id	sid	tid	token	lemma	pos
cana-4665	1	1	optical	optical	ADJ
cana-4665	1	2	solitons	soliton	NOUN
cana-4665	1	3	and	and	CCONJ
cana-4665	1	4	lie	lie	NOUN
cana-4665	1	5	symmetry	symmetry	NOUN
cana-4665	1	6	analysis	analysis	NOUN
cana-4665	1	7	of	of	ADP
cana-4665	1	8	kaup	kaup	PROPN
cana-4665	1	9	–	–	PUNCT
cana-4665	1	10	newell	newell	NOUN
cana-4665	1	11	equation	equation	NOUN
cana-4665	1	12	arshdeep	arshdeep	NOUN
cana-4665	1	13	kaur1	kaur1	PROPN
cana-4665	1	14	,	,	PUNCT
cana-4665	1	15	anupma	anupma	PROPN
cana-4665	1	16	bansal2	bansal2	PROPN
cana-4665	1	17	,	,	PUNCT
cana-4665	1	18	rajeev	rajeev	PROPN
cana-4665	1	19	budhiraja3	budhiraja3	PROPN
cana-4665	2	1	1,3department	1,3department	NUM
cana-4665	2	2	of	of	ADP
cana-4665	2	3	mathematics	mathematic	NOUN
cana-4665	2	4	mmec	mmec	NOUN
cana-4665	2	5	,	,	PUNCT
cana-4665	2	6	maharishi	maharishi	PROPN
cana-4665	2	7	markandeshwar	markandeshwar	NOUN
cana-4665	2	8	(	(	PUNCT
cana-4665	2	9	deemed	deem	VERB
cana-4665	2	10	to	to	PART
cana-4665	2	11	be	be	AUX
cana-4665	2	12	university	university	NOUN
cana-4665	2	13	)	)	PUNCT
cana-4665	2	14	mullana	mullana	PROPN
cana-4665	2	15	,	,	PUNCT
cana-4665	2	16	ambala-133203	ambala-133203	PROPN
cana-4665	2	17	(	(	PUNCT
cana-4665	2	18	haryana	haryana	PROPN
cana-4665	2	19	)	)	PUNCT
cana-4665	2	20	,	,	PUNCT
cana-4665	2	21	india	india	PROPN
cana-4665	2	22	e	e	PROPN
cana-4665	2	23	-	-	NOUN
cana-4665	2	24	mail	mail	NOUN
cana-4665	2	25	:	:	PUNCT
cana-4665	3	1	dhimanarshdeep500@gmail.com	dhimanarshdeep500@gmail.com	PROPN
cana-4665	3	2	2department	2department	NUM
cana-4665	3	3	of	of	ADP
cana-4665	3	4	mathematics	mathematics	PROPN
cana-4665	3	5	d.a.v	d.a.v	NOUN
cana-4665	3	6	.	.	PUNCT
cana-4665	4	1	college	college	NOUN
cana-4665	4	2	for	for	ADP
cana-4665	4	3	women	woman	NOUN
cana-4665	4	4	,	,	PUNCT
cana-4665	4	5	ferozepur-152001(punjab	ferozepur-152001(punjab	ADJ
cana-4665	4	6	)	)	PUNCT
cana-4665	4	7	,	,	PUNCT
cana-4665	4	8	india	india	PROPN
cana-4665	4	9	.	.	PUNCT
cana-4665	5	1	e	e	X
cana-4665	5	2	-	-	NOUN
cana-4665	5	3	mail	mail	NOUN
cana-4665	5	4	:	:	PUNCT
cana-4665	5	5	anupma2512@yahoo.co.in	anupma2512@yahoo.co.in	ADJ
cana-4665	5	6	abstract	abstract	ADV
cana-4665	5	7	this	this	DET
cana-4665	5	8	manuscript	manuscript	NOUN
cana-4665	5	9	is	be	AUX
cana-4665	5	10	based	base	VERB
cana-4665	5	11	on	on	ADP
cana-4665	5	12	the	the	DET
cana-4665	5	13	kaup	kaup	PROPN
cana-4665	5	14	-	-	PROPN
cana-4665	5	15	newell	newell	PROPN
cana-4665	5	16	equation	equation	NOUN
cana-4665	5	17	,	,	PUNCT
cana-4665	5	18	specifically	specifically	ADV
cana-4665	5	19	contemplated	contemplate	VERB
cana-4665	5	20	to	to	PART
cana-4665	5	21	be	be	AUX
cana-4665	5	22	a	a	DET
cana-4665	5	23	kind	kind	NOUN
cana-4665	5	24	of	of	ADP
cana-4665	5	25	nonlinear	nonlinear	ADJ
cana-4665	5	26	schrödinger	schrödinger	NOUN
cana-4665	5	27	equation	equation	NOUN
cana-4665	5	28	.	.	PUNCT
cana-4665	6	1	one	one	NUM
cana-4665	6	2	of	of	ADP
cana-4665	6	3	the	the	DET
cana-4665	6	4	frameworks	framework	NOUN
cana-4665	6	5	derived	derive	VERB
cana-4665	6	6	from	from	ADP
cana-4665	6	7	the	the	DET
cana-4665	6	8	well	well	ADV
cana-4665	6	9	-	-	PUNCT
cana-4665	6	10	known	know	VERB
cana-4665	6	11	nonlinear	nonlinear	NOUN
cana-4665	6	12	schrödinger	schrödinger	NOUN
cana-4665	6	13	equation	equation	NOUN
cana-4665	6	14	is	be	AUX
cana-4665	6	15	the	the	DET
cana-4665	6	16	kaup	kaup	PROPN
cana-4665	6	17	–	–	PUNCT
cana-4665	6	18	newell	newell	PROPN
cana-4665	6	19	equation	equation	NOUN
cana-4665	6	20	which	which	PRON
cana-4665	6	21	is	be	AUX
cana-4665	6	22	one	one	NUM
cana-4665	6	23	of	of	ADP
cana-4665	6	24	the	the	DET
cana-4665	6	25	three	three	NUM
cana-4665	6	26	derivative	derivative	ADJ
cana-4665	6	27	forms	form	NOUN
cana-4665	6	28	of	of	ADP
cana-4665	6	29	the	the	DET
cana-4665	6	30	nonlinear	nonlinear	ADJ
cana-4665	6	31	schrödinger	schrödinger	NOUN
cana-4665	6	32	equation	equation	NOUN
cana-4665	6	33	that	that	PRON
cana-4665	6	34	is	be	AUX
cana-4665	6	35	frequently	frequently	ADV
cana-4665	6	36	explored	explore	VERB
cana-4665	6	37	in	in	ADP
cana-4665	6	38	nonlinear	nonlinear	ADJ
cana-4665	6	39	optics	optic	NOUN
cana-4665	6	40	.	.	PUNCT
cana-4665	7	1	a	a	DET
cana-4665	7	2	systematic	systematic	ADJ
cana-4665	7	3	investigation	investigation	NOUN
cana-4665	7	4	of	of	ADP
cana-4665	7	5	lie	lie	NOUN
cana-4665	7	6	symmetry	symmetry	NOUN
cana-4665	7	7	method	method	NOUN
cana-4665	7	8	is	be	AUX
cana-4665	7	9	pertained	pertain	VERB
cana-4665	7	10	to	to	PART
cana-4665	7	11	derive	derive	VERB
cana-4665	7	12	the	the	DET
cana-4665	7	13	symmetry	symmetry	NOUN
cana-4665	7	14	reductions	reduction	NOUN
cana-4665	7	15	of	of	ADP
cana-4665	7	16	the	the	DET
cana-4665	7	17	given	give	VERB
cana-4665	7	18	equation	equation	NOUN
cana-4665	7	19	.	.	PUNCT
cana-4665	8	1	by	by	ADP
cana-4665	8	2	utilizing	utilize	VERB
cana-4665	8	3	these	these	DET
cana-4665	8	4	symmetry	symmetry	NOUN
cana-4665	8	5	reductions	reduction	NOUN
cana-4665	8	6	,	,	PUNCT
cana-4665	8	7	the	the	DET
cana-4665	8	8	nonlinear	nonlinear	ADJ
cana-4665	8	9	partial	partial	ADJ
cana-4665	8	10	differential	differential	NOUN
cana-4665	8	11	equation	equation	NOUN
cana-4665	8	12	are	be	AUX
cana-4665	8	13	transformed	transform	VERB
cana-4665	8	14	into	into	ADP
cana-4665	8	15	the	the	DET
cana-4665	8	16	ordinary	ordinary	ADJ
cana-4665	8	17	differential	differential	ADJ
cana-4665	8	18	equations	equation	NOUN
cana-4665	8	19	.	.	PUNCT
cana-4665	9	1	consequently	consequently	ADV
cana-4665	9	2	,	,	PUNCT
cana-4665	9	3	the	the	DET
cana-4665	9	4	solutions	solution	NOUN
cana-4665	9	5	are	be	AUX
cana-4665	9	6	obtained	obtain	VERB
cana-4665	9	7	with	with	ADP
cana-4665	9	8	arbitrary	arbitrary	ADJ
cana-4665	9	9	parameters	parameter	NOUN
cana-4665	9	10	through	through	ADP
cana-4665	9	11	various	various	ADJ
cana-4665	9	12	methods	method	NOUN
cana-4665	9	13	which	which	PRON
cana-4665	9	14	are	be	AUX
cana-4665	9	15	in	in	ADP
cana-4665	9	16	the	the	DET
cana-4665	9	17	form	form	NOUN
cana-4665	9	18	of	of	ADP
cana-4665	9	19	hyperbolic	hyperbolic	ADJ
cana-4665	9	20	functions	function	NOUN
cana-4665	9	21	,	,	PUNCT
cana-4665	9	22	rational	rational	ADJ
cana-4665	9	23	functions	function	NOUN
cana-4665	9	24	and	and	CCONJ
cana-4665	9	25	trigonometric	trigonometric	ADJ
cana-4665	9	26	functions	function	NOUN
cana-4665	9	27	.	.	PUNCT
cana-4665	10	1	keywords	keyword	NOUN
cana-4665	10	2	:	:	PUNCT
cana-4665	10	3	lie	lie	VERB
cana-4665	10	4	classical	classical	ADJ
cana-4665	10	5	method	method	NOUN
cana-4665	10	6	,	,	PUNCT
cana-4665	10	7	kaup	kaup	PROPN
cana-4665	10	8	–	–	PUNCT
cana-4665	10	9	newell	newell	PROPN
cana-4665	10	10	equation	equation	NOUN
cana-4665	10	11	,	,	PUNCT
cana-4665	10	12	g	g	NOUN
cana-4665	10	13	′	′	NUM
cana-4665	10	14	g	g	NOUN
cana-4665	10	15	–	–	PUNCT
cana-4665	10	16	expansion	expansion	NOUN
cana-4665	10	17	method	method	NOUN
cana-4665	10	18	,	,	PUNCT
cana-4665	10	19	symmetry	symmetry	NOUN
cana-4665	10	20	reductions	reduction	NOUN
cana-4665	10	21	,	,	PUNCT
cana-4665	10	22	optical	optical	ADJ
cana-4665	10	23	solitons	soliton	NOUN
cana-4665	10	24	.	.	PUNCT
cana-4665	11	1	1	1	NUM
cana-4665	11	2	introduction	introduction	NOUN
cana-4665	11	3	the	the	DET
cana-4665	11	4	schrödinger	schrödinger	NOUN
cana-4665	11	5	equation	equation	NOUN
cana-4665	11	6	is	be	AUX
cana-4665	11	7	a	a	DET
cana-4665	11	8	core	core	NOUN
cana-4665	11	9	concept	concept	NOUN
cana-4665	11	10	in	in	ADP
cana-4665	11	11	quantum	quantum	ADJ
cana-4665	11	12	mechanics	mechanic	NOUN
cana-4665	11	13	with	with	ADP
cana-4665	11	14	widespread	widespread	ADJ
cana-4665	11	15	applications	application	NOUN
cana-4665	11	16	in	in	ADP
cana-4665	11	17	different	different	ADJ
cana-4665	11	18	areas	area	NOUN
cana-4665	11	19	.	.	PUNCT
cana-4665	12	1	this	this	DET
cana-4665	12	2	equation	equation	NOUN
cana-4665	12	3	is	be	AUX
cana-4665	12	4	referred	refer	VERB
cana-4665	12	5	as	as	ADP
cana-4665	12	6	a	a	DET
cana-4665	12	7	partial	partial	ADJ
cana-4665	12	8	differential	differential	NOUN
cana-4665	12	9	equation	equation	NOUN
cana-4665	12	10	that	that	PRON
cana-4665	12	11	describes	describe	VERB
cana-4665	12	12	wave	wave	NOUN
cana-4665	12	13	function	function	NOUN
cana-4665	12	14	of	of	ADP
cana-4665	12	15	physical	physical	ADJ
cana-4665	12	16	systems	system	NOUN
cana-4665	12	17	like	like	ADP
cana-4665	12	18	fluid	fluid	NOUN
cana-4665	12	19	dynamics	dynamic	NOUN
cana-4665	12	20	,	,	PUNCT
cana-4665	12	21	waves	wave	NOUN
cana-4665	12	22	in	in	ADP
cana-4665	12	23	water	water	NOUN
cana-4665	12	24	,	,	PUNCT
cana-4665	12	25	etc	etc	X
cana-4665	12	26	.	.	X
cana-4665	12	27	optical	optical	ADJ
cana-4665	12	28	outcomes	outcome	NOUN
cana-4665	12	29	[	[	X
cana-4665	12	30	1	1	NUM
cana-4665	12	31	-	-	SYM
cana-4665	12	32	5	5	NUM
cana-4665	12	33	]	]	PUNCT
cana-4665	12	34	of	of	ADP
cana-4665	12	35	nonlinear	nonlinear	ADJ
cana-4665	12	36	schrödinger	schrödinger	NOUN
cana-4665	12	37	equation	equation	NOUN
cana-4665	12	38	are	be	AUX
cana-4665	12	39	fundamental	fundamental	ADJ
cana-4665	12	40	solutions	solution	NOUN
cana-4665	12	41	to	to	PART
cana-4665	12	42	design	design	VERB
cana-4665	12	43	the	the	DET
cana-4665	12	44	high	high	ADJ
cana-4665	12	45	-	-	PUNCT
cana-4665	12	46	performance	performance	NOUN
cana-4665	12	47	communication	communication	NOUN
cana-4665	12	48	systems	system	NOUN
cana-4665	12	49	,	,	PUNCT
cana-4665	12	50	understanding	understand	VERB
cana-4665	12	51	wave	wave	NOUN
cana-4665	12	52	interactions	interaction	NOUN
cana-4665	12	53	in	in	ADP
cana-4665	12	54	nonlinear	nonlinear	ADJ
cana-4665	12	55	media	medium	NOUN
cana-4665	12	56	and	and	CCONJ
cana-4665	12	57	pushing	push	VERB
cana-4665	12	58	forward	forward	ADP
cana-4665	12	59	technologies	technology	NOUN
cana-4665	12	60	such	such	ADJ
cana-4665	12	61	as	as	ADP
cana-4665	12	62	super	super	ADJ
cana-4665	12	63	continuum	continuum	ADJ
cana-4665	12	64	generation	generation	NOUN
cana-4665	12	65	and	and	CCONJ
cana-4665	12	66	pulse	pulse	NOUN
cana-4665	12	67	compression	compression	NOUN
cana-4665	12	68	.	.	PUNCT
cana-4665	13	1	in	in	ADP
cana-4665	13	2	this	this	DET
cana-4665	13	3	direction	direction	NOUN
cana-4665	13	4	,	,	PUNCT
cana-4665	13	5	exact	exact	ADJ
cana-4665	13	6	traveling	traveling	ADJ
cana-4665	13	7	wave	wave	NOUN
cana-4665	13	8	solutions	solution	NOUN
cana-4665	13	9	are	be	AUX
cana-4665	13	10	key	key	ADJ
cana-4665	13	11	to	to	ADP
cana-4665	13	12	grasping	grasp	VERB
cana-4665	13	13	wave	wave	NOUN
cana-4665	13	14	dynamics	dynamic	NOUN
cana-4665	13	15	in	in	ADP
cana-4665	13	16	nonlinear	nonlinear	ADJ
cana-4665	13	17	media	medium	NOUN
cana-4665	13	18	,	,	PUNCT
cana-4665	13	19	influencing	influence	VERB
cana-4665	13	20	fields	field	NOUN
cana-4665	13	21	such	such	ADJ
cana-4665	13	22	as	as	ADP
cana-4665	13	23	optics	optic	NOUN
cana-4665	13	24	,	,	PUNCT
cana-4665	13	25	fluid	fluid	ADJ
cana-4665	13	26	dynamics	dynamic	NOUN
cana-4665	13	27	and	and	CCONJ
cana-4665	13	28	more	more	ADJ
cana-4665	13	29	.	.	PUNCT
cana-4665	14	1	they	they	PRON
cana-4665	14	2	provide	provide	VERB
cana-4665	14	3	insights	insight	NOUN
cana-4665	14	4	into	into	ADP
cana-4665	14	5	pulse	pulse	NOUN
cana-4665	14	6	behavior	behavior	NOUN
cana-4665	14	7	in	in	ADP
cana-4665	14	8	optical	optical	ADJ
cana-4665	14	9	fibers	fiber	NOUN
cana-4665	14	10	and	and	CCONJ
cana-4665	14	11	other	other	ADJ
cana-4665	14	12	nonlinear	nonlinear	ADJ
cana-4665	14	13	systems	system	NOUN
cana-4665	14	14	.	.	PUNCT
cana-4665	15	1	communications	communication	NOUN
cana-4665	15	2	on	on	ADP
cana-4665	15	3	applied	apply	VERB
cana-4665	15	4	nonlinear	nonlinear	ADJ
cana-4665	15	5	analysis	analysis	NOUN
cana-4665	15	6	issn	issn	NOUN
cana-4665	15	7	:	:	PUNCT
cana-4665	15	8	1074	1074	NUM
cana-4665	15	9	-	-	PUNCT
cana-4665	15	10	133x	133x	NUM
cana-4665	15	11	vol	vol	VERB
cana-4665	15	12	32	32	NUM
cana-4665	15	13	no	no	NOUN
cana-4665	15	14	.	.	PUNCT
cana-4665	16	1	10s	10	NOUN
cana-4665	16	2	(	(	PUNCT
cana-4665	16	3	2025	2025	NUM
cana-4665	16	4	)	)	PUNCT
cana-4665	16	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-4665	16	6	89	89	NUM
cana-4665	16	7	article	article	NOUN
cana-4665	16	8	history	history	NOUN
cana-4665	16	9	:	:	PUNCT
cana-4665	16	10	received	receive	VERB
cana-4665	16	11	:	:	PUNCT
cana-4665	16	12	12	12	NUM
cana-4665	16	13	-	-	SYM
cana-4665	16	14	01	01	NUM
cana-4665	16	15	-	-	PUNCT
cana-4665	16	16	2025	2025	NUM
cana-4665	16	17	,	,	PUNCT
cana-4665	16	18	revised	revise	VERB
cana-4665	16	19	:	:	PUNCT
cana-4665	16	20	15	15	NUM
cana-4665	16	21	-	-	NUM
cana-4665	16	22	02	02	NUM
cana-4665	16	23	-	-	PUNCT
cana-4665	16	24	2025	2025	NUM
cana-4665	16	25	,	,	PUNCT
cana-4665	16	26	accepted	accept	VERB
cana-4665	16	27	:	:	PUNCT
cana-4665	16	28	01	01	NUM
cana-4665	16	29	-	-	SYM
cana-4665	16	30	03	03	NUM
cana-4665	16	31	-	-	PUNCT
cana-4665	16	32	2025	2025	NUM
cana-4665	16	33	thereby	thereby	ADV
cana-4665	16	34	,	,	PUNCT
cana-4665	16	35	in	in	ADP
cana-4665	16	36	this	this	DET
cana-4665	16	37	supervision	supervision	NOUN
cana-4665	16	38	,	,	PUNCT
cana-4665	16	39	multivarious	multivarious	ADJ
cana-4665	16	40	adequate	adequate	ADJ
cana-4665	16	41	methods	method	NOUN
cana-4665	16	42	for	for	ADP
cana-4665	16	43	finding	find	VERB
cana-4665	16	44	out	out	ADP
cana-4665	16	45	accurate	accurate	ADJ
cana-4665	16	46	and	and	CCONJ
cana-4665	16	47	exact	exact	ADJ
cana-4665	16	48	solutions	solution	NOUN
cana-4665	16	49	to	to	ADP
cana-4665	16	50	the	the	DET
cana-4665	16	51	schrödinger	schrödinger	NOUN
cana-4665	16	52	equation	equation	NOUN
cana-4665	16	53	are	be	AUX
cana-4665	16	54	determined	determine	VERB
cana-4665	16	55	and	and	CCONJ
cana-4665	16	56	evolved	evolve	VERB
cana-4665	16	57	in	in	ADP
cana-4665	16	58	the	the	DET
cana-4665	16	59	course	course	NOUN
cana-4665	16	60	of	of	ADP
cana-4665	16	61	the	the	DET
cana-4665	16	62	numerous	numerous	ADJ
cana-4665	16	63	former	former	ADJ
cana-4665	16	64	decades	decade	NOUN
cana-4665	16	65	.	.	PUNCT
cana-4665	17	1	besides	besides	SCONJ
cana-4665	17	2	the	the	DET
cana-4665	17	3	assorted	assorted	ADJ
cana-4665	17	4	distinct	distinct	ADJ
cana-4665	17	5	methods	method	NOUN
cana-4665	17	6	,	,	PUNCT
cana-4665	17	7	lie	lie	NOUN
cana-4665	17	8	group	group	NOUN
cana-4665	17	9	method	method	NOUN
cana-4665	17	10	,	,	PUNCT
cana-4665	17	11	also	also	ADV
cana-4665	17	12	stated	state	VERB
cana-4665	17	13	as	as	ADP
cana-4665	17	14	lie	lie	NOUN
cana-4665	17	15	symmetry	symmetry	NOUN
cana-4665	17	16	method	method	NOUN
cana-4665	17	17	[	[	X
cana-4665	17	18	11	11	NUM
cana-4665	17	19	-	-	SYM
cana-4665	17	20	20	20	NUM
cana-4665	17	21	]	]	PUNCT
cana-4665	17	22	,	,	PUNCT
cana-4665	17	23	is	be	AUX
cana-4665	17	24	apparently	apparently	ADV
cana-4665	17	25	a	a	DET
cana-4665	17	26	significant	significant	ADJ
cana-4665	17	27	method	method	NOUN
cana-4665	17	28	to	to	PART
cana-4665	17	29	calculate	calculate	VERB
cana-4665	17	30	the	the	DET
cana-4665	17	31	solutions	solution	NOUN
cana-4665	17	32	of	of	ADP
cana-4665	17	33	nonlinear	nonlinear	ADJ
cana-4665	17	34	partial	partial	ADJ
cana-4665	17	35	differential	differential	NOUN
cana-4665	17	36	equations	equation	NOUN
cana-4665	17	37	.	.	PUNCT
cana-4665	18	1	the	the	DET
cana-4665	18	2	lie	lie	NOUN
cana-4665	18	3	symmetry	symmetry	NOUN
cana-4665	18	4	methodology	methodology	NOUN
cana-4665	18	5	is	be	AUX
cana-4665	18	6	smoothly	smoothly	ADV
cana-4665	18	7	appertained	appertain	VERB
cana-4665	18	8	to	to	ADP
cana-4665	18	9	many	many	ADJ
cana-4665	18	10	physical	physical	ADJ
cana-4665	18	11	and	and	CCONJ
cana-4665	18	12	engineering	engineering	NOUN
cana-4665	18	13	methods	method	NOUN
cana-4665	18	14	.	.	PUNCT
cana-4665	19	1	under	under	ADP
cana-4665	19	2	the	the	DET
cana-4665	19	3	lie	lie	NOUN
cana-4665	19	4	group	group	NOUN
cana-4665	19	5	of	of	ADP
cana-4665	19	6	point	point	NOUN
cana-4665	19	7	transformations	transformation	NOUN
cana-4665	19	8	when	when	SCONJ
cana-4665	19	9	particular	particular	ADJ
cana-4665	19	10	differential	differential	ADJ
cana-4665	19	11	equations	equation	NOUN
cana-4665	19	12	are	be	AUX
cana-4665	19	13	invariant	invariant	ADJ
cana-4665	19	14	then	then	ADV
cana-4665	19	15	reduction	reduction	NOUN
cana-4665	19	16	exists	exist	VERB
cana-4665	19	17	.	.	PUNCT
cana-4665	20	1	by	by	ADP
cana-4665	20	2	utilizing	utilize	VERB
cana-4665	20	3	these	these	DET
cana-4665	20	4	symmetry	symmetry	NOUN
cana-4665	20	5	reductions	reduction	NOUN
cana-4665	20	6	,	,	PUNCT
cana-4665	20	7	the	the	DET
cana-4665	20	8	nonlinear	nonlinear	ADJ
cana-4665	20	9	partial	partial	ADJ
cana-4665	20	10	differential	differential	NOUN
cana-4665	20	11	equations	equation	NOUN
cana-4665	20	12	are	be	AUX
cana-4665	20	13	transformed	transform	VERB
cana-4665	20	14	into	into	ADP
cana-4665	20	15	ordinary	ordinary	ADJ
cana-4665	20	16	differential	differential	ADJ
cana-4665	20	17	equations	equation	NOUN
cana-4665	20	18	.	.	PUNCT
cana-4665	21	1	then	then	ADV
cana-4665	21	2	employing	employ	VERB
cana-4665	21	3	various	various	ADJ
cana-4665	21	4	methods	method	NOUN
cana-4665	21	5	and	and	CCONJ
cana-4665	21	6	techniques	technique	NOUN
cana-4665	21	7	exact	exact	ADJ
cana-4665	21	8	traveling	travel	VERB
cana-4665	21	9	wave	wave	NOUN
cana-4665	21	10	solutions	solution	NOUN
cana-4665	21	11	are	be	AUX
cana-4665	21	12	accumulated	accumulate	VERB
cana-4665	21	13	.	.	PUNCT
cana-4665	22	1	1.1	1.1	NUM
cana-4665	22	2	governing	governing	NOUN
cana-4665	22	3	model	model	NOUN
cana-4665	22	4	the	the	DET
cana-4665	22	5	kaup	kaup	PROPN
cana-4665	22	6	–	–	PUNCT
cana-4665	22	7	newell	newell	PROPN
cana-4665	22	8	equation	equation	NOUN
cana-4665	22	9	is	be	AUX
cana-4665	22	10	given	give	VERB
cana-4665	22	11	by	by	ADP
cana-4665	22	12	:	:	PUNCT
cana-4665	22	13	qt	qt	NOUN
cana-4665	22	14	+	+	CCONJ
cana-4665	22	15	ιaqxx	ιaqxx	PROPN
cana-4665	22	16	+	+	CCONJ
cana-4665	22	17	b(|q|2q)x	b(|q|2q)x	NOUN
cana-4665	22	18	=	=	SYM
cana-4665	22	19	0	0	NUM
cana-4665	22	20	,	,	PUNCT
cana-4665	22	21	(	(	PUNCT
cana-4665	22	22	1.1	1.1	NUM
cana-4665	22	23	)	)	PUNCT
cana-4665	22	24	where	where	SCONJ
cana-4665	22	25	‘	'	PUNCT
cana-4665	22	26	q(x	q(x	PROPN
cana-4665	22	27	,	,	PUNCT
cana-4665	22	28	t)′	t)′	PROPN
cana-4665	22	29	is	be	AUX
cana-4665	22	30	a	a	DET
cana-4665	22	31	complex	complex	ADV
cana-4665	22	32	-	-	PUNCT
cana-4665	22	33	valued	value	VERB
cana-4665	22	34	function	function	NOUN
cana-4665	22	35	,	,	PUNCT
cana-4665	22	36	‘	'	PUNCT
cana-4665	22	37	a′	a′	PROPN
cana-4665	22	38	demonstrates	demonstrate	VERB
cana-4665	22	39	velocity	velocity	NOUN
cana-4665	22	40	dispersion	dispersion	NOUN
cana-4665	22	41	parameter	parameter	NOUN
cana-4665	22	42	,	,	PUNCT
cana-4665	22	43	‘	'	PUNCT
cana-4665	22	44	b′	b′	NUM
cana-4665	22	45	the	the	DET
cana-4665	22	46	nonlinearity	nonlinearity	NOUN
cana-4665	22	47	coefficient	coefficient	NOUN
cana-4665	22	48	.	.	PUNCT
cana-4665	23	1	the	the	DET
cana-4665	23	2	kaup	kaup	PROPN
cana-4665	23	3	-	-	PUNCT
cana-4665	23	4	newell	newell	PROPN
cana-4665	23	5	equation	equation	NOUN
cana-4665	23	6	is	be	AUX
cana-4665	23	7	a	a	DET
cana-4665	23	8	specific	specific	ADJ
cana-4665	23	9	type	type	NOUN
cana-4665	23	10	of	of	ADP
cana-4665	23	11	nonlinear	nonlinear	ADJ
cana-4665	23	12	partial	partial	ADJ
cana-4665	23	13	differential	differential	NOUN
cana-4665	23	14	equation	equation	NOUN
cana-4665	23	15	derived	derive	VERB
cana-4665	23	16	from	from	ADP
cana-4665	23	17	the	the	DET
cana-4665	23	18	nonlinear	nonlinear	ADJ
cana-4665	23	19	schrödinger	schrödinger	NOUN
cana-4665	23	20	equation	equation	NOUN
cana-4665	23	21	.	.	PUNCT
cana-4665	24	1	it	it	PRON
cana-4665	24	2	describes	describe	VERB
cana-4665	24	3	wave	wave	NOUN
cana-4665	24	4	phenomena	phenomenon	NOUN
cana-4665	24	5	and	and	CCONJ
cana-4665	24	6	is	be	AUX
cana-4665	24	7	particularly	particularly	ADV
cana-4665	24	8	relevant	relevant	ADJ
cana-4665	24	9	in	in	ADP
cana-4665	24	10	field	field	NOUN
cana-4665	24	11	such	such	ADJ
cana-4665	24	12	as	as	ADP
cana-4665	24	13	plasma	plasma	NOUN
cana-4665	24	14	physics	physic	NOUN
cana-4665	24	15	and	and	CCONJ
cana-4665	24	16	optics	optic	NOUN
cana-4665	24	17	.	.	PUNCT
cana-4665	25	1	the	the	DET
cana-4665	25	2	kaup	kaup	PROPN
cana-4665	25	3	-	-	PROPN
cana-4665	25	4	newell	newell	PROPN
cana-4665	25	5	equation	equation	NOUN
cana-4665	25	6	can	can	AUX
cana-4665	25	7	model	model	VERB
cana-4665	25	8	various	various	ADJ
cana-4665	25	9	physical	physical	ADJ
cana-4665	25	10	situations	situation	NOUN
cana-4665	25	11	involving	involve	VERB
cana-4665	25	12	stability	stability	NOUN
cana-4665	25	13	,	,	PUNCT
cana-4665	25	14	interactions	interaction	NOUN
cana-4665	25	15	and	and	CCONJ
cana-4665	25	16	soliton	soliton	NOUN
cana-4665	25	17	solutions	solution	NOUN
cana-4665	25	18	.	.	PUNCT
cana-4665	26	1	2	2	NUM
cana-4665	26	2	lie	lie	NOUN
cana-4665	26	3	symmetry	symmetry	NOUN
cana-4665	26	4	analysis	analysis	NOUN
cana-4665	26	5	recently	recently	ADV
cana-4665	26	6	,	,	PUNCT
cana-4665	26	7	symmetry	symmetry	NOUN
cana-4665	26	8	analysis	analysis	NOUN
cana-4665	26	9	has	have	AUX
cana-4665	26	10	become	become	VERB
cana-4665	26	11	popular	popular	ADJ
cana-4665	26	12	for	for	ADP
cana-4665	26	13	studying	study	VERB
cana-4665	26	14	differential	differential	ADJ
cana-4665	26	15	equations	equation	NOUN
cana-4665	26	16	.	.	PUNCT
cana-4665	27	1	lie	lie	PROPN
cana-4665	27	2	symmetry	symmetry	NOUN
cana-4665	27	3	analysis	analysis	NOUN
cana-4665	27	4	is	be	AUX
cana-4665	27	5	the	the	DET
cana-4665	27	6	most	most	ADV
cana-4665	27	7	effective	effective	ADJ
cana-4665	27	8	method	method	NOUN
cana-4665	27	9	for	for	ADP
cana-4665	27	10	evaluating	evaluate	VERB
cana-4665	27	11	the	the	DET
cana-4665	27	12	precise	precise	ADJ
cana-4665	27	13	and	and	CCONJ
cana-4665	27	14	exact	exact	ADJ
cana-4665	27	15	solutions	solution	NOUN
cana-4665	27	16	of	of	ADP
