id	sid	tid	token	lemma	pos
ap-7669	1	1	acta	acta	PROPN
ap-7669	1	2	polytechnica	polytechnica	PROPN
ap-7669	1	3	https://doi.org/10.14311/ap.2022.62.0190	https://doi.org/10.14311/ap.2022.62.0190	PROPN
ap-7669	1	4	acta	acta	PROPN
ap-7669	1	5	polytechnica	polytechnica	PROPN
ap-7669	1	6	62(1):190–196	62(1):190–196	PROPN
ap-7669	1	7	,	,	PUNCT
ap-7669	1	8	2022	2022	NUM
ap-7669	1	9	©	©	ADP
ap-7669	1	10	2022	2022	NUM
ap-7669	1	11	the	the	DET
ap-7669	1	12	author(s	author(s	NOUN
ap-7669	1	13	)	)	PUNCT
ap-7669	1	14	.	.	PUNCT
ap-7669	2	1	licensed	license	VERB
ap-7669	2	2	under	under	ADP
ap-7669	2	3	a	a	DET
ap-7669	2	4	cc	cc	NOUN
ap-7669	2	5	-	-	PUNCT
ap-7669	2	6	by	by	ADP
ap-7669	2	7	4.0	4.0	NUM
ap-7669	2	8	licence	licence	NOUN
ap-7669	2	9	published	publish	VERB
ap-7669	2	10	by	by	ADP
ap-7669	2	11	the	the	DET
ap-7669	2	12	czech	czech	PROPN
ap-7669	2	13	technical	technical	PROPN
ap-7669	2	14	university	university	PROPN
ap-7669	2	15	in	in	ADP
ap-7669	2	16	prague	prague	PROPN
ap-7669	2	17	modified	modify	VERB
ap-7669	2	18	korteweg	korteweg	PROPN
ap-7669	2	19	-	-	PUNCT
ap-7669	2	20	de	de	NOUN
ap-7669	2	21	vries	vries	PROPN
ap-7669	2	22	equation	equation	NOUN
ap-7669	2	23	as	as	ADP
ap-7669	2	24	a	a	DET
ap-7669	2	25	system	system	NOUN
ap-7669	2	26	with	with	ADP
ap-7669	2	27	benign	benign	ADJ
ap-7669	2	28	ghosts	ghost	NOUN
ap-7669	2	29	andrei	andrei	PROPN
ap-7669	2	30	smilga	smilga	PROPN
ap-7669	2	31	university	university	PROPN
ap-7669	2	32	of	of	ADP
ap-7669	2	33	nantes	nante	NOUN
ap-7669	2	34	,	,	PUNCT
ap-7669	2	35	subatech	subatech	NOUN
ap-7669	2	36	,	,	PUNCT
ap-7669	2	37	4	4	NUM
ap-7669	2	38	rue	rue	NOUN
ap-7669	2	39	alfred	alfred	PROPN
ap-7669	2	40	kastler	kastler	PROPN
ap-7669	2	41	,	,	PUNCT
ap-7669	2	42	bp	bp	PROPN
ap-7669	2	43	20722	20722	NUM
ap-7669	2	44	,	,	PUNCT
ap-7669	2	45	nantes	nante	NOUN
ap-7669	2	46	44307	44307	NUM
ap-7669	2	47	,	,	PUNCT
ap-7669	2	48	france	france	PROPN
ap-7669	2	49	correspondence	correspondence	NOUN
ap-7669	2	50	:	:	PUNCT
ap-7669	2	51	smilga@subatech.in2p3.fr	smilga@subatech.in2p3.fr	NOUN
ap-7669	2	52	abstract	abstract	NOUN
ap-7669	2	53	.	.	PUNCT
ap-7669	3	1	we	we	PRON
ap-7669	3	2	consider	consider	VERB
ap-7669	3	3	the	the	DET
ap-7669	3	4	modified	modify	VERB
ap-7669	3	5	korteweg	korteweg	NOUN
ap-7669	3	6	-	-	PUNCT
ap-7669	3	7	de	de	NOUN
ap-7669	3	8	vries	vries	PROPN
ap-7669	3	9	equation	equation	NOUN
ap-7669	3	10	,	,	PUNCT
ap-7669	3	11	uxxx	uxxx	PROPN
ap-7669	3	12	+	+	CCONJ
ap-7669	3	13	6u2ux	6u2ux	NUM
ap-7669	3	14	+	+	CCONJ
ap-7669	3	15	ut	ut	PROPN
ap-7669	3	16	=	=	SYM
ap-7669	3	17	0	0	PROPN
ap-7669	3	18	,	,	PUNCT
ap-7669	3	19	and	and	CCONJ
ap-7669	3	20	explore	explore	VERB
ap-7669	3	21	its	its	PRON
ap-7669	3	22	dynamics	dynamic	NOUN
ap-7669	3	23	in	in	ADP
ap-7669	3	24	spatial	spatial	ADJ
ap-7669	3	25	direction	direction	NOUN
ap-7669	3	26	.	.	PUNCT
ap-7669	4	1	higher	high	ADJ
ap-7669	4	2	x	x	ADP
ap-7669	4	3	derivatives	derivative	NOUN
ap-7669	4	4	bring	bring	VERB
ap-7669	4	5	about	about	ADP
ap-7669	4	6	the	the	DET
ap-7669	4	7	ghosts	ghost	NOUN
ap-7669	4	8	.	.	PUNCT
ap-7669	5	1	we	we	PRON
ap-7669	5	2	argue	argue	VERB
ap-7669	5	3	that	that	SCONJ
ap-7669	5	4	these	these	DET
ap-7669	5	5	ghosts	ghost	NOUN
ap-7669	5	6	are	be	AUX
ap-7669	5	7	benign	benign	ADJ
ap-7669	5	8	,	,	PUNCT
ap-7669	5	9	i.e.	i.e.	X
ap-7669	5	10	,	,	PUNCT
ap-7669	5	11	the	the	DET
ap-7669	5	12	classical	classical	ADJ
ap-7669	5	13	dynamics	dynamic	NOUN
ap-7669	5	14	of	of	ADP
ap-7669	5	15	this	this	DET
ap-7669	5	16	system	system	NOUN
ap-7669	5	17	does	do	AUX
ap-7669	5	18	not	not	PART
ap-7669	5	19	involve	involve	VERB
ap-7669	5	20	a	a	DET
ap-7669	5	21	blow	blow	NOUN
ap-7669	5	22	-	-	PUNCT
ap-7669	5	23	up	up	NOUN
ap-7669	5	24	.	.	PUNCT
ap-7669	6	1	this	this	PRON
ap-7669	6	2	probably	probably	ADV
ap-7669	6	3	means	mean	VERB
ap-7669	6	4	that	that	SCONJ
ap-7669	6	5	the	the	DET
ap-7669	6	6	associated	associated	ADJ
ap-7669	6	7	quantum	quantum	NOUN
ap-7669	6	8	problem	problem	NOUN
ap-7669	6	9	is	be	AUX
ap-7669	6	10	also	also	ADV
ap-7669	6	11	well	well	ADV
ap-7669	6	12	defined	define	VERB
ap-7669	6	13	.	.	PUNCT
ap-7669	7	1	keywords	keyword	NOUN
ap-7669	7	2	:	:	PUNCT
ap-7669	7	3	benign	benign	ADJ
ap-7669	7	4	ghosts	ghost	NOUN
ap-7669	7	5	,	,	PUNCT
ap-7669	7	6	kdv	kdv	NOUN
ap-7669	7	7	equation	equation	NOUN
ap-7669	7	8	,	,	PUNCT
ap-7669	7	9	integrability	integrability	NOUN
ap-7669	7	10	.	.	PUNCT
ap-7669	8	1	1	1	X
ap-7669	8	2	.	.	X
ap-7669	8	3	introduction	introduction	NOUN
ap-7669	8	4	a	a	DET
ap-7669	8	5	system	system	NOUN
ap-7669	8	6	with	with	ADP
ap-7669	8	7	ghosts	ghost	NOUN
ap-7669	8	8	is	be	AUX
ap-7669	8	9	,	,	PUNCT
ap-7669	8	10	by	by	ADP
ap-7669	8	11	definition	definition	NOUN
ap-7669	8	12	,	,	PUNCT
ap-7669	8	13	a	a	DET
ap-7669	8	14	system	system	NOUN
ap-7669	8	15	where	where	SCONJ
ap-7669	8	16	the	the	DET
ap-7669	8	17	quantum	quantum	ADJ
ap-7669	8	18	hamiltonian	hamiltonian	NOUN
ap-7669	8	19	has	have	VERB
ap-7669	8	20	no	no	DET
ap-7669	8	21	ground	ground	NOUN
ap-7669	8	22	state	state	NOUN
ap-7669	8	23	so	so	SCONJ
ap-7669	8	24	its	its	PRON
ap-7669	8	25	spectrum	spectrum	NOUN
ap-7669	8	26	involves	involve	VERB
ap-7669	8	27	the	the	DET
ap-7669	8	28	states	state	NOUN
ap-7669	8	29	with	with	ADP
ap-7669	8	30	arbitrarily	arbitrarily	ADV
ap-7669	8	31	low	low	ADJ
ap-7669	8	32	and	and	CCONJ
ap-7669	8	33	arbitrarily	arbitrarily	ADV
ap-7669	8	34	high	high	ADJ
ap-7669	8	35	energies	energy	NOUN
ap-7669	8	36	.	.	PUNCT
ap-7669	9	1	in	in	ADP
ap-7669	9	2	particular	particular	ADJ
ap-7669	9	3	,	,	PUNCT
ap-7669	9	4	all	all	DET
ap-7669	9	5	nondegenerate	nondegenerate	ADJ
ap-7669	9	6	theories	theory	NOUN
ap-7669	9	7	with	with	ADP
ap-7669	9	8	higher	high	ADJ
ap-7669	9	9	derivatives	derivative	NOUN
ap-7669	9	10	in	in	ADP
ap-7669	9	11	the	the	DET
ap-7669	9	12	lagrangian	lagrangian	ADJ
ap-7669	9	13	(	(	PUNCT
ap-7669	9	14	but	but	CCONJ
ap-7669	9	15	not	not	PART
ap-7669	9	16	only	only	ADV
ap-7669	9	17	them	they	PRON
ap-7669	9	18	!	!	PUNCT
ap-7669	9	19	)	)	PUNCT
ap-7669	9	20	involve	involve	VERB
ap-7669	9	21	ghosts	ghost	NOUN
ap-7669	9	22	.	.	PUNCT
ap-7669	10	1	the	the	DET
ap-7669	10	2	ghosts	ghost	NOUN
ap-7669	10	3	show	show	VERB
ap-7669	10	4	up	up	ADV
ap-7669	10	5	there	there	ADV
ap-7669	10	6	already	already	ADV
ap-7669	10	7	at	at	ADP
ap-7669	10	8	the	the	DET
ap-7669	10	9	classical	classical	ADJ
ap-7669	10	10	level	level	NOUN
ap-7669	10	11	:	:	PUNCT
ap-7669	10	12	the	the	DET
ap-7669	10	13	ostrogradsky	ostrogradsky	ADJ
ap-7669	10	14	hamiltonians	hamiltonian	NOUN
ap-7669	10	15	of	of	ADP
ap-7669	10	16	higher	high	ADJ
ap-7669	10	17	derivative	derivative	ADJ
ap-7669	10	18	systems	system	NOUN
ap-7669	10	19	[	[	X
ap-7669	10	20	1	1	X
ap-7669	10	21	]	]	PUNCT
ap-7669	10	22	include	include	VERB
ap-7669	10	23	the	the	DET
ap-7669	10	24	linear	linear	NOUN
ap-7669	10	25	in	in	ADP
ap-7669	10	26	momenta	momenta	ADJ
ap-7669	10	27	terms	term	NOUN
ap-7669	10	28	and	and	CCONJ
ap-7669	10	29	are	be	AUX
ap-7669	10	30	thus	thus	ADV
ap-7669	10	31	not	not	PART
ap-7669	10	32	positive	positive	ADJ
ap-7669	10	33	definite	definite	ADJ
ap-7669	10	34	[	[	X
ap-7669	10	35	2	2	NUM
ap-7669	10	36	]	]	PUNCT
ap-7669	10	37	.	.	PUNCT
ap-7669	11	1	this	this	PRON
ap-7669	11	2	brings	bring	VERB
ap-7669	11	3	about	about	ADP
ap-7669	11	4	the	the	DET
ap-7669	11	5	ghosts	ghost	NOUN
ap-7669	11	6	in	in	ADP
ap-7669	11	7	the	the	DET
ap-7669	11	8	quantum	quantum	ADJ
ap-7669	11	9	problem	problem	NOUN
ap-7669	11	10	[	[	X
ap-7669	11	11	3	3	NUM
ap-7669	11	12	,	,	PUNCT
ap-7669	11	13	4	4	NUM
ap-7669	11	14	]	]	PUNCT
ap-7669	11	15	.	.	PUNCT
ap-7669	12	1	in	in	ADP
ap-7669	12	2	many	many	ADJ
ap-7669	12	3	cases	case	NOUN
ap-7669	12	4	,	,	PUNCT
ap-7669	12	5	ghost	ghost	NOUN
ap-7669	12	6	-	-	PUNCT
ap-7669	12	7	ridden	ride	VERB
ap-7669	12	8	systems	system	NOUN
ap-7669	12	9	are	be	AUX
ap-7669	12	10	sick	sick	ADJ
ap-7669	12	11	–	–	PUNCT
ap-7669	12	12	the	the	DET
ap-7669	12	13	schrödinger	schrödinger	ADJ
ap-7669	12	14	problem	problem	NOUN
ap-7669	12	15	is	be	AUX
ap-7669	12	16	not	not	PART
ap-7669	12	17	well	well	ADV
ap-7669	12	18	posed	pose	VERB
ap-7669	12	19	and	and	CCONJ
ap-7669	12	20	unitarity	unitarity	NOUN
ap-7669	12	21	is	be	AUX
ap-7669	12	22	violated	violate	VERB
ap-7669	12	23	.	.	PUNCT
ap-7669	13	1	probably	probably	ADV
ap-7669	13	2	,	,	PUNCT
ap-7669	13	3	the	the	DET
ap-7669	13	4	simplest	simple	ADJ
ap-7669	13	5	example	example	NOUN
ap-7669	13	6	of	of	ADP
ap-7669	13	7	such	such	DET
ap-7669	13	8	a	a	DET
ap-7669	13	9	system	system	NOUN
ap-7669	13	10	is	be	AUX
ap-7669	13	11	a	a	DET
ap-7669	13	12	system	system	NOUN
ap-7669	13	13	with	with	ADP
ap-7669	13	14	the	the	DET
ap-7669	13	15	hamiltonian	hamiltonian	NOUN
ap-7669	13	16	describing	describe	VERB
ap-7669	13	17	the	the	DET
ap-7669	13	18	3	3	NUM
ap-7669	13	19	-	-	PUNCT
ap-7669	13	20	dimensional	dimensional	ADJ
ap-7669	13	21	motion	motion	NOUN
ap-7669	13	22	of	of	ADP
ap-7669	13	23	a	a	DET
ap-7669	13	24	particle	particle	NOUN
ap-7669	13	25	in	in	ADP
ap-7669	13	26	an	an	DET
ap-7669	13	27	attractive	attractive	ADJ
ap-7669	13	28	1	1	NUM
ap-7669	13	29	r2	r2	NOUN
ap-7669	13	30	potential	potential	NOUN
ap-7669	13	31	:	:	PUNCT
ap-7669	13	32	h	h	NOUN
ap-7669	13	33	=	=	PUNCT
ap-7669	13	34	p⃗2	p⃗2	NOUN
ap-7669	13	35	2	2	NUM
ap-7669	13	36	m	m	NOUN
ap-7669	13	37	−	−	NOUN
ap-7669	13	38	κ	κ	NOUN
ap-7669	13	39	r2	r2	PROPN
ap-7669	13	40	.	.	PUNCT
ap-7669	14	1	(	(	PUNCT
ap-7669	14	2	1	1	X
ap-7669	14	3	)	)	PUNCT
ap-7669	14	4	for	for	ADP
ap-7669	14	5	certain	certain	ADJ
ap-7669	14	6	initial	initial	ADJ
ap-7669	14	7	conditions	condition	NOUN
ap-7669	14	8	,	,	PUNCT
ap-7669	14	9	the	the	DET
ap-7669	14	10	particle	particle	NOUN
ap-7669	14	11	falls	fall	VERB
ap-7669	14	12	to	to	ADP
ap-7669	14	13	the	the	DET
ap-7669	14	14	center	center	NOUN
ap-7669	14	15	in	in	ADP
ap-7669	14	16	a	a	DET
ap-7669	14	17	finite	finite	ADJ
ap-7669	14	18	time	time	NOUN
ap-7669	14	19	,	,	PUNCT
ap-7669	14	20	as	as	SCONJ
ap-7669	14	21	is	be	AUX
ap-7669	14	22	shown	show	VERB
ap-7669	14	23	in	in	ADP
ap-7669	14	24	figure	figure	NOUN
ap-7669	14	25	1	1	NUM
ap-7669	14	26	.	.	PUNCT
ap-7669	15	1	the	the	DET
ap-7669	15	2	quantum	quantum	ADJ
ap-7669	15	3	dynamics	dynamic	NOUN
ap-7669	15	4	of	of	ADP
ap-7669	15	5	this	this	DET
ap-7669	15	6	system	system	NOUN
ap-7669	15	7	depends	depend	VERB
ap-7669	15	8	on	on	ADP
ap-7669	15	9	the	the	DET
ap-7669	15	10	value	value	NOUN
ap-7669	15	11	of	of	ADP
ap-7669	15	12	κ	κ	NOUN
ap-7669	15	13	.	.	PUNCT
ap-7669	16	1	if	if	SCONJ
ap-7669	16	2	mκ	mκ	PROPN
ap-7669	16	3	<	<	X
ap-7669	16	4	1/8	1/8	NUM
ap-7669	16	5	,	,	PUNCT
ap-7669	16	6	the	the	DET
ap-7669	16	7	ground	ground	NOUN
ap-7669	16	8	state	state	NOUN
ap-7669	16	9	exists	exist	VERB
ap-7669	16	10	and	and	CCONJ
ap-7669	16	11	unitarity	unitarity	NOUN
ap-7669	16	12	is	be	AUX
ap-7669	16	13	preserved	preserve	VERB
ap-7669	16	14	.	.	PUNCT
ap-7669	17	1	if	if	SCONJ
ap-7669	17	2	mκ	mκ	PROPN
ap-7669	17	3	>	>	X
ap-7669	17	4	1/8	1/8	NUM
ap-7669	17	5	,	,	PUNCT
ap-7669	17	6	the	the	DET
ap-7669	17	7	spectrum	spectrum	NOUN
ap-7669	17	8	is	be	AUX
ap-7669	17	9	not	not	PART
ap-7669	17	10	bounded	bound	VERB
ap-7669	17	11	from	from	ADP
ap-7669	17	12	below	below	ADP
ap-7669	17	13	and	and	CCONJ
ap-7669	17	14	,	,	PUNCT
ap-7669	17	15	what	what	PRON
ap-7669	17	16	is	be	AUX
ap-7669	17	17	worse	bad	ADJ
ap-7669	17	18	,	,	PUNCT
ap-7669	17	19	the	the	DET
ap-7669	17	20	quantum	quantum	NOUN
ap-7669	17	21	problem	problem	NOUN
ap-7669	17	22	can	can	AUX
ap-7669	17	23	not	not	PART
ap-7669	17	24	be	be	AUX
ap-7669	17	25	well	well	ADV
ap-7669	17	26	posed	pose	VERB
ap-7669	17	27	until	until	SCONJ
ap-7669	17	28	the	the	DET
ap-7669	17	29	singularity	singularity	NOUN
ap-7669	17	30	at	at	ADP
ap-7669	17	31	the	the	DET
ap-7669	17	32	origin	origin	NOUN
ap-7669	17	33	is	be	AUX
ap-7669	17	34	smoothed	smooth	VERB
ap-7669	17	35	out	out	ADP
ap-7669	18	1	[	[	X
ap-7669	18	2	5–7	5–7	NOUN
ap-7669	18	3	]	]	X
ap-7669	18	4	.	.	PUNCT
ap-7669	19	1	one	one	PRON
ap-7669	19	2	can	can	AUX
ap-7669	19	3	say	say	VERB
ap-7669	19	4	that	that	SCONJ
ap-7669	19	5	for	for	ADP
ap-7669	19	6	mκ	mκ	PROPN
ap-7669	19	7	<	<	X
ap-7669	19	8	1/8	1/8	NUM
ap-7669	19	9	,	,	PUNCT
ap-7669	19	10	the	the	DET
ap-7669	19	11	quantum	quantum	NOUN
ap-7669	19	12	fluctuations	fluctuation	NOUN
ap-7669	19	13	cope	cope	VERB
ap-7669	19	14	successfully	successfully	ADV
ap-7669	19	15	with	with	ADP
ap-7669	19	16	the	the	DET
ap-7669	19	17	attractive	attractive	ADJ
ap-7669	19	18	force	force	NOUN
ap-7669	19	19	of	of	ADP
ap-7669	19	20	the	the	DET
ap-7669	19	21	potential	potential	NOUN
ap-7669	19	22	and	and	CCONJ
ap-7669	19	23	prevent	prevent	VERB
ap-7669	19	24	the	the	DET
ap-7669	19	25	system	system	NOUN
ap-7669	19	26	from	from	ADP
ap-7669	19	27	collapsing	collapse	VERB
ap-7669	19	28	.	.	PUNCT
ap-7669	20	1	the	the	DET
ap-7669	20	2	latter	latter	ADJ
ap-7669	20	3	example	example	NOUN
ap-7669	20	4	suggests	suggest	VERB
ap-7669	20	5	that	that	SCONJ
ap-7669	20	6	quantum	quantum	NOUN
ap-7669	20	7	fluctuations	fluctuation	NOUN
ap-7669	20	8	can	can	AUX
ap-7669	20	9	only	only	ADV
ap-7669	20	10	make	make	VERB
ap-7669	20	11	a	a	DET
ap-7669	20	12	ghost	ghost	NOUN
ap-7669	20	13	-	-	PUNCT
ap-7669	20	14	ridden	ride	VERB
ap-7669	20	15	system	system	NOUN
ap-7669	20	16	better	well	ADJ
ap-7669	20	17	,	,	PUNCT
ap-7669	20	18	not	not	PART
ap-7669	20	19	worse	bad	ADJ
ap-7669	20	20	.	.	PUNCT
ap-7669	21	1	we	we	PRON
ap-7669	21	2	,	,	PUNCT
ap-7669	21	3	therefore	therefore	ADV
ap-7669	21	4	,	,	PUNCT
ap-7669	21	5	conjecture	conjecture	VERB
ap-7669	21	6	that	that	SCONJ
ap-7669	21	7	,	,	PUNCT
ap-7669	21	8	if	if	SCONJ
ap-7669	21	9	the	the	DET
ap-7669	21	10	classical	classical	ADJ
ap-7669	21	11	dynamics	dynamic	NOUN
ap-7669	21	12	of	of	ADP
ap-7669	21	13	the	the	DET
ap-7669	21	14	system	system	NOUN
ap-7669	21	15	is	be	AUX
ap-7669	21	16	benign	benign	ADJ
ap-7669	21	17	,	,	PUNCT
ap-7669	21	18	i.e.	i.e.	X
ap-7669	21	19	,	,	PUNCT
ap-7669	21	20	the	the	DET
ap-7669	21	21	system	system	NOUN
ap-7669	21	22	does	do	AUX
ap-7669	21	23	not	not	PART
ap-7669	21	24	run	run	VERB
ap-7669	21	25	into	into	ADP
ap-7669	21	26	singularity	singularity	NOUN
ap-7669	21	27	in	in	ADP
ap-7669	21	28	finite	finite	PROPN
ap-7669	21	29	time,1	time,1	NOUN
ap-7669	21	30	its	its	PRON
ap-7669	21	31	quantum	quantum	PROPN
ap-7669	21	32	1we	1we	NOUN
ap-7669	21	33	still	still	ADV
ap-7669	21	34	call	call	VERB
ap-7669	21	35	a	a	DET
ap-7669	21	36	system	system	NOUN
ap-7669	21	37	benign	benign	ADJ
ap-7669	21	38	if	if	SCONJ
ap-7669	21	39	it	it	PRON
ap-7669	21	40	runs	run	VERB
ap-7669	21	41	into	into	ADP
ap-7669	21	42	a	a	DET
ap-7669	21	43	singularity	singularity	NOUN
ap-7669	21	44	at	at	ADP
ap-7669	21	45	t	t	PROPN
ap-7669	21	46	=	=	SYM
ap-7669	21	47	∞.	∞.	PROPN
ap-7669	21	48	such	such	ADJ
ap-7669	21	49	systems	system	NOUN
ap-7669	21	50	have	have	VERB
ap-7669	21	51	well	well	ADV
ap-7669	21	52	-	-	PUNCT
ap-7669	21	53	defined	define	VERB
ap-7669	21	54	quantum	quantum	NOUN
ap-7669	21	55	dynamics	dynamic	NOUN
ap-7669	21	56	.	.	PUNCT
ap-7669	22	1	this	this	PRON
ap-7669	22	2	refers	refer	VERB
ap-7669	22	3	,	,	PUNCT
ap-7669	22	4	for	for	ADP
ap-7669	22	5	example	example	NOUN
ap-7669	22	6	,	,	PUNCT
ap-7669	22	7	to	to	ADP
ap-7669	22	8	the	the	DET
ap-7669	22	9	problem	problem	NOUN
ap-7669	22	10	of	of	ADP
ap-7669	22	11	motion	motion	NOUN
ap-7669	22	12	in	in	ADP
ap-7669	22	13	a	a	DET
ap-7669	22	14	uniform	uniform	ADJ
ap-7669	22	15	electric	electric	ADJ
ap-7669	22	16	field	field	NOUN
ap-7669	22	17	(	(	PUNCT
ap-7669	22	18	see	see	VERB
ap-7669	22	19	e.g.	e.g.	ADV
ap-7669	22	20	[	[	X
ap-7669	22	21	8	8	NUM
ap-7669	22	22	]	]	PUNCT
ap-7669	22	23	,	,	PUNCT
ap-7669	22	24	$	$	SYM
ap-7669	22	25	24	24	NUM
ap-7669	22	26	)	)	PUNCT
ap-7669	22	27	and	and	CCONJ
ap-7669	22	28	also	also	ADV
ap-7669	22	29	to	to	ADP
ap-7669	22	30	the	the	DET
ap-7669	22	31	inversed	inversed	ADJ
ap-7669	22	32	oscillator	oscillator	NOUN
ap-7669	22	33	-0.5	-0.5	X
ap-7669	22	34	0.5	0.5	NUM
ap-7669	22	35	1.0	1.0	NUM
ap-7669	22	36	x	x	SYM
ap-7669	22	37	-0.4	-0.4	NUM
ap-7669	22	38	-0.2	-0.2	PROPN
ap-7669	22	39	0.2	0.2	NUM
ap-7669	22	40	0.4	0.4	NUM
ap-7669	22	41	0.6	0.6	NUM
ap-7669	22	42	0.8	0.8	NUM
ap-7669	22	43	y	y	PROPN
ap-7669	22	44	figure	figure	NOUN
ap-7669	22	45	1	1	NUM
ap-7669	22	46	.	.	PUNCT
ap-7669	23	1	falling	fall	VERB
ap-7669	23	2	on	on	ADP
ap-7669	23	3	the	the	DET
ap-7669	23	4	center	center	NOUN
ap-7669	23	5	for	for	ADP
ap-7669	23	6	the	the	DET
ap-7669	23	7	hamiltonian	hamiltonian	NOUN
ap-7669	23	8	(	(	PUNCT
ap-7669	23	9	1	1	NUM
ap-7669	23	10	)	)	PUNCT
ap-7669	23	11	with	with	ADP
ap-7669	23	12	m	m	PROPN
ap-7669	23	13	=	=	SYM
ap-7669	23	14	1	1	NUM
ap-7669	23	15	and	and	CCONJ
ap-7669	23	16	κ	κ	X
ap-7669	23	17	=	=	SYM
ap-7669	23	18	.05	.05	NUM
ap-7669	23	19	.	.	PUNCT
ap-7669	24	1	the	the	DET
ap-7669	24	2	energy	energy	NOUN
ap-7669	24	3	is	be	AUX
ap-7669	24	4	slightly	slightly	ADV
ap-7669	24	5	negative	negative	ADJ
ap-7669	24	6	.	.	PUNCT
ap-7669	25	1	the	the	DET
ap-7669	25	2	particles	particle	NOUN
ap-7669	25	3	with	with	ADP
ap-7669	25	4	positive	positive	ADJ
ap-7669	25	5	energies	energy	NOUN
ap-7669	25	6	escape	escape	VERB
ap-7669	25	7	to	to	ADP
ap-7669	25	8	infinity	infinity	NOUN
ap-7669	25	9	.	.	PUNCT
ap-7669	26	1	dynamics	dynamic	NOUN
ap-7669	26	2	will	will	AUX
ap-7669	26	3	also	also	ADV
ap-7669	26	4	be	be	AUX
ap-7669	26	5	benign	benign	ADJ
ap-7669	26	6	,	,	PUNCT
ap-7669	26	7	irrespectively	irrespectively	ADV
ap-7669	26	8	of	of	ADP
ap-7669	26	9	whether	whether	SCONJ
ap-7669	26	10	the	the	DET
ap-7669	26	11	spectrum	spectrum	NOUN
ap-7669	26	12	has	have	AUX
ap-7669	26	13	,	,	PUNCT
ap-7669	26	14	or	or	CCONJ
ap-7669	26	15	does	do	AUX
ap-7669	26	16	not	not	PART
ap-7669	26	17	have	have	VERB
ap-7669	26	18	,	,	PUNCT
ap-7669	26	19	a	a	DET
ap-7669	26	20	bottom	bottom	NOUN
ap-7669	26	21	.	.	PUNCT
ap-7669	27	1	this	this	PRON
ap-7669	27	2	all	all	PRON
ap-7669	27	3	refers	refer	VERB
ap-7669	27	4	to	to	ADP
ap-7669	27	5	ordinary	ordinary	ADJ
ap-7669	27	6	mechanical	mechanical	ADJ
ap-7669	27	7	or	or	CCONJ
ap-7669	27	8	field	field	NOUN
ap-7669	27	9	theory	theory	NOUN
ap-7669	27	10	systems	system	NOUN
ap-7669	27	11	,	,	PUNCT
ap-7669	27	12	where	where	SCONJ
ap-7669	27	13	energy	energy	NOUN
ap-7669	27	14	is	be	AUX
ap-7669	27	15	conserved	conserve	VERB
ap-7669	27	16	and	and	CCONJ
ap-7669	27	17	the	the	DET
ap-7669	27	18	notion	notion	NOUN
ap-7669	27	19	of	of	ADP
ap-7669	27	20	hamiltonian	hamiltonian	ADJ
ap-7669	27	21	exists	exist	VERB
ap-7669	27	22	.	.	PUNCT
ap-7669	28	1	the	the	DET
ap-7669	28	2	ghosts	ghost	NOUN
ap-7669	28	3	in	in	ADP
ap-7669	28	4	gravity	gravity	NOUN
ap-7669	28	5	(	(	PUNCT
ap-7669	28	6	especially	especially	ADV
ap-7669	28	7	,	,	PUNCT
ap-7669	28	8	in	in	ADP
ap-7669	28	9	higher	high	ADJ
ap-7669	28	10	-	-	PUNCT
ap-7669	28	11	derivative	derivative	ADJ
ap-7669	28	12	gravity	gravity	NOUN
ap-7669	28	13	)	)	PUNCT
ap-7669	28	14	are	be	AUX
ap-7669	28	15	special	special	ADJ
ap-7669	28	16	issue	issue	NOUN
ap-7669	28	17	that	that	SCONJ
ap-7669	28	18	we	we	PRON
ap-7669	28	19	are	be	AUX
ap-7669	28	20	not	not	PART
ap-7669	28	21	discussing	discuss	VERB
ap-7669	28	22	here	here	ADV
ap-7669	28	23	.	.	PUNCT
ap-7669	29	1	besides	besides	SCONJ
ap-7669	29	2	malignant	malignant	ADJ
ap-7669	29	3	ghost	ghost	NOUN
ap-7669	29	4	-	-	PUNCT
ap-7669	29	5	ridden	ride	VERB
ap-7669	29	6	systems	system	NOUN
ap-7669	29	7	,	,	PUNCT
ap-7669	29	8	of	of	ADP
ap-7669	29	9	which	which	PRON
ap-7669	29	10	the	the	DET
ap-7669	29	11	system	system	NOUN
ap-7669	29	12	(	(	PUNCT
ap-7669	29	13	1	1	NUM
ap-7669	29	14	)	)	PUNCT
ap-7669	29	15	with	with	ADP
