock	shock	NOUN
ejpam-4971	14	32	profiles	profile	NOUN
ejpam-4971	14	33	as	as	ADP
ejpam-4971	14	34	traveling	travel	VERB
ejpam-4971	14	35	waves	wave	NOUN
ejpam-4971	14	36	.	.	PUNCT
ejpam-4971	15	1	nonlinear	nonlinear	ADJ
ejpam-4971	15	2	partial	partial	ADJ
ejpam-4971	15	3	differential	differential	NOUN
ejpam-4971	15	4	equations	equation	NOUN
ejpam-4971	15	5	(	(	PUNCT
ejpam-4971	15	6	nlpdes)[31	nlpdes)[31	X
ejpam-4971	15	7	]	]	PUNCT
ejpam-4971	15	8	,	,	PUNCT
ejpam-4971	15	9	which	which	PRON
ejpam-4971	15	10	include	include	VERB
ejpam-4971	15	11	time	time	NOUN
ejpam-4971	15	12	as	as	ADP
ejpam-4971	15	13	an	an	DET
ejpam-4971	15	14	independent	independent	ADJ
ejpam-4971	15	15	variable	variable	NOUN
ejpam-4971	15	16	,	,	PUNCT
ejpam-4971	15	17	are	be	AUX
ejpam-4971	15	18	helpful	helpful	ADJ
ejpam-4971	15	19	in	in	ADP
ejpam-4971	15	20	characterizing	characterize	VERB
ejpam-4971	15	21	many	many	ADJ
ejpam-4971	15	22	nonlinear	nonlinear	ADJ
ejpam-4971	15	23	phenomena	phenomenon	NOUN
ejpam-4971	15	24	that	that	PRON
ejpam-4971	15	25	occur	occur	VERB
ejpam-4971	15	26	in	in	ADP
ejpam-4971	15	27	fields	field	NOUN
ejpam-4971	15	28	such	such	ADJ
ejpam-4971	15	29	as	as	ADP
ejpam-4971	15	30	plasma	plasma	NOUN
ejpam-4971	15	31	physics	physic	NOUN
ejpam-4971	15	32	,	,	PUNCT
ejpam-4971	15	33	hydrodynamics	hydrodynamic	NOUN
ejpam-4971	15	34	,	,	PUNCT
ejpam-4971	15	35	solid	solid	ADJ
ejpam-4971	15	36	-	-	PUNCT
ejpam-4971	15	37	state	state	NOUN
ejpam-4971	15	38	physics	physics	NOUN
ejpam-4971	15	39	,	,	PUNCT
ejpam-4971	15	40	fluid	fluid	ADJ
ejpam-4971	15	41	dynamics	dynamic	NOUN
ejpam-4971	15	42	,	,	PUNCT
ejpam-4971	15	43	optics	optic	NOUN
ejpam-4971	15	44	,	,	PUNCT
ejpam-4971	15	45	and	and	CCONJ
ejpam-4971	15	46	applied	apply	VERB
ejpam-4971	15	47	mathematics	mathematic	NOUN
ejpam-4971	15	48	.	.	PUNCT
ejpam-4971	16	1	work	work	NOUN
ejpam-4971	16	2	on	on	ADP
ejpam-4971	16	3	nlpdes	nlpde	NOUN
ejpam-4971	16	4	is	be	AUX
ejpam-4971	16	5	becoming	become	VERB
ejpam-4971	16	6	very	very	ADV
ejpam-4971	16	7	important	important	ADJ
ejpam-4971	16	8	following	follow	VERB
ejpam-4971	16	9	evolutions	evolution	NOUN
ejpam-4971	16	10	in	in	ADP
ejpam-4971	16	11	nonlinear	nonlinear	ADJ
ejpam-4971	16	12	dynamics	dynamic	NOUN
ejpam-4971	16	13	.	.	PUNCT
ejpam-4971	17	1	doi	doi	NOUN
ejpam-4971	17	2	:	:	PUNCT
ejpam-4971	17	3	https://doi.org/10.29020/nybg.ejpam.v16i4.4607	https://doi.org/10.29020/nybg.ejpam.v16i4.4607	ADJ
ejpam-4971	17	4	email	email	NOUN
ejpam-4971	17	5	address	address	NOUN
ejpam-4971	17	6	:	:	PUNCT
ejpam-4971	17	7	marab@kfu.edu.sa	marab@kfu.edu.sa	PROPN
ejpam-4971	17	8	(	(	PUNCT
ejpam-4971	17	9	m.arab	m.arab	NOUN
ejpam-4971	17	10	)	)	PUNCT
ejpam-4971	17	11	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4971	17	12	2643	2643	NUM
ejpam-4971	17	13	©	©	PROPN
ejpam-4971	17	14	2023	2023	NUM
ejpam-4971	17	15	ejpam	ejpam	NOUN
ejpam-4971	17	16	all	all	DET
ejpam-4971	17	17	rights	right	NOUN
ejpam-4971	17	18	reserved	reserve	VERB
ejpam-4971	17	19	.	.	PUNCT
ejpam-4971	18	1	m.arab	m.arab	NOUN
ejpam-4971	18	2	/	/	SYM
ejpam-4971	18	3	eur	eur	PROPN
ejpam-4971	18	4	.	.	PUNCT
ejpam-4971	19	1	j.	j.	PROPN
ejpam-4971	19	2	pure	pure	PROPN
ejpam-4971	19	3	appl	appl	PROPN
ejpam-4971	19	4	.	.	PROPN
ejpam-4971	19	5	math	math	PROPN
ejpam-4971	19	6	,	,	PUNCT
ejpam-4971	19	7	16	16	NUM
ejpam-4971	19	8	(	(	PUNCT
ejpam-4971	19	9	4	4	NUM
ejpam-4971	19	10	)	)	PUNCT
ejpam-4971	19	11	(	(	PUNCT
ejpam-4971	19	12	2023	2023	NUM
ejpam-4971	19	13	)	)	PUNCT
ejpam-4971	19	14	,	,	PUNCT
ejpam-4971	19	15	2643	2643	NUM
ejpam-4971	19	16	-	-	SYM
ejpam-4971	19	17	2661	2661	NUM
ejpam-4971	19	18	2644	2644	NUM
ejpam-4971	19	19	blackseveral	blackseveral	ADJ
ejpam-4971	19	20	aspects	aspect	NOUN
ejpam-4971	19	21	of	of	ADP
ejpam-4971	19	22	engineering	engineering	NOUN
ejpam-4971	19	23	and	and	CCONJ
ejpam-4971	19	24	nonlinear	nonlinear	ADJ
ejpam-4971	19	25	science	science	NOUN
ejpam-4971	19	26	are	be	AUX
ejpam-4971	19	27	affected	affect	VERB
ejpam-4971	19	28	by	by	ADP
ejpam-4971	19	29	solitary	solitary	ADJ
ejpam-4971	19	30	wave	wave	NOUN
ejpam-4971	19	31	theory	theory	NOUN
ejpam-4971	19	32	.	.	PUNCT
ejpam-4971	20	1	these	these	DET
ejpam-4971	20	2	types	type	NOUN
ejpam-4971	20	3	of	of	ADP
ejpam-4971	20	4	wave	wave	NOUN
ejpam-4971	20	5	can	can	AUX
ejpam-4971	20	6	travel	travel	VERB
ejpam-4971	20	7	large	large	ADJ
ejpam-4971	20	8	distances	distance	NOUN
ejpam-4971	20	9	with	with	ADP
ejpam-4971	20	10	only	only	ADJ
ejpam-4971	20	11	slight	slight	ADJ
ejpam-4971	20	12	losses	loss	NOUN
ejpam-4971	20	13	.	.	PUNCT
ejpam-4971	21	1	a	a	DET
ejpam-4971	21	2	key	key	ADJ
ejpam-4971	21	3	component	component	NOUN
ejpam-4971	21	4	of	of	ADP
ejpam-4971	21	5	solitary	solitary	ADJ
ejpam-4971	21	6	wave	wave	NOUN
ejpam-4971	21	7	theory	theory	NOUN
ejpam-4971	21	8	is	be	AUX
ejpam-4971	21	9	the	the	DET
ejpam-4971	21	10	investigation	investigation	NOUN
ejpam-4971	21	11	of	of	ADP
ejpam-4971	21	12	exact	exact	ADJ
ejpam-4971	21	13	traveling	traveling	ADJ
ejpam-4971	21	14	wave	wave	NOUN
ejpam-4971	21	15	solutions	solution	NOUN
ejpam-4971	21	16	,	,	PUNCT
ejpam-4971	21	17	particularly	particularly	ADV
ejpam-4971	21	18	exact	exact	ADJ
ejpam-4971	21	19	solitary	solitary	ADJ
ejpam-4971	21	20	wave	wave	NOUN
ejpam-4971	21	21	solutions	solution	NOUN
ejpam-4971	21	22	.	.	PUNCT
ejpam-4971	22	1	there	there	PRON
ejpam-4971	22	2	have	have	AUX
ejpam-4971	22	3	been	be	AUX
ejpam-4971	22	4	many	many	ADJ
ejpam-4971	22	5	novel	novel	ADJ
ejpam-4971	22	6	approaches	approach	NOUN
ejpam-4971	22	7	to	to	ADP
ejpam-4971	22	8	problem	problem	NOUN
ejpam-4971	22	9	-	-	PUNCT
ejpam-4971	22	10	solving	solve	VERB
ejpam-4971	22	11	and	and	CCONJ
ejpam-4971	22	12	different	different	ADJ
ejpam-4971	22	13	varieties	variety	NOUN
ejpam-4971	22	14	of	of	ADP
ejpam-4971	22	15	solitary	solitary	ADJ
ejpam-4971	22	16	wave	wave	NOUN
ejpam-4971	22	17	solutions	solution	NOUN
ejpam-4971	22	18	over	over	ADP
ejpam-4971	22	19	the	the	DET
ejpam-4971	22	20	past	past	ADJ
ejpam-4971	22	21	decade	decade	NOUN
ejpam-4971	22	22	.	.	PUNCT
ejpam-4971	23	1	in	in	ADP
ejpam-4971	23	2	mathematical	mathematical	ADJ
ejpam-4971	23	3	physics	physics	NOUN
ejpam-4971	23	4	,	,	PUNCT
ejpam-4971	23	5	soliton	soliton	NOUN
ejpam-4971	23	6	dynamics	dynamic	NOUN
ejpam-4971	23	7	is	be	AUX
ejpam-4971	23	8	a	a	DET
ejpam-4971	23	9	novel	novel	ADJ
ejpam-4971	23	10	domain	domain	NOUN
ejpam-4971	23	11	with	with	ADP
ejpam-4971	23	12	several	several	ADJ
ejpam-4971	23	13	applications	application	NOUN
ejpam-4971	23	14	,	,	PUNCT
ejpam-4971	23	15	especially	especially	ADV
ejpam-4971	23	16	in	in	ADP
ejpam-4971	23	17	optics	optic	NOUN
ejpam-4971	23	18	and	and	CCONJ
ejpam-4971	23	19	optical	optical	ADJ
ejpam-4971	23	20	fibers	fiber	NOUN
ejpam-4971	23	21	.	.	PUNCT
ejpam-4971	24	1	solitons	soliton	NOUN
ejpam-4971	24	2	are	be	AUX
ejpam-4971	24	3	the	the	DET
ejpam-4971	24	4	main	main	ADJ
ejpam-4971	24	5	components	component	NOUN
ejpam-4971	24	6	of	of	ADP
ejpam-4971	24	7	data	datum	NOUN
ejpam-4971	24	8	transference	transference	NOUN
ejpam-4971	24	9	over	over	ADP
ejpam-4971	24	10	long	long	ADJ
ejpam-4971	24	11	distances	distance	NOUN
ejpam-4971	24	12	using	use	VERB
ejpam-4971	24	13	optical	optical	ADJ
ejpam-4971	24	14	fibers[7	fibers[7	ADJ
ejpam-4971	24	15	,	,	PUNCT
ejpam-4971	24	16	24–31	24–31	NUM
ejpam-4971	24	17	]	]	PUNCT
ejpam-4971	24	18	.	.	PUNCT
ejpam-4971	25	1	blackvarious	blackvarious	ADJ
ejpam-4971	25	2	methods	method	NOUN
ejpam-4971	25	3	for	for	ADP
ejpam-4971	25	4	producing	produce	VERB
ejpam-4971	25	5	exact	exact	ADJ
ejpam-4971	25	6	solutions	solution	NOUN
ejpam-4971	25	7	of	of	ADP
ejpam-4971	25	8	nonlinear	nonlinear	ADJ
ejpam-4971	25	9	mathematical	mathematical	ADJ
ejpam-4971	25	10	models	model	NOUN
ejpam-4971	25	11	using	use	VERB
ejpam-4971	25	12	a	a	DET
ejpam-4971	25	13	traveling	travel	VERB
ejpam-4971	25	14	wave	wave	NOUN
ejpam-4971	25	15	transformation	transformation	NOUN
ejpam-4971	25	16	have	have	AUX
ejpam-4971	25	17	been	be	AUX
ejpam-4971	25	18	developed	develop	VERB
ejpam-4971	25	19	.	.	PUNCT
ejpam-4971	26	1	this	this	PRON
ejpam-4971	26	2	typically	typically	ADV
ejpam-4971	26	3	involves	involve	VERB
ejpam-4971	26	4	converting	convert	VERB
ejpam-4971	26	5	the	the	DET
ejpam-4971	26	6	blacknlpde	blacknlpde	NOUN
ejpam-4971	26	7	into	into	ADP
ejpam-4971	26	8	ordinary	ordinary	ADJ
ejpam-4971	26	9	differential	differential	ADJ
ejpam-4971	26	10	equations.[33	equations.[33	NOUN
ejpam-4971	26	11	,	,	PUNCT
ejpam-4971	26	12	46	46	NUM
ejpam-4971	26	13	,	,	PUNCT
ejpam-4971	26	14	50	50	NUM
ejpam-4971	26	15	,	,	PUNCT
ejpam-4971	26	16	52	52	NUM
ejpam-4971	26	17	]	]	PUNCT
ejpam-4971	26	18	existing	exist	VERB
ejpam-4971	26	19	methods	method	NOUN
ejpam-4971	26	20	can	can	AUX
ejpam-4971	26	21	be	be	AUX
ejpam-4971	26	22	split	split	VERB
ejpam-4971	26	23	into	into	ADP
ejpam-4971	26	24	two	two	NUM
ejpam-4971	26	25	categories	category	NOUN
ejpam-4971	26	26	.	.	PUNCT
ejpam-4971	27	1	the	the	DET
ejpam-4971	27	2	first	first	ADJ
ejpam-4971	27	3	type	type	NOUN
ejpam-4971	27	4	of	of	ADP
ejpam-4971	27	5	approach	approach	NOUN
ejpam-4971	27	6	creates	create	VERB
ejpam-4971	27	7	a	a	DET
ejpam-4971	27	8	limited	limited	ADJ
ejpam-4971	27	9	set	set	NOUN
ejpam-4971	27	10	of	of	ADP
ejpam-4971	27	11	exact	exact	ADJ
ejpam-4971	27	12	solutions	solution	NOUN
ejpam-4971	27	13	by	by	ADP
ejpam-4971	27	14	simple	simple	ADJ
ejpam-4971	27	15	computations	computation	NOUN
ejpam-4971	27	16	,	,	PUNCT
ejpam-4971	27	17	whereas	whereas	SCONJ
ejpam-4971	27	18	the	the	DET
ejpam-4971	27	19	second	second	ADJ
ejpam-4971	27	20	approach	approach	NOUN
ejpam-4971	27	21	,	,	PUNCT
ejpam-4971	27	22	such	such	DET
ejpam-4971	27	23	the	the	DET
ejpam-4971	27	24	symbolic	symbolic	ADJ
ejpam-4971	27	25	computation	computation	NOUN
ejpam-4971	27	26	method	method	NOUN
ejpam-4971	27	27	,	,	PUNCT
ejpam-4971	27	28	requires	require	VERB
ejpam-4971	27	29	complex	complex	ADJ
ejpam-4971	27	30	computations	computation	NOUN
ejpam-4971	27	31	,	,	PUNCT
ejpam-4971	27	32	but	but	CCONJ
ejpam-4971	27	33	produces	produce	VERB
ejpam-4971	27	34	abundant	abundant	ADJ
ejpam-4971	27	35	wave	wave	NOUN
ejpam-4971	27	36	solutions	solution	NOUN
ejpam-4971	27	37	.	.	PUNCT
ejpam-4971	28	1	the	the	DET
ejpam-4971	28	2	structure	structure	NOUN
ejpam-4971	28	3	of	of	ADP
ejpam-4971	28	4	exact	exact	ADJ
ejpam-4971	28	5	solutions	solution	NOUN
ejpam-4971	28	6	for	for	ADP
ejpam-4971	28	7	nlpdes	nlpde	NOUN
ejpam-4971	28	8	characterizing	characterize	VERB
ejpam-4971	28	9	natural	natural	ADJ
ejpam-4971	28	10	phenomena	phenomenon	NOUN
ejpam-4971	28	11	is	be	AUX
ejpam-4971	28	12	essential	essential	ADJ
ejpam-4971	28	13	in	in	ADP
ejpam-4971	28	14	describing	describe	VERB
ejpam-4971	28	15	these	these	DET
ejpam-4971	28	16	phenomena	phenomenon	NOUN
ejpam-4971	28	17	effectively	effectively	ADV
ejpam-4971	28	18	.	.	PUNCT
ejpam-4971	29	1	solutions	solution	NOUN
ejpam-4971	29	2	can	can	AUX
ejpam-4971	29	3	be	be	AUX
ejpam-4971	29	4	generated	generate	VERB
ejpam-4971	29	5	using	use	VERB
ejpam-4971	29	6	the	the	DET
ejpam-4971	29	7	miura	miura	PROPN
ejpam-4971	29	8	transformation	transformation	NOUN
ejpam-4971	30	1	[	[	X
ejpam-4971	30	2	10	10	NUM
ejpam-4971	30	3	]	]	PUNCT
ejpam-4971	30	4	,	,	PUNCT
ejpam-4971	30	5	adomian	adomian	NOUN
ejpam-4971	30	6	decomposition	decomposition	NOUN
ejpam-4971	30	7	method	method	NOUN
ejpam-4971	30	8	[	[	X
ejpam-4971	30	9	1	1	NUM
ejpam-4971	30	10	,	,	PUNCT
ejpam-4971	30	11	55	55	NUM
ejpam-4971	30	12	]	]	PUNCT
ejpam-4971	30	13	,	,	PUNCT
ejpam-4971	30	14	bifurcation	bifurcation	NOUN
ejpam-4971	30	15	theory	theory	NOUN
ejpam-4971	30	16	[	[	X
ejpam-4971	30	17	6	6	NUM
ejpam-4971	30	18	,	,	PUNCT
ejpam-4971	30	19	14–20	14–20	NUM
ejpam-4971	30	20	,	,	PUNCT
ejpam-4971	30	21	34	34	NUM
ejpam-4971	30	22	,	,	PUNCT
ejpam-4971	30	23	36	36	NUM
ejpam-4971	30	24	,	,	PUNCT
ejpam-4971	30	25	38	38	NUM
ejpam-4971	30	26	,	,	PUNCT
ejpam-4971	30	27	42–45	42–45	NUM
ejpam-4971	30	28	,	,	PUNCT
ejpam-4971	30	29	53	53	NUM
ejpam-4971	30	30	,	,	PUNCT
ejpam-4971	30	31	62	62	NUM
ejpam-4971	30	32	]	]	PUNCT
ejpam-4971	30	33	,	,	PUNCT
ejpam-4971	30	34	cole	cole	PROPN
ejpam-4971	30	35	–	–	PUNCT
ejpam-4971	30	36	hopf	hopf	X
ejpam-4971	30	37	transformation	transformation	NOUN
ejpam-4971	30	38	[	[	X
ejpam-4971	30	39	47	47	NUM
ejpam-4971	30	40	]	]	PUNCT
ejpam-4971	30	41	,	,	PUNCT
ejpam-4971	30	42	g	g	PROPN
ejpam-4971	30	43	′	′	NUM
ejpam-4971	30	44	/g	/g	SYM
ejpam-4971	30	45	-	-	PUNCT
ejpam-4971	30	46	expansion	expansion	NOUN
ejpam-4971	30	47	method	method	NOUN
ejpam-4971	30	48	and	and	CCONJ
ejpam-4971	30	49	its	its	PRON
ejpam-4971	30	50	variants	variant	NOUN
ejpam-4971	31	1	[	[	X
ejpam-4971	31	2	4	4	NUM
ejpam-4971	31	3	,	,	PUNCT
ejpam-4971	31	4	37	37	NUM
ejpam-4971	31	5	,	,	PUNCT
ejpam-4971	31	6	46	46	NUM
ejpam-4971	31	7	,	,	PUNCT
ejpam-4971	31	8	51	51	NUM
ejpam-4971	31	9	,	,	PUNCT
ejpam-4971	31	10	59–61	59–61	NUM
ejpam-4971	31	11	]	]	PUNCT
ejpam-4971	31	12	,	,	PUNCT
ejpam-4971	31	13	hirota	hirota	PROPN
ejpam-4971	31	14	bilinear	bilinear	NOUN
ejpam-4971	31	15	form	form	NOUN
ejpam-4971	31	16	[	[	X
ejpam-4971	31	17	54	54	NUM
ejpam-4971	31	18	]	]	PUNCT
ejpam-4971	31	19	,	,	PUNCT
ejpam-4971	31	20	wronskian	wronskian	ADJ
ejpam-4971	31	21	technique	technique	NOUN
ejpam-4971	31	22	[	[	X
ejpam-4971	31	23	39	39	NUM
ejpam-4971	31	24	]	]	PUNCT
ejpam-4971	31	25	,	,	PUNCT
ejpam-4971	31	26	darboux	darboux	VERB
ejpam-4971	31	27	transformation	transformation	NOUN
ejpam-4971	31	28	[	[	X
ejpam-4971	31	29	35	35	NUM
ejpam-4971	31	30	]	]	PUNCT
ejpam-4971	31	31	,	,	PUNCT
ejpam-4971	31	32	modified	modify	VERB
ejpam-4971	31	33	khater	khater	NOUN
ejpam-4971	31	34	method	method	NOUN
ejpam-4971	31	35	,	,	PUNCT
ejpam-4971	31	36	auxiliary	auxiliary	ADJ
ejpam-4971	31	37	equation	equation	NOUN
ejpam-4971	31	38	approach	approach	NOUN
ejpam-4971	31	39	,	,	PUNCT
ejpam-4971	31	40	khater	khater	PROPN
ejpam-4971	31	41	ii	ii	PROPN
ejpam-4971	31	42	method	method	NOUN
ejpam-4971	31	43	[	[	X
ejpam-4971	31	44	5	5	NUM
ejpam-4971	31	45	]	]	PUNCT
ejpam-4971	31	46	,	,	PUNCT
ejpam-4971	31	47	transformed	transform	VERB
ejpam-4971	31	48	rational	rational	ADJ
ejpam-4971	31	49	function	function	NOUN
ejpam-4971	31	50	method	method	NOUN
ejpam-4971	31	51	[	[	X
ejpam-4971	31	52	40	40	NUM
ejpam-4971	31	53	]	]	PUNCT
ejpam-4971	31	54	,	,	PUNCT
ejpam-4971	31	55	modified	modify	VERB
ejpam-4971	31	56	simple	simple	ADJ
ejpam-4971	31	57	equation	equation	NOUN
ejpam-4971	31	58	method	method	NOUN
ejpam-4971	31	59	[	[	X
ejpam-4971	31	60	3	3	NUM
ejpam-4971	31	61	]	]	PUNCT
ejpam-4971	31	62	,	,	PUNCT
ejpam-4971	31	63	extended	extend	VERB
ejpam-4971	31	64	rational	rational	ADJ
ejpam-4971	31	65	sin	sin	NOUN
ejpam-4971	31	66	–	–	PUNCT
ejpam-4971	31	67	cos	cos	PROPN
ejpam-4971	31	68	and	and	CCONJ
ejpam-4971	31	69	sinh	sinh	PROPN
ejpam-4971	31	70	–	–	PUNCT
ejpam-4971	31	71	cosh	cosh	NOUN
ejpam-4971	31	72	method	method	NOUN
ejpam-4971	31	73	[	[	X
ejpam-4971	31	74	2	2	NUM
ejpam-4971	31	75	]	]	PUNCT
ejpam-4971	31	76	,	,	PUNCT
ejpam-4971	31	77	extended	extend	VERB
ejpam-4971	31	78	rational	rational	ADJ
ejpam-4971	31	79	method	method	NOUN
ejpam-4971	31	80	[	[	X
ejpam-4971	31	81	57	57	NUM
ejpam-4971	31	82	]	]	PUNCT
ejpam-4971	31	83	,	,	PUNCT
ejpam-4971	31	84	and	and	CCONJ
ejpam-4971	31	85	methods	method	NOUN
ejpam-4971	31	86	based	base	VERB
ejpam-4971	31	87	on	on	ADP
ejpam-4971	31	88	numerical	numerical	ADJ
ejpam-4971	31	89	solutions	solution	NOUN
ejpam-4971	31	90	[	[	X
ejpam-4971	31	91	21	21	NUM
ejpam-4971	31	92	,	,	PUNCT
ejpam-4971	31	93	22	22	NUM
ejpam-4971	31	94	,	,	PUNCT
ejpam-4971	31	95	24	24	NUM
ejpam-4971	31	96	,	,	PUNCT
ejpam-4971	31	97	27	27	NUM
ejpam-4971	31	98	,	,	PUNCT
ejpam-4971	31	99	32	32	NUM
ejpam-4971	31	100	,	,	PUNCT
ejpam-4971	31	101	58	58	NUM
ejpam-4971	31	102	]	]	PUNCT
ejpam-4971	31	103	.	.	PUNCT
ejpam-4971	32	1	the	the	DET
ejpam-4971	32	2	present	present	ADJ
ejpam-4971	32	3	article	article	NOUN
ejpam-4971	32	4	studies	study	VERB
ejpam-4971	32	5	the	the	DET
ejpam-4971	32	6	nonlinear	nonlinear	PROPN
ejpam-4971	32	7	klein	klein	PROPN
ejpam-4971	32	8	–	–	PUNCT
ejpam-4971	32	9	gordon	gordon	PROPN
ejpam-4971	32	10	(	(	PUNCT
ejpam-4971	32	11	kg	kg	NOUN
ejpam-4971	32	12	)	)	PUNCT
ejpam-4971	32	13	equation	equation	NOUN
ejpam-4971	32	14	,	,	PUNCT
ejpam-4971	32	15	which	which	PRON
ejpam-4971	32	16	has	have	VERB
ejpam-4971	32	17	the	the	DET
ejpam-4971	32	18	form	form	NOUN
ejpam-4971	32	19	utt	utt	PROPN
ejpam-4971	32	20	−	−	PROPN
ejpam-4971	32	21	uxx	uxx	NOUN
ejpam-4971	32	22	+	+	CCONJ
ejpam-4971	32	23	αu−	αu−	PUNCT
ejpam-4971	32	24	βu3	βu3	NOUN
ejpam-4971	32	25	=	=	SYM
ejpam-4971	32	26	0	0	NUM
ejpam-4971	32	27	,	,	PUNCT
ejpam-4971	32	28	(	(	PUNCT
ejpam-4971	32	29	1	1	X
ejpam-4971	32	30	)	)	PUNCT
ejpam-4971	32	31	where	where	SCONJ
ejpam-4971	32	32	α	α	X
ejpam-4971	32	33	,	,	PUNCT
ejpam-4971	32	34	β	β	X
ejpam-4971	32	35	are	be	AUX
ejpam-4971	32	36	nonzero	nonzero	PROPN
ejpam-4971	32	37	constants	constant	NOUN
ejpam-4971	32	38	.	.	PUNCT
ejpam-4971	33	1	equation	equation	NOUN
ejpam-4971	33	2	(	(	PUNCT
ejpam-4971	33	3	1	1	X
ejpam-4971	33	4	)	)	PUNCT
ejpam-4971	33	5	appears	appear	VERB
ejpam-4971	33	6	in	in	ADP
ejpam-4971	33	7	many	many	ADJ
ejpam-4971	33	8	physical	physical	ADJ
ejpam-4971	33	9	problems	problem	NOUN
ejpam-4971	33	10	of	of	ADP
ejpam-4971	33	11	nonlinear	nonlinear	ADJ
ejpam-4971	33	12	dispersion	dispersion	NOUN
ejpam-4971	33	13	[	[	X
ejpam-4971	33	14	49	49	NUM
ejpam-4971	33	15	,	,	PUNCT
ejpam-4971	33	16	56	56	NUM
ejpam-4971	33	17	]	]	PUNCT
ejpam-4971	33	18	and	and	CCONJ
ejpam-4971	33	19	nonlinear	nonlinear	ADJ
ejpam-4971	33	20	meson	meson	PROPN
ejpam-4971	33	21	theory	theory	NOUN
ejpam-4971	33	22	[	[	X
ejpam-4971	33	23	13	13	NUM
ejpam-4971	33	24	,	,	PUNCT
ejpam-4971	33	25	48	48	NUM
ejpam-4971	33	26	]	]	PUNCT
ejpam-4971	33	27	.	.	PUNCT
ejpam-4971	34	1	the	the	DET
ejpam-4971	34	2	theory	theory	NOUN
ejpam-4971	34	3	of	of	ADP
ejpam-4971	34	4	planar	planar	ADJ
ejpam-4971	34	5	dynamical	dynamical	ADJ
ejpam-4971	34	6	systems	system	NOUN
ejpam-4971	34	7	is	be	AUX
ejpam-4971	34	8	employed	employ	VERB
ejpam-4971	34	9	to	to	PART
ejpam-4971	34	10	explore	explore	VERB
ejpam-4971	34	11	the	the	DET
ejpam-4971	34	12	dynamical	dynamical	ADJ
ejpam-4971	34	13	behaviors	behavior	NOUN
ejpam-4971	34	14	of	of	ADP
ejpam-4971	34	15	the	the	DET
ejpam-4971	34	16	traveling	travel	VERB
ejpam-4971	34	17	wave	wave	NOUN
ejpam-4971	34	18	solutions	solution	NOUN
ejpam-4971	34	19	for	for	ADP
ejpam-4971	34	20	eq	eq	PROPN
ejpam-4971	34	21	.	.	PUNCT
ejpam-4971	35	1	(	(	PUNCT
ejpam-4971	35	2	1	1	NUM
ejpam-4971	35	3	)	)	PUNCT
ejpam-4971	35	4	.	.	PUNCT
ejpam-4971	36	1	in	in	ADP
ejpam-4971	36	2	the	the	DET
ejpam-4971	36	3	present	present	ADJ
ejpam-4971	36	4	work	work	NOUN
ejpam-4971	36	5	,	,	PUNCT
ejpam-4971	36	6	we	we	PRON
ejpam-4971	36	7	construct	construct	VERB
ejpam-4971	36	8	some	some	DET
ejpam-4971	36	9	new	new	ADJ
ejpam-4971	36	10	traveling	travel	VERB
ejpam-4971	36	11	wave	wave	NOUN
ejpam-4971	36	12	solutions	solution	NOUN
ejpam-4971	36	13	for	for	ADP
ejpam-4971	36	14	the	the	DET
ejpam-4971	36	15	nonlinear	nonlinear	ADJ
ejpam-4971	36	16	kg	kg	PROPN
ejpam-4971	36	17	equation	equation	NOUN
ejpam-4971	36	18	(	(	PUNCT
ejpam-4971	36	19	1	1	NUM
ejpam-4971	36	20	)	)	PUNCT
ejpam-4971	36	21	.	.	PUNCT
ejpam-4971	37	1	bifurcation	bifurcation	NOUN
ejpam-4971	37	2	theory	theory	NOUN
ejpam-4971	37	3	is	be	AUX
ejpam-4971	37	4	applied	apply	VERB
ejpam-4971	37	5	to	to	ADP
ejpam-4971	37	6	the	the	DET
ejpam-4971	37	7	traveling	travel	VERB
ejpam-4971	37	8	wave	wave	NOUN
ejpam-4971	37	9	system	system	NOUN
ejpam-4971	37	10	corresponding	correspond	VERB
ejpam-4971	37	11	to	to	ADP
ejpam-4971	37	12	eq	eq	PROPN
ejpam-4971	37	13	.	.	PUNCT
ejpam-4971	38	1	(	(	PUNCT
ejpam-4971	38	2	1	1	NUM
ejpam-4971	38	3	)	)	PUNCT
ejpam-4971	38	4	.	.	PUNCT
ejpam-4971	39	1	bifurcation	bifurcation	NOUN
ejpam-4971	39	2	theory	theory	NOUN
ejpam-4971	39	3	is	be	AUX
ejpam-4971	39	4	useful	useful	ADJ
ejpam-4971	39	5	for	for	ADP
ejpam-4971	39	6	constructing	construct	VERB
ejpam-4971	39	7	wave	wave	NOUN
ejpam-4971	39	8	solutions	solution	NOUN
ejpam-4971	39	9	because	because	SCONJ
ejpam-4971	39	10	we	we	PRON
ejpam-4971	39	11	can	can	AUX
ejpam-4971	39	12	determine	determine	VERB
ejpam-4971	39	13	the	the	DET
ejpam-4971	39	14	type	type	NOUN
ejpam-4971	39	15	of	of	ADP
ejpam-4971	39	16	solution	solution	NOUN
ejpam-4971	39	17	before	before	SCONJ
ejpam-4971	39	18	the	the	DET
ejpam-4971	39	19	precise	precise	ADJ
ejpam-4971	39	20	form	form	NOUN
ejpam-4971	39	21	is	be	AUX
ejpam-4971	39	22	identified	identify	VERB
ejpam-4971	39	23	,	,	PUNCT
ejpam-4971	39	24	which	which	PRON
ejpam-4971	39	25	enables	enable	VERB
ejpam-4971	39	26	us	we	PRON
ejpam-4971	39	27	to	to	PART
ejpam-4971	39	28	find	find	VERB
ejpam-4971	39	29	all	all	DET
ejpam-4971	39	30	possible	possible	ADJ
ejpam-4971	39	31	wave	wave	NOUN
ejpam-4971	39	32	solutions	solution	NOUN
ejpam-4971	39	33	for	for	ADP
ejpam-4971	39	34	the	the	DET
ejpam-4971	39	35	equation	equation	NOUN
ejpam-4971	39	36	under	under	ADP
ejpam-4971	39	37	consideration	consideration	NOUN
ejpam-4971	39	38	.	.	PUNCT
ejpam-4971	40	1	this	this	PRON
ejpam-4971	40	2	motivates	motivate	VERB
ejpam-4971	40	3	us	we	PRON
ejpam-4971	40	4	to	to	PART
ejpam-4971	40	5	apply	apply	VERB
ejpam-4971	40	6	this	this	DET
ejpam-4971	40	7	method	method	NOUN
ejpam-4971	40	8	in	in	ADP
ejpam-4971	40	9	the	the	DET
ejpam-4971	40	10	current	current	ADJ
ejpam-4971	40	11	work	work	NOUN
ejpam-4971	40	12	.	.	PUNCT
ejpam-4971	41	1	the	the	DET
ejpam-4971	41	2	blackreminder	blackreminder	NOUN
ejpam-4971	41	3	of	of	ADP
ejpam-4971	41	4	this	this	DET
ejpam-4971	41	5	article	article	NOUN
ejpam-4971	41	6	is	be	AUX
ejpam-4971	41	7	structured	structure	VERB
ejpam-4971	41	8	in	in	ADP
ejpam-4971	41	9	the	the	DET
ejpam-4971	41	10	following	follow	VERB
ejpam-4971	41	11	steps	step	NOUN
ejpam-4971	41	12	.	.	PUNCT
ejpam-4971	42	1	in	in	ADP
ejpam-4971	42	2	sec	sec	PROPN
ejpam-4971	42	3	.	.	PROPN
ejpam-4971	42	4	ii	ii	PROPN
ejpam-4971	42	5	,	,	PUNCT
ejpam-4971	42	6	to	to	PART
ejpam-4971	42	7	get	get	VERB
ejpam-4971	42	8	the	the	DET
ejpam-4971	42	9	traveling	travel	VERB
ejpam-4971	42	10	wave	wave	NOUN
ejpam-4971	42	11	system	system	NOUN
ejpam-4971	42	12	we	we	PRON
ejpam-4971	42	13	apply	apply	VERB
ejpam-4971	42	14	a	a	DET
ejpam-4971	42	15	specific	specific	ADJ
ejpam-4971	42	16	transformation	transformation	NOUN
ejpam-4971	42	17	.	.	PUNCT
ejpam-4971	43	1	moreover	moreover	ADV
ejpam-4971	43	2	,	,	PUNCT
ejpam-4971	43	3	we	we	PRON
ejpam-4971	43	4	illustrate	illustrate	VERB
ejpam-4971	43	5	the	the	DET
ejpam-4971	43	6	system	system	NOUN
ejpam-4971	43	7	in	in	ADP
ejpam-4971	43	8	the	the	DET
ejpam-4971	43	9	form	form	NOUN
ejpam-4971	43	10	of	of	ADP
ejpam-4971	43	11	a	a	DET
ejpam-4971	43	12	hamiltonian	hamiltonian	NOUN
ejpam-4971	43	13	with	with	ADP
ejpam-4971	43	14	one	one	NUM
ejpam-4971	43	15	degree	degree	NOUN
ejpam-4971	43	16	of	of	ADP
ejpam-4971	43	17	freedom	freedom	NOUN
ejpam-4971	43	18	.	.	PUNCT
ejpam-4971	44	1	section	section	NOUN
ejpam-4971	44	2	iii	iii	PROPN
ejpam-4971	44	3	looks	look	VERB
ejpam-4971	44	4	at	at	ADP
ejpam-4971	44	5	the	the	DET
ejpam-4971	44	6	resulting	result	VERB
ejpam-4971	44	7	bifurcations	bifurcation	NOUN
ejpam-4971	44	8	and	and	CCONJ
ejpam-4971	44	9	phase	phase	NOUN
ejpam-4971	44	10	portraits	portrait	NOUN
ejpam-4971	44	11	,	,	PUNCT
ejpam-4971	44	12	before	before	ADP
ejpam-4971	44	13	sec	sec	PROPN
ejpam-4971	44	14	.	.	PROPN
ejpam-4971	45	1	iv	iv	NUM
ejpam-4971	45	2	derives	derive	VERB
ejpam-4971	45	3	exact	exact	ADJ
ejpam-4971	45	4	solutions	solution	NOUN
ejpam-4971	45	5	to	to	ADP
ejpam-4971	45	6	the	the	DET
ejpam-4971	45	7	kg	kg	PROPN
ejpam-4971	45	8	equation	equation	NOUN
ejpam-4971	45	9	.	.	PUNCT
ejpam-4971	46	1	in	in	ADP
ejpam-4971	46	2	sec	sec	PROPN
ejpam-4971	46	3	.	.	PROPN
ejpam-4971	46	4	v	v	NOUN
ejpam-4971	46	5	,	,	PUNCT
ejpam-4971	46	6	we	we	PRON
ejpam-4971	46	7	present	present	VERB
ejpam-4971	46	8	some	some	DET
ejpam-4971	46	9	new	new	ADJ
ejpam-4971	46	10	traveling	travel	VERB
ejpam-4971	46	11	wave	wave	NOUN
ejpam-4971	46	12	solutions	solution	NOUN
ejpam-4971	46	13	and	and	CCONJ
ejpam-4971	46	14	illustrates	illustrate	VERB
ejpam-4971	46	15	them	they	PRON
ejpam-4971	46	16	graphically	graphically	ADV
ejpam-4971	46	17	.	.	PUNCT
ejpam-4971	47	1	finally	finally	ADV
ejpam-4971	47	2	,	,	PUNCT
ejpam-4971	47	3	sec	sec	PROPN
ejpam-4971	47	4	.	.	PROPN
ejpam-4971	47	5	vi	vi	PROPN
ejpam-4971	47	6	summarizes	summarize	NOUN
ejpam-4971	47	7	the	the	DET
ejpam-4971	47	8	conclusions	conclusion	NOUN
ejpam-4971	47	9	to	to	ADP
ejpam-4971	47	10	this	this	DET
ejpam-4971	47	11	study	study	NOUN
ejpam-4971	47	12	.	.	PUNCT
ejpam-4971	48	1	m.arab	m.arab	NOUN
ejpam-4971	48	2	/	/	SYM
ejpam-4971	48	3	eur	eur	PROPN
ejpam-4971	48	4	.	.	PUNCT
ejpam-4971	49	1	j.	j.	PROPN
ejpam-4971	49	2	pure	pure	PROPN
ejpam-4971	49	3	appl	appl	PROPN
ejpam-4971	49	4	.	.	PROPN
ejpam-4971	49	5	math	math	PROPN
ejpam-4971	49	6	,	,	PUNCT
ejpam-4971	49	7	16	16	NUM
ejpam-4971	49	8	(	(	PUNCT
ejpam-4971	49	9	4	4	NUM
ejpam-4971	49	10	)	)	PUNCT
ejpam-4971	49	11	(	(	PUNCT
ejpam-4971	49	12	2023	2023	NUM
ejpam-4971	49	13	)	)	PUNCT
ejpam-4971	49	14	,	,	PUNCT
ejpam-4971	49	15	2643	2643	NUM
ejpam-4971	49	16	-	-	SYM
ejpam-4971	49	17	2661	2661	NUM
ejpam-4971	49	18	2645	2645	NUM
ejpam-4971	49	19	2	2	NUM
ejpam-4971	49	20	.	.	PUNCT
ejpam-4971	50	1	traveling	travel	VERB
ejpam-4971	50	2	wave	wave	NOUN
ejpam-4971	50	3	solution	solution	NOUN
ejpam-4971	50	4	applying	apply	VERB
ejpam-4971	50	5	the	the	DET
ejpam-4971	50	6	traveling	travel	VERB
ejpam-4971	50	7	wave	wave	NOUN
ejpam-4971	50	8	transformation	transformation	NOUN
ejpam-4971	50	9	ξ	ξ	PROPN
ejpam-4971	50	10	=	=	SYM
ejpam-4971	50	11	x−	x−	PROPN
ejpam-4971	50	12	ωt	ωt	PROPN
ejpam-4971	50	13	,	,	PUNCT
ejpam-4971	50	14	u	u	NOUN
ejpam-4971	50	15	=	=	SYM
ejpam-4971	50	16	φ(ξ	φ(ξ	PROPN
ejpam-4971	50	17	)	)	PUNCT
ejpam-4971	50	18	(	(	PUNCT
ejpam-4971	50	19	2	2	X
ejpam-4971	50	20	)	)	PUNCT
ejpam-4971	50	21	to	to	ADP
ejpam-4971	50	22	eq	eq	NOUN
ejpam-4971	50	23	.	.	PUNCT
ejpam-4971	51	1	(	(	PUNCT
ejpam-4971	51	2	1	1	X
ejpam-4971	51	3	)	)	PUNCT
ejpam-4971	51	4	yields	yield	VERB
ejpam-4971	51	5	d2φ	d2φ	PUNCT
ejpam-4971	51	6	dξ2	dξ2	NOUN
ejpam-4971	51	7	+	+	CCONJ
ejpam-4971	51	8	α0φ−	α0φ−	NOUN
ejpam-4971	51	9	β0φ	β0φ	PUNCT
ejpam-4971	51	10	3	3	NUM
ejpam-4971	51	11	=	=	SYM
ejpam-4971	51	12	0	0	NUM
ejpam-4971	51	13	,	,	PUNCT
ejpam-4971	51	14	(	(	PUNCT
ejpam-4971	51	15	3	3	X
ejpam-4971	51	16	)	)	PUNCT
ejpam-4971	51	17	where	where	SCONJ
ejpam-4971	51	18	α0	α0	ADJ
ejpam-4971	51	19	=	=	SYM
ejpam-4971	51	20	α	α	X
ejpam-4971	51	21	ω2−1	ω2−1	X
ejpam-4971	51	22	,	,	PUNCT
ejpam-4971	51	23	β0	β0	PROPN
ejpam-4971	51	24	=	=	PUNCT
ejpam-4971	51	25	β	β	X
ejpam-4971	51	26	ω2−1	ω2−1	NOUN
ejpam-4971	51	27	with	with	ADP
ejpam-4971	51	28	ω	ω	PROPN
ejpam-4971	51	29	̸=	̸=	PROPN
ejpam-4971	51	30	1	1	NUM
ejpam-4971	51	31	.	.	PUNCT
ejpam-4971	52	1	equation	equation	NOUN
ejpam-4971	52	2	(	(	PUNCT
ejpam-4971	52	3	3	3	X
ejpam-4971	52	4	)	)	PUNCT
ejpam-4971	52	5	can	can	AUX
ejpam-4971	52	6	be	be	AUX
ejpam-4971	52	7	expressed	express	VERB
ejpam-4971	52	8	as	as	ADP
ejpam-4971	52	9	a	a	DET
ejpam-4971	52	10	twodimensional	twodimensional	ADJ
ejpam-4971	52	11	(	(	PUNCT
ejpam-4971	52	12	2d	2d	NOUN
ejpam-4971	52	13	)	)	PUNCT
ejpam-4971	52	14	dynamical	dynamical	ADJ
ejpam-4971	52	15	system	system	NOUN
ejpam-4971	52	16	of	of	ADP
ejpam-4971	52	17	the	the	DET
ejpam-4971	52	18	form	form	NOUN
ejpam-4971	52	19	dφ	dφ	ADP
ejpam-4971	52	20	dξ	dξ	PROPN
ejpam-4971	52	21	=	=	SYM
ejpam-4971	52	22	y	y	PROPN
ejpam-4971	52	23	,	,	PUNCT
ejpam-4971	52	24	dy	dy	X
ejpam-4971	52	25	dξ	dξ	PROPN
ejpam-4971	53	1	=	=	PUNCT
ejpam-4971	53	2	β0φ	β0φ	PUNCT
ejpam-4971	53	3	3	3	NUM
ejpam-4971	53	4	−	−	PROPN
ejpam-4971	53	5	α0φ	α0φ	PROPN
ejpam-4971	53	6	.	.	PUNCT
ejpam-4971	54	1	(	(	PUNCT
ejpam-4971	54	2	4	4	X
ejpam-4971	54	3	)	)	PUNCT
ejpam-4971	54	4	this	this	PRON
ejpam-4971	54	5	is	be	AUX
ejpam-4971	54	6	considered	consider	VERB
ejpam-4971	54	7	a	a	DET
ejpam-4971	54	8	conservative	conservative	ADJ
ejpam-4971	54	9	hamiltonian	hamiltonian	ADJ
ejpam-4971	54	10	system	system	NOUN
ejpam-4971	54	11	with	with	ADP
ejpam-4971	54	12	one	one	NUM
ejpam-4971	54	13	degree	degree	NOUN
ejpam-4971	54	14	of	of	ADP
ejpam-4971	54	15	freedom	freedom	NOUN
ejpam-4971	54	16	,	,	PUNCT
ejpam-4971	54	17	which	which	PRON
ejpam-4971	54	18	has	have	VERB
ejpam-4971	54	19	the	the	DET
ejpam-4971	54	20	hamiltonian	hamiltonian	ADJ
ejpam-4971	54	21	function	function	NOUN
ejpam-4971	54	22	h	h	NOUN
ejpam-4971	54	23	=	=	NOUN
ejpam-4971	54	24	1	1	NUM
ejpam-4971	54	25	2	2	NUM
ejpam-4971	54	26	(	(	PUNCT
ejpam-4971	54	27	dφ	dφ	X
ejpam-4971	54	28	dξ	dξ	PROPN
ejpam-4971	54	29	)	)	PUNCT
ejpam-4971	54	30	2	2	NUM
ejpam-4971	55	1	+	+	CCONJ
ejpam-4971	55	2	α0	α0	ADJ
ejpam-4971	55	3	2	2	NUM
ejpam-4971	55	4	φ2	φ2	NOUN
ejpam-4971	55	5	−	−	PROPN
ejpam-4971	55	6	β0	β0	PROPN
ejpam-4971	55	7	4	4	NUM
ejpam-4971	55	8	φ4	φ4	NOUN
ejpam-4971	55	9	.	.	PUNCT
ejpam-4971	56	1	(	(	PUNCT
ejpam-4971	56	2	5	5	X
ejpam-4971	56	3	)	)	PUNCT
ejpam-4971	56	4	the	the	DET
ejpam-4971	56	5	hamiltonian	hamiltonian	ADJ
ejpam-4971	56	6	function	function	NOUN
ejpam-4971	56	7	(	(	PUNCT
ejpam-4971	56	8	5	5	NUM
ejpam-4971	56	9	)	)	PUNCT
ejpam-4971	56	10	does	do	AUX
ejpam-4971	56	11	not	not	PART
ejpam-4971	56	12	depend	depend	VERB
ejpam-4971	56	13	explicitly	explicitly	ADV
ejpam-4971	56	14	on	on	ADP
ejpam-4971	56	15	ξ	ξ	PROPN
ejpam-4971	56	16	,	,	PUNCT
ejpam-4971	56	17	so	so	SCONJ
ejpam-4971	56	18	it	it	PRON
ejpam-4971	56	19	has	have	VERB
ejpam-4971	56	20	an	an	DET
ejpam-4971	56	21	energy	energy	NOUN
ejpam-4971	56	22	integral	integral	ADJ
ejpam-4971	56	23	1	1	NUM
ejpam-4971	56	24	2	2	NUM
ejpam-4971	56	25	(	(	PUNCT
ejpam-4971	56	26	dφ	dφ	X
ejpam-4971	56	27	dξ	dξ	PROPN
ejpam-4971	56	28	)	)	PUNCT
ejpam-4971	56	29	2	2	NUM
ejpam-4971	57	1	+	+	CCONJ
ejpam-4971	57	2	α0	α0	ADJ
ejpam-4971	57	3	2	2	NUM
ejpam-4971	57	4	φ2	φ2	NOUN
ejpam-4971	57	5	−	−	PROPN
ejpam-4971	57	6	β0	β0	PROPN
ejpam-4971	57	7	4	4	NUM
ejpam-4971	57	8	φ4	φ4	NOUN
ejpam-4971	57	9	=	=	SYM
ejpam-4971	57	10	h	h	NOUN
ejpam-4971	57	11	,	,	PUNCT
ejpam-4971	57	12	(	(	PUNCT
ejpam-4971	57	13	6	6	NUM
ejpam-4971	57	14	)	)	PUNCT
ejpam-4971	57	15	where	where	SCONJ
ejpam-4971	57	16	h	h	NOUN
ejpam-4971	57	17	is	be	AUX
ejpam-4971	57	18	an	an	DET
ejpam-4971	57	19	arbitrary	arbitrary	ADJ
ejpam-4971	57	20	parameter	parameter	NOUN
ejpam-4971	57	21	that	that	PRON
ejpam-4971	57	22	specifies	specify	VERB
ejpam-4971	57	23	the	the	DET
ejpam-4971	57	24	total	total	ADJ
ejpam-4971	57	25	energy	energy	NOUN
ejpam-4971	57	26	.	.	PUNCT
ejpam-4971	58	1	analogous	analogous	ADJ
ejpam-4971	58	2	to	to	ADP
ejpam-4971	58	3	hamiltonian	hamiltonian	ADJ
ejpam-4971	58	4	mechanics	mechanic	NOUN
ejpam-4971	58	5	,	,	PUNCT
ejpam-4971	58	6	the	the	DET
ejpam-4971	58	7	first	first	ADJ
ejpam-4971	58	8	expression	expression	NOUN
ejpam-4971	58	9	in	in	ADP
ejpam-4971	58	10	eq	eq	ADP
ejpam-4971	58	11	.	.	PUNCT
ejpam-4971	59	1	(	(	PUNCT
ejpam-4971	59	2	6	6	NUM
ejpam-4971	59	3	)	)	PUNCT
ejpam-4971	59	4	represents	represent	VERB
ejpam-4971	59	5	the	the	DET
ejpam-4971	59	6	kinetic	kinetic	ADJ
ejpam-4971	59	7	energy	energy	NOUN
ejpam-4971	59	8	,	,	PUNCT
ejpam-4971	59	9	whereas	whereas	SCONJ
ejpam-4971	59	10	the	the	DET
ejpam-4971	59	11	second	second	ADJ
ejpam-4971	59	12	part	part	NOUN
ejpam-4971	59	13	,	,	PUNCT
ejpam-4971	59	14	u	u	NOUN
ejpam-4971	59	15	=	=	SYM
ejpam-4971	59	16	α0	α0	PROPN
ejpam-4971	59	17	2	2	NUM
ejpam-4971	59	18	φ2	φ2	NOUN
ejpam-4971	59	19	−	−	PROPN
ejpam-4971	59	20	β0	β0	PROPN
ejpam-4971	59	21	4	4	NUM
ejpam-4971	59	22	φ4	φ4	ADJ
ejpam-4971	59	23	,	,	PUNCT
ejpam-4971	59	24	(	(	PUNCT
ejpam-4971	59	25	7	7	X
ejpam-4971	59	26	)	)	PUNCT
ejpam-4971	59	27	is	be	AUX
ejpam-4971	59	28	the	the	DET
ejpam-4971	59	29	potential	potential	ADJ
ejpam-4971	59	30	function	function	NOUN
ejpam-4971	59	31	.	.	PUNCT
ejpam-4971	60	1	the	the	DET
ejpam-4971	60	2	hamiltonian	hamiltonian	NOUN
ejpam-4971	60	3	(	(	PUNCT
ejpam-4971	60	4	5	5	NUM
ejpam-4971	60	5	)	)	PUNCT
ejpam-4971	60	6	is	be	AUX
ejpam-4971	60	7	a	a	DET
ejpam-4971	60	8	one	one	NUM
ejpam-4971	60	9	-	-	PUNCT
ejpam-4971	60	10	dimensional	dimensional	ADJ
ejpam-4971	60	11	integrable	integrable	ADJ
ejpam-4971	60	12	system	system	NOUN
ejpam-4971	60	13	which	which	PRON
ejpam-4971	60	14	physically	physically	ADV
ejpam-4971	60	15	characterizes	characterize	VERB
ejpam-4971	60	16	the	the	DET
ejpam-4971	60	17	movement	movement	NOUN
ejpam-4971	60	18	of	of	ADP
ejpam-4971	60	19	a	a	DET
ejpam-4971	60	20	particle	particle	NOUN
ejpam-4971	60	21	in	in	ADP
ejpam-4971	60	22	the	the	DET
ejpam-4971	60	23	plane	plane	NOUN
ejpam-4971	60	24	under	under	ADP
ejpam-4971	60	25	the	the	DET
ejpam-4971	60	26	influence	influence	NOUN
ejpam-4971	60	27	of	of	ADP
ejpam-4971	60	28	a	a	DET
ejpam-4971	60	29	conservative	conservative	ADJ
ejpam-4971	60	30	field	field	NOUN
ejpam-4971	60	31	with	with	ADP
ejpam-4971	60	32	a	a	DET
ejpam-4971	60	33	potential	potential	ADJ
ejpam-4971	60	34	function	function	NOUN
ejpam-4971	60	35	(	(	PUNCT
ejpam-4971	60	36	7	7	NUM
ejpam-4971	60	37	)	)	PUNCT
ejpam-4971	60	38	.	.	PUNCT
ejpam-4971	61	1	thus	thus	ADV
ejpam-4971	61	2	,	,	PUNCT
ejpam-4971	61	3	eq	eq	ADJ
ejpam-4971	61	4	.	.	PUNCT