cana-4665	27	17	nonlinear	nonlinear	ADJ
cana-4665	27	18	partial	partial	ADJ
cana-4665	27	19	differential	differential	NOUN
cana-4665	27	20	equations	equation	NOUN
cana-4665	27	21	.	.	PUNCT
cana-4665	28	1	in	in	ADP
cana-4665	28	2	this	this	DET
cana-4665	28	3	document	document	NOUN
cana-4665	28	4	,	,	PUNCT
cana-4665	28	5	we	we	PRON
cana-4665	28	6	procure	procure	VERB
cana-4665	28	7	symmetry	symmetry	NOUN
cana-4665	28	8	reductions	reduction	NOUN
cana-4665	28	9	,	,	PUNCT
cana-4665	28	10	the	the	DET
cana-4665	28	11	symmetries	symmetry	NOUN
cana-4665	28	12	and	and	CCONJ
cana-4665	28	13	the	the	DET
cana-4665	28	14	solutions	solution	NOUN
cana-4665	28	15	of	of	ADP
cana-4665	28	16	kaup	kaup	PROPN
cana-4665	28	17	-	-	PROPN
cana-4665	28	18	newell	newell	PROPN
cana-4665	28	19	equation	equation	NOUN
cana-4665	28	20	[	[	X
cana-4665	28	21	6	6	NUM
cana-4665	28	22	-	-	SYM
cana-4665	28	23	10	10	NUM
cana-4665	28	24	]	]	PUNCT
cana-4665	28	25	by	by	ADP
cana-4665	28	26	emphasizing	emphasize	VERB
cana-4665	28	27	lie	lie	NOUN
cana-4665	28	28	classical	classical	ADJ
cana-4665	28	29	method	method	NOUN
cana-4665	28	30	.	.	PUNCT
cana-4665	29	1	to	to	PART
cana-4665	29	2	determine	determine	VERB
cana-4665	29	3	the	the	DET
cana-4665	29	4	symmetries	symmetry	NOUN
cana-4665	29	5	of	of	ADP
cana-4665	29	6	the	the	DET
cana-4665	29	7	kaup	kaup	PROPN
cana-4665	29	8	-	-	PROPN
cana-4665	29	9	newell	newell	PROPN
cana-4665	29	10	equation	equation	NOUN
cana-4665	29	11	,	,	PUNCT
cana-4665	29	12	firstly	firstly	ADV
cana-4665	29	13	we	we	PRON
cana-4665	29	14	consider	consider	VERB
cana-4665	29	15	the	the	DET
cana-4665	29	16	complex	complex	ADJ
cana-4665	29	17	function	function	NOUN
cana-4665	29	18	q(x	q(x	PROPN
cana-4665	29	19	,	,	PUNCT
cana-4665	29	20	t	t	PROPN
cana-4665	29	21	)	)	PUNCT
cana-4665	29	22	as	as	ADP
cana-4665	29	23	q(x	q(x	PROPN
cana-4665	29	24	,	,	PUNCT
cana-4665	29	25	t	t	PROPN
cana-4665	29	26	)	)	PUNCT
cana-4665	30	1	=	=	SYM
cana-4665	30	2	u(x	u(x	PROPN
cana-4665	30	3	,	,	PUNCT
cana-4665	30	4	t	t	PROPN
cana-4665	30	5	)	)	PUNCT
cana-4665	30	6	+	+	CCONJ
cana-4665	30	7	ιv(x	ιv(x	NUM
cana-4665	30	8	,	,	PUNCT
cana-4665	30	9	t	t	PROPN
cana-4665	30	10	)	)	PUNCT
cana-4665	30	11	.	.	PUNCT
cana-4665	31	1	(	(	PUNCT
cana-4665	31	2	2.1	2.1	NUM
cana-4665	31	3	)	)	PUNCT
cana-4665	31	4	the	the	DET
cana-4665	31	5	equation	equation	NOUN
cana-4665	31	6	can	can	AUX
cana-4665	31	7	be	be	AUX
cana-4665	31	8	expressed	express	VERB
cana-4665	31	9	in	in	ADP
cana-4665	31	10	terms	term	NOUN
cana-4665	31	11	of	of	ADP
cana-4665	31	12	its	its	PRON
cana-4665	31	13	real	real	ADJ
cana-4665	31	14	and	and	CCONJ
cana-4665	31	15	imaginary	imaginary	ADJ
cana-4665	31	16	components	component	NOUN
cana-4665	31	17	asut	asut	NOUN
cana-4665	31	18	−	−	PROPN
cana-4665	32	1	avxx	avxx	NOUN
cana-4665	33	1	+	+	CCONJ
cana-4665	34	1	2bu2ux	2bu2ux	NUM
cana-4665	34	2	+	+	CCONJ
cana-4665	34	3	2buvvx	2buvvx	NUM
cana-4665	34	4	+	+	NUM
cana-4665	34	5	bu2ux	bu2ux	NOUN
cana-4665	34	6	+	+	CCONJ
cana-4665	34	7	bv2ux	bv2ux	PROPN
cana-4665	34	8	=	=	SYM
cana-4665	34	9	0	0	NUM
cana-4665	34	10	,	,	PUNCT
cana-4665	34	11	(	(	PUNCT
cana-4665	34	12	2.2	2.2	NUM
cana-4665	34	13	)	)	PUNCT
cana-4665	34	14	vt	vt	NOUN
cana-4665	34	15	+	+	NUM
cana-4665	34	16	auxx	auxx	ADJ
cana-4665	34	17	+	+	CCONJ
cana-4665	34	18	2buvux	2buvux	NUM
cana-4665	35	1	+	+	SYM
cana-4665	35	2	2bv2vx	2bv2vx	NUM
cana-4665	35	3	+	+	CCONJ
cana-4665	35	4	bu2vx	bu2vx	ADV
cana-4665	35	5	+	+	CCONJ
cana-4665	35	6	bv2vx	bv2vx	NOUN
cana-4665	35	7	=	=	SYM
cana-4665	35	8	0	0	NUM
cana-4665	35	9	.	.	PUNCT
cana-4665	36	1	(	(	PUNCT
cana-4665	36	2	2.3	2.3	NUM
cana-4665	36	3	)	)	PUNCT
cana-4665	36	4	communications	communication	NOUN
cana-4665	36	5	on	on	ADP
cana-4665	36	6	applied	apply	VERB
cana-4665	36	7	nonlinear	nonlinear	ADJ
cana-4665	36	8	analysis	analysis	NOUN
cana-4665	36	9	issn	issn	NOUN
cana-4665	36	10	:	:	PUNCT
cana-4665	36	11	1074	1074	NUM
cana-4665	36	12	-	-	PUNCT
cana-4665	36	13	133x	133x	NUM
cana-4665	36	14	vol	vol	VERB
cana-4665	36	15	32	32	NUM
cana-4665	36	16	no	no	NOUN
cana-4665	36	17	.	.	PUNCT
cana-4665	37	1	10s	10	NOUN
cana-4665	37	2	(	(	PUNCT
cana-4665	37	3	2025	2025	NUM
cana-4665	37	4	)	)	PUNCT
cana-4665	37	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-4665	37	6	90	90	NUM
cana-4665	37	7	the	the	DET
cana-4665	37	8	one	one	NUM
cana-4665	37	9	parameter	parameter	NOUN
cana-4665	37	10	lie	lie	NOUN
cana-4665	37	11	group	group	NOUN
cana-4665	37	12	of	of	ADP
cana-4665	37	13	infinitesimal	infinitesimal	ADJ
cana-4665	37	14	transformations	transformation	NOUN
cana-4665	37	15	constitutes	constitute	VERB
cana-4665	37	16	as	as	ADP
cana-4665	37	17	aforementionedũ	aforementionedũ	NOUN
cana-4665	37	18	=	=	SYM
cana-4665	37	19	u+	u+	NOUN
cana-4665	37	20	εη(x	εη(x	PROPN
cana-4665	37	21	,	,	PUNCT
cana-4665	37	22	t	t	PROPN
cana-4665	37	23	,	,	PUNCT
cana-4665	37	24	u	u	NOUN
cana-4665	37	25	,	,	PUNCT
cana-4665	37	26	v	v	NOUN
cana-4665	37	27	)	)	PUNCT
cana-4665	38	1	+	+	NOUN
cana-4665	38	2	o(ε2	o(ε2	NOUN
cana-4665	38	3	)	)	PUNCT
cana-4665	38	4	,	,	PUNCT
cana-4665	38	5	ṽ	ṽ	PROPN
cana-4665	38	6	=	=	SYM
cana-4665	38	7	v	v	PROPN
cana-4665	38	8	+	+	CCONJ
cana-4665	38	9	εφ(x	εφ(x	PROPN
cana-4665	38	10	,	,	PUNCT
cana-4665	38	11	t	t	PROPN
cana-4665	38	12	,	,	PUNCT
cana-4665	38	13	u	u	NOUN
cana-4665	38	14	,	,	PUNCT
cana-4665	38	15	v	v	NOUN
cana-4665	38	16	)	)	PUNCT
cana-4665	39	1	+	+	NOUN
cana-4665	39	2	o(ε2	o(ε2	NOUN
cana-4665	39	3	)	)	PUNCT
cana-4665	39	4	,	,	PUNCT
cana-4665	39	5	x̃	x̃	PROPN
cana-4665	39	6	=	=	PUNCT
cana-4665	39	7	x+	x+	X
cana-4665	39	8	εξ(x	εξ(x	X
cana-4665	39	9	,	,	PUNCT
cana-4665	39	10	t	t	PROPN
cana-4665	39	11	,	,	PUNCT
cana-4665	39	12	u	u	NOUN
cana-4665	39	13	,	,	PUNCT
cana-4665	39	14	v	v	NOUN
cana-4665	39	15	)	)	PUNCT
cana-4665	39	16	+	+	NOUN
cana-4665	39	17	o(ε2	o(ε2	NOUN
cana-4665	39	18	)	)	PUNCT
cana-4665	39	19	,	,	PUNCT
cana-4665	39	20	t̃	t̃	PROPN
cana-4665	39	21	=	=	SYM
cana-4665	39	22	t+	t+	NOUN
cana-4665	39	23	ετ(x	ετ(x	NUM
cana-4665	39	24	,	,	PUNCT
cana-4665	39	25	t	t	PROPN
cana-4665	39	26	,	,	PUNCT
cana-4665	39	27	u	u	NOUN
cana-4665	39	28	,	,	PUNCT
cana-4665	39	29	v	v	NOUN
cana-4665	39	30	)	)	PUNCT
cana-4665	40	1	+	+	NOUN
cana-4665	40	2	o(ε2	o(ε2	NOUN
cana-4665	40	3	)	)	PUNCT
cana-4665	40	4	,	,	PUNCT
cana-4665	40	5	(	(	PUNCT
cana-4665	40	6	2.4	2.4	NUM
cana-4665	40	7	)	)	PUNCT
cana-4665	40	8	where	where	SCONJ
cana-4665	40	9	ε	ε	PROPN
cana-4665	40	10	is	be	AUX
cana-4665	40	11	group	group	NOUN
cana-4665	40	12	parameter	parameter	NOUN
cana-4665	40	13	.	.	PUNCT
cana-4665	41	1	applying	apply	VERB
cana-4665	41	2	these	these	DET
cana-4665	41	3	one	one	NUM
cana-4665	41	4	-	-	PUNCT
cana-4665	41	5	parameter	parameter	NOUN
cana-4665	41	6	lie	lie	NOUN
cana-4665	41	7	group	group	NOUN
cana-4665	41	8	of	of	ADP
cana-4665	41	9	infinitesimal	infinitesimal	ADJ
cana-4665	41	10	transformations	transformation	NOUN
cana-4665	41	11	,	,	PUNCT
cana-4665	41	12	we	we	PRON
cana-4665	41	13	obtain	obtain	VERB
cana-4665	41	14	the	the	DET
cana-4665	41	15	invariance	invariance	NOUN
cana-4665	41	16	condition	condition	NOUN
cana-4665	41	17	of	of	ADP
cana-4665	41	18	the	the	DET
cana-4665	41	19	equation	equation	NOUN
cana-4665	41	20	(	(	PUNCT
cana-4665	41	21	1.1	1.1	NUM
cana-4665	41	22	):	):	PUNCT
cana-4665	41	23	ηt	ηt	ADP
cana-4665	41	24	−	−	NOUN
cana-4665	41	25	aφxx	aφxx	ADJ
cana-4665	42	1	+	+	CCONJ
cana-4665	43	1	2bu2ηx	2bu2ηx	NUM
cana-4665	43	2	+	+	NUM
cana-4665	43	3	4buuxη	4buuxη	NUM
cana-4665	44	1	+	+	CCONJ
cana-4665	44	2	2buvxφ+	2buvxφ+	NUM
cana-4665	44	3	2buvφx	2buvφx	NUM
cana-4665	44	4	+	+	CCONJ
cana-4665	44	5	2bvvxη	2bvvxη	NUM
cana-4665	44	6	+	+	SYM
cana-4665	44	7	bu2ηx	bu2ηx	NOUN
cana-4665	44	8	+	+	CCONJ
cana-4665	44	9	2buuxη	2buuxη	NUM
cana-4665	45	1	+	+	PRON
cana-4665	45	2	bv2ηx	bv2ηx	NOUN
cana-4665	45	3	+	+	SYM
cana-4665	45	4	2bvuxφ	2bvuxφ	NUM
cana-4665	45	5	=	=	SYM
cana-4665	45	6	0	0	NUM
cana-4665	45	7	,	,	PUNCT
cana-4665	45	8	(	(	PUNCT
cana-4665	45	9	2.5	2.5	NUM
cana-4665	45	10	)	)	PUNCT
cana-4665	45	11	φt	φt	NOUN
cana-4665	45	12	+	+	CCONJ
cana-4665	45	13	aηxx	aηxx	NOUN
cana-4665	45	14	+	+	CCONJ
cana-4665	45	15	2buvηx	2buvηx	NUM
cana-4665	45	16	+	+	CCONJ
cana-4665	45	17	2buuxφ+	2buuxφ+	NUM
cana-4665	46	1	2bvuxη	2bvuxη	NUM
cana-4665	47	1	+	+	CCONJ
cana-4665	48	1	2bv2φx	2bv2φx	NUM
cana-4665	48	2	+	+	CCONJ
cana-4665	48	3	4bvvxφ+	4bvvxφ+	NUM
cana-4665	48	4	bu2φx	bu2φx	NOUN
cana-4665	48	5	+	+	CCONJ
cana-4665	48	6	2buvxη	2buvxη	NUM
cana-4665	48	7	+	+	ADJ
cana-4665	48	8	bv2φx	bv2φx	NOUN
cana-4665	48	9	+	+	CCONJ
cana-4665	48	10	2bvvxφ	2bvvxφ	NUM
cana-4665	48	11	=	=	SYM
cana-4665	48	12	0	0	NUM
cana-4665	48	13	,	,	PUNCT
cana-4665	48	14	(	(	PUNCT
cana-4665	48	15	2.6	2.6	NUM
cana-4665	48	16	)	)	PUNCT
cana-4665	48	17	the	the	DET
cana-4665	48	18	mentioned	mention	VERB
cana-4665	48	19	transformation	transformation	NOUN
cana-4665	48	20	abandons	abandon	VERB
cana-4665	48	21	the	the	DET
cana-4665	48	22	entire	entire	ADJ
cana-4665	48	23	set	set	NOUN
cana-4665	48	24	of	of	ADP
cana-4665	48	25	resolutions	resolution	NOUN
cana-4665	48	26	of	of	ADP
cana-4665	48	27	the	the	DET
cana-4665	48	28	equation	equation	NOUN
cana-4665	48	29	(	(	PUNCT
cana-4665	48	30	1.1	1.1	NUM
cana-4665	48	31	)	)	PUNCT
cana-4665	48	32	invariant	invariant	ADJ
cana-4665	48	33	and	and	CCONJ
cana-4665	48	34	brings	bring	VERB
cana-4665	48	35	about	about	ADP
cana-4665	48	36	an	an	DET
cana-4665	48	37	over	over	ADP
cana-4665	48	38	determined	determined	ADJ
cana-4665	48	39	linear	linear	NOUN
cana-4665	48	40	system	system	NOUN
cana-4665	48	41	of	of	ADP
cana-4665	48	42	equations	equation	NOUN
cana-4665	48	43	for	for	ADP
cana-4665	48	44	the	the	DET
cana-4665	48	45	infinitesimals	infinitesimal	NOUN
cana-4665	48	46	ξ(x	ξ(x	NOUN
cana-4665	48	47	,	,	PUNCT
cana-4665	48	48	t	t	PROPN
cana-4665	48	49	,	,	PUNCT
cana-4665	48	50	u	u	NOUN
cana-4665	48	51	,	,	PUNCT
cana-4665	48	52	v	v	NOUN
cana-4665	48	53	)	)	PUNCT
cana-4665	48	54	,	,	PUNCT
cana-4665	48	55	τ(x	τ(x	PROPN
cana-4665	48	56	,	,	PUNCT
cana-4665	48	57	t	t	PROPN
cana-4665	48	58	,	,	PUNCT
cana-4665	48	59	u	u	NOUN
cana-4665	48	60	,	,	PUNCT
cana-4665	48	61	v	v	NOUN
cana-4665	48	62	)	)	PUNCT
cana-4665	48	63	,	,	PUNCT
cana-4665	48	64	η(x	η(x	PROPN
cana-4665	48	65	,	,	PUNCT
cana-4665	48	66	t	t	PROPN
cana-4665	48	67	,	,	PUNCT
cana-4665	48	68	u	u	NOUN
cana-4665	48	69	,	,	PUNCT
cana-4665	48	70	v	v	NOUN
cana-4665	48	71	)	)	PUNCT
cana-4665	48	72	.	.	PUNCT
cana-4665	49	1	by	by	ADP
cana-4665	49	2	using	use	VERB
cana-4665	49	3	these	these	DET
cana-4665	49	4	values	value	NOUN
cana-4665	49	5	of	of	ADP
cana-4665	49	6	the	the	DET
cana-4665	49	7	infinitesimal	infinitesimal	ADJ
cana-4665	49	8	ηt	ηt	ADP
cana-4665	49	9	,	,	PUNCT
cana-4665	49	10	φt	φt	NOUN
cana-4665	49	11	,	,	PUNCT
cana-4665	49	12	ηx	ηx	ADJ
cana-4665	49	13	,	,	PUNCT
cana-4665	49	14	φx	φx	ADJ
cana-4665	49	15	,	,	PUNCT
cana-4665	49	16	ηxx	ηxx	NOUN
cana-4665	49	17	and	and	CCONJ
cana-4665	49	18	φxx	φxx	VERB
cana-4665	49	19	into	into	ADP
cana-4665	49	20	equation	equation	NOUN
cana-4665	49	21	(	(	PUNCT
cana-4665	49	22	2.5	2.5	NUM
cana-4665	49	23	)	)	PUNCT
cana-4665	49	24	and	and	CCONJ
cana-4665	49	25	(	(	PUNCT
cana-4665	49	26	2.6	2.6	NUM
cana-4665	49	27	)	)	PUNCT
cana-4665	49	28	,	,	PUNCT
cana-4665	49	29	we	we	PRON
cana-4665	49	30	equalize	equalize	VERB
cana-4665	49	31	the	the	DET
cana-4665	49	32	alike	alike	ADJ
cana-4665	49	33	powers	power	NOUN
cana-4665	49	34	of	of	ADP
cana-4665	49	35	differentials	differential	NOUN
cana-4665	49	36	to	to	ADP
cana-4665	49	37	0	0	NUM
cana-4665	49	38	.	.	PUNCT
cana-4665	50	1	after	after	ADP
cana-4665	50	2	this	this	PRON
cana-4665	50	3	,	,	PUNCT
cana-4665	50	4	we	we	PRON
cana-4665	50	5	will	will	AUX
cana-4665	50	6	be	be	AUX
cana-4665	50	7	able	able	ADJ
cana-4665	50	8	to	to	PART
cana-4665	50	9	pertain	pertain	VERB
cana-4665	50	10	the	the	DET
cana-4665	50	11	system	system	NOUN
cana-4665	50	12	of	of	ADP
cana-4665	50	13	determining	determine	VERB
cana-4665	50	14	equations	equation	NOUN
cana-4665	50	15	as	as	ADP
cana-4665	50	16	under	under	ADV
cana-4665	50	17	:	:	PUNCT
cana-4665	50	18	(	(	PUNCT
cana-4665	50	19	i	i	NOUN
cana-4665	50	20	)	)	PUNCT
cana-4665	50	21	τx	τx	PROPN
cana-4665	51	1	=	=	SYM
cana-4665	51	2	0	0	PROPN
cana-4665	51	3	,	,	PUNCT
cana-4665	51	4	τu	τu	ADP
cana-4665	51	5	=	=	NOUN
cana-4665	51	6	0	0	NUM
cana-4665	51	7	,	,	PUNCT
cana-4665	51	8	τv	τv	NOUN
cana-4665	51	9	=	=	SYM
cana-4665	51	10	0	0	NUM
cana-4665	51	11	(	(	PUNCT
cana-4665	51	12	ii	ii	NOUN
cana-4665	51	13	)	)	PUNCT
cana-4665	51	14	ξu	ξu	NOUN
cana-4665	51	15	=	=	SYM
cana-4665	51	16	0	0	PROPN
cana-4665	51	17	,	,	PUNCT
cana-4665	51	18	ξv	ξv	X
cana-4665	51	19	=	=	SYM
cana-4665	51	20	0	0	NUM
cana-4665	51	21	(	(	PUNCT
cana-4665	51	22	iii	iii	NOUN
cana-4665	51	23	)	)	PUNCT
cana-4665	51	24	−	−	ADP
cana-4665	51	25	aφv	aφv	NOUN
cana-4665	51	26	+	+	CCONJ
cana-4665	51	27	aηu	aηu	ADJ
cana-4665	51	28	+	+	NUM
cana-4665	51	29	2aξx	2aξx	NUM
cana-4665	51	30	−	−	NOUN
cana-4665	51	31	aτt	aτt	NOUN
cana-4665	51	32	=	=	SYM
cana-4665	51	33	0	0	NUM
cana-4665	51	34	(	(	PUNCT
cana-4665	51	35	iv	iv	NOUN
cana-4665	51	36	)	)	PUNCT
cana-4665	51	37	φuu	φuu	NOUN
cana-4665	51	38	=	=	SYM
cana-4665	51	39	0	0	NUM
cana-4665	51	40	,	,	PUNCT
cana-4665	51	41	φuv	φuv	NOUN
cana-4665	51	42	=	=	SYM
cana-4665	51	43	0	0	NUM
cana-4665	51	44	,	,	PUNCT
cana-4665	51	45	φvv	φvv	NOUN
cana-4665	51	46	=	=	SYM
cana-4665	51	47	0	0	NUM
cana-4665	51	48	(	(	PUNCT
cana-4665	51	49	v	v	NOUN
cana-4665	51	50	)	)	PUNCT
cana-4665	51	51	−	−	PROPN
cana-4665	51	52	3u2ξx	3u2ξx	NUM
cana-4665	51	53	+	+	SYM
cana-4665	51	54	3u2τtb+	3u2τtb+	NUM
cana-4665	51	55	2uvbφu	2uvbφu	NUM
cana-4665	51	56	−	−	PROPN
cana-4665	51	57	2uvbηv	2uvbηv	NUM
cana-4665	51	58	−	−	NOUN
cana-4665	51	59	v2bξx	v2bξx	X
cana-4665	52	1	+	+	SYM
cana-4665	52	2	v2bτt	v2bτt	NUM
cana-4665	53	1	+	+	CCONJ
cana-4665	53	2	6buη	6buη	PROPN
cana-4665	53	3	+	+	NUM
cana-4665	53	4	2bvφ−	2bvφ−	ADJ
cana-4665	53	5	2aφxu	2aφxu	NUM
cana-4665	53	6	−	−	PROPN
cana-4665	53	7	ξt	ξt	INTJ
cana-4665	53	8	=	=	SYM
cana-4665	53	9	0	0	NUM
cana-4665	53	10	(	(	PUNCT
cana-4665	53	11	vi	vi	NOUN
cana-4665	53	12	)	)	PUNCT
cana-4665	53	13	2u2bηv	2u2bηv	NUM
cana-4665	54	1	+	+	CCONJ
cana-4665	55	1	2uvbφv	2uvbφv	NUM
cana-4665	56	1	−	−	NUM
cana-4665	56	2	2uvbηu	2uvbηu	NUM
cana-4665	56	3	−	−	PROPN
cana-4665	56	4	2uvbξx	2uvbξx	NUM
cana-4665	56	5	+	+	PUNCT
cana-4665	56	6	2uvbτt	2uvbτt	NUM
cana-4665	57	1	−	−	NUM
cana-4665	57	2	2bv2ηv	2bv2ηv	NUM
cana-4665	57	3	+	+	NUM
cana-4665	57	4	2buφ+	2buφ+	NUM
cana-4665	57	5	2bvη	2bvη	NOUN
cana-4665	57	6	+	+	CCONJ
cana-4665	57	7	aξxx	aξxx	NOUN
cana-4665	57	8	−	−	PROPN
cana-4665	57	9	2aφxv	2aφxv	NUM
cana-4665	57	10	=	=	SYM
cana-4665	57	11	0	0	NUM
cana-4665	57	12	(	(	PUNCT
cana-4665	57	13	vii	vii	PROPN
cana-4665	57	14	)	)	PUNCT
cana-4665	57	15	φu	φu	NOUN
cana-4665	57	16	=	=	SYM
cana-4665	57	17	−ηv	−ηv	PROPN
cana-4665	57	18	(	(	PUNCT
cana-4665	57	19	viii	viii	NOUN
cana-4665	57	20	)	)	PUNCT
cana-4665	58	1	v2bηx	v2bηx	PROPN
cana-4665	59	1	+	+	CCONJ
cana-4665	59	2	2uvbφx	2uvbφx	NUM
cana-4665	59	3	−	−	NOUN
cana-4665	59	4	aφxx	aφxx	ADJ
cana-4665	59	5	+	+	CCONJ
cana-4665	59	6	ηt	ηt	ADP
cana-4665	59	7	+	+	ADJ
cana-4665	59	8	3u2bηx	3u2bηx	NUM
cana-4665	59	9	=	=	SYM
cana-4665	59	10	0	0	PUNCT
cana-4665	59	11	(	(	PUNCT
cana-4665	59	12	ix	ix	ADJ
cana-4665	59	13	)	)	PUNCT
cana-4665	59	14	ηvv	ηvv	NOUN
cana-4665	59	15	=	=	SYM
cana-4665	59	16	0	0	NUM
cana-4665	59	17	,	,	PUNCT
cana-4665	59	18	ηuu	ηuu	NOUN
cana-4665	59	19	=	=	SYM
cana-4665	59	20	0	0	NUM
cana-4665	59	21	,	,	PUNCT
cana-4665	59	22	ηuv	ηuv	NOUN
cana-4665	59	23	=	=	SYM
cana-4665	59	24	0	0	PUNCT
cana-4665	59	25	(	(	PUNCT
cana-4665	59	26	x	x	NOUN
cana-4665	59	27	)	)	PUNCT
cana-4665	59	28	−	−	VERB
cana-4665	59	29	bu2ξx	bu2ξx	NOUN
cana-4665	60	1	+	+	CCONJ
cana-4665	60	2	bu2τt	bu2τt	ADP
cana-4665	60	3	−	−	X
cana-4665	60	4	2buvφu	2buvφu	NUM
cana-4665	60	5	+	+	PROPN
cana-4665	60	6	2buvηv	2buvηv	NUM
cana-4665	60	7	−	−	NUM
cana-4665	61	1	3bv2ξx	3bv2ξx	NUM
cana-4665	61	2	+	+	NUM
cana-4665	62	1	3bv2τt	3bv2τt	NUM
cana-4665	62	2	+	+	CCONJ
cana-4665	62	3	2buη	2buη	NUM
cana-4665	62	4	+	+	CCONJ
cana-4665	62	5	6bvφ+	6bvφ+	NUM
cana-4665	62	6	2aηxv	2aηxv	NUM
cana-4665	62	7	−	−	NOUN
cana-4665	62	8	ξx	ξx	NOUN
cana-4665	62	9	=	=	SYM
cana-4665	62	10	0	0	PROPN
cana-4665	62	11	(	(	PUNCT
cana-4665	62	12	xi	xi	PROPN
cana-4665	62	13	)	)	PUNCT
cana-4665	62	14	−	−	PROPN
cana-4665	63	1	2bu2φu	2bu2φu	NUM
cana-4665	64	1	−	−	NOUN
cana-4665	64	2	2buvξx	2buvξx	NUM
cana-4665	64	3	+	+	CCONJ
cana-4665	64	4	2buvηu	2buvηu	NUM
cana-4665	64	5	+	+	NUM
cana-4665	64	6	2buvτt	2buvτt	NUM
cana-4665	64	7	−	−	PROPN
cana-4665	64	8	2buvφv	2buvφv	NUM
cana-4665	64	9	+	+	CCONJ
cana-4665	64	10	2bv2φu	2bv2φu	NUM
cana-4665	64	11	+	+	NUM
cana-4665	64	12	2buφ+	2buφ+	NUM
cana-4665	64	13	2bvη	2bvη	NOUN
cana-4665	64	14	+	+	CCONJ
cana-4665	64	15	2aηxu	2aηxu	NUM
cana-4665	64	16	−	−	NOUN
cana-4665	64	17	aξxx	aξxx	NOUN
cana-4665	64	18	=	=	SYM
cana-4665	64	19	0	0	PUNCT
cana-4665	65	1	(	(	PUNCT
cana-4665	65	2	xii	xii	NOUN
cana-4665	65	3	)	)	PUNCT
cana-4665	66	1	−	−	PROPN
cana-4665	66	2	2aξx	2aξx	NUM
cana-4665	66	3	+	+	CCONJ
cana-4665	66	4	aηu	aηu	PROPN
cana-4665	67	1	+	+	CCONJ
cana-4665	67	2	aτt	aτt	ADP
cana-4665	67	3	−	−	PROPN
cana-4665	67	4	aφv	aφv	NOUN
cana-4665	67	5	=	=	SYM
cana-4665	67	6	0	0	NUM
cana-4665	67	7	(	(	PUNCT
cana-4665	67	8	xiii	xiii	PROPN
cana-4665	67	9	)	)	PUNCT
cana-4665	67	10	φu	φu	NOUN
cana-4665	68	1	+	+	CCONJ
cana-4665	68	2	ηv	ηv	ADJ
cana-4665	68	3	=	=	SYM
cana-4665	68	4	0	0	NUM
cana-4665	68	5	(	(	PUNCT
cana-4665	68	6	xiv	xiv	NOUN
cana-4665	68	7	)	)	PUNCT
cana-4665	68	8	aηxx	aηxx	NOUN
cana-4665	69	1	+	+	CCONJ
cana-4665	70	1	2buvηx	2buvηx	NUM
cana-4665	70	2	+	+	CCONJ
cana-4665	70	3	3bv2φx	3bv2φx	NUM
cana-4665	71	1	+	+	CCONJ
cana-4665	71	2	bu2φx	bu2φx	NOUN
cana-4665	71	3	+	+	CCONJ
cana-4665	71	4	φt	φt	NOUN
cana-4665	71	5	=	=	SYM
cana-4665	71	6	0	0	NUM
cana-4665	71	7	(	(	PUNCT
cana-4665	71	8	2.7	2.7	NUM
cana-4665	71	9	)	)	PUNCT
cana-4665	71	10	communications	communication	NOUN
cana-4665	71	11	on	on	ADP
cana-4665	71	12	applied	apply	VERB
cana-4665	71	13	nonlinear	nonlinear	ADJ
cana-4665	71	14	analysis	analysis	NOUN
cana-4665	71	15	issn	issn	NOUN
cana-4665	71	16	:	:	PUNCT
cana-4665	71	17	1074	1074	NUM
cana-4665	71	18	-	-	PUNCT
cana-4665	71	19	133x	133x	NUM
cana-4665	71	20	vol	vol	VERB
cana-4665	71	21	32	32	NUM
cana-4665	71	22	no	no	NOUN
cana-4665	71	23	.	.	PUNCT
cana-4665	72	1	10s	10	NOUN
cana-4665	72	2	(	(	PUNCT
cana-4665	72	3	2025	2025	NUM
cana-4665	72	4	)	)	PUNCT
cana-4665	72	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-4665	72	6	91	91	NUM
cana-4665	72	7	by	by	ADP
cana-4665	72	8	working	work	VERB
cana-4665	72	9	through	through	ADP
cana-4665	72	10	these	these	DET
cana-4665	72	11	determining	determine	VERB
cana-4665	72	12	equations	equation	NOUN
cana-4665	72	13	,	,	PUNCT
cana-4665	72	14	the	the	DET
cana-4665	72	15	below	below	ADV
cana-4665	72	16	-	-	PUNCT
cana-4665	72	17	mentioned	mention	VERB
cana-4665	72	18	solutions	solution	NOUN
cana-4665	72	19	will	will	AUX
cana-4665	72	20	be	be	AUX
cana-4665	72	21	obtainedη	obtainedη	VERB
cana-4665	72	22	=	=	PUNCT
cana-4665	73	1	uc2	uc2	NOUN
cana-4665	74	1	−	−	NOUN
cana-4665	74	2	vc1	vc1	PROPN
cana-4665	74	3	,	,	PUNCT
cana-4665	74	4	φ	φ	PROPN
cana-4665	74	5	=	=	SYM
cana-4665	74	6	uc1	uc1	PROPN
cana-4665	74	7	+	+	CCONJ
cana-4665	74	8	vc2	vc2	PROPN
cana-4665	74	9	,	,	PUNCT
cana-4665	74	10	ξ	ξ	X
cana-4665	74	11	=	=	SYM
cana-4665	74	12	−2xc2	−2xc2	NOUN
cana-4665	74	13	+	+	CCONJ
cana-4665	74	14	c3	c3	PROPN
cana-4665	74	15	,	,	PUNCT
cana-4665	74	16	τ	τ	PROPN
cana-4665	74	17	=	=	SYM
cana-4665	74	18	−4tc2	−4tc2	PROPN
cana-4665	74	19	+	+	CCONJ
cana-4665	74	20	c4	c4	NOUN
cana-4665	74	21	,	,	PUNCT
cana-4665	74	22	(	(	PUNCT
cana-4665	74	23	2.8	2.8	NUM
cana-4665	74	24	)	)	PUNCT
cana-4665	74	25	where	where	SCONJ
cana-4665	74	26	c1	c1	PROPN
cana-4665	74	27	,	,	PUNCT
cana-4665	74	28	c2	c2	PROPN
cana-4665	74	29	,	,	PUNCT
cana-4665	74	30	c3	c3	PROPN
cana-4665	74	31	,	,	PUNCT
cana-4665	74	32	c4	c4	NOUN
cana-4665	74	33	illustrates	illustrate	VERB
cana-4665	74	34	the	the	DET
cana-4665	74	35	arbitrary	arbitrary	ADJ
cana-4665	74	36	constants	constant	NOUN
cana-4665	74	37	.	.	PUNCT
cana-4665	75	1	from	from	ADP
cana-4665	75	2	the	the	DET
cana-4665	75	3	above	above	ADJ
cana-4665	75	4	obtained	obtain	VERB
cana-4665	75	5	lie	lie	NOUN
cana-4665	75	6	symmetries	symmetry	NOUN
cana-4665	75	7	the	the	DET
cana-4665	75	8	vector	vector	NOUN
cana-4665	75	9	fields	field	NOUN
cana-4665	75	10	are	be	AUX
cana-4665	75	11	as	as	SCONJ
cana-4665	75	12	follows	follow	VERB
cana-4665	75	13	:	:	PUNCT
cana-4665	75	14	v1	v1	NOUN
cana-4665	75	15	=	=	SYM
cana-4665	75	16	u	u	PROPN
cana-4665	75	17	∂	∂	NOUN
cana-4665	76	1	∂v	∂v	NOUN
cana-4665	76	2	−	−	PROPN
cana-4665	76	3	v	v	NOUN
cana-4665	76	4	∂	∂	NOUN
cana-4665	76	5	∂u	∂u	NOUN
cana-4665	76	6	,	,	PUNCT
cana-4665	76	7	v2	v2	PROPN
cana-4665	76	8	=	=	SYM
cana-4665	76	9	v	v	NOUN
cana-4665	76	10	∂	∂	NOUN
cana-4665	77	1	∂v	∂v	NOUN
cana-4665	77	2	−	−	PROPN
cana-4665	77	3	u	u	PROPN
cana-4665	77	4	∂	∂	NOUN
cana-4665	77	5	∂u	∂u	PROPN
cana-4665	77	6	−	−	PROPN
cana-4665	77	7	2x	2x	NUM
cana-4665	77	8	∂	∂	NUM
cana-4665	77	9	∂x	∂x	NOUN
cana-4665	77	10	−	−	NUM
cana-4665	77	11	4	4	NUM
cana-4665	77	12	t	t	NOUN
cana-4665	77	13	∂∂t	∂∂t	PROPN
cana-4665	77	14	,	,	PUNCT
cana-4665	77	15	v3	v3	PROPN
cana-4665	77	16	=	=	SYM
cana-4665	77	17	∂	∂	NUM
cana-4665	77	18	∂x	∂x	PROPN
cana-4665	77	19	,	,	PUNCT
cana-4665	77	20	v4	v4	PROPN
cana-4665	77	21	=	=	SYM
cana-4665	77	22	∂	∂	NUM
cana-4665	77	23	∂t	∂t	PROPN
cana-4665	77	24	.	.	PUNCT
cana-4665	78	1	(	(	PUNCT
cana-4665	78	2	2.9	2.9	NUM
cana-4665	78	3	)	)	PUNCT
cana-4665	78	4	by	by	ADP