ap-7669	29	16	mκ	mκ	PROPN
ap-7669	29	17	>	>	SYM
ap-7669	29	18	1/8	1/8	NUM
ap-7669	29	19	represents	represent	VERB
ap-7669	29	20	an	an	DET
ap-7669	29	21	example	example	NOUN
ap-7669	29	22	,	,	PUNCT
ap-7669	29	23	there	there	PRON
ap-7669	29	24	are	be	VERB
ap-7669	29	25	also	also	ADV
ap-7669	29	26	many	many	ADJ
ap-7669	29	27	systems	system	NOUN
ap-7669	29	28	with	with	ADP
ap-7669	29	29	ghosts	ghost	NOUN
ap-7669	29	30	,	,	PUNCT
ap-7669	29	31	which	which	PRON
ap-7669	29	32	are	be	AUX
ap-7669	29	33	benign	benign	ADJ
ap-7669	29	34	–	–	PUNCT
ap-7669	29	35	unitarity	unitarity	NOUN
ap-7669	29	36	is	be	AUX
ap-7669	29	37	preserved	preserve	VERB
ap-7669	29	38	and	and	CCONJ
ap-7669	29	39	the	the	DET
ap-7669	29	40	quantum	quantum	ADJ
ap-7669	29	41	hamiltonian	hamiltonian	NOUN
ap-7669	29	42	is	be	AUX
ap-7669	29	43	self	self	NOUN
ap-7669	29	44	-	-	PUNCT
ap-7669	29	45	adjoint	adjoint	NOUN
ap-7669	29	46	with	with	ADP
ap-7669	29	47	a	a	DET
ap-7669	29	48	well	well	ADV
ap-7669	29	49	-	-	PUNCT
ap-7669	29	50	defined	define	VERB
ap-7669	29	51	real	real	ADJ
ap-7669	29	52	spectrum	spectrum	NOUN
ap-7669	29	53	.	.	PUNCT
ap-7669	30	1	to	to	PART
ap-7669	30	2	begin	begin	VERB
ap-7669	30	3	with	with	ADP
ap-7669	30	4	,	,	PUNCT
ap-7669	30	5	such	such	ADJ
ap-7669	30	6	is	be	AUX
ap-7669	30	7	the	the	DET
ap-7669	30	8	famous	famous	ADJ
ap-7669	30	9	paisuhlenbeck	paisuhlenbeck	NOUN
ap-7669	30	10	oscillator	oscillator	NOUN
ap-7669	30	11	[	[	X
ap-7669	30	12	10	10	NUM
ap-7669	30	13	]	]	PUNCT
ap-7669	30	14	–	–	PUNCT
ap-7669	30	15	a	a	DET
ap-7669	30	16	higher	high	ADJ
ap-7669	30	17	derivative	derivative	ADJ
ap-7669	30	18	system	system	NOUN
ap-7669	30	19	with	with	ADP
ap-7669	30	20	the	the	DET
ap-7669	30	21	hamiltonian	hamiltonian	ADJ
ap-7669	30	22	h	h	NOUN
ap-7669	30	23	=	=	SYM
ap-7669	30	24	(	(	PUNCT
ap-7669	30	25	p2	p2	PROPN
ap-7669	30	26	−	−	PROPN
ap-7669	30	27	x2)/2	x2)/2	PROPN
ap-7669	30	28	.	.	PUNCT
ap-7669	31	1	in	in	ADP
ap-7669	31	2	the	the	DET
ap-7669	31	3	latter	latter	ADJ
ap-7669	31	4	problem	problem	NOUN
ap-7669	31	5	,	,	PUNCT
ap-7669	31	6	the	the	DET
ap-7669	31	7	classical	classical	ADJ
ap-7669	31	8	trajectories	trajectory	NOUN
ap-7669	31	9	x(t	x(t	PROPN
ap-7669	31	10	)	)	PUNCT
ap-7669	31	11	grow	grow	VERB
ap-7669	31	12	exponentially	exponentially	ADV
ap-7669	31	13	with	with	ADP
ap-7669	31	14	time	time	NOUN
ap-7669	31	15	,	,	PUNCT
ap-7669	31	16	but	but	CCONJ
ap-7669	31	17	the	the	DET
ap-7669	31	18	quantum	quantum	ADJ
ap-7669	31	19	problem	problem	NOUN
ap-7669	31	20	is	be	AUX
ap-7669	31	21	still	still	ADV
ap-7669	31	22	benign	benign	ADJ
ap-7669	31	23	(	(	PUNCT
ap-7669	31	24	see	see	VERB
ap-7669	32	1	e.g.	e.g.	ADV
ap-7669	32	2	[	[	X
ap-7669	32	3	9	9	NUM
ap-7669	32	4	]	]	PUNCT
ap-7669	32	5	,	,	PUNCT
ap-7669	32	6	ch	ch	NOUN
ap-7669	32	7	.	.	PROPN
ap-7669	32	8	3	3	NUM
ap-7669	32	9	,	,	PUNCT
ap-7669	32	10	corollary	corollary	ADJ
ap-7669	32	11	13	13	NUM
ap-7669	32	12	)	)	PUNCT
ap-7669	32	13	.	.	PUNCT
ap-7669	33	1	the	the	DET
ap-7669	33	2	spectrum	spectrum	NOUN
ap-7669	33	3	in	in	ADP
ap-7669	33	4	this	this	DET
ap-7669	33	5	case	case	NOUN
ap-7669	33	6	is	be	AUX
ap-7669	33	7	continuous	continuous	ADJ
ap-7669	33	8	,	,	PUNCT
ap-7669	33	9	as	as	SCONJ
ap-7669	33	10	it	it	PRON
ap-7669	33	11	is	be	AUX
ap-7669	33	12	for	for	ADP
ap-7669	33	13	the	the	DET
ap-7669	33	14	uniform	uniform	ADJ
ap-7669	33	15	field	field	NOUN
ap-7669	33	16	problem	problem	NOUN
ap-7669	33	17	.	.	PUNCT
ap-7669	34	1	190	190	NUM
ap-7669	34	2	https://doi.org/10.14311/ap.2022.62.0190	https://doi.org/10.14311/ap.2022.62.0190	PROPN
ap-7669	34	3	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-7669	34	4	https://www.cvut.cz/en	https://www.cvut.cz/en	NOUN
ap-7669	34	5	vol	vol	NOUN
ap-7669	34	6	.	.	PROPN
ap-7669	35	1	62	62	NUM
ap-7669	35	2	no	no	INTJ
ap-7669	35	3	.	.	PUNCT
ap-7669	36	1	1/2022	1/2022	NUM
ap-7669	36	2	modified	modify	VERB
ap-7669	36	3	kdv	kdv	NOUN
ap-7669	36	4	equation	equation	NOUN
ap-7669	36	5	as	as	ADP
ap-7669	36	6	a	a	DET
ap-7669	36	7	system	system	NOUN
ap-7669	36	8	with	with	ADP
ap-7669	36	9	benign	benign	ADJ
ap-7669	36	10	ghosts	ghost	NOUN
ap-7669	36	11	with	with	ADP
ap-7669	36	12	the	the	DET
ap-7669	36	13	lagrangian	lagrangian	ADJ
ap-7669	36	14	l	l	NOUN
ap-7669	36	15	=	=	SYM
ap-7669	36	16	1	1	NUM
ap-7669	36	17	2	2	NUM
ap-7669	36	18	[	[	PUNCT
ap-7669	36	19	ẍ2	ẍ2	NOUN
ap-7669	36	20	−	−	PROPN
ap-7669	37	1	(	(	PUNCT
ap-7669	37	2	ω2	ω2	NOUN
ap-7669	37	3	1	1	NUM
ap-7669	37	4	+	+	CCONJ
ap-7669	37	5	ω2	ω2	ADJ
ap-7669	37	6	2)ẋ2	2)ẋ2	NUM
ap-7669	37	7	+	+	CCONJ
ap-7669	37	8	ω2	ω2	ADJ
ap-7669	37	9	1ω	1ω	PROPN
ap-7669	37	10	2	2	NUM
ap-7669	37	11	2x	2x	NUM
ap-7669	37	12	2	2	NUM
ap-7669	37	13	]	]	PUNCT
ap-7669	37	14	.	.	PUNCT
ap-7669	38	1	(	(	PUNCT
ap-7669	38	2	2	2	X
ap-7669	38	3	)	)	PUNCT
ap-7669	38	4	this	this	DET
ap-7669	38	5	system	system	NOUN
ap-7669	38	6	is	be	AUX
ap-7669	38	7	free	free	ADJ
ap-7669	38	8	,	,	PUNCT
ap-7669	38	9	its	its	PRON
ap-7669	38	10	canonical	canonical	ADJ
ap-7669	38	11	hamiltonian	hamiltonian	NOUN
ap-7669	38	12	can	can	AUX
ap-7669	38	13	be	be	AUX
ap-7669	38	14	reduced	reduce	VERB
ap-7669	38	15	to	to	ADP
ap-7669	38	16	the	the	DET
ap-7669	38	17	difference	difference	NOUN
ap-7669	38	18	of	of	ADP
ap-7669	38	19	the	the	DET
ap-7669	38	20	two	two	NUM
ap-7669	38	21	oscillator	oscillator	NOUN
ap-7669	38	22	hamiltonians	hamiltonian	NOUN
ap-7669	38	23	by	by	ADP
ap-7669	38	24	a	a	DET
ap-7669	38	25	canonical	canonical	ADJ
ap-7669	38	26	transformation	transformation	NOUN
ap-7669	38	27	[	[	X
ap-7669	38	28	11	11	NUM
ap-7669	38	29	]	]	PUNCT
ap-7669	38	30	.	.	PUNCT
ap-7669	39	1	the	the	DET
ap-7669	39	2	first	first	ADJ
ap-7669	39	3	example	example	NOUN
ap-7669	39	4	of	of	ADP
ap-7669	39	5	a	a	DET
ap-7669	39	6	nontrivial	nontrivial	ADJ
ap-7669	39	7	benign	benign	ADJ
ap-7669	39	8	ghost	ghost	NOUN
ap-7669	39	9	system	system	NOUN
ap-7669	39	10	involving	involve	VERB
ap-7669	39	11	nonlinear	nonlinear	ADJ
ap-7669	39	12	interactions	interaction	NOUN
ap-7669	39	13	was	be	AUX
ap-7669	39	14	built	build	VERB
ap-7669	39	15	up	up	ADP
ap-7669	39	16	in	in	ADP
ap-7669	39	17	[	[	X
ap-7669	39	18	12	12	NUM
ap-7669	39	19	]	]	PUNCT
ap-7669	39	20	.	.	PUNCT
ap-7669	40	1	for	for	ADP
ap-7669	40	2	other	other	ADJ
ap-7669	40	3	such	such	ADJ
ap-7669	40	4	examples	example	NOUN
ap-7669	40	5	,	,	PUNCT
ap-7669	40	6	see	see	VERB
ap-7669	40	7	refs	ref	NOUN
ap-7669	40	8	.	.	PUNCT
ap-7669	41	1	[	[	X
ap-7669	41	2	13–17	13–17	NUM
ap-7669	41	3	]	]	PUNCT
ap-7669	41	4	.	.	PUNCT
ap-7669	42	1	in	in	ADP
ap-7669	42	2	recent	recent	ADJ
ap-7669	42	3	[	[	X
ap-7669	42	4	18	18	NUM
ap-7669	42	5	]	]	PUNCT
ap-7669	42	6	,	,	PUNCT
ap-7669	42	7	we	we	PRON
ap-7669	42	8	outlined	outline	VERB
ap-7669	42	9	two	two	NUM
ap-7669	42	10	wide	wide	ADJ
ap-7669	42	11	classes	class	NOUN
ap-7669	42	12	of	of	ADP
ap-7669	42	13	benign	benign	ADJ
ap-7669	42	14	ghost	ghost	NOUN
ap-7669	42	15	systems	system	NOUN
ap-7669	42	16	:	:	PUNCT
ap-7669	42	17	(	(	PUNCT
ap-7669	42	18	i	i	NOUN
ap-7669	42	19	)	)	PUNCT
ap-7669	42	20	the	the	DET
ap-7669	42	21	systems	system	NOUN
ap-7669	42	22	obtained	obtain	VERB
ap-7669	42	23	by	by	ADP
ap-7669	42	24	a	a	DET
ap-7669	42	25	variation	variation	NOUN
ap-7669	42	26	of	of	ADP
ap-7669	42	27	ordinary	ordinary	ADJ
ap-7669	42	28	systems	system	NOUN
ap-7669	42	29	and	and	CCONJ
ap-7669	42	30	involving	involve	VERB
ap-7669	42	31	,	,	PUNCT
ap-7669	42	32	compared	compare	VERB
ap-7669	42	33	to	to	ADP
ap-7669	42	34	them	they	PRON
ap-7669	42	35	,	,	PUNCT
ap-7669	42	36	a	a	DET
ap-7669	42	37	double	double	ADJ
ap-7669	42	38	set	set	NOUN
ap-7669	42	39	of	of	ADP
ap-7669	42	40	dynamic	dynamic	ADJ
ap-7669	42	41	variables	variable	NOUN
ap-7669	42	42	and	and	CCONJ
ap-7669	42	43	(	(	PUNCT
ap-7669	42	44	ii	ii	NOUN
ap-7669	42	45	)	)	PUNCT
ap-7669	42	46	the	the	DET
ap-7669	42	47	systems	system	NOUN
ap-7669	42	48	describing	describe	VERB
ap-7669	42	49	geodesic	geodesic	ADJ
ap-7669	42	50	motion	motion	NOUN
ap-7669	42	51	over	over	ADP
ap-7669	42	52	lorenzian	lorenzian	PROPN
ap-7669	42	53	manifolds	manifold	NOUN
ap-7669	42	54	.	.	PUNCT
ap-7669	43	1	in	in	ADP
ap-7669	43	2	addition	addition	NOUN
ap-7669	43	3	,	,	PUNCT
ap-7669	43	4	we	we	PRON
ap-7669	43	5	noticed	notice	VERB
ap-7669	43	6	that	that	SCONJ
ap-7669	43	7	the	the	DET
ap-7669	43	8	evolution	evolution	NOUN
ap-7669	43	9	of	of	ADP
ap-7669	43	10	the	the	DET
ap-7669	43	11	modified	modify	VERB
ap-7669	43	12	korteweg	korteweg	NOUN
ap-7669	43	13	-	-	PUNCT
ap-7669	43	14	de	de	NOUN
ap-7669	43	15	vries	vries	PROPN
ap-7669	43	16	(	(	PUNCT
ap-7669	43	17	mkdv	mkdv	NOUN
ap-7669	43	18	)	)	PUNCT
ap-7669	43	19	system	system	NOUN
ap-7669	43	20	(	(	PUNCT
ap-7669	43	21	9	9	NUM
ap-7669	43	22	)	)	PUNCT
ap-7669	43	23	in	in	ADP
ap-7669	43	24	the	the	DET
ap-7669	43	25	spatial	spatial	ADJ
ap-7669	43	26	direction	direction	NOUN
ap-7669	43	27	also	also	ADV
ap-7669	43	28	exhibits	exhibit	VERB
ap-7669	43	29	a	a	DET
ap-7669	43	30	benign	benign	ADJ
ap-7669	43	31	ghost	ghost	NOUN
ap-7669	43	32	dynamics	dynamic	NOUN
ap-7669	43	33	.	.	PUNCT
ap-7669	44	1	this	this	DET
ap-7669	44	2	report	report	NOUN
ap-7669	44	3	is	be	AUX
ap-7669	44	4	mostly	mostly	ADV
ap-7669	44	5	based	base	VERB
ap-7669	44	6	on	on	ADP
ap-7669	44	7	section	section	NOUN
ap-7669	44	8	4	4	NUM
ap-7669	44	9	of	of	ADP
ap-7669	44	10	[	[	X
ap-7669	44	11	18	18	NUM
ap-7669	44	12	]	]	PUNCT
ap-7669	44	13	that	that	PRON
ap-7669	44	14	deals	deal	VERB
ap-7669	44	15	with	with	ADP
ap-7669	44	16	mkdv	mkdv	NOUN
ap-7669	44	17	dynamics	dynamic	NOUN
ap-7669	44	18	.	.	PUNCT
ap-7669	45	1	2	2	X
ap-7669	45	2	.	.	X
ap-7669	45	3	spatial	spatial	ADJ
ap-7669	45	4	dynamics	dynamic	NOUN
ap-7669	45	5	of	of	ADP
ap-7669	45	6	kdv	kdv	NOUN
ap-7669	45	7	and	and	CCONJ
ap-7669	45	8	mkdv	mkdv	VERB
ap-7669	45	9	equations	equation	NOUN
ap-7669	45	10	first	first	ADV
ap-7669	45	11	,	,	PUNCT
ap-7669	45	12	consider	consider	VERB
ap-7669	45	13	the	the	DET
ap-7669	45	14	ordinary	ordinary	ADJ
ap-7669	45	15	kdv	kdv	NOUN
ap-7669	45	16	equation	equation	NOUN
ap-7669	45	17	,	,	PUNCT
ap-7669	45	18	uxxx	uxxx	PROPN
ap-7669	45	19	+	+	CCONJ
ap-7669	45	20	6uux	6uux	NUM
ap-7669	45	21	+	+	CCONJ
ap-7669	45	22	ut	ut	PROPN
ap-7669	45	23	=	=	SYM
ap-7669	45	24	0	0	PROPN
ap-7669	45	25	,	,	PUNCT
ap-7669	45	26	(	(	PUNCT
ap-7669	45	27	3	3	X
ap-7669	45	28	)	)	PUNCT
ap-7669	45	29	where	where	SCONJ
ap-7669	45	30	ux	ux	PROPN
ap-7669	45	31	=	=	SYM
ap-7669	45	32	∂u/∂x	∂u/∂x	PROPN
ap-7669	45	33	,	,	PUNCT
ap-7669	45	34	ut	ut	X
ap-7669	45	35	=	=	SYM
ap-7669	45	36	∂u/∂t	∂u/∂t	PROPN
ap-7669	45	37	etc	etc	X
ap-7669	45	38	.	.	X
ap-7669	46	1	it	it	PRON
ap-7669	46	2	has	have	VERB
ap-7669	46	3	an	an	DET
ap-7669	46	4	infinite	infinite	ADJ
ap-7669	46	5	number	number	NOUN
ap-7669	46	6	of	of	ADP
ap-7669	46	7	integrals	integral	NOUN
ap-7669	46	8	of	of	ADP
ap-7669	46	9	motion	motion	NOUN
ap-7669	46	10	and	and	CCONJ
ap-7669	46	11	is	be	AUX
ap-7669	46	12	exactly	exactly	ADV
ap-7669	46	13	soluble.2	soluble.2	DET
ap-7669	46	14	the	the	DET
ap-7669	46	15	kdv	kdv	NOUN
ap-7669	46	16	equation	equation	NOUN
ap-7669	46	17	is	be	AUX
ap-7669	46	18	derived	derive	VERB
ap-7669	46	19	from	from	ADP
ap-7669	46	20	the	the	DET
ap-7669	46	21	field	field	NOUN
ap-7669	46	22	lagrangian	lagrangian	ADJ
ap-7669	46	23	l[ψ(t	l[ψ(t	PROPN
ap-7669	46	24	,	,	PUNCT
ap-7669	46	25	x	x	NOUN
ap-7669	46	26	)	)	PUNCT
ap-7669	46	27	]	]	PUNCT
ap-7669	47	1	=	=	SYM
ap-7669	47	2	1	1	NUM
ap-7669	47	3	2ψ	2ψ	NUM
ap-7669	47	4	2	2	NUM
ap-7669	47	5	xx	xx	NUM
ap-7669	47	6	−	−	PROPN
ap-7669	47	7	ψ3	ψ3	NOUN
ap-7669	47	8	x	x	PUNCT
ap-7669	47	9	−	−	PROPN
ap-7669	47	10	1	1	NUM
ap-7669	47	11	2ψtψx	2ψtψx	NUM
ap-7669	47	12	(	(	PUNCT
ap-7669	47	13	4	4	NUM
ap-7669	47	14	)	)	PUNCT
ap-7669	47	15	if	if	SCONJ
ap-7669	47	16	one	one	NUM
ap-7669	47	17	denotes	denote	VERB
ap-7669	47	18	u(t	u(t	NOUN
ap-7669	47	19	,	,	PUNCT
ap-7669	47	20	x	x	X
ap-7669	47	21	)	)	PUNCT
ap-7669	47	22	≡	≡	PROPN
ap-7669	47	23	ψx	ψx	X
ap-7669	47	24	after	after	ADP
ap-7669	47	25	having	having	AUX
ap-7669	47	26	varied	vary	VERB
ap-7669	47	27	over	over	ADP
ap-7669	47	28	ψ(t	ψ(t	PROPN
ap-7669	47	29	,	,	PUNCT
ap-7669	47	30	x	x	NOUN
ap-7669	47	31	)	)	PUNCT
ap-7669	47	32	.	.	PUNCT
ap-7669	48	1	this	this	DET
ap-7669	48	2	lagrangian	lagrangian	ADJ
ap-7669	48	3	involves	involve	VERB
ap-7669	48	4	higher	high	ADJ
ap-7669	48	5	spatial	spatial	ADJ
ap-7669	48	6	derivatives	derivative	NOUN
ap-7669	48	7	,	,	PUNCT
ap-7669	48	8	but	but	CCONJ
ap-7669	48	9	not	not	PART
ap-7669	48	10	higher	high	ADJ
ap-7669	48	11	time	time	NOUN
ap-7669	48	12	derivatives	derivative	NOUN
ap-7669	48	13	and	and	CCONJ
ap-7669	48	14	does	do	AUX
ap-7669	48	15	not	not	PART
ap-7669	48	16	involve	involve	VERB
ap-7669	48	17	ghosts	ghost	NOUN
ap-7669	48	18	in	in	ADP
ap-7669	48	19	the	the	DET
ap-7669	48	20	ordinary	ordinary	ADJ
ap-7669	48	21	sense	sense	NOUN
ap-7669	48	22	.	.	PUNCT
ap-7669	49	1	we	we	PRON
ap-7669	49	2	can	can	AUX
ap-7669	49	3	,	,	PUNCT
ap-7669	49	4	however	however	ADV
ap-7669	49	5	,	,	PUNCT
ap-7669	49	6	simply	simply	ADV
ap-7669	49	7	rename	rename	ADJ
ap-7669	49	8	t	t	NOUN
ap-7669	49	9	→	→	SYM
ap-7669	49	10	x	x	SYM
ap-7669	49	11	,	,	PUNCT
ap-7669	49	12	x	x	PROPN
ap-7669	49	13	→	→	SYM
ap-7669	49	14	t	t	PROPN
ap-7669	49	15	,	,	PUNCT
ap-7669	49	16	(	(	PUNCT
ap-7669	49	17	5	5	NUM
ap-7669	49	18	)	)	PUNCT
ap-7669	49	19	in	in	ADP
ap-7669	49	20	which	which	DET
ap-7669	49	21	case	case	NOUN
ap-7669	49	22	the	the	DET
ap-7669	49	23	equation	equation	NOUN
ap-7669	49	24	acquires	acquire	VERB
ap-7669	49	25	the	the	DET
ap-7669	49	26	form	form	NOUN
ap-7669	49	27	ut	ut	PROPN
ap-7669	49	28	t	t	PROPN
ap-7669	49	29	t	t	PROPN
ap-7669	49	30	+	+	CCONJ
ap-7669	49	31	6uut	6uut	PROPN
ap-7669	50	1	+	+	CCONJ
ap-7669	50	2	ux	ux	NOUN
ap-7669	50	3	=	=	SYM
ap-7669	50	4	0	0	NUM
ap-7669	51	1	(	(	PUNCT
ap-7669	51	2	6	6	NUM
ap-7669	51	3	)	)	PUNCT
ap-7669	51	4	and	and	CCONJ
ap-7669	51	5	higher	high	ADJ
ap-7669	51	6	time	time	NOUN
ap-7669	51	7	derivatives	derivative	NOUN
ap-7669	51	8	appear	appear	VERB
ap-7669	51	9	.	.	PUNCT
ap-7669	52	1	according	accord	VERB
ap-7669	52	2	to	to	ADP
ap-7669	52	3	our	our	PRON
ap-7669	52	4	conjecture	conjecture	NOUN
ap-7669	52	5	,	,	PUNCT
ap-7669	52	6	to	to	PART
ap-7669	52	7	study	study	VERB
ap-7669	52	8	the	the	DET
ap-7669	52	9	question	question	NOUN
ap-7669	52	10	of	of	ADP
ap-7669	52	11	whether	whether	SCONJ
ap-7669	52	12	the	the	DET
ap-7669	52	13	quantum	quantum	ADJ
ap-7669	52	14	hamiltonian	hamiltonian	NOUN
ap-7669	52	15	corresponding	correspond	VERB
ap-7669	52	16	to	to	ADP
ap-7669	52	17	the	the	DET
ap-7669	52	18	thus	thus	ADV
ap-7669	52	19	rotated	rotate	VERB
ap-7669	52	20	lagrangian	lagrangian	ADJ
ap-7669	52	21	(	(	PUNCT
ap-7669	52	22	4	4	NUM
ap-7669	52	23	)	)	PUNCT
ap-7669	52	24	is	be	AUX
ap-7669	52	25	hermitian	hermitian	ADJ
ap-7669	52	26	and	and	CCONJ
ap-7669	52	27	unitarity	unitarity	NOUN
ap-7669	52	28	is	be	AUX
ap-7669	52	29	preserved	preserve	VERB
ap-7669	52	30	,	,	PUNCT
ap-7669	52	31	it	it	PRON
ap-7669	52	32	is	be	AUX
ap-7669	52	33	sufficient	sufficient	ADJ
ap-7669	52	34	to	to	PART
ap-7669	52	35	study	study	VERB
ap-7669	52	36	its	its	PRON
ap-7669	52	37	classical	classical	ADJ
ap-7669	52	38	dynamics	dynamic	NOUN
ap-7669	52	39	:	:	PUNCT
ap-7669	52	40	if	if	SCONJ
ap-7669	52	41	it	it	PRON
ap-7669	52	42	does	do	AUX
ap-7669	52	43	not	not	PART
ap-7669	52	44	involve	involve	VERB
ap-7669	52	45	a	a	DET
ap-7669	52	46	blow	blow	NOUN
ap-7669	52	47	-	-	PUNCT
ap-7669	52	48	up	up	NOUN
ap-7669	52	49	and	and	CCONJ
ap-7669	52	50	all	all	DET
ap-7669	52	51	classical	classical	ADJ
ap-7669	52	52	trajectories	trajectory	NOUN
ap-7669	52	53	exist	exist	VERB
ap-7669	52	54	at	at	ADP
ap-7669	52	55	all	all	DET
ap-7669	52	56	times	time	NOUN
ap-7669	52	57	t	t	NOUN
ap-7669	52	58	,	,	PUNCT
ap-7669	52	59	one	one	PRON
ap-7669	52	60	can	can	AUX
ap-7669	52	61	be	be	AUX
ap-7669	52	62	sure	sure	ADJ
ap-7669	52	63	that	that	SCONJ
ap-7669	52	64	the	the	DET
ap-7669	52	65	quantum	quantum	ADJ
ap-7669	52	66	system	system	NOUN
ap-7669	52	67	is	be	AUX
ap-7669	52	68	also	also	ADV
ap-7669	52	69	benign	benign	ADJ
ap-7669	52	70	.	.	PUNCT
ap-7669	53	1	note	note	VERB
ap-7669	53	2	that	that	SCONJ
ap-7669	53	3	the	the	DET
ap-7669	53	4	question	question	NOUN
ap-7669	53	5	whether	whether	SCONJ
ap-7669	53	6	or	or	CCONJ
ap-7669	53	7	not	not	PART
ap-7669	53	8	blowing	blow	VERB
ap-7669	53	9	up	up	ADP
ap-7669	53	10	trajectories	trajectory	NOUN
ap-7669	53	11	are	be	AUX
ap-7669	53	12	present	present	ADJ
ap-7669	53	13	is	be	AUX
ap-7669	53	14	far	far	ADV
ap-7669	53	15	from	from	ADP
ap-7669	53	16	being	be	AUX
ap-7669	53	17	trivial	trivial	ADJ
ap-7669	53	18	.	.	PUNCT
ap-7669	54	1	the	the	DET
ap-7669	54	2	ordinary	ordinary	ADJ
ap-7669	54	3	cauchy	cauchy	ADJ
ap-7669	54	4	problem	problem	NOUN
ap-7669	54	5	for	for	ADP
ap-7669	54	6	the	the	DET
ap-7669	54	7	equation	equation	NOUN
ap-7669	54	8	(	(	PUNCT
ap-7669	54	9	4	4	X
ap-7669	54	10	)	)	PUNCT
ap-7669	54	11	consists	consist	VERB
ap-7669	54	12	2exact	2exact	NUM
ap-7669	54	13	solvability	solvability	NOUN
ap-7669	54	14	always	always	ADV
ap-7669	54	15	makes	make	VERB
ap-7669	54	16	the	the	DET
ap-7669	54	17	behaviour	behaviour	NOUN
ap-7669	54	18	of	of	ADP
ap-7669	54	19	a	a	DET
ap-7669	54	20	system	system	NOUN
ap-7669	54	21	more	more	ADV
ap-7669	54	22	handy	handy	ADJ
ap-7669	54	23	.	.	PUNCT
ap-7669	55	1	in	in	ADP
ap-7669	55	2	particular	particular	ADJ
ap-7669	55	3	,	,	PUNCT
ap-7669	55	4	many	many	ADJ
ap-7669	55	5	mechanical	mechanical	ADJ
ap-7669	55	6	models	model	NOUN
ap-7669	55	7	including	include	VERB
ap-7669	55	8	benign	benign	ADJ
ap-7669	55	9	ghosts	ghost	NOUN
ap-7669	55	10	,	,	PUNCT
ap-7669	55	11	which	which	PRON
ap-7669	55	12	were	be	AUX
ap-7669	55	13	mentioned	mention	VERB
ap-7669	55	14	above	above	ADV
ap-7669	55	15	,	,	PUNCT
ap-7669	55	16	are	be	AUX
ap-7669	55	17	exactly	exactly	ADV
ap-7669	55	18	solvable	solvable	ADJ
ap-7669	55	19	.	.	PUNCT
ap-7669	56	1	in	in	ADP
ap-7669	56	2	setting	set	VERB
ap-7669	56	3	the	the	DET
ap-7669	56	4	initial	initial	ADJ
ap-7669	56	5	value	value	NOUN
ap-7669	56	6	of	of	ADP
ap-7669	56	7	u(t0	u(t0	NOUN
ap-7669	56	8	,	,	PUNCT
ap-7669	56	9	x	x	NOUN
ap-7669	56	10	)	)	PUNCT
ap-7669	56	11	at	at	ADP
ap-7669	56	12	a	a	DET
ap-7669	56	13	given	give	VERB
ap-7669	56	14	time	time	NOUN
ap-7669	56	15	moment	moment	NOUN
ap-7669	56	16	,	,	PUNCT
ap-7669	56	17	say	say	VERB
ap-7669	56	18	,	,	PUNCT
ap-7669	56	19	t0	t0	X
ap-7669	56	20	=	=	PUNCT
ap-7669	57	1	0	0	PROPN
ap-7669	57	2	.	.	PUNCT
ap-7669	58	1	and	and	CCONJ
ap-7669	58	2	we	we	PRON
ap-7669	58	3	are	be	AUX
ap-7669	58	4	now	now	ADV
ap-7669	58	5	interested	interested	ADJ
ap-7669	58	6	[	[	PUNCT
ap-7669	58	7	staying	stay	VERB
ap-7669	58	8	with	with	ADP
ap-7669	58	9	eq	eq	NOUN
ap-7669	58	10	.	.	PUNCT
ap-7669	59	1	(	(	PUNCT
ap-7669	59	2	4	4	NUM
ap-7669	59	3	)	)	PUNCT
ap-7669	59	4	and	and	CCONJ
ap-7669	59	5	not	not	PART
ap-7669	59	6	changing	change	VERB
ap-7669	59	7	the	the	DET
ap-7669	59	8	name	name	NOUN
ap-7669	59	9	of	of	ADP
ap-7669	59	10	the	the	DET
ap-7669	59	11	variables	variable	NOUN
ap-7669	59	12	according	accord	VERB
ap-7669	59	13	to	to	ADP
ap-7669	59	14	(	(	PUNCT
ap-7669	59	15	5	5	NUM
ap-7669	59	16	)	)	PUNCT
ap-7669	59	17	]	]	PUNCT
ap-7669	59	18	in	in	ADP
ap-7669	59	19	the	the	DET
ap-7669	59	20	cauchy	cauchy	ADJ
ap-7669	59	21	problem	problem	NOUN
ap-7669	59	22	in	in	ADP
ap-7669	59	23	x	x	PROPN
ap-7669	59	24	direction	direction	NOUN
ap-7669	59	25	.	.	PUNCT
ap-7669	60	1	the	the	DET
ap-7669	60	2	presence	presence	NOUN
ap-7669	60	3	of	of	ADP
ap-7669	60	4	third	third	ADJ
ap-7669	60	5	spatial	spatial	ADJ