ejpam-4971	62	1	(	(	PUNCT
ejpam-4971	62	2	4	4	X
ejpam-4971	62	3	)	)	PUNCT
ejpam-4971	62	4	is	be	AUX
ejpam-4971	62	5	the	the	DET
ejpam-4971	62	6	hamiltonian	hamiltonian	ADJ
ejpam-4971	62	7	system	system	NOUN
ejpam-4971	62	8	corresponding	correspond	VERB
ejpam-4971	62	9	to	to	ADP
ejpam-4971	62	10	the	the	DET
ejpam-4971	62	11	hamiltonian	hamiltonian	ADJ
ejpam-4971	62	12	function	function	NOUN
ejpam-4971	62	13	(	(	PUNCT
ejpam-4971	62	14	6	6	NUM
ejpam-4971	62	15	)	)	PUNCT
ejpam-4971	62	16	.	.	PUNCT
ejpam-4971	63	1	the	the	DET
ejpam-4971	63	2	solution	solution	NOUN
ejpam-4971	63	3	of	of	ADP
ejpam-4971	63	4	the	the	DET
ejpam-4971	63	5	kg	kg	PROPN
ejpam-4971	63	6	equation	equation	NOUN
ejpam-4971	63	7	is	be	AUX
ejpam-4971	63	8	equivalent	equivalent	ADJ
ejpam-4971	63	9	to	to	ADP
ejpam-4971	63	10	finding	find	VERB
ejpam-4971	63	11	the	the	DET
ejpam-4971	63	12	solution	solution	NOUN
ejpam-4971	63	13	of	of	ADP
ejpam-4971	63	14	the	the	DET
ejpam-4971	63	15	hamiltonian	hamiltonian	ADJ
ejpam-4971	63	16	system	system	NOUN
ejpam-4971	63	17	(	(	PUNCT
ejpam-4971	63	18	4	4	NUM
ejpam-4971	63	19	)	)	PUNCT
ejpam-4971	63	20	.	.	PUNCT
ejpam-4971	64	1	including	include	VERB
ejpam-4971	64	2	the	the	DET
ejpam-4971	64	3	first	first	ADJ
ejpam-4971	64	4	equation	equation	NOUN
ejpam-4971	64	5	in	in	ADP
ejpam-4971	64	6	eq	eq	ADP
ejpam-4971	64	7	.	.	PUNCT
ejpam-4971	65	1	(	(	PUNCT
ejpam-4971	65	2	4	4	NUM
ejpam-4971	65	3	)	)	PUNCT
ejpam-4971	65	4	into	into	ADP
ejpam-4971	65	5	energy	energy	NOUN
ejpam-4971	65	6	integral	integral	ADJ
ejpam-4971	65	7	(	(	PUNCT
ejpam-4971	65	8	6	6	NUM
ejpam-4971	65	9	)	)	PUNCT
ejpam-4971	65	10	and	and	CCONJ
ejpam-4971	65	11	separating	separate	VERB
ejpam-4971	65	12	the	the	DET
ejpam-4971	65	13	variables	variable	NOUN
ejpam-4971	65	14	,	,	PUNCT
ejpam-4971	65	15	we	we	PRON
ejpam-4971	65	16	get	get	VERB
ejpam-4971	65	17	the	the	DET
ejpam-4971	65	18	differential	differential	ADJ
ejpam-4971	65	19	shape	shape	NOUN
ejpam-4971	65	20	as	as	SCONJ
ejpam-4971	65	21	follows	follow	VERB
ejpam-4971	65	22	dφ√	dφ√	NOUN
ejpam-4971	65	23	p4(φ	p4(φ	NOUN
ejpam-4971	65	24	)	)	PUNCT
ejpam-4971	65	25	=	=	SYM
ejpam-4971	65	26	dξ	dξ	PROPN
ejpam-4971	65	27	,	,	PUNCT
ejpam-4971	65	28	(	(	PUNCT
ejpam-4971	65	29	8)	8)	NUM
ejpam-4971	65	30	where	where	SCONJ
ejpam-4971	65	31	p4(φ	p4(φ	VERB
ejpam-4971	65	32	)	)	PUNCT
ejpam-4971	65	33	is	be	AUX
ejpam-4971	65	34	a	a	DET
ejpam-4971	65	35	polynomial	polynomial	NOUN
ejpam-4971	65	36	in	in	ADP
ejpam-4971	65	37	φ	φ	PROPN
ejpam-4971	65	38	of	of	ADP
ejpam-4971	65	39	degree	degree	NOUN
ejpam-4971	65	40	4	4	NUM
ejpam-4971	65	41	,	,	PUNCT
ejpam-4971	65	42	which	which	PRON
ejpam-4971	65	43	is	be	AUX
ejpam-4971	65	44	given	give	VERB
ejpam-4971	65	45	by	by	ADP
ejpam-4971	65	46	p4(φ	p4(φ	PROPN
ejpam-4971	65	47	)	)	PUNCT
ejpam-4971	65	48	=	=	SYM
ejpam-4971	65	49	2	2	X
ejpam-4971	65	50	[	[	PUNCT
ejpam-4971	65	51	h−	h−	X
ejpam-4971	65	52	α0	α0	ADJ
ejpam-4971	65	53	2	2	NUM
ejpam-4971	65	54	φ2	φ2	NOUN
ejpam-4971	65	55	+	+	CCONJ
ejpam-4971	66	1	β0	β0	PROPN
ejpam-4971	66	2	4	4	NUM
ejpam-4971	66	3	φ4	φ4	NOUN
ejpam-4971	66	4	]	]	PUNCT
ejpam-4971	66	5	.	.	PUNCT
ejpam-4971	67	1	(	(	PUNCT
ejpam-4971	67	2	9	9	X
ejpam-4971	67	3	)	)	PUNCT
ejpam-4971	67	4	m.arab	m.arab	NOUN
ejpam-4971	67	5	/	/	SYM
ejpam-4971	67	6	eur	eur	NOUN
ejpam-4971	67	7	.	.	PUNCT
ejpam-4971	68	1	j.	j.	PROPN
ejpam-4971	68	2	pure	pure	PROPN
ejpam-4971	68	3	appl	appl	PROPN
ejpam-4971	68	4	.	.	PROPN
ejpam-4971	68	5	math	math	PROPN
ejpam-4971	68	6	,	,	PUNCT
ejpam-4971	68	7	16	16	NUM
ejpam-4971	68	8	(	(	PUNCT
ejpam-4971	68	9	4	4	NUM
ejpam-4971	68	10	)	)	PUNCT
ejpam-4971	68	11	(	(	PUNCT
ejpam-4971	68	12	2023	2023	NUM
ejpam-4971	68	13	)	)	PUNCT
ejpam-4971	68	14	,	,	PUNCT
ejpam-4971	68	15	2643	2643	NUM
ejpam-4971	68	16	-	-	SYM
ejpam-4971	68	17	2661	2661	NUM
ejpam-4971	68	18	2646	2646	NUM
ejpam-4971	68	19	integrating	integrate	VERB
ejpam-4971	68	20	eq	eq	ADP
ejpam-4971	68	21	.	.	PUNCT
ejpam-4971	69	1	(	(	PUNCT
ejpam-4971	69	2	8)	8)	NUM
ejpam-4971	69	3	requires	require	VERB
ejpam-4971	69	4	the	the	DET
ejpam-4971	69	5	range	range	NOUN
ejpam-4971	69	6	of	of	ADP
ejpam-4971	69	7	the	the	DET
ejpam-4971	69	8	parameters	parameter	NOUN
ejpam-4971	69	9	α0	α0	ADJ
ejpam-4971	69	10	,	,	PUNCT
ejpam-4971	69	11	β0	β0	NOUN
ejpam-4971	69	12	,	,	PUNCT
ejpam-4971	69	13	and	and	CCONJ
ejpam-4971	69	14	h.	h.	PROPN
ejpam-4971	69	15	there	there	PRON
ejpam-4971	69	16	are	be	VERB
ejpam-4971	69	17	several	several	ADJ
ejpam-4971	69	18	methods	method	NOUN
ejpam-4971	69	19	that	that	PRON
ejpam-4971	69	20	can	can	AUX
ejpam-4971	69	21	be	be	AUX
ejpam-4971	69	22	applied	apply	VERB
ejpam-4971	69	23	to	to	PART
ejpam-4971	69	24	find	find	VERB
ejpam-4971	69	25	this	this	DET
ejpam-4971	69	26	range	range	NOUN
ejpam-4971	69	27	,	,	PUNCT
ejpam-4971	69	28	like	like	ADP
ejpam-4971	69	29	the	the	DET
ejpam-4971	69	30	complete	complete	ADJ
ejpam-4971	69	31	discriminant	discriminant	NOUN
ejpam-4971	69	32	system	system	NOUN
ejpam-4971	69	33	for	for	ADP
ejpam-4971	69	34	the	the	DET
ejpam-4971	69	35	polynomial	polynomial	ADJ
ejpam-4971	69	36	(	(	PUNCT
ejpam-4971	69	37	9	9	NUM
ejpam-4971	69	38	)	)	PUNCT
ejpam-4971	70	1	[	[	X
ejpam-4971	70	2	41	41	NUM
ejpam-4971	70	3	]	]	PUNCT
ejpam-4971	70	4	and	and	CCONJ
ejpam-4971	70	5	bifurcation	bifurcation	NOUN
ejpam-4971	70	6	analysis	analysis	NOUN
ejpam-4971	70	7	[	[	X
ejpam-4971	70	8	6	6	NUM
ejpam-4971	70	9	,	,	PUNCT
ejpam-4971	70	10	14–16	14–16	NUM
ejpam-4971	70	11	,	,	PUNCT
ejpam-4971	70	12	18–20	18–20	NUM
ejpam-4971	70	13	,	,	PUNCT
ejpam-4971	70	14	43	43	NUM
ejpam-4971	70	15	]	]	PUNCT
ejpam-4971	70	16	.	.	PUNCT
ejpam-4971	71	1	blackbifurcation	blackbifurcation	NOUN
ejpam-4971	71	2	analysis	analysis	NOUN
ejpam-4971	71	3	is	be	AUX
ejpam-4971	71	4	more	more	ADV
ejpam-4971	71	5	blackapplicable	blackapplicable	ADJ
ejpam-4971	71	6	because	because	SCONJ
ejpam-4971	71	7	it	it	PRON
ejpam-4971	71	8	affords	afford	VERB
ejpam-4971	71	9	the	the	DET
ejpam-4971	71	10	zone	zone	NOUN
ejpam-4971	71	11	of	of	ADP
ejpam-4971	71	12	those	those	DET
ejpam-4971	71	13	parameters	parameter	NOUN
ejpam-4971	71	14	and	and	CCONJ
ejpam-4971	71	15	also	also	ADV
ejpam-4971	71	16	determines	determine	VERB
ejpam-4971	71	17	the	the	DET
ejpam-4971	71	18	sort	sort	NOUN
ejpam-4971	71	19	of	of	ADP
ejpam-4971	71	20	solutions	solution	NOUN
ejpam-4971	71	21	before	before	SCONJ
ejpam-4971	71	22	they	they	PRON
ejpam-4971	71	23	are	be	AUX
ejpam-4971	71	24	constructed	construct	VERB
ejpam-4971	71	25	by	by	ADP
ejpam-4971	71	26	providing	provide	VERB
ejpam-4971	71	27	the	the	DET
ejpam-4971	71	28	orbits	orbit	NOUN
ejpam-4971	71	29	.	.	PUNCT
ejpam-4971	72	1	3	3	X
ejpam-4971	72	2	.	.	X
ejpam-4971	72	3	bifurcations	bifurcation	NOUN
ejpam-4971	72	4	and	and	CCONJ
ejpam-4971	72	5	phase	phase	NOUN
ejpam-4971	72	6	portraits	portrait	NOUN
ejpam-4971	72	7	in	in	ADP
ejpam-4971	72	8	this	this	DET
ejpam-4971	72	9	section	section	NOUN
ejpam-4971	72	10	,	,	PUNCT
ejpam-4971	72	11	we	we	PRON
ejpam-4971	72	12	examine	examine	VERB
ejpam-4971	72	13	the	the	DET
ejpam-4971	72	14	phase	phase	NOUN
ejpam-4971	72	15	portraits	portrait	NOUN
ejpam-4971	72	16	of	of	ADP
ejpam-4971	72	17	the	the	DET
ejpam-4971	72	18	traveling	travel	VERB
ejpam-4971	72	19	wave	wave	NOUN
ejpam-4971	72	20	system	system	NOUN
ejpam-4971	72	21	using	use	VERB
ejpam-4971	72	22	the	the	DET
ejpam-4971	72	23	qualitative	qualitative	ADJ
ejpam-4971	72	24	theory	theory	NOUN
ejpam-4971	72	25	of	of	ADP
ejpam-4971	72	26	differential	differential	ADJ
ejpam-4971	72	27	equations	equation	NOUN
ejpam-4971	72	28	and	and	CCONJ
ejpam-4971	72	29	the	the	DET
ejpam-4971	72	30	bifurcation	bifurcation	NOUN
ejpam-4971	72	31	theory	theory	NOUN
ejpam-4971	72	32	of	of	ADP
ejpam-4971	72	33	planar	planar	ADJ
ejpam-4971	72	34	dynamical	dynamical	ADJ
ejpam-4971	72	35	systems	system	NOUN
ejpam-4971	72	36	corresponding	correspond	VERB
ejpam-4971	72	37	to	to	ADP
ejpam-4971	72	38	the	the	DET
ejpam-4971	72	39	nonlinear	nonlinear	ADJ
ejpam-4971	72	40	kg	kg	PROPN
ejpam-4971	72	41	equation	equation	NOUN
ejpam-4971	72	42	.	.	PUNCT
ejpam-4971	73	1	we	we	PRON
ejpam-4971	73	2	now	now	ADV
ejpam-4971	73	3	investigate	investigate	VERB
ejpam-4971	73	4	the	the	DET
ejpam-4971	73	5	phase	phase	NOUN
ejpam-4971	73	6	portrait	portrait	NOUN
ejpam-4971	73	7	of	of	ADP
ejpam-4971	73	8	the	the	DET
ejpam-4971	73	9	kg	kg	PROPN
ejpam-4971	73	10	equation	equation	NOUN
ejpam-4971	73	11	,	,	PUNCT
ejpam-4971	73	12	which	which	PRON
ejpam-4971	73	13	is	be	AUX
ejpam-4971	73	14	the	the	DET
ejpam-4971	73	15	same	same	ADJ
ejpam-4971	73	16	as	as	ADP
ejpam-4971	73	17	the	the	DET
ejpam-4971	73	18	phase	phase	NOUN
ejpam-4971	73	19	portrait	portrait	NOUN
ejpam-4971	73	20	of	of	ADP
ejpam-4971	73	21	eq	eq	PROPN
ejpam-4971	73	22	.	.	PUNCT
ejpam-4971	74	1	(	(	PUNCT
ejpam-4971	74	2	3	3	NUM
ejpam-4971	74	3	)	)	PUNCT
ejpam-4971	74	4	.	.	PUNCT
ejpam-4971	75	1	therefore	therefore	ADV
ejpam-4971	75	2	,	,	PUNCT
ejpam-4971	75	3	the	the	DET
ejpam-4971	75	4	equilibrium	equilibrium	NOUN
ejpam-4971	75	5	points	point	NOUN
ejpam-4971	75	6	should	should	AUX
ejpam-4971	75	7	be	be	AUX
ejpam-4971	75	8	found	find	VERB
ejpam-4971	75	9	.	.	PUNCT
ejpam-4971	76	1	so	so	ADV
ejpam-4971	76	2	,	,	PUNCT
ejpam-4971	76	3	we	we	PRON
ejpam-4971	76	4	introduce	introduce	VERB
ejpam-4971	76	5	the	the	DET
ejpam-4971	76	6	next	next	ADJ
ejpam-4971	76	7	theorem	theorem	NOUN
ejpam-4971	76	8	.	.	PUNCT
ejpam-4971	76	9	theorem	theorem	NOUN
ejpam-4971	76	10	1	1	NUM
ejpam-4971	76	11	.	.	PUNCT
ejpam-4971	76	12	considering	consider	VERB
ejpam-4971	76	13	the	the	DET
ejpam-4971	76	14	hamiltonian	hamiltonian	ADJ
ejpam-4971	76	15	system	system	NOUN
ejpam-4971	76	16	(	(	PUNCT
ejpam-4971	76	17	4	4	X
ejpam-4971	76	18	)	)	PUNCT
ejpam-4971	76	19	corresponding	correspond	VERB
ejpam-4971	76	20	to	to	ADP
ejpam-4971	76	21	the	the	DET
ejpam-4971	76	22	hamiltonian	hamiltonian	ADJ
ejpam-4971	76	23	function	function	NOUN
ejpam-4971	76	24	(	(	PUNCT
ejpam-4971	76	25	6	6	NUM
ejpam-4971	76	26	)	)	PUNCT
ejpam-4971	76	27	,	,	PUNCT
ejpam-4971	76	28	we	we	PRON
ejpam-4971	76	29	have	have	VERB
ejpam-4971	76	30	a	a	DET
ejpam-4971	76	31	maximum	maximum	NOUN
ejpam-4971	76	32	of	of	ADP
ejpam-4971	76	33	three	three	NUM
ejpam-4971	76	34	equilibrium	equilibrium	NOUN
ejpam-4971	76	35	points	point	NOUN
ejpam-4971	76	36	.	.	PUNCT
ejpam-4971	77	1	furthermore	furthermore	ADV
ejpam-4971	77	2	,	,	PUNCT
ejpam-4971	77	3	if	if	SCONJ
ejpam-4971	77	4	α0β0	α0β0	PROPN
ejpam-4971	77	5	≤	≤	NUM
ejpam-4971	77	6	0	0	NUM
ejpam-4971	77	7	,	,	PUNCT
ejpam-4971	77	8	then	then	ADV
ejpam-4971	77	9	e1	e1	NOUN
ejpam-4971	77	10	=	=	SYM
ejpam-4971	77	11	(	(	PUNCT
ejpam-4971	77	12	0	0	NUM
ejpam-4971	77	13	,	,	PUNCT
ejpam-4971	77	14	0	0	NUM
ejpam-4971	77	15	)	)	PUNCT
ejpam-4971	77	16	is	be	AUX
ejpam-4971	77	17	the	the	DET
ejpam-4971	77	18	unique	unique	ADJ
ejpam-4971	77	19	equilibrium	equilibrium	NOUN
ejpam-4971	77	20	point	point	NOUN
ejpam-4971	77	21	,	,	PUNCT
ejpam-4971	77	22	whereas	whereas	SCONJ
ejpam-4971	77	23	if	if	SCONJ
ejpam-4971	77	24	α0β0	α0β0	PROPN
ejpam-4971	77	25	>	>	X
ejpam-4971	77	26	0	0	NUM
ejpam-4971	77	27	,	,	PUNCT
ejpam-4971	77	28	there	there	PRON
ejpam-4971	77	29	are	be	VERB
ejpam-4971	77	30	3	3	NUM
ejpam-4971	77	31	equilibrium	equilibrium	NOUN
ejpam-4971	77	32	points	point	NOUN
ejpam-4971	77	33	e1	e1	NOUN
ejpam-4971	77	34	=	=	SYM
ejpam-4971	77	35	(	(	PUNCT
ejpam-4971	77	36	0	0	NUM
ejpam-4971	77	37	,	,	PUNCT
ejpam-4971	77	38	0	0	NUM
ejpam-4971	77	39	)	)	PUNCT
ejpam-4971	77	40	,	,	PUNCT
ejpam-4971	78	1	e2,3	e2,3	NOUN
ejpam-4971	78	2	=	=	SYM
ejpam-4971	78	3	(	(	PUNCT
ejpam-4971	78	4	±	±	NOUN
ejpam-4971	78	5	√	√	PROPN
ejpam-4971	78	6	α0	α0	PROPN
ejpam-4971	78	7	β0	β0	NOUN
ejpam-4971	78	8	,	,	PUNCT
ejpam-4971	78	9	0	0	NUM
ejpam-4971	78	10	)	)	PUNCT
ejpam-4971	78	11	.	.	PUNCT
ejpam-4971	79	1	black	black	ADJ
ejpam-4971	79	2	proof	proof	NOUN
ejpam-4971	79	3	.	.	PUNCT
ejpam-4971	80	1	the	the	DET
ejpam-4971	80	2	equilibrium	equilibrium	NOUN
ejpam-4971	80	3	points	point	NOUN
ejpam-4971	80	4	for	for	ADP
ejpam-4971	80	5	the	the	DET
ejpam-4971	80	6	hamiltonian	hamiltonian	NOUN
ejpam-4971	80	7	(	(	PUNCT
ejpam-4971	80	8	5	5	NUM
ejpam-4971	80	9	)	)	PUNCT
ejpam-4971	80	10	are	be	AUX
ejpam-4971	80	11	the	the	DET
ejpam-4971	80	12	critical	critical	ADJ
ejpam-4971	80	13	points	point	NOUN
ejpam-4971	80	14	for	for	ADP
ejpam-4971	80	15	the	the	DET
ejpam-4971	80	16	potential	potential	ADJ
ejpam-4971	80	17	function	function	NOUN
ejpam-4971	80	18	.	.	PUNCT
ejpam-4971	81	1	hence	hence	ADV
ejpam-4971	81	2	,	,	PUNCT
ejpam-4971	81	3	they	they	PRON
ejpam-4971	81	4	are	be	AUX
ejpam-4971	81	5	(	(	PUNCT
ejpam-4971	81	6	φ0	φ0	ADJ
ejpam-4971	81	7	,	,	PUNCT
ejpam-4971	81	8	0	0	NUM
ejpam-4971	81	9	)	)	PUNCT
ejpam-4971	81	10	,	,	PUNCT
ejpam-4971	81	11	where	where	SCONJ
ejpam-4971	81	12	φ0	φ0	ADJ
ejpam-4971	81	13	satisfies	satisfie	NOUN
ejpam-4971	81	14	β0φ	β0φ	PUNCT
ejpam-4971	81	15	3	3	NUM
ejpam-4971	81	16	−	−	PROPN
ejpam-4971	81	17	α0φ	α0φ	NOUN
ejpam-4971	81	18	=	=	SYM
ejpam-4971	81	19	0	0	PROPN
ejpam-4971	81	20	,	,	PUNCT
ejpam-4971	81	21	(	(	PUNCT
ejpam-4971	81	22	10	10	NUM
ejpam-4971	81	23	)	)	PUNCT
ejpam-4971	81	24	which	which	PRON
ejpam-4971	81	25	is	be	AUX
ejpam-4971	81	26	equivalent	equivalent	ADJ
ejpam-4971	81	27	to	to	PART
ejpam-4971	81	28	set	set	VERB
ejpam-4971	81	29	φ′	φ′	NUM
ejpam-4971	81	30	=	=	SYM
ejpam-4971	81	31	y′	y′	NOUN
ejpam-4971	81	32	=	=	SYM
ejpam-4971	81	33	0	0	NUM
ejpam-4971	81	34	in	in	ADP
ejpam-4971	81	35	system	system	NOUN
ejpam-4971	81	36	(	(	PUNCT
ejpam-4971	81	37	4	4	NUM
ejpam-4971	81	38	)	)	PUNCT
ejpam-4971	81	39	.	.	PUNCT
ejpam-4971	82	1	eq.(10	eq.(10	PROPN
ejpam-4971	82	2	)	)	PUNCT
ejpam-4971	82	3	has	have	VERB
ejpam-4971	82	4	the	the	DET
ejpam-4971	82	5	solution	solution	NOUN
ejpam-4971	82	6	ϕ0	ϕ0	NOUN
ejpam-4971	82	7	=	=	SYM
ejpam-4971	82	8	0	0	NUM
ejpam-4971	82	9	,	,	PUNCT
ejpam-4971	82	10	ϕ0	ϕ0	NOUN
ejpam-4971	82	11	=	=	SYM
ejpam-4971	82	12	±	±	NOUN
ejpam-4971	82	13	√	√	PROPN
ejpam-4971	83	1	α0	α0	PROPN
ejpam-4971	83	2	β0	β0	NOUN
ejpam-4971	83	3	,	,	PUNCT
ejpam-4971	83	4	where	where	SCONJ
ejpam-4971	83	5	the	the	DET
ejpam-4971	83	6	second	second	ADJ
ejpam-4971	83	7	solution	solution	NOUN
ejpam-4971	83	8	exists	exist	VERB
ejpam-4971	83	9	if	if	SCONJ
ejpam-4971	83	10	α0β0	α0β0	PROPN
ejpam-4971	83	11	>	>	X
ejpam-4971	83	12	0	0	X
ejpam-4971	83	13	.	.	PUNCT
ejpam-4971	84	1	hence	hence	ADV
ejpam-4971	84	2	,	,	PUNCT
ejpam-4971	84	3	if	if	SCONJ
ejpam-4971	84	4	α0β	α0β	ADJ
ejpam-4971	84	5	>	>	X
ejpam-4971	84	6	0	0	NUM
ejpam-4971	84	7	,	,	PUNCT
ejpam-4971	84	8	there	there	PRON
ejpam-4971	84	9	are	be	VERB
ejpam-4971	84	10	three	three	NUM
ejpam-4971	84	11	equilibrium	equilibrium	NOUN
ejpam-4971	84	12	points	point	NOUN
ejpam-4971	84	13	e1	e1	NOUN
ejpam-4971	84	14	and	and	CCONJ
ejpam-4971	84	15	e2,3	e2,3	ADJ
ejpam-4971	84	16	while	while	SCONJ
ejpam-4971	84	17	if	if	SCONJ
ejpam-4971	84	18	α0β0	α0β0	PROPN
ejpam-4971	84	19	<	<	X
ejpam-4971	84	20	0	0	NUM
ejpam-4971	84	21	,	,	PUNCT
ejpam-4971	84	22	there	there	PRON
ejpam-4971	84	23	is	be	VERB
ejpam-4971	84	24	a	a	DET
ejpam-4971	84	25	single	single	ADJ
ejpam-4971	84	26	equilibrium	equilibrium	NOUN
ejpam-4971	84	27	point	point	NOUN
ejpam-4971	84	28	e1	e1	PROPN
ejpam-4971	84	29	.	.	PUNCT
ejpam-4971	85	1	the	the	DET
ejpam-4971	85	2	determinant	determinant	NOUN
ejpam-4971	85	3	of	of	ADP
ejpam-4971	85	4	the	the	DET
ejpam-4971	85	5	jacobian	jacobian	ADJ
ejpam-4971	85	6	matrix	matrix	NOUN
ejpam-4971	85	7	related	relate	VERB
ejpam-4971	85	8	to	to	ADP
ejpam-4971	85	9	the	the	DET
ejpam-4971	85	10	hamiltonian	hamiltonian	ADJ
ejpam-4971	85	11	system	system	NOUN
ejpam-4971	85	12	(	(	PUNCT
ejpam-4971	85	13	4	4	NUM
ejpam-4971	85	14	)	)	PUNCT
ejpam-4971	85	15	is	be	AUX
ejpam-4971	85	16	j(φ0	j(φ0	ADJ
ejpam-4971	85	17	,	,	PUNCT
ejpam-4971	85	18	0	0	NUM
ejpam-4971	85	19	)	)	PUNCT
ejpam-4971	85	20	=	=	SYM
ejpam-4971	85	21	−2α0	−2α0	NOUN
ejpam-4971	85	22	.	.	PUNCT
ejpam-4971	86	1	considering	consider	VERB
ejpam-4971	86	2	bifurcation	bifurcation	NOUN
ejpam-4971	86	3	theory	theory	NOUN
ejpam-4971	86	4	for	for	ADP
ejpam-4971	86	5	planar	planar	ADJ
ejpam-4971	86	6	integrable	integrable	ADJ
ejpam-4971	86	7	dynamical	dynamical	ADJ
ejpam-4971	86	8	systems	system	NOUN
ejpam-4971	86	9	,	,	PUNCT
ejpam-4971	86	10	the	the	DET
ejpam-4971	86	11	equilibrium	equilibrium	NOUN
ejpam-4971	86	12	point	point	NOUN
ejpam-4971	86	13	(	(	PUNCT
ejpam-4971	86	14	φ0	φ0	VERB
ejpam-4971	86	15	,	,	PUNCT
ejpam-4971	86	16	0	0	NUM
ejpam-4971	86	17	)	)	PUNCT
ejpam-4971	86	18	is	be	AUX
ejpam-4971	86	19	a	a	DET
ejpam-4971	86	20	center	center	NOUN
ejpam-4971	86	21	if	if	SCONJ
ejpam-4971	86	22	j(φ0	j(φ0	ADJ
ejpam-4971	86	23	,	,	PUNCT
ejpam-4971	86	24	0	0	NUM
ejpam-4971	86	25	)	)	PUNCT
ejpam-4971	86	26	>	>	X
ejpam-4971	86	27	0	0	NUM
ejpam-4971	86	28	,	,	PUNCT
ejpam-4971	86	29	a	a	DET
ejpam-4971	86	30	saddle	saddle	NOUN
ejpam-4971	86	31	if	if	SCONJ
ejpam-4971	86	32	j(φ0	j(φ0	ADJ
ejpam-4971	86	33	,	,	PUNCT
ejpam-4971	86	34	0	0	NUM
ejpam-4971	86	35	)	)	PUNCT
ejpam-4971	86	36	<	<	X
ejpam-4971	86	37	0	0	NUM
ejpam-4971	86	38	,	,	PUNCT
ejpam-4971	86	39	and	and	CCONJ
ejpam-4971	86	40	a	a	DET
ejpam-4971	86	41	cusp	cusp	NOUN
ejpam-4971	86	42	if	if	SCONJ
ejpam-4971	86	43	j(φ0	j(φ0	ADJ
ejpam-4971	86	44	,	,	PUNCT
ejpam-4971	86	45	0	0	NUM
ejpam-4971	86	46	)	)	PUNCT
ejpam-4971	86	47	=	=	SYM
ejpam-4971	86	48	0	0	NUM
ejpam-4971	86	49	and	and	CCONJ
ejpam-4971	86	50	its	its	PRON
ejpam-4971	86	51	poincaré	poincaré	ADJ
ejpam-4971	86	52	index	index	NOUN
ejpam-4971	86	53	is	be	AUX
ejpam-4971	86	54	0	0	NUM
ejpam-4971	86	55	.	.	PUNCT
ejpam-4971	87	1	using	use	VERB
ejpam-4971	87	2	this	this	DET
ejpam-4971	87	3	information	information	NOUN
ejpam-4971	87	4	,	,	PUNCT
ejpam-4971	87	5	we	we	PRON
ejpam-4971	87	6	can	can	AUX
ejpam-4971	87	7	characterize	characterize	VERB
ejpam-4971	87	8	the	the	DET
ejpam-4971	87	9	equilibrium	equilibrium	NOUN
ejpam-4971	87	10	points	point	NOUN
ejpam-4971	87	11	ei	ei	X
ejpam-4971	87	12	,	,	PUNCT
ejpam-4971	87	13	i	i	PRON
ejpam-4971	87	14	=	=	NOUN
ejpam-4971	87	15	1	1	NUM
ejpam-4971	87	16	,	,	PUNCT
ejpam-4971	87	17	2	2	NUM
ejpam-4971	87	18	,	,	PUNCT
ejpam-4971	87	19	3	3	NUM
ejpam-4971	87	20	.	.	X
ejpam-4971	87	21	we	we	PRON
ejpam-4971	87	22	now	now	ADV
ejpam-4971	87	23	examine	examine	VERB
ejpam-4971	87	24	the	the	DET
ejpam-4971	87	25	bifurcations	bifurcation	NOUN
ejpam-4971	87	26	and	and	CCONJ
ejpam-4971	87	27	phase	phase	NOUN
ejpam-4971	87	28	forms	form	NOUN
ejpam-4971	87	29	of	of	ADP
ejpam-4971	87	30	the	the	DET
ejpam-4971	87	31	hamiltonian	hamiltonian	ADJ
ejpam-4971	87	32	system	system	NOUN
ejpam-4971	87	33	(	(	PUNCT
ejpam-4971	87	34	4	4	NUM
ejpam-4971	87	35	)	)	PUNCT
ejpam-4971	87	36	for	for	ADP
ejpam-4971	87	37	different	different	ADJ
ejpam-4971	87	38	parameters	parameter	NOUN
ejpam-4971	87	39	α0	α0	ADJ
ejpam-4971	87	40	and	and	CCONJ
ejpam-4971	87	41	β0	β0	NOUN
ejpam-4971	87	42	.	.	PUNCT
ejpam-4971	88	1	the	the	DET
ejpam-4971	88	2	energy	energy	NOUN
ejpam-4971	88	3	corresponding	correspond	VERB
ejpam-4971	88	4	to	to	ADP
ejpam-4971	88	5	these	these	DET
ejpam-4971	88	6	equilibrium	equilibrium	NOUN
ejpam-4971	88	7	points	point	NOUN
ejpam-4971	88	8	is	be	AUX
ejpam-4971	88	9	h1	h1	ADJ
ejpam-4971	88	10	=	=	SYM
ejpam-4971	88	11	h(0	h(0	PROPN
ejpam-4971	88	12	,	,	PUNCT
ejpam-4971	88	13	0	0	NUM
ejpam-4971	88	14	)	)	PUNCT
ejpam-4971	88	15	=	=	SYM
ejpam-4971	88	16	0	0	NUM
ejpam-4971	88	17	,	,	PUNCT
ejpam-4971	88	18	h2	h2	NOUN
ejpam-4971	88	19	=	=	SYM
ejpam-4971	88	20	h(±	h(±	NOUN
ejpam-4971	88	21	√	√	ADP
ejpam-4971	88	22	α0	α0	PROPN
ejpam-4971	88	23	β0	β0	NOUN
ejpam-4971	88	24	,	,	PUNCT
ejpam-4971	88	25	0	0	NUM
ejpam-4971	88	26	)	)	PUNCT
ejpam-4971	88	27	=	=	VERB
ejpam-4971	89	1	α2	α2	ADJ
ejpam-4971	89	2	0	0	NUM
ejpam-4971	89	3	4β0	4β0	NUM
ejpam-4971	89	4	.	.	PUNCT
ejpam-4971	90	1	(	(	PUNCT
ejpam-4971	90	2	11	11	NUM
ejpam-4971	90	3	)	)	PUNCT
ejpam-4971	90	4	there	there	PRON
ejpam-4971	90	5	are	be	VERB
ejpam-4971	90	6	two	two	NUM
ejpam-4971	90	7	bifurcation	bifurcation	NOUN
ejpam-4971	90	8	curves	curve	NOUN
ejpam-4971	90	9	,	,	PUNCT
ejpam-4971	90	10	l1	l1	PROPN
ejpam-4971	90	11	:	:	PUNCT
ejpam-4971	90	12	α0	α0	ADJ
ejpam-4971	90	13	=	=	SYM
ejpam-4971	90	14	0	0	NUM
ejpam-4971	90	15	,	,	PUNCT
ejpam-4971	90	16	l2	l2	NOUN
ejpam-4971	90	17	:	:	PUNCT
ejpam-4971	90	18	β0	β0	NOUN
ejpam-4971	90	19	=	=	SYM
ejpam-4971	90	20	0	0	NUM
ejpam-4971	90	21	,	,	PUNCT
ejpam-4971	90	22	m.arab	m.arab	NOUN
ejpam-4971	90	23	/	/	SYM
ejpam-4971	90	24	eur	eur	NOUN
ejpam-4971	90	25	.	.	PUNCT
ejpam-4971	91	1	j.	j.	PROPN
ejpam-4971	91	2	pure	pure	PROPN
ejpam-4971	91	3	appl	appl	PROPN
ejpam-4971	91	4	.	.	PROPN
ejpam-4971	91	5	math	math	PROPN
ejpam-4971	91	6	,	,	PUNCT
ejpam-4971	91	7	16	16	NUM
ejpam-4971	91	8	(	(	PUNCT
ejpam-4971	91	9	4	4	NUM
ejpam-4971	91	10	)	)	PUNCT
ejpam-4971	91	11	(	(	PUNCT
ejpam-4971	91	12	2023	2023	NUM
ejpam-4971	91	13	)	)	PUNCT
ejpam-4971	91	14	,	,	PUNCT
ejpam-4971	91	15	2643	2643	NUM
ejpam-4971	91	16	-	-	SYM
ejpam-4971	91	17	2661	2661	NUM
ejpam-4971	91	18	2647	2647	NUM
ejpam-4971	91	19	that	that	PRON
ejpam-4971	91	20	split	split	VERB
ejpam-4971	91	21	the	the	DET
ejpam-4971	91	22	plane	plane	NOUN
ejpam-4971	91	23	of	of	ADP
ejpam-4971	91	24	the	the	DET
ejpam-4971	91	25	parameters	parameter	NOUN
ejpam-4971	91	26	(	(	PUNCT
ejpam-4971	91	27	α0	α0	ADJ
ejpam-4971	91	28	,	,	PUNCT
ejpam-4971	91	29	β0	β0	NOUN
ejpam-4971	91	30	)	)	PUNCT
ejpam-4971	91	31	into	into	ADP
ejpam-4971	91	32	five	five	NUM
ejpam-4971	91	33	regions	region	NOUN
ejpam-4971	91	34	.	.	PUNCT
ejpam-4971	92	1	these	these	DET
ejpam-4971	92	2	regions	region	NOUN
ejpam-4971	92	3	are	be	AUX
ejpam-4971	92	4	represented	represent	VERB
ejpam-4971	92	5	as	as	ADP
ejpam-4971	92	6	r1	r1	NOUN
ejpam-4971	92	7	=	=	SYM
ejpam-4971	92	8	{	{	PUNCT
ejpam-4971	92	9	(	(	PUNCT
ejpam-4971	92	10	α0	α0	ADJ
ejpam-4971	92	11	,	,	PUNCT
ejpam-4971	92	12	β0	β0	NOUN
ejpam-4971	92	13	)	)	PUNCT
ejpam-4971	92	14	|α0	|α0	PROPN
ejpam-4971	92	15	>	>	X
ejpam-4971	92	16	0	0	NUM
ejpam-4971	92	17	,	,	PUNCT
ejpam-4971	92	18	β0	β0	NOUN
ejpam-4971	92	19	>	>	X
ejpam-4971	92	20	0	0	NUM
ejpam-4971	92	21	}	}	PUNCT
ejpam-4971	92	22	,	,	PUNCT
ejpam-4971	92	23	r2	r2	PROPN
ejpam-4971	92	24	=	=	SYM
ejpam-4971	92	25	{	{	PUNCT
ejpam-4971	92	26	(	(	PUNCT
ejpam-4971	92	27	α0	α0	ADJ
ejpam-4971	92	28	,	,	PUNCT
ejpam-4971	92	29	β0	β0	NOUN
ejpam-4971	92	30	)	)	PUNCT
ejpam-4971	92	31	|α0	|α0	PROPN
ejpam-4971	92	32	>	>	X
ejpam-4971	92	33	0	0	NUM
ejpam-4971	92	34	,	,	PUNCT
ejpam-4971	92	35	β0	β0	NOUN
ejpam-4971	92	36	<	<	X
ejpam-4971	92	37	0	0	NUM
ejpam-4971	92	38	}	}	PUNCT
ejpam-4971	92	39	,	,	PUNCT
ejpam-4971	92	40	r3	r3	PROPN
ejpam-4971	92	41	=	=	SYM
ejpam-4971	92	42	{	{	PUNCT
ejpam-4971	92	43	(	(	PUNCT
ejpam-4971	92	44	α0	α0	ADJ
ejpam-4971	92	45	,	,	PUNCT
ejpam-4971	92	46	β0	β0	NOUN
ejpam-4971	92	47	)	)	PUNCT
ejpam-4971	92	48	|α0	|α0	NOUN
ejpam-4971	92	49	<	<	X
ejpam-4971	92	50	0	0	NUM
ejpam-4971	92	51	,	,	PUNCT
ejpam-4971	92	52	β0	β0	NOUN
ejpam-4971	92	53	>	>	X
ejpam-4971	92	54	0	0	NUM
ejpam-4971	92	55	}	}	PUNCT
ejpam-4971	92	56	,	,	PUNCT
ejpam-4971	92	57	r4	r4	NOUN
ejpam-4971	92	58	=	=	SYM
ejpam-4971	92	59	{	{	PUNCT
ejpam-4971	92	60	(	(	PUNCT
ejpam-4971	92	61	α0	α0	ADJ
ejpam-4971	92	62	,	,	PUNCT
ejpam-4971	92	63	β0	β0	NOUN
ejpam-4971	92	64	)	)	PUNCT
ejpam-4971	92	65	|α0	|α0	NOUN
ejpam-4971	92	66	<	<	X
ejpam-4971	92	67	0	0	NUM
ejpam-4971	92	68	,	,	PUNCT
ejpam-4971	92	69	β0	β0	NOUN
ejpam-4971	92	70	<	<	X
ejpam-4971	92	71	0	0	NUM
ejpam-4971	92	72	}	}	PUNCT
ejpam-4971	92	73	,	,	PUNCT
ejpam-4971	92	74	r5	r5	PROPN
ejpam-4971	92	75	=	=	SYM
ejpam-4971	92	76	{	{	PUNCT
ejpam-4971	92	77	(	(	PUNCT
ejpam-4971	92	78	α0	α0	ADJ
ejpam-4971	92	79	,	,	PUNCT
ejpam-4971	92	80	β0	β0	NOUN
ejpam-4971	92	81	)	)	PUNCT
ejpam-4971	92	82	|α0	|α0	PROPN
ejpam-4971	93	1	=	=	SYM
ejpam-4971	93	2	0	0	NUM
ejpam-4971	93	3	,	,	PUNCT
ejpam-4971	93	4	β0	β0	NOUN
ejpam-4971	93	5	>	>	NOUN
ejpam-4971	93	6	0	0	NUM
ejpam-4971	93	7	}	}	PUNCT
ejpam-4971	93	8	∪	∪	X
ejpam-4971	93	9	{	{	PUNCT
ejpam-4971	93	10	(	(	PUNCT
ejpam-4971	93	11	α0	α0	ADJ
ejpam-4971	93	12	,	,	PUNCT
ejpam-4971	93	13	β0	β0	NOUN
ejpam-4971	93	14	)	)	PUNCT
ejpam-4971	93	15	|α0	|α0	PROPN
ejpam-4971	94	1	=	=	SYM
ejpam-4971	94	2	0	0	NUM
ejpam-4971	94	3	,	,	PUNCT
ejpam-4971	94	4	β0	β0	NOUN
ejpam-4971	94	5	<	<	X
ejpam-4971	94	6	0	0	NUM
ejpam-4971	94	7	}	}	PUNCT
ejpam-4971	94	8	.	.	PUNCT
ejpam-4971	95	1	(	(	PUNCT
ejpam-4971	95	2	12	12	NUM
ejpam-4971	95	3	)	)	PUNCT
ejpam-4971	95	4	considering	consider	VERB
ejpam-4971	95	5	the	the	DET
ejpam-4971	95	6	abovementioned	abovementione	VERB
ejpam-4971	95	7	restrictions	restriction	NOUN
ejpam-4971	95	8	on	on	ADP
ejpam-4971	95	9	the	the	DET
ejpam-4971	95	10	parameters	parameter	NOUN
ejpam-4971	95	11	and	and	CCONJ
ejpam-4971	95	12	employing	employ	VERB
ejpam-4971	95	13	the	the	DET
ejpam-4971	95	14	maple	maple	NOUN
ejpam-4971	95	15	software	software	NOUN
ejpam-4971	95	16	to	to	PART
ejpam-4971	95	17	perform	perform	VERB
ejpam-4971	95	18	the	the	DET
ejpam-4971	95	19	symbolic	symbolic	ADJ
ejpam-4971	95	20	calculations	calculation	NOUN
ejpam-4971	95	21	,	,	PUNCT
ejpam-4971	95	22	we	we	PRON
ejpam-4971	95	23	introduce	introduce	VERB
ejpam-4971	95	24	phase	phase	NOUN
ejpam-4971	95	25	portraits	portrait	NOUN
ejpam-4971	95	26	for	for	ADP
ejpam-4971	95	27	system	system	NOUN
ejpam-4971	95	28	(	(	PUNCT
ejpam-4971	95	29	4	4	NUM
ejpam-4971	95	30	)	)	PUNCT
ejpam-4971	95	31	in	in	ADP
ejpam-4971	95	32	the	the	DET
ejpam-4971	95	33	plane	plane	NOUN
ejpam-4971	95	34	(	(	PUNCT
ejpam-4971	95	35	φ	φ	NOUN
ejpam-4971	95	36	,	,	PUNCT
ejpam-4971	95	37	dφdξ	dφdξ	NOUN
ejpam-4971	95	38	)	)	PUNCT
ejpam-4971	95	39	.	.	PUNCT
ejpam-4971	96	1	case	case	NOUN
ejpam-4971	96	2	i	i	PRON
ejpam-4971	96	3	assume	assume	VERB
ejpam-4971	96	4	that	that	SCONJ
ejpam-4971	96	5	(	(	PUNCT
ejpam-4971	96	6	α0	α0	ADJ
ejpam-4971	96	7	,	,	PUNCT
ejpam-4971	96	8	β0	β0	ADJ
ejpam-4971	96	9	)	)	PUNCT
ejpam-4971	96	10	∈	∈	PROPN
ejpam-4971	96	11	r1	r1	NOUN
ejpam-4971	96	12	,	,	PUNCT
ejpam-4971	96	13	and	and	CCONJ
ejpam-4971	96	14	so	so	ADV
ejpam-4971	96	15	α0β0	α0β0	X
ejpam-4971	96	16	>	>	X
ejpam-4971	96	17	0	0	X
ejpam-4971	96	18	.	.	PUNCT
ejpam-4971	97	1	the	the	DET
ejpam-4971	97	2	dynamical	dynamical	ADJ
ejpam-4971	97	3	system	system	NOUN
ejpam-4971	97	4	(	(	PUNCT
ejpam-4971	97	5	4	4	NUM
ejpam-4971	97	6	)	)	PUNCT
ejpam-4971	97	7	has	have	VERB
ejpam-4971	97	8	three	three	NUM
ejpam-4971	97	9	equilibrium	equilibrium	NOUN
ejpam-4971	97	10	points	point	NOUN
ejpam-4971	97	11	ei	ei	NOUN
ejpam-4971	97	12	,	,	PUNCT
ejpam-4971	97	13	i	i	PRON
ejpam-4971	97	14	=	=	NOUN
ejpam-4971	97	15	1	1	NUM
ejpam-4971	97	16	,	,	PUNCT
ejpam-4971	97	17	2	2	NUM
ejpam-4971	97	18	,	,	PUNCT
ejpam-4971	97	19	3	3	NUM
ejpam-4971	97	20	.	.	PUNCT
ejpam-4971	97	21	equilibrium	equilibrium	NOUN
ejpam-4971	97	22	point	point	NOUN
ejpam-4971	97	23	e1	e1	PROPN
ejpam-4971	97	24	is	be	AUX
ejpam-4971	97	25	a	a	DET
ejpam-4971	97	26	center	center	NOUN
ejpam-4971	97	27	point	point	NOUN
ejpam-4971	97	28	because	because	SCONJ
ejpam-4971	97	29	j(e1	j(e1	NOUN
ejpam-4971	97	30	)	)	PUNCT
ejpam-4971	98	1	=	=	PUNCT
ejpam-4971	99	1	α0	α0	VERB
ejpam-4971	99	2	>	>	X
ejpam-4971	99	3	0	0	X
ejpam-4971	99	4	.	.	PUNCT
ejpam-4971	100	1	the	the	DET
ejpam-4971	100	2	other	other	ADJ
ejpam-4971	100	3	two	two	NUM
ejpam-4971	100	4	equilibrium	equilibrium	NOUN
ejpam-4971	100	5	points	point	NOUN
ejpam-4971	100	6	e2,3	e2,3	X
ejpam-4971	100	7	are	be	AUX
ejpam-4971	100	8	saddle	saddle	NOUN
ejpam-4971	100	9	points	point	NOUN
ejpam-4971	100	10	because	because	SCONJ
ejpam-4971	100	11	j(e2,3	j(e2,3	VERB
ejpam-4971	100	12	)	)	PUNCT
ejpam-4971	100	13	=	=	SYM
ejpam-4971	100	14	−2α0	−2α0	X
ejpam-4971	100	15	<	<	X
ejpam-4971	100	16	0	0	NUM
ejpam-4971	100	17	.	.	PUNCT
ejpam-4971	101	1	the	the	DET
ejpam-4971	101	2	phase	phase	NOUN
ejpam-4971	101	3	portrait	portrait	NOUN
ejpam-4971	101	4	for	for	ADP
ejpam-4971	101	5	this	this	DET
ejpam-4971	101	6	case	case	NOUN
ejpam-4971	101	7	is	be	AUX
ejpam-4971	101	8	summarized	summarize	VERB
ejpam-4971	101	9	in	in	ADP
ejpam-4971	101	10	fig	fig	NOUN
ejpam-4971	101	11	.	.	PUNCT
ejpam-4971	102	1	1(a	1(a	NUM
ejpam-4971	102	2	)	)	PUNCT
ejpam-4971	102	3	.	.	PUNCT
ejpam-4971	103	1	case	case	NOUN
ejpam-4971	103	2	ii	ii	PRON
ejpam-4971	103	3	if	if	SCONJ
ejpam-4971	103	4	(	(	PUNCT
ejpam-4971	103	5	α0	α0	ADJ
ejpam-4971	103	6	,	,	PUNCT
ejpam-4971	103	7	β0	β0	ADJ
ejpam-4971	103	8	)	)	PUNCT
ejpam-4971	103	9	∈	∈	PROPN
ejpam-4971	103	10	r2	r2	NOUN
ejpam-4971	103	11	,	,	PUNCT
ejpam-4971	103	12	then	then	ADV
ejpam-4971	103	13	α0β0	α0β0	X
ejpam-4971	103	14	<	<	X
ejpam-4971	103	15	0	0	NUM
ejpam-4971	103	16	.	.	PUNCT
ejpam-4971	104	1	consequently	consequently	ADV
ejpam-4971	104	2	,	,	PUNCT
ejpam-4971	104	3	the	the	DET
ejpam-4971	104	4	dynamical	dynamical	ADJ
ejpam-4971	104	5	system	system	NOUN
ejpam-4971	104	6	(	(	PUNCT
ejpam-4971	104	7	4	4	X
ejpam-4971	104	8	)	)	PUNCT
ejpam-4971	104	9	has	have	VERB
ejpam-4971	104	10	a	a	DET
ejpam-4971	104	11	unique	unique	ADJ
ejpam-4971	104	12	equilibrium	equilibrium	NOUN
ejpam-4971	104	13	point	point	NOUN
ejpam-4971	104	14	e1	e1	PROPN
ejpam-4971	104	15	.	.	PUNCT
ejpam-4971	105	1	because	because	SCONJ
ejpam-4971	105	2	j(e1	j(e1	NOUN
ejpam-4971	105	3	)	)	PUNCT
ejpam-4971	106	1	=	=	PUNCT
ejpam-4971	107	1	α0	α0	VERB
ejpam-4971	107	2	>	>	SYM
ejpam-4971	107	3	0	0	NUM
ejpam-4971	107	4	,	,	PUNCT
ejpam-4971	107	5	e1	e1	NOUN
ejpam-4971	107	6	is	be	AUX
ejpam-4971	107	7	a	a	DET
ejpam-4971	107	8	center	center	ADJ
ejpam-4971	107	9	point	point	NOUN
ejpam-4971	107	10	.	.	PUNCT
ejpam-4971	108	1	the	the	DET
ejpam-4971	108	2	phase	phase	NOUN
ejpam-4971	108	3	portrait	portrait	NOUN
ejpam-4971	108	4	for	for	ADP
ejpam-4971	108	5	the	the	DET
ejpam-4971	108	6	dynamical	dynamical	ADJ
ejpam-4971	108	7	system	system	NOUN
ejpam-4971	108	8	(	(	PUNCT
ejpam-4971	108	9	4	4	NUM
ejpam-4971	108	10	)	)	PUNCT
ejpam-4971	108	11	in	in	ADP
ejpam-4971	108	12	this	this	DET
ejpam-4971	108	13	case	case	NOUN
ejpam-4971	108	14	is	be	AUX
ejpam-4971	108	15	appeared	appear	VERB
ejpam-4971	108	16	in	in	ADP
ejpam-4971	108	17	fig	fig	NOUN
ejpam-4971	108	18	.	.	PUNCT
ejpam-4971	109	1	1(b	1(b	NUM
ejpam-4971	109	2	)	)	PUNCT
ejpam-4971	109	3	.	.	PUNCT
ejpam-4971	110	1	case	case	NOUN
ejpam-4971	110	2	iii	iii	PRON
ejpam-4971	110	3	if	if	SCONJ
ejpam-4971	110	4	(	(	PUNCT
ejpam-4971	110	5	α0	α0	ADJ
ejpam-4971	110	6	,	,	PUNCT
ejpam-4971	110	7	β0	β0	ADJ
ejpam-4971	110	8	)	)	PUNCT
ejpam-4971	110	9	∈	∈	PROPN
ejpam-4971	110	10	r3	r3	PROPN
ejpam-4971	110	11	,	,	PUNCT
ejpam-4971	110	12	we	we	PRON
ejpam-4971	110	13	have	have	VERB
ejpam-4971	110	14	α0β0	α0β0	X
ejpam-4971	110	15	<	<	X
ejpam-4971	110	16	0	0	NUM
ejpam-4971	110	17	.	.	PUNCT
ejpam-4971	111	1	thus	thus	ADV
ejpam-4971	111	2	,	,	PUNCT
ejpam-4971	111	3	the	the	DET
ejpam-4971	111	4	dynamical	dynamical	ADJ
ejpam-4971	111	5	system	system	NOUN
ejpam-4971	111	6	(	(	PUNCT
ejpam-4971	111	7	4	4	X
ejpam-4971	111	8	)	)	PUNCT
ejpam-4971	111	9	has	have	VERB
ejpam-4971	111	10	a	a	DET
ejpam-4971	111	11	unique	unique	ADJ
ejpam-4971	111	12	equilibrium	equilibrium	NOUN
ejpam-4971	111	13	point	point	NOUN
ejpam-4971	111	14	e1	e1	NOUN
ejpam-4971	111	15	,	,	PUNCT
ejpam-4971	111	16	and	and	CCONJ
ejpam-4971	111	17	this	this	PRON
ejpam-4971	111	18	is	be	AUX
ejpam-4971	111	19	a	a	DET
ejpam-4971	111	20	saddle	saddle	NOUN
ejpam-4971	111	21	point	point	NOUN
ejpam-4971	111	22	because	because	SCONJ
ejpam-4971	111	23	j(e1	j(e1	NOUN
ejpam-4971	111	24	)	)	PUNCT
ejpam-4971	112	1	=	=	PUNCT
ejpam-4971	113	1	α0	α0	ADJ
ejpam-4971	113	2	<	<	X
ejpam-4971	113	3	0	0	NUM
ejpam-4971	113	4	.	.	PUNCT
ejpam-4971	114	1	the	the	DET
ejpam-4971	114	2	phase	phase	NOUN
ejpam-4971	114	3	portrait	portrait	NOUN
ejpam-4971	114	4	for	for	ADP
ejpam-4971	114	5	the	the	DET
ejpam-4971	114	6	dynamical	dynamical	ADJ
ejpam-4971	114	7	system	system	NOUN
ejpam-4971	114	8	(	(	PUNCT
ejpam-4971	114	9	4	4	NUM
ejpam-4971	114	10	)	)	PUNCT
ejpam-4971	114	11	in	in	ADP
ejpam-4971	114	12	this	this	DET
ejpam-4971	114	13	case	case	NOUN
ejpam-4971	114	14	is	be	AUX
ejpam-4971	114	15	presented	present	VERB
ejpam-4971	114	16	in	in	ADP
ejpam-4971	114	17	fig	fig	NOUN
ejpam-4971	114	18	.	.	PUNCT
ejpam-4971	115	1	1(c	1(c	NUM
ejpam-4971	115	2	)	)	PUNCT
ejpam-4971	115	3	.	.	PUNCT
ejpam-4971	116	1	case	case	NOUN
ejpam-4971	116	2	iv	iv	X
ejpam-4971	116	3	for	for	ADP
ejpam-4971	116	4	(	(	PUNCT
ejpam-4971	116	5	α0	α0	ADJ
ejpam-4971	116	6	,	,	PUNCT
ejpam-4971	116	7	β0	β0	ADJ
ejpam-4971	116	8	)	)	PUNCT
ejpam-4971	116	9	∈	∈	PROPN
ejpam-4971	116	10	r4	r4	NOUN
ejpam-4971	116	11	,	,	PUNCT
ejpam-4971	116	12	we	we	PRON
ejpam-4971	116	13	have	have	VERB
ejpam-4971	116	14	α0β0	α0β0	X
ejpam-4971	116	15	>	>	X
ejpam-4971	116	16	0	0	NUM
ejpam-4971	116	17	.	.	PUNCT
ejpam-4971	117	1	thus	thus	ADV
ejpam-4971	117	2	,	,	PUNCT
ejpam-4971	117	3	the	the	DET
ejpam-4971	117	4	dynamical	dynamical	ADJ
ejpam-4971	117	5	system	system	NOUN
ejpam-4971	117	6	(	(	PUNCT
ejpam-4971	117	7	4	4	NUM
ejpam-4971	117	8	)	)	PUNCT
ejpam-4971	117	9	has	have	VERB
ejpam-4971	117	10	three	three	NUM
ejpam-4971	117	11	equilibrium	equilibrium	NOUN
ejpam-4971	117	12	points	point	NOUN
ejpam-4971	117	13	ei	ei	NOUN
ejpam-4971	117	14	,	,	PUNCT
ejpam-4971	117	15	i	i	PRON
ejpam-4971	117	16	=	=	NOUN
ejpam-4971	117	17	1	1	NUM
