id	sid	tid	token	lemma	pos
ma-342	1	1	2025	2025	NUM
ma-342	1	2	ada	ada	PROPN
ma-342	1	3	academica	academica	PROPN
ma-342	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-342	1	5	.	.	PUNCT
ma-342	2	1	j.	j.	PROPN
ma-342	2	2	math	math	PROPN
ma-342	2	3	.	.	PUNCT
ma-342	3	1	anal	anal	ADJ
ma-342	3	2	.	.	PUNCT
ma-342	4	1	5	5	NUM
ma-342	4	2	(	(	PUNCT
ma-342	4	3	2025	2025	NUM
ma-342	4	4	)	)	PUNCT
ma-342	4	5	14doi	14doi	NOUN
ma-342	4	6	:	:	PUNCT
ma-342	4	7	10.28924	10.28924	NUM
ma-342	4	8	/	/	SYM
ma-342	4	9	ada	ada	PROPN
ma-342	4	10	/	/	SYM
ma-342	4	11	ma.5.14	ma.5.14	NOUN
ma-342	4	12	modulation	modulation	NOUN
ma-342	4	13	instability	instability	NOUN
ma-342	4	14	,	,	PUNCT
ma-342	4	15	dark	dark	ADJ
ma-342	4	16	and	and	CCONJ
ma-342	4	17	singular	singular	ADJ
ma-342	4	18	soliton	soliton	NOUN
ma-342	4	19	for	for	ADP
ma-342	4	20	weakly	weakly	ADJ
ma-342	4	21	nonlocal	nonlocal	ADJ
ma-342	4	22	schrodinger	schrodinger	NOUN
ma-342	4	23	equation	equation	NOUN
ma-342	4	24	ali	ali	PROPN
ma-342	4	25	danladi1,∗	danladi1,∗	PROPN
ma-342	4	26	,	,	PUNCT
ma-342	4	27	alhaji	alhaji	PROPN
ma-342	4	28	tahir2	tahir2	PROPN
ma-342	4	29	,	,	PUNCT
ma-342	4	30	hadi	hadi	PROPN
ma-342	4	31	rezazadeh3	rezazadeh3	PROPN
ma-342	4	32	1department	1department	NUM
ma-342	4	33	of	of	ADP
ma-342	4	34	mathematics	mathematic	NOUN
ma-342	4	35	,	,	PUNCT
ma-342	4	36	federal	federal	ADJ
ma-342	4	37	university	university	NOUN
ma-342	4	38	,	,	PUNCT
ma-342	4	39	dutse	dutse	PROPN
ma-342	4	40	,	,	PUNCT
ma-342	4	41	nigeria	nigeria	PROPN
ma-342	5	1	alidanladi14@gmail.com	alidanladi14@gmail.com	PROPN
ma-342	5	2	,	,	PUNCT
ma-342	5	3	ali.danladi@fud.edu.ng	ali.danladi@fud.edu.ng	NOUN
ma-342	5	4	2department	2department	NUM
ma-342	5	5	of	of	ADP
ma-342	5	6	mathematics	mathematic	NOUN
ma-342	5	7	,	,	PUNCT
ma-342	5	8	faculty	faculty	NOUN
ma-342	5	9	of	of	ADP
ma-342	5	10	physical	physical	ADJ
ma-342	5	11	sciences	science	NOUN
ma-342	5	12	,	,	PUNCT
ma-342	5	13	modibbo	modibbo	PROPN
ma-342	5	14	adama	adama	PROPN
ma-342	5	15	university	university	PROPN
ma-342	5	16	,	,	PUNCT
ma-342	5	17	yola	yola	PROPN
ma-342	5	18	,	,	PUNCT
ma-342	5	19	nigeria	nigeria	PROPN
ma-342	6	1	atahir@mau.edu.ng	atahir@mau.edu.ng	PROPN
ma-342	6	2	3faculty	3faculty	NUM
ma-342	6	3	of	of	ADP
ma-342	6	4	engineering	engineering	NOUN
ma-342	6	5	technology	technology	NOUN
ma-342	6	6	,	,	PUNCT
ma-342	6	7	amol	amol	PROPN
ma-342	6	8	university	university	PROPN
ma-342	6	9	of	of	ADP
ma-342	6	10	special	special	ADJ
ma-342	6	11	modern	modern	ADJ
ma-342	6	12	technologies	technology	NOUN
ma-342	6	13	,	,	PUNCT
ma-342	6	14	amol	amol	PROPN
ma-342	6	15	,	,	PUNCT
ma-342	6	16	iran	iran	PROPN
ma-342	6	17	h.rezazadeh@ausmt.ac.ir	h.rezazadeh@ausmt.ac.ir	PROPN
ma-342	6	18	∗correspondence	∗correspondence	NOUN
ma-342	6	19	:	:	PUNCT
ma-342	6	20	alidanladi14@gmail.com	alidanladi14@gmail.com	ADJ
ma-342	6	21	,	,	PUNCT
ma-342	6	22	ali.danladi@fud.edu.ng	ali.danladi@fud.edu.ng	NOUN
ma-342	6	23	abstract	abstract	ADJ
ma-342	6	24	.	.	PUNCT
ma-342	7	1	the	the	DET
ma-342	7	2	optical	optical	ADJ
ma-342	7	3	soliton	soliton	NOUN
ma-342	7	4	solution	solution	NOUN
ma-342	7	5	of	of	ADP
ma-342	7	6	nonlinear	nonlinear	ADJ
ma-342	7	7	complex	complex	ADJ
ma-342	7	8	models	model	NOUN
ma-342	7	9	holds	hold	VERB
ma-342	7	10	significant	significant	ADJ
ma-342	7	11	importance	importance	NOUN
ma-342	7	12	innonlinear	innonlinear	ADJ
ma-342	7	13	optics	optic	NOUN
ma-342	7	14	and	and	CCONJ
ma-342	7	15	communication	communication	NOUN
ma-342	7	16	systems	system	NOUN
ma-342	7	17	.	.	PUNCT
ma-342	8	1	considering	consider	VERB
ma-342	8	2	nonlinear	nonlinear	ADJ
ma-342	8	3	complex	complex	ADJ
ma-342	8	4	models	model	NOUN
ma-342	8	5	,	,	PUNCT
ma-342	8	6	often	often	ADV
ma-342	8	7	describedby	describedby	ADJ
ma-342	8	8	equations	equation	NOUN
ma-342	8	9	like	like	ADP
ma-342	8	10	the	the	DET
ma-342	8	11	nonlinear	nonlinear	ADJ
ma-342	8	12	schrodinger	schrodinger	PROPN
ma-342	8	13	equation	equation	NOUN
ma-342	8	14	(	(	PUNCT
ma-342	8	15	nlse	nlse	ADJ
ma-342	8	16	)	)	PUNCT
ma-342	8	17	,	,	PUNCT
ma-342	8	18	plays	play	VERB
ma-342	8	19	a	a	DET
ma-342	8	20	crucial	crucial	ADJ
ma-342	8	21	role	role	NOUN
ma-342	8	22	in	in	ADP
ma-342	8	23	defining	define	VERB
ma-342	8	24	thebalance	thebalance	NOUN
ma-342	8	25	between	between	ADP
ma-342	8	26	dispersive	dispersive	ADJ
ma-342	8	27	and	and	CCONJ
ma-342	8	28	nonlinear	nonlinear	ADJ
ma-342	8	29	effects	effect	NOUN
ma-342	8	30	,	,	PUNCT
ma-342	8	31	enabling	enable	VERB
ma-342	8	32	the	the	DET
ma-342	8	33	formation	formation	NOUN
ma-342	8	34	and	and	CCONJ
ma-342	8	35	maintenance	maintenance	NOUN
ma-342	8	36	of	of	ADP
ma-342	8	37	solitonsover	solitonsover	NOUN
ma-342	8	38	long	long	ADJ
ma-342	8	39	distances	distance	NOUN
ma-342	8	40	.	.	PUNCT
ma-342	9	1	this	this	DET
ma-342	9	2	stability	stability	NOUN
ma-342	9	3	is	be	AUX
ma-342	9	4	crucial	crucial	ADJ
ma-342	9	5	for	for	ADP
ma-342	9	6	signal	signal	ADJ
ma-342	9	7	integrity	integrity	NOUN
ma-342	9	8	in	in	ADP
ma-342	9	9	optical	optical	ADJ
ma-342	9	10	communication	communication	NOUN
ma-342	9	11	systems.the	systems.the	DET
ma-342	9	12	investigation	investigation	NOUN
ma-342	9	13	of	of	ADP
ma-342	9	14	optical	optical	ADJ
ma-342	9	15	soliton	soliton	NOUN
ma-342	9	16	solutions	solution	NOUN
ma-342	9	17	from	from	ADP
ma-342	9	18	nonlinear	nonlinear	ADJ
ma-342	9	19	complex	complex	ADJ
ma-342	9	20	models	model	NOUN
ma-342	9	21	is	be	AUX
ma-342	9	22	sometimes	sometimes	ADV
ma-342	9	23	compli	compli	ADJ
ma-342	9	24	-	-	PUNCT
ma-342	9	25	cated	cat	VERB
ma-342	9	26	.	.	PUNCT
ma-342	10	1	with	with	ADP
ma-342	10	2	this	this	PRON
ma-342	10	3	in	in	ADP
ma-342	10	4	mind	mind	NOUN
ma-342	10	5	,	,	PUNCT
ma-342	10	6	we	we	PRON
ma-342	10	7	employed	employ	VERB
ma-342	10	8	an	an	DET
ma-342	10	9	effective	effective	ADJ
ma-342	10	10	method	method	NOUN
ma-342	10	11	of	of	ADP
ma-342	10	12	extended	extend	VERB
ma-342	10	13	tanh	tanh	NOUN
ma-342	10	14	function	function	NOUN
ma-342	10	15	with	with	ADP
ma-342	10	16	a	a	DET
ma-342	10	17	riccattidifferential	riccattidifferential	ADJ
ma-342	10	18	equation	equation	NOUN
ma-342	10	19	to	to	PART
ma-342	10	20	retrieve	retrieve	VERB
ma-342	10	21	the	the	DET
ma-342	10	22	dark	dark	ADJ
ma-342	10	23	,	,	PUNCT
ma-342	10	24	singular	singular	ADJ
ma-342	10	25	and	and	CCONJ
ma-342	10	26	periodic	periodic	ADJ
ma-342	10	27	wave	wave	NOUN
ma-342	10	28	solutions	solution	NOUN
ma-342	10	29	for	for	ADP
ma-342	10	30	the	the	DET
ma-342	10	31	weakly	weakly	ADJ
ma-342	10	32	nonlocalnonlinear	nonlocalnonlinear	ADP
ma-342	10	33	schrodinger	schrodinger	PROPN
ma-342	10	34	equation	equation	NOUN
ma-342	10	35	with	with	ADP
ma-342	10	36	parabolic	parabolic	ADJ
ma-342	10	37	law	law	NOUN
ma-342	10	38	.	.	PUNCT
ma-342	11	1	the	the	DET
ma-342	11	2	obtained	obtain	VERB
ma-342	11	3	solutions	solution	NOUN
ma-342	11	4	were	be	AUX
ma-342	11	5	verified	verify	VERB
ma-342	11	6	by	by	ADP
ma-342	11	7	back	back	ADJ
ma-342	11	8	-	-	PUNCT
ma-342	11	9	substitution	substitution	NOUN
ma-342	11	10	in	in	ADP
ma-342	11	11	the	the	DET
ma-342	11	12	original	original	ADJ
ma-342	11	13	equations	equation	NOUN
ma-342	11	14	,	,	PUNCT
ma-342	11	15	with	with	ADP
ma-342	11	16	the	the	DET
ma-342	11	17	aid	aid	NOUN
ma-342	11	18	of	of	ADP
ma-342	11	19	a	a	DET
ma-342	11	20	mathematica	mathematica	PROPN
ma-342	11	21	to	to	PART
ma-342	11	22	affirm	affirm	VERB
ma-342	11	23	the	the	DET
ma-342	11	24	robustness	robustness	NOUN
ma-342	11	25	of	of	ADP
ma-342	11	26	thechosen	thechosen	NOUN
ma-342	11	27	approach	approach	NOUN
ma-342	11	28	.	.	PUNCT
ma-342	12	1	respective	respective	ADJ
ma-342	12	2	2d	2d	NOUN
ma-342	12	3	and	and	CCONJ
ma-342	12	4	3d	3d	NUM
ma-342	12	5	graphs	graph	NOUN
ma-342	12	6	for	for	ADP
ma-342	12	7	some	some	PRON
ma-342	12	8	of	of	ADP
ma-342	12	9	the	the	DET
ma-342	12	10	obtained	obtain	VERB
ma-342	12	11	results	result	NOUN
ma-342	12	12	was	be	AUX
ma-342	12	13	portrayed	portray	VERB
ma-342	12	14	bychoosing	bychoose	VERB
ma-342	12	15	suitable	suitable	ADJ
ma-342	12	16	values	value	NOUN
ma-342	12	17	of	of	ADP
ma-342	12	18	the	the	DET
ma-342	12	19	parameters	parameter	NOUN
ma-342	12	20	that	that	PRON
ma-342	12	21	were	be	AUX
ma-342	12	22	involved	involve	VERB
ma-342	12	23	.	.	PUNCT
ma-342	13	1	an	an	DET
ma-342	13	2	analysis	analysis	NOUN
ma-342	13	3	of	of	ADP
ma-342	13	4	instability	instability	NOUN
ma-342	13	5	that	that	PRON
ma-342	13	6	resultsin	resultsin	VERB
ma-342	13	7	the	the	DET
ma-342	13	8	modulation	modulation	NOUN
ma-342	13	9	of	of	ADP
ma-342	13	10	the	the	DET
ma-342	13	11	steady	steady	ADJ
ma-342	13	12	-	-	PUNCT
ma-342	13	13	state	state	NOUN
ma-342	13	14	as	as	ADP
ma-342	13	15	a	a	DET
ma-342	13	16	result	result	NOUN
ma-342	13	17	of	of	ADP
ma-342	13	18	co	co	NOUN
ma-342	13	19	-	-	NOUN
ma-342	13	20	action	action	NOUN
ma-342	13	21	between	between	ADP
ma-342	13	22	the	the	DET
ma-342	13	23	nonlinear	nonlinear	NOUN
ma-342	13	24	and	and	CCONJ
ma-342	13	25	dispersiveeffects	dispersiveeffect	NOUN
ma-342	13	26	was	be	AUX
ma-342	13	27	performed	perform	VERB
ma-342	13	28	on	on	ADP
ma-342	13	29	the	the	DET
ma-342	13	30	proposed	propose	VERB
ma-342	13	31	model	model	NOUN
ma-342	13	32	where	where	SCONJ
ma-342	13	33	the	the	DET
ma-342	13	34	condition	condition	NOUN
ma-342	13	35	for	for	ADP
ma-342	13	36	stable	stable	ADJ
ma-342	13	37	wave	wave	NOUN
ma-342	13	38	under	under	ADP
ma-342	13	39	small	small	ADJ
ma-342	13	40	per	per	ADP
ma-342	13	41	-	-	PUNCT
ma-342	13	42	turbation	turbation	NOUN
ma-342	13	43	was	be	AUX
ma-342	13	44	obtained	obtain	VERB
ma-342	13	45	and	and	CCONJ
ma-342	13	46	presented	present	VERB
ma-342	13	47	.	.	PUNCT
ma-342	14	1	the	the	DET
ma-342	14	2	gain	gain	NOUN
ma-342	14	3	spectrum	spectrum	NOUN
ma-342	14	4	plot	plot	NOUN
ma-342	14	5	for	for	ADP
ma-342	14	6	the	the	DET
ma-342	14	7	modulation	modulation	NOUN
ma-342	14	8	instability	instability	NOUN
ma-342	14	9	wasportrayed	wasportraye	VERB
ma-342	14	10	.	.	PUNCT
ma-342	15	1	1	1	X
ma-342	15	2	.	.	X
ma-342	15	3	introductionpartial	introductionpartial	ADJ
ma-342	15	4	differential	differential	NOUN
ma-342	15	5	equations	equation	NOUN
ma-342	15	6	(	(	PUNCT
ma-342	15	7	pdes	pde	NOUN
ma-342	15	8	)	)	PUNCT
ma-342	15	9	serve	serve	VERB
ma-342	15	10	as	as	ADP
ma-342	15	11	powerful	powerful	ADJ
ma-342	15	12	mathematical	mathematical	ADJ
ma-342	15	13	tools	tool	NOUN
ma-342	15	14	for	for	ADP
ma-342	15	15	modeling	modeling	NOUN
ma-342	15	16	and	and	CCONJ
ma-342	15	17	under	under	ADV
ma-342	15	18	-	-	PUNCT
ma-342	15	19	standing	stand	VERB
ma-342	15	20	diverse	diverse	ADJ
ma-342	15	21	phenomena	phenomenon	NOUN
ma-342	15	22	in	in	ADP
ma-342	15	23	science	science	NOUN
ma-342	15	24	and	and	CCONJ
ma-342	15	25	engineering	engineering	NOUN
ma-342	15	26	.	.	PUNCT
ma-342	16	1	these	these	DET
ma-342	16	2	equations	equation	NOUN
ma-342	16	3	involve	involve	VERB
ma-342	16	4	multiple	multiple	ADJ
ma-342	16	5	variablesand	variablesand	NOUN
ma-342	16	6	their	their	PRON
ma-342	16	7	partial	partial	ADJ
ma-342	16	8	derivatives	derivative	NOUN
ma-342	16	9	,	,	PUNCT
ma-342	16	10	making	make	VERB
ma-342	16	11	them	they	PRON
ma-342	16	12	well	well	ADV
ma-342	16	13	-	-	PUNCT
ma-342	16	14	suited	suited	ADJ
ma-342	16	15	for	for	ADP
ma-342	16	16	describing	describe	VERB
ma-342	16	17	complex	complex	ADJ
ma-342	16	18	physical	physical	ADJ
ma-342	16	19	processessuch	processessuch	NOUN
ma-342	16	20	as	as	ADP
ma-342	16	21	heat	heat	NOUN
ma-342	16	22	conduction	conduction	NOUN
ma-342	16	23	,	,	PUNCT
ma-342	16	24	fluid	fluid	ADJ
ma-342	16	25	dynamics	dynamic	NOUN
ma-342	16	26	,	,	PUNCT
ma-342	16	27	and	and	CCONJ
ma-342	16	28	electromagnetic	electromagnetic	ADJ
ma-342	16	29	fields	field	NOUN
ma-342	16	30	.	.	PUNCT
ma-342	17	1	the	the	DET
ma-342	17	2	investigation	investigation	NOUN
ma-342	17	3	of	of	ADP
ma-342	17	4	pdesencompasses	pdesencompasse	NOUN
ma-342	17	5	various	various	ADJ
ma-342	17	6	aspects	aspect	NOUN
ma-342	17	7	,	,	PUNCT
ma-342	17	8	including	include	VERB
ma-342	17	9	analytical	analytical	ADJ
ma-342	17	10	and	and	CCONJ
ma-342	17	11	numerical	numerical	ADJ
ma-342	17	12	methods	method	NOUN
ma-342	17	13	for	for	ADP
ma-342	17	14	solving	solve	VERB
ma-342	17	15	these	these	DET
ma-342	17	16	equa	equa	NOUN
ma-342	17	17	-	-	PUNCT
ma-342	17	18	tions	tion	NOUN
ma-342	17	19	.	.	PUNCT
ma-342	18	1	analytically	analytically	ADV
ma-342	18	2	,	,	PUNCT
ma-342	18	3	researchers	researcher	NOUN
ma-342	18	4	explore	explore	VERB
ma-342	18	5	techniques	technique	NOUN
ma-342	18	6	like	like	ADP
ma-342	18	7	separation	separation	NOUN
ma-342	18	8	of	of	ADP
ma-342	18	9	variables	variable	NOUN
ma-342	18	10	,	,	PUNCT
ma-342	18	11	integral	integral	ADJ
ma-342	18	12	transforms	transform	NOUN
ma-342	18	13	,	,	PUNCT
ma-342	18	14	received	receive	VERB
ma-342	18	15	:	:	PUNCT
ma-342	18	16	3	3	NUM
ma-342	18	17	mar	mar	PROPN
ma-342	18	18	2025	2025	NUM
ma-342	18	19	.	.	PUNCT
ma-342	19	1	key	key	ADJ
ma-342	19	2	words	word	NOUN
ma-342	19	3	and	and	CCONJ
ma-342	19	4	phrases	phrase	NOUN
ma-342	19	5	.	.	PUNCT
ma-342	20	1	nonlocal	nonlocal	ADJ
ma-342	20	2	schrodinger	schrodinger	ADJ
ma-342	20	3	equation	equation	NOUN
ma-342	20	4	with	with	ADP
ma-342	20	5	pl	pl	PROPN
ma-342	20	6	;	;	PUNCT
ma-342	20	7	extended	extended	ADJ
ma-342	20	8	tanh	tanh	PROPN
ma-342	20	9	approach	approach	NOUN
ma-342	20	10	;	;	PUNCT
ma-342	20	11	modulation	modulation	NOUN
ma-342	20	12	instability.1	instability.1	PROPN
ma-342	20	13	https://adac.ee	https://adac.ee	PROPN
ma-342	20	14	https://doi.org/10.28924/ada/ma.5.14	https://doi.org/10.28924/ada/ma.5.14	PROPN
ma-342	20	15	eur	eur	PROPN
ma-342	20	16	.	.	PUNCT
ma-342	21	1	j.	j.	PROPN
ma-342	21	2	math	math	PROPN
ma-342	21	3	.	.	PUNCT
ma-342	22	1	anal	anal	PROPN
ma-342	22	2	.	.	PUNCT
ma-342	23	1	10.28924	10.28924	NUM
ma-342	23	2	/	/	SYM
ma-342	23	3	ada	ada	PROPN
ma-342	23	4	/	/	SYM
ma-342	23	5	ma.5.14	ma.5.14	PROPN
ma-342	23	6	2and	2and	NUM
ma-342	23	7	series	series	NOUN
ma-342	23	8	solutions	solution	NOUN
ma-342	23	9	to	to	PART
ma-342	23	10	obtain	obtain	VERB
ma-342	23	11	exact	exact	ADJ
ma-342	23	12	solutions	solution	NOUN
ma-342	23	13	or	or	CCONJ
ma-342	23	14	gain	gain	VERB
ma-342	23	15	insights	insight	NOUN
ma-342	23	16	into	into	ADP
ma-342	23	17	the	the	DET
ma-342	23	18	behavior	behavior	NOUN
ma-342	23	19	of	of	ADP
ma-342	23	20	solutions	solution	NOUN
ma-342	23	21	.	.	PUNCT
ma-342	24	1	onthe	onthe	ADJ
ma-342	24	2	other	other	ADJ
ma-342	24	3	hand	hand	NOUN
ma-342	24	4	,	,	PUNCT
ma-342	24	5	numerical	numerical	ADJ
ma-342	24	6	methods	method	NOUN
ma-342	24	7	,	,	PUNCT
ma-342	24	8	such	such	ADJ
ma-342	24	9	as	as	ADP
ma-342	24	10	finite	finite	ADJ
ma-342	24	11	difference	difference	NOUN
ma-342	24	12	,	,	PUNCT
ma-342	24	13	finite	finite	NOUN
ma-342	24	14	element	element	NOUN
ma-342	24	15	,	,	PUNCT
ma-342	24	16	and	and	CCONJ
ma-342	24	17	spectral	spectral	ADJ
ma-342	24	18	methods	method	NOUN
ma-342	24	19	,	,	PUNCT
ma-342	24	20	provide	provide	VERB
ma-342	24	21	computational	computational	ADJ
ma-342	24	22	tools	tool	NOUN
ma-342	24	23	to	to	PART
ma-342	24	24	approximate	approximate	VERB
ma-342	24	25	solutions	solution	NOUN
ma-342	24	26	for	for	ADP
ma-342	24	27	pdes	pde	NOUN
ma-342	24	28	in	in	ADP
ma-342	24	29	cases	case	NOUN
ma-342	24	30	where	where	SCONJ
ma-342	24	31	analytical	analytical	ADJ
ma-342	24	32	solu	solu	NOUN
ma-342	24	33	-	-	PUNCT
ma-342	24	34	tions	tion	NOUN
ma-342	24	35	are	be	AUX
ma-342	24	36	challenging	challenge	VERB
ma-342	24	37	or	or	CCONJ
ma-342	24	38	impossible	impossible	ADJ
ma-342	24	39	to	to	PART
ma-342	24	40	obtain	obtain	VERB
ma-342	24	41	.	.	PUNCT
ma-342	25	1	additionally	additionally	ADV
ma-342	25	2	,	,	PUNCT
ma-342	25	3	the	the	DET
ma-342	25	4	study	study	NOUN
ma-342	25	5	of	of	ADP
ma-342	25	6	stability	stability	NOUN
ma-342	25	7	,	,	PUNCT
ma-342	25	8	existence	existence	NOUN
ma-342	25	9	,	,	PUNCT
ma-342	25	10	anduniqueness	anduniqueness	ADV
ma-342	25	11	of	of	ADP
ma-342	25	12	solutions	solution	NOUN
ma-342	25	13	,	,	PUNCT
ma-342	25	14	as	as	ADV
ma-342	25	15	well	well	ADV
ma-342	25	16	as	as	ADP
ma-342	25	17	the	the	DET
ma-342	25	18	development	development	NOUN
ma-342	25	19	of	of	ADP
ma-342	25	20	new	new	ADJ
ma-342	25	21	solution	solution	NOUN
ma-342	25	22	methods	method	NOUN
ma-342	25	23	,	,	PUNCT
ma-342	25	24	continues	continue	VERB
ma-342	25	25	to	to	PART
ma-342	25	26	be	be	AUX
ma-342	25	27	avibrant	avibrant	ADJ
ma-342	25	28	area	area	NOUN
ma-342	25	29	of	of	ADP
ma-342	25	30	research	research	NOUN
ma-342	25	31	within	within	ADP
ma-342	25	32	the	the	DET
ma-342	25	33	broader	broad	ADJ
ma-342	25	34	field	field	NOUN
ma-342	25	35	of	of	ADP
ma-342	25	36	partial	partial	ADJ
ma-342	25	37	differential	differential	NOUN
ma-342	25	38	equations	equation	NOUN
ma-342	25	39	.	.	PUNCT
ma-342	26	1	understandingand	understandingand	PROPN
ma-342	26	2	harnessing	harness	VERB
ma-342	26	3	the	the	DET
ma-342	26	4	mathematical	mathematical	ADJ
ma-342	26	5	intricacies	intricacy	NOUN
ma-342	26	6	of	of	ADP
ma-342	26	7	pdes	pde	NOUN
ma-342	26	8	play	play	VERB
ma-342	26	9	a	a	DET
ma-342	26	10	crucial	crucial	ADJ
ma-342	26	11	role	role	NOUN
ma-342	26	12	in	in	ADP
ma-342	26	13	advancing	advance	VERB
ma-342	26	14	our	our	PRON
ma-342	26	15	compre	compre	NOUN
ma-342	26	16	-	-	PUNCT
ma-342	26	17	hension	hension	NOUN
ma-342	26	18	of	of	ADP
ma-342	26	19	the	the	DET
ma-342	26	20	natural	natural	ADJ
ma-342	26	21	world	world	NOUN
ma-342	26	22	and	and	CCONJ
ma-342	26	23	technological	technological	ADJ
ma-342	26	24	applications	application	NOUN
ma-342	26	25	.	.	PUNCT
ma-342	27	1	numerous	numerous	ADJ
ma-342	27	2	scholars	scholar	NOUN
ma-342	27	3	have	have	AUX
ma-342	27	4	focused	focus	VERB
ma-342	27	5	theirefforts	theireffort	NOUN
ma-342	27	6	on	on	ADP
ma-342	27	7	determining	determine	VERB
ma-342	27	8	exact	exact	ADJ
ma-342	27	9	solutions	solution	NOUN
ma-342	27	10	for	for	ADP
ma-342	27	11	npdes	npde	NOUN
ma-342	27	12	,	,	PUNCT
ma-342	27	13	with	with	ADP
ma-342	27	14	these	these	DET
ma-342	27	15	equations	equation	NOUN
ma-342	27	16	finding	find	VERB
ma-342	27	17	applications	application	NOUN
ma-342	27	18	acrossdiverse	acrossdiverse	VERB
ma-342	27	19	scientific	scientific	ADJ
ma-342	27	20	and	and	CCONJ
ma-342	27	21	technological	technological	ADJ
ma-342	27	22	domains	domain	NOUN
ma-342	27	23	,	,	PUNCT
ma-342	27	24	including	include	VERB
ma-342	27	25	but	but	CCONJ
ma-342	27	26	not	not	PART
ma-342	27	27	limited	limit	VERB
ma-342	27	28	to	to	ADP
ma-342	27	29	mathematical	mathematical	ADJ
ma-342	27	30	physics	physics	NOUN
ma-342	27	31	,	,	PUNCT
ma-342	27	32	fluid	fluid	ADJ
ma-342	27	33	dynamics	dynamic	NOUN
ma-342	27	34	,	,	PUNCT
ma-342	27	35	optical	optical	ADJ
ma-342	27	36	fibers	fiber	NOUN
ma-342	27	37	,	,	PUNCT
ma-342	27	38	and	and	CCONJ
ma-342	27	39	economics	economic	NOUN
ma-342	28	1	[	[	X
ma-342	28	2	10	10	NUM
ma-342	28	3	,	,	PUNCT
ma-342	28	4	14	14	NUM
ma-342	28	5	,	,	PUNCT
ma-342	28	6	27].in	27].in	NUM
ma-342	28	7	recent	recent	ADJ
ma-342	28	8	years	year	NOUN
ma-342	28	9	,	,	PUNCT
ma-342	28	10	various	various	ADJ
ma-342	28	11	methodologies	methodology	NOUN
ma-342	28	12	have	have	AUX
ma-342	28	13	been	be	AUX
ma-342	28	14	developed	develop	VERB
ma-342	28	15	for	for	ADP
ma-342	28	16	determining	determine	VERB
ma-342	28	17	precise	precise	ADJ
ma-342	28	18	solutions	solution	NOUN
ma-342	28	19	tonpdes	tonpde	NOUN
ma-342	28	20	.	.	PUNCT
ma-342	29	1	these	these	DET
ma-342	29	2	approaches	approach	NOUN
ma-342	29	3	include	include	VERB
ma-342	29	4	the	the	DET
ma-342	29	5	lie	lie	NOUN
ma-342	29	6	symmetry	symmetry	NOUN
ma-342	29	7	method	method	NOUN
ma-342	29	8	[	[	X
ma-342	29	9	16	16	NUM
ma-342	29	10	,	,	PUNCT
ma-342	29	11	18	18	NUM
ma-342	29	12	,	,	PUNCT
ma-342	29	13	20	20	NUM
ma-342	29	14	,	,	PUNCT
ma-342	29	15	26	26	NUM
ma-342	29	16	,	,	PUNCT
ma-342	29	17	30	30	NUM
ma-342	29	18	]	]	PUNCT
ma-342	29	19	,	,	PUNCT
ma-342	29	20	the	the	DET
ma-342	29	21	kudryashovmethod	kudryashovmethod	NOUN
ma-342	29	22	[	[	X
ma-342	29	23	21	21	NUM
ma-342	29	24	,	,	PUNCT
ma-342	29	25	22	22	NUM
ma-342	29	26	,	,	PUNCT
ma-342	29	27	33	33	NUM
ma-342	29	28	]	]	PUNCT
ma-342	29	29	,	,	PUNCT
ma-342	29	30	the	the	DET
ma-342	29	31	sine	sine	NOUN
ma-342	29	32	-	-	PUNCT
ma-342	29	33	gordon	gordon	PROPN
ma-342	29	34	expansion	expansion	NOUN
ma-342	29	35	method	method	NOUN
ma-342	29	36	[	[	X
ma-342	29	37	6	6	NUM
ma-342	29	38	]	]	PUNCT
ma-342	29	39	,	,	PUNCT
ma-342	29	40	the	the	DET
ma-342	29	41	invariant	invariant	ADJ
ma-342	29	42	subspace	subspace	NOUN
ma-342	29	43	method	method	NOUN
ma-342	29	44	[	[	X
ma-342	29	45	13	13	NUM
ma-342	29	46	,	,	PUNCT
ma-342	29	47	28],the	28],the	NUM
ma-342	29	48	sardar	sardar	NOUN
ma-342	29	49	subequation	subequation	NOUN
ma-342	29	50	method	method	NOUN
ma-342	29	51	[	[	X
ma-342	29	52	3	3	NUM
ma-342	29	53	,	,	PUNCT
ma-342	29	54	11	11	NUM
ma-342	29	55	]	]	PUNCT
ma-342	29	56	,	,	PUNCT
ma-342	29	57	and	and	CCONJ
ma-342	29	58	others	other	NOUN
ma-342	30	1	[	[	X
ma-342	30	2	1	1	NUM
ma-342	30	3	,	,	PUNCT
ma-342	30	4	5	5	NUM
ma-342	30	5	,	,	PUNCT
ma-342	30	6	8	8	NUM
ma-342	30	7	,	,	PUNCT
ma-342	30	8	9	9	NUM
ma-342	30	9	,	,	PUNCT
ma-342	30	10	29	29	NUM
ma-342	30	11	]	]	PUNCT
ma-342	30	12	.	.	PUNCT
ma-342	31	1	these	these	DET
ma-342	31	2	techniques	technique	NOUN
ma-342	31	3	contributeto	contributeto	VERB
ma-342	31	4	the	the	DET
ma-342	31	5	exploration	exploration	NOUN
ma-342	31	6	of	of	ADP
ma-342	31	7	exact	exact	ADJ
ma-342	31	8	solutions	solution	NOUN
ma-342	31	9	for	for	ADP
ma-342	31	10	a	a	DET
ma-342	31	11	wide	wide	ADJ
ma-342	31	12	range	range	NOUN
ma-342	31	13	of	of	ADP
ma-342	31	14	pdes	pde	NOUN
ma-342	31	15	.	.	PUNCT
ma-342	32	1	the	the	DET
ma-342	32	2	nlse	nlse	NOUN
ma-342	32	3	is	be	AUX
ma-342	32	4	a	a	DET
ma-342	32	5	complex	complex	ADJ
ma-342	32	6	pdethat	pdethat	NOUN
ma-342	32	7	plays	play	VERB
ma-342	32	8	a	a	DET
ma-342	32	9	crucial	crucial	ADJ
ma-342	32	10	role	role	NOUN
ma-342	32	11	in	in	ADP
ma-342	32	12	various	various	ADJ
ma-342	32	13	fields	field	NOUN
ma-342	32	14	of	of	ADP
ma-342	32	15	physics	physics	NOUN
ma-342	32	16	and	and	CCONJ
ma-342	32	17	engineering	engineering	NOUN
ma-342	32	18	,	,	PUNCT
ma-342	32	19	describing	describe	VERB
ma-342	32	20	the	the	DET
ma-342	32	21	evolution	evolution	NOUN
ma-342	32	22	ofcomplex	ofcomplex	PROPN
ma-342	32	23	wave	wave	NOUN
ma-342	32	24	packets	packet	NOUN
ma-342	32	25	.	.	PUNCT
ma-342	33	1	it	it	PRON
ma-342	33	2	arises	arise	VERB
ma-342	33	3	in	in	ADP
ma-342	33	4	different	different	ADJ
ma-342	33	5	contexts	contexts	NOUN
ma-342	33	6	,	,	PUNCT
ma-342	33	7	including	include	VERB
ma-342	33	8	nonlinear	nonlinear	ADJ
ma-342	33	9	optics	optic	NOUN