ap-7669	60	6	derivatives	derivative	NOUN
ap-7669	60	7	in	in	ADP
ap-7669	60	8	(	(	PUNCT
ap-7669	60	9	4	4	X
ap-7669	60	10	)	)	PUNCT
ap-7669	60	11	makes	make	VERB
ap-7669	60	12	it	it	PRON
ap-7669	60	13	necessary	necessary	ADJ
ap-7669	60	14	to	to	PART
ap-7669	60	15	define	define	VERB
ap-7669	60	16	,	,	PUNCT
ap-7669	60	17	at	at	ADP
ap-7669	60	18	the	the	DET
ap-7669	60	19	line	line	NOUN
ap-7669	60	20	x	x	X
ap-7669	60	21	=	=	SYM
ap-7669	60	22	x0	x0	PROPN
ap-7669	60	23	,	,	PUNCT
ap-7669	60	24	three	three	NUM
ap-7669	60	25	different	different	ADJ
ap-7669	60	26	functions	function	NOUN
ap-7669	60	27	:	:	PUNCT
ap-7669	60	28	u(t	u(t	NOUN
ap-7669	60	29	,	,	PUNCT
ap-7669	60	30	x0	x0	PROPN
ap-7669	60	31	)	)	PUNCT
ap-7669	60	32	,	,	PUNCT
ap-7669	60	33	ux(t	ux(t	PRON
ap-7669	60	34	,	,	PUNCT
ap-7669	60	35	x0	x0	PROPN
ap-7669	60	36	)	)	PUNCT
ap-7669	60	37	and	and	CCONJ
ap-7669	60	38	uxx(t	uxx(t	PROPN
ap-7669	60	39	,	,	PUNCT
ap-7669	60	40	x0	x0	PROPN
ap-7669	60	41	)	)	PUNCT
ap-7669	60	42	.	.	PUNCT
ap-7669	61	1	the	the	DET
ap-7669	61	2	presence	presence	NOUN
ap-7669	61	3	of	of	ADP
ap-7669	61	4	three	three	NUM
ap-7669	61	5	arbitrary	arbitrary	ADJ
ap-7669	61	6	functions	function	NOUN
ap-7669	61	7	makes	make	VERB
ap-7669	61	8	the	the	DET
ap-7669	61	9	space	space	NOUN
ap-7669	61	10	of	of	ADP
ap-7669	61	11	solutions	solution	NOUN
ap-7669	61	12	to	to	ADP
ap-7669	61	13	the	the	DET
ap-7669	61	14	spatial	spatial	ADJ
ap-7669	61	15	cauchy	cauchy	PROPN
ap-7669	61	16	problem	problem	NOUN
ap-7669	61	17	much	much	ADV
ap-7669	61	18	larger	large	ADJ
ap-7669	61	19	than	than	ADP
ap-7669	61	20	for	for	ADP
ap-7669	61	21	the	the	DET
ap-7669	61	22	ordinary	ordinary	ADJ
ap-7669	61	23	cauchy	cauchy	ADJ
ap-7669	61	24	problem	problem	NOUN
ap-7669	61	25	.	.	PUNCT
ap-7669	62	1	the	the	DET
ap-7669	62	2	solutions	solution	NOUN
ap-7669	62	3	to	to	ADP
ap-7669	62	4	the	the	DET
ap-7669	62	5	latter	latter	ADJ
ap-7669	62	6	represent	represent	VERB
ap-7669	62	7	a	a	DET
ap-7669	62	8	subset	subset	NOUN
ap-7669	62	9	of	of	ADP
ap-7669	62	10	measure	measure	NOUN
ap-7669	62	11	zero	zero	NUM
ap-7669	62	12	in	in	ADP
ap-7669	62	13	the	the	DET
ap-7669	62	14	set	set	NOUN
ap-7669	62	15	of	of	ADP
ap-7669	62	16	the	the	DET
ap-7669	62	17	solutions	solution	NOUN
ap-7669	62	18	in	in	ADP
ap-7669	62	19	the	the	DET
ap-7669	62	20	former	former	ADJ
ap-7669	62	21	,	,	PUNCT
ap-7669	62	22	and	and	CCONJ
ap-7669	62	23	the	the	DET
ap-7669	62	24	fact	fact	NOUN
ap-7669	62	25	that	that	SCONJ
ap-7669	62	26	the	the	DET
ap-7669	62	27	solutions	solution	NOUN
ap-7669	62	28	to	to	ADP
ap-7669	62	29	the	the	DET
ap-7669	62	30	ordinary	ordinary	ADJ
ap-7669	62	31	cauchy	cauchy	ADJ
ap-7669	62	32	problem	problem	NOUN
ap-7669	62	33	are	be	AUX
ap-7669	62	34	all	all	ADV
ap-7669	62	35	benign	benign	ADJ
ap-7669	62	36	does	do	AUX
ap-7669	62	37	not	not	PART
ap-7669	62	38	mean	mean	VERB
ap-7669	62	39	that	that	SCONJ
ap-7669	62	40	it	it	PRON
ap-7669	62	41	is	be	AUX
ap-7669	62	42	also	also	ADV
ap-7669	62	43	the	the	DET
ap-7669	62	44	case	case	NOUN
ap-7669	62	45	for	for	ADP
ap-7669	62	46	the	the	DET
ap-7669	62	47	rotated	rotated	ADJ
ap-7669	62	48	x	x	ADJ
ap-7669	62	49	-	-	ADJ
ap-7669	62	50	directed	direct	VERB
ap-7669	62	51	problem	problem	NOUN
ap-7669	62	52	.	.	PUNCT
ap-7669	63	1	and	and	CCONJ
ap-7669	63	2	,	,	PUNCT
ap-7669	63	3	indeed	indeed	ADV
ap-7669	63	4	,	,	PUNCT
ap-7669	63	5	for	for	ADP
ap-7669	63	6	the	the	DET
ap-7669	63	7	ordinary	ordinary	ADJ
ap-7669	63	8	kdv	kdv	NOUN
ap-7669	63	9	equation	equation	NOUN
ap-7669	63	10	(	(	PUNCT
ap-7669	63	11	4	4	NUM
ap-7669	63	12	)	)	PUNCT
ap-7669	63	13	,	,	PUNCT
ap-7669	63	14	the	the	DET
ap-7669	63	15	problem	problem	NOUN
ap-7669	63	16	is	be	AUX
ap-7669	63	17	not	not	PART
ap-7669	63	18	benign	benign	ADJ
ap-7669	63	19	.	.	PUNCT
ap-7669	64	1	it	it	PRON
ap-7669	64	2	is	be	AUX
ap-7669	64	3	best	well	ADV
ap-7669	64	4	seen	see	VERB
ap-7669	64	5	if	if	SCONJ
ap-7669	64	6	we	we	PRON
ap-7669	64	7	choose	choose	VERB
ap-7669	64	8	a	a	DET
ap-7669	64	9	t	t	NOUN
ap-7669	64	10	-	-	PUNCT
ap-7669	64	11	independent	independent	ADJ
ap-7669	64	12	ansatz	ansatz	ADJ
ap-7669	64	13	u(t	u(t	NOUN
ap-7669	64	14	,	,	PUNCT
ap-7669	64	15	x	x	NOUN
ap-7669	64	16	)	)	PUNCT
ap-7669	64	17	→	→	SYM
ap-7669	64	18	u(x	u(x	NOUN
ap-7669	64	19	)	)	PUNCT
ap-7669	64	20	and	and	CCONJ
ap-7669	64	21	plug	plug	VERB
ap-7669	64	22	it	it	PRON
ap-7669	64	23	into	into	ADP
ap-7669	64	24	(	(	PUNCT
ap-7669	64	25	3	3	NUM
ap-7669	64	26	)	)	PUNCT
ap-7669	64	27	.	.	PUNCT
ap-7669	65	1	the	the	DET
ap-7669	65	2	equation	equation	NOUN
ap-7669	65	3	is	be	AUX
ap-7669	65	4	reduced	reduce	VERB
ap-7669	65	5	to	to	ADP
ap-7669	65	6	∂x(uxx	∂x(uxx	PROPN
ap-7669	65	7	+	+	X
ap-7669	66	1	3u2	3u2	NUM
ap-7669	66	2	)	)	PUNCT
ap-7669	66	3	=	=	SYM
ap-7669	66	4	0	0	PUNCT
ap-7669	67	1	=	=	VERB
ap-7669	67	2	⇒	⇒	X
ap-7669	67	3	uxx	uxx	NOUN
ap-7669	68	1	+	+	CCONJ
ap-7669	68	2	3u2	3u2	NUM
ap-7669	68	3	=	=	SYM
ap-7669	68	4	c	c	NOUN
ap-7669	68	5	.	.	PUNCT
ap-7669	69	1	(	(	PUNCT
ap-7669	69	2	7	7	X
ap-7669	69	3	)	)	PUNCT
ap-7669	69	4	this	this	DET
ap-7669	69	5	equation	equation	NOUN
ap-7669	69	6	describes	describe	VERB
ap-7669	69	7	the	the	DET
ap-7669	69	8	motion	motion	NOUN
ap-7669	69	9	in	in	ADP
ap-7669	69	10	the	the	DET
ap-7669	69	11	cubic	cubic	ADJ
ap-7669	69	12	potential	potential	ADJ
ap-7669	69	13	v	v	X
ap-7669	69	14	(	(	PUNCT
ap-7669	69	15	u	u	NOUN
ap-7669	69	16	)	)	PUNCT
ap-7669	69	17	=	=	NOUN
ap-7669	69	18	u3	u3	PROPN
ap-7669	69	19	−	−	PROPN
ap-7669	69	20	cu	cu	PROPN
ap-7669	69	21	.	.	PUNCT
ap-7669	70	1	it	it	PRON
ap-7669	70	2	has	have	VERB
ap-7669	70	3	blow	blow	NOUN
ap-7669	70	4	-	-	PUNCT
ap-7669	70	5	up	up	ADP
ap-7669	70	6	solutions	solution	NOUN
ap-7669	70	7	.	.	PUNCT
ap-7669	71	1	if	if	SCONJ
ap-7669	71	2	c	c	NOUN
ap-7669	71	3	=	=	SYM
ap-7669	71	4	0	0	NUM
ap-7669	71	5	,	,	PUNCT
ap-7669	71	6	they	they	PRON
ap-7669	71	7	read	read	VERB
ap-7669	71	8	u(x	u(x	NOUN
ap-7669	71	9	)	)	PUNCT
ap-7669	72	1	=	=	SYM
ap-7669	73	1	−	−	PROPN
ap-7669	73	2	2	2	NUM
ap-7669	73	3	(	(	PUNCT
ap-7669	73	4	x−	x−	PROPN
ap-7669	73	5	x0)2	x0)2	PROPN
ap-7669	73	6	.	.	PUNCT
ap-7669	74	1	(	(	PUNCT
ap-7669	74	2	8)	8)	NUM
ap-7669	74	3	however	however	ADV
ap-7669	74	4	,	,	PUNCT
ap-7669	74	5	the	the	DET
ap-7669	74	6	situation	situation	NOUN
ap-7669	74	7	is	be	AUX
ap-7669	74	8	completely	completely	ADV
ap-7669	74	9	different	different	ADJ
ap-7669	74	10	for	for	ADP
ap-7669	74	11	the	the	DET
ap-7669	74	12	modified	modified	ADJ
ap-7669	74	13	kdv	kdv	NOUN
ap-7669	74	14	equation,3	equation,3	X
ap-7669	74	15	uxxx	uxxx	PROPN
ap-7669	75	1	+	+	CCONJ
ap-7669	75	2	6u2ux	6u2ux	NUM
ap-7669	75	3	+	+	CCONJ
ap-7669	75	4	ut	ut	PROPN
ap-7669	75	5	=	=	NOUN
ap-7669	75	6	0	0	PROPN
ap-7669	75	7	.	.	PUNCT
ap-7669	76	1	(	(	PUNCT
ap-7669	76	2	9	9	X
ap-7669	76	3	)	)	PUNCT
ap-7669	76	4	this	this	DET
ap-7669	76	5	equation	equation	NOUN
ap-7669	76	6	admits	admit	VERB
ap-7669	76	7	an	an	DET
ap-7669	76	8	infinite	infinite	ADJ
ap-7669	76	9	number	number	NOUN
ap-7669	76	10	of	of	ADP
ap-7669	76	11	integrals	integral	NOUN
ap-7669	76	12	of	of	ADP
ap-7669	76	13	motion	motion	NOUN
ap-7669	76	14	,	,	PUNCT
ap-7669	76	15	as	as	SCONJ
ap-7669	76	16	the	the	DET
ap-7669	76	17	ordinary	ordinary	ADJ
ap-7669	76	18	kdv	kdv	NOUN
ap-7669	76	19	equation	equation	NOUN
ap-7669	76	20	does	do	VERB
ap-7669	76	21	.	.	PUNCT
ap-7669	77	1	the	the	DET
ap-7669	77	2	first	first	ADJ
ap-7669	77	3	three	three	NUM
ap-7669	77	4	local	local	ADJ
ap-7669	77	5	conservation	conservation	NOUN
ap-7669	77	6	laws	law	NOUN
ap-7669	77	7	are	be	AUX
ap-7669	77	8	∂tu	∂tu	ADJ
ap-7669	77	9	=	=	SYM
ap-7669	77	10	−∂x(uxx	−∂x(uxx	PROPN
ap-7669	77	11	+	+	CCONJ
ap-7669	77	12	2u3	2u3	NUM
ap-7669	77	13	)	)	PUNCT
ap-7669	77	14	,	,	PUNCT
ap-7669	77	15	(	(	PUNCT
ap-7669	77	16	10	10	NUM
ap-7669	77	17	)	)	PUNCT
ap-7669	77	18	∂tu	∂tu	ADV
ap-7669	77	19	2	2	NUM
ap-7669	77	20	=	=	SYM
ap-7669	77	21	−2∂x	−2∂x	X
ap-7669	77	22	[	[	PUNCT
ap-7669	77	23	3	3	NUM
ap-7669	77	24	2u	2u	NOUN
ap-7669	77	25	4	4	NUM
ap-7669	77	26	+	+	NUM
ap-7669	77	27	uuxx	uuxx	ADJ
ap-7669	77	28	−	−	PROPN
ap-7669	77	29	1	1	NUM
ap-7669	77	30	2u	2u	PROPN
ap-7669	77	31	2	2	NUM
ap-7669	77	32	x	x	SYM
ap-7669	77	33	]	]	X
ap-7669	77	34	,	,	PUNCT
ap-7669	77	35	(	(	PUNCT
ap-7669	77	36	11	11	NUM
ap-7669	77	37	)	)	PUNCT
ap-7669	77	38	∂t	∂t	PROPN
ap-7669	77	39	(	(	PUNCT
ap-7669	77	40	1	1	NUM
ap-7669	77	41	2u	2u	PROPN
ap-7669	77	42	4	4	NUM
ap-7669	77	43	−	−	NOUN
ap-7669	77	44	1	1	NUM
ap-7669	77	45	2u	2u	PROPN
ap-7669	77	46	2	2	NUM
ap-7669	77	47	x	x	SYM
ap-7669	77	48	)	)	PUNCT
ap-7669	78	1	=	=	SYM
ap-7669	78	2	∂x	∂x	PROPN
ap-7669	78	3	[	[	PUNCT
ap-7669	78	4	ux(2u2ux	ux(2u2ux	PROPN
ap-7669	78	5	+	+	CCONJ
ap-7669	78	6	1	1	NUM
ap-7669	78	7	2uxxx	2uxxx	NUM
ap-7669	78	8	)	)	PUNCT
ap-7669	78	9	−	−	PROPN
ap-7669	78	10	1	1	NUM
ap-7669	78	11	2u	2u	PROPN
ap-7669	78	12	2	2	NUM
ap-7669	78	13	xx	xx	NUM
ap-7669	78	14	−	−	PROPN
ap-7669	78	15	2u3uxx	2u3uxx	NUM
ap-7669	78	16	−	−	NOUN
ap-7669	78	17	2u6	2u6	NUM
ap-7669	78	18	]	]	PUNCT
ap-7669	78	19	(	(	PUNCT
ap-7669	78	20	12	12	NUM
ap-7669	78	21	)	)	PUNCT
ap-7669	78	22	for	for	ADP
ap-7669	78	23	the	the	DET
ap-7669	78	24	time	time	NOUN
ap-7669	78	25	-	-	PUNCT
ap-7669	78	26	independent	independent	ADJ
ap-7669	78	27	ansatz	ansatz	NOUN
ap-7669	78	28	,	,	PUNCT
ap-7669	78	29	we	we	PRON
ap-7669	78	30	obtain	obtain	VERB
ap-7669	78	31	,	,	PUNCT
ap-7669	78	32	instead	instead	ADV
ap-7669	78	33	of	of	ADP
ap-7669	78	34	(	(	PUNCT
ap-7669	78	35	7	7	NUM
ap-7669	78	36	)	)	PUNCT
ap-7669	78	37	,	,	PUNCT
ap-7669	78	38	∂x(uxx	∂x(uxx	X
ap-7669	78	39	+	+	CCONJ
ap-7669	78	40	2u3	2u3	NUM
ap-7669	78	41	)	)	PUNCT
ap-7669	78	42	=	=	SYM
ap-7669	78	43	0	0	PUNCT
ap-7669	79	1	=	=	VERB
ap-7669	79	2	⇒	⇒	X
ap-7669	79	3	uxx	uxx	NOUN
ap-7669	79	4	+	+	CCONJ
ap-7669	79	5	2u3	2u3	NUM
ap-7669	79	6	=	=	SYM
ap-7669	79	7	c	c	NOUN
ap-7669	79	8	.	.	PUNCT
ap-7669	80	1	(	(	PUNCT
ap-7669	80	2	13	13	NUM
ap-7669	80	3	)	)	PUNCT
ap-7669	80	4	this	this	PRON
ap-7669	80	5	describes	describe	VERB
ap-7669	80	6	the	the	DET
ap-7669	80	7	motion	motion	NOUN
ap-7669	80	8	in	in	ADP
ap-7669	80	9	a	a	DET
ap-7669	80	10	quartic	quartic	ADJ
ap-7669	80	11	potential	potential	ADJ
ap-7669	80	12	v	v	NOUN
ap-7669	80	13	(	(	PUNCT
ap-7669	80	14	u	u	NOUN
ap-7669	80	15	)	)	PUNCT
ap-7669	80	16	=	=	SYM
ap-7669	80	17	u4/2	u4/2	NUM
ap-7669	80	18	−	−	PROPN
ap-7669	80	19	cu	cu	PROPN
ap-7669	80	20	.	.	PUNCT
ap-7669	81	1	this	this	DET
ap-7669	81	2	motion	motion	NOUN
ap-7669	81	3	is	be	AUX
ap-7669	81	4	bounded	bound	VERB
ap-7669	81	5	,	,	PUNCT
ap-7669	81	6	the	the	DET
ap-7669	81	7	solutions	solution	NOUN
ap-7669	81	8	being	be	AUX
ap-7669	81	9	elliptic	elliptic	ADJ
ap-7669	81	10	functions	function	NOUN
ap-7669	81	11	.	.	PUNCT
ap-7669	82	1	3	3	NUM
ap-7669	82	2	in	in	ADP
ap-7669	82	3	ref	ref	NOUN
ap-7669	82	4	.	.	PUNCT
ap-7669	83	1	[	[	X
ap-7669	83	2	18	18	NUM
ap-7669	83	3	]	]	PUNCT
ap-7669	83	4	,	,	PUNCT
ap-7669	83	5	we	we	PRON
ap-7669	83	6	wrote	write	VERB
ap-7669	83	7	this	this	DET
ap-7669	83	8	equation	equation	NOUN
ap-7669	83	9	as	as	ADP
ap-7669	83	10	uxxx	uxxx	PROPN
ap-7669	83	11	+	+	CCONJ
ap-7669	83	12	12κu2ux	12κu2ux	NUM
ap-7669	83	13	+	+	CCONJ
ap-7669	83	14	ut	ut	PROPN
ap-7669	83	15	=	=	SYM
ap-7669	83	16	0	0	PUNCT
ap-7669	84	1	and	and	CCONJ
ap-7669	84	2	kept	keep	VERB
ap-7669	84	3	κ	κ	PROPN
ap-7669	84	4	in	in	ADP
ap-7669	84	5	all	all	DET
ap-7669	84	6	subsequent	subsequent	ADJ
ap-7669	84	7	formulas	formula	NOUN
ap-7669	84	8	.	.	PUNCT
ap-7669	85	1	but	but	CCONJ
ap-7669	85	2	here	here	ADV
ap-7669	85	3	,	,	PUNCT
ap-7669	85	4	we	we	PRON
ap-7669	85	5	have	have	AUX
ap-7669	85	6	chosen	choose	VERB
ap-7669	85	7	,	,	PUNCT
ap-7669	85	8	for	for	ADP
ap-7669	85	9	simplicity	simplicity	NOUN
ap-7669	85	10	,	,	PUNCT
ap-7669	85	11	to	to	PART
ap-7669	85	12	fix	fix	VERB
ap-7669	85	13	κ	κ	X
ap-7669	85	14	=	=	SYM
ap-7669	85	15	1/2	1/2	NUM
ap-7669	85	16	.	.	PUNCT
ap-7669	86	1	191	191	NUM
ap-7669	86	2	andrei	andrei	PROPN
ap-7669	86	3	smilga	smilga	PROPN
ap-7669	86	4	acta	acta	PROPN
ap-7669	86	5	polytechnica	polytechnica	PROPN
ap-7669	86	6	this	this	DET
ap-7669	86	7	observation	observation	NOUN
ap-7669	86	8	presents	present	VERB
ap-7669	86	9	an	an	DET
ap-7669	86	10	argument	argument	NOUN
ap-7669	86	11	that	that	SCONJ
ap-7669	86	12	the	the	DET
ap-7669	86	13	rotated	rotate	VERB
ap-7669	86	14	cauchy	cauchy	NOUN
ap-7669	86	15	problem	problem	NOUN
ap-7669	86	16	for	for	ADP
ap-7669	86	17	the	the	DET
ap-7669	86	18	equation	equation	NOUN
ap-7669	86	19	(	(	PUNCT
ap-7669	86	20	9	9	NUM
ap-7669	86	21	)	)	PUNCT
ap-7669	86	22	with	with	ADP
ap-7669	86	23	arbitrary	arbitrary	ADJ
ap-7669	86	24	initial	initial	ADJ
ap-7669	86	25	conditions	condition	NOUN
ap-7669	86	26	on	on	ADP
ap-7669	86	27	the	the	DET
ap-7669	86	28	line	line	NOUN
ap-7669	86	29	x	x	PUNCT
ap-7669	87	1	=	=	PRON
ap-7669	87	2	const	const	NOUN
ap-7669	87	3	might	might	AUX
ap-7669	87	4	be	be	AUX
ap-7669	87	5	benign	benign	ADJ
ap-7669	87	6	.	.	PUNCT
ap-7669	88	1	note	note	VERB
ap-7669	88	2	that	that	SCONJ
ap-7669	88	3	this	this	DET
ap-7669	88	4	behaviour	behaviour	NOUN
ap-7669	88	5	is	be	AUX
ap-7669	88	6	specific	specific	ADJ
ap-7669	88	7	for	for	ADP
ap-7669	88	8	the	the	DET
ap-7669	88	9	equation	equation	NOUN
ap-7669	88	10	(	(	PUNCT
ap-7669	88	11	9	9	NUM
ap-7669	88	12	)	)	PUNCT
ap-7669	88	13	with	with	ADP
ap-7669	88	14	the	the	DET
ap-7669	88	15	positive	positive	ADJ
ap-7669	88	16	sign	sign	NOUN
ap-7669	88	17	of	of	ADP
ap-7669	88	18	the	the	DET
ap-7669	88	19	middle	middle	ADJ
ap-7669	88	20	term	term	NOUN
ap-7669	88	21	(	(	PUNCT
ap-7669	88	22	the	the	DET
ap-7669	88	23	socalled	socalled	ADJ
ap-7669	88	24	focusing	focus	VERB
ap-7669	88	25	case	case	NOUN
ap-7669	88	26	)	)	PUNCT
ap-7669	88	27	.	.	PUNCT
ap-7669	89	1	plugging	plug	VERB
ap-7669	89	2	the	the	DET
ap-7669	89	3	time	time	NOUN
ap-7669	89	4	-	-	PUNCT
ap-7669	89	5	independent	independent	ADJ
ap-7669	89	6	ansatz	ansatz	NOUN
ap-7669	89	7	in	in	ADP
ap-7669	89	8	the	the	DET
ap-7669	89	9	defocusing	defocuse	VERB
ap-7669	89	10	mkdv	mkdv	NOUN
ap-7669	89	11	equation,4	equation,4	AUX
ap-7669	89	12	uxxx	uxxx	ADJ
ap-7669	89	13	−	−	PROPN
ap-7669	89	14	6u2ux	6u2ux	NUM
ap-7669	89	15	+	+	CCONJ
ap-7669	89	16	ut	ut	PROPN
ap-7669	89	17	=	=	SYM
ap-7669	89	18	0	0	PROPN
ap-7669	89	19	,	,	PUNCT
ap-7669	89	20	(	(	PUNCT
ap-7669	89	21	14	14	NUM
ap-7669	89	22	)	)	PUNCT
ap-7669	89	23	the	the	DET
ap-7669	89	24	problem	problem	NOUN
ap-7669	89	25	would	would	AUX
ap-7669	89	26	be	be	AUX
ap-7669	89	27	reduced	reduce	VERB
ap-7669	89	28	to	to	ADP
ap-7669	89	29	the	the	DET
ap-7669	89	30	motion	motion	NOUN
ap-7669	89	31	in	in	ADP
ap-7669	89	32	the	the	DET
ap-7669	89	33	potential	potential	ADJ
ap-7669	89	34	v	v	NOUN
ap-7669	89	35	(	(	PUNCT
ap-7669	89	36	u	u	NOUN
ap-7669	89	37	)	)	PUNCT
ap-7669	89	38	=	=	SYM
ap-7669	90	1	−u4/2−cu	−u4/2−cu	VERB
ap-7669	90	2	characterized	characterize	VERB
ap-7669	90	3	by	by	ADP
ap-7669	90	4	a	a	DET
ap-7669	90	5	blowup	blowup	NOUN
ap-7669	90	6	.	.	PUNCT
ap-7669	91	1	this	this	PRON
ap-7669	91	2	conforms	conform	VERB
ap-7669	91	3	to	to	ADP
ap-7669	91	4	the	the	DET
ap-7669	91	5	well	well	ADV
ap-7669	91	6	-	-	PUNCT
ap-7669	91	7	known	know	VERB
ap-7669	91	8	fact	fact	NOUN
ap-7669	91	9	that	that	SCONJ
ap-7669	91	10	any	any	DET
ap-7669	91	11	solution	solution	NOUN
ap-7669	91	12	u(t	u(t	NOUN
ap-7669	91	13	,	,	PUNCT
ap-7669	91	14	x	x	NOUN
ap-7669	91	15	)	)	PUNCT
ap-7669	91	16	of	of	ADP
ap-7669	91	17	the	the	DET
ap-7669	91	18	ordinary	ordinary	ADJ
ap-7669	91	19	kdv	kdv	NOUN
ap-7669	91	20	equation	equation	NOUN
ap-7669	91	21	is	be	AUX
ap-7669	91	22	related	relate	VERB
ap-7669	91	23	to	to	ADP
ap-7669	91	24	a	a	DET
ap-7669	91	25	solution	solution	NOUN
ap-7669	91	26	v(t	v(t	NOUN
ap-7669	91	27	,	,	PUNCT
ap-7669	91	28	x	x	NOUN
ap-7669	91	29	)	)	PUNCT
ap-7669	91	30	of	of	ADP
ap-7669	91	31	the	the	DET
ap-7669	91	32	defocusing	defocuse	VERB
ap-7669	91	33	mkdv	mkdv	NOUN
ap-7669	91	34	equation	equation	NOUN
ap-7669	91	35	by	by	ADP
ap-7669	91	36	the	the	DET
ap-7669	91	37	miura	miura	PROPN
ap-7669	91	38	transformation	transformation	PROPN
ap-7669	91	39	,	,	PUNCT
ap-7669	91	40	u	u	NOUN
ap-7669	91	41	=	=	NOUN
ap-7669	91	42	−(v2	−(v2	X
ap-7669	91	43	+	+	CCONJ
ap-7669	91	44	vx	vx	PROPN
ap-7669	91	45	)	)	PUNCT
ap-7669	91	46	.	.	PUNCT
ap-7669	92	1	(	(	PUNCT
ap-7669	92	2	15	15	X
ap-7669	92	3	)	)	PUNCT
ap-7669	92	4	a	a	DET
ap-7669	92	5	different	different	ADJ
ap-7669	92	6	(	(	PUNCT
ap-7669	92	7	though	though	SCONJ
ap-7669	92	8	related	relate	VERB
ap-7669	92	9	)	)	PUNCT
ap-7669	92	10	analytic	analytic	ADJ
ap-7669	92	11	argument	argument	NOUN
ap-7669	92	12	indicating	indicate	VERB
ap-7669	92	13	the	the	DET
ap-7669	92	14	absence	absence	NOUN
ap-7669	92	15	of	of	ADP
ap-7669	92	16	real	real	ADJ
ap-7669	92	17	blow	blow	NOUN
ap-7669	92	18	-	-	PUNCT
ap-7669	92	19	up	up	ADP
ap-7669	92	20	solutions	solution	NOUN
ap-7669	92	21	for	for	ADP
ap-7669	92	22	the	the	DET
ap-7669	92	23	focusing	focus	VERB
ap-7669	92	24	mkdv	mkdv	NOUN
ap-7669	92	25	equation	equation	NOUN
ap-7669	92	26	comes	come	VERB
ap-7669	92	27	from	from	ADP
ap-7669	92	28	the	the	DET
ap-7669	92	29	analysis	analysis	NOUN
ap-7669	92	30	of	of	ADP
ap-7669	92	31	its	its	PRON
ap-7669	92	32	scaling	scale	VERB
ap-7669	92	33	properties	property	NOUN
ap-7669	92	34	.	.	PUNCT
ap-7669	93	1	it	it	PRON
ap-7669	93	2	is	be	AUX
ap-7669	93	3	easily	easily	ADV
ap-7669	93	4	seen	see	VERB
ap-7669	93	5	that	that	SCONJ
ap-7669	93	6	eq	eq	ADP
ap-7669	93	7	.	.	PUNCT
ap-7669	94	1	(	(	PUNCT
ap-7669	94	2	9	9	X
ap-7669	94	3	)	)	PUNCT
ap-7669	94	4	is	be	AUX
ap-7669	94	5	invariant	invariant	ADJ
ap-7669	94	6	under	under	ADP
ap-7669	94	7	the	the	DET
ap-7669	94	8	rescalings	rescaling	NOUN
ap-7669	94	9	u	u	NOUN
ap-7669	94	10	=	=	PROPN
ap-7669	94	11	λuū	λuū	PROPN
ap-7669	94	12	,	,	PUNCT
ap-7669	94	13	x	x	X
ap-7669	95	1	=	=	SYM
ap-7669	95	2	λxx̄	λxx̄	PROPN
ap-7669	95	3	,	,	PUNCT
ap-7669	95	4	t	t	NOUN
ap-7669	95	5	=	=	SYM
ap-7669	95	6	λtt̄	λtt̄	NOUN
ap-7669	96	1	if	if	SCONJ
ap-7669	96	2	λt	λt	ADP
ap-7669	96	3	=	=	PUNCT
ap-7669	96	4	λ3	λ3	PROPN
ap-7669	96	5	x	x	PROPN
ap-7669	96	6	,	,	PUNCT
ap-7669	96	7	λu	λu	X
ap-7669	97	1	=	=	PUNCT
ap-7669	97	2	λ−1	λ−1	PROPN
ap-7669	97	3	x	x	X
ap-7669	97	4	.	.	PUNCT
ap-7669	98	1	(	(	PUNCT
ap-7669	98	2	16	16	NUM
ap-7669	98	3	)	)	PUNCT
ap-7669	98	4	the	the	DET
ap-7669	98	5	quantities	quantity	NOUN
ap-7669	98	6	xu	xu	PROPN
ap-7669	99	1	and	and	CCONJ
ap-7669	99	2	x	x	X
ap-7669	99	3	/	/	SYM
ap-7669	99	4	t1/3	t1/3	PROPN
ap-7669	99	5	are	be	AUX
ap-7669	99	6	invariant	invariant	ADJ
ap-7669	99	7	under	under	ADP
ap-7669	99	8	these	these	DET
ap-7669	99	9	rescalings	rescaling	NOUN
ap-7669	99	10	.	.	PUNCT
ap-7669	100	1	using	use	VERB
ap-7669	100	2	also	also	ADV
ap-7669	100	3	the	the	DET
ap-7669	100	4	space	space	NOUN
ap-7669	100	5	and	and	CCONJ
ap-7669	100	6	time	time	NOUN
ap-7669	100	7	translational	translational	ADJ
ap-7669	100	8	invariance	invariance	NOUN
ap-7669	100	9	of	of	ADP
ap-7669	100	10	the	the	DET
ap-7669	100	11	mkdv	mkdv	NOUN
ap-7669	100	12	equation	equation	NOUN
ap-7669	100	13	,	,	PUNCT
ap-7669	100	14	we	we	PRON
ap-7669	100	15	can	can	AUX
ap-7669	100	16	look	look	VERB
ap-7669	100	17	for	for	ADP
ap-7669	100	18	scaling	scale	VERB
ap-7669	100	19	solutions	solution	NOUN
ap-7669	100	20	of	of	ADP
ap-7669	100	21	the	the	DET
ap-7669	100	22	type	type	NOUN
ap-7669	100	23	u(t	u(t	NOUN
ap-7669	100	24	,	,	PUNCT
ap-7669	100	25	x	x	X
ap-7669	100	26	)	)	PUNCT
ap-7669	100	27	=	=	SYM
ap-7669	101	1	1	1	NUM
ap-7669	102	1	[	[	X
ap-7669	102	2	3(t−	3(t−	NUM
ap-7669	102	3	t0)]1/3w(z	t0)]1/3w(z	PROPN
ap-7669	102	4	)	)	PUNCT
ap-7669	102	5	,	,	PUNCT