ejpam-4971	117	18	,	,	PUNCT
ejpam-4971	117	19	2	2	NUM
ejpam-4971	117	20	,	,	PUNCT
ejpam-4971	117	21	3	3	NUM
ejpam-4971	117	22	.	.	X
ejpam-4971	118	1	e1	e1	NOUN
ejpam-4971	118	2	is	be	AUX
ejpam-4971	118	3	a	a	DET
ejpam-4971	118	4	saddle	saddle	NOUN
ejpam-4971	118	5	point	point	NOUN
ejpam-4971	118	6	and	and	CCONJ
ejpam-4971	118	7	e2,3	e2,3	NOUN
ejpam-4971	118	8	are	be	AUX
ejpam-4971	118	9	center	center	NOUN
ejpam-4971	118	10	points	point	NOUN
ejpam-4971	118	11	.	.	PUNCT
ejpam-4971	119	1	the	the	DET
ejpam-4971	119	2	phase	phase	NOUN
ejpam-4971	119	3	portrait	portrait	NOUN
ejpam-4971	119	4	for	for	ADP
ejpam-4971	119	5	this	this	DET
ejpam-4971	119	6	case	case	NOUN
ejpam-4971	119	7	is	be	AUX
ejpam-4971	119	8	appeared	appear	VERB
ejpam-4971	119	9	in	in	ADP
ejpam-4971	119	10	fig	fig	NOUN
ejpam-4971	119	11	.	.	PUNCT
ejpam-4971	120	1	1(d	1(d	NUM
ejpam-4971	120	2	)	)	PUNCT
ejpam-4971	120	3	.	.	PUNCT
ejpam-4971	121	1	case	case	NOUN
ejpam-4971	121	2	v	v	ADP
ejpam-4971	121	3	finally	finally	ADV
ejpam-4971	121	4	,	,	PUNCT
ejpam-4971	121	5	for	for	ADP
ejpam-4971	121	6	(	(	PUNCT
ejpam-4971	121	7	α0	α0	ADJ
ejpam-4971	121	8	,	,	PUNCT
ejpam-4971	121	9	β0	β0	ADJ
ejpam-4971	121	10	)	)	PUNCT
ejpam-4971	121	11	∈	∈	PROPN
ejpam-4971	121	12	r5	r5	PROPN
ejpam-4971	121	13	,	,	PUNCT
ejpam-4971	121	14	the	the	DET
ejpam-4971	121	15	dynamical	dynamical	ADJ
ejpam-4971	121	16	system	system	NOUN
ejpam-4971	121	17	(	(	PUNCT
ejpam-4971	121	18	4	4	X
ejpam-4971	121	19	)	)	PUNCT
ejpam-4971	121	20	has	have	VERB
ejpam-4971	121	21	a	a	DET
ejpam-4971	121	22	unique	unique	ADJ
ejpam-4971	121	23	equilibrium	equilibrium	NOUN
ejpam-4971	121	24	point	point	NOUN
ejpam-4971	121	25	e1	e1	NOUN
ejpam-4971	121	26	.	.	PUNCT
ejpam-4971	122	1	this	this	PRON
ejpam-4971	122	2	is	be	AUX
ejpam-4971	122	3	a	a	DET
ejpam-4971	122	4	saddle	saddle	NOUN
ejpam-4971	122	5	point	point	NOUN
ejpam-4971	122	6	when	when	SCONJ
ejpam-4971	122	7	β0	β0	PROPN
ejpam-4971	122	8	>	>	X
ejpam-4971	122	9	0	0	NUM
ejpam-4971	122	10	,	,	PUNCT
ejpam-4971	122	11	as	as	SCONJ
ejpam-4971	122	12	appeared	appear	VERB
ejpam-4971	122	13	in	in	ADP
ejpam-4971	122	14	fig	fig	NOUN
ejpam-4971	122	15	.	.	PUNCT
ejpam-4971	123	1	1(e	1(e	NUM
ejpam-4971	123	2	)	)	PUNCT
ejpam-4971	123	3	,	,	PUNCT
ejpam-4971	123	4	and	and	CCONJ
ejpam-4971	123	5	a	a	DET
ejpam-4971	123	6	center	center	NOUN
ejpam-4971	123	7	point	point	NOUN
ejpam-4971	123	8	when	when	SCONJ
ejpam-4971	123	9	β0	β0	ADV
ejpam-4971	123	10	<	<	X
ejpam-4971	123	11	0	0	NUM
ejpam-4971	123	12	,	,	PUNCT
ejpam-4971	123	13	as	as	SCONJ
ejpam-4971	123	14	appeared	appear	VERB
ejpam-4971	123	15	in	in	ADP
ejpam-4971	123	16	fig	fig	NOUN
ejpam-4971	123	17	.	.	PUNCT
ejpam-4971	124	1	1(f	1(f	NUM
ejpam-4971	124	2	)	)	PUNCT
ejpam-4971	124	3	.	.	PUNCT
ejpam-4971	125	1	3.1	3.1	NUM
ejpam-4971	125	2	.	.	NOUN
ejpam-4971	125	3	phase	phase	NOUN
ejpam-4971	125	4	portrait	portrait	NOUN
ejpam-4971	125	5	description	description	NOUN
ejpam-4971	125	6	the	the	DET
ejpam-4971	125	7	phase	phase	NOUN
ejpam-4971	125	8	orbits	orbit	NOUN
ejpam-4971	125	9	are	be	AUX
ejpam-4971	125	10	energy	energy	NOUN
ejpam-4971	125	11	level	level	NOUN
ejpam-4971	125	12	curves	curve	NOUN
ejpam-4971	125	13	that	that	PRON
ejpam-4971	125	14	take	take	VERB
ejpam-4971	125	15	the	the	DET
ejpam-4971	125	16	form	form	NOUN
ejpam-4971	125	17	ch	ch	NOUN
ejpam-4971	125	18	=	=	SYM
ejpam-4971	125	19	{	{	PUNCT
ejpam-4971	125	20	(	(	PUNCT
ejpam-4971	125	21	ϕ	ϕ	NOUN
ejpam-4971	125	22	,	,	PUNCT
ejpam-4971	125	23	y	y	NOUN
ejpam-4971	125	24	)	)	PUNCT
ejpam-4971	125	25	∈	∈	PROPN
ejpam-4971	125	26	r2	r2	NOUN
ejpam-4971	125	27	:	:	PUNCT
ejpam-4971	125	28	h	h	NOUN
ejpam-4971	126	1	=	=	NOUN
ejpam-4971	126	2	h	h	NOUN
ejpam-4971	126	3	}	}	PUNCT
ejpam-4971	126	4	.	.	PUNCT
ejpam-4971	127	1	(	(	PUNCT
ejpam-4971	127	2	13	13	NUM
ejpam-4971	127	3	)	)	PUNCT
ejpam-4971	127	4	for	for	ADP
ejpam-4971	127	5	(	(	PUNCT
ejpam-4971	127	6	α0	α0	ADJ
ejpam-4971	127	7	,	,	PUNCT
ejpam-4971	127	8	β0	β0	ADJ
ejpam-4971	127	9	)	)	PUNCT
ejpam-4971	127	10	∈	∈	PROPN
ejpam-4971	127	11	r1	r1	PROPN
ejpam-4971	127	12	,	,	PUNCT
ejpam-4971	127	13	fig	fig	NOUN
ejpam-4971	127	14	.	.	PUNCT
ejpam-4971	128	1	1(a	1(a	NUM
ejpam-4971	128	2	)	)	PUNCT
ejpam-4971	128	3	shows	show	VERB
ejpam-4971	128	4	that	that	SCONJ
ejpam-4971	128	5	the	the	DET
ejpam-4971	128	6	hamiltonian	hamiltonian	ADJ
ejpam-4971	128	7	system	system	NOUN
ejpam-4971	128	8	(	(	PUNCT
ejpam-4971	128	9	4	4	X
ejpam-4971	128	10	)	)	PUNCT
ejpam-4971	128	11	has	have	VERB
ejpam-4971	128	12	boundless	boundless	ADJ
ejpam-4971	128	13	families	family	NOUN
ejpam-4971	128	14	of	of	ADP
ejpam-4971	128	15	orbits	orbit	NOUN
ejpam-4971	128	16	ch	ch	PROPN
ejpam-4971	128	17	,	,	PUNCT
ejpam-4971	128	18	appeared	appear	VERB
ejpam-4971	128	19	in	in	ADP
ejpam-4971	128	20	green	green	ADJ
ejpam-4971	128	21	,	,	PUNCT
ejpam-4971	128	22	brown	brown	ADJ
ejpam-4971	128	23	,	,	PUNCT
ejpam-4971	128	24	and	and	CCONJ
ejpam-4971	128	25	black	black	ADJ
ejpam-4971	128	26	for	for	ADP
ejpam-4971	128	27	h	h	NOUN
ejpam-4971	128	28	∈]h2,∞[∪	∈]h2,∞[∪	ADJ
ejpam-4971	128	29	]	]	PUNCT
ejpam-4971	128	30	−	−	PROPN
ejpam-4971	128	31	∞	∞	PROPN
ejpam-4971	128	32	,	,	PUNCT
ejpam-4971	128	33	0[∪{0	0[∪{0	PROPN
ejpam-4971	128	34	}	}	PUNCT
ejpam-4971	128	35	,	,	PUNCT
ejpam-4971	128	36	respectively	respectively	ADV
ejpam-4971	128	37	.	.	PUNCT
ejpam-4971	129	1	of	of	ADP
ejpam-4971	129	2	the	the	DET
ejpam-4971	129	3	three	three	NUM
ejpam-4971	129	4	families	family	NOUN
ejpam-4971	129	5	of	of	ADP
ejpam-4971	129	6	orbits	orbit	NOUN
ejpam-4971	129	7	that	that	PRON
ejpam-4971	129	8	appeared	appear	VERB
ejpam-4971	129	9	in	in	ADP
ejpam-4971	129	10	blue	blue	ADJ
ejpam-4971	129	11	,	,	PUNCT
ejpam-4971	129	12	two	two	NUM
ejpam-4971	129	13	of	of	ADP
ejpam-4971	129	14	them	they	PRON
ejpam-4971	129	15	are	be	AUX
ejpam-4971	129	16	boundless	boundless	ADJ
ejpam-4971	129	17	and	and	CCONJ
ejpam-4971	129	18	lie	lie	VERB
ejpam-4971	129	19	outside	outside	ADP
ejpam-4971	129	20	the	the	DET
ejpam-4971	129	21	heteroclinic	heteroclinic	ADJ
ejpam-4971	129	22	orbit	orbit	NOUN
ejpam-4971	129	23	{	{	PUNCT
ejpam-4971	129	24	ch	ch	NOUN
ejpam-4971	130	1	:	:	PUNCT
ejpam-4971	130	2	h	h	NOUN
ejpam-4971	130	3	=	=	SYM
ejpam-4971	130	4	h2	h2	PROPN
ejpam-4971	130	5	}	}	PUNCT
ejpam-4971	130	6	appeared	appear	VERB
ejpam-4971	130	7	in	in	ADP
ejpam-4971	130	8	black	black	ADJ
ejpam-4971	130	9	,	,	PUNCT
ejpam-4971	130	10	while	while	SCONJ
ejpam-4971	130	11	m.arab	m.arab	ADJ
ejpam-4971	130	12	/	/	SYM
ejpam-4971	130	13	eur	eur	NOUN
ejpam-4971	130	14	.	.	PUNCT
ejpam-4971	131	1	j.	j.	PROPN
ejpam-4971	131	2	pure	pure	PROPN
ejpam-4971	131	3	appl	appl	PROPN
ejpam-4971	131	4	.	.	PROPN
ejpam-4971	131	5	math	math	PROPN
ejpam-4971	131	6	,	,	PUNCT
ejpam-4971	131	7	16	16	NUM
ejpam-4971	131	8	(	(	PUNCT
ejpam-4971	131	9	4	4	NUM
ejpam-4971	131	10	)	)	PUNCT
ejpam-4971	131	11	(	(	PUNCT
ejpam-4971	131	12	2023	2023	NUM
ejpam-4971	131	13	)	)	PUNCT
ejpam-4971	131	14	,	,	PUNCT
ejpam-4971	131	15	2643	2643	NUM
ejpam-4971	131	16	-	-	SYM
ejpam-4971	131	17	2661	2661	NUM
ejpam-4971	131	18	2648	2648	NUM
ejpam-4971	131	19	(	(	PUNCT
ejpam-4971	131	20	(	(	PUNCT
ejpam-4971	131	21	)	)	PUNCT
ejpam-4971	131	22	(	(	PUNCT
ejpam-4971	131	23	a	a	X
ejpam-4971	131	24	)	)	PUNCT
ejpam-4971	131	25	(	(	PUNCT
ejpam-4971	131	26	b	b	X
ejpam-4971	131	27	)	)	PUNCT
ejpam-4971	131	28	(	(	PUNCT
ejpam-4971	131	29	c	c	X
ejpam-4971	131	30	)	)	PUNCT
ejpam-4971	131	31	(	(	PUNCT
ejpam-4971	131	32	d	d	X
ejpam-4971	131	33	)	)	PUNCT
ejpam-4971	131	34	(	(	PUNCT
ejpam-4971	131	35	e	e	NOUN
ejpam-4971	131	36	)	)	PUNCT
ejpam-4971	131	37	(	(	PUNCT
ejpam-4971	131	38	f	f	X
ejpam-4971	131	39	)	)	PUNCT
ejpam-4971	131	40	figure	figure	NOUN
ejpam-4971	131	41	1	1	NUM
ejpam-4971	131	42	:	:	PUNCT
ejpam-4971	131	43	phase	phase	NOUN
ejpam-4971	131	44	portraits	portrait	NOUN
ejpam-4971	131	45	of	of	ADP
ejpam-4971	131	46	the	the	DET
ejpam-4971	131	47	one	one	NUM
ejpam-4971	131	48	-	-	PUNCT
ejpam-4971	131	49	dimensional	dimensional	ADJ
ejpam-4971	131	50	hamiltonian	hamiltonian	ADJ
ejpam-4971	131	51	system	system	NOUN
ejpam-4971	131	52	(	(	PUNCT
ejpam-4971	131	53	4	4	NUM
ejpam-4971	131	54	)	)	PUNCT
ejpam-4971	131	55	for	for	ADP
ejpam-4971	131	56	different	different	ADJ
ejpam-4971	131	57	values	value	NOUN
ejpam-4971	131	58	of	of	ADP
ejpam-4971	131	59	α0	α0	ADJ
ejpam-4971	131	60	,	,	PUNCT
ejpam-4971	131	61	β0	β0	NOUN
ejpam-4971	131	62	in	in	ADP
ejpam-4971	131	63	the	the	DET
ejpam-4971	131	64	plane	plane	NOUN
ejpam-4971	131	65	(	(	PUNCT
ejpam-4971	131	66	φ	φ	PROPN
ejpam-4971	131	67	,	,	PUNCT
ejpam-4971	131	68	dφ	dφ	X
ejpam-4971	131	69	dξ	dξ	PROPN
ejpam-4971	131	70	)	)	PUNCT
ejpam-4971	131	71	.	.	PUNCT
ejpam-4971	132	1	the	the	DET
ejpam-4971	132	2	solid	solid	ADJ
ejpam-4971	132	3	black	black	ADJ
ejpam-4971	132	4	boxes	box	NOUN
ejpam-4971	132	5	denote	denote	VERB
ejpam-4971	132	6	the	the	DET
ejpam-4971	132	7	equilibrium	equilibrium	NOUN
ejpam-4971	132	8	points	point	NOUN
ejpam-4971	132	9	.	.	PUNCT
ejpam-4971	133	1	(	(	PUNCT
ejpam-4971	133	2	a	a	X
ejpam-4971	133	3	)	)	PUNCT
ejpam-4971	133	4	α0	α0	ADJ
ejpam-4971	133	5	>	>	X
ejpam-4971	133	6	0	0	NUM
ejpam-4971	133	7	,	,	PUNCT
ejpam-4971	133	8	β0	β0	NOUN
ejpam-4971	133	9	>	>	X
ejpam-4971	133	10	0	0	NUM
ejpam-4971	133	11	,	,	PUNCT
ejpam-4971	133	12	(	(	PUNCT
ejpam-4971	133	13	b	b	X
ejpam-4971	133	14	)	)	PUNCT
ejpam-4971	133	15	α0	α0	ADJ
ejpam-4971	133	16	>	>	X
ejpam-4971	133	17	0	0	NUM
ejpam-4971	133	18	,	,	PUNCT
ejpam-4971	133	19	β0	β0	NOUN
ejpam-4971	133	20	<	<	X
ejpam-4971	133	21	0	0	NUM
ejpam-4971	133	22	,	,	PUNCT
ejpam-4971	133	23	(	(	PUNCT
ejpam-4971	133	24	c	c	X
ejpam-4971	133	25	)	)	PUNCT
ejpam-4971	134	1	α0	α0	ADJ
ejpam-4971	134	2	<	<	X
ejpam-4971	134	3	0	0	NUM
ejpam-4971	134	4	,	,	PUNCT
ejpam-4971	134	5	β0	β0	NOUN
ejpam-4971	134	6	>	>	X
ejpam-4971	134	7	0	0	NUM
ejpam-4971	134	8	,	,	PUNCT
ejpam-4971	134	9	(	(	PUNCT
ejpam-4971	134	10	d	d	X
ejpam-4971	134	11	)	)	PUNCT
ejpam-4971	134	12	α0	α0	ADJ
ejpam-4971	134	13	<	<	X
ejpam-4971	134	14	0	0	NUM
ejpam-4971	134	15	,	,	PUNCT
ejpam-4971	134	16	β0	β0	NOUN
ejpam-4971	134	17	<	<	X
ejpam-4971	134	18	0	0	NUM
ejpam-4971	134	19	,	,	PUNCT
ejpam-4971	134	20	(	(	PUNCT
ejpam-4971	134	21	e	e	NOUN
ejpam-4971	134	22	)	)	PUNCT
ejpam-4971	134	23	α0	α0	ADJ
ejpam-4971	134	24	=	=	SYM
ejpam-4971	134	25	0	0	NUM
ejpam-4971	134	26	,	,	PUNCT
ejpam-4971	134	27	β0	β0	NOUN
ejpam-4971	134	28	>	>	X
ejpam-4971	134	29	0	0	NUM
ejpam-4971	134	30	,	,	PUNCT
ejpam-4971	134	31	and	and	CCONJ
ejpam-4971	134	32	(	(	PUNCT
ejpam-4971	134	33	f	f	X
ejpam-4971	134	34	)	)	PUNCT
ejpam-4971	134	35	α0	α0	ADJ
ejpam-4971	134	36	=	=	SYM
ejpam-4971	134	37	0	0	NUM
ejpam-4971	134	38	,	,	PUNCT
ejpam-4971	134	39	β0	β0	NOUN
ejpam-4971	134	40	<	<	X
ejpam-4971	134	41	0	0	NUM
ejpam-4971	134	42	.	.	PUNCT
ejpam-4971	135	1	the	the	DET
ejpam-4971	135	2	remaining	remain	VERB
ejpam-4971	135	3	one	one	NUM
ejpam-4971	135	4	is	be	AUX
ejpam-4971	135	5	a	a	DET
ejpam-4971	135	6	bounded	bounded	ADJ
ejpam-4971	135	7	periodic	periodic	ADJ
ejpam-4971	135	8	orbit	orbit	NOUN
ejpam-4971	135	9	that	that	PRON
ejpam-4971	135	10	lies	lie	VERB
ejpam-4971	135	11	inside	inside	ADP
ejpam-4971	135	12	the	the	DET
ejpam-4971	135	13	heteroclinic	heteroclinic	ADJ
ejpam-4971	135	14	orbit	orbit	NOUN
ejpam-4971	135	15	.	.	PUNCT
ejpam-4971	136	1	for	for	ADP
ejpam-4971	136	2	(	(	PUNCT
ejpam-4971	136	3	α0	α0	ADJ
ejpam-4971	136	4	,	,	PUNCT
ejpam-4971	136	5	β0	β0	ADJ
ejpam-4971	136	6	)	)	PUNCT
ejpam-4971	136	7	∈	∈	PROPN
ejpam-4971	136	8	r2	r2	NOUN
ejpam-4971	136	9	∪	∪	NOUN
ejpam-4971	136	10	{	{	PUNCT
ejpam-4971	136	11	(	(	PUNCT
ejpam-4971	136	12	α0	α0	ADJ
ejpam-4971	136	13	,	,	PUNCT
ejpam-4971	136	14	β0	β0	NOUN
ejpam-4971	136	15	)	)	PUNCT
ejpam-4971	136	16	|	|	ADV
ejpam-4971	136	17	α0	α0	ADJ
ejpam-4971	136	18	=	=	SYM
ejpam-4971	136	19	0	0	NUM
ejpam-4971	136	20	,	,	PUNCT
ejpam-4971	136	21	β0	β0	NOUN
ejpam-4971	136	22	<	<	X
ejpam-4971	136	23	0	0	NUM
ejpam-4971	136	24	}	}	PUNCT
ejpam-4971	136	25	,	,	PUNCT
ejpam-4971	136	26	the	the	DET
ejpam-4971	136	27	hamilton	hamilton	PROPN
ejpam-4971	136	28	system	system	NOUN
ejpam-4971	136	29	(	(	PUNCT
ejpam-4971	136	30	4	4	X
ejpam-4971	136	31	)	)	PUNCT
ejpam-4971	136	32	has	have	VERB
ejpam-4971	136	33	one	one	NUM
ejpam-4971	136	34	family	family	NOUN
ejpam-4971	136	35	of	of	ADP
ejpam-4971	136	36	bounded	bounded	ADJ
ejpam-4971	136	37	periodic	periodic	ADJ
ejpam-4971	136	38	orbits	orbit	NOUN
ejpam-4971	136	39	for	for	ADP
ejpam-4971	136	40	h	h	PROPN
ejpam-4971	136	41	>	>	X
ejpam-4971	136	42	0	0	NUM
ejpam-4971	136	43	,	,	PUNCT
ejpam-4971	136	44	as	as	SCONJ
ejpam-4971	136	45	appeared	appear	VERB
ejpam-4971	136	46	in	in	ADP
ejpam-4971	136	47	figs	fig	NOUN
ejpam-4971	136	48	.	.	PUNCT
ejpam-4971	137	1	1(b	1(b	NUM
ejpam-4971	137	2	)	)	PUNCT
ejpam-4971	137	3	and	and	CCONJ
ejpam-4971	137	4	1(f	1(f	NUM
ejpam-4971	137	5	)	)	PUNCT
ejpam-4971	137	6	.	.	PUNCT
ejpam-4971	138	1	if	if	SCONJ
ejpam-4971	138	2	(	(	PUNCT
ejpam-4971	138	3	α0	α0	ADJ
ejpam-4971	138	4	,	,	PUNCT
ejpam-4971	138	5	β0	β0	ADJ
ejpam-4971	138	6	)	)	PUNCT
ejpam-4971	138	7	∈	∈	PROPN
ejpam-4971	138	8	r3	r3	PROPN
ejpam-4971	138	9	∪	∪	X
ejpam-4971	138	10	{	{	PUNCT
ejpam-4971	138	11	(	(	PUNCT
ejpam-4971	138	12	α0	α0	ADJ
ejpam-4971	138	13	,	,	PUNCT
ejpam-4971	138	14	β0	β0	NOUN
ejpam-4971	138	15	)	)	PUNCT
ejpam-4971	138	16	|	|	ADV
ejpam-4971	138	17	α0	α0	ADJ
ejpam-4971	138	18	=	=	SYM
ejpam-4971	138	19	0	0	NUM
ejpam-4971	138	20	,	,	PUNCT
ejpam-4971	138	21	β0	β0	NOUN
ejpam-4971	138	22	>	>	X
ejpam-4971	138	23	0	0	NUM
ejpam-4971	138	24	}	}	PUNCT
ejpam-4971	138	25	,	,	PUNCT
ejpam-4971	138	26	then	then	ADV
ejpam-4971	138	27	all	all	DET
ejpam-4971	138	28	phase	phase	NOUN
ejpam-4971	138	29	orbits	orbit	NOUN
ejpam-4971	138	30	are	be	AUX
ejpam-4971	138	31	boundless	boundless	ADJ
ejpam-4971	138	32	for	for	ADP
ejpam-4971	138	33	all	all	DET
ejpam-4971	138	34	amounts	amount	NOUN
ejpam-4971	138	35	of	of	ADP
ejpam-4971	138	36	the	the	DET
ejpam-4971	138	37	parameter	parameter	NOUN
ejpam-4971	138	38	h	h	NOUN
ejpam-4971	138	39	,	,	PUNCT
ejpam-4971	138	40	as	as	SCONJ
ejpam-4971	138	41	appeared	appear	VERB
ejpam-4971	138	42	in	in	ADP
ejpam-4971	138	43	figs	fig	NOUN
ejpam-4971	138	44	.	.	PUNCT
ejpam-4971	139	1	1(c	1(c	NUM
ejpam-4971	139	2	)	)	PUNCT
ejpam-4971	139	3	and	and	CCONJ
ejpam-4971	139	4	1(e	1(e	NUM
ejpam-4971	139	5	)	)	PUNCT
ejpam-4971	139	6	.	.	PUNCT
ejpam-4971	140	1	if	if	SCONJ
ejpam-4971	140	2	(	(	PUNCT
ejpam-4971	140	3	α0	α0	ADJ
ejpam-4971	140	4	,	,	PUNCT
ejpam-4971	140	5	β0	β0	ADJ
ejpam-4971	140	6	)	)	PUNCT
ejpam-4971	140	7	∈	∈	PROPN
ejpam-4971	140	8	r4	r4	NOUN
ejpam-4971	140	9	,	,	PUNCT
ejpam-4971	140	10	then	then	ADV
ejpam-4971	140	11	all	all	DET
ejpam-4971	140	12	phase	phase	NOUN
ejpam-4971	140	13	orbits	orbit	NOUN
ejpam-4971	140	14	of	of	ADP
ejpam-4971	140	15	the	the	DET
ejpam-4971	140	16	hamiltonian	hamiltonian	ADJ
ejpam-4971	140	17	system	system	NOUN
ejpam-4971	140	18	(	(	PUNCT
ejpam-4971	140	19	4	4	X
ejpam-4971	140	20	)	)	PUNCT
ejpam-4971	140	21	are	be	AUX
ejpam-4971	140	22	bounded	bound	VERB
ejpam-4971	140	23	.	.	PUNCT
ejpam-4971	141	1	for	for	ADP
ejpam-4971	141	2	h	h	PROPN
ejpam-4971	141	3	>	>	X
ejpam-4971	141	4	0	0	PROPN
ejpam-4971	141	5	,	,	PUNCT
ejpam-4971	141	6	there	there	PRON
ejpam-4971	141	7	is	be	VERB
ejpam-4971	141	8	a	a	DET
ejpam-4971	141	9	family	family	NOUN
ejpam-4971	141	10	of	of	ADP
ejpam-4971	141	11	periodic	periodic	ADJ
ejpam-4971	141	12	orbits	orbit	NOUN
ejpam-4971	141	13	(	(	PUNCT
ejpam-4971	141	14	appeared	appear	VERB
ejpam-4971	141	15	in	in	ADP
ejpam-4971	141	16	blue	blue	ADJ
ejpam-4971	141	17	)	)	PUNCT
ejpam-4971	141	18	that	that	PRON
ejpam-4971	141	19	lie	lie	VERB
ejpam-4971	141	20	outside	outside	ADP
ejpam-4971	141	21	the	the	DET
ejpam-4971	141	22	homoclinic	homoclinic	ADJ
ejpam-4971	141	23	orbit	orbit	NOUN
ejpam-4971	141	24	ch	ch	NOUN
ejpam-4971	141	25	:	:	PUNCT
ejpam-4971	141	26	h	h	NOUN
ejpam-4971	141	27	=	=	SYM
ejpam-4971	141	28	0	0	PUNCT
ejpam-4971	141	29	(	(	PUNCT
ejpam-4971	141	30	appeared	appear	VERB
ejpam-4971	141	31	in	in	ADP
ejpam-4971	141	32	black	black	NOUN
ejpam-4971	141	33	)	)	PUNCT
ejpam-4971	141	34	,	,	PUNCT
ejpam-4971	141	35	while	while	SCONJ
ejpam-4971	141	36	for	for	ADP
ejpam-4971	141	37	h	h	PROPN
ejpam-4971	141	38	∈]h2	∈]h2	PROPN
ejpam-4971	141	39	,	,	PUNCT
ejpam-4971	141	40	0	0	PUNCT
ejpam-4971	142	1	[	[	X
ejpam-4971	142	2	,	,	PUNCT
ejpam-4971	142	3	there	there	PRON
ejpam-4971	142	4	are	be	VERB
ejpam-4971	142	5	two	two	NUM
ejpam-4971	142	6	families	family	NOUN
ejpam-4971	142	7	of	of	ADP
ejpam-4971	142	8	periodic	periodic	ADJ
ejpam-4971	142	9	orbits	orbit	NOUN
ejpam-4971	142	10	(	(	PUNCT
ejpam-4971	142	11	appeared	appear	VERB
ejpam-4971	142	12	in	in	ADP
ejpam-4971	142	13	green	green	ADJ
ejpam-4971	142	14	)	)	PUNCT
ejpam-4971	142	15	that	that	PRON
ejpam-4971	142	16	lie	lie	VERB
ejpam-4971	142	17	inside	inside	ADP
ejpam-4971	142	18	the	the	DET
ejpam-4971	142	19	homoclinic	homoclinic	ADJ
ejpam-4971	142	20	orbit	orbit	NOUN
ejpam-4971	142	21	.	.	PUNCT
ejpam-4971	143	1	black	black	ADJ
ejpam-4971	143	2	lemma	lemma	PROPN
ejpam-4971	143	3	1	1	NUM
ejpam-4971	143	4	.	.	PUNCT
ejpam-4971	144	1	(	(	PUNCT
ejpam-4971	144	2	see	see	VERB
ejpam-4971	144	3	,	,	PUNCT
ejpam-4971	144	4	e.g.	e.g.	ADV
ejpam-4971	144	5	,	,	PUNCT
ejpam-4971	144	6	[	[	X
ejpam-4971	144	7	8	8	NUM
ejpam-4971	144	8	,	,	PUNCT
ejpam-4971	144	9	9	9	NUM
ejpam-4971	144	10	,	,	PUNCT
ejpam-4971	144	11	41	41	NUM
ejpam-4971	144	12	]	]	PUNCT
ejpam-4971	144	13	)	)	PUNCT
ejpam-4971	144	14	.	.	PUNCT
ejpam-4971	145	1	let	let	VERB
ejpam-4971	145	2	system	system	NOUN
ejpam-4971	145	3	(	(	PUNCT
ejpam-4971	145	4	4	4	NUM
ejpam-4971	145	5	)	)	PUNCT
ejpam-4971	145	6	has	have	VERB
ejpam-4971	145	7	a	a	DET
ejpam-4971	145	8	continuous	continuous	ADJ
ejpam-4971	145	9	solution	solution	NOUN
ejpam-4971	145	10	u	u	NOUN
ejpam-4971	145	11	=	=	PUNCT
ejpam-4971	145	12	φ(x	φ(x	PROPN
ejpam-4971	145	13	−	−	PROPN
ejpam-4971	145	14	ωt	ωt	PROPN
ejpam-4971	145	15	)	)	PUNCT
ejpam-4971	145	16	=	=	SYM
ejpam-4971	145	17	u(ξ	u(ξ	NOUN
ejpam-4971	145	18	)	)	PUNCT
ejpam-4971	145	19	for	for	ADP
ejpam-4971	145	20	ξ	ξ	PROPN
ejpam-4971	145	21	∈]−∞,∞	∈]−∞,∞	PROPN
ejpam-4971	145	22	[	[	PUNCT
ejpam-4971	145	23	and	and	CCONJ
ejpam-4971	145	24	assume	assume	VERB
ejpam-4971	145	25	limξ→∞	limξ→∞	ADJ
ejpam-4971	145	26	u(ξ	u(ξ	NOUN
ejpam-4971	145	27	)	)	PUNCT
ejpam-4971	145	28	=	=	SYM
ejpam-4971	145	29	κ1	κ1	NOUN
ejpam-4971	145	30	,	,	PUNCT
ejpam-4971	145	31	and	and	CCONJ
ejpam-4971	145	32	limξ→−∞	limξ→−∞	NOUN
ejpam-4971	145	33	u(ξ	u(ξ	NOUN
ejpam-4971	145	34	)	)	PUNCT
ejpam-4971	145	35	=	=	SYM
ejpam-4971	145	36	κ2	κ2	NOUN
ejpam-4971	145	37	m.arab	m.arab	VERB
ejpam-4971	145	38	/	/	SYM
ejpam-4971	145	39	eur	eur	NOUN
ejpam-4971	145	40	.	.	PUNCT
ejpam-4971	146	1	j.	j.	PROPN
ejpam-4971	146	2	pure	pure	PROPN
ejpam-4971	146	3	appl	appl	PROPN
ejpam-4971	146	4	.	.	PROPN
ejpam-4971	146	5	math	math	PROPN
ejpam-4971	146	6	,	,	PUNCT
ejpam-4971	146	7	16	16	NUM
ejpam-4971	146	8	(	(	PUNCT
ejpam-4971	146	9	4	4	NUM
ejpam-4971	146	10	)	)	PUNCT
ejpam-4971	146	11	(	(	PUNCT
ejpam-4971	146	12	2023	2023	NUM
ejpam-4971	146	13	)	)	PUNCT
ejpam-4971	146	14	,	,	PUNCT
ejpam-4971	146	15	2643	2643	NUM
ejpam-4971	146	16	-	-	SYM
ejpam-4971	146	17	2661	2661	NUM
ejpam-4971	146	18	2649	2649	NUM
ejpam-4971	146	19	(	(	PUNCT
ejpam-4971	146	20	i	i	NOUN
ejpam-4971	146	21	)	)	PUNCT
ejpam-4971	146	22	if	if	SCONJ
ejpam-4971	146	23	κ1	κ1	NOUN
ejpam-4971	146	24	=	=	SYM
ejpam-4971	146	25	κ2	κ2	PROPN
ejpam-4971	146	26	,	,	PUNCT
ejpam-4971	146	27	then	then	ADV
ejpam-4971	146	28	the	the	DET
ejpam-4971	146	29	solution	solution	NOUN
ejpam-4971	146	30	u(ξ	u(ξ	NOUN
ejpam-4971	146	31	)	)	PUNCT
ejpam-4971	146	32	is	be	AUX
ejpam-4971	146	33	solitary	solitary	ADJ
ejpam-4971	146	34	which	which	PRON
ejpam-4971	146	35	corresponds	correspond	VERB
ejpam-4971	146	36	to	to	ADP
ejpam-4971	146	37	a	a	DET
ejpam-4971	146	38	homoclinic	homoclinic	ADJ
ejpam-4971	146	39	orbit	orbit	NOUN
ejpam-4971	146	40	for	for	ADP
ejpam-4971	146	41	the	the	DET
ejpam-4971	146	42	system	system	NOUN
ejpam-4971	146	43	(	(	PUNCT
ejpam-4971	146	44	4	4	NUM
ejpam-4971	146	45	)	)	PUNCT
ejpam-4971	146	46	.	.	PUNCT
ejpam-4971	147	1	(	(	PUNCT
ejpam-4971	147	2	ii	ii	NOUN
ejpam-4971	147	3	)	)	PUNCT
ejpam-4971	147	4	if	if	SCONJ
ejpam-4971	147	5	κ1	κ1	PROPN
ejpam-4971	147	6	̸=	̸=	PROPN
ejpam-4971	147	7	κ2	κ2	PROPN
ejpam-4971	147	8	,	,	PUNCT
ejpam-4971	147	9	then	then	ADV
ejpam-4971	147	10	the	the	DET
ejpam-4971	147	11	solution	solution	NOUN
ejpam-4971	147	12	u(ξ	u(ξ	NOUN
ejpam-4971	147	13	)	)	PUNCT
ejpam-4971	147	14	is	be	AUX
ejpam-4971	147	15	a	a	DET
ejpam-4971	147	16	kink	kink	NOUN
ejpam-4971	147	17	(	(	PUNCT
ejpam-4971	147	18	or	or	CCONJ
ejpam-4971	147	19	anti	anti	ADJ
ejpam-4971	147	20	-	-	ADJ
ejpam-4971	147	21	kink	kink	ADJ
ejpam-4971	147	22	)	)	PUNCT
ejpam-4971	147	23	wave	wave	NOUN
ejpam-4971	147	24	that	that	PRON
ejpam-4971	147	25	corresponds	correspond	VERB
ejpam-4971	147	26	to	to	ADP
ejpam-4971	147	27	a	a	DET
ejpam-4971	147	28	heteroclinic	heteroclinic	ADJ
ejpam-4971	147	29	orbit	orbit	NOUN
ejpam-4971	147	30	for	for	ADP
ejpam-4971	147	31	the	the	DET
ejpam-4971	147	32	system	system	NOUN
ejpam-4971	147	33	(	(	PUNCT
ejpam-4971	147	34	4	4	NUM
ejpam-4971	147	35	)	)	PUNCT
ejpam-4971	147	36	.	.	PUNCT
ejpam-4971	148	1	(	(	PUNCT
ejpam-4971	148	2	iii	iii	X
ejpam-4971	148	3	)	)	PUNCT
ejpam-4971	148	4	if	if	SCONJ
ejpam-4971	148	5	system	system	NOUN
ejpam-4971	148	6	(	(	PUNCT
ejpam-4971	148	7	4	4	X
ejpam-4971	148	8	)	)	PUNCT
ejpam-4971	148	9	possesses	possess	VERB
ejpam-4971	148	10	a	a	DET
ejpam-4971	148	11	periodic	periodic	ADJ
ejpam-4971	148	12	orbit	orbit	NOUN
ejpam-4971	148	13	,	,	PUNCT
ejpam-4971	148	14	then	then	ADV
ejpam-4971	148	15	its	its	PRON
ejpam-4971	148	16	corresponding	corresponding	ADJ
ejpam-4971	148	17	solution	solution	NOUN
ejpam-4971	148	18	u(ξ	u(ξ	NOUN
ejpam-4971	148	19	)	)	PUNCT
ejpam-4971	148	20	is	be	AUX
ejpam-4971	148	21	also	also	ADV
ejpam-4971	148	22	periodic	periodic	ADJ
ejpam-4971	148	23	.	.	PUNCT
ejpam-4971	149	1	(	(	PUNCT
ejpam-4971	149	2	iv	iv	X
ejpam-4971	149	3	)	)	PUNCT
ejpam-4971	149	4	if	if	SCONJ
ejpam-4971	149	5	system	system	NOUN
ejpam-4971	149	6	(	(	PUNCT
ejpam-4971	149	7	4	4	NUM
ejpam-4971	149	8	)	)	PUNCT
ejpam-4971	149	9	has	have	VERB
ejpam-4971	149	10	a	a	DET
ejpam-4971	149	11	closed	closed	ADJ
ejpam-4971	149	12	orbit	orbit	NOUN
ejpam-4971	149	13	in	in	ADP
ejpam-4971	149	14	the	the	DET
ejpam-4971	149	15	phase	phase	NOUN
ejpam-4971	149	16	portrait	portrait	NOUN
ejpam-4971	149	17	evolved	evolve	VERB
ejpam-4971	149	18	by	by	ADP
ejpam-4971	149	19	at	at	ADV
ejpam-4971	149	20	least	least	ADV
ejpam-4971	149	21	two	two	NUM
ejpam-4971	149	22	centers	center	NOUN
ejpam-4971	149	23	and	and	CCONJ
ejpam-4971	149	24	one	one	NUM
ejpam-4971	149	25	separatrix	separatrix	NOUN
ejpam-4971	149	26	layer	layer	NOUN
ejpam-4971	149	27	,	,	PUNCT
ejpam-4971	149	28	then	then	ADV
ejpam-4971	149	29	its	its	PRON
ejpam-4971	149	30	corresponding	corresponding	ADJ
ejpam-4971	149	31	solution	solution	NOUN
ejpam-4971	149	32	u(ξ	u(ξ	NOUN
ejpam-4971	149	33	)	)	PUNCT
ejpam-4971	149	34	is	be	AUX
ejpam-4971	149	35	a	a	DET
ejpam-4971	149	36	super	super	ADJ
ejpam-4971	149	37	periodic	periodic	ADJ
ejpam-4971	149	38	wave	wave	NOUN
ejpam-4971	149	39	.	.	PUNCT
ejpam-4971	150	1	black	black	ADJ
ejpam-4971	150	2	theorem	theorem	NOUN
ejpam-4971	150	3	2	2	X
ejpam-4971	150	4	.	.	PUNCT
ejpam-4971	151	1	if	if	SCONJ
ejpam-4971	151	2	the	the	DET
ejpam-4971	151	3	solution	solution	NOUN
ejpam-4971	151	4	of	of	ADP
ejpam-4971	151	5	the	the	DET
ejpam-4971	151	6	nonlinear	nonlinear	ADJ
ejpam-4971	151	7	kg	kg	PROPN
ejpam-4971	151	8	equation	equation	NOUN
ejpam-4971	151	9	(	(	PUNCT
ejpam-4971	151	10	1	1	X
ejpam-4971	151	11	)	)	PUNCT
ejpam-4971	151	12	has	have	VERB
ejpam-4971	151	13	the	the	DET
ejpam-4971	151	14	form	form	NOUN
ejpam-4971	151	15	u(x	u(x	NOUN
ejpam-4971	151	16	,	,	PUNCT
ejpam-4971	151	17	t	t	NOUN
ejpam-4971	151	18	)	)	PUNCT
ejpam-4971	152	1	=	=	SYM
ejpam-4971	152	2	φ(x−	φ(x−	NOUN
ejpam-4971	152	3	blackωt	blackωt	NOUN
ejpam-4971	152	4	)	)	PUNCT
ejpam-4971	152	5	,	,	PUNCT
ejpam-4971	152	6	then	then	ADV
ejpam-4971	152	7	(	(	PUNCT
ejpam-4971	152	8	a	a	X
ejpam-4971	152	9	)	)	PUNCT
ejpam-4971	152	10	it	it	PRON
ejpam-4971	152	11	is	be	AUX
ejpam-4971	152	12	a	a	DET
ejpam-4971	152	13	periodic	periodic	ADJ
ejpam-4971	152	14	wave	wave	NOUN
ejpam-4971	152	15	solution	solution	NOUN
ejpam-4971	152	16	if	if	SCONJ
ejpam-4971	152	17	(	(	PUNCT
ejpam-4971	152	18	α0	α0	ADJ
ejpam-4971	152	19	,	,	PUNCT
ejpam-4971	152	20	β0	β0	ADJ
ejpam-4971	152	21	)	)	PUNCT
ejpam-4971	152	22	∈	∈	PROPN
ejpam-4971	152	23	r1	r1	NOUN
ejpam-4971	152	24	∪	∪	X
ejpam-4971	152	25	{	{	PUNCT
ejpam-4971	152	26	(	(	PUNCT
ejpam-4971	152	27	α0	α0	ADJ
ejpam-4971	152	28	,	,	PUNCT
ejpam-4971	152	29	β0	β0	NOUN
ejpam-4971	152	30	)	)	PUNCT
ejpam-4971	152	31	|	|	ADV
ejpam-4971	152	32	α0	α0	ADJ
ejpam-4971	152	33	=	=	SYM
ejpam-4971	152	34	0	0	NUM
ejpam-4971	152	35	,	,	PUNCT
ejpam-4971	152	36	β0	β0	NOUN
ejpam-4971	152	37	<	<	X
ejpam-4971	152	38	0	0	NUM
ejpam-4971	152	39	}	}	PUNCT
ejpam-4971	152	40	,	,	PUNCT
ejpam-4971	152	41	or	or	CCONJ
ejpam-4971	152	42	if	if	SCONJ
ejpam-4971	152	43	(	(	PUNCT
ejpam-4971	152	44	α0	α0	ADJ
ejpam-4971	152	45	,	,	PUNCT
ejpam-4971	152	46	β0	β0	ADJ
ejpam-4971	152	47	)	)	PUNCT
ejpam-4971	152	48	∈	∈	PROPN
ejpam-4971	152	49	r2	r2	NOUN
ejpam-4971	152	50	,	,	PUNCT
ejpam-4971	152	51	h	h	NOUN
ejpam-4971	152	52	∈]0,∞	∈]0,∞	PROPN
ejpam-4971	153	1	[	[	X
ejpam-4971	153	2	,	,	PUNCT
ejpam-4971	153	3	or	or	CCONJ
ejpam-4971	153	4	if	if	SCONJ
ejpam-4971	153	5	(	(	PUNCT
ejpam-4971	153	6	α0	α0	ADJ
ejpam-4971	153	7	,	,	PUNCT
ejpam-4971	153	8	β0	β0	ADJ
ejpam-4971	153	9	)	)	PUNCT
ejpam-4971	153	10	∈	∈	PROPN
ejpam-4971	153	11	r4	r4	NOUN
ejpam-4971	153	12	,	,	PUNCT
ejpam-4971	153	13	h	h	PROPN
ejpam-4971	153	14	∈]h2	∈]h2	PROPN
ejpam-4971	153	15	,	,	PUNCT
ejpam-4971	153	16	0[∪]0,∞	0[∪]0,∞	NUM
ejpam-4971	153	17	[	[	X
ejpam-4971	153	18	;	;	PUNCT
ejpam-4971	153	19	(	(	PUNCT
ejpam-4971	153	20	b	b	X
ejpam-4971	153	21	)	)	PUNCT
ejpam-4971	153	22	it	it	PRON
ejpam-4971	153	23	is	be	AUX
ejpam-4971	153	24	a	a	DET
ejpam-4971	153	25	kink	kink	NOUN
ejpam-4971	153	26	(	(	PUNCT
ejpam-4971	153	27	anti	anti	ADJ
ejpam-4971	153	28	-	-	ADJ
ejpam-4971	153	29	kink	kink	ADJ
ejpam-4971	153	30	)	)	PUNCT
ejpam-4971	153	31	solution	solution	NOUN
ejpam-4971	153	32	if	if	SCONJ
ejpam-4971	153	33	(	(	PUNCT
ejpam-4971	153	34	α0	α0	ADJ
ejpam-4971	153	35	,	,	PUNCT
ejpam-4971	153	36	β0	β0	ADJ
ejpam-4971	153	37	)	)	PUNCT
ejpam-4971	153	38	∈	∈	PROPN
ejpam-4971	153	39	r1	r1	NOUN
ejpam-4971	153	40	,	,	PUNCT
ejpam-4971	153	41	h	h	NOUN
ejpam-4971	153	42	=	=	SYM
ejpam-4971	153	43	h2	h2	NOUN
ejpam-4971	153	44	;	;	PUNCT
ejpam-4971	153	45	(	(	PUNCT
ejpam-4971	153	46	c	c	X
ejpam-4971	153	47	)	)	PUNCT
ejpam-4971	153	48	it	it	PRON
ejpam-4971	153	49	is	be	AUX
ejpam-4971	153	50	a	a	DET
ejpam-4971	153	51	solitary	solitary	ADJ
ejpam-4971	153	52	wave	wave	NOUN
ejpam-4971	153	53	solution	solution	NOUN
ejpam-4971	153	54	if	if	SCONJ
ejpam-4971	153	55	(	(	PUNCT
ejpam-4971	153	56	α0	α0	ADJ
ejpam-4971	153	57	,	,	PUNCT
ejpam-4971	153	58	β0	β0	ADJ
ejpam-4971	153	59	)	)	PUNCT
ejpam-4971	153	60	∈	∈	PROPN
ejpam-4971	153	61	r4	r4	NOUN
ejpam-4971	153	62	,	,	PUNCT
ejpam-4971	153	63	h	h	NOUN
ejpam-4971	153	64	=	=	NOUN
ejpam-4971	153	65	0	0	X
ejpam-4971	153	66	.	.	PUNCT
ejpam-4971	154	1	black	black	ADJ
ejpam-4971	154	2	proof	proof	NOUN
ejpam-4971	154	3	.	.	PUNCT
ejpam-4971	155	1	taking	take	VERB
ejpam-4971	155	2	into	into	ADP
ejpam-4971	155	3	account	account	NOUN
ejpam-4971	155	4	lemma	lemma	PROPN
ejpam-4971	155	5	1	1	NUM
ejpam-4971	155	6	and	and	CCONJ
ejpam-4971	155	7	the	the	DET
ejpam-4971	155	8	bifurcation	bifurcation	NOUN
ejpam-4971	155	9	analysis	analysis	NOUN
ejpam-4971	155	10	,	,	PUNCT
ejpam-4971	155	11	the	the	DET
ejpam-4971	155	12	theorem	theorem	NOUN
ejpam-4971	155	13	is	be	AUX
ejpam-4971	155	14	proved	prove	VERB
ejpam-4971	155	15	directly	directly	ADV
ejpam-4971	155	16	.	.	PUNCT
ejpam-4971	156	1	4	4	X
ejpam-4971	156	2	.	.	X
ejpam-4971	156	3	exact	exact	ADJ
ejpam-4971	156	4	traveling	travel	VERB
ejpam-4971	156	5	wave	wave	NOUN
ejpam-4971	156	6	solutions	solution	NOUN
ejpam-4971	156	7	to	to	ADP
ejpam-4971	156	8	the	the	DET
ejpam-4971	156	9	kg	kg	PROPN
ejpam-4971	156	10	equation	equation	NOUN
ejpam-4971	156	11	considering	consider	VERB
ejpam-4971	156	12	the	the	DET
ejpam-4971	156	13	bifurcation	bifurcation	NOUN
ejpam-4971	156	14	constraints	constraint	NOUN
ejpam-4971	156	15	on	on	ADP
ejpam-4971	156	16	the	the	DET
ejpam-4971	156	17	parameters	parameter	NOUN
ejpam-4971	156	18	α0	α0	ADJ
ejpam-4971	156	19	,	,	PUNCT
ejpam-4971	156	20	β0	β0	NOUN
ejpam-4971	156	21	,	,	PUNCT
ejpam-4971	156	22	we	we	PRON
ejpam-4971	156	23	integrate	integrate	VERB
ejpam-4971	156	24	both	both	DET
ejpam-4971	156	25	sides	side	NOUN
ejpam-4971	156	26	of	of	ADP
ejpam-4971	156	27	eq	eq	PROPN
ejpam-4971	156	28	.	.	PUNCT
ejpam-4971	157	1	(	(	PUNCT
ejpam-4971	157	2	8)	8)	NUM
ejpam-4971	157	3	and	and	CCONJ
ejpam-4971	157	4	construct	construct	VERB
ejpam-4971	157	5	some	some	DET
ejpam-4971	157	6	wave	wave	NOUN
ejpam-4971	157	7	solutions	solution	NOUN
ejpam-4971	157	8	.	.	PUNCT
ejpam-4971	158	1	4.1	4.1	NUM
ejpam-4971	158	2	.	.	PUNCT
ejpam-4971	158	3	case	case	NOUN
ejpam-4971	158	4	of	of	ADP
ejpam-4971	158	5	(	(	PUNCT
ejpam-4971	158	6	α0	α0	ADJ
ejpam-4971	158	7	,	,	PUNCT
ejpam-4971	158	8	β0	β0	ADJ
ejpam-4971	158	9	)	)	PUNCT
ejpam-4971	158	10	∈	∈	PROPN
ejpam-4971	158	11	r1	r1	NOUN
ejpam-4971	158	12	we	we	PRON
ejpam-4971	158	13	first	first	ADV
ejpam-4971	158	14	construct	construct	VERB
ejpam-4971	158	15	exact	exact	ADJ
ejpam-4971	158	16	traveling	travel	VERB
ejpam-4971	158	17	wave	wave	NOUN
ejpam-4971	158	18	solutions	solution	NOUN
ejpam-4971	158	19	to	to	ADP
ejpam-4971	158	20	the	the	DET
ejpam-4971	158	21	kg	kg	PROPN
ejpam-4971	158	22	equation	equation	NOUN
ejpam-4971	158	23	(	(	PUNCT
ejpam-4971	158	24	1	1	NUM
ejpam-4971	158	25	)	)	PUNCT
ejpam-4971	158	26	for	for	ADP
ejpam-4971	158	27	different	different	ADJ
ejpam-4971	158	28	energy	energy	NOUN
ejpam-4971	158	29	parameters	parameter	NOUN
ejpam-4971	158	30	h.	h.	PROPN
ejpam-4971	158	31	•	•	NOUN
ejpam-4971	158	32	on	on	ADP
ejpam-4971	158	33	a	a	DET
ejpam-4971	158	34	fixed	fix	VERB
ejpam-4971	158	35	energy	energy	NOUN
ejpam-4971	158	36	level	level	NOUN
ejpam-4971	158	37	h	h	NOUN
ejpam-4971	158	38	=	=	PUNCT
ejpam-4971	158	39	α2	α2	PROPN
ejpam-4971	158	40	0	0	NUM
ejpam-4971	159	1	4β0	4β0	NUM
ejpam-4971	159	2	,	,	PUNCT
ejpam-4971	159	3	there	there	PRON
ejpam-4971	159	4	exists	exist	VERB
ejpam-4971	159	5	a	a	DET
ejpam-4971	159	6	heteroclinic	heteroclinic	ADJ
ejpam-4971	159	7	orbit	orbit	NOUN
ejpam-4971	159	8	connecting	connect	VERB
ejpam-4971	159	9	the	the	DET
ejpam-4971	159	10	two	two	NUM
ejpam-4971	159	11	saddle	saddle	NOUN
ejpam-4971	159	12	points	point	NOUN
ejpam-4971	159	13	e2,3	e2,3	NOUN
ejpam-4971	159	14	;	;	PUNCT
ejpam-4971	159	15	see	see	VERB
ejpam-4971	159	16	fig	fig	NOUN
ejpam-4971	159	17	.	.	PUNCT
ejpam-4971	160	1	1(a	1(a	NUM
ejpam-4971	160	2	)	)	PUNCT
ejpam-4971	160	3	.	.	PUNCT
ejpam-4971	161	1	this	this	DET
ejpam-4971	161	2	orbit	orbit	NOUN
ejpam-4971	161	3	intersects	intersect	NOUN
ejpam-4971	161	4	with	with	ADP
ejpam-4971	161	5	the	the	DET
ejpam-4971	161	6	φ	φ	PROPN
ejpam-4971	161	7	axis	axis	NOUN
ejpam-4971	161	8	at	at	ADP
ejpam-4971	161	9	the	the	DET
ejpam-4971	161	10	two	two	NUM
ejpam-4971	161	11	points	point	NOUN
ejpam-4971	161	12	(	(	PUNCT
ejpam-4971	161	13	±α0	±α0	PROPN
ejpam-4971	161	14	β0	β0	NOUN
ejpam-4971	161	15	,	,	PUNCT
ejpam-4971	161	16	0	0	NUM
ejpam-4971	161	17	)	)	PUNCT
ejpam-4971	161	18	,	,	PUNCT
ejpam-4971	161	19	and	and	CCONJ
ejpam-4971	161	20	so	so	ADV
ejpam-4971	161	21	the	the	DET
ejpam-4971	161	22	quartic	quartic	ADJ
ejpam-4971	161	23	polynomial	polynomial	ADJ
ejpam-4971	161	24	(	(	PUNCT
ejpam-4971	161	25	9	9	NUM
ejpam-4971	161	26	)	)	PUNCT
ejpam-4971	161	27	takes	take	VERB
ejpam-4971	161	28	the	the	DET
ejpam-4971	161	29	form	form	NOUN
ejpam-4971	161	30	p4(φ	p4(φ	NOUN
ejpam-4971	161	31	)	)	PUNCT
ejpam-4971	162	1	=	=	SYM
ejpam-4971	162	2	β0	β0	NOUN
ejpam-4971	162	3	2	2	NUM
ejpam-4971	162	4	(	(	PUNCT
ejpam-4971	162	5	α0	α0	PROPN
ejpam-4971	162	6	β0	β0	NOUN
ejpam-4971	162	7	−	−	PROPN
ejpam-4971	162	8	φ2	φ2	PROPN
ejpam-4971	162	9	)	)	PUNCT
ejpam-4971	162	10	2	2	NUM
ejpam-4971	162	11	.	.	PUNCT
ejpam-4971	163	1	(	(	PUNCT
ejpam-4971	163	2	14	14	NUM
ejpam-4971	163	3	)	)	PUNCT
ejpam-4971	163	4	using	use	VERB
ejpam-4971	163	5	eq	eq	X
ejpam-4971	163	6	.	.	PUNCT
ejpam-4971	164	1	(	(	PUNCT
ejpam-4971	164	2	8)	8)	NUM
ejpam-4971	164	3	,	,	PUNCT
ejpam-4971	164	4	we	we	PRON
ejpam-4971	164	5	obtain	obtain	VERB
ejpam-4971	164	6	a	a	DET
ejpam-4971	164	7	kink	kink	NOUN
ejpam-4971	164	8	(	(	PUNCT
ejpam-4971	164	9	or	or	CCONJ
ejpam-4971	164	10	anti	anti	ADJ
ejpam-4971	164	11	-	-	ADJ
ejpam-4971	164	12	kink	kink	ADJ
ejpam-4971	164	13	)	)	PUNCT
ejpam-4971	164	14	wave	wave	NOUN
ejpam-4971	164	15	solution	solution	NOUN
ejpam-4971	164	16	for	for	ADP
ejpam-4971	164	17	eq	eq	PROPN
ejpam-4971	164	18	.	.	PUNCT
ejpam-4971	165	1	(	(	PUNCT
ejpam-4971	165	2	1	1	X
ejpam-4971	165	3	)	)	PUNCT
ejpam-4971	165	4	as	as	ADP
ejpam-4971	165	5	φ(ξ	φ(ξ	NOUN
ejpam-4971	165	6	)	)	PUNCT