ma-342	33	10	,	,	PUNCT
ma-342	33	11	plasma	plasma	NOUN
ma-342	33	12	physics	physics	NOUN
ma-342	33	13	,	,	PUNCT
ma-342	33	14	fluid	fluid	ADJ
ma-342	33	15	dynamics	dynamic	NOUN
ma-342	33	16	,	,	PUNCT
ma-342	33	17	and	and	CCONJ
ma-342	33	18	condensed	condense	VERB
ma-342	33	19	matter	matter	NOUN
ma-342	33	20	physics	physics	NOUN
ma-342	33	21	.	.	PUNCT
ma-342	34	1	the	the	DET
ma-342	34	2	nlse	nlse	NOUN
ma-342	34	3	and	and	CCONJ
ma-342	34	4	its	its	PRON
ma-342	34	5	variants	variant	NOUN
ma-342	34	6	have	have	VERB
ma-342	34	7	significant	significant	ADJ
ma-342	34	8	impor	impor	NOUN
ma-342	34	9	-	-	PUNCT
ma-342	34	10	tance	tance	NOUN
ma-342	34	11	in	in	ADP
ma-342	34	12	understanding	understanding	NOUN
ma-342	34	13	and	and	CCONJ
ma-342	34	14	predicting	predict	VERB
ma-342	34	15	the	the	DET
ma-342	34	16	behavior	behavior	NOUN
ma-342	34	17	of	of	ADP
ma-342	34	18	wave	wave	NOUN
ma-342	34	19	-	-	PUNCT
ma-342	34	20	like	like	ADJ
ma-342	34	21	phenomena	phenomenon	NOUN
ma-342	34	22	in	in	ADP
ma-342	34	23	diverse	diverse	ADJ
ma-342	34	24	real-worldapplications.in	real-worldapplications.in	NOUN
ma-342	34	25	nonlinear	nonlinear	ADJ
ma-342	34	26	optics	optic	NOUN
ma-342	34	27	,	,	PUNCT
ma-342	34	28	the	the	DET
ma-342	34	29	nlse	nlse	NOUN
ma-342	34	30	governs	govern	VERB
ma-342	34	31	the	the	DET
ma-342	34	32	propagation	propagation	NOUN
ma-342	34	33	of	of	ADP
ma-342	34	34	intense	intense	ADJ
ma-342	34	35	laser	laser	NOUN
ma-342	34	36	beams	beam	NOUN
ma-342	34	37	through	through	ADP
ma-342	34	38	nonlinearmedia	nonlinearmedia	PROPN
ma-342	34	39	.	.	PUNCT
ma-342	35	1	this	this	DET
ma-342	35	2	equation	equation	NOUN
ma-342	35	3	describes	describe	VERB
ma-342	35	4	the	the	DET
ma-342	35	5	interactions	interaction	NOUN
ma-342	35	6	among	among	ADP
ma-342	35	7	optical	optical	ADJ
ma-342	35	8	waves	wave	NOUN
ma-342	35	9	,	,	PUNCT
ma-342	35	10	considering	consider	VERB
ma-342	35	11	effects	effect	NOUN
ma-342	35	12	suchas	suchas	VERB
ma-342	35	13	self	self	NOUN
ma-342	35	14	-	-	PUNCT
ma-342	35	15	focusing	focus	VERB
ma-342	35	16	,	,	PUNCT
ma-342	35	17	self	self	NOUN
ma-342	35	18	-	-	PUNCT
ma-342	35	19	phase	phase	NOUN
ma-342	35	20	modulation	modulation	NOUN
ma-342	35	21	,	,	PUNCT
ma-342	35	22	and	and	CCONJ
ma-342	35	23	optical	optical	ADJ
ma-342	35	24	solitons	soliton	NOUN
ma-342	35	25	.	.	PUNCT
ma-342	36	1	optical	optical	ADJ
ma-342	36	2	solitons	soliton	NOUN
ma-342	36	3	,	,	PUNCT
ma-342	36	4	which	which	PRON
ma-342	36	5	are	be	AUX
ma-342	36	6	stable	stable	ADJ
ma-342	36	7	,	,	PUNCT
ma-342	36	8	localized	localized	ADJ
ma-342	36	9	wave	wave	NOUN
ma-342	36	10	packets	packet	NOUN
ma-342	36	11	that	that	PRON
ma-342	36	12	can	can	AUX
ma-342	36	13	maintain	maintain	VERB
ma-342	36	14	their	their	PRON
ma-342	36	15	shape	shape	NOUN
ma-342	36	16	during	during	ADP
ma-342	36	17	propagation	propagation	NOUN
ma-342	36	18	,	,	PUNCT
ma-342	36	19	and	and	CCONJ
ma-342	36	20	applications	application	NOUN
ma-342	36	21	in	in	ADP
ma-342	36	22	long	long	ADJ
ma-342	36	23	-	-	PUNCT
ma-342	36	24	distance	distance	NOUN
ma-342	36	25	communication	communication	NOUN
ma-342	36	26	systems	system	NOUN
ma-342	36	27	.	.	PUNCT
ma-342	37	1	the	the	DET
ma-342	37	2	nlse	nlse	NOUN
ma-342	37	3	helps	help	VERB
ma-342	37	4	optimize	optimize	VERB
ma-342	37	5	and	and	CCONJ
ma-342	37	6	control	control	VERB
ma-342	37	7	these	these	DET
ma-342	37	8	phenomena	phenomenon	NOUN
ma-342	37	9	in	in	ADP
ma-342	37	10	thedesign	thedesign	NOUN
ma-342	37	11	of	of	ADP
ma-342	37	12	optical	optical	ADJ
ma-342	37	13	communication	communication	NOUN
ma-342	37	14	systems	system	NOUN
ma-342	37	15	and	and	CCONJ
ma-342	37	16	laser	laser	VERB
ma-342	37	17	technologies.the	technologies.the	DET
ma-342	37	18	nlse	nlse	NOUN
ma-342	37	19	also	also	ADV
ma-342	37	20	appears	appear	VERB
ma-342	37	21	in	in	ADP
ma-342	37	22	the	the	DET
ma-342	37	23	study	study	NOUN
ma-342	37	24	of	of	ADP
ma-342	37	25	ultra	ultra	ADJ
ma-342	37	26	-	-	ADJ
ma-342	37	27	cold	cold	ADJ
ma-342	37	28	atomic	atomic	ADJ
ma-342	37	29	gases	gas	NOUN
ma-342	37	30	,	,	PUNCT
ma-342	37	31	particularly	particularly	ADV
ma-342	37	32	in	in	ADP
ma-342	37	33	the	the	DET
ma-342	37	34	context	context	NOUN
ma-342	37	35	ofbose	ofbose	NOUN
ma-342	37	36	-	-	PUNCT
ma-342	37	37	einstein	einstein	NOUN
ma-342	37	38	condensates	condensate	NOUN
ma-342	37	39	.	.	PUNCT
ma-342	38	1	in	in	ADP
ma-342	38	2	this	this	DET
ma-342	38	3	scenario	scenario	NOUN
ma-342	38	4	,	,	PUNCT
ma-342	38	5	the	the	DET
ma-342	38	6	nlse	nlse	NOUN
ma-342	38	7	describes	describe	VERB
ma-342	38	8	the	the	DET
ma-342	38	9	dynamics	dynamic	NOUN
ma-342	38	10	of	of	ADP
ma-342	38	11	the	the	DET
ma-342	38	12	macroscopicwave	macroscopicwave	NOUN
ma-342	38	13	function	function	NOUN
ma-342	38	14	of	of	ADP
ma-342	38	15	the	the	DET
ma-342	38	16	condensate	condensate	NOUN
ma-342	38	17	.	.	PUNCT
ma-342	39	1	understanding	understand	VERB
ma-342	39	2	the	the	DET
ma-342	39	3	nlse	nlse	NOUN
ma-342	39	4	for	for	ADP
ma-342	39	5	becs	becs	PROPN
ma-342	39	6	is	be	AUX
ma-342	39	7	crucial	crucial	ADJ
ma-342	39	8	for	for	ADP
ma-342	39	9	investigatingphenomena	investigatingphenomena	NOUN
ma-342	39	10	such	such	ADJ
ma-342	39	11	as	as	ADP
ma-342	39	12	matter	matter	NOUN
ma-342	39	13	-	-	PUNCT
ma-342	39	14	wave	wave	NOUN
ma-342	39	15	solitons	soliton	NOUN
ma-342	39	16	and	and	CCONJ
ma-342	39	17	vortices	vortex	NOUN
ma-342	39	18	,	,	PUNCT
ma-342	39	19	which	which	PRON
ma-342	39	20	have	have	VERB
ma-342	39	21	applications	application	NOUN
ma-342	39	22	in	in	ADP
ma-342	39	23	precision	precision	NOUN
ma-342	39	24	mea	mea	NOUN
ma-342	39	25	-	-	PUNCT
ma-342	39	26	surements	surement	NOUN
ma-342	39	27	and	and	CCONJ
ma-342	39	28	quantum	quantum	NOUN
ma-342	39	29	information	information	NOUN
ma-342	39	30	processing.the	processing.the	PRON
ma-342	39	31	nlse	nlse	PROPN
ma-342	39	32	arises	arise	VERB
ma-342	39	33	in	in	ADP
ma-342	39	34	the	the	DET
ma-342	39	35	study	study	NOUN
ma-342	39	36	of	of	ADP
ma-342	39	37	langmuir	langmuir	PROPN
ma-342	39	38	waves	wave	NOUN
ma-342	39	39	in	in	ADP
ma-342	39	40	plasmas	plasma	NOUN
ma-342	39	41	,	,	PUNCT
ma-342	39	42	where	where	SCONJ
ma-342	39	43	it	it	PRON
ma-342	39	44	describes	describe	VERB
ma-342	39	45	the	the	DET
ma-342	39	46	evolution	evolution	NOUN
ma-342	39	47	of	of	ADP
ma-342	39	48	theelectron	theelectron	NOUN
ma-342	39	49	plasma	plasma	NOUN
ma-342	39	50	wave	wave	NOUN
ma-342	39	51	.	.	PUNCT
ma-342	40	1	nonlinear	nonlinear	ADJ
ma-342	40	2	effects	effect	NOUN
ma-342	40	3	become	become	VERB
ma-342	40	4	significant	significant	ADJ
ma-342	40	5	in	in	ADP
ma-342	40	6	high	high	ADJ
ma-342	40	7	-	-	PUNCT
ma-342	40	8	intensity	intensity	NOUN
ma-342	40	9	laser	laser	NOUN
ma-342	40	10	-	-	PUNCT
ma-342	40	11	plasma	plasma	NOUN
ma-342	40	12	inter	inter	NOUN
ma-342	40	13	-	-	NOUN
ma-342	40	14	actions	action	NOUN
ma-342	40	15	and	and	CCONJ
ma-342	40	16	can	can	AUX
ma-342	40	17	lead	lead	VERB
ma-342	40	18	to	to	ADP
ma-342	40	19	the	the	DET
ma-342	40	20	generation	generation	NOUN
ma-342	40	21	of	of	ADP
ma-342	40	22	harmonics	harmonic	NOUN
ma-342	40	23	and	and	CCONJ
ma-342	40	24	other	other	ADJ
ma-342	40	25	phenomena	phenomenon	NOUN
ma-342	40	26	.	.	PUNCT
ma-342	41	1	this	this	PRON
ma-342	41	2	has	have	VERB
ma-342	41	3	applicationsin	applicationsin	NOUN
ma-342	41	4	areas	area	NOUN
ma-342	41	5	such	such	ADJ
ma-342	41	6	as	as	ADP
ma-342	41	7	controlled	control	VERB
ma-342	41	8	nuclear	nuclear	ADJ
ma-342	41	9	fusion	fusion	NOUN
ma-342	41	10	research	research	NOUN
ma-342	41	11	and	and	CCONJ
ma-342	41	12	the	the	DET
ma-342	41	13	development	development	NOUN
ma-342	41	14	of	of	ADP
ma-342	41	15	high	high	ADJ
ma-342	41	16	-	-	PUNCT
ma-342	41	17	power	power	NOUN
ma-342	41	18	particle	particle	NOUN
ma-342	41	19	https://doi.org/10.28924/ada/ma.5.14	https://doi.org/10.28924/ada/ma.5.14	PROPN
ma-342	41	20	eur	eur	PROPN
ma-342	41	21	.	.	PUNCT
ma-342	42	1	j.	j.	PROPN
ma-342	42	2	math	math	PROPN
ma-342	42	3	.	.	PUNCT
ma-342	43	1	anal	anal	PROPN
ma-342	43	2	.	.	PUNCT
ma-342	44	1	10.28924	10.28924	NUM
ma-342	44	2	/	/	SYM
ma-342	44	3	ada	ada	PROPN
ma-342	44	4	/	/	SYM
ma-342	44	5	ma.5.14	ma.5.14	NOUN
ma-342	44	6	3accelerators.nlse	3accelerators.nlse	PRON
ma-342	44	7	is	be	AUX
ma-342	44	8	fundamental	fundamental	ADJ
ma-342	44	9	in	in	ADP
ma-342	44	10	understanding	understand	VERB
ma-342	44	11	the	the	DET
ma-342	44	12	behavior	behavior	NOUN
ma-342	44	13	of	of	ADP
ma-342	44	14	optical	optical	ADJ
ma-342	44	15	pulses	pulse	NOUN
ma-342	44	16	in	in	ADP
ma-342	44	17	fiber	fiber	NOUN
ma-342	44	18	optic	optic	PROPN
ma-342	44	19	communica	communica	PROPN
ma-342	44	20	-	-	PUNCT
ma-342	44	21	tion	tion	NOUN
ma-342	44	22	systems	system	NOUN
ma-342	44	23	.	.	PUNCT
ma-342	45	1	fiber	fiber	NOUN
ma-342	45	2	optic	optic	ADJ
ma-342	45	3	channels	channel	NOUN
ma-342	45	4	exhibit	exhibit	VERB
ma-342	45	5	nonlinear	nonlinear	ADJ
ma-342	45	6	effects	effect	NOUN
ma-342	45	7	such	such	ADJ
ma-342	45	8	as	as	ADP
ma-342	45	9	self	self	NOUN
ma-342	45	10	-	-	PUNCT
ma-342	45	11	phase	phase	NOUN
ma-342	45	12	modulation	modulation	NOUN
ma-342	45	13	andcross	andcross	NOUN
ma-342	45	14	-	-	NOUN
ma-342	45	15	phase	phase	NOUN
ma-342	45	16	modulation	modulation	NOUN
ma-342	45	17	,	,	PUNCT
ma-342	45	18	which	which	PRON
ma-342	45	19	can	can	AUX
ma-342	45	20	distort	distort	VERB
ma-342	45	21	transmitted	transmit	VERB
ma-342	45	22	signals	signal	NOUN
ma-342	45	23	.	.	PUNCT
ma-342	46	1	the	the	DET
ma-342	46	2	nlse	nlse	NOUN
ma-342	46	3	is	be	AUX
ma-342	46	4	essential	essential	ADJ
ma-342	46	5	for	for	ADP
ma-342	46	6	modelingand	modelingand	NOUN
ma-342	46	7	mitigating	mitigate	VERB
ma-342	46	8	these	these	DET
ma-342	46	9	effects	effect	NOUN
ma-342	46	10	,	,	PUNCT
ma-342	46	11	ensuring	ensure	VERB
ma-342	46	12	the	the	DET
ma-342	46	13	reliability	reliability	NOUN
ma-342	46	14	and	and	CCONJ
ma-342	46	15	efficiency	efficiency	NOUN
ma-342	46	16	of	of	ADP
ma-342	46	17	long	long	ADJ
ma-342	46	18	-	-	PUNCT
ma-342	46	19	distance	distance	NOUN
ma-342	46	20	communicationnetworks.variants	communicationnetworks.variant	NOUN
ma-342	46	21	of	of	ADP
ma-342	46	22	the	the	DET
ma-342	46	23	nlse	nlse	NOUN
ma-342	46	24	are	be	AUX
ma-342	46	25	used	use	VERB
ma-342	46	26	to	to	PART
ma-342	46	27	model	model	VERB
ma-342	46	28	the	the	DET
ma-342	46	29	propagation	propagation	NOUN
ma-342	46	30	of	of	ADP
ma-342	46	31	water	water	NOUN
ma-342	46	32	waves	wave	NOUN
ma-342	46	33	in	in	ADP
ma-342	46	34	oceans	ocean	NOUN
ma-342	46	35	and	and	CCONJ
ma-342	46	36	otherbodies	otherbodie	NOUN
ma-342	46	37	of	of	ADP
ma-342	46	38	water	water	NOUN
ma-342	46	39	.	.	PUNCT
ma-342	47	1	nonlinear	nonlinear	ADJ
ma-342	47	2	effects	effect	NOUN
ma-342	47	3	,	,	PUNCT
ma-342	47	4	such	such	ADJ
ma-342	47	5	as	as	ADP
ma-342	47	6	wave	wave	NOUN
ma-342	47	7	steepening	steepening	NOUN
ma-342	47	8	and	and	CCONJ
ma-342	47	9	wave	wave	NOUN
ma-342	47	10	breaking	breaking	NOUN
ma-342	47	11	,	,	PUNCT
ma-342	47	12	can	can	AUX
ma-342	47	13	be	be	AUX
ma-342	47	14	describedusing	describeduse	VERB
ma-342	47	15	these	these	DET
ma-342	47	16	equations	equation	NOUN
ma-342	47	17	.	.	PUNCT
ma-342	48	1	understanding	understand	VERB
ma-342	48	2	these	these	DET
ma-342	48	3	phenomena	phenomenon	NOUN
ma-342	48	4	is	be	AUX
ma-342	48	5	crucial	crucial	ADJ
ma-342	48	6	for	for	ADP
ma-342	48	7	predicting	predict	VERB
ma-342	48	8	and	and	CCONJ
ma-342	48	9	mitigating	mitigate	VERB
ma-342	48	10	theimpact	theimpact	NOUN
ma-342	48	11	of	of	ADP
ma-342	48	12	tsunamis	tsunamis	NOUN
ma-342	48	13	,	,	PUNCT
ma-342	48	14	storm	storm	NOUN
ma-342	48	15	surges	surge	VERB
ma-342	48	16	,	,	PUNCT
ma-342	48	17	and	and	CCONJ
ma-342	48	18	other	other	ADJ
ma-342	48	19	oceanic	oceanic	ADJ
ma-342	48	20	events.nlse	events.nlse	X
ma-342	48	21	variants	variant	NOUN
ma-342	48	22	are	be	AUX
ma-342	48	23	employed	employ	VERB
ma-342	48	24	in	in	ADP
ma-342	48	25	the	the	DET
ma-342	48	26	study	study	NOUN
ma-342	48	27	of	of	ADP
ma-342	48	28	biological	biological	ADJ
ma-342	48	29	systems	system	NOUN
ma-342	48	30	,	,	PUNCT
ma-342	48	31	such	such	ADJ
ma-342	48	32	as	as	ADP
ma-342	48	33	modeling	model	VERB
ma-342	48	34	the	the	DET
ma-342	48	35	propagationof	propagationof	NOUN
ma-342	48	36	nerve	nerve	NOUN
ma-342	48	37	impulses	impulse	NOUN
ma-342	48	38	.	.	PUNCT
ma-342	49	1	the	the	DET
ma-342	49	2	nlse	nlse	NOUN
ma-342	49	3	can	can	AUX
ma-342	49	4	describe	describe	VERB
ma-342	49	5	the	the	DET
ma-342	49	6	nonlinear	nonlinear	ADJ
ma-342	49	7	dynamics	dynamic	NOUN
ma-342	49	8	of	of	ADP
ma-342	49	9	excitable	excitable	ADJ
ma-342	49	10	media	medium	NOUN
ma-342	49	11	,	,	PUNCT
ma-342	49	12	providinginsights	providinginsight	NOUN
ma-342	49	13	into	into	ADP
ma-342	49	14	the	the	DET
ma-342	49	15	behavior	behavior	NOUN
ma-342	49	16	of	of	ADP
ma-342	49	17	electrical	electrical	ADJ
ma-342	49	18	signals	signal	NOUN
ma-342	49	19	in	in	ADP
ma-342	49	20	biological	biological	ADJ
ma-342	49	21	tissues.moreover	tissues.moreover	NUM
ma-342	49	22	,	,	PUNCT
ma-342	49	23	the	the	DET
ma-342	49	24	nlse	nlse	ADJ
ma-342	50	1	[	[	X
ma-342	50	2	4	4	NUM
ma-342	50	3	,	,	PUNCT
ma-342	50	4	12	12	NUM
ma-342	50	5	,	,	PUNCT
ma-342	50	6	23	23	NUM
ma-342	50	7	]	]	PUNCT
ma-342	50	8	,	,	PUNCT
ma-342	50	9	which	which	PRON
ma-342	50	10	is	be	AUX
ma-342	50	11	an	an	DET
ma-342	50	12	essential	essential	ADJ
ma-342	50	13	fully	fully	ADV
ma-342	50	14	-	-	PUNCT
ma-342	50	15	integrated	integrate	VERB
ma-342	50	16	nonlinear	nonlinear	ADJ
ma-342	50	17	dispersive	dispersive	ADJ
ma-342	50	18	par	par	ADJ
ma-342	50	19	-	-	PUNCT
ma-342	50	20	tial	tial	ADJ
ma-342	50	21	differential	differential	ADJ
ma-342	50	22	equation	equation	NOUN
ma-342	50	23	(	(	PUNCT
ma-342	50	24	pde	pde	NOUN
ma-342	50	25	)	)	PUNCT
ma-342	50	26	,	,	PUNCT
ma-342	50	27	has	have	AUX
ma-342	50	28	found	find	VERB
ma-342	50	29	extensive	extensive	ADJ
ma-342	50	30	application	application	NOUN
ma-342	50	31	in	in	ADP
ma-342	50	32	elucidating	elucidate	VERB
ma-342	50	33	diverse	diverse	ADJ
ma-342	50	34	phenomenalike	phenomenalike	ADP
ma-342	50	35	deep	deep	ADJ
ma-342	50	36	water	water	NOUN
ma-342	50	37	waves	wave	NOUN
ma-342	50	38	,	,	PUNCT
ma-342	50	39	rogue	rogue	NOUN
ma-342	50	40	waves	wave	NOUN
ma-342	50	41	,	,	PUNCT
ma-342	50	42	plasmas	plasma	NOUN
ma-342	50	43	,	,	PUNCT
ma-342	50	44	and	and	CCONJ
ma-342	50	45	nonlinear	nonlinear	ADJ
ma-342	50	46	optics	optic	NOUN
ma-342	50	47	,	,	PUNCT
ma-342	50	48	including	include	VERB
ma-342	50	49	atomic	atomic	ADJ
ma-342	50	50	physics	physic	NOUN
ma-342	50	51	.	.	PUNCT
ma-342	51	1	thenlse	thenlse	PROPN
ma-342	51	2	serves	serve	VERB
ma-342	51	3	as	as	ADP
ma-342	51	4	a	a	DET
ma-342	51	5	comprehensive	comprehensive	ADJ
ma-342	51	6	description	description	NOUN
ma-342	51	7	of	of	ADP
ma-342	51	8	nonlinear	nonlinear	ADJ
ma-342	51	9	dispersive	dispersive	ADJ
ma-342	51	10	processes	process	NOUN
ma-342	51	11	.	.	PUNCT
ma-342	52	1	zhou	zhou	PROPN
ma-342	52	2	et	et	PROPN
ma-342	52	3	al	al	PROPN
ma-342	52	4	.	.	PUNCT
ma-342	53	1	[	[	X
ma-342	53	2	34]considered	34]considered	NUM
ma-342	53	3	the	the	DET
ma-342	53	4	weakly	weakly	ADJ
ma-342	53	5	nonlocal	nonlocal	ADJ
ma-342	53	6	nlse	nlse	NOUN
ma-342	53	7	having	have	VERB
ma-342	53	8	pl	pl	X
ma-342	53	9	nonlinearity	nonlinearity	NOUN
ma-342	53	10	with	with	ADP
ma-342	53	11	external	external	ADJ
ma-342	53	12	potential	potential	NOUN
ma-342	53	13	as	as	ADP
ma-342	53	14	iφt	iφt	PROPN
ma-342	53	15	+	+	CCONJ
ma-342	53	16	λ1φxx	λ1φxx	PUNCT
ma-342	54	1	+	+	CCONJ
ma-342	54	2	(	(	PUNCT
ma-342	54	3	λ2|φ|2xx	λ2|φ|2xx	NOUN
ma-342	55	1	+	+	CCONJ
ma-342	55	2	λ3|φ|2	λ3|φ|2	PROPN
ma-342	55	3	+	+	CCONJ
ma-342	55	4	λ4|φ|4	λ4|φ|4	PROPN
ma-342	55	5	)	)	PUNCT
ma-342	55	6	φ	φ	PROPN
ma-342	55	7	=	=	SYM
ma-342	55	8	0	0	PROPN
ma-342	55	9	.	.	PUNCT
ma-342	56	1	(	(	PUNCT
ma-342	56	2	1	1	X
ma-342	56	3	)	)	PUNCT
ma-342	56	4	the	the	DET
ma-342	56	5	study	study	NOUN
ma-342	56	6	of	of	ADP
ma-342	56	7	schrodinger	schrodinger	PROPN
ma-342	56	8	equations	equation	NOUN
ma-342	56	9	with	with	ADP
ma-342	56	10	nonlinearity	nonlinearity	NOUN
ma-342	56	11	is	be	AUX
ma-342	56	12	an	an	DET
ma-342	56	13	important	important	ADJ
ma-342	56	14	area	area	NOUN
ma-342	56	15	of	of	ADP
ma-342	56	16	research	research	NOUN
ma-342	56	17	in	in	ADP
ma-342	56	18	math	math	NOUN
ma-342	56	19	-	-	PUNCT
ma-342	56	20	ematical	ematical	ADJ
ma-342	56	21	physics	physics	NOUN
ma-342	56	22	.	.	PUNCT
ma-342	57	1	in	in	ADP
ma-342	57	2	recent	recent	ADJ
ma-342	57	3	years	year	NOUN
ma-342	57	4	,	,	PUNCT
ma-342	57	5	the	the	DET
ma-342	57	6	weakly	weakly	ADJ
ma-342	57	7	nonlocal	nonlocal	ADJ
ma-342	57	8	schrodinger	schrodinger	NOUN
ma-342	57	9	equation	equation	NOUN
ma-342	57	10	with	with	ADP
ma-342	57	11	parabolic	parabolic	ADJ
ma-342	57	12	lawnonlinearity	lawnonlinearity	NOUN
ma-342	57	13	has	have	AUX
ma-342	57	14	gained	gain	VERB
ma-342	57	15	significant	significant	ADJ
ma-342	57	16	attention	attention	NOUN
ma-342	57	17	due	due	ADP
ma-342	57	18	to	to	ADP
ma-342	57	19	its	its	PRON
ma-342	57	20	numerous	numerous	ADJ
ma-342	57	21	applications	application	NOUN
ma-342	57	22	in	in	ADP
ma-342	57	23	various	various	ADJ
ma-342	57	24	fields	field	NOUN
ma-342	57	25	suchas	suchas	VERB
ma-342	57	26	quantum	quantum	NOUN
ma-342	57	27	mechanics	mechanic	NOUN
ma-342	57	28	,	,	PUNCT
ma-342	57	29	nonlinear	nonlinear	ADJ
ma-342	57	30	optics	optic	NOUN
ma-342	57	31	,	,	PUNCT
ma-342	57	32	and	and	CCONJ
ma-342	57	33	fluid	fluid	NOUN
ma-342	57	34	dynamics.in	dynamics.in	PRON
ma-342	57	35	this	this	DET
ma-342	57	36	paper	paper	NOUN
ma-342	57	37	,	,	PUNCT
ma-342	57	38	we	we	PRON
ma-342	57	39	present	present	VERB
ma-342	57	40	modulation	modulation	NOUN
ma-342	57	41	instability	instability	NOUN
ma-342	57	42	analysis	analysis	NOUN
ma-342	57	43	and	and	CCONJ
ma-342	57	44	the	the	DET
ma-342	57	45	novel	novel	ADJ
ma-342	57	46	exact	exact	ADJ
ma-342	57	47	solutions	solution	NOUN
ma-342	57	48	for	for	ADP
ma-342	57	49	theweakly	theweakly	DET
ma-342	57	50	nonlocal	nonlocal	ADJ
ma-342	57	51	schrodinger	schrodinger	NOUN
ma-342	57	52	equation	equation	NOUN
ma-342	57	53	with	with	ADP
ma-342	57	54	parabolic	parabolic	ADJ
ma-342	57	55	law	law	NOUN
ma-342	57	56	nonlinearity	nonlinearity	NOUN
ma-342	57	57	,	,	PUNCT
ma-342	57	58	derived	derive	VERB
ma-342	57	59	using	use	VERB
ma-342	57	60	the	the	DET
ma-342	57	61	methodextended	methodextende	VERB
ma-342	57	62	tanh	tanh	NOUN
ma-342	57	63	function	function	NOUN
ma-342	57	64	.	.	PUNCT
ma-342	58	1	the	the	DET
ma-342	58	2	solutions	solution	NOUN
ma-342	58	3	we	we	PRON
ma-342	58	4	obtain	obtain	VERB
ma-342	58	5	,	,	PUNCT
ma-342	58	6	which	which	PRON
ma-342	58	7	include	include	VERB
ma-342	58	8	dark	dark	ADJ
ma-342	58	9	soliton	soliton	NOUN
ma-342	58	10	,	,	PUNCT
ma-342	58	11	bright	bright	ADJ
ma-342	58	12	soliton	soliton	NOUN
ma-342	58	13	,	,	PUNCT
ma-342	58	14	andtraveling	andtravele	VERB
ma-342	58	15	wave	wave	NOUN
ma-342	58	16	solutions	solution	NOUN
ma-342	58	17	,	,	PUNCT
ma-342	58	18	have	have	AUX
ma-342	58	19	not	not	PART
ma-342	58	20	been	be	AUX
ma-342	58	21	previously	previously	ADV
ma-342	58	22	reported	report	VERB
ma-342	58	23	in	in	ADP
ma-342	58	24	the	the	DET
ma-342	58	25	literature	literature	NOUN
ma-342	58	26	and	and	CCONJ
ma-342	58	27	demonstrate	demonstrate	VERB
ma-342	58	28	thecomplex	thecomplex	ADJ
ma-342	58	29	dynamics	dynamic	NOUN
ma-342	58	30	of	of	ADP
ma-342	58	31	the	the	DET
ma-342	58	32	considered	consider	VERB
ma-342	58	33	equation	equation	NOUN
ma-342	58	34	.	.	PUNCT
ma-342	59	1	dark	dark	ADJ
ma-342	59	2	optical	optical	ADJ
ma-342	59	3	soliton	soliton	NOUN
ma-342	59	4	describes	describe	VERB
ma-342	59	5	the	the	DET
ma-342	59	6	solitary	solitary	ADJ
ma-342	59	7	waveswith	waveswith	ADP
ma-342	59	8	lower	low	ADJ
ma-342	59	9	intensity	intensity	NOUN
ma-342	59	10	than	than	ADP
ma-342	59	11	the	the	DET
ma-342	59	12	background	background	NOUN
ma-342	59	13	,	,	PUNCT
ma-342	59	14	bright	bright	ADJ
ma-342	59	15	optical	optical	ADJ
ma-342	59	16	soliton	soliton	NOUN
ma-342	59	17	describes	describe	VERB
ma-342	59	18	the	the	DET
ma-342	59	19	solitary	solitary	ADJ
ma-342	59	20	waves	wave	NOUN
ma-342	59	21	whosepeak	whosepeak	NOUN
ma-342	59	22	intensity	intensity	NOUN
ma-342	59	23	is	be	AUX
ma-342	59	24	larger	large	ADJ
ma-342	59	25	than	than	ADP
ma-342	59	26	the	the	DET
ma-342	59	27	background	background	NOUN
ma-342	59	28	and	and	CCONJ
ma-342	59	29	the	the	DET
ma-342	59	30	singular	singular	ADJ
ma-342	59	31	optical	optical	ADJ
ma-342	59	32	soliton	soliton	NOUN
ma-342	59	33	is	be	AUX
ma-342	59	34	a	a	DET
ma-342	59	35	solitary	solitary	ADJ
ma-342	59	36	wavewith	wavewith	NOUN
ma-342	59	37	discontinuous	discontinuous	ADJ
ma-342	59	38	derivatives	derivative	NOUN
ma-342	59	39	;	;	PUNCT
ma-342	59	40	examples	example	NOUN
ma-342	59	41	of	of	ADP
ma-342	59	42	such	such	ADJ
ma-342	59	43	solitary	solitary	ADJ
ma-342	59	44	waves	wave	NOUN
ma-342	59	45	include	include	VERB
ma-342	59	46	compactions	compaction	NOUN
ma-342	59	47	,	,	PUNCT
ma-342	59	48	which	which	PRON
ma-342	59	49	havefinite	havefinite	NOUN
ma-342	59	50	(	(	PUNCT
ma-342	59	51	compact	compact	ADJ
ma-342	59	52	)	)	PUNCT
ma-342	59	53	support	support	NOUN
ma-342	59	54	,	,	PUNCT
ma-342	59	55	and	and	CCONJ
ma-342	59	56	peakons	peakon	NOUN
ma-342	59	57	,	,	PUNCT
ma-342	59	58	whose	whose	DET
ma-342	59	59	peaks	peak	NOUN
ma-342	59	60	have	have	VERB
ma-342	59	61	a	a	DET
ma-342	59	62	discontinuous	discontinuous	ADJ
ma-342	59	63	first	first	ADJ
ma-342	59	64	derivative	derivative	ADJ
ma-342	59	65	[	[	X
ma-342	59	66	35	35	NUM
ma-342	59	67	,	,	PUNCT
ma-342	59	68	36].dark	36].dark	ADJ
ma-342	59	69	soliton	soliton	NOUN
ma-342	59	70	propagates	propagate	VERB
ma-342	59	71	without	without	ADP
ma-342	59	72	changing	change	VERB
ma-342	59	73	its	its	PRON
ma-342	59	74	shape	shape	NOUN
ma-342	59	75	,	,	PUNCT
ma-342	59	76	but	but	CCONJ
ma-342	59	77	it	it	PRON
ma-342	59	78	is	be	AUX
ma-342	59	79	not	not	PART
ma-342	59	80	made	make	VERB
ma-342	59	81	by	by	ADP
ma-342	59	82	a	a	DET
ma-342	59	83	normal	normal	ADJ
ma-342	59	84	pulse	pulse	NOUN
ma-342	59	85	;	;	PUNCT
ma-342	59	86	rather	rather	ADV
ma-342	59	87	,	,	PUNCT
ma-342	59	88	it	it	PRON
ma-342	59	89	is	be	AUX
ma-342	59	90	a	a	DET
ma-342	59	91	lack	lack	NOUN
ma-342	59	92	of	of	ADP
ma-342	59	93	energy	energy	NOUN
ma-342	59	94	in	in	ADP
ma-342	59	95	a	a	DET
ma-342	59	96	continuous	continuous	ADJ
ma-342	59	97	-	-	PUNCT
ma-342	59	98	time	time	NOUN
ma-342	59	99	beam	beam	NOUN
ma-342	59	100	.	.	PUNCT
ma-342	60	1	the	the	DET
ma-342	60	2	intensity	intensity	NOUN
ma-342	60	3	is	be	AUX
ma-342	60	4	constant	constant	ADJ