ap-7669	102	6	(	(	PUNCT
ap-7669	102	7	17	17	NUM
ap-7669	102	8	)	)	PUNCT
ap-7669	102	9	where	where	SCONJ
ap-7669	102	10	z	z	NOUN
ap-7669	103	1	=	=	PUNCT
ap-7669	103	2	x−	x−	X
ap-7669	103	3	x0	x0	PROPN
ap-7669	104	1	[	[	X
ap-7669	104	2	3(t−	3(t−	NUM
ap-7669	104	3	t0)]1/3	t0)]1/3	INTJ
ap-7669	104	4	.	.	PUNCT
ap-7669	105	1	(	(	PUNCT
ap-7669	105	2	18	18	NUM
ap-7669	105	3	)	)	PUNCT
ap-7669	105	4	inserting	insert	VERB
ap-7669	105	5	the	the	DET
ap-7669	105	6	ansatz	ansatz	ADJ
ap-7669	105	7	(	(	PUNCT
ap-7669	105	8	17	17	NUM
ap-7669	105	9	)	)	PUNCT
ap-7669	105	10	in	in	ADP
ap-7669	105	11	eq	eq	ADP
ap-7669	105	12	.	.	PUNCT
ap-7669	106	1	(	(	PUNCT
ap-7669	106	2	9	9	NUM
ap-7669	106	3	)	)	PUNCT
ap-7669	106	4	,	,	PUNCT
ap-7669	106	5	one	one	NUM
ap-7669	106	6	easily	easily	ADV
ap-7669	106	7	verifies	verifie	NOUN
ap-7669	106	8	that	that	SCONJ
ap-7669	106	9	the	the	DET
ap-7669	106	10	function	function	NOUN
ap-7669	106	11	w(z	w(z	NOUN
ap-7669	106	12	)	)	PUNCT
ap-7669	106	13	satisfies	satisfy	VERB
ap-7669	106	14	the	the	DET
ap-7669	106	15	equation	equation	NOUN
ap-7669	106	16	0	0	NUM
ap-7669	106	17	=	=	SYM
ap-7669	107	1	w′′′	w′′′	NOUN
ap-7669	107	2	+	+	CCONJ
ap-7669	107	3	(	(	PUNCT
ap-7669	107	4	6w2	6w2	NUM
ap-7669	107	5	−	−	PROPN
ap-7669	107	6	z)w′	z)w′	NOUN
ap-7669	107	7	−	−	PROPN
ap-7669	108	1	w	w	PROPN
ap-7669	108	2	=	=	SYM
ap-7669	108	3	d	d	X
ap-7669	108	4	dz	dz	X
ap-7669	108	5	[	[	PUNCT
ap-7669	108	6	w′′	w′′	NOUN
ap-7669	108	7	+	+	CCONJ
ap-7669	108	8	2w3	2w3	NUM
ap-7669	108	9	−	−	NOUN
ap-7669	108	10	zw	zw	X
ap-7669	108	11	]	]	PUNCT
ap-7669	108	12	(	(	PUNCT
ap-7669	108	13	19	19	NUM
ap-7669	108	14	)	)	PUNCT
ap-7669	108	15	denoting	denote	VERB
ap-7669	108	16	the	the	DET
ap-7669	108	17	constant	constant	ADJ
ap-7669	108	18	value	value	NOUN
ap-7669	108	19	of	of	ADP
ap-7669	108	20	the	the	DET
ap-7669	108	21	bracket	bracket	NOUN
ap-7669	108	22	in	in	ADP
ap-7669	108	23	the	the	DET
ap-7669	108	24	last	last	ADJ
ap-7669	108	25	right	right	ADJ
ap-7669	108	26	-	-	PUNCT
ap-7669	108	27	hand	hand	NOUN
ap-7669	108	28	side	side	NOUN
ap-7669	108	29	as	as	ADP
ap-7669	108	30	c	c	NOUN
ap-7669	108	31	,	,	PUNCT
ap-7669	108	32	we	we	PRON
ap-7669	108	33	conclude	conclude	VERB
ap-7669	108	34	that	that	SCONJ
ap-7669	108	35	w(z	w(z	PROPN
ap-7669	108	36	)	)	PUNCT
ap-7669	108	37	satisfies	satisfy	VERB
ap-7669	108	38	a	a	DET
ap-7669	108	39	second	second	ADJ
ap-7669	108	40	-	-	PUNCT
ap-7669	108	41	order	order	NOUN
ap-7669	108	42	equation	equation	NOUN
ap-7669	108	43	,	,	PUNCT
ap-7669	108	44	w′′	w′′	NOUN
ap-7669	108	45	=	=	PUNCT
ap-7669	108	46	−2w3	−2w3	PUNCT
ap-7669	109	1	+	+	CCONJ
ap-7669	109	2	zw	zw	X
ap-7669	109	3	+	+	CCONJ
ap-7669	109	4	c	c	NOUN
ap-7669	109	5	.	.	PUNCT
ap-7669	110	1	(	(	PUNCT
ap-7669	110	2	20	20	NUM
ap-7669	110	3	)	)	PUNCT
ap-7669	110	4	for	for	ADP
ap-7669	110	5	the	the	DET
ap-7669	110	6	equation	equation	NOUN
ap-7669	110	7	(	(	PUNCT
ap-7669	110	8	14	14	NUM
ap-7669	110	9	)	)	PUNCT
ap-7669	110	10	,	,	PUNCT
ap-7669	110	11	the	the	DET
ap-7669	110	12	same	same	ADJ
ap-7669	110	13	analysis	analysis	NOUN
ap-7669	110	14	would	would	AUX
ap-7669	110	15	give	give	VERB
ap-7669	110	16	the	the	DET
ap-7669	110	17	equation	equation	NOUN
ap-7669	110	18	w′′	w′′	NOUN
ap-7669	110	19	=	=	SYM
ap-7669	110	20	2w3	2w3	NUM
ap-7669	110	21	+	+	CCONJ
ap-7669	110	22	zw	zw	X
ap-7669	110	23	+	+	CCONJ
ap-7669	110	24	c	c	NOUN
ap-7669	110	25	.	.	PUNCT
ap-7669	111	1	(	(	PUNCT
ap-7669	111	2	21	21	NUM
ap-7669	111	3	)	)	PUNCT
ap-7669	111	4	these	these	PRON
ap-7669	111	5	are	be	AUX
ap-7669	111	6	painlevé	painlevé	PROPN
ap-7669	111	7	ii	ii	PROPN
ap-7669	111	8	equations	equation	NOUN
ap-7669	111	9	[	[	X
ap-7669	111	10	19	19	NUM
ap-7669	111	11	]	]	PUNCT
ap-7669	111	12	.	.	PUNCT
ap-7669	112	1	in	in	ADP
ap-7669	112	2	general	general	ADJ
ap-7669	112	3	,	,	PUNCT
ap-7669	112	4	painlevé	painlevé	NOUN
ap-7669	112	5	equations	equation	NOUN
ap-7669	112	6	have	have	VERB
ap-7669	112	7	pole	pole	NOUN
ap-7669	112	8	singularities	singularity	NOUN
ap-7669	112	9	.	.	PUNCT
ap-7669	113	1	and	and	CCONJ
ap-7669	113	2	indeed	indeed	ADV
ap-7669	113	3	,	,	PUNCT
ap-7669	113	4	a	a	DET
ap-7669	113	5	local	local	ADJ
ap-7669	113	6	analysis	analysis	NOUN
ap-7669	113	7	of	of	ADP
ap-7669	113	8	eq	eq	PROPN
ap-7669	113	9	.	.	PUNCT
ap-7669	114	1	(	(	PUNCT
ap-7669	114	2	21	21	NUM
ap-7669	114	3	)	)	PUNCT
ap-7669	114	4	(	(	PUNCT
ap-7669	114	5	keeping	keep	VERB
ap-7669	114	6	the	the	DET
ap-7669	114	7	leadingorder	leadingorder	NOUN
ap-7669	114	8	terms	term	NOUN
ap-7669	114	9	w′′	w′′	PROPN
ap-7669	114	10	≈	≈	PROPN
ap-7669	114	11	2w3	2w3	PROPN
ap-7669	114	12	)	)	PUNCT
ap-7669	114	13	shows	show	VERB
ap-7669	114	14	that	that	SCONJ
ap-7669	114	15	(	(	PUNCT
ap-7669	114	16	21	21	NUM
ap-7669	114	17	)	)	PUNCT
ap-7669	114	18	admits	admit	VERB
ap-7669	114	19	simple	simple	ADJ
ap-7669	114	20	poles	pole	NOUN
ap-7669	114	21	,	,	PUNCT
ap-7669	114	22	w(z	w(z	PROPN
ap-7669	114	23	)	)	PUNCT
ap-7669	115	1	≈	≈	NUM
ap-7669	115	2	±1/(z	±1/(z	X
ap-7669	115	3	−	−	PROPN
ap-7669	115	4	z0	z0	PROPN
ap-7669	115	5	)	)	PUNCT
ap-7669	115	6	.	.	PUNCT
ap-7669	116	1	the	the	DET
ap-7669	116	2	existence	existence	NOUN
ap-7669	116	3	of	of	ADP
ap-7669	116	4	4the	4the	NUM
ap-7669	116	5	coefficient	coefficient	NOUN
ap-7669	116	6	6	6	NUM
ap-7669	116	7	is	be	AUX
ap-7669	116	8	a	a	DET
ap-7669	116	9	convention	convention	NOUN
ap-7669	116	10	.	.	PUNCT
ap-7669	117	1	it	it	PRON
ap-7669	117	2	can	can	AUX
ap-7669	117	3	be	be	AUX
ap-7669	117	4	changed	change	VERB
ap-7669	117	5	by	by	ADP
ap-7669	117	6	rescaling	rescale	VERB
ap-7669	117	7	t	t	PROPN
ap-7669	117	8	and	and	CCONJ
ap-7669	117	9	x.	x.	PROPN
ap-7669	118	1	but	but	CCONJ
ap-7669	118	2	the	the	DET
ap-7669	118	3	sign	sign	NOUN
ap-7669	118	4	stays	stay	VERB
ap-7669	118	5	invariant	invariant	ADJ
ap-7669	118	6	under	under	ADP
ap-7669	118	7	rescaling	rescaling	NOUN
ap-7669	118	8	.	.	PUNCT
ap-7669	119	1	1	1	NUM
ap-7669	119	2	2	2	NUM
ap-7669	119	3	3	3	NUM
ap-7669	119	4	4	4	NUM
ap-7669	119	5	5	5	NUM
ap-7669	119	6	6	6	NUM
ap-7669	119	7	t	t	NOUN
ap-7669	119	8	-300	-300	NUM
ap-7669	120	1	-200	-200	NUM
ap-7669	120	2	-100	-100	PROPN
ap-7669	120	3	100	100	NUM
ap-7669	120	4	200	200	NUM
ap-7669	120	5	300	300	NUM
ap-7669	120	6	u	u	NOUN
ap-7669	120	7	figure	figure	NOUN
ap-7669	120	8	2	2	NUM
ap-7669	120	9	.	.	PUNCT
ap-7669	121	1	u(t	u(t	NOUN
ap-7669	121	2	,	,	PUNCT
ap-7669	121	3	x	x	SYM
ap-7669	121	4	=	=	NOUN
ap-7669	121	5	2.26	2.26	NUM
ap-7669	121	6	)	)	PUNCT
ap-7669	121	7	for	for	ADP
ap-7669	121	8	the	the	DET
ap-7669	121	9	defocusing	defocuse	VERB
ap-7669	121	10	mkdv	mkdv	NOUN
ap-7669	121	11	.	.	PUNCT
ap-7669	122	1	a	a	DET
ap-7669	122	2	real	real	ADJ
ap-7669	122	3	simple	simple	ADJ
ap-7669	122	4	pole	pole	NOUN
ap-7669	122	5	at	at	ADP
ap-7669	122	6	z	z	NOUN
ap-7669	122	7	=	=	SYM
ap-7669	122	8	z0	z0	PROPN
ap-7669	122	9	would	would	AUX
ap-7669	122	10	then	then	ADV
ap-7669	122	11	correspond	correspond	VERB
ap-7669	122	12	to	to	ADP
ap-7669	122	13	a	a	DET
ap-7669	122	14	singular	singular	NOUN
ap-7669	122	15	(	(	PUNCT
ap-7669	122	16	blow	blow	NOUN
ap-7669	122	17	-	-	PUNCT
ap-7669	122	18	up	up	NOUN
ap-7669	122	19	)	)	PUNCT
ap-7669	122	20	behavior	behavior	NOUN
ap-7669	122	21	of	of	ADP
ap-7669	122	22	u(t	u(t	NOUN
ap-7669	122	23	,	,	PUNCT
ap-7669	122	24	x	x	NOUN
ap-7669	122	25	)	)	PUNCT
ap-7669	122	26	of	of	ADP
ap-7669	122	27	the	the	DET
ap-7669	122	28	form	form	NOUN
ap-7669	122	29	u(t	u(t	NOUN
ap-7669	122	30	,	,	PUNCT
ap-7669	122	31	x	x	X
ap-7669	122	32	)	)	PUNCT
ap-7669	122	33	∝	∝	PROPN
ap-7669	122	34	[	[	PUNCT
ap-7669	122	35	x−	x−	PROPN
ap-7669	122	36	x0	x0	PROPN
ap-7669	123	1	−	−	PROPN
ap-7669	124	1	z0[3(t−	z0[3(t−	NUM
ap-7669	124	2	t0)]1/3]−1	t0)]1/3]−1	NOUN
ap-7669	124	3	.	.	PUNCT
ap-7669	125	1	but	but	CCONJ
ap-7669	125	2	for	for	ADP
ap-7669	125	3	the	the	DET
ap-7669	125	4	equation	equation	NOUN
ap-7669	125	5	(	(	PUNCT
ap-7669	125	6	20	20	NUM
ap-7669	125	7	)	)	PUNCT
ap-7669	126	1	[	[	X
ap-7669	126	2	and	and	CCONJ
ap-7669	126	3	hence	hence	ADV
ap-7669	126	4	for	for	ADP
ap-7669	126	5	(	(	PUNCT
ap-7669	126	6	9	9	NUM
ap-7669	126	7	)	)	PUNCT
ap-7669	126	8	]	]	PUNCT
ap-7669	126	9	,	,	PUNCT
ap-7669	126	10	the	the	DET
ap-7669	126	11	singularities	singularity	NOUN
ap-7669	126	12	are	be	AUX
ap-7669	126	13	absent	absent	ADJ
ap-7669	126	14	.	.	PUNCT
ap-7669	127	1	the	the	DET
ap-7669	127	2	third	third	ADJ
ap-7669	127	3	argument	argument	NOUN
ap-7669	127	4	in	in	ADP
ap-7669	127	5	favor	favor	NOUN
ap-7669	127	6	of	of	ADP
ap-7669	127	7	the	the	DET
ap-7669	127	8	conjecture	conjecture	NOUN
ap-7669	127	9	that	that	SCONJ
ap-7669	127	10	the	the	DET
ap-7669	127	11	x	x	SYM
ap-7669	127	12	evolution	evolution	NOUN
ap-7669	127	13	of	of	ADP
ap-7669	127	14	sufficiently	sufficiently	ADV
ap-7669	127	15	smooth	smooth	ADJ
ap-7669	127	16	cauchy	cauchy	ADJ
ap-7669	127	17	data	datum	NOUN
ap-7669	127	18	on	on	ADP
ap-7669	127	19	the	the	DET
ap-7669	127	20	line	line	NOUN
ap-7669	127	21	x	x	PUNCT
ap-7669	128	1	=	=	PUNCT
ap-7669	128	2	const	const	NOUN
ap-7669	128	3	for	for	ADP
ap-7669	128	4	the	the	DET
ap-7669	128	5	mkdv	mkdv	NOUN
ap-7669	128	6	equation	equation	NOUN
ap-7669	128	7	(	(	PUNCT
ap-7669	128	8	9	9	NUM
ap-7669	128	9	)	)	PUNCT
ap-7669	128	10	does	do	AUX
ap-7669	128	11	not	not	PART
ap-7669	128	12	bring	bring	VERB
ap-7669	128	13	about	about	ADP
ap-7669	128	14	singularities	singularity	NOUN
ap-7669	128	15	in	in	ADP
ap-7669	128	16	u(t	u(t	NOUN
ap-7669	128	17	,	,	PUNCT
ap-7669	128	18	x	x	PRON
ap-7669	128	19	)	)	PUNCT
ap-7669	128	20	comes	come	VERB
ap-7669	128	21	from	from	ADP
ap-7669	128	22	numerical	numerical	ADJ
ap-7669	128	23	simulations	simulation	NOUN
ap-7669	128	24	.	.	PUNCT
ap-7669	129	1	to	to	PART
ap-7669	129	2	simplify	simplify	VERB
ap-7669	129	3	the	the	DET
ap-7669	129	4	numerical	numerical	ADJ
ap-7669	129	5	analysis	analysis	NOUN
ap-7669	129	6	,	,	PUNCT
ap-7669	129	7	we	we	PRON
ap-7669	129	8	considered	consider	VERB
ap-7669	129	9	the	the	DET
ap-7669	129	10	problem	problem	NOUN
ap-7669	129	11	on	on	ADP
ap-7669	129	12	the	the	DET
ap-7669	129	13	band	band	NOUN
ap-7669	129	14	0	0	NUM
ap-7669	129	15	≤	≤	NUM
ap-7669	129	16	t	t	NOUN
ap-7669	129	17	≤	≤	ADJ
ap-7669	129	18	2π	2π	NOUN
ap-7669	129	19	,	,	PUNCT
ap-7669	129	20	where	where	SCONJ
ap-7669	129	21	we	we	PRON
ap-7669	129	22	imposed	impose	VERB
ap-7669	129	23	[	[	PUNCT
ap-7669	129	24	as	as	SCONJ
ap-7669	129	25	is	be	AUX
ap-7669	129	26	allowed	allow	VERB
ap-7669	129	27	by	by	ADP
ap-7669	129	28	eq	eq	PROPN
ap-7669	129	29	.	.	PUNCT
ap-7669	130	1	(	(	PUNCT
ap-7669	130	2	9	9	NUM
ap-7669	130	3	)	)	PUNCT
ap-7669	130	4	]	]	PUNCT
ap-7669	130	5	periodic	periodic	ADJ
ap-7669	130	6	boundary	boundary	ADJ
ap-7669	130	7	conditions	condition	NOUN
ap-7669	130	8	:	:	PUNCT
ap-7669	131	1	u(t+	u(t+	ADP
ap-7669	131	2	2π	2π	NOUN
ap-7669	131	3	,	,	PUNCT
ap-7669	131	4	x	x	X
ap-7669	131	5	)	)	PUNCT
ap-7669	131	6	=	=	SYM
ap-7669	131	7	u(t	u(t	NOUN
ap-7669	131	8	,	,	PUNCT
ap-7669	131	9	x	x	NOUN
ap-7669	131	10	)	)	PUNCT
ap-7669	131	11	.	.	PUNCT
ap-7669	132	1	(	(	PUNCT
ap-7669	132	2	22	22	X
ap-7669	132	3	)	)	PUNCT
ap-7669	132	4	we	we	PRON
ap-7669	132	5	have	have	AUX
ap-7669	132	6	chosen	choose	VERB
ap-7669	132	7	the	the	DET
ap-7669	132	8	cauchy	cauchy	PROPN
ap-7669	132	9	data	datum	NOUN
ap-7669	132	10	u(t	u(t	NOUN
ap-7669	132	11	,	,	PUNCT
ap-7669	132	12	0	0	NUM
ap-7669	132	13	)	)	PUNCT
ap-7669	132	14	=	=	VERB
ap-7669	132	15	sin	sin	NOUN
ap-7669	132	16	t	t	PROPN
ap-7669	132	17	,	,	PUNCT
ap-7669	132	18	ux(t	ux(t	PRON
ap-7669	132	19	,	,	PUNCT
ap-7669	132	20	0	0	NUM
ap-7669	132	21	)	)	PUNCT
ap-7669	132	22	=	=	SYM
ap-7669	132	23	uxx(t	uxx(t	PROPN
ap-7669	132	24	,	,	PUNCT
ap-7669	132	25	0	0	NUM
ap-7669	132	26	)	)	PUNCT
ap-7669	132	27	=	=	SYM
ap-7669	132	28	0	0	X
ap-7669	132	29	.	.	PUNCT
ap-7669	133	1	(	(	PUNCT
ap-7669	133	2	23	23	NUM
ap-7669	133	3	)	)	PUNCT
ap-7669	133	4	we	we	PRON
ap-7669	133	5	first	first	ADV
ap-7669	133	6	checked	check	VERB
ap-7669	133	7	that	that	SCONJ
ap-7669	133	8	the	the	DET
ap-7669	133	9	use	use	NOUN
ap-7669	133	10	of	of	ADP
ap-7669	133	11	such	such	ADJ
ap-7669	133	12	cauchy	cauchy	ADJ
ap-7669	133	13	data	datum	NOUN
ap-7669	133	14	for	for	ADP
ap-7669	133	15	the	the	DET
ap-7669	133	16	defocusing	defocuse	VERB
ap-7669	133	17	mkdv	mkdv	NOUN
ap-7669	133	18	equation	equation	NOUN
ap-7669	133	19	(	(	PUNCT
ap-7669	133	20	14	14	NUM
ap-7669	133	21	)	)	PUNCT
ap-7669	133	22	was	be	AUX
ap-7669	133	23	leading	lead	VERB
ap-7669	133	24	to	to	ADP
ap-7669	133	25	a	a	DET
ap-7669	133	26	blow	blow	NOUN
ap-7669	133	27	-	-	PUNCT
ap-7669	133	28	up	up	NOUN
ap-7669	133	29	rather	rather	ADV
ap-7669	133	30	fast	fast	ADV
ap-7669	133	31	(	(	PUNCT
ap-7669	133	32	at	at	ADP
ap-7669	133	33	x	x	X
ap-7669	133	34	=	=	PUNCT
ap-7669	133	35	2.2630	2.2630	NUM
ap-7669	133	36	.	.	PUNCT
ap-7669	133	37	.	.	PUNCT
ap-7669	133	38	.	.	PUNCT
ap-7669	133	39	)	)	PUNCT
ap-7669	133	40	.	.	PUNCT
ap-7669	134	1	this	this	PRON
ap-7669	134	2	is	be	AUX
ap-7669	134	3	illustrated	illustrate	VERB
ap-7669	134	4	in	in	ADP
ap-7669	134	5	figure	figure	NOUN
ap-7669	134	6	2	2	NUM
ap-7669	134	7	,	,	PUNCT
ap-7669	134	8	where	where	SCONJ
ap-7669	134	9	the	the	DET
ap-7669	134	10	function	function	NOUN
ap-7669	134	11	u(t	u(t	NOUN
ap-7669	134	12	,	,	PUNCT
ap-7669	134	13	x	x	X
ap-7669	134	14	)	)	PUNCT
ap-7669	134	15	is	be	AUX
ap-7669	134	16	plotted	plot	VERB
ap-7669	134	17	just	just	ADV
ap-7669	134	18	before	before	ADP
ap-7669	134	19	the	the	DET
ap-7669	134	20	blow	blow	NOUN
ap-7669	134	21	-	-	PUNCT
ap-7669	134	22	up	up	NOUN
ap-7669	134	23	,	,	PUNCT
ap-7669	134	24	at	at	ADP
ap-7669	134	25	x	x	X
ap-7669	134	26	=	=	SYM
ap-7669	134	27	2.26	2.26	NUM
ap-7669	134	28	.	.	PUNCT
ap-7669	135	1	by	by	ADP
ap-7669	135	2	contrast	contrast	NOUN
ap-7669	135	3	,	,	PUNCT
ap-7669	135	4	our	our	PRON
ap-7669	135	5	numerical	numerical	ADJ
ap-7669	135	6	simulations	simulation	NOUN
ap-7669	135	7	of	of	ADP
ap-7669	135	8	the	the	DET
ap-7669	135	9	x	x	ADJ
ap-7669	135	10	evolution	evolution	NOUN
ap-7669	135	11	of	of	ADP
ap-7669	135	12	the	the	DET
ap-7669	135	13	focusing	focus	VERB
ap-7669	135	14	mkdv	mkdv	NOUN
ap-7669	135	15	equation	equation	NOUN
ap-7669	135	16	showed	show	VERB
ap-7669	135	17	that	that	SCONJ
ap-7669	135	18	u(t	u(t	NOUN
ap-7669	135	19	,	,	PUNCT
ap-7669	135	20	x	x	PRON
ap-7669	135	21	)	)	PUNCT
ap-7669	135	22	stayed	stay	VERB
ap-7669	135	23	bounded	bounded	ADJ
ap-7669	135	24	for	for	ADP
ap-7669	135	25	all	all	DET
ap-7669	135	26	the	the	DET
ap-7669	135	27	values	value	NOUN
ap-7669	135	28	of	of	ADP
ap-7669	135	29	x	x	PUNCT
ap-7669	135	30	that	that	SCONJ
ap-7669	135	31	we	we	PRON
ap-7669	135	32	explored	explore	VERB
ap-7669	135	33	.	.	PUNCT
ap-7669	136	1	we	we	PRON
ap-7669	136	2	met	meet	VERB
ap-7669	136	3	,	,	PUNCT
ap-7669	136	4	however	however	ADV
ap-7669	136	5	,	,	PUNCT
ap-7669	136	6	another	another	DET
ap-7669	136	7	problem	problem	NOUN
ap-7669	136	8	associated	associate	VERB
ap-7669	136	9	with	with	ADP
ap-7669	136	10	the	the	DET
ap-7669	136	11	instability	instability	NOUN
ap-7669	136	12	of	of	ADP
ap-7669	136	13	eq	eq	PROPN
ap-7669	136	14	.	.	PUNCT
ap-7669	137	1	(	(	PUNCT
ap-7669	137	2	9	9	NUM
ap-7669	137	3	)	)	PUNCT
ap-7669	137	4	under	under	ADP
ap-7669	137	5	highfrequency	highfrequency	NOUN
ap-7669	137	6	(	(	PUNCT
ap-7669	137	7	hf	hf	NOUN
ap-7669	137	8	)	)	PUNCT
ap-7669	137	9	perturbations	perturbation	NOUN
ap-7669	137	10	.	.	PUNCT
ap-7669	138	1	suppressing	suppress	VERB
ap-7669	138	2	the	the	DET
ap-7669	138	3	nonlinear	nonlinear	ADJ
ap-7669	138	4	term	term	NOUN
ap-7669	138	5	in	in	ADP
ap-7669	138	6	the	the	DET
ap-7669	138	7	kdv	kdv	NOUN
ap-7669	138	8	or	or	CCONJ
ap-7669	138	9	mkdv	mkdv	NOUN
ap-7669	138	10	equations	equation	NOUN
ap-7669	138	11	,	,	PUNCT
ap-7669	138	12	we	we	PRON
ap-7669	138	13	obtain	obtain	VERB
ap-7669	138	14	uxxx	uxxx	ADJ
ap-7669	138	15	+	+	CCONJ
ap-7669	138	16	ut	ut	PROPN
ap-7669	138	17	=	=	NOUN
ap-7669	138	18	0	0	PROPN
ap-7669	138	19	.	.	PUNCT
ap-7669	139	1	(	(	PUNCT
ap-7669	139	2	24	24	NUM
ap-7669	139	3	)	)	PUNCT
ap-7669	139	4	this	this	DET
ap-7669	139	5	equation	equation	NOUN
ap-7669	139	6	describes	describe	VERB
ap-7669	139	7	the	the	DET
ap-7669	139	8	fluctuations	fluctuation	NOUN
ap-7669	139	9	around	around	ADP
ap-7669	139	10	the	the	DET
ap-7669	139	11	solution	solution	NOUN
ap-7669	139	12	u(t	u(t	NOUN
ap-7669	139	13	,	,	PUNCT
ap-7669	139	14	x	x	NOUN
ap-7669	139	15	)	)	PUNCT
ap-7669	139	16	=	=	SYM
ap-7669	140	1	0	0	X
ap-7669	140	2	.	.	PUNCT
ap-7669	141	1	its	its	PRON
ap-7669	141	2	analysis	analysis	NOUN
ap-7669	141	3	gives	give	VERB
ap-7669	141	4	us	we	PRON
ap-7669	141	5	an	an	DET
ap-7669	141	6	idea	idea	NOUN
ap-7669	141	7	about	about	ADP
ap-7669	141	8	the	the	DET
ap-7669	141	9	behaviour	behaviour	NOUN
ap-7669	141	10	of	of	ADP
ap-7669	141	11	fluctuations	fluctuation	NOUN
ap-7669	141	12	around	around	ADP
ap-7669	141	13	other	other	ADJ
ap-7669	141	14	solutions	solution	NOUN
ap-7669	141	15	.	.	PUNCT
ap-7669	142	1	decomposing	decompose	VERB
ap-7669	142	2	u(t	u(t	NOUN
ap-7669	142	3	,	,	PUNCT
ap-7669	142	4	x	x	NOUN
ap-7669	142	5	)	)	PUNCT
ap-7669	142	6	as	as	ADP
ap-7669	142	7	a	a	DET
ap-7669	142	8	fourier	fourier	NOUN
ap-7669	142	9	integral	integral	ADJ
ap-7669	142	10	,	,	PUNCT
ap-7669	142	11	in	in	ADP
ap-7669	142	12	plane	plane	NOUN
ap-7669	142	13	waves	wave	NOUN
ap-7669	142	14	ei(ωt+kx	ei(ωt+kx	NOUN
ap-7669	142	15	)	)	PUNCT
ap-7669	142	16	,	,	PUNCT
ap-7669	142	17	we	we	PRON
ap-7669	142	18	obtain	obtain	VERB
ap-7669	142	19	the	the	DET
ap-7669	142	20	dispersion	dispersion	NOUN
ap-7669	142	21	law	law	NOUN
ap-7669	142	22	ω	ω	NOUN
ap-7669	142	23	=	=	PUNCT
ap-7669	142	24	k3	k3	VERB
ap-7669	142	25	.	.	PUNCT
ap-7669	143	1	(	(	PUNCT
ap-7669	143	2	25	25	NUM
ap-7669	143	3	)	)	PUNCT
ap-7669	143	4	192	192	NUM
ap-7669	143	5	vol	vol	NOUN
ap-7669	143	6	.	.	PUNCT
ap-7669	144	1	62	62	NUM
ap-7669	144	2	no	no	INTJ
ap-7669	144	3	.	.	PUNCT
ap-7669	145	1	1/2022	1/2022	NUM
ap-7669	145	2	modified	modify	VERB
ap-7669	145	3	kdv	kdv	NOUN
ap-7669	145	4	equation	equation	NOUN
ap-7669	145	5	as	as	ADP
ap-7669	145	6	a	a	DET
ap-7669	145	7	system	system	NOUN
ap-7669	145	8	with	with	ADP
ap-7669	145	9	benign	benign	ADJ
ap-7669	145	10	ghosts	ghost	NOUN
ap-7669	145	11	if	if	SCONJ
ap-7669	145	12	one	one	PRON
ap-7669	145	13	poses	pose	VERB
ap-7669	145	14	the	the	DET
ap-7669	145	15	conventional	conventional	ADJ
ap-7669	145	16	cauchy	cauchy	ADJ
ap-7669	145	17	problem	problem	NOUN
ap-7669	145	18	with	with	ADP
ap-7669	145	19	some	some	DET
ap-7669	145	20	fourier	fourier	ADJ
ap-7669	145	21	-	-	PUNCT
ap-7669	145	22	transformable	transformable	ADJ
ap-7669	145	23	initial	initial	ADJ
ap-7669	145	24	data	datum	NOUN
ap-7669	145	25	u(0	u(0	PROPN
ap-7669	145	26	,	,	PUNCT
ap-7669	145	27	x	x	NOUN
ap-7669	145	28	)	)	PUNCT
ap-7669	145	29	=	=	SYM
ap-7669	145	30	v(x	v(x	PROPN
ap-7669	145	31	)	)	PUNCT
ap-7669	146	1	≡	≡	PROPN
ap-7669	146	2	∫	∫	PROPN
ap-7669	147	1	dk	dk	PROPN
ap-7669	147	2	2π	2π	PROPN
ap-7669	147	3	v(k)eikx	v(k)eikx	NUM
ap-7669	147	4	,	,	PUNCT
ap-7669	147	5	(	(	PUNCT
ap-7669	147	6	26	26	NUM
ap-7669	147	7	)	)	PUNCT
ap-7669	147	8	the	the	DET
ap-7669	147	9	time	time	NOUN
ap-7669	147	10	evolution	evolution	NOUN
ap-7669	147	11	of	of	ADP
ap-7669	147	12	the	the	DET
ap-7669	147	13	initial	initial	ADJ
ap-7669	147	14	data	datum	NOUN
ap-7669	147	15	v(x	v(x	NUM
ap-7669	147	16	)	)	PUNCT
ap-7669	147	17	yields	yield	VERB
ap-7669	147	18	the	the	DET
ap-7669	147	19	solution	solution	NOUN
ap-7669	147	20	u(t	u(t	NOUN
ap-7669	147	21	,	,	PUNCT
ap-7669	147	22	x	x	NOUN
ap-7669	147	23	)	)	PUNCT
ap-7669	147	24	=	=	SYM
ap-7669	148	1	∫	∫	PROPN