ejpam-4971	165	7	=	=	SYM
ejpam-4971	165	8	√	√	PROPN
ejpam-4971	165	9	α0	α0	ADJ
ejpam-4971	165	10	β0	β0	PROPN
ejpam-4971	165	11	tanh	tanh	PROPN
ejpam-4971	166	1	[	[	X
ejpam-4971	166	2	√	√	ADV
ejpam-4971	166	3	α0	α0	ADJ
ejpam-4971	166	4	2	2	NUM
ejpam-4971	166	5	ξ	ξ	X
ejpam-4971	166	6	+	+	SYM
ejpam-4971	166	7	c	c	NOUN
ejpam-4971	166	8	]	]	PUNCT
ejpam-4971	166	9	,	,	PUNCT
ejpam-4971	166	10	(	(	PUNCT
ejpam-4971	166	11	15	15	NUM
ejpam-4971	166	12	)	)	PUNCT
ejpam-4971	166	13	where	where	SCONJ
ejpam-4971	166	14	c	c	NOUN
ejpam-4971	166	15	is	be	AUX
ejpam-4971	166	16	the	the	DET
ejpam-4971	166	17	integration	integration	NOUN
ejpam-4971	166	18	constant	constant	ADJ
ejpam-4971	166	19	.	.	PUNCT
ejpam-4971	167	1	m.arab	m.arab	NOUN
ejpam-4971	167	2	/	/	SYM
ejpam-4971	167	3	eur	eur	PROPN
ejpam-4971	167	4	.	.	PUNCT
ejpam-4971	168	1	j.	j.	PROPN
ejpam-4971	168	2	pure	pure	PROPN
ejpam-4971	168	3	appl	appl	PROPN
ejpam-4971	168	4	.	.	PROPN
ejpam-4971	168	5	math	math	PROPN
ejpam-4971	168	6	,	,	PUNCT
ejpam-4971	168	7	16	16	NUM
ejpam-4971	168	8	(	(	PUNCT
ejpam-4971	168	9	4	4	NUM
ejpam-4971	168	10	)	)	PUNCT
ejpam-4971	168	11	(	(	PUNCT
ejpam-4971	168	12	2023	2023	NUM
ejpam-4971	168	13	)	)	PUNCT
ejpam-4971	168	14	,	,	PUNCT
ejpam-4971	168	15	2643	2643	NUM
ejpam-4971	168	16	-	-	SYM
ejpam-4971	168	17	2661	2661	NUM
ejpam-4971	168	18	2650	2650	NUM
ejpam-4971	168	19	•	•	NOUN
ejpam-4971	168	20	on	on	ADP
ejpam-4971	168	21	energy	energy	NOUN
ejpam-4971	168	22	level	level	NOUN
ejpam-4971	168	23	h	h	NOUN
ejpam-4971	168	24	∈]0	∈]0	NOUN
ejpam-4971	168	25	,	,	PUNCT
ejpam-4971	168	26	α2	α2	PROPN
ejpam-4971	168	27	0	0	NUM
ejpam-4971	168	28	4β0	4β0	NUM
ejpam-4971	169	1	[	[	X
ejpam-4971	169	2	,	,	PUNCT
ejpam-4971	169	3	there	there	PRON
ejpam-4971	169	4	is	be	VERB
ejpam-4971	169	5	a	a	DET
ejpam-4971	169	6	group	group	NOUN
ejpam-4971	169	7	of	of	ADP
ejpam-4971	169	8	periodic	periodic	ADJ
ejpam-4971	169	9	orbits	orbit	NOUN
ejpam-4971	169	10	around	around	ADP
ejpam-4971	169	11	the	the	DET
ejpam-4971	169	12	center	center	NOUN
ejpam-4971	169	13	point	point	NOUN
ejpam-4971	169	14	e1	e1	NOUN
ejpam-4971	169	15	=	=	SYM
ejpam-4971	169	16	(	(	PUNCT
ejpam-4971	169	17	0	0	NUM
ejpam-4971	169	18	,	,	PUNCT
ejpam-4971	169	19	0	0	NUM
ejpam-4971	169	20	)	)	PUNCT
ejpam-4971	169	21	.	.	PUNCT
ejpam-4971	170	1	this	this	DET
ejpam-4971	170	2	type	type	NOUN
ejpam-4971	170	3	of	of	ADP
ejpam-4971	170	4	orbit	orbit	NOUN
ejpam-4971	170	5	always	always	ADV
ejpam-4971	170	6	corresponds	correspond	VERB
ejpam-4971	170	7	to	to	ADP
ejpam-4971	170	8	the	the	DET
ejpam-4971	170	9	existence	existence	NOUN
ejpam-4971	170	10	of	of	ADP
ejpam-4971	170	11	a	a	DET
ejpam-4971	170	12	periodic	periodic	ADJ
ejpam-4971	170	13	traveling	travel	VERB
ejpam-4971	170	14	wave	wave	NOUN
ejpam-4971	170	15	solution	solution	NOUN
ejpam-4971	170	16	to	to	ADP
ejpam-4971	170	17	eq	eq	PROPN
ejpam-4971	170	18	.	.	PUNCT
ejpam-4971	171	1	(	(	PUNCT
ejpam-4971	171	2	1	1	NUM
ejpam-4971	171	3	)	)	PUNCT
ejpam-4971	171	4	.	.	PUNCT
ejpam-4971	172	1	as	as	SCONJ
ejpam-4971	172	2	appeared	appear	VERB
ejpam-4971	172	3	in	in	ADP
ejpam-4971	172	4	fig	fig	NOUN
ejpam-4971	172	5	.	.	PUNCT
ejpam-4971	173	1	1(a	1(a	NUM
ejpam-4971	173	2	)	)	PUNCT
ejpam-4971	173	3	,	,	PUNCT
ejpam-4971	173	4	these	these	DET
ejpam-4971	173	5	orbits	orbit	NOUN
ejpam-4971	173	6	cut	cut	VERB
ejpam-4971	173	7	off	off	ADP
ejpam-4971	173	8	the	the	DET
ejpam-4971	173	9	φ	φ	PROPN
ejpam-4971	173	10	axis	axis	NOUN
ejpam-4971	173	11	at	at	ADP
ejpam-4971	173	12	four	four	NUM
ejpam-4971	173	13	points	point	NOUN
ejpam-4971	173	14	,	,	PUNCT
ejpam-4971	173	15	(	(	PUNCT
ejpam-4971	173	16	±φ1	±φ1	PROPN
ejpam-4971	173	17	,	,	PUNCT
ejpam-4971	173	18	0	0	NUM
ejpam-4971	173	19	)	)	PUNCT
ejpam-4971	173	20	,	,	PUNCT
ejpam-4971	173	21	(	(	PUNCT
ejpam-4971	173	22	±φ2	±φ2	PROPN
ejpam-4971	173	23	,	,	PUNCT
ejpam-4971	173	24	0	0	NUM
ejpam-4971	173	25	)	)	PUNCT
ejpam-4971	173	26	.	.	PUNCT
ejpam-4971	174	1	thus	thus	ADV
ejpam-4971	174	2	,	,	PUNCT
ejpam-4971	174	3	the	the	DET
ejpam-4971	174	4	polynomial	polynomial	ADJ
ejpam-4971	174	5	(	(	PUNCT
ejpam-4971	174	6	9	9	NUM
ejpam-4971	174	7	)	)	PUNCT
ejpam-4971	174	8	takes	take	VERB
ejpam-4971	174	9	the	the	DET
ejpam-4971	174	10	form	form	NOUN
ejpam-4971	174	11	p4(φ	p4(φ	NOUN
ejpam-4971	174	12	)	)	PUNCT
ejpam-4971	174	13	=	=	SYM
ejpam-4971	175	1	β0	β0	NOUN
ejpam-4971	175	2	2	2	NUM
ejpam-4971	175	3	(	(	PUNCT
ejpam-4971	175	4	φ2	φ2	PROPN
ejpam-4971	175	5	−	−	PROPN
ejpam-4971	175	6	φ2	φ2	PROPN
ejpam-4971	175	7	1)(φ	1)(φ	NUM
ejpam-4971	175	8	2	2	NUM
ejpam-4971	175	9	−	−	NOUN
ejpam-4971	175	10	φ2	φ2	NOUN
ejpam-4971	175	11	2	2	NUM
ejpam-4971	175	12	)	)	PUNCT
ejpam-4971	175	13	.	.	PUNCT
ejpam-4971	176	1	(	(	PUNCT
ejpam-4971	176	2	16	16	NUM
ejpam-4971	176	3	)	)	PUNCT
ejpam-4971	176	4	using	use	VERB
ejpam-4971	176	5	eqs	eqs	PROPN
ejpam-4971	176	6	.	.	PUNCT
ejpam-4971	177	1	(	(	PUNCT
ejpam-4971	177	2	16	16	NUM
ejpam-4971	177	3	)	)	PUNCT
ejpam-4971	177	4	and	and	CCONJ
ejpam-4971	177	5	(	(	PUNCT
ejpam-4971	177	6	8)	8)	NUM
ejpam-4971	177	7	,	,	PUNCT
ejpam-4971	177	8	we	we	PRON
ejpam-4971	177	9	obtain	obtain	VERB
ejpam-4971	177	10	φ(ξ	φ(ξ	NOUN
ejpam-4971	177	11	)	)	PUNCT
ejpam-4971	178	1	=	=	X
ejpam-4971	178	2	φ2sn	φ2sn	PUNCT
ejpam-4971	178	3	(	(	PUNCT
ejpam-4971	178	4	√	√	NUM
ejpam-4971	178	5	β0	β0	NOUN
ejpam-4971	178	6	2	2	NUM
ejpam-4971	178	7	φ1(ξ	φ1(ξ	PROPN
ejpam-4971	178	8	+	+	NUM
ejpam-4971	178	9	c	c	NOUN
ejpam-4971	178	10	)	)	PUNCT
ejpam-4971	178	11	,	,	PUNCT
ejpam-4971	178	12	φ2	φ2	PROPN
ejpam-4971	178	13	φ1	φ1	PROPN
ejpam-4971	178	14	)	)	PUNCT
ejpam-4971	178	15	,	,	PUNCT
ejpam-4971	178	16	(	(	PUNCT
ejpam-4971	178	17	17	17	NUM
ejpam-4971	178	18	)	)	PUNCT
ejpam-4971	178	19	where	where	SCONJ
ejpam-4971	178	20	sn(u	sn(u	NOUN
ejpam-4971	178	21	,	,	PUNCT
ejpam-4971	178	22	k	k	NOUN
ejpam-4971	178	23	)	)	PUNCT
ejpam-4971	178	24	,	,	PUNCT
ejpam-4971	178	25	cn(u	cn(u	NOUN
ejpam-4971	178	26	,	,	PUNCT
ejpam-4971	178	27	k),dn(u	k),dn(u	PROPN
ejpam-4971	178	28	,	,	PUNCT
ejpam-4971	178	29	k	k	NOUN
ejpam-4971	178	30	)	)	PUNCT
ejpam-4971	178	31	are	be	AUX
ejpam-4971	178	32	the	the	DET
ejpam-4971	178	33	jacobian	jacobian	ADJ
ejpam-4971	178	34	elliptic	elliptic	ADJ
ejpam-4971	178	35	functions	function	NOUN
ejpam-4971	179	1	[	[	X
ejpam-4971	179	2	11	11	NUM
ejpam-4971	179	3	]	]	PUNCT
ejpam-4971	179	4	.	.	PUNCT
ejpam-4971	180	1	equation	equation	NOUN
ejpam-4971	180	2	(	(	PUNCT
ejpam-4971	180	3	17	17	NUM
ejpam-4971	180	4	)	)	PUNCT
ejpam-4971	180	5	is	be	AUX
ejpam-4971	180	6	a	a	DET
ejpam-4971	180	7	periodic	periodic	ADJ
ejpam-4971	180	8	traveling	travel	VERB
ejpam-4971	180	9	wave	wave	NOUN
ejpam-4971	180	10	solution	solution	NOUN
ejpam-4971	180	11	with	with	ADP
ejpam-4971	180	12	period	period	NOUN
ejpam-4971	180	13	4	4	NUM
ejpam-4971	180	14	φ1	φ1	NOUN
ejpam-4971	180	15	√	√	ADV
ejpam-4971	180	16	2	2	NUM
ejpam-4971	180	17	β0	β0	NOUN
ejpam-4971	180	18	k(φ2	k(φ2	NOUN
ejpam-4971	180	19	φ1	φ1	PROPN
ejpam-4971	180	20	)	)	PUNCT
ejpam-4971	180	21	,	,	PUNCT
ejpam-4971	180	22	where	where	SCONJ
ejpam-4971	180	23	k(k	k(k	PROPN
ejpam-4971	180	24	)	)	PUNCT
ejpam-4971	180	25	is	be	AUX
ejpam-4971	180	26	an	an	DET
ejpam-4971	180	27	exact	exact	ADJ
ejpam-4971	180	28	elliptic	elliptic	ADJ
ejpam-4971	180	29	integral	integral	NOUN
ejpam-4971	180	30	of	of	ADP
ejpam-4971	180	31	the	the	DET
ejpam-4971	180	32	first	first	ADJ
ejpam-4971	180	33	type	type	NOUN
ejpam-4971	180	34	.	.	PUNCT
ejpam-4971	181	1	•	•	NUM
ejpam-4971	181	2	on	on	ADP
ejpam-4971	181	3	the	the	DET
ejpam-4971	181	4	zero	zero	NUM
ejpam-4971	181	5	energy	energy	NOUN
ejpam-4971	181	6	level	level	NOUN
ejpam-4971	181	7	h	h	NOUN
ejpam-4971	181	8	=	=	SYM
ejpam-4971	181	9	0	0	NUM
ejpam-4971	181	10	,	,	PUNCT
ejpam-4971	181	11	there	there	PRON
ejpam-4971	181	12	is	be	VERB
ejpam-4971	181	13	a	a	DET
ejpam-4971	181	14	group	group	NOUN
ejpam-4971	181	15	of	of	ADP
ejpam-4971	181	16	orbits	orbit	NOUN
ejpam-4971	181	17	that	that	PRON
ejpam-4971	181	18	cut	cut	VERB
ejpam-4971	181	19	off	off	ADP
ejpam-4971	181	20	with	with	ADP
ejpam-4971	181	21	the	the	DET
ejpam-4971	181	22	φ	φ	PROPN
ejpam-4971	181	23	axis	axis	NOUN
ejpam-4971	181	24	at	at	ADP
ejpam-4971	181	25	two	two	NUM
ejpam-4971	181	26	points	point	NOUN
ejpam-4971	181	27	if	if	SCONJ
ejpam-4971	181	28	|φ|	|φ|	PROPN
ejpam-4971	181	29	≥	≥	NOUN
ejpam-4971	181	30	√	√	PROPN
ejpam-4971	181	31	2α0	2α0	NUM
ejpam-4971	181	32	β0	β0	NOUN
ejpam-4971	181	33	;	;	PUNCT
ejpam-4971	181	34	see	see	VERB
ejpam-4971	181	35	fig	fig	NOUN
ejpam-4971	181	36	.	.	PUNCT
ejpam-4971	182	1	1(a	1(a	NUM
ejpam-4971	182	2	)	)	PUNCT
ejpam-4971	182	3	.	.	PUNCT
ejpam-4971	183	1	setting	set	VERB
ejpam-4971	183	2	h	h	NOUN
ejpam-4971	183	3	=	=	NOUN
ejpam-4971	183	4	0	0	NUM
ejpam-4971	183	5	in	in	ADP
ejpam-4971	183	6	the	the	DET
ejpam-4971	183	7	quartic	quartic	ADJ
ejpam-4971	183	8	polynomial	polynomial	ADJ
ejpam-4971	183	9	(	(	PUNCT
ejpam-4971	183	10	9	9	NUM
ejpam-4971	183	11	)	)	PUNCT
ejpam-4971	183	12	and	and	CCONJ
ejpam-4971	183	13	using	use	VERB
ejpam-4971	183	14	eq	eq	ADP
ejpam-4971	183	15	.	.	PUNCT
ejpam-4971	184	1	(	(	PUNCT
ejpam-4971	184	2	8)	8)	NUM
ejpam-4971	184	3	,	,	PUNCT
ejpam-4971	184	4	we	we	PRON
ejpam-4971	184	5	obtain	obtain	VERB
ejpam-4971	184	6	φ(ξ	φ(ξ	NOUN
ejpam-4971	184	7	)	)	PUNCT
ejpam-4971	184	8	=	=	SYM
ejpam-4971	184	9	√	√	NUM
ejpam-4971	184	10	2α0	2α0	NUM
ejpam-4971	184	11	β0	β0	PROPN
ejpam-4971	184	12	sec	sec	PROPN
ejpam-4971	184	13	(	(	PUNCT
ejpam-4971	184	14	√	√	NUM
ejpam-4971	184	15	α0ξ	α0ξ	NOUN
ejpam-4971	184	16	+	+	CCONJ
ejpam-4971	184	17	c	c	X
ejpam-4971	184	18	)	)	PUNCT
ejpam-4971	184	19	.	.	PUNCT
ejpam-4971	185	1	(	(	PUNCT
ejpam-4971	185	2	18	18	NUM
ejpam-4971	185	3	)	)	PUNCT
ejpam-4971	185	4	•	•	NOUN
ejpam-4971	185	5	at	at	ADP
ejpam-4971	185	6	negative	negative	ADJ
ejpam-4971	185	7	energy	energy	NOUN
ejpam-4971	185	8	levels	level	NOUN
ejpam-4971	185	9	h	h	VERB
ejpam-4971	185	10	<	<	X
ejpam-4971	185	11	0	0	PROPN
ejpam-4971	185	12	,	,	PUNCT
ejpam-4971	185	13	there	there	PRON
ejpam-4971	185	14	is	be	VERB
ejpam-4971	185	15	a	a	DET
ejpam-4971	185	16	group	group	NOUN
ejpam-4971	185	17	of	of	ADP
ejpam-4971	185	18	periodic	periodic	ADJ
ejpam-4971	185	19	orbits	orbit	NOUN
ejpam-4971	185	20	about	about	ADP
ejpam-4971	185	21	the	the	DET
ejpam-4971	185	22	center	center	NOUN
ejpam-4971	185	23	point	point	NOUN
ejpam-4971	185	24	e1	e1	NOUN
ejpam-4971	185	25	=	=	SYM
ejpam-4971	185	26	(	(	PUNCT
ejpam-4971	185	27	0	0	NUM
ejpam-4971	185	28	,	,	PUNCT
ejpam-4971	185	29	0	0	NUM
ejpam-4971	185	30	)	)	PUNCT
ejpam-4971	185	31	,	,	PUNCT
ejpam-4971	185	32	as	as	SCONJ
ejpam-4971	185	33	appeared	appear	VERB
ejpam-4971	185	34	in	in	ADP
ejpam-4971	185	35	fig	fig	NOUN
ejpam-4971	185	36	.	.	PUNCT
ejpam-4971	186	1	1(a	1(a	NUM
ejpam-4971	186	2	)	)	PUNCT
ejpam-4971	186	3	.	.	PUNCT
ejpam-4971	187	1	these	these	DET
ejpam-4971	187	2	orbits	orbit	NOUN
ejpam-4971	187	3	indicate	indicate	VERB
ejpam-4971	187	4	the	the	DET
ejpam-4971	187	5	existence	existence	NOUN
ejpam-4971	187	6	of	of	ADP
ejpam-4971	187	7	periodic	periodic	ADJ
ejpam-4971	187	8	traveling	travel	VERB
ejpam-4971	187	9	wave	wave	NOUN
ejpam-4971	187	10	solutions	solution	NOUN
ejpam-4971	187	11	.	.	PUNCT
ejpam-4971	188	1	when	when	SCONJ
ejpam-4971	188	2	h	h	ADP
ejpam-4971	188	3	<	<	X
ejpam-4971	188	4	0	0	PROPN
ejpam-4971	188	5	,	,	PUNCT
ejpam-4971	188	6	the	the	DET
ejpam-4971	188	7	quartic	quartic	ADJ
ejpam-4971	188	8	polynomial	polynomial	NOUN
ejpam-4971	188	9	takes	take	VERB
ejpam-4971	188	10	the	the	DET
ejpam-4971	188	11	form	form	NOUN
ejpam-4971	188	12	p4(φ	p4(φ	NOUN
ejpam-4971	188	13	)	)	PUNCT
ejpam-4971	188	14	=	=	PUNCT
ejpam-4971	189	1	√	√	NUM
ejpam-4971	189	2	β0	β0	NOUN
ejpam-4971	189	3	2	2	NUM
ejpam-4971	189	4	[	[	PUNCT
ejpam-4971	189	5	(	(	PUNCT
ejpam-4971	189	6	φ2	φ2	PROPN
ejpam-4971	189	7	−	−	PROPN
ejpam-4971	189	8	φ2	φ2	PROPN
ejpam-4971	189	9	1)(φ	1)(φ	NUM
ejpam-4971	189	10	2	2	NUM
ejpam-4971	189	11	+	+	CCONJ
ejpam-4971	189	12	φ2	φ2	PROPN
ejpam-4971	189	13	)	)	PUNCT
ejpam-4971	189	14	]	]	PUNCT
ejpam-4971	189	15	,	,	PUNCT
ejpam-4971	189	16	(	(	PUNCT
ejpam-4971	189	17	19	19	NUM
ejpam-4971	189	18	)	)	PUNCT
ejpam-4971	189	19	where	where	SCONJ
ejpam-4971	189	20	±φ1	±φ1	NOUN
ejpam-4971	189	21	and	and	CCONJ
ejpam-4971	189	22	±iφ2	±iφ2	NOUN
ejpam-4971	189	23	are	be	AUX
ejpam-4971	189	24	the	the	DET
ejpam-4971	189	25	roots	root	NOUN
ejpam-4971	189	26	of	of	ADP
ejpam-4971	189	27	the	the	DET
ejpam-4971	189	28	polynomial	polynomial	ADJ
ejpam-4971	189	29	(	(	PUNCT
ejpam-4971	189	30	9	9	NUM
ejpam-4971	189	31	)	)	PUNCT
ejpam-4971	189	32	,	,	PUNCT
ejpam-4971	189	33	φ2	φ2	PROPN
ejpam-4971	189	34	>	>	X
ejpam-4971	189	35	φ1	φ1	PROPN
ejpam-4971	189	36	.	.	PUNCT
ejpam-4971	190	1	inserting	insert	VERB
ejpam-4971	190	2	eq	eq	X
ejpam-4971	190	3	.	.	PUNCT
ejpam-4971	191	1	(	(	PUNCT
ejpam-4971	191	2	19	19	NUM
ejpam-4971	191	3	)	)	PUNCT
ejpam-4971	191	4	into	into	ADP
ejpam-4971	191	5	eq	eq	NOUN
ejpam-4971	191	6	.	.	PUNCT
ejpam-4971	192	1	(	(	PUNCT
ejpam-4971	192	2	8)	8)	NUM
ejpam-4971	192	3	,	,	PUNCT
ejpam-4971	192	4	we	we	PRON
ejpam-4971	192	5	obtain	obtain	VERB
ejpam-4971	192	6	φ(ξ	φ(ξ	NOUN
ejpam-4971	192	7	)	)	PUNCT
ejpam-4971	193	1	=	=	SYM
ejpam-4971	193	2	cn	cn	PROPN
ejpam-4971	193	3	(	(	PUNCT
ejpam-4971	193	4	√	√	PROPN
ejpam-4971	193	5	β0	β0	NOUN
ejpam-4971	193	6	2	2	NUM
ejpam-4971	193	7	(	(	PUNCT
ejpam-4971	193	8	φ	φ	PROPN
ejpam-4971	193	9	2	2	NUM
ejpam-4971	193	10	1	1	NUM
ejpam-4971	193	11	+	+	NUM
ejpam-4971	193	12	φ2	φ2	PROPN
ejpam-4971	193	13	2)(ξ	2)(ξ	NUM
ejpam-4971	193	14	+	+	CCONJ
ejpam-4971	193	15	c	c	X
ejpam-4971	193	16	)	)	PUNCT
ejpam-4971	193	17	,	,	PUNCT
ejpam-4971	193	18	φ2√	φ2√	PROPN
ejpam-4971	193	19	φ2	φ2	PROPN
ejpam-4971	193	20	1+φ2	1+φ2	NUM
ejpam-4971	193	21	2	2	NUM
ejpam-4971	193	22	)	)	PUNCT
ejpam-4971	193	23	dn	dn	NOUN
ejpam-4971	193	24	(	(	PUNCT
ejpam-4971	193	25	√	√	PROPN
ejpam-4971	193	26	β0	β0	NOUN
ejpam-4971	193	27	2	2	NUM
ejpam-4971	193	28	(	(	PUNCT
ejpam-4971	193	29	φ	φ	PROPN
ejpam-4971	193	30	2	2	NUM
ejpam-4971	193	31	1	1	NUM
ejpam-4971	193	32	+	+	NUM
ejpam-4971	193	33	φ2	φ2	PROPN
ejpam-4971	193	34	2)(ξ	2)(ξ	NUM
ejpam-4971	193	35	+	+	CCONJ
ejpam-4971	193	36	c	c	X
ejpam-4971	193	37	)	)	PUNCT
ejpam-4971	193	38	,	,	PUNCT
ejpam-4971	193	39	φ2√	φ2√	PROPN
ejpam-4971	193	40	φ2	φ2	PROPN
ejpam-4971	193	41	1+φ2	1+φ2	NUM
ejpam-4971	193	42	2	2	NUM
ejpam-4971	193	43	)	)	PUNCT
ejpam-4971	193	44	black	black	NOUN
ejpam-4971	193	45	.	.	PUNCT
ejpam-4971	194	1	(	(	PUNCT
ejpam-4971	194	2	20	20	NUM
ejpam-4971	194	3	)	)	PUNCT
ejpam-4971	194	4	this	this	DET
ejpam-4971	194	5	solution	solution	NOUN
ejpam-4971	194	6	represents	represent	VERB
ejpam-4971	194	7	a	a	DET
ejpam-4971	194	8	periodic	periodic	ADJ
ejpam-4971	194	9	traveling	travel	VERB
ejpam-4971	194	10	wave	wave	NOUN
ejpam-4971	194	11	solution	solution	NOUN
ejpam-4971	194	12	and	and	CCONJ
ejpam-4971	194	13	is	be	AUX
ejpam-4971	194	14	illustrated	illustrate	VERB
ejpam-4971	194	15	in	in	ADP
ejpam-4971	194	16	fig	fig	NOUN
ejpam-4971	194	17	.	.	PUNCT
ejpam-4971	195	1	1(a	1(a	NUM
ejpam-4971	195	2	)	)	PUNCT
ejpam-4971	195	3	.	.	PUNCT
ejpam-4971	196	1	4.2	4.2	NUM
ejpam-4971	196	2	.	.	PUNCT
ejpam-4971	196	3	case	case	NOUN
ejpam-4971	196	4	of	of	ADP
ejpam-4971	196	5	(	(	PUNCT
ejpam-4971	196	6	α0	α0	ADJ
ejpam-4971	196	7	,	,	PUNCT
ejpam-4971	196	8	β0	β0	ADJ
ejpam-4971	196	9	)	)	PUNCT
ejpam-4971	196	10	∈	∈	PROPN
ejpam-4971	196	11	r2	r2	PROPN
ejpam-4971	196	12	for	for	ADP
ejpam-4971	196	13	(	(	PUNCT
ejpam-4971	196	14	α0	α0	ADJ
ejpam-4971	196	15	,	,	PUNCT
ejpam-4971	196	16	β0	β0	ADJ
ejpam-4971	196	17	)	)	PUNCT
ejpam-4971	196	18	∈	∈	PROPN
ejpam-4971	196	19	r2	r2	NOUN
ejpam-4971	196	20	,	,	PUNCT
ejpam-4971	196	21	there	there	PRON
ejpam-4971	196	22	are	be	VERB
ejpam-4971	196	23	groups	group	NOUN
ejpam-4971	196	24	of	of	ADP
ejpam-4971	196	25	periodic	periodic	ADJ
ejpam-4971	196	26	orbits	orbit	NOUN
ejpam-4971	196	27	about	about	ADP
ejpam-4971	196	28	a	a	DET
ejpam-4971	196	29	center	center	NOUN
ejpam-4971	196	30	point	point	NOUN
ejpam-4971	196	31	e1	e1	NOUN
ejpam-4971	196	32	=	=	SYM
ejpam-4971	196	33	(	(	PUNCT
ejpam-4971	196	34	0	0	NUM
ejpam-4971	196	35	,	,	PUNCT
ejpam-4971	196	36	0	0	NUM
ejpam-4971	196	37	)	)	PUNCT
ejpam-4971	196	38	.	.	PUNCT
ejpam-4971	197	1	these	these	DET
ejpam-4971	197	2	orbits	orbit	NOUN
ejpam-4971	197	3	indicate	indicate	VERB
ejpam-4971	197	4	the	the	DET
ejpam-4971	197	5	existence	existence	NOUN
ejpam-4971	197	6	of	of	ADP
ejpam-4971	197	7	periodic	periodic	ADJ
ejpam-4971	197	8	traveling	travel	VERB
ejpam-4971	197	9	wave	wave	NOUN
ejpam-4971	197	10	solutions	solution	NOUN
ejpam-4971	197	11	,	,	PUNCT
ejpam-4971	197	12	as	as	SCONJ
ejpam-4971	197	13	appeared	appear	VERB
ejpam-4971	197	14	in	in	ADP
ejpam-4971	197	15	m.arab	m.arab	NOUN
ejpam-4971	197	16	/	/	SYM
ejpam-4971	197	17	eur	eur	NOUN
ejpam-4971	197	18	.	.	PUNCT
ejpam-4971	198	1	j.	j.	PROPN
ejpam-4971	198	2	pure	pure	PROPN
ejpam-4971	198	3	appl	appl	PROPN
ejpam-4971	198	4	.	.	PROPN
ejpam-4971	198	5	math	math	PROPN
ejpam-4971	198	6	,	,	PUNCT
ejpam-4971	198	7	16	16	NUM
ejpam-4971	198	8	(	(	PUNCT
ejpam-4971	198	9	4	4	NUM
ejpam-4971	198	10	)	)	PUNCT
ejpam-4971	198	11	(	(	PUNCT
ejpam-4971	198	12	2023	2023	NUM
ejpam-4971	198	13	)	)	PUNCT
ejpam-4971	198	14	,	,	PUNCT
ejpam-4971	198	15	2643	2643	NUM
ejpam-4971	198	16	-	-	SYM
ejpam-4971	198	17	2661	2661	NUM
ejpam-4971	198	18	2651	2651	NUM
ejpam-4971	198	19	fig	fig	NOUN
ejpam-4971	198	20	.	.	PUNCT
ejpam-4971	199	1	1(b	1(b	NUM
ejpam-4971	199	2	)	)	PUNCT
ejpam-4971	199	3	.	.	PUNCT
ejpam-4971	200	1	because	because	SCONJ
ejpam-4971	200	2	α0	α0	ADJ
ejpam-4971	200	3	>	>	X
ejpam-4971	200	4	0	0	NUM
ejpam-4971	200	5	,	,	PUNCT
ejpam-4971	200	6	β0	β0	NOUN
ejpam-4971	200	7	<	<	X
ejpam-4971	200	8	0	0	PROPN
ejpam-4971	200	9	,	,	PUNCT
ejpam-4971	200	10	the	the	DET
ejpam-4971	200	11	energy	energy	NOUN
ejpam-4971	200	12	constant	constant	ADJ
ejpam-4971	200	13	h	h	NOUN
ejpam-4971	200	14	should	should	AUX
ejpam-4971	200	15	be	be	AUX
ejpam-4971	200	16	positive	positive	ADJ
ejpam-4971	200	17	,	,	PUNCT
ejpam-4971	200	18	i.e.	i.e.	X
ejpam-4971	200	19	,	,	PUNCT
ejpam-4971	200	20	h	h	NOUN
ejpam-4971	200	21	>	>	X
ejpam-4971	200	22	0	0	NUM
ejpam-4971	200	23	,	,	PUNCT
ejpam-4971	200	24	and	and	CCONJ
ejpam-4971	200	25	so	so	ADV
ejpam-4971	200	26	the	the	DET
ejpam-4971	200	27	quartic	quartic	ADJ
ejpam-4971	200	28	polynomial	polynomial	ADJ
ejpam-4971	200	29	(	(	PUNCT
ejpam-4971	200	30	9	9	NUM
ejpam-4971	200	31	)	)	PUNCT
ejpam-4971	200	32	takes	take	VERB
ejpam-4971	200	33	the	the	DET
ejpam-4971	200	34	form	form	NOUN
ejpam-4971	200	35	p4(φ	p4(φ	NOUN
ejpam-4971	200	36	)	)	PUNCT
ejpam-4971	201	1	=	=	SYM
ejpam-4971	201	2	2	2	X
ejpam-4971	201	3	[	[	PUNCT
ejpam-4971	201	4	h−	h−	X
ejpam-4971	201	5	α0	α0	ADJ
ejpam-4971	201	6	2	2	NUM
ejpam-4971	201	7	φ2	φ2	NOUN
ejpam-4971	201	8	+	+	CCONJ
ejpam-4971	202	1	β0	β0	PROPN
ejpam-4971	202	2	4	4	NUM
ejpam-4971	202	3	φ4	φ4	NOUN
ejpam-4971	202	4	]	]	PUNCT
ejpam-4971	202	5	=	=	PUNCT
ejpam-4971	203	1	−β0	−β0	PROPN
ejpam-4971	203	2	2	2	NUM
ejpam-4971	203	3	(	(	PUNCT
ejpam-4971	203	4	φ2	φ2	PROPN
ejpam-4971	203	5	1	1	NUM
ejpam-4971	203	6	−	−	NOUN
ejpam-4971	203	7	φ2)(φ2	φ2)(φ2	X
ejpam-4971	203	8	2	2	NUM
ejpam-4971	203	9	+	+	CCONJ
ejpam-4971	203	10	φ2	φ2	PROPN
ejpam-4971	203	11	)	)	PUNCT
ejpam-4971	203	12	.	.	PUNCT
ejpam-4971	204	1	(	(	PUNCT
ejpam-4971	204	2	21	21	NUM
ejpam-4971	204	3	)	)	PUNCT
ejpam-4971	204	4	this	this	PRON
ejpam-4971	204	5	means	mean	VERB
ejpam-4971	204	6	that	that	SCONJ
ejpam-4971	204	7	the	the	DET
ejpam-4971	204	8	polynomial	polynomial	ADJ
ejpam-4971	204	9	(	(	PUNCT
ejpam-4971	204	10	21	21	NUM
ejpam-4971	204	11	)	)	PUNCT
ejpam-4971	204	12	has	have	VERB
ejpam-4971	204	13	two	two	NUM
ejpam-4971	204	14	real	real	ADJ
ejpam-4971	204	15	roots	root	NOUN
ejpam-4971	204	16	,	,	PUNCT
ejpam-4971	204	17	with	with	ADP
ejpam-4971	204	18	the	the	DET
ejpam-4971	204	19	other	other	ADJ
ejpam-4971	204	20	roots	root	NOUN
ejpam-4971	204	21	being	be	AUX
ejpam-4971	204	22	imaginary	imaginary	ADJ
ejpam-4971	204	23	.	.	PUNCT
ejpam-4971	205	1	inserting	insert	VERB
ejpam-4971	205	2	eq	eq	X
ejpam-4971	205	3	.	.	PUNCT
ejpam-4971	206	1	(	(	PUNCT
ejpam-4971	206	2	21	21	NUM
ejpam-4971	206	3	)	)	PUNCT
ejpam-4971	206	4	into	into	ADP
ejpam-4971	206	5	eq	eq	NOUN
ejpam-4971	206	6	.	.	PUNCT
ejpam-4971	207	1	(	(	PUNCT
ejpam-4971	207	2	8)	8)	NUM
ejpam-4971	207	3	,	,	PUNCT
ejpam-4971	207	4	we	we	PRON
ejpam-4971	207	5	obtain	obtain	VERB
ejpam-4971	207	6	φ(ξ	φ(ξ	NOUN
ejpam-4971	207	7	)	)	PUNCT
ejpam-4971	208	1	=	=	SYM
ejpam-4971	208	2	φ2√	φ2√	NOUN
ejpam-4971	208	3	φ2	φ2	NOUN
ejpam-4971	208	4	1	1	NUM
ejpam-4971	208	5	+	+	CCONJ
ejpam-4971	208	6	φ2	φ2	PROPN
ejpam-4971	208	7	2	2	NUM
ejpam-4971	208	8	sd	sd	NOUN
ejpam-4971	208	9	(	(	PUNCT
ejpam-4971	208	10	√	√	PROPN
ejpam-4971	208	11	−β0	−β0	PROPN
ejpam-4971	208	12	2	2	NUM
ejpam-4971	208	13	(	(	PUNCT
ejpam-4971	208	14	φ2	φ2	NOUN
ejpam-4971	208	15	1	1	NUM
ejpam-4971	208	16	+	+	CCONJ
ejpam-4971	208	17	φ2	φ2	PROPN
ejpam-4971	208	18	2)(ξ	2)(ξ	NUM
ejpam-4971	208	19	+	+	CCONJ
ejpam-4971	208	20	c	c	X
ejpam-4971	208	21	)	)	PUNCT
ejpam-4971	208	22	,	,	PUNCT
ejpam-4971	208	23	φ1√	φ1√	NOUN
ejpam-4971	208	24	φ2	φ2	NOUN
ejpam-4971	208	25	1	1	NUM
ejpam-4971	208	26	+	+	CCONJ
ejpam-4971	208	27	φ2	φ2	PROPN
ejpam-4971	208	28	2	2	NUM
ejpam-4971	208	29	)	)	PUNCT
ejpam-4971	208	30	.	.	PUNCT
ejpam-4971	209	1	(	(	PUNCT
ejpam-4971	209	2	22	22	NUM
ejpam-4971	209	3	)	)	PUNCT
ejpam-4971	209	4	4.3	4.3	NUM
ejpam-4971	209	5	.	.	PUNCT
ejpam-4971	210	1	case	case	NOUN
ejpam-4971	210	2	of	of	ADP
ejpam-4971	210	3	(	(	PUNCT
ejpam-4971	210	4	α0	α0	ADJ
ejpam-4971	210	5	,	,	PUNCT
ejpam-4971	210	6	β0	β0	ADJ
ejpam-4971	210	7	)	)	PUNCT
ejpam-4971	210	8	∈	∈	PROPN
ejpam-4971	210	9	r3	r3	PROPN
ejpam-4971	210	10	in	in	ADP
ejpam-4971	210	11	this	this	DET
ejpam-4971	210	12	case	case	NOUN
ejpam-4971	210	13	,	,	PUNCT
ejpam-4971	210	14	there	there	PRON
ejpam-4971	210	15	is	be	VERB
ejpam-4971	210	16	a	a	DET
ejpam-4971	210	17	unique	unique	ADJ
ejpam-4971	210	18	equilibrium	equilibrium	NOUN
ejpam-4971	210	19	(	(	PUNCT
ejpam-4971	210	20	saddle	saddle	NOUN
ejpam-4971	210	21	)	)	PUNCT
ejpam-4971	210	22	point	point	NOUN
ejpam-4971	210	23	.	.	PUNCT
ejpam-4971	211	1	the	the	DET
ejpam-4971	211	2	family	family	NOUN
ejpam-4971	211	3	of	of	ADP
ejpam-4971	211	4	orbits	orbit	NOUN
ejpam-4971	211	5	for	for	ADP
ejpam-4971	211	6	various	various	ADJ
ejpam-4971	211	7	energy	energy	NOUN
ejpam-4971	211	8	levels	level	NOUN
ejpam-4971	211	9	is	be	AUX
ejpam-4971	211	10	appeared	appear	VERB
ejpam-4971	211	11	in	in	ADP
ejpam-4971	211	12	fig	fig	NOUN
ejpam-4971	211	13	.	.	PUNCT
ejpam-4971	212	1	1(c	1(c	NUM
ejpam-4971	212	2	)	)	PUNCT
ejpam-4971	212	3	.	.	PUNCT
ejpam-4971	213	1	we	we	PRON
ejpam-4971	213	2	now	now	ADV
ejpam-4971	213	3	derive	derive	VERB
ejpam-4971	213	4	an	an	DET
ejpam-4971	213	5	explicit	explicit	ADJ
ejpam-4971	213	6	formulation	formulation	NOUN
ejpam-4971	213	7	for	for	ADP
ejpam-4971	213	8	the	the	DET
ejpam-4971	213	9	traveling	travel	VERB
ejpam-4971	213	10	wave	wave	NOUN
ejpam-4971	213	11	solution	solution	NOUN
ejpam-4971	213	12	at	at	ADP
ejpam-4971	213	13	these	these	DET
ejpam-4971	213	14	energy	energy	NOUN
ejpam-4971	213	15	levels	level	NOUN
ejpam-4971	213	16	.	.	PUNCT
ejpam-4971	214	1	•	•	NOUN
ejpam-4971	214	2	at	at	ADP
ejpam-4971	214	3	the	the	DET
ejpam-4971	214	4	zero	zero	NUM
ejpam-4971	214	5	energy	energy	NOUN
ejpam-4971	214	6	level	level	NOUN
ejpam-4971	214	7	,	,	PUNCT
ejpam-4971	214	8	there	there	PRON
ejpam-4971	214	9	exists	exist	VERB
ejpam-4971	214	10	an	an	DET
ejpam-4971	214	11	orbit	orbit	NOUN
ejpam-4971	214	12	that	that	PRON
ejpam-4971	214	13	passes	pass	VERB
ejpam-4971	214	14	through	through	ADP
ejpam-4971	214	15	the	the	DET
ejpam-4971	214	16	equilibrium	equilibrium	NOUN
ejpam-4971	214	17	point	point	NOUN
ejpam-4971	214	18	,	,	PUNCT
ejpam-4971	214	19	as	as	SCONJ
ejpam-4971	214	20	appeared	appear	VERB
ejpam-4971	214	21	in	in	ADP
ejpam-4971	214	22	fig	fig	NOUN
ejpam-4971	214	23	.	.	PUNCT
ejpam-4971	215	1	1(c	1(c	NUM
ejpam-4971	215	2	)	)	PUNCT
ejpam-4971	215	3	.	.	PUNCT
ejpam-4971	216	1	in	in	ADP
ejpam-4971	216	2	this	this	DET
ejpam-4971	216	3	case	case	NOUN
ejpam-4971	216	4	,	,	PUNCT
ejpam-4971	216	5	eq	eq	NOUN
ejpam-4971	216	6	.	.	PUNCT
ejpam-4971	217	1	(	(	PUNCT
ejpam-4971	217	2	8)	8)	NUM
ejpam-4971	217	3	gives	give	VERB
ejpam-4971	217	4	the	the	DET
ejpam-4971	217	5	following	follow	VERB
ejpam-4971	217	6	solitary	solitary	ADJ
ejpam-4971	217	7	traveling	travel	VERB
ejpam-4971	217	8	wave	wave	NOUN
ejpam-4971	217	9	solution	solution	NOUN
ejpam-4971	217	10	:	:	PUNCT
ejpam-4971	217	11	φ(ξ	φ(ξ	NOUN
ejpam-4971	217	12	)	)	PUNCT
ejpam-4971	217	13	=	=	SYM
ejpam-4971	217	14	√	√	PROPN
ejpam-4971	218	1	−α0sech	−α0sech	INTJ
ejpam-4971	218	2	(	(	PUNCT
ejpam-4971	218	3	√	√	PROPN
ejpam-4971	218	4	−α0β0	−α0β0	NUM
ejpam-4971	218	5	2	2	NUM
ejpam-4971	218	6	ξ	ξ	NOUN
ejpam-4971	218	7	+	+	SYM
ejpam-4971	218	8	c	c	NOUN
ejpam-4971	218	9	)	)	PUNCT
ejpam-4971	218	10	.	.	PUNCT
ejpam-4971	219	1	(	(	PUNCT
ejpam-4971	219	2	23	23	NUM
ejpam-4971	219	3	)	)	PUNCT
ejpam-4971	219	4	•	•	NOUN
ejpam-4971	219	5	at	at	ADP
ejpam-4971	219	6	positive	positive	ADJ
ejpam-4971	219	7	energy	energy	NOUN
ejpam-4971	219	8	levels	level	NOUN
ejpam-4971	219	9	h	h	VERB
ejpam-4971	219	10	>	>	X
ejpam-4971	219	11	0	0	NUM
ejpam-4971	219	12	,	,	PUNCT
ejpam-4971	219	13	there	there	PRON
ejpam-4971	219	14	exists	exist	VERB
ejpam-4971	219	15	a	a	DET
ejpam-4971	219	16	group	group	NOUN
ejpam-4971	219	17	of	of	ADP
ejpam-4971	219	18	unbounded	unbounded	ADJ
ejpam-4971	219	19	orbits	orbit	NOUN
ejpam-4971	219	20	,	,	PUNCT
ejpam-4971	219	21	as	as	SCONJ
ejpam-4971	219	22	appeared	appear	VERB
ejpam-4971	219	23	in	in	ADP
ejpam-4971	219	24	fig	fig	NOUN
ejpam-4971	219	25	.	.	PUNCT
ejpam-4971	220	1	1(c	1(c	NUM
ejpam-4971	220	2	)	)	PUNCT
ejpam-4971	220	3	.	.	PUNCT
ejpam-4971	221	1	under	under	ADP
ejpam-4971	221	2	these	these	DET
ejpam-4971	221	3	conditions	condition	NOUN
ejpam-4971	221	4	on	on	ADP
ejpam-4971	221	5	α0	α0	ADJ
ejpam-4971	221	6	,	,	PUNCT
ejpam-4971	221	7	β0	β0	NOUN
ejpam-4971	221	8	,	,	PUNCT
ejpam-4971	221	9	and	and	CCONJ
ejpam-4971	221	10	h	h	NOUN
ejpam-4971	221	11	,	,	PUNCT
ejpam-4971	221	12	the	the	DET
ejpam-4971	221	13	quartic	quartic	ADJ
ejpam-4971	221	14	polynomial	polynomial	ADJ
ejpam-4971	221	15	(	(	PUNCT
ejpam-4971	221	16	9	9	NUM
ejpam-4971	221	17	)	)	PUNCT
ejpam-4971	221	18	becomes	become	VERB
ejpam-4971	221	19	p4(φ	p4(φ	NOUN
ejpam-4971	221	20	)	)	PUNCT
ejpam-4971	222	1	=	=	SYM
ejpam-4971	222	2	β0	β0	NOUN
ejpam-4971	222	3	2	2	NUM
ejpam-4971	222	4	(	(	PUNCT
ejpam-4971	222	5	φ2	φ2	NOUN
ejpam-4971	222	6	1	1	NUM
ejpam-4971	222	7	+	+	CCONJ
ejpam-4971	222	8	φ2)(φ2	φ2)(φ2	X
ejpam-4971	222	9	2	2	NUM
ejpam-4971	222	10	+	+	CCONJ
ejpam-4971	222	11	φ2	φ2	PROPN
ejpam-4971	222	12	)	)	PUNCT
ejpam-4971	222	13	.	.	PUNCT
ejpam-4971	223	1	(	(	PUNCT
ejpam-4971	223	2	24	24	NUM
ejpam-4971	223	3	)	)	PUNCT
ejpam-4971	223	4	this	this	PRON
ejpam-4971	223	5	means	mean	VERB
ejpam-4971	223	6	that	that	SCONJ
ejpam-4971	223	7	there	there	PRON
ejpam-4971	223	8	are	be	VERB
ejpam-4971	223	9	four	four	NUM
ejpam-4971	223	10	purely	purely	ADV
ejpam-4971	223	11	imaginary	imaginary	ADJ
ejpam-4971	223	12	roots	root	NOUN
ejpam-4971	223	13	.	.	PUNCT
ejpam-4971	224	1	inserting	insert	VERB
ejpam-4971	224	2	eq	eq	X
ejpam-4971	224	3	.	.	PUNCT
ejpam-4971	225	1	(	(	PUNCT
ejpam-4971	225	2	24	24	NUM
ejpam-4971	225	3	)	)	PUNCT
ejpam-4971	225	4	into	into	ADP
ejpam-4971	225	5	eq	eq	NOUN
ejpam-4971	225	6	.	.	PUNCT
ejpam-4971	226	1	(	(	PUNCT
ejpam-4971	226	2	8)	8)	NUM
ejpam-4971	226	3	,	,	PUNCT
ejpam-4971	226	4	we	we	PRON
ejpam-4971	226	5	obtain	obtain	VERB
ejpam-4971	226	6	φ(ξ	φ(ξ	NOUN
ejpam-4971	226	7	)	)	PUNCT
ejpam-4971	227	1	=	=	PUNCT
ejpam-4971	227	2	−φ1	−φ1	PROPN
ejpam-4971	227	3	sn	sn	PROPN
ejpam-4971	227	4	(	(	PUNCT
ejpam-4971	227	5	√	√	PROPN
ejpam-4971	227	6	β0	β0	PROPN
ejpam-4971	227	7	2	2	NUM
ejpam-4971	227	8	φ2(ξ	φ2(ξ	NOUN
ejpam-4971	227	9	+	+	CCONJ
ejpam-4971	227	10	c	c	NOUN
ejpam-4971	227	11	)	)	PUNCT
ejpam-4971	227	12	,	,	PUNCT
ejpam-4971	227	13	√	√	PROPN
ejpam-4971	227	14	1−	1−	NUM
ejpam-4971	227	15	φ2	φ2	PROPN
ejpam-4971	227	16	1	1	NUM
ejpam-4971	227	17	φ2	φ2	PROPN
ejpam-4971	227	18	2	2	NUM
ejpam-4971	227	19	)	)	PUNCT
ejpam-4971	227	20	cn	cn	PROPN
ejpam-4971	227	21	(	(	PUNCT
ejpam-4971	227	22	√	√	PROPN
ejpam-4971	227	23	β0	β0	PROPN
ejpam-4971	227	24	2	2	NUM
ejpam-4971	227	25	φ2(ξ	φ2(ξ	NOUN
ejpam-4971	227	26	+	+	CCONJ
ejpam-4971	227	27	c	c	NOUN
ejpam-4971	227	28	)	)	PUNCT
ejpam-4971	227	29	,	,	PUNCT
ejpam-4971	227	30	√	√	PROPN
ejpam-4971	227	31	1−	1−	NUM
ejpam-4971	227	32	φ2	φ2	PROPN
ejpam-4971	227	33	1	1	NUM
ejpam-4971	227	34	φ2	φ2	PROPN
ejpam-4971	227	35	2	2	NUM
ejpam-4971	227	36	)	)	PUNCT
ejpam-4971	227	37	.	.	PUNCT
ejpam-4971	228	1	(	(	PUNCT
ejpam-4971	228	2	25	25	NUM
ejpam-4971	228	3	)	)	PUNCT
ejpam-4971	228	4	•	•	NOUN
ejpam-4971	228	5	at	at	ADP
ejpam-4971	228	6	negative	negative	ADJ
ejpam-4971	228	7	energy	energy	NOUN
ejpam-4971	228	8	levels	level	NOUN
ejpam-4971	228	9	,	,	PUNCT
ejpam-4971	228	10	there	there	PRON
ejpam-4971	228	11	exists	exist	VERB
ejpam-4971	228	12	a	a	DET
ejpam-4971	228	13	group	group	NOUN
ejpam-4971	228	14	of	of	ADP
ejpam-4971	228	15	orbits	orbit	NOUN
ejpam-4971	228	16	that	that	PRON
ejpam-4971	228	17	cut	cut	VERB
ejpam-4971	228	18	off	off	ADP
ejpam-4971	228	19	the	the	DET
ejpam-4971	228	20	φ	φ	PROPN
ejpam-4971	228	21	axis	axis	NOUN
ejpam-4971	228	22	,	,	PUNCT
ejpam-4971	228	23	as	as	SCONJ
ejpam-4971	228	24	appeared	appear	VERB
ejpam-4971	228	25	in	in	ADP
ejpam-4971	228	26	fig	fig	NOUN
ejpam-4971	228	27	.	.	PUNCT
ejpam-4971	229	1	1(c	1(c	NUM
ejpam-4971	229	2	)	)	PUNCT
ejpam-4971	229	3	.	.	PUNCT
ejpam-4971	230	1	thus	thus	ADV
ejpam-4971	230	2	,	,	PUNCT
ejpam-4971	230	3	the	the	DET
ejpam-4971	230	4	polynomial	polynomial	ADJ
ejpam-4971	230	5	(	(	PUNCT
ejpam-4971	230	6	9	9	NUM
ejpam-4971	230	7	)	)	PUNCT
ejpam-4971	230	8	takes	take	VERB
ejpam-4971	230	9	the	the	DET
ejpam-4971	230	10	form	form	NOUN
ejpam-4971	230	11	p4(φ	p4(φ	NOUN
ejpam-4971	230	12	)	)	PUNCT
ejpam-4971	230	13	=	=	SYM
ejpam-4971	231	1	β0	β0	NOUN
ejpam-4971	231	2	2	2	NUM
ejpam-4971	231	3	(	(	PUNCT
ejpam-4971	231	4	φ2	φ2	PROPN
ejpam-4971	231	5	−	−	PROPN
ejpam-4971	231	6	φ2	φ2	PROPN
ejpam-4971	231	7	1)(φ	1)(φ	NUM
ejpam-4971	231	8	2	2	NUM
ejpam-4971	231	9	+	+	CCONJ
ejpam-4971	231	10	φ2	φ2	PROPN
ejpam-4971	231	11	2	2	NUM
ejpam-4971	231	12	)	)	PUNCT
ejpam-4971	231	13	.	.	PUNCT
ejpam-4971	232	1	(	(	PUNCT
ejpam-4971	232	2	26	26	NUM
ejpam-4971	232	3	)	)	PUNCT
ejpam-4971	232	4	m.arab	m.arab	NOUN
ejpam-4971	232	5	/	/	SYM
ejpam-4971	232	6	eur	eur	NOUN
ejpam-4971	232	7	.	.	PUNCT
ejpam-4971	233	1	j.	j.	PROPN
ejpam-4971	233	2	pure	pure	PROPN
ejpam-4971	233	3	appl	appl	PROPN
ejpam-4971	233	4	.	.	PROPN
ejpam-4971	233	5	math	math	PROPN
ejpam-4971	233	6	,	,	PUNCT
ejpam-4971	233	7	16	16	NUM
ejpam-4971	233	8	(	(	PUNCT
ejpam-4971	233	9	4	4	NUM
ejpam-4971	233	10	)	)	PUNCT
ejpam-4971	233	11	(	(	PUNCT
ejpam-4971	233	12	2023	2023	NUM
ejpam-4971	233	13	)	)	PUNCT
ejpam-4971	233	14	,	,	PUNCT
ejpam-4971	233	15	2643	2643	NUM
ejpam-4971	233	16	-	-	SYM
ejpam-4971	233	17	2661	2661	NUM
ejpam-4971	233	18	2652	2652	NUM
ejpam-4971	233	19	inserting	insert	VERB
ejpam-4971	233	20	eq	eq	ADP
ejpam-4971	233	21	.	.	PUNCT
ejpam-4971	234	1	(	(	PUNCT
ejpam-4971	234	2	26	26	NUM
ejpam-4971	234	3	)	)	PUNCT
ejpam-4971	234	4	into	into	ADP
ejpam-4971	234	5	eq	eq	NOUN
ejpam-4971	234	6	.	.	PUNCT
ejpam-4971	235	1	(	(	PUNCT
ejpam-4971	235	2	8)	8)	NUM
ejpam-4971	235	3	,	,	PUNCT
ejpam-4971	235	4	the	the	DET
ejpam-4971	235	5	parametric	parametric	ADJ
ejpam-4971	235	6	representation	representation	NOUN
ejpam-4971	235	7	of	of	ADP
ejpam-4971	235	8	the	the	DET
ejpam-4971	235	9	traveling	travel	VERB
ejpam-4971	235	10	wave	wave	NOUN
ejpam-4971	235	11	solution	solution	NOUN
ejpam-4971	235	12	for	for	ADP
ejpam-4971	235	13	eq	eq	PROPN
ejpam-4971	235	14	.	.	PUNCT
ejpam-4971	236	1	(	(	PUNCT
ejpam-4971	236	2	1	1	X
ejpam-4971	236	3	)	)	PUNCT
ejpam-4971	236	4	is	be	AUX
ejpam-4971	236	5	φ(ξ	φ(ξ	PROPN
ejpam-4971	236	6	)	)	PUNCT
ejpam-4971	236	7	=	=	SYM
ejpam-4971	236	8	cn	cn	PROPN
ejpam-4971	236	9	(	(	PUNCT
ejpam-4971	236	10	√	√	PROPN
ejpam-4971	236	11	β0	β0	NOUN
ejpam-4971	236	12	2	2	NUM
ejpam-4971	236	13	(	(	PUNCT
ejpam-4971	236	14	φ2	φ2	NOUN
ejpam-4971	236	15	1	1	NUM
ejpam-4971	236	16	+	+	CCONJ
ejpam-4971	236	17	φ2	φ2	PROPN
ejpam-4971	236	18	2)(ξ	2)(ξ	NUM
ejpam-4971	236	19	+	+	CCONJ
ejpam-4971	236	20	c	c	X
ejpam-4971	236	21	)	)	PUNCT
ejpam-4971	236	22	,	,	PUNCT
ejpam-4971	236	23	φ2√	φ2√	PROPN
ejpam-4971	236	24	φ2	φ2	PROPN
ejpam-4971	236	25	1+φ2	1+φ2	NUM
ejpam-4971	236	26	2	2	NUM
ejpam-4971	236	27	)	)	PUNCT
ejpam-4971	236	28	dn2	dn2	NOUN
ejpam-4971	236	29	(	(	PUNCT
ejpam-4971	236	30	√	√	PROPN
ejpam-4971	236	31	β0	β0	NOUN
ejpam-4971	236	32	2	2	NUM
ejpam-4971	236	33	(	(	PUNCT
ejpam-4971	236	34	φ2	φ2	NOUN
ejpam-4971	236	35	1	1	NUM
ejpam-4971	236	36	+	+	CCONJ
ejpam-4971	236	37	φ2	φ2	PROPN
ejpam-4971	236	38	2)(ξ	2)(ξ	NUM
ejpam-4971	236	39	+	+	CCONJ
ejpam-4971	236	40	c	c	X
ejpam-4971	236	41	)	)	PUNCT
ejpam-4971	236	42	,	,	PUNCT
ejpam-4971	236	43	φ2√	φ2√	PROPN
ejpam-4971	236	44	φ2	φ2	PROPN
ejpam-4971	236	45	1+φ2	1+φ2	NUM
ejpam-4971	236	46	2	2	NUM
ejpam-4971	236	47	)	)	PUNCT
ejpam-4971	236	48	.	.	PUNCT