ma-342	60	5	,	,	PUNCT
ma-342	60	6	but	but	CCONJ
ma-342	60	7	for	for	ADP
ma-342	60	8	a	a	DET
ma-342	60	9	short	short	ADJ
ma-342	60	10	timeduring	timeduring	NOUN
ma-342	60	11	which	which	PRON
ma-342	60	12	it	it	PRON
ma-342	60	13	jumps	jump	VERB
ma-342	60	14	to	to	ADP
ma-342	60	15	zero	zero	NUM
ma-342	60	16	and	and	CCONJ
ma-342	60	17	back	back	ADV
ma-342	60	18	again	again	ADV
ma-342	60	19	,	,	PUNCT
ma-342	60	20	thus	thus	ADV
ma-342	60	21	generating	generate	VERB
ma-342	60	22	a	a	DET
ma-342	60	23	"	"	PUNCT
ma-342	60	24	dark	dark	ADJ
ma-342	60	25	pulse	pulse	NOUN
ma-342	60	26	"	"	PUNCT
ma-342	60	27	’	'	PUNCT
ma-342	60	28	.	.	PUNCT
ma-342	61	1	those	those	DET
ma-342	61	2	solitons	soliton	NOUN
ma-342	61	3	can	can	AUX
ma-342	61	4	https://doi.org/10.28924/ada/ma.5.14	https://doi.org/10.28924/ada/ma.5.14	PROPN
ma-342	61	5	eur	eur	PROPN
ma-342	61	6	.	.	PUNCT
ma-342	62	1	j.	j.	PROPN
ma-342	62	2	math	math	PROPN
ma-342	62	3	.	.	PUNCT
ma-342	63	1	anal	anal	PROPN
ma-342	63	2	.	.	PUNCT
ma-342	64	1	10.28924	10.28924	NUM
ma-342	64	2	/	/	SYM
ma-342	64	3	ada	ada	PROPN
ma-342	64	4	/	/	SYM
ma-342	64	5	ma.5.14	ma.5.14	NOUN
ma-342	64	6	4actually	4actually	ADV
ma-342	64	7	be	be	AUX
ma-342	64	8	generated	generate	VERB
ma-342	64	9	introducing	introduce	VERB
ma-342	64	10	short	short	ADJ
ma-342	64	11	dark	dark	ADJ
ma-342	64	12	pulses	pulse	NOUN
ma-342	64	13	in	in	ADP
ma-342	64	14	much	much	ADV
ma-342	64	15	longer	long	ADJ
ma-342	64	16	standard	standard	ADJ
ma-342	64	17	pulses	pulse	NOUN
ma-342	64	18	.	.	PUNCT
ma-342	65	1	dark	dark	ADJ
ma-342	65	2	soli	solo	NOUN
ma-342	65	3	-	-	PUNCT
ma-342	65	4	tons	ton	NOUN
ma-342	65	5	are	be	AUX
ma-342	65	6	more	more	ADV
ma-342	65	7	difficult	difficult	ADJ
ma-342	65	8	to	to	PART
ma-342	65	9	handle	handle	VERB
ma-342	65	10	than	than	ADP
ma-342	65	11	standard	standard	ADJ
ma-342	65	12	solitons	soliton	NOUN
ma-342	65	13	,	,	PUNCT
ma-342	65	14	but	but	CCONJ
ma-342	65	15	they	they	PRON
ma-342	65	16	have	have	AUX
ma-342	65	17	shown	show	VERB
ma-342	65	18	to	to	PART
ma-342	65	19	be	be	AUX
ma-342	65	20	more	more	ADJ
ma-342	65	21	stableand	stableand	NOUN
ma-342	65	22	robust	robust	ADJ
ma-342	65	23	to	to	ADP
ma-342	65	24	losses	loss	NOUN
ma-342	65	25	.	.	PUNCT
ma-342	66	1	bright	bright	ADJ
ma-342	66	2	optical	optical	ADJ
ma-342	66	3	soliton	soliton	NOUN
ma-342	66	4	causes	cause	VERB
ma-342	66	5	a	a	DET
ma-342	66	6	temporary	temporary	ADJ
ma-342	66	7	increase	increase	NOUN
ma-342	66	8	in	in	ADP
ma-342	66	9	an	an	DET
ma-342	66	10	associated	associated	ADJ
ma-342	66	11	waveamplitude	waveamplitude	NOUN
ma-342	66	12	[	[	X
ma-342	66	13	52	52	NUM
ma-342	66	14	]	]	PUNCT
ma-342	66	15	.	.	PUNCT
ma-342	67	1	the	the	DET
ma-342	67	2	combined	combine	VERB
ma-342	67	3	dark	dark	ADJ
ma-342	67	4	-	-	PUNCT
ma-342	67	5	bright	bright	ADJ
ma-342	67	6	optical	optical	ADJ
ma-342	67	7	soliton	soliton	NOUN
ma-342	67	8	carries	carry	VERB
ma-342	67	9	the	the	DET
ma-342	67	10	combine	combine	NOUN
ma-342	67	11	features	feature	NOUN
ma-342	67	12	of	of	ADP
ma-342	67	13	the	the	DET
ma-342	67	14	darkand	darkand	ADJ
ma-342	67	15	bright	bright	ADJ
ma-342	67	16	optical	optical	ADJ
ma-342	67	17	solitons	soliton	NOUN
ma-342	67	18	.	.	PUNCT
ma-342	68	1	moreover	moreover	ADV
ma-342	68	2	,	,	PUNCT
ma-342	68	3	the	the	DET
ma-342	68	4	modulation	modulation	NOUN
ma-342	68	5	instability	instability	NOUN
ma-342	68	6	analysis	analysis	NOUN
ma-342	68	7	for	for	ADP
ma-342	68	8	the	the	DET
ma-342	68	9	weakly	weakly	ADJ
ma-342	68	10	nonlocalnlse	nonlocalnlse	NOUN
ma-342	68	11	having	have	VERB
ma-342	68	12	pl	pl	X
ma-342	68	13	nonlinearity	nonlinearity	NOUN
ma-342	68	14	with	with	ADP
ma-342	68	15	external	external	ADJ
ma-342	68	16	potential	potential	NOUN
ma-342	68	17	will	will	AUX
ma-342	68	18	also	also	ADV
ma-342	68	19	be	be	AUX
ma-342	68	20	presented.our	presented.our	DET
ma-342	68	21	findings	finding	NOUN
ma-342	68	22	have	have	VERB
ma-342	68	23	significant	significant	ADJ
ma-342	68	24	implications	implication	NOUN
ma-342	68	25	for	for	ADP
ma-342	68	26	the	the	DET
ma-342	68	27	study	study	NOUN
ma-342	68	28	of	of	ADP
ma-342	68	29	nonlinear	nonlinear	ADJ
ma-342	68	30	phenomena	phenomenon	NOUN
ma-342	68	31	in	in	ADP
ma-342	68	32	physical	physical	ADJ
ma-342	68	33	sys	sys	PROPN
ma-342	68	34	-	-	NOUN
ma-342	68	35	tems	tem	NOUN
ma-342	68	36	.	.	PUNCT
ma-342	69	1	the	the	DET
ma-342	69	2	ability	ability	NOUN
ma-342	69	3	to	to	PART
ma-342	69	4	obtain	obtain	VERB
ma-342	69	5	exact	exact	ADJ
ma-342	69	6	solutions	solution	NOUN
ma-342	69	7	to	to	ADP
ma-342	69	8	such	such	ADJ
ma-342	69	9	complex	complex	ADJ
ma-342	69	10	equations	equation	NOUN
ma-342	69	11	is	be	AUX
ma-342	69	12	crucial	crucial	ADJ
ma-342	69	13	in	in	ADP
ma-342	69	14	understandingthe	understandingthe	ADJ
ma-342	69	15	underlying	underlying	ADJ
ma-342	69	16	physics	physics	NOUN
ma-342	69	17	and	and	CCONJ
ma-342	69	18	designing	design	VERB
ma-342	69	19	new	new	ADJ
ma-342	69	20	experiments	experiment	NOUN
ma-342	69	21	.	.	PUNCT
ma-342	70	1	additionally	additionally	ADV
ma-342	70	2	,	,	PUNCT
ma-342	70	3	with	with	ADP
ma-342	70	4	the	the	DET
ma-342	70	5	aid	aid	NOUN
ma-342	70	6	of	of	ADP
ma-342	70	7	mathemat	mathemat	PROPN
ma-342	70	8	-	-	PUNCT
ma-342	70	9	ica	ica	PROPN
ma-342	70	10	,	,	PUNCT
ma-342	70	11	our	our	PRON
ma-342	70	12	results	result	NOUN
ma-342	70	13	are	be	AUX
ma-342	70	14	verified	verify	VERB
ma-342	70	15	by	by	ADP
ma-342	70	16	back	back	ADJ
ma-342	70	17	-	-	PUNCT
ma-342	70	18	substitution	substitution	NOUN
ma-342	70	19	in	in	ADP
ma-342	70	20	the	the	DET
ma-342	70	21	original	original	ADJ
ma-342	70	22	equations	equation	NOUN
ma-342	70	23	,	,	PUNCT
ma-342	70	24	affrming	affrme	VERB
ma-342	70	25	the	the	DET
ma-342	70	26	robustnessof	robustnessof	NOUN
ma-342	70	27	our	our	PRON
ma-342	70	28	approach	approach	NOUN
ma-342	70	29	.	.	PUNCT
ma-342	71	1	the	the	DET
ma-342	71	2	suggested	suggest	VERB
ma-342	71	3	is	be	AUX
ma-342	71	4	not	not	PART
ma-342	71	5	only	only	ADV
ma-342	71	6	direct	direct	ADJ
ma-342	71	7	and	and	CCONJ
ma-342	71	8	simple	simple	ADJ
ma-342	71	9	but	but	CCONJ
ma-342	71	10	also	also	ADV
ma-342	71	11	suitable	suitable	ADJ
ma-342	71	12	for	for	ADP
ma-342	71	13	constructingnew	constructingnew	ADJ
ma-342	71	14	results	result	NOUN
ma-342	71	15	,	,	PUNCT
ma-342	71	16	paving	pave	VERB
ma-342	71	17	the	the	DET
ma-342	71	18	way	way	NOUN
ma-342	71	19	for	for	ADP
ma-342	71	20	future	future	ADJ
ma-342	71	21	applications	application	NOUN
ma-342	71	22	on	on	ADP
ma-342	71	23	nlses	nlse	NOUN
ma-342	71	24	with	with	ADP
ma-342	71	25	dual	dual	ADJ
ma-342	71	26	power	power	NOUN
ma-342	71	27	law	law	NOUN
ma-342	71	28	and	and	CCONJ
ma-342	71	29	perturbednlses	perturbednlse	NOUN
ma-342	71	30	with	with	ADP
ma-342	71	31	kerr	kerr	PROPN
ma-342	71	32	law	law	PROPN
ma-342	71	33	.	.	PUNCT
ma-342	72	1	this	this	PRON
ma-342	72	2	is	be	AUX
ma-342	72	3	particularly	particularly	ADV
ma-342	72	4	useful	useful	ADJ
ma-342	72	5	for	for	ADP
ma-342	72	6	identifying	identify	VERB
ma-342	72	7	solitons	soliton	NOUN
ma-342	72	8	in	in	ADP
ma-342	72	9	photorefractive	photorefractive	ADJ
ma-342	72	10	andpolymer	andpolymer	NOUN
ma-342	72	11	materials	material	NOUN
ma-342	72	12	.	.	PUNCT
ma-342	73	1	the	the	DET
ma-342	73	2	proposed	propose	VERB
ma-342	73	3	technique	technique	NOUN
ma-342	73	4	holds	hold	VERB
ma-342	73	5	potential	potential	NOUN
ma-342	73	6	for	for	ADP
ma-342	73	7	further	further	ADJ
ma-342	73	8	applications	application	NOUN
ma-342	73	9	in	in	ADP
ma-342	73	10	natural	natural	ADJ
ma-342	73	11	sci	sci	PROPN
ma-342	73	12	-	-	PUNCT
ma-342	73	13	ence	ence	NOUN
ma-342	73	14	models	model	NOUN
ma-342	73	15	,	,	PUNCT
ma-342	73	16	aiding	aid	VERB
ma-342	73	17	in	in	ADP
ma-342	73	18	the	the	DET
ma-342	73	19	investigation	investigation	NOUN
ma-342	73	20	of	of	ADP
ma-342	73	21	other	other	ADJ
ma-342	73	22	mathematical	mathematical	ADJ
ma-342	73	23	challenges	challenge	NOUN
ma-342	73	24	and	and	CCONJ
ma-342	73	25	characterizing	characterize	VERB
ma-342	73	26	thebehavior	thebehavior	NOUN
ma-342	73	27	of	of	ADP
ma-342	73	28	nonlinear	nonlinear	ADJ
ma-342	73	29	models.the	models.the	DET
ma-342	73	30	remaining	remain	VERB
ma-342	73	31	sections	section	NOUN
ma-342	73	32	of	of	ADP
ma-342	73	33	this	this	DET
ma-342	73	34	manuscript	manuscript	NOUN
ma-342	73	35	are	be	AUX
ma-342	73	36	organized	organize	VERB
ma-342	73	37	as	as	SCONJ
ma-342	73	38	follows	follow	VERB
ma-342	73	39	:	:	PUNCT
ma-342	73	40	in	in	ADP
ma-342	73	41	section	section	NOUN
ma-342	73	42	2	2	NUM
ma-342	73	43	,	,	PUNCT
ma-342	73	44	we	we	PRON
ma-342	73	45	give	give	VERB
ma-342	73	46	thedescription	thedescription	NOUN
ma-342	73	47	of	of	ADP
ma-342	73	48	the	the	DET
ma-342	73	49	approach.in	approach.in	PROPN
ma-342	73	50	section	section	NOUN
ma-342	73	51	3	3	NUM
ma-342	73	52	,	,	PUNCT
ma-342	73	53	we	we	PRON
ma-342	73	54	apply	apply	VERB
ma-342	73	55	the	the	DET
ma-342	73	56	method	method	NOUN
ma-342	73	57	the	the	DET
ma-342	73	58	governing	govern	VERB
ma-342	73	59	equation	equation	NOUN
ma-342	73	60	.	.	PUNCT
ma-342	74	1	insection4	insection4	PROPN
ma-342	74	2	,	,	PUNCT
ma-342	74	3	we	we	PRON
ma-342	74	4	give	give	VERB
ma-342	74	5	the	the	DET
ma-342	74	6	graphical	graphical	ADJ
ma-342	74	7	representation	representation	NOUN
ma-342	74	8	of	of	ADP
ma-342	74	9	some	some	PRON
ma-342	74	10	of	of	ADP
ma-342	74	11	the	the	DET
ma-342	74	12	obtained	obtain	VERB
ma-342	74	13	results	result	NOUN
ma-342	74	14	.	.	PUNCT
ma-342	75	1	in	in	ADP
ma-342	75	2	section	section	NOUN
ma-342	75	3	5	5	NUM
ma-342	75	4	,	,	PUNCT
ma-342	75	5	we	we	PRON
ma-342	75	6	presentthe	presentthe	VERB
ma-342	75	7	analysis	analysis	NOUN
ma-342	75	8	of	of	ADP
ma-342	75	9	modulation	modulation	NOUN
ma-342	75	10	instability	instability	NOUN
ma-342	75	11	for	for	ADP
ma-342	75	12	the	the	DET
ma-342	75	13	model	model	NOUN
ma-342	75	14	and	and	CCONJ
ma-342	75	15	its	its	PRON
ma-342	75	16	physical	physical	ADJ
ma-342	75	17	description	description	NOUN
ma-342	75	18	.	.	PUNCT
ma-342	76	1	in	in	ADP
ma-342	76	2	section	section	NOUN
ma-342	76	3	6	6	NUM
ma-342	76	4	,	,	PUNCT
ma-342	76	5	weprovide	weprovide	ADP
ma-342	76	6	the	the	DET
ma-342	76	7	conclusion	conclusion	NOUN
ma-342	76	8	of	of	ADP
ma-342	76	9	the	the	DET
ma-342	76	10	study	study	NOUN
ma-342	76	11	.	.	PUNCT
ma-342	77	1	2	2	X
ma-342	77	2	.	.	X
ma-342	77	3	description	description	NOUN
ma-342	77	4	of	of	ADP
ma-342	77	5	the	the	DET
ma-342	77	6	approachthe	approachthe	ADJ
ma-342	77	7	method	method	NOUN
ma-342	77	8	of	of	ADP
ma-342	77	9	extended	extended	ADJ
ma-342	77	10	tanh	tanh	NOUN
ma-342	77	11	is	be	AUX
ma-342	77	12	often	often	ADV
ma-342	77	13	employed	employ	VERB
ma-342	77	14	in	in	ADP
ma-342	77	15	obtaining	obtain	VERB
ma-342	77	16	soliton	soliton	NOUN
ma-342	77	17	solutions	solution	NOUN
ma-342	77	18	due	due	ADJ
ma-342	77	19	to	to	ADP
ma-342	77	20	is	be	AUX
ma-342	77	21	effectivenessin	effectivenessin	NOUN
ma-342	77	22	capturing	capture	VERB
ma-342	77	23	the	the	DET
ma-342	77	24	inherent	inherent	ADJ
ma-342	77	25	characteristics	characteristic	NOUN
ma-342	77	26	of	of	ADP
ma-342	77	27	solitons	soliton	NOUN
ma-342	77	28	such	such	ADJ
ma-342	77	29	as	as	ADP
ma-342	77	30	their	their	PRON
ma-342	77	31	amplitude	amplitude	NOUN
ma-342	77	32	,	,	PUNCT
ma-342	77	33	width	width	ADJ
ma-342	77	34	,	,	PUNCT
ma-342	77	35	and	and	CCONJ
ma-342	77	36	velocity.the	velocity.the	DET
ma-342	77	37	following	follow	VERB
ma-342	77	38	are	be	AUX
ma-342	77	39	some	some	PRON
ma-342	77	40	of	of	ADP
ma-342	77	41	the	the	DET
ma-342	77	42	rationale	rationale	NOUN
ma-342	77	43	for	for	ADP
ma-342	77	44	using	use	VERB
ma-342	77	45	the	the	DET
ma-342	77	46	method	method	NOUN
ma-342	77	47	:	:	PUNCT
ma-342	77	48	flexibility	flexibility	NOUN
ma-342	77	49	,	,	PUNCT
ma-342	77	50	asymptotic	asymptotic	ADJ
ma-342	77	51	behavior	behavior	NOUN
ma-342	77	52	,	,	PUNCT
ma-342	77	53	easeof	easeof	ADJ
ma-342	77	54	manipulation	manipulation	NOUN
ma-342	77	55	accuracy	accuracy	NOUN
ma-342	77	56	,	,	PUNCT
ma-342	77	57	existence	existence	NOUN
ma-342	77	58	of	of	ADP
ma-342	77	59	exact	exact	ADJ
ma-342	77	60	solutions.in	solutions.in	X
ma-342	77	61	order	order	NOUN
ma-342	77	62	to	to	PART
ma-342	77	63	present	present	VERB
ma-342	77	64	the	the	DET
ma-342	77	65	modified	modify	VERB
ma-342	77	66	extended	extend	VERB
ma-342	77	67	tanh	tanh	NOUN
ma-342	77	68	approach	approach	NOUN
ma-342	77	69	,	,	PUNCT
ma-342	77	70	we	we	PRON
ma-342	77	71	need	need	VERB
ma-342	77	72	to	to	PART
ma-342	77	73	consider	consider	VERB
ma-342	77	74	the	the	DET
ma-342	77	75	nonlinear	nonlinear	ADJ
ma-342	77	76	partialdifferential	partialdifferential	ADJ
ma-342	77	77	equation	equation	NOUN
ma-342	77	78	of	of	ADP
ma-342	77	79	the	the	DET
ma-342	77	80	form	form	NOUN
ma-342	77	81	:	:	PUNCT
ma-342	78	1	ρ	ρ	PROPN
ma-342	78	2	(	(	PUNCT
ma-342	78	3	u	u	NOUN
ma-342	78	4	,	,	PUNCT
ma-342	78	5	ux	ux	PROPN
ma-342	78	6	,	,	PUNCT
ma-342	78	7	uxx	uxx	PROPN
ma-342	78	8	,	,	PUNCT
ma-342	78	9	utux	utux	INTJ
ma-342	78	10	,	,	PUNCT
ma-342	78	11	...	...	PUNCT
ma-342	78	12	)	)	PUNCT
ma-342	79	1	=	=	PUNCT
ma-342	79	2	0	0	NUM
ma-342	79	3	;	;	PUNCT
ma-342	79	4	(	(	PUNCT
ma-342	79	5	2	2	X
ma-342	79	6	)	)	PUNCT
ma-342	79	7	in	in	ADP
ma-342	79	8	transforming	transform	VERB
ma-342	79	9	(	(	PUNCT
ma-342	79	10	2	2	NUM
ma-342	79	11	)	)	PUNCT
ma-342	79	12	;	;	PUNCT
ma-342	79	13	we	we	PRON
ma-342	79	14	use	use	VERB
ma-342	79	15	the	the	DET
ma-342	79	16	wave	wave	NOUN
ma-342	79	17	transformations	transformation	NOUN
ma-342	79	18	:	:	PUNCT
ma-342	79	19	u(x	u(x	NOUN
ma-342	79	20	,	,	PUNCT
ma-342	79	21	t	t	NOUN
ma-342	79	22	)	)	PUNCT
ma-342	79	23	=	=	SYM
ma-342	79	24	u(ξ	u(ξ	NOUN
ma-342	79	25	)	)	PUNCT
ma-342	79	26	;	;	PUNCT
ma-342	80	1	ξ	ξ	X
ma-342	80	2	=	=	SYM
ma-342	80	3	(	(	PUNCT
ma-342	80	4	x	x	NOUN
ma-342	80	5	−	−	NOUN
ma-342	80	6	µt	µt	NUM
ma-342	80	7	)	)	PUNCT
ma-342	80	8	(	(	PUNCT
ma-342	80	9	3	3	X
ma-342	80	10	)	)	PUNCT
ma-342	80	11	where	where	SCONJ
ma-342	80	12	µ	µ	NOUN
ma-342	80	13	is	be	AUX
ma-342	80	14	a	a	DET
ma-342	80	15	nonzero	nonzero	ADJ
ma-342	80	16	constant	constant	ADJ
ma-342	80	17	.	.	PUNCT
ma-342	80	18	substitution	substitution	NOUN
ma-342	80	19	of	of	ADP
ma-342	80	20	the	the	DET
ma-342	80	21	transformation	transformation	NOUN
ma-342	80	22	(	(	PUNCT
ma-342	80	23	3	3	NUM
ma-342	80	24	)	)	PUNCT
ma-342	80	25	into	into	ADP
ma-342	80	26	eq	eq	NOUN
ma-342	80	27	.	.	PUNCT
ma-342	80	28	(	(	PUNCT
ma-342	80	29	2	2	NUM
ma-342	80	30	)	)	PUNCT
ma-342	80	31	,	,	PUNCT
ma-342	80	32	it	it	PRON
ma-342	80	33	reduces	reduce	VERB
ma-342	80	34	to	to	ADP
ma-342	80	35	anordinary	anordinary	ADJ
ma-342	80	36	differential	differential	ADJ
ma-342	80	37	equation	equation	NOUN
ma-342	80	38	of	of	ADP
ma-342	80	39	the	the	DET
ma-342	80	40	polynomial	polynomial	ADJ
ma-342	80	41	form	form	NOUN
ma-342	80	42	:	:	PUNCT
ma-342	80	43	ξ	ξ	X
ma-342	80	44	(	(	PUNCT
ma-342	80	45	u(ξ	u(ξ	NOUN
ma-342	80	46	)	)	PUNCT
ma-342	80	47	,	,	PUNCT
ma-342	80	48	u	u	NOUN
ma-342	80	49	′(ξ	′(ξ	NOUN
ma-342	80	50	)	)	PUNCT
ma-342	80	51	,	,	PUNCT
ma-342	80	52	u	u	NOUN
ma-342	80	53	′′(ξ	′′(ξ	PROPN
ma-342	80	54	)	)	PUNCT
ma-342	80	55	,	,	PUNCT
ma-342	80	56	u	u	PROPN
ma-342	80	57	′′′(ξ	′′′(ξ	PROPN
ma-342	80	58	)	)	PUNCT
ma-342	80	59	,	,	PUNCT
ma-342	80	60	...	...	PUNCT
ma-342	80	61	)	)	PUNCT
ma-342	81	1	=	=	PUNCT
ma-342	81	2	0	0	X
ma-342	81	3	.	.	PUNCT
ma-342	82	1	(	(	PUNCT
ma-342	82	2	4	4	X
ma-342	82	3	)	)	PUNCT
ma-342	82	4	https://doi.org/10.28924/ada/ma.5.14	https://doi.org/10.28924/ada/ma.5.14	PROPN
ma-342	82	5	eur	eur	PROPN
ma-342	82	6	.	.	PUNCT
ma-342	83	1	j.	j.	PROPN
ma-342	83	2	math	math	PROPN
ma-342	83	3	.	.	PUNCT
ma-342	84	1	anal	anal	PROPN
ma-342	84	2	.	.	PUNCT
ma-342	85	1	10.28924	10.28924	NUM
ma-342	85	2	/	/	SYM
ma-342	85	3	ada	ada	PROPN
ma-342	85	4	/	/	SYM
ma-342	85	5	ma.5.14	ma.5.14	NOUN
ma-342	85	6	5furthermore	5furthermore	NUM
ma-342	85	7	,	,	PUNCT
ma-342	85	8	the	the	DET
ma-342	85	9	solution	solution	NOUN
ma-342	85	10	is	be	AUX
ma-342	85	11	considered	consider	VERB
ma-342	85	12	to	to	PART
ma-342	85	13	be	be	AUX
ma-342	85	14	a	a	DET
ma-342	85	15	finite	finite	ADJ
ma-342	85	16	series	series	NOUN
ma-342	85	17	of	of	ADP
ma-342	85	18	the	the	DET
ma-342	85	19	form	form	NOUN
ma-342	85	20	:	:	PUNCT
ma-342	85	21	u(ξ	u(ξ	NOUN
ma-342	85	22	)	)	PUNCT
ma-342	85	23	=	=	SYM
ma-342	85	24	a0	a0	PROPN
ma-342	85	25	+	+	CCONJ
ma-342	85	26	n	n	CCONJ
ma-342	85	27	=	=	PROPN
ma-342	85	28	n∑	n∑	PROPN
ma-342	85	29	n=1	n=1	PROPN
ma-342	85	30	anψ	anψ	PROPN
ma-342	85	31	n(ξ	n(ξ	PROPN
ma-342	85	32	)	)	PUNCT
ma-342	85	33	+	+	NUM
ma-342	85	34	n	n	CCONJ
ma-342	85	35	=	=	PROPN
ma-342	85	36	n∑	n∑	NOUN
ma-342	85	37	n=1	n=1	PROPN
ma-342	85	38	bn	bn	ADP
ma-342	85	39	ψn	ψn	INTJ
ma-342	85	40	(	(	PUNCT
ma-342	85	41	ξ	ξ	NOUN
ma-342	85	42	)	)	PUNCT
ma-342	85	43	(	(	PUNCT
ma-342	85	44	5	5	NUM
ma-342	85	45	)	)	PUNCT
ma-342	85	46	where	where	SCONJ
ma-342	85	47	,	,	PUNCT
ma-342	85	48	a0	a0	PROPN
ma-342	85	49	,	,	PUNCT
ma-342	85	50	an	an	PRON
ma-342	85	51	,	,	PUNCT
ma-342	85	52	bn	bn	NOUN
ma-342	85	53	,	,	PUNCT
ma-342	85	54	n	n	NOUN
ma-342	85	55	=	=	SYM
ma-342	85	56	1	1	NUM
ma-342	85	57	,	,	PUNCT
ma-342	85	58	2	2	NUM
ma-342	85	59	,	,	PUNCT
ma-342	85	60	3	3	NUM
ma-342	85	61	,	,	PUNCT
ma-342	85	62	...	...	PUNCT
ma-342	85	63	n	n	PRON
ma-342	85	64	are	be	AUX
ma-342	85	65	constants	constant	NOUN
ma-342	85	66	which	which	PRON
ma-342	85	67	to	to	PART
ma-342	85	68	be	be	AUX
ma-342	85	69	computed	compute	VERB
ma-342	85	70	;	;	PUNCT
ma-342	85	71	and	and	CCONJ
ma-342	85	72	n	n	PRON
ma-342	85	73	is	be	AUX
ma-342	85	74	a	a	DET
ma-342	85	75	positive	positive	ADJ
ma-342	85	76	integerwhich	integerwhich	NOUN
ma-342	85	77	is	be	AUX
ma-342	85	78	to	to	PART
ma-342	85	79	be	be	AUX
ma-342	85	80	determined	determine	VERB
ma-342	85	81	by	by	ADP
ma-342	85	82	balancing	balance	VERB
ma-342	85	83	the	the	DET
ma-342	85	84	highest	high	ADJ
ma-342	85	85	order	order	NOUN
ma-342	85	86	derivative	derivative	NOUN
ma-342	85	87	and	and	CCONJ
ma-342	85	88	with	with	ADP
ma-342	85	89	the	the	DET
ma-342	85	90	highest	high	ADJ
ma-342	85	91	nonlinearterms	nonlinearterm	NOUN
ma-342	85	92	in	in	ADP
ma-342	85	93	the	the	DET
ma-342	85	94	equation	equation	NOUN
ma-342	85	95	.	.	PUNCT
ma-342	86	1	also	also	ADV
ma-342	86	2	,	,	PUNCT
ma-342	86	3	ψ(ξ	ψ(ξ	PROPN
ma-342	86	4	)	)	PUNCT
ma-342	86	5	satisfies	satisfy	VERB
ma-342	86	6	the	the	DET
ma-342	86	7	riccati	riccati	NOUN
ma-342	86	8	’s	’s	PART
ma-342	86	9	differential	differential	ADJ
ma-342	86	10	equation	equation	NOUN
ma-342	86	11	:	:	PUNCT
ma-342	86	12	ψ′(ξ	ψ′(ξ	X
ma-342	86	13	)	)	PUNCT
ma-342	87	1	=	=	PUNCT
ma-342	87	2	ψ2(ξ	ψ2(ξ	NOUN
ma-342	87	3	)	)	PUNCT
ma-342	88	1	+	+	NUM
ma-342	88	2	b	b	X
ma-342	88	3	(	(	PUNCT
ma-342	88	4	6	6	NUM
ma-342	88	5	)	)	PUNCT
ma-342	88	6	where	where	SCONJ
ma-342	88	7	b	b	NOUN
ma-342	88	8	is	be	AUX
ma-342	88	9	a	a	DET
ma-342	88	10	constant	constant	ADJ
ma-342	88	11	.	.	PUNCT
ma-342	89	1	furthermore	furthermore	ADV
ma-342	89	2	,	,	PUNCT
ma-342	89	3	the	the	DET
ma-342	89	4	riccati	riccati	PROPN
ma-342	89	5	differential	differential	NOUN
ma-342	89	6	equation	equation	NOUN
ma-342	89	7	in	in	ADP
ma-342	89	8	(	(	PUNCT
ma-342	89	9	6	6	NUM
ma-342	89	10	)	)	PUNCT
ma-342	89	11	has	have	VERB
ma-342	89	12	solutions	solution	NOUN
ma-342	89	13	of	of	ADP
ma-342	89	14	theform	theform	NOUN
ma-342	89	15	:	:	PUNCT
ma-342	89	16	•	•	NOUN
ma-342	89	17	for	for	ADP
ma-342	89	18	hyperbolic	hyperbolic	ADJ
ma-342	89	19	solution	solution	NOUN
ma-342	89	20	,	,	PUNCT
ma-342	89	21	if	if	SCONJ
ma-342	89	22	b	b	PROPN
ma-342	89	23	<	<	X
ma-342	89	24	0	0	NUM
ma-342	89	25	,	,	PUNCT
ma-342	89	26	then	then	ADV
ma-342	89	27	φ(ξ	φ(ξ	PROPN
ma-342	89	28	)	)	PUNCT
ma-342	89	29	=	=	PUNCT
ma-342	89	30	−	−	PROPN
ma-342	89	31	√	√	NUM
ma-342	89	32	−b	−b	VERB
ma-342	89	33	tanh	tanh	PROPN
ma-342	89	34	√	√	PROPN
ma-342	89	35	−b	−b	ADP
ma-342	89	36	ξ	ξ	PROPN
ma-342	89	37	,	,	PUNCT
ma-342	89	38	φ(ξ	φ(ξ	PROPN
ma-342	89	39	)	)	PUNCT
ma-342	89	40	=	=	PUNCT
ma-342	90	1	−	−	PROPN
ma-342	90	2	√	√	NUM
ma-342	90	3	−b	−b	NOUN
ma-342	90	4	coth	coth	PROPN
ma-342	90	5	√	√	PROPN
ma-342	91	1	−b	−b	ADP
ma-342	91	2	ξ	ξ	NOUN
ma-342	91	3	•	•	NOUN
ma-342	91	4	for	for	ADP
ma-342	91	5	rational	rational	ADJ
ma-342	91	6	solution	solution	NOUN
ma-342	91	7	,	,	PUNCT
ma-342	91	8	if	if	SCONJ
ma-342	91	9	b	b	NOUN
ma-342	91	10	=	=	SYM
ma-342	91	11	0	0	NUM
ma-342	91	12	,	,	PUNCT
ma-342	91	13	then	then	ADV
ma-342	91	14	1	1	NUM
ma-342	91	15	ξ	ξ	NOUN
ma-342	91	16	•	•	NOUN
ma-342	91	17	for	for	ADP
ma-342	91	18	periodic	periodic	ADJ
ma-342	91	19	solution	solution	NOUN
ma-342	91	20	,	,	PUNCT
ma-342	91	21	if	if	SCONJ
ma-342	91	22	b	b	PROPN
ma-342	91	23	>	>	X
ma-342	91	24	0	0	NUM
ma-342	91	25	,	,	PUNCT
ma-342	91	26	then	then	ADV
ma-342	91	27	φ(ξ	φ(ξ	PROPN
ma-342	91	28	)	)	PUNCT
ma-342	91	29	=	=	SYM
ma-342	92	1	√	√	NUM
ma-342	92	2	b	b	X
ma-342	92	3	tan	tan	PROPN
ma-342	92	4	√	√	PROPN
ma-342	92	5	b	b	SYM
ma-342	92	6	ξ	ξ	PROPN
ma-342	92	7	,	,	PUNCT
ma-342	92	8	φ(ξ	φ(ξ	NOUN
ma-342	92	9	)	)	PUNCT
ma-342	92	10	=	=	SYM
ma-342	92	11	√	√	NUM
ma-342	92	12	b	b	NOUN
ma-342	92	13	cot	cot	NOUN
ma-342	92	14	−	−	NOUN
ma-342	92	15	√	√	PROPN
ma-342	92	16	−b	−b	ADJ
ma-342	92	17	ξnow	ξnow	NOUN
ma-342	92	18	,	,	PUNCT
ma-342	92	19	after	after	SCONJ
ma-342	92	20	we	we	PRON
ma-342	92	21	substitute	substitute	VERB
ma-342	92	22	eq	eq	ADP
ma-342	92	23	.	.	PUNCT
ma-342	93	1	(	(	PUNCT
ma-342	93	2	5	5	NUM
ma-342	93	3	)	)	PUNCT
ma-342	93	4	and	and	CCONJ
ma-342	93	5	its	its	PRON
ma-342	93	6	derivatives	derivative	NOUN
ma-342	93	7	together	together	ADV
ma-342	93	8	with	with	ADP
ma-342	93	9	the	the	DET
ma-342	93	10	riccati	riccati	PROPN
ma-342	93	11	eq	eq	PROPN
ma-342	93	12	.	.	PUNCT
ma-342	94	1	(	(	PUNCT
ma-342	94	2	6	6	NUM
ma-342	94	3	)	)	PUNCT
ma-342	94	4	,	,	PUNCT
ma-342	94	5	into	into	ADP
ma-342	94	6	eq.(4	eq.(4	ADJ
ma-342	94	7	)	)	PUNCT
ma-342	94	8	,	,	PUNCT
ma-342	94	9	it	it	PRON
ma-342	94	10	gives	give	VERB
ma-342	94	11	a	a	DET
ma-342	94	12	polynomial	polynomial	NOUN
ma-342	94	13	in	in	ADP
ma-342	94	14	φ(ξ	φ(ξ	PROPN
ma-342	94	15	)	)	PUNCT
ma-342	94	16	.	.	PUNCT
ma-342	95	1	collecting	collect	VERB
ma-342	95	2	the	the	DET
ma-342	95	3	coefficients	coefficient	NOUN
ma-342	95	4	of	of	ADP
ma-342	95	5	the	the	DET
ma-342	95	6	same	same	ADJ
ma-342	95	7	power	power	NOUN
ma-342	95	8	of	of	ADP
ma-342	95	9	φ(ξ	φ(ξ	PROPN
ma-342	95	10	)	)	PUNCT
ma-342	95	11	in	in	ADP
ma-342	95	12	thepolynomial	thepolynomial	ADJ
ma-342	95	13	and	and	CCONJ
ma-342	95	14	setting	set	VERB
ma-342	95	15	each	each	PRON
ma-342	95	16	of	of	ADP
ma-342	95	17	them	they	PRON
ma-342	95	18	to	to	ADP
ma-342	95	19	zero	zero	NUM