cana-4665	78	5	utilizing	utilize	VERB
cana-4665	78	6	the	the	DET
cana-4665	78	7	various	various	ADJ
cana-4665	78	8	linear	linear	ADJ
cana-4665	78	9	combinations	combination	NOUN
cana-4665	78	10	of	of	ADP
cana-4665	78	11	the	the	DET
cana-4665	78	12	above	above	ADJ
cana-4665	78	13	mentioned	mention	VERB
cana-4665	78	14	vector	vector	NOUN
cana-4665	78	15	fields	field	NOUN
cana-4665	78	16	i.e.	i.e.	X
cana-4665	78	17	,	,	PUNCT
cana-4665	78	18	v1	v1	NOUN
cana-4665	78	19	,	,	PUNCT
cana-4665	78	20	v2	v2	PROPN
cana-4665	78	21	,	,	PUNCT
cana-4665	78	22	v3	v3	PROPN
cana-4665	78	23	,	,	PUNCT
cana-4665	78	24	v4	v4	NOUN
cana-4665	78	25	we	we	PRON
cana-4665	78	26	avail	avail	VERB
cana-4665	78	27	the	the	DET
cana-4665	78	28	similarity	similarity	NOUN
cana-4665	78	29	reductions	reduction	NOUN
cana-4665	78	30	of	of	ADP
cana-4665	78	31	the	the	DET
cana-4665	78	32	kaup	kaup	PROPN
cana-4665	78	33	-	-	PROPN
cana-4665	78	34	newell	newell	PROPN
cana-4665	78	35	equation	equation	NOUN
cana-4665	78	36	.	.	PUNCT
cana-4665	79	1	3	3	NUM
cana-4665	79	2	reductions	reduction	NOUN
cana-4665	79	3	and	and	CCONJ
cana-4665	79	4	exact	exact	ADJ
cana-4665	79	5	solutions	solution	NOUN
cana-4665	79	6	of	of	ADP
cana-4665	79	7	kaup	kaup	PROPN
cana-4665	79	8	-	-	PROPN
cana-4665	79	9	newell	newell	PROPN
cana-4665	79	10	equation	equation	NOUN
cana-4665	79	11	a	a	DET
cana-4665	79	12	prominent	prominent	ADJ
cana-4665	79	13	motive	motive	NOUN
cana-4665	79	14	to	to	PART
cana-4665	79	15	calculate	calculate	VERB
cana-4665	79	16	symmetries	symmetry	NOUN
cana-4665	79	17	of	of	ADP
cana-4665	79	18	differential	differential	ADJ
cana-4665	79	19	equations	equation	NOUN
cana-4665	79	20	aims	aim	VERB
cana-4665	79	21	to	to	PART
cana-4665	79	22	utilize	utilize	VERB
cana-4665	79	23	those	those	PRON
cana-4665	79	24	to	to	PART
cana-4665	79	25	generate	generate	VERB
cana-4665	79	26	the	the	DET
cana-4665	79	27	exact	exact	ADJ
cana-4665	79	28	solutions	solution	NOUN
cana-4665	79	29	and	and	CCONJ
cana-4665	79	30	obtain	obtain	VERB
cana-4665	79	31	symmetry	symmetry	NOUN
cana-4665	79	32	reductions	reduction	NOUN
cana-4665	79	33	.	.	PUNCT
cana-4665	80	1	in	in	ADP
cana-4665	80	2	this	this	DET
cana-4665	80	3	subsection	subsection	NOUN
cana-4665	80	4	,	,	PUNCT
cana-4665	80	5	we	we	PRON
cana-4665	80	6	use	use	VERB
cana-4665	80	7	the	the	DET
cana-4665	80	8	different	different	ADJ
cana-4665	80	9	combinations	combination	NOUN
cana-4665	80	10	of	of	ADP
cana-4665	80	11	vector	vector	NOUN
cana-4665	80	12	fields	field	NOUN
cana-4665	80	13	and	and	CCONJ
cana-4665	80	14	reduce	reduce	VERB
cana-4665	80	15	the	the	DET
cana-4665	80	16	kaup	kaup	PROPN
cana-4665	80	17	-	-	PROPN
cana-4665	80	18	newell	newell	PROPN
cana-4665	80	19	equation	equation	NOUN
cana-4665	80	20	to	to	ADP
cana-4665	80	21	ordinary	ordinary	ADJ
cana-4665	80	22	differential	differential	ADJ
cana-4665	80	23	equations	equation	NOUN
cana-4665	80	24	in	in	ADP
cana-4665	80	25	each	each	DET
cana-4665	80	26	case	case	NOUN
cana-4665	80	27	to	to	PART
cana-4665	80	28	further	far	ADV
cana-4665	80	29	explore	explore	VERB
cana-4665	80	30	the	the	DET
cana-4665	80	31	exact	exact	ADJ
cana-4665	80	32	solutions	solution	NOUN
cana-4665	80	33	.	.	PUNCT
cana-4665	81	1	we	we	PRON
cana-4665	81	2	will	will	AUX
cana-4665	81	3	consider	consider	VERB
cana-4665	81	4	the	the	DET
cana-4665	81	5	following	follow	VERB
cana-4665	81	6	vector	vector	NOUN
cana-4665	81	7	fields	field	NOUN
cana-4665	81	8	for	for	ADP
cana-4665	81	9	the	the	DET
cana-4665	81	10	reduction	reduction	NOUN
cana-4665	81	11	of	of	ADP
cana-4665	81	12	the	the	DET
cana-4665	81	13	system	system	NOUN
cana-4665	81	14	of	of	ADP
cana-4665	81	15	equations	equation	NOUN
cana-4665	81	16	:	:	PUNCT
cana-4665	81	17	(	(	PUNCT
cana-4665	81	18	1	1	X
cana-4665	81	19	)	)	PUNCT
cana-4665	81	20	v1	v1	NOUN
cana-4665	81	21	+	+	CCONJ
cana-4665	81	22	αv3	αv3	NOUN
cana-4665	81	23	+	+	CCONJ
cana-4665	81	24	βv4	βv4	PROPN
cana-4665	81	25	,	,	PUNCT
cana-4665	81	26	(	(	PUNCT
cana-4665	81	27	2	2	X
cana-4665	81	28	)	)	PUNCT
cana-4665	81	29	v2	v2	PROPN
cana-4665	81	30	,	,	PUNCT
cana-4665	81	31	(	(	PUNCT
cana-4665	81	32	3	3	X
cana-4665	81	33	)	)	PUNCT
cana-4665	81	34	v3	v3	PROPN
cana-4665	81	35	+	+	CCONJ
cana-4665	81	36	ωv4	ωv4	PROPN
cana-4665	81	37	.	.	PUNCT
cana-4665	82	1	(	(	PUNCT
cana-4665	82	2	3.1	3.1	NUM
cana-4665	82	3	)	)	PUNCT
cana-4665	82	4	in	in	ADP
cana-4665	82	5	each	each	DET
cana-4665	82	6	case	case	NOUN
cana-4665	82	7	,	,	PUNCT
cana-4665	82	8	by	by	ADP
cana-4665	82	9	using	use	VERB
cana-4665	82	10	characteristics	characteristic	NOUN
cana-4665	82	11	equation	equation	NOUN
cana-4665	82	12	,	,	PUNCT
cana-4665	82	13	as	as	SCONJ
cana-4665	82	14	under	under	ADV
cana-4665	82	15	,	,	PUNCT
cana-4665	82	16	we	we	PRON
cana-4665	82	17	will	will	AUX
cana-4665	82	18	try	try	VERB
cana-4665	82	19	to	to	PART
cana-4665	82	20	obtain	obtain	VERB
cana-4665	82	21	the	the	DET
cana-4665	82	22	reductions	reduction	NOUN
cana-4665	82	23	:	:	PUNCT
cana-4665	82	24	dx	dx	PROPN
cana-4665	82	25	ξ	ξ	X
cana-4665	82	26	=	=	X
cana-4665	82	27	dt	dt	X
cana-4665	82	28	τ	τ	PROPN
cana-4665	82	29	=	=	SYM
cana-4665	82	30	du	du	PROPN
cana-4665	82	31	η	η	PROPN
cana-4665	82	32	=	=	PROPN
cana-4665	82	33	dv	dv	PROPN
cana-4665	82	34	φ	φ	PROPN
cana-4665	82	35	.	.	PUNCT
cana-4665	83	1	(	(	PUNCT
cana-4665	83	2	3.2	3.2	NUM
cana-4665	83	3	)	)	PUNCT
cana-4665	83	4	3.1	3.1	NUM
cana-4665	83	5	vector	vector	NOUN
cana-4665	83	6	field	field	NOUN
cana-4665	83	7	v1	v1	NOUN
cana-4665	83	8	+	+	CCONJ
cana-4665	83	9	αv3	αv3	NOUN
cana-4665	84	1	+	+	CCONJ
cana-4665	84	2	βv4	βv4	NOUN
cana-4665	84	3	on	on	ADP
cana-4665	84	4	using	use	VERB
cana-4665	84	5	the	the	DET
cana-4665	84	6	characteristic	characteristic	ADJ
cana-4665	84	7	equations	equation	NOUN
cana-4665	84	8	(	(	PUNCT
cana-4665	84	9	3.2	3.2	NUM
cana-4665	84	10	)	)	PUNCT
cana-4665	84	11	we	we	PRON
cana-4665	84	12	acquire	acquire	VERB
cana-4665	84	13	the	the	DET
cana-4665	84	14	similarity	similarity	NOUN
cana-4665	84	15	variables	variable	NOUN
cana-4665	84	16	as	as	SCONJ
cana-4665	84	17	shown	show	VERB
cana-4665	84	18	belowq	belowq	NOUN
cana-4665	84	19	=	=	SYM
cana-4665	84	20	f	f	PROPN
cana-4665	84	21	(	(	PUNCT
cana-4665	84	22	ξ)e	ξ)e	VERB
cana-4665	84	23	ι	ι	X
cana-4665	84	24	(	(	PUNCT
cana-4665	84	25	t	t	NOUN
cana-4665	84	26	β	β	X
cana-4665	85	1	+	+	PROPN
cana-4665	86	1	g(ξ	g(ξ	PROPN
cana-4665	86	2	)	)	PUNCT
cana-4665	86	3	)	)	PUNCT
cana-4665	87	1	,	,	PUNCT
cana-4665	87	2	ξ	ξ	X
cana-4665	87	3	=	=	SYM
cana-4665	87	4	βx−	βx−	NUM
cana-4665	87	5	αt	αt	PROPN
cana-4665	87	6	.	.	PUNCT
cana-4665	87	7	(	(	PUNCT
cana-4665	87	8	3.3	3.3	NUM
cana-4665	87	9	)	)	PUNCT
cana-4665	87	10	using	use	VERB
cana-4665	87	11	equation	equation	NOUN
cana-4665	87	12	(	(	PUNCT
cana-4665	87	13	3.3	3.3	NUM
cana-4665	87	14	)	)	PUNCT
cana-4665	87	15	in	in	ADP
cana-4665	87	16	equation	equation	NOUN
cana-4665	87	17	(	(	PUNCT
cana-4665	87	18	2.2	2.2	NUM
cana-4665	87	19	)	)	PUNCT
cana-4665	87	20	and	and	CCONJ
cana-4665	87	21	(	(	PUNCT
cana-4665	87	22	2.3	2.3	NUM
cana-4665	87	23	)	)	PUNCT
cana-4665	87	24	,	,	PUNCT
cana-4665	87	25	we	we	PRON
cana-4665	87	26	get	get	VERB
cana-4665	87	27	ordinary	ordinary	ADJ
cana-4665	87	28	differential	differential	ADJ
cana-4665	87	29	equation	equation	NOUN
cana-4665	87	30	as	as	ADP
cana-4665	87	31	:	:	PUNCT
cana-4665	87	32	−aβ2f	−aβ2f	PROPN
cana-4665	87	33	(	(	PUNCT
cana-4665	87	34	ξ)g′(ξ	ξ)g′(ξ	NOUN
cana-4665	87	35	)	)	PUNCT
cana-4665	87	36	2	2	NUM
cana-4665	88	1	+	+	CCONJ
cana-4665	88	2	f	f	X
cana-4665	88	3	(	(	PUNCT
cana-4665	88	4	ξ	ξ	NOUN
cana-4665	88	5	)	)	PUNCT
cana-4665	88	6	(	(	PUNCT
cana-4665	88	7	1	1	NUM
cana-4665	88	8	β	β	NOUN
cana-4665	88	9	−	−	NOUN
cana-4665	88	10	αg′(ξ	αg′(ξ	NOUN
cana-4665	88	11	)	)	PUNCT
cana-4665	88	12	)	)	PUNCT
cana-4665	89	1	+	+	CCONJ
cana-4665	89	2	aβ2f	aβ2f	ADJ
cana-4665	89	3	′′(ξ	′′(ξ	PROPN
cana-4665	89	4	)	)	PUNCT
cana-4665	90	1	+	+	CCONJ
cana-4665	90	2	bβf	bβf	PROPN
cana-4665	90	3	(	(	PUNCT
cana-4665	90	4	ξ)3g′(ξ	ξ)3g′(ξ	NOUN
cana-4665	90	5	)	)	PUNCT
cana-4665	90	6	=	=	SYM
cana-4665	90	7	0	0	NUM
cana-4665	90	8	,	,	PUNCT
cana-4665	90	9	(	(	PUNCT
cana-4665	90	10	3.4	3.4	NUM
cana-4665	90	11	)	)	PUNCT
cana-4665	90	12	communications	communication	NOUN
cana-4665	90	13	on	on	ADP
cana-4665	90	14	applied	apply	VERB
cana-4665	90	15	nonlinear	nonlinear	ADJ
cana-4665	90	16	analysis	analysis	NOUN
cana-4665	90	17	issn	issn	NOUN
cana-4665	90	18	:	:	PUNCT
cana-4665	90	19	1074	1074	NUM
cana-4665	90	20	-	-	PUNCT
cana-4665	90	21	133x	133x	NUM
cana-4665	90	22	vol	vol	VERB
cana-4665	90	23	32	32	NUM
cana-4665	90	24	no	no	NOUN
cana-4665	90	25	.	.	PUNCT
cana-4665	91	1	10s	10	NOUN
cana-4665	91	2	(	(	PUNCT
cana-4665	91	3	2025	2025	NUM
cana-4665	91	4	)	)	PUNCT
cana-4665	91	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-4665	91	6	92	92	NUM
cana-4665	91	7	and	and	CCONJ
cana-4665	91	8	2β2f	2β2f	NUM
cana-4665	91	9	′(ξ)g′(ξ	′(ξ)g′(ξ	NOUN
cana-4665	91	10	)	)	PUNCT
cana-4665	92	1	+	+	CCONJ
cana-4665	92	2	β2f	β2f	PROPN
cana-4665	92	3	(	(	PUNCT
cana-4665	92	4	ξ)g′′(ξ	ξ)g′′(ξ	NOUN
cana-4665	92	5	)	)	PUNCT
cana-4665	93	1	+	+	CCONJ
cana-4665	93	2	3bβf	3bβf	PROPN
cana-4665	93	3	′(ξ)f	′(ξ)f	PROPN
cana-4665	93	4	(	(	PUNCT
cana-4665	93	5	ξ)2	ξ)2	PROPN
cana-4665	93	6	−	−	PROPN
cana-4665	93	7	αf	αf	NOUN
cana-4665	93	8	′(ξ	′(ξ	NOUN
cana-4665	93	9	)	)	PUNCT
cana-4665	93	10	=	=	SYM
cana-4665	93	11	0	0	X
cana-4665	93	12	.	.	PUNCT
cana-4665	93	13	(	(	PUNCT
cana-4665	93	14	3.5	3.5	NUM
cana-4665	93	15	)	)	PUNCT
cana-4665	93	16	in	in	ADP
cana-4665	93	17	this	this	DET
cana-4665	93	18	context	context	NOUN
cana-4665	93	19	,	,	PUNCT
cana-4665	93	20	the	the	DET
cana-4665	93	21	prime	prime	NOUN
cana-4665	93	22	(	(	PUNCT
cana-4665	93	23	’	'	PUNCT
cana-4665	93	24	)	)	PUNCT
cana-4665	93	25	signifies	signify	VERB
cana-4665	93	26	the	the	DET
cana-4665	93	27	differentiation	differentiation	NOUN
cana-4665	93	28	w.r.t	w.r.t	VERB
cana-4665	93	29	variable	variable	PROPN
cana-4665	93	30	ξ	ξ	PROPN
cana-4665	93	31	.	.	PUNCT
cana-4665	94	1	on	on	ADP
cana-4665	94	2	solving	solve	VERB
cana-4665	94	3	these	these	DET
cana-4665	94	4	equations	equation	NOUN
cana-4665	94	5	we	we	PRON
cana-4665	94	6	get	get	VERB
cana-4665	94	7	f	f	PROPN
cana-4665	94	8	(	(	PUNCT
cana-4665	94	9	ξ	ξ	PROPN
cana-4665	94	10	)	)	PUNCT
cana-4665	94	11	=	=	SYM
cana-4665	94	12	k1	k1	NOUN
cana-4665	94	13	,	,	PUNCT
cana-4665	94	14	(	(	PUNCT
cana-4665	94	15	3.6	3.6	NUM
cana-4665	94	16	)	)	PUNCT
cana-4665	94	17	where	where	SCONJ
cana-4665	94	18	k1	k1	NOUN
cana-4665	94	19	is	be	AUX
cana-4665	94	20	any	any	DET
cana-4665	94	21	constant	constant	ADJ
cana-4665	94	22	and	and	CCONJ
cana-4665	94	23	g(ξ	g(ξ	PROPN
cana-4665	94	24	)	)	PUNCT
cana-4665	94	25	=	=	PRON
cana-4665	94	26	(	(	PUNCT
cana-4665	94	27	bc2β	bc2β	ADJ
cana-4665	94	28	−	−	PROPN
cana-4665	94	29	α+	α+	PUNCT
cana-4665	94	30	√	√	NOUN
cana-4665	94	31	b2c4β2	b2c4β2	NOUN
cana-4665	94	32	−	−	PROPN
cana-4665	94	33	2bc2αβ	2bc2αβ	NUM
cana-4665	94	34	+	+	CCONJ
cana-4665	94	35	4aβ	4aβ	NOUN
cana-4665	94	36	+	+	CCONJ
cana-4665	94	37	α2	α2	ADJ
cana-4665	94	38	2aβ2	2aβ2	NUM
cana-4665	94	39	)	)	PUNCT
cana-4665	95	1	ξ	ξ	X
cana-4665	95	2	+	+	NUM
cana-4665	95	3	c1	c1	NOUN
cana-4665	95	4	.	.	PUNCT
cana-4665	96	1	(	(	PUNCT
cana-4665	96	2	3.7	3.7	NUM
cana-4665	96	3	)	)	PUNCT
cana-4665	96	4	using	use	VERB
cana-4665	96	5	these	these	DET
cana-4665	96	6	values	value	NOUN
cana-4665	96	7	we	we	PRON
cana-4665	96	8	get	get	VERB
cana-4665	96	9	the	the	DET
cana-4665	96	10	solution	solution	NOUN
cana-4665	96	11	of	of	ADP
cana-4665	96	12	kaup	kaup	PROPN
cana-4665	96	13	-	-	PROPN
cana-4665	96	14	newell	newell	PROPN
cana-4665	96	15	equation	equation	NOUN
cana-4665	96	16	as	as	ADP
cana-4665	96	17	q(x	q(x	PROPN
cana-4665	96	18	,	,	PUNCT
cana-4665	96	19	t	t	PROPN
cana-4665	96	20	)	)	PUNCT
cana-4665	96	21	=	=	X
cana-4665	97	1	k1e	k1e	X
cana-4665	97	2	ι	ι	X
cana-4665	97	3	(	(	PUNCT
cana-4665	97	4	t	t	NOUN
cana-4665	97	5	β	β	X
cana-4665	97	6	+	+	CCONJ
cana-4665	97	7	(	(	PUNCT
cana-4665	97	8	bc2β−α+	bc2β−α+	ADV
cana-4665	97	9	√	√	INTJ
cana-4665	97	10	b2c4β2−2bc2αβ+4aβ+α2	b2c4β2−2bc2αβ+4aβ+α2	NOUN
cana-4665	97	11	2aβ2	2aβ2	NUM
cana-4665	97	12	)	)	PUNCT
cana-4665	97	13	(	(	PUNCT
cana-4665	97	14	βx−αt)+c1	βx−αt)+c1	NOUN
cana-4665	97	15	)	)	PUNCT
cana-4665	97	16	.	.	PUNCT
cana-4665	98	1	(	(	PUNCT
cana-4665	98	2	3.8	3.8	NUM
cana-4665	98	3	)	)	PUNCT
cana-4665	98	4	3.2	3.2	NUM
cana-4665	98	5	vector	vector	NOUN
cana-4665	98	6	field	field	NOUN
cana-4665	98	7	v2	v2	NOUN
cana-4665	98	8	by	by	ADP
cana-4665	98	9	solving	solve	VERB
cana-4665	98	10	the	the	DET
cana-4665	98	11	characteristic	characteristic	ADJ
cana-4665	98	12	equation	equation	NOUN
cana-4665	98	13	(	(	PUNCT
cana-4665	98	14	3.2	3.2	NUM
cana-4665	98	15	)	)	PUNCT
cana-4665	98	16	aforementioned	aforementione	VERB
cana-4665	98	17	similarity	similarity	NOUN
cana-4665	98	18	variable	variable	NOUN
cana-4665	98	19	is	be	AUX
cana-4665	98	20	calculated	calculate	VERB
cana-4665	98	21	as	as	ADP
cana-4665	98	22	u	u	PROPN
cana-4665	98	23	=	=	PROPN
cana-4665	98	24	f	f	PROPN
cana-4665	98	25	(	(	PUNCT
cana-4665	98	26	ξ)t	ξ)t	NOUN
cana-4665	98	27	−1	−1	NOUN
cana-4665	98	28	4	4	NUM
cana-4665	98	29	,	,	PUNCT
cana-4665	98	30	v	v	NOUN
cana-4665	98	31	=	=	SYM
cana-4665	98	32	g(ξ)t	g(ξ)t	PROPN
cana-4665	98	33	−1	−1	NOUN
cana-4665	98	34	4	4	NUM
cana-4665	98	35	,	,	PUNCT
cana-4665	98	36	ξ	ξ	X
cana-4665	98	37	=	=	SYM
cana-4665	98	38	x2	x2	PROPN
cana-4665	98	39	t	t	PROPN
cana-4665	98	40	,	,	PUNCT
cana-4665	98	41	(	(	PUNCT
cana-4665	98	42	3.9	3.9	NUM
cana-4665	98	43	)	)	PUNCT
cana-4665	98	44	on	on	ADP
cana-4665	98	45	using	use	VERB
cana-4665	98	46	equation	equation	NOUN
cana-4665	98	47	(	(	PUNCT
cana-4665	98	48	3.9	3.9	NUM
cana-4665	98	49	)	)	PUNCT
cana-4665	98	50	in	in	ADP
cana-4665	98	51	equation	equation	NOUN
cana-4665	98	52	(	(	PUNCT
cana-4665	98	53	2.2	2.2	NUM
cana-4665	98	54	)	)	PUNCT
cana-4665	98	55	and	and	CCONJ
cana-4665	98	56	(	(	PUNCT
cana-4665	98	57	2.3	2.3	NUM
cana-4665	98	58	)	)	PUNCT
cana-4665	98	59	,	,	PUNCT
cana-4665	98	60	we	we	PRON
cana-4665	98	61	get	get	VERB
cana-4665	98	62	ordinary	ordinary	ADJ
cana-4665	98	63	differential	differential	ADJ
cana-4665	98	64	equation	equation	NOUN
cana-4665	98	65	as	as	ADP
cana-4665	98	66	:	:	PUNCT
cana-4665	98	67	−1	−1	NOUN
cana-4665	98	68	4	4	NUM
cana-4665	98	69	f	f	NOUN
cana-4665	98	70	(	(	PUNCT
cana-4665	98	71	ξ)−ξf	ξ)−ξf	PROPN
cana-4665	98	72	′(ξ)−4aξg′′(ξ)−2ag′(ξ)+6b	′(ξ)−4aξg′′(ξ)−2ag′(ξ)+6b	NOUN
cana-4665	98	73	√	√	PROPN
cana-4665	98	74	ξf	ξf	PROPN
cana-4665	98	75	′(ξ)+2b	′(ξ)+2b	PROPN
cana-4665	98	76	√	√	PROPN
cana-4665	98	77	ξg2(ξ)f	ξg2(ξ)f	PROPN
cana-4665	98	78	′(ξ)+4b	′(ξ)+4b	PROPN
cana-4665	98	79	√	√	NUM
cana-4665	98	80	ξg(ξ)g′(ξ	ξg(ξ)g′(ξ	PROPN
cana-4665	98	81	)	)	PUNCT
cana-4665	98	82	=	=	SYM
cana-4665	98	83	0	0	NUM
cana-4665	98	84	,	,	PUNCT
cana-4665	98	85	and	and	CCONJ
cana-4665	98	86	−1	−1	NOUN
cana-4665	98	87	4	4	NUM
cana-4665	98	88	g(ξ)−ξg′(ξ)+2af	g(ξ)−ξg′(ξ)+2af	NOUN
cana-4665	98	89	′(ξ)+4aξf	′(ξ)+4aξf	PUNCT
cana-4665	98	90	′′(ξ)+4bf	′′(ξ)+4bf	X
cana-4665	98	91	(	(	PUNCT
cana-4665	98	92	ξ)g(ξ)f	ξ)g(ξ)f	PROPN
cana-4665	98	93	′(ξ	′(ξ	PROPN
cana-4665	98	94	)	)	PUNCT
cana-4665	98	95	√	√	PUNCT
cana-4665	99	1	ξ+6b	ξ+6b	NOUN
cana-4665	99	2	√	√	NUM
cana-4665	99	3	ξg2(ξ)g′(ξ)+2b	ξg2(ξ)g′(ξ)+2b	PRON
cana-4665	99	4	√	√	NOUN
cana-4665	99	5	ξf	ξf	DET
cana-4665	99	6	2(ξ)g′(ξ	2(ξ)g′(ξ	PROPN
cana-4665	99	7	)	)	PUNCT
cana-4665	99	8	=	=	NOUN
cana-4665	100	1	0	0	X
cana-4665	100	2	.	.	PUNCT
cana-4665	100	3	(	(	PUNCT
cana-4665	100	4	3.10	3.10	NUM
cana-4665	100	5	)	)	PUNCT
cana-4665	100	6	where	where	SCONJ
cana-4665	100	7	prime	prime	ADJ
cana-4665	100	8	(	(	PUNCT
cana-4665	100	9	’	'	PUNCT
cana-4665	100	10	)	)	PUNCT
cana-4665	100	11	denotes	denote	VERB
cana-4665	100	12	the	the	DET
cana-4665	100	13	differentiation	differentiation	NOUN
cana-4665	100	14	w.r.t	w.r.t	VERB
cana-4665	100	15	variable	variable	NOUN
cana-4665	100	16	ξ	ξ	PROPN
cana-4665	100	17	.	.	PROPN
cana-4665	101	1	due	due	ADP
cana-4665	101	2	to	to	ADP
cana-4665	101	3	complexity	complexity	NOUN
cana-4665	101	4	of	of	ADP
cana-4665	101	5	the	the	DET
cana-4665	101	6	reduced	reduce	VERB
cana-4665	101	7	equations	equation	NOUN
cana-4665	101	8	,	,	PUNCT
cana-4665	101	9	we	we	PRON
cana-4665	101	10	just	just	ADV
cana-4665	101	11	obtain	obtain	VERB
cana-4665	101	12	a	a	DET
cana-4665	101	13	constant	constant	ADJ
cana-4665	101	14	solution	solution	NOUN
cana-4665	101	15	for	for	ADP
cana-4665	101	16	the	the	DET
cana-4665	101	17	equation	equation	NOUN
cana-4665	101	18	.	.	PUNCT
cana-4665	102	1	3.3	3.3	NUM
cana-4665	102	2	vector	vector	NOUN
cana-4665	102	3	field	field	NOUN
cana-4665	102	4	v3	v3	PROPN
cana-4665	102	5	+	+	CCONJ
cana-4665	102	6	ωv4	ωv4	ADP
cana-4665	102	7	similarity	similarity	NOUN
cana-4665	102	8	variables	variable	NOUN
cana-4665	102	9	are	be	AUX
cana-4665	102	10	acquired	acquire	VERB
cana-4665	102	11	in	in	ADP
cana-4665	102	12	the	the	DET
cana-4665	102	13	light	light	NOUN
cana-4665	102	14	of	of	ADP
cana-4665	102	15	the	the	DET
cana-4665	102	16	characteristic	characteristic	ADJ
cana-4665	102	17	equation	equation	NOUN
cana-4665	102	18	as	as	ADP
cana-4665	102	19	:	:	PUNCT
cana-4665	102	20	ξ	ξ	PROPN
cana-4665	102	21	=	=	SYM
cana-4665	102	22	x−	x−	PROPN
cana-4665	102	23	t	t	PROPN
cana-4665	102	24	ω	ω	PROPN
cana-4665	102	25	,	,	PUNCT
cana-4665	102	26	q	q	PROPN
cana-4665	102	27	=	=	SYM
cana-4665	102	28	f	f	X
cana-4665	102	29	(	(	PUNCT
cana-4665	102	30	ξ)eιg(ξ	ξ)eιg(ξ	PROPN
cana-4665	102	31	)	)	PUNCT
cana-4665	102	32	.	.	PUNCT
cana-4665	103	1	(	(	PUNCT
cana-4665	103	2	3.11	3.11	NUM
cana-4665	103	3	)	)	PUNCT
cana-4665	103	4	on	on	ADP
cana-4665	103	5	applying	apply	VERB
cana-4665	103	6	these	these	DET
cana-4665	103	7	values	value	NOUN
cana-4665	103	8	we	we	PRON
cana-4665	103	9	acquire	acquire	VERB
cana-4665	103	10	the	the	DET
cana-4665	103	11	aforementioned	aforementioned	ADJ
cana-4665	103	12	system	system	NOUN
cana-4665	103	13	of	of	ADP
cana-4665	103	14	ordinary	ordinary	ADJ
cana-4665	103	15	differential	differential	ADJ
cana-4665	103	16	equations	equation	NOUN
cana-4665	103	17	as	as	ADP
cana-4665	103	18	−	−	PROPN
cana-4665	103	19	1	1	NUM
cana-4665	103	20	ω	ω	NUM
cana-4665	103	21	f	f	X
cana-4665	103	22	(	(	PUNCT
cana-4665	103	23	ξ)g′(ξ	ξ)g′(ξ	PROPN
cana-4665	103	24	)	)	PUNCT
cana-4665	104	1	+	+	CCONJ
cana-4665	104	2	af	af	PROPN
cana-4665	104	3	′′(ξ)−	′′(ξ)−	PROPN
cana-4665	104	4	af	af	NOUN
cana-4665	104	5	(	(	PUNCT
cana-4665	104	6	ξ)(g′(ξ))2	ξ)(g′(ξ))2	NOUN
cana-4665	104	7	+	+	CCONJ
cana-4665	104	8	bf	bf	NOUN
cana-4665	104	9	(	(	PUNCT
cana-4665	104	10	ξ)3g′(ξ	ξ)3g′(ξ	NOUN
cana-4665	104	11	)	)	PUNCT
cana-4665	104	12	=	=	SYM
cana-4665	104	13	0	0	NUM
cana-4665	104	14	,	,	PUNCT
cana-4665	104	15	(	(	PUNCT
cana-4665	104	16	3.12	3.12	NUM
cana-4665	104	17	)	)	PUNCT
cana-4665	104	18	communications	communication	NOUN
cana-4665	104	19	on	on	ADP
cana-4665	104	20	applied	apply	VERB
cana-4665	104	21	nonlinear	nonlinear	ADJ
cana-4665	104	22	analysis	analysis	NOUN
cana-4665	104	23	issn	issn	NOUN
cana-4665	104	24	:	:	PUNCT
cana-4665	104	25	1074	1074	NUM
cana-4665	104	26	-	-	PUNCT
cana-4665	104	27	133x	133x	NUM
cana-4665	104	28	vol	vol	VERB
cana-4665	104	29	32	32	NUM
cana-4665	104	30	no	no	NOUN
cana-4665	104	31	.	.	PUNCT
cana-4665	105	1	10s	10	NOUN
cana-4665	105	2	(	(	PUNCT
cana-4665	105	3	2025	2025	NUM
cana-4665	105	4	)	)	PUNCT
cana-4665	105	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-4665	105	6	93	93	NUM
cana-4665	105	7	and	and	CCONJ
cana-4665	105	8	−	−	PROPN
cana-4665	105	9	1	1	NUM
cana-4665	105	10	ω	ω	NUM
cana-4665	105	11	f	f	NOUN
cana-4665	105	12	′(ξ)−	′(ξ)−	PROPN
cana-4665	105	13	2af	2af	PROPN
cana-4665	105	14	′(ξ)g′(ξ)−	′(ξ)g′(ξ)−	PROPN
cana-4665	105	15	af	af	PROPN
cana-4665	105	16	(	(	PUNCT
cana-4665	105	17	ξ)g′′(ξ	ξ)g′′(ξ	PROPN
cana-4665	105	18	)	)	PUNCT
cana-4665	106	1	+	+	X
cana-4665	106	2	3bf	3bf	ADJ
cana-4665	106	3	(	(	PUNCT
cana-4665	106	4	ξ)2f	ξ)2f	NOUN
cana-4665	106	5	′(ξ	′(ξ	PROPN
cana-4665	106	6	)	)	PUNCT
cana-4665	106	7	=	=	SYM
cana-4665	107	1	0	0	X
cana-4665	107	2	.	.	PUNCT
cana-4665	108	1	(	(	PUNCT
cana-4665	108	2	3.13	3.13	NUM
cana-4665	108	3	)	)	PUNCT
cana-4665	108	4	multiply	multiply	NOUN
cana-4665	108	5	equation(3.13	equation(3.13	NUM
cana-4665	108	6	)	)	PUNCT
cana-4665	108	7	with	with	ADP
cana-4665	108	8	f	f	PROPN
cana-4665	108	9	(	(	PUNCT
cana-4665	108	10	ξ	ξ	NOUN
cana-4665	108	11	)	)	PUNCT
cana-4665	108	12	and	and	CCONJ
cana-4665	108	13	on	on	ADP
cana-4665	108	14	integrating	integrate	VERB
cana-4665	108	15	we	we	PRON
cana-4665	108	16	obtain	obtain	VERB
cana-4665	108	17	−ag′(ξ)f	−ag′(ξ)f	PROPN
cana-4665	108	18	(	(	PUNCT
cana-4665	108	19	ξ)2	ξ)2	PROPN
cana-4665	108	20	−	−	PROPN
cana-4665	108	21	f	f	PROPN
cana-4665	108	22	(	(	PUNCT
cana-4665	108	23	ξ)2	ξ)2	PROPN
cana-4665	108	24	2ω	2ω	PROPN
cana-4665	109	1	+	+	CCONJ
cana-4665	109	2	3	3	NUM
cana-4665	109	3	4	4	NUM
cana-4665	109	4	bf	bf	NOUN
cana-4665	109	5	(	(	PUNCT
cana-4665	109	6	ξ)4	ξ)4	X
cana-4665	109	7	=	=	SYM
cana-4665	109	8	0	0	NUM
cana-4665	109	9	,	,	PUNCT
cana-4665	109	10	(	(	PUNCT
cana-4665	109	11	3.14	3.14	NUM
cana-4665	109	12	)	)	PUNCT
cana-4665	109	13	above	above	ADP
cana-4665	109	14	equation	equation	NOUN
cana-4665	109	15	leads	lead	VERB
cana-4665	109	16	to	to	ADP
cana-4665	109	17	:	:	PUNCT
cana-4665	109	18	g′(ξ	g′(ξ	X
cana-4665	109	19	)	)	PUNCT
cana-4665	110	1	=	=	SYM
cana-4665	110	2	−12aω	−12aω	NOUN
cana-4665	110	3	+	+	NUM
cana-4665	110	4	3b	3b	NUM
cana-4665	110	5	4a	4a	X
cana-4665	110	6	f	f	X
cana-4665	110	7	(	(	PUNCT
cana-4665	110	8	ξ)2	ξ)2	PROPN
cana-4665	110	9	+	+	PROPN
cana-4665	110	10	b	b	PROPN
cana-4665	110	11	,	,	PUNCT
cana-4665	110	12	(	(	PUNCT
cana-4665	110	13	3.15	3.15	NUM
