id	sid	tid	token	lemma	pos
cana-951	1	1	communications	communication	NOUN
cana-951	1	2	on	on	ADP
cana-951	1	3	applied	apply	VERB
cana-951	1	4	nonlinear	nonlinear	ADJ
cana-951	1	5	analysis	analysis	NOUN
cana-951	1	6	issn	issn	NOUN
cana-951	1	7	:	:	PUNCT
cana-951	1	8	1074	1074	NUM
cana-951	1	9	-	-	PUNCT
cana-951	1	10	133x	133x	NUM
cana-951	1	11	vol	vol	NOUN
cana-951	1	12	31	31	NUM
cana-951	1	13	no	no	NOUN
cana-951	1	14	.	.	PUNCT
cana-951	2	1	4s	4s	NUM
cana-951	2	2	(	(	PUNCT
cana-951	2	3	2024	2024	NUM
cana-951	2	4	)	)	PUNCT
cana-951	2	5	572	572	NUM
cana-951	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-951	2	7	application	application	NOUN
cana-951	2	8	of	of	ADP
cana-951	2	9	the	the	DET
cana-951	2	10	𝑮’/𝑮	𝑮’/𝑮	PROPN
cana-951	2	11	expansion	expansion	NOUN
cana-951	2	12	method	method	NOUN
cana-951	2	13	for	for	ADP
cana-951	2	14	solving	solve	VERB
cana-951	2	15	new	new	ADJ
cana-951	2	16	form	form	NOUN
cana-951	2	17	of	of	ADP
cana-951	2	18	nonlinear	nonlinear	ADJ
cana-951	2	19	schrödinger	schrödinger	ADJ
cana-951	2	20	equation	equation	NOUN
cana-951	2	21	in	in	ADP
cana-951	2	22	bi	bi	ADJ
cana-951	2	23	-	-	ADJ
cana-951	2	24	isotropic	isotropic	ADJ
cana-951	2	25	fiber	fiber	NOUN
cana-951	2	26	ourahmoun	ourahmoun	NOUN
cana-951	2	27	abbes1	abbes1	NOUN
cana-951	2	28	,	,	PUNCT
cana-951	2	29	mezache	mezache	PROPN
cana-951	2	30	zinelabiddine2	zinelabiddine2	PROPN
cana-951	2	31	1	1	NUM
cana-951	2	32	,	,	PUNCT
cana-951	2	33	2	2	NUM
cana-951	2	34	institute	institute	NOUN
cana-951	2	35	of	of	ADP
cana-951	2	36	optics	optic	NOUN
cana-951	2	37	and	and	CCONJ
cana-951	2	38	fine	fine	ADJ
cana-951	2	39	mechanics	mechanic	NOUN
cana-951	2	40	,	,	PUNCT
cana-951	2	41	university	university	NOUN
cana-951	2	42	of	of	ADP
cana-951	2	43	ferhat	ferhat	PROPN
cana-951	2	44	abbas	abbas	PROPN
cana-951	2	45	setif	setif	PROPN
cana-951	2	46	1	1	NUM
cana-951	2	47	,	,	PUNCT
cana-951	2	48	setif	setif	NOUN
cana-951	2	49	,	,	PUNCT
cana-951	2	50	algeria	algeria	PROPN
cana-951	2	51	.	.	PUNCT
cana-951	3	1	abbes.ourahmoun@univ-setif.dz	abbes.ourahmoun@univ-setif.dz	PROPN
cana-951	3	2	zinemezaache@yahoo.fr	zinemezaache@yahoo.fr	NOUN
cana-951	3	3	article	article	NOUN
cana-951	3	4	history	history	NOUN
cana-951	3	5	:	:	PUNCT
cana-951	3	6	received	receive	VERB
cana-951	3	7	:	:	PUNCT
cana-951	3	8	21	21	NUM
cana-951	3	9	-	-	PUNCT
cana-951	3	10	04	04	NUM
cana-951	3	11	-	-	PUNCT
cana-951	3	12	2024	2024	NUM
cana-951	3	13	revised	revise	VERB
cana-951	3	14	:	:	PUNCT
cana-951	3	15	19	19	NUM
cana-951	3	16	-	-	PUNCT
cana-951	3	17	06	06	NUM
cana-951	3	18	-	-	PUNCT
cana-951	3	19	2024	2024	NUM
cana-951	3	20	accepted	accept	VERB
cana-951	3	21	:	:	PUNCT
cana-951	3	22	27	27	NUM
cana-951	3	23	-	-	SYM
cana-951	3	24	06	06	NUM
cana-951	3	25	-	-	PUNCT
cana-951	3	26	2024	2024	NUM
cana-951	3	27	abstract	abstract	NOUN
cana-951	3	28	:	:	PUNCT
cana-951	3	29	bi	bi	ADJ
cana-951	3	30	-	-	ADJ
cana-951	3	31	isotropic	isotropic	ADJ
cana-951	3	32	media	medium	NOUN
cana-951	3	33	(	(	PUNCT
cana-951	3	34	chiral	chiral	ADJ
cana-951	3	35	and	and	CCONJ
cana-951	3	36	non	non	ADJ
cana-951	3	37	-	-	ADJ
cana-951	3	38	reciprocal	reciprocal	ADJ
cana-951	3	39	)	)	PUNCT
cana-951	3	40	present	present	VERB
cana-951	3	41	an	an	DET
cana-951	3	42	outstanding	outstanding	ADJ
cana-951	3	43	challenge	challenge	NOUN
cana-951	3	44	for	for	ADP
cana-951	3	45	the	the	DET
cana-951	3	46	scientific	scientific	ADJ
cana-951	3	47	community	community	NOUN
cana-951	3	48	.	.	PUNCT
cana-951	4	1	their	their	PRON
cana-951	4	2	characteristics	characteristic	NOUN
cana-951	4	3	have	have	AUX
cana-951	4	4	facilitated	facilitate	VERB
cana-951	4	5	the	the	DET
cana-951	4	6	emergence	emergence	NOUN
cana-951	4	7	of	of	ADP
cana-951	4	8	new	new	ADJ
cana-951	4	9	and	and	CCONJ
cana-951	4	10	remarkable	remarkable	ADJ
cana-951	4	11	applications	application	NOUN
cana-951	4	12	.	.	PUNCT
cana-951	5	1	in	in	ADP
cana-951	5	2	this	this	DET
cana-951	5	3	paper	paper	NOUN
cana-951	5	4	,	,	PUNCT
cana-951	5	5	we	we	PRON
cana-951	5	6	focus	focus	VERB
cana-951	5	7	on	on	ADP
cana-951	5	8	the	the	DET
cana-951	5	9	novel	novel	ADJ
cana-951	5	10	effect	effect	NOUN
cana-951	5	11	of	of	ADP
cana-951	5	12	chirality	chirality	NOUN
cana-951	5	13	,	,	PUNCT
cana-951	5	14	characterized	characterize	VERB
cana-951	5	15	through	through	ADP
cana-951	5	16	a	a	DET
cana-951	5	17	newly	newly	ADV
cana-951	5	18	proposed	propose	VERB
cana-951	5	19	formalism	formalism	NOUN
cana-951	5	20	,	,	PUNCT
cana-951	5	21	to	to	PART
cana-951	5	22	highlight	highlight	VERB
cana-951	5	23	the	the	DET
cana-951	5	24	nonlinear	nonlinear	ADJ
cana-951	5	25	effect	effect	NOUN
cana-951	5	26	induced	induce	VERB
cana-951	5	27	by	by	ADP
cana-951	5	28	the	the	DET
cana-951	5	29	magnetization	magnetization	NOUN
cana-951	5	30	vector	vector	NOUN
cana-951	5	31	under	under	ADP
cana-951	5	32	the	the	DET
cana-951	5	33	influence	influence	NOUN
cana-951	5	34	of	of	ADP
cana-951	5	35	a	a	DET
cana-951	5	36	strong	strong	ADJ
cana-951	5	37	electric	electric	ADJ
cana-951	5	38	field	field	NOUN
cana-951	5	39	.	.	PUNCT
cana-951	6	1	this	this	DET
cana-951	6	2	research	research	NOUN
cana-951	6	3	work	work	NOUN
cana-951	6	4	is	be	AUX
cana-951	6	5	concerned	concern	VERB
cana-951	6	6	with	with	ADP
cana-951	6	7	a	a	DET
cana-951	6	8	new	new	ADJ
cana-951	6	9	formulation	formulation	NOUN
cana-951	6	10	of	of	ADP
cana-951	6	11	constitutive	constitutive	ADJ
cana-951	6	12	relations	relation	NOUN
cana-951	6	13	.	.	PUNCT
cana-951	7	1	we	we	PRON
cana-951	7	2	delve	delve	VERB
cana-951	7	3	into	into	ADP
cana-951	7	4	the	the	DET
cana-951	7	5	analysis	analysis	NOUN
cana-951	7	6	and	and	CCONJ
cana-951	7	7	discussion	discussion	NOUN
cana-951	7	8	of	of	ADP
cana-951	7	9	the	the	DET
cana-951	7	10	family	family	NOUN
cana-951	7	11	of	of	ADP
cana-951	7	12	solutions	solution	NOUN
cana-951	7	13	of	of	ADP
cana-951	7	14	the	the	DET
cana-951	7	15	nonlinear	nonlinear	ADJ
cana-951	7	16	schrödinger	schrödinger	ADJ
cana-951	7	17	equation	equation	NOUN
cana-951	7	18	,	,	PUNCT
cana-951	7	19	describing	describe	VERB
cana-951	7	20	the	the	DET
cana-951	7	21	pulse	pulse	NOUN
cana-951	7	22	propagation	propagation	NOUN
cana-951	7	23	in	in	ADP
cana-951	7	24	nonlinear	nonlinear	ADJ
cana-951	7	25	bi	bi	ADJ
cana-951	7	26	-	-	ADJ
cana-951	7	27	isotropic	isotropic	ADJ
cana-951	7	28	media	medium	NOUN
cana-951	7	29	,	,	PUNCT
cana-951	7	30	with	with	ADP
cana-951	7	31	a	a	DET
cana-951	7	32	novel	novel	ADJ
cana-951	7	33	approach	approach	NOUN
cana-951	7	34	to	to	ADP
cana-951	7	35	constitutive	constitutive	ADJ
cana-951	7	36	equations	equation	NOUN
cana-951	7	37	.	.	PUNCT
cana-951	8	1	we	we	PRON
cana-951	8	2	apply	apply	VERB
cana-951	8	3	the	the	DET
cana-951	8	4	extended	extended	ADJ
cana-951	8	5	𝐺’/𝐺-expansion	𝐺’/𝐺-expansion	NOUN
cana-951	8	6	method	method	NOUN
cana-951	8	7	with	with	ADP
cana-951	8	8	varying	vary	VERB
cana-951	8	9	dispersion	dispersion	NOUN
cana-951	8	10	and	and	CCONJ
cana-951	8	11	nonlinearity	nonlinearity	NOUN
cana-951	8	12	to	to	PART
cana-951	8	13	define	define	VERB
cana-951	8	14	certain	certain	ADJ
cana-951	8	15	families	family	NOUN
cana-951	8	16	of	of	ADP
cana-951	8	17	solutions	solution	NOUN
cana-951	8	18	of	of	ADP
cana-951	8	19	the	the	DET
cana-951	8	20	nonlinear	nonlinear	ADJ
cana-951	8	21	schrödinger	schrödinger	ADJ
cana-951	8	22	equation	equation	NOUN
cana-951	8	23	in	in	ADP
cana-951	8	24	bi	bi	ADJ
cana-951	8	25	-	-	ADJ
cana-951	8	26	isotropic	isotropic	ADJ
cana-951	8	27	(	(	PUNCT
cana-951	8	28	chiral	chiral	ADJ
cana-951	8	29	and	and	CCONJ
cana-951	8	30	non	non	ADJ
cana-951	8	31	-	-	ADJ
cana-951	8	32	reciprocal	reciprocal	ADJ
cana-951	8	33	)	)	PUNCT
cana-951	8	34	optical	optical	ADJ
cana-951	8	35	fibers	fiber	NOUN
cana-951	8	36	.	.	PUNCT
cana-951	9	1	this	this	DET
cana-951	9	2	clarification	clarification	NOUN
cana-951	9	3	aids	aid	VERB
cana-951	9	4	in	in	ADP
cana-951	9	5	understanding	understand	VERB
cana-951	9	6	the	the	DET
cana-951	9	7	propagation	propagation	NOUN
cana-951	9	8	of	of	ADP
cana-951	9	9	light	light	NOUN
cana-951	9	10	with	with	ADP
cana-951	9	11	two	two	NUM
cana-951	9	12	modes	mode	NOUN
cana-951	9	13	of	of	ADP
cana-951	9	14	propagation	propagation	NOUN
cana-951	9	15	:	:	PUNCT
cana-951	9	16	a	a	DET
cana-951	9	17	right	right	ADJ
cana-951	9	18	circular	circular	ADJ
cana-951	9	19	polarized	polarize	VERB
cana-951	9	20	wave	wave	NOUN
cana-951	9	21	(	(	PUNCT
cana-951	9	22	rcp	rcp	PROPN
cana-951	9	23	)	)	PUNCT
cana-951	9	24	and	and	CCONJ
cana-951	9	25	a	a	DET
cana-951	9	26	left	left	ADJ
cana-951	9	27	circular	circular	ADJ
cana-951	9	28	polarized	polarize	VERB
cana-951	9	29	wave	wave	NOUN
cana-951	9	30	(	(	PUNCT
cana-951	9	31	lcp	lcp	PROPN
cana-951	9	32	)	)	PUNCT
cana-951	9	33	,	,	PUNCT
cana-951	9	34	each	each	PRON
cana-951	9	35	having	have	VERB
cana-951	9	36	two	two	NUM
cana-951	9	37	different	different	ADJ
cana-951	9	38	wave	wave	NOUN
cana-951	9	39	vectors	vector	NOUN
cana-951	9	40	in	in	ADP
cana-951	9	41	nonlinear	nonlinear	ADJ
cana-951	9	42	bi	bi	ADJ
cana-951	9	43	-	-	ADJ
cana-951	9	44	isotropic	isotropic	ADJ
cana-951	9	45	media	medium	NOUN
cana-951	9	46	.	.	PUNCT
cana-951	10	1	various	various	ADJ
cana-951	10	2	novel	novel	ADJ
cana-951	10	3	exact	exact	ADJ
cana-951	10	4	solutions	solution	NOUN
cana-951	10	5	of	of	ADP
cana-951	10	6	bi	bi	ADJ
cana-951	10	7	-	-	ADJ
cana-951	10	8	isotropic	isotropic	ADJ
cana-951	10	9	optical	optical	ADJ
cana-951	10	10	solitons	soliton	NOUN
cana-951	10	11	are	be	AUX
cana-951	10	12	reported	report	VERB
cana-951	10	13	in	in	ADP
cana-951	10	14	this	this	DET
cana-951	10	15	study	study	NOUN
cana-951	10	16	.	.	PUNCT
cana-951	11	1	introduction	introduction	NOUN
cana-951	11	2	:	:	PUNCT
cana-951	11	3	the	the	DET
cana-951	11	4	investigation	investigation	NOUN
cana-951	11	5	of	of	ADP
cana-951	11	6	exact	exact	ADJ
cana-951	11	7	solutions	solution	NOUN
cana-951	11	8	for	for	ADP
cana-951	11	9	nonlinear	nonlinear	ADJ
cana-951	11	10	partial	partial	ADJ
cana-951	11	11	differential	differential	NOUN