ma-342	95	20	,	,	PUNCT
ma-342	95	21	we	we	PRON
ma-342	95	22	shall	shall	AUX
ma-342	95	23	get	get	VERB
ma-342	95	24	a	a	DET
ma-342	95	25	set	set	NOUN
ma-342	95	26	of	of	ADP
ma-342	95	27	algebraic	algebraic	ADJ
ma-342	95	28	equations	equation	NOUN
ma-342	95	29	.	.	PUNCT
ma-342	96	1	solvingthese	solvingthese	ADJ
ma-342	96	2	system	system	NOUN
ma-342	96	3	of	of	ADP
ma-342	96	4	algebraic	algebraic	ADJ
ma-342	96	5	equation	equation	NOUN
ma-342	96	6	with	with	ADP
ma-342	96	7	the	the	DET
ma-342	96	8	aid	aid	NOUN
ma-342	96	9	of	of	ADP
ma-342	96	10	symbolic	symbolic	ADJ
ma-342	96	11	computation	computation	NOUN
ma-342	96	12	using	use	VERB
ma-342	96	13	mathematica	mathematica	PROPN
ma-342	96	14	to	to	ADP
ma-342	96	15	getthe	getthe	VERB
ma-342	96	16	values	value	NOUN
ma-342	96	17	of	of	ADP
ma-342	96	18	a0	a0	PROPN
ma-342	96	19	,	,	PUNCT
ma-342	96	20	an	an	PRON
ma-342	96	21	,	,	PUNCT
ma-342	96	22	bn	bn	NOUN
ma-342	96	23	,	,	PUNCT
ma-342	96	24	(	(	PUNCT
ma-342	96	25	n	n	NOUN
ma-342	96	26	=	=	SYM
ma-342	96	27	1	1	NUM
ma-342	96	28	,	,	PUNCT
ma-342	96	29	2	2	NUM
ma-342	96	30	,	,	PUNCT
ma-342	96	31	3	3	NUM
ma-342	96	32	,	,	PUNCT
ma-342	96	33	...	...	PUNCT
ma-342	96	34	)	)	PUNCT
ma-342	96	35	and	and	CCONJ
ma-342	96	36	b.	b.	PROPN
ma-342	96	37	finally	finally	ADV
ma-342	96	38	,	,	PUNCT
ma-342	96	39	substituting	substitute	VERB
ma-342	96	40	these	these	DET
ma-342	96	41	values	value	NOUN
ma-342	96	42	into	into	ADP
ma-342	96	43	eq	eq	NOUN
ma-342	96	44	.	.	PUNCT
ma-342	97	1	(	(	PUNCT
ma-342	97	2	5	5	X
ma-342	97	3	)	)	PUNCT
ma-342	97	4	fromwhich	fromwhich	NOUN
ma-342	97	5	we	we	PRON
ma-342	97	6	obtain	obtain	VERB
ma-342	97	7	the	the	DET
ma-342	97	8	solution	solution	NOUN
ma-342	97	9	of	of	ADP
ma-342	97	10	eq	eq	PROPN
ma-342	97	11	.	.	PUNCT
ma-342	98	1	(	(	PUNCT
ma-342	98	2	4	4	NUM
ma-342	98	3	)	)	PUNCT
ma-342	98	4	.	.	PUNCT
ma-342	99	1	3	3	X
ma-342	99	2	.	.	X
ma-342	99	3	applicationin	applicationin	ADJ
ma-342	99	4	this	this	DET
ma-342	99	5	section	section	NOUN
ma-342	99	6	,	,	PUNCT
ma-342	99	7	the	the	DET
ma-342	99	8	application	application	NOUN
ma-342	99	9	of	of	ADP
ma-342	99	10	the	the	DET
ma-342	99	11	modified	modify	VERB
ma-342	99	12	extended	extend	VERB
ma-342	99	13	tanh	tanh	NOUN
ma-342	99	14	expansion	expansion	NOUN
ma-342	99	15	method	method	NOUN
ma-342	99	16	with	with	ADP
ma-342	99	17	riccati	riccati	PROPN
ma-342	99	18	differ	differ	VERB
ma-342	99	19	-	-	PUNCT
ma-342	99	20	ential	ential	ADJ
ma-342	99	21	equation	equation	NOUN
ma-342	99	22	[	[	X
ma-342	99	23	49	49	NUM
ma-342	99	24	]	]	PUNCT
ma-342	99	25	to	to	ADP
ma-342	99	26	our	our	PRON
ma-342	99	27	equation	equation	NOUN
ma-342	99	28	(	(	PUNCT
ma-342	99	29	1	1	X
ma-342	99	30	)	)	PUNCT
ma-342	99	31	shall	shall	AUX
ma-342	99	32	be	be	AUX
ma-342	99	33	presented.consider	presented.consider	NUM
ma-342	99	34	the	the	DET
ma-342	99	35	transformation	transformation	NOUN
ma-342	99	36	:	:	PUNCT
ma-342	99	37	φ(x	φ(x	PROPN
ma-342	99	38	,	,	PUNCT
ma-342	99	39	t	t	NOUN
ma-342	99	40	)	)	PUNCT
ma-342	99	41	=	=	PRON
ma-342	100	1	φ(ξ)e	φ(ξ)e	VERB
ma-342	100	2	i$	i$	NOUN
ma-342	100	3	;	;	PUNCT
ma-342	100	4	ξ	ξ	X
ma-342	100	5	=	=	SYM
ma-342	100	6	x	x	SYM
ma-342	100	7	−	−	NOUN
ma-342	100	8	νt	νt	NOUN
ma-342	100	9	and	and	CCONJ
ma-342	100	10	$	$	SYM
ma-342	100	11	=	=	PRON
ma-342	100	12	ωx	ωx	NUM
ma-342	100	13	−	−	NOUN
ma-342	100	14	r	r	NOUN
ma-342	100	15	t	t	NOUN
ma-342	100	16	+	+	CCONJ
ma-342	100	17	δ	δ	PROPN
ma-342	100	18	(	(	PUNCT
ma-342	100	19	7	7	X
ma-342	100	20	)	)	PUNCT
ma-342	100	21	substituting	substitute	VERB
ma-342	100	22	equation	equation	NOUN
ma-342	100	23	(	(	PUNCT
ma-342	100	24	7	7	NUM
ma-342	100	25	)	)	PUNCT
ma-342	100	26	into	into	ADP
ma-342	100	27	equation	equation	NOUN
ma-342	100	28	(	(	PUNCT
ma-342	100	29	1	1	NUM
ma-342	100	30	)	)	PUNCT
ma-342	100	31	,	,	PUNCT
ma-342	100	32	gives	give	VERB
ma-342	100	33	the	the	DET
ma-342	100	34	following	follow	VERB
ma-342	100	35	nonlinear	nonlinear	ADJ
ma-342	100	36	ode	ode	NOUN
ma-342	100	37	:	:	PUNCT
ma-342	100	38	2λ2φ2φ′′	2λ2φ2φ′′	NUM
ma-342	101	1	+	+	CCONJ
ma-342	101	2	λ1φ′′	λ1φ′′	ADV
ma-342	101	3	+	+	CCONJ
ma-342	101	4	λ4φ5	λ4φ5	PROPN
ma-342	101	5	+	+	CCONJ
ma-342	101	6	λ3φ3	λ3φ3	X
ma-342	101	7	+	+	NUM
ma-342	101	8	φ	φ	PROPN
ma-342	101	9	(	(	PUNCT
ma-342	101	10	2λ2φ′2	2λ2φ′2	NUM
ma-342	101	11	−	−	NOUN
ma-342	101	12	λ1ω	λ1ω	ADP
ma-342	101	13	2	2	NUM
ma-342	101	14	+	+	CCONJ
ma-342	101	15	r	r	NOUN
ma-342	101	16	)	)	PUNCT
ma-342	101	17	=	=	SYM
ma-342	101	18	0	0	X
ma-342	101	19	.	.	PUNCT
ma-342	102	1	(	(	PUNCT
ma-342	102	2	8)	8)	NUM
ma-342	102	3	from	from	ADP
ma-342	102	4	the	the	DET
ma-342	102	5	real	real	ADJ
ma-342	102	6	part	part	NOUN
ma-342	102	7	and	and	CCONJ
ma-342	102	8	(	(	PUNCT
ma-342	102	9	v	v	NOUN
ma-342	102	10	−	−	PROPN
ma-342	102	11	2λ1ω	2λ1ω	NUM
ma-342	102	12	)	)	PUNCT
ma-342	102	13	φ′	φ′	NUM
ma-342	102	14	=	=	SYM
ma-342	102	15	0	0	X
ma-342	102	16	.	.	PUNCT
ma-342	103	1	(	(	PUNCT
ma-342	103	2	9	9	NUM
ma-342	103	3	)	)	PUNCT
ma-342	103	4	from	from	ADP
ma-342	103	5	the	the	DET
ma-342	103	6	imaginary	imaginary	ADJ
ma-342	103	7	part	part	NOUN
ma-342	103	8	.	.	PUNCT
ma-342	104	1	thus	thus	ADV
ma-342	104	2	,	,	PUNCT
ma-342	104	3	we	we	PRON
ma-342	104	4	have	have	VERB
ma-342	104	5	the	the	DET
ma-342	104	6	constraint	constraint	NOUN
ma-342	104	7	condition	condition	NOUN
ma-342	104	8	as	as	ADP
ma-342	104	9	v	v	NOUN
ma-342	104	10	=	=	SYM
ma-342	104	11	2λ1ω	2λ1ω	ADJ
ma-342	104	12	.	.	PUNCT
ma-342	105	1	(	(	PUNCT
ma-342	105	2	10	10	NUM
ma-342	105	3	)	)	PUNCT
ma-342	105	4	https://doi.org/10.28924/ada/ma.5.14	https://doi.org/10.28924/ada/ma.5.14	PROPN
ma-342	105	5	eur	eur	PROPN
ma-342	105	6	.	.	PUNCT
ma-342	106	1	j.	j.	PROPN
ma-342	106	2	math	math	PROPN
ma-342	106	3	.	.	PUNCT
ma-342	107	1	anal	anal	PROPN
ma-342	107	2	.	.	PUNCT
ma-342	108	1	10.28924	10.28924	NUM
ma-342	108	2	/	/	SYM
ma-342	108	3	ada	ada	PROPN
ma-342	108	4	/	/	SYM
ma-342	108	5	ma.5.14	ma.5.14	NOUN
ma-342	109	1	6balancing	6balancing	NUM
ma-342	109	2	between	between	ADP
ma-342	109	3	φ2φ′′	φ2φ′′	PROPN
ma-342	109	4	and	and	CCONJ
ma-342	109	5	φ5	φ5	PROPN
ma-342	109	6	,	,	PUNCT
ma-342	109	7	that	that	ADV
ma-342	109	8	is	be	AUX
ma-342	109	9	:	:	PUNCT
ma-342	109	10	2n	2n	NUM
ma-342	109	11	+	+	CCONJ
ma-342	109	12	n	n	PROPN
ma-342	109	13	+	+	CCONJ
ma-342	109	14	2	2	NUM
ma-342	109	15	=	=	NOUN
ma-342	109	16	5n	5n	NOUN
ma-342	109	17	=	=	NOUN
ma-342	109	18	⇒	⇒	NOUN
ma-342	109	19	n	n	NOUN
ma-342	109	20	=	=	SYM
ma-342	109	21	1	1	X
ma-342	109	22	.	.	PUNCT
ma-342	110	1	(	(	PUNCT
ma-342	110	2	11	11	NUM
ma-342	110	3	)	)	PUNCT
ma-342	110	4	with	with	ADP
ma-342	110	5	equation	equation	NOUN
ma-342	110	6	(	(	PUNCT
ma-342	110	7	11	11	NUM
ma-342	110	8	)	)	PUNCT
ma-342	110	9	,	,	PUNCT
ma-342	110	10	our	our	PRON
ma-342	110	11	equation	equation	NOUN
ma-342	110	12	(	(	PUNCT
ma-342	110	13	5	5	X
ma-342	110	14	)	)	PUNCT
ma-342	110	15	takes	take	VERB
ma-342	110	16	the	the	DET
ma-342	110	17	form	form	NOUN
ma-342	110	18	:	:	PUNCT
ma-342	110	19	φ(ω	φ(ω	X
ma-342	110	20	)	)	PUNCT
ma-342	110	21	=	=	SYM
ma-342	110	22	a1φ(ω	a1φ(ω	PROPN
ma-342	110	23	)	)	PUNCT
ma-342	111	1	+	+	CCONJ
ma-342	111	2	a0	a0	NOUN
ma-342	111	3	+	+	CCONJ
ma-342	111	4	b1	b1	PROPN
ma-342	111	5	φ(ω	φ(ω	PROPN
ma-342	111	6	)	)	PUNCT
ma-342	111	7	(	(	PUNCT
ma-342	111	8	12	12	X
ma-342	111	9	)	)	PUNCT
ma-342	111	10	substituting	substitute	VERB
ma-342	111	11	eq	eq	NOUN
ma-342	111	12	.	.	PUNCT
ma-342	112	1	(	(	PUNCT
ma-342	112	2	12	12	NUM
ma-342	112	3	)	)	PUNCT
ma-342	112	4	,	,	PUNCT
ma-342	112	5	its	its	PRON
ma-342	112	6	first	first	ADJ
ma-342	112	7	and	and	CCONJ
ma-342	112	8	second	second	ADJ
ma-342	112	9	derivative	derivative	NOUN
ma-342	112	10	along	along	ADP
ma-342	112	11	with	with	ADP
ma-342	112	12	equation	equation	NOUN
ma-342	112	13	(	(	PUNCT
ma-342	112	14	6	6	NUM
ma-342	112	15	)	)	PUNCT
ma-342	112	16	into	into	ADP
ma-342	112	17	equation	equation	NOUN
ma-342	112	18	(	(	PUNCT
ma-342	112	19	8)	8)	NUM
ma-342	112	20	,	,	PUNCT
ma-342	112	21	weget	weget	VERB
ma-342	112	22	a	a	DET
ma-342	112	23	polynomial	polynomial	NOUN
ma-342	112	24	in	in	ADP
ma-342	112	25	powers	power	NOUN
ma-342	112	26	of	of	ADP
ma-342	112	27	φ(ω	φ(ω	PROPN
ma-342	112	28	)	)	PUNCT
ma-342	112	29	.	.	PUNCT
ma-342	113	1	summing	sum	VERB
ma-342	113	2	the	the	DET
ma-342	113	3	coefficients	coefficient	NOUN
ma-342	113	4	of	of	ADP
ma-342	113	5	φ(ω	φ(ω	NOUN
ma-342	113	6	)	)	PUNCT
ma-342	113	7	with	with	ADP
ma-342	113	8	the	the	DET
ma-342	113	9	same	same	ADJ
ma-342	113	10	power	power	NOUN
ma-342	113	11	andequating	andequate	VERB
ma-342	113	12	each	each	DET
ma-342	113	13	summation	summation	NOUN
ma-342	113	14	to	to	ADP
ma-342	113	15	zero	zero	NUM
ma-342	113	16	,	,	PUNCT
ma-342	113	17	gives	give	VERB
ma-342	113	18	a	a	DET
ma-342	113	19	set	set	NOUN
ma-342	113	20	of	of	ADP
ma-342	113	21	algebraic	algebraic	ADJ
ma-342	113	22	equations	equation	NOUN
ma-342	113	23	.	.	PUNCT
ma-342	114	1	solving	solve	VERB
ma-342	114	2	these	these	DET
ma-342	114	3	set	set	NOUN
ma-342	114	4	of	of	ADP
ma-342	114	5	algebraicequations	algebraicequation	NOUN
ma-342	114	6	,	,	PUNCT
ma-342	114	7	yields	yield	VERB
ma-342	114	8	the	the	DET
ma-342	114	9	following	follow	VERB
ma-342	114	10	cases	case	NOUN
ma-342	114	11	of	of	ADP
ma-342	114	12	solutions	solution	NOUN
ma-342	114	13	:	:	PUNCT
ma-342	114	14	case	case	NOUN
ma-342	114	15	onewhen	onewhen	ADV
ma-342	114	16	a0	a0	PROPN
ma-342	114	17	=	=	PROPN
ma-342	114	18	0	0	NUM
ma-342	114	19	;	;	PUNCT
ma-342	114	20	a1	a1	NOUN
ma-342	114	21	=	=	PUNCT
ma-342	114	22	−	−	PROPN
ma-342	115	1	i	i	PRON
ma-342	115	2	√	√	VERB
ma-342	115	3	6	6	NUM
ma-342	115	4	√	√	NOUN
ma-342	115	5	λ2√	λ2√	NUM
ma-342	115	6	λ4	λ4	NOUN
ma-342	115	7	;	;	PUNCT
ma-342	115	8	b1	b1	NOUN
ma-342	115	9	=	=	SYM
ma-342	115	10	0	0	NUM
ma-342	115	11	;	;	PUNCT
ma-342	115	12	r	r	NOUN
ma-342	115	13	→	→	SYM
ma-342	115	14	1	1	NUM
ma-342	115	15	16	16	NUM
ma-342	115	16	(	(	PUNCT
ma-342	115	17	λ1	λ1	PROPN
ma-342	115	18	(	(	PUNCT
ma-342	115	19	2λ3	2λ3	NUM
ma-342	115	20	λ2	λ2	NOUN
ma-342	115	21	+	+	CCONJ
ma-342	115	22	16ω2	16ω2	NUM
ma-342	115	23	)	)	PUNCT
ma-342	115	24	−	−	PROPN
ma-342	116	1	λ4λ	λ4λ	X
ma-342	116	2	2	2	NUM
ma-342	116	3	1	1	NUM
ma-342	116	4	λ2	λ2	NOUN
ma-342	116	5	2	2	NUM
ma-342	116	6	+	+	CCONJ
ma-342	116	7	3λ2	3λ2	NUM
ma-342	116	8	3	3	NUM
ma-342	116	9	λ4	λ4	NOUN
ma-342	116	10	)	)	PUNCT
ma-342	116	11	;	;	PUNCT
ma-342	116	12	w	w	X
ma-342	116	13	=	=	VERB
ma-342	116	14	λ1λ4−3λ2λ3	λ1λ4−3λ2λ3	NOUN
ma-342	116	15	24λ2	24λ2	NUM
ma-342	116	16	2	2	NUM
ma-342	116	17	,	,	PUNCT
ma-342	116	18	we	we	PRON
ma-342	116	19	obtain	obtain	VERB
ma-342	116	20	the	the	DET
ma-342	116	21	following	follow	VERB
ma-342	116	22	solutions	solution	NOUN
ma-342	116	23	to	to	ADP
ma-342	116	24	equation	equation	NOUN
ma-342	116	25	(	(	PUNCT
ma-342	116	26	3):if	3):if	NUM
ma-342	116	27	w	w	ADP
ma-342	116	28	<	<	X
ma-342	116	29	0	0	NUM
ma-342	116	30	,	,	PUNCT
ma-342	116	31	then	then	ADV
ma-342	116	32	we	we	PRON
ma-342	116	33	have	have	VERB
ma-342	116	34	φ1(ξ	φ1(ξ	NUM
ma-342	116	35	)	)	PUNCT
ma-342	116	36	=	=	SYM
ma-342	116	37	±	±	NOUN
ma-342	117	1	i	i	NOUN
ma-342	117	2	√	√	VERB
ma-342	117	3	3λ2λ3	3λ2λ3	NUM
ma-342	117	4	−	−	NOUN
ma-342	118	1	λ1λ4	λ1λ4	NOUN
ma-342	118	2	tanh	tanh	PROPN
ma-342	118	3	(	(	PUNCT
ma-342	118	4	√	√	NUM
ma-342	118	5	3λ2λ3−λ1λ4ω	3λ2λ3−λ1λ4ω	NUM
ma-342	118	6	2	2	NUM
ma-342	118	7	√	√	NUM
ma-342	118	8	6λ2	6λ2	NUM
ma-342	118	9	)	)	PUNCT
ma-342	118	10	2	2	NUM
ma-342	118	11	√	√	NUM
ma-342	118	12	λ2	λ2	NOUN
ma-342	118	13	√	√	PUNCT
ma-342	118	14	λ4	λ4	PROPN
ma-342	118	15	e	e	PROPN
ma-342	118	16	i(ωx−r	i(ωx−r	NOUN
ma-342	118	17	t+δ	t+δ	PROPN
ma-342	118	18	)	)	PUNCT
ma-342	118	19	.	.	PUNCT
ma-342	119	1	(	(	PUNCT
ma-342	119	2	13	13	NUM
ma-342	119	3	)	)	PUNCT
ma-342	119	4	φ2(ξ	φ2(ξ	NOUN
ma-342	119	5	)	)	PUNCT
ma-342	119	6	=	=	SYM
ma-342	119	7	±	±	NOUN
ma-342	120	1	i	i	PRON
ma-342	120	2	√	√	VERB
ma-342	120	3	3λ2λ3	3λ2λ3	NUM
ma-342	120	4	−	−	NOUN
ma-342	121	1	λ1λ4	λ1λ4	INTJ
ma-342	121	2	coth	coth	NOUN
ma-342	121	3	(	(	PUNCT
ma-342	121	4	√	√	NUM
ma-342	121	5	3λ2λ3−λ1λ4ω	3λ2λ3−λ1λ4ω	NUM
ma-342	121	6	2	2	NUM
ma-342	121	7	√	√	NUM
ma-342	121	8	6λ2	6λ2	NUM
ma-342	121	9	)	)	PUNCT
ma-342	121	10	2	2	NUM
ma-342	121	11	√	√	NUM
ma-342	121	12	λ2	λ2	NOUN
ma-342	121	13	√	√	PUNCT
ma-342	121	14	λ4	λ4	PROPN
ma-342	121	15	e	e	PROPN
ma-342	121	16	i(ωx−r	i(ωx−r	NOUN
ma-342	121	17	t+δ	t+δ	PROPN
ma-342	121	18	)	)	PUNCT
ma-342	121	19	.	.	PUNCT
ma-342	122	1	(	(	PUNCT
ma-342	122	2	14)if	14)if	NUM
ma-342	122	3	w	w	ADP
ma-342	122	4	>	>	X
ma-342	122	5	0	0	NUM
ma-342	122	6	,	,	PUNCT
ma-342	122	7	then	then	ADV
ma-342	122	8	we	we	PRON
ma-342	122	9	have	have	VERB
ma-342	122	10	φ3(ξ	φ3(ξ	PRON
ma-342	122	11	)	)	PUNCT
ma-342	122	12	=	=	PUNCT
ma-342	123	1	∓−	∓−	NOUN
ma-342	124	1	i	i	PRON
ma-342	124	2	√	√	VERB
ma-342	125	1	λ1λ4	λ1λ4	ADP
ma-342	125	2	−	−	PROPN
ma-342	125	3	3λ2λ3	3λ2λ3	NUM
ma-342	125	4	tan	tan	NOUN
ma-342	125	5	(	(	PUNCT
ma-342	125	6	√	√	ADP
ma-342	125	7	λ1λ4−3λ2λ3ω	λ1λ4−3λ2λ3ω	ADJ
ma-342	125	8	2	2	NUM
ma-342	125	9	√	√	NUM
ma-342	125	10	6λ2	6λ2	NUM
ma-342	125	11	)	)	PUNCT
ma-342	125	12	2	2	NUM
ma-342	125	13	√	√	NUM
ma-342	125	14	λ2	λ2	NOUN
ma-342	125	15	√	√	PUNCT
ma-342	125	16	λ4	λ4	PROPN
ma-342	125	17	e	e	PROPN
ma-342	125	18	i(ωx−r	i(ωx−r	NOUN
ma-342	125	19	t+δ	t+δ	PROPN
ma-342	125	20	)	)	PUNCT
ma-342	125	21	.	.	PUNCT
ma-342	126	1	(	(	PUNCT
ma-342	126	2	15	15	X
ma-342	126	3	)	)	PUNCT
ma-342	126	4	φ4(ξ	φ4(ξ	NOUN
ma-342	126	5	)	)	PUNCT
ma-342	126	6	=	=	SYM
ma-342	126	7	±	±	NOUN
ma-342	127	1	i	i	PRON
ma-342	127	2	√	√	VERB
ma-342	128	1	λ1λ4	λ1λ4	ADP
ma-342	128	2	−	−	PROPN
ma-342	128	3	3λ2λ3	3λ2λ3	NUM
ma-342	128	4	cot	cot	NOUN
ma-342	128	5	(	(	PUNCT
ma-342	128	6	√	√	ADP
ma-342	128	7	λ1λ4−3λ2λ3ω	λ1λ4−3λ2λ3ω	ADJ
ma-342	128	8	2	2	NUM
ma-342	128	9	√	√	NUM
ma-342	128	10	6λ2	6λ2	NUM
ma-342	128	11	)	)	PUNCT
ma-342	128	12	2	2	NUM
ma-342	128	13	√	√	NUM
ma-342	128	14	λ2	λ2	NOUN
ma-342	128	15	√	√	PUNCT
ma-342	128	16	λ4	λ4	PROPN
ma-342	128	17	e	e	PROPN
ma-342	128	18	i(ωx−r	i(ωx−r	NOUN
ma-342	128	19	t+δ	t+δ	PROPN
ma-342	128	20	)	)	PUNCT
ma-342	128	21	.	.	PUNCT
ma-342	129	1	(	(	PUNCT
ma-342	129	2	16	16	NUM
ma-342	129	3	)	)	PUNCT
ma-342	129	4	case	case	NOUN
ma-342	129	5	twowhen	twowhen	NOUN
ma-342	129	6	a0	a0	PROPN
ma-342	129	7	=	=	SYM
ma-342	129	8	0	0	NUM
ma-342	129	9	;	;	PUNCT
ma-342	129	10	a1	a1	NOUN
ma-342	129	11	=	=	NOUN
ma-342	129	12	i	i	NOUN
ma-342	129	13	√	√	VERB
ma-342	129	14	6	6	NUM
ma-342	129	15	√	√	NOUN
ma-342	129	16	λ2√	λ2√	NUM
ma-342	129	17	λ4	λ4	NOUN
ma-342	129	18	;	;	PUNCT
ma-342	129	19	b1	b1	NOUN
ma-342	129	20	=	=	SYM
ma-342	130	1	i(3λ2λ3−λ1λ4	i(3λ2λ3−λ1λ4	ADJ
ma-342	130	2	)	)	PUNCT
ma-342	130	3	8	8	NUM
ma-342	130	4	√	√	NUM
ma-342	130	5	6λ	6λ	NUM
ma-342	130	6	3/2	3/2	NUM
ma-342	130	7	2	2	NUM
ma-342	130	8	√	√	NOUN
ma-342	130	9	λ4	λ4	NOUN
ma-342	130	10	;	;	PUNCT
ma-342	131	1	r	r	NOUN
ma-342	131	2	=	=	SYM
ma-342	131	3	λ1(3λ2(4λ2ω	λ1(3λ2(4λ2ω	PROPN
ma-342	131	4	2+λ3)−λ1λ4	2+λ3)−λ1λ4	PROPN
ma-342	131	5	)	)	PUNCT
ma-342	131	6	12λ2	12λ2	NUM
ma-342	131	7	2	2	NUM
ma-342	131	8	;	;	PUNCT
ma-342	131	9	w	w	X
ma-342	131	10	=	=	PUNCT
ma-342	131	11	3λ2λ3−λ1λ4	3λ2λ3−λ1λ4	NUM
ma-342	131	12	48λ2	48λ2	NUM
ma-342	131	13	2	2	NUM
ma-342	131	14	;	;	PUNCT
ma-342	131	15	we	we	PRON
ma-342	131	16	obtain	obtain	VERB
ma-342	131	17	the	the	DET
ma-342	131	18	following	follow	VERB
ma-342	131	19	solutions	solution	NOUN
ma-342	131	20	to	to	ADP
ma-342	131	21	equation	equation	NOUN
ma-342	131	22	(	(	PUNCT
ma-342	131	23	1):if	1):if	NUM
ma-342	131	24	w	w	NOUN
ma-342	131	25	<	<	X
ma-342	131	26	0	0	NUM
ma-342	131	27	,	,	PUNCT
ma-342	131	28	then	then	ADV
ma-342	131	29	we	we	PRON
ma-342	131	30	have	have	VERB
ma-342	131	31	φ5(ξ	φ5(ξ	NUM
ma-342	131	32	)	)	PUNCT
ma-342	131	33	=	=	SYM
ma-342	131	34	±	±	NOUN
ma-342	132	1	i	i	PRON
ma-342	132	2	√	√	VERB
ma-342	133	1	λ1λ4	λ1λ4	ADP
ma-342	133	2	−	−	NUM
ma-342	134	1	3λ2λ3csch(√	3λ2λ3csch(√	NUM
ma-342	134	2	λ1λ4	λ1λ4	NOUN
ma-342	134	3	3	3	NUM
ma-342	134	4	−λ2λ3ω	−λ2λ3ω	ADV
ma-342	134	5	2λ2	2λ2	NUM
ma-342	134	6	)	)	PUNCT
ma-342	134	7	√	√	ADV
ma-342	135	1	2	2	NUM
ma-342	135	2	√	√	NUM
ma-342	135	3	λ2	λ2	NOUN
ma-342	135	4	√	√	PUNCT
ma-342	135	5	λ4	λ4	PROPN
ma-342	135	6	e	e	PROPN
ma-342	135	7	i(ωx−r	i(ωx−r	NOUN
ma-342	135	8	t+δ	t+δ	PROPN
ma-342	135	9	)	)	PUNCT
ma-342	135	10	.	.	PUNCT
ma-342	136	1	(	(	PUNCT
ma-342	136	2	17	17	NUM
ma-342	136	3	)	)	PUNCT
ma-342	136	4	if	if	SCONJ
ma-342	136	5	w	w	PROPN
ma-342	136	6	>	>	X
ma-342	136	7	0	0	NUM
ma-342	136	8	,	,	PUNCT
ma-342	136	9	then	then	ADV
ma-342	136	10	we	we	PRON
ma-342	136	11	have	have	VERB
ma-342	136	12	φ6(ξ	φ6(ξ	NOUN
ma-342	136	13	)	)	PUNCT
ma-342	136	14	=	=	VERB
ma-342	137	1	∓	∓	NOUN
ma-342	138	1	i	i	PRON
ma-342	138	2	√	√	VERB
ma-342	138	3	3λ2λ3	3λ2λ3	NUM
ma-342	138	4	−	−	NOUN
ma-342	139	1	λ1λ4	λ1λ4	INTJ
ma-342	139	2	csc	csc	PROPN
ma-342	139	3	(	(	PUNCT
ma-342	139	4	√	√	PROPN
ma-342	139	5	λ2λ3−	λ2λ3−	CCONJ
ma-342	139	6	λ1λ4	λ1λ4	PROPN
ma-342	139	7	3	3	NUM
ma-342	139	8	ω	ω	NUM
ma-342	139	9	2λ2	2λ2	NUM
ma-342	139	10	)	)	PUNCT
ma-342	139	11	√	√	ADV
ma-342	139	12	2	2	NUM
ma-342	139	13	√	√	NUM
ma-342	139	14	λ2	λ2	NOUN
ma-342	139	15	√	√	PUNCT
ma-342	139	16	λ4	λ4	PROPN
ma-342	139	17	e	e	PROPN
ma-342	139	18	i(ωx−r	i(ωx−r	NOUN
ma-342	139	19	t+δ	t+δ	PROPN
ma-342	139	20	)	)	PUNCT
ma-342	139	21	.	.	PUNCT
ma-342	140	1	(	(	PUNCT
ma-342	140	2	18	18	NUM
ma-342	140	3	)	)	PUNCT
ma-342	140	4	https://doi.org/10.28924/ada/ma.5.14	https://doi.org/10.28924/ada/ma.5.14	PROPN
ma-342	140	5	eur	eur	PROPN
ma-342	140	6	.	.	PUNCT
ma-342	141	1	j.	j.	PROPN
ma-342	141	2	math	math	PROPN
ma-342	141	3	.	.	PUNCT
ma-342	142	1	anal	anal	PROPN
ma-342	142	2	.	.	PUNCT
ma-342	143	1	10.28924	10.28924	NUM
ma-342	143	2	/	/	SYM
ma-342	143	3	ada	ada	PROPN
ma-342	143	4	/	/	SYM
ma-342	143	5	ma.5.14	ma.5.14	PROPN
ma-342	143	6	7	7	NUM
ma-342	143	7	4	4	NUM
ma-342	143	8	.	.	PUNCT
ma-342	143	9	graphical	graphical	ADJ
ma-342	143	10	representations	representation	NOUN
ma-342	143	11	of	of	ADP
ma-342	143	12	resultsin	resultsin	NOUN
ma-342	143	13	this	this	DET
ma-342	143	14	section	section	NOUN
ma-342	143	15	,	,	PUNCT
ma-342	143	16	the	the	DET
ma-342	143	17	2d	2d	NOUN
ma-342	143	18	and	and	CCONJ
ma-342	143	19	3d	3d	NUM
ma-342	143	20	graphical	graphical	ADJ
ma-342	143	21	representation	representation	NOUN
ma-342	143	22	for	for	ADP
ma-342	143	23	some	some	PRON
ma-342	143	24	of	of	ADP
ma-342	143	25	the	the	DET
ma-342	143	26	obtained	obtain	VERB
ma-342	143	27	results	result	NOUN
ma-342	143	28	for	for	ADP
ma-342	143	29	theweakly	theweakly	DET
ma-342	143	30	nonlocal	nonlocal	ADJ
ma-342	143	31	nlse	nlse	NOUN
ma-342	143	32	having	have	VERB
ma-342	143	33	pl	pl	NOUN
ma-342	143	34	nonlinearity	nonlinearity	NOUN
ma-342	143	35	,	,	PUNCT
ma-342	143	36	which	which	PRON
ma-342	143	37	is	be	AUX
ma-342	143	38	given	give	VERB
ma-342	143	39	by	by	ADP
ma-342	143	40	equations	equation	NOUN
ma-342	143	41	(	(	PUNCT
ma-342	143	42	1	1	X
ma-342	143	43	)	)	PUNCT
ma-342	143	44	shall	shall	AUX
ma-342	143	45	be	be	AUX
ma-342	143	46	presentedby	presentedby	ADV
ma-342	143	47	choosing	choose	VERB
ma-342	143	48	different	different	ADJ
ma-342	143	49	values	value	NOUN
ma-342	143	50	of	of	ADP
ma-342	143	51	parameters	parameter	NOUN
ma-342	143	52	that	that	PRON
ma-342	143	53	are	be	AUX
ma-342	143	54	involved	involve	VERB
ma-342	143	55	.	.	PUNCT
ma-342	144	1	figure	figure	VERB
ma-342	144	2	1	1	NUM
ma-342	144	3	.	.	X
ma-342	145	1	3d	3d	NUM
ma-342	145	2	and	and	CCONJ
ma-342	145	3	2d	2d	NUM
ma-342	145	4	abs	ab	NOUN
ma-342	145	5	plot	plot	NOUN
ma-342	145	6	for	for	ADP
ma-342	145	7	φ1(ξ	φ1(ξ	NOUN
ma-342	145	8	)	)	PUNCT
ma-342	145	9	.	.	PUNCT
ma-342	146	1	in	in	ADP
ma-342	146	2	figure	figure	NOUN
ma-342	146	3	(	(	PUNCT
ma-342	146	4	1	1	NUM
ma-342	146	5	)	)	PUNCT
ma-342	146	6	above	above	ADV
ma-342	146	7	,	,	PUNCT
ma-342	146	8	we	we	PRON
ma-342	146	9	have	have	VERB
ma-342	146	10	the	the	DET
ma-342	146	11	surface	surface	NOUN
ma-342	146	12	profile	profile	NOUN
ma-342	146	13	of	of	ADP
ma-342	146	14	2d	2d	NUM
ma-342	146	15	and	and	CCONJ
ma-342	146	16	3d	3d	NUM
ma-342	146	17	absolute	absolute	ADJ
ma-342	146	18	plot	plot	NOUN
ma-342	146	19	represen	represen	NOUN
ma-342	146	20	-	-	PUNCT
ma-342	146	21	tation	tation	NOUN
ma-342	146	22	of	of	ADP
ma-342	146	23	equation	equation	NOUN
ma-342	146	24	(	(	PUNCT
ma-342	146	25	13	13	NUM
ma-342	146	26	)	)	PUNCT
ma-342	146	27	(	(	PUNCT
ma-342	146	28	that	that	ADV
ma-342	146	29	is	is	ADV
ma-342	146	30	,	,	PUNCT
ma-342	146	31	φ1(ξ	φ1(ξ	PROPN
ma-342	146	32	)	)	PUNCT
ma-342	146	33	)	)	PUNCT
ma-342	146	34	by	by	ADP
ma-342	146	35	taking	take	VERB
ma-342	146	36	the	the	DET
ma-342	146	37	following	follow	VERB
ma-342	146	38	parameter	parameter	NOUN
ma-342	146	39	values	value	NOUN
ma-342	146	40	(	(	PUNCT
ma-342	146	41	δ	δ	X
ma-342	146	42	=	=	SYM
ma-342	146	43	−1.5	−1.5	PROPN
ma-342	146	44	;	;	PUNCT
ma-342	146	45	)	)	PUNCT
ma-342	146	46	(	(	PUNCT
ma-342	146	47	λ4	λ4	NOUN
ma-342	146	48	=	=	NOUN
ma-342	146	49	1.5	1.5	NUM
ma-342	146	50	;	;	PUNCT
ma-342	146	51	)	)	PUNCT
ma-342	146	52	(	(	PUNCT
ma-342	146	53	λ1	λ1	PROPN
ma-342	146	54	=	=	SYM
ma-342	146	55	0.5	0.5	NUM
ma-342	146	56	;	;	PUNCT
ma-342	146	57	)	)	PUNCT
ma-342	146	58	(	(	PUNCT
ma-342	146	59	λ3	λ3	PROPN
ma-342	146	60	=	=	NOUN
ma-342	146	61	1.5	1.5	NUM
ma-342	146	62	;	;	PUNCT
ma-342	146	63	)	)	PUNCT
ma-342	146	64	(	(	PUNCT
ma-342	146	65	λ2	λ2	NOUN
ma-342	146	66	=	=	SYM
ma-342	146	67	1.15	1.15	NUM
ma-342	146	68	;	;	PUNCT
ma-342	146	69	)	)	PUNCT
ma-342	146	70	(	(	PUNCT
ma-342	146	71	ω	ω	NOUN
ma-342	146	72	=	=	SYM
ma-342	146	73	1.5	1.5	NUM
ma-342	146	74	;	;	PUNCT
ma-342	146	75	)	)	PUNCT
ma-342	146	76	.	.	PUNCT
ma-342	147	1	the	the	DET
ma-342	147	2	range	range	NOUN
ma-342	147	3	of	of	ADP
ma-342	147	4	values	value	NOUN
ma-342	147	5	of	of	ADP
ma-342	147	6	xfor	xfor	ADP
ma-342	147	7	which	which	PRON
ma-342	147	8	the	the	DET
ma-342	147	9	graphs	graph	NOUN
ma-342	147	10	were	be	AUX
ma-342	147	11	plotted	plot	VERB
ma-342	147	12	is	be	AUX
ma-342	147	13	[	[	X
ma-342	147	14	-10,10	-10,10	X
ma-342	147	15	]	]	X
ma-342	147	16	.	.	PUNCT
ma-342	148	1	the	the	DET
ma-342	148	2	2d	2d	NUM
ma-342	148	3	graphs	graph	NOUN
ma-342	148	4	was	be	AUX
ma-342	148	5	plotted	plot	VERB
ma-342	148	6	by	by	ADP
ma-342	148	7	taking	take	VERB
ma-342	148	8	values	value	NOUN
ma-342	148	9	of	of	ADP
ma-342	148	10	t	t	PROPN
ma-342	148	11	at	at	ADP
ma-342	148	12	0	0	NUM
ma-342	148	13	,	,	PUNCT
ma-342	148	14	2	2	NUM
ma-342	148	15	,	,	PUNCT
ma-342	148	16	4	4	NUM
ma-342	148	17	,	,	PUNCT
ma-342	148	18	.	.	PUNCT
ma-342	149	1	figure	figure	NOUN
ma-342	149	2	2	2	NUM
ma-342	149	3	.	.	NUM
ma-342	149	4	3d	3d	NUM
ma-342	149	5	and	and	CCONJ
ma-342	149	6	2d	2d	NUM