ap-7669	149	1	dk	dk	PROPN
ap-7669	149	2	2π	2π	PROPN
ap-7669	149	3	v(k)ei(k3t+kx	v(k)ei(k3t+kx	NOUN
ap-7669	149	4	)	)	PUNCT
ap-7669	149	5	.	.	PUNCT
ap-7669	150	1	(	(	PUNCT
ap-7669	150	2	27	27	NUM
ap-7669	150	3	)	)	PUNCT
ap-7669	150	4	the	the	DET
ap-7669	150	5	important	important	ADJ
ap-7669	150	6	point	point	NOUN
ap-7669	150	7	here	here	ADV
ap-7669	150	8	is	be	AUX
ap-7669	150	9	that	that	SCONJ
ap-7669	150	10	u(t	u(t	NOUN
ap-7669	150	11	,	,	PUNCT
ap-7669	150	12	x	x	X
ap-7669	150	13	)	)	PUNCT
ap-7669	150	14	is	be	AUX
ap-7669	150	15	obtained	obtain	VERB
ap-7669	150	16	from	from	ADP
ap-7669	150	17	v(k	v(k	NOUN
ap-7669	150	18	)	)	PUNCT
ap-7669	150	19	by	by	ADP
ap-7669	150	20	a	a	DET
ap-7669	150	21	purely	purely	ADV
ap-7669	150	22	oscillatory	oscillatory	ADJ
ap-7669	150	23	complex	complex	ADJ
ap-7669	150	24	kernel	kernel	NOUN
ap-7669	150	25	ei(k3t+kx	ei(k3t+kx	NOUN
ap-7669	150	26	)	)	PUNCT
ap-7669	150	27	of	of	ADP
ap-7669	150	28	unit	unit	NOUN
ap-7669	150	29	modulus	modulus	NOUN
ap-7669	150	30	.	.	PUNCT
ap-7669	151	1	it	it	PRON
ap-7669	151	2	has	have	AUX
ap-7669	151	3	been	be	AUX
ap-7669	151	4	shown	show	VERB
ap-7669	151	5	that	that	SCONJ
ap-7669	151	6	this	this	DET
ap-7669	151	7	oscillatory	oscillatory	ADJ
ap-7669	151	8	kernel	kernel	NOUN
ap-7669	151	9	has	have	AUX
ap-7669	151	10	smoothing	smooth	VERB
ap-7669	151	11	properties	property	NOUN
ap-7669	151	12	(	(	PUNCT
ap-7669	151	13	see	see	VERB
ap-7669	151	14	,	,	PUNCT
ap-7669	151	15	e.g.	e.g.	ADV
ap-7669	151	16	,	,	PUNCT
ap-7669	151	17	[	[	X
ap-7669	151	18	20	20	NUM
ap-7669	151	19	]	]	NUM
ap-7669	151	20	)	)	PUNCT
ap-7669	151	21	.	.	PUNCT
ap-7669	152	1	this	this	PRON
ap-7669	152	2	allows	allow	VERB
ap-7669	152	3	one	one	PRON
ap-7669	152	4	to	to	PART
ap-7669	152	5	take	take	VERB
ap-7669	152	6	the	the	DET
ap-7669	152	7	initial	initial	ADJ
ap-7669	152	8	data	datum	NOUN
ap-7669	152	9	in	in	ADP
ap-7669	152	10	low	low	ADJ
ap-7669	152	11	-	-	PUNCT
ap-7669	152	12	s	s	NOUN
ap-7669	152	13	sobolev	sobolev	NOUN
ap-7669	152	14	spaces	space	NOUN
ap-7669	152	15	hs	hs	PROPN
ap-7669	152	16	(	(	PUNCT
ap-7669	152	17	describing	describe	VERB
ap-7669	152	18	pretty	pretty	ADV
ap-7669	152	19	rough	rough	ADJ
ap-7669	152	20	initial	initial	ADJ
ap-7669	152	21	data	datum	NOUN
ap-7669	152	22	)	)	PUNCT
ap-7669	152	23	.	.	PUNCT
ap-7669	153	1	however	however	ADV
ap-7669	153	2	,	,	PUNCT
ap-7669	153	3	if	if	SCONJ
ap-7669	153	4	one	one	PRON
ap-7669	153	5	considers	consider	VERB
ap-7669	153	6	the	the	DET
ap-7669	153	7	x	x	NOUN
ap-7669	153	8	-	-	NOUN
ap-7669	153	9	evolution	evolution	ADJ
ap-7669	153	10	cauchy	cauchy	PROPN
ap-7669	153	11	problem	problem	NOUN
ap-7669	153	12	,	,	PUNCT
ap-7669	153	13	one	one	NUM
ap-7669	153	14	starts	start	VERB
ap-7669	153	15	from	from	ADP
ap-7669	153	16	three	three	NUM
ap-7669	153	17	independent	independent	ADJ
ap-7669	153	18	functions	function	NOUN
ap-7669	153	19	of	of	ADP
ap-7669	153	20	t	t	PROPN
ap-7669	153	21	along	along	ADP
ap-7669	153	22	the	the	DET
ap-7669	153	23	x	x	SYM
ap-7669	153	24	=	=	SYM
ap-7669	153	25	0	0	NUM
ap-7669	153	26	axis	axis	NOUN
ap-7669	153	27	:	:	PUNCT
ap-7669	153	28	u(t	u(t	NOUN
ap-7669	153	29	,	,	PUNCT
ap-7669	153	30	0	0	NUM
ap-7669	153	31	)	)	PUNCT
ap-7669	153	32	=	=	SYM
ap-7669	154	1	u0(t	u0(t	PROPN
ap-7669	154	2	)	)	PUNCT
ap-7669	154	3	,	,	PUNCT
ap-7669	154	4	ux(t	ux(t	PROPN
ap-7669	154	5	,	,	PUNCT
ap-7669	154	6	0	0	NUM
ap-7669	154	7	)	)	PUNCT
ap-7669	154	8	=	=	SYM
ap-7669	155	1	u1(t	u1(t	X
ap-7669	155	2	)	)	PUNCT
ap-7669	155	3	and	and	CCONJ
ap-7669	155	4	uxx(t	uxx(t	PROPN
ap-7669	155	5	,	,	PUNCT
ap-7669	155	6	0	0	NUM
ap-7669	155	7	)	)	PUNCT
ap-7669	155	8	=	=	SYM
ap-7669	155	9	u2(t	u2(t	NOUN
ap-7669	155	10	)	)	PUNCT
ap-7669	155	11	,	,	PUNCT
ap-7669	155	12	as	as	ADP
ap-7669	155	13	in	in	ADP
ap-7669	155	14	(	(	PUNCT
ap-7669	155	15	23	23	NUM
ap-7669	155	16	)	)	PUNCT
ap-7669	155	17	.	.	PUNCT
ap-7669	156	1	assuming	assume	VERB
ap-7669	156	2	that	that	SCONJ
ap-7669	156	3	the	the	DET
ap-7669	156	4	three	three	NUM
ap-7669	156	5	cauchy	cauchy	PROPN
ap-7669	156	6	data	datum	NOUN
ap-7669	156	7	ua(t	ua(t	PROPN
ap-7669	156	8	)	)	PUNCT
ap-7669	156	9	,	,	PUNCT
ap-7669	156	10	a	a	DET
ap-7669	156	11	=	=	SYM
ap-7669	156	12	0	0	NUM
ap-7669	156	13	,	,	PUNCT
ap-7669	156	14	1	1	NUM
ap-7669	156	15	,	,	PUNCT
ap-7669	156	16	2	2	NUM
ap-7669	156	17	,	,	PUNCT
ap-7669	156	18	are	be	AUX
ap-7669	156	19	fourier	fourier	NOUN
ap-7669	156	20	-	-	PUNCT
ap-7669	156	21	transformable	transformable	ADJ
ap-7669	156	22	,	,	PUNCT
ap-7669	156	23	we	we	PRON
ap-7669	156	24	can	can	AUX
ap-7669	156	25	represent	represent	VERB
ap-7669	156	26	them	they	PRON
ap-7669	156	27	as	as	ADP
ap-7669	156	28	ua(t	ua(t	NOUN
ap-7669	156	29	)	)	PUNCT
ap-7669	156	30	=	=	SYM
ap-7669	157	1	∫	∫	PROPN
ap-7669	157	2	dω	dω	PROPN
ap-7669	157	3	2π	2π	PROPN
ap-7669	157	4	ua(ω)eiωt	ua(ω)eiωt	NOUN
ap-7669	157	5	.	.	PUNCT
ap-7669	158	1	(	(	PUNCT
ap-7669	158	2	28	28	NUM
ap-7669	158	3	)	)	PUNCT
ap-7669	158	4	the	the	DET
ap-7669	158	5	three	three	NUM
ap-7669	158	6	cauchy	cauchy	PROPN
ap-7669	158	7	data	datum	NOUN
ap-7669	158	8	determine	determine	VERB
ap-7669	158	9	a	a	DET
ap-7669	158	10	unique	unique	ADJ
ap-7669	158	11	solution	solution	NOUN
ap-7669	158	12	which	which	PRON
ap-7669	158	13	,	,	PUNCT
ap-7669	158	14	when	when	SCONJ
ap-7669	158	15	decomposed	decompose	VERB
ap-7669	158	16	in	in	ADP
ap-7669	158	17	plane	plane	NOUN
ap-7669	158	18	waves	wave	NOUN
ap-7669	158	19	,	,	PUNCT
ap-7669	158	20	satisfies	satisfy	VERB
ap-7669	158	21	the	the	DET
ap-7669	158	22	same	same	ADJ
ap-7669	158	23	dispersion	dispersion	NOUN
ap-7669	158	24	law	law	NOUN
ap-7669	158	25	(	(	PUNCT
ap-7669	158	26	25	25	NUM
ap-7669	158	27	)	)	PUNCT
ap-7669	158	28	as	as	ADP
ap-7669	158	29	before	before	ADV
ap-7669	158	30	.	.	PUNCT
ap-7669	159	1	however	however	ADV
ap-7669	159	2	,	,	PUNCT
ap-7669	159	3	the	the	DET
ap-7669	159	4	dispersion	dispersion	NOUN
ap-7669	159	5	law	law	NOUN
ap-7669	159	6	(	(	PUNCT
ap-7669	159	7	25	25	NUM
ap-7669	159	8	)	)	PUNCT
ap-7669	159	9	must	must	AUX
ap-7669	159	10	now	now	ADV
ap-7669	159	11	be	be	AUX
ap-7669	159	12	solved	solve	VERB
ap-7669	159	13	for	for	ADP
ap-7669	159	14	k	k	PROPN
ap-7669	159	15	in	in	ADP
ap-7669	159	16	terms	term	NOUN
ap-7669	159	17	of	of	ADP
ap-7669	159	18	ω	ω	PROPN
ap-7669	159	19	.	.	PUNCT
ap-7669	160	1	as	as	SCONJ
ap-7669	160	2	it	it	PRON
ap-7669	160	3	is	be	AUX
ap-7669	160	4	a	a	DET
ap-7669	160	5	cubic	cubic	ADJ
ap-7669	160	6	equation	equation	NOUN
ap-7669	160	7	in	in	ADP
ap-7669	160	8	k	k	PROPN
ap-7669	160	9	,	,	PUNCT
ap-7669	160	10	it	it	PRON
ap-7669	160	11	has	have	VERB
ap-7669	160	12	three	three	NUM
ap-7669	160	13	different	different	ADJ
ap-7669	160	14	roots	root	NOUN
ap-7669	160	15	:	:	PUNCT
ap-7669	160	16	ka(ω	ka(ω	NOUN
ap-7669	160	17	)	)	PUNCT
ap-7669	160	18	=	=	SYM
ap-7669	161	1	ω	ω	NUM
ap-7669	161	2	1	1	NUM
ap-7669	161	3	3	3	NUM
ap-7669	161	4	e2πia/3	e2πia/3	PROPN
ap-7669	161	5	a	a	DET
ap-7669	161	6	=	=	NOUN
ap-7669	161	7	0	0	NUM
ap-7669	161	8	,	,	PUNCT
ap-7669	161	9	1	1	NUM
ap-7669	161	10	,	,	PUNCT
ap-7669	161	11	2	2	NUM
ap-7669	161	12	.	.	PUNCT
ap-7669	162	1	(	(	PUNCT
ap-7669	162	2	29	29	NUM
ap-7669	162	3	)	)	PUNCT
ap-7669	162	4	this	this	PRON
ap-7669	162	5	yields	yield	VERB
ap-7669	162	6	a	a	DET
ap-7669	162	7	solution	solution	NOUN
ap-7669	162	8	for	for	ADP
ap-7669	162	9	u(t	u(t	NOUN
ap-7669	162	10	,	,	PUNCT
ap-7669	162	11	x	x	NOUN
ap-7669	162	12	)	)	PUNCT
ap-7669	162	13	of	of	ADP
ap-7669	162	14	the	the	DET
ap-7669	162	15	form	form	NOUN
ap-7669	162	16	u(t	u(t	NOUN
ap-7669	162	17	,	,	PUNCT
ap-7669	162	18	x	x	NOUN
ap-7669	162	19	)	)	PUNCT
ap-7669	162	20	=	=	SYM
ap-7669	163	1	∑	∑	PUNCT
ap-7669	163	2	a=0,1,2	a=0,1,2	NUM
ap-7669	163	3	∫	∫	PROPN
ap-7669	163	4	dω	dω	PROPN
ap-7669	163	5	2π	2π	PROPN
ap-7669	163	6	va(ω)ei(ωt+kax	va(ω)ei(ωt+kax	ADV
ap-7669	163	7	)	)	PUNCT
ap-7669	163	8	,	,	PUNCT
ap-7669	163	9	(	(	PUNCT
ap-7669	163	10	30	30	NUM
ap-7669	163	11	)	)	PUNCT
ap-7669	163	12	where	where	SCONJ
ap-7669	163	13	the	the	DET
ap-7669	163	14	three	three	NUM
ap-7669	163	15	coefficients	coefficient	NOUN
ap-7669	163	16	va(ω	va(ω	NOUN
ap-7669	163	17	)	)	PUNCT
ap-7669	163	18	are	be	AUX
ap-7669	163	19	uniquely	uniquely	ADV
ap-7669	163	20	determined	determine	VERB
ap-7669	163	21	by	by	ADP
ap-7669	163	22	the	the	DET
ap-7669	163	23	three	three	NUM
ap-7669	163	24	initial	initial	ADJ
ap-7669	163	25	conditions	condition	NOUN
ap-7669	163	26	at	at	ADP
ap-7669	163	27	x	x	X
ap-7669	163	28	=	=	NOUN
ap-7669	163	29	0	0	NUM
ap-7669	163	30	.	.	PUNCT
ap-7669	164	1	the	the	DET
ap-7669	164	2	point	point	NOUN
ap-7669	164	3	of	of	ADP
ap-7669	164	4	this	this	DET
ap-7669	164	5	exercise	exercise	NOUN
ap-7669	164	6	was	be	AUX
ap-7669	164	7	to	to	PART
ap-7669	164	8	exhibit	exhibit	VERB
ap-7669	164	9	the	the	DET
ap-7669	164	10	fact	fact	NOUN
ap-7669	164	11	that	that	SCONJ
ap-7669	164	12	,	,	PUNCT
ap-7669	164	13	when	when	SCONJ
ap-7669	164	14	considering	consider	VERB
ap-7669	164	15	the	the	DET
ap-7669	164	16	x	x	ADJ
ap-7669	164	17	evolution	evolution	NOUN
ap-7669	164	18	with	with	ADP
ap-7669	164	19	arbitrary	arbitrary	ADJ
ap-7669	164	20	cauchy	cauchy	ADJ
ap-7669	164	21	data	datum	NOUN
ap-7669	164	22	u0(t	u0(t	PROPN
ap-7669	164	23	)	)	PUNCT
ap-7669	164	24	,	,	PUNCT
ap-7669	164	25	u1(t	u1(t	PROPN
ap-7669	164	26	)	)	PUNCT
ap-7669	164	27	,	,	PUNCT
ap-7669	164	28	u2(t	u2(t	PROPN
ap-7669	164	29	)	)	PUNCT
ap-7669	164	30	,	,	PUNCT
ap-7669	164	31	the	the	DET
ap-7669	164	32	solution	solution	NOUN
ap-7669	164	33	involves	involve	VERB
ap-7669	164	34	exponentially	exponentially	ADV
ap-7669	164	35	growing	grow	VERB
ap-7669	164	36	modes	mode	NOUN
ap-7669	164	37	in	in	ADP
ap-7669	164	38	the	the	DET
ap-7669	164	39	x	x	NOUN
ap-7669	164	40	direction	direction	NOUN
ap-7669	164	41	,	,	PUNCT
ap-7669	164	42	linked	link	VERB
ap-7669	164	43	to	to	ADP
ap-7669	164	44	the	the	DET
ap-7669	164	45	imaginary	imaginary	ADJ
ap-7669	164	46	parts	part	NOUN
ap-7669	164	47	of	of	ADP
ap-7669	164	48	k1(ω	k1(ω	NOUN
ap-7669	164	49	)	)	PUNCT
ap-7669	164	50	and	and	CCONJ
ap-7669	164	51	k2(ω	k2(ω	PROPN
ap-7669	164	52	)	)	PUNCT
ap-7669	164	53	.	.	PUNCT
ap-7669	165	1	this	this	PRON
ap-7669	165	2	can	can	AUX
ap-7669	165	3	be	be	AUX
ap-7669	165	4	avoided	avoid	VERB
ap-7669	165	5	if	if	SCONJ
ap-7669	165	6	the	the	DET
ap-7669	165	7	initial	initial	ADJ
ap-7669	165	8	data	datum	NOUN
ap-7669	165	9	are	be	AUX
ap-7669	165	10	sufficiently	sufficiently	ADV
ap-7669	165	11	smooth	smooth	ADJ
ap-7669	165	12	,	,	PUNCT
ap-7669	165	13	not	not	PART
ap-7669	165	14	involving	involve	VERB
ap-7669	165	15	hf	hf	ADJ
ap-7669	165	16	modes	mode	NOUN
ap-7669	165	17	.	.	PUNCT
ap-7669	166	1	as	as	ADP
ap-7669	166	2	a	a	DET
ap-7669	166	3	minimum	minimum	NOUN
ap-7669	166	4	condition	condition	NOUN
ap-7669	166	5	for	for	ADP
ap-7669	166	6	a	a	DET
ap-7669	166	7	local	local	ADJ
ap-7669	166	8	existence	existence	NOUN
ap-7669	166	9	theorem	theorem	VERB
ap-7669	166	10	,	,	PUNCT
ap-7669	166	11	one	one	PRON
ap-7669	166	12	should	should	AUX
ap-7669	166	13	require	require	VERB
ap-7669	166	14	the	the	DET
ap-7669	166	15	fourier	fourier	NOUN
ap-7669	166	16	transforms	transform	VERB
ap-7669	166	17	va(ω	va(ω	NOUN
ap-7669	166	18	)	)	PUNCT
ap-7669	166	19	to	to	PART
ap-7669	166	20	decrease	decrease	VERB
ap-7669	166	21	like	like	ADP
ap-7669	166	22	e−α|ω|	e−α|ω|	PROPN
ap-7669	166	23	1	1	NUM
ap-7669	166	24	3	3	NUM
ap-7669	166	25	for	for	ADP
ap-7669	166	26	some	some	DET
ap-7669	166	27	positive	positive	ADJ
ap-7669	166	28	constant	constant	ADJ
ap-7669	166	29	α.5	α.5	PRON
ap-7669	166	30	however	however	ADV
ap-7669	166	31	,	,	PUNCT
ap-7669	166	32	it	it	PRON
ap-7669	166	33	is	be	AUX
ap-7669	166	34	difficult	difficult	ADJ
ap-7669	166	35	to	to	PART
ap-7669	166	36	respect	respect	VERB
ap-7669	166	37	these	these	DET
ap-7669	166	38	essential	essential	ADJ
ap-7669	166	39	smoothness	smoothness	ADJ
ap-7669	166	40	constraints	constraint	NOUN
ap-7669	166	41	on	on	ADP
ap-7669	166	42	the	the	DET
ap-7669	166	43	behavour	behavour	NOUN
ap-7669	166	44	of	of	ADP
ap-7669	166	45	u(t	u(t	PROPN
ap-7669	166	46	,	,	PUNCT
ap-7669	166	47	x	x	NOUN
ap-7669	166	48	)	)	PUNCT
ap-7669	166	49	in	in	ADP
ap-7669	166	50	the	the	DET
ap-7669	166	51	numerical	numerical	ADJ
ap-7669	166	52	calculations	calculation	NOUN
ap-7669	166	53	.	.	PUNCT
ap-7669	167	1	the	the	DET
ap-7669	167	2	standard	standard	PROPN
ap-7669	167	3	mathematica	mathematica	PROPN
ap-7669	167	4	algorithms	algorithm	NOUN
ap-7669	167	5	do	do	AUX
ap-7669	167	6	not	not	PART
ap-7669	167	7	do	do	VERB
ap-7669	167	8	so	so	ADV
ap-7669	167	9	,	,	PUNCT
ap-7669	167	10	and	and	CCONJ
ap-7669	167	11	that	that	PRON
ap-7669	167	12	is	be	AUX
ap-7669	167	13	why	why	SCONJ
ap-7669	167	14	we	we	PRON
ap-7669	167	15	,	,	PUNCT
ap-7669	167	16	starting	start	VERB
ap-7669	167	17	from	from	ADP
ap-7669	167	18	some	some	DET
ap-7669	167	19	values	value	NOUN
ap-7669	167	20	of	of	ADP
ap-7669	167	21	x	x	PRON
ap-7669	167	22	,	,	PUNCT
ap-7669	167	23	observe	observe	VERB
ap-7669	167	24	the	the	DET
ap-7669	167	25	hf	hf	PROPN
ap-7669	167	26	noise	noise	NOUN
ap-7669	167	27	in	in	ADP
ap-7669	167	28	our	our	PRON
ap-7669	167	29	results	result	NOUN
ap-7669	167	30	.	.	PUNCT
ap-7669	168	1	5see	5see	NUM
ap-7669	168	2	ref	ref	NOUN
ap-7669	168	3	.	.	PUNCT
ap-7669	169	1	[	[	X
ap-7669	169	2	18	18	NUM
ap-7669	169	3	]	]	PUNCT
ap-7669	169	4	for	for	ADP
ap-7669	169	5	more	more	ADV
ap-7669	169	6	detailed	detailed	ADJ
ap-7669	169	7	discussion	discussion	NOUN
ap-7669	169	8	.	.	PUNCT
ap-7669	170	1	1	1	NUM
ap-7669	170	2	2	2	NUM
ap-7669	170	3	3	3	NUM
ap-7669	170	4	4	4	NUM
ap-7669	170	5	5	5	NUM
ap-7669	170	6	6	6	NUM
ap-7669	170	7	t	t	NOUN
ap-7669	170	8	-2	-2	INTJ
ap-7669	170	9	-1	-1	NOUN
ap-7669	170	10	1	1	NUM
ap-7669	170	11	2	2	NUM
ap-7669	170	12	u	u	NOUN
ap-7669	170	13	figure	figure	NOUN
ap-7669	170	14	3	3	NUM
ap-7669	170	15	.	.	PUNCT
ap-7669	171	1	u(t	u(t	NOUN
ap-7669	171	2	,	,	PUNCT
ap-7669	171	3	x	x	SYM
ap-7669	171	4	=	=	SYM
ap-7669	171	5	3	3	NUM
ap-7669	171	6	)	)	PUNCT
ap-7669	171	7	for	for	ADP
ap-7669	171	8	the	the	DET
ap-7669	171	9	focusing	focus	VERB
ap-7669	171	10	mkdv	mkdv	NOUN
ap-7669	171	11	.	.	PUNCT
ap-7669	172	1	1	1	NUM
ap-7669	172	2	2	2	NUM
ap-7669	172	3	3	3	NUM
ap-7669	172	4	4	4	NUM
ap-7669	172	5	5	5	NUM
ap-7669	172	6	6	6	NUM
ap-7669	172	7	t	t	NOUN
ap-7669	173	1	-6	-6	INTJ
ap-7669	173	2	-4	-4	INTJ
ap-7669	174	1	-2	-2	INTJ
ap-7669	174	2	2	2	NUM
ap-7669	174	3	4	4	NUM
ap-7669	174	4	6	6	NUM
ap-7669	174	5	du	du	NOUN
ap-7669	174	6	figure	figure	NOUN
ap-7669	174	7	4	4	NUM
ap-7669	174	8	.	.	PUNCT
ap-7669	175	1	ux(t	ux(t	NOUN
ap-7669	175	2	,	,	PUNCT
ap-7669	175	3	x	x	SYM
ap-7669	175	4	=	=	SYM
ap-7669	175	5	3	3	NUM
ap-7669	175	6	)	)	PUNCT
ap-7669	175	7	for	for	ADP
ap-7669	175	8	the	the	DET
ap-7669	175	9	focusing	focus	VERB
ap-7669	175	10	mkdv	mkdv	NOUN
ap-7669	175	11	.	.	PUNCT
ap-7669	176	1	in	in	ADP
ap-7669	176	2	figures	figure	NOUN
ap-7669	176	3	3	3	NUM
ap-7669	176	4	,	,	PUNCT
ap-7669	176	5	4	4	NUM
ap-7669	176	6	,	,	PUNCT
ap-7669	176	7	we	we	PRON
ap-7669	176	8	present	present	VERB
ap-7669	176	9	the	the	DET
ap-7669	176	10	results	result	NOUN
ap-7669	176	11	of	of	ADP
ap-7669	176	12	numerical	numerical	ADJ
ap-7669	176	13	calculations	calculation	NOUN
ap-7669	176	14	of	of	ADP
ap-7669	176	15	u(t	u(t	NOUN
ap-7669	176	16	,	,	PUNCT
ap-7669	176	17	x	x	NOUN
ap-7669	176	18	)	)	PUNCT
ap-7669	176	19	and	and	CCONJ
ap-7669	176	20	ux(t	ux(t	PROPN
ap-7669	176	21	,	,	PUNCT
ap-7669	176	22	x	x	NOUN
ap-7669	176	23	)	)	PUNCT
ap-7669	176	24	for	for	ADP
ap-7669	176	25	x	x	SYM
ap-7669	176	26	=	=	SYM
ap-7669	176	27	3	3	X
ap-7669	176	28	.	.	X
ap-7669	177	1	there	there	PRON
ap-7669	177	2	is	be	VERB
ap-7669	177	3	no	no	DET
ap-7669	177	4	trace	trace	NOUN
ap-7669	177	5	of	of	ADP
ap-7669	177	6	a	a	DET
ap-7669	177	7	blow	blow	NOUN
ap-7669	177	8	-	-	PUNCT
ap-7669	177	9	up	up	NOUN
ap-7669	177	10	.	.	PUNCT
ap-7669	178	1	for	for	ADP
ap-7669	178	2	the	the	DET
ap-7669	178	3	plot	plot	NOUN
ap-7669	178	4	of	of	ADP
ap-7669	178	5	u(t	u(t	NOUN
ap-7669	178	6	,	,	PUNCT
ap-7669	178	7	x	x	NOUN
ap-7669	178	8	)	)	PUNCT
ap-7669	178	9	,	,	PUNCT
ap-7669	178	10	one	one	PRON
ap-7669	178	11	also	also	ADV
ap-7669	178	12	does	do	AUX
ap-7669	178	13	not	not	PART
ap-7669	178	14	see	see	VERB
ap-7669	178	15	a	a	DET
ap-7669	178	16	hf	hf	NOUN
ap-7669	178	17	noise	noise	NOUN
ap-7669	178	18	,	,	PUNCT
ap-7669	178	19	but	but	CCONJ
ap-7669	178	20	it	it	PRON
ap-7669	178	21	is	be	AUX
ap-7669	178	22	seen	see	VERB
ap-7669	178	23	in	in	ADP
ap-7669	178	24	the	the	DET
ap-7669	178	25	plot	plot	NOUN
ap-7669	178	26	for	for	ADP
ap-7669	178	27	ux(t	ux(t	NOUN
ap-7669	178	28	,	,	PUNCT
ap-7669	178	29	x	x	NOUN
ap-7669	178	30	)	)	PUNCT
ap-7669	178	31	.	.	PUNCT
ap-7669	179	1	for	for	ADP
ap-7669	179	2	larger	large	ADJ
ap-7669	179	3	values	value	NOUN
ap-7669	179	4	of	of	ADP
ap-7669	179	5	x	x	PRON
ap-7669	179	6	,	,	PUNCT
ap-7669	179	7	the	the	DET
ap-7669	179	8	noise	noise	NOUN
ap-7669	179	9	also	also	ADV
ap-7669	179	10	shows	show	VERB
ap-7669	179	11	up	up	ADP
ap-7669	179	12	in	in	ADP
ap-7669	179	13	the	the	DET
ap-7669	179	14	plot	plot	NOUN
ap-7669	179	15	of	of	ADP
ap-7669	179	16	u(t	u(t	NOUN
ap-7669	179	17	,	,	PUNCT
ap-7669	179	18	x	x	NOUN
ap-7669	179	19	)	)	PUNCT
ap-7669	179	20	.	.	PUNCT
ap-7669	180	1	at	at	ADP
ap-7669	180	2	x	x	X
ap-7669	180	3	>	>	PUNCT
ap-7669	180	4	∼	∼	NOUN
ap-7669	180	5	3.8	3.8	NUM
ap-7669	180	6	,	,	PUNCT
ap-7669	180	7	the	the	DET
ap-7669	180	8	noise	noise	NOUN
ap-7669	180	9	overwhelms	overwhelm	VERB
ap-7669	180	10	the	the	DET
ap-7669	180	11	signal	signal	NOUN
ap-7669	180	12	.	.	PUNCT
ap-7669	181	1	the	the	DET
ap-7669	181	2	observed	observed	ADJ
ap-7669	181	3	noise	noise	NOUN
ap-7669	181	4	is	be	AUX
ap-7669	181	5	a	a	DET
ap-7669	181	6	numerical	numerical	ADJ
ap-7669	181	7	effect	effect	NOUN
ap-7669	181	8	associated	associate	VERB
ap-7669	181	9	with	with	ADP
ap-7669	181	10	a	a	DET
ap-7669	181	11	finite	finite	ADJ
ap-7669	181	12	computer	computer	NOUN
ap-7669	181	13	accuracy	accuracy	NOUN
ap-7669	181	14	.	.	PUNCT
ap-7669	182	1	to	to	PART
ap-7669	182	2	confirm	confirm	VERB
ap-7669	182	3	this	this	PRON
ap-7669	182	4	,	,	PUNCT
ap-7669	182	5	we	we	PRON
ap-7669	182	6	performed	perform	VERB
ap-7669	182	7	a	a	DET
ap-7669	182	8	different	different	ADJ
ap-7669	182	9	calculation	calculation	NOUN
ap-7669	182	10	choosing	choose	VERB
ap-7669	182	11	the	the	DET
ap-7669	182	12	initial	initial	ADJ
ap-7669	182	13	conditions	condition	NOUN
ap-7669	182	14	which	which	PRON
ap-7669	182	15	correspond	correspond	VERB
ap-7669	182	16	to	to	ADP
ap-7669	182	17	the	the	DET
ap-7669	182	18	exact	exact	ADJ
ap-7669	182	19	solitonic	solitonic	ADJ
ap-7669	182	20	solution	solution	NOUN
ap-7669	182	21	to	to	ADP
ap-7669	182	22	eq	eq	PROPN
ap-7669	182	23	.	.	PUNCT
ap-7669	183	1	(	(	PUNCT
ap-7669	183	2	9	9	NUM
ap-7669	183	3	)	)	PUNCT
ap-7669	183	4	.	.	PUNCT
ap-7669	184	1	the	the	DET
ap-7669	184	2	soliton	soliton	NOUN
ap-7669	184	3	is	be	AUX
ap-7669	184	4	a	a	DET
ap-7669	184	5	travelling	travel	VERB
ap-7669	184	6	wave	wave	NOUN
ap-7669	184	7	,	,	PUNCT
ap-7669	184	8	u(t	u(t	NOUN
ap-7669	184	9	,	,	PUNCT
ap-7669	184	10	x	x	NOUN
ap-7669	184	11	)	)	PUNCT
ap-7669	184	12	=	=	SYM
ap-7669	184	13	u(x−ct	u(x−ct	ADJ
ap-7669	184	14	)	)	PUNCT
ap-7669	184	15	≡	≡	PROPN
ap-7669	184	16	u(x̄	u(x̄	NUM
ap-7669	184	17	)	)	PUNCT
ap-7669	184	18	.	.	PUNCT
ap-7669	185	1	plugging	plug	VERB
ap-7669	185	2	this	this	DET
ap-7669	185	3	ansatz	ansatz	ADV
ap-7669	185	4	into	into	ADP
ap-7669	185	5	(	(	PUNCT
ap-7669	185	6	9	9	NUM
ap-7669	185	7	)	)	PUNCT
ap-7669	185	8	,	,	PUNCT
ap-7669	185	9	we	we	PRON