cana-951	11	12	equations	equation	NOUN
cana-951	11	13	(	(	PUNCT
cana-951	11	14	pdes	pde	NOUN
cana-951	11	15	)	)	PUNCT
cana-951	11	16	holds	hold	VERB
cana-951	11	17	significant	significant	ADJ
cana-951	11	18	importance	importance	NOUN
cana-951	11	19	in	in	ADP
cana-951	11	20	understanding	understand	VERB
cana-951	11	21	nonlinear	nonlinear	ADJ
cana-951	11	22	physical	physical	ADJ
cana-951	11	23	phenomena	phenomenon	NOUN
cana-951	11	24	.	.	PUNCT
cana-951	12	1	nonlinear	nonlinear	ADJ
cana-951	12	2	waves	wave	NOUN
cana-951	12	3	manifest	manifest	VERB
cana-951	12	4	across	across	ADP
cana-951	12	5	various	various	ADJ
cana-951	12	6	scientific	scientific	ADJ
cana-951	12	7	domains	domain	NOUN
cana-951	12	8	,	,	PUNCT
cana-951	12	9	notably	notably	ADV
cana-951	12	10	in	in	ADP
cana-951	12	11	optical	optical	ADJ
cana-951	12	12	fibers	fiber	NOUN
cana-951	12	13	and	and	CCONJ
cana-951	12	14	solid	solid	ADJ
cana-951	12	15	-	-	PUNCT
cana-951	12	16	state	state	NOUN
cana-951	12	17	physics	physics	NOUN
cana-951	12	18	.	.	PUNCT
cana-951	13	1	in	in	ADP
cana-951	13	2	recent	recent	ADJ
cana-951	13	3	years	year	NOUN
cana-951	13	4	,	,	PUNCT
cana-951	13	5	several	several	ADJ
cana-951	13	6	potent	potent	ADJ
cana-951	13	7	methodologies	methodology	NOUN
cana-951	13	8	have	have	AUX
cana-951	13	9	emerged	emerge	VERB
cana-951	13	10	for	for	ADP
cana-951	13	11	identifying	identify	VERB
cana-951	13	12	solitons	soliton	NOUN
cana-951	13	13	and	and	CCONJ
cana-951	13	14	periodic	periodic	ADJ
cana-951	13	15	wave	wave	NOUN
cana-951	13	16	solutions	solution	NOUN
cana-951	13	17	of	of	ADP
cana-951	13	18	nonlinear	nonlinear	ADJ
cana-951	13	19	pdes	pde	NOUN
cana-951	13	20	.	.	PUNCT
cana-951	14	1	these	these	PRON
cana-951	14	2	include	include	VERB
cana-951	14	3	the	the	DET
cana-951	14	4	𝐺’/𝐺	𝐺’/𝐺	PROPN
cana-951	14	5	-expansion	-expansion	PROPN
cana-951	14	6	method	method	NOUN
cana-951	14	7	[	[	X
cana-951	14	8	1	1	NUM
cana-951	14	9	-	-	SYM
cana-951	14	10	6	6	NUM
cana-951	14	11	]	]	PUNCT
cana-951	14	12	,	,	PUNCT
cana-951	14	13	the	the	DET
cana-951	14	14	new	new	ADJ
cana-951	14	15	mapping	mapping	NOUN
cana-951	14	16	method	method	NOUN
cana-951	14	17	[	[	X
cana-951	14	18	9	9	NUM
cana-951	14	19	-	-	SYM
cana-951	14	20	10	10	NUM
cana-951	14	21	]	]	PUNCT
cana-951	14	22	,	,	PUNCT
cana-951	14	23	the	the	DET
cana-951	14	24	method	method	NOUN
cana-951	14	25	of	of	ADP
cana-951	14	26	generalized	generalized	ADJ
cana-951	14	27	projective	projective	ADJ
cana-951	14	28	riccati	riccati	PROPN
cana-951	14	29	equations	equation	NOUN
cana-951	14	30	[	[	X
cana-951	14	31	11	11	NUM
cana-951	14	32	-	-	SYM
cana-951	14	33	16	16	NUM
cana-951	14	34	]	]	PUNCT
cana-951	14	35	,	,	PUNCT
cana-951	14	36	and	and	CCONJ
cana-951	14	37	the	the	DET
cana-951	14	38	𝐺’/𝐺	𝐺’/𝐺	PROPN
cana-951	14	39	expansion	expansion	NOUN
cana-951	14	40	method	method	NOUN
cana-951	14	41	[	[	X
cana-951	14	42	17	17	NUM
cana-951	14	43	]	]	PUNCT
cana-951	14	44	.	.	PUNCT
cana-951	15	1	consequently	consequently	ADV
cana-951	15	2	,	,	PUNCT
cana-951	15	3	an	an	DET
cana-951	15	4	original	original	ADJ
cana-951	15	5	mathematical	mathematical	ADJ
cana-951	15	6	approach	approach	NOUN
cana-951	15	7	is	be	AUX
cana-951	15	8	proposed	propose	VERB
cana-951	15	9	to	to	PART
cana-951	15	10	evaluate	evaluate	VERB
cana-951	15	11	nonlinear	nonlinear	ADJ
cana-951	15	12	effects	effect	NOUN
cana-951	15	13	in	in	ADP
cana-951	15	14	bi	bi	ADJ
cana-951	15	15	-	-	ADJ
cana-951	15	16	isotropic	isotropic	ADJ
cana-951	15	17	optical	optical	ADJ
cana-951	15	18	fibers	fiber	NOUN
cana-951	15	19	,	,	PUNCT
cana-951	15	20	stemming	stem	VERB
cana-951	15	21	from	from	ADP
cana-951	15	22	magnetization	magnetization	NOUN
cana-951	15	23	under	under	ADP
cana-951	15	24	the	the	DET
cana-951	15	25	influence	influence	NOUN
cana-951	15	26	of	of	ADP
cana-951	15	27	a	a	DET
cana-951	15	28	strong	strong	ADJ
cana-951	15	29	electric	electric	ADJ
cana-951	15	30	field	field	NOUN
cana-951	15	31	[	[	X
cana-951	15	32	19	19	NUM
cana-951	15	33	-	-	SYM
cana-951	15	34	20	20	NUM
cana-951	15	35	]	]	PUNCT
cana-951	15	36	.	.	PUNCT
cana-951	16	1	the	the	DET
cana-951	16	2	extended	extended	ADJ
cana-951	16	3	𝐺’/𝐺-expansion	𝐺’/𝐺-expansion	NOUN
cana-951	16	4	method	method	NOUN
cana-951	16	5	emerges	emerge	VERB
cana-951	16	6	as	as	ADP
cana-951	16	7	a	a	DET
cana-951	16	8	potent	potent	ADJ
cana-951	16	9	technique	technique	NOUN
cana-951	16	10	for	for	ADP
cana-951	16	11	deriving	derive	VERB
cana-951	16	12	solution	solution	NOUN
cana-951	16	13	families	family	NOUN
cana-951	16	14	of	of	ADP
cana-951	16	15	the	the	DET
cana-951	16	16	nonlinear	nonlinear	ADJ
cana-951	16	17	schrödinger	schrödinger	ADJ
cana-951	16	18	equation	equation	NOUN
cana-951	16	19	in	in	ADP
cana-951	16	20	bi	bi	ADJ
cana-951	16	21	-	-	ADJ
cana-951	16	22	isotropic	isotropic	ADJ
cana-951	16	23	optical	optical	ADJ
cana-951	16	24	fibers	fiber	NOUN
cana-951	16	25	.	.	PUNCT
cana-951	17	1	this	this	DET
cana-951	17	2	method	method	NOUN
cana-951	17	3	employs	employ	VERB
cana-951	17	4	a	a	DET
cana-951	17	5	perturbation	perturbation	NOUN
cana-951	17	6	expansion	expansion	NOUN
cana-951	17	7	in	in	ADP
cana-951	17	8	powers	power	NOUN
cana-951	17	9	of	of	ADP
cana-951	17	10	the	the	DET
cana-951	17	11	dimensionless	dimensionless	NOUN
cana-951	17	12	parameter	parameter	NOUN
cana-951	17	13	and	and	CCONJ
cana-951	17	14	is	be	AUX
cana-951	17	15	applicable	applicable	ADJ
cana-951	17	16	for	for	ADP
cana-951	17	17	both	both	CCONJ
cana-951	17	18	weak	weak	ADJ
cana-951	17	19	and	and	CCONJ
cana-951	17	20	strong	strong	ADJ
cana-951	17	21	nonlinearities	nonlinearitie	NOUN
cana-951	17	22	.	.	PUNCT
cana-951	18	1	it	it	PRON
cana-951	18	2	accommodates	accommodate	VERB
cana-951	18	3	varying	vary	VERB
cana-951	18	4	dispersion	dispersion	NOUN
cana-951	18	5	and	and	CCONJ
cana-951	18	6	nonlinearity	nonlinearity	NOUN
cana-951	18	7	,	,	PUNCT
cana-951	18	8	rendering	render	VERB
cana-951	18	9	it	it	PRON
cana-951	18	10	suitable	suitable	ADJ
cana-951	18	11	for	for	ADP
cana-951	18	12	modeling	model	VERB
cana-951	18	13	a	a	DET
cana-951	18	14	wide	wide	ADJ
cana-951	18	15	array	array	NOUN
cana-951	18	16	of	of	ADP
cana-951	18	17	optical	optical	ADJ
cana-951	18	18	fibers	fiber	NOUN
cana-951	18	19	.	.	PUNCT
cana-951	19	1	results	result	NOUN
cana-951	19	2	and	and	CCONJ
cana-951	19	3	conclusion	conclusion	NOUN
cana-951	19	4	:	:	PUNCT
cana-951	19	5	this	this	DET
cana-951	19	6	investigate	investigate	NOUN
cana-951	19	7	is	be	AUX
cana-951	19	8	concerned	concern	VERB
cana-951	19	9	with	with	ADP
cana-951	19	10	a	a	DET
cana-951	19	11	new	new	ADJ
cana-951	19	12	formulation	formulation	NOUN
cana-951	19	13	of	of	ADP
cana-951	19	14	constitutive	constitutive	ADJ
cana-951	19	15	relation	relation	NOUN
cana-951	19	16	linking	link	VERB
cana-951	19	17	to	to	ADP
cana-951	19	18	the	the	DET
cana-951	19	19	magnetic	magnetic	ADJ
cana-951	19	20	effect	effect	NOUN
cana-951	19	21	,	,	PUNCT
cana-951	19	22	to	to	PART
cana-951	19	23	understand	understand	VERB
cana-951	19	24	rigorously	rigorously	ADV
cana-951	19	25	the	the	DET
cana-951	19	26	physical	physical	ADJ
cana-951	19	27	nature	nature	NOUN
cana-951	19	28	of	of	ADP
cana-951	19	29	biisotropic	biisotropic	ADJ
cana-951	19	30	effects	effect	NOUN
cana-951	19	31	and	and	CCONJ
cana-951	19	32	to	to	PART
cana-951	19	33	generalize	generalize	VERB
cana-951	19	34	the	the	DET
cana-951	19	35	main	main	ADJ
cana-951	19	36	macroscopic	macroscopic	ADJ
cana-951	19	37	models	model	NOUN
cana-951	19	38	.	.	PUNCT
cana-951	20	1	we	we	PRON
cana-951	20	2	inferred	infer	VERB
cana-951	20	3	the	the	DET
cana-951	20	4	nonlinear	nonlinear	ADJ
cana-951	20	5	schrodinger	schrodinger	PROPN
cana-951	20	6	equation	equation	NOUN
cana-951	20	7	for	for	ADP
cana-951	20	8	a	a	DET
cana-951	20	9	bi	bi	ADJ
cana-951	20	10	-	-	ADJ
cana-951	20	11	isotropic	isotropic	ADJ
cana-951	20	12	medium	medium	ADJ
cana-951	20	13	term	term	NOUN
cana-951	20	14	with	with	ADP
cana-951	20	15	a	a	DET
cana-951	20	16	nonlinear	nonlinear	ADJ
cana-951	20	17	term	term	NOUN
cana-951	20	18	of	of	ADP
cana-951	20	19	magnetizing	magnetize	VERB
cana-951	20	20	.	.	PUNCT
cana-951	21	1	in	in	ADP
cana-951	21	2	this	this	DET
cana-951	21	3	article	article	NOUN
cana-951	21	4	,	,	PUNCT
cana-951	21	5	the	the	DET
cana-951	21	6	extended	extended	ADJ
cana-951	21	7	𝐺’/𝐺-expansion	𝐺’/𝐺-expansion	NOUN
cana-951	21	8	method	method	NOUN
cana-951	21	9	is	be	AUX
cana-951	21	10	a	a	DET
cana-951	21	11	communications	communication	NOUN
cana-951	21	12	on	on	ADP
cana-951	21	13	applied	apply	VERB
cana-951	21	14	nonlinear	nonlinear	ADJ
cana-951	21	15	analysis	analysis	NOUN
cana-951	21	16	issn	issn	NOUN
cana-951	21	17	:	:	PUNCT
cana-951	21	18	1074	1074	NUM
cana-951	21	19	-	-	PUNCT
cana-951	21	20	133x	133x	NUM
cana-951	21	21	vol	vol	NOUN
cana-951	21	22	31	31	NUM
cana-951	21	23	no	no	NOUN
cana-951	21	24	.	.	PUNCT
cana-951	22	1	4s	4s	NUM
cana-951	22	2	(	(	PUNCT
cana-951	22	3	2024	2024	NUM
cana-951	22	4	)	)	PUNCT
cana-951	22	5	573	573	NUM
cana-951	22	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-951	22	7	powerful	powerful	ADJ
cana-951	22	8	technique	technique	NOUN
cana-951	22	9	for	for	ADP
cana-951	22	10	determining	determine	VERB
cana-951	22	11	a	a	DET
cana-951	22	12	family	family	NOUN
cana-951	22	13	of	of	ADP
cana-951	22	14	solutions	solution	NOUN
cana-951	22	15	of	of	ADP
cana-951	22	16	the	the	DET
cana-951	22	17	nonlinear	nonlinear	ADJ
cana-951	22	18	schrödinger	schrödinger	ADJ
cana-951	22	19	equation	equation	NOUN
cana-951	22	20	in	in	ADP
cana-951	22	21	bi	bi	ADJ
cana-951	22	22	-	-	ADJ
cana-951	22	23	isotropic	isotropic	ADJ
cana-951	22	24	optical	optical	ADJ
cana-951	22	25	fibers	fiber	NOUN
cana-951	22	26	.	.	PUNCT
cana-951	23	1	this	this	DET
cana-951	23	2	method	method	NOUN
cana-951	23	3	is	be	AUX
cana-951	23	4	based	base	VERB
cana-951	23	5	on	on	ADP
cana-951	23	6	the	the	DET
cana-951	23	7	use	use	NOUN
cana-951	23	8	of	of	ADP
cana-951	23	9	a	a	DET
cana-951	23	10	perturbation	perturbation	NOUN
cana-951	23	11	expansion	expansion	NOUN