ma-342	149	7	abs	ab	NOUN
ma-342	149	8	plot	plot	NOUN
ma-342	149	9	for	for	ADP
ma-342	149	10	φ3(ξ	φ3(ξ	X
ma-342	149	11	)	)	PUNCT
ma-342	149	12	.	.	PUNCT
ma-342	150	1	in	in	ADP
ma-342	150	2	figure	figure	NOUN
ma-342	150	3	(	(	PUNCT
ma-342	150	4	2	2	NUM
ma-342	150	5	)	)	PUNCT
ma-342	150	6	below	below	ADV
ma-342	150	7	,	,	PUNCT
ma-342	150	8	we	we	PRON
ma-342	150	9	have	have	VERB
ma-342	150	10	the	the	DET
ma-342	150	11	surface	surface	NOUN
ma-342	150	12	profile	profile	NOUN
ma-342	150	13	of	of	ADP
ma-342	150	14	2d	2d	NUM
ma-342	150	15	and	and	CCONJ
ma-342	150	16	3d	3d	NUM
ma-342	150	17	absolute	absolute	ADJ
ma-342	150	18	plot	plot	NOUN
ma-342	150	19	represen	represen	NOUN
ma-342	150	20	-	-	PUNCT
ma-342	150	21	tation	tation	NOUN
ma-342	150	22	of	of	ADP
ma-342	150	23	equation	equation	NOUN
ma-342	150	24	(	(	PUNCT
ma-342	150	25	15	15	NUM
ma-342	150	26	)	)	PUNCT
ma-342	150	27	(	(	PUNCT
ma-342	150	28	that	that	ADV
ma-342	150	29	is	is	ADV
ma-342	150	30	,	,	PUNCT
ma-342	150	31	φ3(ξ	φ3(ξ	X
ma-342	150	32	)	)	PUNCT
ma-342	150	33	)	)	PUNCT
ma-342	150	34	by	by	ADP
ma-342	150	35	taking	take	VERB
ma-342	150	36	the	the	DET
ma-342	150	37	following	follow	VERB
ma-342	150	38	parameter	parameter	NOUN
ma-342	150	39	values	value	NOUN
ma-342	150	40	(	(	PUNCT
ma-342	150	41	δ	δ	X
ma-342	150	42	=	=	SYM
ma-342	150	43	−1.5	−1.5	PROPN
ma-342	150	44	;	;	PUNCT
ma-342	150	45	)	)	PUNCT
ma-342	150	46	(	(	PUNCT
ma-342	150	47	λ4	λ4	NOUN
ma-342	150	48	=	=	NOUN
ma-342	150	49	1.5	1.5	NUM
ma-342	150	50	;	;	PUNCT
ma-342	150	51	)	)	PUNCT
ma-342	150	52	(	(	PUNCT
ma-342	150	53	λ1	λ1	PROPN
ma-342	150	54	=	=	SYM
ma-342	150	55	0.5	0.5	NUM
ma-342	150	56	;	;	PUNCT
ma-342	150	57	)	)	PUNCT
ma-342	150	58	(	(	PUNCT
ma-342	150	59	λ3	λ3	PROPN
ma-342	150	60	=	=	NOUN
ma-342	150	61	1.5	1.5	NUM
ma-342	150	62	;	;	PUNCT
ma-342	150	63	)	)	PUNCT
ma-342	150	64	(	(	PUNCT
ma-342	150	65	λ2	λ2	NOUN
ma-342	150	66	=	=	SYM
ma-342	150	67	1.15	1.15	NUM
ma-342	150	68	;	;	PUNCT
ma-342	150	69	)	)	PUNCT
ma-342	150	70	(	(	PUNCT
ma-342	150	71	ω	ω	NOUN
ma-342	150	72	=	=	SYM
ma-342	150	73	1.5	1.5	NUM
ma-342	150	74	;	;	PUNCT
ma-342	150	75	)	)	PUNCT
ma-342	150	76	.	.	PUNCT
ma-342	151	1	the	the	DET
ma-342	151	2	range	range	NOUN
ma-342	151	3	of	of	ADP
ma-342	151	4	values	value	NOUN
ma-342	151	5	of	of	ADP
ma-342	151	6	xfor	xfor	ADP
ma-342	151	7	which	which	PRON
ma-342	151	8	the	the	DET
ma-342	151	9	graphs	graph	NOUN
ma-342	151	10	were	be	AUX
ma-342	151	11	plotted	plot	VERB
ma-342	151	12	is	be	AUX
ma-342	151	13	[	[	X
ma-342	151	14	-10,10	-10,10	X
ma-342	151	15	]	]	X
ma-342	151	16	.	.	PUNCT
ma-342	152	1	the	the	DET
ma-342	152	2	2d	2d	NUM
ma-342	152	3	graphs	graph	NOUN
ma-342	152	4	was	be	AUX
ma-342	152	5	plotted	plot	VERB
ma-342	152	6	by	by	ADP
ma-342	152	7	taking	take	VERB
ma-342	152	8	values	value	NOUN
ma-342	152	9	of	of	ADP
ma-342	152	10	t	t	PROPN
ma-342	152	11	at	at	ADP
ma-342	152	12	https://doi.org/10.28924/ada/ma.5.14	https://doi.org/10.28924/ada/ma.5.14	PROPN
ma-342	152	13	eur	eur	PROPN
ma-342	152	14	.	.	PUNCT
ma-342	153	1	j.	j.	PROPN
ma-342	153	2	math	math	PROPN
ma-342	153	3	.	.	PUNCT
ma-342	154	1	anal	anal	PROPN
ma-342	154	2	.	.	PUNCT
ma-342	155	1	10.28924	10.28924	NUM
ma-342	155	2	/	/	SYM
ma-342	155	3	ada	ada	PROPN
ma-342	155	4	/	/	SYM
ma-342	155	5	ma.5.14	ma.5.14	PROPN
ma-342	155	6	8	8	NUM
ma-342	155	7	figure	figure	NOUN
ma-342	155	8	3	3	NUM
ma-342	155	9	.	.	X
ma-342	155	10	3d	3d	NOUN
ma-342	155	11	and	and	CCONJ
ma-342	155	12	2d	2d	NUM
ma-342	156	1	i	i	NOUN
ma-342	156	2	m	m	VERB
ma-342	156	3	plot	plot	NOUN
ma-342	156	4	for	for	ADP
ma-342	156	5	φ3(ξ	φ3(ξ	X
ma-342	156	6	)	)	PUNCT
ma-342	156	7	.	.	PUNCT
ma-342	157	1	the	the	DET
ma-342	157	2	origin	origin	NOUN
ma-342	157	3	.	.	PUNCT
ma-342	158	1	in	in	ADP
ma-342	158	2	figure	figure	NOUN
ma-342	158	3	(	(	PUNCT
ma-342	158	4	3	3	NUM
ma-342	158	5	)	)	PUNCT
ma-342	158	6	above	above	ADV
ma-342	158	7	,	,	PUNCT
ma-342	158	8	we	we	PRON
ma-342	158	9	have	have	VERB
ma-342	158	10	the	the	DET
ma-342	158	11	surface	surface	NOUN
ma-342	158	12	profile	profile	NOUN
ma-342	158	13	of	of	ADP
ma-342	158	14	2d	2d	NUM
ma-342	158	15	and	and	CCONJ
ma-342	158	16	3d	3d	NUM
ma-342	158	17	imaginary	imaginary	ADJ
ma-342	158	18	plot	plot	NOUN
ma-342	158	19	represen	represen	NOUN
ma-342	158	20	-	-	PUNCT
ma-342	158	21	tation	tation	NOUN
ma-342	158	22	of	of	ADP
ma-342	158	23	equation	equation	NOUN
ma-342	158	24	(	(	PUNCT
ma-342	158	25	15	15	NUM
ma-342	158	26	)	)	PUNCT
ma-342	158	27	(	(	PUNCT
ma-342	158	28	that	that	ADV
ma-342	158	29	is	is	ADV
ma-342	158	30	,	,	PUNCT
ma-342	158	31	φ3(ξ	φ3(ξ	X
ma-342	158	32	)	)	PUNCT
ma-342	158	33	)	)	PUNCT
ma-342	158	34	by	by	ADP
ma-342	158	35	taking	take	VERB
ma-342	158	36	the	the	DET
ma-342	158	37	following	follow	VERB
ma-342	158	38	parameter	parameter	NOUN
ma-342	158	39	values	value	NOUN
ma-342	158	40	(	(	PUNCT
ma-342	158	41	δ	δ	X
ma-342	158	42	=	=	SYM
ma-342	158	43	−1.5	−1.5	PROPN
ma-342	158	44	;	;	PUNCT
ma-342	158	45	)	)	PUNCT
ma-342	158	46	(	(	PUNCT
ma-342	158	47	λ4	λ4	NOUN
ma-342	158	48	=	=	NOUN
ma-342	158	49	1.5	1.5	NUM
ma-342	158	50	;	;	PUNCT
ma-342	158	51	)	)	PUNCT
ma-342	158	52	(	(	PUNCT
ma-342	158	53	λ1	λ1	PROPN
ma-342	158	54	=	=	SYM
ma-342	158	55	0.5	0.5	NUM
ma-342	158	56	;	;	PUNCT
ma-342	158	57	)	)	PUNCT
ma-342	158	58	(	(	PUNCT
ma-342	158	59	λ3	λ3	PROPN
ma-342	158	60	=	=	NOUN
ma-342	158	61	1.5	1.5	NUM
ma-342	158	62	;	;	PUNCT
ma-342	158	63	)	)	PUNCT
ma-342	158	64	(	(	PUNCT
ma-342	158	65	λ2	λ2	NOUN
ma-342	158	66	=	=	SYM
ma-342	158	67	1.15	1.15	NUM
ma-342	158	68	;	;	PUNCT
ma-342	158	69	)	)	PUNCT
ma-342	158	70	(	(	PUNCT
ma-342	158	71	ω	ω	NOUN
ma-342	158	72	=	=	SYM
ma-342	158	73	1.5	1.5	NUM
ma-342	158	74	;	;	PUNCT
ma-342	158	75	)	)	PUNCT
ma-342	158	76	.	.	PUNCT
ma-342	159	1	the	the	DET
ma-342	159	2	range	range	NOUN
ma-342	159	3	of	of	ADP
ma-342	159	4	values	value	NOUN
ma-342	159	5	of	of	ADP
ma-342	159	6	xfor	xfor	ADP
ma-342	159	7	which	which	PRON
ma-342	159	8	the	the	DET
ma-342	159	9	graphs	graph	NOUN
ma-342	159	10	were	be	AUX
ma-342	159	11	plotted	plot	VERB
ma-342	159	12	is	be	AUX
ma-342	159	13	[	[	X
ma-342	159	14	-10,10	-10,10	X
ma-342	159	15	]	]	X
ma-342	159	16	.	.	PUNCT
ma-342	160	1	the	the	DET
ma-342	160	2	2d	2d	NUM
ma-342	160	3	graphs	graph	NOUN
ma-342	160	4	was	be	AUX
ma-342	160	5	plotted	plot	VERB
ma-342	160	6	by	by	ADP
ma-342	160	7	taking	take	VERB
ma-342	160	8	values	value	NOUN
ma-342	160	9	of	of	ADP
ma-342	160	10	t	t	PROPN
ma-342	160	11	atthe	atthe	ADJ
ma-342	160	12	origin	origin	NOUN
ma-342	160	13	.	.	PUNCT
ma-342	161	1	figure	figure	NOUN
ma-342	161	2	4	4	NUM
ma-342	161	3	.	.	X
ma-342	162	1	3d	3d	NUM
ma-342	162	2	and	and	CCONJ
ma-342	162	3	2d	2d	NUM
ma-342	162	4	abs	ab	NOUN
ma-342	162	5	plot	plot	NOUN
ma-342	162	6	for	for	ADP
ma-342	162	7	φ5(ξ	φ5(ξ	NOUN
ma-342	162	8	)	)	PUNCT
ma-342	162	9	.	.	PUNCT
ma-342	163	1	in	in	ADP
ma-342	163	2	figure	figure	NOUN
ma-342	163	3	(	(	PUNCT
ma-342	163	4	4	4	NUM
ma-342	163	5	)	)	PUNCT
ma-342	163	6	above	above	ADV
ma-342	163	7	,	,	PUNCT
ma-342	163	8	we	we	PRON
ma-342	163	9	have	have	VERB
ma-342	163	10	the	the	DET
ma-342	163	11	surface	surface	NOUN
ma-342	163	12	profile	profile	NOUN
ma-342	163	13	of	of	ADP
ma-342	163	14	2d	2d	NUM
ma-342	163	15	and	and	CCONJ
ma-342	163	16	3d	3d	NUM
ma-342	163	17	absolute	absolute	ADJ
ma-342	163	18	plot	plot	NOUN
ma-342	163	19	represen	represen	NOUN
ma-342	163	20	-	-	PUNCT
ma-342	163	21	tation	tation	NOUN
ma-342	163	22	of	of	ADP
ma-342	163	23	equation	equation	NOUN
ma-342	163	24	(	(	PUNCT
ma-342	163	25	17	17	NUM
ma-342	163	26	)	)	PUNCT
ma-342	163	27	(	(	PUNCT
ma-342	163	28	that	that	ADV
ma-342	163	29	is	is	ADV
ma-342	163	30	,	,	PUNCT
ma-342	163	31	φ5(ξ	φ5(ξ	NOUN
ma-342	163	32	)	)	PUNCT
ma-342	163	33	)	)	PUNCT
ma-342	163	34	by	by	ADP
ma-342	163	35	taking	take	VERB
ma-342	163	36	the	the	DET
ma-342	163	37	following	follow	VERB
ma-342	163	38	parameter	parameter	NOUN
ma-342	163	39	values	value	NOUN
ma-342	163	40	(	(	PUNCT
ma-342	163	41	δ	δ	X
ma-342	163	42	=	=	SYM
ma-342	163	43	−1.5	−1.5	PROPN
ma-342	163	44	;	;	PUNCT
ma-342	163	45	)	)	PUNCT
ma-342	163	46	(	(	PUNCT
ma-342	163	47	λ4	λ4	NOUN
ma-342	163	48	=	=	NOUN
ma-342	163	49	1.5	1.5	NUM
ma-342	163	50	;	;	PUNCT
ma-342	163	51	)	)	PUNCT
ma-342	163	52	(	(	PUNCT
ma-342	163	53	λ1	λ1	PROPN
ma-342	163	54	=	=	SYM
ma-342	163	55	0.5	0.5	NUM
ma-342	163	56	;	;	PUNCT
ma-342	163	57	)	)	PUNCT
ma-342	163	58	(	(	PUNCT
ma-342	163	59	λ3	λ3	PROPN
ma-342	163	60	=	=	NOUN
ma-342	163	61	1.5	1.5	NUM
ma-342	163	62	;	;	PUNCT
ma-342	163	63	)	)	PUNCT
ma-342	163	64	(	(	PUNCT
ma-342	163	65	λ2	λ2	NOUN
ma-342	163	66	=	=	SYM
ma-342	163	67	1.15	1.15	NUM
ma-342	163	68	;	;	PUNCT
ma-342	163	69	)	)	PUNCT
ma-342	163	70	(	(	PUNCT
ma-342	163	71	ω	ω	NOUN
ma-342	163	72	=	=	SYM
ma-342	163	73	1.5	1.5	NUM
ma-342	163	74	;	;	PUNCT
ma-342	163	75	)	)	PUNCT
ma-342	163	76	.	.	PUNCT
ma-342	164	1	the	the	DET
ma-342	164	2	range	range	NOUN
ma-342	164	3	of	of	ADP
ma-342	164	4	values	value	NOUN
ma-342	164	5	of	of	ADP
ma-342	164	6	xfor	xfor	ADP
ma-342	164	7	which	which	PRON
ma-342	164	8	the	the	DET
ma-342	164	9	graphs	graph	NOUN
ma-342	164	10	were	be	AUX
ma-342	164	11	plotted	plot	VERB
ma-342	164	12	is	be	AUX
ma-342	164	13	[	[	X
ma-342	164	14	-10,10	-10,10	X
ma-342	164	15	]	]	X
ma-342	164	16	.	.	PUNCT
ma-342	165	1	the	the	DET
ma-342	165	2	2d	2d	NUM
ma-342	165	3	graphs	graph	NOUN
ma-342	165	4	was	be	AUX
ma-342	165	5	plotted	plot	VERB
ma-342	165	6	by	by	ADP
ma-342	165	7	taking	take	VERB
ma-342	165	8	values	value	NOUN
ma-342	165	9	of	of	ADP
ma-342	165	10	t	t	PROPN
ma-342	165	11	atthe	atthe	NOUN
ma-342	165	12	origin.in	origin.in	X
ma-342	165	13	figure	figure	NOUN
ma-342	165	14	(	(	PUNCT
ma-342	165	15	5	5	NUM
ma-342	165	16	)	)	PUNCT
ma-342	165	17	above	above	ADV
ma-342	165	18	,	,	PUNCT
ma-342	165	19	we	we	PRON
ma-342	165	20	have	have	VERB
ma-342	165	21	the	the	DET
ma-342	165	22	surface	surface	NOUN
ma-342	165	23	profile	profile	NOUN
ma-342	165	24	of	of	ADP
ma-342	165	25	2d	2d	NUM
ma-342	165	26	and	and	CCONJ
ma-342	165	27	3d	3d	NUM
ma-342	165	28	real	real	ADJ
ma-342	165	29	plot	plot	NOUN
ma-342	165	30	representa	representa	NOUN
ma-342	165	31	-	-	PUNCT
ma-342	165	32	tion	tion	NOUN
ma-342	165	33	of	of	ADP
ma-342	165	34	equation	equation	NOUN
ma-342	165	35	(	(	PUNCT
ma-342	165	36	17	17	NUM
ma-342	165	37	)	)	PUNCT
ma-342	165	38	(	(	PUNCT
ma-342	165	39	that	that	ADV
ma-342	165	40	is	is	ADV
ma-342	165	41	,	,	PUNCT
ma-342	165	42	φ5(ξ	φ5(ξ	NOUN
ma-342	165	43	)	)	PUNCT
ma-342	165	44	)	)	PUNCT
ma-342	165	45	by	by	ADP
ma-342	165	46	taking	take	VERB
ma-342	165	47	the	the	DET
ma-342	165	48	following	follow	VERB
ma-342	165	49	parameter	parameter	NOUN
ma-342	165	50	values	value	NOUN
ma-342	165	51	(	(	PUNCT
ma-342	165	52	δ	δ	X
ma-342	165	53	=	=	SYM
ma-342	165	54	−1.5	−1.5	PROPN
ma-342	165	55	;	;	PUNCT
ma-342	165	56	)	)	PUNCT
ma-342	165	57	(	(	PUNCT
ma-342	165	58	λ4	λ4	NOUN
ma-342	165	59	=	=	NOUN
ma-342	165	60	1.5	1.5	NUM
ma-342	165	61	;	;	PUNCT
ma-342	165	62	)	)	PUNCT
ma-342	165	63	(	(	PUNCT
ma-342	165	64	λ1	λ1	PROPN
ma-342	165	65	=	=	SYM
ma-342	165	66	0.5	0.5	NUM
ma-342	165	67	;	;	PUNCT
ma-342	165	68	)	)	PUNCT
ma-342	165	69	(	(	PUNCT
ma-342	165	70	λ3	λ3	PROPN
ma-342	165	71	=	=	NOUN
ma-342	165	72	1.5	1.5	NUM
ma-342	165	73	;	;	PUNCT
ma-342	165	74	)	)	PUNCT
ma-342	165	75	(	(	PUNCT
ma-342	165	76	λ2	λ2	NOUN
ma-342	165	77	=	=	SYM
ma-342	165	78	1.15	1.15	NUM
ma-342	165	79	;	;	PUNCT
ma-342	165	80	)	)	PUNCT
ma-342	165	81	(	(	PUNCT
ma-342	165	82	ω	ω	NOUN
ma-342	165	83	=	=	SYM
ma-342	165	84	1.5	1.5	NUM
ma-342	165	85	;	;	PUNCT
ma-342	165	86	)	)	PUNCT
ma-342	165	87	.	.	PUNCT
ma-342	166	1	the	the	DET
ma-342	166	2	range	range	NOUN
ma-342	166	3	of	of	ADP
ma-342	166	4	values	value	NOUN
ma-342	166	5	of	of	ADP
ma-342	166	6	x	x	PUNCT
ma-342	166	7	https://doi.org/10.28924/ada/ma.5.14	https://doi.org/10.28924/ada/ma.5.14	PROPN
ma-342	166	8	eur	eur	PROPN
ma-342	166	9	.	.	PUNCT
ma-342	167	1	j.	j.	PROPN
ma-342	167	2	math	math	PROPN
ma-342	167	3	.	.	PUNCT
ma-342	168	1	anal	anal	PROPN
ma-342	168	2	.	.	PUNCT
ma-342	169	1	10.28924	10.28924	NUM
ma-342	169	2	/	/	SYM
ma-342	169	3	ada	ada	PROPN
ma-342	169	4	/	/	SYM
ma-342	169	5	ma.5.14	ma.5.14	PROPN
ma-342	169	6	9	9	NUM
ma-342	169	7	figure	figure	NOUN
ma-342	169	8	5	5	NUM
ma-342	169	9	.	.	X
ma-342	169	10	3d	3d	NUM
ma-342	169	11	and	and	CCONJ
ma-342	169	12	2d	2d	NUM
ma-342	169	13	real	real	ADJ
ma-342	169	14	plot	plot	NOUN
ma-342	169	15	for	for	ADP
ma-342	169	16	φ5(ξ	φ5(ξ	NOUN
ma-342	169	17	)	)	PUNCT
ma-342	169	18	.	.	PUNCT
ma-342	170	1	for	for	ADP
ma-342	170	2	which	which	PRON
ma-342	170	3	the	the	DET
ma-342	170	4	graphs	graph	NOUN
ma-342	170	5	were	be	AUX
ma-342	170	6	plotted	plot	VERB
ma-342	170	7	is	be	AUX
ma-342	170	8	[	[	X
ma-342	170	9	-10,10	-10,10	X
ma-342	170	10	]	]	X
ma-342	170	11	.	.	PUNCT
ma-342	171	1	the	the	DET
ma-342	171	2	2d	2d	NUM
ma-342	171	3	graphs	graph	NOUN
ma-342	171	4	was	be	AUX
ma-342	171	5	plotted	plot	VERB
ma-342	171	6	by	by	ADP
ma-342	171	7	taking	take	VERB
ma-342	171	8	values	value	NOUN
ma-342	171	9	of	of	ADP
ma-342	171	10	t	t	PROPN
ma-342	171	11	atthe	atthe	ADJ
ma-342	171	12	origin	origin	NOUN
ma-342	171	13	.	.	PUNCT
ma-342	172	1	figure	figure	NOUN
ma-342	172	2	6	6	NUM
ma-342	172	3	.	.	X
ma-342	173	1	3d	3d	NUM
ma-342	173	2	and	and	CCONJ
ma-342	173	3	2d	2d	NUM
ma-342	173	4	real	real	ADJ
ma-342	173	5	plot	plot	NOUN
ma-342	173	6	for	for	ADP
ma-342	173	7	φ6(ξ	φ6(ξ	NOUN
ma-342	173	8	)	)	PUNCT
ma-342	173	9	.	.	PUNCT
ma-342	174	1	in	in	ADP
ma-342	174	2	figure	figure	NOUN
ma-342	174	3	(	(	PUNCT
ma-342	174	4	6	6	NUM
ma-342	174	5	)	)	PUNCT
ma-342	174	6	above	above	ADV
ma-342	174	7	,	,	PUNCT
ma-342	174	8	we	we	PRON
ma-342	174	9	have	have	VERB
ma-342	174	10	the	the	DET
ma-342	174	11	surface	surface	NOUN
ma-342	174	12	profile	profile	NOUN
ma-342	174	13	of	of	ADP
ma-342	174	14	2d	2d	NUM
ma-342	174	15	and	and	CCONJ
ma-342	174	16	3d	3d	NUM
ma-342	174	17	real	real	ADJ
ma-342	174	18	plot	plot	NOUN
ma-342	174	19	representa	representa	NOUN
ma-342	174	20	-	-	PUNCT
ma-342	174	21	tion	tion	NOUN
ma-342	174	22	of	of	ADP
ma-342	174	23	equation	equation	NOUN
ma-342	174	24	(	(	PUNCT
ma-342	174	25	18	18	NUM
ma-342	174	26	)	)	PUNCT
ma-342	174	27	(	(	PUNCT
ma-342	174	28	that	that	ADV
ma-342	174	29	is	be	AUX
ma-342	174	30	,	,	PUNCT
ma-342	174	31	φ6(ξ	φ6(ξ	NOUN
ma-342	174	32	)	)	PUNCT
ma-342	174	33	)	)	PUNCT
ma-342	174	34	by	by	ADP
ma-342	174	35	taking	take	VERB
ma-342	174	36	the	the	DET
ma-342	174	37	following	follow	VERB
ma-342	174	38	parameter	parameter	NOUN
ma-342	174	39	values	value	NOUN
ma-342	174	40	(	(	PUNCT
ma-342	174	41	δ	δ	X
ma-342	174	42	=	=	SYM
ma-342	174	43	−1.5	−1.5	PROPN
ma-342	174	44	;	;	PUNCT
ma-342	174	45	)	)	PUNCT
ma-342	174	46	(	(	PUNCT
ma-342	174	47	λ4	λ4	NOUN
ma-342	174	48	=	=	NOUN
ma-342	174	49	1.5	1.5	NUM
ma-342	174	50	;	;	PUNCT
ma-342	174	51	)	)	PUNCT
ma-342	174	52	(	(	PUNCT
ma-342	174	53	λ1	λ1	PROPN
ma-342	174	54	=	=	SYM
ma-342	174	55	0.5	0.5	NUM
ma-342	174	56	;	;	PUNCT
ma-342	174	57	)	)	PUNCT
ma-342	174	58	(	(	PUNCT
ma-342	174	59	λ3	λ3	PROPN
ma-342	174	60	=	=	NOUN
ma-342	174	61	1.5	1.5	NUM
ma-342	174	62	;	;	PUNCT
ma-342	174	63	)	)	PUNCT
ma-342	174	64	(	(	PUNCT
ma-342	174	65	λ2	λ2	NOUN
ma-342	174	66	=	=	SYM
ma-342	174	67	1.15	1.15	NUM
ma-342	174	68	;	;	PUNCT
ma-342	174	69	)	)	PUNCT
ma-342	174	70	(	(	PUNCT
ma-342	174	71	ω	ω	NOUN
ma-342	174	72	=	=	SYM
ma-342	174	73	1.5	1.5	NUM
ma-342	174	74	;	;	PUNCT
ma-342	174	75	)	)	PUNCT
ma-342	174	76	.	.	PUNCT
ma-342	175	1	the	the	DET
ma-342	175	2	range	range	NOUN
ma-342	175	3	of	of	ADP
ma-342	175	4	values	value	NOUN
ma-342	175	5	of	of	ADP
ma-342	175	6	xfor	xfor	ADP
ma-342	175	7	which	which	PRON
ma-342	175	8	the	the	DET
ma-342	175	9	graphs	graph	NOUN
ma-342	175	10	were	be	AUX
ma-342	175	11	plotted	plot	VERB
ma-342	175	12	is	be	AUX
ma-342	175	13	[	[	X
ma-342	175	14	-10,10	-10,10	X
ma-342	175	15	]	]	X
ma-342	175	16	.	.	PUNCT
ma-342	176	1	the	the	DET
ma-342	176	2	2d	2d	NUM
ma-342	176	3	graphs	graph	NOUN
ma-342	176	4	was	be	AUX
ma-342	176	5	plotted	plot	VERB
ma-342	176	6	by	by	ADP
ma-342	176	7	taking	take	VERB
ma-342	176	8	values	value	NOUN
ma-342	176	9	of	of	ADP
ma-342	176	10	t	t	PROPN
ma-342	176	11	atthe	atthe	ADJ
ma-342	176	12	origin	origin	NOUN
ma-342	176	13	.	.	PUNCT
ma-342	177	1	5	5	X
ma-342	177	2	.	.	X
ma-342	177	3	modulation	modulation	NOUN
ma-342	177	4	instability	instability	NOUN
ma-342	177	5	(	(	PUNCT
ma-342	177	6	mi	mi	NOUN
ma-342	177	7	)	)	PUNCT
ma-342	177	8	analysisvarious	analysisvarious	ADJ
ma-342	177	9	nonlinear	nonlinear	ADJ
ma-342	177	10	phenomena	phenomenon	NOUN
ma-342	177	11	display	display	VERB
ma-342	177	12	an	an	DET
ma-342	177	13	instability	instability	NOUN
ma-342	177	14	that	that	PRON
ma-342	177	15	results	result	VERB
ma-342	177	16	in	in	ADP
ma-342	177	17	the	the	DET
ma-342	177	18	modulation	modulation	NOUN
ma-342	177	19	of	of	ADP
ma-342	177	20	the	the	DET
ma-342	177	21	steady	steady	ADJ
ma-342	177	22	-	-	PUNCT
ma-342	177	23	state	state	NOUN
ma-342	177	24	as	as	ADP
ma-342	177	25	a	a	DET
ma-342	177	26	result	result	NOUN
ma-342	177	27	of	of	ADP
ma-342	177	28	co	co	NOUN
ma-342	177	29	-	-	NOUN
ma-342	177	30	action	action	NOUN
ma-342	177	31	between	between	ADP
ma-342	177	32	the	the	DET
ma-342	177	33	nonlinear	nonlinear	ADJ
ma-342	177	34	and	and	CCONJ
ma-342	177	35	dispersive	dispersive	ADJ
ma-342	177	36	effects	effect	NOUN
ma-342	177	37	[	[	X
ma-342	177	38	37	37	NUM
ma-342	177	39	]	]	PUNCT
ma-342	177	40	.	.	PUNCT
ma-342	178	1	in	in	ADP
ma-342	178	2	this	this	DET
ma-342	178	3	section	section	NOUN
ma-342	178	4	,	,	PUNCT
ma-342	178	5	wederive	wederive	ADJ
ma-342	178	6	modulation	modulation	NOUN
ma-342	178	7	instability	instability	NOUN
ma-342	178	8	for	for	ADP
ma-342	178	9	the	the	DET
ma-342	178	10	weakly	weakly	ADJ
ma-342	178	11	nonlocal	nonlocal	ADJ
ma-342	178	12	schrodinger	schrodinger	NOUN
ma-342	178	13	equation	equation	NOUN
ma-342	178	14	with	with	ADP
ma-342	178	15	parabolic	parabolic	ADJ
ma-342	178	16	law	law	NOUN
ma-342	178	17	.	.	PUNCT
ma-342	179	1	theorem	theorem	NOUN
ma-342	179	2	1	1	NUM
ma-342	179	3	:	:	PUNCT
ma-342	179	4	suppose	suppose	VERB
ma-342	179	5	that	that	SCONJ
ma-342	179	6	equation	equation	NOUN
ma-342	179	7	(	(	PUNCT
ma-342	179	8	1	1	X
ma-342	179	9	)	)	PUNCT
ma-342	179	10	characterizes	characterize	VERB
ma-342	179	11	a	a	DET
ma-342	179	12	wave	wave	NOUN
ma-342	179	13	system	system	NOUN
ma-342	179	14	featuring	feature	VERB
ma-342	179	15	a	a	DET
ma-342	179	16	non	non	ADJ
ma-342	179	17	-	-	ADJ
ma-342	179	18	trivial	trivial	ADJ
ma-342	179	19	disper	disper	NOUN
ma-342	179	20	-	-	PUNCT
ma-342	179	21	sion	sion	NOUN
ma-342	179	22	relation	relation	NOUN
ma-342	179	23	,	,	PUNCT
ma-342	179	24	alongside	alongside	ADP
ma-342	179	25	nonlinear	nonlinear	ADJ
ma-342	179	26	components	component	NOUN
ma-342	179	27	.	.	PUNCT
ma-342	180	1	given	give	VERB
ma-342	180	2	that	that	SCONJ
ma-342	180	3	φ(x	φ(x	PROPN
ma-342	180	4	,	,	PUNCT
ma-342	180	5	t	t	PROPN
ma-342	180	6	)	)	PUNCT
ma-342	180	7	represents	represent	VERB
ma-342	180	8	a	a	DET
ma-342	180	9	solution	solution	NOUN
ma-342	180	10	to	to	ADP
ma-342	180	11	equation	equation	NOUN
ma-342	180	12	,	,	PUNCT
ma-342	180	13	it	it	PRON
ma-342	180	14	is	be	AUX
ma-342	180	15	possible	possible	ADJ
ma-342	180	16	,	,	PUNCT
ma-342	180	17	under	under	ADP
ma-342	180	18	appropriate	appropriate	ADJ
ma-342	180	19	circumstances	circumstance	NOUN
ma-342	180	20	,	,	PUNCT
ma-342	180	21	for	for	SCONJ
ma-342	180	22	a	a	DET
ma-342	180	23	range	range	NOUN
ma-342	180	24	of	of	ADP
ma-342	180	25	parameters	parameter	NOUN
ma-342	180	26	to	to	PART
ma-342	180	27	exist	exist	VERB
ma-342	180	28	where	where	SCONJ
ma-342	180	29	mi	mi	PROPN
ma-342	180	30	takesplace	takesplace	NOUN
ma-342	180	31	.	.	PUNCT
ma-342	181	1	over	over	ADP
ma-342	181	2	time	time	NOUN
ma-342	181	3	,	,	PUNCT
ma-342	181	4	the	the	DET
ma-342	181	5	amplitude	amplitude	NOUN
ma-342	181	6	and	and	CCONJ
ma-342	181	7	configuration	configuration	NOUN
ma-342	181	8	of	of	ADP
ma-342	181	9	the	the	DET
ma-342	181	10	wave	wave	NOUN
ma-342	181	11	undergo	undergo	VERB
ma-342	181	12	significant	significant	ADJ
ma-342	181	13	alterations	alteration	NOUN
ma-342	181	14	dueto	dueto	NOUN
ma-342	181	15	instability	instability	NOUN
ma-342	181	16	,	,	PUNCT
ma-342	181	17	resulting	result	VERB
ma-342	181	18	in	in	ADP
ma-342	181	19	a	a	DET
ma-342	181	20	rapid	rapid	ADJ
ma-342	181	21	growth	growth	NOUN
ma-342	181	22	of	of	ADP
ma-342	181	23	small	small	ADJ
ma-342	181	24	perturbations	perturbation	NOUN
ma-342	181	25	.	.	PUNCT
ma-342	182	1	https://doi.org/10.28924/ada/ma.5.14	https://doi.org/10.28924/ada/ma.5.14	PROPN
ma-342	182	2	eur	eur	PROPN
ma-342	182	3	.	.	PUNCT
ma-342	183	1	j.	j.	PROPN
ma-342	183	2	math	math	PROPN
ma-342	183	3	.	.	PUNCT
ma-342	184	1	anal	anal	PROPN
ma-342	184	2	.	.	PUNCT
ma-342	185	1	10.28924	10.28924	NUM
ma-342	185	2	/	/	SYM
ma-342	185	3	ada	ada	PROPN
ma-342	185	4	/	/	SYM
ma-342	185	5	ma.5.14	ma.5.14	PROPN
ma-342	185	6	10	10	NUM
ma-342	185	7	proof	proof	NOUN
ma-342	185	8	:	:	PUNCT
ma-342	185	9	to	to	PART
ma-342	185	10	explore	explore	VERB
ma-342	185	11	the	the	DET
ma-342	185	12	mi	mi	PROPN
ma-342	185	13	of	of	ADP
ma-342	185	14	equation	equation	NOUN
ma-342	185	15	(	(	PUNCT
ma-342	185	16	1	1	NUM
ma-342	185	17	)	)	PUNCT
ma-342	185	18	,	,	PUNCT
ma-342	185	19	let	let	VERB
ma-342	185	20	take	take	VERB
ma-342	185	21	the	the	DET
ma-342	185	22	initial	initial	ADJ
ma-342	185	23	assumption	assumption	NOUN
ma-342	185	24	that	that	SCONJ
ma-342	185	25	equation	equation	NOUN
ma-342	185	26	(	(	PUNCT
ma-342	185	27	1	1	X
ma-342	185	28	)	)	PUNCT
ma-342	185	29	issubjected	issubjecte	VERB
ma-342	185	30	to	to	ADP
ma-342	185	31	a	a	DET
ma-342	185	32	small	small	ADJ
ma-342	185	33	perturbation	perturbation	NOUN
ma-342	185	34	in	in	ADP
ma-342	185	35	the	the	DET
ma-342	185	36	following	following	ADJ
ma-342	185	37	manner	manner	NOUN
ma-342	185	38	:	:	PUNCT
ma-342	185	39	φ(x	φ(x	PROPN
ma-342	185	40	,	,	PUNCT
ma-342	185	41	t	t	PROPN
ma-342	185	42	)	)	PUNCT
ma-342	185	43	=	=	PUNCT
ma-342	185	44	(	(	PUNCT
ma-342	185	45	√	√	NUM
ma-342	185	46	m	m	VERB
ma-342	185	47	+	+	X
ma-342	185	48	φ(x	φ(x	PROPN
ma-342	185	49	,	,	PUNCT
ma-342	185	50	t	t	PROPN
ma-342	185	51	)	)	PUNCT
ma-342	185	52	)	)	PUNCT
ma-342	186	1	e	e	X
ma-342	186	2	imx	imx	PROPN
ma-342	186	3	;	;	PUNCT
ma-342	186	4	(	(	PUNCT
ma-342	186	5	19	19	NUM
ma-342	186	6	)	)	PUNCT
ma-342	186	7	where	where	SCONJ
ma-342	186	8	m	m	NOUN
ma-342	186	9	is	be	AUX
ma-342	186	10	the	the	DET
ma-342	186	11	normalized	normalize	VERB
ma-342	186	12	optical	optical	ADJ
ma-342	186	13	power	power	NOUN
ma-342	186	14	,	,	PUNCT
ma-342	186	15	φ(x	φ(x	PROPN
ma-342	186	16	,	,	PUNCT