cana-4665	110	14	)	)	PUNCT
cana-4665	110	15	where	where	SCONJ
cana-4665	110	16	b	b	NOUN
cana-4665	110	17	is	be	AUX
cana-4665	110	18	referred	refer	VERB
cana-4665	110	19	to	to	ADP
cana-4665	110	20	as	as	ADP
cana-4665	110	21	the	the	DET
cana-4665	110	22	arbitrary	arbitrary	ADJ
cana-4665	110	23	constant	constant	ADJ
cana-4665	110	24	.	.	PUNCT
cana-4665	111	1	on	on	ADP
cana-4665	111	2	substituting	substitute	VERB
cana-4665	111	3	this	this	DET
cana-4665	111	4	value	value	NOUN
cana-4665	111	5	in	in	ADP
cana-4665	111	6	(	(	PUNCT
cana-4665	111	7	3.12	3.12	NUM
cana-4665	111	8	)	)	PUNCT
cana-4665	111	9	and	and	CCONJ
cana-4665	111	10	again	again	ADV
cana-4665	111	11	multiply	multiply	VERB
cana-4665	111	12	with	with	ADP
cana-4665	111	13	f	f	PROPN
cana-4665	111	14	′(ξ	′(ξ	PROPN
cana-4665	111	15	)	)	PUNCT
cana-4665	111	16	and	and	CCONJ
cana-4665	111	17	integrating	integrating	NOUN
cana-4665	111	18	,	,	PUNCT
cana-4665	111	19	we	we	PRON
cana-4665	111	20	get	get	VERB
cana-4665	111	21	b2	b2	NOUN
cana-4665	111	22	32a	32a	NOUN
cana-4665	111	23	f	f	PROPN
cana-4665	111	24	(	(	PUNCT
cana-4665	111	25	ξ)6	ξ)6	VERB
cana-4665	111	26	−	−	PROPN
cana-4665	111	27	b	b	NUM
cana-4665	111	28	8aw	8aw	NOUN
cana-4665	111	29	f	f	PROPN
cana-4665	111	30	(	(	PUNCT
cana-4665	111	31	ξ)4	ξ)4	X
cana-4665	111	32	+	+	X
cana-4665	111	33	1	1	NUM
cana-4665	111	34	8aω2	8aω2	NUM
cana-4665	111	35	f	f	NOUN
cana-4665	111	36	(	(	PUNCT
cana-4665	111	37	ξ)2	ξ)2	PROPN
cana-4665	111	38	+	+	CCONJ
cana-4665	111	39	a	a	DET
cana-4665	111	40	2	2	NUM
cana-4665	111	41	(	(	PUNCT
cana-4665	111	42	f	f	NOUN
cana-4665	111	43	′(ξ))2	′(ξ))2	NOUN
cana-4665	111	44	=	=	NOUN
cana-4665	111	45	0	0	PROPN
cana-4665	111	46	,	,	PUNCT
cana-4665	111	47	(	(	PUNCT
cana-4665	111	48	3.16	3.16	NUM
cana-4665	111	49	)	)	PUNCT
cana-4665	111	50	substitute	substitute	NOUN
cana-4665	111	51	(	(	PUNCT
cana-4665	111	52	f	f	X
cana-4665	111	53	(	(	PUNCT
cana-4665	111	54	ξ))2	ξ))2	X
cana-4665	111	55	=	=	SYM
cana-4665	111	56	p	p	X
cana-4665	111	57	(	(	PUNCT
cana-4665	111	58	ξ	ξ	NOUN
cana-4665	111	59	)	)	PUNCT
cana-4665	111	60	into	into	ADP
cana-4665	111	61	(	(	PUNCT
cana-4665	111	62	3.16	3.16	NUM
cana-4665	111	63	)	)	PUNCT
cana-4665	111	64	equation	equation	NOUN
cana-4665	111	65	,	,	PUNCT
cana-4665	111	66	we	we	PRON
cana-4665	111	67	get	get	VERB
cana-4665	111	68	b2ω2p	b2ω2p	PUNCT
cana-4665	111	69	(	(	PUNCT
cana-4665	111	70	ξ)4	ξ)4	VERB
cana-4665	111	71	−	−	PROPN
cana-4665	111	72	4bωp	4bωp	NUM
cana-4665	111	73	(	(	PUNCT
cana-4665	111	74	ξ)3	ξ)3	PROPN
cana-4665	111	75	+	+	X
cana-4665	111	76	4p	4p	NUM
cana-4665	111	77	(	(	PUNCT
cana-4665	111	78	ξ)2	ξ)2	PROPN
cana-4665	111	79	+	+	NUM
cana-4665	111	80	4a2ω2(p	4a2ω2(p	NOUN
cana-4665	111	81	′(ξ))2	′(ξ))2	NOUN
cana-4665	111	82	=	=	NOUN
cana-4665	111	83	0	0	PROPN
cana-4665	111	84	.	.	PUNCT
cana-4665	112	1	(	(	PUNCT
cana-4665	112	2	3.17	3.17	NUM
cana-4665	112	3	)	)	PUNCT
cana-4665	112	4	on	on	ADP
cana-4665	112	5	solving	solve	VERB
cana-4665	112	6	the	the	DET
cana-4665	112	7	equation	equation	NOUN
cana-4665	112	8	(	(	PUNCT
cana-4665	112	9	3.17	3.17	NUM
cana-4665	112	10	)	)	PUNCT
cana-4665	112	11	,	,	PUNCT
cana-4665	112	12	we	we	PRON
cana-4665	112	13	acquire	acquire	VERB
cana-4665	112	14	the	the	DET
cana-4665	112	15	solutions	solution	NOUN
cana-4665	112	16	which	which	PRON
cana-4665	112	17	are	be	AUX
cana-4665	112	18	given	give	VERB
cana-4665	112	19	underneath	underneath	NOUN
cana-4665	112	20	:	:	PUNCT
cana-4665	112	21	(	(	PUNCT
cana-4665	112	22	i)q(x	i)q(x	INTJ
cana-4665	112	23	,	,	PUNCT
cana-4665	112	24	t	t	PROPN
cana-4665	112	25	)	)	PUNCT
cana-4665	112	26	=	=	SYM
cana-4665	113	1	√	√	NUM
cana-4665	113	2	2	2	NUM
cana-4665	113	3	bωe	bωe	X
cana-4665	113	4	ι(−12aω+	ι(−12aω+	PROPN
cana-4665	113	5	3ω	3ω	NOUN
cana-4665	113	6	2a	2a	NUM
cana-4665	113	7	+	+	CCONJ
cana-4665	113	8	b)(x−	b)(x−	PROPN
cana-4665	113	9	t	t	PROPN
cana-4665	113	10	ω	ω	PROPN
cana-4665	113	11	)	)	PUNCT
cana-4665	114	1	+	+	NOUN
cana-4665	114	2	c2	c2	PROPN
cana-4665	114	3	,	,	PUNCT
cana-4665	114	4	(	(	PUNCT
cana-4665	114	5	ii)q(x	ii)q(x	PROPN
cana-4665	114	6	,	,	PUNCT
cana-4665	114	7	t	t	PROPN
cana-4665	114	8	)	)	PUNCT
cana-4665	114	9	=	=	SYM
cana-4665	114	10	√	√	NUM
cana-4665	114	11	1	1	NUM
cana-4665	114	12	bω	bω	NOUN
cana-4665	114	13	−	−	PROPN
cana-4665	114	14	tanh	tanh	PROPN
cana-4665	114	15	(	(	PUNCT
cana-4665	114	16	c1−	c1−	PROPN
cana-4665	114	17	1	1	NUM
cana-4665	114	18	2	2	NUM
cana-4665	114	19	ι(x−	ι(x−	PROPN
cana-4665	114	20	t	t	PROPN
cana-4665	114	21	ω	ω	PROPN
cana-4665	114	22	)	)	PUNCT
cana-4665	114	23	ωa	ωa	PROPN
cana-4665	114	24	)	)	PUNCT
cana-4665	114	25	bω	bω	PROPN
cana-4665	114	26	×	×	PROPN
cana-4665	114	27	e	e	PROPN
cana-4665	114	28	ι	ι	PROPN
cana-4665	114	29	(	(	PUNCT
cana-4665	114	30	−12aω(x−	−12aω(x−	PROPN
cana-4665	114	31	t	t	PROPN
cana-4665	114	32	ω	ω	PROPN
cana-4665	114	33	)	)	PUNCT
cana-4665	115	1	+	+	CCONJ
cana-4665	115	2	3(x−	3(x−	NUM
cana-4665	115	3	t	t	PROPN
cana-4665	115	4	ω	ω	NUM
cana-4665	115	5	)	)	PUNCT
cana-4665	116	1	4aω	4aω	NOUN
cana-4665	117	1	+	+	X
cana-4665	117	2	3ι	3ι	NUM
cana-4665	117	3	log(tanh(c1−	log(tanh(c1−	NOUN
cana-4665	117	4	ι	ι	X
cana-4665	117	5	2	2	NUM
cana-4665	117	6	(	(	PUNCT
cana-4665	117	7	x−	x−	PROPN
cana-4665	117	8	t	t	PROPN
cana-4665	117	9	ω	ω	PROPN
cana-4665	117	10	)	)	PUNCT
cana-4665	117	11	)	)	PUNCT
cana-4665	117	12	−1	−1	NOUN
cana-4665	117	13	)	)	PUNCT
cana-4665	117	14	4aω	4aω	NOUN
cana-4665	118	1	+	+	X
cana-4665	118	2	3ι	3ι	NUM
cana-4665	118	3	log(tanh(c1−	log(tanh(c1−	NOUN
cana-4665	118	4	ι	ι	X
cana-4665	118	5	2	2	NUM
cana-4665	118	6	(	(	PUNCT
cana-4665	118	7	x−	x−	PROPN
cana-4665	118	8	t	t	PROPN
cana-4665	118	9	ω	ω	PROPN
cana-4665	118	10	)	)	PUNCT
cana-4665	118	11	)	)	PUNCT
cana-4665	119	1	+1	+1	X
cana-4665	119	2	)	)	PUNCT
cana-4665	119	3	4aω	4aω	NOUN
cana-4665	120	1	+	+	NOUN
cana-4665	120	2	b(x−	b(x−	NOUN
cana-4665	120	3	t	t	PROPN
cana-4665	120	4	ω	ω	NUM
cana-4665	120	5	)	)	PUNCT
cana-4665	120	6	)	)	PUNCT
cana-4665	121	1	(	(	PUNCT
cana-4665	121	2	3.18	3.18	NUM
cana-4665	121	3	)	)	PUNCT
cana-4665	121	4	3.4	3.4	NUM
cana-4665	121	5	exact	exact	ADJ
cana-4665	121	6	traveling	travel	VERB
cana-4665	121	7	wave	wave	NOUN
cana-4665	121	8	solutions	solution	NOUN
cana-4665	121	9	using	use	VERB
cana-4665	121	10	(	(	PUNCT
cana-4665	121	11	g	g	NOUN
cana-4665	121	12	′	′	NUM
cana-4665	121	13	g	g	NOUN
cana-4665	121	14	)	)	PUNCT
cana-4665	121	15	-expansion	-expansion	PROPN
cana-4665	121	16	method	method	NOUN
cana-4665	121	17	in	in	ADP
cana-4665	121	18	this	this	DET
cana-4665	121	19	section	section	NOUN
cana-4665	121	20	,	,	PUNCT
cana-4665	121	21	we	we	PRON
cana-4665	121	22	aim	aim	VERB
cana-4665	121	23	to	to	PART
cana-4665	121	24	determine	determine	VERB
cana-4665	121	25	wave	wave	NOUN
cana-4665	121	26	solutions	solution	NOUN
cana-4665	121	27	by	by	ADP
cana-4665	121	28	using	use	VERB
cana-4665	121	29	(	(	PUNCT
cana-4665	121	30	g	g	NOUN
cana-4665	121	31	′	′	NUM
cana-4665	121	32	g	g	NOUN
cana-4665	121	33	)	)	PUNCT
cana-4665	121	34	-expansion	-expansion	PROPN
cana-4665	121	35	method	method	NOUN
cana-4665	121	36	for	for	ADP
cana-4665	121	37	equation	equation	NOUN
cana-4665	121	38	(	(	PUNCT
cana-4665	121	39	3.17	3.17	NUM
cana-4665	121	40	)	)	PUNCT
cana-4665	121	41	.	.	PUNCT
cana-4665	122	1	the	the	DET
cana-4665	122	2	progression	progression	NOUN
cana-4665	122	3	of	of	ADP
cana-4665	122	4	wave	wave	NOUN
cana-4665	122	5	solutions	solution	NOUN
cana-4665	122	6	originates	originate	NOUN
cana-4665	122	7	from	from	ADP
cana-4665	122	8	these	these	DET
cana-4665	122	9	procedures	procedure	NOUN
cana-4665	122	10	:	:	PUNCT
cana-4665	122	11	1	1	X
cana-4665	122	12	.	.	X
cana-4665	122	13	taking	take	VERB
cana-4665	122	14	into	into	ADP
cana-4665	122	15	consideration	consideration	NOUN
cana-4665	122	16	,	,	PUNCT
cana-4665	122	17	the	the	DET
cana-4665	122	18	structure	structure	NOUN
cana-4665	122	19	of	of	ADP
cana-4665	122	20	ordinary	ordinary	ADJ
cana-4665	122	21	differential	differential	ADJ
cana-4665	122	22	equation	equation	NOUN
cana-4665	122	23	(	(	PUNCT
cana-4665	122	24	3.17	3.17	NUM
cana-4665	122	25	)	)	PUNCT
cana-4665	122	26	is	be	AUX
cana-4665	122	27	formulated	formulate	VERB
cana-4665	122	28	as	as	ADP
cana-4665	122	29	(	(	PUNCT
cana-4665	122	30	g′	g′	NOUN
cana-4665	122	31	g	g	NOUN
cana-4665	122	32	)	)	PUNCT
cana-4665	122	33	:	:	PUNCT
cana-4665	123	1	f̃	f̃	PROPN
cana-4665	123	2	(	(	PUNCT
cana-4665	123	3	χ	χ	X
cana-4665	123	4	)	)	PUNCT
cana-4665	123	5	=	=	SYM
cana-4665	123	6	aq	aq	PROPN
cana-4665	123	7	(	(	PUNCT
cana-4665	123	8	g′	g′	NOUN
cana-4665	123	9	g	g	NOUN
cana-4665	123	10	)	)	PUNCT
cana-4665	123	11	q	q	PROPN
cana-4665	124	1	+	+	CCONJ
cana-4665	124	2	aq−1	aq−1	NOUN
cana-4665	124	3	(	(	PUNCT
cana-4665	124	4	g′	g′	NOUN
cana-4665	124	5	g	g	NOUN
cana-4665	124	6	)	)	PUNCT
cana-4665	124	7	q−1	q−1	PROPN
cana-4665	125	1	+	+	CCONJ
cana-4665	125	2	........	........	PUNCT
cana-4665	125	3	(	(	PUNCT
cana-4665	125	4	3.19	3.19	NUM
cana-4665	125	5	)	)	PUNCT
cana-4665	125	6	here	here	ADV
cana-4665	125	7	aq	aq	VERB
cana-4665	125	8	are	be	AUX
cana-4665	125	9	constants	constant	NOUN
cana-4665	125	10	to	to	PART
cana-4665	125	11	be	be	AUX
cana-4665	125	12	determine	determine	NOUN
cana-4665	125	13	,	,	PUNCT
cana-4665	125	14	where	where	SCONJ
cana-4665	125	15	q	q	PROPN
cana-4665	125	16	ranges	range	VERB
cana-4665	125	17	from	from	ADP
cana-4665	125	18	0	0	NUM
cana-4665	125	19	to	to	ADP
cana-4665	125	20	infinity	infinity	NOUN
cana-4665	125	21	.	.	PUNCT
cana-4665	126	1	as	as	SCONJ
cana-4665	126	2	g	g	PROPN
cana-4665	126	3	=	=	SYM
cana-4665	126	4	g(χ	g(χ	PROPN
cana-4665	126	5	)	)	PUNCT
cana-4665	126	6	persuades	persuade	VERB
cana-4665	126	7	the	the	DET
cana-4665	126	8	lde	lde	NOUN
cana-4665	126	9	of	of	ADP
cana-4665	126	10	second	second	ADJ
cana-4665	126	11	order	order	NOUN
cana-4665	126	12	which	which	PRON
cana-4665	126	13	is	be	AUX
cana-4665	126	14	of	of	ADP
cana-4665	126	15	the	the	DET
cana-4665	126	16	form	form	NOUN
cana-4665	126	17	written	write	VERB
cana-4665	126	18	below	below	ADV
cana-4665	126	19	:	:	PUNCT
cana-4665	126	20	g′′	g′′	PROPN
cana-4665	126	21	+	+	PROPN
cana-4665	126	22	λ̃g′	λ̃g′	PROPN
cana-4665	126	23	+	+	ADJ
cana-4665	126	24	µ̃g	µ̃g	NOUN
cana-4665	126	25	=	=	NOUN
cana-4665	126	26	0	0	NUM
cana-4665	126	27	.	.	PUNCT
cana-4665	127	1	(	(	PUNCT
cana-4665	127	2	3.20	3.20	NUM
cana-4665	127	3	)	)	PUNCT
cana-4665	127	4	where	where	SCONJ
cana-4665	127	5	aq(aq	aq(aq	PROPN
cana-4665	127	6	6=	6=	PROPN
cana-4665	127	7	0	0	NUM
cana-4665	127	8	)	)	PUNCT
cana-4665	127	9	;	;	PUNCT
cana-4665	127	10	where	where	SCONJ
cana-4665	127	11	q	q	NOUN
cana-4665	127	12	is	be	AUX
cana-4665	127	13	called	call	VERB
cana-4665	127	14	the	the	DET
cana-4665	127	15	balance	balance	NOUN
cana-4665	127	16	number	number	NOUN
cana-4665	127	17	,	,	PUNCT
cana-4665	127	18	aq−1,	aq−1,	NOUN
cana-4665	127	19	.....	.....	SYM
cana-4665	127	20	a0	a0	PROPN
cana-4665	127	21	,	,	PUNCT
cana-4665	127	22	λ̃	λ̃	PROPN
cana-4665	127	23	and	and	CCONJ
cana-4665	127	24	µ̃	µ̃	PROPN
cana-4665	127	25	are	be	AUX
cana-4665	127	26	constants	constant	NOUN
cana-4665	127	27	to	to	PART
cana-4665	127	28	be	be	AUX
cana-4665	127	29	determine	determine	VERB
cana-4665	127	30	later	later	ADV
cana-4665	127	31	.	.	PUNCT
cana-4665	128	1	communications	communication	NOUN
cana-4665	128	2	on	on	ADP
cana-4665	128	3	applied	apply	VERB
cana-4665	128	4	nonlinear	nonlinear	ADJ
cana-4665	128	5	analysis	analysis	NOUN
cana-4665	128	6	issn	issn	NOUN
cana-4665	128	7	:	:	PUNCT
cana-4665	128	8	1074	1074	NUM
cana-4665	128	9	-	-	PUNCT
cana-4665	128	10	133x	133x	NUM
cana-4665	128	11	vol	vol	VERB
cana-4665	128	12	32	32	NUM
cana-4665	128	13	no	no	NOUN
cana-4665	128	14	.	.	PUNCT
cana-4665	129	1	10s	10	NOUN
cana-4665	129	2	(	(	PUNCT
cana-4665	129	3	2025	2025	NUM
cana-4665	129	4	)	)	PUNCT
cana-4665	129	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-4665	129	6	94	94	NUM
cana-4665	129	7	2	2	NUM
cana-4665	129	8	.	.	PUNCT
cana-4665	129	9	determining	determine	VERB
cana-4665	129	10	the	the	DET
cana-4665	129	11	positive	positive	ADJ
cana-4665	129	12	integer	integer	NOUN
cana-4665	129	13	q	q	NOUN
cana-4665	129	14	in	in	ADP
cana-4665	129	15	(	(	PUNCT
cana-4665	129	16	3.19	3.19	NUM
cana-4665	129	17	)	)	PUNCT
cana-4665	129	18	,	,	PUNCT
cana-4665	129	19	by	by	ADP
cana-4665	129	20	equalizing	equalize	VERB
cana-4665	129	21	the	the	DET
cana-4665	129	22	higher	high	ADJ
cana-4665	129	23	order	order	NOUN
cana-4665	129	24	nonlinear	nonlinear	ADJ
cana-4665	129	25	terms	term	NOUN
cana-4665	129	26	to	to	ADP
cana-4665	129	27	the	the	DET
cana-4665	129	28	higher	high	ADJ
cana-4665	129	29	order	order	NOUN
cana-4665	129	30	derivatives	derivative	NOUN
cana-4665	129	31	in	in	ADP
cana-4665	129	32	(	(	PUNCT
cana-4665	129	33	3.17	3.17	NUM
cana-4665	129	34	)	)	PUNCT
cana-4665	129	35	3	3	NUM
cana-4665	129	36	.	.	X
cana-4665	130	1	replacing	replace	VERB
cana-4665	130	2	(	(	PUNCT
cana-4665	130	3	3.19	3.19	NUM
cana-4665	130	4	)	)	PUNCT
cana-4665	130	5	into	into	ADP
cana-4665	130	6	(	(	PUNCT
cana-4665	130	7	3.17	3.17	NUM
cana-4665	130	8	)	)	PUNCT
cana-4665	130	9	and	and	CCONJ
cana-4665	130	10	pertain	pertain	VERB
cana-4665	130	11	the	the	DET
cana-4665	130	12	ode	ode	NOUN
cana-4665	130	13	(	(	PUNCT
cana-4665	130	14	3.20	3.20	NUM
cana-4665	130	15	)	)	PUNCT
cana-4665	130	16	,	,	PUNCT
cana-4665	130	17	then	then	ADV
cana-4665	130	18	gather	gather	VERB
cana-4665	130	19	all	all	DET
cana-4665	130	20	the	the	DET
cana-4665	130	21	entire	entire	ADJ
cana-4665	130	22	terms	term	NOUN
cana-4665	130	23	of	of	ADP
cana-4665	130	24	(	(	PUNCT
cana-4665	130	25	g′	g′	NOUN
cana-4665	130	26	g	g	NOUN
cana-4665	130	27	)	)	PUNCT
cana-4665	130	28	containing	contain	VERB
cana-4665	130	29	homogeneous	homogeneous	ADJ
cana-4665	130	30	power	power	NOUN
cana-4665	130	31	,	,	PUNCT
cana-4665	130	32	and	and	CCONJ
cana-4665	130	33	equalize	equalize	VERB
cana-4665	130	34	each	each	DET
cana-4665	130	35	coefficient	coefficient	NOUN
cana-4665	130	36	to	to	ADP
cana-4665	130	37	zero	zero	NUM
cana-4665	130	38	,	,	PUNCT
cana-4665	130	39	resulting	result	VERB
cana-4665	130	40	in	in	ADP
cana-4665	130	41	a	a	DET
cana-4665	130	42	variety	variety	NOUN
cana-4665	130	43	of	of	ADP
cana-4665	130	44	algebraic	algebraic	ADJ
cana-4665	130	45	equations	equation	NOUN
cana-4665	130	46	for	for	ADP
cana-4665	130	47	anaysis	anaysis	NOUN
cana-4665	130	48	aq	aq	ADP
cana-4665	130	49	,	,	PUNCT
cana-4665	130	50	aq−1	aq−1	PROPN
cana-4665	130	51	,	,	PUNCT
cana-4665	130	52	.....	.....	PUNCT
cana-4665	131	1	a0	a0	PROPN
cana-4665	131	2	,	,	PUNCT
cana-4665	131	3	c	c	X
cana-4665	131	4	,	,	PUNCT
cana-4665	131	5	λ̃	λ̃	PROPN
cana-4665	131	6	and	and	CCONJ
cana-4665	131	7	µ̃.	µ̃.	NOUN
cana-4665	131	8	4	4	NUM
cana-4665	131	9	.	.	PUNCT
cana-4665	132	1	the	the	DET
cana-4665	132	2	general	general	ADJ
cana-4665	132	3	solution	solution	NOUN
cana-4665	132	4	of	of	ADP
cana-4665	132	5	(	(	PUNCT
cana-4665	132	6	3.20	3.20	NUM
cana-4665	132	7	)	)	PUNCT
cana-4665	132	8	is	be	AUX
cana-4665	132	9	noted	note	VERB
cana-4665	132	10	,	,	PUNCT
cana-4665	132	11	then	then	ADV
cana-4665	132	12	substituting	substitute	VERB
cana-4665	132	13	the	the	DET
cana-4665	132	14	values	value	NOUN
cana-4665	132	15	of	of	ADP
cana-4665	132	16	aq	aq	NOUN
cana-4665	132	17	in	in	ADP
cana-4665	132	18	(	(	PUNCT
cana-4665	132	19	3.19	3.19	NUM
cana-4665	132	20	)	)	PUNCT
cana-4665	132	21	we	we	PRON
cana-4665	132	22	will	will	AUX
cana-4665	132	23	get	get	VERB
cana-4665	132	24	the	the	DET
cana-4665	132	25	exact	exact	ADJ
cana-4665	132	26	solutions	solution	NOUN
cana-4665	132	27	of	of	ADP
cana-4665	132	28	(	(	PUNCT
cana-4665	132	29	1.1	1.1	NUM
cana-4665	132	30	)	)	PUNCT
cana-4665	132	31	the	the	DET
cana-4665	132	32	general	general	ADJ
cana-4665	132	33	solutions	solution	NOUN
cana-4665	132	34	of	of	ADP
cana-4665	132	35	equation(3.20	equation(3.20	NUM
cana-4665	132	36	)	)	PUNCT
cana-4665	132	37	can	can	AUX
cana-4665	132	38	be	be	AUX
cana-4665	132	39	written	write	VERB
cana-4665	132	40	as	as	ADP
cana-4665	132	41	(	(	PUNCT
cana-4665	132	42	g′	g′	NOUN
cana-4665	132	43	g	g	NOUN
cana-4665	132	44	)	)	PUNCT
cana-4665	133	1	=	=	PUNCT
cana-4665	133	2			PROPN
cana-4665	134	1	√	√	NOUN
cana-4665	135	1	λ̃2−4µ̃	λ̃2−4µ̃	PRON
cana-4665	135	2	2	2	NUM
cana-4665	135	3	(	(	PUNCT
cana-4665	135	4	c1sinh	c1sinh	ADV
cana-4665	135	5	(	(	PUNCT
cana-4665	135	6	1	1	NUM
cana-4665	135	7	2	2	NUM
cana-4665	135	8	√	√	PROPN
cana-4665	135	9	λ̃2−4µ̃	λ̃2−4µ̃	PROPN
cana-4665	135	10	)	)	PUNCT
cana-4665	135	11	χ+c2cosh	χ+c2cosh	PROPN
cana-4665	135	12	(	(	PUNCT
cana-4665	135	13	1	1	NUM
cana-4665	135	14	2	2	NUM
cana-4665	135	15	√	√	PROPN
cana-4665	135	16	λ̃2−4µ̃	λ̃2−4µ̃	PROPN
cana-4665	135	17	)	)	PUNCT
cana-4665	135	18	χ	χ	PRON
cana-4665	135	19	c1cosh	c1cosh	NOUN
cana-4665	135	20	(	(	PUNCT
cana-4665	135	21	1	1	NUM
cana-4665	135	22	2	2	NUM
cana-4665	135	23	√	√	PROPN
cana-4665	135	24	λ̃2−4µ̃	λ̃2−4µ̃	PROPN
cana-4665	135	25	)	)	PUNCT
cana-4665	135	26	χ+c2sinh	χ+c2sinh	PROPN
cana-4665	135	27	(	(	PUNCT
cana-4665	135	28	1	1	NUM
cana-4665	135	29	2	2	NUM
cana-4665	135	30	√	√	PROPN
cana-4665	135	31	λ̃2−4µ̃	λ̃2−4µ̃	PROPN
cana-4665	135	32	)	)	PUNCT
cana-4665	135	33	χ	χ	X
cana-4665	135	34	)	)	PUNCT
cana-4665	135	35	−	−	PROPN
cana-4665	136	1	λ̃	λ̃	PROPN
cana-4665	136	2	2	2	NUM
cana-4665	136	3	,	,	PUNCT
cana-4665	136	4	λ̃	λ̃	PROPN
cana-4665	136	5	2	2	NUM
cana-4665	136	6	−	−	PROPN
cana-4665	136	7	4µ̃	4µ̃	NOUN
cana-4665	136	8	>	>	SYM
cana-4665	136	9	0	0	PUNCT
cana-4665	137	1	√	√	NUM
cana-4665	137	2	4µ̃−λ̃2	4µ̃−λ̃2	NOUN
cana-4665	137	3	2	2	NUM
cana-4665	137	4	(	(	PUNCT
cana-4665	137	5	−c1sin	−c1sin	NOUN
cana-4665	137	6	(	(	PUNCT
cana-4665	137	7	1	1	NUM
cana-4665	137	8	2	2	NUM
cana-4665	137	9	√	√	PROPN
cana-4665	137	10	4µ̃−λ̃2	4µ̃−λ̃2	NOUN
cana-4665	137	11	)	)	PUNCT
cana-4665	137	12	χ+c2cos	χ+c2cos	X
cana-4665	137	13	(	(	PUNCT
cana-4665	137	14	1	1	NUM
cana-4665	137	15	2	2	NUM
cana-4665	137	16	√	√	PROPN
cana-4665	137	17	4µ̃−λ̃2	4µ̃−λ̃2	NOUN
cana-4665	137	18	)	)	PUNCT
cana-4665	138	1	χ	χ	DET
cana-4665	138	2	c1cos	c1cos	PROPN
cana-4665	138	3	(	(	PUNCT
cana-4665	138	4	1	1	NUM
cana-4665	138	5	2	2	NUM
cana-4665	138	6	√	√	PROPN
cana-4665	138	7	4µ̃−λ̃2	4µ̃−λ̃2	PROPN
cana-4665	138	8	)	)	PUNCT
cana-4665	138	9	χ+c2sin	χ+c2sin	PROPN
cana-4665	138	10	(	(	PUNCT
cana-4665	138	11	1	1	NUM
cana-4665	138	12	2	2	NUM
cana-4665	138	13	√	√	PROPN
cana-4665	138	14	4µ̃−λ̃2	4µ̃−λ̃2	NOUN
cana-4665	138	15	)	)	PUNCT
cana-4665	139	1	χ	χ	X
cana-4665	139	2	)	)	PUNCT
cana-4665	139	3	−	−	PROPN
cana-4665	140	1	λ̃	λ̃	PROPN
cana-4665	140	2	2	2	NUM
cana-4665	140	3	,	,	PUNCT
cana-4665	140	4	λ̃	λ̃	PROPN
cana-4665	140	5	2	2	NUM
cana-4665	140	6	−	−	PROPN
cana-4665	140	7	4µ̃	4µ̃	NOUN
cana-4665	140	8	<	<	X
cana-4665	140	9	0	0	NUM
cana-4665	140	10	c2	c2	PROPN
cana-4665	140	11	c1+c2χ	c1+c2χ	PROPN
cana-4665	140	12	−	−	PROPN
cana-4665	140	13	λ̃	λ̃	PROPN
cana-4665	140	14	2	2	NUM
cana-4665	140	15	,	,	PUNCT
cana-4665	140	16	λ̃2	λ̃2	PROPN
cana-4665	140	17	−	−	PROPN
cana-4665	140	18	4µ̃	4µ̃	PROPN
cana-4665	140	19	=	=	SYM
cana-4665	140	20	0	0	X
cana-4665	140	21	.	.	PUNCT
cana-4665	140	22	(	(	PUNCT
cana-4665	140	23	3.21	3.21	NUM
cana-4665	140	24	)	)	PUNCT
cana-4665	140	25	in	in	ADP
cana-4665	140	26	this	this	DET
cana-4665	140	27	context	context	NOUN
cana-4665	140	28	,	,	PUNCT
cana-4665	140	29	c1	c1	PROPN
cana-4665	140	30	and	and	CCONJ
cana-4665	140	31	c2	c2	PROPN
cana-4665	140	32	both	both	PRON
cana-4665	140	33	illustrates	illustrate	VERB
cana-4665	140	34	the	the	DET
cana-4665	140	35	arbitrary	arbitrary	ADJ
cana-4665	140	36	constants	constant	NOUN
cana-4665	140	37	.	.	PUNCT
cana-4665	141	1	considering	consider	VERB
cana-4665	141	2	equation	equation	NOUN
cana-4665	141	3	(	(	PUNCT
cana-4665	141	4	3.17	3.17	NUM
cana-4665	141	5	)	)	PUNCT
cana-4665	141	6	,	,	PUNCT
cana-4665	141	7	balancing	balance	VERB
cana-4665	141	8	with	with	ADP
cana-4665	141	9	p	p	PROPN
cana-4665	141	10	′(ξ)2	′(ξ)2	PROPN
cana-4665	141	11	and	and	CCONJ
cana-4665	141	12	p	p	X
cana-4665	141	13	(	(	PUNCT
cana-4665	141	14	ξ)4	ξ)4	X
cana-4665	141	15	bestows	bestow	VERB
cana-4665	141	16	q	q	NOUN
cana-4665	141	17	=	=	SYM
cana-4665	141	18	1	1	NUM
cana-4665	141	19	,	,	PUNCT
cana-4665	141	20	thus	thus	ADV
cana-4665	141	21	,	,	PUNCT
cana-4665	141	22	the	the	DET
cana-4665	141	23	result	result	NOUN
cana-4665	141	24	is	be	AUX
cana-4665	141	25	of	of	ADP
cana-4665	141	26	the	the	DET
cana-4665	141	27	below	below	ADV
cana-4665	141	28	-	-	PUNCT
cana-4665	141	29	stated	state	VERB
cana-4665	141	30	form	form	NOUN
cana-4665	141	31	p	p	X
cana-4665	141	32	(	(	PUNCT
cana-4665	141	33	ξ	ξ	NOUN
cana-4665	141	34	)	)	PUNCT
cana-4665	141	35	=	=	SYM
cana-4665	141	36	a0	a0	PROPN
cana-4665	141	37	+	+	CCONJ
cana-4665	141	38	a1	a1	PROPN
cana-4665	141	39	(	(	PUNCT
cana-4665	141	40	g′	g′	NOUN
cana-4665	141	41	g	g	PROPN
cana-4665	141	42	)	)	PUNCT
cana-4665	141	43	,	,	PUNCT
cana-4665	141	44	(	(	PUNCT
cana-4665	141	45	3.22	3.22	NUM
cana-4665	141	46	)	)	PUNCT
cana-4665	141	47	we	we	PRON
cana-4665	141	48	substitute	substitute	VERB
cana-4665	141	49	the	the	DET
cana-4665	141	50	equation	equation	NOUN
cana-4665	141	51	(	(	PUNCT
cana-4665	141	52	3.22	3.22	NUM
cana-4665	141	53	)	)	PUNCT
cana-4665	141	54	in	in	ADP
cana-4665	141	55	the	the	DET
cana-4665	141	56	equation(3.17	equation(3.17	NOUN
cana-4665	141	57	)	)	PUNCT
cana-4665	141	58	and	and	CCONJ
cana-4665	141	59	after	after	ADP
cana-4665	141	60	this	this	PRON
cana-4665	141	61	,	,	PUNCT
cana-4665	141	62	we	we	PRON
cana-4665	141	63	equalize	equalize	VERB
cana-4665	141	64	the	the	DET
cana-4665	141	65	coefficients	coefficient	NOUN
cana-4665	141	66	of	of	ADP
cana-4665	141	67	the	the	DET
cana-4665	141	68	algebraic	algebraic	ADJ
cana-4665	141	69	equation	equation	NOUN