cana-951	23	12	in	in	ADP
cana-951	23	13	powers	power	NOUN
cana-951	23	14	of	of	ADP
cana-951	23	15	the	the	DET
cana-951	23	16	dimensionless	dimensionless	NOUN
cana-951	23	17	parameter	parameter	NOUN
cana-951	23	18	,	,	PUNCT
cana-951	23	19	and	and	CCONJ
cana-951	23	20	it	it	PRON
cana-951	23	21	is	be	AUX
cana-951	23	22	valid	valid	ADJ
cana-951	23	23	for	for	ADP
cana-951	23	24	both	both	CCONJ
cana-951	23	25	weak	weak	ADJ
cana-951	23	26	and	and	CCONJ
cana-951	23	27	strong	strong	ADJ
cana-951	23	28	nonlinearities	nonlinearitie	NOUN
cana-951	23	29	.	.	PUNCT
cana-951	24	1	the	the	DET
cana-951	24	2	method	method	NOUN
cana-951	24	3	allows	allow	VERB
cana-951	24	4	for	for	ADP
cana-951	24	5	the	the	DET
cana-951	24	6	inclusion	inclusion	NOUN
cana-951	24	7	of	of	ADP
cana-951	24	8	varying	vary	VERB
cana-951	24	9	dispersion	dispersion	NOUN
cana-951	24	10	and	and	CCONJ
cana-951	24	11	nonlinearity	nonlinearity	NOUN
cana-951	24	12	,	,	PUNCT
cana-951	24	13	making	make	VERB
cana-951	24	14	it	it	PRON
cana-951	24	15	wellsuited	wellsuite	VERB
cana-951	24	16	for	for	ADP
cana-951	24	17	modeling	model	VERB
cana-951	24	18	a	a	DET
cana-951	24	19	wide	wide	ADJ
cana-951	24	20	range	range	NOUN
cana-951	24	21	of	of	ADP
cana-951	24	22	optical	optical	ADJ
cana-951	24	23	fibres	fibre	NOUN
cana-951	24	24	.	.	PUNCT
cana-951	25	1	overall	overall	ADV
cana-951	25	2	,	,	PUNCT
cana-951	25	3	the	the	DET
cana-951	25	4	extended	extended	ADJ
cana-951	25	5	𝐺’/𝐺	𝐺’/𝐺	PROPN
cana-951	25	6	-expansion	-expansion	PROPN
cana-951	25	7	method	method	NOUN
cana-951	25	8	is	be	AUX
cana-951	25	9	a	a	DET
cana-951	25	10	valuable	valuable	ADJ
cana-951	25	11	tool	tool	NOUN
cana-951	25	12	for	for	ADP
cana-951	25	13	understanding	understand	VERB
cana-951	25	14	the	the	DET
cana-951	25	15	dynamics	dynamic	NOUN
cana-951	25	16	of	of	ADP
cana-951	25	17	nonlinear	nonlinear	ADJ
cana-951	25	18	optical	optical	ADJ
cana-951	25	19	systems	system	NOUN
cana-951	25	20	,	,	PUNCT
cana-951	25	21	and	and	CCONJ
cana-951	25	22	it	it	PRON
cana-951	25	23	is	be	AUX
cana-951	25	24	expected	expect	VERB
cana-951	25	25	to	to	PART
cana-951	25	26	have	have	VERB
cana-951	25	27	a	a	DET
cana-951	25	28	wide	wide	ADJ
cana-951	25	29	range	range	NOUN
cana-951	25	30	of	of	ADP
cana-951	25	31	applications	application	NOUN
cana-951	25	32	in	in	ADP
cana-951	25	33	the	the	DET
cana-951	25	34	field	field	NOUN
cana-951	25	35	of	of	ADP
cana-951	25	36	nonlinear	nonlinear	ADJ
cana-951	25	37	optics	optic	NOUN
cana-951	25	38	.	.	PUNCT
cana-951	26	1	keywords	keyword	NOUN
cana-951	26	2	:	:	PUNCT
cana-951	26	3	nonlinear	nonlinear	ADJ
cana-951	26	4	bi	bi	ADJ
cana-951	26	5	-	-	ADJ
cana-951	26	6	isotropic	isotropic	ADJ
cana-951	26	7	media	medium	NOUN
cana-951	26	8	,	,	PUNCT
cana-951	26	9	schrödinger	schrödinger	ADJ
cana-951	26	10	equation	equation	NOUN
cana-951	26	11	,	,	PUNCT
cana-951	26	12	optical	optical	ADJ
cana-951	26	13	fiber	fiber	NOUN
cana-951	26	14	,	,	PUNCT
cana-951	26	15	the	the	DET
cana-951	26	16	𝐺’/𝐺	𝐺’/𝐺	PROPN
cana-951	26	17	expansion	expansion	NOUN
cana-951	26	18	method	method	NOUN
cana-951	26	19	,	,	PUNCT
cana-951	26	20	chiratity	chiratity	NOUN
cana-951	26	21	,	,	PUNCT
cana-951	26	22	non	non	ADJ
cana-951	26	23	-	-	NOUN
cana-951	26	24	reciprocity	reciprocity	NOUN
cana-951	26	25	.	.	PUNCT
cana-951	27	1	1	1	X
cana-951	27	2	.	.	X
cana-951	27	3	introduction	introduction	NOUN
cana-951	27	4	the	the	DET
cana-951	27	5	investigation	investigation	NOUN
cana-951	27	6	of	of	ADP
cana-951	27	7	exact	exact	ADJ
cana-951	27	8	solutions	solution	NOUN
cana-951	27	9	for	for	ADP
cana-951	27	10	nonlinear	nonlinear	ADJ
cana-951	27	11	partial	partial	ADJ
cana-951	27	12	differential	differential	NOUN
cana-951	27	13	equations	equation	NOUN
cana-951	27	14	(	(	PUNCT
cana-951	27	15	pdes	pde	NOUN
cana-951	27	16	)	)	PUNCT
cana-951	27	17	holds	hold	VERB
cana-951	27	18	significant	significant	ADJ
cana-951	27	19	importance	importance	NOUN
cana-951	27	20	in	in	ADP
cana-951	27	21	understanding	understand	VERB
cana-951	27	22	nonlinear	nonlinear	ADJ
cana-951	27	23	physical	physical	ADJ
cana-951	27	24	phenomena	phenomenon	NOUN
cana-951	27	25	.	.	PUNCT
cana-951	28	1	nonlinear	nonlinear	ADJ
cana-951	28	2	waves	wave	NOUN
cana-951	28	3	manifest	manifest	VERB
cana-951	28	4	across	across	ADP
cana-951	28	5	various	various	ADJ
cana-951	28	6	scientific	scientific	ADJ
cana-951	28	7	domains	domain	NOUN
cana-951	28	8	,	,	PUNCT
cana-951	28	9	notably	notably	ADV
cana-951	28	10	in	in	ADP
cana-951	28	11	optical	optical	ADJ
cana-951	28	12	fibers	fiber	NOUN
cana-951	28	13	and	and	CCONJ
cana-951	28	14	solid	solid	ADJ
cana-951	28	15	-	-	PUNCT
cana-951	28	16	state	state	NOUN
cana-951	28	17	physics	physics	NOUN
cana-951	28	18	.	.	PUNCT
cana-951	29	1	in	in	ADP
cana-951	29	2	recent	recent	ADJ
cana-951	29	3	years	year	NOUN
cana-951	29	4	,	,	PUNCT
cana-951	29	5	several	several	ADJ
cana-951	29	6	potent	potent	ADJ
cana-951	29	7	methodologies	methodology	NOUN
cana-951	29	8	have	have	AUX
cana-951	29	9	emerged	emerge	VERB
cana-951	29	10	for	for	ADP
cana-951	29	11	identifying	identify	VERB
cana-951	29	12	solitons	soliton	NOUN
cana-951	29	13	and	and	CCONJ
cana-951	29	14	periodic	periodic	ADJ
cana-951	29	15	wave	wave	NOUN
cana-951	29	16	solutions	solution	NOUN
cana-951	29	17	of	of	ADP
cana-951	29	18	nonlinear	nonlinear	ADJ
cana-951	29	19	pdes	pde	NOUN
cana-951	29	20	.	.	PUNCT
cana-951	30	1	these	these	PRON
cana-951	30	2	include	include	VERB
cana-951	30	3	the	the	DET
cana-951	30	4	𝐺’/𝐺	𝐺’/𝐺	PROPN
cana-951	30	5	-expansion	-expansion	PROPN
cana-951	30	6	method	method	NOUN
cana-951	30	7	[	[	X
cana-951	30	8	1	1	NUM
cana-951	30	9	-	-	SYM
cana-951	30	10	6	6	NUM
cana-951	30	11	]	]	PUNCT
cana-951	30	12	,	,	PUNCT
cana-951	30	13	the	the	DET
cana-951	30	14	new	new	ADJ
cana-951	30	15	mapping	mapping	NOUN
cana-951	30	16	method	method	NOUN
cana-951	30	17	[	[	X
cana-951	30	18	9	9	NUM
cana-951	30	19	-	-	SYM
cana-951	30	20	10	10	NUM
cana-951	30	21	]	]	PUNCT
cana-951	30	22	,	,	PUNCT
cana-951	30	23	the	the	DET
cana-951	30	24	method	method	NOUN
cana-951	30	25	of	of	ADP
cana-951	30	26	generalized	generalized	ADJ
cana-951	30	27	projective	projective	ADJ
cana-951	30	28	riccati	riccati	PROPN
cana-951	30	29	equations	equation	NOUN
cana-951	30	30	[	[	X
cana-951	30	31	11	11	NUM
cana-951	30	32	-	-	SYM
cana-951	30	33	16	16	NUM
cana-951	30	34	]	]	PUNCT
cana-951	30	35	,	,	PUNCT
cana-951	30	36	and	and	CCONJ
cana-951	30	37	the	the	DET
cana-951	30	38	𝐺’/𝐺	𝐺’/𝐺	PROPN
cana-951	30	39	-expansion	-expansion	PROPN
cana-951	30	40	method	method	NOUN
cana-951	30	41	[	[	X
cana-951	30	42	17	17	NUM
cana-951	30	43	]	]	PUNCT
cana-951	30	44	.	.	PUNCT
cana-951	31	1	conte	conte	PROPN
cana-951	31	2	and	and	CCONJ
cana-951	31	3	musette	musette	PROPN
cana-951	32	1	[	[	X
cana-951	32	2	11	11	NUM
cana-951	32	3	]	]	PUNCT
cana-951	32	4	introduced	introduce	VERB
cana-951	32	5	an	an	DET
cana-951	32	6	indirect	indirect	ADJ
cana-951	32	7	approach	approach	NOUN
cana-951	32	8	to	to	PART
cana-951	32	9	uncover	uncover	VERB
cana-951	32	10	solitary	solitary	ADJ
cana-951	32	11	wave	wave	NOUN
cana-951	32	12	solutions	solution	NOUN
cana-951	32	13	of	of	ADP
cana-951	32	14	specific	specific	ADJ
cana-951	32	15	nonlinear	nonlinear	ADJ
cana-951	32	16	pdes	pde	NOUN
cana-951	32	17	expressible	expressible	ADJ
cana-951	32	18	as	as	ADP
cana-951	32	19	polynomials	polynomial	NOUN
cana-951	32	20	in	in	ADP
cana-951	32	21	two	two	NUM
cana-951	32	22	elementary	elementary	ADJ
cana-951	32	23	functions	function	NOUN
cana-951	32	24	satisfying	satisfy	VERB
cana-951	32	25	a	a	DET
cana-951	32	26	projective	projective	ADJ
cana-951	32	27	riccati	riccati	NOUN
cana-951	32	28	equation	equation	NOUN
cana-951	32	29	[	[	X
cana-951	32	30	18	18	NUM
cana-951	32	31	]	]	PUNCT
cana-951	32	32	.	.	PUNCT
cana-951	33	1	this	this	DET
cana-951	33	2	method	method	NOUN
cana-951	33	3	has	have	AUX
cana-951	33	4	been	be	AUX
cana-951	33	5	successfully	successfully	ADV
cana-951	33	6	applied	apply	VERB
cana-951	33	7	to	to	ADP
cana-951	33	8	numerous	numerous	ADJ
cana-951	33	9	nonlinear	nonlinear	ADJ
cana-951	33	10	pdes	pde	NOUN
cana-951	33	11	,	,	PUNCT
cana-951	33	12	with	with	ADP
cana-951	33	13	resulting	result	VERB
cana-951	33	14	solitary	solitary	ADJ
cana-951	33	15	wave	wave	NOUN
cana-951	33	16	solutions	solution	NOUN
cana-951	33	17	documented	document	VERB
cana-951	33	18	in	in	ADP
cana-951	33	19	[	[	PUNCT
cana-951	33	20	12	12	NUM
cana-951	33	21	-	-	SYM
cana-951	33	22	16	16	NUM
cana-951	33	23	]	]	PUNCT
cana-951	33	24	.	.	PUNCT
cana-951	34	1	the	the	DET
cana-951	34	2	𝐺’/𝐺	𝐺’/𝐺	PROPN
cana-951	34	3	-expansion	-expansion	PROPN
cana-951	34	4	method	method	NOUN
cana-951	34	5	exhibits	exhibit	VERB
cana-951	34	6	broad	broad	ADJ
cana-951	34	7	applicability	applicability	NOUN
cana-951	34	8	for	for	ADP
cana-951	34	9	tackling	tackle	VERB
cana-951	34	10	various	various	ADJ
cana-951	34	11	other	other	ADJ
cana-951	34	12	nonlinear	nonlinear	ADJ
cana-951	34	13	evolution	evolution	NOUN
cana-951	34	14	equations	equation	NOUN
cana-951	34	15	in	in	ADP
cana-951	34	16	mathematical	mathematical	ADJ
cana-951	34	17	physics	physics	NOUN
cana-951	34	18	.	.	PUNCT
cana-951	35	1	in	in	ADP
cana-951	35	2	recent	recent	ADJ
cana-951	35	3	years	year	NOUN
cana-951	35	4	,	,	PUNCT
cana-951	35	5	research	research	NOUN
cana-951	35	6	endeavors	endeavor	NOUN
cana-951	35	7	have	have	AUX
cana-951	35	8	actively	actively	ADV
cana-951	35	9	explored	explore	VERB
cana-951	35	10	novel	novel	ADJ
cana-951	35	11	types	type	NOUN
cana-951	35	12	of	of	ADP
cana-951	35	13	heterogeneous	heterogeneous	ADJ
cana-951	35	14	absorbent	absorbent	ADJ
cana-951	35	15	materials	material	NOUN
cana-951	35	16	,	,	PUNCT
cana-951	35	17	notably	notably	ADV
cana-951	35	18	bi	bi	ADJ
cana-951	35	19	-	-	ADJ
cana-951	35	20	isotropic	isotropic	ADJ
cana-951	35	21	materials	material	NOUN
cana-951	35	22	.	.	PUNCT
cana-951	36	1	bi	bi	ADJ
cana-951	36	2	-	-	ADJ
cana-951	36	3	isotropic	isotropic	ADJ
cana-951	36	4	materials	material	NOUN
cana-951	36	5	comprise	comprise	VERB