ap-7669	185	10	obtain	obtain	VERB
ap-7669	185	11	an	an	DET
ap-7669	185	12	ordinary	ordinary	ADJ
ap-7669	185	13	differential	differential	ADJ
ap-7669	185	14	equation	equation	NOUN
ap-7669	185	15	∂	∂	NUM
ap-7669	186	1	∂x̄	∂x̄	PROPN
ap-7669	186	2	[	[	PUNCT
ap-7669	186	3	ux̄x̄	ux̄x̄	PROPN
ap-7669	187	1	+	+	CCONJ
ap-7669	187	2	2u3	2u3	NUM
ap-7669	187	3	−	−	PROPN
ap-7669	187	4	cu	cu	NOUN
ap-7669	187	5	]	]	PUNCT
ap-7669	187	6	=	=	PUNCT
ap-7669	187	7	0	0	X
ap-7669	187	8	.	.	PUNCT
ap-7669	188	1	(	(	PUNCT
ap-7669	188	2	31	31	NUM
ap-7669	188	3	)	)	PUNCT
ap-7669	188	4	denoting	denote	VERB
ap-7669	188	5	the	the	DET
ap-7669	188	6	constant	constant	ADJ
ap-7669	188	7	quantity	quantity	NOUN
ap-7669	188	8	within	within	ADP
ap-7669	188	9	the	the	DET
ap-7669	188	10	bracket	bracket	NOUN
ap-7669	188	11	as	as	ADP
ap-7669	188	12	c	c	NOUN
ap-7669	188	13	′	′	NUM
ap-7669	188	14	,	,	PUNCT
ap-7669	188	15	we	we	PRON
ap-7669	188	16	then	then	ADV
ap-7669	188	17	get	get	VERB
ap-7669	188	18	the	the	DET
ap-7669	188	19	following	follow	VERB
ap-7669	188	20	second	second	ADJ
ap-7669	188	21	-	-	PUNCT
ap-7669	188	22	order	order	NOUN
ap-7669	188	23	equation	equation	NOUN
ap-7669	188	24	for	for	ADP
ap-7669	188	25	the	the	DET
ap-7669	188	26	function	function	NOUN
ap-7669	188	27	u(x̄	u(x̄	NOUN
ap-7669	188	28	):	):	PUNCT
ap-7669	188	29	ux̄x̄	ux̄x̄	PROPN
ap-7669	188	30	=	=	SYM
ap-7669	189	1	−	−	PROPN
ap-7669	189	2	d	d	X
ap-7669	189	3	du	du	PROPN
ap-7669	189	4	v(u	v(u	NOUN
ap-7669	189	5	)	)	PUNCT
ap-7669	189	6	,	,	PUNCT
ap-7669	189	7	(	(	PUNCT
ap-7669	189	8	32	32	NUM
ap-7669	189	9	)	)	SYM
ap-7669	189	10	193	193	NUM
ap-7669	189	11	andrei	andrei	PROPN
ap-7669	189	12	smilga	smilga	PROPN
ap-7669	189	13	acta	acta	PROPN
ap-7669	189	14	polytechnica	polytechnica	PROPN
ap-7669	189	15	with	with	ADP
ap-7669	189	16	a	a	DET
ap-7669	189	17	potential	potential	ADJ
ap-7669	189	18	function	function	NOUN
ap-7669	189	19	v(u	v(u	NOUN
ap-7669	189	20	)	)	PUNCT
ap-7669	189	21	now	now	ADV
ap-7669	189	22	given	give	VERB
ap-7669	189	23	by	by	ADP
ap-7669	189	24	v(u	v(u	NOUN
ap-7669	189	25	)	)	PUNCT
ap-7669	189	26	=	=	SYM
ap-7669	189	27	u4	u4	PROPN
ap-7669	189	28	−	−	PROPN
ap-7669	189	29	cu2	cu2	NOUN
ap-7669	189	30	2	2	NUM
ap-7669	189	31	−	−	PROPN
ap-7669	189	32	c	c	NOUN
ap-7669	189	33	′u	′u	PROPN
ap-7669	189	34	.	.	PUNCT
ap-7669	190	1	(	(	PUNCT
ap-7669	190	2	33	33	NUM
ap-7669	190	3	)	)	PUNCT
ap-7669	190	4	as	as	SCONJ
ap-7669	190	5	was	be	AUX
ap-7669	190	6	also	also	ADV
ap-7669	190	7	the	the	DET
ap-7669	190	8	case	case	NOUN
ap-7669	190	9	for	for	ADP
ap-7669	190	10	the	the	DET
ap-7669	190	11	time	time	NOUN
ap-7669	190	12	-	-	PUNCT
ap-7669	190	13	independent	independent	ADJ
ap-7669	190	14	ansatz	ansatz	NOUN
ap-7669	190	15	,	,	PUNCT
ap-7669	190	16	the	the	DET
ap-7669	190	17	problem	problem	NOUN
ap-7669	190	18	is	be	AUX
ap-7669	190	19	reduced	reduce	VERB
ap-7669	190	20	to	to	ADP
ap-7669	190	21	the	the	DET
ap-7669	190	22	dynamics	dynamic	NOUN
ap-7669	190	23	of	of	ADP
ap-7669	190	24	a	a	DET
ap-7669	190	25	particle	particle	NOUN
ap-7669	190	26	moving	move	VERB
ap-7669	190	27	in	in	ADP
ap-7669	190	28	the	the	DET
ap-7669	190	29	confining	confining	ADJ
ap-7669	190	30	quartic	quartic	ADJ
ap-7669	190	31	potential	potential	NOUN
ap-7669	190	32	v(u	v(u	NOUN
ap-7669	190	33	)	)	PUNCT
ap-7669	190	34	.	.	PUNCT
ap-7669	191	1	the	the	DET
ap-7669	191	2	trajectory	trajectory	NOUN
ap-7669	191	3	of	of	ADP
ap-7669	191	4	the	the	DET
ap-7669	191	5	particle	particle	NOUN
ap-7669	191	6	depends	depend	VERB
ap-7669	191	7	on	on	ADP
ap-7669	191	8	three	three	NUM
ap-7669	191	9	parameters	parameter	NOUN
ap-7669	191	10	:	:	PUNCT
ap-7669	191	11	the	the	DET
ap-7669	191	12	celerity	celerity	NOUN
ap-7669	191	13	c	c	NOUN
ap-7669	191	14	,	,	PUNCT
ap-7669	191	15	the	the	DET
ap-7669	191	16	constant	constant	ADJ
ap-7669	191	17	c	c	NOUN
ap-7669	191	18	′	′	NOUN
ap-7669	191	19	,	,	PUNCT
ap-7669	191	20	and	and	CCONJ
ap-7669	191	21	the	the	DET
ap-7669	191	22	particle	particle	NOUN
ap-7669	191	23	energy	energy	NOUN
ap-7669	191	24	,	,	PUNCT
ap-7669	191	25	e	e	NOUN
ap-7669	191	26	=	=	SYM
ap-7669	191	27	1	1	NUM
ap-7669	191	28	2u	2u	PROPN
ap-7669	191	29	2	2	NUM
ap-7669	191	30	x̄	x̄	NOUN
ap-7669	191	31	+	+	CCONJ
ap-7669	191	32	v(u	v(u	NUM
ap-7669	191	33	)	)	PUNCT
ap-7669	191	34	.	.	PUNCT
ap-7669	192	1	(	(	PUNCT
ap-7669	192	2	34	34	NUM
ap-7669	192	3	)	)	PUNCT
ap-7669	192	4	the	the	DET
ap-7669	192	5	usually	usually	ADV
ap-7669	192	6	considered	consider	VERB
ap-7669	192	7	solitonic	solitonic	ADJ
ap-7669	192	8	solutions	solution	NOUN
ap-7669	192	9	(	(	PUNCT
ap-7669	192	10	such	such	ADJ
ap-7669	192	11	that	that	SCONJ
ap-7669	192	12	u(x̄	u(x̄	NUM
ap-7669	192	13	)	)	PUNCT
ap-7669	192	14	tends	tend	VERB
ap-7669	192	15	to	to	ADP
ap-7669	192	16	zero	zero	NUM
ap-7669	192	17	when	when	SCONJ
ap-7669	192	18	x̄	x̄	PROPN
ap-7669	192	19	→	→	SYM
ap-7669	192	20	±∞	±∞	PROPN
ap-7669	192	21	)	)	PUNCT
ap-7669	192	22	are	be	AUX
ap-7669	192	23	obtained	obtain	VERB
ap-7669	192	24	by	by	ADP
ap-7669	192	25	taking	take	VERB
ap-7669	192	26	c	c	PROPN
ap-7669	192	27	>	>	X
ap-7669	192	28	0	0	NUM
ap-7669	192	29	,	,	PUNCT
ap-7669	192	30	c	c	NOUN
ap-7669	192	31	′	′	NOUN
ap-7669	193	1	=	=	SYM
ap-7669	193	2	0	0	PUNCT
ap-7669	194	1	(	(	PUNCT
ap-7669	194	2	so	so	SCONJ
ap-7669	194	3	that	that	SCONJ
ap-7669	194	4	the	the	DET
ap-7669	194	5	potential	potential	NOUN
ap-7669	194	6	represents	represent	VERB
ap-7669	194	7	a	a	DET
ap-7669	194	8	symmetric	symmetric	ADJ
ap-7669	194	9	double	double	ADJ
ap-7669	194	10	-	-	PUNCT
ap-7669	194	11	well	well	NOUN
ap-7669	194	12	potential	potential	NOUN
ap-7669	194	13	)	)	PUNCT
ap-7669	194	14	and	and	CCONJ
ap-7669	194	15	e	e	X
ap-7669	194	16	=	=	NOUN
ap-7669	194	17	0	0	PROPN
ap-7669	194	18	.	.	PUNCT
ap-7669	195	1	the	the	DET
ap-7669	195	2	zero	zero	NUM
ap-7669	195	3	-	-	PUNCT
ap-7669	195	4	energy	energy	NOUN
ap-7669	195	5	trajectory	trajectory	NOUN
ap-7669	195	6	describes	describe	VERB
ap-7669	195	7	a	a	DET
ap-7669	195	8	particle	particle	NOUN
ap-7669	195	9	starting	start	VERB
ap-7669	195	10	at	at	ADP
ap-7669	195	11	“	"	PUNCT
ap-7669	195	12	time	time	NOUN
ap-7669	195	13	"	"	PUNCT
ap-7669	195	14	x̄	x̄	NOUN
ap-7669	195	15	=	=	PUNCT
ap-7669	195	16	−∞	−∞	PROPN
ap-7669	195	17	,	,	PUNCT
ap-7669	195	18	at	at	ADP
ap-7669	195	19	u	u	NOUN
ap-7669	195	20	=	=	NOUN
ap-7669	195	21	0	0	NUM
ap-7669	195	22	with	with	ADP
ap-7669	195	23	zero	zero	NUM
ap-7669	195	24	“	"	PUNCT
ap-7669	195	25	velocity	velocity	NOUN
ap-7669	195	26	"	"	PUNCT
ap-7669	195	27	ux̄	ux̄	NOUN
ap-7669	195	28	,	,	PUNCT
ap-7669	195	29	gliding	glide	VERB
ap-7669	195	30	down	down	ADP
ap-7669	195	31	,	,	PUNCT
ap-7669	195	32	say	say	INTJ
ap-7669	195	33	,	,	PUNCT
ap-7669	195	34	to	to	ADP
ap-7669	195	35	the	the	DET
ap-7669	195	36	right	right	NOUN
ap-7669	195	37	,	,	PUNCT
ap-7669	195	38	reflecting	reflect	VERB
ap-7669	195	39	on	on	ADP
ap-7669	195	40	the	the	DET
ap-7669	195	41	right	right	ADJ
ap-7669	195	42	wall	wall	NOUN
ap-7669	195	43	of	of	ADP
ap-7669	195	44	the	the	DET
ap-7669	195	45	double	double	ADJ
ap-7669	195	46	well	well	NOUN
ap-7669	195	47	and	and	CCONJ
ap-7669	195	48	then	then	ADV
ap-7669	195	49	turning	turn	VERB
ap-7669	195	50	back	back	ADV
ap-7669	195	51	to	to	PART
ap-7669	195	52	end	end	VERB
ap-7669	195	53	up	up	ADP
ap-7669	195	54	,	,	PUNCT
ap-7669	195	55	again	again	ADV
ap-7669	195	56	,	,	PUNCT
ap-7669	195	57	at	at	ADP
ap-7669	195	58	u	u	NOUN
ap-7669	195	59	=	=	NOUN
ap-7669	195	60	0	0	NUM
ap-7669	195	61	when	when	SCONJ
ap-7669	195	62	x̄	x̄	NOUN
ap-7669	195	63	=	=	PUNCT
ap-7669	196	1	+	+	NUM
ap-7669	196	2	∞.	∞.	PROPN
ap-7669	196	3	the	the	DET
ap-7669	196	4	explicit	explicit	ADJ
ap-7669	196	5	form	form	NOUN
ap-7669	196	6	of	of	ADP
ap-7669	196	7	the	the	DET
ap-7669	196	8	corresponding	corresponding	ADJ
ap-7669	196	9	solution	solution	NOUN
ap-7669	196	10	defined	define	VERB
ap-7669	196	11	on	on	ADP
ap-7669	196	12	the	the	DET
ap-7669	196	13	infinite	infinite	NOUN
ap-7669	196	14	(	(	PUNCT
ap-7669	196	15	t	t	PROPN
ap-7669	196	16	,	,	PUNCT
ap-7669	196	17	x	x	NOUN
ap-7669	196	18	)	)	PUNCT
ap-7669	196	19	plane	plane	NOUN
ap-7669	196	20	is	be	AUX
ap-7669	196	21	u(t	u(t	NOUN
ap-7669	196	22	,	,	PUNCT
ap-7669	196	23	x	x	NOUN
ap-7669	196	24	)	)	PUNCT
ap-7669	196	25	=	=	SYM
ap-7669	196	26	√	√	PROPN
ap-7669	196	27	c	c	NOUN
ap-7669	196	28	cosh	cosh	NOUN
ap-7669	196	29	[	[	PUNCT
ap-7669	196	30	√	√	PROPN
ap-7669	196	31	c	c	NOUN
ap-7669	196	32	(	(	PUNCT
ap-7669	196	33	x−	x−	PROPN
ap-7669	196	34	ct	ct	PROPN
ap-7669	196	35	)	)	PUNCT
ap-7669	196	36	]	]	PUNCT
ap-7669	196	37	.	.	PUNCT
ap-7669	197	1	(	(	PUNCT
ap-7669	197	2	35	35	NUM
ap-7669	197	3	)	)	PUNCT
ap-7669	197	4	however	however	ADV
ap-7669	197	5	,	,	PUNCT
ap-7669	197	6	to	to	PART
ap-7669	197	7	make	make	VERB
ap-7669	197	8	contact	contact	NOUN
ap-7669	197	9	with	with	ADP
ap-7669	197	10	our	our	PRON
ap-7669	197	11	numerical	numerical	ADJ
ap-7669	197	12	calculations	calculation	NOUN
ap-7669	197	13	,	,	PUNCT
ap-7669	197	14	we	we	PRON
ap-7669	197	15	need	need	VERB
ap-7669	197	16	a	a	DET
ap-7669	197	17	periodic	periodic	ADJ
ap-7669	197	18	soliton	soliton	NOUN
ap-7669	197	19	solution	solution	NOUN
ap-7669	197	20	.	.	PUNCT
ap-7669	198	1	such	such	ADJ
ap-7669	198	2	solutions	solution	NOUN
ap-7669	198	3	can	can	AUX
ap-7669	198	4	be	be	AUX
ap-7669	198	5	easily	easily	ADV
ap-7669	198	6	constructed	construct	VERB
ap-7669	198	7	by	by	ADP
ap-7669	198	8	considering	consider	VERB
ap-7669	198	9	bounded	bound	VERB
ap-7669	198	10	mechanical	mechanical	ADJ
ap-7669	198	11	motions	motion	NOUN
ap-7669	198	12	in	in	ADP
ap-7669	198	13	the	the	DET
ap-7669	198	14	potential	potential	ADJ
ap-7669	198	15	v(u	v(u	NOUN
ap-7669	198	16	)	)	PUNCT
ap-7669	198	17	having	have	VERB
ap-7669	198	18	a	a	DET
ap-7669	198	19	non	non	ADJ
ap-7669	198	20	-	-	ADJ
ap-7669	198	21	zero	zero	NUM
ap-7669	198	22	energy	energy	NOUN
ap-7669	198	23	.	.	PUNCT
ap-7669	199	1	periodic	periodic	ADJ
ap-7669	199	2	solutions	solution	NOUN
ap-7669	199	3	exist	exist	VERB
ap-7669	199	4	both	both	CCONJ
ap-7669	199	5	for	for	ADP
ap-7669	199	6	positive	positive	ADJ
ap-7669	199	7	and	and	CCONJ
ap-7669	199	8	negative	negative	ADJ
ap-7669	199	9	c.	c.	NOUN
ap-7669	199	10	the	the	DET
ap-7669	199	11	trajectories	trajectory	NOUN
ap-7669	199	12	are	be	AUX
ap-7669	199	13	the	the	DET
ap-7669	199	14	elliptic	elliptic	ADJ
ap-7669	199	15	functions	function	NOUN
ap-7669	199	16	.	.	PUNCT
ap-7669	200	1	it	it	PRON
ap-7669	200	2	was	be	AUX
ap-7669	200	3	more	more	ADV
ap-7669	200	4	convenient	convenient	ADJ
ap-7669	200	5	for	for	SCONJ
ap-7669	200	6	us	we	PRON
ap-7669	200	7	to	to	PART
ap-7669	200	8	assume	assume	VERB
ap-7669	200	9	c	c	NOUN
ap-7669	200	10	=	=	SYM
ap-7669	200	11	−|c|	−|c|	PROPN
ap-7669	200	12	,	,	PUNCT
ap-7669	200	13	in	in	ADP
ap-7669	200	14	which	which	DET
ap-7669	200	15	case	case	NOUN
ap-7669	200	16	we	we	PRON
ap-7669	200	17	could	could	AUX
ap-7669	200	18	make	make	VERB
ap-7669	200	19	contact	contact	NOUN
ap-7669	200	20	with	with	ADP
ap-7669	200	21	ref	ref	NOUN
ap-7669	200	22	.	.	PUNCT
ap-7669	201	1	[	[	X
ap-7669	201	2	12	12	NUM
ap-7669	201	3	]	]	PUNCT
ap-7669	201	4	,	,	PUNCT
ap-7669	201	5	where	where	SCONJ
ap-7669	201	6	the	the	DET
ap-7669	201	7	expressions	expression	NOUN
ap-7669	201	8	for	for	ADP
ap-7669	201	9	the	the	DET
ap-7669	201	10	trajectories	trajectory	NOUN
ap-7669	201	11	of	of	ADP
ap-7669	201	12	motion	motion	NOUN
ap-7669	201	13	in	in	ADP
ap-7669	201	14	the	the	DET
ap-7669	201	15	same	same	ADJ
ap-7669	201	16	quartic	quartic	ADJ
ap-7669	201	17	potential	potential	NOUN
ap-7669	201	18	were	be	AUX
ap-7669	201	19	explicitly	explicitly	ADV
ap-7669	201	20	written	write	VERB
ap-7669	201	21	,	,	PUNCT
ap-7669	201	22	one	one	NUM
ap-7669	201	23	only	only	ADV
ap-7669	201	24	had	have	VERB
ap-7669	201	25	to	to	PART
ap-7669	201	26	rename	rename	VERB
ap-7669	201	27	the	the	DET
ap-7669	201	28	parameters	parameter	NOUN
ap-7669	201	29	.	.	PUNCT
ap-7669	202	1	choosing	choose	VERB
ap-7669	202	2	e	e	NOUN
ap-7669	202	3	=	=	SYM
ap-7669	202	4	1	1	NUM
ap-7669	202	5	and	and	CCONJ
ap-7669	202	6	c	c	NOUN
ap-7669	202	7	=	=	SYM
ap-7669	202	8	−1	−1	NOUN
ap-7669	202	9	,	,	PUNCT
ap-7669	202	10	we	we	PRON
ap-7669	202	11	obtain	obtain	VERB
ap-7669	202	12	the	the	DET
ap-7669	202	13	following	follow	VERB
ap-7669	202	14	solution	solution	NOUN
ap-7669	202	15	:	:	PUNCT
ap-7669	202	16	u(t	u(t	NOUN
ap-7669	202	17	,	,	PUNCT
ap-7669	202	18	x	x	NOUN
ap-7669	202	19	)	)	PUNCT
ap-7669	202	20	=	=	SYM
ap-7669	203	1	cn	cn	PROPN
ap-7669	204	1	[	[	X
ap-7669	204	2	√	√	PROPN
ap-7669	204	3	3(x+	3(x+	NUM
ap-7669	204	4	t),m	t),m	PROPN
ap-7669	204	5	]	]	PUNCT
ap-7669	204	6	,	,	PUNCT
ap-7669	204	7	(	(	PUNCT
ap-7669	204	8	36	36	NUM
ap-7669	204	9	)	)	PUNCT
ap-7669	204	10	where	where	SCONJ
ap-7669	204	11	cn(z	cn(z	NUM
ap-7669	204	12	)	)	PUNCT
ap-7669	204	13	is	be	AUX
ap-7669	204	14	the	the	DET
ap-7669	204	15	jacobi	jacobi	PROPN
ap-7669	204	16	elliptic	elliptic	PROPN
ap-7669	204	17	cosine	cosine	NOUN
ap-7669	204	18	function	function	NOUN
ap-7669	204	19	with	with	ADP
ap-7669	204	20	the	the	DET
ap-7669	204	21	elliptic	elliptic	ADJ
ap-7669	204	22	modulus	modulus	NOUN
ap-7669	204	23	m	m	PROPN
ap-7669	204	24	=	=	SYM
ap-7669	204	25	1/3	1/3	NUM
ap-7669	204	26	.	.	PUNCT
ap-7669	205	1	the	the	DET
ap-7669	205	2	function	function	NOUN
ap-7669	205	3	(	(	PUNCT
ap-7669	205	4	36	36	NUM
ap-7669	205	5	)	)	PUNCT
ap-7669	205	6	is	be	AUX
ap-7669	205	7	periodic	periodic	ADJ
ap-7669	205	8	both	both	CCONJ
ap-7669	205	9	in	in	ADP
ap-7669	205	10	t	t	PROPN
ap-7669	205	11	and	and	CCONJ
ap-7669	205	12	x	x	PUNCT
ap-7669	205	13	with	with	ADP
ap-7669	205	14	the	the	DET
ap-7669	205	15	period	period	NOUN
ap-7669	205	16	t	t	NOUN
ap-7669	205	17	=	=	SYM
ap-7669	205	18	l	l	NOUN
ap-7669	206	1	=	=	SYM
ap-7669	206	2	4√	4√	PROPN
ap-7669	206	3	3	3	NUM
ap-7669	206	4	k	k	NOUN
ap-7669	206	5	(	(	PUNCT
ap-7669	206	6	1	1	NUM
ap-7669	206	7	3	3	NUM
ap-7669	206	8	)	)	PUNCT
ap-7669	206	9	≈	≈	PROPN
ap-7669	206	10	4	4	NUM
ap-7669	206	11	.	.	PUNCT
ap-7669	207	1	(	(	PUNCT
ap-7669	207	2	37	37	NUM
ap-7669	207	3	)	)	PUNCT
ap-7669	207	4	we	we	PRON
ap-7669	207	5	fixed	fix	VERB
ap-7669	207	6	the	the	DET
ap-7669	207	7	initial	initial	ADJ
ap-7669	207	8	conditions	condition	NOUN
ap-7669	207	9	for	for	ADP
ap-7669	207	10	x	x	SYM
ap-7669	207	11	=	=	SYM
ap-7669	207	12	0	0	NUM
ap-7669	207	13	and	and	CCONJ
ap-7669	207	14	periodic	periodic	ADJ
ap-7669	207	15	conditions	condition	NOUN
ap-7669	207	16	in	in	ADP
ap-7669	207	17	time	time	NOUN
ap-7669	207	18	as	as	SCONJ
ap-7669	207	19	is	be	AUX
ap-7669	207	20	dictated	dictate	VERB
ap-7669	207	21	by	by	ADP
ap-7669	207	22	(	(	PUNCT
ap-7669	207	23	36	36	NUM
ap-7669	207	24	)	)	PUNCT
ap-7669	207	25	,	,	PUNCT
ap-7669	207	26	and	and	CCONJ
ap-7669	207	27	then	then	ADV
ap-7669	207	28	numerically	numerically	ADV
ap-7669	207	29	solved	solve	VERB
ap-7669	207	30	(	(	PUNCT
ap-7669	207	31	9	9	NUM
ap-7669	207	32	)	)	PUNCT
ap-7669	207	33	.	.	PUNCT
ap-7669	208	1	the	the	DET
ap-7669	208	2	numerical	numerical	ADJ
ap-7669	208	3	solution	solution	NOUN
ap-7669	208	4	should	should	AUX
ap-7669	208	5	reproduce	reproduce	VERB
ap-7669	208	6	the	the	DET
ap-7669	208	7	exact	exact	ADJ
ap-7669	208	8	one	one	NUM
ap-7669	208	9	,	,	PUNCT
ap-7669	208	10	and	and	CCONJ
ap-7669	208	11	it	it	PRON
ap-7669	208	12	does	do	AUX
ap-7669	208	13	for	for	ADP
ap-7669	208	14	x	x	SYM
ap-7669	208	15	<	<	X
ap-7669	208	16	∼	∼	NOUN
ap-7669	208	17	4	4	NUM
ap-7669	208	18	.	.	PUNCT
ap-7669	209	1	however	however	ADV
ap-7669	209	2	,	,	PUNCT
ap-7669	209	3	at	at	ADP
ap-7669	209	4	larger	large	ADJ
ap-7669	209	5	values	value	NOUN
ap-7669	209	6	of	of	ADP
ap-7669	209	7	x	x	PRON
ap-7669	209	8	,	,	PUNCT
ap-7669	209	9	the	the	DET
ap-7669	209	10	hf	hf	PROPN
ap-7669	209	11	noise	noise	NOUN
ap-7669	209	12	appears	appear	VERB
ap-7669	209	13	.	.	PUNCT
ap-7669	210	1	the	the	DET
ap-7669	210	2	result	result	NOUN
ap-7669	210	3	of	of	ADP
ap-7669	210	4	the	the	DET
ap-7669	210	5	calculation	calculation	NOUN
ap-7669	210	6	for	for	ADP
ap-7669	210	7	x	x	SYM
ap-7669	210	8	=	=	SYM
ap-7669	210	9	4.5	4.5	NUM
ap-7669	210	10	is	be	AUX
ap-7669	210	11	given	give	VERB
ap-7669	210	12	in	in	ADP
ap-7669	210	13	figure	figure	NOUN
ap-7669	210	14	5	5	NUM
ap-7669	210	15	.	.	PUNCT
ap-7669	211	1	one	one	PRON
ap-7669	211	2	can	can	AUX
ap-7669	211	3	suppress	suppress	VERB
ap-7669	211	4	the	the	DET
ap-7669	211	5	hf	hf	NOUN
ap-7669	211	6	noise	noise	NOUN
ap-7669	211	7	by	by	ADP
ap-7669	211	8	increasing	increase	VERB
ap-7669	211	9	the	the	DET
ap-7669	211	10	step	step	NOUN
ap-7669	211	11	size	size	NOUN
ap-7669	211	12	,	,	PUNCT
ap-7669	211	13	but	but	CCONJ
ap-7669	211	14	then	then	ADV
ap-7669	211	15	the	the	DET
ap-7669	211	16	form	form	NOUN
ap-7669	211	17	of	of	ADP
ap-7669	211	18	the	the	DET
ap-7669	211	19	soliton	soliton	NOUN
ap-7669	211	20	is	be	AUX
ap-7669	211	21	distorted	distort	VERB
ap-7669	211	22	.	.	PUNCT
ap-7669	212	1	to	to	PART
ap-7669	212	2	find	find	VERB
ap-7669	212	3	a	a	DET
ap-7669	212	4	numerical	numerical	ADJ
ap-7669	212	5	procedure	procedure	NOUN
ap-7669	212	6	that	that	PRON
ap-7669	212	7	suppresses	suppress	VERB
ap-7669	212	8	the	the	DET
ap-7669	212	9	noise	noise	NOUN
ap-7669	212	10	and	and	CCONJ
ap-7669	212	11	gives	give	VERB
ap-7669	212	12	correct	correct	ADJ
ap-7669	212	13	results	result	NOUN
ap-7669	212	14	for	for	ADP
ap-7669	212	15	large	large	ADJ
ap-7669	212	16	values	value	NOUN
ap-7669	212	17	of	of	ADP
ap-7669	212	18	x	x	PUNCT
ap-7669	212	19	remains	remain	VERB
ap-7669	212	20	a	a	DET
ap-7669	212	21	challenge	challenge	NOUN
ap-7669	212	22	for	for	ADP
ap-7669	212	23	future	future	ADJ
ap-7669	212	24	studies	study	NOUN
ap-7669	212	25	.	.	PUNCT
ap-7669	213	1	1	1	NUM
ap-7669	213	2	2	2	NUM
ap-7669	213	3	3	3	NUM
ap-7669	213	4	4	4	NUM
ap-7669	213	5	t	t	PROPN
ap-7669	213	6	-1.0	-1.0	PROPN
ap-7669	213	7	-0.5	-0.5	PROPN
ap-7669	213	8	0.5	0.5	NUM
ap-7669	213	9	1.0	1.0	NUM
ap-7669	213	10	u	u	NOUN
ap-7669	213	11	figure	figure	NOUN
ap-7669	213	12	5	5	NUM
ap-7669	213	13	.	.	PUNCT
ap-7669	213	14	hf	hf	NOUN
ap-7669	213	15	noise	noise	NOUN
ap-7669	213	16	for	for	ADP
ap-7669	213	17	the	the	DET
ap-7669	213	18	periodic	periodic	ADJ
ap-7669	213	19	soliton	soliton	NOUN
ap-7669	213	20	evolution	evolution	NOUN
ap-7669	213	21	.	.	PUNCT
ap-7669	214	1	x	x	X
ap-7669	215	1	=	=	NOUN
ap-7669	215	2	4.5	4.5	NUM
ap-7669	215	3	.	.	PUNCT
ap-7669	216	1	3	3	X
ap-7669	216	2	.	.	NOUN
ap-7669	216	3	discrete	discrete	ADJ
ap-7669	216	4	models	model	NOUN
ap-7669	216	5	with	with	ADP
ap-7669	216	6	benign	benign	ADJ
ap-7669	216	7	ghosts	ghost	NOUN
ap-7669	216	8	one	one	NUM
ap-7669	216	9	of	of	ADP
ap-7669	216	10	the	the	DET
ap-7669	216	11	possible	possible	ADJ
ap-7669	216	12	solutions	solution	NOUN
ap-7669	216	13	to	to	ADP
ap-7669	216	14	this	this	DET
ap-7669	216	15	numerical	numerical	ADJ
ap-7669	216	16	problem	problem	NOUN
ap-7669	216	17	could	could	AUX
ap-7669	216	18	consist	consist	VERB
ap-7669	216	19	in	in	ADP
ap-7669	216	20	discretizing	discretize	VERB
ap-7669	216	21	the	the	DET
ap-7669	216	22	model	model	NOUN
ap-7669	216	23	in	in	ADP
ap-7669	216	24	time	time	NOUN
ap-7669	216	25	direction	direction	NOUN
ap-7669	216	26	and	and	CCONJ
ap-7669	216	27	assuming	assume	VERB
ap-7669	216	28	that	that	SCONJ
ap-7669	216	29	the	the	DET
ap-7669	216	30	variable	variable	ADJ
ap-7669	216	31	t	t	NOUN
ap-7669	216	32	takes	take	VERB
ap-7669	216	33	only	only	ADV
ap-7669	216	34	the	the	DET
ap-7669	216	35	discrete	discrete	ADJ
ap-7669	216	36	values	value	NOUN
ap-7669	216	37	t	t	NOUN
ap-7669	216	38	=	=	SYM
ap-7669	216	39	h	h	NOUN
ap-7669	216	40	,	,	PUNCT