cana-4665	141	70	to	to	ADP
cana-4665	141	71	zero	zero	NUM
cana-4665	141	72	,	,	PUNCT
cana-4665	141	73	we	we	PRON
cana-4665	141	74	will	will	AUX
cana-4665	141	75	get	get	VERB
cana-4665	141	76	the	the	DET
cana-4665	141	77	following	follow	VERB
cana-4665	141	78	algebraic	algebraic	ADJ
cana-4665	141	79	system	system	NOUN
cana-4665	141	80	of	of	ADP
cana-4665	141	81	equations:(g	equations:(g	NOUN
cana-4665	141	82	′	′	NUM
cana-4665	142	1	g	g	NOUN
cana-4665	142	2	)	)	PUNCT
cana-4665	142	3	4	4	NUM
cana-4665	142	4	:	:	PUNCT
cana-4665	143	1	b2w2a41	b2w2a41	ADJ
cana-4665	143	2	+	+	X
cana-4665	143	3	4w2a2a21	4w2a2a21	PROPN
cana-4665	143	4	=	=	SYM
cana-4665	143	5	0	0	NUM
cana-4665	143	6	,	,	PUNCT
cana-4665	143	7	(	(	PUNCT
cana-4665	143	8	g	g	NOUN
cana-4665	143	9	′	′	NUM
cana-4665	143	10	g	g	NOUN
cana-4665	143	11	)	)	PUNCT
cana-4665	143	12	3	3	NUM
cana-4665	143	13	:	:	PUNCT
cana-4665	143	14	−4ba31	−4ba31	PROPN
cana-4665	143	15	+	+	NUM
cana-4665	143	16	8w2a2a21λ+	8w2a2a21λ+	NOUN
cana-4665	143	17	4b2w2a0a	4b2w2a0a	ADJ
cana-4665	143	18	3	3	NUM
cana-4665	143	19	1	1	NUM
cana-4665	143	20	=	=	SYM
cana-4665	143	21	0	0	NUM
cana-4665	143	22	,	,	PUNCT
cana-4665	143	23	(	(	PUNCT
cana-4665	143	24	g	g	NOUN
cana-4665	143	25	′	′	NUM
cana-4665	143	26	g	g	NOUN
cana-4665	143	27	)	)	PUNCT
cana-4665	143	28	2	2	NUM
cana-4665	143	29	:	:	PUNCT
cana-4665	143	30	−12ba0a	−12ba0a	PROPN
cana-4665	143	31	2	2	NUM
cana-4665	143	32	1	1	NUM
cana-4665	143	33	+	+	CCONJ
cana-4665	143	34	4a21	4a21	NUM
cana-4665	144	1	+	+	CCONJ
cana-4665	144	2	6b2w2a20a	6b2w2a20a	NUM
cana-4665	144	3	2	2	NUM
cana-4665	144	4	1	1	NUM
cana-4665	144	5	+	+	NUM
cana-4665	144	6	4w2a2a21λ	4w2a2a21λ	NUM
cana-4665	144	7	2	2	NUM
cana-4665	144	8	+	+	NUM
cana-4665	144	9	8w2a2a21µ	8w2a2a21µ	NUM
cana-4665	144	10	=	=	SYM
cana-4665	144	11	0	0	NUM
cana-4665	144	12	,	,	PUNCT
cana-4665	144	13	(	(	PUNCT
cana-4665	144	14	g	g	NOUN
cana-4665	144	15	′	′	NUM
cana-4665	144	16	g	g	NOUN
cana-4665	144	17	)	)	PUNCT
cana-4665	144	18	1	1	NUM
cana-4665	144	19	:	:	PUNCT
cana-4665	144	20	−12ba20a1	−12ba20a1	PROPN
cana-4665	144	21	+	+	NUM
cana-4665	144	22	8a0a1	8a0a1	NUM
cana-4665	144	23	+	+	SYM
cana-4665	144	24	4b2w2a2a21µλ	4b2w2a2a21µλ	NUM
cana-4665	144	25	=	=	SYM
cana-4665	144	26	0	0	NUM
cana-4665	144	27	,	,	PUNCT
cana-4665	144	28	(	(	PUNCT
cana-4665	144	29	g	g	NOUN
cana-4665	144	30	′	′	NUM
cana-4665	144	31	g	g	NOUN
cana-4665	144	32	)	)	PUNCT
cana-4665	144	33	0	0	NUM
cana-4665	145	1	:	:	PUNCT
cana-4665	145	2	b2w2a40	b2w2a40	PROPN
cana-4665	145	3	−	−	PROPN
cana-4665	145	4	4ba30	4ba30	PROPN
cana-4665	146	1	+	+	NUM
cana-4665	146	2	4w2a2a21µ	4w2a2a21µ	PROPN
cana-4665	146	3	2	2	NUM
cana-4665	146	4	+	+	NUM
cana-4665	146	5	4a20	4a20	NOUN
cana-4665	146	6	=	=	SYM
cana-4665	146	7	0	0	PROPN
cana-4665	146	8	.	.	PUNCT
cana-4665	147	1	(	(	PUNCT
cana-4665	147	2	3.23	3.23	NUM
cana-4665	147	3	)	)	PUNCT
cana-4665	147	4	resolving	resolve	VERB
cana-4665	147	5	the	the	DET
cana-4665	147	6	overhead	overhead	ADJ
cana-4665	147	7	algebraic	algebraic	ADJ
cana-4665	147	8	equations	equation	NOUN
cana-4665	147	9	;	;	PUNCT
cana-4665	147	10	yields	yield	VERB
cana-4665	147	11	the	the	DET
cana-4665	147	12	following	follow	VERB
cana-4665	147	13	cases	case	NOUN
cana-4665	147	14	:	:	PUNCT
cana-4665	147	15	case	case	NOUN
cana-4665	147	16	-	-	PUNCT
cana-4665	147	17	i	i	PRON
cana-4665	147	18	v	v	NOUN
cana-4665	147	19	=	=	SYM
cana-4665	147	20	v	v	NOUN
cana-4665	147	21	,	,	PUNCT
cana-4665	147	22	a	a	DET
cana-4665	147	23	=	=	SYM
cana-4665	147	24	1	1	NUM
cana-4665	147	25	2	2	NUM
cana-4665	147	26	ιa1b,−	ιa1b,−	NOUN
cana-4665	147	27	1	1	NUM
cana-4665	147	28	2	2	NUM
cana-4665	147	29	ιa1b	ιa1b	PROPN
cana-4665	147	30	,	,	PUNCT
cana-4665	147	31	b	b	X
cana-4665	147	32	=	=	SYM
cana-4665	147	33	b	b	PROPN
cana-4665	147	34	,	,	PUNCT
cana-4665	147	35	µ	µ	NOUN
cana-4665	147	36	=	=	NOUN
cana-4665	147	37	a0(−2	a0(−2	NOUN
cana-4665	147	38	+	+	CCONJ
cana-4665	147	39	ba0	ba0	X
cana-4665	147	40	)	)	PUNCT
cana-4665	148	1	ba21	ba21	PROPN
cana-4665	148	2	,	,	PUNCT
cana-4665	148	3	w	w	PROPN
cana-4665	148	4	=	=	SYM
cana-4665	148	5	1	1	NUM
cana-4665	148	6	,	,	PUNCT
cana-4665	148	7	λ	λ	X
cana-4665	148	8	=	=	SYM
cana-4665	148	9	2(−1	2(−1	NUM
cana-4665	148	10	+	+	CCONJ
cana-4665	148	11	ba0	ba0	ADJ
cana-4665	148	12	)	)	PUNCT
cana-4665	148	13	ba1	ba1	NOUN
cana-4665	148	14	,	,	PUNCT
cana-4665	148	15	a0	a0	PROPN
cana-4665	148	16	=	=	SYM
cana-4665	148	17	a0	a0	PROPN
cana-4665	148	18	,	,	PUNCT
cana-4665	148	19	a1	a1	NOUN
cana-4665	148	20	=	=	PUNCT
cana-4665	148	21	a1	a1	NOUN
cana-4665	148	22	.	.	PUNCT
cana-4665	149	1	(	(	PUNCT
cana-4665	149	2	3.24	3.24	NUM
cana-4665	149	3	)	)	PUNCT
cana-4665	149	4	case	case	NOUN
cana-4665	149	5	-	-	PUNCT
cana-4665	149	6	ii	ii	NOUN
cana-4665	149	7	v	v	NOUN
cana-4665	149	8	=	=	SYM
cana-4665	149	9	v	v	NOUN
cana-4665	149	10	,	,	PUNCT
cana-4665	149	11	a	a	DET
cana-4665	149	12	=	=	SYM
cana-4665	149	13	1	1	NUM
cana-4665	149	14	2	2	NUM
cana-4665	149	15	ιa1b,−	ιa1b,−	NOUN
cana-4665	149	16	1	1	NUM
cana-4665	149	17	2	2	NUM
cana-4665	149	18	ιa1b	ιa1b	PROPN
cana-4665	149	19	,	,	PUNCT
cana-4665	149	20	b	b	X
cana-4665	149	21	=	=	SYM
cana-4665	149	22	b	b	PROPN
cana-4665	149	23	,	,	PUNCT
cana-4665	149	24	µ	µ	NOUN
cana-4665	149	25	=	=	NOUN
cana-4665	149	26	a0(−2	a0(−2	NOUN
cana-4665	149	27	+	+	CCONJ
cana-4665	149	28	ba0	ba0	X
cana-4665	149	29	)	)	PUNCT
cana-4665	150	1	ba21	ba21	PROPN
cana-4665	150	2	,	,	PUNCT
cana-4665	150	3	w	w	PROPN
cana-4665	150	4	=	=	SYM
cana-4665	150	5	−1	−1	NOUN
cana-4665	150	6	,	,	PUNCT
cana-4665	150	7	λ	λ	X
cana-4665	150	8	=	=	SYM
cana-4665	150	9	2(−1	2(−1	NUM
cana-4665	150	10	+	+	CCONJ
cana-4665	150	11	ba0	ba0	ADJ
cana-4665	150	12	)	)	PUNCT
cana-4665	150	13	ba1	ba1	NOUN
cana-4665	150	14	,	,	PUNCT
cana-4665	150	15	a0	a0	PROPN
cana-4665	150	16	=	=	SYM
cana-4665	150	17	a0	a0	PROPN
cana-4665	150	18	,	,	PUNCT
cana-4665	150	19	a1	a1	NOUN
cana-4665	150	20	=	=	PUNCT
cana-4665	150	21	a1	a1	NOUN
cana-4665	150	22	.	.	PUNCT
cana-4665	151	1	(	(	PUNCT
cana-4665	151	2	3.25	3.25	NUM
cana-4665	151	3	)	)	PUNCT
cana-4665	151	4	communications	communication	NOUN
cana-4665	151	5	on	on	ADP
cana-4665	151	6	applied	apply	VERB
cana-4665	151	7	nonlinear	nonlinear	ADJ
cana-4665	151	8	analysis	analysis	NOUN
cana-4665	151	9	issn	issn	NOUN
cana-4665	151	10	:	:	PUNCT
cana-4665	151	11	1074	1074	NUM
cana-4665	151	12	-	-	PUNCT
cana-4665	151	13	133x	133x	NUM
cana-4665	151	14	vol	vol	VERB
cana-4665	151	15	32	32	NUM
cana-4665	151	16	no	no	NOUN
cana-4665	151	17	.	.	PUNCT
cana-4665	152	1	10s	10	NOUN
cana-4665	152	2	(	(	PUNCT
cana-4665	152	3	2025	2025	NUM
cana-4665	152	4	)	)	PUNCT
cana-4665	152	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-4665	152	6	95	95	NUM
cana-4665	152	7	corresponding	correspond	VERB
cana-4665	152	8	to	to	ADP
cana-4665	152	9	the	the	DET
cana-4665	152	10	above	above	ADJ
cana-4665	152	11	cases	case	NOUN
cana-4665	152	12	we	we	PRON
cana-4665	152	13	will	will	AUX
cana-4665	152	14	obtain	obtain	VERB
cana-4665	152	15	the	the	DET
cana-4665	152	16	traveling	travel	VERB
cana-4665	152	17	wave	wave	NOUN
cana-4665	152	18	solutions	solution	NOUN
cana-4665	152	19	.	.	PUNCT
cana-4665	153	1	the	the	DET
cana-4665	153	2	general	general	ADJ
cana-4665	153	3	outcomes	outcome	NOUN
cana-4665	153	4	of	of	ADP
cana-4665	153	5	the	the	DET
cana-4665	153	6	equation	equation	NOUN
cana-4665	153	7	(	(	PUNCT
cana-4665	153	8	3.24	3.24	NUM
cana-4665	153	9	)	)	PUNCT
cana-4665	153	10	can	can	AUX
cana-4665	153	11	be	be	AUX
cana-4665	153	12	expressed	express	VERB
cana-4665	153	13	as	as	ADP
cana-4665	153	14	:	:	PUNCT
cana-4665	153	15	subcase	subcase	VERB
cana-4665	153	16	-	-	PUNCT
cana-4665	153	17	i	i	PRON
cana-4665	153	18	when	when	SCONJ
cana-4665	153	19	λ2	λ2	PROPN
cana-4665	153	20	−	−	PROPN
cana-4665	153	21	4µ	4µ	NOUN
cana-4665	153	22	>	>	X
cana-4665	153	23	0	0	NUM
cana-4665	153	24	,	,	PUNCT
cana-4665	153	25	then	then	ADV
cana-4665	153	26	solution	solution	NOUN
cana-4665	153	27	is	be	AUX
cana-4665	153	28	:	:	PUNCT
cana-4665	153	29	p	p	X
cana-4665	153	30	(	(	PUNCT
cana-4665	153	31	ξ	ξ	NOUN
cana-4665	153	32	)	)	PUNCT
cana-4665	153	33	=	=	SYM
cana-4665	153	34	a0	a0	PROPN
cana-4665	153	35	+	+	CCONJ
cana-4665	153	36	a1	a1	NOUN
cana-4665	153	37	−	−	X
cana-4665	153	38	(	(	PUNCT
cana-4665	153	39	−1+ba0	−1+ba0	NOUN
cana-4665	153	40	)	)	PUNCT
cana-4665	153	41	a1b	a1b	PROPN
cana-4665	154	1	+	+	CCONJ
cana-4665	154	2	√	√	PROPN
cana-4665	154	3	(	(	PUNCT
cana-4665	154	4	−1+ba0)2	−1+ba0)2	NOUN
cana-4665	154	5	a21b	a21b	NOUN
cana-4665	154	6	2	2	NUM
cana-4665	154	7	−	−	PROPN
cana-4665	154	8	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	154	9	)	)	PUNCT
cana-4665	154	10	ba21	ba21	PROPN
cana-4665	154	11			NOUN
cana-4665	154	12	c1sinh	c1sinh	VERB
cana-4665	154	13	√	√	PROPN
cana-4665	154	14	(	(	PUNCT
cana-4665	154	15	−1+ba0)2	−1+ba0)2	INTJ
cana-4665	154	16	a21b	a21b	NOUN
cana-4665	154	17	2	2	NUM
cana-4665	154	18	−	−	PROPN
cana-4665	154	19	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	154	20	)	)	PUNCT
cana-4665	154	21	ba21	ba21	PROPN
cana-4665	154	22	(	(	PUNCT
cana-4665	154	23	x−	x−	PROPN
cana-4665	154	24	t	t	PROPN
cana-4665	154	25	ω	ω	PROPN
cana-4665	154	26	)	)	PUNCT
cana-4665	155	1	+	+	NOUN
cana-4665	155	2	c2cosh	c2cosh	PROPN
cana-4665	155	3	√	√	PROPN
cana-4665	155	4	(	(	PUNCT
cana-4665	155	5	−1+ba0)2	−1+ba0)2	NOUN
cana-4665	155	6	a21b	a21b	NOUN
cana-4665	155	7	2	2	NUM
cana-4665	155	8	−	−	PROPN
cana-4665	155	9	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	155	10	)	)	PUNCT
cana-4665	155	11	ba21	ba21	PROPN
cana-4665	155	12	(	(	PUNCT
cana-4665	155	13	x−	x−	PROPN
cana-4665	155	14	t	t	PROPN
cana-4665	155	15	ω	ω	PROPN
cana-4665	155	16	)	)	PUNCT
cana-4665	155	17	c1cosh	c1cosh	NOUN
cana-4665	155	18	√	√	PROPN
cana-4665	155	19	(	(	PUNCT
cana-4665	155	20	−1+ba0)2	−1+ba0)2	NOUN
cana-4665	155	21	a21b	a21b	NOUN
cana-4665	155	22	2	2	NUM
cana-4665	155	23	−	−	PROPN
cana-4665	155	24	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	155	25	)	)	PUNCT
cana-4665	155	26	ba21	ba21	PROPN
cana-4665	155	27	(	(	PUNCT
cana-4665	155	28	x−	x−	PROPN
cana-4665	155	29	t	t	PROPN
cana-4665	155	30	ω	ω	PROPN
cana-4665	155	31	)	)	PUNCT
cana-4665	156	1	+	+	NOUN
cana-4665	156	2	c2sinh	c2sinh	NOUN
cana-4665	156	3	√√√√	√√√√	ADP
cana-4665	156	4	(	(	PUNCT
cana-4665	156	5	−1+ba20	−1+ba20	NOUN
cana-4665	156	6	)	)	PUNCT
cana-4665	156	7	a21b	a21b	NOUN
cana-4665	156	8	2	2	NUM
cana-4665	156	9	−	−	NOUN
cana-4665	156	10	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	156	11	)	)	PUNCT
cana-4665	156	12	ba21	ba21	PROPN
cana-4665	156	13	(	(	PUNCT
cana-4665	156	14	x−	x−	PROPN
cana-4665	156	15	t	t	PROPN
cana-4665	156	16	ω	ω	PROPN
cana-4665	156	17	)	)	PUNCT
cana-4665	156	18			NOUN
cana-4665	156	19			NOUN
cana-4665	156	20	.	.	PUNCT
cana-4665	157	1	(	(	PUNCT
cana-4665	157	2	3.26	3.26	NUM
cana-4665	157	3	)	)	PUNCT
cana-4665	157	4	f	f	PROPN
cana-4665	157	5	(	(	PUNCT
cana-4665	157	6	ξ	ξ	NOUN
cana-4665	157	7	)	)	PUNCT
cana-4665	157	8	=	=	NOUN
cana-4665	157	9	√√√√√√√√√a0	√√√√√√√√√a0	NOUN
cana-4665	157	10	+	+	CCONJ
cana-4665	157	11	a1	a1	NOUN
cana-4665	157	12	−	−	NOUN
cana-4665	157	13	(	(	PUNCT
cana-4665	157	14	−1+ba0	−1+ba0	NOUN
cana-4665	157	15	)	)	PUNCT
cana-4665	157	16	a1b	a1b	PROPN
cana-4665	158	1	+	+	CCONJ
cana-4665	158	2	√	√	PROPN
cana-4665	158	3	(	(	PUNCT
cana-4665	158	4	−1+ba0)2	−1+ba0)2	NOUN
cana-4665	158	5	a21b	a21b	NOUN
cana-4665	158	6	2	2	NUM
cana-4665	158	7	−	−	PROPN
cana-4665	158	8	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	158	9	)	)	PUNCT
cana-4665	158	10	ba21	ba21	PROPN
cana-4665	158	11			NOUN
cana-4665	158	12	c1sinh	c1sinh	VERB
cana-4665	158	13	√	√	PROPN
cana-4665	158	14	(	(	PUNCT
cana-4665	158	15	−1+ba0)2	−1+ba0)2	INTJ
cana-4665	158	16	a21b	a21b	NOUN
cana-4665	158	17	2	2	NUM
cana-4665	158	18	−	−	PROPN
cana-4665	158	19	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	158	20	)	)	PUNCT
cana-4665	158	21	ba21	ba21	PROPN
cana-4665	158	22	(	(	PUNCT
cana-4665	158	23	x−	x−	PROPN
cana-4665	158	24	t	t	PROPN
cana-4665	158	25	ω	ω	PROPN
cana-4665	158	26	)	)	PUNCT
cana-4665	159	1	+	+	NOUN
cana-4665	159	2	c2cosh	c2cosh	PROPN
cana-4665	159	3	√	√	PROPN
cana-4665	159	4	(	(	PUNCT
cana-4665	159	5	−1+ba0)2	−1+ba0)2	NOUN
cana-4665	159	6	a21b	a21b	NOUN
cana-4665	159	7	2	2	NUM
cana-4665	159	8	−	−	PROPN
cana-4665	159	9	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	159	10	)	)	PUNCT
cana-4665	159	11	ba21	ba21	PROPN
cana-4665	159	12	(	(	PUNCT
cana-4665	159	13	x−	x−	PROPN
cana-4665	159	14	t	t	PROPN
cana-4665	159	15	ω	ω	PROPN
cana-4665	159	16	)	)	PUNCT
cana-4665	159	17	c1cosh	c1cosh	NOUN
cana-4665	159	18	√	√	PROPN
cana-4665	159	19	(	(	PUNCT
cana-4665	159	20	−1+ba0)2	−1+ba0)2	NOUN
cana-4665	159	21	a21b	a21b	NOUN
cana-4665	159	22	2	2	NUM
cana-4665	159	23	−	−	PROPN
cana-4665	159	24	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	159	25	)	)	PUNCT
cana-4665	159	26	ba21	ba21	PROPN
cana-4665	159	27	(	(	PUNCT
cana-4665	159	28	x−	x−	PROPN
cana-4665	159	29	t	t	PROPN
cana-4665	159	30	ω	ω	PROPN
cana-4665	159	31	)	)	PUNCT
cana-4665	160	1	+	+	NOUN
cana-4665	160	2	c2sinh	c2sinh	NOUN
cana-4665	160	3	√√√√	√√√√	ADP
cana-4665	160	4	(	(	PUNCT
cana-4665	160	5	−1+ba20	−1+ba20	NOUN
cana-4665	160	6	)	)	PUNCT
cana-4665	160	7	a21b	a21b	NOUN
cana-4665	160	8	2	2	NUM
cana-4665	160	9	−	−	NOUN
cana-4665	160	10	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	160	11	)	)	PUNCT
cana-4665	160	12	ba21	ba21	PROPN
cana-4665	160	13	(	(	PUNCT
cana-4665	160	14	x−	x−	PROPN
cana-4665	160	15	t	t	PROPN
cana-4665	160	16	ω	ω	PROPN
cana-4665	160	17	)	)	PUNCT
cana-4665	160	18			NOUN
cana-4665	160	19			NOUN
cana-4665	160	20	,	,	PUNCT
cana-4665	160	21	(	(	PUNCT
cana-4665	160	22	3.27	3.27	NUM
cana-4665	160	23	)	)	PUNCT
cana-4665	160	24	g(ξ	g(ξ	PROPN
cana-4665	160	25	)	)	PUNCT
cana-4665	161	1	=	=	PUNCT
cana-4665	162	1	6ιa1bξ	6ιa1bξ	NUM
cana-4665	162	2	−	−	NUM
cana-4665	162	3	3	3	NUM
cana-4665	162	4	2	2	NUM
cana-4665	162	5	ι	ι	PRON
cana-4665	162	6	√	√	DET
cana-4665	162	7	(	(	PUNCT
cana-4665	162	8	−1+ba0	−1+ba0	PROPN
cana-4665	162	9	)	)	PUNCT
cana-4665	162	10	2	2	NUM
cana-4665	162	11	b2a21	b2a21	NOUN
cana-4665	162	12	−a0(−2+ba0	−a0(−2+ba0	NOUN
cana-4665	162	13	)	)	PUNCT
cana-4665	163	1	ba21	ba21	PROPN
cana-4665	163	2	log	log	NOUN
cana-4665	163	3	(	(	PUNCT
cana-4665	163	4	c1	c1	PROPN
cana-4665	163	5	cosh	cosh	PROPN
cana-4665	163	6	(	(	PUNCT
cana-4665	163	7	√	√	PROPN
cana-4665	163	8	1	1	NUM
cana-4665	163	9	b2a21	b2a21	PROPN
cana-4665	163	10	ξ)+c2	ξ)+c2	X
cana-4665	163	11	sinh	sinh	NOUN
cana-4665	163	12	(	(	PUNCT
cana-4665	163	13	√	√	PROPN
cana-4665	163	14	1	1	NUM
cana-4665	163	15	b2a21	b2a21	PROPN
cana-4665	163	16	ξ	ξ	NUM
cana-4665	163	17	)	)	PUNCT
cana-4665	163	18	)	)	PUNCT
cana-4665	163	19	√	√	ADP
cana-4665	163	20	1	1	NUM
cana-4665	163	21	b2a21	b2a21	NOUN
cana-4665	163	22	−	−	NOUN
cana-4665	163	23	3ιξ	3ιξ	ADJ
cana-4665	163	24	2a1b	2a1b	NUM
cana-4665	164	1	+	+	ADJ
cana-4665	164	2	bξ	bξ	ADJ
cana-4665	164	3	,	,	PUNCT
cana-4665	164	4	(	(	PUNCT
cana-4665	164	5	3.28	3.28	NUM
cana-4665	164	6	)	)	PUNCT
cana-4665	164	7	using	use	VERB
cana-4665	164	8	these	these	DET
cana-4665	164	9	values	value	NOUN
cana-4665	164	10	we	we	PRON
cana-4665	164	11	get	get	VERB
cana-4665	164	12	solution	solution	NOUN
cana-4665	164	13	q(x	q(x	PROPN
cana-4665	164	14	,	,	PUNCT
cana-4665	164	15	t	t	PROPN
cana-4665	164	16	)	)	PUNCT
cana-4665	165	1	=	=	NOUN
cana-4665	165	2	√√√√√√√√√a0	√√√√√√√√√a0	NOUN
cana-4665	165	3	+	+	CCONJ
cana-4665	165	4	a1	a1	NOUN
cana-4665	165	5	−	−	NOUN
cana-4665	165	6	(	(	PUNCT
cana-4665	165	7	−1+ba0	−1+ba0	NOUN
cana-4665	165	8	)	)	PUNCT
cana-4665	165	9	a1b	a1b	PROPN
cana-4665	166	1	+	+	CCONJ
cana-4665	166	2	√	√	PROPN
cana-4665	166	3	(	(	PUNCT
cana-4665	166	4	−1+ba0)2	−1+ba0)2	NOUN
cana-4665	166	5	a21b	a21b	NOUN
cana-4665	166	6	2	2	NUM
cana-4665	166	7	−	−	PROPN
cana-4665	166	8	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	166	9	)	)	PUNCT
cana-4665	166	10	ba21	ba21	PROPN
cana-4665	166	11			NOUN
cana-4665	166	12	c1sinh	c1sinh	VERB
cana-4665	166	13	√	√	PROPN
cana-4665	166	14	(	(	PUNCT
cana-4665	166	15	−1+ba0)2	−1+ba0)2	INTJ
cana-4665	166	16	a21b	a21b	NOUN
cana-4665	166	17	2	2	NUM
cana-4665	166	18	−	−	PROPN
cana-4665	166	19	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	166	20	)	)	PUNCT
cana-4665	166	21	ba21	ba21	PROPN
cana-4665	166	22	(	(	PUNCT
cana-4665	166	23	x−	x−	PROPN
cana-4665	166	24	t	t	PROPN
cana-4665	166	25	ω	ω	PROPN
cana-4665	166	26	)	)	PUNCT
cana-4665	167	1	+	+	NOUN
cana-4665	167	2	c2cosh	c2cosh	PROPN
cana-4665	167	3	√	√	PROPN
cana-4665	167	4	(	(	PUNCT
cana-4665	167	5	−1+ba0)2	−1+ba0)2	NOUN
cana-4665	167	6	a21b	a21b	NOUN
cana-4665	167	7	2	2	NUM
cana-4665	167	8	−	−	PROPN
cana-4665	167	9	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	167	10	)	)	PUNCT
cana-4665	167	11	ba21	ba21	PROPN
cana-4665	167	12	(	(	PUNCT
cana-4665	167	13	x−	x−	PROPN
cana-4665	167	14	t	t	PROPN
cana-4665	167	15	ω	ω	PROPN
cana-4665	167	16	)	)	PUNCT
cana-4665	167	17	c1cosh	c1cosh	NOUN
cana-4665	167	18	√	√	PROPN
cana-4665	167	19	(	(	PUNCT
cana-4665	167	20	−1+ba0)2	−1+ba0)2	NOUN
cana-4665	167	21	a21b	a21b	NOUN
cana-4665	167	22	2	2	NUM
cana-4665	167	23	−	−	PROPN
cana-4665	167	24	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	167	25	)	)	PUNCT
cana-4665	167	26	ba21	ba21	PROPN
cana-4665	167	27	(	(	PUNCT
cana-4665	167	28	x−	x−	PROPN
cana-4665	167	29	t	t	PROPN
cana-4665	167	30	ω	ω	PROPN
cana-4665	167	31	)	)	PUNCT
cana-4665	168	1	+	+	NOUN
cana-4665	168	2	c2sinh	c2sinh	NOUN
cana-4665	168	3	√√√√	√√√√	ADP
cana-4665	168	4	(	(	PUNCT
cana-4665	168	5	−1+ba20	−1+ba20	NOUN
cana-4665	168	6	)	)	PUNCT
cana-4665	168	7	a21b	a21b	NOUN
cana-4665	168	8	2	2	NUM
cana-4665	168	9	−	−	NOUN
cana-4665	168	10	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	168	11	)	)	PUNCT
cana-4665	168	12	ba21	ba21	PROPN
cana-4665	168	13	(	(	PUNCT
cana-4665	168	14	x−	x−	PROPN
cana-4665	168	15	t	t	PROPN
cana-4665	168	16	ω	ω	PROPN
cana-4665	168	17	)	)	PUNCT
cana-4665	168	18			NOUN
cana-4665	168	19			NOUN
cana-4665	168	20	e	e	X
cana-4665	168	21	ι(6ιa1b(x−	ι(6ιa1b(x−	PROPN
cana-4665	168	22	t	t	PROPN
cana-4665	168	23	ω	ω	PROPN
cana-4665	168	24	)	)	PUNCT
cana-4665	168	25	−	−	PROPN
cana-4665	168	26	3	3	NUM
cana-4665	168	27	2	2	NUM
cana-4665	168	28	ι	ι	PART
cana-4665	168	29	√	√	INTJ
cana-4665	168	30	(	(	PUNCT
cana-4665	168	31	−1+ba0)2	−1+ba0)2	X
cana-4665	168	32	b2a21	b2a21	X
cana-4665	168	33	−	−	PROPN
cana-4665	168	34	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	168	35	)	)	PUNCT
cana-4665	169	1	ba21	ba21	PROPN
cana-4665	169	2	log	log	VERB
cana-4665	169	3	c1	c1	PUNCT
cana-4665	169	4	cosh	cosh	PROPN
cana-4665	169	5	(	(	PUNCT
cana-4665	169	6	√	√	PROPN
cana-4665	169	7	1	1	NUM
cana-4665	169	8	b2a21	b2a21	X
cana-4665	169	9	(	(	PUNCT
cana-4665	169	10	x−	x−	PROPN
cana-4665	169	11	t	t	PROPN
cana-4665	169	12	ω	ω	PROPN
cana-4665	169	13	)	)	PUNCT
cana-4665	169	14	)	)	PUNCT
cana-4665	170	1	+	+	ADJ
cana-4665	170	2	c2	c2	PROPN
cana-4665	170	3	sinh	sinh	PROPN
cana-4665	170	4	(	(	PUNCT
cana-4665	170	5	√	√	PROPN
cana-4665	170	6	1	1	NUM
cana-4665	170	7	b2a21	b2a21	X
cana-4665	170	8	(	(	PUNCT
cana-4665	170	9	x−	x−	PROPN
cana-4665	170	10	t	t	PROPN
cana-4665	170	11	ω	ω	PROPN
cana-4665	170	12	)	)	PUNCT
cana-4665	170	13	)	)	PUNCT
cana-4665	171	1			PROPN
cana-4665	171	2	√	√	ADJ
cana-4665	171	3	1	1	NUM
cana-4665	171	4	b2a21	b2a21	NOUN
cana-4665	171	5	−	−	PROPN
cana-4665	171	6	3ι(x−	3ι(x−	NUM
cana-4665	171	7	t	t	PROPN
cana-4665	171	8	ω	ω	NUM
cana-4665	171	9	)	)	PUNCT
cana-4665	171	10	2a1b	2a1b	NUM
cana-4665	172	1	+	+	ADV
cana-4665	172	2	b(x−	b(x−	NOUN
cana-4665	172	3	t	t	PROPN
cana-4665	172	4	ω	ω	NUM
cana-4665	172	5	)	)	PUNCT
cana-4665	172	6	)	)	PUNCT
cana-4665	172	7	.	.	PUNCT
cana-4665	173	1	(	(	PUNCT
cana-4665	173	2	3.29	3.29	NUM
cana-4665	173	3	)	)	PUNCT
cana-4665	173	4	the	the	DET
cana-4665	173	5	graphical	graphical	ADJ
cana-4665	173	6	representation	representation	NOUN
cana-4665	173	7	of	of	ADP
cana-4665	173	8	this	this	DET
cana-4665	173	9	case	case	NOUN
cana-4665	173	10	is	be	AUX
cana-4665	173	11	represented	represent	VERB
cana-4665	173	12	in	in	ADP
cana-4665	173	13	figure	figure	NOUN
cana-4665	173	14	1	1	NUM
cana-4665	173	15	and	and	CCONJ
cana-4665	173	16	in	in	ADP
cana-4665	173	17	figure	figure	NOUN
cana-4665	173	18	2	2	NUM
cana-4665	173	19	.	.	PUNCT
cana-4665	173	20	subcase	subcase	PROPN
cana-4665	173	21	-	-	PUNCT
cana-4665	173	22	ii	ii	NOUN
cana-4665	173	23	when	when	SCONJ
cana-4665	173	24	λ2	λ2	PROPN
cana-4665	173	25	−	−	PROPN
cana-4665	173	26	4µ	4µ	NOUN
cana-4665	173	27	<	<	X
cana-4665	173	28	0	0	NUM
cana-4665	173	29	,	,	PUNCT
cana-4665	173	30	then	then	ADV
cana-4665	173	31	solution	solution	NOUN
cana-4665	173	32	is	be	AUX
cana-4665	173	33	:	:	PUNCT
cana-4665	173	34	p	p	X
cana-4665	173	35	(	(	PUNCT
cana-4665	173	36	x	x	PROPN
cana-4665	173	37	,	,	PUNCT
cana-4665	173	38	t	t	PROPN
cana-4665	173	39	)	)	PUNCT
cana-4665	174	1	=	=	PROPN
cana-4665	174	2	a0	a0	PROPN
cana-4665	174	3	+	+	CCONJ
cana-4665	174	4	a1	a1	NOUN
cana-4665	174	5	−	−	NOUN
cana-4665	174	6	(	(	PUNCT
cana-4665	174	7	−1+ba0	−1+ba0	NOUN
cana-4665	174	8	)	)	PUNCT
cana-4665	174	9	a1b	a1b	PROPN
cana-4665	174	10	+	+	CCONJ
cana-4665	174	11	√	√	NUM
cana-4665	174	12	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	174	13	)	)	PUNCT
cana-4665	175	1	ba21	ba21	PROPN
cana-4665	175	2	−	−	PROPN
cana-4665	175	3	(	(	PUNCT
cana-4665	175	4	−1+ba0)2	−1+ba0)2	INTJ
cana-4665	175	5	a21b	a21b	NOUN
cana-4665	175	6	2	2	NUM
cana-4665	175	7	−c1sin	−c1sin	ADJ
cana-4665	175	8	√	√	CCONJ
cana-4665	175	9	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	175	10	)	)	PUNCT
cana-4665	175	11	ba21	ba21	PROPN
cana-4665	175	12	−	−	PROPN
cana-4665	176	1	(	(	PUNCT
cana-4665	176	2	−1+ba0)2	−1+ba0)2	INTJ
cana-4665	176	3	a21b	a21b	NOUN