ejpam-4971	237	1	(	(	PUNCT
ejpam-4971	237	2	27	27	NUM
ejpam-4971	237	3	)	)	PUNCT
ejpam-4971	237	4	4.4	4.4	NUM
ejpam-4971	237	5	.	.	PUNCT
ejpam-4971	238	1	case	case	NOUN
ejpam-4971	238	2	of	of	ADP
ejpam-4971	238	3	(	(	PUNCT
ejpam-4971	238	4	α0	α0	ADJ
ejpam-4971	238	5	,	,	PUNCT
ejpam-4971	238	6	β0	β0	ADJ
ejpam-4971	238	7	)	)	PUNCT
ejpam-4971	238	8	∈	∈	PROPN
ejpam-4971	238	9	r4	r4	NOUN
ejpam-4971	238	10	under	under	ADP
ejpam-4971	238	11	these	these	DET
ejpam-4971	238	12	conditions	condition	NOUN
ejpam-4971	238	13	,	,	PUNCT
ejpam-4971	238	14	the	the	DET
ejpam-4971	238	15	phase	phase	NOUN
ejpam-4971	238	16	portrait	portrait	NOUN
ejpam-4971	238	17	for	for	ADP
ejpam-4971	238	18	the	the	DET
ejpam-4971	238	19	dynamical	dynamical	ADJ
ejpam-4971	238	20	system	system	NOUN
ejpam-4971	238	21	(	(	PUNCT
ejpam-4971	238	22	4	4	NUM
ejpam-4971	238	23	)	)	PUNCT
ejpam-4971	238	24	has	have	VERB
ejpam-4971	238	25	three	three	NUM
ejpam-4971	238	26	equilibrium	equilibrium	NOUN
ejpam-4971	238	27	points	point	NOUN
ejpam-4971	238	28	,	,	PUNCT
ejpam-4971	238	29	in	in	ADP
ejpam-4971	238	30	which	which	PRON
ejpam-4971	238	31	e1	e1	NOUN
ejpam-4971	238	32	is	be	AUX
ejpam-4971	238	33	a	a	DET
ejpam-4971	238	34	saddle	saddle	NOUN
ejpam-4971	238	35	and	and	CCONJ
ejpam-4971	238	36	e2,3	e2,3	NOUN
ejpam-4971	238	37	are	be	AUX
ejpam-4971	238	38	centers	center	NOUN
ejpam-4971	238	39	.	.	PUNCT
ejpam-4971	239	1	we	we	PRON
ejpam-4971	239	2	now	now	ADV
ejpam-4971	239	3	study	study	VERB
ejpam-4971	239	4	the	the	DET
ejpam-4971	239	5	traveling	travel	VERB
ejpam-4971	239	6	wave	wave	NOUN
ejpam-4971	239	7	solutions	solution	NOUN
ejpam-4971	239	8	according	accord	VERB
ejpam-4971	239	9	to	to	ADP
ejpam-4971	239	10	the	the	DET
ejpam-4971	239	11	value	value	NOUN
ejpam-4971	239	12	of	of	ADP
ejpam-4971	239	13	the	the	DET
ejpam-4971	239	14	energy	energy	NOUN
ejpam-4971	239	15	constant	constant	ADJ
ejpam-4971	239	16	h.	h.	PROPN
ejpam-4971	239	17	•	•	NOUN
ejpam-4971	239	18	at	at	ADP
ejpam-4971	239	19	the	the	DET
ejpam-4971	239	20	zero	zero	NUM
ejpam-4971	239	21	energy	energy	NOUN
ejpam-4971	239	22	level	level	NOUN
ejpam-4971	239	23	,	,	PUNCT
ejpam-4971	239	24	there	there	PRON
ejpam-4971	239	25	is	be	VERB
ejpam-4971	239	26	a	a	DET
ejpam-4971	239	27	certain	certain	ADJ
ejpam-4971	239	28	orbit	orbit	NOUN
ejpam-4971	239	29	that	that	PRON
ejpam-4971	239	30	repeatedly	repeatedly	ADV
ejpam-4971	239	31	passes	pass	VERB
ejpam-4971	239	32	through	through	ADP
ejpam-4971	239	33	the	the	DET
ejpam-4971	239	34	saddle	saddle	NOUN
ejpam-4971	239	35	point	point	NOUN
ejpam-4971	239	36	.	.	PUNCT
ejpam-4971	240	1	this	this	PRON
ejpam-4971	240	2	is	be	AUX
ejpam-4971	240	3	a	a	DET
ejpam-4971	240	4	separatrix	separatrix	NOUN
ejpam-4971	240	5	closed	closed	ADJ
ejpam-4971	240	6	loop	loop	NOUN
ejpam-4971	240	7	(	(	PUNCT
ejpam-4971	240	8	homoclinic	homoclinic	ADJ
ejpam-4971	240	9	loop	loop	NOUN
ejpam-4971	240	10	)	)	PUNCT
ejpam-4971	240	11	.	.	PUNCT
ejpam-4971	241	1	the	the	DET
ejpam-4971	241	2	existence	existence	NOUN
ejpam-4971	241	3	of	of	ADP
ejpam-4971	241	4	such	such	DET
ejpam-4971	241	5	an	an	DET
ejpam-4971	241	6	orbit	orbit	NOUN
ejpam-4971	241	7	indicates	indicate	VERB
ejpam-4971	241	8	a	a	DET
ejpam-4971	241	9	solitary	solitary	ADJ
ejpam-4971	241	10	wave	wave	NOUN
ejpam-4971	241	11	solution	solution	NOUN
ejpam-4971	241	12	for	for	ADP
ejpam-4971	241	13	eq	eq	PROPN
ejpam-4971	241	14	.	.	PUNCT
ejpam-4971	242	1	(	(	PUNCT
ejpam-4971	242	2	1	1	NUM
ejpam-4971	242	3	)	)	PUNCT
ejpam-4971	242	4	.	.	PUNCT
ejpam-4971	243	1	figure	figure	NOUN
ejpam-4971	243	2	1(d	1(d	NUM
ejpam-4971	243	3	)	)	PUNCT
ejpam-4971	243	4	clearly	clearly	ADV
ejpam-4971	243	5	shows	show	VERB
ejpam-4971	243	6	that	that	SCONJ
ejpam-4971	243	7	polynomial	polynomial	ADJ
ejpam-4971	243	8	(	(	PUNCT
ejpam-4971	243	9	9	9	NUM
ejpam-4971	243	10	)	)	PUNCT
ejpam-4971	243	11	has	have	VERB
ejpam-4971	243	12	4	4	NUM
ejpam-4971	243	13	real	real	ADJ
ejpam-4971	243	14	roots	root	NOUN
ejpam-4971	243	15	,	,	PUNCT
ejpam-4971	243	16	and	and	CCONJ
ejpam-4971	243	17	could	could	AUX
ejpam-4971	243	18	be	be	AUX
ejpam-4971	243	19	written	write	VERB
ejpam-4971	243	20	in	in	ADP
ejpam-4971	243	21	the	the	DET
ejpam-4971	243	22	form	form	NOUN
ejpam-4971	243	23	p4(φ	p4(φ	NOUN
ejpam-4971	243	24	)	)	PUNCT
ejpam-4971	244	1	=	=	SYM
ejpam-4971	244	2	−β0	−β0	PROPN
ejpam-4971	244	3	2	2	NUM
ejpam-4971	244	4	φ2	φ2	NOUN
ejpam-4971	244	5	[	[	PUNCT
ejpam-4971	244	6	2α0	2α0	NUM
ejpam-4971	244	7	β0	β0	NUM
ejpam-4971	244	8	−	−	PROPN
ejpam-4971	244	9	φ2	φ2	PROPN
ejpam-4971	244	10	]	]	PUNCT
ejpam-4971	244	11	.	.	PUNCT
ejpam-4971	245	1	(	(	PUNCT
ejpam-4971	245	2	28	28	NUM
ejpam-4971	245	3	)	)	PUNCT
ejpam-4971	245	4	using	use	VERB
ejpam-4971	245	5	eqs	eqs	PROPN
ejpam-4971	245	6	.	.	PUNCT
ejpam-4971	246	1	(	(	PUNCT
ejpam-4971	246	2	28	28	NUM
ejpam-4971	246	3	)	)	PUNCT
ejpam-4971	246	4	and	and	CCONJ
ejpam-4971	246	5	(	(	PUNCT
ejpam-4971	246	6	8)	8)	NUM
ejpam-4971	246	7	,	,	PUNCT
ejpam-4971	246	8	we	we	PRON
ejpam-4971	246	9	obtain	obtain	VERB
ejpam-4971	246	10	φ(ξ	φ(ξ	NOUN
ejpam-4971	246	11	)	)	PUNCT
ejpam-4971	246	12	=	=	SYM
ejpam-4971	246	13	√	√	NUM
ejpam-4971	246	14	2α0	2α0	NUM
ejpam-4971	246	15	β0	β0	PROPN
ejpam-4971	246	16	sech	sech	NOUN
ejpam-4971	246	17	√	√	PROPN
ejpam-4971	246	18	−α0(ξ	−α0(ξ	PROPN
ejpam-4971	246	19	+	+	CCONJ
ejpam-4971	246	20	c	c	NOUN
ejpam-4971	246	21	)	)	PUNCT
ejpam-4971	246	22	.	.	PUNCT
ejpam-4971	247	1	(	(	PUNCT
ejpam-4971	247	2	29	29	NUM
ejpam-4971	247	3	)	)	PUNCT
ejpam-4971	247	4	•	•	NOUN
ejpam-4971	247	5	at	at	ADP
ejpam-4971	247	6	negative	negative	ADJ
ejpam-4971	247	7	energy	energy	NOUN
ejpam-4971	247	8	levels	level	NOUN
ejpam-4971	247	9	,	,	PUNCT
ejpam-4971	247	10	there	there	PRON
ejpam-4971	247	11	exists	exist	VERB
ejpam-4971	247	12	a	a	DET
ejpam-4971	247	13	group	group	NOUN
ejpam-4971	247	14	of	of	ADP
ejpam-4971	247	15	periodic	periodic	ADJ
ejpam-4971	247	16	orbits	orbit	NOUN
ejpam-4971	247	17	around	around	ADP
ejpam-4971	247	18	the	the	DET
ejpam-4971	247	19	two	two	NUM
ejpam-4971	247	20	centers	center	NOUN
ejpam-4971	247	21	,	,	PUNCT
ejpam-4971	247	22	as	as	SCONJ
ejpam-4971	247	23	appeared	appear	VERB
ejpam-4971	247	24	in	in	ADP
ejpam-4971	247	25	fig	fig	NOUN
ejpam-4971	247	26	.	.	PUNCT
ejpam-4971	248	1	1(d	1(d	NUM
ejpam-4971	248	2	)	)	PUNCT
ejpam-4971	248	3	.	.	PUNCT
ejpam-4971	249	1	these	these	DET
ejpam-4971	249	2	orbits	orbit	NOUN
ejpam-4971	249	3	correspond	correspond	VERB
ejpam-4971	249	4	to	to	ADP
ejpam-4971	249	5	periodic	periodic	ADJ
ejpam-4971	249	6	traveling	travel	VERB
ejpam-4971	249	7	wave	wave	NOUN
ejpam-4971	249	8	solutions	solution	NOUN
ejpam-4971	249	9	.	.	PUNCT
ejpam-4971	250	1	such	such	ADJ
ejpam-4971	250	2	orbits	orbit	NOUN
ejpam-4971	250	3	cut	cut	VERB
ejpam-4971	250	4	off	off	ADP
ejpam-4971	250	5	the	the	DET
ejpam-4971	250	6	φ	φ	PROPN
ejpam-4971	250	7	axis	axis	NOUN
ejpam-4971	250	8	at	at	ADP
ejpam-4971	250	9	four	four	NUM
ejpam-4971	250	10	points	point	NOUN
ejpam-4971	250	11	,	,	PUNCT
ejpam-4971	250	12	and	and	CCONJ
ejpam-4971	250	13	so	so	ADV
ejpam-4971	250	14	the	the	DET
ejpam-4971	250	15	quartic	quartic	ADJ
ejpam-4971	250	16	polynomial	polynomial	ADJ
ejpam-4971	250	17	(	(	PUNCT
ejpam-4971	250	18	9	9	NUM
ejpam-4971	250	19	)	)	PUNCT
ejpam-4971	250	20	has	have	VERB
ejpam-4971	250	21	four	four	NUM
ejpam-4971	250	22	real	real	ADJ
ejpam-4971	250	23	roots	root	NOUN
ejpam-4971	250	24	,	,	PUNCT
ejpam-4971	250	25	±φ1,±φ2	±φ1,±φ2	NOUN
ejpam-4971	250	26	.	.	PUNCT
ejpam-4971	251	1	thus	thus	ADV
ejpam-4971	251	2	,	,	PUNCT
ejpam-4971	251	3	the	the	DET
ejpam-4971	251	4	polynomial	polynomial	ADJ
ejpam-4971	251	5	(	(	PUNCT
ejpam-4971	251	6	8)	8)	NUM
ejpam-4971	251	7	admits	admit	VERB
ejpam-4971	251	8	the	the	DET
ejpam-4971	251	9	form	form	NOUN
ejpam-4971	251	10	p4(φ	p4(φ	NOUN
ejpam-4971	251	11	)	)	PUNCT
ejpam-4971	251	12	=	=	SYM
ejpam-4971	251	13	−β0	−β0	PROPN
ejpam-4971	251	14	2	2	NUM
ejpam-4971	251	15	(	(	PUNCT
ejpam-4971	251	16	φ2	φ2	PROPN
ejpam-4971	251	17	1	1	NUM
ejpam-4971	251	18	−	−	NOUN
ejpam-4971	251	19	φ2)(φ2	φ2)(φ2	NOUN
ejpam-4971	251	20	−	−	PROPN
ejpam-4971	251	21	φ2	φ2	PROPN
ejpam-4971	251	22	2	2	NUM
ejpam-4971	251	23	)	)	PUNCT
ejpam-4971	251	24	.	.	PUNCT
ejpam-4971	252	1	(	(	PUNCT
ejpam-4971	252	2	30	30	X
ejpam-4971	252	3	)	)	PUNCT
ejpam-4971	252	4	using	use	VERB
ejpam-4971	252	5	eqs	eqs	PROPN
ejpam-4971	252	6	.	.	PUNCT
ejpam-4971	253	1	(	(	PUNCT
ejpam-4971	253	2	30	30	NUM
ejpam-4971	253	3	)	)	PUNCT
ejpam-4971	253	4	and	and	CCONJ
ejpam-4971	253	5	(	(	PUNCT
ejpam-4971	253	6	8)	8)	NUM
ejpam-4971	253	7	,	,	PUNCT
ejpam-4971	253	8	we	we	PRON
ejpam-4971	253	9	obtain	obtain	VERB
ejpam-4971	253	10	the	the	DET
ejpam-4971	253	11	periodic	periodic	ADJ
ejpam-4971	253	12	traveling	travel	VERB
ejpam-4971	253	13	wave	wave	NOUN
ejpam-4971	253	14	solution	solution	NOUN
ejpam-4971	253	15	φ(ξ	φ(ξ	NOUN
ejpam-4971	253	16	)	)	PUNCT
ejpam-4971	253	17	=	=	SYM
ejpam-4971	254	1	φ2	φ2	PROPN
ejpam-4971	254	2	dn	dn	PROPN
ejpam-4971	254	3	(	(	PUNCT
ejpam-4971	254	4	√	√	PROPN
ejpam-4971	254	5	−β0	−β0	PROPN
ejpam-4971	254	6	2	2	NUM
ejpam-4971	254	7	φ1(ξ	φ1(ξ	VERB
ejpam-4971	254	8	+	+	NUM
ejpam-4971	254	9	c	c	NOUN
ejpam-4971	254	10	)	)	PUNCT
ejpam-4971	254	11	,	,	PUNCT
ejpam-4971	254	12	√	√	PROPN
ejpam-4971	254	13	1−	1−	NUM
ejpam-4971	254	14	φ2	φ2	PROPN
ejpam-4971	254	15	2	2	NUM
ejpam-4971	254	16	φ2	φ2	NOUN
ejpam-4971	254	17	1	1	NUM
ejpam-4971	254	18	)	)	PUNCT
ejpam-4971	254	19	.	.	PUNCT
ejpam-4971	255	1	(	(	PUNCT
ejpam-4971	255	2	31	31	NUM
ejpam-4971	255	3	)	)	PUNCT
ejpam-4971	255	4	•	•	NOUN
ejpam-4971	255	5	at	at	ADP
ejpam-4971	255	6	positive	positive	ADJ
ejpam-4971	255	7	energy	energy	NOUN
ejpam-4971	255	8	levels	level	NOUN
ejpam-4971	255	9	,	,	PUNCT
ejpam-4971	255	10	there	there	PRON
ejpam-4971	255	11	exists	exist	VERB
ejpam-4971	255	12	a	a	DET
ejpam-4971	255	13	group	group	NOUN
ejpam-4971	255	14	of	of	ADP
ejpam-4971	255	15	orbits	orbit	NOUN
ejpam-4971	255	16	that	that	PRON
ejpam-4971	255	17	cut	cut	VERB
ejpam-4971	255	18	off	off	ADP
ejpam-4971	255	19	the	the	DET
ejpam-4971	255	20	φ	φ	PROPN
ejpam-4971	255	21	axis	axis	NOUN
ejpam-4971	255	22	at	at	ADP
ejpam-4971	255	23	two	two	NUM
ejpam-4971	255	24	points	point	NOUN
ejpam-4971	255	25	.	.	PUNCT
ejpam-4971	256	1	thus	thus	ADV
ejpam-4971	256	2	,	,	PUNCT
ejpam-4971	256	3	the	the	DET
ejpam-4971	256	4	polynomial	polynomial	ADJ
ejpam-4971	256	5	(	(	PUNCT
ejpam-4971	256	6	9	9	NUM
ejpam-4971	256	7	)	)	PUNCT
ejpam-4971	256	8	has	have	VERB
ejpam-4971	256	9	2	2	NUM
ejpam-4971	256	10	real	real	ADJ
ejpam-4971	256	11	roots	root	NOUN
ejpam-4971	256	12	±φ1	±φ1	NOUN
ejpam-4971	256	13	due	due	ADP
ejpam-4971	256	14	to	to	ADP
ejpam-4971	256	15	the	the	DET
ejpam-4971	256	16	symmetry	symmetry	NOUN
ejpam-4971	256	17	about	about	ADP
ejpam-4971	256	18	the	the	DET
ejpam-4971	256	19	φ	φ	PROPN
ejpam-4971	256	20	=	=	SYM
ejpam-4971	256	21	0	0	NUM
ejpam-4971	256	22	axis	axis	NOUN
ejpam-4971	257	1	[	[	X
ejpam-4971	257	2	see	see	VERB
ejpam-4971	257	3	fig	fig	NOUN
ejpam-4971	257	4	.	.	PUNCT
ejpam-4971	258	1	1(d	1(d	NUM
ejpam-4971	258	2	)	)	PUNCT
ejpam-4971	258	3	]	]	PUNCT
ejpam-4971	258	4	.	.	PUNCT
ejpam-4971	259	1	in	in	ADP
ejpam-4971	259	2	this	this	DET
ejpam-4971	259	3	case	case	NOUN
ejpam-4971	259	4	,	,	PUNCT
ejpam-4971	259	5	the	the	DET
ejpam-4971	259	6	polynomial	polynomial	ADJ
ejpam-4971	259	7	(	(	PUNCT
ejpam-4971	259	8	9	9	NUM
ejpam-4971	259	9	)	)	PUNCT
ejpam-4971	259	10	takes	take	VERB
ejpam-4971	259	11	the	the	DET
ejpam-4971	259	12	form	form	NOUN
ejpam-4971	259	13	p4(φ	p4(φ	NOUN
ejpam-4971	259	14	)	)	PUNCT
ejpam-4971	259	15	=	=	SYM
ejpam-4971	259	16	−β0	−β0	PROPN
ejpam-4971	259	17	2	2	NUM
ejpam-4971	259	18	(	(	PUNCT
ejpam-4971	259	19	φ2	φ2	NOUN
ejpam-4971	259	20	2	2	NUM
ejpam-4971	259	21	+	+	CCONJ
ejpam-4971	259	22	φ2)(φ2	φ2)(φ2	X
ejpam-4971	259	23	1	1	NUM
ejpam-4971	259	24	−	−	PROPN
ejpam-4971	259	25	φ2	φ2	PROPN
ejpam-4971	259	26	)	)	PUNCT
ejpam-4971	259	27	.	.	PUNCT
ejpam-4971	260	1	(	(	PUNCT
ejpam-4971	260	2	32	32	NUM
ejpam-4971	260	3	)	)	PUNCT
ejpam-4971	260	4	employing	employ	VERB
ejpam-4971	260	5	eqs	eqs	PROPN
ejpam-4971	260	6	.	.	PUNCT
ejpam-4971	261	1	(	(	PUNCT
ejpam-4971	261	2	8)	8)	NUM
ejpam-4971	261	3	and	and	CCONJ
ejpam-4971	261	4	(	(	PUNCT
ejpam-4971	261	5	32	32	NUM
ejpam-4971	261	6	)	)	PUNCT
ejpam-4971	261	7	,	,	PUNCT
ejpam-4971	261	8	we	we	PRON
ejpam-4971	261	9	obtain	obtain	VERB
ejpam-4971	261	10	φ(ξ	φ(ξ	NOUN
ejpam-4971	261	11	)	)	PUNCT
ejpam-4971	262	1	=	=	SYM
ejpam-4971	262	2	φ2√	φ2√	NOUN
ejpam-4971	262	3	φ2	φ2	NOUN
ejpam-4971	262	4	1	1	NUM
ejpam-4971	262	5	+	+	CCONJ
ejpam-4971	262	6	φ2	φ2	PROPN
ejpam-4971	262	7	2	2	NUM
ejpam-4971	262	8	sd	sd	NOUN
ejpam-4971	262	9	(	(	PUNCT
ejpam-4971	262	10	√	√	PROPN
ejpam-4971	262	11	−β0	−β0	PROPN
ejpam-4971	262	12	2	2	NUM
ejpam-4971	262	13	(	(	PUNCT
ejpam-4971	262	14	φ2	φ2	NOUN
ejpam-4971	262	15	1	1	NUM
ejpam-4971	262	16	+	+	CCONJ
ejpam-4971	262	17	φ2	φ2	PROPN
ejpam-4971	262	18	2)(ξ	2)(ξ	NUM
ejpam-4971	262	19	+	+	CCONJ
ejpam-4971	262	20	c),−	c),−	PROPN
ejpam-4971	262	21	φ1√	φ1√	ADJ
ejpam-4971	262	22	φ2	φ2	NOUN
ejpam-4971	262	23	1	1	NUM
ejpam-4971	262	24	+	+	CCONJ
ejpam-4971	262	25	φ2	φ2	PROPN
ejpam-4971	262	26	2	2	NUM
ejpam-4971	262	27	)	)	PUNCT
ejpam-4971	262	28	.	.	PUNCT
ejpam-4971	263	1	(	(	PUNCT
ejpam-4971	263	2	33	33	NUM
ejpam-4971	263	3	)	)	PUNCT
ejpam-4971	263	4	m.arab	m.arab	NOUN
ejpam-4971	263	5	/	/	SYM
ejpam-4971	263	6	eur	eur	NOUN
ejpam-4971	263	7	.	.	PUNCT
ejpam-4971	264	1	j.	j.	PROPN
ejpam-4971	264	2	pure	pure	PROPN
ejpam-4971	264	3	appl	appl	PROPN
ejpam-4971	264	4	.	.	PROPN
ejpam-4971	264	5	math	math	PROPN
ejpam-4971	264	6	,	,	PUNCT
ejpam-4971	264	7	16	16	NUM
ejpam-4971	264	8	(	(	PUNCT
ejpam-4971	264	9	4	4	NUM
ejpam-4971	264	10	)	)	PUNCT
ejpam-4971	264	11	(	(	PUNCT
ejpam-4971	264	12	2023	2023	NUM
ejpam-4971	264	13	)	)	PUNCT
ejpam-4971	264	14	,	,	PUNCT
ejpam-4971	264	15	2643	2643	NUM
ejpam-4971	264	16	-	-	SYM
ejpam-4971	264	17	2661	2661	NUM
ejpam-4971	264	18	2653	2653	NUM
ejpam-4971	264	19	4.5	4.5	NUM
ejpam-4971	264	20	.	.	PUNCT
ejpam-4971	265	1	case	case	NOUN
ejpam-4971	265	2	of	of	ADP
ejpam-4971	265	3	(	(	PUNCT
ejpam-4971	265	4	α0	α0	ADJ
ejpam-4971	265	5	,	,	PUNCT
ejpam-4971	265	6	β0	β0	ADJ
ejpam-4971	265	7	)	)	PUNCT
ejpam-4971	265	8	∈	∈	PROPN
ejpam-4971	265	9	r5	r5	PROPN
ejpam-4971	265	10	we	we	PRON
ejpam-4971	265	11	set	set	VERB
ejpam-4971	265	12	α0	α0	ADJ
ejpam-4971	265	13	in	in	ADP
ejpam-4971	265	14	the	the	DET
ejpam-4971	265	15	dynamical	dynamical	ADJ
ejpam-4971	265	16	system	system	NOUN
ejpam-4971	265	17	(	(	PUNCT
ejpam-4971	265	18	4	4	NUM
ejpam-4971	265	19	)	)	PUNCT
ejpam-4971	265	20	and	and	CCONJ
ejpam-4971	265	21	study	study	VERB
ejpam-4971	265	22	the	the	DET
ejpam-4971	265	23	following	follow	VERB
ejpam-4971	265	24	two	two	NUM
ejpam-4971	265	25	cases	case	NOUN
ejpam-4971	265	26	:	:	PUNCT
ejpam-4971	265	27	case	case	NOUN
ejpam-4971	265	28	1	1	NUM
ejpam-4971	265	29	:	:	PUNCT
ejpam-4971	265	30	β0	β0	ADV
ejpam-4971	265	31	>	>	X
ejpam-4971	265	32	0	0	PROPN
ejpam-4971	265	33	.	.	PUNCT
ejpam-4971	266	1	the	the	DET
ejpam-4971	266	2	phase	phase	NOUN
ejpam-4971	266	3	portrait	portrait	NOUN
ejpam-4971	266	4	for	for	ADP
ejpam-4971	266	5	the	the	DET
ejpam-4971	266	6	dynamical	dynamical	ADJ
ejpam-4971	266	7	system	system	NOUN
ejpam-4971	266	8	(	(	PUNCT
ejpam-4971	266	9	4	4	NUM
ejpam-4971	266	10	)	)	PUNCT
ejpam-4971	266	11	is	be	AUX
ejpam-4971	266	12	appeared	appear	VERB
ejpam-4971	266	13	in	in	ADP
ejpam-4971	266	14	fig	fig	NOUN
ejpam-4971	266	15	.	.	PUNCT
ejpam-4971	267	1	1(e	1(e	NUM
ejpam-4971	267	2	)	)	PUNCT
ejpam-4971	267	3	.	.	PUNCT
ejpam-4971	268	1	we	we	PRON
ejpam-4971	268	2	study	study	VERB
ejpam-4971	268	3	the	the	DET
ejpam-4971	268	4	types	type	NOUN
ejpam-4971	268	5	of	of	ADP
ejpam-4971	268	6	traveling	travel	VERB
ejpam-4971	268	7	wave	wave	NOUN
ejpam-4971	268	8	solutions	solution	NOUN
ejpam-4971	268	9	for	for	ADP
ejpam-4971	268	10	eq	eq	PROPN
ejpam-4971	268	11	.	.	PUNCT
ejpam-4971	269	1	(	(	PUNCT
ejpam-4971	269	2	1	1	NUM
ejpam-4971	269	3	)	)	PUNCT
ejpam-4971	269	4	according	accord	VERB
ejpam-4971	269	5	to	to	ADP
ejpam-4971	269	6	the	the	DET
ejpam-4971	269	7	value	value	NOUN
ejpam-4971	269	8	of	of	ADP
ejpam-4971	269	9	the	the	DET
ejpam-4971	269	10	energy	energy	NOUN
ejpam-4971	269	11	constant	constant	ADJ
ejpam-4971	269	12	h.	h.	PROPN
ejpam-4971	269	13	•	•	NOUN
ejpam-4971	269	14	at	at	ADP
ejpam-4971	269	15	the	the	DET
ejpam-4971	269	16	zero	zero	NUM
ejpam-4971	269	17	energy	energy	NOUN
ejpam-4971	269	18	level	level	NOUN
ejpam-4971	269	19	,	,	PUNCT
ejpam-4971	269	20	i.e.	i.e.	X
ejpam-4971	269	21	,	,	PUNCT
ejpam-4971	269	22	h	h	NOUN
ejpam-4971	269	23	=	=	SYM
ejpam-4971	269	24	0	0	NUM
ejpam-4971	269	25	,	,	PUNCT
ejpam-4971	269	26	there	there	PRON
ejpam-4971	269	27	exist	exist	VERB
ejpam-4971	269	28	groups	group	NOUN
ejpam-4971	269	29	of	of	ADP
ejpam-4971	269	30	orbits	orbit	NOUN
ejpam-4971	269	31	passing	pass	VERB
ejpam-4971	269	32	out	out	ADP
ejpam-4971	269	33	of	of	ADP
ejpam-4971	269	34	the	the	DET
ejpam-4971	269	35	equilibrium	equilibrium	NOUN
ejpam-4971	269	36	point	point	NOUN
ejpam-4971	269	37	e1	e1	NOUN
ejpam-4971	269	38	[	[	X
ejpam-4971	269	39	see	see	VERB
ejpam-4971	269	40	fig	fig	NOUN
ejpam-4971	269	41	.	.	PUNCT
ejpam-4971	270	1	1(e	1(e	NUM
ejpam-4971	270	2	)	)	PUNCT
ejpam-4971	270	3	]	]	PUNCT
ejpam-4971	270	4	.	.	PUNCT
ejpam-4971	271	1	under	under	ADP
ejpam-4971	271	2	these	these	DET
ejpam-4971	271	3	conditions	condition	NOUN
ejpam-4971	271	4	,	,	PUNCT
ejpam-4971	271	5	eq	eq	NOUN
ejpam-4971	271	6	.	.	PUNCT
ejpam-4971	272	1	(	(	PUNCT
ejpam-4971	272	2	8)	8)	NUM
ejpam-4971	272	3	gives	give	VERB
ejpam-4971	272	4	a	a	DET
ejpam-4971	272	5	kink	kink	NOUN
ejpam-4971	272	6	(	(	PUNCT
ejpam-4971	272	7	or	or	CCONJ
ejpam-4971	272	8	anti	anti	ADJ
ejpam-4971	272	9	-	-	ADJ
ejpam-4971	272	10	kink	kink	ADJ
ejpam-4971	272	11	)	)	PUNCT
ejpam-4971	272	12	traveling	travel	VERB
ejpam-4971	272	13	wave	wave	NOUN
ejpam-4971	272	14	solution	solution	NOUN
ejpam-4971	272	15	for	for	ADP
ejpam-4971	272	16	eq	eq	PROPN
ejpam-4971	272	17	.	.	PUNCT
ejpam-4971	273	1	(	(	PUNCT
ejpam-4971	273	2	1	1	NUM
ejpam-4971	273	3	):	):	PUNCT
ejpam-4971	273	4	φ(ξ	φ(ξ	NOUN
ejpam-4971	273	5	)	)	PUNCT
ejpam-4971	273	6	=	=	SYM
ejpam-4971	273	7	1√	1√	PROPN
ejpam-4971	273	8	β0	β0	NOUN
ejpam-4971	273	9	2	2	NUM
ejpam-4971	273	10	(	(	PUNCT
ejpam-4971	273	11	c−	c−	NOUN
ejpam-4971	273	12	ξ	ξ	NOUN
ejpam-4971	273	13	)	)	PUNCT
ejpam-4971	273	14	.	.	PUNCT
ejpam-4971	274	1	(	(	PUNCT
ejpam-4971	274	2	34	34	NUM
ejpam-4971	274	3	)	)	PUNCT
ejpam-4971	274	4	•	•	NOUN
ejpam-4971	274	5	at	at	ADP
ejpam-4971	274	6	negative	negative	ADJ
ejpam-4971	274	7	energy	energy	NOUN
ejpam-4971	274	8	levels	level	NOUN
ejpam-4971	274	9	,	,	PUNCT
ejpam-4971	274	10	i.e.	i.e.	X
ejpam-4971	274	11	,	,	PUNCT
ejpam-4971	274	12	h	h	NOUN
ejpam-4971	274	13	<	<	X
ejpam-4971	274	14	0	0	NUM
ejpam-4971	274	15	,	,	PUNCT
ejpam-4971	274	16	there	there	PRON
ejpam-4971	274	17	is	be	VERB
ejpam-4971	274	18	a	a	DET
ejpam-4971	274	19	group	group	NOUN
ejpam-4971	274	20	of	of	ADP
ejpam-4971	274	21	trajectories	trajectory	NOUN
ejpam-4971	274	22	that	that	PRON
ejpam-4971	274	23	cut	cut	VERB
ejpam-4971	274	24	off	off	ADP
ejpam-4971	274	25	the	the	DET
ejpam-4971	274	26	φ	φ	PROPN
ejpam-4971	274	27	axis	axis	NOUN
ejpam-4971	274	28	at	at	ADP
ejpam-4971	274	29	two	two	NUM
ejpam-4971	274	30	points	point	NOUN
ejpam-4971	274	31	,	,	PUNCT
ejpam-4971	274	32	say	say	INTJ
ejpam-4971	274	33	(	(	PUNCT
ejpam-4971	274	34	±φ1	±φ1	PROPN
ejpam-4971	274	35	,	,	PUNCT
ejpam-4971	274	36	0	0	NUM
ejpam-4971	274	37	)	)	PUNCT
ejpam-4971	274	38	.	.	PUNCT
ejpam-4971	275	1	the	the	DET
ejpam-4971	275	2	polynomial	polynomial	ADJ
ejpam-4971	275	3	(	(	PUNCT
ejpam-4971	275	4	9	9	NUM
ejpam-4971	275	5	)	)	PUNCT
ejpam-4971	275	6	takes	take	VERB
ejpam-4971	275	7	the	the	DET
ejpam-4971	275	8	form	form	NOUN
ejpam-4971	275	9	[	[	X
ejpam-4971	275	10	see	see	VERB
ejpam-4971	275	11	fig	fig	NOUN
ejpam-4971	275	12	.	.	PUNCT
ejpam-4971	276	1	1(e	1(e	NUM
ejpam-4971	276	2	)	)	PUNCT
ejpam-4971	276	3	]	]	PUNCT
ejpam-4971	277	1	p4(φ	p4(φ	PROPN
ejpam-4971	277	2	)	)	PUNCT
ejpam-4971	277	3	=	=	SYM
ejpam-4971	278	1	β0	β0	NOUN
ejpam-4971	278	2	2	2	NUM
ejpam-4971	278	3	(	(	PUNCT
ejpam-4971	278	4	φ2	φ2	PROPN
ejpam-4971	278	5	−	−	PROPN
ejpam-4971	278	6	φ2	φ2	PROPN
ejpam-4971	278	7	1)(φ	1)(φ	NUM
ejpam-4971	278	8	2	2	NUM
ejpam-4971	278	9	+	+	CCONJ
ejpam-4971	278	10	φ2	φ2	PROPN
ejpam-4971	278	11	1	1	NUM
ejpam-4971	278	12	)	)	PUNCT
ejpam-4971	278	13	.	.	PUNCT
ejpam-4971	279	1	(	(	PUNCT
ejpam-4971	279	2	35	35	NUM
ejpam-4971	279	3	)	)	PUNCT
ejpam-4971	279	4	inserting	insert	VERB
ejpam-4971	279	5	eq	eq	X
ejpam-4971	279	6	.	.	PUNCT
ejpam-4971	280	1	(	(	PUNCT
ejpam-4971	280	2	35	35	NUM
ejpam-4971	280	3	)	)	PUNCT
ejpam-4971	280	4	into	into	ADP
ejpam-4971	280	5	eq	eq	NOUN
ejpam-4971	280	6	.	.	PUNCT
ejpam-4971	281	1	(	(	PUNCT
ejpam-4971	281	2	8)	8)	NUM
ejpam-4971	281	3	,	,	PUNCT
ejpam-4971	281	4	we	we	PRON
ejpam-4971	281	5	obtain	obtain	VERB
ejpam-4971	281	6	φ(ξ	φ(ξ	NOUN
ejpam-4971	281	7	)	)	PUNCT
ejpam-4971	281	8	=	=	SYM
ejpam-4971	281	9	φ1	φ1	PROPN
ejpam-4971	281	10	cn	cn	PROPN
ejpam-4971	281	11	(	(	PUNCT
ejpam-4971	281	12	φ1	φ1	PROPN
ejpam-4971	281	13	√	√	VERB
ejpam-4971	281	14	β0(ξ	β0(ξ	PROPN
ejpam-4971	281	15	+	+	NUM
ejpam-4971	281	16	c	c	X
ejpam-4971	281	17	)	)	PUNCT
ejpam-4971	281	18	,	,	PUNCT
ejpam-4971	281	19	1√	1√	PROPN
ejpam-4971	281	20	2	2	NUM
ejpam-4971	281	21	)	)	PUNCT
ejpam-4971	281	22	.	.	PUNCT
ejpam-4971	282	1	(	(	PUNCT
ejpam-4971	282	2	36	36	NUM
ejpam-4971	282	3	)	)	PUNCT
ejpam-4971	282	4	•	•	NOUN
ejpam-4971	282	5	at	at	ADP
ejpam-4971	282	6	positive	positive	ADJ
ejpam-4971	282	7	energy	energy	NOUN
ejpam-4971	282	8	levels	level	NOUN
ejpam-4971	282	9	h	h	VERB
ejpam-4971	282	10	>	>	X
ejpam-4971	282	11	0	0	NUM
ejpam-4971	282	12	,	,	PUNCT
ejpam-4971	282	13	there	there	PRON
ejpam-4971	282	14	are	be	VERB
ejpam-4971	282	15	groups	group	NOUN
ejpam-4971	282	16	of	of	ADP
ejpam-4971	282	17	orbits	orbit	NOUN
ejpam-4971	282	18	in	in	ADP
ejpam-4971	282	19	which	which	PRON
ejpam-4971	282	20	there	there	PRON
ejpam-4971	282	21	is	be	VERB
ejpam-4971	282	22	no	no	DET
ejpam-4971	282	23	intersection	intersection	NOUN
ejpam-4971	282	24	with	with	ADP
ejpam-4971	282	25	the	the	DET
ejpam-4971	282	26	ϕ	ϕ	NOUN
ejpam-4971	282	27	axis	axis	NOUN
ejpam-4971	282	28	.	.	PUNCT
ejpam-4971	283	1	hence	hence	ADV
ejpam-4971	283	2	,	,	PUNCT
ejpam-4971	283	3	the	the	DET
ejpam-4971	283	4	polynomial	polynomial	ADJ
ejpam-4971	283	5	(	(	PUNCT
ejpam-4971	283	6	9	9	NUM
ejpam-4971	283	7	)	)	PUNCT
ejpam-4971	283	8	has	have	VERB
ejpam-4971	283	9	no	no	DET
ejpam-4971	283	10	real	real	ADJ
ejpam-4971	283	11	roots	root	NOUN
ejpam-4971	283	12	and	and	CCONJ
ejpam-4971	283	13	has	have	VERB
ejpam-4971	283	14	the	the	DET
ejpam-4971	283	15	shape	shape	NOUN
ejpam-4971	284	1	[	[	X
ejpam-4971	284	2	see	see	VERB
ejpam-4971	284	3	fig	fig	NOUN
ejpam-4971	284	4	.	.	PUNCT
ejpam-4971	285	1	1(e	1(e	NUM
ejpam-4971	285	2	)	)	PUNCT
ejpam-4971	285	3	]	]	PUNCT
ejpam-4971	286	1	φ(ξ	φ(ξ	PROPN
ejpam-4971	286	2	)	)	PUNCT
ejpam-4971	286	3	=	=	SYM
ejpam-4971	287	1	β0	β0	NOUN
ejpam-4971	287	2	2	2	NUM
ejpam-4971	287	3	(	(	PUNCT
ejpam-4971	287	4	φ2	φ2	PROPN
ejpam-4971	287	5	+	+	CCONJ
ejpam-4971	287	6	φ2	φ2	PROPN
ejpam-4971	287	7	1	1	NUM
ejpam-4971	287	8	)	)	PUNCT
ejpam-4971	287	9	2	2	NUM
ejpam-4971	287	10	.	.	PUNCT
ejpam-4971	288	1	(	(	PUNCT
ejpam-4971	288	2	37	37	NUM
ejpam-4971	288	3	)	)	PUNCT
ejpam-4971	288	4	inserting	insert	VERB
ejpam-4971	288	5	eq	eq	ADP
ejpam-4971	288	6	.	.	PUNCT
ejpam-4971	289	1	(	(	PUNCT
ejpam-4971	289	2	37	37	NUM
ejpam-4971	289	3	)	)	PUNCT
ejpam-4971	289	4	into	into	ADP
ejpam-4971	289	5	eq	eq	NOUN
ejpam-4971	289	6	.	.	PUNCT
ejpam-4971	290	1	(	(	PUNCT
ejpam-4971	290	2	8)	8)	NUM
ejpam-4971	290	3	,	,	PUNCT
ejpam-4971	290	4	we	we	PRON
ejpam-4971	290	5	obtain	obtain	VERB
ejpam-4971	290	6	φ(ξ	φ(ξ	NOUN
ejpam-4971	290	7	)	)	PUNCT
ejpam-4971	290	8	=	=	SYM
ejpam-4971	290	9	φ1	φ1	PROPN
ejpam-4971	290	10	tan	tan	PROPN
ejpam-4971	290	11	(	(	PUNCT
ejpam-4971	290	12	√	√	PROPN
ejpam-4971	290	13	β0	β0	NOUN
ejpam-4971	290	14	2	2	NUM
ejpam-4971	290	15	(	(	PUNCT
ejpam-4971	290	16	ξ	ξ	PROPN
ejpam-4971	290	17	+	+	SYM
ejpam-4971	290	18	c	c	NOUN
ejpam-4971	290	19	)	)	PUNCT
ejpam-4971	290	20	)	)	PUNCT
ejpam-4971	290	21	.	.	PUNCT
ejpam-4971	291	1	(	(	PUNCT
ejpam-4971	291	2	38	38	NUM
ejpam-4971	291	3	)	)	PUNCT
ejpam-4971	291	4	case	case	NOUN
ejpam-4971	291	5	2	2	NUM
ejpam-4971	291	6	:	:	PUNCT
ejpam-4971	291	7	β0	β0	ADV
ejpam-4971	291	8	<	<	X
ejpam-4971	291	9	0	0	NUM
ejpam-4971	291	10	.	.	PUNCT
ejpam-4971	292	1	on	on	ADP
ejpam-4971	292	2	a	a	DET
ejpam-4971	292	3	positive	positive	ADJ
ejpam-4971	292	4	level	level	NOUN
ejpam-4971	292	5	h	h	NOUN
ejpam-4971	292	6	>	>	X
ejpam-4971	292	7	0	0	PROPN
ejpam-4971	292	8	,	,	PUNCT
ejpam-4971	292	9	the	the	DET
ejpam-4971	292	10	phase	phase	NOUN
ejpam-4971	292	11	form	form	NOUN
ejpam-4971	292	12	for	for	ADP
ejpam-4971	292	13	the	the	DET
ejpam-4971	292	14	dynamical	dynamical	ADJ
ejpam-4971	292	15	system	system	NOUN
ejpam-4971	292	16	(	(	PUNCT
ejpam-4971	292	17	4	4	NUM
ejpam-4971	292	18	)	)	PUNCT
ejpam-4971	292	19	is	be	AUX
ejpam-4971	292	20	as	as	SCONJ
ejpam-4971	292	21	appeared	appear	VERB
ejpam-4971	292	22	in	in	ADP
ejpam-4971	292	23	fig	fig	NOUN
ejpam-4971	292	24	.	.	PUNCT
ejpam-4971	293	1	1(f	1(f	NUM
ejpam-4971	293	2	)	)	PUNCT
ejpam-4971	293	3	.	.	PUNCT
ejpam-4971	294	1	there	there	PRON
ejpam-4971	294	2	exists	exist	VERB
ejpam-4971	294	3	a	a	DET
ejpam-4971	294	4	group	group	NOUN
ejpam-4971	294	5	of	of	ADP
ejpam-4971	294	6	periodic	periodic	ADJ
ejpam-4971	294	7	orbits	orbit	NOUN
ejpam-4971	294	8	about	about	ADP
ejpam-4971	294	9	the	the	DET
ejpam-4971	294	10	equilibrium	equilibrium	NOUN
ejpam-4971	294	11	point	point	NOUN
ejpam-4971	294	12	e1	e1	NOUN
ejpam-4971	294	13	that	that	PRON
ejpam-4971	294	14	cut	cut	VERB
ejpam-4971	294	15	off	off	ADP
ejpam-4971	294	16	with	with	ADP
ejpam-4971	294	17	the	the	DET
ejpam-4971	294	18	φ	φ	PROPN
ejpam-4971	294	19	axis	axis	NOUN
ejpam-4971	294	20	at	at	ADP
ejpam-4971	294	21	two	two	NUM
ejpam-4971	294	22	points	point	NOUN
ejpam-4971	294	23	,	,	PUNCT
ejpam-4971	294	24	say	say	VERB
ejpam-4971	294	25	(	(	PUNCT
ejpam-4971	294	26	±φ	±φ	ADJ
ejpam-4971	294	27	,	,	PUNCT
ejpam-4971	294	28	0	0	NUM
ejpam-4971	294	29	)	)	PUNCT
ejpam-4971	294	30	.	.	PUNCT
ejpam-4971	295	1	these	these	DET
ejpam-4971	295	2	orbits	orbit	NOUN
ejpam-4971	295	3	indicate	indicate	VERB
ejpam-4971	295	4	the	the	DET
ejpam-4971	295	5	existence	existence	NOUN
ejpam-4971	295	6	of	of	ADP
ejpam-4971	295	7	periodic	periodic	ADJ
ejpam-4971	295	8	traveling	travel	VERB
ejpam-4971	295	9	wave	wave	NOUN
ejpam-4971	295	10	solutions	solution	NOUN
ejpam-4971	295	11	.	.	PUNCT
ejpam-4971	296	1	the	the	DET
ejpam-4971	296	2	quartic	quartic	ADJ
ejpam-4971	296	3	polynomial	polynomial	ADJ
ejpam-4971	296	4	(	(	PUNCT
ejpam-4971	296	5	9	9	NUM
ejpam-4971	296	6	)	)	PUNCT
ejpam-4971	296	7	takes	take	VERB
ejpam-4971	296	8	the	the	DET
ejpam-4971	296	9	form	form	NOUN
ejpam-4971	296	10	p4(φ	p4(φ	NOUN
ejpam-4971	296	11	)	)	PUNCT
ejpam-4971	296	12	=	=	SYM
ejpam-4971	296	13	−β0	−β0	PROPN
ejpam-4971	296	14	2	2	NUM
ejpam-4971	296	15	(	(	PUNCT
ejpam-4971	296	16	φ2	φ2	PROPN
ejpam-4971	296	17	1	1	NUM
ejpam-4971	296	18	−	−	NOUN
ejpam-4971	296	19	φ2)(φ2	φ2)(φ2	NOUN
ejpam-4971	296	20	1	1	NUM
ejpam-4971	296	21	+	+	NUM
ejpam-4971	296	22	φ2	φ2	PROPN
ejpam-4971	296	23	)	)	PUNCT
ejpam-4971	296	24	.	.	PUNCT
ejpam-4971	297	1	(	(	PUNCT
ejpam-4971	297	2	39	39	NUM
ejpam-4971	297	3	)	)	PUNCT
ejpam-4971	297	4	inserting	insert	VERB
ejpam-4971	297	5	eq	eq	ADP
ejpam-4971	297	6	.	.	PUNCT
ejpam-4971	298	1	(	(	PUNCT
ejpam-4971	298	2	39	39	NUM
ejpam-4971	298	3	)	)	PUNCT
ejpam-4971	298	4	into	into	ADP
ejpam-4971	298	5	eq	eq	NOUN
ejpam-4971	298	6	.	.	PUNCT
ejpam-4971	299	1	(	(	PUNCT
ejpam-4971	299	2	8)	8)	NUM
ejpam-4971	299	3	,	,	PUNCT
ejpam-4971	299	4	we	we	PRON
ejpam-4971	299	5	obtain	obtain	VERB
ejpam-4971	299	6	the	the	DET
ejpam-4971	299	7	following	follow	VERB
ejpam-4971	299	8	periodic	periodic	ADJ
ejpam-4971	299	9	traveling	travel	VERB
ejpam-4971	299	10	wave	wave	NOUN
ejpam-4971	299	11	solution	solution	NOUN
ejpam-4971	299	12	:	:	PUNCT
ejpam-4971	299	13	φ(ξ	φ(ξ	NOUN
ejpam-4971	299	14	)	)	PUNCT
ejpam-4971	299	15	=	=	SYM
ejpam-4971	299	16	1√	1√	NUM
ejpam-4971	299	17	2	2	NUM
ejpam-4971	299	18	sd	sd	NOUN
ejpam-4971	299	19	(	(	PUNCT
ejpam-4971	299	20	φ1	φ1	NOUN
ejpam-4971	299	21	√	√	VERB
ejpam-4971	299	22	−β0(ξ	−β0(ξ	NOUN
ejpam-4971	299	23	+	+	CCONJ
ejpam-4971	299	24	c),−	c),−	PROPN
ejpam-4971	299	25	1√	1√	PROPN
ejpam-4971	299	26	2	2	NUM
ejpam-4971	299	27	)	)	PUNCT
ejpam-4971	299	28	.	.	PUNCT
ejpam-4971	300	1	(	(	PUNCT
ejpam-4971	300	2	40	40	NUM
ejpam-4971	300	3	)	)	PUNCT
ejpam-4971	300	4	black	black	NOUN
ejpam-4971	300	5	in	in	ADP
ejpam-4971	300	6	the	the	DET
ejpam-4971	300	7	comparison	comparison	NOUN
ejpam-4971	300	8	with	with	ADP
ejpam-4971	300	9	previous	previous	ADJ
ejpam-4971	300	10	works	work	NOUN
ejpam-4971	300	11	such	such	ADJ
ejpam-4971	300	12	as	as	ADP
ejpam-4971	300	13	[	[	X
ejpam-4971	300	14	12	12	NUM
ejpam-4971	300	15	,	,	PUNCT
ejpam-4971	300	16	63	63	NUM
ejpam-4971	300	17	]	]	PUNCT
ejpam-4971	300	18	,	,	PUNCT
ejpam-4971	300	19	the	the	DET
ejpam-4971	300	20	majority	majority	NOUN
ejpam-4971	300	21	of	of	ADP
ejpam-4971	300	22	obtained	obtain	VERB
ejpam-4971	300	23	solutions	solution	NOUN
ejpam-4971	300	24	in	in	ADP
ejpam-4971	300	25	the	the	DET
ejpam-4971	300	26	current	current	ADJ
ejpam-4971	300	27	work	work	NOUN
ejpam-4971	300	28	are	be	AUX
ejpam-4971	300	29	expressed	express	VERB
ejpam-4971	300	30	as	as	ADP
ejpam-4971	300	31	jacobi	jacobi	NOUN
ejpam-4971	300	32	-	-	PUNCT
ejpam-4971	300	33	elliptic	elliptic	ADJ
ejpam-4971	300	34	functions	function	NOUN
ejpam-4971	300	35	.	.	PUNCT
ejpam-4971	301	1	therefore	therefore	ADV
ejpam-4971	301	2	,	,	PUNCT
ejpam-4971	301	3	our	our	PRON
ejpam-4971	301	4	results	result	NOUN
ejpam-4971	301	5	are	be	AUX
ejpam-4971	301	6	new	new	ADJ
ejpam-4971	301	7	.	.	PUNCT
ejpam-4971	302	1	m.arab	m.arab	NOUN
ejpam-4971	302	2	/	/	SYM
ejpam-4971	302	3	eur	eur	PROPN
ejpam-4971	302	4	.	.	PUNCT
ejpam-4971	303	1	j.	j.	PROPN
ejpam-4971	303	2	pure	pure	PROPN
ejpam-4971	303	3	appl	appl	PROPN
ejpam-4971	303	4	.	.	PROPN
ejpam-4971	303	5	math	math	PROPN
ejpam-4971	303	6	,	,	PUNCT
ejpam-4971	303	7	16	16	NUM
ejpam-4971	303	8	(	(	PUNCT
ejpam-4971	303	9	4	4	NUM
ejpam-4971	303	10	)	)	PUNCT
ejpam-4971	303	11	(	(	PUNCT
ejpam-4971	303	12	2023	2023	NUM
ejpam-4971	303	13	)	)	PUNCT
ejpam-4971	303	14	,	,	PUNCT
ejpam-4971	303	15	2643	2643	NUM
ejpam-4971	303	16	-	-	SYM
ejpam-4971	303	17	2661	2661	NUM
ejpam-4971	303	18	2654	2654	NUM
ejpam-4971	303	19	(	(	PUNCT
ejpam-4971	303	20	a	a	NOUN
ejpam-4971	303	21	)	)	PUNCT
ejpam-4971	303	22	(	(	PUNCT
ejpam-4971	303	23	b	b	X
ejpam-4971	303	24	)	)	PUNCT
ejpam-4971	303	25	(	(	PUNCT
ejpam-4971	303	26	c	c	X
ejpam-4971	303	27	)	)	PUNCT
ejpam-4971	303	28	figure	figure	NOUN
ejpam-4971	303	29	2	2	NUM
ejpam-4971	303	30	:	:	PUNCT
ejpam-4971	303	31	graphical	graphical	ADJ
ejpam-4971	303	32	representation	representation	NOUN
ejpam-4971	303	33	of	of	ADP
ejpam-4971	303	34	the	the	DET
ejpam-4971	303	35	kink	kink	NOUN
ejpam-4971	303	36	solution	solution	NOUN
ejpam-4971	303	37	(	(	PUNCT
ejpam-4971	303	38	15	15	NUM
ejpam-4971	303	39	)	)	PUNCT
ejpam-4971	303	40	for	for	ADP
ejpam-4971	303	41	α0	α0	PROPN
ejpam-4971	303	42	=	=	SYM
ejpam-4971	303	43	β0	β0	PROPN
ejpam-4971	303	44	=	=	SYM
ejpam-4971	303	45	1	1	NUM
ejpam-4971	303	46	,	,	PUNCT
ejpam-4971	303	47	h	h	NOUN
ejpam-4971	303	48	=	=	NOUN
ejpam-4971	303	49	0.25	0.25	NUM
ejpam-4971	303	50	.	.	PUNCT
ejpam-4971	304	1	(	(	PUNCT
ejpam-4971	304	2	a	a	X
ejpam-4971	304	3	)	)	PUNCT
ejpam-4971	304	4	3d	3d	NOUN
ejpam-4971	304	5	representation	representation	NOUN
ejpam-4971	304	6	,	,	PUNCT
ejpam-4971	304	7	(	(	PUNCT
ejpam-4971	304	8	b	b	X
ejpam-4971	304	9	)	)	PUNCT
ejpam-4971	304	10	2d	2d	NOUN
ejpam-4971	304	11	representation	representation	NOUN
ejpam-4971	304	12	,	,	PUNCT
ejpam-4971	304	13	and	and	CCONJ
ejpam-4971	304	14	(	(	PUNCT
ejpam-4971	304	15	c	c	NOUN
ejpam-4971	304	16	)	)	PUNCT
ejpam-4971	304	17	phase	phase	NOUN
ejpam-4971	304	18	orbit	orbit	NOUN
ejpam-4971	304	19	.	.	PUNCT
ejpam-4971	305	1	5	5	X
ejpam-4971	305	2	.	.	X
ejpam-4971	305	3	graphical	graphical	ADJ
ejpam-4971	305	4	representation	representation	NOUN
ejpam-4971	305	5	black	black	ADJ
ejpam-4971	305	6	this	this	DET
ejpam-4971	305	7	section	section	NOUN
ejpam-4971	305	8	presents	present	VERB
ejpam-4971	305	9	a	a	DET
ejpam-4971	305	10	graphical	graphical	ADJ
ejpam-4971	305	11	illustration	illustration	NOUN
ejpam-4971	305	12	of	of	ADP
ejpam-4971	305	13	some	some	PRON
ejpam-4971	305	14	of	of	ADP
ejpam-4971	305	15	the	the	DET
ejpam-4971	305	16	newly	newly	ADV
ejpam-4971	305	17	obtained	obtain	VERB
ejpam-4971	305	18	solutions	solution	NOUN
ejpam-4971	305	19	for	for	ADP
ejpam-4971	305	20	the	the	DET
ejpam-4971	305	21	nonlinear	nonlinear	ADJ
ejpam-4971	305	22	kg	kg	PROPN
ejpam-4971	305	23	equation	equation	NOUN
ejpam-4971	305	24	by	by	ADP
ejpam-4971	305	25	introducing	introduce	VERB
ejpam-4971	305	26	three	three	NUM
ejpam-4971	305	27	-	-	PUNCT
ejpam-4971	305	28	dimensional	dimensional	ADJ
ejpam-4971	305	29	(	(	PUNCT
ejpam-4971	305	30	3d	3d	NOUN