ma-342	186	17	t	t	PROPN
ma-342	186	18	)	)	PUNCT
ma-342	186	19	shows	show	VERB
ma-342	186	20	real	real	ADV
ma-342	186	21	valued	value	VERB
ma-342	186	22	amplitude	amplitude	NOUN
ma-342	186	23	of	of	ADP
ma-342	186	24	perturbation	perturbation	NOUN
ma-342	186	25	withrelatively	withrelatively	ADV
ma-342	186	26	dispersion	dispersion	NOUN
ma-342	186	27	.	.	PUNCT
ma-342	187	1	substituting	substitute	VERB
ma-342	187	2	equation	equation	NOUN
ma-342	187	3	(	(	PUNCT
ma-342	187	4	19	19	NUM
ma-342	187	5	)	)	PUNCT
ma-342	187	6	into	into	ADP
ma-342	187	7	equation	equation	NOUN
ma-342	187	8	(	(	PUNCT
ma-342	187	9	1	1	NUM
ma-342	187	10	)	)	PUNCT
ma-342	187	11	and	and	CCONJ
ma-342	187	12	linearizing	linearize	VERB
ma-342	187	13	,	,	PUNCT
ma-342	187	14	gives	give	VERB
ma-342	187	15	iφt	iφt	PROPN
ma-342	188	1	+	+	CCONJ
ma-342	188	2	(	(	PUNCT
ma-342	188	3	λ1	λ1	ADJ
ma-342	188	4	+	+	SYM
ma-342	188	5	λ2	λ2	PROPN
ma-342	188	6	m	m	NOUN
ma-342	188	7	)	)	PUNCT
ma-342	189	1	φxx	φxx	PROPN
ma-342	189	2	+	+	CCONJ
ma-342	189	3	iλ1	iλ1	X
ma-342	189	4	m	m	PROPN
ma-342	189	5	(	(	PUNCT
ma-342	189	6	φx	φx	PROPN
ma-342	189	7	+	+	ADJ
ma-342	189	8	φ∗x	φ∗x	NUM
ma-342	189	9	)	)	PUNCT
ma-342	190	1	+	+	CCONJ
ma-342	190	2	(	(	PUNCT
ma-342	190	3	(	(	PUNCT
ma-342	190	4	λ4	λ4	ADJ
ma-342	190	5	−	−	PROPN
ma-342	190	6	λ1)m2	λ1)m2	PROPN
ma-342	190	7	+	+	NUM
ma-342	190	8	λ3	λ3	PROPN
ma-342	190	9	m	m	PROPN
ma-342	190	10	)	)	PUNCT
ma-342	190	11	(	(	PUNCT
ma-342	190	12	φ	φ	PROPN
ma-342	190	13	+	+	CCONJ
ma-342	190	14	φ∗	φ∗	NOUN
ma-342	190	15	)	)	PUNCT
ma-342	190	16	=	=	SYM
ma-342	190	17	0	0	NUM
ma-342	190	18	,	,	PUNCT
ma-342	190	19	(	(	PUNCT
ma-342	190	20	20	20	NUM
ma-342	190	21	)	)	PUNCT
ma-342	190	22	where	where	SCONJ
ma-342	190	23	φ∗	φ∗	NOUN
ma-342	190	24	denotes	denote	NOUN
ma-342	190	25	complex	complex	ADJ
ma-342	190	26	conjugate.assume	conjugate.assume	PRON
ma-342	190	27	the	the	DET
ma-342	190	28	solutions	solution	NOUN
ma-342	190	29	of	of	ADP
ma-342	190	30	equation	equation	NOUN
ma-342	190	31	(	(	PUNCT
ma-342	190	32	20	20	NUM
ma-342	190	33	)	)	PUNCT
ma-342	190	34	to	to	PART
ma-342	190	35	be	be	AUX
ma-342	190	36	of	of	ADP
ma-342	190	37	the	the	DET
ma-342	190	38	form	form	NOUN
ma-342	190	39	φ(x	φ(x	PROPN
ma-342	190	40	,	,	PUNCT
ma-342	190	41	t	t	NOUN
ma-342	190	42	)	)	PUNCT
ma-342	190	43	=	=	SYM
ma-342	190	44	a1e	a1e	PROPN
ma-342	190	45	(	(	PUNCT
ma-342	190	46	i(x$−ξt	i(x$−ξt	NOUN
ma-342	190	47	)	)	PUNCT
ma-342	190	48	)	)	PUNCT
ma-342	191	1	+	+	CCONJ
ma-342	191	2	a2e	a2e	X
ma-342	191	3	(	(	PUNCT
ma-342	191	4	−i(x$−ξt	−i(x$−ξt	NOUN
ma-342	191	5	)	)	PUNCT
ma-342	191	6	)	)	PUNCT
ma-342	191	7	(	(	PUNCT
ma-342	191	8	21	21	NUM
ma-342	191	9	)	)	PUNCT
ma-342	191	10	φ(x	φ(x	NOUN
ma-342	191	11	,	,	PUNCT
ma-342	191	12	t)∗	t)∗	NOUN
ma-342	191	13	=	=	SYM
ma-342	191	14	a1e	a1e	PROPN
ma-342	191	15	(	(	PUNCT
ma-342	191	16	−i(x$−ξt	−i(x$−ξt	NOUN
ma-342	191	17	)	)	PUNCT
ma-342	191	18	)	)	PUNCT
ma-342	192	1	+	+	CCONJ
ma-342	192	2	a2e	a2e	PROPN
ma-342	192	3	(	(	PUNCT
ma-342	192	4	i(x$−ξt	i(x$−ξt	NOUN
ma-342	192	5	)	)	PUNCT
ma-342	192	6	)	)	PUNCT
ma-342	193	1	(	(	PUNCT
ma-342	193	2	22)where	22)where	NUM
ma-342	193	3	$	$	SYM
ma-342	193	4	and	and	CCONJ
ma-342	193	5	ξ	ξ	PROPN
ma-342	193	6	represent	represent	NOUN
ma-342	193	7	normalize	normalize	VERB
ma-342	193	8	wave	wave	NOUN
ma-342	193	9	number	number	NOUN
ma-342	193	10	and	and	CCONJ
ma-342	193	11	frequency	frequency	NOUN
ma-342	193	12	of	of	ADP
ma-342	193	13	perturbation	perturbation	NOUN
ma-342	193	14	respectively.substituting	respectively.substitute	VERB
ma-342	193	15	(	(	PUNCT
ma-342	193	16	21	21	NUM
ma-342	193	17	)	)	PUNCT
ma-342	193	18	and	and	CCONJ
ma-342	193	19	(	(	PUNCT
ma-342	193	20	22	22	NUM
ma-342	193	21	)	)	PUNCT
ma-342	193	22	into	into	ADP
ma-342	193	23	(	(	PUNCT
ma-342	193	24	20	20	NUM
ma-342	193	25	)	)	PUNCT
ma-342	193	26	and	and	CCONJ
ma-342	193	27	collect	collect	VERB
ma-342	193	28	the	the	DET
ma-342	193	29	coefficients	coefficient	NOUN
ma-342	193	30	of	of	ADP
ma-342	193	31	e(−i(x$−ξt	e(−i(x$−ξt	PROPN
ma-342	193	32	)	)	PUNCT
ma-342	193	33	)	)	PUNCT
ma-342	193	34	,	,	PUNCT
ma-342	193	35	and	and	CCONJ
ma-342	193	36	e(i(x$−ξt	e(i(x$−ξt	NOUN
ma-342	193	37	)	)	PUNCT
ma-342	193	38	)	)	PUNCT
ma-342	193	39	,	,	PUNCT
ma-342	193	40	and	and	CCONJ
ma-342	193	41	solve	solve	VERB
ma-342	193	42	the	the	DET
ma-342	193	43	determinant	determinant	NOUN
ma-342	193	44	of	of	ADP
ma-342	193	45	the	the	DET
ma-342	193	46	resulting	result	VERB
ma-342	193	47	matrix	matrix	NOUN
ma-342	193	48	of	of	ADP
ma-342	193	49	coefficients	coefficient	NOUN
ma-342	193	50	we	we	PRON
ma-342	193	51	obtain	obtain	VERB
ma-342	193	52	the	the	DET
ma-342	193	53	followingdispersion	followingdispersion	NOUN
ma-342	193	54	relation	relation	NOUN
ma-342	193	55	:	:	PUNCT
ma-342	193	56	−λ2	−λ2	NOUN
ma-342	193	57	1	1	NUM
ma-342	193	58	$	$	SYM
ma-342	193	59	4	4	NUM
ma-342	193	60	−	−	NUM
ma-342	193	61	2λ1λ2	2λ1λ2	NUM
ma-342	193	62	m	m	NOUN
ma-342	193	63	3$2	3$2	NUM
ma-342	193	64	+	+	NUM
ma-342	193	65	2λ2λ4	2λ2λ4	NUM
ma-342	193	66	m	m	PROPN
ma-342	193	67	3$2	3$2	NUM
ma-342	193	68	−	−	NUM
ma-342	193	69	λ2	λ2	NOUN
ma-342	193	70	2	2	NUM
ma-342	193	71	m	m	NOUN
ma-342	193	72	2$4	2$4	NUM
ma-342	193	73	−	−	NUM
ma-342	193	74	2λ2	2λ2	NUM
ma-342	193	75	1	1	NUM
ma-342	193	76	m	m	NUM
ma-342	193	77	2$2	2$2	NUM
ma-342	193	78	+	+	NUM
ma-342	193	79	2λ2λ3	2λ2λ3	NUM
ma-342	193	80	m	m	NOUN
ma-342	193	81	2$2	2$2	NUM
ma-342	193	82	2λ1λ4	2λ1λ4	NUM
ma-342	193	83	m	m	NOUN
ma-342	193	84	2$2	2$2	NUM
ma-342	193	85	−	−	NOUN
ma-342	193	86	2λ1mξ$	2λ1mξ$	NUM
ma-342	193	87	−	−	PROPN
ma-342	193	88	2λ1λ2m$	2λ1λ2m$	NUM
ma-342	193	89	4	4	NUM
ma-342	194	1	+	+	CCONJ
ma-342	195	1	2λ1λ3m$	2λ1λ3m$	NUM
ma-342	195	2	2	2	NUM
ma-342	195	3	+	+	CCONJ
ma-342	195	4	ξ2	ξ2	NOUN
ma-342	195	5	=	=	SYM
ma-342	195	6	0	0	NUM
ma-342	195	7	(	(	PUNCT
ma-342	195	8	23	23	NUM
ma-342	195	9	)	)	PUNCT
ma-342	195	10	solving	solve	VERB
ma-342	195	11	the	the	DET
ma-342	195	12	dispersion	dispersion	NOUN
ma-342	195	13	relation(23	relation(23	NOUN
ma-342	195	14	)	)	PUNCT
ma-342	195	15	for	for	ADP
ma-342	195	16	ξ	ξ	PROPN
ma-342	195	17	,	,	PUNCT
ma-342	195	18	we	we	PRON
ma-342	195	19	obtain	obtain	VERB
ma-342	195	20	:	:	PUNCT
ma-342	195	21	ξ	ξ	X
ma-342	195	22	=	=	PUNCT
ma-342	195	23	λ1m$	λ1m$	X
ma-342	195	24	∓	∓	NOUN
ma-342	195	25	(	(	PUNCT
ma-342	195	26	λ2	λ2	NOUN
ma-342	195	27	1	1	NUM
ma-342	195	28	$	$	SYM
ma-342	195	29	4	4	NUM
ma-342	195	30	+	+	NUM
ma-342	195	31	2λ1λ2	2λ1λ2	NUM
ma-342	195	32	m	m	NOUN
ma-342	195	33	3$2	3$2	NUM
ma-342	195	34	+	+	CCONJ
ma-342	195	35	λ2	λ2	NOUN
ma-342	195	36	2	2	NUM
ma-342	195	37	m	m	NOUN
ma-342	195	38	2$4	2$4	NUM
ma-342	195	39	+	+	CCONJ
ma-342	195	40	3λ2	3λ2	NUM
ma-342	195	41	1	1	NUM
ma-342	195	42	m	m	NUM
ma-342	195	43	2$2	2$2	NUM
ma-342	195	44	+	+	CCONJ
ma-342	195	45	2λ1λ2m$	2λ1λ2m$	NUM
ma-342	195	46	4	4	NUM
ma-342	195	47	−2λ2λ4	−2λ2λ4	VERB
ma-342	195	48	m	m	VERB
ma-342	195	49	3$2	3$2	NUM
ma-342	195	50	−	−	PROPN
ma-342	195	51	2λ2λ3	2λ2λ3	NOUN
ma-342	195	52	m	m	VERB
ma-342	195	53	2$2	2$2	NUM
ma-342	195	54	−	−	NOUN
ma-342	195	55	2λ1λ4	2λ1λ4	NUM
ma-342	195	56	m	m	NOUN
ma-342	195	57	2$2	2$2	NUM
ma-342	195	58	−	−	NOUN
ma-342	195	59	2λ1λ3m$	2λ1λ3m$	NUM
ma-342	195	60	2	2	NUM
ma-342	195	61	)	)	PUNCT
ma-342	195	62	1	1	NUM
ma-342	195	63	2	2	NUM
ma-342	195	64	.	.	PUNCT
ma-342	196	1	(	(	PUNCT
ma-342	196	2	24	24	NUM
ma-342	196	3	)	)	PUNCT
ma-342	196	4	in	in	ADP
ma-342	196	5	a	a	DET
ma-342	196	6	situation	situation	NOUN
ma-342	196	7	whereby	whereby	ADV
ma-342	196	8	(	(	PUNCT
ma-342	196	9	λ2	λ2	NOUN
ma-342	196	10	1	1	NUM
ma-342	196	11	$	$	SYM
ma-342	196	12	4	4	NUM
ma-342	196	13	+	+	NUM
ma-342	196	14	2λ1λ2	2λ1λ2	NUM
ma-342	196	15	m	m	NOUN
ma-342	196	16	3$2	3$2	NUM
ma-342	196	17	+	+	CCONJ
ma-342	196	18	λ2	λ2	NOUN
ma-342	196	19	2	2	NUM
ma-342	196	20	m	m	NOUN
ma-342	196	21	2$4	2$4	NUM
ma-342	196	22	+	+	CCONJ
ma-342	196	23	3λ2	3λ2	NUM
ma-342	196	24	1	1	NUM
ma-342	196	25	m	m	NUM
ma-342	196	26	2$2	2$2	NUM
ma-342	197	1	+	+	CCONJ
ma-342	197	2	2λ1λ2m$	2λ1λ2m$	NUM
ma-342	197	3	4	4	NUM
ma-342	197	4	−2λ2λ4	−2λ2λ4	VERB
ma-342	197	5	m	m	VERB
ma-342	197	6	3$2	3$2	NUM
ma-342	197	7	−	−	PROPN
ma-342	197	8	2λ2λ3	2λ2λ3	NOUN
ma-342	197	9	m	m	VERB
ma-342	197	10	2$2	2$2	NUM
ma-342	197	11	−	−	NOUN
ma-342	197	12	2λ1λ4	2λ1λ4	NUM
ma-342	197	13	m	m	NOUN
ma-342	197	14	2$2	2$2	NUM
ma-342	197	15	−	−	NOUN
ma-342	198	1	2λ1λ3m$	2λ1λ3m$	NUM
ma-342	198	2	2	2	NUM
ma-342	198	3	)	)	PUNCT
ma-342	198	4	>	>	X
ma-342	198	5	0	0	PUNCT
ma-342	198	6	,	,	PUNCT
ma-342	198	7	the	the	DET
ma-342	198	8	wave	wave	NOUN
ma-342	198	9	number	number	NOUN
ma-342	198	10	is	be	AUX
ma-342	198	11	real	real	ADJ
ma-342	198	12	for	for	ADP
ma-342	198	13	any	any	DET
ma-342	198	14	real	real	ADJ
ma-342	198	15	value	value	NOUN
ma-342	198	16	of	of	ADP
ma-342	198	17	m	m	PROPN
ma-342	198	18	and	and	CCONJ
ma-342	198	19	the	the	DET
ma-342	198	20	steady	steady	ADJ
ma-342	198	21	-	-	PUNCT
ma-342	198	22	state	state	NOUN
ma-342	198	23	is	be	AUX
ma-342	198	24	stable	stable	ADJ
ma-342	198	25	against	against	ADP
ma-342	198	26	small	small	ADJ
ma-342	198	27	perturbations	perturbation	NOUN
ma-342	198	28	.	.	PUNCT
ma-342	199	1	however	however	ADV
ma-342	199	2	,	,	PUNCT
ma-342	199	3	in	in	ADP
ma-342	199	4	contraryto	contraryto	NOUN
ma-342	199	5	the	the	DET
ma-342	199	6	above	above	ADJ
ma-342	199	7	condition	condition	NOUN
ma-342	199	8	,	,	PUNCT
ma-342	199	9	the	the	DET
ma-342	199	10	steady	steady	ADJ
ma-342	199	11	-	-	PUNCT
ma-342	199	12	state	state	NOUN
ma-342	199	13	solution	solution	NOUN
ma-342	199	14	turns	turn	VERB
ma-342	199	15	to	to	PART
ma-342	199	16	be	be	AUX
ma-342	199	17	unstable	unstable	ADJ
ma-342	199	18	,	,	PUNCT
ma-342	199	19	that	that	ADV
ma-342	199	20	is	is	ADV
ma-342	199	21	,	,	PUNCT
ma-342	199	22	the	the	DET
ma-342	199	23	wave	wave	NOUN
ma-342	199	24	number	number	NOUN
ma-342	199	25	becomes	become	VERB
ma-342	199	26	imaginary	imaginary	ADJ
ma-342	199	27	,	,	PUNCT
ma-342	199	28	when	when	SCONJ
ma-342	199	29	(	(	PUNCT
ma-342	199	30	λ2	λ2	NOUN
ma-342	199	31	1	1	NUM
ma-342	199	32	$	$	SYM
ma-342	199	33	4	4	NUM
ma-342	199	34	+	+	NUM
ma-342	199	35	2λ1λ2	2λ1λ2	NUM
ma-342	199	36	m	m	NOUN
ma-342	199	37	3$2	3$2	NUM
ma-342	199	38	+	+	CCONJ
ma-342	199	39	λ2	λ2	NOUN
ma-342	199	40	2	2	NUM
ma-342	199	41	m	m	NOUN
ma-342	199	42	2$4	2$4	NUM
ma-342	199	43	+	+	CCONJ
ma-342	200	1	3λ2	3λ2	NUM
ma-342	200	2	1	1	NUM
ma-342	200	3	m	m	NUM
ma-342	200	4	2$2	2$2	NUM
ma-342	200	5	+	+	CCONJ
ma-342	200	6	2λ1λ2m$	2λ1λ2m$	NUM
ma-342	200	7	4	4	NUM
ma-342	200	8	−2λ2λ4	−2λ2λ4	VERB
ma-342	200	9	m	m	VERB
ma-342	200	10	3$2	3$2	NUM
ma-342	200	11	−	−	PROPN
ma-342	200	12	2λ2λ3	2λ2λ3	NOUN
ma-342	200	13	m	m	VERB
ma-342	200	14	2$2	2$2	NUM
ma-342	200	15	−	−	NOUN
ma-342	200	16	2λ1λ4	2λ1λ4	NUM
ma-342	200	17	m	m	NOUN
ma-342	200	18	2$2	2$2	NUM
ma-342	200	19	−	−	NOUN
ma-342	201	1	2λ1λ3m$	2λ1λ3m$	NUM
ma-342	201	2	2	2	NUM
ma-342	201	3	)	)	PUNCT
ma-342	201	4	<	<	X
ma-342	201	5	0	0	PUNCT
ma-342	201	6	and	and	CCONJ
ma-342	201	7	the	the	DET
ma-342	201	8	perturbation	perturbation	NOUN
ma-342	201	9	grows	grow	VERB
ma-342	201	10	exponentially	exponentially	ADV
ma-342	201	11	.	.	PUNCT
ma-342	202	1	under	under	ADP
ma-342	202	2	this	this	DET
ma-342	202	3	condition	condition	NOUN
ma-342	202	4	,	,	PUNCT
ma-342	202	5	the	the	DET
ma-342	202	6	growth	growth	NOUN
ma-342	202	7	rate	rate	NOUN
ma-342	202	8	of	of	ADP
ma-342	202	9	modulationstability	modulationstability	NOUN
ma-342	202	10	gain	gain	VERB
ma-342	202	11	spectrum	spectrum	NOUN
ma-342	202	12	g(m	g(m	NOUN
ma-342	202	13	)	)	PUNCT
ma-342	202	14	may	may	AUX
ma-342	202	15	be	be	AUX
ma-342	202	16	given	give	VERB
ma-342	202	17	as	as	ADP
ma-342	202	18	g(r	g(r	NOUN
ma-342	202	19	)	)	PUNCT
ma-342	202	20	=	=	PUNCT
ma-342	203	1	2im(ξ)=	2im(ξ)=	NUM
ma-342	203	2	2im	2im	NOUN
ma-342	203	3	(	(	PUNCT
ma-342	203	4	λ1m$	λ1m$	X
ma-342	203	5	∓	∓	NOUN
ma-342	203	6	(	(	PUNCT
ma-342	203	7	λ2	λ2	NOUN
ma-342	203	8	1	1	NUM
ma-342	203	9	$	$	SYM
ma-342	203	10	4	4	NUM
ma-342	203	11	+	+	NUM
ma-342	203	12	2λ1λ2	2λ1λ2	NUM
ma-342	203	13	m	m	NOUN
ma-342	203	14	3$2	3$2	NUM
ma-342	203	15	+	+	CCONJ
ma-342	203	16	λ2	λ2	NOUN
ma-342	203	17	2	2	NUM
ma-342	203	18	m	m	NOUN
ma-342	203	19	2$4	2$4	NUM
ma-342	203	20	+	+	CCONJ
ma-342	203	21	3λ2	3λ2	NUM
ma-342	203	22	1	1	NUM
ma-342	203	23	m	m	NUM
ma-342	203	24	2$2	2$2	NUM
ma-342	203	25	+	+	CCONJ
ma-342	203	26	2λ1λ2m$	2λ1λ2m$	NUM
ma-342	203	27	4	4	NUM
ma-342	203	28	−2λ2λ4	−2λ2λ4	VERB
ma-342	203	29	m	m	VERB
ma-342	203	30	3$2	3$2	NUM
ma-342	203	31	−	−	PROPN
ma-342	203	32	2λ2λ3	2λ2λ3	NOUN
ma-342	203	33	m	m	VERB
ma-342	203	34	2$2	2$2	NUM
ma-342	203	35	−	−	NOUN
ma-342	203	36	2λ1λ4	2λ1λ4	NUM
ma-342	203	37	m	m	NOUN
ma-342	203	38	2$2	2$2	NUM
ma-342	203	39	−	−	NOUN
ma-342	203	40	2λ1λ3m$	2λ1λ3m$	NUM
ma-342	203	41	2	2	NUM
ma-342	203	42	)	)	PUNCT
ma-342	203	43	)	)	PUNCT
ma-342	203	44	.	.	PUNCT
ma-342	204	1	(	(	PUNCT
ma-342	204	2	25	25	NUM
ma-342	204	3	)	)	PUNCT
ma-342	204	4	the	the	DET
ma-342	204	5	figure	figure	NOUN
ma-342	204	6	below	below	ADV
ma-342	204	7	shows	show	VERB
ma-342	204	8	the	the	DET
ma-342	204	9	gained	gain	VERB
ma-342	204	10	dispersion	dispersion	NOUN
ma-342	204	11	relation	relation	NOUN
ma-342	204	12	to	to	PART
ma-342	204	13	investigate	investigate	VERB
ma-342	204	14	the	the	DET
ma-342	204	15	steady	steady	ADJ
ma-342	204	16	-	-	PUNCT
ma-342	204	17	state	state	NOUN
ma-342	204	18	stabilityby	stabilityby	NOUN
ma-342	204	19	taking	take	VERB
ma-342	204	20	the	the	DET
ma-342	204	21	following	follow	VERB
ma-342	204	22	parameter	parameter	NOUN
ma-342	204	23	values	value	NOUN
ma-342	204	24	λ1	λ1	PROPN
ma-342	204	25	→	→	SYM
ma-342	204	26	2	2	NUM
ma-342	204	27	,	,	PUNCT
ma-342	204	28	λ2	λ2	NOUN
ma-342	204	29	→	→	SYM
ma-342	204	30	2.4	2.4	NUM
ma-342	204	31	,	,	PUNCT
ma-342	204	32	λ3	λ3	PROPN
ma-342	204	33	→	→	SYM
ma-342	204	34	1.5	1.5	NUM
ma-342	204	35	,	,	PUNCT
ma-342	204	36	λ4	λ4	PROPN
ma-342	204	37	→	→	ADP
ma-342	204	38	2.3	2.3	NUM
ma-342	204	39	under	under	ADP
ma-342	204	40	distinct	distinct	ADJ
ma-342	204	41	https://doi.org/10.28924/ada/ma.5.14	https://doi.org/10.28924/ada/ma.5.14	PROPN
ma-342	204	42	eur	eur	PROPN
ma-342	204	43	.	.	PUNCT
ma-342	205	1	j.	j.	PROPN
ma-342	205	2	math	math	PROPN
ma-342	205	3	.	.	PUNCT
ma-342	206	1	anal	anal	PROPN
ma-342	206	2	.	.	PUNCT
ma-342	207	1	10.28924	10.28924	NUM
ma-342	207	2	/	/	SYM
ma-342	207	3	ada	ada	PROPN
ma-342	207	4	/	/	SYM
ma-342	207	5	ma.5.14	ma.5.14	PROPN
ma-342	207	6	11	11	NUM
ma-342	207	7	figure	figure	NOUN
ma-342	207	8	7	7	NUM
ma-342	207	9	.	.	PUNCT
ma-342	208	1	gain	gain	VERB
ma-342	208	2	spectrum	spectrum	NOUN
ma-342	208	3	of	of	ADP
ma-342	208	4	mi	mi	PROPN
ma-342	208	5	under	under	ADP
ma-342	208	6	different	different	ADJ
ma-342	208	7	values	value	NOUN
ma-342	208	8	of	of	ADP
ma-342	208	9	m	m	PROPN
ma-342	208	10	values	value	NOUN
ma-342	208	11	of	of	ADP
ma-342	208	12	m.	m.	NOUN
ma-342	208	13	6	6	NUM
ma-342	208	14	.	.	PUNCT
ma-342	209	1	conclusionsvariants	conclusionsvariant	NOUN
ma-342	209	2	of	of	ADP
ma-342	209	3	the	the	DET
ma-342	209	4	nlse	nlse	NOUN
ma-342	209	5	are	be	AUX
ma-342	209	6	used	use	VERB
ma-342	209	7	to	to	PART
ma-342	209	8	model	model	VERB
ma-342	209	9	the	the	DET
ma-342	209	10	propagation	propagation	NOUN
ma-342	209	11	of	of	ADP
ma-342	209	12	water	water	NOUN
ma-342	209	13	waves	wave	NOUN
ma-342	209	14	in	in	ADP
ma-342	209	15	oceans	ocean	NOUN
ma-342	209	16	and	and	CCONJ
ma-342	209	17	otherbodies	otherbodie	NOUN
ma-342	209	18	of	of	ADP
ma-342	209	19	water	water	NOUN
ma-342	209	20	.	.	PUNCT
ma-342	210	1	nonlinear	nonlinear	ADJ
ma-342	210	2	effects	effect	NOUN
ma-342	210	3	,	,	PUNCT
ma-342	210	4	such	such	ADJ
ma-342	210	5	as	as	ADP
ma-342	210	6	wave	wave	NOUN
ma-342	210	7	steepening	steepening	NOUN
ma-342	210	8	and	and	CCONJ
ma-342	210	9	wave	wave	NOUN
ma-342	210	10	breaking	breaking	NOUN
ma-342	210	11	,	,	PUNCT
ma-342	210	12	can	can	AUX
ma-342	210	13	be	be	AUX
ma-342	210	14	describedusing	describeduse	VERB
ma-342	210	15	these	these	DET
ma-342	210	16	equations	equation	NOUN
ma-342	210	17	.	.	PUNCT
ma-342	211	1	understanding	understand	VERB
ma-342	211	2	these	these	DET
ma-342	211	3	phenomena	phenomenon	NOUN
ma-342	211	4	is	be	AUX
ma-342	211	5	crucial	crucial	ADJ
ma-342	211	6	for	for	ADP
ma-342	211	7	predicting	predict	VERB
ma-342	211	8	and	and	CCONJ
ma-342	211	9	mitigatingthe	mitigatingthe	DET
ma-342	211	10	impact	impact	NOUN
ma-342	211	11	of	of	ADP
ma-342	211	12	tsunamis	tsunamis	NOUN
ma-342	211	13	,	,	PUNCT
ma-342	211	14	storm	storm	NOUN
ma-342	211	15	surges	surge	VERB
ma-342	211	16	,	,	PUNCT
ma-342	211	17	and	and	CCONJ
ma-342	211	18	other	other	ADJ
ma-342	211	19	oceanic	oceanic	ADJ
ma-342	211	20	events	event	NOUN
ma-342	211	21	.	.	PUNCT
ma-342	212	1	furthermore	furthermore	ADV
ma-342	212	2	,	,	PUNCT
ma-342	212	3	nlse	nlse	ADJ
ma-342	212	4	variant	variant	NOUN
ma-342	212	5	areemployed	areemploye	VERB
ma-342	212	6	in	in	ADP
ma-342	212	7	the	the	DET
ma-342	212	8	study	study	NOUN
ma-342	212	9	of	of	ADP
ma-342	212	10	biological	biological	ADJ
ma-342	212	11	systems	system	NOUN
ma-342	212	12	,	,	PUNCT
ma-342	212	13	such	such	ADJ
ma-342	212	14	as	as	ADP
ma-342	212	15	modeling	model	VERB
ma-342	212	16	the	the	DET
ma-342	212	17	propagation	propagation	NOUN
ma-342	212	18	of	of	ADP
ma-342	212	19	nerve	nerve	NOUN
ma-342	212	20	impulses.the	impulses.the	DET
ma-342	212	21	nlse	nlse	ADJ
ma-342	212	22	can	can	AUX
ma-342	212	23	describe	describe	VERB
ma-342	212	24	the	the	DET
ma-342	212	25	nonlinear	nonlinear	ADJ
ma-342	212	26	dynamics	dynamic	NOUN
ma-342	212	27	of	of	ADP
ma-342	212	28	excitable	excitable	ADJ
ma-342	212	29	media	medium	NOUN
ma-342	212	30	,	,	PUNCT
ma-342	212	31	providing	provide	VERB
ma-342	212	32	insights	insight	NOUN
ma-342	212	33	into	into	ADP
ma-342	212	34	the	the	DET
ma-342	212	35	be	be	NOUN
ma-342	212	36	-	-	PUNCT
ma-342	212	37	havior	havior	ADJ
ma-342	212	38	of	of	ADP
ma-342	212	39	electrical	electrical	ADJ
ma-342	212	40	signals	signal	NOUN
ma-342	212	41	in	in	ADP
ma-342	212	42	biological	biological	ADJ
ma-342	212	43	tissues	tissue	NOUN
ma-342	212	44	.	.	PUNCT
ma-342	213	1	also	also	ADV
ma-342	213	2	,	,	PUNCT
ma-342	213	3	nlse	nlse	ADJ
ma-342	213	4	which	which	PRON
ma-342	213	5	are	be	AUX
ma-342	213	6	essential	essential	ADJ
ma-342	213	7	in	in	ADP
ma-342	213	8	fully	fully	ADV
ma-342	213	9	-	-	PUNCT
ma-342	213	10	integratednonlinear	integratednonlinear	ADJ
ma-342	213	11	dispersive	dispersive	ADJ
ma-342	213	12	partial	partial	ADJ
ma-342	213	13	differential	differential	NOUN
ma-342	213	14	equation	equation	NOUN
ma-342	213	15	(	(	PUNCT
ma-342	213	16	pde	pde	NOUN
ma-342	213	17	)	)	PUNCT
ma-342	213	18	,	,	PUNCT
ma-342	213	19	have	have	AUX
ma-342	213	20	found	find	VERB
ma-342	213	21	extensive	extensive	ADJ
ma-342	213	22	application	application	NOUN
ma-342	213	23	in	in	ADP
ma-342	213	24	elu	elu	PROPN
ma-342	213	25	-	-	PUNCT
ma-342	213	26	cidating	cidate	VERB
ma-342	213	27	diverse	diverse	ADJ
ma-342	213	28	phenomena	phenomenon	NOUN
ma-342	213	29	like	like	ADP
ma-342	213	30	deep	deep	ADJ
ma-342	213	31	water	water	NOUN
ma-342	213	32	waves	wave	NOUN
ma-342	213	33	,	,	PUNCT
ma-342	213	34	rogue	rogue	NOUN
ma-342	213	35	waves	wave	NOUN
ma-342	213	36	,	,	PUNCT
ma-342	213	37	plasmas	plasma	NOUN
ma-342	213	38	,	,	PUNCT
ma-342	213	39	and	and	CCONJ
ma-342	213	40	nonlinear	nonlinear	ADJ
ma-342	213	41	optics	optic	NOUN
ma-342	213	42	,	,	PUNCT
ma-342	213	43	including	include	VERB
ma-342	213	44	atomic	atomic	ADJ
ma-342	213	45	physics	physic	NOUN
ma-342	213	46	.	.	PUNCT
ma-342	214	1	the	the	DET
ma-342	214	2	nlse	nlse	PROPN
ma-342	214	3	serves	serve	VERB
ma-342	214	4	as	as	ADP
ma-342	214	5	a	a	DET
ma-342	214	6	comprehensive	comprehensive	ADJ
ma-342	214	7	description	description	NOUN
ma-342	214	8	of	of	ADP
ma-342	214	9	nonlinear	nonlinear	ADJ
ma-342	214	10	dispersiveprocesses	dispersiveprocesse	NOUN
ma-342	214	11	.	.	PUNCT
ma-342	215	1	with	with	ADP
ma-342	215	2	all	all	PRON
ma-342	215	3	of	of	ADP
ma-342	215	4	these	these	PRON
ma-342	215	5	in	in	ADP
ma-342	215	6	mind	mind	NOUN
ma-342	215	7	,	,	PUNCT
ma-342	215	8	we	we	PRON
ma-342	215	9	found	find	VERB
ma-342	215	10	the	the	DET
ma-342	215	11	courage	courage	NOUN
ma-342	215	12	and	and	CCONJ
ma-342	215	13	motivation	motivation	NOUN
ma-342	215	14	in	in	ADP
ma-342	215	15	this	this	DET
ma-342	215	16	study	study	NOUN
ma-342	215	17	to	to	ADP
ma-342	215	18	providethe	providethe	DET
ma-342	215	19	distinct	distinct	ADJ
ma-342	215	20	types	type	NOUN
ma-342	215	21	of	of	ADP
ma-342	215	22	exact	exact	ADJ
ma-342	215	23	soliton	soliton	NOUN
ma-342	215	24	solutions	solution	NOUN
ma-342	215	25	for	for	ADP
ma-342	215	26	the	the	DET
ma-342	215	27	weakly	weakly	ADJ
ma-342	215	28	nonlocal	nonlocal	ADJ
ma-342	215	29	schrodinger	schrodinger	NOUN
ma-342	215	30	equation	equation	NOUN
ma-342	215	31	.	.	PUNCT
ma-342	216	1	we	we	PRON
ma-342	216	2	ob	ob	ADJ
ma-342	216	3	-	-	PUNCT
ma-342	216	4	tain	tain	NOUN
ma-342	216	5	dark	dark	ADJ
ma-342	216	6	and	and	CCONJ
ma-342	216	7	periodic	periodic	ADJ
ma-342	216	8	singular	singular	ADJ
ma-342	216	9	soliton	soliton	NOUN
ma-342	216	10	solutions	solution	NOUN
ma-342	216	11	via	via	ADP
ma-342	216	12	the	the	DET
ma-342	216	13	reliable	reliable	ADJ
ma-342	216	14	approach	approach	NOUN
ma-342	216	15	of	of	ADP
ma-342	216	16	the	the	DET
ma-342	216	17	modified	modify	VERB
ma-342	216	18	extendedtanh	extendedtanh	ADJ
ma-342	216	19	function	function	NOUN
ma-342	216	20	method	method	NOUN
ma-342	216	21	.	.	PUNCT
ma-342	217	1	the	the	DET
ma-342	217	2	obtained	obtain	VERB
ma-342	217	3	solutions	solution	NOUN
ma-342	217	4	were	be	AUX
ma-342	217	5	verified	verify	VERB
ma-342	217	6	by	by	ADP
ma-342	217	7	back	back	ADJ
ma-342	217	8	-	-	PUNCT
ma-342	217	9	substitution	substitution	NOUN
ma-342	217	10	in	in	ADP
ma-342	217	11	the	the	DET
ma-342	217	12	originalequations	originalequation	NOUN
ma-342	217	13	,	,	PUNCT
ma-342	217	14	with	with	ADP
ma-342	217	15	the	the	DET
ma-342	217	16	aid	aid	NOUN
ma-342	217	17	of	of	ADP
ma-342	217	18	a	a	DET
ma-342	217	19	mathematica	mathematica	PROPN
ma-342	217	20	to	to	PART
ma-342	217	21	affirm	affirm	VERB
ma-342	217	22	the	the	DET
ma-342	217	23	robustness	robustness	NOUN
ma-342	217	24	of	of	ADP
ma-342	217	25	the	the	DET
ma-342	217	26	chosen	choose	VERB
ma-342	217	27	approach	approach	NOUN
ma-342	217	28	.	.	PUNCT
ma-342	218	1	the	the	DET
ma-342	218	2	ob	ob	NOUN
ma-342	218	3	-	-	PUNCT
ma-342	218	4	tained	taine	VERB
ma-342	218	5	results	result	NOUN
ma-342	218	6	were	be	AUX
ma-342	218	7	portrayed	portray	VERB
ma-342	218	8	using	use	VERB
ma-342	218	9	two	two	NUM
ma-342	218	10	-	-	PUNCT
ma-342	218	11	dimensional	dimensional	ADJ