cana-4665	176	4	2	2	NUM
cana-4665	176	5	(	(	PUNCT
cana-4665	176	6	x−	x−	PROPN
cana-4665	176	7	t	t	PROPN
cana-4665	176	8	ω	ω	PROPN
cana-4665	176	9	)	)	PUNCT
cana-4665	176	10	+	+	NUM
cana-4665	176	11	c2cos	c2co	NOUN
cana-4665	176	12	√	√	CCONJ
cana-4665	176	13	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	176	14	)	)	PUNCT
cana-4665	176	15	ba21	ba21	PROPN
cana-4665	176	16	−	−	PROPN
cana-4665	176	17	(	(	PUNCT
cana-4665	176	18	−1+ba0)2	−1+ba0)2	INTJ
cana-4665	176	19	a21b	a21b	NOUN
cana-4665	176	20	2	2	NUM
cana-4665	176	21	(	(	PUNCT
cana-4665	176	22	x−	x−	PROPN
cana-4665	176	23	t	t	PROPN
cana-4665	176	24	ω	ω	PROPN
cana-4665	176	25	)	)	PUNCT
cana-4665	176	26	c1cos	c1co	NOUN
cana-4665	176	27	√	√	NUM
cana-4665	176	28	a0(−2+ba0	a0(−2+ba0	NOUN
cana-4665	176	29	)	)	PUNCT
cana-4665	177	1	ba21	ba21	PROPN
cana-4665	177	2	−	−	PROPN
cana-4665	177	3	(	(	PUNCT
cana-4665	177	4	−1+ba0)2	−1+ba0)2	INTJ
cana-4665	177	5	a21b	a21b	NOUN
cana-4665	177	6	2	2	NUM
cana-4665	177	7	(	(	PUNCT
cana-4665	177	8	x−	x−	PROPN
cana-4665	177	9	t	t	PROPN
cana-4665	177	10	ω	ω	PROPN
cana-4665	177	11	)	)	PUNCT
cana-4665	178	1	+	+	ADJ
cana-4665	178	2	c2	c2	PROPN
cana-4665	178	3	√	√	PUNCT
cana-4665	178	4	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	178	5	)	)	PUNCT
cana-4665	178	6	ba21	ba21	PROPN
cana-4665	178	7	−	−	PROPN
cana-4665	178	8	(	(	PUNCT
cana-4665	178	9	−1+ba0)2	−1+ba0)2	INTJ
cana-4665	178	10	a21b	a21b	NOUN
cana-4665	178	11	2	2	NUM
cana-4665	178	12	(	(	PUNCT
cana-4665	178	13	x−	x−	PROPN
cana-4665	178	14	t	t	PROPN
cana-4665	178	15	ω	ω	PROPN
cana-4665	178	16	)	)	PUNCT
cana-4665	178	17			NOUN
cana-4665	178	18			NOUN
cana-4665	178	19	.	.	PUNCT
cana-4665	179	1	(	(	PUNCT
cana-4665	179	2	3.30	3.30	NUM
cana-4665	179	3	)	)	PUNCT
cana-4665	179	4	f	f	PROPN
cana-4665	179	5	(	(	PUNCT
cana-4665	179	6	ξ	ξ	NOUN
cana-4665	179	7	)	)	PUNCT
cana-4665	179	8	=	=	NOUN
cana-4665	179	9	√√√√√√√a0	√√√√√√√a0	X
cana-4665	180	1	+	+	CCONJ
cana-4665	180	2	a1	a1	NOUN
cana-4665	180	3	−	−	NOUN
cana-4665	180	4	(	(	PUNCT
cana-4665	180	5	−1+ba0	−1+ba0	NOUN
cana-4665	180	6	)	)	PUNCT
cana-4665	180	7	a1b	a1b	PROPN
cana-4665	180	8	+	+	CCONJ
cana-4665	180	9	√	√	NUM
cana-4665	180	10	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	180	11	)	)	PUNCT
cana-4665	180	12	ba21	ba21	PROPN
cana-4665	180	13	−	−	PROPN
cana-4665	180	14	(	(	PUNCT
cana-4665	180	15	−1+ba0)2	−1+ba0)2	INTJ
cana-4665	180	16	a21b	a21b	NOUN
cana-4665	180	17	2	2	NUM
cana-4665	180	18	−c1sin	−c1sin	ADJ
cana-4665	180	19	√	√	CCONJ
cana-4665	180	20	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	180	21	)	)	PUNCT
cana-4665	180	22	ba21	ba21	PROPN
cana-4665	180	23	−	−	PROPN
cana-4665	180	24	(	(	PUNCT
cana-4665	180	25	−1+ba0)2	−1+ba0)2	INTJ
cana-4665	180	26	a21b	a21b	NOUN
cana-4665	180	27	2	2	NUM
cana-4665	180	28	(	(	PUNCT
cana-4665	180	29	x−	x−	PROPN
cana-4665	180	30	t	t	PROPN
cana-4665	180	31	ω	ω	PROPN
cana-4665	180	32	)	)	PUNCT
cana-4665	180	33	+	+	NUM
cana-4665	180	34	c2cos	c2co	NOUN
cana-4665	180	35	√	√	CCONJ
cana-4665	180	36	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	180	37	)	)	PUNCT
cana-4665	180	38	ba21	ba21	PROPN
cana-4665	180	39	−	−	PROPN
cana-4665	180	40	(	(	PUNCT
cana-4665	180	41	−1+ba0)2	−1+ba0)2	INTJ
cana-4665	180	42	a21b	a21b	NOUN
cana-4665	180	43	2	2	NUM
cana-4665	180	44	(	(	PUNCT
cana-4665	180	45	x−	x−	PROPN
cana-4665	180	46	t	t	PROPN
cana-4665	180	47	ω	ω	PROPN
cana-4665	180	48	)	)	PUNCT
cana-4665	180	49	c1cos	c1co	NOUN
cana-4665	180	50	√	√	NUM
cana-4665	180	51	a0(−2+ba0	a0(−2+ba0	NOUN
cana-4665	180	52	)	)	PUNCT
cana-4665	180	53	ba21	ba21	PROPN
cana-4665	180	54	−	−	PROPN
cana-4665	180	55	(	(	PUNCT
cana-4665	180	56	−1+ba0)2	−1+ba0)2	INTJ
cana-4665	180	57	a21b	a21b	NOUN
cana-4665	180	58	2	2	NUM
cana-4665	180	59	(	(	PUNCT
cana-4665	180	60	x−	x−	PROPN
cana-4665	180	61	t	t	PROPN
cana-4665	180	62	ω	ω	PROPN
cana-4665	180	63	)	)	PUNCT
cana-4665	181	1	+	+	ADJ
cana-4665	181	2	c2	c2	PROPN
cana-4665	181	3	√	√	PUNCT
cana-4665	181	4	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	181	5	)	)	PUNCT
cana-4665	181	6	ba21	ba21	PROPN
cana-4665	181	7	−	−	PROPN
cana-4665	181	8	(	(	PUNCT
cana-4665	181	9	−1+ba0)2	−1+ba0)2	INTJ
cana-4665	181	10	a21b	a21b	NOUN
cana-4665	181	11	2	2	NUM
cana-4665	181	12	(	(	PUNCT
cana-4665	181	13	x−	x−	PROPN
cana-4665	181	14	t	t	PROPN
cana-4665	181	15	ω	ω	PROPN
cana-4665	181	16	)	)	PUNCT
cana-4665	181	17			NOUN
cana-4665	181	18			NOUN
cana-4665	181	19	,	,	PUNCT
cana-4665	181	20	(	(	PUNCT
cana-4665	181	21	3.31	3.31	NUM
cana-4665	181	22	)	)	PUNCT
cana-4665	181	23	g(ξ	g(ξ	PROPN
cana-4665	181	24	)	)	PUNCT
cana-4665	181	25	=	=	PUNCT
cana-4665	182	1	−12aωξ	−12aωξ	ADJ
cana-4665	182	2	+	+	PUNCT
cana-4665	182	3	bξ	bξ	ADJ
cana-4665	182	4	3b	3b	NOUN
cana-4665	182	5	8a	8a	NUM
cana-4665	182	6	√√√√√√−2(−2a0c1	√√√√√√−2(−2a0c1	NOUN
cana-4665	182	7	cos	cos	ADP
cana-4665	182	8	(	(	PUNCT
cana-4665	182	9	√	√	NUM
cana-4665	182	10	4µ−λ2	4µ−λ2	NUM
cana-4665	182	11	2	2	NUM
cana-4665	182	12	)	)	PUNCT
cana-4665	182	13	−2a0c2	−2a0c2	ADJ
cana-4665	182	14	sin	sin	NOUN
cana-4665	182	15	(	(	PUNCT
cana-4665	182	16	√	√	PROPN
cana-4665	182	17	4µ−λ2	4µ−λ2	NUM
cana-4665	182	18	2	2	NUM
cana-4665	182	19	)	)	PUNCT
cana-4665	182	20	+	+	CCONJ
cana-4665	182	21	√	√	NUM
cana-4665	182	22	4µ−λ2	4µ−λ2	NUM
cana-4665	182	23	2	2	NUM
cana-4665	182	24	a1c1	a1c1	PRON
cana-4665	182	25	sin	sin	NOUN
cana-4665	182	26	(	(	PUNCT
cana-4665	182	27	√	√	NUM
cana-4665	182	28	4µ−λ2	4µ−λ2	NUM
cana-4665	182	29	2	2	NUM
cana-4665	182	30	)	)	PUNCT
cana-4665	182	31	−	−	NOUN
cana-4665	182	32	√	√	PROPN
cana-4665	182	33	4µ−λ2a1c2	4µ−λ2a1c2	PROPN
cana-4665	182	34	cos	cos	PROPN
cana-4665	182	35	(	(	PUNCT
cana-4665	182	36	√	√	NUM
cana-4665	182	37	4µ−λ2	4µ−λ2	NUM
cana-4665	182	38	2	2	NUM
cana-4665	182	39	)	)	PUNCT
cana-4665	183	1	+	+	PUNCT
cana-4665	183	2	λc1	λc1	X
cana-4665	183	3	cos	cos	ADJ
cana-4665	183	4	(	(	PUNCT
cana-4665	183	5	√	√	NUM
cana-4665	183	6	4µ−λ2	4µ−λ2	NUM
cana-4665	183	7	2	2	NUM
cana-4665	183	8	)	)	PUNCT
cana-4665	184	1	+	+	CCONJ
cana-4665	184	2	λc2	λc2	NOUN
cana-4665	184	3	sin	sin	NOUN
cana-4665	184	4	(	(	PUNCT
cana-4665	184	5	√	√	NUM
cana-4665	184	6	4µ−λ2	4µ−λ2	NUM
cana-4665	184	7	2	2	X
cana-4665	184	8	)	)	PUNCT
cana-4665	184	9	c1	c1	PROPN
cana-4665	184	10	cos	cos	PROPN
cana-4665	184	11	(	(	PUNCT
cana-4665	184	12	√	√	NUM
cana-4665	184	13	4µ−λ2	4µ−λ2	NUM
cana-4665	184	14	2	2	NUM
cana-4665	184	15	)	)	PUNCT
cana-4665	185	1	+	+	NOUN
cana-4665	185	2	c2	c2	PROPN
cana-4665	185	3	sin	sin	NOUN
cana-4665	185	4	(	(	PUNCT
cana-4665	185	5	√	√	PROPN
cana-4665	185	6	4µ−λ2	4µ−λ2	NUM
cana-4665	185	7	2	2	NUM
cana-4665	185	8	)	)	PUNCT
cana-4665	185	9			NOUN
cana-4665	186	1	ξ	ξ	PROPN
cana-4665	186	2	.	.	PUNCT
cana-4665	187	1	(	(	PUNCT
cana-4665	187	2	3.32	3.32	NUM
cana-4665	187	3	)	)	PUNCT
cana-4665	187	4	using	use	VERB
cana-4665	187	5	these	these	DET
cana-4665	187	6	values	value	NOUN
cana-4665	187	7	we	we	PRON
cana-4665	187	8	get	get	VERB
cana-4665	187	9	the	the	DET
cana-4665	187	10	solution	solution	NOUN
cana-4665	187	11	q(x	q(x	PROPN
cana-4665	187	12	,	,	PUNCT
cana-4665	187	13	t	t	PROPN
cana-4665	187	14	)	)	PUNCT
cana-4665	187	15	=	=	PUNCT
cana-4665	187	16	√√√√√√√a0	√√√√√√√a0	X
cana-4665	187	17	+	+	CCONJ
cana-4665	187	18	a1	a1	NOUN
cana-4665	187	19	−	−	NOUN
cana-4665	187	20	(	(	PUNCT
cana-4665	187	21	−1+ba0	−1+ba0	NOUN
cana-4665	187	22	)	)	PUNCT
cana-4665	187	23	a1b	a1b	PROPN
cana-4665	187	24	+	+	CCONJ
cana-4665	187	25	√	√	NUM
cana-4665	187	26	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	187	27	)	)	PUNCT
cana-4665	187	28	ba21	ba21	PROPN
cana-4665	187	29	−	−	PROPN
cana-4665	187	30	(	(	PUNCT
cana-4665	187	31	−1+ba0)2	−1+ba0)2	INTJ
cana-4665	187	32	a21b	a21b	NOUN
cana-4665	187	33	2	2	NUM
cana-4665	187	34	−c1sin	−c1sin	ADJ
cana-4665	187	35	√	√	CCONJ
cana-4665	187	36	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	187	37	)	)	PUNCT
cana-4665	187	38	ba21	ba21	PROPN
cana-4665	187	39	−	−	PROPN
cana-4665	188	1	(	(	PUNCT
cana-4665	188	2	−1+ba0)2	−1+ba0)2	INTJ
cana-4665	188	3	a21b	a21b	NOUN
cana-4665	188	4	2	2	NUM
cana-4665	188	5	(	(	PUNCT
cana-4665	188	6	x−	x−	PROPN
cana-4665	188	7	t	t	PROPN
cana-4665	188	8	ω	ω	PROPN
cana-4665	188	9	)	)	PUNCT
cana-4665	188	10	+	+	NUM
cana-4665	188	11	c2cos	c2co	NOUN
cana-4665	188	12	√	√	CCONJ
cana-4665	188	13	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	188	14	)	)	PUNCT
cana-4665	188	15	ba21	ba21	PROPN
cana-4665	188	16	−	−	PROPN
cana-4665	188	17	(	(	PUNCT
cana-4665	188	18	−1+ba0)2	−1+ba0)2	INTJ
cana-4665	188	19	a21b	a21b	NOUN
cana-4665	188	20	2	2	NUM
cana-4665	188	21	(	(	PUNCT
cana-4665	188	22	x−	x−	PROPN
cana-4665	188	23	t	t	PROPN
cana-4665	188	24	ω	ω	PROPN
cana-4665	188	25	)	)	PUNCT
cana-4665	188	26	c1cos	c1co	NOUN
cana-4665	188	27	√	√	NUM
cana-4665	188	28	a0(−2+ba0	a0(−2+ba0	NOUN
cana-4665	188	29	)	)	PUNCT
cana-4665	189	1	ba21	ba21	PROPN
cana-4665	189	2	−	−	PROPN
cana-4665	189	3	(	(	PUNCT
cana-4665	189	4	−1+ba0)2	−1+ba0)2	INTJ
cana-4665	189	5	a21b	a21b	NOUN
cana-4665	189	6	2	2	NUM
cana-4665	189	7	(	(	PUNCT
cana-4665	189	8	x−	x−	PROPN
cana-4665	189	9	t	t	PROPN
cana-4665	189	10	ω	ω	PROPN
cana-4665	189	11	)	)	PUNCT
cana-4665	190	1	+	+	ADJ
cana-4665	190	2	c2	c2	PROPN
cana-4665	190	3	√	√	PUNCT
cana-4665	190	4	a0(−2+ba0	a0(−2+ba0	PROPN
cana-4665	190	5	)	)	PUNCT
cana-4665	190	6	ba21	ba21	PROPN
cana-4665	190	7	−	−	PROPN
cana-4665	190	8	(	(	PUNCT
cana-4665	190	9	−1+ba0)2	−1+ba0)2	INTJ
cana-4665	190	10	a21b	a21b	NOUN
cana-4665	190	11	2	2	NUM
cana-4665	190	12	(	(	PUNCT
cana-4665	190	13	x−	x−	PROPN
cana-4665	190	14	t	t	PROPN
cana-4665	190	15	ω	ω	PROPN
cana-4665	190	16	)	)	PUNCT
cana-4665	190	17			NOUN
cana-4665	190	18			NOUN
cana-4665	190	19	eι(−12aωξ+bξ)×	eι(−12aωξ+bξ)×	NOUN
cana-4665	190	20	e	e	X
cana-4665	190	21	ι	ι	PROPN
cana-4665	190	22			NOUN
cana-4665	190	23	3b	3b	NOUN
cana-4665	190	24	8a	8a	NUM
cana-4665	190	25	√√√√√√√√−2(−2a0c1	√√√√√√√√−2(−2a0c1	NOUN
cana-4665	190	26	cos	cos	ADJ
cana-4665	190	27	(	(	PUNCT
cana-4665	190	28	√	√	NUM
cana-4665	190	29	4µ−λ2	4µ−λ2	NUM
cana-4665	190	30	2	2	NUM
cana-4665	190	31	)	)	PUNCT
cana-4665	190	32	−2a0c2	−2a0c2	ADJ
cana-4665	190	33	sin	sin	NOUN
cana-4665	190	34	(	(	PUNCT
cana-4665	190	35	√	√	PROPN
cana-4665	190	36	4µ−λ2	4µ−λ2	NUM
cana-4665	190	37	2	2	NUM
cana-4665	190	38	)	)	PUNCT
cana-4665	190	39	+	+	CCONJ
cana-4665	190	40	√	√	NUM
cana-4665	190	41	4µ−λ2	4µ−λ2	NUM
cana-4665	190	42	2	2	NUM
cana-4665	190	43	a1c1	a1c1	DET
cana-4665	190	44	sin	sin	NOUN
cana-4665	190	45	(	(	PUNCT
cana-4665	190	46	√	√	NUM
cana-4665	190	47	4µ−λ2	4µ−λ2	NUM
cana-4665	190	48	2	2	NUM
cana-4665	190	49	)	)	PUNCT
cana-4665	190	50	−	−	NOUN
cana-4665	190	51	√	√	PROPN
cana-4665	190	52	4µ−λ2a1c2	4µ−λ2a1c2	PROPN
cana-4665	190	53	cos	cos	PROPN
cana-4665	190	54	(	(	PUNCT
cana-4665	190	55	√	√	NUM
cana-4665	190	56	4µ−λ2	4µ−λ2	NUM
cana-4665	190	57	2	2	NUM
cana-4665	190	58	)	)	PUNCT
cana-4665	191	1	+	+	PUNCT
cana-4665	191	2	λc1	λc1	X
cana-4665	191	3	cos	cos	ADJ
cana-4665	191	4	(	(	PUNCT
cana-4665	191	5	√	√	NUM
cana-4665	191	6	4µ−λ2	4µ−λ2	NUM
cana-4665	191	7	2	2	NUM
cana-4665	191	8	)	)	PUNCT
cana-4665	192	1	+	+	CCONJ
cana-4665	192	2	λc2	λc2	NOUN
cana-4665	192	3	sin	sin	NOUN
cana-4665	192	4	(	(	PUNCT
cana-4665	192	5	√	√	NUM
cana-4665	192	6	4µ−λ2	4µ−λ2	NUM
cana-4665	192	7	2	2	X
cana-4665	192	8	)	)	PUNCT
cana-4665	192	9	c1	c1	PROPN
cana-4665	192	10	cos	cos	PROPN
cana-4665	192	11	(	(	PUNCT
cana-4665	192	12	√	√	NUM
cana-4665	192	13	4µ−λ2	4µ−λ2	NUM
cana-4665	192	14	2	2	NUM
cana-4665	192	15	)	)	PUNCT
cana-4665	193	1	+	+	NOUN
cana-4665	193	2	c2	c2	PROPN
cana-4665	193	3	sin	sin	NOUN
cana-4665	193	4	(	(	PUNCT
cana-4665	193	5	√	√	PROPN
cana-4665	193	6	4µ−λ2	4µ−λ2	NUM
cana-4665	193	7	2	2	NUM
cana-4665	193	8	)	)	PUNCT
cana-4665	193	9	ξ	ξ	NOUN
cana-4665	193	10	.	.	PUNCT
cana-4665	194	1	(	(	PUNCT
cana-4665	194	2	3.33	3.33	NUM
cana-4665	194	3	)	)	PUNCT
cana-4665	194	4	communications	communication	NOUN
cana-4665	194	5	on	on	ADP
cana-4665	194	6	applied	apply	VERB
cana-4665	194	7	nonlinear	nonlinear	ADJ
cana-4665	194	8	analysis	analysis	NOUN
cana-4665	194	9	issn	issn	NOUN
cana-4665	194	10	:	:	PUNCT
cana-4665	194	11	1074	1074	NUM
cana-4665	194	12	-	-	PUNCT
cana-4665	194	13	133x	133x	NUM
cana-4665	194	14	vol	vol	VERB
cana-4665	194	15	32	32	NUM
cana-4665	194	16	no	no	NOUN
cana-4665	194	17	.	.	PUNCT
cana-4665	195	1	10s	10	NOUN
cana-4665	195	2	(	(	PUNCT
cana-4665	195	3	2025	2025	NUM
cana-4665	195	4	)	)	PUNCT
cana-4665	195	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-4665	195	6	96	96	NUM
cana-4665	195	7	figure	figure	NOUN
cana-4665	195	8	1	1	NUM
cana-4665	195	9	:	:	PUNCT
cana-4665	195	10	traveling	travel	VERB
cana-4665	195	11	wave	wave	NOUN
cana-4665	195	12	solution	solution	NOUN
cana-4665	195	13	of	of	ADP
cana-4665	195	14	|q(x	|q(x	PROPN
cana-4665	195	15	,	,	PUNCT
cana-4665	195	16	t)|	t)|	NOUN
cana-4665	195	17	of	of	ADP
cana-4665	195	18	equation	equation	NOUN
cana-4665	195	19	(	(	PUNCT
cana-4665	195	20	3.29	3.29	NUM
cana-4665	195	21	)	)	PUNCT
cana-4665	195	22	when	when	SCONJ
cana-4665	195	23	λ2−	λ2−	NOUN
cana-4665	195	24	4µ	4µ	NOUN
cana-4665	195	25	>	>	X
cana-4665	195	26	0	0	PUNCT
cana-4665	196	1	for	for	SCONJ
cana-4665	196	2	case	case	NOUN
cana-4665	196	3	-	-	PUNCT
cana-4665	196	4	i	i	PRON
cana-4665	196	5	a0	a0	NOUN
cana-4665	196	6	=	=	SYM
cana-4665	196	7	2	2	NUM
cana-4665	196	8	,	,	PUNCT
cana-4665	196	9	a1	a1	NOUN
cana-4665	196	10	=	=	SYM
cana-4665	196	11	1	1	NUM
cana-4665	196	12	,	,	PUNCT
cana-4665	196	13	c1	c1	NOUN
cana-4665	196	14	=	=	PROPN
cana-4665	196	15	4	4	NUM
cana-4665	196	16	,	,	PUNCT
cana-4665	196	17	c2	c2	PROPN
cana-4665	196	18	=	=	SYM
cana-4665	196	19	5	5	NUM
cana-4665	196	20	,	,	PUNCT
cana-4665	196	21	w	w	NOUN
cana-4665	196	22	=	=	SYM
cana-4665	196	23	1	1	NUM
cana-4665	196	24	,	,	PUNCT
cana-4665	196	25	b	b	NOUN
cana-4665	196	26	=	=	SYM
cana-4665	196	27	1	1	NUM
cana-4665	196	28	,	,	PUNCT
cana-4665	196	29	ξ	ξ	PROPN
cana-4665	196	30	=	=	SYM
cana-4665	196	31	x−	x−	PROPN
cana-4665	196	32	t	t	PROPN
cana-4665	196	33	w	w	PROPN
cana-4665	196	34	.	.	PUNCT
cana-4665	196	35	figure	figure	NOUN
cana-4665	196	36	2	2	NUM
cana-4665	196	37	:	:	PUNCT
cana-4665	196	38	traveling	travel	VERB
cana-4665	196	39	wave	wave	NOUN
cana-4665	196	40	solution	solution	NOUN
cana-4665	196	41	of	of	ADP
cana-4665	196	42	|q(x	|q(x	PROPN
cana-4665	196	43	,	,	PUNCT
cana-4665	196	44	t)|	t)|	NOUN
cana-4665	196	45	of	of	ADP
cana-4665	196	46	equation	equation	NOUN
cana-4665	196	47	(	(	PUNCT
cana-4665	196	48	3.29	3.29	NUM
cana-4665	196	49	)	)	PUNCT
cana-4665	196	50	when	when	SCONJ
cana-4665	196	51	λ2−	λ2−	NOUN
cana-4665	196	52	4µ	4µ	NOUN
cana-4665	196	53	>	>	X
cana-4665	196	54	0	0	PUNCT
cana-4665	196	55	for	for	ADP
cana-4665	196	56	case	case	NOUN
cana-4665	196	57	-	-	PUNCT
cana-4665	196	58	ii	ii	NOUN
cana-4665	196	59	a0	a0	NOUN
cana-4665	196	60	=	=	SYM
cana-4665	196	61	2	2	NUM
cana-4665	196	62	,	,	PUNCT
cana-4665	196	63	a1	a1	NOUN
cana-4665	196	64	=	=	SYM
cana-4665	196	65	1	1	NUM
cana-4665	196	66	,	,	PUNCT
cana-4665	196	67	c1	c1	NOUN
cana-4665	196	68	=	=	PROPN
cana-4665	196	69	4	4	NUM
cana-4665	196	70	,	,	PUNCT
cana-4665	196	71	c2	c2	PROPN
cana-4665	196	72	=	=	SYM
cana-4665	196	73	5	5	NUM
cana-4665	196	74	,	,	PUNCT
cana-4665	196	75	w	w	NOUN
cana-4665	196	76	=	=	SYM
cana-4665	196	77	−1	−1	NOUN
cana-4665	196	78	,	,	PUNCT
cana-4665	196	79	b	b	NOUN
cana-4665	196	80	=	=	SYM
cana-4665	196	81	1	1	NUM
cana-4665	196	82	,	,	PUNCT
cana-4665	196	83	ξ	ξ	PROPN
cana-4665	196	84	=	=	SYM
cana-4665	196	85	x−	x−	PROPN
cana-4665	196	86	t	t	PROPN
cana-4665	196	87	w	w	PROPN
cana-4665	196	88	.	.	PUNCT
cana-4665	196	89	communications	communication	NOUN
cana-4665	196	90	on	on	ADP
cana-4665	196	91	applied	apply	VERB
cana-4665	196	92	nonlinear	nonlinear	ADJ
cana-4665	196	93	analysis	analysis	NOUN
cana-4665	196	94	issn	issn	NOUN
cana-4665	196	95	:	:	PUNCT
cana-4665	196	96	1074	1074	NUM
cana-4665	196	97	-	-	PUNCT
cana-4665	196	98	133x	133x	NUM
cana-4665	196	99	vol	vol	VERB
cana-4665	196	100	32	32	NUM
cana-4665	196	101	no	no	NOUN
cana-4665	196	102	.	.	PUNCT
cana-4665	197	1	10s	10	NOUN
cana-4665	197	2	(	(	PUNCT
cana-4665	197	3	2025	2025	NUM
cana-4665	197	4	)	)	PUNCT
cana-4665	197	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-4665	197	6	97	97	NUM
cana-4665	197	7	where	where	SCONJ
cana-4665	197	8	ξ	ξ	PROPN
cana-4665	197	9	=	=	SYM
cana-4665	198	1	x−	x−	PROPN
cana-4665	198	2	t	t	PROPN
cana-4665	198	3	w	w	PROPN
cana-4665	198	4	.	.	PUNCT
cana-4665	198	5	subcase	subcase	PROPN
cana-4665	198	6	-	-	PUNCT
cana-4665	198	7	iii	iii	NOUN
cana-4665	198	8	when	when	SCONJ
cana-4665	198	9	λ2	λ2	NOUN
cana-4665	198	10	−	−	PROPN
cana-4665	198	11	4µ	4µ	NOUN
cana-4665	198	12	=	=	SYM
cana-4665	198	13	0	0	NUM
cana-4665	198	14	,	,	PUNCT
cana-4665	198	15	then	then	ADV
cana-4665	198	16	solution	solution	NOUN
cana-4665	198	17	is	be	AUX
cana-4665	198	18	:	:	PUNCT
cana-4665	198	19	p	p	X
cana-4665	198	20	(	(	PUNCT
cana-4665	198	21	x	x	PROPN
cana-4665	198	22	,	,	PUNCT
cana-4665	198	23	t	t	PROPN
cana-4665	198	24	)	)	PUNCT
cana-4665	198	25	=	=	SYM
cana-4665	199	1	(	(	PUNCT
cana-4665	199	2	−(−1	−(−1	INTJ
cana-4665	199	3	+	+	CCONJ
cana-4665	199	4	ba0	ba0	ADJ
cana-4665	199	5	)	)	PUNCT
cana-4665	199	6	a1b	a1b	PROPN
cana-4665	200	1	+	+	CCONJ
cana-4665	200	2	c2	c2	PROPN
cana-4665	200	3	c1	c1	PROPN
cana-4665	200	4	+	+	CCONJ
cana-4665	200	5	c2ξ	c2ξ	PROPN
cana-4665	200	6	)	)	PUNCT
cana-4665	200	7	.	.	PUNCT
cana-4665	201	1	(	(	PUNCT
cana-4665	201	2	3.34	3.34	NUM
cana-4665	201	3	)	)	PUNCT
cana-4665	201	4	in	in	ADP
cana-4665	201	5	this	this	DET
cana-4665	201	6	instance	instance	NOUN
cana-4665	201	7	,	,	PUNCT
cana-4665	201	8	both	both	CCONJ
cana-4665	201	9	c1	c1	PROPN
cana-4665	201	10	and	and	CCONJ
cana-4665	201	11	c2	c2	PROPN
cana-4665	201	12	are	be	AUX
cana-4665	201	13	treated	treat	VERB
cana-4665	201	14	the	the	DET
cana-4665	201	15	arbitrary	arbitrary	ADJ
cana-4665	201	16	constants	constant	NOUN
cana-4665	201	17	.	.	PUNCT
cana-4665	202	1	f	f	X
cana-4665	202	2	(	(	PUNCT
cana-4665	202	3	x	x	PROPN
cana-4665	202	4	,	,	PUNCT
cana-4665	202	5	t	t	PROPN
cana-4665	202	6	)	)	PUNCT
cana-4665	202	7	=	=	SYM
cana-4665	202	8	√	√	PROPN
cana-4665	202	9	−k2	−k2	NOUN
cana-4665	202	10	+	+	CCONJ
cana-4665	202	11	(	(	PUNCT
cana-4665	202	12	c2	c2	PROPN
cana-4665	202	13	c1	c1	PROPN
cana-4665	202	14	+	+	CCONJ
cana-4665	202	15	c2ξ	c2ξ	PROPN
cana-4665	202	16	)	)	PUNCT
cana-4665	202	17	,	,	PUNCT
cana-4665	202	18	(	(	PUNCT
cana-4665	202	19	3.35	3.35	NUM
cana-4665	202	20	)	)	PUNCT
cana-4665	202	21	where	where	SCONJ
cana-4665	202	22	k2	k2	PROPN
cana-4665	202	23	=	=	SYM
cana-4665	202	24	−1+ba0	−1+ba0	ADJ
cana-4665	202	25	a1b	a1b	PROPN
cana-4665	202	26	.	.	PUNCT
cana-4665	203	1	is	be	AUX
cana-4665	203	2	any	any	PRON
cana-4665	203	3	constant	constant	ADJ
cana-4665	203	4	.	.	PUNCT
cana-4665	204	1	g(x	g(x	NOUN
cana-4665	204	2	,	,	PUNCT
cana-4665	204	3	t	t	PROPN
cana-4665	204	4	)	)	PUNCT
cana-4665	204	5	=	=	VERB
cana-4665	205	1	−12aξ	−12aξ	NOUN
cana-4665	205	2	+	+	CCONJ
cana-4665	205	3	3	3	NUM
cana-4665	205	4	8	8	NUM
cana-4665	205	5			NOUN
cana-4665	205	6	b	b	NOUN
cana-4665	205	7	√	√	NOUN
cana-4665	205	8	−(k2c1+k2c2ξ−c2	−(k2c1+k2c2ξ−c2	NOUN
cana-4665	205	9	)	)	PUNCT
cana-4665	205	10	(	(	PUNCT
cana-4665	205	11	c1+c2ξ	c1+c2ξ	NUM
cana-4665	205	12	)	)	PUNCT
cana-4665	205	13	(	(	PUNCT
cana-4665	205	14	c1+c2ξ)(2	c1+c2ξ)(2	ADV
cana-4665	205	15	√	√	NOUN
cana-4665	205	16	−(k2c1+k2c2ξ−c2)(c1+c2ξ	−(k2c1+k2c2ξ−c2)(c1+c2ξ	PROPN
cana-4665	205	17	)	)	PUNCT
cana-4665	205	18	√	√	PROPN
cana-4665	206	1	k2c	k2c	NOUN
cana-4665	206	2	2	2	NUM
cana-4665	206	3	2+c2	2+c2	NUM
cana-4665	206	4	2arctan	2arctan	NUM
cana-4665	206	5	(	(	PUNCT
cana-4665	206	6	√	√	NUM
cana-4665	206	7	k2c	k2c	PROPN
cana-4665	206	8	2	2	NUM
cana-4665	206	9	2(2k2c2ξ+2k2c1−c2	2(2k2c2ξ+2k2c1−c2	NUM
cana-4665	206	10	)	)	PUNCT
cana-4665	206	11	)	)	PUNCT
cana-4665	206	12	2k2c2	2k2c2	NUM
cana-4665	207	1	√	√	NUM
cana-4665	207	2	−(k2c1+k2c2ξ−c2)(c1+c2ξ	−(k2c1+k2c2ξ−c2)(c1+c2ξ	PROPN
cana-4665	207	3	)	)	PUNCT
cana-4665	207	4	)	)	PUNCT
cana-4665	208	1	ac2	ac2	PROPN
cana-4665	208	2	√	√	PROPN
cana-4665	208	3	−(k2c1+k2c2ξ−c2)(c1+c2ξ	−(k2c1+k2c2ξ−c2)(c1+c2ξ	PROPN
cana-4665	208	4	)	)	PUNCT
cana-4665	209	1	√	√	PROPN
cana-4665	210	1	k2c	k2c	NOUN
cana-4665	210	2	2	2	NUM
cana-4665	210	3	2	2	NUM
cana-4665	210	4			NOUN
cana-4665	210	5	+	+	CCONJ
cana-4665	210	6	bξ	bξ	PROPN
cana-4665	210	7	.	.	PUNCT
cana-4665	211	1	(	(	PUNCT
cana-4665	211	2	3.36	3.36	NUM
cana-4665	211	3	)	)	PUNCT
cana-4665	211	4	using	use	VERB
cana-4665	211	5	these	these	DET
cana-4665	211	6	values	value	NOUN
cana-4665	211	7	we	we	PRON
cana-4665	211	8	get	get	VERB
cana-4665	211	9	solution	solution	NOUN
cana-4665	211	10	q(x	q(x	PROPN
cana-4665	211	11	,	,	PUNCT
cana-4665	211	12	t	t	PROPN
cana-4665	211	13	)	)	PUNCT
cana-4665	211	14	=	=	SYM
cana-4665	212	1	√	√	PROPN
cana-4665	212	2	−k2	−k2	NOUN
cana-4665	212	3	+	+	CCONJ
cana-4665	212	4	(	(	PUNCT
cana-4665	212	5	c2	c2	PROPN
cana-4665	212	6	c1+c2ξ	c1+c2ξ	PROPN
cana-4665	212	7	)	)	PUNCT
cana-4665	212	8	×	×	NOUN
cana-4665	212	9	e	e	NOUN
cana-4665	212	10	ι	ι	X
cana-4665	212	11	−12aξ+3	−12aξ+3	PROPN
cana-4665	212	12	8	8	NUM
cana-4665	212	13			NOUN
cana-4665	212	14	b	b	NOUN
cana-4665	212	15	√	√	NOUN
cana-4665	212	16	−(k2c1+k2c2ξ−c2	−(k2c1+k2c2ξ−c2	NOUN
cana-4665	212	17	)	)	PUNCT
cana-4665	212	18	(	(	PUNCT
cana-4665	212	19	c1+c2ξ	c1+c2ξ	NUM
cana-4665	212	20	)	)	PUNCT
cana-4665	212	21	(	(	PUNCT
cana-4665	212	22	c1+c2ξ)(2	c1+c2ξ)(2	ADV
cana-4665	212	23	√	√	NOUN
cana-4665	212	24	−(k2c1+k2c2ξ−c2)(c1+c2ξ	−(k2c1+k2c2ξ−c2)(c1+c2ξ	PROPN
cana-4665	212	25	)	)	PUNCT
cana-4665	212	26	√	√	PROPN
cana-4665	213	1	k2c	k2c	NOUN
cana-4665	213	2	2	2	NUM
cana-4665	213	3	2+c2	2+c2	NUM
cana-4665	213	4	2arctan	2arctan	NUM
cana-4665	213	5	(	(	PUNCT