ejpam-4971	305	31	)	)	PUNCT
ejpam-4971	305	32	and	and	CCONJ
ejpam-4971	305	33	2d	2d	NUM
ejpam-4971	305	34	representations	representation	NOUN
ejpam-4971	305	35	of	of	ADP
ejpam-4971	305	36	the	the	DET
ejpam-4971	305	37	solutions	solution	NOUN
ejpam-4971	305	38	.	.	PUNCT
ejpam-4971	306	1	in	in	ADP
ejpam-4971	306	2	addition	addition	NOUN
ejpam-4971	306	3	,	,	PUNCT
ejpam-4971	306	4	we	we	PRON
ejpam-4971	306	5	provide	provide	VERB
ejpam-4971	306	6	graphical	graphical	ADJ
ejpam-4971	306	7	evidence	evidence	NOUN
ejpam-4971	306	8	that	that	SCONJ
ejpam-4971	306	9	the	the	DET
ejpam-4971	306	10	type	type	NOUN
ejpam-4971	306	11	of	of	ADP
ejpam-4971	306	12	solution	solution	NOUN
ejpam-4971	306	13	agrees	agree	VERB
ejpam-4971	306	14	with	with	ADP
ejpam-4971	306	15	the	the	DET
ejpam-4971	306	16	type	type	NOUN
ejpam-4971	306	17	of	of	ADP
ejpam-4971	306	18	phase	phase	NOUN
ejpam-4971	306	19	orbit	orbit	NOUN
ejpam-4971	306	20	.	.	PUNCT
ejpam-4971	307	1	•	•	NUM
ejpam-4971	307	2	for	for	ADP
ejpam-4971	307	3	h	h	NOUN
ejpam-4971	307	4	=	=	NOUN
ejpam-4971	307	5	0.25	0.25	NUM
ejpam-4971	307	6	,	,	PUNCT
ejpam-4971	307	7	α0	α0	PROPN
ejpam-4971	307	8	=	=	SYM
ejpam-4971	307	9	β0	β0	NOUN
ejpam-4971	307	10	=	=	SYM
ejpam-4971	307	11	1	1	NUM
ejpam-4971	307	12	,	,	PUNCT
ejpam-4971	307	13	the	the	DET
ejpam-4971	307	14	dynamical	dynamical	ADJ
ejpam-4971	307	15	system	system	NOUN
ejpam-4971	307	16	(	(	PUNCT
ejpam-4971	307	17	4	4	X
ejpam-4971	307	18	)	)	PUNCT
ejpam-4971	307	19	has	have	VERB
ejpam-4971	307	20	heteroclinic	heteroclinic	ADJ
ejpam-4971	307	21	phase	phase	NOUN
ejpam-4971	307	22	orbits	orbit	NOUN
ejpam-4971	307	23	,	,	PUNCT
ejpam-4971	307	24	as	as	SCONJ
ejpam-4971	307	25	summarized	summarize	VERB
ejpam-4971	307	26	by	by	ADP
ejpam-4971	307	27	fig	fig	NOUN
ejpam-4971	307	28	.	.	PUNCT
ejpam-4971	308	1	2(c	2(c	NUM
ejpam-4971	308	2	)	)	PUNCT
ejpam-4971	308	3	.	.	PUNCT
ejpam-4971	309	1	based	base	VERB
ejpam-4971	309	2	on	on	ADP
ejpam-4971	309	3	theorem	theorem	NOUN
ejpam-4971	309	4	2	2	NUM
ejpam-4971	309	5	,	,	PUNCT
ejpam-4971	309	6	this	this	PRON
ejpam-4971	309	7	implies	imply	VERB
ejpam-4971	309	8	that	that	SCONJ
ejpam-4971	309	9	the	the	DET
ejpam-4971	309	10	kg	kg	PROPN
ejpam-4971	309	11	equation	equation	NOUN
ejpam-4971	309	12	(	(	PUNCT
ejpam-4971	309	13	1	1	X
ejpam-4971	309	14	)	)	PUNCT
ejpam-4971	309	15	has	have	VERB
ejpam-4971	309	16	a	a	DET
ejpam-4971	309	17	kink	kink	ADJ
ejpam-4971	309	18	wave	wave	NOUN
ejpam-4971	309	19	solution	solution	NOUN
ejpam-4971	309	20	,	,	PUNCT
ejpam-4971	309	21	which	which	PRON
ejpam-4971	309	22	is	be	AUX
ejpam-4971	309	23	described	describe	VERB
ejpam-4971	309	24	by	by	ADP
ejpam-4971	309	25	figs	fig	NOUN
ejpam-4971	309	26	.	.	PUNCT
ejpam-4971	310	1	2(a	2(a	NUM
ejpam-4971	310	2	)	)	PUNCT
ejpam-4971	310	3	and	and	CCONJ
ejpam-4971	310	4	2(b	2(b	NUM
ejpam-4971	310	5	)	)	PUNCT
ejpam-4971	310	6	.	.	PUNCT
ejpam-4971	311	1	•	•	NUM
ejpam-4971	311	2	the	the	DET
ejpam-4971	311	3	dynamical	dynamical	ADJ
ejpam-4971	311	4	system	system	NOUN
ejpam-4971	311	5	(	(	PUNCT
ejpam-4971	311	6	4	4	NUM
ejpam-4971	311	7	)	)	PUNCT
ejpam-4971	311	8	has	have	VERB
ejpam-4971	311	9	a	a	DET
ejpam-4971	311	10	homoclinic	homoclinic	ADJ
ejpam-4971	311	11	phase	phase	NOUN
ejpam-4971	311	12	orbit	orbit	NOUN
ejpam-4971	311	13	when	when	SCONJ
ejpam-4971	311	14	α0	α0	PROPN
ejpam-4971	311	15	=	=	SYM
ejpam-4971	311	16	β0	β0	PROPN
ejpam-4971	311	17	=	=	SYM
ejpam-4971	311	18	−1	−1	NOUN
ejpam-4971	311	19	,	,	PUNCT
ejpam-4971	311	20	h	h	NOUN
ejpam-4971	312	1	=	=	NOUN
ejpam-4971	312	2	0	0	NUM
ejpam-4971	312	3	,	,	PUNCT
ejpam-4971	312	4	as	as	SCONJ
ejpam-4971	312	5	illustrated	illustrate	VERB
ejpam-4971	312	6	by	by	ADP
ejpam-4971	312	7	fig	fig	NOUN
ejpam-4971	312	8	.	.	PUNCT
ejpam-4971	313	1	3(c	3(c	NUM
ejpam-4971	313	2	)	)	PUNCT
ejpam-4971	313	3	.	.	PUNCT
ejpam-4971	314	1	consequently	consequently	ADV
ejpam-4971	314	2	,	,	PUNCT
ejpam-4971	314	3	the	the	DET
ejpam-4971	314	4	kg	kg	PROPN
ejpam-4971	314	5	equation	equation	NOUN
ejpam-4971	314	6	(	(	PUNCT
ejpam-4971	314	7	1	1	X
ejpam-4971	314	8	)	)	PUNCT
ejpam-4971	314	9	has	have	VERB
ejpam-4971	314	10	a	a	DET
ejpam-4971	314	11	solitary	solitary	ADJ
ejpam-4971	314	12	wave	wave	NOUN
ejpam-4971	314	13	solution	solution	NOUN
ejpam-4971	314	14	in	in	ADP
ejpam-4971	314	15	the	the	DET
ejpam-4971	314	16	form	form	NOUN
ejpam-4971	314	17	of	of	ADP
ejpam-4971	314	18	eq	eq	PROPN
ejpam-4971	314	19	.	.	PUNCT
ejpam-4971	315	1	(	(	PUNCT
ejpam-4971	315	2	29	29	NUM
ejpam-4971	315	3	)	)	PUNCT
ejpam-4971	315	4	.	.	PUNCT
ejpam-4971	316	1	the	the	DET
ejpam-4971	316	2	3d	3d	NOUN
ejpam-4971	316	3	and	and	CCONJ
ejpam-4971	316	4	2d	2d	NUM
ejpam-4971	316	5	representations	representation	NOUN
ejpam-4971	316	6	of	of	ADP
ejpam-4971	316	7	this	this	DET
ejpam-4971	316	8	solution	solution	NOUN
ejpam-4971	316	9	are	be	AUX
ejpam-4971	316	10	appeared	appear	VERB
ejpam-4971	316	11	in	in	ADP
ejpam-4971	316	12	figs	fig	NOUN
ejpam-4971	316	13	.	.	PUNCT
ejpam-4971	317	1	3(a	3(a	NUM
ejpam-4971	317	2	)	)	PUNCT
ejpam-4971	317	3	and	and	CCONJ
ejpam-4971	317	4	3(b	3(b	NUM
ejpam-4971	317	5	)	)	PUNCT
ejpam-4971	317	6	.	.	PUNCT
ejpam-4971	318	1	•	•	NUM
ejpam-4971	318	2	the	the	DET
ejpam-4971	318	3	dynamical	dynamical	ADJ
ejpam-4971	318	4	system	system	NOUN
ejpam-4971	318	5	(	(	PUNCT
ejpam-4971	318	6	4	4	X
ejpam-4971	318	7	)	)	PUNCT
ejpam-4971	318	8	possesses	possess	VERB
ejpam-4971	318	9	a	a	DET
ejpam-4971	318	10	periodic	periodic	ADJ
ejpam-4971	318	11	phase	phase	NOUN
ejpam-4971	318	12	orbit	orbit	NOUN
ejpam-4971	318	13	when	when	SCONJ
ejpam-4971	318	14	α0	α0	PROPN
ejpam-4971	318	15	=	=	SYM
ejpam-4971	318	16	β0	β0	NOUN
ejpam-4971	318	17	=	=	SYM
ejpam-4971	318	18	1	1	NUM
ejpam-4971	318	19	,	,	PUNCT
ejpam-4971	318	20	h	h	NOUN
ejpam-4971	318	21	=	=	NOUN
ejpam-4971	318	22	0.125	0.125	NUM
ejpam-4971	318	23	,	,	PUNCT
ejpam-4971	318	24	as	as	SCONJ
ejpam-4971	318	25	outlined	outline	VERB
ejpam-4971	318	26	by	by	ADP
ejpam-4971	318	27	fig	fig	NOUN
ejpam-4971	318	28	.	.	PUNCT
ejpam-4971	319	1	4(c	4(c	NUM
ejpam-4971	319	2	)	)	PUNCT
ejpam-4971	319	3	.	.	PUNCT
ejpam-4971	320	1	based	base	VERB
ejpam-4971	320	2	on	on	ADP
ejpam-4971	320	3	theorem	theorem	NOUN
ejpam-4971	320	4	2	2	NUM
ejpam-4971	320	5	,	,	PUNCT
ejpam-4971	320	6	the	the	DET
ejpam-4971	320	7	kg	kg	NOUN
ejpam-4971	320	8	equation	equation	NOUN
ejpam-4971	320	9	(	(	PUNCT
ejpam-4971	320	10	1	1	X
ejpam-4971	320	11	)	)	PUNCT
ejpam-4971	320	12	has	have	VERB
ejpam-4971	320	13	a	a	DET
ejpam-4971	320	14	periodic	periodic	ADJ
ejpam-4971	320	15	wave	wave	NOUN
ejpam-4971	320	16	solution	solution	NOUN
ejpam-4971	320	17	in	in	ADP
ejpam-4971	320	18	the	the	DET
ejpam-4971	320	19	form	form	NOUN
ejpam-4971	320	20	of	of	ADP
ejpam-4971	320	21	eq	eq	PROPN
ejpam-4971	320	22	.	.	PUNCT
ejpam-4971	321	1	(	(	PUNCT
ejpam-4971	321	2	17	17	NUM
ejpam-4971	321	3	)	)	PUNCT
ejpam-4971	321	4	.	.	PUNCT
ejpam-4971	322	1	the	the	DET
ejpam-4971	322	2	3d	3d	NOUN
ejpam-4971	322	3	and	and	CCONJ
ejpam-4971	322	4	2d	2d	NUM
ejpam-4971	322	5	representations	representation	NOUN
ejpam-4971	322	6	of	of	ADP
ejpam-4971	322	7	this	this	DET
ejpam-4971	322	8	solution	solution	NOUN
ejpam-4971	322	9	are	be	AUX
ejpam-4971	322	10	outlined	outline	VERB
ejpam-4971	322	11	in	in	ADP
ejpam-4971	322	12	figs	fig	NOUN
ejpam-4971	322	13	.	.	PUNCT
ejpam-4971	323	1	4(b	4(b	NUM
ejpam-4971	323	2	)	)	PUNCT
ejpam-4971	323	3	and	and	CCONJ
ejpam-4971	323	4	4(c	4(c	NUM
ejpam-4971	323	5	)	)	PUNCT
ejpam-4971	323	6	.	.	PUNCT
ejpam-4971	324	1	m.arab	m.arab	NOUN
ejpam-4971	324	2	/	/	SYM
ejpam-4971	324	3	eur	eur	PROPN
ejpam-4971	324	4	.	.	PUNCT
ejpam-4971	325	1	j.	j.	PROPN
ejpam-4971	325	2	pure	pure	PROPN
ejpam-4971	325	3	appl	appl	PROPN
ejpam-4971	325	4	.	.	PROPN
ejpam-4971	325	5	math	math	PROPN
ejpam-4971	325	6	,	,	PUNCT
ejpam-4971	325	7	16	16	NUM
ejpam-4971	325	8	(	(	PUNCT
ejpam-4971	325	9	4	4	NUM
ejpam-4971	325	10	)	)	PUNCT
ejpam-4971	325	11	(	(	PUNCT
ejpam-4971	325	12	2023	2023	NUM
ejpam-4971	325	13	)	)	PUNCT
ejpam-4971	325	14	,	,	PUNCT
ejpam-4971	325	15	2643	2643	NUM
ejpam-4971	325	16	-	-	SYM
ejpam-4971	325	17	2661	2661	NUM
ejpam-4971	325	18	2655	2655	NUM
ejpam-4971	325	19	(	(	PUNCT
ejpam-4971	325	20	a	a	NOUN
ejpam-4971	325	21	)	)	PUNCT
ejpam-4971	325	22	(	(	PUNCT
ejpam-4971	325	23	b	b	X
ejpam-4971	325	24	)	)	PUNCT
ejpam-4971	325	25	(	(	PUNCT
ejpam-4971	325	26	c	c	X
ejpam-4971	325	27	)	)	PUNCT
ejpam-4971	325	28	figure	figure	NOUN
ejpam-4971	325	29	3	3	NUM
ejpam-4971	325	30	:	:	PUNCT
ejpam-4971	325	31	graphical	graphical	ADJ
ejpam-4971	325	32	representation	representation	NOUN
ejpam-4971	325	33	of	of	ADP
ejpam-4971	325	34	the	the	DET
ejpam-4971	325	35	solitary	solitary	ADJ
ejpam-4971	325	36	wave	wave	NOUN
ejpam-4971	325	37	solution	solution	NOUN
ejpam-4971	325	38	(	(	PUNCT
ejpam-4971	325	39	29	29	NUM
ejpam-4971	325	40	)	)	PUNCT
ejpam-4971	325	41	for	for	ADP
ejpam-4971	325	42	α0	α0	PROPN
ejpam-4971	325	43	=	=	SYM
ejpam-4971	325	44	β0	β0	PROPN
ejpam-4971	325	45	=	=	SYM
ejpam-4971	325	46	−1	−1	NOUN
ejpam-4971	325	47	,	,	PUNCT
ejpam-4971	325	48	h	h	NOUN
ejpam-4971	325	49	=	=	NOUN
ejpam-4971	325	50	0	0	PROPN
ejpam-4971	325	51	.	.	PUNCT
ejpam-4971	326	1	(	(	PUNCT
ejpam-4971	326	2	a	a	X
ejpam-4971	326	3	)	)	PUNCT
ejpam-4971	326	4	3d	3d	NOUN
ejpam-4971	326	5	representation	representation	NOUN
ejpam-4971	326	6	,	,	PUNCT
ejpam-4971	326	7	(	(	PUNCT
ejpam-4971	326	8	b	b	X
ejpam-4971	326	9	)	)	PUNCT
ejpam-4971	326	10	2d	2d	NOUN
ejpam-4971	326	11	representation	representation	NOUN
ejpam-4971	326	12	,	,	PUNCT
ejpam-4971	326	13	and	and	CCONJ
ejpam-4971	326	14	(	(	PUNCT
ejpam-4971	326	15	c	c	NOUN
ejpam-4971	326	16	)	)	PUNCT
ejpam-4971	326	17	phase	phase	NOUN
ejpam-4971	326	18	orbit	orbit	NOUN
ejpam-4971	326	19	.	.	PUNCT
ejpam-4971	327	1	6	6	X
ejpam-4971	327	2	.	.	X
ejpam-4971	327	3	conclusion	conclusion	NOUN
ejpam-4971	327	4	this	this	DET
ejpam-4971	327	5	work	work	NOUN
ejpam-4971	327	6	has	have	AUX
ejpam-4971	327	7	focused	focus	VERB
ejpam-4971	327	8	on	on	ADP
ejpam-4971	327	9	building	build	VERB
ejpam-4971	327	10	several	several	ADJ
ejpam-4971	327	11	traveling	travel	VERB
ejpam-4971	327	12	wave	wave	NOUN
ejpam-4971	327	13	solutions	solution	NOUN
ejpam-4971	327	14	of	of	ADP
ejpam-4971	327	15	the	the	DET
ejpam-4971	327	16	nonlinear	nonlinear	ADJ
ejpam-4971	327	17	kg	kg	PROPN
ejpam-4971	327	18	equation	equation	NOUN
ejpam-4971	327	19	.	.	PUNCT
ejpam-4971	328	1	a	a	DET
ejpam-4971	328	2	familiar	familiar	ADJ
ejpam-4971	328	3	wave	wave	NOUN
ejpam-4971	328	4	transformation	transformation	NOUN
ejpam-4971	328	5	was	be	AUX
ejpam-4971	328	6	used	use	VERB
ejpam-4971	328	7	for	for	ADP
ejpam-4971	328	8	the	the	DET
ejpam-4971	328	9	kg	kg	PROPN
ejpam-4971	328	10	equation	equation	NOUN
ejpam-4971	328	11	to	to	PART
ejpam-4971	328	12	convert	convert	VERB
ejpam-4971	328	13	it	it	PRON
ejpam-4971	328	14	into	into	ADP
ejpam-4971	328	15	an	an	DET
ejpam-4971	328	16	ordinary	ordinary	ADJ
ejpam-4971	328	17	differential	differential	ADJ
ejpam-4971	328	18	equation	equation	NOUN
ejpam-4971	328	19	in	in	ADP
ejpam-4971	328	20	the	the	DET
ejpam-4971	328	21	form	form	NOUN
ejpam-4971	328	22	of	of	ADP
ejpam-4971	328	23	a	a	DET
ejpam-4971	328	24	one	one	NUM
ejpam-4971	328	25	-	-	PUNCT
ejpam-4971	328	26	dimensional	dimensional	ADJ
ejpam-4971	328	27	hamiltonian	hamiltonian	ADJ
ejpam-4971	328	28	system	system	NOUN
ejpam-4971	328	29	describing	describe	VERB
ejpam-4971	328	30	the	the	DET
ejpam-4971	328	31	motion	motion	NOUN
ejpam-4971	328	32	of	of	ADP
ejpam-4971	328	33	a	a	DET
ejpam-4971	328	34	unit	unit	NOUN
ejpam-4971	328	35	mass	mass	NOUN
ejpam-4971	328	36	particle	particle	NOUN
ejpam-4971	328	37	under	under	ADP
ejpam-4971	328	38	the	the	DET
ejpam-4971	328	39	effect	effect	NOUN
ejpam-4971	328	40	of	of	ADP
ejpam-4971	328	41	a	a	DET
ejpam-4971	328	42	conservative	conservative	ADJ
ejpam-4971	328	43	potential	potential	NOUN
ejpam-4971	328	44	.	.	PUNCT
ejpam-4971	329	1	the	the	DET
ejpam-4971	329	2	qualitative	qualitative	ADJ
ejpam-4971	329	3	theory	theory	NOUN
ejpam-4971	329	4	for	for	ADP
ejpam-4971	329	5	planar	planar	ADJ
ejpam-4971	329	6	dynamical	dynamical	ADJ
ejpam-4971	329	7	systems	system	NOUN
ejpam-4971	329	8	was	be	AUX
ejpam-4971	329	9	used	use	VERB
ejpam-4971	329	10	to	to	PART
ejpam-4971	329	11	study	study	VERB
ejpam-4971	329	12	the	the	DET
ejpam-4971	329	13	bifurcations	bifurcation	NOUN
ejpam-4971	329	14	and	and	CCONJ
ejpam-4971	329	15	phase	phase	NOUN
ejpam-4971	329	16	portraits	portrait	NOUN
ejpam-4971	329	17	of	of	ADP
ejpam-4971	329	18	this	this	DET
ejpam-4971	329	19	system	system	NOUN
ejpam-4971	329	20	.	.	PUNCT
ejpam-4971	330	1	blackthe	blackthe	DET
ejpam-4971	330	2	application	application	NOUN
ejpam-4971	330	3	of	of	ADP
ejpam-4971	330	4	the	the	DET
ejpam-4971	330	5	qualitative	qualitative	ADJ
ejpam-4971	330	6	theory	theory	NOUN
ejpam-4971	330	7	for	for	ADP
ejpam-4971	330	8	planar	planar	ADJ
ejpam-4971	330	9	dynamical	dynamical	ADJ
ejpam-4971	330	10	systems	system	NOUN
ejpam-4971	330	11	has	have	VERB
ejpam-4971	330	12	the	the	DET
ejpam-4971	330	13	following	following	ADJ
ejpam-4971	330	14	advantages	advantage	NOUN
ejpam-4971	330	15	over	over	ADP
ejpam-4971	330	16	other	other	ADJ
ejpam-4971	330	17	methods	method	NOUN
ejpam-4971	330	18	:	:	PUNCT
ejpam-4971	330	19	(	(	PUNCT
ejpam-4971	330	20	a	a	X
ejpam-4971	330	21	)	)	PUNCT
ejpam-4971	330	22	it	it	PRON
ejpam-4971	330	23	enables	enable	VERB
ejpam-4971	330	24	us	we	PRON
ejpam-4971	330	25	to	to	PART
ejpam-4971	330	26	find	find	VERB
ejpam-4971	330	27	the	the	DET
ejpam-4971	330	28	required	require	VERB
ejpam-4971	330	29	range	range	NOUN
ejpam-4971	330	30	of	of	ADP
ejpam-4971	330	31	the	the	DET
ejpam-4971	330	32	parameters	parameter	NOUN
ejpam-4971	330	33	h	h	NOUN
ejpam-4971	330	34	,	,	PUNCT
ejpam-4971	330	35	α0	α0	ADJ
ejpam-4971	330	36	,	,	PUNCT
ejpam-4971	330	37	β0	β0	NOUN
ejpam-4971	330	38	that	that	PRON
ejpam-4971	330	39	is	be	AUX
ejpam-4971	330	40	necessary	necessary	ADJ
ejpam-4971	330	41	to	to	PART
ejpam-4971	330	42	integrate	integrate	VERB
ejpam-4971	330	43	both	both	DET
ejpam-4971	330	44	sides	side	NOUN
ejpam-4971	330	45	of	of	ADP
ejpam-4971	330	46	the	the	DET
ejpam-4971	330	47	differential	differential	ADJ
ejpam-4971	330	48	form	form	NOUN
ejpam-4971	330	49	(	(	PUNCT
ejpam-4971	330	50	8)	8)	NUM
ejpam-4971	330	51	.	.	PUNCT
ejpam-4971	331	1	(	(	PUNCT
ejpam-4971	331	2	b	b	X
ejpam-4971	331	3	)	)	PUNCT
ejpam-4971	331	4	it	it	PRON
ejpam-4971	331	5	helps	help	VERB
ejpam-4971	331	6	us	we	PRON
ejpam-4971	331	7	to	to	PART
ejpam-4971	331	8	define	define	VERB
ejpam-4971	331	9	the	the	DET
ejpam-4971	331	10	shape	shape	NOUN
ejpam-4971	331	11	of	of	ADP
ejpam-4971	331	12	solutions	solution	NOUN
ejpam-4971	331	13	before	before	ADP
ejpam-4971	331	14	constructing	construct	VERB
ejpam-4971	331	15	them	they	PRON
ejpam-4971	331	16	because	because	SCONJ
ejpam-4971	331	17	it	it	PRON
ejpam-4971	331	18	links	link	VERB
ejpam-4971	331	19	the	the	DET
ejpam-4971	331	20	shape	shape	NOUN
ejpam-4971	331	21	of	of	ADP
ejpam-4971	331	22	solution	solution	NOUN
ejpam-4971	331	23	with	with	ADP
ejpam-4971	331	24	the	the	DET
ejpam-4971	331	25	phase	phase	NOUN
ejpam-4971	331	26	orbit	orbit	NOUN
ejpam-4971	331	27	.	.	PUNCT
ejpam-4971	332	1	for	for	ADP
ejpam-4971	332	2	example	example	NOUN
ejpam-4971	332	3	,	,	PUNCT
ejpam-4971	332	4	the	the	DET
ejpam-4971	332	5	existence	existence	NOUN
ejpam-4971	332	6	of	of	ADP
ejpam-4971	332	7	periodic	periodic	ADJ
ejpam-4971	332	8	,	,	PUNCT
ejpam-4971	332	9	homoclinic	homoclinic	ADJ
ejpam-4971	332	10	,	,	PUNCT
ejpam-4971	332	11	and	and	CCONJ
ejpam-4971	332	12	heteroclinic	heteroclinic	ADJ
ejpam-4971	332	13	orbits	orbit	NOUN
ejpam-4971	332	14	in	in	ADP
ejpam-4971	332	15	the	the	DET
ejpam-4971	332	16	phase	phase	NOUN
ejpam-4971	332	17	plane	plane	NOUN
ejpam-4971	332	18	indicate	indicate	VERB
ejpam-4971	332	19	the	the	DET
ejpam-4971	332	20	presence	presence	NOUN
ejpam-4971	332	21	of	of	ADP
ejpam-4971	332	22	periodic	periodic	ADJ
ejpam-4971	332	23	,	,	PUNCT
ejpam-4971	332	24	solitary	solitary	ADJ
ejpam-4971	332	25	,	,	PUNCT
ejpam-4971	332	26	and	and	CCONJ
ejpam-4971	332	27	kink	kink	PROPN
ejpam-4971	332	28	(	(	PUNCT
ejpam-4971	332	29	or	or	CCONJ
ejpam-4971	332	30	anti	anti	ADJ
ejpam-4971	332	31	-	-	ADJ
ejpam-4971	332	32	kink	kink	ADJ
ejpam-4971	332	33	)	)	PUNCT
ejpam-4971	332	34	solutions	solution	NOUN
ejpam-4971	332	35	,	,	PUNCT
ejpam-4971	332	36	as	as	SCONJ
ejpam-4971	332	37	outlined	outline	VERB
ejpam-4971	332	38	by	by	ADP
ejpam-4971	332	39	theorem	theorem	NOUN
ejpam-4971	332	40	2	2	NUM
ejpam-4971	332	41	.	.	PUNCT
ejpam-4971	332	42	(	(	PUNCT
ejpam-4971	332	43	c	c	X
ejpam-4971	332	44	)	)	PUNCT
ejpam-4971	332	45	it	it	PRON
ejpam-4971	332	46	illustrates	illustrate	VERB
ejpam-4971	332	47	the	the	DET
ejpam-4971	332	48	reliance	reliance	NOUN
ejpam-4971	332	49	of	of	ADP
ejpam-4971	332	50	the	the	DET
ejpam-4971	332	51	solutions	solution	NOUN
ejpam-4971	332	52	on	on	ADP
ejpam-4971	332	53	the	the	DET
ejpam-4971	332	54	initial	initial	ADJ
ejpam-4971	332	55	conditions	condition	NOUN
ejpam-4971	332	56	over	over	ADP
ejpam-4971	332	57	the	the	DET
ejpam-4971	332	58	parameter	parameter	NOUN
ejpam-4971	332	59	h	h	NOUN
ejpam-4971	332	60	,	,	PUNCT
ejpam-4971	332	61	which	which	PRON
ejpam-4971	332	62	is	be	AUX
ejpam-4971	332	63	determined	determine	VERB
ejpam-4971	332	64	by	by	ADP
ejpam-4971	332	65	the	the	DET
ejpam-4971	332	66	initial	initial	ADJ
ejpam-4971	332	67	conditions	condition	NOUN
ejpam-4971	332	68	.	.	PUNCT
ejpam-4971	333	1	for	for	ADP
ejpam-4971	333	2	clarification	clarification	NOUN
ejpam-4971	333	3	,	,	PUNCT
ejpam-4971	333	4	if	if	SCONJ
ejpam-4971	333	5	(	(	PUNCT
ejpam-4971	333	6	α0	α0	ADJ
ejpam-4971	333	7	,	,	PUNCT
ejpam-4971	333	8	β0	β0	ADJ
ejpam-4971	333	9	)	)	PUNCT
ejpam-4971	333	10	∈	∈	PROPN
ejpam-4971	333	11	r1	r1	NOUN
ejpam-4971	333	12	,	,	PUNCT
ejpam-4971	333	13	there	there	PRON
ejpam-4971	333	14	are	be	VERB
ejpam-4971	333	15	entirely	entirely	ADV
ejpam-4971	333	16	other	other	ADJ
ejpam-4971	333	17	solutions	solution	NOUN
ejpam-4971	333	18	from	from	ADP
ejpam-4971	333	19	the	the	DET
ejpam-4971	333	20	point	point	NOUN
ejpam-4971	333	21	of	of	ADP
ejpam-4971	333	22	view	view	NOUN
ejpam-4971	333	23	of	of	ADP
ejpam-4971	333	24	the	the	DET
ejpam-4971	333	25	mathematical	mathematical	ADJ
ejpam-4971	333	26	and	and	CCONJ
ejpam-4971	333	27	physical	physical	ADJ
ejpam-4971	333	28	researchers	researcher	NOUN
ejpam-4971	333	29	.	.	PUNCT
ejpam-4971	334	1	for	for	ADP
ejpam-4971	334	2	example	example	NOUN
ejpam-4971	334	3	,	,	PUNCT
ejpam-4971	334	4	when	when	SCONJ
ejpam-4971	334	5	h	h	NOUN
ejpam-4971	334	6	=	=	SYM
ejpam-4971	334	7	α2	α2	PROPN
ejpam-4971	334	8	0	0	NUM
ejpam-4971	334	9	4β0	4β0	NUM
ejpam-4971	334	10	,	,	PUNCT
ejpam-4971	334	11	there	there	PRON
ejpam-4971	334	12	is	be	VERB
ejpam-4971	334	13	a	a	DET
ejpam-4971	334	14	kink	kink	NOUN
ejpam-4971	334	15	solution	solution	NOUN
ejpam-4971	334	16	,	,	PUNCT
ejpam-4971	334	17	whereas	whereas	SCONJ
ejpam-4971	334	18	if	if	SCONJ
ejpam-4971	334	19	h	h	PROPN
ejpam-4971	334	20	∈]0	∈]0	ADJ
ejpam-4971	334	21	,	,	PUNCT
ejpam-4971	334	22	α2	α2	PROPN
ejpam-4971	334	23	0	0	NUM
ejpam-4971	334	24	4β0	4β0	NUM
ejpam-4971	335	1	[	[	X
ejpam-4971	335	2	,	,	PUNCT
ejpam-4971	335	3	there	there	PRON
ejpam-4971	335	4	is	be	VERB
ejpam-4971	335	5	a	a	DET
ejpam-4971	335	6	periodic	periodic	ADJ
ejpam-4971	335	7	solution	solution	NOUN
ejpam-4971	335	8	.	.	PUNCT
ejpam-4971	336	1	this	this	DET
ejpam-4971	336	2	study	study	NOUN
ejpam-4971	336	3	has	have	AUX
ejpam-4971	336	4	derived	derive	VERB
ejpam-4971	336	5	some	some	DET
ejpam-4971	336	6	new	new	ADJ
ejpam-4971	336	7	periodic	periodic	NOUN
ejpam-4971	336	8	,	,	PUNCT
ejpam-4971	336	9	kink	kink	PROPN
ejpam-4971	336	10	(	(	PUNCT
ejpam-4971	336	11	anti	anti	ADJ
ejpam-4971	336	12	-	-	ADJ
ejpam-4971	336	13	kink	kink	ADJ
ejpam-4971	336	14	)	)	PUNCT
ejpam-4971	336	15	,	,	PUNCT
ejpam-4971	336	16	and	and	CCONJ
ejpam-4971	336	17	solitary	solitary	ADJ
ejpam-4971	336	18	wave	wave	NOUN
ejpam-4971	336	19	solutions	solution	NOUN
ejpam-4971	336	20	.	.	PUNCT
ejpam-4971	337	1	some	some	PRON
ejpam-4971	337	2	of	of	ADP
ejpam-4971	337	3	these	these	DET
ejpam-4971	337	4	solutions	solution	NOUN
ejpam-4971	337	5	have	have	AUX
ejpam-4971	337	6	been	be	AUX
ejpam-4971	337	7	outlined	outline	VERB
ejpam-4971	337	8	graphically	graphically	ADV
ejpam-4971	337	9	in	in	ADP
ejpam-4971	337	10	connection	connection	NOUN
ejpam-4971	337	11	with	with	ADP
ejpam-4971	337	12	the	the	DET
ejpam-4971	337	13	corresponding	corresponding	ADJ
ejpam-4971	337	14	phase	phase	NOUN
ejpam-4971	337	15	orbits	orbit	NOUN
ejpam-4971	337	16	.	.	PUNCT
ejpam-4971	338	1	references	reference	NOUN
ejpam-4971	338	2	2656	2656	NUM
ejpam-4971	338	3	(	(	PUNCT
ejpam-4971	338	4	a	a	NOUN
ejpam-4971	338	5	)	)	PUNCT
ejpam-4971	338	6	(	(	PUNCT
ejpam-4971	338	7	b	b	X
ejpam-4971	338	8	)	)	PUNCT
ejpam-4971	338	9	(	(	PUNCT
ejpam-4971	338	10	c	c	X
ejpam-4971	338	11	)	)	PUNCT
ejpam-4971	338	12	figure	figure	NOUN
ejpam-4971	338	13	4	4	NUM
ejpam-4971	338	14	:	:	PUNCT
ejpam-4971	338	15	graphical	graphical	ADJ
ejpam-4971	338	16	representation	representation	NOUN
ejpam-4971	338	17	of	of	ADP
ejpam-4971	338	18	the	the	DET
ejpam-4971	338	19	periodic	periodic	ADJ
ejpam-4971	338	20	wave	wave	NOUN
ejpam-4971	338	21	solution	solution	NOUN
ejpam-4971	338	22	(	(	PUNCT
ejpam-4971	338	23	17	17	NUM
ejpam-4971	338	24	)	)	PUNCT
ejpam-4971	338	25	for	for	ADP
ejpam-4971	338	26	α0	α0	PROPN
ejpam-4971	338	27	=	=	SYM
ejpam-4971	338	28	β0	β0	PROPN
ejpam-4971	338	29	=	=	SYM
ejpam-4971	338	30	1	1	NUM
ejpam-4971	338	31	,	,	PUNCT
ejpam-4971	338	32	h	h	NOUN
ejpam-4971	338	33	=	=	NOUN
ejpam-4971	338	34	0.125	0.125	NUM
ejpam-4971	338	35	.	.	PUNCT
ejpam-4971	339	1	(	(	PUNCT
ejpam-4971	339	2	a	a	X
ejpam-4971	339	3	)	)	PUNCT
ejpam-4971	339	4	3d	3d	NOUN
ejpam-4971	339	5	representation	representation	NOUN
ejpam-4971	339	6	,	,	PUNCT
ejpam-4971	339	7	(	(	PUNCT
ejpam-4971	339	8	b	b	X
ejpam-4971	339	9	)	)	PUNCT
ejpam-4971	339	10	2d	2d	NOUN
ejpam-4971	339	11	representation	representation	NOUN
ejpam-4971	339	12	,	,	PUNCT
ejpam-4971	339	13	and	and	CCONJ
ejpam-4971	339	14	(	(	PUNCT
ejpam-4971	339	15	c	c	NOUN
ejpam-4971	339	16	)	)	PUNCT
ejpam-4971	339	17	phase	phase	NOUN
ejpam-4971	339	18	orbit	orbit	NOUN
ejpam-4971	339	19	.	.	PUNCT
ejpam-4971	340	1	acknowledgements	acknowledgement	NOUN
ejpam-4971	340	2	this	this	DET
ejpam-4971	340	3	work	work	NOUN
ejpam-4971	340	4	was	be	AUX
ejpam-4971	340	5	supported	support	VERB
ejpam-4971	340	6	by	by	ADP
ejpam-4971	340	7	the	the	DET
ejpam-4971	340	8	deanship	deanship	NOUN
ejpam-4971	340	9	of	of	ADP
ejpam-4971	340	10	scientific	scientific	ADJ
ejpam-4971	340	11	research	research	NOUN
ejpam-4971	340	12	,	,	PUNCT
ejpam-4971	340	13	vice	vice	NOUN
ejpam-4971	340	14	presidency	presidency	NOUN
ejpam-4971	340	15	for	for	ADP
ejpam-4971	340	16	graduate	graduate	NOUN
ejpam-4971	340	17	studies	study	NOUN
ejpam-4971	340	18	and	and	CCONJ
ejpam-4971	340	19	scientific	scientific	ADJ
ejpam-4971	340	20	research	research	NOUN
ejpam-4971	340	21	,	,	PUNCT
ejpam-4971	340	22	king	king	PROPN
ejpam-4971	340	23	faisal	faisal	PROPN
ejpam-4971	340	24	university	university	PROPN
ejpam-4971	340	25	,	,	PUNCT
ejpam-4971	340	26	saudi	saudi	PROPN
ejpam-4971	340	27	arabia	arabia	PROPN
ejpam-4971	341	1	[	[	X
ejpam-4971	341	2	grant	grant	VERB
ejpam-4971	341	3	no	no	INTJ
ejpam-4971	341	4	.	.	PUNCT
ejpam-4971	341	5	4607	4607	NUM
ejpam-4971	341	6	]	]	PUNCT
ejpam-4971	341	7	.	.	PUNCT
ejpam-4971	342	1	competing	compete	VERB
ejpam-4971	342	2	interests	interest	NOUN
ejpam-4971	342	3	the	the	DET
ejpam-4971	342	4	authors	author	NOUN
ejpam-4971	342	5	declare	declare	VERB
ejpam-4971	342	6	that	that	SCONJ
ejpam-4971	342	7	they	they	PRON
ejpam-4971	342	8	have	have	VERB
ejpam-4971	342	9	no	no	DET
ejpam-4971	342	10	competing	compete	VERB
ejpam-4971	342	11	interests	interest	NOUN
ejpam-4971	342	12	.	.	PUNCT
ejpam-4971	343	1	references	reference	NOUN
ejpam-4971	343	2	[	[	X
ejpam-4971	343	3	1	1	NUM
ejpam-4971	343	4	]	]	PUNCT
ejpam-4971	343	5	g	g	NOUN
ejpam-4971	343	6	adomian	adomian	NOUN
ejpam-4971	343	7	.	.	PUNCT
ejpam-4971	344	1	solving	solve	VERB
ejpam-4971	344	2	frontier	frontier	NOUN
ejpam-4971	344	3	problems	problem	NOUN
ejpam-4971	344	4	of	of	ADP
ejpam-4971	344	5	physics	physics	NOUN
ejpam-4971	344	6	:	:	PUNCT
ejpam-4971	344	7	the	the	DET
ejpam-4971	344	8	decomposition	decomposition	NOUN
ejpam-4971	344	9	method	method	NOUN
ejpam-4971	344	10	.	.	PUNCT
ejpam-4971	344	11	1994	1994	NUM
ejpam-4971	344	12	.	.	PUNCT
ejpam-4971	345	1	klumer	klumer	PROPN
ejpam-4971	345	2	,	,	PUNCT
ejpam-4971	345	3	boston	boston	PROPN
ejpam-4971	345	4	.	.	PUNCT
ejpam-4971	346	1	[	[	X
ejpam-4971	346	2	2	2	X
ejpam-4971	346	3	]	]	PUNCT
ejpam-4971	346	4	nikan	nikan	PROPN
ejpam-4971	346	5	ahmadi	ahmadi	PROPN
ejpam-4971	346	6	karchi	karchi	PROPN
ejpam-4971	346	7	,	,	PUNCT
ejpam-4971	346	8	mohammad	mohammad	PROPN
ejpam-4971	346	9	bagher	bagher	PROPN
ejpam-4971	346	10	ghaemi	ghaemi	PROPN
ejpam-4971	346	11	,	,	PUNCT
ejpam-4971	346	12	and	and	CCONJ
ejpam-4971	346	13	javad	javad	PROPN
ejpam-4971	346	14	vahidi	vahidi	PROPN
ejpam-4971	346	15	.	.	PUNCT
ejpam-4971	347	1	new	new	ADJ
ejpam-4971	347	2	exact	exact	ADJ
ejpam-4971	347	3	solutions	solution	NOUN
ejpam-4971	347	4	of	of	ADP
ejpam-4971	347	5	nonlinear	nonlinear	ADJ
ejpam-4971	347	6	schrödinger	schrödinger	NOUN
ejpam-4971	347	7	equation	equation	NOUN
ejpam-4971	347	8	with	with	ADP
ejpam-4971	347	9	extended	extended	ADJ
ejpam-4971	347	10	rational	rational	ADJ
ejpam-4971	347	11	sin	sin	NOUN
ejpam-4971	347	12	–	–	PUNCT
ejpam-4971	347	13	cos	cos	PROPN
ejpam-4971	347	14	and	and	CCONJ
ejpam-4971	347	15	sinh	sinh	PROPN
ejpam-4971	347	16	–	–	PUNCT
ejpam-4971	347	17	cosh	cosh	NOUN
ejpam-4971	347	18	method	method	NOUN
ejpam-4971	347	19	.	.	PUNCT
ejpam-4971	348	1	aip	aip	PROPN
ejpam-4971	348	2	advances	advance	NOUN
ejpam-4971	348	3	,	,	PUNCT
ejpam-4971	348	4	12(8	12(8	NUM
ejpam-4971	348	5	)	)	PUNCT
ejpam-4971	348	6	,	,	PUNCT
ejpam-4971	348	7	2022	2022	NUM
ejpam-4971	348	8	.	.	PUNCT
ejpam-4971	349	1	[	[	X
ejpam-4971	349	2	3	3	X
ejpam-4971	349	3	]	]	PUNCT
ejpam-4971	349	4	mohammed	mohammed	PROPN
ejpam-4971	349	5	o	o	PROPN
ejpam-4971	349	6	al	al	PROPN
ejpam-4971	349	7	-	-	PUNCT
ejpam-4971	349	8	amr	amr	PROPN
ejpam-4971	349	9	.	.	PROPN
ejpam-4971	349	10	exact	exact	ADJ
ejpam-4971	349	11	solutions	solution	NOUN
ejpam-4971	349	12	of	of	ADP
ejpam-4971	349	13	the	the	DET
ejpam-4971	349	14	generalized	generalized	ADJ
ejpam-4971	349	15	(	(	PUNCT
ejpam-4971	349	16	2	2	NUM
ejpam-4971	349	17	+	+	NUM
ejpam-4971	349	18	1)-dimensional	1)-dimensional	NUM
ejpam-4971	349	19	nonlinear	nonlinear	ADJ
ejpam-4971	349	20	evolution	evolution	NOUN
ejpam-4971	349	21	equations	equation	NOUN
ejpam-4971	349	22	via	via	ADP
ejpam-4971	349	23	the	the	DET
ejpam-4971	349	24	modified	modify	VERB
ejpam-4971	349	25	simple	simple	ADJ
ejpam-4971	349	26	equation	equation	NOUN
ejpam-4971	349	27	method	method	NOUN
ejpam-4971	349	28	.	.	PUNCT
ejpam-4971	350	1	computers	computer	NOUN
ejpam-4971	350	2	&	&	CCONJ
ejpam-4971	350	3	mathematics	mathematics	PROPN
ejpam-4971	350	4	with	with	ADP
ejpam-4971	350	5	applications	application	NOUN
ejpam-4971	350	6	,	,	PUNCT
ejpam-4971	350	7	69(5):390–397	69(5):390–397	PROPN
ejpam-4971	350	8	,	,	PUNCT
ejpam-4971	350	9	2015	2015	NUM
ejpam-4971	350	10	.	.	PUNCT
ejpam-4971	351	1	[	[	X
ejpam-4971	351	2	4	4	X
ejpam-4971	351	3	]	]	X
ejpam-4971	351	4	md	md	PROPN
ejpam-4971	351	5	nur	nur	VERB
ejpam-4971	351	6	alam	alam	PROPN
ejpam-4971	351	7	and	and	CCONJ
ejpam-4971	351	8	m	m	PROPN
ejpam-4971	351	9	ali	ali	PROPN
ejpam-4971	351	10	akbar	akbar	NOUN
ejpam-4971	351	11	.	.	PUNCT
ejpam-4971	352	1	traveling	travel	VERB
ejpam-4971	352	2	wave	wave	NOUN
ejpam-4971	352	3	solutions	solution	NOUN
ejpam-4971	352	4	of	of	ADP
ejpam-4971	352	5	the	the	DET
ejpam-4971	352	6	nonlinear	nonlinear	NOUN
ejpam-4971	352	7	(	(	PUNCT
ejpam-4971	352	8	1	1	NUM
ejpam-4971	352	9	+	+	NUM
ejpam-4971	352	10	1)-dimensional	1)-dimensional	NUM
ejpam-4971	352	11	modified	modify	VERB
ejpam-4971	352	12	benjamin	benjamin	NOUN
ejpam-4971	352	13	-	-	PUNCT
ejpam-4971	352	14	bona	bona	ADJ
ejpam-4971	352	15	-	-	PUNCT
ejpam-4971	352	16	mahony	mahony	NOUN
ejpam-4971	352	17	equation	equation	NOUN
ejpam-4971	352	18	by	by	ADP
ejpam-4971	352	19	using	use	VERB
ejpam-4971	352	20	novel	novel	NOUN
ejpam-4971	352	21	(	(	PUNCT
ejpam-4971	352	22	g’/g)expansion	g’/g)expansion	NOUN
ejpam-4971	352	23	method	method	NOUN
ejpam-4971	352	24	.	.	PUNCT
ejpam-4971	353	1	physical	physical	ADJ
ejpam-4971	353	2	science	science	PROPN
ejpam-4971	353	3	international	international	PROPN
ejpam-4971	353	4	journal	journal	PROPN
ejpam-4971	353	5	,	,	PUNCT
ejpam-4971	353	6	4(1):147–165	4(1):147–165	NUM
ejpam-4971	353	7	,	,	PUNCT
ejpam-4971	353	8	2013	2013	NUM
ejpam-4971	353	9	.	.	PUNCT
ejpam-4971	354	1	references	reference	NOUN
ejpam-4971	354	2	2657	2657	NUM
ejpam-4971	355	1	[	[	X
ejpam-4971	355	2	5	5	NUM
ejpam-4971	355	3	]	]	PUNCT
ejpam-4971	355	4	am	be	AUX
ejpam-4971	355	5	algelany	algelany	NOUN
ejpam-4971	355	6	,	,	PUNCT
ejpam-4971	355	7	ma	ma	PROPN
ejpam-4971	355	8	el	el	PROPN
ejpam-4971	355	9	-	-	PUNCT
ejpam-4971	355	10	shorbagy	shorbagy	ADJ
ejpam-4971	355	11	,	,	PUNCT
ejpam-4971	355	12	and	and	CCONJ
ejpam-4971	355	13	mostafa	mostafa	PROPN
ejpam-4971	355	14	khater	khater	PROPN
ejpam-4971	355	15	.	.	PUNCT
ejpam-4971	356	1	dimensionless	dimensionless	ADJ
ejpam-4971	356	2	zakharov	zakharov	PROPN
ejpam-4971	356	3	equation	equation	NOUN
ejpam-4971	356	4	;	;	PUNCT
ejpam-4971	356	5	high	high	ADJ
ejpam-4971	356	6	-	-	PUNCT
ejpam-4971	356	7	frequency	frequency	NOUN
ejpam-4971	356	8	langmuir	langmuir	NOUN
ejpam-4971	356	9	waves	wave	NOUN
ejpam-4971	356	10	and	and	CCONJ
ejpam-4971	356	11	low	low	ADJ
ejpam-4971	356	12	-	-	PUNCT
ejpam-4971	356	13	frequency	frequency	NOUN
ejpam-4971	356	14	ion	ion	NOUN
ejpam-4971	356	15	-	-	PUNCT
ejpam-4971	356	16	acoustic	acoustic	ADJ
ejpam-4971	356	17	waves	wave	NOUN
ejpam-4971	356	18	’	'	PUNCT
ejpam-4971	356	19	interaction	interaction	NOUN
ejpam-4971	356	20	.	.	PUNCT
ejpam-4971	357	1	aip	aip	PROPN
ejpam-4971	357	2	advances	advance	NOUN
ejpam-4971	357	3	,	,	PUNCT
ejpam-4971	357	4	12(12	12(12	NUM
ejpam-4971	357	5	)	)	PUNCT
ejpam-4971	357	6	,	,	PUNCT
ejpam-4971	357	7	2022	2022	NUM
ejpam-4971	357	8	.	.	PUNCT
ejpam-4971	358	1	[	[	X
ejpam-4971	358	2	6	6	NUM
ejpam-4971	358	3	]	]	SYM
ejpam-4971	358	4	mm	mm	PROPN
ejpam-4971	358	5	arab	arab	PROPN
ejpam-4971	358	6	.	.	PUNCT
ejpam-4971	359	1	a	a	DET
ejpam-4971	359	2	(	(	PUNCT
ejpam-4971	359	3	3	3	NUM
ejpam-4971	359	4	+	+	NUM
ejpam-4971	359	5	1)-dimensional	1)-dimensional	NUM
ejpam-4971	359	6	nonlinear	nonlinear	ADJ
ejpam-4971	359	7	extended	extend	VERB
ejpam-4971	359	8	zakharov	zakharov	ADJ
ejpam-4971	359	9	–	–	PUNCT
ejpam-4971	359	10	kuznetsov	kuznetsov	ADJ
ejpam-4971	359	11	dynamical	dynamical	ADJ
ejpam-4971	359	12	equation	equation	NOUN
ejpam-4971	359	13	:	:	PUNCT
ejpam-4971	359	14	bifurcation	bifurcation	NOUN
ejpam-4971	359	15	and	and	CCONJ
ejpam-4971	359	16	traveling	travel	VERB
ejpam-4971	359	17	wave	wave	NOUN
ejpam-4971	359	18	solutions	solution	NOUN
ejpam-4971	359	19	.	.	PUNCT
ejpam-4971	360	1	aip	aip	PROPN
ejpam-4971	360	2	advances	advance	NOUN
ejpam-4971	360	3	,	,	PUNCT
ejpam-4971	360	4	10(12	10(12	NUM
ejpam-4971	360	5	)	)	PUNCT
ejpam-4971	360	6	,	,	PUNCT
ejpam-4971	360	7	2020	2020	NUM
ejpam-4971	360	8	.	.	PUNCT
ejpam-4971	361	1	[	[	X
ejpam-4971	361	2	7	7	NUM
ejpam-4971	361	3	]	]	X
ejpam-4971	361	4	raghda	raghda	NOUN
ejpam-4971	361	5	am	be	AUX
ejpam-4971	361	6	attia	attia	PROPN
ejpam-4971	361	7	,	,	PUNCT
ejpam-4971	361	8	xiao	xiao	PROPN
ejpam-4971	361	9	zhang	zhang	PROPN
ejpam-4971	361	10	,	,	PUNCT
ejpam-4971	361	11	and	and	CCONJ
ejpam-4971	361	12	mostafa	mostafa	PROPN
ejpam-4971	361	13	ma	ma	PROPN
ejpam-4971	361	14	khater	khater	PROPN
ejpam-4971	361	15	.	.	PUNCT
ejpam-4971	362	1	analytical	analytical	ADJ
ejpam-4971	362	2	and	and	CCONJ
ejpam-4971	362	3	hybrid	hybrid	ADJ
ejpam-4971	362	4	numerical	numerical	ADJ
ejpam-4971	362	5	simulations	simulation	NOUN
ejpam-4971	362	6	for	for	ADP
ejpam-4971	362	7	the	the	DET
ejpam-4971	362	8	(	(	PUNCT
ejpam-4971	362	9	2	2	NUM
ejpam-4971	362	10	+	+	NUM
ejpam-4971	362	11	1)-dimensional	1)-dimensional	PROPN
ejpam-4971	362	12	heisenberg	heisenberg	PROPN
ejpam-4971	362	13	ferromagnetic	ferromagnetic	ADJ
ejpam-4971	362	14	spin	spin	NOUN
ejpam-4971	362	15	chain	chain	NOUN
ejpam-4971	362	16	.	.	PUNCT
ejpam-4971	363	1	results	result	NOUN
ejpam-4971	363	2	in	in	ADP
ejpam-4971	363	3	physics	physics	NOUN
ejpam-4971	363	4	,	,	PUNCT
ejpam-4971	363	5	43:106045	43:106045	NUM
ejpam-4971	363	6	,	,	PUNCT
ejpam-4971	363	7	2022	2022	NUM
ejpam-4971	363	8	.	.	PUNCT
ejpam-4971	364	1	[	[	X
ejpam-4971	364	2	8	8	NUM
ejpam-4971	364	3	]	]	X
ejpam-4971	364	4	kn	kn	PROPN
ejpam-4971	364	5	bhat	bhat	PROPN
ejpam-4971	364	6	and	and	CCONJ
ejpam-4971	364	7	a	a	DET
ejpam-4971	364	8	dasgupta	dasgupta	PROPN
ejpam-4971	364	9	.	.	PUNCT
ejpam-4971	364	10	physics	physics	PROPN
ejpam-4971	364	11	of	of	ADP
ejpam-4971	364	12	semiconductor	semiconductor	NOUN
ejpam-4971	364	13	devices	device	NOUN
ejpam-4971	364	14	:	:	PUNCT
ejpam-4971	364	15	iwpsd-2003	iwpsd-2003	NOUN
ejpam-4971	364	16	,	,	PUNCT
ejpam-4971	364	17	twovolume	twovolume	PROPN