ma-342	218	12	and	and	CCONJ
ma-342	218	13	three	three	NUM
ma-342	218	14	-	-	PUNCT
ma-342	218	15	dimensional	dimensional	ADJ
ma-342	218	16	graphs	graph	NOUN
ma-342	218	17	.	.	PUNCT
ma-342	219	1	additionally	additionally	ADV
ma-342	219	2	,	,	PUNCT
ma-342	219	3	https://doi.org/10.28924/ada/ma.5.14	https://doi.org/10.28924/ada/ma.5.14	PROPN
ma-342	219	4	eur	eur	PROPN
ma-342	219	5	.	.	PUNCT
ma-342	220	1	j.	j.	PROPN
ma-342	220	2	math	math	PROPN
ma-342	220	3	.	.	PUNCT
ma-342	221	1	anal	anal	PROPN
ma-342	221	2	.	.	PUNCT
ma-342	222	1	10.28924	10.28924	NUM
ma-342	222	2	/	/	SYM
ma-342	222	3	ada	ada	PROPN
ma-342	222	4	/	/	SYM
ma-342	222	5	ma.5.14	ma.5.14	PROPN
ma-342	222	6	12modulation	12modulation	NUM
ma-342	222	7	instability	instability	NOUN
ma-342	222	8	was	be	AUX
ma-342	222	9	performed	perform	VERB
ma-342	222	10	to	to	PART
ma-342	222	11	study	study	VERB
ma-342	222	12	the	the	DET
ma-342	222	13	stationary	stationary	ADJ
ma-342	222	14	state	state	NOUN
ma-342	222	15	of	of	ADP
ma-342	222	16	the	the	DET
ma-342	222	17	governing	govern	VERB
ma-342	222	18	model	model	NOUN
ma-342	222	19	.	.	PUNCT
ma-342	223	1	resultsare	resultsare	NOUN
ma-342	223	2	helpful	helpful	ADJ
ma-342	223	3	in	in	ADP
ma-342	223	4	the	the	DET
ma-342	223	5	progress	progress	NOUN
ma-342	223	6	of	of	ADP
ma-342	223	7	the	the	DET
ma-342	223	8	concerned	concerned	ADJ
ma-342	223	9	system	system	NOUN
ma-342	223	10	.	.	PUNCT
ma-342	224	1	the	the	DET
ma-342	224	2	gained	gain	VERB
ma-342	224	3	results	result	NOUN
ma-342	224	4	will	will	AUX
ma-342	224	5	be	be	AUX
ma-342	224	6	of	of	ADP
ma-342	224	7	high	high	ADJ
ma-342	224	8	importancein	importancein	ADJ
ma-342	224	9	the	the	DET
ma-342	224	10	interaction	interaction	NOUN
ma-342	224	11	of	of	ADP
ma-342	224	12	quantum	quantum	NOUN
ma-342	224	13	-	-	ADJ
ma-342	224	14	mechanical	mechanical	ADJ
ma-342	224	15	fluctuations	fluctuation	NOUN
ma-342	224	16	,	,	PUNCT
ma-342	224	17	granular	granular	ADJ
ma-342	224	18	matters	matter	NOUN
ma-342	224	19	,	,	PUNCT
ma-342	224	20	and	and	CCONJ
ma-342	224	21	other	other	ADJ
ma-342	224	22	fields	field	NOUN
ma-342	224	23	of	of	ADP
ma-342	224	24	weaklynonlocal	weaklynonlocal	ADJ
ma-342	224	25	schrodinger	schrodinger	NOUN
ma-342	224	26	with	with	ADP
ma-342	224	27	parabolic	parabolic	ADJ
ma-342	224	28	law	law	NOUN
ma-342	224	29	applications	application	NOUN
ma-342	224	30	.	.	PUNCT
ma-342	225	1	the	the	DET
ma-342	225	2	achieved	achieve	VERB
ma-342	225	3	results	result	NOUN
ma-342	225	4	are	be	AUX
ma-342	225	5	also	also	ADV
ma-342	225	6	useful	useful	ADJ
ma-342	225	7	in	in	ADP
ma-342	225	8	var	var	NOUN
ma-342	225	9	-	-	PUNCT
ma-342	225	10	ious	ious	ADJ
ma-342	225	11	naturally	naturally	ADV
ma-342	225	12	occurring	occur	VERB
ma-342	225	13	phenomena	phenomenon	NOUN
ma-342	225	14	,	,	PUNCT
ma-342	225	15	industries	industry	NOUN
ma-342	225	16	,	,	PUNCT
ma-342	225	17	geophysics	geophysic	NOUN
ma-342	225	18	,	,	PUNCT
ma-342	225	19	civil	civil	ADJ
ma-342	225	20	engineering	engineering	NOUN
ma-342	225	21	,	,	PUNCT
ma-342	225	22	pharmaceutical	pharmaceutical	NOUN
ma-342	225	23	,	,	PUNCT
ma-342	225	24	andmany	andmany	NOUN
ma-342	225	25	others	other	NOUN
ma-342	225	26	.	.	PUNCT
ma-342	226	1	it	it	PRON
ma-342	226	2	is	be	AUX
ma-342	226	3	suggested	suggest	VERB
ma-342	226	4	that	that	SCONJ
ma-342	226	5	the	the	DET
ma-342	226	6	method	method	NOUN
ma-342	226	7	used	use	VERB
ma-342	226	8	is	be	AUX
ma-342	226	9	also	also	ADV
ma-342	226	10	useful	useful	ADJ
ma-342	226	11	for	for	SCONJ
ma-342	226	12	the	the	DET
ma-342	226	13	other	other	ADJ
ma-342	226	14	nonlinear	nonlinear	ADJ
ma-342	226	15	models	model	NOUN
ma-342	226	16	ofdifferent	ofdifferent	VERB
ma-342	226	17	fields	field	NOUN
ma-342	226	18	of	of	ADP
ma-342	226	19	science	science	NOUN
ma-342	226	20	and	and	CCONJ
ma-342	226	21	engineering	engineering	NOUN
ma-342	226	22	.	.	PUNCT
ma-342	227	1	references	reference	NOUN
ma-342	227	2	[	[	X
ma-342	227	3	1	1	NUM
ma-342	227	4	]	]	X
ma-342	227	5	m.j	m.j	PROPN
ma-342	227	6	.	.	PROPN
ma-342	227	7	ablowitz	ablowitz	PROPN
ma-342	227	8	,	,	PUNCT
ma-342	227	9	nonlinear	nonlinear	ADJ
ma-342	227	10	dispersive	dispersive	ADJ
ma-342	227	11	waves	wave	NOUN
ma-342	227	12	:	:	PUNCT
ma-342	227	13	asymptotic	asymptotic	ADJ
ma-342	227	14	analysis	analysis	NOUN
ma-342	227	15	and	and	CCONJ
ma-342	227	16	solitons	soliton	NOUN
ma-342	227	17	,	,	PUNCT
ma-342	227	18	cambridge	cambridge	PROPN
ma-342	227	19	univ	univ	PROPN
ma-342	227	20	.	.	PUNCT
ma-342	228	1	press	press	PROPN
ma-342	228	2	,	,	PUNCT
ma-342	228	3	47	47	NUM
ma-342	228	4	(	(	PUNCT
ma-342	228	5	2011).[2	2011).[2	X
ma-342	228	6	]	]	X
ma-342	228	7	a.r.z.u	a.r.z.u	PROPN
ma-342	228	8	.	.	PROPN
ma-342	228	9	akbulut	akbulut	PROPN
ma-342	228	10	,	,	PUNCT
ma-342	228	11	m.	m.	NOUN
ma-342	228	12	mirzazadeh	mirzazadeh	PROPN
ma-342	228	13	,	,	PUNCT
ma-342	228	14	m.s	m.s	PROPN
ma-342	228	15	.	.	PROPN
ma-342	228	16	hashemi	hashemi	PROPN
ma-342	228	17	,	,	PUNCT
ma-342	228	18	k.	k.	PROPN
ma-342	228	19	hosseini	hosseini	PROPN
ma-342	228	20	,	,	PUNCT
ma-342	228	21	s.	s.	PROPN
ma-342	228	22	salahshour	salahshour	PROPN
ma-342	228	23	,	,	PUNCT
ma-342	228	24	c.	c.	PROPN
ma-342	228	25	park	park	PROPN
ma-342	228	26	,	,	PUNCT
ma-342	228	27	triki?biswas	triki?biswa	VERB
ma-342	228	28	model	model	NOUN
ma-342	228	29	:	:	PUNCT
ma-342	228	30	itssymmetry	itssymmetry	NOUN
ma-342	228	31	reduction	reduction	NOUN
ma-342	228	32	,	,	PUNCT
ma-342	228	33	nucci	nucci	PROPN
ma-342	228	34	’s	’s	PART
ma-342	228	35	reduction	reduction	NOUN
ma-342	228	36	and	and	CCONJ
ma-342	228	37	conservation	conservation	NOUN
ma-342	228	38	laws	law	NOUN
ma-342	228	39	,	,	PUNCT
ma-342	228	40	int	int	NOUN
ma-342	228	41	.	.	PUNCT
ma-342	229	1	j.	j.	PROPN
ma-342	229	2	mod	mod	PROPN
ma-342	229	3	.	.	PUNCT
ma-342	230	1	phys	phy	NOUN
ma-342	230	2	.	.	PUNCT
ma-342	231	1	b	b	X
ma-342	231	2	37	37	NUM
ma-342	231	3	(	(	PUNCT
ma-342	231	4	2023	2023	NUM
ma-342	231	5	)	)	PUNCT
ma-342	231	6	,	,	PUNCT
ma-342	231	7	2350063.[3	2350063.[3	NUM
ma-342	231	8	]	]	X
ma-342	231	9	l.	l.	PROPN
ma-342	231	10	akinyemi	akinyemi	PROPN
ma-342	231	11	,	,	PUNCT
ma-342	231	12	u.	u.	PROPN
ma-342	231	13	akpan	akpan	PROPN
ma-342	231	14	,	,	PUNCT
ma-342	231	15	p.	p.	PROPN
ma-342	231	16	veeresha	veeresha	PROPN
ma-342	231	17	,	,	PUNCT
ma-342	231	18	h.	h.	PROPN
ma-342	231	19	rezazadeh	rezazadeh	PROPN
ma-342	231	20	,	,	PUNCT
ma-342	231	21	m.	m.	PROPN
ma-342	231	22	inc	inc	PROPN
ma-342	231	23	,	,	PUNCT
ma-342	231	24	computational	computational	ADJ
ma-342	231	25	techniques	technique	NOUN
ma-342	231	26	to	to	PART
ma-342	231	27	study	study	VERB
ma-342	231	28	the	the	DET
ma-342	231	29	dynamics	dynamic	NOUN
ma-342	231	30	ofgeneralized	ofgeneralize	VERB
ma-342	231	31	unstable	unstable	ADJ
ma-342	231	32	nonlinear	nonlinear	ADJ
ma-342	231	33	schrodinger	schrodinger	PROPN
ma-342	231	34	equation	equation	NOUN
ma-342	231	35	,	,	PUNCT
ma-342	231	36	j.	j.	PROPN
ma-342	231	37	ocean	ocean	PROPN
ma-342	231	38	eng	eng	PROPN
ma-342	231	39	.	.	PUNCT
ma-342	232	1	sci	sci	PROPN
ma-342	232	2	.	.	PUNCT
ma-342	233	1	(	(	PUNCT
ma-342	233	2	2022).[4	2022).[4	NUM
ma-342	233	3	]	]	X
ma-342	233	4	l.	l.	PROPN
ma-342	233	5	akinyemi	akinyemi	PROPN
ma-342	233	6	,	,	PUNCT
ma-342	233	7	m.	m.	NOUN
ma-342	233	8	?	?	PUNCT
ma-342	233	9	enol	enol	NOUN
ma-342	233	10	,	,	PUNCT
ma-342	233	11	m.	m.	NOUN
ma-342	233	12	mirzazadeh	mirzazadeh	PROPN
ma-342	233	13	,	,	PUNCT
ma-342	233	14	m.	m.	NOUN
ma-342	233	15	eslami	eslami	PROPN
ma-342	233	16	,	,	PUNCT
ma-342	233	17	optical	optical	ADJ
ma-342	233	18	solitons	soliton	NOUN
ma-342	233	19	for	for	ADP
ma-342	233	20	weakly	weakly	ADJ
ma-342	233	21	nonlocal	nonlocal	ADJ
ma-342	233	22	schrodinger	schrodinger	NOUN
ma-342	233	23	equation	equation	NOUN
ma-342	233	24	withparabolic	withparabolic	PROPN
ma-342	233	25	law	law	NOUN
ma-342	233	26	nonlinearity	nonlinearity	NOUN
ma-342	233	27	and	and	CCONJ
ma-342	233	28	external	external	ADJ
ma-342	233	29	potential	potential	NOUN
ma-342	233	30	,	,	PUNCT
ma-342	233	31	optik	optik	PROPN
ma-342	233	32	230	230	NUM
ma-342	233	33	(	(	PUNCT
ma-342	233	34	2021	2021	NUM
ma-342	233	35	)	)	PUNCT
ma-342	233	36	,	,	PUNCT
ma-342	233	37	166281.[5	166281.[5	NUM
ma-342	233	38	]	]	X
ma-342	233	39	g.	g.	PROPN
ma-342	233	40	akram	akram	PROPN
ma-342	233	41	,	,	PUNCT
ma-342	233	42	h.u	h.u	PROPN
ma-342	233	43	.	.	PUNCT
ma-342	233	44	rehman	rehman	PROPN
ma-342	233	45	,	,	PUNCT
ma-342	233	46	numerical	numerical	ADJ
ma-342	233	47	solution	solution	NOUN
ma-342	233	48	of	of	ADP
ma-342	233	49	eighth	eighth	ADJ
ma-342	233	50	order	order	NOUN
ma-342	233	51	boundary	boundary	ADJ
ma-342	233	52	value	value	NOUN
ma-342	233	53	problems	problem	NOUN
ma-342	233	54	in	in	ADP
ma-342	233	55	reproducing	reproduce	VERB
ma-342	233	56	kernelspace	kernelspace	NOUN
ma-342	233	57	,	,	PUNCT
ma-342	233	58	numer	numer	NOUN
ma-342	233	59	.	.	PUNCT
ma-342	234	1	algorithms	algorithms	PROPN
ma-342	234	2	62	62	NUM
ma-342	234	3	(	(	PUNCT
ma-342	234	4	2013	2013	NUM
ma-342	234	5	)	)	PUNCT
ma-342	234	6	,	,	PUNCT
ma-342	234	7	527–540.[6	527–540.[6	NUM
ma-342	234	8	]	]	X
ma-342	234	9	k.k	k.k	PROPN
ma-342	234	10	.	.	PROPN
ma-342	234	11	ali	ali	PROPN
ma-342	234	12	,	,	PUNCT
ma-342	234	13	a.m.	a.m.	PROPN
ma-342	234	14	wazwaz	wazwaz	PROPN
ma-342	234	15	,	,	PUNCT
ma-342	234	16	m.s	m.s	PROPN
ma-342	234	17	.	.	PROPN
ma-342	234	18	osman	osman	PROPN
ma-342	234	19	,	,	PUNCT
ma-342	234	20	optical	optical	ADJ
ma-342	234	21	soliton	soliton	NOUN
ma-342	234	22	solutions	solution	NOUN
ma-342	234	23	to	to	ADP
ma-342	234	24	the	the	DET
ma-342	234	25	generalized	generalized	ADJ
ma-342	234	26	nonautonomous	nonautonomous	ADJ
ma-342	234	27	nonlinearschrodinger	nonlinearschrodinger	ADJ
ma-342	234	28	equations	equation	NOUN
ma-342	234	29	in	in	ADP
ma-342	234	30	optical	optical	ADJ
ma-342	234	31	fibers	fiber	NOUN
ma-342	234	32	via	via	ADP
ma-342	234	33	the	the	DET
ma-342	234	34	sine	sine	ADJ
ma-342	234	35	-	-	PUNCT
ma-342	234	36	gordon	gordon	PROPN
ma-342	234	37	expansion	expansion	NOUN
ma-342	234	38	method	method	NOUN
ma-342	234	39	,	,	PUNCT
ma-342	234	40	optik	optik	PROPN
ma-342	234	41	208	208	NUM
ma-342	234	42	(	(	PUNCT
ma-342	234	43	2020	2020	NUM
ma-342	234	44	)	)	PUNCT
ma-342	234	45	,	,	PUNCT
ma-342	234	46	164132.[7	164132.[7	NUM
ma-342	234	47	]	]	X
ma-342	234	48	m.o	m.o	PROPN
ma-342	234	49	.	.	PROPN
ma-342	234	50	al	al	PROPN
ma-342	234	51	-	-	PUNCT
ma-342	234	52	amr	amr	PROPN
ma-342	234	53	,	,	PUNCT
ma-342	234	54	h.	h.	PROPN
ma-342	234	55	rezazadeh	rezazadeh	PROPN
ma-342	234	56	,	,	PUNCT
ma-342	234	57	k.k	k.k	PROPN
ma-342	234	58	.	.	PROPN
ma-342	234	59	ali	ali	PROPN
ma-342	234	60	,	,	PUNCT
ma-342	234	61	a.	a.	PROPN
ma-342	234	62	korkmazki	korkmazki	PROPN
ma-342	234	63	,	,	PUNCT
ma-342	234	64	n1	n1	ADJ
ma-342	234	65	-	-	PUNCT
ma-342	234	66	soliton	soliton	NOUN
ma-342	234	67	solution	solution	NOUN
ma-342	234	68	for	for	ADP
ma-342	234	69	schrodinger	schrodinger	ADJ
ma-342	234	70	equation	equation	NOUN
ma-342	234	71	with	with	ADP
ma-342	234	72	competingweakly	competingweakly	ADJ
ma-342	234	73	nonlocal	nonlocal	ADJ
ma-342	234	74	and	and	CCONJ
ma-342	234	75	parabolic	parabolic	ADJ
ma-342	234	76	law	law	NOUN
ma-342	234	77	nonlinearities	nonlinearitie	NOUN
ma-342	234	78	,	,	PUNCT
ma-342	234	79	commun	commun	PROPN
ma-342	234	80	.	.	PUNCT
ma-342	235	1	theor	theor	PROPN
ma-342	235	2	.	.	PUNCT
ma-342	236	1	phys	phy	NOUN
ma-342	236	2	.	.	PUNCT
ma-342	237	1	72	72	NUM
ma-342	237	2	(	(	PUNCT
ma-342	237	3	2020	2020	NUM
ma-342	237	4	)	)	PUNCT
ma-342	237	5	,	,	PUNCT
ma-342	237	6	065503.[8	065503.[8	NUM
ma-342	238	1	]	]	X
ma-342	238	2	t.	t.	X
ma-342	238	3	an	an	PRON
ma-342	238	4	,	,	PUNCT
ma-342	238	5	n.h.m	n.h.m	ADJ
ma-342	238	6	.	.	PUNCT
ma-342	239	1	shahen	shahen	PROPN
ma-342	239	2	,	,	PUNCT
ma-342	239	3	s.n	s.n	PROPN
ma-342	239	4	.	.	PROPN
ma-342	239	5	ananna	ananna	PROPN
ma-342	239	6	,	,	PUNCT
ma-342	239	7	m.f	m.f	PROPN
ma-342	239	8	.	.	PROPN
ma-342	239	9	hossain	hossain	PROPN
ma-342	239	10	,	,	PUNCT
ma-342	239	11	t.	t.	NOUN
ma-342	239	12	muazu	muazu	NOUN
ma-342	239	13	,	,	PUNCT
ma-342	239	14	exact	exact	ADJ
ma-342	239	15	and	and	CCONJ
ma-342	239	16	explicit	explicit	ADJ
ma-342	239	17	travelling	travelling	ADJ
ma-342	239	18	-	-	PUNCT
ma-342	239	19	wave	wave	NOUN
ma-342	239	20	solutions	solution	NOUN
ma-342	239	21	to	to	ADP
ma-342	239	22	thefamily	thefamily	ADV
ma-342	239	23	of	of	ADP
ma-342	239	24	new	new	ADJ
ma-342	239	25	3d	3d	PROPN
ma-342	239	26	fractional	fractional	ADJ
ma-342	239	27	wbbm	wbbm	PROPN
ma-342	239	28	equations	equation	NOUN
ma-342	239	29	in	in	ADP
ma-342	239	30	mathematical	mathematical	ADJ
ma-342	239	31	physics	physics	NOUN
ma-342	239	32	,	,	PUNCT
ma-342	239	33	results	result	VERB
ma-342	239	34	phys	phy	NOUN
ma-342	239	35	.	.	PUNCT
ma-342	240	1	19	19	NUM
ma-342	240	2	(	(	PUNCT
ma-342	240	3	2020	2020	NUM
ma-342	240	4	)	)	PUNCT
ma-342	240	5	,	,	PUNCT
ma-342	240	6	103517.[9	103517.[9	NUM
ma-342	240	7	]	]	X
ma-342	240	8	s.n	s.n	PROPN
ma-342	240	9	.	.	PROPN
ma-342	240	10	ananna	ananna	PROPN
ma-342	240	11	,	,	PUNCT
ma-342	240	12	p.p	p.p	PROPN
ma-342	240	13	.	.	PROPN
ma-342	240	14	gharami	gharami	NOUN
ma-342	240	15	,	,	PUNCT
ma-342	240	16	t.	t.	PROPN
ma-342	240	17	an	an	PRON
ma-342	240	18	,	,	PUNCT
ma-342	240	19	m.	m.	NOUN
ma-342	240	20	asaduzzaman	asaduzzaman	NOUN
ma-342	240	21	,	,	PUNCT
ma-342	240	22	the	the	DET
ma-342	240	23	improved	improve	VERB
ma-342	240	24	modified	modify	VERB
ma-342	240	25	extended	extended	ADJ
ma-342	240	26	tanh	tanh	NOUN
ma-342	240	27	-	-	PUNCT
ma-342	240	28	function	function	NOUN
ma-342	240	29	method	method	NOUN
ma-342	240	30	todevelop	todevelop	VERB
ma-342	240	31	the	the	DET
ma-342	240	32	exact	exact	ADJ
ma-342	240	33	travelling	travel	VERB
ma-342	240	34	wave	wave	NOUN
ma-342	240	35	solutions	solution	NOUN
ma-342	240	36	of	of	ADP
ma-342	240	37	a	a	DET
ma-342	240	38	family	family	NOUN
ma-342	240	39	of	of	ADP
ma-342	240	40	3d	3d	PROPN
ma-342	240	41	fractional	fractional	ADJ
ma-342	240	42	wbbm	wbbm	PROPN
ma-342	240	43	equations	equation	NOUN
ma-342	240	44	,	,	PUNCT
ma-342	240	45	results	result	VERB
ma-342	240	46	phys	phy	NOUN
ma-342	240	47	.	.	PUNCT
ma-342	241	1	41(2022	41(2022	NOUN
ma-342	241	2	)	)	PUNCT
ma-342	241	3	,	,	PUNCT
ma-342	241	4	105969.[10	105969.[10	NUM
ma-342	241	5	]	]	X
ma-342	241	6	m.i	m.i	PROPN
ma-342	241	7	.	.	PROPN
ma-342	241	8	asjad	asjad	PROPN
ma-342	241	9	,	,	PUNCT
ma-342	241	10	n.	n.	PROPN
ma-342	241	11	ullah	ullah	PROPN
ma-342	241	12	,	,	PUNCT
ma-342	241	13	h.u	h.u	PROPN
ma-342	242	1	.	.	PUNCT
ma-342	242	2	rehman	rehman	PROPN
ma-342	242	3	,	,	PUNCT
ma-342	242	4	d.	d.	PROPN
ma-342	242	5	baleanu	baleanu	PROPN
ma-342	242	6	,	,	PUNCT
ma-342	242	7	optical	optical	ADJ
ma-342	242	8	solitons	soliton	NOUN
ma-342	242	9	for	for	ADP
ma-342	242	10	conformable	conformable	ADJ
ma-342	242	11	space	space	NOUN
ma-342	242	12	-	-	PUNCT
ma-342	242	13	time	time	NOUN
ma-342	242	14	fractional	fractional	ADJ
ma-342	242	15	non	non	ADJ
ma-342	242	16	-	-	ADJ
ma-342	242	17	linearmodel	linearmodel	ADJ
ma-342	242	18	,	,	PUNCT
ma-342	242	19	j.	j.	PROPN
ma-342	242	20	math	math	PROPN
ma-342	242	21	.	.	PUNCT
ma-342	243	1	comput	comput	NOUN
ma-342	243	2	.	.	PUNCT
ma-342	244	1	sci	sci	PROPN
ma-342	244	2	.	.	PROPN
ma-342	244	3	27	27	NUM
ma-342	244	4	(	(	PUNCT
ma-342	244	5	2022	2022	NUM
ma-342	244	6	)	)	PUNCT
ma-342	244	7	,	,	PUNCT
ma-342	244	8	1–9.[11	1–9.[11	NUM
ma-342	244	9	]	]	X
ma-342	244	10	h.m	h.m	PROPN
ma-342	244	11	.	.	PROPN
ma-342	244	12	baskonus	baskonus	PROPN
ma-342	244	13	,	,	PUNCT
ma-342	244	14	m.s	m.s	PROPN
ma-342	244	15	.	.	PROPN
ma-342	244	16	osman	osman	PROPN
ma-342	244	17	,	,	PUNCT
ma-342	244	18	h.u	h.u	PROPN
ma-342	244	19	.	.	PUNCT
ma-342	244	20	rehman	rehman	PROPN
ma-342	244	21	,	,	PUNCT
ma-342	244	22	m.	m.	PROPN
ma-342	244	23	ramzan	ramzan	PROPN
ma-342	244	24	,	,	PUNCT
ma-342	244	25	m.	m.	PROPN
ma-342	244	26	tahir	tahir	PROPN
ma-342	244	27	,	,	PUNCT
ma-342	244	28	s.	s.	PROPN
ma-342	244	29	ashraf	ashraf	PROPN
ma-342	244	30	,	,	PUNCT
ma-342	244	31	on	on	ADP
ma-342	244	32	pulse	pulse	NOUN
ma-342	244	33	propagation	propagation	NOUN
ma-342	244	34	of	of	ADP
ma-342	244	35	soliton	soliton	NOUN
ma-342	244	36	wavesolutions	wavesolution	NOUN
ma-342	244	37	related	relate	VERB
ma-342	244	38	to	to	ADP
ma-342	244	39	the	the	DET
ma-342	244	40	perturbed	perturb	VERB
ma-342	244	41	chen?lee?liu	chen?lee?liu	PROPN
ma-342	244	42	equation	equation	NOUN
ma-342	244	43	in	in	ADP
ma-342	244	44	an	an	DET
ma-342	244	45	optical	optical	ADJ
ma-342	244	46	fiber	fiber	NOUN
ma-342	244	47	,	,	PUNCT
ma-342	244	48	opt	opt	PROPN
ma-342	244	49	.	.	PUNCT
ma-342	245	1	quantum	quantum	PROPN
ma-342	245	2	electron	electron	NOUN
ma-342	245	3	.	.	PUNCT
ma-342	246	1	53	53	NUM
ma-342	246	2	(	(	PUNCT
ma-342	246	3	2021),1–17.[12	2021),1–17.[12	NUM
ma-342	246	4	]	]	X
ma-342	246	5	m.d	m.d	PROPN
ma-342	246	6	.	.	PROPN
ma-342	246	7	feit	feit	PROPN
ma-342	246	8	,	,	PUNCT
ma-342	246	9	j.a	j.a	PROPN
ma-342	246	10	.	.	PROPN
ma-342	246	11	fleck	fleck	PROPN
ma-342	246	12	jr	jr	PROPN
ma-342	246	13	.	.	PROPN
ma-342	246	14	,	,	PUNCT
ma-342	246	15	a.	a.	NOUN
ma-342	246	16	steiger	steiger	PROPN
ma-342	246	17	,	,	PUNCT
ma-342	246	18	solution	solution	NOUN
ma-342	246	19	of	of	ADP
ma-342	246	20	the	the	DET
ma-342	246	21	schrodinger	schrodinger	ADJ
ma-342	246	22	equation	equation	NOUN
ma-342	246	23	by	by	ADP
ma-342	246	24	a	a	DET
ma-342	246	25	spectral	spectral	ADJ
ma-342	246	26	method	method	NOUN
ma-342	246	27	,	,	PUNCT
ma-342	246	28	j.	j.	PROPN
ma-342	246	29	comput	comput	PROPN
ma-342	246	30	.	.	PUNCT
ma-342	247	1	phys.47	phys.47	PROPN
ma-342	247	2	(	(	PUNCT
ma-342	247	3	1982	1982	NUM
ma-342	247	4	)	)	PUNCT
ma-342	247	5	,	,	PUNCT
ma-342	247	6	412–433.[13	412–433.[13	NOUN
ma-342	247	7	]	]	X
ma-342	247	8	r.k	r.k	PROPN
ma-342	247	9	.	.	PROPN
ma-342	247	10	gazizov	gazizov	PROPN
ma-342	247	11	,	,	PUNCT
ma-342	247	12	a.a	a.a	PROPN
ma-342	247	13	.	.	PROPN
ma-342	247	14	kasatkin	kasatkin	PROPN
ma-342	247	15	,	,	PUNCT
ma-342	247	16	construction	construction	NOUN
ma-342	247	17	of	of	ADP
ma-342	247	18	exact	exact	ADJ
ma-342	247	19	solutions	solution	NOUN
ma-342	247	20	for	for	ADP
ma-342	247	21	fractional	fractional	ADJ
ma-342	247	22	order	order	NOUN
ma-342	247	23	differential	differential	ADJ
ma-342	247	24	equations	equation	NOUN
ma-342	247	25	by	by	ADP
ma-342	247	26	invariantsubspace	invariantsubspace	NOUN
ma-342	247	27	method	method	NOUN
ma-342	247	28	,	,	PUNCT
ma-342	247	29	comput	comput	NOUN
ma-342	247	30	.	.	PUNCT
ma-342	248	1	math	math	NOUN
ma-342	248	2	.	.	PUNCT
ma-342	249	1	appl	appl	PROPN
ma-342	249	2	.	.	PUNCT
ma-342	250	1	66	66	NUM
ma-342	250	2	(	(	PUNCT
ma-342	250	3	2013	2013	NUM
ma-342	250	4	)	)	PUNCT
ma-342	250	5	,	,	PUNCT
ma-342	250	6	576–584.[14	576–584.[14	PROPN
ma-342	250	7	]	]	PUNCT
ma-342	251	1	v.	v.	CCONJ
ma-342	251	2	gokulakrishnan	gokulakrishnan	PROPN
ma-342	251	3	,	,	PUNCT
ma-342	251	4	r.	r.	PROPN
ma-342	251	5	srinivasan	srinivasan	PROPN
ma-342	251	6	,	,	PUNCT
ma-342	251	7	impulsive	impulsive	ADJ
ma-342	251	8	effects	effect	NOUN
ma-342	251	9	on	on	ADP
ma-342	251	10	stabilization	stabilization	NOUN
ma-342	251	11	of	of	ADP
ma-342	251	12	stochastic	stochastic	ADJ
ma-342	251	13	nonlinear	nonlinear	ADJ
ma-342	251	14	reaction	reaction	NOUN
ma-342	251	15	-	-	PUNCT
ma-342	251	16	diffusionsystems	diffusionsystem	NOUN
ma-342	251	17	with	with	ADP
ma-342	251	18	time	time	NOUN
ma-342	251	19	delays	delay	NOUN
ma-342	251	20	and	and	CCONJ
ma-342	251	21	boundary	boundary	ADJ
ma-342	251	22	feedback	feedback	NOUN
ma-342	251	23	control	control	NOUN
ma-342	251	24	,	,	PUNCT
ma-342	251	25	j.	j.	PROPN
ma-342	251	26	math	math	PROPN
ma-342	251	27	.	.	PUNCT
ma-342	252	1	comput	comput	NOUN
ma-342	252	2	.	.	PUNCT
ma-342	253	1	sci	sci	PROPN
ma-342	253	2	.	.	PROPN
ma-342	253	3	28	28	NUM
ma-342	253	4	(	(	PUNCT
ma-342	253	5	2023	2023	NUM
ma-342	253	6	)	)	PUNCT
ma-342	253	7	,	,	PUNCT
ma-342	253	8	350–362.[15	350–362.[15	PROPN
ma-342	253	9	]	]	X
ma-342	253	10	m.s	m.s	PROPN
ma-342	253	11	.	.	PROPN
ma-342	253	12	hashemi	hashemi	PROPN
ma-342	253	13	,	,	PUNCT
ma-342	253	14	a	a	DET
ma-342	253	15	novel	novel	ADJ
ma-342	253	16	approach	approach	NOUN
ma-342	253	17	to	to	PART
ma-342	253	18	find	find	VERB
ma-342	253	19	exact	exact	ADJ
ma-342	253	20	solutions	solution	NOUN
ma-342	253	21	of	of	ADP
ma-342	253	22	fractional	fractional	ADJ
ma-342	253	23	evolution	evolution	NOUN
ma-342	253	24	equations	equation	NOUN
ma-342	253	25	with	with	ADP
ma-342	253	26	non	non	ADJ
ma-342	253	27	-	-	ADJ
ma-342	253	28	singularkernel	singularkernel	ADJ
ma-342	253	29	derivative	derivative	NOUN
ma-342	253	30	,	,	PUNCT
ma-342	253	31	chaos	chaos	NOUN
ma-342	253	32	solitons	soliton	NOUN
ma-342	253	33	fractals	fractal	VERB
ma-342	253	34	152	152	NUM
ma-342	253	35	(	(	PUNCT
ma-342	253	36	2021	2021	NUM
ma-342	253	37	)	)	PUNCT
ma-342	253	38	,	,	PUNCT
ma-342	253	39	111367.[16	111367.[16	NUM
ma-342	253	40	]	]	X
ma-342	253	41	m.s	m.s	PROPN
ma-342	253	42	.	.	PROPN
ma-342	253	43	hashemi	hashemi	PROPN
ma-342	253	44	,	,	PUNCT
ma-342	253	45	d.	d.	PROPN
ma-342	253	46	baleanu	baleanu	PROPN
ma-342	253	47	,	,	PUNCT
ma-342	253	48	lie	lie	NOUN
ma-342	253	49	symmetry	symmetry	NOUN
ma-342	253	50	analysis	analysis	NOUN
ma-342	253	51	of	of	ADP
ma-342	253	52	fractional	fractional	ADJ
ma-342	253	53	differential	differential	ADJ
ma-342	253	54	equations	equation	NOUN
ma-342	253	55	,	,	PUNCT
ma-342	253	56	chapman	chapman	NOUN
ma-342	253	57	and	and	CCONJ
ma-342	253	58	hall	hall	PROPN
ma-342	253	59	/	/	SYM
ma-342	253	60	crc	crc	PROPN
ma-342	253	61	,	,	PUNCT
ma-342	253	62	new	new	PROPN
ma-342	253	63	york	york	PROPN
ma-342	253	64	,	,	PUNCT
ma-342	253	65	2020	2020	NUM
ma-342	253	66	.	.	PUNCT
ma-342	254	1	https://doi.org/10.28924/ada/ma.5.14	https://doi.org/10.28924/ada/ma.5.14	PROPN
ma-342	254	2	eur	eur	PROPN
ma-342	254	3	.	.	PUNCT
ma-342	255	1	j.	j.	PROPN
ma-342	255	2	math	math	PROPN
ma-342	255	3	.	.	PUNCT
ma-342	256	1	anal	anal	PROPN
ma-342	256	2	.	.	PUNCT
ma-342	257	1	10.28924	10.28924	NUM
ma-342	257	2	/	/	SYM
ma-342	257	3	ada	ada	PROPN
ma-342	257	4	/	/	SYM
ma-342	257	5	ma.5.14	ma.5.14	NOUN
ma-342	257	6	13	13	NUM
ma-342	258	1	[	[	X
ma-342	258	2	17	17	NUM
ma-342	258	3	]	]	X
ma-342	258	4	m.s	m.s	PROPN
ma-342	258	5	.	.	PROPN
ma-342	258	6	hashemi	hashemi	PROPN
ma-342	258	7	,	,	PUNCT
ma-342	258	8	m.	m.	PROPN
ma-342	258	9	inc	inc	PROPN
ma-342	258	10	,	,	PUNCT
ma-342	258	11	b.	b.	PROPN
ma-342	258	12	kilic	kilic	PROPN
ma-342	258	13	,	,	PUNCT
ma-342	258	14	a.	a.	NOUN
ma-342	258	15	akcol	akcol	PROPN
ma-342	258	16	,	,	PUNCT
ma-342	258	17	on	on	ADP
ma-342	258	18	solitons	soliton	NOUN
ma-342	258	19	and	and	CCONJ