cana-951	36	6	a	a	DET
cana-951	36	7	random	random	ADJ
cana-951	36	8	dispersion	dispersion	NOUN
cana-951	36	9	of	of	ADP
cana-951	36	10	inclusions	inclusion	NOUN
cana-951	36	11	within	within	ADP
cana-951	36	12	a	a	DET
cana-951	36	13	polymeric	polymeric	ADJ
cana-951	36	14	or	or	CCONJ
cana-951	36	15	ceramic	ceramic	ADJ
cana-951	36	16	matrix	matrix	NOUN
cana-951	36	17	.	.	PUNCT
cana-951	37	1	lindman	lindman	NOUN
cana-951	37	2	in	in	ADP
cana-951	37	3	1920	1920	NUM
cana-951	37	4	and	and	CCONJ
cana-951	37	5	pickering	pickere	VERB
cana-951	37	6	in	in	ADP
cana-951	37	7	1945	1945	NUM
cana-951	37	8	specifically	specifically	ADV
cana-951	37	9	investigated	investigate	VERB
cana-951	37	10	the	the	DET
cana-951	37	11	interaction	interaction	NOUN
cana-951	37	12	of	of	ADP
cana-951	37	13	electromagnetic	electromagnetic	ADJ
cana-951	37	14	waves	wave	NOUN
cana-951	37	15	with	with	ADP
cana-951	37	16	a	a	DET
cana-951	37	17	collection	collection	NOUN
cana-951	37	18	of	of	ADP
cana-951	37	19	randomly	randomly	ADV
cana-951	37	20	distributed	distribute	VERB
cana-951	37	21	metal	metal	NOUN
cana-951	37	22	helices	helix	NOUN
cana-951	37	23	of	of	ADP
cana-951	37	24	the	the	DET
cana-951	37	25	same	same	ADJ
cana-951	37	26	enantiomorph	enantiomorph	NOUN
cana-951	37	27	form	form	NOUN
cana-951	37	28	[	[	X
cana-951	37	29	19	19	NUM
cana-951	37	30	-	-	SYM
cana-951	37	31	23	23	NUM
cana-951	37	32	]	]	PUNCT
cana-951	37	33	.	.	PUNCT
cana-951	38	1	they	they	PRON
cana-951	38	2	observed	observe	VERB
cana-951	38	3	polarization	polarization	NOUN
cana-951	38	4	plane	plane	NOUN
cana-951	38	5	rotation	rotation	NOUN
cana-951	38	6	of	of	ADP
cana-951	38	7	electromagnetic	electromagnetic	ADJ
cana-951	38	8	waves	wave	NOUN
cana-951	38	9	post	post	NOUN
cana-951	38	10	-	-	NOUN
cana-951	38	11	interaction	interaction	NOUN
cana-951	38	12	with	with	ADP
cana-951	38	13	the	the	DET
cana-951	38	14	helices	helix	NOUN
cana-951	38	15	.	.	PUNCT
cana-951	39	1	in	in	ADP
cana-951	39	2	1979	1979	NUM
cana-951	39	3	,	,	PUNCT
cana-951	39	4	jaggard	jaggard	PROPN
cana-951	39	5	,	,	PUNCT
cana-951	39	6	mickelson	mickelson	PROPN
cana-951	39	7	,	,	PUNCT
cana-951	39	8	and	and	CCONJ
cana-951	39	9	papas	papa	NOUN
cana-951	39	10	proposed	propose	VERB
cana-951	39	11	a	a	DET
cana-951	39	12	macroscopic	macroscopic	ADJ
cana-951	39	13	model	model	NOUN
cana-951	39	14	detailing	detail	VERB
cana-951	39	15	the	the	DET
cana-951	39	16	interaction	interaction	NOUN
cana-951	39	17	of	of	ADP
cana-951	39	18	electromagnetic	electromagnetic	ADJ
cana-951	39	19	waves	wave	NOUN
cana-951	39	20	with	with	ADP
cana-951	39	21	chiral	chiral	ADJ
cana-951	39	22	structures	structure	NOUN
cana-951	39	23	(	(	PUNCT
cana-951	39	24	bi	bi	ADJ
cana-951	39	25	-	-	ADJ
cana-951	39	26	isotropic	isotropic	ADJ
cana-951	39	27	materials	material	NOUN
cana-951	39	28	)	)	PUNCT
cana-951	40	1	[	[	X
cana-951	40	2	19	19	NUM
cana-951	40	3	-	-	SYM
cana-951	40	4	20	20	NUM
cana-951	40	5	]	]	PUNCT
cana-951	40	6	.	.	PUNCT
cana-951	41	1	the	the	DET
cana-951	41	2	general	general	ADJ
cana-951	41	3	bi	bi	ADJ
cana-951	41	4	-	-	ADJ
cana-951	41	5	isotropic	isotropic	ADJ
cana-951	41	6	medium	medium	NOUN
cana-951	41	7	is	be	AUX
cana-951	41	8	chiral	chiral	ADJ
cana-951	41	9	and	and	CCONJ
cana-951	41	10	non	non	ADJ
cana-951	41	11	-	-	ADJ
cana-951	41	12	reciprocal	reciprocal	ADJ
cana-951	41	13	,	,	PUNCT
cana-951	41	14	involving	involve	VERB
cana-951	41	15	a	a	DET
cana-951	41	16	complex	complex	ADJ
cana-951	41	17	parameter	parameter	NOUN
cana-951	41	18	in	in	ADP
cana-951	41	19	the	the	DET
cana-951	41	20	general	general	ADJ
cana-951	41	21	case	case	NOUN
cana-951	41	22	.	.	PUNCT
cana-951	42	1	the	the	DET
cana-951	42	2	effects	effect	NOUN
cana-951	42	3	of	of	ADP
cana-951	42	4	two	two	NUM
cana-951	42	5	parameters	parameter	NOUN
cana-951	42	6	,	,	PUNCT
cana-951	42	7	nonlinear	nonlinear	ADJ
cana-951	42	8	chirality	chirality	NOUN
cana-951	42	9	,	,	PUNCT
cana-951	42	10	and	and	CCONJ
cana-951	42	11	non	non	ADJ
cana-951	42	12	-	-	NOUN
cana-951	42	13	reciprocity	reciprocity	NOUN
cana-951	42	14	,	,	PUNCT
cana-951	42	15	are	be	AUX
cana-951	42	16	crucial	crucial	ADJ
cana-951	42	17	for	for	ADP
cana-951	42	18	estimating	estimate	VERB
cana-951	42	19	non	non	ADJ
cana-951	42	20	-	-	ADJ
cana-951	42	21	linearity	linearity	NOUN
cana-951	42	22	in	in	ADP
cana-951	42	23	bi	bi	ADJ
cana-951	42	24	-	-	ADJ
cana-951	42	25	isotropic	isotropic	ADJ
cana-951	42	26	fibers	fiber	NOUN
cana-951	42	27	.	.	PUNCT
cana-951	43	1	this	this	DET
cana-951	43	2	paper	paper	NOUN
cana-951	43	3	examines	examine	VERB
cana-951	43	4	a	a	DET
cana-951	43	5	direct	direct	ADJ
cana-951	43	6	method	method	NOUN
cana-951	43	7	to	to	PART
cana-951	43	8	determine	determine	VERB
cana-951	43	9	numerous	numerous	ADJ
cana-951	43	10	solution	solution	NOUN
cana-951	43	11	families	family	NOUN
cana-951	43	12	for	for	ADP
cana-951	43	13	the	the	DET
cana-951	43	14	nonlinear	nonlinear	ADJ
cana-951	43	15	schrödinger	schrödinger	ADJ
cana-951	43	16	equation	equation	NOUN
cana-951	43	17	in	in	ADP
cana-951	43	18	bi	bi	ADJ
cana-951	43	19	-	-	ADJ
cana-951	43	20	isotropic	isotropic	ADJ
cana-951	43	21	optical	optical	ADJ
cana-951	43	22	fiber	fiber	NOUN
cana-951	43	23	,	,	PUNCT
cana-951	43	24	alongside	alongside	ADP
cana-951	43	25	𝐺’/𝐺-expansion	𝐺’/𝐺-expansion	NOUN
cana-951	43	26	.	.	PUNCT
cana-951	44	1	this	this	PRON
cana-951	44	2	contributes	contribute	VERB
cana-951	44	3	to	to	ADP
cana-951	44	4	a	a	DET
cana-951	44	5	deeper	deep	ADJ
cana-951	44	6	understanding	understanding	NOUN
cana-951	44	7	of	of	ADP
cana-951	44	8	the	the	DET
cana-951	44	9	interaction	interaction	NOUN
cana-951	44	10	between	between	ADP
cana-951	44	11	electromagnetic	electromagnetic	ADJ
cana-951	44	12	waves	wave	NOUN
cana-951	44	13	and	and	CCONJ
cana-951	44	14	nonlinear	nonlinear	ADJ
cana-951	44	15	bi	bi	ADJ
cana-951	44	16	-	-	ADJ
cana-951	44	17	isotropic	isotropic	ADJ
cana-951	44	18	media	medium	NOUN
cana-951	44	19	,	,	PUNCT
cana-951	44	20	facilitating	facilitate	VERB
cana-951	44	21	the	the	DET
cana-951	44	22	design	design	NOUN
cana-951	44	23	of	of	ADP
cana-951	44	24	potential	potential	ADJ
cana-951	44	25	applications	application	NOUN
cana-951	44	26	in	in	ADP
cana-951	44	27	microwave	microwave	NOUN
cana-951	44	28	and	and	CCONJ
cana-951	44	29	optical	optical	ADJ
cana-951	44	30	domains	domain	NOUN
cana-951	44	31	.	.	PUNCT
cana-951	45	1	consequently	consequently	ADV
cana-951	45	2	,	,	PUNCT
cana-951	45	3	an	an	DET
cana-951	45	4	original	original	ADJ
cana-951	45	5	mathematical	mathematical	ADJ
cana-951	45	6	approach	approach	NOUN
cana-951	45	7	is	be	AUX
cana-951	45	8	proposed	propose	VERB
cana-951	45	9	to	to	PART
cana-951	45	10	evaluate	evaluate	VERB
cana-951	45	11	nonlinear	nonlinear	ADJ
cana-951	45	12	effects	effect	NOUN
cana-951	45	13	in	in	ADP
cana-951	45	14	bi	bi	ADJ
cana-951	45	15	-	-	ADJ
cana-951	45	16	isotropic	isotropic	ADJ
cana-951	45	17	optical	optical	ADJ
cana-951	45	18	fibers	fiber	NOUN
cana-951	45	19	,	,	PUNCT
cana-951	45	20	stemming	stem	VERB
cana-951	45	21	from	from	ADP
cana-951	45	22	magnetization	magnetization	NOUN
cana-951	45	23	under	under	ADP
cana-951	45	24	the	the	DET
cana-951	45	25	influence	influence	NOUN
cana-951	45	26	of	of	ADP
cana-951	45	27	a	a	DET
cana-951	45	28	strong	strong	ADJ
cana-951	45	29	electric	electric	ADJ
cana-951	45	30	field	field	NOUN
cana-951	45	31	communications	communication	NOUN
cana-951	45	32	on	on	ADP
cana-951	45	33	applied	apply	VERB
cana-951	45	34	nonlinear	nonlinear	ADJ
cana-951	45	35	analysis	analysis	NOUN
cana-951	45	36	issn	issn	NOUN
cana-951	45	37	:	:	PUNCT
cana-951	45	38	1074	1074	NUM
cana-951	45	39	-	-	PUNCT
cana-951	45	40	133x	133x	NUM
cana-951	45	41	vol	vol	NOUN
cana-951	45	42	31	31	NUM
cana-951	45	43	no	no	NOUN
cana-951	45	44	.	.	PUNCT
cana-951	46	1	4s	4s	NUM
cana-951	46	2	(	(	PUNCT
cana-951	46	3	2024	2024	NUM
cana-951	46	4	)	)	PUNCT
cana-951	46	5	574	574	NUM
cana-951	46	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-951	47	1	[	[	X
cana-951	47	2	19	19	NUM
cana-951	47	3	-	-	SYM
cana-951	47	4	20	20	NUM
cana-951	47	5	]	]	PUNCT
cana-951	47	6	.	.	PUNCT
cana-951	48	1	the	the	DET
cana-951	48	2	extended	extended	ADJ
cana-951	48	3	𝐺’/𝐺	𝐺’/𝐺	PROPN
cana-951	48	4	-expansion	-expansion	PROPN
cana-951	48	5	method	method	NOUN
cana-951	48	6	emerges	emerge	VERB
cana-951	48	7	as	as	ADP
cana-951	48	8	a	a	DET
cana-951	48	9	potent	potent	ADJ
cana-951	48	10	technique	technique	NOUN
cana-951	48	11	for	for	ADP
cana-951	48	12	deriving	derive	VERB
cana-951	48	13	solution	solution	NOUN
cana-951	48	14	families	family	NOUN
cana-951	48	15	of	of	ADP
cana-951	48	16	the	the	DET
cana-951	48	17	nonlinear	nonlinear	ADJ
cana-951	48	18	schrödinger	schrödinger	ADJ
cana-951	48	19	equation	equation	NOUN
cana-951	48	20	in	in	ADP
cana-951	48	21	bi	bi	ADJ
cana-951	48	22	-	-	ADJ
cana-951	48	23	isotropic	isotropic	ADJ
cana-951	48	24	optical	optical	ADJ
cana-951	48	25	fibers	fiber	NOUN
cana-951	48	26	.	.	PUNCT
cana-951	49	1	this	this	DET
cana-951	49	2	method	method	NOUN
cana-951	49	3	employs	employ	VERB
cana-951	49	4	a	a	DET
cana-951	49	5	perturbation	perturbation	NOUN
cana-951	49	6	expansion	expansion	NOUN
cana-951	49	7	in	in	ADP
cana-951	49	8	powers	power	NOUN
cana-951	49	9	of	of	ADP
cana-951	49	10	the	the	DET
cana-951	49	11	dimensionless	dimensionless	NOUN
cana-951	49	12	parameter	parameter	NOUN
cana-951	49	13	and	and	CCONJ
cana-951	49	14	is	be	AUX
cana-951	49	15	applicable	applicable	ADJ
cana-951	49	16	for	for	ADP
cana-951	49	17	both	both	CCONJ
cana-951	49	18	weak	weak	ADJ
cana-951	49	19	and	and	CCONJ
cana-951	49	20	strong	strong	ADJ
cana-951	49	21	nonlinearities	nonlinearitie	NOUN
cana-951	49	22	.	.	PUNCT
cana-951	50	1	it	it	PRON
cana-951	50	2	accommodates	accommodate	VERB
cana-951	50	3	varying	vary	VERB
cana-951	50	4	dispersion	dispersion	NOUN
cana-951	50	5	and	and	CCONJ
cana-951	50	6	nonlinearity	nonlinearity	NOUN
cana-951	50	7	,	,	PUNCT
cana-951	50	8	rendering	render	VERB
cana-951	50	9	it	it	PRON