ejpam-4971	364	18	set	set	NOUN
ejpam-4971	364	19	,	,	PUNCT
ejpam-4971	364	20	volume	volume	NOUN
ejpam-4971	364	21	1	1	NUM
ejpam-4971	364	22	.	.	PUNCT
ejpam-4971	365	1	alpha	alpha	PROPN
ejpam-4971	365	2	science	science	PROPN
ejpam-4971	365	3	int’l	int’l	NUM
ejpam-4971	365	4	ltd	ltd	PROPN
ejpam-4971	365	5	.	.	PROPN
ejpam-4971	365	6	,	,	PUNCT
ejpam-4971	365	7	2004	2004	NUM
ejpam-4971	365	8	.	.	PUNCT
ejpam-4971	366	1	[	[	X
ejpam-4971	366	2	9	9	NUM
ejpam-4971	366	3	]	]	PUNCT
ejpam-4971	366	4	he	he	PROPN
ejpam-4971	366	5	bin	bin	PROPN
ejpam-4971	366	6	,	,	PUNCT
ejpam-4971	366	7	li	li	PROPN
ejpam-4971	366	8	jibin	jibin	PROPN
ejpam-4971	366	9	,	,	PUNCT
ejpam-4971	366	10	long	long	ADJ
ejpam-4971	366	11	yao	yao	NOUN
ejpam-4971	366	12	,	,	PUNCT
ejpam-4971	366	13	and	and	CCONJ
ejpam-4971	366	14	rui	rui	PROPN
ejpam-4971	366	15	weiguo	weiguo	PROPN
ejpam-4971	366	16	.	.	PUNCT
ejpam-4971	367	1	bifurcations	bifurcation	NOUN
ejpam-4971	367	2	of	of	ADP
ejpam-4971	367	3	travelling	travel	VERB
ejpam-4971	367	4	wave	wave	NOUN
ejpam-4971	367	5	solutions	solution	NOUN
ejpam-4971	367	6	for	for	ADP
ejpam-4971	367	7	a	a	DET
ejpam-4971	367	8	variant	variant	NOUN
ejpam-4971	367	9	of	of	ADP
ejpam-4971	367	10	camassa	camassa	ADJ
ejpam-4971	367	11	–	–	PUNCT
ejpam-4971	367	12	holm	holm	NOUN
ejpam-4971	367	13	equation	equation	NOUN
ejpam-4971	367	14	.	.	PUNCT
ejpam-4971	368	1	nonlinear	nonlinear	ADJ
ejpam-4971	368	2	analysis	analysis	NOUN
ejpam-4971	368	3	:	:	PUNCT
ejpam-4971	368	4	real	real	ADJ
ejpam-4971	368	5	world	world	NOUN
ejpam-4971	368	6	applications	application	NOUN
ejpam-4971	368	7	,	,	PUNCT
ejpam-4971	368	8	9(2):222–232	9(2):222–232	NUM
ejpam-4971	368	9	,	,	PUNCT
ejpam-4971	368	10	2008	2008	NUM
ejpam-4971	368	11	.	.	PUNCT
ejpam-4971	369	1	[	[	X
ejpam-4971	369	2	10	10	NUM
ejpam-4971	369	3	]	]	X
ejpam-4971	369	4	timothy	timothy	PROPN
ejpam-4971	369	5	l	l	PROPN
ejpam-4971	369	6	bock	bock	NOUN
ejpam-4971	369	7	and	and	CCONJ
ejpam-4971	369	8	martin	martin	PROPN
ejpam-4971	369	9	d	d	PROPN
ejpam-4971	369	10	kruskal	kruskal	PROPN
ejpam-4971	369	11	.	.	PUNCT
ejpam-4971	370	1	a	a	DET
ejpam-4971	370	2	two	two	NUM
ejpam-4971	370	3	-	-	PUNCT
ejpam-4971	370	4	parameter	parameter	NOUN
ejpam-4971	370	5	miura	miura	PROPN
ejpam-4971	370	6	transformation	transformation	NOUN
ejpam-4971	370	7	of	of	ADP
ejpam-4971	370	8	the	the	DET
ejpam-4971	370	9	benjamin	benjamin	PROPN
ejpam-4971	370	10	-	-	PUNCT
ejpam-4971	370	11	ono	ono	PROPN
ejpam-4971	370	12	equation	equation	NOUN
ejpam-4971	370	13	.	.	PUNCT
ejpam-4971	371	1	physics	physics	NOUN
ejpam-4971	371	2	letters	letter	NOUN
ejpam-4971	371	3	a	a	DET
ejpam-4971	371	4	,	,	PUNCT
ejpam-4971	371	5	74(3	74(3	PROPN
ejpam-4971	371	6	-	-	NOUN
ejpam-4971	371	7	4):173–176	4):173–176	NOUN
ejpam-4971	371	8	,	,	PUNCT
ejpam-4971	371	9	1979	1979	NUM
ejpam-4971	371	10	.	.	PUNCT
ejpam-4971	372	1	[	[	X
ejpam-4971	372	2	11	11	NUM
ejpam-4971	372	3	]	]	X
ejpam-4971	372	4	p	p	PROPN
ejpam-4971	372	5	friedman	friedman	PROPN
ejpam-4971	372	6	byrd	byrd	PROPN
ejpam-4971	372	7	.	.	PUNCT
ejpam-4971	373	1	pf	pf	PROPN
ejpam-4971	373	2	and	and	CCONJ
ejpam-4971	373	3	md	md	PROPN
ejpam-4971	373	4	friedman	friedman	PROPN
ejpam-4971	373	5	,	,	PUNCT
ejpam-4971	373	6	handbook	handbook	NOUN
ejpam-4971	373	7	of	of	ADP
ejpam-4971	373	8	elliptic	elliptic	ADJ
ejpam-4971	373	9	integrals	integral	NOUN
ejpam-4971	373	10	for	for	ADP
ejpam-4971	373	11	engineers	engineer	NOUN
ejpam-4971	373	12	and	and	CCONJ
ejpam-4971	373	13	scientists	scientist	NOUN
ejpam-4971	373	14	,	,	PUNCT
ejpam-4971	373	15	1971	1971	NUM
ejpam-4971	373	16	.	.	PUNCT
ejpam-4971	374	1	[	[	X
ejpam-4971	374	2	12	12	NUM
ejpam-4971	374	3	]	]	X
ejpam-4971	374	4	liu	liu	PROPN
ejpam-4971	374	5	cheng	cheng	PROPN
ejpam-4971	374	6	-	-	PUNCT
ejpam-4971	374	7	shi	shi	PROPN
ejpam-4971	374	8	.	.	PUNCT
ejpam-4971	375	1	exact	exact	ADJ
ejpam-4971	375	2	travelling	travel	VERB
ejpam-4971	375	3	wave	wave	NOUN
ejpam-4971	375	4	solutions	solution	NOUN
ejpam-4971	375	5	for	for	ADP
ejpam-4971	375	6	(	(	PUNCT
ejpam-4971	375	7	1	1	NUM
ejpam-4971	375	8	+	+	NUM
ejpam-4971	375	9	1)-dimensional	1)-dimensional	NUM
ejpam-4971	375	10	dispersive	dispersive	ADJ
ejpam-4971	375	11	long	long	ADJ
ejpam-4971	375	12	wave	wave	NOUN
ejpam-4971	375	13	equation	equation	NOUN
ejpam-4971	375	14	.	.	PUNCT
ejpam-4971	376	1	chinese	chinese	ADJ
ejpam-4971	376	2	physics	physics	PROPN
ejpam-4971	376	3	,	,	PUNCT
ejpam-4971	376	4	14(9):1710	14(9):1710	NUM
ejpam-4971	376	5	,	,	PUNCT
ejpam-4971	376	6	2005	2005	NUM
ejpam-4971	376	7	.	.	PUNCT
ejpam-4971	377	1	[	[	X
ejpam-4971	377	2	13	13	NUM
ejpam-4971	377	3	]	]	PUNCT
ejpam-4971	377	4	lokenath	lokenath	NOUN
ejpam-4971	377	5	debnath	debnath	NOUN
ejpam-4971	377	6	and	and	CCONJ
ejpam-4971	377	7	lokenath	lokenath	PROPN
ejpam-4971	377	8	debnath	debnath	PROPN
ejpam-4971	377	9	.	.	PUNCT
ejpam-4971	378	1	nonlinear	nonlinear	ADJ
ejpam-4971	378	2	partial	partial	ADJ
ejpam-4971	378	3	differential	differential	ADJ
ejpam-4971	378	4	equations	equation	NOUN
ejpam-4971	378	5	for	for	ADP
ejpam-4971	378	6	scientists	scientist	NOUN
ejpam-4971	378	7	and	and	CCONJ
ejpam-4971	378	8	engineers	engineer	NOUN
ejpam-4971	378	9	.	.	PUNCT
ejpam-4971	379	1	springer	springer	NOUN
ejpam-4971	379	2	,	,	PUNCT
ejpam-4971	379	3	2005	2005	NUM
ejpam-4971	379	4	.	.	PUNCT
ejpam-4971	380	1	[	[	X
ejpam-4971	380	2	14	14	NUM
ejpam-4971	380	3	]	]	X
ejpam-4971	380	4	me	i	PRON
ejpam-4971	380	5	elbrolosy	elbrolosy	VERB
ejpam-4971	380	6	.	.	PUNCT
ejpam-4971	381	1	qualitative	qualitative	ADJ
ejpam-4971	381	2	analysis	analysis	NOUN
ejpam-4971	381	3	and	and	CCONJ
ejpam-4971	381	4	new	new	ADJ
ejpam-4971	381	5	soliton	soliton	NOUN
ejpam-4971	381	6	solutions	solution	NOUN
ejpam-4971	381	7	for	for	ADP
ejpam-4971	381	8	the	the	DET
ejpam-4971	381	9	coupled	couple	VERB
ejpam-4971	381	10	nonlinear	nonlinear	ADJ
ejpam-4971	381	11	schrödinger	schrödinger	NOUN
ejpam-4971	381	12	type	type	NOUN
ejpam-4971	381	13	equations	equation	NOUN
ejpam-4971	381	14	.	.	PUNCT
ejpam-4971	382	1	physica	physica	PROPN
ejpam-4971	382	2	scripta	scripta	PROPN
ejpam-4971	382	3	,	,	PUNCT
ejpam-4971	382	4	96(12):125275	96(12):125275	NUM
ejpam-4971	382	5	,	,	PUNCT
ejpam-4971	382	6	2021	2021	NUM
ejpam-4971	382	7	.	.	PUNCT
ejpam-4971	383	1	[	[	X
ejpam-4971	383	2	15	15	NUM
ejpam-4971	383	3	]	]	X
ejpam-4971	383	4	me	i	PRON
ejpam-4971	383	5	elbrolosy	elbrolosy	VERB
ejpam-4971	383	6	and	and	CCONJ
ejpam-4971	383	7	aa	aa	NOUN
ejpam-4971	383	8	elmandouh	elmandouh	NOUN
ejpam-4971	383	9	.	.	PUNCT
ejpam-4971	384	1	bifurcation	bifurcation	NOUN
ejpam-4971	384	2	and	and	CCONJ
ejpam-4971	384	3	new	new	ADJ
ejpam-4971	384	4	traveling	travel	VERB
ejpam-4971	384	5	wave	wave	NOUN
ejpam-4971	384	6	solutions	solution	NOUN
ejpam-4971	384	7	for	for	ADP
ejpam-4971	384	8	(	(	PUNCT
ejpam-4971	384	9	2	2	NUM
ejpam-4971	384	10	+	+	NUM
ejpam-4971	384	11	1)-dimensional	1)-dimensional	NUM
ejpam-4971	384	12	nonlinear	nonlinear	ADJ
ejpam-4971	384	13	nizhnik	nizhnik	NOUN
ejpam-4971	384	14	–	–	PUNCT
ejpam-4971	384	15	novikov	novikov	ADJ
ejpam-4971	384	16	–	–	PUNCT
ejpam-4971	384	17	veselov	veselov	NOUN
ejpam-4971	384	18	dynamical	dynamical	ADJ
ejpam-4971	384	19	equation	equation	NOUN
ejpam-4971	384	20	.	.	PUNCT
ejpam-4971	385	1	the	the	DET
ejpam-4971	385	2	european	european	PROPN
ejpam-4971	385	3	physical	physical	PROPN
ejpam-4971	385	4	journal	journal	PROPN
ejpam-4971	385	5	plus	plus	CCONJ
ejpam-4971	385	6	,	,	PUNCT
ejpam-4971	385	7	135(6):533	135(6):533	NUM
ejpam-4971	385	8	,	,	PUNCT
ejpam-4971	385	9	2020	2020	NUM
ejpam-4971	385	10	.	.	PUNCT
ejpam-4971	386	1	[	[	X
ejpam-4971	386	2	16	16	NUM
ejpam-4971	386	3	]	]	X
ejpam-4971	386	4	me	i	PRON
ejpam-4971	386	5	elbrolosy	elbrolosy	VERB
ejpam-4971	386	6	and	and	CCONJ
ejpam-4971	386	7	aa	aa	NOUN
ejpam-4971	386	8	elmandouh	elmandouh	NOUN
ejpam-4971	386	9	.	.	PUNCT
ejpam-4971	387	1	dynamical	dynamical	ADJ
ejpam-4971	387	2	behaviour	behaviour	NOUN
ejpam-4971	387	3	of	of	ADP
ejpam-4971	387	4	nondissipative	nondissipative	ADJ
ejpam-4971	387	5	double	double	ADJ
ejpam-4971	387	6	dispersive	dispersive	ADJ
ejpam-4971	387	7	microstrain	microstrain	NOUN
ejpam-4971	387	8	wave	wave	NOUN
ejpam-4971	387	9	in	in	ADP
ejpam-4971	387	10	the	the	DET
ejpam-4971	387	11	microstructured	microstructured	ADJ
ejpam-4971	387	12	solids	solid	NOUN
ejpam-4971	387	13	.	.	PUNCT
ejpam-4971	388	1	the	the	DET
ejpam-4971	388	2	european	european	PROPN
ejpam-4971	388	3	physical	physical	PROPN
ejpam-4971	388	4	journal	journal	PROPN
ejpam-4971	388	5	plus	plus	CCONJ
ejpam-4971	388	6	,	,	PUNCT
ejpam-4971	388	7	136(9):1–20	136(9):1–20	NUM
ejpam-4971	388	8	,	,	PUNCT
ejpam-4971	388	9	2021	2021	NUM
ejpam-4971	388	10	.	.	PUNCT
ejpam-4971	389	1	[	[	X
ejpam-4971	389	2	17	17	NUM
ejpam-4971	389	3	]	]	X
ejpam-4971	389	4	mohammed	mohammed	PROPN
ejpam-4971	389	5	fathy	fathy	PROPN
ejpam-4971	389	6	elettreby	elettreby	PROPN
ejpam-4971	389	7	,	,	PUNCT
ejpam-4971	389	8	aisha	aisha	PROPN
ejpam-4971	389	9	khawagi	khawagi	PROPN
ejpam-4971	389	10	,	,	PUNCT
ejpam-4971	389	11	and	and	CCONJ
ejpam-4971	389	12	tamer	tame	ADJ
ejpam-4971	389	13	nabil	nabil	NOUN
ejpam-4971	389	14	.	.	PUNCT
ejpam-4971	390	1	dynamics	dynamic	NOUN
ejpam-4971	390	2	of	of	ADP
ejpam-4971	390	3	a	a	DET
ejpam-4971	390	4	discrete	discrete	ADJ
ejpam-4971	390	5	prey	prey	NOUN
ejpam-4971	390	6	–	–	PUNCT
ejpam-4971	390	7	predator	predator	NOUN
ejpam-4971	390	8	model	model	NOUN
ejpam-4971	390	9	with	with	ADP
ejpam-4971	390	10	mixed	mixed	ADJ
ejpam-4971	390	11	functional	functional	ADJ
ejpam-4971	390	12	response	response	NOUN
ejpam-4971	390	13	.	.	PUNCT
ejpam-4971	391	1	international	international	ADJ
ejpam-4971	391	2	journal	journal	NOUN
ejpam-4971	391	3	of	of	ADP
ejpam-4971	391	4	bifurcation	bifurcation	NOUN
ejpam-4971	391	5	and	and	CCONJ
ejpam-4971	391	6	chaos	chaos	NOUN
ejpam-4971	391	7	,	,	PUNCT
ejpam-4971	391	8	29(14):1950199	29(14):1950199	NUM
ejpam-4971	391	9	,	,	PUNCT
ejpam-4971	391	10	2019	2019	NUM
ejpam-4971	391	11	.	.	PUNCT
ejpam-4971	392	1	[	[	X
ejpam-4971	392	2	18	18	NUM
ejpam-4971	392	3	]	]	X
ejpam-4971	392	4	aa	aa	NOUN
ejpam-4971	392	5	elmandouh	elmandouh	NOUN
ejpam-4971	392	6	.	.	PUNCT
ejpam-4971	393	1	bifurcation	bifurcation	NOUN
ejpam-4971	393	2	and	and	CCONJ
ejpam-4971	393	3	new	new	ADJ
ejpam-4971	393	4	traveling	travel	VERB
ejpam-4971	393	5	wave	wave	NOUN
ejpam-4971	393	6	solutions	solution	NOUN
ejpam-4971	393	7	for	for	ADP
ejpam-4971	393	8	the	the	DET
ejpam-4971	393	9	2d	2d	NUM
ejpam-4971	393	10	ginzburg	ginzburg	NOUN
ejpam-4971	393	11	–	–	PUNCT
ejpam-4971	393	12	landau	landau	VERB
ejpam-4971	393	13	equation	equation	NOUN
ejpam-4971	393	14	.	.	PUNCT
ejpam-4971	394	1	the	the	DET
ejpam-4971	394	2	european	european	PROPN
ejpam-4971	394	3	physical	physical	PROPN
ejpam-4971	394	4	journal	journal	PROPN
ejpam-4971	394	5	plus	plus	CCONJ
ejpam-4971	394	6	,	,	PUNCT
ejpam-4971	394	7	135(8):648	135(8):648	NUM
ejpam-4971	394	8	,	,	PUNCT
ejpam-4971	394	9	2020	2020	NUM
ejpam-4971	394	10	.	.	PUNCT
ejpam-4971	395	1	references	reference	NOUN
ejpam-4971	395	2	2658	2658	NUM
ejpam-4971	395	3	[	[	X
ejpam-4971	395	4	19	19	NUM
ejpam-4971	395	5	]	]	X
ejpam-4971	395	6	aa	aa	NOUN
ejpam-4971	395	7	elmandouh	elmandouh	PROPN
ejpam-4971	395	8	.	.	PUNCT
ejpam-4971	396	1	integrability	integrability	NOUN
ejpam-4971	396	2	,	,	PUNCT
ejpam-4971	396	3	qualitative	qualitative	ADJ
ejpam-4971	396	4	analysis	analysis	NOUN
ejpam-4971	396	5	and	and	CCONJ
ejpam-4971	396	6	the	the	DET
ejpam-4971	396	7	dynamics	dynamic	NOUN
ejpam-4971	396	8	of	of	ADP
ejpam-4971	396	9	wave	wave	NOUN
ejpam-4971	396	10	solutions	solution	NOUN
ejpam-4971	396	11	for	for	ADP
ejpam-4971	396	12	biswas	biswas	PROPN
ejpam-4971	396	13	–	–	PUNCT
ejpam-4971	396	14	milovic	milovic	ADJ
ejpam-4971	396	15	equation	equation	NOUN
ejpam-4971	396	16	.	.	PUNCT
ejpam-4971	397	1	the	the	DET
ejpam-4971	397	2	european	european	PROPN
ejpam-4971	397	3	physical	physical	PROPN
ejpam-4971	397	4	journal	journal	PROPN
ejpam-4971	397	5	plus	plus	CCONJ
ejpam-4971	397	6	,	,	PUNCT
ejpam-4971	397	7	136(6):1–17	136(6):1–17	NUM
ejpam-4971	397	8	,	,	PUNCT
ejpam-4971	397	9	2021	2021	NUM
ejpam-4971	397	10	.	.	PUNCT
ejpam-4971	398	1	[	[	X
ejpam-4971	398	2	20	20	NUM
ejpam-4971	398	3	]	]	X
ejpam-4971	398	4	aa	aa	NOUN
ejpam-4971	398	5	elmandouha	elmandouha	NOUN
ejpam-4971	398	6	and	and	CCONJ
ejpam-4971	398	7	ag	ag	PROPN
ejpam-4971	398	8	ibrahim	ibrahim	PROPN
ejpam-4971	398	9	.	.	PUNCT
ejpam-4971	399	1	bifurcation	bifurcation	NOUN
ejpam-4971	399	2	and	and	CCONJ
ejpam-4971	399	3	travelling	travel	VERB
ejpam-4971	399	4	wave	wave	NOUN
ejpam-4971	399	5	solutions	solution	NOUN
ejpam-4971	399	6	for	for	ADP
ejpam-4971	399	7	a	a	DET
ejpam-4971	399	8	(	(	PUNCT
ejpam-4971	399	9	2	2	NUM
ejpam-4971	399	10	+	+	NUM
ejpam-4971	399	11	1)-dimensional	1)-dimensional	NUM
ejpam-4971	399	12	kdv	kdv	NOUN
ejpam-4971	399	13	equation	equation	NOUN
ejpam-4971	399	14	.	.	PUNCT
ejpam-4971	400	1	journal	journal	PROPN
ejpam-4971	400	2	of	of	ADP
ejpam-4971	400	3	taibah	taibah	PROPN
ejpam-4971	400	4	university	university	PROPN
ejpam-4971	400	5	for	for	ADP
ejpam-4971	400	6	science	science	NOUN
ejpam-4971	400	7	,	,	PUNCT
ejpam-4971	400	8	14(1):139	14(1):139	NUM
ejpam-4971	400	9	–	–	PUNCT
ejpam-4971	400	10	147	147	NUM
ejpam-4971	400	11	,	,	PUNCT
ejpam-4971	400	12	2020	2020	NUM
ejpam-4971	400	13	.	.	PUNCT
ejpam-4971	401	1	[	[	X
ejpam-4971	401	2	21	21	NUM
ejpam-4971	401	3	]	]	X
ejpam-4971	401	4	berat	berat	PROPN
ejpam-4971	401	5	karaagac	karaagac	PROPN
ejpam-4971	401	6	.	.	PUNCT
ejpam-4971	402	1	a	a	DET
ejpam-4971	402	2	study	study	NOUN
ejpam-4971	402	3	on	on	ADP
ejpam-4971	402	4	fractional	fractional	PROPN
ejpam-4971	402	5	klein	klein	PROPN
ejpam-4971	402	6	gordon	gordon	PROPN
ejpam-4971	402	7	equation	equation	NOUN
ejpam-4971	402	8	with	with	ADP
ejpam-4971	402	9	non	non	ADJ
ejpam-4971	402	10	-	-	ADJ
ejpam-4971	402	11	local	local	ADJ
ejpam-4971	402	12	and	and	CCONJ
ejpam-4971	402	13	non	non	ADJ
ejpam-4971	402	14	-	-	ADJ
ejpam-4971	402	15	singular	singular	ADJ
ejpam-4971	402	16	kernel	kernel	NOUN
ejpam-4971	402	17	.	.	PUNCT
ejpam-4971	403	1	chaos	chaos	NOUN
ejpam-4971	403	2	,	,	PUNCT
ejpam-4971	403	3	solitons	soliton	NOUN
ejpam-4971	403	4	&	&	CCONJ
ejpam-4971	403	5	fractals	fractal	NOUN
ejpam-4971	403	6	,	,	PUNCT
ejpam-4971	403	7	126:218–229	126:218–229	NUM
ejpam-4971	403	8	,	,	PUNCT
ejpam-4971	403	9	2019	2019	NUM
ejpam-4971	403	10	.	.	PUNCT
ejpam-4971	404	1	[	[	X
ejpam-4971	404	2	22	22	NUM
ejpam-4971	404	3	]	]	X
ejpam-4971	404	4	berat	berat	PROPN
ejpam-4971	404	5	karaagac	karaagac	PROPN
ejpam-4971	404	6	,	,	PUNCT
ejpam-4971	404	7	ucar	ucar	PROPN
ejpam-4971	404	8	yusuf	yusuf	PROPN
ejpam-4971	404	9	,	,	PUNCT
ejpam-4971	404	10	n	n	PROPN
ejpam-4971	404	11	murat	murat	PROPN
ejpam-4971	404	12	yagmurlu	yagmurlu	NOUN
ejpam-4971	404	13	,	,	PUNCT
ejpam-4971	404	14	and	and	CCONJ
ejpam-4971	404	15	esen	esen	ADJ
ejpam-4971	404	16	alaattin	alaattin	NOUN
ejpam-4971	404	17	.	.	PUNCT
ejpam-4971	405	1	a	a	DET
ejpam-4971	405	2	new	new	ADJ
ejpam-4971	405	3	perspective	perspective	NOUN
ejpam-4971	405	4	on	on	ADP
ejpam-4971	405	5	the	the	DET
ejpam-4971	405	6	numerical	numerical	ADJ
ejpam-4971	405	7	solution	solution	NOUN
ejpam-4971	405	8	for	for	ADP
ejpam-4971	405	9	fractional	fractional	PROPN
ejpam-4971	405	10	klein	klein	PROPN
ejpam-4971	405	11	gordon	gordon	PROPN
ejpam-4971	405	12	equation	equation	PROPN
ejpam-4971	405	13	.	.	PUNCT
ejpam-4971	406	1	politeknik	politeknik	PROPN
ejpam-4971	406	2	dergisi	dergisi	PROPN
ejpam-4971	406	3	,	,	PUNCT
ejpam-4971	406	4	22(2):443–451	22(2):443–451	PROPN
ejpam-4971	406	5	,	,	PUNCT
ejpam-4971	406	6	2019	2019	NUM
ejpam-4971	406	7	.	.	PUNCT
ejpam-4971	407	1	[	[	X
ejpam-4971	407	2	23	23	NUM
ejpam-4971	407	3	]	]	X
ejpam-4971	407	4	mostafa	mostafa	PROPN
ejpam-4971	407	5	ma	ma	PROPN
ejpam-4971	407	6	khater	khater	PROPN
ejpam-4971	407	7	.	.	PUNCT
ejpam-4971	408	1	a	a	DET
ejpam-4971	408	2	hybrid	hybrid	ADJ
ejpam-4971	408	3	analytical	analytical	ADJ
ejpam-4971	408	4	and	and	CCONJ
ejpam-4971	408	5	numerical	numerical	ADJ
ejpam-4971	408	6	analysis	analysis	NOUN
ejpam-4971	408	7	of	of	ADP
ejpam-4971	408	8	ultra	ultra	ADJ
ejpam-4971	408	9	-	-	ADJ
ejpam-4971	408	10	short	short	ADJ
ejpam-4971	408	11	pulse	pulse	NOUN
ejpam-4971	408	12	phase	phase	NOUN
ejpam-4971	408	13	shifts	shift	NOUN
ejpam-4971	408	14	.	.	PUNCT
ejpam-4971	409	1	chaos	chaos	NOUN
ejpam-4971	409	2	,	,	PUNCT
ejpam-4971	409	3	solitons	soliton	NOUN
ejpam-4971	409	4	&	&	CCONJ
ejpam-4971	409	5	fractals	fractal	NOUN
ejpam-4971	409	6	,	,	PUNCT
ejpam-4971	409	7	169:113232	169:113232	NUM
ejpam-4971	409	8	,	,	PUNCT
ejpam-4971	409	9	2023	2023	NUM
ejpam-4971	409	10	.	.	PUNCT
ejpam-4971	410	1	[	[	X
ejpam-4971	410	2	24	24	NUM
ejpam-4971	410	3	]	]	X
ejpam-4971	410	4	mostafa	mostafa	PROPN
ejpam-4971	410	5	ma	ma	PROPN
ejpam-4971	410	6	khater	khater	PROPN
ejpam-4971	410	7	.	.	PUNCT
ejpam-4971	411	1	in	in	ADP
ejpam-4971	411	2	solid	solid	ADJ
ejpam-4971	411	3	physics	physics	NOUN
ejpam-4971	411	4	equations	equation	NOUN
ejpam-4971	411	5	,	,	PUNCT
ejpam-4971	411	6	accurate	accurate	ADJ
ejpam-4971	411	7	and	and	CCONJ
ejpam-4971	411	8	novel	novel	ADJ
ejpam-4971	411	9	soliton	soliton	NOUN
ejpam-4971	411	10	wave	wave	NOUN
ejpam-4971	411	11	structures	structure	NOUN
ejpam-4971	411	12	for	for	ADP
ejpam-4971	411	13	heating	heat	VERB
ejpam-4971	411	14	a	a	DET
ejpam-4971	411	15	single	single	ADJ
ejpam-4971	411	16	crystal	crystal	NOUN
ejpam-4971	411	17	of	of	ADP
ejpam-4971	411	18	sodium	sodium	NOUN
ejpam-4971	411	19	fluoride	fluoride	NOUN
ejpam-4971	411	20	.	.	PUNCT
ejpam-4971	412	1	international	international	ADJ
ejpam-4971	412	2	journal	journal	NOUN
ejpam-4971	412	3	of	of	ADP
ejpam-4971	412	4	modern	modern	ADJ
ejpam-4971	412	5	physics	physics	PROPN
ejpam-4971	412	6	b	b	PROPN
ejpam-4971	412	7	,	,	PUNCT
ejpam-4971	412	8	37(07):2350068	37(07):2350068	NUM
ejpam-4971	412	9	,	,	PUNCT
ejpam-4971	412	10	2023	2023	NUM
ejpam-4971	412	11	.	.	PUNCT
ejpam-4971	413	1	[	[	X
ejpam-4971	413	2	25	25	NUM
ejpam-4971	413	3	]	]	X
ejpam-4971	413	4	mostafa	mostafa	PROPN
ejpam-4971	413	5	ma	ma	PROPN
ejpam-4971	413	6	khater	khater	PROPN
ejpam-4971	413	7	.	.	PUNCT
ejpam-4971	414	1	multi	multi	ADJ
ejpam-4971	414	2	-	-	NOUN
ejpam-4971	414	3	vector	vector	NOUN
ejpam-4971	414	4	with	with	ADP
ejpam-4971	414	5	nonlocal	nonlocal	ADJ
ejpam-4971	414	6	and	and	CCONJ
ejpam-4971	414	7	non	non	ADJ
ejpam-4971	414	8	-	-	ADJ
ejpam-4971	414	9	singular	singular	ADJ
ejpam-4971	414	10	kernel	kernel	PROPN
ejpam-4971	414	11	ultrashort	ultrashort	VERB
ejpam-4971	414	12	optical	optical	ADJ
ejpam-4971	414	13	solitons	soliton	NOUN
ejpam-4971	414	14	pulses	pulse	NOUN
ejpam-4971	414	15	waves	wave	NOUN
ejpam-4971	414	16	in	in	ADP
ejpam-4971	414	17	birefringent	birefringent	NOUN
ejpam-4971	414	18	fibers	fiber	NOUN
ejpam-4971	414	19	.	.	PUNCT
ejpam-4971	415	1	chaos	chaos	NOUN
ejpam-4971	415	2	,	,	PUNCT
ejpam-4971	415	3	solitons	soliton	NOUN
ejpam-4971	415	4	&	&	CCONJ
ejpam-4971	415	5	fractals	fractal	NOUN
ejpam-4971	415	6	,	,	PUNCT
ejpam-4971	415	7	167:113098	167:113098	NUM
ejpam-4971	415	8	,	,	PUNCT
ejpam-4971	415	9	2023	2023	NUM
ejpam-4971	415	10	.	.	PUNCT
ejpam-4971	416	1	[	[	X
ejpam-4971	416	2	26	26	NUM
ejpam-4971	416	3	]	]	X
ejpam-4971	416	4	mostafa	mostafa	PROPN
ejpam-4971	416	5	ma	ma	PROPN
ejpam-4971	416	6	khater	khater	PROPN
ejpam-4971	416	7	.	.	PUNCT
ejpam-4971	417	1	nonlinear	nonlinear	ADJ
ejpam-4971	417	2	elastic	elastic	ADJ
ejpam-4971	417	3	circular	circular	ADJ
ejpam-4971	417	4	rod	rod	NOUN
ejpam-4971	417	5	with	with	ADP
ejpam-4971	417	6	lateral	lateral	ADJ
ejpam-4971	417	7	inertia	inertia	NOUN
ejpam-4971	417	8	and	and	CCONJ
ejpam-4971	417	9	finite	finite	ADJ
ejpam-4971	417	10	radius	radius	NOUN
ejpam-4971	417	11	:	:	PUNCT
ejpam-4971	417	12	dynamical	dynamical	ADJ
ejpam-4971	417	13	attributive	attributive	NOUN
ejpam-4971	417	14	of	of	ADP
ejpam-4971	417	15	longitudinal	longitudinal	ADJ
ejpam-4971	417	16	oscillation	oscillation	NOUN
ejpam-4971	417	17	.	.	PUNCT
ejpam-4971	418	1	international	international	ADJ
ejpam-4971	418	2	journal	journal	NOUN
ejpam-4971	418	3	of	of	ADP
ejpam-4971	418	4	modern	modern	ADJ
ejpam-4971	418	5	physics	physics	PROPN
ejpam-4971	418	6	b	b	PROPN
ejpam-4971	418	7	,	,	PUNCT
ejpam-4971	418	8	37(06):2350052	37(06):2350052	NUM
ejpam-4971	418	9	,	,	PUNCT
ejpam-4971	418	10	2023	2023	NUM
ejpam-4971	418	11	.	.	PUNCT
ejpam-4971	419	1	[	[	X
ejpam-4971	419	2	27	27	NUM
ejpam-4971	419	3	]	]	X
ejpam-4971	419	4	mostafa	mostafa	PROPN
ejpam-4971	419	5	ma	ma	PROPN
ejpam-4971	419	6	khater	khater	PROPN
ejpam-4971	419	7	.	.	PUNCT
ejpam-4971	420	1	novel	novel	ADJ
ejpam-4971	420	2	computational	computational	ADJ
ejpam-4971	420	3	simulation	simulation	NOUN
ejpam-4971	420	4	of	of	ADP
ejpam-4971	420	5	the	the	DET
ejpam-4971	420	6	propagation	propagation	NOUN
ejpam-4971	420	7	of	of	ADP
ejpam-4971	420	8	pulses	pulse	NOUN
ejpam-4971	420	9	in	in	ADP
ejpam-4971	420	10	optical	optical	ADJ
ejpam-4971	420	11	fibers	fiber	NOUN
ejpam-4971	420	12	regarding	regard	VERB
ejpam-4971	420	13	the	the	DET
ejpam-4971	420	14	dispersion	dispersion	NOUN
ejpam-4971	420	15	effect	effect	NOUN
ejpam-4971	420	16	.	.	PUNCT
ejpam-4971	421	1	international	international	ADJ
ejpam-4971	421	2	journal	journal	NOUN
ejpam-4971	421	3	of	of	ADP
ejpam-4971	421	4	modern	modern	ADJ
ejpam-4971	421	5	physics	physics	PROPN
ejpam-4971	421	6	b	b	PROPN
ejpam-4971	421	7	,	,	PUNCT
ejpam-4971	421	8	37(09):2350083	37(09):2350083	NUM
ejpam-4971	421	9	,	,	PUNCT
ejpam-4971	421	10	2023	2023	NUM
ejpam-4971	421	11	.	.	PUNCT
ejpam-4971	422	1	[	[	X
ejpam-4971	422	2	28	28	NUM
ejpam-4971	422	3	]	]	X
ejpam-4971	422	4	mostafa	mostafa	PROPN
ejpam-4971	422	5	ma	ma	PROPN
ejpam-4971	422	6	khater	khater	PROPN
ejpam-4971	422	7	.	.	PUNCT
ejpam-4971	423	1	physics	physics	PROPN
ejpam-4971	423	2	of	of	ADP
ejpam-4971	423	3	crystal	crystal	NOUN
ejpam-4971	423	4	lattices	lattice	NOUN
ejpam-4971	423	5	and	and	CCONJ
ejpam-4971	423	6	plasma	plasma	NOUN
ejpam-4971	423	7	;	;	PUNCT
ejpam-4971	423	8	analytical	analytical	ADJ
ejpam-4971	423	9	and	and	CCONJ
ejpam-4971	423	10	numerical	numerical	ADJ
ejpam-4971	423	11	simulations	simulation	NOUN
ejpam-4971	423	12	of	of	ADP
ejpam-4971	423	13	the	the	DET
ejpam-4971	423	14	gilson	gilson	PROPN
ejpam-4971	423	15	–	–	PUNCT
ejpam-4971	423	16	pickering	pickering	NOUN
ejpam-4971	423	17	equation	equation	NOUN
ejpam-4971	423	18	.	.	PUNCT
ejpam-4971	424	1	results	result	NOUN
ejpam-4971	424	2	in	in	ADP
ejpam-4971	424	3	physics	physics	NOUN
ejpam-4971	424	4	,	,	PUNCT
ejpam-4971	424	5	44:106193	44:106193	NOUN
ejpam-4971	424	6	,	,	PUNCT
ejpam-4971	424	7	2023	2023	NUM
ejpam-4971	424	8	.	.	PUNCT
ejpam-4971	425	1	[	[	X
ejpam-4971	425	2	29	29	NUM
ejpam-4971	425	3	]	]	X
ejpam-4971	425	4	mostafa	mostafa	PROPN
ejpam-4971	425	5	ma	ma	PROPN
ejpam-4971	425	6	khater	khater	PROPN
ejpam-4971	425	7	.	.	PUNCT
ejpam-4971	426	1	prorogation	prorogation	NOUN
ejpam-4971	426	2	of	of	ADP
ejpam-4971	426	3	waves	wave	NOUN
ejpam-4971	426	4	in	in	ADP
ejpam-4971	426	5	shallow	shallow	ADJ
ejpam-4971	426	6	water	water	NOUN
ejpam-4971	426	7	through	through	ADP
ejpam-4971	426	8	unidirectional	unidirectional	ADJ
ejpam-4971	426	9	dullin	dullin	NOUN
ejpam-4971	426	10	–	–	PUNCT
ejpam-4971	426	11	gottwald	gottwald	NOUN
ejpam-4971	426	12	–	–	PUNCT
ejpam-4971	426	13	holm	holm	PROPN
ejpam-4971	426	14	model	model	NOUN
ejpam-4971	426	15	;	;	PUNCT
ejpam-4971	426	16	computational	computational	ADJ
ejpam-4971	426	17	simulations	simulation	NOUN
ejpam-4971	426	18	.	.	PUNCT
ejpam-4971	427	1	international	international	ADJ
ejpam-4971	427	2	journal	journal	NOUN
ejpam-4971	427	3	of	of	ADP
ejpam-4971	427	4	modern	modern	ADJ
ejpam-4971	427	5	physics	physics	PROPN
ejpam-4971	427	6	b	b	PROPN
ejpam-4971	427	7	,	,	PUNCT
ejpam-4971	427	8	37(08):2350071	37(08):2350071	NUM
ejpam-4971	427	9	,	,	PUNCT
ejpam-4971	427	10	2023	2023	NUM
ejpam-4971	427	11	.	.	PUNCT
ejpam-4971	428	1	[	[	X
ejpam-4971	428	2	30	30	NUM
ejpam-4971	428	3	]	]	X
ejpam-4971	428	4	mostafa	mostafa	PROPN
ejpam-4971	428	5	ma	ma	PROPN
ejpam-4971	428	6	khater	khater	PROPN
ejpam-4971	428	7	,	,	PUNCT
ejpam-4971	428	8	suleman	suleman	PROPN
ejpam-4971	428	9	h	h	PROPN
ejpam-4971	428	10	alfalqi	alfalqi	PROPN
ejpam-4971	428	11	,	,	PUNCT
ejpam-4971	428	12	jameel	jameel	PROPN
ejpam-4971	428	13	f	f	PROPN
ejpam-4971	428	14	alzaidi	alzaidi	PROPN
ejpam-4971	428	15	,	,	PUNCT
ejpam-4971	428	16	and	and	CCONJ
ejpam-4971	428	17	raghda	raghda	NOUN
ejpam-4971	428	18	am	be	AUX
ejpam-4971	428	19	attia	attia	NOUN
ejpam-4971	428	20	.	.	PUNCT
ejpam-4971	429	1	analytically	analytically	ADV
ejpam-4971	429	2	and	and	CCONJ
ejpam-4971	429	3	numerically	numerically	ADV
ejpam-4971	429	4	,	,	PUNCT
ejpam-4971	429	5	dispersive	dispersive	ADJ
ejpam-4971	429	6	,	,	PUNCT
ejpam-4971	429	7	weakly	weakly	ADJ
ejpam-4971	429	8	nonlinear	nonlinear	ADJ
ejpam-4971	429	9	wave	wave	NOUN
ejpam-4971	429	10	packets	packet	NOUN
ejpam-4971	429	11	are	be	AUX
ejpam-4971	429	12	presented	present	VERB
ejpam-4971	429	13	in	in	ADP
ejpam-4971	429	14	a	a	DET
ejpam-4971	429	15	quasi	quasi	ADJ
ejpam-4971	429	16	-	-	ADJ
ejpam-4971	429	17	monochromatic	monochromatic	ADJ
ejpam-4971	429	18	medium	medium	NOUN
ejpam-4971	429	19	.	.	PUNCT
ejpam-4971	430	1	results	result	NOUN
ejpam-4971	430	2	in	in	ADP
ejpam-4971	430	3	physics	physics	NOUN
ejpam-4971	430	4	,	,	PUNCT
ejpam-4971	430	5	46:106312	46:106312	PROPN
ejpam-4971	430	6	,	,	PUNCT
ejpam-4971	430	7	2023	2023	NUM
ejpam-4971	430	8	.	.	PUNCT
ejpam-4971	431	1	[	[	X
ejpam-4971	431	2	31	31	NUM
ejpam-4971	431	3	]	]	PUNCT
ejpam-4971	431	4	mostafa	mostafa	PROPN
ejpam-4971	431	5	ma	ma	PROPN
ejpam-4971	431	6	khater	khater	PROPN
ejpam-4971	431	7	,	,	PUNCT
ejpam-4971	431	8	xiao	xiao	PROPN
ejpam-4971	431	9	zhang	zhang	PROPN
ejpam-4971	431	10	,	,	PUNCT
ejpam-4971	431	11	and	and	CCONJ
ejpam-4971	431	12	raghda	raghda	NOUN
ejpam-4971	431	13	am	be	AUX
ejpam-4971	431	14	attia	attia	NOUN
ejpam-4971	431	15	.	.	PUNCT
ejpam-4971	432	1	accurate	accurate	ADJ
ejpam-4971	432	2	computational	computational	ADJ
ejpam-4971	432	3	simulations	simulation	NOUN
ejpam-4971	432	4	of	of	ADP
ejpam-4971	432	5	perturbed	perturb	VERB
ejpam-4971	432	6	chen	chen	PROPN
ejpam-4971	432	7	–	–	PUNCT
ejpam-4971	432	8	lee	lee	PROPN
ejpam-4971	432	9	–	–	PUNCT
ejpam-4971	432	10	liu	liu	PROPN
ejpam-4971	432	11	equation	equation	NOUN
ejpam-4971	432	12	.	.	PUNCT
ejpam-4971	433	1	results	result	NOUN
ejpam-4971	433	2	in	in	ADP
ejpam-4971	433	3	physics	physics	NOUN
ejpam-4971	433	4	,	,	PUNCT
ejpam-4971	433	5	45:106227	45:106227	PROPN
ejpam-4971	433	6	,	,	PUNCT
ejpam-4971	433	7	2023	2023	NUM
ejpam-4971	433	8	.	.	PUNCT
ejpam-4971	434	1	references	reference	NOUN
ejpam-4971	434	2	2659	2659	NUM
ejpam-4971	434	3	[	[	X
ejpam-4971	434	4	32	32	NUM
ejpam-4971	434	5	]	]	PUNCT
ejpam-4971	434	6	s	s	VERB
ejpam-4971	434	7	kumbinarasaiah	kumbinarasaiah	PROPN
ejpam-4971	434	8	,	,	PUNCT
ejpam-4971	434	9	hs	hs	PROPN
ejpam-4971	434	10	ramane	ramane	PROPN
ejpam-4971	434	11	,	,	PUNCT
ejpam-4971	434	12	ks	ks	NOUN
ejpam-4971	434	13	pise	pise	NOUN
ejpam-4971	434	14	,	,	PUNCT
ejpam-4971	434	15	and	and	CCONJ
ejpam-4971	434	16	g	g	PROPN
ejpam-4971	434	17	hariharan	hariharan	PROPN
ejpam-4971	434	18	.	.	PUNCT
ejpam-4971	435	1	numerical	numerical	PROPN
ejpam-4971	435	2	-	-	PUNCT
ejpam-4971	435	3	solutionfor	solutionfor	NOUN
ejpam-4971	435	4	-	-	PUNCT
ejpam-4971	435	5	nonlinear	nonlinear	ADJ
ejpam-4971	435	6	-	-	PUNCT
ejpam-4971	435	7	klein	klein	NOUN
ejpam-4971	435	8	–	–	PUNCT
ejpam-4971	435	9	gordon	gordon	PROPN
ejpam-4971	435	10	equation	equation	NOUN
ejpam-4971	435	11	via	via	ADP
ejpam-4971	435	12	operational	operational	ADJ
ejpam-4971	435	13	-	-	PUNCT
ejpam-4971	435	14	matrix	matrix	NOUN
ejpam-4971	435	15	by	by	ADP
ejpam-4971	435	16	clique	clique	ADJ
ejpam-4971	435	17	polynomial	polynomial	NOUN
ejpam-4971	435	18	of	of	ADP
ejpam-4971	435	19	complete	complete	ADJ
ejpam-4971	435	20	graphs	graph	NOUN
ejpam-4971	435	21	.	.	PUNCT
ejpam-4971	436	1	international	international	ADJ
ejpam-4971	436	2	journal	journal	PROPN
ejpam-4971	436	3	of	of	ADP
ejpam-4971	436	4	applied	applied	ADJ
ejpam-4971	436	5	and	and	CCONJ
ejpam-4971	436	6	computational	computational	ADJ
ejpam-4971	436	7	mathematics	mathematic	NOUN
ejpam-4971	436	8	,	,	PUNCT
ejpam-4971	436	9	7:1–19	7:1–19	NUM
ejpam-4971	436	10	,	,	PUNCT
ejpam-4971	436	11	2021	2021	NUM
ejpam-4971	436	12	.	.	PUNCT
ejpam-4971	437	1	[	[	X
ejpam-4971	437	2	33	33	NUM
ejpam-4971	437	3	]	]	PUNCT
ejpam-4971	437	4	chun	chun	PROPN
ejpam-4971	437	5	-	-	PUNCT
ejpam-4971	437	6	ku	ku	PROPN
ejpam-4971	437	7	kuo	kuo	PROPN
ejpam-4971	437	8	,	,	PUNCT
ejpam-4971	437	9	b	b	X
ejpam-4971	437	10	gunay	gunay	PROPN
ejpam-4971	437	11	,	,	PUNCT
ejpam-4971	437	12	and	and	CCONJ
ejpam-4971	437	13	chieh	chieh	PROPN
ejpam-4971	437	14	-	-	PROPN
ejpam-4971	437	15	ju	ju	PROPN
ejpam-4971	437	16	juan	juan	PROPN
ejpam-4971	437	17	.	.	PUNCT
ejpam-4971	438	1	the	the	DET
ejpam-4971	438	2	applications	application	NOUN
ejpam-4971	438	3	of	of	ADP
ejpam-4971	438	4	symbolic	symbolic	ADJ
ejpam-4971	438	5	computation	computation	NOUN
ejpam-4971	438	6	to	to	ADP
ejpam-4971	438	7	exact	exact	ADJ
ejpam-4971	438	8	wave	wave	NOUN
ejpam-4971	438	9	solutions	solution	NOUN
ejpam-4971	438	10	of	of	ADP
ejpam-4971	438	11	two	two	NUM
ejpam-4971	438	12	hsi	hsi	PROPN
ejpam-4971	438	13	-	-	PUNCT
ejpam-4971	438	14	like	like	ADJ
ejpam-4971	438	15	equations	equation	NOUN
ejpam-4971	438	16	in	in	ADP
ejpam-4971	438	17	(	(	PUNCT
ejpam-4971	438	18	2	2	NUM
ejpam-4971	438	19	+	+	NUM
ejpam-4971	438	20	1)-dimensional	1)-dimensional	PROPN
ejpam-4971	438	21	.	.	NOUN
ejpam-4971	438	22	frontiers	frontier	NOUN
ejpam-4971	438	23	in	in	ADP
ejpam-4971	438	24	physics	physics	PROPN
ejpam-4971	438	25	,	,	PUNCT
ejpam-4971	438	26	11:26	11:26	NUM
ejpam-4971	438	27	,	,	PUNCT
ejpam-4971	438	28	2023	2023	NUM
ejpam-4971	438	29	.	.	PUNCT
ejpam-4971	439	1	[	[	X
ejpam-4971	439	2	34	34	NUM
ejpam-4971	439	3	]	]	X
ejpam-4971	439	4	jibin	jibin	PROPN
ejpam-4971	439	5	li	li	PROPN
ejpam-4971	439	6	and	and	CCONJ
ejpam-4971	439	7	zhengrong	zhengrong	PROPN
ejpam-4971	439	8	liu	liu	PROPN
ejpam-4971	439	9	.	.	PROPN
ejpam-4971	440	1	smooth	smooth	PROPN
ejpam-4971	440	2	and	and	CCONJ
ejpam-4971	440	3	non	non	ADJ
ejpam-4971	440	4	-	-	ADJ
ejpam-4971	440	5	smooth	smooth	ADJ
ejpam-4971	440	6	traveling	travel	VERB
ejpam-4971	440	7	waves	wave	NOUN
ejpam-4971	440	8	in	in	ADP
ejpam-4971	440	9	a	a	DET
ejpam-4971	440	10	nonlinearly	nonlinearly	ADV
ejpam-4971	440	11	dispersive	dispersive	ADJ
ejpam-4971	440	12	equation	equation	NOUN
ejpam-4971	440	13	.	.	PUNCT
ejpam-4971	441	1	applied	apply	VERB
ejpam-4971	441	2	mathematical	mathematical	ADJ
ejpam-4971	441	3	modelling	modelling	NOUN
ejpam-4971	441	4	,	,	PUNCT
ejpam-4971	441	5	25(1):41–56	25(1):41–56	NUM
ejpam-4971	441	6	,	,	PUNCT
ejpam-4971	441	7	2000	2000	NUM
ejpam-4971	441	8	.	.	PUNCT
ejpam-4971	442	1	[	[	X
ejpam-4971	442	2	35	35	NUM
ejpam-4971	442	3	]	]	PUNCT
ejpam-4971	442	4	xuemei	xuemei	PROPN
ejpam-4971	442	5	li	li	PROPN
ejpam-4971	442	6	and	and	CCONJ
ejpam-4971	442	7	aihua	aihua	PROPN
ejpam-4971	442	8	chen	chen	PROPN
ejpam-4971	442	9	.	.	PUNCT
ejpam-4971	443	1	darboux	darboux	VERB
ejpam-4971	443	2	transformation	transformation	NOUN
ejpam-4971	443	3	and	and	CCONJ
ejpam-4971	443	4	multi	multi	ADJ
ejpam-4971	443	5	-	-	ADJ
ejpam-4971	443	6	soliton	soliton	ADJ
ejpam-4971	443	7	solutions	solution	NOUN
ejpam-4971	443	8	of	of	ADP
ejpam-4971	443	9	boussinesq	boussinesq	ADJ
ejpam-4971	443	10	–	–	PUNCT
ejpam-4971	443	11	burgers	burger	NOUN
ejpam-4971	443	12	equation	equation	NOUN
ejpam-4971	443	13	.	.	PUNCT
ejpam-4971	444	1	physics	physics	NOUN
ejpam-4971	444	2	letters	letter	NOUN
ejpam-4971	444	3	a	a	PRON
ejpam-4971	444	4	,	,	PUNCT
ejpam-4971	444	5	342(5	342(5	NUM
ejpam-4971	444	6	-	-	SYM
ejpam-4971	444	7	6):413–420	6):413–420	NOUN
ejpam-4971	444	8	,	,	PUNCT
ejpam-4971	444	9	2005	2005	NUM
ejpam-4971	444	10	.	.	PUNCT
ejpam-4971	445	1	[	[	X
ejpam-4971	445	2	36	36	NUM
ejpam-4971	445	3	]	]	X
ejpam-4971	445	4	haihong	haihong	PROPN
ejpam-4971	445	5	liu	liu	PROPN
ejpam-4971	445	6	,	,	PUNCT
ejpam-4971	445	7	fang	fang	PROPN
ejpam-4971	445	8	yan	yan	PROPN
ejpam-4971	445	9	,	,	PUNCT
ejpam-4971	445	10	and	and	CCONJ
ejpam-4971	445	11	chenglin	chenglin	PROPN
ejpam-4971	445	12	xu	xu	PROPN
ejpam-4971	445	13	.	.	PUNCT
ejpam-4971	446	1	the	the	DET
ejpam-4971	446	2	bifurcation	bifurcation	NOUN
ejpam-4971	446	3	and	and	CCONJ
ejpam-4971	446	4	exact	exact	ADJ
ejpam-4971	446	5	travelling	travelling	ADJ
ejpam-4971	446	6	wave	wave	NOUN
ejpam-4971	446	7	solutions	solution	NOUN
ejpam-4971	446	8	of	of	ADP
ejpam-4971	446	9	(	(	PUNCT
ejpam-4971	446	10	1	1	NUM
ejpam-4971	446	11	+	+	NUM
ejpam-4971	446	12	2)-dimensional	2)-dimensional	NUM
ejpam-4971	446	13	nonlinear	nonlinear	NOUN
ejpam-4971	446	14	schrödinger	schrödinger	NOUN
ejpam-4971	446	15	equation	equation	NOUN
ejpam-4971	446	16	with	with	ADP
ejpam-4971	446	17	dual	dual	ADJ
ejpam-4971	446	18	-	-	PUNCT
ejpam-4971	446	19	power	power	NOUN
ejpam-4971	446	20	law	law	NOUN
ejpam-4971	446	21	nonlinearity	nonlinearity	NOUN
ejpam-4971	446	22	.	.	PUNCT
ejpam-4971	447	1	nonlinear	nonlinear	ADJ
ejpam-4971	447	2	dynamics	dynamic	NOUN
ejpam-4971	447	3	,	,	PUNCT
ejpam-4971	447	4	67:465–473	67:465–473	NUM
ejpam-4971	447	5	,	,	PUNCT