ap-7669	216	41	2h	2h	NUM
ap-7669	216	42	,	,	PUNCT
ap-7669	216	43	·	·	PUNCT
ap-7669	216	44	·	·	PUNCT
ap-7669	216	45	·	·	PUNCT
ap-7669	216	46	,	,	PUNCT
ap-7669	216	47	nh	nh	PROPN
ap-7669	216	48	,	,	PUNCT
ap-7669	216	49	for	for	ADP
ap-7669	216	50	some	some	DET
ap-7669	216	51	integer	integer	NOUN
ap-7669	216	52	n	n	PRON
ap-7669	216	53	≥	≥	NOUN
ap-7669	216	54	3	3	NUM
ap-7669	216	55	and	and	CCONJ
ap-7669	216	56	by	by	ADP
ap-7669	216	57	replacing	replace	VERB
ap-7669	216	58	the	the	DET
ap-7669	216	59	continuous	continuous	ADJ
ap-7669	216	60	time	time	NOUN
ap-7669	216	61	derivative	derivative	NOUN
ap-7669	216	62	ψt	ψt	NOUN
ap-7669	216	63	by	by	ADP
ap-7669	216	64	a	a	DET
ap-7669	216	65	discrete	discrete	ADJ
ap-7669	216	66	(	(	PUNCT
ap-7669	216	67	symmetric	symmetric	ADJ
ap-7669	216	68	)	)	PUNCT
ap-7669	216	69	time	time	NOUN
ap-7669	216	70	derivative	derivative	ADJ
ap-7669	216	71	[	[	X
ap-7669	216	72	ψ(t+h	ψ(t+h	X
ap-7669	216	73	,	,	PUNCT
ap-7669	216	74	x	x	X
ap-7669	216	75	)	)	PUNCT
ap-7669	216	76	−ψ(t−h	−ψ(t−h	NOUN
ap-7669	216	77	,	,	PUNCT
ap-7669	216	78	x)]/(2h	x)]/(2h	PROPN
ap-7669	216	79	)	)	PUNCT
ap-7669	216	80	.	.	PUNCT
ap-7669	217	1	then	then	ADV
ap-7669	217	2	the	the	DET
ap-7669	217	3	lagrangian6	lagrangian6	NOUN
ap-7669	217	4	l[ψ(t	l[ψ(t	PROPN
ap-7669	217	5	,	,	PUNCT
ap-7669	217	6	x	x	NOUN
ap-7669	217	7	)	)	PUNCT
ap-7669	217	8	]	]	PUNCT
ap-7669	218	1	=	=	PUNCT
ap-7669	218	2	ψ2	ψ2	NOUN
ap-7669	218	3	xx	xx	NUM
ap-7669	218	4	−	−	PROPN
ap-7669	219	1	ψ4	ψ4	NOUN
ap-7669	219	2	x	x	X
ap-7669	219	3	−	−	X
ap-7669	219	4	ψxψt	ψxψt	X
ap-7669	219	5	2	2	NUM
ap-7669	219	6	(	(	PUNCT
ap-7669	219	7	38	38	NUM
ap-7669	219	8	)	)	PUNCT
ap-7669	219	9	acquires	acquire	VERB
ap-7669	219	10	the	the	DET
ap-7669	219	11	form	form	NOUN
ap-7669	219	12	ln	ln	NOUN
ap-7669	219	13	=	=	PUNCT
ap-7669	219	14	n∑	n∑	NOUN
ap-7669	219	15	k=1	k=1	X
ap-7669	220	1	{	{	PUNCT
ap-7669	221	1	[	[	X
ap-7669	221	2	ψxx(kh	ψxx(kh	X
ap-7669	221	3	,	,	PUNCT
ap-7669	221	4	x)]2	x)]2	PROPN
ap-7669	221	5	−	−	PROPN
ap-7669	222	1	[	[	X
ap-7669	222	2	ψx(kh	ψx(kh	PROPN
ap-7669	222	3	,	,	PUNCT
ap-7669	222	4	x)]4	x)]4	X
ap-7669	222	5	2	2	NUM
ap-7669	222	6	−	−	NOUN
ap-7669	222	7	1	1	NUM
ap-7669	222	8	2ψx(kh	2ψx(kh	NUM
ap-7669	222	9	,	,	PUNCT
ap-7669	222	10	x)ψ[(k	x)ψ[(k	PROPN
ap-7669	223	1	+	+	CCONJ
ap-7669	223	2	1)h	1)h	NUM
ap-7669	223	3	,	,	PUNCT
ap-7669	223	4	x	x	X
ap-7669	223	5	]	]	X
ap-7669	223	6	−	−	PROPN
ap-7669	223	7	ψ[(k	ψ[(k	NOUN
ap-7669	223	8	−	−	PROPN
ap-7669	223	9	1)h	1)h	NUM
ap-7669	223	10	,	,	PUNCT
ap-7669	223	11	x	x	X
ap-7669	223	12	]	]	X
ap-7669	223	13	2h	2h	NUM
ap-7669	223	14	}	}	PUNCT
ap-7669	223	15	,	,	PUNCT
ap-7669	223	16	(	(	PUNCT
ap-7669	223	17	39	39	NUM
ap-7669	223	18	)	)	PUNCT
ap-7669	223	19	where	where	SCONJ
ap-7669	223	20	we	we	PRON
ap-7669	223	21	impose	impose	VERB
ap-7669	223	22	the	the	DET
ap-7669	223	23	periodicity	periodicity	NOUN
ap-7669	223	24	:	:	PUNCT
ap-7669	223	25	ψ(0	ψ(0	ADJ
ap-7669	223	26	,	,	PUNCT
ap-7669	223	27	x	x	ADJ
ap-7669	223	28	)	)	PUNCT
ap-7669	223	29	≡	≡	PROPN
ap-7669	223	30	ψ(nh	ψ(nh	PROPN
ap-7669	223	31	,	,	PUNCT
ap-7669	223	32	x	x	NOUN
ap-7669	223	33	)	)	PUNCT
ap-7669	223	34	and	and	CCONJ
ap-7669	223	35	ψ[(n	ψ[(n	PROPN
ap-7669	223	36	+	+	CCONJ
ap-7669	223	37	1)h	1)h	NUM
ap-7669	223	38	,	,	PUNCT
ap-7669	223	39	x	x	X
ap-7669	223	40	]	]	X
ap-7669	223	41	≡	≡	PROPN
ap-7669	223	42	ψ(h	ψ(h	PROPN
ap-7669	223	43	,	,	PUNCT
ap-7669	223	44	x).7	x).7	PROPN
ap-7669	223	45	the	the	DET
ap-7669	223	46	lagrangian	lagrangian	ADJ
ap-7669	223	47	(	(	PUNCT
ap-7669	223	48	39	39	NUM
ap-7669	223	49	)	)	PUNCT
ap-7669	223	50	includes	include	VERB
ap-7669	223	51	a	a	DET
ap-7669	223	52	finite	finite	ADJ
ap-7669	223	53	number	number	NOUN
ap-7669	223	54	of	of	ADP
ap-7669	223	55	degrees	degree	NOUN
ap-7669	223	56	of	of	ADP
ap-7669	223	57	freedom	freedom	NOUN
ap-7669	223	58	and	and	CCONJ
ap-7669	223	59	represents	represent	VERB
ap-7669	223	60	a	a	DET
ap-7669	223	61	mechanical	mechanical	ADJ
ap-7669	223	62	system	system	NOUN
ap-7669	223	63	.	.	PUNCT
ap-7669	224	1	this	this	DET
ap-7669	224	2	system	system	NOUN
ap-7669	224	3	involves	involve	VERB
ap-7669	224	4	higher	high	ADJ
ap-7669	224	5	derivatives	derivative	NOUN
ap-7669	224	6	in	in	ADP
ap-7669	224	7	x	x	PROPN
ap-7669	224	8	(	(	PUNCT
ap-7669	224	9	playing	play	VERB
ap-7669	224	10	the	the	DET
ap-7669	224	11	role	role	NOUN
ap-7669	224	12	of	of	ADP
ap-7669	224	13	time	time	NOUN
ap-7669	224	14	)	)	PUNCT
ap-7669	224	15	and	and	CCONJ
ap-7669	224	16	hence	hence	ADV
ap-7669	224	17	involves	involve	VERB
ap-7669	224	18	ghosts	ghost	NOUN
ap-7669	224	19	.	.	PUNCT
ap-7669	225	1	defining	define	VERB
ap-7669	225	2	the	the	DET
ap-7669	225	3	new	new	ADJ
ap-7669	225	4	dynamical	dynamical	ADJ
ap-7669	225	5	variables	variable	NOUN
ap-7669	225	6	ak(x	ak(x	NOUN
ap-7669	225	7	)	)	PUNCT
ap-7669	225	8	=	=	SYM
ap-7669	225	9	ψx(kh	ψx(kh	PROPN
ap-7669	225	10	,	,	PUNCT
ap-7669	225	11	x	x	NOUN
ap-7669	225	12	)	)	PUNCT
ap-7669	225	13	,	,	PUNCT
ap-7669	225	14	the	the	DET
ap-7669	225	15	equations	equation	NOUN
ap-7669	225	16	of	of	ADP
ap-7669	225	17	motion	motion	NOUN
ap-7669	225	18	derived	derive	VERB
ap-7669	225	19	from	from	ADP
ap-7669	225	20	the	the	DET
ap-7669	225	21	lagrangian	lagrangian	ADJ
ap-7669	225	22	(	(	PUNCT
ap-7669	225	23	39	39	NUM
ap-7669	225	24	)	)	PUNCT
ap-7669	225	25	read	read	VERB
ap-7669	225	26	ak	ak	PROPN
ap-7669	225	27	xxx	xxx	PROPN
ap-7669	226	1	+	+	CCONJ
ap-7669	227	1	6(ak)2ak	6(ak)2ak	NUM
ap-7669	227	2	x	x	SYM
ap-7669	227	3	+	+	CCONJ
ap-7669	227	4	ak+1	ak+1	VERB
ap-7669	227	5	−	−	NOUN
ap-7669	227	6	ak−1	ak−1	ADV
ap-7669	227	7	2h	2h	NUM
ap-7669	227	8	=	=	SYM
ap-7669	227	9	0	0	NUM
ap-7669	227	10	.	.	PUNCT
ap-7669	228	1	(	(	PUNCT
ap-7669	228	2	40	40	NUM
ap-7669	228	3	)	)	PUNCT
ap-7669	228	4	there	there	PRON
ap-7669	228	5	are	be	VERB
ap-7669	228	6	two	two	NUM
ap-7669	228	7	integrals	integral	NOUN
ap-7669	228	8	of	of	ADP
ap-7669	228	9	motion	motion	NOUN
ap-7669	228	10	:	:	PUNCT
ap-7669	228	11	the	the	DET
ap-7669	228	12	energy	energy	NOUN
ap-7669	228	13	e	e	NOUN
ap-7669	228	14	=	=	NOUN
ap-7669	229	1	n∑	n∑	NOUN
ap-7669	229	2	k=1	k=1	PUNCT
ap-7669	230	1	[	[	PUNCT
ap-7669	230	2	(	(	PUNCT
ap-7669	230	3	ak	ak	PROPN
ap-7669	230	4	x)2	x)2	PROPN
ap-7669	230	5	−	−	PROPN
ap-7669	230	6	3(ak)4	3(ak)4	NOUN
ap-7669	230	7	2	2	NUM
ap-7669	230	8	−	−	NOUN
ap-7669	230	9	akak	akak	NOUN
ap-7669	230	10	xx	xx	X
ap-7669	230	11	]	]	PUNCT
ap-7669	230	12	(	(	PUNCT
ap-7669	230	13	41	41	NUM
ap-7669	230	14	)	)	PUNCT
ap-7669	230	15	6it	6it	NOUN
ap-7669	230	16	is	be	AUX
ap-7669	230	17	quite	quite	ADV
ap-7669	230	18	analogous	analogous	ADJ
ap-7669	230	19	to	to	ADP
ap-7669	230	20	(	(	PUNCT
ap-7669	230	21	4	4	NUM
ap-7669	230	22	)	)	PUNCT
ap-7669	230	23	.	.	PUNCT
ap-7669	231	1	after	after	ADP
ap-7669	231	2	variation	variation	NOUN
ap-7669	231	3	with	with	ADP
ap-7669	231	4	respect	respect	NOUN
ap-7669	231	5	to	to	ADP
ap-7669	231	6	ψ(t	ψ(t	PROPN
ap-7669	231	7	,	,	PUNCT
ap-7669	231	8	x	x	NOUN
ap-7669	231	9	)	)	PUNCT
ap-7669	231	10	,	,	PUNCT
ap-7669	231	11	one	one	PRON
ap-7669	231	12	gets	get	VERB
ap-7669	231	13	eq	eq	NOUN
ap-7669	231	14	.	.	PUNCT
ap-7669	232	1	(	(	PUNCT
ap-7669	232	2	9	9	NUM
ap-7669	232	3	)	)	PUNCT
ap-7669	232	4	after	after	ADP
ap-7669	232	5	posing	pose	VERB
ap-7669	232	6	u(t	u(t	NOUN
ap-7669	232	7	,	,	PUNCT
ap-7669	232	8	x	x	NOUN
ap-7669	232	9	)	)	PUNCT
ap-7669	232	10	=	=	SYM
ap-7669	232	11	ψx(t	ψx(t	NOUN
ap-7669	232	12	,	,	PUNCT
ap-7669	232	13	x	x	NOUN
ap-7669	232	14	)	)	PUNCT
ap-7669	232	15	.	.	PUNCT
ap-7669	233	1	7it	7it	ADJ
ap-7669	233	2	is	be	AUX
ap-7669	233	3	also	also	ADV
ap-7669	233	4	possible	possible	ADJ
ap-7669	233	5	to	to	PART
ap-7669	233	6	impose	impose	VERB
ap-7669	233	7	the	the	DET
ap-7669	233	8	dirichlet	dirichlet	NOUN
ap-7669	233	9	-	-	PUNCT
ap-7669	233	10	type	type	NOUN
ap-7669	233	11	boundary	boundary	ADJ
ap-7669	233	12	conditions	condition	NOUN
ap-7669	233	13	,	,	PUNCT
ap-7669	233	14	ψ(0h	ψ(0h	PROPN
ap-7669	233	15	,	,	PUNCT
ap-7669	233	16	x	x	X
ap-7669	233	17	)	)	PUNCT
ap-7669	233	18	=	=	VERB
ap-7669	233	19	ψ[(n	ψ[(n	PROPN
ap-7669	233	20	+	+	CCONJ
ap-7669	233	21	1)h	1)h	NUM
ap-7669	233	22	,	,	PUNCT
ap-7669	233	23	x	x	X
ap-7669	233	24	]	]	X
ap-7669	233	25	=	=	SYM
ap-7669	233	26	0	0	X
ap-7669	233	27	.	.	PUNCT
ap-7669	234	1	for	for	ADP
ap-7669	234	2	n	n	NOUN
ap-7669	234	3	=	=	SYM
ap-7669	234	4	2	2	NUM
ap-7669	234	5	,	,	PUNCT
ap-7669	234	6	periodicity	periodicity	NOUN
ap-7669	234	7	can	can	AUX
ap-7669	234	8	not	not	PART
ap-7669	234	9	be	be	AUX
ap-7669	234	10	imposed	impose	VERB
ap-7669	234	11	and	and	CCONJ
ap-7669	234	12	dirichlet	dirichlet	PROPN
ap-7669	234	13	conditions	condition	NOUN
ap-7669	234	14	are	be	AUX
ap-7669	234	15	the	the	DET
ap-7669	234	16	only	only	ADJ
ap-7669	234	17	option	option	NOUN
ap-7669	234	18	.	.	PUNCT
ap-7669	235	1	194	194	NUM
ap-7669	235	2	vol	vol	NOUN
ap-7669	235	3	.	.	PUNCT
ap-7669	236	1	62	62	NUM
ap-7669	236	2	no	no	INTJ
ap-7669	236	3	.	.	PUNCT
ap-7669	237	1	1/2022	1/2022	NUM
ap-7669	237	2	modified	modify	VERB
ap-7669	237	3	kdv	kdv	NOUN
ap-7669	237	4	equation	equation	NOUN
ap-7669	237	5	as	as	ADP
ap-7669	237	6	a	a	DET
ap-7669	237	7	system	system	NOUN
ap-7669	237	8	with	with	ADP
ap-7669	237	9	benign	benign	ADJ
ap-7669	237	10	ghosts	ghost	NOUN
ap-7669	237	11	5	5	NUM
ap-7669	237	12	10	10	NUM
ap-7669	237	13	15	15	NUM
ap-7669	237	14	20	20	NUM
ap-7669	237	15	x	x	SYM
ap-7669	237	16	-8	-8	NOUN
ap-7669	238	1	-6	-6	INTJ
ap-7669	238	2	-4	-4	INTJ
ap-7669	238	3	-2	-2	INTJ
ap-7669	238	4	2	2	NUM
ap-7669	238	5	4	4	NUM
ap-7669	238	6	6	6	NUM
ap-7669	238	7	a	a	DET
ap-7669	238	8	n	n	PRON
ap-7669	238	9	figure	figure	NOUN
ap-7669	238	10	6	6	NUM
ap-7669	238	11	.	.	PUNCT
ap-7669	239	1	the	the	DET
ap-7669	239	2	solution	solution	NOUN
ap-7669	239	3	of	of	ADP
ap-7669	239	4	the	the	DET
ap-7669	239	5	system	system	NOUN
ap-7669	239	6	(	(	PUNCT
ap-7669	239	7	40	40	NUM
ap-7669	239	8	)	)	PUNCT
ap-7669	239	9	for	for	ADP
ap-7669	239	10	an	an	DET
ap-7669	239	11	(	(	PUNCT
ap-7669	239	12	x	x	NOUN
ap-7669	239	13	)	)	PUNCT
ap-7669	239	14	(	(	PUNCT
ap-7669	239	15	n	n	NOUN
ap-7669	239	16	=	=	SYM
ap-7669	239	17	350	350	NUM
ap-7669	239	18	,	,	PUNCT
ap-7669	239	19	h	h	NOUN
ap-7669	239	20	=	=	SYM
ap-7669	239	21	t	t	PROPN
ap-7669	239	22	/	/	SYM
ap-7669	239	23	n	n	CCONJ
ap-7669	239	24	)	)	PUNCT
ap-7669	239	25	.	.	PUNCT
ap-7669	240	1	and	and	CCONJ
ap-7669	240	2	q	q	X
ap-7669	240	3	=	=	SYM
ap-7669	240	4	n∑	n∑	NOUN
ap-7669	240	5	k=1	k=1	PUNCT
ap-7669	241	1	[	[	PUNCT
ap-7669	241	2	ak	ak	PROPN
ap-7669	241	3	xx	xx	X
ap-7669	241	4	+	+	CCONJ
ap-7669	241	5	2(ak)3	2(ak)3	NUM
ap-7669	241	6	]	]	PUNCT
ap-7669	241	7	.	.	PUNCT
ap-7669	242	1	(	(	PUNCT
ap-7669	242	2	42	42	NUM
ap-7669	242	3	)	)	PUNCT
ap-7669	242	4	the	the	DET
ap-7669	242	5	expression	expression	NOUN
ap-7669	242	6	(	(	PUNCT
ap-7669	242	7	41	41	NUM
ap-7669	242	8	)	)	PUNCT
ap-7669	242	9	is	be	AUX
ap-7669	242	10	the	the	DET
ap-7669	242	11	discretized	discretized	ADJ
ap-7669	242	12	version	version	NOUN
ap-7669	242	13	of	of	ADP
ap-7669	242	14	the	the	DET
ap-7669	242	15	integral	integral	ADJ
ap-7669	242	16	∫	∫	PROPN
ap-7669	242	17	dt	dt	X
ap-7669	242	18	[	[	PUNCT
ap-7669	242	19	(	(	PUNCT
ap-7669	242	20	ux)2	ux)2	NOUN
ap-7669	242	21	−	−	NOUN
ap-7669	242	22	3u4	3u4	NUM
ap-7669	242	23	2	2	NUM
ap-7669	242	24	−	−	NOUN
ap-7669	242	25	uuxx	uuxx	NOUN
ap-7669	242	26	]	]	PUNCT
ap-7669	242	27	(	(	PUNCT
ap-7669	242	28	43	43	NUM
ap-7669	242	29	)	)	PUNCT
ap-7669	242	30	in	in	ADP
ap-7669	242	31	the	the	DET
ap-7669	242	32	continuous	continuous	ADJ
ap-7669	242	33	mkdv	mkdv	NOUN
ap-7669	242	34	system	system	NOUN
ap-7669	242	35	,	,	PUNCT
ap-7669	242	36	which	which	PRON
ap-7669	242	37	is	be	AUX
ap-7669	242	38	conserved	conserve	VERB
ap-7669	242	39	during	during	ADP
ap-7669	242	40	the	the	DET
ap-7669	242	41	x	x	SYM
ap-7669	242	42	evolution	evolution	NOUN
ap-7669	242	43	,	,	PUNCT
ap-7669	242	44	as	as	SCONJ
ap-7669	242	45	follows	follow	VERB
ap-7669	242	46	from	from	ADP
ap-7669	242	47	the	the	DET
ap-7669	242	48	local	local	ADJ
ap-7669	242	49	conservation	conservation	NOUN
ap-7669	242	50	law	law	NOUN
ap-7669	242	51	(	(	PUNCT
ap-7669	242	52	11	11	NUM
ap-7669	242	53	)	)	PUNCT
ap-7669	242	54	.	.	PUNCT
ap-7669	243	1	the	the	DET
ap-7669	243	2	second	second	ADJ
ap-7669	243	3	integral	integral	NOUN
ap-7669	243	4	of	of	ADP
ap-7669	243	5	motion	motion	NOUN
ap-7669	243	6	is	be	AUX
ap-7669	243	7	related	relate	VERB
ap-7669	243	8	to	to	ADP
ap-7669	243	9	the	the	DET
ap-7669	243	10	conservation	conservation	NOUN
ap-7669	243	11	law	law	NOUN
ap-7669	243	12	(	(	PUNCT
ap-7669	243	13	10	10	NUM
ap-7669	243	14	)	)	PUNCT
ap-7669	243	15	.	.	PUNCT
ap-7669	244	1	by	by	ADP
ap-7669	244	2	contrast	contrast	NOUN
ap-7669	244	3	,	,	PUNCT
ap-7669	244	4	the	the	DET
ap-7669	244	5	currents	current	NOUN
ap-7669	244	6	in	in	ADP
ap-7669	244	7	the	the	DET
ap-7669	244	8	higher	high	ADJ
ap-7669	244	9	conservation	conservation	NOUN
ap-7669	244	10	laws	law	NOUN
ap-7669	244	11	of	of	ADP
ap-7669	244	12	the	the	DET
ap-7669	244	13	mkdv	mkdv	NOUN
ap-7669	244	14	equation	equation	NOUN
ap-7669	244	15	,	,	PUNCT
ap-7669	244	16	starting	start	VERB
ap-7669	244	17	with	with	ADP
ap-7669	244	18	eq.(12	eq.(12	NOUN
ap-7669	244	19	)	)	PUNCT
ap-7669	244	20	,	,	PUNCT
ap-7669	244	21	do	do	AUX
ap-7669	244	22	not	not	PART
ap-7669	244	23	translate	translate	VERB
ap-7669	244	24	into	into	ADP
ap-7669	244	25	integrals	integral	NOUN
ap-7669	244	26	of	of	ADP
ap-7669	244	27	motion	motion	NOUN
ap-7669	244	28	of	of	ADP
ap-7669	244	29	the	the	DET
ap-7669	244	30	discrete	discrete	ADJ
ap-7669	244	31	systems	system	NOUN
ap-7669	244	32	.	.	PUNCT
ap-7669	245	1	we	we	PRON
ap-7669	245	2	have	have	VERB
ap-7669	245	3	only	only	ADV
ap-7669	245	4	two	two	NUM
ap-7669	245	5	integrals	integral	NOUN
ap-7669	245	6	of	of	ADP
ap-7669	245	7	motion	motion	NOUN
ap-7669	245	8	and	and	CCONJ
ap-7669	245	9	many	many	ADJ
ap-7669	245	10	variables	variable	NOUN
ap-7669	245	11	,	,	PUNCT
ap-7669	245	12	which	which	PRON
ap-7669	245	13	means	mean	VERB
ap-7669	245	14	that	that	SCONJ
ap-7669	245	15	the	the	DET
ap-7669	245	16	equation	equation	NOUN
ap-7669	245	17	system	system	NOUN
ap-7669	245	18	(	(	PUNCT
ap-7669	245	19	40	40	NUM
ap-7669	245	20	)	)	PUNCT
ap-7669	245	21	is	be	AUX
ap-7669	245	22	not	not	PART
ap-7669	245	23	integrable	integrable	ADJ
ap-7669	245	24	and	and	CCONJ
ap-7669	245	25	exhibits	exhibit	VERB
ap-7669	245	26	a	a	DET
ap-7669	245	27	chaotic	chaotic	ADJ
ap-7669	245	28	behaviour	behaviour	NOUN
ap-7669	245	29	.	.	PUNCT
ap-7669	246	1	we	we	PRON
ap-7669	246	2	fed	feed	VERB
ap-7669	246	3	these	these	DET
ap-7669	246	4	equations	equation	NOUN
ap-7669	246	5	to	to	ADP
ap-7669	246	6	mathematica	mathematica	PROPN
ap-7669	246	7	and	and	CCONJ
ap-7669	246	8	found	find	VERB
ap-7669	246	9	out	out	ADP
ap-7669	246	10	that	that	SCONJ
ap-7669	246	11	their	their	PRON
ap-7669	246	12	solution	solution	NOUN
ap-7669	246	13	stays	stay	VERB
ap-7669	246	14	bounded	bound	VERB
ap-7669	246	15	up	up	ADP
ap-7669	246	16	to	to	ADP
ap-7669	246	17	x	x	X
ap-7669	246	18	=	=	SYM
ap-7669	246	19	10000	10000	NUM
ap-7669	246	20	and	and	CCONJ
ap-7669	246	21	more	more	ADJ
ap-7669	246	22	–	–	PUNCT
ap-7669	246	23	the	the	DET
ap-7669	246	24	ghosts	ghost	NOUN
ap-7669	246	25	are	be	AUX
ap-7669	246	26	benign	benign	ADJ
ap-7669	246	27	!	!	PUNCT
ap-7669	247	1	this	this	PRON
ap-7669	247	2	represents	represent	VERB
ap-7669	247	3	a	a	DET
ap-7669	247	4	further	further	ADJ
ap-7669	247	5	argument	argument	NOUN
ap-7669	247	6	in	in	ADP
ap-7669	247	7	favour	favour	NOUN
ap-7669	247	8	of	of	ADP
ap-7669	247	9	the	the	DET
ap-7669	247	10	conjecture	conjecture	NOUN
ap-7669	247	11	that	that	SCONJ
ap-7669	247	12	in	in	ADP
ap-7669	247	13	the	the	DET
ap-7669	247	14	continuous	continuous	ADJ
ap-7669	247	15	theory	theory	NOUN
ap-7669	247	16	the	the	DET
ap-7669	247	17	evolution	evolution	NOUN
ap-7669	247	18	in	in	ADP
ap-7669	247	19	spatial	spatial	ADJ
ap-7669	247	20	direction	direction	NOUN
ap-7669	247	21	is	be	AUX
ap-7669	247	22	also	also	ADV
ap-7669	247	23	benign	benign	ADJ
ap-7669	247	24	.	.	PUNCT
ap-7669	248	1	indeed	indeed	ADV
ap-7669	248	2	,	,	PUNCT
ap-7669	248	3	one	one	PRON
ap-7669	248	4	may	may	AUX
ap-7669	248	5	expect	expect	VERB
ap-7669	248	6	that	that	SCONJ
ap-7669	248	7	taking	take	VERB
ap-7669	248	8	larger	large	ADJ
ap-7669	248	9	and	and	CCONJ
ap-7669	248	10	larger	large	ADJ
ap-7669	248	11	values	value	NOUN
ap-7669	248	12	of	of	ADP
ap-7669	248	13	n	n	PRON
ap-7669	248	14	would	would	AUX
ap-7669	248	15	allow	allow	VERB
ap-7669	248	16	one	one	PRON
ap-7669	248	17	to	to	PART
ap-7669	248	18	simulate	simulate	VERB
ap-7669	248	19	better	well	ADV
ap-7669	248	20	and	and	CCONJ
ap-7669	248	21	better	well	ADJ
ap-7669	248	22	the	the	DET
ap-7669	248	23	continuous	continuous	ADJ
ap-7669	248	24	theory	theory	NOUN
ap-7669	248	25	(	(	PUNCT
ap-7669	248	26	though	though	SCONJ
ap-7669	248	27	the	the	DET
ap-7669	248	28	presence	presence	NOUN
ap-7669	248	29	of	of	ADP
ap-7669	248	30	chaos	chaos	NOUN
ap-7669	248	31	might	might	AUX
ap-7669	248	32	make	make	VERB
ap-7669	248	33	such	such	DET
ap-7669	248	34	a	a	DET
ap-7669	248	35	convergence	convergence	NOUN
ap-7669	248	36	non	non	ADJ
ap-7669	248	37	uniform	uniform	NOUN
ap-7669	248	38	in	in	ADP
ap-7669	248	39	x	x	NOUN
ap-7669	248	40	)	)	PUNCT
ap-7669	248	41	.	.	PUNCT
ap-7669	249	1	anyway	anyway	INTJ
ap-7669	249	2	,	,	PUNCT
ap-7669	249	3	we	we	PRON
ap-7669	249	4	tried	try	VERB
ap-7669	249	5	the	the	DET
ap-7669	249	6	solitonic	solitonic	ADJ
ap-7669	249	7	initial	initial	ADJ
ap-7669	249	8	conditions	condition	NOUN
ap-7669	249	9	and	and	CCONJ
ap-7669	249	10	found	find	VERB
ap-7669	249	11	out	out	ADP
ap-7669	249	12	that	that	SCONJ
ap-7669	249	13	the	the	DET
ap-7669	249	14	discrete	discrete	ADJ
ap-7669	249	15	system	system	NOUN
ap-7669	249	16	for	for	ADP
ap-7669	249	17	large	large	ADJ
ap-7669	249	18	n	n	NOUN
ap-7669	249	19	=	=	SYM
ap-7669	249	20	350	350	NUM
ap-7669	249	21	(	(	PUNCT
ap-7669	249	22	the	the	DET
ap-7669	249	23	limit	limit	NOUN
ap-7669	249	24	of	of	ADP
ap-7669	249	25	mathematica	mathematica	PROPN
ap-7669	249	26	skills	skill	NOUN
ap-7669	249	27	)	)	PUNCT
ap-7669	249	28	behaves	behave	VERB
ap-7669	249	29	better	well	ADV
ap-7669	249	30	than	than	ADP
ap-7669	249	31	the	the	DET
ap-7669	249	32	pde	pde	NOUN
ap-7669	249	33	.	.	PUNCT
ap-7669	250	1	as	as	SCONJ
ap-7669	250	2	is	be	AUX
ap-7669	250	3	seen	see	VERB
ap-7669	250	4	from	from	ADP
ap-7669	250	5	figure	figure	NOUN
ap-7669	250	6	6	6	NUM
ap-7669	250	7	,	,	PUNCT
ap-7669	250	8	the	the	DET
ap-7669	250	9	discrete	discrete	ADJ
ap-7669	250	10	solution	solution	NOUN
ap-7669	250	11	stays	stay	VERB
ap-7669	250	12	close	close	ADV
ap-7669	250	13	to	to	ADP
ap-7669	250	14	the	the	DET
ap-7669	250	15	exact	exact	ADJ
ap-7669	250	16	soliton	soliton	NOUN
ap-7669	250	17	solution	solution	NOUN
ap-7669	250	18	up	up	ADP
ap-7669	250	19	to	to	ADP
ap-7669	250	20	x	x	PROPN
ap-7669	250	21	≈	≈	PROPN
ap-7669	250	22	10	10	NUM
ap-7669	250	23	,	,	PUNCT
ap-7669	250	24	to	to	PART
ap-7669	250	25	be	be	AUX
ap-7669	250	26	compared	compare	VERB
ap-7669	250	27	to	to	ADP
ap-7669	250	28	x	x	PROPN
ap-7669	250	29	≈	≈	PROPN
ap-7669	250	30	4.5	4.5	NUM
ap-7669	250	31	,	,	PUNCT
ap-7669	250	32	which	which	PRON
ap-7669	250	33	was	be	AUX
ap-7669	250	34	the	the	DET
ap-7669	250	35	horizon	horizon	NOUN
ap-7669	250	36	of	of	ADP
ap-7669	250	37	the	the	DET
ap-7669	250	38	numerical	numerical	ADJ
ap-7669	250	39	procedure	procedure	NOUN
ap-7669	250	40	of	of	ADP
ap-7669	250	41	the	the	DET
ap-7669	250	42	previous	previous	ADJ
ap-7669	250	43	section	section	NOUN