cana-4665	213	6	√	√	NUM
cana-4665	213	7	k2c	k2c	PROPN
cana-4665	213	8	2	2	NUM
cana-4665	213	9	2(2k2c2ξ+2k2c1−c2	2(2k2c2ξ+2k2c1−c2	NUM
cana-4665	213	10	)	)	PUNCT
cana-4665	213	11	)	)	PUNCT
cana-4665	213	12	2k2c2	2k2c2	NUM
cana-4665	214	1	√	√	NUM
cana-4665	214	2	−(k2c1+k2c2ξ−c2)(c1+c2ξ	−(k2c1+k2c2ξ−c2)(c1+c2ξ	PROPN
cana-4665	214	3	)	)	PUNCT
cana-4665	214	4	)	)	PUNCT
cana-4665	215	1	ac2	ac2	PROPN
cana-4665	215	2	√	√	PROPN
cana-4665	215	3	−(k2c1+k2c2ξ−c2)(c1+c2ξ	−(k2c1+k2c2ξ−c2)(c1+c2ξ	PROPN
cana-4665	215	4	)	)	PUNCT
cana-4665	216	1	√	√	PROPN
cana-4665	217	1	k2c	k2c	NOUN
cana-4665	217	2	2	2	NUM
cana-4665	217	3	2	2	NUM
cana-4665	217	4	+bξ	+bξ	NOUN
cana-4665	217	5			NOUN
cana-4665	217	6	.	.	PUNCT
cana-4665	218	1	(	(	PUNCT
cana-4665	218	2	3.37	3.37	NUM
cana-4665	218	3	)	)	PUNCT
cana-4665	218	4	where	where	SCONJ
cana-4665	218	5	ξ	ξ	X
cana-4665	218	6	=	=	SYM
cana-4665	218	7	x−	x−	PROPN
cana-4665	218	8	t	t	PROPN
cana-4665	218	9	w	w	PROPN
cana-4665	218	10	.	.	PUNCT
cana-4665	219	1	4	4	NUM
cana-4665	219	2	conclusion	conclusion	NOUN
cana-4665	219	3	the	the	DET
cana-4665	219	4	goal	goal	NOUN
cana-4665	219	5	of	of	ADP
cana-4665	219	6	this	this	DET
cana-4665	219	7	study	study	NOUN
cana-4665	219	8	was	be	AUX
cana-4665	219	9	to	to	PART
cana-4665	219	10	explore	explore	VERB
cana-4665	219	11	the	the	DET
cana-4665	219	12	various	various	ADJ
cana-4665	219	13	lie	lie	NOUN
cana-4665	219	14	symmetries	symmetry	NOUN
cana-4665	219	15	and	and	CCONJ
cana-4665	219	16	the	the	DET
cana-4665	219	17	invariant	invariant	ADJ
cana-4665	219	18	solutions	solution	NOUN
cana-4665	219	19	of	of	ADP
cana-4665	219	20	kaup	kaup	PROPN
cana-4665	219	21	-	-	PROPN
cana-4665	219	22	newell	newell	PROPN
cana-4665	219	23	equations	equation	NOUN
cana-4665	219	24	.	.	PUNCT
cana-4665	220	1	the	the	DET
cana-4665	220	2	first	first	ADJ
cana-4665	220	3	step	step	NOUN
cana-4665	220	4	is	be	AUX
cana-4665	220	5	to	to	PART
cana-4665	220	6	determine	determine	VERB
cana-4665	220	7	the	the	DET
cana-4665	220	8	infinitesmal	infinitesmal	ADJ
cana-4665	220	9	generators	generator	NOUN
cana-4665	220	10	of	of	ADP
cana-4665	220	11	the	the	DET
cana-4665	220	12	equation	equation	NOUN
cana-4665	220	13	using	use	VERB
cana-4665	220	14	the	the	DET
cana-4665	220	15	lie	lie	NOUN
cana-4665	220	16	group	group	NOUN
cana-4665	220	17	method	method	NOUN
cana-4665	220	18	.	.	PUNCT
cana-4665	221	1	we	we	PRON
cana-4665	221	2	then	then	ADV
cana-4665	221	3	used	use	VERB
cana-4665	221	4	the	the	DET
cana-4665	221	5	g′	g′	NOUN
cana-4665	221	6	g	g	PROPN
cana-4665	221	7	-expansion	-expansion	NOUN
cana-4665	221	8	procedure	procedure	NOUN
cana-4665	221	9	to	to	PART
cana-4665	221	10	derive	derive	VERB
cana-4665	221	11	the	the	DET
cana-4665	221	12	traveling	travel	VERB
cana-4665	221	13	wave	wave	NOUN
cana-4665	221	14	solutions	solution	NOUN
cana-4665	221	15	.	.	PUNCT
cana-4665	222	1	these	these	DET
cana-4665	222	2	traveling	travel	VERB
cana-4665	222	3	wave	wave	NOUN
cana-4665	222	4	solutions	solution	NOUN
cana-4665	222	5	are	be	AUX
cana-4665	222	6	expressed	express	VERB
cana-4665	222	7	using	use	VERB
cana-4665	222	8	hyperbolic	hyperbolic	ADJ
cana-4665	222	9	,	,	PUNCT
cana-4665	222	10	trigonometric	trigonometric	ADJ
cana-4665	222	11	,	,	PUNCT
cana-4665	222	12	and	and	CCONJ
cana-4665	222	13	rational	rational	ADJ
cana-4665	222	14	functions	function	NOUN
cana-4665	222	15	that	that	PRON
cana-4665	222	16	incorporate	incorporate	VERB
cana-4665	222	17	arbitrary	arbitrary	ADJ
cana-4665	222	18	parameters	parameter	NOUN
cana-4665	222	19	.	.	PUNCT
cana-4665	223	1	we	we	PRON
cana-4665	223	2	derived	derive	VERB
cana-4665	223	3	exact	exact	ADJ
cana-4665	223	4	soliton	soliton	NOUN
cana-4665	223	5	solutions	solution	NOUN
cana-4665	223	6	for	for	ADP
cana-4665	223	7	the	the	DET
cana-4665	223	8	kaup	kaup	PROPN
cana-4665	223	9	-	-	PROPN
cana-4665	223	10	newell	newell	PROPN
cana-4665	223	11	equation	equation	NOUN
cana-4665	223	12	.	.	PUNCT
cana-4665	224	1	these	these	DET
cana-4665	224	2	solutions	solution	NOUN
cana-4665	224	3	may	may	AUX
cana-4665	224	4	hold	hold	VERB
cana-4665	224	5	importance	importance	NOUN
cana-4665	224	6	across	across	ADP
cana-4665	224	7	various	various	ADJ
cana-4665	224	8	scientific	scientific	ADJ
cana-4665	224	9	disciplines	discipline	NOUN
cana-4665	224	10	.	.	PUNCT
cana-4665	225	1	the	the	DET
cana-4665	225	2	availability	availability	NOUN
cana-4665	225	3	of	of	ADP
cana-4665	225	4	advanced	advanced	ADJ
cana-4665	225	5	mathematical	mathematical	ADJ
cana-4665	225	6	software	software	NOUN
cana-4665	225	7	such	such	ADJ
cana-4665	225	8	as	as	ADP
cana-4665	225	9	maple	maple	NOUN
cana-4665	225	10	simplifies	simplifie	NOUN
cana-4665	225	11	the	the	DET
cana-4665	225	12	complex	complex	ADJ
cana-4665	225	13	algebraic	algebraic	ADJ
cana-4665	225	14	computations	computation	NOUN
cana-4665	225	15	.	.	PUNCT
cana-4665	226	1	5	5	NUM
cana-4665	226	2	author	author	NOUN
cana-4665	226	3	contribution	contribution	NOUN
cana-4665	226	4	anupma	anupma	PROPN
cana-4665	226	5	bansal	bansal	NOUN
cana-4665	226	6	;	;	PUNCT
cana-4665	226	7	editing	edit	VERB
cana-4665	226	8	,	,	PUNCT
cana-4665	226	9	original	original	ADJ
cana-4665	226	10	graph	graph	NOUN
cana-4665	226	11	plotting	plotting	NOUN
cana-4665	226	12	and	and	CCONJ
cana-4665	226	13	investigation	investigation	NOUN
cana-4665	226	14	.	.	PUNCT
cana-4665	227	1	arshdeep	arshdeep	PROPN
cana-4665	227	2	kaur	kaur	PROPN
cana-4665	227	3	;	;	PUNCT
cana-4665	227	4	writting	writting	NOUN
cana-4665	227	5	,	,	PUNCT
cana-4665	227	6	editing	edit	VERB
cana-4665	227	7	and	and	CCONJ
cana-4665	227	8	original	original	ADJ
cana-4665	227	9	graph	graph	NOUN
cana-4665	227	10	plotting	plotting	NOUN
cana-4665	227	11	.	.	PUNCT
cana-4665	228	1	rajeev	rajeev	PROPN
cana-4665	228	2	budhiraja	budhiraja	PROPN
cana-4665	228	3	;	;	PUNCT
cana-4665	228	4	editing	editing	NOUN
cana-4665	228	5	and	and	CCONJ
cana-4665	228	6	investigation	investigation	NOUN
cana-4665	228	7	.	.	PUNCT
cana-4665	229	1	6	6	NUM
cana-4665	229	2	competing	compete	VERB
cana-4665	229	3	interest	interest	NOUN
cana-4665	229	4	the	the	DET
cana-4665	229	5	authors	author	NOUN
cana-4665	229	6	declare	declare	VERB
cana-4665	229	7	that	that	SCONJ
cana-4665	229	8	they	they	PRON
cana-4665	229	9	have	have	VERB
cana-4665	229	10	no	no	DET
cana-4665	229	11	known	know	VERB
cana-4665	229	12	competing	compete	VERB
cana-4665	229	13	interest	interest	NOUN
cana-4665	229	14	.	.	PUNCT
cana-4665	230	1	communications	communication	NOUN
cana-4665	230	2	on	on	ADP
cana-4665	230	3	applied	apply	VERB
cana-4665	230	4	nonlinear	nonlinear	ADJ
cana-4665	230	5	analysis	analysis	NOUN
cana-4665	230	6	issn	issn	NOUN
cana-4665	230	7	:	:	PUNCT
cana-4665	230	8	1074	1074	NUM
cana-4665	230	9	-	-	PUNCT
cana-4665	230	10	133x	133x	NUM
cana-4665	230	11	vol	vol	VERB
cana-4665	230	12	32	32	NUM
cana-4665	230	13	no	no	NOUN
cana-4665	230	14	.	.	PUNCT
cana-4665	231	1	10s	10	NOUN
cana-4665	231	2	(	(	PUNCT
cana-4665	231	3	2025	2025	NUM
cana-4665	231	4	)	)	PUNCT
cana-4665	231	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-4665	231	6	98	98	NUM
cana-4665	231	7	references	reference	NOUN
cana-4665	231	8	[	[	X
cana-4665	231	9	1	1	NUM
cana-4665	231	10	]	]	PUNCT
cana-4665	231	11	chou	chou	PROPN
cana-4665	231	12	dean	dean	PROPN
cana-4665	231	13	,	,	PUNCT
cana-4665	231	14	boulaaras	boulaaras	NOUN
cana-4665	231	15	sm	sm	PROPN
cana-4665	231	16	,	,	PUNCT
cana-4665	231	17	rehman	rehman	PROPN
cana-4665	231	18	h	h	PROPN
cana-4665	231	19	ur	ur	VERB
cana-4665	231	20	,	,	PUNCT
cana-4665	231	21	iqbal	iqbal	PROPN
cana-4665	231	22	i	i	PROPN
cana-4665	231	23	,	,	PUNCT
cana-4665	231	24	abbas	abbas	PROPN
cana-4665	231	25	m	m	PROPN
cana-4665	231	26	(	(	PUNCT
cana-4665	231	27	2024	2024	NUM
cana-4665	231	28	)	)	PUNCT
cana-4665	231	29	lie	lie	NOUN
cana-4665	231	30	symmetries	symmetry	NOUN
cana-4665	231	31	,	,	PUNCT
cana-4665	231	32	soliton	soliton	NOUN
cana-4665	231	33	dynamics	dynamic	NOUN
cana-4665	231	34	,	,	PUNCT
cana-4665	231	35	bifurcation	bifurcation	NOUN
cana-4665	231	36	analysis	analysis	NOUN
cana-4665	231	37	and	and	CCONJ
cana-4665	231	38	chaotic	chaotic	ADJ
cana-4665	231	39	behaviour	behaviour	NOUN
cana-4665	231	40	in	in	ADP
cana-4665	231	41	the	the	DET
cana-4665	231	42	reduced	reduced	ADJ
cana-4665	231	43	ostrovsky	ostrovsky	ADJ
cana-4665	231	44	equation	equation	NOUN
cana-4665	231	45	.	.	PUNCT
cana-4665	232	1	rendiconti	rendiconti	ADJ
cana-4665	232	2	lincei	lincei	NOUN
cana-4665	232	3	.	.	PUNCT
cana-4665	233	1	science	science	PROPN
cana-4665	233	2	fisiche	fisiche	PROPN
cana-4665	233	3	naturali	naturali	VERB
cana-4665	233	4	.	.	PUNCT
cana-4665	234	1	[	[	X
cana-4665	234	2	2	2	NUM
cana-4665	234	3	]	]	PUNCT
cana-4665	234	4	bansal	bansal	NOUN
cana-4665	234	5	a	a	PROPN
cana-4665	234	6	,	,	PUNCT
cana-4665	234	7	kara	kara	PROPN
cana-4665	234	8	ah	ah	INTJ
cana-4665	234	9	,	,	PUNCT
cana-4665	234	10	biswas	biswas	PROPN
cana-4665	234	11	a	a	PROPN
cana-4665	234	12	,	,	PUNCT
cana-4665	234	13	moshokoa	moshokoa	NOUN
cana-4665	234	14	sp	sp	NOUN
cana-4665	234	15	and	and	CCONJ
cana-4665	234	16	belic	belic	ADJ
cana-4665	234	17	m	m	PROPN
cana-4665	234	18	(	(	PUNCT
cana-4665	234	19	2018)optical	2018)optical	ADJ
cana-4665	234	20	soliton	soliton	NOUN
cana-4665	234	21	perturbation	perturbation	NOUN
cana-4665	234	22	,	,	PUNCT
cana-4665	234	23	group	group	NOUN
cana-4665	234	24	invariants	invariant	NOUN
cana-4665	234	25	and	and	CCONJ
cana-4665	234	26	conservation	conservation	NOUN
cana-4665	234	27	laws	law	NOUN
cana-4665	234	28	of	of	ADP
cana-4665	234	29	perturbed	perturb	VERB
cana-4665	234	30	fokas	fokas	ADJ
cana-4665	234	31	-	-	PUNCT
cana-4665	234	32	lenells	lenell	NOUN
cana-4665	234	33	equation	equation	NOUN
cana-4665	234	34	,	,	PUNCT
cana-4665	234	35	chaos	chaos	NOUN
cana-4665	234	36	solitons	soliton	NOUN
cana-4665	234	37	fractals	fractal	NOUN
cana-4665	234	38	(	(	PUNCT
cana-4665	234	39	vol.114):275–280	vol.114):275–280	VERB
cana-4665	234	40	[	[	X
cana-4665	234	41	3	3	NUM
cana-4665	234	42	]	]	X
cana-4665	234	43	bansal	bansal	NOUN
cana-4665	234	44	a	a	PROPN
cana-4665	234	45	,	,	PUNCT
cana-4665	234	46	kara	kara	PROPN
cana-4665	234	47	ah	ah	INTJ
cana-4665	234	48	,	,	PUNCT
cana-4665	234	49	biswas	biswas	PROPN
cana-4665	234	50	a	a	PROPN
cana-4665	234	51	,	,	PUNCT
cana-4665	234	52	khan	khan	PROPN
cana-4665	234	53	s	s	PROPN
cana-4665	234	54	,	,	PUNCT
cana-4665	234	55	zhou	zhou	PROPN
cana-4665	234	56	q	q	PROPN
cana-4665	234	57	,	,	PUNCT
cana-4665	234	58	moshokoa	moshokoa	AUX
cana-4665	234	59	sp(2019)optical	sp(2019)optical	ADJ
cana-4665	234	60	solitons	soliton	NOUN
cana-4665	234	61	and	and	CCONJ
cana-4665	234	62	conservation	conservation	NOUN
cana-4665	234	63	laws	law	NOUN
cana-4665	234	64	with	with	ADP
cana-4665	234	65	polarization	polarization	NOUN
cana-4665	234	66	-	-	PUNCT
cana-4665	234	67	mode	mode	NOUN
cana-4665	234	68	dispersion	dispersion	NOUN
cana-4665	234	69	for	for	ADP
cana-4665	234	70	coupled	couple	VERB
cana-4665	234	71	fokas	fokas	ADJ
cana-4665	234	72	-	-	PUNCT
cana-4665	234	73	lenells	lenell	NOUN
cana-4665	234	74	equation	equation	NOUN
cana-4665	234	75	using	use	VERB
cana-4665	234	76	group	group	NOUN
cana-4665	234	77	invariance	invariance	NOUN
cana-4665	234	78	(	(	PUNCT
cana-4665	234	79	vol.120):(245–249	vol.120):(245–249	X
cana-4665	234	80	)	)	PUNCT
cana-4665	235	1	[	[	X
cana-4665	235	2	4	4	NUM
cana-4665	235	3	]	]	PUNCT
cana-4665	235	4	bansal	bansal	NOUN
cana-4665	235	5	a	a	PROPN
cana-4665	235	6	,	,	PUNCT
cana-4665	235	7	biswas	biswas	PROPN
cana-4665	235	8	a	a	PROPN
cana-4665	235	9	,	,	PUNCT
cana-4665	235	10	mahmood	mahmood	PROPN
cana-4665	235	11	mf	mf	PROPN
cana-4665	235	12	,	,	PUNCT
cana-4665	235	13	zhou	zhou	PROPN
cana-4665	235	14	q	q	PROPN
cana-4665	235	15	,	,	PUNCT
cana-4665	235	16	mohammad	mohammad	PROPN
cana-4665	235	17	mirzazadeh	mirzazadeh	PROPN
cana-4665	235	18	,	,	PUNCT
cana-4665	235	19	alshormrani	alshormrani	ADJ
cana-4665	235	20	as	as	ADP
cana-4665	235	21	,	,	PUNCT
cana-4665	235	22	moshokoa	moshokoa	AUX
cana-4665	235	23	sp	sp	NOUN
cana-4665	235	24	,	,	PUNCT
cana-4665	235	25	belic	belic	ADJ
cana-4665	235	26	m	m	PROPN
cana-4665	235	27	(	(	PUNCT
cana-4665	235	28	2018	2018	NUM
cana-4665	235	29	)	)	PUNCT
cana-4665	235	30	optical	optical	ADJ
cana-4665	235	31	soliton	soliton	NOUN
cana-4665	235	32	perturbation	perturbation	NOUN
cana-4665	235	33	with	with	ADP
cana-4665	235	34	radhakrishankundu	radhakrishankundu	NOUN
cana-4665	235	35	-	-	PUNCT
cana-4665	235	36	lakshmanan	lakshmanan	NOUN
cana-4665	235	37	equation	equation	NOUN
cana-4665	235	38	by	by	ADP
cana-4665	235	39	lie	lie	NOUN
cana-4665	235	40	group	group	NOUN
cana-4665	235	41	analysis	analysis	NOUN
cana-4665	235	42	optik	optik	PROPN
cana-4665	235	43	(	(	PUNCT
cana-4665	235	44	vol	vol	NOUN
cana-4665	235	45	.	.	NOUN
cana-4665	235	46	163	163	NUM
cana-4665	235	47	)	)	PUNCT
cana-4665	235	48	:	:	PUNCT
cana-4665	236	1	137–141	137–141	NUM
cana-4665	236	2	[	[	PUNCT
cana-4665	236	3	5	5	NUM
cana-4665	236	4	]	]	PUNCT
cana-4665	236	5	bansal	bansal	NOUN
cana-4665	236	6	a	a	PROPN
cana-4665	236	7	,	,	PUNCT
cana-4665	236	8	biswas	biswas	PROPN
cana-4665	236	9	a	a	PRON
cana-4665	236	10	,	,	PUNCT
cana-4665	236	11	triki	triki	ADJ
cana-4665	236	12	h	h	NOUN
cana-4665	236	13	,	,	PUNCT
cana-4665	236	14	zhou	zhou	PROPN
cana-4665	236	15	q	q	PROPN
cana-4665	236	16	,	,	PUNCT
cana-4665	236	17	moshokoa	moshokoa	PROPN
cana-4665	236	18	sp	sp	NOUN
cana-4665	236	19	,	,	PUNCT
cana-4665	236	20	belic	belic	ADJ
cana-4665	236	21	m	m	PROPN
cana-4665	236	22	(	(	PUNCT
cana-4665	236	23	2018)optical	2018)optical	ADJ
cana-4665	236	24	solitons	soliton	NOUN
cana-4665	236	25	and	and	CCONJ
cana-4665	236	26	group	group	NOUN
cana-4665	236	27	invariant	invariant	ADJ
cana-4665	236	28	solutions	solution	NOUN
cana-4665	236	29	to	to	ADP
cana-4665	236	30	lakshmanan	lakshmanan	ADJ
cana-4665	236	31	–	–	PUNCT
cana-4665	236	32	porsezian	porsezian	ADJ
cana-4665	236	33	–	–	PUNCT
cana-4665	236	34	daniel	daniel	PROPN
cana-4665	236	35	model	model	NOUN
cana-4665	236	36	in	in	ADP
cana-4665	236	37	optical	optical	ADJ
cana-4665	236	38	fibers	fiber	NOUN
cana-4665	236	39	and	and	CCONJ
cana-4665	236	40	pcf	pcf	PROPN
cana-4665	236	41	optik	optik	PROPN
cana-4665	236	42	(	(	PUNCT
cana-4665	236	43	vol	vol	NOUN
cana-4665	236	44	.	.	PUNCT
cana-4665	237	1	160):86–91	160):86–91	NUM
cana-4665	238	1	[	[	X
cana-4665	238	2	6	6	NUM
cana-4665	238	3	]	]	PUNCT
cana-4665	238	4	biswas	biswas	PROPN
cana-4665	238	5	a	a	DET
cana-4665	238	6	,	,	PUNCT
cana-4665	238	7	ekici	ekici	NOUN
cana-4665	238	8	m	m	PROPN
cana-4665	238	9	,	,	PUNCT
cana-4665	238	10	sonmezoglu	sonmezoglu	PROPN
cana-4665	238	11	a	a	PRON
cana-4665	238	12	,	,	PUNCT
cana-4665	238	13	alshomrani	alshomrani	NOUN
cana-4665	238	14	as	as	ADP
cana-4665	238	15	,	,	PUNCT
cana-4665	238	16	zhou	zhou	PROPN
cana-4665	238	17	q	q	PROPN
cana-4665	238	18	,	,	PUNCT
cana-4665	238	19	moshokoa	moshokoa	AUX
cana-4665	238	20	sp	sp	ADP
cana-4665	238	21	and	and	CCONJ
cana-4665	238	22	belic	belic	ADJ
cana-4665	238	23	m	m	PROPN
cana-4665	238	24	(	(	PUNCT
cana-4665	238	25	2018	2018	NUM
cana-4665	238	26	)	)	PUNCT
cana-4665	238	27	chirped	chirp	VERB
cana-4665	238	28	optical	optical	ADJ
cana-4665	238	29	solitons	soliton	NOUN
cana-4665	238	30	of	of	ADP
cana-4665	238	31	chen	chen	PROPN
cana-4665	238	32	-	-	PUNCT
cana-4665	238	33	lee	lee	PROPN
cana-4665	238	34	-	-	PUNCT
cana-4665	238	35	liu	liu	PROPN
cana-4665	238	36	equation	equation	NOUN
cana-4665	238	37	by	by	ADP
cana-4665	238	38	extended	extended	ADJ
cana-4665	238	39	trial	trial	NOUN
cana-4665	238	40	equation	equation	NOUN
cana-4665	238	41	scheme	scheme	NOUN
cana-4665	238	42	optik	optik	PROPN
cana-4665	238	43	(	(	PUNCT
cana-4665	238	44	vol	vol	NOUN
cana-4665	238	45	.	.	PUNCT
cana-4665	239	1	156):999–1006	156):999–1006	NUM
cana-4665	240	1	[	[	X
cana-4665	240	2	7	7	NUM
cana-4665	240	3	]	]	X
cana-4665	240	4	biswas	biswas	PROPN
cana-4665	240	5	a	a	PROPN
cana-4665	240	6	,	,	PUNCT
cana-4665	240	7	yildirim	yildirim	PROPN
cana-4665	240	8	y	y	PROPN
cana-4665	240	9	,	,	PUNCT
cana-4665	240	10	yasar	yasar	PROPN
cana-4665	240	11	e	e	PROPN
cana-4665	240	12	,	,	PUNCT
cana-4665	240	13	triki	triki	PROPN
cana-4665	240	14	h	h	NOUN
cana-4665	240	15	,	,	PUNCT
cana-4665	240	16	alshomrani	alshomrani	NOUN
cana-4665	240	17	as	as	ADP
cana-4665	240	18	,	,	PUNCT
cana-4665	240	19	ullah	ullah	PROPN
cana-4665	240	20	mz	mz	PROPN
cana-4665	240	21	,	,	PUNCT
cana-4665	240	22	zhou	zhou	PROPN
cana-4665	240	23	q	q	PROPN
cana-4665	240	24	,	,	PUNCT
cana-4665	240	25	moshokoa	moshokoa	AUX
cana-4665	240	26	sp	sp	ADP
cana-4665	240	27	and	and	CCONJ
cana-4665	240	28	belic	belic	ADJ
cana-4665	240	29	m	m	PROPN
cana-4665	240	30	(	(	PUNCT
cana-4665	240	31	2018	2018	NUM
cana-4665	240	32	)	)	PUNCT
cana-4665	240	33	optical	optical	ADJ
cana-4665	240	34	soliton	soliton	NOUN
cana-4665	240	35	perturbation	perturbation	NOUN
cana-4665	240	36	with	with	ADP
cana-4665	240	37	complex	complex	ADJ
cana-4665	240	38	ginzburg	ginzburg	NOUN
cana-4665	240	39	-	-	PUNCT
cana-4665	240	40	landau	landau	NOUN
cana-4665	240	41	equation	equation	NOUN
cana-4665	240	42	using	use	VERB
cana-4665	240	43	trial	trial	NOUN
cana-4665	240	44	solution	solution	NOUN
cana-4665	240	45	approach	approach	NOUN
cana-4665	240	46	optik	optik	PROPN
cana-4665	240	47	(	(	PUNCT
cana-4665	240	48	vol	vol	NOUN
cana-4665	240	49	.	.	PUNCT
cana-4665	241	1	160):44–60	160):44–60	NUM
cana-4665	242	1	[	[	X
cana-4665	242	2	8	8	NUM
cana-4665	242	3	]	]	X
cana-4665	242	4	biswas	biswas	NOUN
cana-4665	242	5	(	(	PUNCT
cana-4665	242	6	2018	2018	NUM
cana-4665	242	7	)	)	PUNCT
cana-4665	242	8	a	a	DET
cana-4665	242	9	optical	optical	ADJ
cana-4665	242	10	soliton	soliton	NOUN
cana-4665	242	11	perturbation	perturbation	NOUN
cana-4665	242	12	with	with	ADP
cana-4665	242	13	radhakrishnan	radhakrishnan	PROPN
cana-4665	242	14	-	-	PUNCT
cana-4665	242	15	kundu	kundu	ADJ
cana-4665	242	16	-	-	PUNCT
cana-4665	242	17	lakshmanan	lakshmanan	NOUN
cana-4665	242	18	equation	equation	NOUN
cana-4665	242	19	by	by	ADP
cana-4665	242	20	traveling	travel	VERB
cana-4665	242	21	wave	wave	NOUN
cana-4665	242	22	hypothesis	hypothesis	NOUN
cana-4665	242	23	optik	optik	PROPN
cana-4665	242	24	(	(	PUNCT
cana-4665	242	25	vol	vol	NOUN
cana-4665	242	26	.	.	PROPN
cana-4665	242	27	171	171	NUM
cana-4665	242	28	)	)	PUNCT
cana-4665	242	29	:	:	PUNCT
cana-4665	242	30	217–220	217–220	NUM
cana-4665	242	31	[	[	X
cana-4665	242	32	9	9	NUM
cana-4665	242	33	]	]	PUNCT
cana-4665	242	34	biswas	biswas	NOUN
cana-4665	242	35	a	a	PRON
cana-4665	242	36	,	,	PUNCT
cana-4665	242	37	ekici	ekici	NOUN
cana-4665	242	38	m	m	PROPN
cana-4665	242	39	,	,	PUNCT
cana-4665	242	40	sonmezoglu	sonmezoglu	PROPN
cana-4665	242	41	a	a	PROPN
cana-4665	242	42	and	and	CCONJ
cana-4665	242	43	alqahtani	alqahtani	PROPN
cana-4665	242	44	rt	rt	PROPN
cana-4665	242	45	(	(	PUNCT
cana-4665	242	46	2018)sub	2018)sub	NUM
cana-4665	242	47	-	-	PUNCT
cana-4665	242	48	pico	pico	NOUN
cana-4665	242	49	-	-	PUNCT
cana-4665	242	50	second	second	NOUN
cana-4665	242	51	chirped	chirp	VERB
cana-4665	242	52	optical	optical	ADJ
cana-4665	242	53	solitons	soliton	NOUN
cana-4665	242	54	in	in	ADP
cana-4665	242	55	mono	mono	NOUN
cana-4665	242	56	-	-	PUNCT
cana-4665	242	57	mode	mode	NOUN
cana-4665	242	58	fibers	fiber	NOUN
cana-4665	242	59	with	with	ADP
cana-4665	242	60	kaup	kaup	PROPN
cana-4665	242	61	-	-	PUNCT
cana-4665	242	62	newell	newell	PROPN
cana-4665	242	63	equation	equation	NOUN
cana-4665	242	64	by	by	ADP
cana-4665	242	65	extended	extended	ADJ
cana-4665	242	66	trial	trial	NOUN
cana-4665	242	67	function	function	NOUN
cana-4665	242	68	method	method	NOUN
cana-4665	242	69	optik	optik	PROPN
cana-4665	242	70	(	(	PUNCT
cana-4665	242	71	vol	vol	NOUN
cana-4665	242	72	.	.	PUNCT
cana-4665	242	73	168):208–216	168):208–216	NUM
cana-4665	243	1	[	[	X
cana-4665	243	2	10	10	NUM
cana-4665	243	3	]	]	X
cana-4665	243	4	bansal	bansal	NOUN
cana-4665	243	5	a	a	PROPN
cana-4665	243	6	,	,	PUNCT
cana-4665	243	7	biswas	biswas	PROPN
cana-4665	243	8	a	a	X
cana-4665	243	9	,	,	PUNCT
cana-4665	243	10	zhou	zhou	PROPN
cana-4665	243	11	q	q	PROPN
cana-4665	243	12	and	and	CCONJ
cana-4665	243	13	babatin	babatin	PROPN
cana-4665	243	14	mm	mm	PROPN
cana-4665	243	15	(	(	PUNCT
cana-4665	243	16	2018	2018	NUM
cana-4665	243	17	)	)	PUNCT
cana-4665	243	18	lie	lie	NOUN
cana-4665	243	19	symmetry	symmetry	NOUN
cana-4665	243	20	analysis	analysis	NOUN
cana-4665	243	21	for	for	ADP
cana-4665	243	22	cubicquartic	cubicquartic	ADJ
cana-4665	243	23	nonlinear	nonlinear	ADJ
cana-4665	243	24	schrdinger	schrdinger	NOUN
cana-4665	243	25	equation	equation	NOUN
cana-4665	243	26	optik	optik	NOUN
cana-4665	243	27	(	(	PUNCT
cana-4665	243	28	vol	vol	NOUN
cana-4665	243	29	.	.	PUNCT
cana-4665	244	1	169):12–15	169):12–15	NUM
cana-4665	244	2	[	[	PUNCT
cana-4665	244	3	11	11	NUM
cana-4665	244	4	]	]	X
cana-4665	244	5	bansal	bansal	NOUN
cana-4665	244	6	a	a	PROPN
cana-4665	244	7	,	,	PUNCT
cana-4665	244	8	biswas	biswas	PROPN
cana-4665	244	9	a	a	X
cana-4665	244	10	,	,	PUNCT
cana-4665	244	11	zhou	zhou	PROPN
cana-4665	244	12	q	q	PROPN
cana-4665	244	13	,	,	PUNCT
cana-4665	244	14	arshed	arshe	VERB
cana-4665	244	15	s	s	PROPN
cana-4665	244	16	,	,	PUNCT
cana-4665	244	17	alzahrani	alzahrani	PROPN
cana-4665	244	18	ak	ak	PROPN
cana-4665	244	19	,	,	PUNCT
cana-4665	244	20	belic	belic	ADJ
cana-4665	244	21	m	m	PROPN
cana-4665	244	22	(	(	PUNCT
cana-4665	244	23	2020	2020	NUM
cana-4665	244	24	)	)	PUNCT
cana-4665	244	25	optical	optical	ADJ
cana-4665	244	26	solitons	soliton	NOUN
cana-4665	244	27	with	with	ADP
cana-4665	244	28	chen	chen	PROPN
cana-4665	244	29	–	–	PUNCT
cana-4665	244	30	lee	lee	PROPN
cana-4665	244	31	–	–	PUNCT
cana-4665	244	32	liu	liu	PROPN
cana-4665	244	33	equation	equation	NOUN
cana-4665	244	34	by	by	ADP