cana-951	50	10	suitable	suitable	ADJ
cana-951	50	11	for	for	ADP
cana-951	50	12	modeling	model	VERB
cana-951	50	13	a	a	DET
cana-951	50	14	wide	wide	ADJ
cana-951	50	15	array	array	NOUN
cana-951	50	16	of	of	ADP
cana-951	50	17	optical	optical	ADJ
cana-951	50	18	fibers	fiber	NOUN
cana-951	50	19	.	.	PUNCT
cana-951	51	1	the	the	DET
cana-951	51	2	method	method	NOUN
cana-951	51	3	effectively	effectively	ADV
cana-951	51	4	describes	describe	VERB
cana-951	51	5	the	the	DET
cana-951	51	6	propagation	propagation	NOUN
cana-951	51	7	of	of	ADP
cana-951	51	8	optical	optical	ADJ
cana-951	51	9	pulses	pulse	NOUN
cana-951	51	10	in	in	ADP
cana-951	51	11	bi	bi	ADJ
cana-951	51	12	-	-	ADJ
cana-951	51	13	isotropic	isotropic	ADJ
cana-951	51	14	fibers	fiber	NOUN
cana-951	51	15	and	and	CCONJ
cana-951	51	16	predicts	predict	VERB
cana-951	51	17	their	their	PRON
cana-951	51	18	behavior	behavior	NOUN
cana-951	51	19	under	under	ADP
cana-951	51	20	diverse	diverse	ADJ
cana-951	51	21	conditions	condition	NOUN
cana-951	51	22	.	.	PUNCT
cana-951	52	1	furthermore	furthermore	ADV
cana-951	52	2	,	,	PUNCT
cana-951	52	3	it	it	PRON
cana-951	52	4	facilitates	facilitate	VERB
cana-951	52	5	the	the	DET
cana-951	52	6	study	study	NOUN
cana-951	52	7	of	of	ADP
cana-951	52	8	soliton	soliton	NOUN
cana-951	52	9	dynamics	dynamic	NOUN
cana-951	52	10	,	,	PUNCT
cana-951	52	11	including	include	VERB
cana-951	52	12	stability	stability	NOUN
cana-951	52	13	and	and	CCONJ
cana-951	52	14	interactions	interaction	NOUN
cana-951	52	15	.	.	PUNCT
cana-951	53	1	overall	overall	ADV
cana-951	53	2	,	,	PUNCT
cana-951	53	3	the	the	DET
cana-951	53	4	extended	extended	ADJ
cana-951	53	5	𝐺’/𝐺	𝐺’/𝐺	PROPN
cana-951	53	6	-expansion	-expansion	PROPN
cana-951	53	7	method	method	NOUN
cana-951	53	8	stands	stand	VERB
cana-951	53	9	as	as	ADP
cana-951	53	10	a	a	DET
cana-951	53	11	valuable	valuable	ADJ
cana-951	53	12	tool	tool	NOUN
cana-951	53	13	for	for	ADP
cana-951	53	14	comprehending	comprehend	VERB
cana-951	53	15	the	the	DET
cana-951	53	16	dynamics	dynamic	NOUN
cana-951	53	17	of	of	ADP
cana-951	53	18	nonlinear	nonlinear	ADJ
cana-951	53	19	optical	optical	ADJ
cana-951	53	20	systems	system	NOUN
cana-951	53	21	,	,	PUNCT
cana-951	53	22	with	with	ADP
cana-951	53	23	anticipated	anticipate	VERB
cana-951	53	24	applications	application	NOUN
cana-951	53	25	across	across	ADP
cana-951	53	26	the	the	DET
cana-951	53	27	field	field	NOUN
cana-951	53	28	of	of	ADP
cana-951	53	29	nonlinear	nonlinear	ADJ
cana-951	53	30	optics	optic	NOUN
cana-951	53	31	[	[	X
cana-951	53	32	24	24	NUM
cana-951	53	33	]	]	PUNCT
cana-951	53	34	.	.	PUNCT
cana-951	54	1	2	2	X
cana-951	54	2	.	.	X
cana-951	54	3	description	description	NOUN
cana-951	54	4	of	of	ADP
cana-951	54	5	the	the	PRON
cana-951	54	6	(	(	PUNCT
cana-951	54	7	𝐆′/𝐆)-expansion	𝐆′/𝐆)-expansion	SYM
cana-951	54	8	method	method	NOUN
cana-951	54	9	study	study	VERB
cana-951	54	10	a	a	DET
cana-951	54	11	nonlinear	nonlinear	ADJ
cana-951	54	12	pde	pde	NOUN
cana-951	54	13	in	in	ADP
cana-951	54	14	the	the	DET
cana-951	54	15	following	follow	VERB
cana-951	54	16	form	form	NOUN
cana-951	54	17	p(u	p(u	PROPN
cana-951	54	18	,	,	PUNCT
cana-951	54	19	uz	uz	PROPN
cana-951	54	20	,	,	PUNCT
cana-951	54	21	ut	ut	PROPN
cana-951	54	22	,	,	PUNCT
cana-951	54	23	uzz	uzz	PROPN
cana-951	54	24	,	,	PUNCT
cana-951	54	25	utt	utt	PROPN
cana-951	54	26	)	)	PUNCT
cana-951	54	27	=	=	SYM
cana-951	54	28	0	0	PUNCT
cana-951	55	1	(	(	PUNCT
cana-951	55	2	1	1	NUM
cana-951	55	3	)	)	PUNCT
cana-951	55	4	where	where	SCONJ
cana-951	55	5	u	u	NOUN
cana-951	55	6	=	=	SYM
cana-951	55	7	u(t	u(t	NOUN
cana-951	55	8	,	,	PUNCT
cana-951	55	9	z	z	NOUN
cana-951	55	10	)	)	PUNCT
cana-951	55	11	is	be	AUX
cana-951	55	12	an	an	DET
cana-951	55	13	new	new	ADJ
cana-951	55	14	function	function	NOUN
cana-951	55	15	,	,	PUNCT
cana-951	55	16	p	p	NOUN
cana-951	55	17	is	be	AUX
cana-951	55	18	a	a	DET
cana-951	55	19	polynomial	polynomial	NOUN
cana-951	55	20	in	in	ADP
cana-951	55	21	u	u	NOUN
cana-951	55	22	=	=	SYM
cana-951	55	23	u(t	u(t	NOUN
cana-951	55	24	,	,	PUNCT
cana-951	55	25	z	z	NOUN
cana-951	55	26	)	)	PUNCT
cana-951	55	27	,	,	PUNCT
cana-951	55	28	and	and	CCONJ
cana-951	55	29	its	its	PRON
cana-951	55	30	partial	partial	ADJ
cana-951	55	31	derivatives	derivative	NOUN
cana-951	55	32	in	in	ADP
cana-951	55	33	which	which	PRON
cana-951	55	34	the	the	DET
cana-951	55	35	highest	high	ADJ
cana-951	55	36	order	order	NOUN
cana-951	55	37	derivatives	derivative	NOUN
cana-951	55	38	and	and	CCONJ
cana-951	55	39	nonlinear	nonlinear	ADJ
cana-951	55	40	terms	term	NOUN
cana-951	55	41	are	be	AUX
cana-951	55	42	involved	involve	VERB
cana-951	55	43	.	.	PUNCT
cana-951	56	1	let	let	VERB
cana-951	56	2	us	we	PRON
cana-951	56	3	now	now	ADV
cana-951	56	4	provide	provide	VERB
cana-951	56	5	the	the	DET
cana-951	56	6	main	main	ADJ
cana-951	56	7	steps	step	NOUN
cana-951	56	8	of	of	ADP
cana-951	56	9	the	the	DET
cana-951	56	10	extended	extended	ADJ
cana-951	56	11	(	(	PUNCT
cana-951	56	12	g′/g)expansion	g′/g)expansion	NOUN
cana-951	56	13	method	method	NOUN
cana-951	56	14	.	.	PUNCT
cana-951	57	1	step	step	NOUN
cana-951	57	2	1	1	NUM
cana-951	57	3	.	.	PUNCT
cana-951	58	1	we	we	PRON
cana-951	58	2	usage	usage	VERB
cana-951	58	3	the	the	DET
cana-951	58	4	following	follow	VERB
cana-951	58	5	conversion	conversion	NOUN
cana-951	58	6	u(z	u(z	PROPN
cana-951	58	7	,	,	PUNCT
cana-951	58	8	t	t	PROPN
cana-951	58	9	)	)	PUNCT
cana-951	58	10	=	=	SYM
cana-951	58	11	u(ξ	u(ξ	NOUN
cana-951	58	12	)	)	PUNCT
cana-951	58	13	;	;	PUNCT
cana-951	58	14	ξ	ξ	X
cana-951	58	15	=	=	SYM
cana-951	58	16	z	z	PROPN
cana-951	58	17	−	−	PROPN
cana-951	58	18	vt	vt	NOUN
cana-951	58	19	(	(	PUNCT
cana-951	58	20	2	2	NUM
cana-951	58	21	)	)	PUNCT
cana-951	58	22	to	to	PART
cana-951	58	23	reduce	reduce	VERB
cana-951	58	24	eq.(3	eq.(3	NOUN
cana-951	58	25	)	)	PUNCT
cana-951	58	26	to	to	ADP
cana-951	58	27	the	the	DET
cana-951	58	28	next	next	ADJ
cana-951	58	29	nonlinear	nonlinear	ADJ
cana-951	58	30	ode	ode	PROPN
cana-951	58	31	:	:	PUNCT
cana-951	58	32	k(u	k(u	NOUN
cana-951	58	33	,	,	PUNCT
cana-951	58	34	u′	u′	PROPN
cana-951	58	35	,	,	PUNCT
cana-951	58	36	u′′	u′′	PROPN
cana-951	58	37	,	,	PUNCT
cana-951	58	38	.	.	PUNCT
cana-951	58	39	.	.	PUNCT
cana-951	58	40	.	.	PUNCT
cana-951	58	41	)	)	PUNCT
cana-951	59	1	=	=	SYM
cana-951	59	2	0	0	PUNCT
cana-951	59	3	(	(	PUNCT
cana-951	59	4	3	3	NUM
cana-951	59	5	)	)	PUNCT
cana-951	59	6	where	where	SCONJ
cana-951	59	7	v	v	NOUN
cana-951	59	8	is	be	AUX
cana-951	59	9	velocity	velocity	NOUN
cana-951	59	10	of	of	ADP
cana-951	59	11	the	the	DET
cana-951	59	12	propagation	propagation	NOUN
cana-951	59	13	,	,	PUNCT
cana-951	59	14	k	k	PROPN
cana-951	59	15	is	be	AUX
cana-951	59	16	a	a	DET
cana-951	59	17	polynomial	polynomial	NOUN
cana-951	59	18	of	of	ADP
cana-951	59	19	u(ξ	u(ξ	NOUN
cana-951	59	20	)	)	PUNCT
cana-951	59	21	and	and	CCONJ
cana-951	59	22	its	its	PRON
cana-951	59	23	derivatives	derivative	NOUN
cana-951	59	24	u′(ξ	u′(ξ	PRON
cana-951	59	25	)	)	PUNCT
cana-951	59	26	,	,	PUNCT
cana-951	59	27	u	u	PRON
cana-951	59	28	′′	′′	PROPN
cana-951	59	29	(	(	PUNCT
cana-951	59	30	ξ	ξ	PROPN
cana-951	59	31	)	)	PUNCT
cana-951	59	32	,	,	PUNCT
cana-951	59	33	.	.	PUNCT
cana-951	59	34	.	.	PUNCT
cana-951	59	35	.	.	PUNCT
cana-951	60	1	where	where	SCONJ
cana-951	60	2	u′(ξ	u′(ξ	X
cana-951	60	3	)	)	PUNCT
cana-951	60	4	=	=	PUNCT
cana-951	60	5	du	du	PROPN
cana-951	60	6	∂ξ	∂ξ	PROPN
cana-951	60	7	,	,	PUNCT
cana-951	60	8	u′′(ξ	u′′(ξ	NOUN
cana-951	60	9	)	)	PUNCT
cana-951	60	10	=	=	PUNCT
cana-951	60	11	d2u(ξ	d2u(ξ	PROPN
cana-951	60	12	)	)	PUNCT
cana-951	60	13	dξ2	dξ2	NOUN
cana-951	60	14	,	,	PUNCT
cana-951	60	15	...	...	PUNCT
cana-951	60	16	step	step	NOUN
cana-951	60	17	2	2	NUM
cana-951	60	18	.	.	PUNCT
cana-951	61	1	we	we	PRON
cana-951	61	2	adopt	adopt	VERB
cana-951	61	3	that	that	SCONJ
cana-951	61	4	the	the	DET
cana-951	61	5	solution	solution	NOUN
cana-951	61	6	of	of	ADP
cana-951	61	7	eq.(1	eq.(1	ADJ
cana-951	61	8	)	)	PUNCT
cana-951	61	9	has	have	VERB
cana-951	61	10	the	the	DET
cana-951	61	11	form	form	NOUN
cana-951	61	12	:	:	PUNCT
cana-951	61	13	u(ξ	u(ξ	NOUN
cana-951	61	14	)	)	PUNCT
cana-951	61	15	=	=	SYM
cana-951	61	16	a0(z	a0(z	NUM
cana-951	61	17	)	)	PUNCT
cana-951	62	1	+	+	CCONJ
cana-951	62	2	∑	∑	PROPN
cana-951	62	3	n	n	PRON
cana-951	62	4	i=1	i=1	PROPN
cana-951	62	5	ai	ai	VERB
cana-951	62	6	(	(	PUNCT
cana-951	62	7	g′	g′	NOUN
cana-951	62	8	g	g	NOUN
cana-951	62	9	)	)	PUNCT
cana-951	62	10	i	i	PRON
cana-951	62	11	+	+	X
cana-951	62	12	bi(z	bi(z	NOUN
cana-951	62	13	)	)	PUNCT
cana-951	62	14	(	(	PUNCT
cana-951	62	15	g′	g′	NOUN
cana-951	62	16	g	g	NOUN
cana-951	62	17	)	)	PUNCT
cana-951	63	1	i−1	i−1	PROPN
cana-951	63	2	√1	√1	PROPN
cana-951	63	3	+	+	CCONJ
cana-951	63	4	1	1	NUM
cana-951	63	5	μ	μ	NOUN
cana-951	63	6	(	(	PUNCT
cana-951	63	7	g′	g′	NOUN
cana-951	63	8	g	g	NOUN
cana-951	63	9	)	)	PUNCT
cana-951	63	10	2	2	NUM
cana-951	63	11	(	(	PUNCT
cana-951	63	12	4	4	NUM
cana-951	63	13	)	)	PUNCT
cana-951	63	14	where	where	SCONJ
cana-951	63	15	ai	ai	VERB
cana-951	63	16	=	=	PUNCT
cana-951	63	17	ai(z	ai(z	NOUN
cana-951	63	18	)	)	PUNCT
cana-951	63	19	,	,	PUNCT
cana-951	63	20	bi	bi	NOUN
cana-951	63	21	=	=	NOUN
cana-951	63	22	bi(z	bi(z	X
cana-951	63	23	)	)	PUNCT
cana-951	63	24	(	(	PUNCT
cana-951	63	25	i	i	NOUN
cana-951	63	26	=	=	SYM
cana-951	63	27	1,2	1,2	NUM
cana-951	63	28	,	,	PUNCT
cana-951	63	29	.	.	PUNCT
cana-951	63	30	.	.	PUNCT
cana-951	64	1	n	n	CCONJ
cana-951	64	2	)	)	PUNCT
cana-951	64	3	are	be	AUX
cana-951	64	4	functions	function	NOUN
cana-951	64	5	of	of	ADP
cana-951	64	6	z	z	NOUN
cana-951	64	7	to	to	PART
cana-951	64	8	be	be	AUX
cana-951	64	9	determined	determine	VERB
cana-951	64	10	.	.	PUNCT
cana-951	65	1	g	g	PROPN
cana-951	65	2	=	=	SYM
cana-951	65	3	g(ξ	g(ξ	PROPN
cana-951	65	4	)	)	PUNCT
cana-951	65	5	satisfies	satisfy	VERB
cana-951	65	6	the	the	DET
cana-951	65	7	resulting	result	VERB
cana-951	65	8	second	second	ADJ
cana-951	65	9	order	order	NOUN
cana-951	65	10	ode	ode	ADJ
cana-951	65	11	equation	equation	NOUN
cana-951	65	12	:	:	PUNCT
cana-951	65	13	g′′(ξ	g′′(ξ	NOUN