ma-342	258	20	invariant	invariant	ADJ
ma-342	258	21	solutions	solution	NOUN
ma-342	258	22	of	of	ADP
ma-342	258	23	the	the	DET
ma-342	258	24	magneto	magneto	PROPN
ma-342	258	25	-	-	PUNCT
ma-342	258	26	electro	electro	VERB
ma-342	258	27	-	-	PUNCT
ma-342	258	28	elasticcircular	elasticcircular	ADJ
ma-342	258	29	rod	rod	NOUN
ma-342	258	30	,	,	PUNCT
ma-342	258	31	waves	wave	VERB
ma-342	258	32	random	random	ADJ
ma-342	258	33	complex	complex	ADJ
ma-342	258	34	media	medium	NOUN
ma-342	258	35	26	26	NUM
ma-342	258	36	(	(	PUNCT
ma-342	258	37	2016	2016	NUM
ma-342	258	38	)	)	PUNCT
ma-342	258	39	,	,	PUNCT
ma-342	258	40	259–271.[18	259–271.[18	PROPN
ma-342	258	41	]	]	X
ma-342	258	42	m.s	m.s	PROPN
ma-342	258	43	.	.	PROPN
ma-342	258	44	hashemi	hashemi	PROPN
ma-342	258	45	,	,	PUNCT
ma-342	258	46	m.c	m.c	PROPN
ma-342	258	47	.	.	PROPN
ma-342	258	48	nucci	nucci	PROPN
ma-342	258	49	,	,	PUNCT
ma-342	258	50	s.	s.	PROPN
ma-342	258	51	abbasbandy	abbasbandy	PROPN
ma-342	258	52	,	,	PUNCT
ma-342	258	53	group	group	NOUN
ma-342	258	54	analysis	analysis	NOUN
ma-342	258	55	of	of	ADP
ma-342	258	56	the	the	DET
ma-342	258	57	modified	modify	VERB
ma-342	258	58	generalized	generalize	VERB
ma-342	258	59	vakhnenko	vakhnenko	NOUN
ma-342	258	60	equation	equation	NOUN
ma-342	258	61	,	,	PUNCT
ma-342	258	62	commun	commun	PROPN
ma-342	258	63	.	.	PUNCT
ma-342	259	1	nonlinear	nonlinear	PROPN
ma-342	259	2	sci	sci	PROPN
ma-342	259	3	.	.	PUNCT
ma-342	259	4	numer	numer	PROPN
ma-342	259	5	.	.	PUNCT
ma-342	260	1	simul	simul	PROPN
ma-342	260	2	.	.	PROPN
ma-342	261	1	18	18	NUM
ma-342	261	2	(	(	PUNCT
ma-342	261	3	2013	2013	NUM
ma-342	261	4	)	)	PUNCT
ma-342	261	5	,	,	PUNCT
ma-342	261	6	867–877.[19	867–877.[19	PROPN
ma-342	261	7	]	]	PUNCT
ma-342	261	8	k.	k.	PROPN
ma-342	261	9	hosseini	hosseini	PROPN
ma-342	261	10	,	,	PUNCT
ma-342	261	11	s.	s.	PROPN
ma-342	261	12	salahshour	salahshour	PROPN
ma-342	261	13	,	,	PUNCT
ma-342	261	14	m.	m.	NOUN
ma-342	261	15	mirzazadeh	mirzazadeh	PROPN
ma-342	261	16	,	,	PUNCT
ma-342	261	17	bright	bright	ADJ
ma-342	261	18	and	and	CCONJ
ma-342	261	19	dark	dark	ADJ
ma-342	261	20	solitons	soliton	NOUN
ma-342	261	21	of	of	ADP
ma-342	261	22	a	a	DET
ma-342	261	23	weakly	weakly	ADJ
ma-342	261	24	nonlocal	nonlocal	ADJ
ma-342	261	25	schrodinger	schrodinger	NOUN
ma-342	261	26	equationinvolving	equationinvolve	VERB
ma-342	261	27	the	the	DET
ma-342	261	28	parabolic	parabolic	ADJ
ma-342	261	29	law	law	NOUN
ma-342	261	30	nonlinearity	nonlinearity	NOUN
ma-342	261	31	,	,	PUNCT
ma-342	261	32	optik	optik	PROPN
ma-342	261	33	227	227	NUM
ma-342	261	34	(	(	PUNCT
ma-342	261	35	2021	2021	NUM
ma-342	261	36	)	)	PUNCT
ma-342	261	37	,	,	PUNCT
ma-342	261	38	166042.[20	166042.[20	NUM
ma-342	261	39	]	]	X
ma-342	261	40	l.	l.	PROPN
ma-342	261	41	gagnon	gagnon	PROPN
ma-342	261	42	,	,	PUNCT
ma-342	261	43	p.	p.	PROPN
ma-342	261	44	winternitz	winternitz	PROPN
ma-342	261	45	,	,	PUNCT
ma-342	261	46	lie	lie	NOUN
ma-342	261	47	symmetries	symmetry	NOUN
ma-342	261	48	of	of	ADP
ma-342	261	49	a	a	DET
ma-342	261	50	generalised	generalise	VERB
ma-342	261	51	nonlinear	nonlinear	ADJ
ma-342	261	52	schrodinger	schrodinger	PROPN
ma-342	261	53	equation	equation	NOUN
ma-342	261	54	:	:	PUNCT
ma-342	261	55	i.	i.	NOUN
ma-342	261	56	the	the	DET
ma-342	261	57	symmetrygroup	symmetrygroup	NOUN
ma-342	261	58	and	and	CCONJ
ma-342	261	59	its	its	PRON
ma-342	261	60	subgroups	subgroup	NOUN
ma-342	261	61	,	,	PUNCT
ma-342	261	62	j.	j.	PROPN
ma-342	261	63	phys	phys	PROPN
ma-342	261	64	.	.	PUNCT
ma-342	262	1	a	a	DET
ma-342	262	2	:	:	PUNCT
ma-342	262	3	math	math	NOUN
ma-342	262	4	.	.	PUNCT
ma-342	263	1	gen	gen	PROPN
ma-342	263	2	.	.	PROPN
ma-342	263	3	21	21	NUM
ma-342	263	4	(	(	PUNCT
ma-342	263	5	1988	1988	NUM
ma-342	263	6	)	)	PUNCT
ma-342	263	7	,	,	PUNCT
ma-342	263	8	1493.[21	1493.[21	PROPN
ma-342	263	9	]	]	X
ma-342	263	10	m.a	m.a	PROPN
ma-342	263	11	.	.	PROPN
ma-342	263	12	iqbal	iqbal	PROPN
ma-342	263	13	,	,	PUNCT
ma-342	263	14	y.	y.	PROPN
ma-342	263	15	wang	wang	PROPN
ma-342	263	16	,	,	PUNCT
ma-342	263	17	m.m	m.m	PROPN
ma-342	263	18	.	.	PROPN
ma-342	263	19	miah	miah	PROPN
ma-342	263	20	,	,	PUNCT
ma-342	263	21	m.s	m.s	PROPN
ma-342	263	22	.	.	PROPN
ma-342	263	23	osman	osman	PROPN
ma-342	263	24	,	,	PUNCT
ma-342	263	25	study	study	NOUN
ma-342	263	26	on	on	ADP
ma-342	263	27	date	date	NOUN
ma-342	263	28	jimbo	jimbo	PROPN
ma-342	263	29	kashiwara	kashiwara	PROPN
ma-342	263	30	miwa	miwa	PROPN
ma-342	263	31	equation	equation	NOUN
ma-342	263	32	with	with	ADP
ma-342	263	33	conformablederivative	conformablederivative	ADJ
ma-342	263	34	dependent	dependent	ADJ
ma-342	263	35	on	on	ADP
ma-342	263	36	time	time	NOUN
ma-342	263	37	parameter	parameter	NOUN
ma-342	263	38	to	to	ADP
ma-342	263	39	and	and	CCONJ
ma-342	263	40	the	the	DET
ma-342	263	41	exact	exact	ADJ
ma-342	263	42	dynamic	dynamic	ADJ
ma-342	263	43	wave	wave	NOUN
ma-342	263	44	solutions	solution	NOUN
ma-342	263	45	,	,	PUNCT
ma-342	263	46	fractal	fractal	ADJ
ma-342	263	47	fract	fract	NOUN
ma-342	263	48	.	.	PUNCT
ma-342	264	1	6	6	NUM
ma-342	264	2	(	(	PUNCT
ma-342	264	3	2021	2021	NUM
ma-342	264	4	)	)	PUNCT
ma-342	264	5	,	,	PUNCT
ma-342	264	6	4.[22	4.[22	NUM
ma-342	264	7	]	]	X
ma-342	264	8	n.a	n.a	PROPN
ma-342	264	9	.	.	PROPN
ma-342	264	10	kudryashov	kudryashov	PROPN
ma-342	264	11	,	,	PUNCT
ma-342	264	12	highly	highly	ADV
ma-342	264	13	dispersive	dispersive	ADJ
ma-342	264	14	solitary	solitary	ADJ
ma-342	264	15	wave	wave	NOUN
ma-342	264	16	solutions	solution	NOUN
ma-342	264	17	of	of	ADP
ma-342	264	18	perturbed	perturb	VERB
ma-342	264	19	nonlinear	nonlinear	PROPN
ma-342	264	20	schrodinger	schrodinger	PROPN
ma-342	264	21	equations	equation	NOUN
ma-342	264	22	,	,	PUNCT
ma-342	265	1	appl.math	appl.math	PROPN
ma-342	265	2	.	.	PUNCT
ma-342	265	3	comput	comput	NOUN
ma-342	265	4	.	.	PUNCT
ma-342	266	1	371	371	NUM
ma-342	266	2	(	(	PUNCT
ma-342	266	3	2020	2020	NUM
ma-342	266	4	)	)	PUNCT
ma-342	266	5	,	,	PUNCT
ma-342	266	6	124972.[23	124972.[23	NUM
ma-342	266	7	]	]	X
ma-342	267	1	w.	w.	PROPN
ma-342	267	2	liu	liu	PROPN
ma-342	267	3	,	,	PUNCT
ma-342	267	4	y.	y.	PROPN
ma-342	267	5	zhang	zhang	PROPN
ma-342	267	6	,	,	PUNCT
ma-342	267	7	z.	z.	PROPN
ma-342	267	8	luan	luan	PROPN
ma-342	267	9	,	,	PUNCT
ma-342	267	10	q.	q.	PROPN
ma-342	267	11	zhou	zhou	PROPN
ma-342	267	12	,	,	PUNCT
ma-342	267	13	m.	m.	NOUN
ma-342	267	14	mirzazadeh	mirzazadeh	PROPN
ma-342	267	15	,	,	PUNCT
ma-342	267	16	m.	m.	NOUN
ma-342	267	17	ekici	ekici	PROPN
ma-342	267	18	,	,	PUNCT
ma-342	267	19	a.	a.	PROPN
ma-342	267	20	biswas	biswas	PROPN
ma-342	267	21	,	,	PUNCT
ma-342	267	22	dromion	dromion	NOUN
ma-342	267	23	-	-	PUNCT
ma-342	267	24	like	like	ADJ
ma-342	267	25	soliton	soliton	NOUN
ma-342	267	26	interactions	interaction	NOUN
ma-342	267	27	fornonlinear	fornonlinear	VERB
ma-342	267	28	schrodinger	schrodinger	NOUN
ma-342	267	29	equation	equation	NOUN
ma-342	267	30	with	with	ADP
ma-342	267	31	variable	variable	ADJ
ma-342	267	32	coefficients	coefficient	NOUN
ma-342	267	33	in	in	ADP
ma-342	267	34	inhomogeneous	inhomogeneous	ADJ
ma-342	267	35	optical	optical	ADJ
ma-342	267	36	fibers	fiber	NOUN
ma-342	267	37	,	,	PUNCT
ma-342	267	38	nonlinear	nonlinear	ADJ
ma-342	267	39	dyn	dyn	NOUN
ma-342	267	40	.	.	PUNCT
ma-342	268	1	96(2019	96(2019	NUM
ma-342	268	2	)	)	PUNCT
ma-342	268	3	,	,	PUNCT
ma-342	268	4	729–736.[24	729–736.[24	NOUN
ma-342	268	5	]	]	X
ma-342	268	6	m.	m.	NOUN
ma-342	268	7	mirzazadeh	mirzazadeh	PROPN
ma-342	268	8	,	,	PUNCT
ma-342	268	9	a.	a.	PROPN
ma-342	268	10	sharif	sharif	PROPN
ma-342	268	11	,	,	PUNCT
ma-342	268	12	m.s	m.s	PROPN
ma-342	268	13	.	.	PROPN
ma-342	268	14	hashemi	hashemi	PROPN
ma-342	268	15	,	,	PUNCT
ma-342	268	16	a.	a.	PROPN
ma-342	268	17	akcol	akcol	PROPN
ma-342	268	18	,	,	PUNCT
ma-342	268	19	s.m	s.m	PROPN
ma-342	268	20	.	.	PROPN
ma-342	268	21	el	el	PROPN
ma-342	268	22	din	din	PROPN
ma-342	268	23	,	,	PUNCT
ma-342	268	24	optical	optical	ADJ
ma-342	268	25	solitons	soliton	NOUN
ma-342	268	26	with	with	ADP
ma-342	268	27	an	an	DET
ma-342	268	28	extended	extended	ADJ
ma-342	268	29	(	(	PUNCT
ma-342	268	30	3	3	NUM
ma-342	268	31	+	+	NOUN
ma-342	268	32	1)-dimensional	1)-dimensional	ADJ
ma-342	268	33	nonlinear	nonlinear	ADJ
ma-342	268	34	conformable	conformable	ADJ
ma-342	268	35	schrodinger	schrodinger	NOUN
ma-342	268	36	equation	equation	NOUN
ma-342	268	37	including	include	VERB
ma-342	268	38	cubic	cubic	ADJ
ma-342	268	39	-	-	PUNCT
ma-342	268	40	quintic	quintic	ADJ
ma-342	268	41	nonlinearity	nonlinearity	NOUN
ma-342	268	42	,	,	PUNCT
ma-342	268	43	results	result	VERB
ma-342	268	44	phys.49	phys.49	NOUN
ma-342	268	45	(	(	PUNCT
ma-342	268	46	2023	2023	NUM
ma-342	268	47	)	)	PUNCT
ma-342	268	48	,	,	PUNCT
ma-342	269	1	106521.[25	106521.[25	PROPN
ma-342	269	2	]	]	X
ma-342	269	3	m.c	m.c	PROPN
ma-342	269	4	.	.	PROPN
ma-342	269	5	nucci	nucci	PROPN
ma-342	269	6	,	,	PUNCT
ma-342	269	7	p.g.l	p.g.l	ADJ
ma-342	269	8	.	.	PUNCT
ma-342	269	9	leach	leach	NOUN
ma-342	269	10	,	,	PUNCT
ma-342	269	11	the	the	DET
ma-342	269	12	determination	determination	NOUN
ma-342	269	13	of	of	ADP
ma-342	269	14	nonlocal	nonlocal	ADJ
ma-342	269	15	symmetries	symmetry	NOUN
ma-342	269	16	by	by	ADP
ma-342	269	17	the	the	DET
ma-342	269	18	technique	technique	NOUN
ma-342	269	19	of	of	ADP
ma-342	269	20	reduction	reduction	NOUN
ma-342	269	21	of	of	ADP
ma-342	269	22	order	order	NOUN
ma-342	269	23	,	,	PUNCT
ma-342	269	24	j.math	j.math	NOUN
ma-342	269	25	.	.	PUNCT
ma-342	270	1	anal	anal	PROPN
ma-342	270	2	.	.	PUNCT
ma-342	270	3	appl	appl	PROPN
ma-342	270	4	.	.	PUNCT
ma-342	271	1	251	251	NUM
ma-342	271	2	(	(	PUNCT
ma-342	271	3	2000	2000	NUM
ma-342	271	4	)	)	PUNCT
ma-342	271	5	,	,	PUNCT
ma-342	271	6	871–884.[26	871–884.[26	PROPN
ma-342	271	7	]	]	X
ma-342	271	8	m.s	m.s	PROPN
ma-342	271	9	.	.	PROPN
ma-342	271	10	osman	osman	PROPN
ma-342	271	11	,	,	PUNCT
ma-342	271	12	d.	d.	PROPN
ma-342	271	13	baleanu	baleanu	PROPN
ma-342	271	14	,	,	PUNCT
ma-342	271	15	a.r	a.r	PROPN
ma-342	271	16	.	.	PROPN
ma-342	271	17	adem	adem	PROPN
ma-342	271	18	,	,	PUNCT
ma-342	271	19	k.	k.	PROPN
ma-342	271	20	hosseini	hosseini	PROPN
ma-342	271	21	,	,	PUNCT
ma-342	271	22	m.	m.	NOUN
ma-342	271	23	mirzazadeh	mirzazadeh	PROPN
ma-342	271	24	,	,	PUNCT
ma-342	271	25	m.	m.	NOUN
ma-342	271	26	eslami	eslami	PROPN
ma-342	271	27	,	,	PUNCT
ma-342	271	28	double	double	ADJ
ma-342	271	29	-	-	PUNCT
ma-342	271	30	wave	wave	NOUN
ma-342	271	31	solutions	solution	NOUN
ma-342	271	32	and	and	CCONJ
ma-342	271	33	liesymmetry	liesymmetry	NOUN
ma-342	271	34	analysis	analysis	NOUN
ma-342	271	35	to	to	ADP
ma-342	271	36	the	the	DET
ma-342	271	37	(	(	PUNCT
ma-342	271	38	2	2	NUM
ma-342	271	39	+	+	NOUN
ma-342	271	40	1)-dimensional	1)-dimensional	ADJ
ma-342	271	41	coupled	couple	VERB
ma-342	271	42	burgers	burger	NOUN
ma-342	271	43	equations	equation	NOUN
ma-342	271	44	,	,	PUNCT
ma-342	271	45	chin	chin	PROPN
ma-342	271	46	.	.	PUNCT
ma-342	272	1	j.	j.	PROPN
ma-342	272	2	phys	phys	PROPN
ma-342	272	3	.	.	PUNCT
ma-342	273	1	63	63	NUM
ma-342	273	2	(	(	PUNCT
ma-342	273	3	2020	2020	NUM
ma-342	273	4	)	)	PUNCT
ma-342	273	5	,	,	PUNCT
ma-342	273	6	122–129.[27	122–129.[27	PROPN
ma-342	273	7	]	]	X
ma-342	273	8	m.n	m.n	PROPN
ma-342	273	9	.	.	PROPN
ma-342	273	10	rasoulizadeh	rasoulizadeh	PROPN
ma-342	273	11	,	,	PUNCT
ma-342	273	12	m.j	m.j	PROPN
ma-342	273	13	.	.	PROPN
ma-342	273	14	ebadi	ebadi	PROPN
ma-342	273	15	,	,	PUNCT
ma-342	273	16	z.	z.	PROPN
ma-342	273	17	avazzadeh	avazzadeh	PROPN
ma-342	273	18	,	,	PUNCT
ma-342	273	19	o.	o.	PROPN
ma-342	273	20	nikan	nikan	PROPN
ma-342	273	21	,	,	PUNCT
ma-342	273	22	an	an	DET
ma-342	273	23	efficient	efficient	ADJ
ma-342	273	24	local	local	ADJ
ma-342	273	25	meshless	meshless	ADJ
ma-342	273	26	method	method	NOUN
ma-342	273	27	for	for	ADP
ma-342	273	28	the	the	DET
ma-342	273	29	equal	equal	ADJ
ma-342	273	30	widthequation	widthequation	NOUN
ma-342	273	31	in	in	ADP
ma-342	273	32	fluid	fluid	ADJ
ma-342	273	33	mechanics	mechanic	NOUN
ma-342	273	34	,	,	PUNCT
ma-342	273	35	eng	eng	PROPN
ma-342	273	36	.	.	PROPN
ma-342	273	37	anal	anal	PROPN
ma-342	273	38	.	.	PUNCT
ma-342	274	1	bound	bind	VERB
ma-342	274	2	.	.	PUNCT
ma-342	274	3	elem	elem	NOUN
ma-342	274	4	.	.	PUNCT
ma-342	275	1	131	131	NUM
ma-342	275	2	(	(	PUNCT
ma-342	275	3	2021	2021	NUM
ma-342	275	4	)	)	PUNCT
ma-342	275	5	,	,	PUNCT
ma-342	275	6	258–268.[28	258–268.[28	PROPN
ma-342	275	7	]	]	X
ma-342	275	8	h.u	h.u	PROPN
ma-342	275	9	.	.	PUNCT
ma-342	275	10	rehman	rehman	PROPN
ma-342	275	11	,	,	PUNCT
ma-342	275	12	i.	i.	PROPN
ma-342	275	13	iqbal	iqbal	PROPN
ma-342	275	14	,	,	PUNCT
ma-342	275	15	s.	s.	PROPN
ma-342	275	16	subhi	subhi	PROPN
ma-342	275	17	aiadi	aiadi	PROPN
ma-342	275	18	,	,	PUNCT
ma-342	275	19	n.	n.	PROPN
ma-342	275	20	mlaiki	mlaiki	PROPN
ma-342	275	21	,	,	PUNCT
ma-342	275	22	m.s	m.s	PROPN
ma-342	275	23	.	.	PROPN
ma-342	275	24	saleem	saleem	PROPN
ma-342	275	25	,	,	PUNCT
ma-342	275	26	soliton	soliton	NOUN
ma-342	275	27	solutions	solution	NOUN
ma-342	275	28	of	of	ADP
ma-342	275	29	klein	klein	PROPN
ma-342	275	30	fock	fock	PROPN
ma-342	275	31	gordon	gordon	PROPN
ma-342	275	32	equationusing	equationuse	VERB
ma-342	275	33	sardar	sardar	PROPN
ma-342	275	34	subequation	subequation	PROPN
ma-342	275	35	method	method	NOUN
ma-342	275	36	,	,	PUNCT
ma-342	275	37	mathematics	mathematics	NOUN
ma-342	275	38	10	10	NUM
ma-342	275	39	(	(	PUNCT
ma-342	275	40	2022	2022	NUM
ma-342	275	41	)	)	PUNCT
ma-342	275	42	,	,	PUNCT
ma-342	275	43	3377.[29	3377.[29	X
ma-342	275	44	]	]	X
ma-342	275	45	h.u	h.u	PROPN
ma-342	275	46	.	.	PUNCT
ma-342	275	47	rehman	rehman	PROPN
ma-342	275	48	,	,	PUNCT
ma-342	275	49	n.	n.	PROPN
ma-342	275	50	ullah	ullah	PROPN
ma-342	275	51	,	,	PUNCT
ma-342	275	52	m.a	m.a	PROPN
ma-342	275	53	.	.	PROPN
ma-342	275	54	imran	imran	PROPN
ma-342	275	55	,	,	PUNCT
ma-342	275	56	highly	highly	ADV
ma-342	275	57	dispersive	dispersive	ADJ
ma-342	275	58	optical	optical	ADJ
ma-342	275	59	solitons	soliton	NOUN
ma-342	275	60	using	use	VERB
ma-342	275	61	kudryashov	kudryashov	PROPN
ma-342	275	62	’s	’s	PART
ma-342	275	63	method	method	NOUN
ma-342	275	64	,	,	PUNCT
ma-342	275	65	optik	optik	PROPN
ma-342	275	66	199(2019	199(2019	NUM
ma-342	275	67	)	)	PUNCT
ma-342	275	68	,	,	PUNCT
ma-342	275	69	163349.[30	163349.[30	NUM
ma-342	275	70	]	]	X
ma-342	275	71	r.	r.	PROPN
ma-342	275	72	sahadevan	sahadevan	PROPN
ma-342	275	73	,	,	PUNCT
ma-342	275	74	p.	p.	PROPN
ma-342	275	75	prakash	prakash	PROPN
ma-342	275	76	,	,	PUNCT
ma-342	275	77	on	on	ADP
ma-342	275	78	lie	lie	NOUN
ma-342	275	79	symmetry	symmetry	NOUN
ma-342	275	80	analysis	analysis	NOUN
ma-342	275	81	and	and	CCONJ
ma-342	275	82	invariant	invariant	ADJ
ma-342	275	83	subspace	subspace	NOUN
ma-342	275	84	methods	method	NOUN
ma-342	275	85	of	of	ADP
ma-342	275	86	coupled	couple	VERB
ma-342	275	87	time	time	NOUN
ma-342	275	88	fractionalpartial	fractionalpartial	ADJ
ma-342	275	89	differential	differential	NOUN
ma-342	275	90	equations	equation	NOUN
ma-342	275	91	,	,	PUNCT
ma-342	275	92	chaos	chaos	NOUN
ma-342	275	93	solitons	soliton	NOUN
ma-342	275	94	fractals	fractal	VERB
ma-342	275	95	104	104	NUM
ma-342	275	96	(	(	PUNCT
ma-342	275	97	2017	2017	NUM
ma-342	275	98	)	)	PUNCT
ma-342	275	99	,	,	PUNCT
ma-342	275	100	107–120.[31	107–120.[31	X
ma-342	275	101	]	]	X
ma-342	275	102	f.l	f.l	PROPN
ma-342	275	103	.	.	PROPN
ma-342	275	104	xia	xia	PROPN
ma-342	275	105	,	,	PUNCT
ma-342	275	106	f.	f.	PROPN
ma-342	275	107	jarad	jarad	PROPN
ma-342	275	108	,	,	PUNCT
ma-342	275	109	m.s	m.s	PROPN
ma-342	275	110	.	.	PROPN
ma-342	275	111	hashemi	hashemi	PROPN
ma-342	275	112	,	,	PUNCT
ma-342	275	113	m.b	m.b	PROPN
ma-342	275	114	.	.	PROPN
ma-342	275	115	riaz	riaz	PROPN
ma-342	275	116	,	,	PUNCT
ma-342	275	117	a	a	DET
ma-342	275	118	reduction	reduction	NOUN
ma-342	275	119	technique	technique	NOUN
ma-342	275	120	to	to	PART
ma-342	275	121	solve	solve	VERB
ma-342	275	122	the	the	DET
ma-342	275	123	generalized	generalized	ADJ
ma-342	275	124	nonlinear	nonlinear	NOUN
ma-342	275	125	dispersivemk	dispersivemk	ADJ
ma-342	275	126	(	(	PUNCT
ma-342	275	127	m	m	PROPN
ma-342	275	128	,	,	PUNCT
ma-342	275	129	n	n	CCONJ
ma-342	275	130	)	)	PUNCT
ma-342	275	131	equation	equation	NOUN
ma-342	275	132	with	with	ADP
ma-342	275	133	new	new	ADJ
ma-342	275	134	local	local	ADJ
ma-342	275	135	derivative	derivative	NOUN
ma-342	275	136	,	,	PUNCT
ma-342	275	137	results	result	VERB
ma-342	275	138	phys	phy	NOUN
ma-342	275	139	.	.	PUNCT
ma-342	276	1	38	38	NUM
ma-342	276	2	(	(	PUNCT
ma-342	276	3	2022	2022	NUM
ma-342	276	4	)	)	PUNCT
ma-342	276	5	,	,	PUNCT
ma-342	276	6	105512.[32	105512.[32	NUM
ma-342	276	7	]	]	X
ma-342	276	8	y.	y.	PROPN
ma-342	276	9	xie	xie	PROPN
ma-342	276	10	,	,	PUNCT
ma-342	276	11	l.	l.	PROPN
ma-342	276	12	li	li	PROPN
ma-342	276	13	,	,	PUNCT
ma-342	276	14	y.	y.	PROPN
ma-342	276	15	kang	kang	PROPN
ma-342	276	16	,	,	PUNCT
ma-342	276	17	new	new	ADJ
ma-342	276	18	solitons	soliton	NOUN
ma-342	276	19	and	and	CCONJ
ma-342	276	20	conditional	conditional	ADJ
ma-342	276	21	stability	stability	NOUN
ma-342	276	22	to	to	ADP
ma-342	276	23	the	the	DET
ma-342	276	24	high	high	ADJ
ma-342	276	25	dispersive	dispersive	ADJ
ma-342	276	26	nonlinear	nonlinear	ADJ
ma-342	276	27	schrodingerequation	schrodingerequation	NOUN
ma-342	276	28	with	with	ADP
ma-342	276	29	parabolic	parabolic	ADJ
ma-342	276	30	law	law	NOUN
ma-342	276	31	nonlinearity	nonlinearity	NOUN
ma-342	276	32	,	,	PUNCT
ma-342	276	33	nonlinear	nonlinear	ADJ
ma-342	276	34	dyn	dyn	NOUN
ma-342	276	35	.	.	PUNCT
ma-342	276	36	103	103	NUM
ma-342	276	37	(	(	PUNCT
ma-342	276	38	2021	2021	NUM
ma-342	276	39	)	)	PUNCT
ma-342	276	40	,	,	PUNCT
ma-342	276	41	1011–1021.[33	1011–1021.[33	X
ma-342	276	42	]	]	X
ma-342	276	43	a.	a.	PROPN
ma-342	276	44	zafar	zafar	PROPN
ma-342	276	45	,	,	PUNCT
ma-342	276	46	m.	m.	NOUN
ma-342	276	47	raheel	raheel	PROPN
ma-342	276	48	,	,	PUNCT
ma-342	276	49	m.	m.	NOUN
ma-342	276	50	asif	asif	PROPN
ma-342	276	51	,	,	PUNCT
ma-342	276	52	k.	k.	PROPN
ma-342	276	53	hosseini	hosseini	PROPN
ma-342	276	54	,	,	PUNCT
ma-342	276	55	m.	m.	NOUN
ma-342	276	56	mirzazadeh	mirzazadeh	PROPN
ma-342	276	57	,	,	PUNCT
ma-342	276	58	l.	l.	PROPN
ma-342	276	59	akinyemi	akinyemi	PROPN
ma-342	276	60	,	,	PUNCT
ma-342	276	61	some	some	DET
ma-342	276	62	novel	novel	ADJ
ma-342	276	63	integration	integration	NOUN
ma-342	276	64	techniques	technique	NOUN
ma-342	276	65	toexplore	toexplore	VERB
ma-342	276	66	the	the	DET
ma-342	276	67	conformable	conformable	ADJ
ma-342	276	68	m	m	ADJ
ma-342	276	69	-	-	ADJ
ma-342	276	70	fractional	fractional	ADJ
ma-342	276	71	schrodinger?hirota	schrodinger?hirota	NUM
ma-342	276	72	equation	equation	NOUN
ma-342	276	73	,	,	PUNCT
ma-342	276	74	j.	j.	PROPN
ma-342	276	75	ocean	ocean	PROPN
ma-342	276	76	eng	eng	PROPN
ma-342	276	77	.	.	PUNCT
ma-342	277	1	sci	sci	PROPN
ma-342	277	2	.	.	PROPN
ma-342	277	3	7	7	NUM
ma-342	277	4	(	(	PUNCT
ma-342	277	5	2022	2022	NUM
ma-342	277	6	)	)	PUNCT
ma-342	277	7	,	,	PUNCT
ma-342	277	8	337–344.[34	337–344.[34	PROPN
ma-342	277	9	]	]	PUNCT
ma-342	277	10	q.	q.	PROPN
ma-342	277	11	zhou	zhou	PROPN
ma-342	277	12	,	,	PUNCT
ma-342	277	13	d.	d.	PROPN
ma-342	277	14	yao	yao	PROPN
ma-342	277	15	,	,	PUNCT
ma-342	277	16	s.	s.	PROPN
ma-342	277	17	ding	ding	PROPN
ma-342	277	18	,	,	PUNCT
ma-342	277	19	y.	y.	PROPN
ma-342	277	20	zhang	zhang	PROPN
ma-342	277	21	,	,	PUNCT
ma-342	277	22	f.	f.	PROPN
ma-342	277	23	chen	chen	PROPN
ma-342	277	24	,	,	PUNCT
ma-342	277	25	x.	x.	PROPN
ma-342	277	26	liu	liu	PROPN
ma-342	277	27	,	,	PUNCT
ma-342	277	28	spatial	spatial	ADJ
ma-342	277	29	optical	optical	ADJ
ma-342	277	30	solitons	soliton	NOUN
ma-342	277	31	in	in	ADP
ma-342	277	32	fifth	fifth	ADJ
ma-342	277	33	order	order	NOUN
ma-342	277	34	and	and	CCONJ
ma-342	277	35	seventh	seventh	ADJ
ma-342	277	36	orderweakly	orderweakly	ADV
ma-342	277	37	nonlocal	nonlocal	ADJ
ma-342	277	38	nonlinear	nonlinear	ADJ
ma-342	277	39	media	medium	NOUN
ma-342	277	40	,	,	PUNCT
ma-342	277	41	optik	optik	PROPN
ma-342	277	42	124	124	NUM
ma-342	277	43	(	(	PUNCT
ma-342	277	44	2013	2013	NUM
ma-342	277	45	)	)	PUNCT
ma-342	277	46	,	,	PUNCT
ma-342	277	47	5683–5686.[35	5683–5686.[35	NUM
ma-342	277	48	]	]	PUNCT
ma-342	277	49	m.	m.	NOUN
ma-342	277	50	daniel	daniel	PROPN
ma-342	277	51	,	,	PUNCT
ma-342	277	52	l.	l.	PROPN
ma-342	277	53	kavitha	kavitha	PROPN
ma-342	277	54	,	,	PUNCT
ma-342	277	55	r.	r.	PROPN
ma-342	277	56	amuda	amuda	PROPN
ma-342	277	57	,	,	PUNCT
ma-342	277	58	soliton	soliton	NOUN
ma-342	277	59	spin	spin	NOUN
ma-342	277	60	excitations	excitation	NOUN
ma-342	277	61	in	in	ADP
ma-342	277	62	an	an	DET
ma-342	277	63	anisotropic	anisotropic	NOUN
ma-342	277	64	heisenberg	heisenberg	PROPN
ma-342	277	65	ferromagnet	ferromagnet	NOUN
ma-342	277	66	with	with	ADP
ma-342	277	67	octupole	octupole	ADJ
ma-342	277	68	-	-	PUNCT
ma-342	277	69	dipole	dipole	NOUN
ma-342	277	70	interaction	interaction	NOUN
ma-342	277	71	,	,	PUNCT
ma-342	277	72	phys	phy	NOUN
ma-342	277	73	.	.	PUNCT
ma-342	277	74	rev	rev	PROPN
ma-342	277	75	.	.	PROPN
ma-342	278	1	b	b	PROPN
ma-342	278	2	59	59	NUM
ma-342	278	3	(	(	PUNCT
ma-342	278	4	1999	1999	NUM
ma-342	278	5	)	)	PUNCT
ma-342	278	6	,	,	PUNCT
ma-342	278	7	13774.[36	13774.[36	NUM
ma-342	278	8	]	]	PUNCT
ma-342	278	9	m.	m.	NOUN
ma-342	278	10	daniel	daniel	PROPN
ma-342	278	11	,	,	PUNCT
ma-342	278	12	magnetization	magnetization	NOUN
ma-342	278	13	reversal	reversal	NOUN
ma-342	278	14	through	through	ADP
ma-342	278	15	soliton	soliton	NOUN
ma-342	278	16	flip	flip	NOUN
ma-342	278	17	in	in	ADP
ma-342	278	18	a	a	DET
ma-342	278	19	biquadratic	biquadratic	ADJ
ma-342	278	20	ferromagnet	ferromagnet	NOUN
ma-342	278	21	with	with	ADP
ma-342	278	22	varying	vary	VERB
ma-342	278	23	exchangeinteractions	exchangeinteraction	NOUN
ma-342	278	24	,	,	PUNCT
ma-342	278	25	phys	phy	NOUN
ma-342	278	26	.	.	PUNCT
ma-342	279	1	rev	rev	PROPN
ma-342	279	2	.	.	PROPN
ma-342	280	1	b	b	PROPN
ma-342	280	2	66	66	NUM
ma-342	280	3	(	(	PUNCT
ma-342	280	4	2002	2002	NUM
ma-342	280	5	)	)	PUNCT
ma-342	280	6	,	,	PUNCT
ma-342	280	7	184433.[37	184433.[37	NUM
ma-342	280	8	]	]	X
ma-342	280	9	g.p	g.p	PROPN
ma-342	280	10	.	.	PROPN
ma-342	280	11	agrawal	agrawal	PROPN
ma-342	280	12	,	,	PUNCT
ma-342	280	13	nonlinear	nonlinear	ADJ
ma-342	280	14	fiber	fiber	NOUN
ma-342	280	15	optics	optic	NOUN
ma-342	280	16	,	,	PUNCT
ma-342	280	17	academic	academic	ADJ
ma-342	280	18	press	press	NOUN
ma-342	280	19	,	,	PUNCT
ma-342	280	20	new	new	PROPN
ma-342	280	21	york	york	PROPN
ma-342	280	22	,	,	PUNCT
ma-342	280	23	2013	2013	NUM
ma-342	280	24	.	.	PUNCT
ma-342	281	1	https://doi.org/10.28924/ada/ma.5.14	https://doi.org/10.28924/ada/ma.5.14	PROPN
ma-342	281	2	references	reference	VERB