cana-4665	244	35	lie	lie	NOUN
cana-4665	244	36	symmetry	symmetry	NOUN
cana-4665	244	37	optik	optik	PROPN
cana-4665	244	38	(	(	PUNCT
cana-4665	244	39	vol	vol	NOUN
cana-4665	244	40	.	.	PUNCT
cana-4665	245	1	384(10)):126202	384(10)):126202	PROPN
cana-4665	246	1	[	[	X
cana-4665	246	2	12	12	NUM
cana-4665	246	3	]	]	X
cana-4665	246	4	zeng	zeng	PROPN
cana-4665	246	5	y(1994	y(1994	PROPN
cana-4665	246	6	)	)	PUNCT
cana-4665	246	7	factorization	factorization	NOUN
cana-4665	246	8	of	of	ADP
cana-4665	246	9	the	the	DET
cana-4665	246	10	kaup	kaup	PROPN
cana-4665	246	11	-	-	PROPN
cana-4665	246	12	newell	newell	PROPN
cana-4665	246	13	hierarchy	hierarchy	PROPN
cana-4665	246	14	physica	physica	PROPN
cana-4665	246	15	d	d	PROPN
cana-4665	246	16	(	(	PUNCT
cana-4665	246	17	vol	vol	NOUN
cana-4665	246	18	.	.	PUNCT
cana-4665	247	1	73(3)):171	73(3)):171	NUM
cana-4665	247	2	–	–	PUNCT
cana-4665	247	3	188	188	NUM
cana-4665	247	4	communications	communication	NOUN
cana-4665	247	5	on	on	ADP
cana-4665	247	6	applied	apply	VERB
cana-4665	247	7	nonlinear	nonlinear	ADJ
cana-4665	247	8	analysis	analysis	NOUN
cana-4665	247	9	issn	issn	NOUN
cana-4665	247	10	:	:	PUNCT
cana-4665	247	11	1074	1074	NUM
cana-4665	247	12	-	-	PUNCT
cana-4665	247	13	133x	133x	NUM
cana-4665	247	14	vol	vol	VERB
cana-4665	247	15	32	32	NUM
cana-4665	247	16	no	no	NOUN
cana-4665	247	17	.	.	PUNCT
cana-4665	248	1	10s	10	NOUN
cana-4665	248	2	(	(	PUNCT
cana-4665	248	3	2025	2025	NUM
cana-4665	248	4	)	)	PUNCT
cana-4665	248	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-4665	248	6	99	99	NUM
cana-4665	249	1	[	[	SYM
cana-4665	249	2	13	13	NUM
cana-4665	249	3	]	]	X
cana-4665	249	4	zhu	zhu	PROPN
cana-4665	250	1	f	f	X
cana-4665	250	2	,	,	PUNCT
cana-4665	250	3	ji	ji	PROPN
cana-4665	250	4	j	j	PROPN
cana-4665	250	5	and	and	CCONJ
cana-4665	250	6	zhang	zhang	PROPN
cana-4665	250	7	j	j	PROPN
cana-4665	250	8	(	(	PUNCT
cana-4665	250	9	2008	2008	NUM
cana-4665	250	10	)	)	PUNCT
cana-4665	250	11	two	two	NUM
cana-4665	250	12	hierarchies	hierarchy	NOUN
cana-4665	250	13	of	of	ADP
cana-4665	250	14	multi	multi	ADJ
cana-4665	250	15	-	-	ADJ
cana-4665	250	16	component	component	ADJ
cana-4665	250	17	kaup	kaup	PROPN
cana-4665	250	18	-	-	PUNCT
cana-4665	250	19	newell	newell	PROPN
cana-4665	250	20	equations	equation	NOUN
cana-4665	250	21	and	and	CCONJ
cana-4665	250	22	their	their	PRON
cana-4665	250	23	integrable	integrable	ADJ
cana-4665	250	24	couplings	coupling	NOUN
cana-4665	250	25	physics	physics	NOUN
cana-4665	250	26	letters	letter	NOUN
cana-4665	250	27	a	a	DET
cana-4665	250	28	(	(	PUNCT
cana-4665	250	29	vol	vol	NOUN
cana-4665	250	30	.	.	PUNCT
cana-4665	251	1	372(8)):1244–1249	372(8)):1244–1249	NUM
cana-4665	252	1	[	[	X
cana-4665	252	2	14	14	NUM
cana-4665	252	3	]	]	X
cana-4665	252	4	biswas	biswas	PROPN
cana-4665	252	5	a	a	PROPN
cana-4665	252	6	,	,	PUNCT
cana-4665	252	7	yildirim	yildirim	PROPN
cana-4665	252	8	y	y	PROPN
cana-4665	252	9	,	,	PUNCT
cana-4665	252	10	yasar	yasar	PROPN
cana-4665	252	11	e	e	PROPN
cana-4665	252	12	,	,	PUNCT
cana-4665	252	13	zhou	zhou	PROPN
cana-4665	252	14	q	q	PROPN
cana-4665	252	15	,	,	PUNCT
cana-4665	252	16	moshokoa	moshokoa	AUX
cana-4665	252	17	sp	sp	ADP
cana-4665	252	18	and	and	CCONJ
cana-4665	252	19	belic	belic	ADJ
cana-4665	252	20	m	m	PROPN
cana-4665	252	21	(	(	PUNCT
cana-4665	252	22	2018	2018	NUM
cana-4665	252	23	)	)	PUNCT
cana-4665	252	24	sub	sub	ADJ
cana-4665	252	25	-	-	NOUN
cana-4665	252	26	pico	pico	ADJ
cana-4665	252	27	second	second	ADJ
cana-4665	252	28	pulses	pulse	NOUN
cana-4665	252	29	in	in	ADP
cana-4665	252	30	monomode	monomode	ADJ
cana-4665	252	31	optical	optical	ADJ
cana-4665	252	32	fibers	fiber	NOUN
cana-4665	252	33	with	with	ADP
cana-4665	252	34	kaup	kaup	PROPN
cana-4665	252	35	-	-	PROPN
cana-4665	252	36	newell	newell	PROPN
cana-4665	252	37	equation	equation	NOUN
cana-4665	252	38	by	by	ADP
cana-4665	252	39	a	a	DET
cana-4665	252	40	couple	couple	NOUN
cana-4665	252	41	of	of	ADP
cana-4665	252	42	integration	integration	NOUN
cana-4665	252	43	scheme	scheme	NOUN
cana-4665	252	44	optik	optik	PROPN
cana-4665	252	45	(	(	PUNCT
cana-4665	252	46	vol	vol	NOUN
cana-4665	252	47	.	.	PUNCT
cana-4665	253	1	167):121–128	167):121–128	NUM
cana-4665	254	1	[	[	X
cana-4665	254	2	15	15	NUM
cana-4665	254	3	]	]	X
cana-4665	254	4	biswas	biswas	PROPN
cana-4665	254	5	a	a	PRON
cana-4665	254	6	,	,	PUNCT
cana-4665	254	7	ekici	ekici	NOUN
cana-4665	254	8	m	m	PROPN
cana-4665	254	9	,	,	PUNCT
cana-4665	254	10	sonmezoglu	sonmezoglu	PROPN
cana-4665	254	11	a	a	PROPN
cana-4665	254	12	and	and	CCONJ
cana-4665	254	13	alqahtani	alqahtani	PROPN
cana-4665	254	14	rt	rt	PROPN
cana-4665	254	15	(	(	PUNCT
cana-4665	254	16	2018	2018	NUM
cana-4665	254	17	)	)	PUNCT
cana-4665	254	18	sub	sub	ADJ
cana-4665	254	19	-	-	NOUN
cana-4665	254	20	pico	pico	NOUN
cana-4665	254	21	second	second	ADV
cana-4665	254	22	chirped	chirp	VERB
cana-4665	254	23	optical	optical	ADJ
cana-4665	254	24	solitons	soliton	NOUN
cana-4665	254	25	in	in	ADP
cana-4665	254	26	monomode	monomode	ADJ
cana-4665	254	27	fibers	fiber	NOUN
cana-4665	254	28	with	with	ADP
cana-4665	254	29	kaup	kaup	PROPN
cana-4665	254	30	-	-	PUNCT
cana-4665	254	31	newell	newell	PROPN
cana-4665	254	32	equation	equation	NOUN
cana-4665	254	33	by	by	ADP
cana-4665	254	34	extended	extended	ADJ
cana-4665	254	35	trial	trial	NOUN
cana-4665	254	36	function	function	NOUN
cana-4665	254	37	method	method	NOUN
cana-4665	254	38	optik(vol	optik(vol	NOUN
cana-4665	254	39	.	.	PUNCT
cana-4665	255	1	168):208–216	168):208–216	NUM
cana-4665	256	1	[	[	X
cana-4665	256	2	16	16	NUM
cana-4665	256	3	]	]	PUNCT
cana-4665	256	4	jaafa	jaafa	PROPN
cana-4665	256	5	a	a	PROPN
cana-4665	256	6	,	,	PUNCT
cana-4665	256	7	jawad	jawad	PROPN
cana-4665	256	8	m	m	PROPN
cana-4665	256	9	,	,	PUNCT
cana-4665	256	10	azzawi	azzawi	PROPN
cana-4665	256	11	fji	fji	PROPN
cana-4665	256	12	al	al	PROPN
cana-4665	256	13	,	,	PUNCT
cana-4665	256	14	biswas	biswas	PROPN
cana-4665	256	15	a	a	PROPN
cana-4665	256	16	,	,	PUNCT
cana-4665	256	17	khan	khan	PROPN
cana-4665	256	18	s	s	PROPN
cana-4665	256	19	,	,	PUNCT
cana-4665	256	20	zhou	zhou	PROPN
cana-4665	256	21	q	q	PROPN
cana-4665	256	22	,	,	PUNCT
cana-4665	256	23	moshokoa	moshokoa	AUX
cana-4665	256	24	sp	sp	ADP
cana-4665	256	25	and	and	CCONJ
cana-4665	256	26	belic	belic	VERB
cana-4665	256	27	mr	mr	PROPN
cana-4665	256	28	(	(	PUNCT
cana-4665	256	29	2018	2018	NUM
cana-4665	256	30	)	)	PUNCT
cana-4665	256	31	bright	bright	ADJ
cana-4665	256	32	and	and	CCONJ
cana-4665	256	33	singular	singular	ADJ
cana-4665	256	34	optical	optical	ADJ
cana-4665	256	35	solitons	soliton	NOUN
cana-4665	256	36	for	for	ADP
cana-4665	256	37	kaup	kaup	PROPN
cana-4665	256	38	-	-	PROPN
cana-4665	256	39	newell	newell	PROPN
cana-4665	256	40	equation	equation	NOUN
cana-4665	256	41	with	with	ADP
cana-4665	256	42	two	two	NUM
cana-4665	256	43	fundamental	fundamental	ADJ
cana-4665	256	44	integration	integration	NOUN
cana-4665	256	45	norms	norm	NOUN
cana-4665	256	46	optik	optik	PROPN
cana-4665	256	47	(	(	PUNCT
cana-4665	256	48	vol	vol	NOUN
cana-4665	256	49	.	.	NOUN
cana-4665	256	50	182	182	NUM
cana-4665	256	51	):	):	PUNCT
cana-4665	257	1	594–597	594–597	NUM
cana-4665	257	2	[	[	X
cana-4665	257	3	17	17	NUM
cana-4665	257	4	]	]	PUNCT
cana-4665	257	5	baleanu	baleanu	NOUN
cana-4665	258	1	d	d	PROPN
cana-4665	258	2	,	,	PUNCT
cana-4665	258	3	inc	inc	PROPN
cana-4665	258	4	m	m	PROPN
cana-4665	258	5	,	,	PUNCT
cana-4665	258	6	yusuf	yusuf	PROPN
cana-4665	258	7	a	a	PROPN
cana-4665	258	8	and	and	CCONJ
cana-4665	258	9	aliyu	aliyu	ADV
cana-4665	258	10	ai	ai	VERB
cana-4665	258	11	(	(	PUNCT
cana-4665	258	12	2017	2017	NUM
cana-4665	258	13	)	)	PUNCT
cana-4665	258	14	lie	lie	NOUN
cana-4665	258	15	symmetry	symmetry	NOUN
cana-4665	258	16	analysis	analysis	NOUN
cana-4665	258	17	,	,	PUNCT
cana-4665	258	18	exact	exact	ADJ
cana-4665	258	19	solutions	solution	NOUN
cana-4665	258	20	and	and	CCONJ
cana-4665	258	21	conservation	conservation	NOUN
cana-4665	258	22	laws	law	NOUN
cana-4665	258	23	for	for	ADP
cana-4665	258	24	the	the	DET
cana-4665	258	25	time	time	NOUN
cana-4665	258	26	fractional	fractional	ADJ
cana-4665	258	27	modified	modify	VERB
cana-4665	258	28	zakharov	zakharov	ADJ
cana-4665	258	29	-	-	PUNCT
cana-4665	258	30	kuznetsov	kuznetsov	NOUN
cana-4665	258	31	equation	equation	NOUN
cana-4665	258	32	nonlinear	nonlinear	PROPN
cana-4665	258	33	anal	anal	ADJ
cana-4665	258	34	model	model	NOUN
cana-4665	258	35	control	control	NOUN
cana-4665	258	36	(	(	PUNCT
cana-4665	258	37	vol.22(6	vol.22(6	NOUN
cana-4665	258	38	)	)	PUNCT
cana-4665	258	39	):	):	PUNCT
cana-4665	258	40	861–876	861–876	NUM
cana-4665	258	41	[	[	SYM
cana-4665	258	42	18	18	NUM
cana-4665	258	43	]	]	PUNCT
cana-4665	258	44	olver	olver	NOUN
cana-4665	258	45	pj(1993	pj(1993	PROPN
cana-4665	258	46	)	)	PUNCT
cana-4665	258	47	applications	application	NOUN
cana-4665	258	48	of	of	ADP
cana-4665	258	49	lie	lie	NOUN
cana-4665	258	50	groups	group	NOUN
cana-4665	258	51	to	to	PART
cana-4665	258	52	differential	differential	VERB
cana-4665	258	53	equations	equation	NOUN
cana-4665	258	54	,	,	PUNCT
cana-4665	258	55	graduate	graduate	NOUN
cana-4665	258	56	texts	text	NOUN
cana-4665	258	57	math	math	NOUN
cana-4665	258	58	(	(	PUNCT
cana-4665	258	59	vol	vol	NOUN
cana-4665	258	60	.	.	PUNCT
cana-4665	258	61	107	107	NUM
cana-4665	258	62	)	)	PUNCT
cana-4665	258	63	springer	springer	NOUN
cana-4665	258	64	verlag	verlag	NOUN
cana-4665	258	65	,	,	PUNCT
cana-4665	258	66	new	new	PROPN
cana-4665	258	67	york	york	PROPN
cana-4665	259	1	[	[	X
cana-4665	259	2	19	19	NUM
cana-4665	259	3	]	]	X
cana-4665	259	4	bluman	bluman	PROPN
cana-4665	259	5	gw	gw	PROPN
cana-4665	259	6	,	,	PUNCT
cana-4665	259	7	cole	cole	PROPN
cana-4665	259	8	jd	jd	PROPN
cana-4665	259	9	(	(	PUNCT
cana-4665	259	10	1974	1974	NUM
cana-4665	259	11	)	)	PUNCT
cana-4665	259	12	similarity	similarity	NOUN
cana-4665	259	13	methods	method	NOUN
cana-4665	259	14	for	for	ADP
cana-4665	259	15	differential	differential	ADJ
cana-4665	259	16	equations	equation	NOUN
cana-4665	259	17	,	,	PUNCT
cana-4665	259	18	springer	springer	NOUN
cana-4665	259	19	verlag	verlag	PROPN
cana-4665	259	20	,	,	PUNCT
cana-4665	259	21	new	new	PROPN
cana-4665	259	22	york	york	PROPN
cana-4665	259	23	[	[	X
cana-4665	259	24	20	20	NUM
cana-4665	259	25	]	]	PUNCT
cana-4665	259	26	ovsiannikov	ovsiannikov	PROPN
cana-4665	259	27	lv	lv	PROPN
cana-4665	259	28	group	group	NOUN
cana-4665	259	29	(	(	PUNCT
cana-4665	259	30	1982	1982	NUM
cana-4665	259	31	)	)	PUNCT
cana-4665	259	32	analysis	analysis	NOUN
cana-4665	259	33	of	of	ADP
cana-4665	259	34	differential	differential	ADJ
cana-4665	259	35	equations	equation	NOUN
cana-4665	259	36	,	,	PUNCT
cana-4665	259	37	academic	academic	ADJ
cana-4665	259	38	press	press	NOUN
cana-4665	259	39	,	,	PUNCT
cana-4665	259	40	new	new	PROPN
cana-4665	259	41	york	york	PROPN
cana-4665	259	42	[	[	X
cana-4665	259	43	21	21	NUM
cana-4665	259	44	]	]	X
cana-4665	259	45	bluman	bluman	PROPN
cana-4665	259	46	gw	gw	PROPN
cana-4665	259	47	,	,	PUNCT
cana-4665	259	48	kumei	kumei	NOUN
cana-4665	259	49	s(1989	s(1989	PROPN
cana-4665	259	50	)	)	PUNCT
cana-4665	259	51	symmetries	symmetry	NOUN
cana-4665	259	52	and	and	CCONJ
cana-4665	259	53	differential	differential	ADJ
cana-4665	259	54	equations	equation	NOUN
cana-4665	259	55	,	,	PUNCT
cana-4665	259	56	springer	springer	NOUN
cana-4665	259	57	verlag	verlag	PROPN
cana-4665	259	58	,	,	PUNCT
cana-4665	259	59	new	new	PROPN
cana-4665	259	60	york	york	PROPN
cana-4665	260	1	[	[	X
cana-4665	260	2	22	22	NUM
cana-4665	260	3	]	]	PUNCT
cana-4665	260	4	olver	olver	NOUN
cana-4665	260	5	pj(1993	pj(1993	PROPN
cana-4665	260	6	)	)	PUNCT
cana-4665	260	7	application	application	NOUN
cana-4665	260	8	of	of	ADP
cana-4665	260	9	lie	lie	NOUN
cana-4665	260	10	groups	group	NOUN
cana-4665	260	11	to	to	PART
cana-4665	260	12	differential	differential	VERB
cana-4665	260	13	equations	equation	NOUN
cana-4665	260	14	,	,	PUNCT
cana-4665	260	15	springer	springer	NOUN
cana-4665	260	16	-	-	PUNCT
cana-4665	260	17	verlag	verlag	PROPN
cana-4665	260	18	,	,	PUNCT
cana-4665	260	19	new	new	PROPN
cana-4665	260	20	york	york	PROPN
cana-4665	260	21	,	,	PUNCT
cana-4665	260	22	[	[	X
cana-4665	260	23	23	23	NUM
cana-4665	260	24	]	]	X
cana-4665	260	25	ibragimov	ibragimov	ADJ
cana-4665	260	26	nh	nh	PROPN
cana-4665	260	27	(	(	PUNCT
cana-4665	260	28	1999	1999	NUM
cana-4665	260	29	)	)	PUNCT
cana-4665	260	30	elementary	elementary	ADJ
cana-4665	260	31	lie	lie	NOUN
cana-4665	260	32	group	group	NOUN
cana-4665	260	33	analysis	analysis	NOUN
cana-4665	260	34	and	and	CCONJ
cana-4665	260	35	ordinary	ordinary	ADJ
cana-4665	260	36	differential	differential	ADJ
cana-4665	260	37	equations	equation	NOUN
cana-4665	260	38	,	,	PUNCT
cana-4665	260	39	john	john	PROPN
cana-4665	260	40	wiley	wiley	PROPN
cana-4665	260	41	and	and	CCONJ
cana-4665	260	42	sons	son	NOUN
cana-4665	260	43	,	,	PUNCT
cana-4665	260	44	chichester	chichester	PROPN
cana-4665	261	1	[	[	X
cana-4665	261	2	24	24	NUM
cana-4665	261	3	]	]	X
cana-4665	261	4	adem	adem	PROPN
cana-4665	261	5	ar	ar	PROPN
cana-4665	261	6	and	and	CCONJ
cana-4665	261	7	khalique	khalique	PROPN
cana-4665	261	8	cm	cm	PROPN
cana-4665	261	9	(	(	PUNCT
cana-4665	261	10	2012	2012	NUM
cana-4665	261	11	)	)	PUNCT
cana-4665	261	12	symmetry	symmetry	NOUN
cana-4665	261	13	reductions	reduction	NOUN
cana-4665	261	14	,	,	PUNCT
cana-4665	261	15	exact	exact	ADJ
cana-4665	261	16	solutions	solution	NOUN
cana-4665	261	17	and	and	CCONJ
cana-4665	261	18	conservation	conservation	NOUN
cana-4665	261	19	laws	law	NOUN
cana-4665	261	20	of	of	ADP
cana-4665	261	21	a	a	DET
cana-4665	261	22	new	new	ADJ
cana-4665	261	23	coupled	couple	VERB
cana-4665	261	24	kdv	kdv	NOUN
cana-4665	261	25	system	system	NOUN
cana-4665	261	26	commun	commun	PROPN
cana-4665	261	27	nonlinear	nonlinear	PROPN
cana-4665	261	28	sci	sci	PROPN
cana-4665	261	29	numer	numer	PROPN
cana-4665	261	30	simul	simul	PROPN
cana-4665	261	31	,	,	PUNCT
cana-4665	261	32	(	(	PUNCT
cana-4665	261	33	vol	vol	NOUN
cana-4665	261	34	.	.	PUNCT
cana-4665	261	35	17):3465–3475	17):3465–3475	PROPN
cana-4665	262	1	[	[	X
cana-4665	262	2	25	25	NUM
cana-4665	262	3	]	]	X
cana-4665	262	4	gandarias	gandarias	PROPN
cana-4665	262	5	ml	ml	ADP
cana-4665	262	6	and	and	CCONJ
cana-4665	262	7	khalique	khalique	PROPN
cana-4665	262	8	cm	cm	PROPN
cana-4665	262	9	(	(	PUNCT
cana-4665	262	10	2016)symmetries	2016)symmetrie	NOUN
cana-4665	262	11	,	,	PUNCT
cana-4665	262	12	solutions	solution	NOUN
cana-4665	262	13	and	and	CCONJ
cana-4665	262	14	conservation	conservation	NOUN
cana-4665	262	15	laws	law	NOUN
cana-4665	262	16	of	of	ADP
cana-4665	262	17	a	a	DET
cana-4665	262	18	class	class	NOUN
cana-4665	262	19	of	of	ADP
cana-4665	262	20	nonlinear	nonlinear	ADJ
cana-4665	262	21	dispersive	dispersive	ADJ
cana-4665	262	22	wave	wave	NOUN
cana-4665	262	23	equations	equation	NOUN
cana-4665	262	24	.	.	PUNCT
cana-4665	262	25	”	"	PUNCT
cana-4665	263	1	commun	commun	PROPN
cana-4665	263	2	nonlinear	nonlinear	PROPN
cana-4665	263	3	sci	sci	PROPN
cana-4665	263	4	numer	numer	PROPN
cana-4665	263	5	simul	simul	PROPN
cana-4665	263	6	(	(	PUNCT
cana-4665	263	7	vol	vol	NOUN
cana-4665	263	8	32):114–121	32):114–121	NUM
cana-4665	264	1	[	[	X
cana-4665	264	2	26	26	NUM
cana-4665	264	3	]	]	X
cana-4665	264	4	kumar	kumar	PROPN
cana-4665	264	5	r	r	PROPN
cana-4665	264	6	,	,	PUNCT
cana-4665	264	7	gupta	gupta	PROPN
cana-4665	264	8	rk	rk	PROPN
cana-4665	264	9	and	and	CCONJ
cana-4665	264	10	bhatia	bhatia	PROPN
cana-4665	264	11	ss	ss	PROPN
cana-4665	264	12	(	(	PUNCT
cana-4665	264	13	2016)invariant	2016)invariant	NUM
cana-4665	264	14	solutions	solution	NOUN
cana-4665	264	15	of	of	ADP
cana-4665	264	16	variable	variable	ADJ
cana-4665	264	17	coefficients	coefficient	NOUN
cana-4665	264	18	generalized	generalized	ADJ
cana-4665	264	19	gardner	gardner	NOUN
cana-4665	264	20	equation	equation	NOUN
cana-4665	264	21	(	(	PUNCT
cana-4665	264	22	vol.83	vol.83	PROPN
cana-4665	264	23	)	)	PUNCT
cana-4665	264	24	,	,	PUNCT
cana-4665	264	25	springer:2103–2111	springer:2103–2111	PROPN
cana-4665	264	26	communications	communication	NOUN
cana-4665	264	27	on	on	ADP
cana-4665	264	28	applied	apply	VERB
cana-4665	264	29	nonlinear	nonlinear	ADJ
cana-4665	264	30	analysis	analysis	NOUN
cana-4665	264	31	issn	issn	NOUN
cana-4665	264	32	:	:	PUNCT
cana-4665	264	33	1074	1074	NUM
cana-4665	264	34	-	-	PUNCT
cana-4665	264	35	133x	133x	NUM
cana-4665	264	36	vol	vol	VERB
cana-4665	264	37	32	32	NUM
cana-4665	264	38	no	no	NOUN
cana-4665	264	39	.	.	PUNCT
cana-4665	265	1	10s	10	NOUN
cana-4665	265	2	(	(	PUNCT
cana-4665	265	3	2025	2025	NUM
cana-4665	265	4	)	)	PUNCT
cana-4665	265	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-4665	265	6	100	100	NUM
cana-4665	266	1	[	[	X
cana-4665	266	2	27	27	NUM
cana-4665	266	3	]	]	X
cana-4665	266	4	taha	taha	PROPN
cana-4665	266	5	m	m	PROPN
cana-4665	266	6	waffa	waffa	PROPN
cana-4665	266	7	,	,	PUNCT
cana-4665	266	8	noorani	noorani	ADJ
cana-4665	266	9	msm	msm	NOUN
cana-4665	266	10	and	and	CCONJ
cana-4665	266	11	hashim	hashim	PROPN
cana-4665	266	12	i	i	PRON
cana-4665	266	13	,	,	PUNCT
cana-4665	266	14	new	new	ADJ
cana-4665	266	15	application	application	NOUN
cana-4665	266	16	of	of	ADP
cana-4665	266	17	the	the	DET
cana-4665	266	18	g′	g′	NOUN
cana-4665	266	19	g	g	PROPN
cana-4665	266	20	-expansion	-expansion	PROPN
cana-4665	266	21	method	method	NOUN
cana-4665	266	22	for	for	ADP
cana-4665	266	23	thin	thin	ADJ
cana-4665	266	24	film	film	NOUN
cana-4665	266	25	equations	equation	NOUN
cana-4665	266	26	,	,	PUNCT
cana-4665	266	27	hindwai	hindwai	PROPN
cana-4665	266	28	publishing	publish	VERB
cana-4665	266	29	corporation	corporation	NOUN
cana-4665	266	30	abstract	abstract	ADJ
cana-4665	266	31	and	and	CCONJ
cana-4665	266	32	applied	apply	VERB
cana-4665	266	33	analysis	analysis	NOUN
cana-4665	266	34	(	(	PUNCT
cana-4665	266	35	vol	vol	NOUN
cana-4665	266	36	.	.	PROPN
cana-4665	266	37	2013	2013	NUM
cana-4665	266	38	)	)	PUNCT
cana-4665	266	39	.	.	PUNCT
cana-4665	267	1	[	[	X
cana-4665	267	2	28	28	NUM
cana-4665	267	3	]	]	X
cana-4665	267	4	kumar	kumar	PROPN
cana-4665	267	5	r	r	PROPN
cana-4665	267	6	,	,	PUNCT
cana-4665	267	7	kumar	kumar	PROPN
cana-4665	267	8	r	r	PROPN
cana-4665	267	9	,	,	PUNCT
cana-4665	267	10	bansal	bansal	NOUN
cana-4665	267	11	a	a	PROPN
cana-4665	267	12	,	,	PUNCT
cana-4665	267	13	biswas	biswas	PROPN
cana-4665	267	14	a	a	PROPN
cana-4665	267	15	,	,	PUNCT
cana-4665	267	16	yildirim	yildirim	PROPN
cana-4665	267	17	a	a	PROPN
cana-4665	267	18	,	,	PUNCT
cana-4665	267	19	moshokoa	moshokoa	NOUN
cana-4665	267	20	sp	sp	ADP
cana-4665	267	21	and	and	CCONJ
cana-4665	267	22	sirikr	sirikr	NOUN
cana-4665	267	23	aa	aa	NOUN
cana-4665	267	24	(	(	PUNCT
cana-4665	267	25	2023	2023	NUM
cana-4665	267	26	)	)	PUNCT
cana-4665	267	27	optical	optical	ADJ
cana-4665	267	28	solitons	soliton	NOUN
cana-4665	267	29	and	and	CCONJ
cana-4665	267	30	group	group	NOUN
cana-4665	267	31	invariants	invariant	NOUN
cana-4665	267	32	for	for	ADP
cana-4665	267	33	chen	chen	PROPN
cana-4665	267	34	-	-	PUNCT
cana-4665	267	35	lee	lee	PROPN
cana-4665	267	36	-	-	PUNCT
cana-4665	267	37	liu	liu	PROPN
cana-4665	267	38	equation	equation	NOUN
cana-4665	267	39	with	with	ADP
cana-4665	267	40	timedependent	timedependent	NOUN
cana-4665	267	41	chromatic	chromatic	ADJ
cana-4665	267	42	dispersion	dispersion	NOUN
cana-4665	267	43	and	and	CCONJ
cana-4665	267	44	nonlinearity	nonlinearity	NOUN
cana-4665	267	45	by	by	ADP
cana-4665	267	46	lie	lie	NOUN
cana-4665	267	47	symmetry	symmetry	PROPN
cana-4665	267	48	ukrainian	ukrainian	PROPN
cana-4665	267	49	journal	journal	PROPN
cana-4665	267	50	of	of	ADP
cana-4665	267	51	physical	physical	ADJ
cana-4665	267	52	optics	optic	NOUN
cana-4665	267	53	,	,	PUNCT
cana-4665	267	54	(	(	PUNCT
cana-4665	267	55	vol	vol	NOUN
cana-4665	267	56	24(4)):4021	24(4)):4021	NUM
cana-4665	267	57	7	7	NUM
cana-4665	267	58	statements	statement	NOUN
cana-4665	267	59	and	and	CCONJ
cana-4665	267	60	declarations	declaration	NOUN
cana-4665	267	61	the	the	DET
cana-4665	267	62	authors	author	NOUN
cana-4665	267	63	declares	declare	VERB
cana-4665	267	64	that	that	SCONJ
cana-4665	267	65	this	this	DET
cana-4665	267	66	manuscript	manuscript	NOUN
cana-4665	267	67	presents	present	VERB
cana-4665	267	68	original	original	ADJ
cana-4665	267	69	research	research	NOUN
cana-4665	267	70	and	and	CCONJ
cana-4665	267	71	confirm	confirm	VERB
cana-4665	267	72	that	that	SCONJ
cana-4665	267	73	they	they	PRON
cana-4665	267	74	have	have	VERB
cana-4665	267	75	no	no	DET
cana-4665	267	76	financial	financial	ADJ
cana-4665	267	77	interests	interest	NOUN
cana-4665	267	78	or	or	CCONJ
cana-4665	267	79	personal	personal	ADJ
cana-4665	267	80	relationships	relationship	NOUN
cana-4665	267	81	that	that	PRON
cana-4665	267	82	could	could	AUX
cana-4665	267	83	have	have	AUX
cana-4665	267	84	impacted	impact	VERB
cana-4665	267	85	the	the	DET
cana-4665	267	86	work	work	NOUN
cana-4665	267	87	described	describe	VERB
cana-4665	267	88	in	in	ADP
cana-4665	267	89	this	this	DET
cana-4665	267	90	paper	paper	NOUN
cana-4665	267	91	.	.	PUNCT
cana-4665	268	1	communications	communication	NOUN
cana-4665	268	2	on	on	ADP
cana-4665	268	3	applied	apply	VERB
cana-4665	268	4	nonlinear	nonlinear	ADJ
cana-4665	268	5	analysis	analysis	NOUN
cana-4665	268	6	issn	issn	NOUN
cana-4665	268	7	:	:	PUNCT
cana-4665	268	8	1074	1074	NUM
cana-4665	268	9	-	-	PUNCT
cana-4665	268	10	133x	133x	NUM
cana-4665	268	11	vol	vol	VERB
cana-4665	268	12	32	32	NUM
cana-4665	268	13	no	no	NOUN
cana-4665	268	14	.	.	PUNCT
cana-4665	269	1	10s	10	NOUN
cana-4665	269	2	(	(	PUNCT
cana-4665	269	3	2025	2025	NUM
cana-4665	269	4	)	)	PUNCT
cana-4665	269	5	https://internationalpubls.com	https://internationalpubls.com	X
cana-4665	269	6	101	101	NUM