cana-951	65	14	)	)	PUNCT
cana-951	66	1	+	+	CCONJ
cana-951	66	2	μg(ξ	μg(ξ	X
cana-951	66	3	)	)	PUNCT
cana-951	66	4	=	=	SYM
cana-951	66	5	0	0	PUNCT
cana-951	66	6	(	(	PUNCT
cana-951	66	7	5	5	NUM
cana-951	66	8	)	)	PUNCT
cana-951	66	9	where	where	SCONJ
cana-951	66	10	g′	g′	NOUN
cana-951	66	11	=	=	VERB
cana-951	66	12	dg	dg	X
cana-951	66	13	dξ	dξ	PROPN
cana-951	66	14	,	,	PUNCT
cana-951	66	15	g′′	g′′	PROPN
cana-951	66	16	=	=	SYM
cana-951	66	17	d2	d2	PROPN
cana-951	66	18	g	g	PROPN
cana-951	66	19	dξ2	dξ2	NOUN
cana-951	66	20	.	.	PUNCT
cana-951	67	1	we	we	PRON
cana-951	67	2	describe	describe	VERB
cana-951	67	3	the	the	DET
cana-951	67	4	degree	degree	NOUN
cana-951	67	5	of	of	ADP
cana-951	67	6	u(ξ	u(ξ	NOUN
cana-951	67	7	)	)	PUNCT
cana-951	67	8	as	as	ADP
cana-951	67	9	d[u(ξ	d[u(ξ	NOUN
cana-951	67	10	)	)	PUNCT
cana-951	67	11	]	]	PUNCT
cana-951	68	1	=	=	PUNCT
cana-951	68	2	m	m	ADJ
cana-951	68	3	,	,	PUNCT
cana-951	68	4	then	then	ADV
cana-951	68	5	d	d	X
cana-951	68	6	[	[	PUNCT
cana-951	68	7	dpu(ξ	dpu(ξ	NOUN
cana-951	68	8	)	)	PUNCT
cana-951	68	9	dξp	dξp	NOUN
cana-951	68	10	]	]	PUNCT
cana-951	69	1	=	=	PUNCT
cana-951	69	2	m	m	VERB
cana-951	70	1	+	+	X
cana-951	70	2	p	p	X
cana-951	70	3	;	;	PUNCT
cana-951	70	4	d[up	d[up	X
cana-951	70	5	(	(	PUNCT
cana-951	70	6	dqu(ξ	dqu(ξ	NOUN
cana-951	70	7	)	)	PUNCT
cana-951	70	8	dξq	dξq	NOUN
cana-951	70	9	)	)	PUNCT
cana-951	70	10	s	s	PART
cana-951	70	11	]	]	X
cana-951	70	12	=	=	PUNCT
cana-951	70	13	mp	mp	PROPN
cana-951	70	14	+	+	CCONJ
cana-951	70	15	(	(	PUNCT
cana-951	70	16	m	m	VERB
cana-951	70	17	+	+	ADJ
cana-951	70	18	q)s	q)s	NOUN
cana-951	70	19	(	(	PUNCT
cana-951	70	20	6	6	NUM
cana-951	70	21	)	)	PUNCT
cana-951	70	22	the	the	DET
cana-951	70	23	parameter	parameter	NOUN
cana-951	70	24	n	n	PRON
cana-951	70	25	can	can	AUX
cana-951	70	26	be	be	AUX
cana-951	70	27	start	start	VERB
cana-951	70	28	by	by	ADP
cana-951	70	29	balancing	balance	VERB
cana-951	70	30	the	the	DET
cana-951	70	31	highest	high	ADJ
cana-951	70	32	order	order	NOUN
cana-951	70	33	derivative	derivative	ADJ
cana-951	70	34	term	term	NOUN
cana-951	70	35	and	and	CCONJ
cana-951	70	36	nonlinear	nonlinear	ADJ
cana-951	70	37	terms	term	NOUN
cana-951	70	38	in	in	ADP
cana-951	70	39	eq.(3	eq.(3	NOUN
cana-951	70	40	)	)	PUNCT
cana-951	70	41	.	.	PUNCT
cana-951	71	1	n	n	PRON
cana-951	71	2	is	be	AUX
cana-951	71	3	typically	typically	ADV
cana-951	71	4	a	a	DET
cana-951	71	5	positive	positive	ADJ
cana-951	71	6	integer	integer	NOUN
cana-951	71	7	.	.	PUNCT
cana-951	72	1	substituting	substitute	VERB
cana-951	72	2	eq.(1	eq.(1	ADJ
cana-951	72	3	)	)	PUNCT
cana-951	72	4	along	along	ADP
cana-951	72	5	with	with	ADP
cana-951	72	6	eq.(2	eq.(2	ADJ
cana-951	72	7	)	)	PUNCT
cana-951	72	8	into	into	ADP
cana-951	72	9	eq.(4	eq.(4	ADJ
cana-951	72	10	)	)	PUNCT
cana-951	72	11	,	,	PUNCT
cana-951	72	12	collecting	collect	VERB
cana-951	72	13	all	all	DET
cana-951	72	14	terms	term	NOUN
cana-951	72	15	with	with	ADP
cana-951	72	16	the	the	DET
cana-951	72	17	same	same	ADJ
cana-951	72	18	power	power	NOUN
cana-951	72	19	of	of	ADP
cana-951	72	20	(	(	PUNCT
cana-951	72	21	g′(ξ	g′(ξ	NOUN
cana-951	72	22	)	)	PUNCT
cana-951	72	23	g(ξ	g(ξ	PROPN
cana-951	72	24	)	)	PUNCT
cana-951	72	25	)	)	PUNCT
cana-951	73	1	i(i	i(i	PROPN
cana-951	73	2	=	=	SYM
cana-951	73	3	0	0	NUM
cana-951	73	4	;	;	PUNCT
cana-951	73	5	1	1	NUM
cana-951	73	6	;	;	PUNCT
cana-951	73	7	2;	2;	NUM
cana-951	73	8	...	...	PUNCT
cana-951	73	9	n	n	CCONJ
cana-951	73	10	)	)	PUNCT
cana-951	73	11	,	,	PUNCT
cana-951	73	12	and	and	CCONJ
cana-951	73	13	setting	set	VERB
cana-951	73	14	each	each	DET
cana-951	73	15	coefficients	coefficient	NOUN
cana-951	73	16	to	to	ADP
cana-951	73	17	zero	zero	NUM
cana-951	73	18	,	,	PUNCT
cana-951	73	19	we	we	PRON
cana-951	73	20	get	get	VERB
cana-951	73	21	a	a	DET
cana-951	73	22	system	system	NOUN
cana-951	73	23	of	of	ADP
cana-951	73	24	algebraic	algebraic	ADJ
cana-951	73	25	equations	equation	NOUN
cana-951	73	26	for	for	ADP
cana-951	73	27	ai	ai	NOUN
cana-951	73	28	and	and	CCONJ
cana-951	73	29	bi.the	bi.the	DET
cana-951	73	30	solution	solution	NOUN
cana-951	73	31	of	of	ADP
cana-951	73	32	eq.(5	eq.(5	NOUN
cana-951	73	33	)	)	PUNCT
cana-951	73	34	are	be	AUX
cana-951	73	35	given	give	VERB
cana-951	73	36	as	as	SCONJ
cana-951	73	37	communications	communication	NOUN
cana-951	73	38	on	on	ADP
cana-951	73	39	applied	apply	VERB
cana-951	73	40	nonlinear	nonlinear	ADJ
cana-951	73	41	analysis	analysis	NOUN
cana-951	73	42	issn	issn	NOUN
cana-951	73	43	:	:	PUNCT
cana-951	73	44	1074	1074	NUM
cana-951	73	45	-	-	PUNCT
cana-951	73	46	133x	133x	NUM
cana-951	73	47	vol	vol	NOUN
cana-951	73	48	31	31	NUM
cana-951	73	49	no	no	NOUN
cana-951	73	50	.	.	PUNCT
cana-951	74	1	4s	4s	NUM
cana-951	74	2	(	(	PUNCT
cana-951	74	3	2024	2024	NUM
cana-951	74	4	)	)	PUNCT
cana-951	74	5	575	575	NUM
cana-951	74	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-951	74	7	3	3	NUM
cana-951	74	8	.	.	PUNCT
cana-951	75	1	g′(ξ	g′(ξ	NOUN
cana-951	75	2	)	)	PUNCT
cana-951	75	3	g(ξ	g(ξ	PROPN
cana-951	75	4	)	)	PUNCT
cana-951	76	1	=	=	PRON
cana-951	76	2	{	{	PUNCT
cana-951	76	3	√−μ	√−μ	PROPN
cana-951	76	4	(	(	PUNCT
cana-951	76	5	a1sinh√−μξ+a2cosh√−μξ	a1sinh√−μξ+a2cosh√−μξ	NOUN
cana-951	76	6	a1cosh√−μξ+a2sinh√−μξ	a1cosh√−μξ+a2sinh√−μξ	PROPN
cana-951	76	7	)	)	PUNCT
cana-951	76	8	;	;	PUNCT
cana-951	76	9	μ	μ	PROPN
cana-951	76	10	<	<	X
cana-951	76	11	0	0	NUM
cana-951	76	12	√μ	√μ	NUM
cana-951	76	13	(	(	PUNCT
cana-951	76	14	a1sin√μξ+a2cos√μξ	a1sin√μξ+a2cos√μξ	PROPN
cana-951	76	15	a2sin√μξ−a1cos√μξ	a2sin√μξ−a1cos√μξ	PROPN
cana-951	76	16	)	)	PUNCT
cana-951	76	17	;	;	PUNCT
cana-951	76	18	μ	μ	PROPN
cana-951	76	19	>	>	SYM
cana-951	76	20	0	0	NUM
cana-951	76	21	a2	a2	PROPN
cana-951	76	22	a1+a2ξ	a1+a2ξ	PROPN
cana-951	76	23	;	;	PUNCT
cana-951	76	24	μ	μ	PROPN
cana-951	76	25	=	=	SYM
cana-951	76	26	0	0	PUNCT
cana-951	76	27	(	(	PUNCT
cana-951	76	28	7	7	NUM
cana-951	76	29	)	)	PUNCT
cana-951	76	30	which	which	PRON
cana-951	76	31	can	can	AUX
cana-951	76	32	be	be	AUX
cana-951	76	33	written	write	VERB
cana-951	76	34	in	in	ADP
cana-951	76	35	the	the	DET
cana-951	76	36	following	following	ADJ
cana-951	76	37	simplified	simplified	ADJ
cana-951	76	38	form	form	NOUN
cana-951	76	39	g′(ξ	g′(ξ	NOUN
cana-951	76	40	)	)	PUNCT
cana-951	76	41	g(ξ	g(ξ	PROPN
cana-951	76	42	)	)	PUNCT
cana-951	76	43	=	=	PRON
cana-951	76	44	{	{	PUNCT
cana-951	76	45	√−μtanh(√−μξ	√−μtanh(√−μξ	X
cana-951	76	46	+	+	X
cana-951	76	47	ξ0	ξ0	PROPN
cana-951	76	48	)	)	PUNCT
cana-951	76	49	;	;	PUNCT
cana-951	76	50	μ	μ	PROPN
cana-951	76	51	<	<	X
cana-951	76	52	0	0	PROPN
cana-951	76	53	,	,	PUNCT
cana-951	76	54	tanhξ0	tanhξ0	NOUN
cana-951	76	55	=	=	NOUN
cana-951	76	56	a1	a1	NOUN
cana-951	76	57	a2	a2	PROPN
cana-951	76	58	;	;	PUNCT
cana-951	76	59	|	|	ADV
cana-951	76	60	a2	a2	NOUN
cana-951	76	61	a1	a1	NOUN
cana-951	76	62	|	|	ADV
cana-951	76	63	>	>	X
cana-951	76	64	1	1	NUM
cana-951	76	65	√−μcoth(√−μξ	√−μcoth(√−μξ	NOUN
cana-951	76	66	+	+	X
cana-951	76	67	ξ0	ξ0	NOUN
cana-951	76	68	)	)	PUNCT
cana-951	76	69	;	;	PUNCT
cana-951	76	70	μ	μ	PROPN
cana-951	76	71	<	<	X
cana-951	76	72	0	0	NUM
cana-951	76	73	,	,	PUNCT
cana-951	76	74	cothξ0	cothξ0	NOUN
cana-951	76	75	=	=	SYM
cana-951	76	76	a1	a1	NOUN
cana-951	76	77	a2	a2	PROPN
cana-951	76	78	;	;	PUNCT
cana-951	76	79	|	|	ADV
cana-951	76	80	a2	a2	NOUN
cana-951	76	81	a1	a1	NOUN
cana-951	76	82	|	|	ADV
cana-951	76	83	<	<	X
cana-951	76	84	1	1	NUM
cana-951	76	85	√μcot(√μξ	√μcot(√μξ	PROPN
cana-951	76	86	+	+	CCONJ
cana-951	76	87	ξ0	ξ0	PROPN
cana-951	76	88	)	)	PUNCT
cana-951	76	89	;	;	PUNCT
cana-951	76	90	μ	μ	PROPN
cana-951	76	91	>	>	X
cana-951	76	92	0	0	PROPN
cana-951	76	93	,	,	PUNCT
cana-951	76	94	cosξ0	cosξ0	NOUN
cana-951	76	95	=	=	PUNCT
cana-951	76	96	−	−	PROPN
cana-951	76	97	a2	a2	PROPN
cana-951	76	98	a1	a1	PROPN
cana-951	76	99	a2	a2	PROPN
cana-951	76	100	a1+a2ξ	a1+a2ξ	PROPN
cana-951	76	101	;	;	PUNCT
cana-951	76	102	μ	μ	PROPN
cana-951	76	103	=	=	SYM
cana-951	76	104	0	0	PUNCT
cana-951	76	105	(	(	PUNCT
cana-951	76	106	8)	8)	NUM
cana-951	76	107	4	4	NUM
cana-951	76	108	.	.	PUNCT
cana-951	76	109	by	by	ADP
cana-951	76	110	solving	solve	VERB
cana-951	76	111	the	the	DET
cana-951	76	112	over	over	ADV
cana-951	76	113	-	-	PUNCT
cana-951	76	114	determined	determine	VERB
cana-951	76	115	algebraic	algebraic	ADJ
cana-951	76	116	system	system	NOUN
cana-951	76	117	with	with	ADP
cana-951	76	118	the	the	DET
cana-951	76	119	help	help	NOUN
cana-951	76	120	of	of	ADP
cana-951	76	121	mathematica	mathematica	PROPN
cana-951	76	122	,	,	PUNCT
cana-951	76	123	we	we	PRON
cana-951	76	124	obtain	obtain	VERB
cana-951	76	125	the	the	DET
cana-951	76	126	values	value	NOUN
cana-951	76	127	of	of	ADP
cana-951	76	128	a0	a0	NOUN
cana-951	76	129	;	;	PUNCT
cana-951	76	130	ai	ai	PROPN
cana-951	76	131	and	and	CCONJ
cana-951	76	132	bi	bi	NOUN
cana-951	76	133	.	.	PUNCT
cana-951	77	1	substituting	substitute	VERB
cana-951	77	2	these	these	DET
cana-951	77	3	results	result	NOUN
cana-951	77	4	into	into	ADP
cana-951	77	5	eq.(1	eq.(1	ADJ
cana-951	77	6	)	)	PUNCT
cana-951	77	7	,	,	PUNCT
cana-951	77	8	and	and	CCONJ
cana-951	77	9	combining	combine	VERB
cana-951	77	10	with	with	ADP
cana-951	77	11	the	the	DET
cana-951	77	12	solution	solution	NOUN
cana-951	77	13	of	of	ADP
cana-951	77	14	eq.(5	eq.(5	NOUN
cana-951	77	15	)	)	PUNCT
cana-951	77	16	,	,	PUNCT
cana-951	77	17	we	we	PRON
cana-951	77	18	obtain	obtain	VERB
cana-951	77	19	some	some	DET
cana-951	77	20	exact	exact	ADJ
cana-951	77	21	solutions	solution	NOUN
cana-951	77	22	of	of	ADP
cana-951	77	23	eq.(1	eq.(1	ADJ
cana-951	77	24	)	)	PUNCT
cana-951	77	25	.	.	PUNCT
cana-951	78	1	3	3	X
cana-951	78	2	.	.	X
cana-951	78	3	application	application	NOUN
cana-951	78	4	of	of	ADP
cana-951	78	5	the	the	DET
cana-951	78	6	(	(	PUNCT
cana-951	78	7	𝐆′/𝐆)-expansion	𝐆′/𝐆)-expansion	NOUN
cana-951	78	8	method	method	NOUN
cana-951	78	9	in	in	ADP
cana-951	78	10	bi	bi	ADJ
cana-951	78	11	-	-	ADJ
cana-951	78	12	isotropic	isotropic	ADJ
cana-951	78	13	fiber	fiber	NOUN
cana-951	78	14	the	the	DET
cana-951	78	15	nonlinear	nonlinear	ADJ