ejpam-4971	447	6	2012	2012	NUM
ejpam-4971	447	7	.	.	PUNCT
ejpam-4971	448	1	[	[	X
ejpam-4971	448	2	37	37	NUM
ejpam-4971	448	3	]	]	PUNCT
ejpam-4971	448	4	xun	xun	PROPN
ejpam-4971	448	5	liu	liu	PROPN
ejpam-4971	448	6	,	,	PUNCT
ejpam-4971	448	7	lixin	lixin	PROPN
ejpam-4971	448	8	tian	tian	PROPN
ejpam-4971	448	9	,	,	PUNCT
ejpam-4971	448	10	and	and	CCONJ
ejpam-4971	448	11	yuhai	yuhai	PROPN
ejpam-4971	448	12	wu	wu	PROPN
ejpam-4971	448	13	.	.	PUNCT
ejpam-4971	449	1	application	application	NOUN
ejpam-4971	449	2	of	of	ADP
ejpam-4971	449	3	g	g	PROPN
ejpam-4971	449	4	g	g	NOUN
ejpam-4971	449	5	-	-	PUNCT
ejpam-4971	449	6	expansion	expansion	NOUN
ejpam-4971	449	7	method	method	NOUN
ejpam-4971	449	8	to	to	ADP
ejpam-4971	449	9	two	two	NUM
ejpam-4971	449	10	nonlinear	nonlinear	ADJ
ejpam-4971	449	11	evolution	evolution	NOUN
ejpam-4971	449	12	equations	equation	NOUN
ejpam-4971	449	13	.	.	PUNCT
ejpam-4971	450	1	applied	apply	VERB
ejpam-4971	450	2	mathematics	mathematic	NOUN
ejpam-4971	450	3	and	and	CCONJ
ejpam-4971	450	4	computation	computation	NOUN
ejpam-4971	450	5	,	,	PUNCT
ejpam-4971	450	6	217(4):1376	217(4):1376	NUM
ejpam-4971	450	7	–	–	PUNCT
ejpam-4971	450	8	1384	1384	NUM
ejpam-4971	450	9	,	,	PUNCT
ejpam-4971	450	10	2010	2010	NUM
ejpam-4971	450	11	.	.	PUNCT
ejpam-4971	451	1	[	[	X
ejpam-4971	451	2	38	38	NUM
ejpam-4971	451	3	]	]	PUNCT
ejpam-4971	451	4	zhengrong	zhengrong	PROPN
ejpam-4971	451	5	liu	liu	PROPN
ejpam-4971	451	6	and	and	CCONJ
ejpam-4971	451	7	tifei	tifei	PROPN
ejpam-4971	451	8	qian	qian	PROPN
ejpam-4971	451	9	.	.	PUNCT
ejpam-4971	452	1	peakons	peakon	NOUN
ejpam-4971	452	2	and	and	CCONJ
ejpam-4971	452	3	their	their	PRON
ejpam-4971	452	4	bifurcation	bifurcation	NOUN
ejpam-4971	452	5	in	in	ADP
ejpam-4971	452	6	a	a	DET
ejpam-4971	452	7	generalized	generalized	ADJ
ejpam-4971	452	8	camassa	camassa	ADJ
ejpam-4971	452	9	–	–	PUNCT
ejpam-4971	452	10	holm	holm	NOUN
ejpam-4971	452	11	equation	equation	NOUN
ejpam-4971	452	12	.	.	PUNCT
ejpam-4971	453	1	international	international	ADJ
ejpam-4971	453	2	journal	journal	NOUN
ejpam-4971	453	3	of	of	ADP
ejpam-4971	453	4	bifurcation	bifurcation	NOUN
ejpam-4971	453	5	and	and	CCONJ
ejpam-4971	453	6	chaos	chaos	NOUN
ejpam-4971	453	7	,	,	PUNCT
ejpam-4971	453	8	11(03):781	11(03):781	NUM
ejpam-4971	453	9	–	–	PUNCT
ejpam-4971	453	10	792	792	NUM
ejpam-4971	453	11	,	,	PUNCT
ejpam-4971	453	12	2001	2001	NUM
ejpam-4971	453	13	.	.	PUNCT
ejpam-4971	454	1	[	[	X
ejpam-4971	454	2	39	39	NUM
ejpam-4971	454	3	]	]	X
ejpam-4971	454	4	wen	wen	PROPN
ejpam-4971	454	5	-	-	PROPN
ejpam-4971	454	6	xiu	xiu	PROPN
ejpam-4971	454	7	ma	ma	PROPN
ejpam-4971	454	8	.	.	PROPN
ejpam-4971	454	9	wronskians	wronskian	NOUN
ejpam-4971	454	10	,	,	PUNCT
ejpam-4971	454	11	generalized	generalize	VERB
ejpam-4971	454	12	wronskians	wronskian	NOUN
ejpam-4971	454	13	and	and	CCONJ
ejpam-4971	454	14	solutions	solution	NOUN
ejpam-4971	454	15	to	to	ADP
ejpam-4971	454	16	the	the	DET
ejpam-4971	454	17	korteweg	korteweg	NOUN
ejpam-4971	454	18	–	–	PUNCT
ejpam-4971	454	19	de	de	PROPN
ejpam-4971	454	20	vries	vries	PROPN
ejpam-4971	454	21	equation	equation	NOUN
ejpam-4971	454	22	.	.	PUNCT
ejpam-4971	455	1	chaos	chaos	NOUN
ejpam-4971	455	2	,	,	PUNCT
ejpam-4971	455	3	solitons	soliton	NOUN
ejpam-4971	455	4	&	&	CCONJ
ejpam-4971	455	5	fractals	fractal	NOUN
ejpam-4971	455	6	,	,	PUNCT
ejpam-4971	455	7	19(1):163–170	19(1):163–170	NUM
ejpam-4971	455	8	,	,	PUNCT
ejpam-4971	455	9	2004	2004	NUM
ejpam-4971	455	10	.	.	PUNCT
ejpam-4971	456	1	[	[	X
ejpam-4971	456	2	40	40	NUM
ejpam-4971	456	3	]	]	X
ejpam-4971	456	4	wen	wen	PROPN
ejpam-4971	456	5	-	-	PROPN
ejpam-4971	456	6	xiu	xiu	PROPN
ejpam-4971	456	7	ma	ma	PROPN
ejpam-4971	456	8	and	and	CCONJ
ejpam-4971	456	9	jyh	jyh	PROPN
ejpam-4971	456	10	-	-	PUNCT
ejpam-4971	456	11	hao	hao	PROPN
ejpam-4971	456	12	lee	lee	PROPN
ejpam-4971	456	13	.	.	PUNCT
ejpam-4971	457	1	a	a	DET
ejpam-4971	457	2	transformed	transform	VERB
ejpam-4971	457	3	rational	rational	ADJ
ejpam-4971	457	4	function	function	NOUN
ejpam-4971	457	5	method	method	NOUN
ejpam-4971	457	6	and	and	CCONJ
ejpam-4971	457	7	exact	exact	ADJ
ejpam-4971	457	8	solutions	solution	NOUN
ejpam-4971	457	9	to	to	ADP
ejpam-4971	457	10	the	the	DET
ejpam-4971	457	11	3	3	NUM
ejpam-4971	457	12	+	+	SYM
ejpam-4971	457	13	1	1	NUM
ejpam-4971	457	14	dimensional	dimensional	ADJ
ejpam-4971	457	15	jimbo	jimbo	PROPN
ejpam-4971	457	16	–	–	PUNCT
ejpam-4971	457	17	miwa	miwa	PROPN
ejpam-4971	457	18	equation	equation	NOUN
ejpam-4971	457	19	.	.	PUNCT
ejpam-4971	458	1	chaos	chaos	NOUN
ejpam-4971	458	2	,	,	PUNCT
ejpam-4971	458	3	solitons	soliton	NOUN
ejpam-4971	458	4	&	&	CCONJ
ejpam-4971	458	5	fractals	fractal	NOUN
ejpam-4971	458	6	,	,	PUNCT
ejpam-4971	458	7	42(3):1356–1363	42(3):1356–1363	NUM
ejpam-4971	458	8	,	,	PUNCT
ejpam-4971	458	9	2009	2009	NUM
ejpam-4971	458	10	.	.	PUNCT
ejpam-4971	459	1	[	[	X
ejpam-4971	459	2	41	41	NUM
ejpam-4971	459	3	]	]	X
ejpam-4971	459	4	qing	qing	NOUN
ejpam-4971	459	5	meng	meng	PROPN
ejpam-4971	459	6	,	,	PUNCT
ejpam-4971	459	7	bin	bin	PROPN
ejpam-4971	459	8	he	he	PRON
ejpam-4971	459	9	,	,	PUNCT
ejpam-4971	459	10	yao	yao	PROPN
ejpam-4971	459	11	long	long	ADV
ejpam-4971	459	12	,	,	PUNCT
ejpam-4971	459	13	and	and	CCONJ
ejpam-4971	459	14	weiguo	weiguo	PROPN
ejpam-4971	459	15	rui	rui	PROPN
ejpam-4971	459	16	.	.	PUNCT
ejpam-4971	460	1	bifurcations	bifurcation	NOUN
ejpam-4971	460	2	of	of	ADP
ejpam-4971	460	3	travelling	travel	VERB
ejpam-4971	460	4	wave	wave	NOUN
ejpam-4971	460	5	solutions	solution	NOUN
ejpam-4971	460	6	for	for	ADP
ejpam-4971	460	7	a	a	DET
ejpam-4971	460	8	general	general	ADJ
ejpam-4971	460	9	sine	sine	NOUN
ejpam-4971	460	10	–	–	PUNCT
ejpam-4971	460	11	gordon	gordon	PROPN
ejpam-4971	460	12	equation	equation	NOUN
ejpam-4971	460	13	.	.	PUNCT
ejpam-4971	461	1	chaos	chaos	NOUN
ejpam-4971	461	2	,	,	PUNCT
ejpam-4971	461	3	solitons	soliton	NOUN
ejpam-4971	461	4	&	&	CCONJ
ejpam-4971	461	5	fractals	fractal	NOUN
ejpam-4971	461	6	,	,	PUNCT
ejpam-4971	461	7	29(2):483	29(2):483	NUM
ejpam-4971	461	8	–	–	PUNCT
ejpam-4971	461	9	489	489	NUM
ejpam-4971	461	10	,	,	PUNCT
ejpam-4971	461	11	2006	2006	NUM
ejpam-4971	461	12	.	.	PUNCT
ejpam-4971	462	1	[	[	X
ejpam-4971	462	2	42	42	NUM
ejpam-4971	462	3	]	]	PUNCT
ejpam-4971	462	4	parvaiz	parvaiz	PROPN
ejpam-4971	462	5	ahmad	ahmad	PROPN
ejpam-4971	462	6	naik	naik	PROPN
ejpam-4971	462	7	,	,	PUNCT
ejpam-4971	462	8	zohreh	zohreh	X
ejpam-4971	462	9	eskandari	eskandari	ADJ
ejpam-4971	462	10	,	,	PUNCT
ejpam-4971	462	11	and	and	CCONJ
ejpam-4971	462	12	hossein	hossein	PROPN
ejpam-4971	462	13	eskandari	eskandari	PROPN
ejpam-4971	462	14	shahraki	shahraki	PROPN
ejpam-4971	462	15	.	.	PUNCT
ejpam-4971	463	1	flip	flip	VERB
ejpam-4971	463	2	and	and	CCONJ
ejpam-4971	463	3	generalized	generalized	ADJ
ejpam-4971	463	4	flip	flip	ADJ
ejpam-4971	463	5	bifurcations	bifurcation	NOUN
ejpam-4971	463	6	of	of	ADP
ejpam-4971	463	7	a	a	DET
ejpam-4971	463	8	two	two	NUM
ejpam-4971	463	9	-	-	PUNCT
ejpam-4971	463	10	dimensional	dimensional	ADJ
ejpam-4971	463	11	discrete	discrete	ADJ
ejpam-4971	463	12	-	-	PUNCT
ejpam-4971	463	13	time	time	NOUN
ejpam-4971	463	14	chemical	chemical	NOUN
ejpam-4971	463	15	model	model	NOUN
ejpam-4971	463	16	.	.	PUNCT
ejpam-4971	464	1	mathematical	mathematical	ADJ
ejpam-4971	464	2	modelling	modelling	NOUN
ejpam-4971	464	3	and	and	CCONJ
ejpam-4971	464	4	numerical	numerical	PROPN
ejpam-4971	464	5	simulation	simulation	NOUN
ejpam-4971	464	6	with	with	ADP
ejpam-4971	464	7	applications	application	NOUN
ejpam-4971	464	8	,	,	PUNCT
ejpam-4971	464	9	1(2):95–101	1(2):95–101	NUM
ejpam-4971	464	10	,	,	PUNCT
ejpam-4971	464	11	2021	2021	NUM
ejpam-4971	464	12	.	.	PUNCT
ejpam-4971	465	1	[	[	X
ejpam-4971	465	2	43	43	NUM
ejpam-4971	465	3	]	]	X
ejpam-4971	465	4	m	m	VERB
ejpam-4971	465	5	al	al	PROPN
ejpam-4971	465	6	nuwairan	nuwairan	NOUN
ejpam-4971	465	7	and	and	CCONJ
ejpam-4971	465	8	aa	aa	NOUN
ejpam-4971	465	9	elmandouh	elmandouh	NOUN
ejpam-4971	465	10	.	.	PUNCT
ejpam-4971	466	1	qualitative	qualitative	ADJ
ejpam-4971	466	2	analysis	analysis	NOUN
ejpam-4971	466	3	and	and	CCONJ
ejpam-4971	466	4	wave	wave	NOUN
ejpam-4971	466	5	propagation	propagation	NOUN
ejpam-4971	466	6	of	of	ADP
ejpam-4971	466	7	the	the	DET
ejpam-4971	466	8	nonlinear	nonlinear	ADJ
ejpam-4971	466	9	model	model	NOUN
ejpam-4971	466	10	for	for	ADP
ejpam-4971	466	11	low	low	ADJ
ejpam-4971	466	12	-	-	PUNCT
ejpam-4971	466	13	pass	pass	NOUN
ejpam-4971	466	14	electrical	electrical	ADJ
ejpam-4971	466	15	transmission	transmission	NOUN
ejpam-4971	466	16	lines	line	NOUN
ejpam-4971	466	17	.	.	PUNCT
ejpam-4971	467	1	physica	physica	PROPN
ejpam-4971	467	2	scripta	scripta	PROPN
ejpam-4971	467	3	,	,	PUNCT
ejpam-4971	467	4	96(9):095214	96(9):095214	NUM
ejpam-4971	467	5	,	,	PUNCT
ejpam-4971	467	6	2021	2021	NUM
ejpam-4971	467	7	.	.	PUNCT
ejpam-4971	468	1	references	reference	NOUN
ejpam-4971	468	2	2660	2660	NUM
ejpam-4971	468	3	[	[	X
ejpam-4971	468	4	44	44	NUM
ejpam-4971	468	5	]	]	X
ejpam-4971	468	6	kolade	kolade	ADJ
ejpam-4971	468	7	m	m	NOUN
ejpam-4971	468	8	owolabi	owolabi	NOUN
ejpam-4971	468	9	and	and	CCONJ
ejpam-4971	468	10	dumitru	dumitru	NOUN
ejpam-4971	468	11	baleanu	baleanu	NOUN
ejpam-4971	468	12	.	.	PUNCT
ejpam-4971	469	1	emergent	emergent	ADJ
ejpam-4971	469	2	patterns	pattern	NOUN
ejpam-4971	469	3	in	in	ADP
ejpam-4971	469	4	diffusive	diffusive	ADJ
ejpam-4971	469	5	turinglike	turinglike	NOUN
ejpam-4971	469	6	systems	system	NOUN
ejpam-4971	469	7	with	with	ADP
ejpam-4971	469	8	fractional	fractional	ADJ
ejpam-4971	469	9	-	-	PUNCT
ejpam-4971	469	10	order	order	NOUN
ejpam-4971	469	11	operator	operator	NOUN
ejpam-4971	469	12	.	.	PUNCT
ejpam-4971	470	1	neural	neural	ADJ
ejpam-4971	470	2	computing	computing	NOUN
ejpam-4971	470	3	and	and	CCONJ
ejpam-4971	470	4	applications	application	NOUN
ejpam-4971	470	5	,	,	PUNCT
ejpam-4971	470	6	33(19):12703–12720	33(19):12703–12720	NOUN
ejpam-4971	470	7	,	,	PUNCT
ejpam-4971	470	8	2021	2021	NUM
ejpam-4971	470	9	.	.	PUNCT
ejpam-4971	471	1	[	[	X
ejpam-4971	471	2	45	45	NUM
ejpam-4971	471	3	]	]	X
ejpam-4971	471	4	kolade	kolade	ADJ
ejpam-4971	471	5	m	m	PROPN
ejpam-4971	471	6	owolabi	owolabi	NOUN
ejpam-4971	471	7	,	,	PUNCT
ejpam-4971	471	8	berat	berat	PROPN
ejpam-4971	471	9	karaagac	karaagac	PROPN
ejpam-4971	471	10	,	,	PUNCT
ejpam-4971	471	11	and	and	CCONJ
ejpam-4971	471	12	dumitru	dumitru	PROPN
ejpam-4971	471	13	baleanu	baleanu	NOUN
ejpam-4971	471	14	.	.	PUNCT
ejpam-4971	472	1	pattern	pattern	NOUN
ejpam-4971	472	2	formation	formation	NOUN
ejpam-4971	472	3	in	in	ADP
ejpam-4971	472	4	superdiffusion	superdiffusion	NOUN
ejpam-4971	472	5	predator	predator	NOUN
ejpam-4971	472	6	–	–	PUNCT
ejpam-4971	472	7	prey	prey	NOUN
ejpam-4971	472	8	-	-	PUNCT
ejpam-4971	472	9	like	like	ADJ
ejpam-4971	472	10	problems	problem	NOUN
ejpam-4971	472	11	with	with	ADP
ejpam-4971	472	12	integer	integer	NOUN
ejpam-4971	472	13	-	-	PUNCT
ejpam-4971	472	14	and	and	CCONJ
ejpam-4971	472	15	noninteger	noninteger	NOUN
ejpam-4971	472	16	-	-	PUNCT
ejpam-4971	472	17	order	order	NOUN
ejpam-4971	472	18	derivatives	derivative	NOUN
ejpam-4971	472	19	.	.	PUNCT
ejpam-4971	473	1	mathematical	mathematical	ADJ
ejpam-4971	473	2	methods	method	NOUN
ejpam-4971	473	3	in	in	ADP
ejpam-4971	473	4	the	the	DET
ejpam-4971	473	5	applied	apply	VERB
ejpam-4971	473	6	sciences	science	NOUN
ejpam-4971	473	7	,	,	PUNCT
ejpam-4971	473	8	44(5):4018–4036	44(5):4018–4036	NOUN
ejpam-4971	473	9	,	,	PUNCT
ejpam-4971	473	10	2021	2021	NUM
ejpam-4971	473	11	.	.	PUNCT
ejpam-4971	474	1	[	[	X
ejpam-4971	474	2	46	46	NUM
ejpam-4971	474	3	]	]	X
ejpam-4971	474	4	hadi	hadi	PROPN
ejpam-4971	474	5	rezazadeh	rezazadeh	PROPN
ejpam-4971	474	6	,	,	PUNCT
ejpam-4971	474	7	fiza	fiza	ADJ
ejpam-4971	474	8	batool	batool	NOUN
ejpam-4971	474	9	,	,	PUNCT
ejpam-4971	474	10	mustafa	mustafa	PROPN
ejpam-4971	474	11	inc	inc	PROPN
ejpam-4971	474	12	,	,	PUNCT
ejpam-4971	474	13	lanre	lanre	NOUN
ejpam-4971	474	14	akinyemi	akinyemi	NOUN
ejpam-4971	474	15	,	,	PUNCT
ejpam-4971	474	16	and	and	CCONJ
ejpam-4971	474	17	mir	mir	PROPN
ejpam-4971	474	18	sajjad	sajjad	PROPN
ejpam-4971	474	19	hashemi	hashemi	PROPN
ejpam-4971	474	20	.	.	PUNCT
ejpam-4971	475	1	exact	exact	ADJ
ejpam-4971	475	2	traveling	travel	VERB
ejpam-4971	475	3	wave	wave	NOUN
ejpam-4971	475	4	solutions	solution	NOUN
ejpam-4971	475	5	of	of	ADP
ejpam-4971	475	6	generalized	generalized	ADJ
ejpam-4971	475	7	fractional	fractional	ADJ
ejpam-4971	475	8	tzitz	tzitz	NOUN
ejpam-4971	475	9	e	e	NOUN
ejpam-4971	475	10	´	´	PROPN
ejpam-4971	475	11	ica	ica	PROPN
ejpam-4971	475	12	-	-	PUNCT
ejpam-4971	475	13	type	type	NOUN
ejpam-4971	475	14	nonlinear	nonlinear	ADJ
ejpam-4971	475	15	evolution	evolution	NOUN
ejpam-4971	475	16	equations	equation	NOUN
ejpam-4971	475	17	in	in	ADP
ejpam-4971	475	18	nonlinear	nonlinear	ADJ
ejpam-4971	475	19	optics	optic	NOUN
ejpam-4971	475	20	.	.	PUNCT
ejpam-4971	476	1	optical	optical	ADJ
ejpam-4971	476	2	and	and	CCONJ
ejpam-4971	476	3	quantum	quantum	NOUN
ejpam-4971	476	4	electronics	electronic	NOUN
ejpam-4971	476	5	,	,	PUNCT
ejpam-4971	476	6	55(6):485	55(6):485	NUM
ejpam-4971	476	7	,	,	PUNCT
ejpam-4971	476	8	2023	2023	NUM
ejpam-4971	476	9	.	.	PUNCT
ejpam-4971	477	1	[	[	X
ejpam-4971	477	2	47	47	NUM
ejpam-4971	477	3	]	]	X
ejpam-4971	477	4	alvaro	alvaro	PROPN
ejpam-4971	477	5	h	h	PROPN
ejpam-4971	477	6	salas	salas	PROPN
ejpam-4971	477	7	,	,	PUNCT
ejpam-4971	477	8	cesar	cesar	VERB
ejpam-4971	477	9	a	a	DET
ejpam-4971	477	10	gómez	gómez	NOUN
ejpam-4971	477	11	s	s	PROPN
ejpam-4971	477	12	,	,	PUNCT
ejpam-4971	477	13	et	et	PROPN
ejpam-4971	477	14	al	al	PROPN
ejpam-4971	477	15	.	.	PUNCT
ejpam-4971	477	16	application	application	NOUN
ejpam-4971	477	17	of	of	ADP
ejpam-4971	477	18	the	the	DET
ejpam-4971	477	19	cole	cole	NOUN
ejpam-4971	477	20	-	-	PUNCT
ejpam-4971	477	21	hopf	hopf	ADJ
ejpam-4971	477	22	transformation	transformation	NOUN
ejpam-4971	477	23	for	for	ADP
ejpam-4971	477	24	finding	find	VERB
ejpam-4971	477	25	exact	exact	ADJ
ejpam-4971	477	26	solutions	solution	NOUN
ejpam-4971	477	27	to	to	ADP
ejpam-4971	477	28	several	several	ADJ
ejpam-4971	477	29	forms	form	NOUN
ejpam-4971	477	30	of	of	ADP
ejpam-4971	477	31	the	the	DET
ejpam-4971	477	32	seventh	seventh	ADJ
ejpam-4971	477	33	-	-	PUNCT
ejpam-4971	477	34	order	order	NOUN
ejpam-4971	477	35	kdv	kdv	NOUN
ejpam-4971	477	36	equation	equation	NOUN
ejpam-4971	477	37	.	.	PUNCT
ejpam-4971	478	1	mathematical	mathematical	ADJ
ejpam-4971	478	2	problems	problem	NOUN
ejpam-4971	478	3	in	in	ADP
ejpam-4971	478	4	engineering	engineering	NOUN
ejpam-4971	478	5	,	,	PUNCT
ejpam-4971	478	6	2010	2010	NUM
ejpam-4971	478	7	,	,	PUNCT
ejpam-4971	478	8	2010	2010	NUM
ejpam-4971	478	9	.	.	PUNCT
ejpam-4971	479	1	[	[	X
ejpam-4971	479	2	48	48	NUM
ejpam-4971	479	3	]	]	PUNCT
ejpam-4971	479	4	leonard	leonard	PROPN
ejpam-4971	479	5	isaac	isaac	PROPN
ejpam-4971	479	6	schiff	schiff	PROPN
ejpam-4971	479	7	.	.	PUNCT
ejpam-4971	480	1	nonlinear	nonlinear	PROPN
ejpam-4971	480	2	meson	meson	PROPN
ejpam-4971	480	3	theory	theory	NOUN
ejpam-4971	480	4	of	of	ADP
ejpam-4971	480	5	nuclear	nuclear	ADJ
ejpam-4971	480	6	forces	force	NOUN
ejpam-4971	480	7	.	.	PUNCT
ejpam-4971	481	1	i.	i.	PROPN
ejpam-4971	481	2	neutral	neutral	PROPN
ejpam-4971	481	3	scalar	scalar	ADJ
ejpam-4971	481	4	mesons	meson	NOUN
ejpam-4971	481	5	with	with	ADP
ejpam-4971	481	6	point	point	NOUN
ejpam-4971	481	7	-	-	PUNCT
ejpam-4971	481	8	contact	contact	NOUN
ejpam-4971	481	9	repulsion	repulsion	NOUN
ejpam-4971	481	10	.	.	PUNCT
ejpam-4971	482	1	physical	physical	ADJ
ejpam-4971	482	2	review	review	PROPN
ejpam-4971	482	3	,	,	PUNCT
ejpam-4971	482	4	84(1):1	84(1):1	PROPN
ejpam-4971	482	5	,	,	PUNCT
ejpam-4971	482	6	1951	1951	NUM
ejpam-4971	482	7	.	.	PUNCT
ejpam-4971	483	1	[	[	X
ejpam-4971	483	2	49	49	NUM
ejpam-4971	483	3	]	]	X
ejpam-4971	483	4	alwyn	alwyn	PROPN
ejpam-4971	483	5	c	c	PROPN
ejpam-4971	483	6	scott	scott	PROPN
ejpam-4971	483	7	.	.	PUNCT
ejpam-4971	484	1	a	a	DET
ejpam-4971	484	2	nonlinear	nonlinear	PROPN
ejpam-4971	484	3	klein	klein	PROPN
ejpam-4971	484	4	-	-	PUNCT
ejpam-4971	484	5	gordon	gordon	PROPN
ejpam-4971	484	6	equation	equation	NOUN
ejpam-4971	484	7	.	.	PUNCT
ejpam-4971	485	1	american	american	PROPN
ejpam-4971	485	2	journal	journal	PROPN
ejpam-4971	485	3	of	of	ADP
ejpam-4971	485	4	physics	physics	PROPN
ejpam-4971	485	5	,	,	PUNCT
ejpam-4971	485	6	37(1):52–61	37(1):52–61	NUM
ejpam-4971	485	7	,	,	PUNCT
ejpam-4971	485	8	1969	1969	NUM
ejpam-4971	485	9	.	.	PUNCT
ejpam-4971	486	1	[	[	X
ejpam-4971	486	2	50	50	NUM
ejpam-4971	486	3	]	]	PUNCT
ejpam-4971	486	4	innocent	innocent	ADJ
ejpam-4971	486	5	simbanefayi	simbanefayi	NOUN
ejpam-4971	486	6	,	,	PUNCT
ejpam-4971	486	7	maŕıa	maŕıa	ADP
ejpam-4971	486	8	luz	luz	NOUN
ejpam-4971	486	9	gandarias	gandaria	NOUN
ejpam-4971	486	10	,	,	PUNCT
ejpam-4971	486	11	and	and	CCONJ
ejpam-4971	486	12	chaudry	chaudry	ADJ
ejpam-4971	486	13	masood	masood	PROPN
ejpam-4971	486	14	khalique	khalique	PROPN
ejpam-4971	486	15	.	.	PUNCT
ejpam-4971	487	1	travelling	travel	VERB
ejpam-4971	487	2	wave	wave	NOUN
ejpam-4971	487	3	solutions	solution	NOUN
ejpam-4971	487	4	,	,	PUNCT
ejpam-4971	487	5	symmetry	symmetry	NOUN
ejpam-4971	487	6	reductions	reduction	NOUN
ejpam-4971	487	7	and	and	CCONJ
ejpam-4971	487	8	conserved	conserve	VERB
ejpam-4971	487	9	vectors	vector	NOUN
ejpam-4971	487	10	of	of	ADP
ejpam-4971	487	11	a	a	DET
ejpam-4971	487	12	generalized	generalized	ADJ
ejpam-4971	487	13	hyper	hyper	ADJ
ejpam-4971	487	14	-	-	ADJ
ejpam-4971	487	15	elastic	elastic	ADJ
ejpam-4971	487	16	rod	rod	NOUN
ejpam-4971	487	17	wave	wave	NOUN
ejpam-4971	487	18	equation	equation	NOUN
ejpam-4971	487	19	.	.	PUNCT
ejpam-4971	488	1	partial	partial	ADJ
ejpam-4971	488	2	differential	differential	ADJ
ejpam-4971	488	3	equations	equation	NOUN
ejpam-4971	488	4	in	in	ADP
ejpam-4971	488	5	applied	applied	ADJ
ejpam-4971	488	6	mathematics	mathematic	NOUN
ejpam-4971	488	7	,	,	PUNCT
ejpam-4971	488	8	7:100501	7:100501	NUM
ejpam-4971	488	9	,	,	PUNCT
ejpam-4971	488	10	2023	2023	NUM
ejpam-4971	488	11	.	.	PUNCT
ejpam-4971	489	1	[	[	X
ejpam-4971	489	2	51	51	NUM
ejpam-4971	489	3	]	]	X
ejpam-4971	489	4	ming	ming	NOUN
ejpam-4971	489	5	song	song	NOUN
ejpam-4971	489	6	and	and	CCONJ
ejpam-4971	489	7	yuli	yuli	PROPN
ejpam-4971	489	8	ge	ge	PROPN
ejpam-4971	489	9	.	.	PUNCT
ejpam-4971	490	1	application	application	NOUN
ejpam-4971	490	2	of	of	ADP
ejpam-4971	490	3	the	the	DET
ejpam-4971	490	4	(	(	PUNCT
ejpam-4971	490	5	g	g	PROPN
ejpam-4971	490	6	g)-expansion	g)-expansion	NOUN
ejpam-4971	490	7	method	method	NOUN
ejpam-4971	490	8	to	to	ADP
ejpam-4971	490	9	(	(	PUNCT
ejpam-4971	490	10	3	3	NUM
ejpam-4971	490	11	+	+	SYM
ejpam-4971	490	12	1)dimensional	1)dimensional	NUM
ejpam-4971	490	13	nonlinear	nonlinear	ADJ
ejpam-4971	490	14	evolution	evolution	NOUN
ejpam-4971	490	15	equations	equation	NOUN
ejpam-4971	490	16	.	.	PUNCT
ejpam-4971	491	1	computers	computer	NOUN
ejpam-4971	491	2	&	&	CCONJ
ejpam-4971	491	3	mathematics	mathematics	PROPN
ejpam-4971	491	4	with	with	ADP
ejpam-4971	491	5	applications	application	NOUN
ejpam-4971	491	6	,	,	PUNCT
ejpam-4971	491	7	60(5):1220–1227	60(5):1220–1227	NUM
ejpam-4971	491	8	,	,	PUNCT
ejpam-4971	491	9	2010	2010	NUM
ejpam-4971	491	10	.	.	PUNCT
ejpam-4971	492	1	[	[	X
ejpam-4971	492	2	52	52	NUM
ejpam-4971	492	3	]	]	X
ejpam-4971	492	4	lu	lu	PROPN
ejpam-4971	492	5	tang	tang	PROPN
ejpam-4971	492	6	.	.	PUNCT
ejpam-4971	493	1	bifurcations	bifurcation	NOUN
ejpam-4971	493	2	and	and	CCONJ
ejpam-4971	493	3	traveling	travel	VERB
ejpam-4971	493	4	wave	wave	NOUN
ejpam-4971	493	5	solitons	soliton	NOUN
ejpam-4971	493	6	in	in	ADP
ejpam-4971	493	7	optical	optical	ADJ
ejpam-4971	493	8	fibers	fiber	NOUN
ejpam-4971	493	9	with	with	ADP
ejpam-4971	493	10	the	the	DET
ejpam-4971	493	11	nonlinear	nonlinear	ADJ
ejpam-4971	493	12	kaup	kaup	PROPN
ejpam-4971	493	13	–	–	PUNCT
ejpam-4971	493	14	newell	newell	PROPN
ejpam-4971	493	15	system	system	NOUN
ejpam-4971	493	16	.	.	PUNCT
ejpam-4971	494	1	optik	optik	PROPN
ejpam-4971	494	2	,	,	PUNCT
ejpam-4971	494	3	279:170749	279:170749	NUM
ejpam-4971	494	4	,	,	PUNCT
ejpam-4971	494	5	2023	2023	NUM
ejpam-4971	494	6	.	.	PUNCT
ejpam-4971	495	1	[	[	X
ejpam-4971	495	2	53	53	NUM
ejpam-4971	495	3	]	]	PUNCT
ejpam-4971	495	4	heng	heng	PROPN
ejpam-4971	495	5	wang	wang	PROPN
ejpam-4971	495	6	and	and	CCONJ
ejpam-4971	495	7	shuhua	shuhua	PROPN
ejpam-4971	495	8	zheng	zheng	PROPN
ejpam-4971	495	9	.	.	PUNCT
ejpam-4971	496	1	a	a	DET
ejpam-4971	496	2	note	note	NOUN
ejpam-4971	496	3	on	on	ADP
ejpam-4971	496	4	bifurcations	bifurcation	NOUN
ejpam-4971	496	5	and	and	CCONJ
ejpam-4971	496	6	travelling	travel	VERB
ejpam-4971	496	7	wave	wave	NOUN
ejpam-4971	496	8	solutions	solution	NOUN
ejpam-4971	496	9	of	of	ADP
ejpam-4971	496	10	a	a	DET
ejpam-4971	496	11	(	(	PUNCT
ejpam-4971	496	12	2	2	NUM
ejpam-4971	496	13	+	+	NUM
ejpam-4971	496	14	1)-dimensional	1)-dimensional	NUM
ejpam-4971	496	15	nonlinear	nonlinear	ADJ
ejpam-4971	496	16	schrödinger	schrödinger	NOUN
ejpam-4971	496	17	equation	equation	NOUN
ejpam-4971	496	18	.	.	PUNCT
ejpam-4971	497	1	analysis	analysis	NOUN
ejpam-4971	497	2	and	and	CCONJ
ejpam-4971	497	3	mathematical	mathematical	ADJ
ejpam-4971	497	4	physics	physics	NOUN
ejpam-4971	497	5	,	,	PUNCT
ejpam-4971	497	6	9(1):251–261	9(1):251–261	NOUN
ejpam-4971	497	7	,	,	PUNCT
ejpam-4971	497	8	2019	2019	NUM
ejpam-4971	497	9	.	.	PUNCT
ejpam-4971	498	1	[	[	X
ejpam-4971	498	2	54	54	NUM
ejpam-4971	498	3	]	]	PUNCT
ejpam-4971	498	4	abdul	abdul	PROPN
ejpam-4971	498	5	-	-	PUNCT
ejpam-4971	498	6	majid	majid	PROPN
ejpam-4971	498	7	wazwaz	wazwaz	NOUN
ejpam-4971	498	8	.	.	PUNCT
ejpam-4971	499	1	multiple	multiple	ADJ
ejpam-4971	499	2	-	-	PUNCT
ejpam-4971	499	3	soliton	soliton	NOUN
ejpam-4971	499	4	solutions	solution	NOUN
ejpam-4971	499	5	for	for	ADP
ejpam-4971	499	6	the	the	DET
ejpam-4971	499	7	kp	kp	PROPN
ejpam-4971	499	8	equation	equation	NOUN
ejpam-4971	499	9	by	by	ADP
ejpam-4971	499	10	hirota	hirota	PROPN
ejpam-4971	499	11	’s	’s	PART
ejpam-4971	499	12	bilinear	bilinear	PROPN
ejpam-4971	499	13	method	method	NOUN
ejpam-4971	499	14	and	and	CCONJ
ejpam-4971	499	15	by	by	ADP
ejpam-4971	499	16	the	the	DET
ejpam-4971	499	17	tanh	tanh	PROPN
ejpam-4971	499	18	–	–	PUNCT
ejpam-4971	499	19	coth	coth	NOUN
ejpam-4971	499	20	method	method	NOUN
ejpam-4971	499	21	.	.	PUNCT
ejpam-4971	500	1	applied	apply	VERB
ejpam-4971	500	2	mathematics	mathematic	NOUN
ejpam-4971	500	3	and	and	CCONJ
ejpam-4971	500	4	computation	computation	NOUN
ejpam-4971	500	5	,	,	PUNCT
ejpam-4971	500	6	190(1):633–640	190(1):633–640	NUM
ejpam-4971	500	7	,	,	PUNCT
ejpam-4971	500	8	2007	2007	NUM
ejpam-4971	500	9	.	.	PUNCT
ejpam-4971	501	1	[	[	X
ejpam-4971	501	2	55	55	NUM
ejpam-4971	501	3	]	]	X
ejpam-4971	501	4	abdul	abdul	PROPN
ejpam-4971	501	5	-	-	PUNCT
ejpam-4971	501	6	majid	majid	PROPN
ejpam-4971	501	7	wazwaz	wazwaz	NOUN
ejpam-4971	501	8	.	.	PUNCT
ejpam-4971	502	1	partial	partial	ADJ
ejpam-4971	502	2	differential	differential	ADJ
ejpam-4971	502	3	equations	equation	NOUN
ejpam-4971	502	4	and	and	CCONJ
ejpam-4971	502	5	solitary	solitary	ADJ
ejpam-4971	502	6	waves	wave	NOUN
ejpam-4971	502	7	theory	theory	NOUN
ejpam-4971	502	8	.	.	PUNCT
ejpam-4971	503	1	springer	springer	NOUN
ejpam-4971	503	2	science	science	PROPN
ejpam-4971	503	3	&	&	CCONJ
ejpam-4971	503	4	business	business	NOUN
ejpam-4971	503	5	media	medium	NOUN
ejpam-4971	503	6	,	,	PUNCT
ejpam-4971	503	7	2010	2010	NUM
ejpam-4971	503	8	.	.	PUNCT
ejpam-4971	504	1	[	[	X
ejpam-4971	504	2	56	56	NUM
ejpam-4971	504	3	]	]	X
ejpam-4971	504	4	gerald	gerald	PROPN
ejpam-4971	504	5	beresford	beresford	PROPN
ejpam-4971	504	6	whitham	whitham	PROPN
ejpam-4971	504	7	.	.	PUNCT
ejpam-4971	505	1	linear	linear	PROPN
ejpam-4971	505	2	and	and	CCONJ
ejpam-4971	505	3	nonlinear	nonlinear	ADJ
ejpam-4971	505	4	waves	wave	NOUN
ejpam-4971	505	5	.	.	PUNCT
ejpam-4971	506	1	john	john	PROPN
ejpam-4971	506	2	wiley	wiley	PROPN
ejpam-4971	506	3	&	&	CCONJ
ejpam-4971	506	4	sons	son	NOUN
ejpam-4971	506	5	,	,	PUNCT
ejpam-4971	506	6	2011	2011	NUM
ejpam-4971	506	7	.	.	PUNCT
ejpam-4971	506	8	references	reference	NOUN
ejpam-4971	506	9	2661	2661	NUM
ejpam-4971	506	10	[	[	X
ejpam-4971	506	11	57	57	NUM
ejpam-4971	506	12	]	]	X
ejpam-4971	506	13	shao	shao	PROPN
ejpam-4971	506	14	-	-	PUNCT
ejpam-4971	506	15	wen	wen	PROPN
ejpam-4971	506	16	yao	yao	PROPN
ejpam-4971	506	17	,	,	PUNCT
ejpam-4971	506	18	sayyed	sayyed	PROPN
ejpam-4971	506	19	masood	masood	PROPN
ejpam-4971	506	20	zekavatmand	zekavatmand	PROPN
ejpam-4971	506	21	,	,	PUNCT
ejpam-4971	506	22	hadi	hadi	PROPN
ejpam-4971	506	23	rezazadeh	rezazadeh	PROPN
ejpam-4971	506	24	,	,	PUNCT
ejpam-4971	506	25	javad	javad	PROPN
ejpam-4971	506	26	vahidi	vahidi	PROPN
ejpam-4971	506	27	,	,	PUNCT
ejpam-4971	506	28	mohammad	mohammad	PROPN
ejpam-4971	506	29	bagher	bagher	PROPN
ejpam-4971	506	30	ghaemi	ghaemi	PROPN
ejpam-4971	506	31	,	,	PUNCT
ejpam-4971	506	32	and	and	CCONJ
ejpam-4971	506	33	mustafa	mustafa	PROPN
ejpam-4971	506	34	inc	inc	PROPN
ejpam-4971	506	35	.	.	PUNCT
ejpam-4971	507	1	the	the	DET
ejpam-4971	507	2	solitary	solitary	ADJ
ejpam-4971	507	3	wave	wave	NOUN
ejpam-4971	507	4	solutions	solution	NOUN
ejpam-4971	507	5	to	to	ADP
ejpam-4971	507	6	the	the	DET
ejpam-4971	507	7	klein	klein	PROPN
ejpam-4971	507	8	–	–	PUNCT
ejpam-4971	507	9	gordon	gordon	PROPN
ejpam-4971	507	10	–	–	PUNCT
ejpam-4971	507	11	zakharov	zakharov	ADJ
ejpam-4971	507	12	equations	equation	NOUN
ejpam-4971	507	13	by	by	ADP
ejpam-4971	507	14	extended	extended	ADJ
ejpam-4971	507	15	rational	rational	ADJ
ejpam-4971	507	16	methods	method	NOUN
ejpam-4971	507	17	.	.	PUNCT
ejpam-4971	508	1	aip	aip	PROPN
ejpam-4971	508	2	advances	advance	NOUN
ejpam-4971	508	3	,	,	PUNCT
ejpam-4971	508	4	11(6	11(6	NUM
ejpam-4971	508	5	)	)	PUNCT
ejpam-4971	508	6	,	,	PUNCT
ejpam-4971	508	7	2021	2021	NUM
ejpam-4971	508	8	.	.	PUNCT
ejpam-4971	509	1	[	[	X
ejpam-4971	509	2	58	58	NUM
ejpam-4971	509	3	]	]	X
ejpam-4971	509	4	chen	chen	PROPN
ejpam-4971	509	5	yue	yue	PROPN
ejpam-4971	509	6	,	,	PUNCT
ejpam-4971	509	7	m	m	PROPN
ejpam-4971	509	8	higazy	higazy	NOUN
ejpam-4971	509	9	,	,	PUNCT
ejpam-4971	509	10	omnia	omnia	NOUN
ejpam-4971	509	11	khater	khater	PROPN
ejpam-4971	509	12	,	,	PUNCT
ejpam-4971	509	13	and	and	CCONJ
ejpam-4971	509	14	mostafa	mostafa	PROPN
ejpam-4971	509	15	khater	khater	PROPN
ejpam-4971	509	16	.	.	PUNCT
ejpam-4971	510	1	computational	computational	ADJ
ejpam-4971	510	2	and	and	CCONJ
ejpam-4971	510	3	numerical	numerical	ADJ
ejpam-4971	510	4	simulations	simulation	NOUN
ejpam-4971	510	5	of	of	ADP
ejpam-4971	510	6	the	the	DET
ejpam-4971	510	7	wave	wave	NOUN
ejpam-4971	510	8	propagation	propagation	NOUN
ejpam-4971	510	9	in	in	ADP
ejpam-4971	510	10	nonlinear	nonlinear	ADJ
ejpam-4971	510	11	media	medium	NOUN
ejpam-4971	510	12	with	with	ADP
ejpam-4971	510	13	dispersion	dispersion	NOUN
ejpam-4971	510	14	processes	process	NOUN
ejpam-4971	510	15	.	.	PUNCT
ejpam-4971	511	1	aip	aip	PROPN
ejpam-4971	511	2	advances	advance	NOUN
ejpam-4971	511	3	,	,	PUNCT
ejpam-4971	511	4	13(3	13(3	NUM
ejpam-4971	511	5	)	)	PUNCT
ejpam-4971	511	6	,	,	PUNCT
ejpam-4971	511	7	2023	2023	NUM
ejpam-4971	511	8	.	.	PUNCT
ejpam-4971	512	1	[	[	X
ejpam-4971	512	2	59	59	NUM
ejpam-4971	512	3	]	]	PUNCT
ejpam-4971	512	4	elsayed	elsaye	VERB
ejpam-4971	512	5	me	i	PRON
ejpam-4971	512	6	zayed	zaye	VERB
ejpam-4971	512	7	and	and	CCONJ
ejpam-4971	512	8	khaled	khale	VERB
ejpam-4971	512	9	a	a	DET
ejpam-4971	512	10	gepreel	gepreel	NOUN
ejpam-4971	512	11	.	.	PUNCT
ejpam-4971	513	1	some	some	DET
ejpam-4971	513	2	applications	application	NOUN
ejpam-4971	513	3	of	of	ADP
ejpam-4971	513	4	the	the	DET
ejpam-4971	513	5	g	g	PROPN
ejpam-4971	513	6	g	g	NOUN
ejpam-4971	513	7	-	-	PUNCT
ejpam-4971	513	8	expansion	expansion	NOUN
ejpam-4971	513	9	method	method	NOUN
ejpam-4971	513	10	to	to	ADP
ejpam-4971	513	11	non	non	ADJ
ejpam-4971	513	12	-	-	ADJ
ejpam-4971	513	13	linear	linear	ADJ
ejpam-4971	513	14	partial	partial	ADJ
ejpam-4971	513	15	differential	differential	NOUN
ejpam-4971	513	16	equations	equation	NOUN
ejpam-4971	513	17	.	.	PUNCT
ejpam-4971	514	1	applied	apply	VERB
ejpam-4971	514	2	mathematics	mathematic	NOUN
ejpam-4971	514	3	and	and	CCONJ
ejpam-4971	514	4	computation	computation	NOUN
ejpam-4971	514	5	,	,	PUNCT
ejpam-4971	514	6	212(1):1–13	212(1):1–13	NUM
ejpam-4971	514	7	,	,	PUNCT
ejpam-4971	514	8	2009	2009	NUM
ejpam-4971	514	9	.	.	PUNCT
ejpam-4971	515	1	[	[	X
ejpam-4971	515	2	60	60	NUM
ejpam-4971	515	3	]	]	X
ejpam-4971	515	4	eme	eme	X
ejpam-4971	515	5	zayed	zayed	PROPN
ejpam-4971	515	6	and	and	CCONJ
ejpam-4971	515	7	khaled	khale	VERB
ejpam-4971	515	8	a	a	DET
ejpam-4971	515	9	gepreel	gepreel	NOUN
ejpam-4971	515	10	.	.	PUNCT
ejpam-4971	516	1	the	the	DET
ejpam-4971	516	2	(	(	PUNCT
ejpam-4971	516	3	g	g	NOUN
ejpam-4971	516	4	/	/	SYM
ejpam-4971	516	5	g)-expansion	g)-expansion	NOUN
ejpam-4971	516	6	method	method	NOUN
ejpam-4971	516	7	for	for	ADP
ejpam-4971	516	8	finding	find	VERB
ejpam-4971	516	9	traveling	travel	VERB
ejpam-4971	516	10	wave	wave	NOUN
ejpam-4971	516	11	solutions	solution	NOUN
ejpam-4971	516	12	of	of	ADP
ejpam-4971	516	13	nonlinear	nonlinear	ADJ
ejpam-4971	516	14	partial	partial	ADJ
ejpam-4971	516	15	differential	differential	ADJ
ejpam-4971	516	16	equations	equation	NOUN
ejpam-4971	516	17	in	in	ADP
ejpam-4971	516	18	mathematical	mathematical	ADJ
ejpam-4971	516	19	physics	physics	PROPN
ejpam-4971	516	20	.	.	PUNCT
ejpam-4971	517	1	journal	journal	PROPN
ejpam-4971	517	2	of	of	ADP
ejpam-4971	517	3	mathematical	mathematical	ADJ
ejpam-4971	517	4	physics	physics	NOUN
ejpam-4971	517	5	,	,	PUNCT
ejpam-4971	517	6	50(1	50(1	PROPN
ejpam-4971	517	7	)	)	PUNCT
ejpam-4971	517	8	,	,	PUNCT
ejpam-4971	517	9	2009	2009	NUM
ejpam-4971	517	10	.	.	PUNCT
ejpam-4971	518	1	[	[	X
ejpam-4971	518	2	61	61	NUM
ejpam-4971	518	3	]	]	X
ejpam-4971	518	4	jiao	jiao	PROPN
ejpam-4971	518	5	zhang	zhang	PROPN
ejpam-4971	518	6	,	,	PUNCT
ejpam-4971	518	7	fengli	fengli	PROPN
ejpam-4971	518	8	jiang	jiang	PROPN
ejpam-4971	518	9	,	,	PUNCT
ejpam-4971	518	10	and	and	CCONJ
ejpam-4971	518	11	xiaoying	xiaoye	VERB
ejpam-4971	518	12	zhao	zhao	PROPN
ejpam-4971	518	13	.	.	PUNCT
ejpam-4971	519	1	an	an	DET
ejpam-4971	519	2	improved	improved	ADJ
ejpam-4971	519	3	(	(	PUNCT
ejpam-4971	519	4	g	g	NOUN
ejpam-4971	519	5	/	/	SYM
ejpam-4971	519	6	g)-expansion	g)-expansion	NOUN
ejpam-4971	519	7	method	method	NOUN
ejpam-4971	519	8	for	for	ADP
ejpam-4971	519	9	solving	solve	VERB
ejpam-4971	519	10	nonlinear	nonlinear	ADJ
ejpam-4971	519	11	evolution	evolution	NOUN
ejpam-4971	519	12	equations	equation	NOUN
ejpam-4971	519	13	.	.	PUNCT
ejpam-4971	520	1	international	international	ADJ
ejpam-4971	520	2	journal	journal	PROPN
ejpam-4971	520	3	of	of	ADP
ejpam-4971	520	4	computer	computer	NOUN
ejpam-4971	520	5	mathematics	mathematic	NOUN
ejpam-4971	520	6	,	,	PUNCT
ejpam-4971	520	7	87(8):1716–1725	87(8):1716–1725	PROPN
ejpam-4971	520	8	,	,	PUNCT
ejpam-4971	520	9	2010	2010	NUM
ejpam-4971	520	10	.	.	PUNCT
ejpam-4971	521	1	[	[	X
ejpam-4971	521	2	62	62	NUM
ejpam-4971	521	3	]	]	PUNCT
ejpam-4971	521	4	weiguo	weiguo	PROPN
ejpam-4971	521	5	zhang	zhang	PROPN
ejpam-4971	521	6	,	,	PUNCT
ejpam-4971	521	7	yuli	yuli	PROPN
ejpam-4971	521	8	guo	guo	PROPN
ejpam-4971	521	9	,	,	PUNCT
ejpam-4971	521	10	siyu	siyu	NOUN
ejpam-4971	521	11	hong	hong	PROPN
ejpam-4971	521	12	,	,	PUNCT
ejpam-4971	521	13	and	and	CCONJ
ejpam-4971	521	14	xingqian	xingqian	ADJ
ejpam-4971	521	15	ling	ling	PROPN
ejpam-4971	521	16	.	.	PUNCT
ejpam-4971	522	1	exact	exact	ADJ
ejpam-4971	522	2	solitary	solitary	ADJ
ejpam-4971	522	3	and	and	CCONJ
ejpam-4971	522	4	periodic	periodic	ADJ
ejpam-4971	522	5	wave	wave	NOUN
ejpam-4971	522	6	solutions	solution	NOUN
ejpam-4971	522	7	of	of	ADP
ejpam-4971	522	8	high	high	ADJ
ejpam-4971	522	9	-	-	PUNCT
ejpam-4971	522	10	order	order	NOUN
ejpam-4971	522	11	nonlinear	nonlinear	NOUN
ejpam-4971	522	12	schrödinger	schrödinger	NOUN
ejpam-4971	522	13	equation	equation	NOUN
ejpam-4971	522	14	and	and	CCONJ
ejpam-4971	522	15	their	their	PRON
ejpam-4971	522	16	relationship	relationship	NOUN
ejpam-4971	522	17	with	with	ADP
ejpam-4971	522	18	hamilton	hamilton	PROPN
ejpam-4971	522	19	energy	energy	PROPN
ejpam-4971	522	20	.	.	PUNCT
ejpam-4971	523	1	aip	aip	PROPN
ejpam-4971	523	2	advances	advance	NOUN
ejpam-4971	523	3	,	,	PUNCT
ejpam-4971	523	4	11(8	11(8	NUM
ejpam-4971	523	5	)	)	PUNCT
ejpam-4971	523	6	,	,	PUNCT
ejpam-4971	523	7	2021	2021	NUM
ejpam-4971	523	8	.	.	PUNCT
ejpam-4971	524	1	[	[	X
ejpam-4971	524	2	63	63	NUM
ejpam-4971	524	3	]	]	SYM
ejpam-4971	524	4	zaiyun	zaiyun	PROPN
ejpam-4971	524	5	zhang	zhang	PROPN
ejpam-4971	524	6	.	.	PUNCT
ejpam-4971	525	1	new	new	ADJ
ejpam-4971	525	2	exact	exact	ADJ
ejpam-4971	525	3	traveling	travel	VERB
ejpam-4971	525	4	wave	wave	NOUN
ejpam-4971	525	5	solutions	solution	NOUN
ejpam-4971	525	6	for	for	ADP
ejpam-4971	525	7	the	the	DET
ejpam-4971	525	8	nonlinear	nonlinear	PROPN
ejpam-4971	525	9	klein	klein	PROPN
ejpam-4971	525	10	-	-	PUNCT
ejpam-4971	525	11	gordon	gordon	PROPN
ejpam-4971	525	12	equation	equation	NOUN
ejpam-4971	525	13	.	.	PUNCT
ejpam-4971	526	1	turkish	turkish	ADJ
ejpam-4971	526	2	journal	journal	PROPN
ejpam-4971	526	3	of	of	ADP
ejpam-4971	526	4	physics	physics	PROPN
ejpam-4971	526	5	,	,	PUNCT
ejpam-4971	526	6	32(5):235–240	32(5):235–240	PROPN
ejpam-4971	526	7	,	,	PUNCT
ejpam-4971	526	8	2008	2008	NUM
ejpam-4971	526	9	.	.	PUNCT