ap-7669	250	44	.	.	PUNCT
ap-7669	251	1	hopefully	hopefully	ADV
ap-7669	251	2	,	,	PUNCT
ap-7669	251	3	a	a	DET
ap-7669	251	4	clever	clever	ADJ
ap-7669	251	5	mathematician	mathematician	NOUN
ap-7669	251	6	,	,	PUNCT
ap-7669	251	7	an	an	DET
ap-7669	251	8	expert	expert	NOUN
ap-7669	251	9	in	in	ADP
ap-7669	251	10	numerical	numerical	ADJ
ap-7669	251	11	calculations	calculation	NOUN
ap-7669	251	12	,	,	PUNCT
ap-7669	251	13	would	would	AUX
ap-7669	251	14	be	be	AUX
ap-7669	251	15	able	able	ADJ
ap-7669	251	16	to	to	PART
ap-7669	251	17	increase	increase	VERB
ap-7669	251	18	the	the	DET
ap-7669	251	19	horizon	horizon	NOUN
ap-7669	251	20	even	even	ADV
ap-7669	251	21	more	more	ADV
ap-7669	251	22	...	...	PUNCT
ap-7669	251	23	lastly	lastly	ADV
ap-7669	251	24	,	,	PUNCT
ap-7669	251	25	we	we	PRON
ap-7669	251	26	note	note	VERB
ap-7669	251	27	that	that	SCONJ
ap-7669	251	28	,	,	PUNCT
ap-7669	251	29	irrespectively	irrespectively	ADV
ap-7669	251	30	to	to	ADP
ap-7669	251	31	the	the	DET
ap-7669	251	32	relationship	relationship	NOUN
ap-7669	251	33	of	of	ADP
ap-7669	251	34	the	the	DET
ap-7669	251	35	systems	system	NOUN
ap-7669	251	36	(	(	PUNCT
ap-7669	251	37	39	39	NUM
ap-7669	251	38	)	)	PUNCT
ap-7669	251	39	to	to	ADP
ap-7669	251	40	the	the	DET
ap-7669	251	41	mkdv	mkdv	NOUN
ap-7669	251	42	equation	equation	NOUN
ap-7669	251	43	,	,	PUNCT
ap-7669	251	44	these	these	DET
ap-7669	251	45	systems	system	NOUN
ap-7669	251	46	represent	represent	VERB
ap-7669	251	47	an	an	DET
ap-7669	251	48	interest	interest	NOUN
ap-7669	251	49	by	by	ADP
ap-7669	251	50	their	their	PRON
ap-7669	251	51	own	own	ADJ
ap-7669	251	52	because	because	SCONJ
ap-7669	251	53	they	they	PRON
ap-7669	251	54	provide	provide	VERB
ap-7669	251	55	a	a	DET
ap-7669	251	56	set	set	NOUN
ap-7669	251	57	of	of	ADP
ap-7669	251	58	nontrivial	nontrivial	NOUN
ap-7669	251	59	interacting	interact	VERB
ap-7669	251	60	higher	high	ADJ
ap-7669	251	61	derivative	derivative	ADJ
ap-7669	251	62	systems	system	NOUN
ap-7669	251	63	with	with	ADP
ap-7669	251	64	benign	benign	ADJ
ap-7669	251	65	ghosts	ghost	NOUN
ap-7669	251	66	.	.	PUNCT
ap-7669	252	1	such	such	ADJ
ap-7669	252	2	systems	system	NOUN
ap-7669	252	3	were	be	AUX
ap-7669	252	4	not	not	PART
ap-7669	252	5	known	know	VERB
ap-7669	252	6	before	before	ADV
ap-7669	252	7	.	.	PUNCT
ap-7669	253	1	acknowledgements	acknowledgement	NOUN
ap-7669	253	2	i	i	PRON
ap-7669	253	3	am	be	AUX
ap-7669	253	4	grateful	grateful	ADJ
ap-7669	253	5	to	to	ADP
ap-7669	253	6	the	the	DET
ap-7669	253	7	organizers	organizer	NOUN
ap-7669	253	8	of	of	ADP
ap-7669	253	9	the	the	DET
ap-7669	253	10	aamp	aamp	PROPN
ap-7669	253	11	conference	conference	NOUN
ap-7669	253	12	for	for	ADP
ap-7669	253	13	the	the	DET
ap-7669	253	14	invitation	invitation	NOUN
ap-7669	253	15	to	to	PART
ap-7669	253	16	make	make	VERB
ap-7669	253	17	a	a	DET
ap-7669	253	18	talk	talk	NOUN
ap-7669	253	19	there	there	ADV
ap-7669	253	20	.	.	PUNCT
ap-7669	254	1	working	work	VERB
ap-7669	254	2	on	on	ADP
ap-7669	254	3	our	our	PRON
ap-7669	254	4	paper	paper	NOUN
ap-7669	254	5	[	[	X
ap-7669	254	6	18	18	NUM
ap-7669	254	7	]	]	PUNCT
ap-7669	254	8	,	,	PUNCT
ap-7669	254	9	we	we	PRON
ap-7669	254	10	benefited	benefit	VERB
ap-7669	254	11	a	a	DET
ap-7669	254	12	lot	lot	NOUN
ap-7669	254	13	from	from	ADP
ap-7669	254	14	illuminating	illuminate	VERB
ap-7669	254	15	discussions	discussion	NOUN
ap-7669	254	16	with	with	ADP
ap-7669	254	17	piotr	piotr	PROPN
ap-7669	254	18	chrusciel	chrusciel	PROPN
ap-7669	254	19	,	,	PUNCT
ap-7669	254	20	alberto	alberto	PROPN
ap-7669	254	21	de	de	X
ap-7669	254	22	sole	sole	PROPN
ap-7669	254	23	,	,	PUNCT
ap-7669	254	24	victor	victor	PROPN
ap-7669	254	25	kac	kac	PROPN
ap-7669	254	26	,	,	PUNCT
ap-7669	254	27	nader	nader	PROPN
ap-7669	254	28	masmoudi	masmoudi	PROPN
ap-7669	254	29	,	,	PUNCT
ap-7669	254	30	frank	frank	PROPN
ap-7669	254	31	merle	merle	PROPN
ap-7669	254	32	and	and	CCONJ
ap-7669	254	33	laure	laure	PROPN
ap-7669	254	34	saint	saint	PROPN
ap-7669	254	35	-	-	PUNCT
ap-7669	254	36	raymond	raymond	PROPN
ap-7669	254	37	.	.	PUNCT
ap-7669	255	1	references	reference	NOUN
ap-7669	255	2	[	[	X
ap-7669	255	3	1	1	NUM
ap-7669	255	4	]	]	PUNCT
ap-7669	255	5	m.	m.	NOUN
ap-7669	255	6	ostrogradsky	ostrogradsky	ADJ
ap-7669	255	7	.	.	PUNCT
ap-7669	256	1	mémoire	mémoire	PROPN
ap-7669	256	2	sur	sur	PROPN
ap-7669	256	3	les	les	PROPN
ap-7669	256	4	équations	équation	NOUN
ap-7669	256	5	differéntielles	differéntielle	VERB
ap-7669	256	6	relatives	relative	NOUN
ap-7669	256	7	au	au	ADP
ap-7669	256	8	problème	problème	X
ap-7669	256	9	des	des	X
ap-7669	256	10	isopérimètres	isopérimètres	PROPN
ap-7669	256	11	.	.	PUNCT
ap-7669	257	1	mem	mem	PROPN
ap-7669	257	2	acad	acad	PROPN
ap-7669	257	3	st	st	PROPN
ap-7669	257	4	petersbourg	petersbourg	PROPN
ap-7669	257	5	vi(4):385	vi(4):385	NOUN
ap-7669	257	6	,	,	PUNCT
ap-7669	257	7	1850	1850	NUM
ap-7669	257	8	.	.	PUNCT
ap-7669	258	1	[	[	X
ap-7669	258	2	2	2	NUM
ap-7669	258	3	]	]	X
ap-7669	258	4	r.	r.	PROPN
ap-7669	258	5	p.	p.	PROPN
ap-7669	258	6	woodard	woodard	PROPN
ap-7669	258	7	.	.	PUNCT
ap-7669	259	1	ostrogradsky	ostrogradsky	ADJ
ap-7669	259	2	’s	’s	PART
ap-7669	259	3	theorem	theorem	NOUN
ap-7669	259	4	on	on	ADP
ap-7669	259	5	hamiltonian	hamiltonian	ADJ
ap-7669	259	6	instability	instability	NOUN
ap-7669	259	7	.	.	PUNCT
ap-7669	260	1	scholarpedia	scholarpedia	PROPN
ap-7669	260	2	10(8):32243	10(8):32243	NUM
ap-7669	260	3	,	,	PUNCT
ap-7669	260	4	2015	2015	NUM
ap-7669	260	5	.	.	PUNCT
ap-7669	261	1	https://doi.org/10.4249/scholarpedia.32243	https://doi.org/10.4249/scholarpedia.32243	VERB
ap-7669	261	2	.	.	PUNCT
ap-7669	262	1	[	[	X
ap-7669	262	2	3	3	NUM
ap-7669	262	3	]	]	X
ap-7669	262	4	m.	m.	NOUN
ap-7669	262	5	raidal	raidal	PROPN
ap-7669	262	6	,	,	PUNCT
ap-7669	262	7	h.	h.	PROPN
ap-7669	262	8	veermae	veermae	PROPN
ap-7669	262	9	.	.	PUNCT
ap-7669	263	1	on	on	ADP
ap-7669	263	2	the	the	DET
ap-7669	263	3	quantisation	quantisation	NOUN
ap-7669	263	4	of	of	ADP
ap-7669	263	5	complex	complex	ADJ
ap-7669	263	6	higher	high	ADJ
ap-7669	263	7	derivative	derivative	ADJ
ap-7669	263	8	theories	theory	NOUN
ap-7669	263	9	and	and	CCONJ
ap-7669	263	10	avoiding	avoid	VERB
ap-7669	263	11	the	the	DET
ap-7669	263	12	ostrogradsky	ostrogradsky	ADJ
ap-7669	263	13	ghost	ghost	NOUN
ap-7669	263	14	.	.	PUNCT
ap-7669	264	1	nuclear	nuclear	ADJ
ap-7669	264	2	physics	physics	PROPN
ap-7669	264	3	b	b	PROPN
ap-7669	264	4	916:607–626	916:607–626	NUM
ap-7669	264	5	,	,	PUNCT
ap-7669	264	6	2017	2017	NUM
ap-7669	264	7	.	.	PUNCT
ap-7669	265	1	https://doi.org/10.1016/j.nuclphysb.2017.01.024	https://doi.org/10.1016/j.nuclphysb.2017.01.024	NOUN
ap-7669	265	2	.	.	PUNCT
ap-7669	266	1	[	[	X
ap-7669	266	2	4	4	NUM
ap-7669	266	3	]	]	X
ap-7669	266	4	a.	a.	NOUN
ap-7669	266	5	v.	v.	ADP
ap-7669	266	6	smilga	smilga	ADJ
ap-7669	266	7	.	.	PUNCT
ap-7669	267	1	classical	classical	ADJ
ap-7669	267	2	and	and	CCONJ
ap-7669	267	3	quantum	quantum	NOUN
ap-7669	267	4	dynamics	dynamic	NOUN
ap-7669	267	5	of	of	ADP
ap-7669	267	6	higher	high	ADJ
ap-7669	267	7	-	-	PUNCT
ap-7669	267	8	derivative	derivative	ADJ
ap-7669	267	9	systems	system	NOUN
ap-7669	267	10	.	.	PUNCT
ap-7669	268	1	international	international	ADJ
ap-7669	268	2	journal	journal	NOUN
ap-7669	268	3	of	of	ADP
ap-7669	268	4	modern	modern	ADJ
ap-7669	268	5	physics	physic	NOUN
ap-7669	268	6	a	a	PRON
ap-7669	268	7	32(33):1730025	32(33):1730025	NUM
ap-7669	268	8	,	,	PUNCT
ap-7669	268	9	2017	2017	NUM
ap-7669	268	10	.	.	PUNCT
ap-7669	269	1	https://doi.org/10.1142/s0217751x17300253	https://doi.org/10.1142/s0217751x17300253	NUM
ap-7669	269	2	.	.	PUNCT
ap-7669	270	1	[	[	X
ap-7669	270	2	5	5	X
ap-7669	270	3	]	]	PUNCT
ap-7669	270	4	k.	k.	PROPN
ap-7669	270	5	m.	m.	PROPN
ap-7669	270	6	case	case	NOUN
ap-7669	270	7	.	.	PUNCT
ap-7669	271	1	singular	singular	PROPN
ap-7669	271	2	potentials	potential	VERB
ap-7669	271	3	.	.	PUNCT
ap-7669	272	1	physical	physical	ADJ
ap-7669	272	2	review	review	NOUN
ap-7669	272	3	80(5):797–806	80(5):797–806	PROPN
ap-7669	272	4	,	,	PUNCT
ap-7669	272	5	1950	1950	NUM
ap-7669	272	6	.	.	PUNCT
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ap-7669	274	2	6	6	NUM
ap-7669	274	3	]	]	PUNCT
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ap-7669	275	5	-	-	ADJ
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ap-7669	275	9	.	.	PUNCT
ap-7669	276	1	il	il	PROPN
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ap-7669	276	5	,	,	PUNCT
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ap-7669	276	7	.	.	PUNCT
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ap-7669	278	2	7	7	NUM
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ap-7669	279	10	.	.	PUNCT
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ap-7669	280	6	,	,	PUNCT
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ap-7669	280	8	.	.	PUNCT
ap-7669	281	1	https://doi.org/10.1007/bf01246666	https://doi.org/10.1007/bf01246666	NUM
ap-7669	281	2	.	.	PUNCT
ap-7669	282	1	[	[	X
ap-7669	282	2	8	8	NUM
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ap-7669	282	11	.	.	PUNCT
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ap-7669	283	2	mechanics	mechanic	NOUN
ap-7669	283	3	.	.	PUNCT
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ap-7669	284	2	,	,	PUNCT
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ap-7669	284	4	.	.	PUNCT
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ap-7669	285	2	9	9	NUM
ap-7669	285	3	]	]	PUNCT
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ap-7669	285	14	in	in	ADP
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ap-7669	285	17	.	.	PUNCT
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ap-7669	286	2	,	,	PUNCT
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ap-7669	286	4	.	.	PUNCT
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ap-7669	287	2	.	.	PUNCT
ap-7669	288	1	[	[	X
ap-7669	288	2	10	10	NUM
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ap-7669	289	8	action	action	NOUN
ap-7669	289	9	.	.	PUNCT
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ap-7669	290	4	,	,	PUNCT
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ap-7669	290	6	.	.	PUNCT
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ap-7669	291	2	.	.	PUNCT
ap-7669	292	1	[	[	X
ap-7669	292	2	11	11	NUM
ap-7669	292	3	]	]	PUNCT
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ap-7669	292	5	d.	d.	PROPN
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ap-7669	292	8	a.	a.	PROPN
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ap-7669	292	10	.	.	PUNCT
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ap-7669	294	1	physical	physical	ADJ
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ap-7669	294	5	,	,	PUNCT
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ap-7669	294	7	.	.	PUNCT
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ap-7669	295	2	.	.	PUNCT
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ap-7669	296	2	12	12	NUM
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ap-7669	297	4	.	.	PUNCT
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ap-7669	298	6	,	,	PUNCT
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ap-7669	298	8	.	.	PUNCT
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ap-7669	300	2	13	13	NUM
ap-7669	300	3	]	]	PUNCT
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ap-7669	300	6	.	.	PUNCT
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ap-7669	301	3	-	-	PUNCT
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ap-7669	301	5	pais	pais	PROPN
ap-7669	301	6	-	-	PUNCT
ap-7669	301	7	uhlenbeck	uhlenbeck	PROPN
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ap-7669	302	1	modern	modern	ADJ
ap-7669	302	2	physics	physics	NOUN
ap-7669	302	3	letters	letter	NOUN
ap-7669	302	4	a	a	DET
ap-7669	302	5	28(36):1350165	28(36):1350165	NUM
ap-7669	302	6	,	,	PUNCT
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ap-7669	302	8	.	.	PUNCT
ap-7669	303	1	https://doi.org/10.1142/s0217732313501654	https://doi.org/10.1142/s0217732313501654	NUM
ap-7669	303	2	.	.	NOUN
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ap-7669	304	9	https://doi.org/10.1103/physrev.79.145	https://doi.org/10.1103/physrev.79.145	PROPN
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ap-7669	304	18	14	14	NUM
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ap-7669	305	2	comments	comment	NOUN
ap-7669	305	3	on	on	ADP
ap-7669	305	4	ghosts	ghost	NOUN
ap-7669	305	5	and	and	CCONJ
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ap-7669	305	7	:	:	PUNCT
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ap-7669	305	9	pais	pais	PROPN
ap-7669	305	10	-	-	PUNCT
ap-7669	305	11	uhlenbeck	uhlenbeck	PROPN
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ap-7669	305	14	.	.	PUNCT
ap-7669	306	1	physical	physical	ADJ
ap-7669	306	2	review	review	PROPN
ap-7669	306	3	d	d	PROPN
ap-7669	306	4	88(4):044045	88(4):044045	NUM
ap-7669	306	5	,	,	PUNCT
ap-7669	306	6	2013	2013	NUM
ap-7669	306	7	.	.	PUNCT
ap-7669	307	1	https://doi.org/10.1103/physrevd.88.044045	https://doi.org/10.1103/physrevd.88.044045	NOUN
ap-7669	307	2	.	.	PUNCT
ap-7669	308	1	[	[	X
ap-7669	308	2	15	15	NUM
ap-7669	308	3	]	]	X
ap-7669	308	4	a.	a.	NOUN
ap-7669	308	5	v.	v.	ADP
ap-7669	308	6	smilga	smilga	PROPN
ap-7669	308	7	.	.	PUNCT
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ap-7669	309	2	field	field	NOUN
ap-7669	309	3	theory	theory	NOUN
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ap-7669	309	5	benign	benign	ADJ
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ap-7669	309	7	.	.	PUNCT
ap-7669	310	1	journal	journal	PROPN
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ap-7669	310	5	:	:	PUNCT
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ap-7669	310	9	47(5):052001	47(5):052001	NUM
ap-7669	310	10	,	,	PUNCT
ap-7669	310	11	2014	2014	NUM
ap-7669	310	12	.	.	PUNCT
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ap-7669	311	2	.	.	PUNCT
ap-7669	312	1	[	[	X
ap-7669	312	2	16	16	NUM
ap-7669	312	3	]	]	X
ap-7669	312	4	a.	a.	NOUN
ap-7669	312	5	v.	v.	ADP
ap-7669	312	6	smilga	smilga	ADJ
ap-7669	312	7	.	.	PUNCT
ap-7669	313	1	on	on	ADP
ap-7669	313	2	exactly	exactly	ADV
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ap-7669	313	4	ghost	ghost	NOUN
ap-7669	313	5	-	-	PUNCT
ap-7669	313	6	ridden	ride	VERB
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ap-7669	313	8	.	.	PUNCT
ap-7669	314	1	physics	physics	NOUN
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ap-7669	314	5	,	,	PUNCT
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ap-7669	314	7	.	.	PUNCT
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ap-7669	315	2	.	.	PUNCT
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ap-7669	316	2	17	17	NUM
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ap-7669	316	10	a.	a.	NOUN
ap-7669	316	11	vikman	vikman	NOUN
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ap-7669	317	1	ghosts	ghost	NOUN
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ap-7669	317	5	.	.	PUNCT
ap-7669	318	1	physical	physical	ADJ
ap-7669	318	2	review	review	NOUN
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ap-7669	318	5	,	,	PUNCT
ap-7669	318	6	2022	2022	NUM
ap-7669	318	7	.	.	PUNCT
ap-7669	319	1	https://doi.org/10.1103/physrevlett.128.041301	https://doi.org/10.1103/physrevlett.128.041301	NOUN
ap-7669	319	2	.	.	PUNCT
ap-7669	320	1	[	[	X
ap-7669	320	2	18	18	NUM
ap-7669	320	3	]	]	PUNCT
ap-7669	320	4	t.	t.	PROPN
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ap-7669	320	6	,	,	PUNCT
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ap-7669	320	8	v.	v.	ADP
ap-7669	320	9	smilga	smilga	ADJ
ap-7669	320	10	.	.	PUNCT
ap-7669	321	1	dynamical	dynamical	ADJ
ap-7669	321	2	systems	system	NOUN
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ap-7669	321	4	benign	benign	ADJ
ap-7669	321	5	ghosts	ghost	NOUN
ap-7669	321	6	.	.	PUNCT
ap-7669	322	1	physical	physical	ADJ
ap-7669	322	2	review	review	PROPN
ap-7669	322	3	d	d	X
ap-7669	322	4	(	(	PUNCT
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ap-7669	322	7	)	)	PUNCT
ap-7669	322	8	,	,	PUNCT
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ap-7669	322	10	.	.	PUNCT
ap-7669	323	1	[	[	X
ap-7669	323	2	19	19	NUM
ap-7669	323	3	]	]	X
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ap-7669	324	7	.	.	PUNCT
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ap-7669	325	8	-	-	SYM
ap-7669	325	9	2):127–140	2):127–140	NUM
ap-7669	325	10	,	,	PUNCT
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ap-7669	325	12	.	.	PUNCT
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ap-7669	327	2	20	20	NUM
ap-7669	327	3	]	]	X
ap-7669	327	4	c.	c.	PROPN
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ap-7669	328	2	-	-	PUNCT
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ap-7669	328	5	the	the	DET
ap-7669	328	6	initial	initial	ADJ
ap-7669	328	7	value	value	NOUN
ap-7669	328	8	problem	problem	NOUN
ap-7669	328	9	for	for	ADP
ap-7669	328	10	the	the	DET
ap-7669	328	11	korteweg	korteweg	NOUN
ap-7669	328	12	-	-	PUNCT
ap-7669	328	13	de	de	PROPN
ap-7669	328	14	vries	vries	PROPN
ap-7669	328	15	equation	equation	NOUN
ap-7669	328	16	.	.	PUNCT
ap-7669	329	1	journal	journal	NOUN
ap-7669	329	2	of	of	ADP
ap-7669	329	3	the	the	DET
ap-7669	329	4	american	american	PROPN
ap-7669	329	5	mathematical	mathematical	PROPN
ap-7669	329	6	society	society	PROPN
ap-7669	329	7	4(2):323–347	4(2):323–347	PROPN
ap-7669	329	8	,	,	PUNCT
ap-7669	329	9	1991	1991	NUM
ap-7669	329	10	.	.	PUNCT
ap-7669	330	1	https	https	NOUN
ap-7669	330	2	:	:	PUNCT
ap-7669	330	3	//doi.org/10.1090	//doi.org/10.1090	ADJ
ap-7669	330	4	/	/	SYM
ap-7669	330	5	s0894	s0894	NOUN
ap-7669	330	6	-	-	PUNCT
ap-7669	330	7	0347	0347	NUM
ap-7669	330	8	-	-	PUNCT
ap-7669	330	9	1991	1991	NUM
ap-7669	330	10	-	-	PUNCT
ap-7669	330	11	1086966	1086966	NUM
ap-7669	330	12	-	-	SYM
ap-7669	330	13	0	0	NUM
ap-7669	330	14	.	.	NOUN
ap-7669	330	15	196	196	NUM
ap-7669	330	16	https://doi.org/10.1103/physrevd.88.044045	https://doi.org/10.1103/physrevd.88.044045	NOUN
ap-7669	330	17	https://doi.org/10.1088/1751-8113/47/5/052001	https://doi.org/10.1088/1751-8113/47/5/052001	PROPN
ap-7669	330	18	https://doi.org/10.1016/j.physleta.2020.127104	https://doi.org/10.1016/j.physleta.2020.127104	NOUN
ap-7669	331	1	https://doi.org/10.1103/physrevlett.128.041301	https://doi.org/10.1103/physrevlett.128.041301	PROPN
ap-7669	331	2	http://arxiv.org/abs/2110.11175	http://arxiv.org/abs/2110.11175	NOUN
ap-7669	331	3	https://doi.org/10.1016/s0377-0427(02)00589-7	https://doi.org/10.1016/s0377-0427(02)00589-7	PROPN
ap-7669	331	4	https://doi.org/10.1090/s0894-0347-1991-1086966-0	https://doi.org/10.1090/s0894-0347-1991-1086966-0	PROPN
ap-7669	331	5	https://doi.org/10.1090/s0894-0347-1991-1086966-0	https://doi.org/10.1090/s0894-0347-1991-1086966-0	PROPN
ap-7669	331	6	acta	acta	PROPN
ap-7669	331	7	polytechnica	polytechnica	PROPN
ap-7669	331	8	62(1):190–196	62(1):190–196	PROPN
ap-7669	331	9	,	,	PUNCT
ap-7669	331	10	2022	2022	NUM
ap-7669	331	11	1	1	NUM
ap-7669	331	12	introduction	introduction	NOUN
ap-7669	331	13	2	2	NUM
ap-7669	331	14	spatial	spatial	ADJ
ap-7669	331	15	dynamics	dynamic	NOUN
ap-7669	331	16	of	of	ADP
ap-7669	331	17	kdv	kdv	NOUN
ap-7669	331	18	and	and	CCONJ
ap-7669	331	19	mkdv	mkdv	VERB
ap-7669	331	20	equations	equation	NOUN
ap-7669	331	21	3	3	NUM
ap-7669	331	22	discrete	discrete	ADJ
ap-7669	331	23	models	model	NOUN
ap-7669	331	24	with	with	ADP
ap-7669	331	25	benign	benign	ADJ
ap-7669	331	26	ghosts	ghost	NOUN
ap-7669	331	27	acknowledgements	acknowledgement	NOUN
ap-7669	331	28	references	reference	NOUN