cana-951	78	16	schrödinger	schrödinger	ADJ
cana-951	78	17	equation	equation	NOUN
cana-951	78	18	(	(	PUNCT
cana-951	78	19	esnl	esnl	PROPN
cana-951	78	20	)	)	PUNCT
cana-951	78	21	is	be	AUX
cana-951	78	22	an	an	DET
cana-951	78	23	equation	equation	NOUN
cana-951	78	24	that	that	PRON
cana-951	78	25	occurs	occur	VERB
cana-951	78	26	in	in	ADP
cana-951	78	27	several	several	ADJ
cana-951	78	28	fields	field	NOUN
cana-951	78	29	of	of	ADP
cana-951	78	30	wave	wave	NOUN
cana-951	78	31	physics	physics	NOUN
cana-951	79	1	[	[	X
cana-951	79	2	1	1	NUM
cana-951	79	3	-	-	SYM
cana-951	79	4	24	24	NUM
cana-951	79	5	]	]	PUNCT
cana-951	79	6	.	.	PUNCT
cana-951	80	1	among	among	ADP
cana-951	80	2	other	other	ADJ
cana-951	80	3	things	thing	NOUN
cana-951	80	4	,	,	PUNCT
cana-951	80	5	it	it	PRON
cana-951	80	6	can	can	AUX
cana-951	80	7	be	be	AUX
cana-951	80	8	obtained	obtain	VERB
cana-951	80	9	from	from	ADP
cana-951	80	10	an	an	DET
cana-951	80	11	asymptotic	asymptotic	ADJ
cana-951	80	12	expansion	expansion	NOUN
cana-951	80	13	of	of	ADP
cana-951	80	14	the	the	DET
cana-951	80	15	kortewegde	kortewegde	NOUN
cana-951	80	16	vries	vries	PROPN
cana-951	80	17	(	(	PUNCT
cana-951	80	18	kdv	kdv	NOUN
cana-951	80	19	)	)	PUNCT
cana-951	80	20	equation	equation	NOUN
cana-951	80	21	for	for	ADP
cana-951	80	22	weakly	weakly	ADJ
cana-951	80	23	nonlinear	nonlinear	ADJ
cana-951	80	24	wave	wave	NOUN
cana-951	80	25	packets	packet	NOUN
cana-951	80	26	[	[	X
cana-951	80	27	1	1	NUM
cana-951	80	28	-	-	SYM
cana-951	80	29	5	5	NUM
cana-951	80	30	]	]	PUNCT
cana-951	80	31	.	.	PUNCT
cana-951	81	1	the	the	DET
cana-951	81	2	schrödinger	schrödinger	ADJ
cana-951	81	3	equation	equation	NOUN
cana-951	81	4	then	then	ADV
cana-951	81	5	follows	follow	VERB
cana-951	81	6	from	from	ADP
cana-951	81	7	a	a	DET
cana-951	81	8	first	first	ADJ
cana-951	81	9	order	order	NOUN
cana-951	81	10	approximation	approximation	NOUN
cana-951	81	11	and	and	CCONJ
cana-951	81	12	gives	give	VERB
cana-951	81	13	the	the	DET
cana-951	81	14	evolution	evolution	NOUN
cana-951	81	15	of	of	ADP
cana-951	81	16	the	the	DET
cana-951	81	17	wave	wave	NOUN
cana-951	81	18	packet	packet	NOUN
cana-951	81	19	envelope	envelope	NOUN
cana-951	81	20	[	[	X
cana-951	81	21	1	1	NUM
cana-951	81	22	-	-	SYM
cana-951	81	23	5	5	NUM
cana-951	81	24	]	]	PUNCT
cana-951	81	25	.	.	PUNCT
cana-951	82	1	the	the	DET
cana-951	82	2	characterization	characterization	NOUN
cana-951	82	3	of	of	ADP
cana-951	82	4	the	the	DET
cana-951	82	5	bi	bi	ADJ
cana-951	82	6	-	-	ADJ
cana-951	82	7	isotropic	isotropic	ADJ
cana-951	82	8	nonlinear	nonlinear	ADJ
cana-951	82	9	medium	medium	NOUN
cana-951	82	10	is	be	AUX
cana-951	82	11	achieved	achieve	VERB
cana-951	82	12	through	through	ADP
cana-951	82	13	an	an	DET
cana-951	82	14	electromagnetic	electromagnetic	ADJ
cana-951	82	15	approach	approach	NOUN
cana-951	82	16	utilizing	utilize	VERB
cana-951	82	17	a	a	DET
cana-951	82	18	novel	novel	ADJ
cana-951	82	19	formulation	formulation	NOUN
cana-951	82	20	of	of	ADP
cana-951	82	21	constitutive	constitutive	ADJ
cana-951	82	22	relations	relation	NOUN
cana-951	82	23	[	[	X
cana-951	82	24	22	22	NUM
cana-951	82	25	]	]	PUNCT
cana-951	82	26	.	.	PUNCT
cana-951	83	1	this	this	DET
cana-951	83	2	formulation	formulation	NOUN
cana-951	83	3	enables	enable	VERB
cana-951	83	4	the	the	DET
cana-951	83	5	derivation	derivation	NOUN
cana-951	83	6	of	of	ADP
cana-951	83	7	the	the	DET
cana-951	83	8	nonlinear	nonlinear	ADJ
cana-951	83	9	schrödinger	schrödinger	ADJ
cana-951	83	10	equation	equation	NOUN
cana-951	83	11	for	for	ADP
cana-951	83	12	a	a	DET
cana-951	83	13	chiroptic	chiroptic	ADJ
cana-951	83	14	fiber	fiber	NOUN
cana-951	83	15	,	,	PUNCT
cana-951	83	16	obtained	obtain	VERB
cana-951	83	17	through	through	ADP
cana-951	83	18	a	a	DET
cana-951	83	19	first	first	ADJ
cana-951	83	20	-	-	PUNCT
cana-951	83	21	order	order	NOUN
cana-951	83	22	approximation	approximation	NOUN
cana-951	83	23	,	,	PUNCT
cana-951	83	24	providing	provide	VERB
cana-951	83	25	insight	insight	NOUN
cana-951	83	26	into	into	ADP
cana-951	83	27	the	the	DET
cana-951	83	28	evolution	evolution	NOUN
cana-951	83	29	of	of	ADP
cana-951	83	30	the	the	DET
cana-951	83	31	wave	wave	NOUN
cana-951	83	32	packet	packet	NOUN
cana-951	83	33	envelope	envelope	NOUN
cana-951	83	34	.	.	PUNCT
cana-951	84	1	this	this	DET
cana-951	84	2	endeavor	endeavor	NOUN
cana-951	84	3	promises	promise	VERB
cana-951	84	4	a	a	DET
cana-951	84	5	deeper	deep	ADJ
cana-951	84	6	understanding	understanding	NOUN
cana-951	84	7	of	of	ADP
cana-951	84	8	the	the	DET
cana-951	84	9	interplay	interplay	NOUN
cana-951	84	10	between	between	ADP
cana-951	84	11	electromagnetic	electromagnetic	ADJ
cana-951	84	12	waves	wave	NOUN
cana-951	84	13	and	and	CCONJ
cana-951	84	14	bi	bi	ADJ
cana-951	84	15	-	-	ADJ
cana-951	84	16	isotropic	isotropic	ADJ
cana-951	84	17	nonlinear	nonlinear	ADJ
cana-951	84	18	mediums	medium	NOUN
cana-951	84	19	,	,	PUNCT
cana-951	84	20	paving	pave	VERB
cana-951	84	21	the	the	DET
cana-951	84	22	way	way	NOUN
cana-951	84	23	for	for	ADP
cana-951	84	24	potential	potential	ADJ
cana-951	84	25	applications	application	NOUN
cana-951	84	26	in	in	ADP
cana-951	84	27	optics	optic	NOUN
cana-951	84	28	and	and	CCONJ
cana-951	84	29	microwaves	microwave	NOUN
cana-951	84	30	,	,	PUNCT
cana-951	84	31	exemplified	exemplify	VERB
cana-951	84	32	by	by	ADP
cana-951	84	33	our	our	PRON
cana-951	84	34	case	case	NOUN
cana-951	84	35	study	study	NOUN
cana-951	84	36	on	on	ADP
cana-951	84	37	chiroptic	chiroptic	ADJ
cana-951	84	38	fibers	fiber	NOUN
cana-951	84	39	.	.	PUNCT
cana-951	85	1	within	within	ADP
cana-951	85	2	this	this	DET
cana-951	85	3	section	section	NOUN
cana-951	85	4	,	,	PUNCT
cana-951	85	5	our	our	PRON
cana-951	85	6	focus	focus	NOUN
cana-951	85	7	lies	lie	VERB
cana-951	85	8	on	on	ADP
cana-951	85	9	the	the	DET
cana-951	85	10	analysis	analysis	NOUN
cana-951	85	11	and	and	CCONJ
cana-951	85	12	modeling	modeling	NOUN
cana-951	85	13	of	of	ADP
cana-951	85	14	light	light	ADJ
cana-951	85	15	pulse	pulse	NOUN
cana-951	85	16	propagation	propagation	NOUN
cana-951	85	17	within	within	ADP
cana-951	85	18	a	a	DET
cana-951	85	19	biisotropic	biisotropic	ADJ
cana-951	85	20	fiber	fiber	NOUN
cana-951	85	21	,	,	PUNCT
cana-951	85	22	leveraging	leverage	VERB
cana-951	85	23	our	our	PRON
cana-951	85	24	newly	newly	ADV
cana-951	85	25	formulated	formulate	VERB
cana-951	85	26	constitutive	constitutive	ADJ
cana-951	85	27	equations	equation	NOUN
cana-951	85	28	[	[	X
cana-951	85	29	22	22	NUM
cana-951	85	30	]	]	PUNCT
cana-951	85	31	.	.	PUNCT
cana-951	86	1	hence	hence	ADV
cana-951	86	2	,	,	PUNCT
cana-951	86	3	we	we	PRON
cana-951	86	4	have	have	AUX
cana-951	86	5	employed	employ	VERB
cana-951	86	6	the	the	DET
cana-951	86	7	extended	extended	ADJ
cana-951	86	8	𝐺’/𝐺	𝐺’/𝐺	PROPN
cana-951	86	9	-expansion	-expansion	PROPN
cana-951	86	10	method	method	NOUN
cana-951	86	11	as	as	ADP
cana-951	86	12	our	our	PRON
cana-951	86	13	chosen	choose	VERB
cana-951	86	14	approach	approach	NOUN
cana-951	86	15	for	for	ADP
cana-951	86	16	solving	solve	VERB
cana-951	86	17	the	the	DET
cana-951	86	18	nonlinear	nonlinear	ADJ
cana-951	86	19	schrödinger	schrödinger	ADJ
cana-951	86	20	equation	equation	NOUN
cana-951	86	21	,	,	PUNCT
cana-951	86	22	facilitating	facilitate	VERB
cana-951	86	23	the	the	DET
cana-951	86	24	acquisition	acquisition	NOUN
cana-951	86	25	of	of	ADP
cana-951	86	26	precise	precise	ADJ
cana-951	86	27	solutions	solution	NOUN
cana-951	86	28	for	for	ADP
cana-951	86	29	bi	bi	ADJ
cana-951	86	30	-	-	ADJ
cana-951	86	31	isotropic	isotropic	ADJ
cana-951	86	32	fiber	fiber	NOUN
cana-951	86	33	nonlinearities	nonlinearitie	NOUN
cana-951	86	34	.	.	PUNCT
cana-951	87	1	as	as	ADV
cana-951	87	2	delineated	delineated	ADJ
cana-951	87	3	in	in	ADP
cana-951	87	4	our	our	PRON
cana-951	87	5	formalism	formalism	NOUN
cana-951	87	6	expounded	expound	VERB
cana-951	87	7	in	in	ADP
cana-951	87	8	[	[	PUNCT
cana-951	87	9	19	19	NUM
cana-951	87	10	-	-	SYM
cana-951	87	11	23	23	NUM
cana-951	87	12	]	]	PUNCT
cana-951	87	13	,	,	PUNCT
cana-951	87	14	the	the	DET
cana-951	87	15	constitutive	constitutive	ADJ
cana-951	87	16	equations	equation	NOUN
cana-951	87	17	governing	govern	VERB
cana-951	87	18	the	the	DET
cana-951	87	19	bianisotropic	bianisotropic	ADJ
cana-951	87	20	nonlinear	nonlinear	ADJ
cana-951	87	21	effects	effect	NOUN
cana-951	87	22	are	be	AUX
cana-951	87	23	delineated	delineate	VERB
cana-951	87	24	as	as	SCONJ
cana-951	87	25	follows	follow	VERB
cana-951	87	26	:	:	PUNCT
cana-951	87	27	d⃗⃗	d⃗⃗	PROPN
cana-951	87	28	=	=	PUNCT
cana-951	87	29	ε̅	ε̅	PROPN
cana-951	87	30	e⃗⃗	e⃗⃗	PROPN
cana-951	87	31	+	+	CCONJ
cana-951	87	32	ζ̅𝐸𝐻	ζ̅𝐸𝐻	PUNCT
cana-951	87	33	h⃗⃗	h⃗⃗	PROPN
cana-951	87	34	(	(	PUNCT
cana-951	87	35	9	9	NUM
cana-951	87	36	)	)	PUNCT
cana-951	87	37	b⃗⃗	b⃗⃗	PROPN
cana-951	87	38	=	=	SYM
cana-951	87	39	μ̅h⃗⃗	μ̅h⃗⃗	NOUN
cana-951	87	40	+	+	CCONJ
cana-951	87	41	ζ̅he	ζ̅he	X
cana-951	87	42	g	g	PROPN
cana-951	87	43	e⃗⃗	e⃗⃗	PROPN
cana-951	87	44	(	(	PUNCT
cana-951	87	45	10	10	NUM
cana-951	87	46	)	)	PUNCT
cana-951	87	47	the	the	DET
cana-951	87	48	medium	medium	ADJ
cana-951	87	49	effects	effect	NOUN
cana-951	87	50	are	be	AUX
cana-951	87	51	contained	contain	VERB
cana-951	87	52	in	in	ADP
cana-951	87	53	the	the	DET
cana-951	87	54	dyadic	dyadic	NOUN
cana-951	87	55	:	:	PUNCT
cana-951	87	56	ε̅	ε̅	NOUN
cana-951	87	57	,	,	PUNCT
cana-951	87	58	μ̅	μ̅	PROPN
cana-951	87	59	,	,	PUNCT
cana-951	87	60	ζ̅𝐸𝐻	ζ̅𝐸𝐻	NUM
cana-951	87	61	and	and	CCONJ
cana-951	87	62	ζ̅he	ζ̅he	X
cana-951	87	63	g	g	NOUN
cana-951	87	64	due	due	ADP
cana-951	87	65	to	to	PART
cana-951	87	66	anisotropy	anisotropy	VERB
cana-951	87	67	.	.	PUNCT
cana-951	88	1	the	the	DET
cana-951	88	2	bi	bi	ADJ
cana-951	88	3	-	-	ADJ
cana-951	88	4	isotropic	isotropic	ADJ
cana-951	88	5	medium	medium	NOUN
cana-951	88	6	has	have	VERB
cana-951	88	7	a	a	DET
cana-951	88	8	kerr	kerr	PROPN
cana-951	88	9	type	type	NOUN
cana-951	88	10	nonlinearity	nonlinearity	NOUN
cana-951	88	11	characterized	characterize	VERB
cana-951	88	12	by	by	ADP
cana-951	88	13	[	[	X
cana-951	88	14	1923	1923	NUM
cana-951	88	15	]	]	X
cana-951	88	16	:	:	PUNCT
cana-951	88	17	communications	communication	NOUN
cana-951	88	18	on	on	ADP
cana-951	88	19	applied	apply	VERB
cana-951	88	20	nonlinear	nonlinear	ADJ
cana-951	88	21	analysis	analysis	NOUN
cana-951	88	22	issn	issn	NOUN
cana-951	88	23	:	:	PUNCT
cana-951	88	24	1074	1074	NUM
cana-951	88	25	-	-	PUNCT
cana-951	88	26	133x	133x	NUM
cana-951	88	27	vol	vol	NOUN
cana-951	88	28	31	31	NUM
cana-951	88	29	no	no	NOUN
cana-951	88	30	.	.	PUNCT
cana-951	89	1	4s	4s	NUM
cana-951	89	2	(	(	PUNCT
cana-951	89	3	2024	2024	NUM
cana-951	89	4	)	)	PUNCT
cana-951	89	5	576	576	NUM
cana-951	89	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-951	89	7	εg	εg	PROPN
cana-951	89	8	=	=	SYM
cana-951	89	9	ε	ε	PROPN
cana-951	89	10	+	+	NUM
cana-951	89	11	εkerr|e	εkerr|e	VERB
cana-951	89	12	2|	2|	NUM
cana-951	89	13	(	(	PUNCT
cana-951	89	14	11	11	NUM
cana-951	89	15	)	)	PUNCT
cana-951	89	16	ζhe	ζhe	NOUN
cana-951	89	17	g	g	PROPN
cana-951	89	18	=	=	PROPN
cana-951	89	19	ζeh	ζeh	PROPN
cana-951	89	20	∗	∗	NOUN
cana-951	89	21	+	+	CCONJ
cana-951	89	22	ζhe	ζhe	PROPN
cana-951	89	23	kerr|e2|	kerr|e2|	PROPN
cana-951	89	24	(	(	PUNCT
cana-951	89	25	12	12	NUM
cana-951	89	26	)	)	PUNCT
cana-951	89	27	ζeh	ζeh	NOUN
cana-951	89	28	∗	∗	PROPN
cana-951	89	29	is	be	AUX
cana-951	89	30	the	the	DET
cana-951	89	31	linear	linear	ADJ
cana-951	89	32	bi	bi	NOUN
cana-951	89	33	-	-	ADJ
cana-951	89	34	isotropy	isotropy	ADJ
cana-951	89	35	coefficient	coefficient	NOUN
cana-951	89	36	,	,	PUNCT
cana-951	89	37	and	and	CCONJ
cana-951	89	38	the	the	DET
cana-951	89	39	term	term	NOUN
cana-951	89	40	ζhe	ζhe	NOUN
cana-951	89	41	kerr|e2|corrects	kerr|e2|correct	VERB
cana-951	89	42	the	the	DET
cana-951	89	43	bi	bi	ADJ
cana-951	89	44	-	-	ADJ
cana-951	89	45	isotropic	isotropic	ADJ
cana-951	89	46	coefficient	coefficient	NOUN
cana-951	89	47	with	with	ADP
cana-951	89	48	a	a	DET
cana-951	89	49	quantity	quantity	NOUN
cana-951	89	50	proportional	proportional	ADJ
cana-951	89	51	to	to	ADP
cana-951	89	52	the	the	DET
cana-951	89	53	field	field	NOUN
cana-951	89	54	intensity	intensity	NOUN
cana-951	89	55	[	[	X
cana-951	89	56	19	19	NUM
cana-951	89	57	-	-	SYM
cana-951	89	58	23	23	NUM
cana-951	89	59	]	]	PUNCT
cana-951	89	60	.	.	PUNCT
cana-951	90	1	the	the	DET
cana-951	90	2	linear	linear	ADJ
cana-951	90	3	bi	bi	NOUN
cana-951	90	4	-	-	ADJ
cana-951	90	5	isotropy	isotropy	ADJ
cana-951	90	6	factors	factor	NOUN
cana-951	90	7	are	be	AUX
cana-951	90	8	written	write	VERB
cana-951	90	9	as	as	SCONJ
cana-951	90	10	follows	follow	VERB
cana-951	90	11	[	[	X
cana-951	90	12	19	19	NUM
cana-951	90	13	-	-	SYM
cana-951	90	14	23	23	NUM
cana-951	90	15	]	]	PUNCT
cana-951	90	16	:	:	PUNCT
cana-951	90	17	ζeh	ζeh	X
cana-951	90	18	=	=	PUNCT
cana-951	90	19	γ	γ	X
cana-951	90	20	−	−	X
cana-951	90	21	jκ	jκ	NOUN
cana-951	90	22	(	(	PUNCT
cana-951	90	23	13	13	NUM
cana-951	90	24	)	)	PUNCT
cana-951	90	25	γ	γ	PROPN
cana-951	90	26	is	be	AUX
cana-951	90	27	the	the	DET
cana-951	90	28	non	non	ADJ
cana-951	90	29	-	-	ADJ
cana-951	90	30	reciprocity	reciprocity	ADJ
cana-951	90	31	parameter	parameter	NOUN
cana-951	90	32	,	,	PUNCT
cana-951	90	33	and	and	CCONJ
cana-951	90	34	κ	κ	PROPN
cana-951	90	35	is	be	AUX
cana-951	90	36	the	the	DET
cana-951	90	37	linear	linear	PROPN
cana-951	90	38	chirality	chirality	NOUN
cana-951	90	39	parameter	parameter	NOUN
cana-951	90	40	.	.	PUNCT
cana-951	91	1	γkerr	γkerr	PROPN
cana-951	91	2	is	be	AUX
cana-951	91	3	the	the	DET
cana-951	91	4	nonlinear	nonlinear	ADJ
cana-951	91	5	non	non	ADJ
cana-951	91	6	-	-	ADJ
cana-951	91	7	reciprocity	reciprocity	ADJ
cana-951	91	8	parameter	parameter	NOUN
cana-951	91	9	,	,	PUNCT
cana-951	91	10	and	and	CCONJ
cana-951	91	11	κkerr	κkerr	NOUN
cana-951	91	12	is	be	AUX
cana-951	91	13	the	the	DET
cana-951	91	14	nonlinear	nonlinear	ADJ
cana-951	91	15	chirality	chirality	NOUN
cana-951	91	16	parameter	parameter	NOUN
cana-951	91	17	.	.	PUNCT
cana-951	92	1	there	there	PRON
cana-951	92	2	exist	exist	VERB
cana-951	92	3	three	three	NUM
cana-951	92	4	distinct	distinct	ADJ
cana-951	92	5	cases	case	NOUN
cana-951	92	6	for	for	ADP
cana-951	92	7	the	the	DET
cana-951	92	8	biisotropic	biisotropic	ADJ
cana-951	92	9	medium	medium	NOUN
cana-951	92	10	:	:	PUNCT
cana-951	93	1	1	1	X
cana-951	93	2	.	.	PUNCT
cana-951	94	1	the	the	DET
cana-951	94	2	chiral	chiral	ADJ
cana-951	94	3	medium	medium	NOUN
cana-951	94	4	,	,	PUNCT
cana-951	94	5	which	which	PRON
cana-951	94	6	is	be	AUX
cana-951	94	7	reciprocal	reciprocal	ADJ
cana-951	94	8	(	(	PUNCT
cana-951	94	9	purely	purely	ADV
cana-951	94	10	imaginary	imaginary	ADJ
cana-951	94	11	)	)	PUNCT
cana-951	94	12	,	,	PUNCT
cana-951	94	13	denoted	denote	VERB
cana-951	94	14	by	by	ADP
cana-951	94	15	κ≠0	κ≠0	NOUN
cana-951	94	16	and	and	CCONJ
cana-951	94	17	γ=0	γ=0	NOUN
cana-951	94	18	.	.	NOUN
cana-951	95	1	2	2	X
cana-951	95	2	.	.	X
cana-951	95	3	the	the	DET
cana-951	95	4	tellegen	tellegen	PROPN
cana-951	95	5	medium	medium	NOUN
cana-951	95	6	,	,	PUNCT
cana-951	95	7	which	which	PRON
cana-951	95	8	is	be	AUX
cana-951	95	9	non	non	ADJ
cana-951	95	10	-	-	ADJ
cana-951	95	11	reciprocal	reciprocal	ADJ
cana-951	95	12	(	(	PUNCT
cana-951	95	13	purely	purely	ADV
cana-951	95	14	real	real	ADJ
cana-951	95	15	)	)	PUNCT
cana-951	95	16	,	,	PUNCT
cana-951	95	17	indicated	indicate	VERB
cana-951	95	18	by	by	ADP
cana-951	95	19	κ=0	κ=0	PROPN
cana-951	95	20	and	and	CCONJ
cana-951	95	21	γ≠0	γ≠0	PROPN
cana-951	95	22	.	.	PUNCT
cana-951	96	1	3	3	X
cana-951	96	2	.	.	X
cana-951	96	3	the	the	DET
cana-951	96	4	biisotropic	biisotropic	NOUN
cana-951	96	5	medium	medium	NOUN
cana-951	96	6	,	,	PUNCT
cana-951	96	7	characterized	characterize	VERB
cana-951	96	8	by	by	ADP
cana-951	96	9	both	both	PRON
cana-951	96	10	chirality	chirality	NOUN
cana-951	96	11	and	and	CCONJ
cana-951	96	12	non	non	ADJ
cana-951	96	13	-	-	NOUN
cana-951	96	14	reciprocity	reciprocity	NOUN
cana-951	96	15	(	(	PUNCT
cana-951	96	16	complex	complex	ADJ
cana-951	96	17	numbers	number	NOUN
cana-951	96	18	)	)	PUNCT
cana-951	96	19	,	,	PUNCT
cana-951	96	20	with	with	ADP
cana-951	96	21	κ≠0	κ≠0	NOUN
cana-951	96	22	and	and	CCONJ
cana-951	96	23	γ≠0	γ≠0	NOUN
cana-951	96	24	.	.	PUNCT
cana-951	97	1	in	in	ADP
cana-951	97	2	this	this	DET
cana-951	97	3	study	study	NOUN
cana-951	97	4	,	,	PUNCT
cana-951	97	5	our	our	PRON
cana-951	97	6	focus	focus	NOUN
cana-951	97	7	centers	center	NOUN
cana-951	97	8	on	on	ADP
cana-951	97	9	the	the	DET
cana-951	97	10	third	third	ADJ
cana-951	97	11	case	case	NOUN
cana-951	97	12	.	.	PUNCT
cana-951	98	1	a	a	DET
cana-951	98	2	biisotropic	biisotropic	NOUN
cana-951	98	3	fiber	fiber	NOUN
cana-951	98	4	refers	refer	VERB
cana-951	98	5	to	to	ADP
cana-951	98	6	an	an	DET
cana-951	98	7	optical	optical	ADJ
cana-951	98	8	fiber	fiber	NOUN
cana-951	98	9	featuring	feature	VERB
cana-951	98	10	a	a	DET
cana-951	98	11	chiral	chiral	ADJ
cana-951	98	12	core	core	NOUN
cana-951	98	13	enveloped	envelop	VERB
cana-951	98	14	by	by	ADP
cana-951	98	15	an	an	DET
cana-951	98	16	optical	optical	ADJ
cana-951	98	17	cladding	cladding	NOUN
cana-951	98	18	.	.	PUNCT
cana-951	99	1	the	the	DET
cana-951	99	2	core	core	NOUN
cana-951	99	3	of	of	ADP
cana-951	99	4	the	the	DET
cana-951	99	5	biisotropic	biisotropic	NOUN
cana-951	99	6	fiber	fiber	NOUN
cana-951	99	7	possesses	possess	VERB
cana-951	99	8	a	a	DET
cana-951	99	9	slightly	slightly	ADV
cana-951	99	10	higher	high	ADJ
cana-951	99	11	refractive	refractive	ADJ
cana-951	99	12	index	index	NOUN
cana-951	99	13	compared	compare	VERB
cana-951	99	14	to	to	ADP
cana-951	99	15	the	the	DET
cana-951	99	16	sheath	sheath	NOUN
cana-951	99	17	.	.	PUNCT
cana-951	100	1	this	this	DET
cana-951	100	2	variation	variation	NOUN
cana-951	100	3	in	in	ADP
cana-951	100	4	refractive	refractive	ADJ
cana-951	100	5	index	index	NOUN
cana-951	100	6	induces	induce	VERB
cana-951	100	7	total	total	ADJ
cana-951	100	8	internal	internal	ADJ
cana-951	100	9	reflection	reflection	NOUN
cana-951	100	10	of	of	ADP
cana-951	100	11	light	light	NOUN
cana-951	100	12	within	within	ADP
cana-951	100	13	the	the	DET
cana-951	100	14	chiral	chiral	ADJ
cana-951	100	15	core	core	NOUN
cana-951	100	16	,	,	PUNCT
cana-951	100	17	enabling	enable	VERB
cana-951	100	18	the	the	DET
cana-951	100	19	propagation	propagation	NOUN
cana-951	100	20	of	of	ADP
cana-951	100	21	light	light	NOUN
cana-951	100	22	with	with	ADP
cana-951	100	23	two	two	NUM
cana-951	100	24	distinct	distinct	ADJ
cana-951	100	25	modes	mode	NOUN
cana-951	100	26	:	:	PUNCT
cana-951	100	27	a	a	DET
cana-951	100	28	right	right	ADJ
cana-951	100	29	circular	circular	ADJ
cana-951	100	30	polarized	polarize	VERB
cana-951	100	31	wave	wave	NOUN
cana-951	100	32	(	(	PUNCT
cana-951	100	33	rcp	rcp	PROPN
cana-951	100	34	)	)	PUNCT
cana-951	100	35	and	and	CCONJ
cana-951	100	36	a	a	DET
cana-951	100	37	left	left	ADJ
cana-951	100	38	circular	circular	ADJ
cana-951	100	39	polarized	polarize	VERB
cana-951	100	40	wave	wave	NOUN
cana-951	100	41	(	(	PUNCT
cana-951	100	42	lcp	lcp	PROPN
cana-951	100	43	)	)	PUNCT
cana-951	100	44	,	,	PUNCT
cana-951	100	45	each	each	PRON
cana-951	100	46	exhibiting	exhibit	VERB
cana-951	100	47	different	different	ADJ
cana-951	100	48	wave	wave	NOUN
cana-951	100	49	vectors	vector	NOUN
cana-951	100	50	.	.	PUNCT
cana-951	101	1	from	from	ADP
cana-951	101	2	maxwell	maxwell	PROPN
cana-951	101	3	's	's	PART
cana-951	101	4	equations	equation	NOUN
cana-951	101	5	,	,	PUNCT
cana-951	101	6	which	which	PRON
cana-951	101	7	serve	serve	VERB
cana-951	101	8	as	as	ADP
cana-951	101	9	the	the	DET
cana-951	101	10	cornerstone	cornerstone	NOUN
cana-951	101	11	of	of	ADP
cana-951	101	12	electromagnetism	electromagnetism	NOUN
cana-951	101	13	and	and	CCONJ
cana-951	101	14	locally	locally	ADV
cana-951	101	15	describe	describe	VERB
cana-951	101	16	the	the	DET
cana-951	101	17	evolution	evolution	NOUN
cana-951	101	18	and	and	CCONJ
cana-951	101	19	properties	property	NOUN
cana-951	101	20	of	of	ADP
cana-951	101	21	electric	electric	ADJ
cana-951	101	22	and	and	CCONJ
cana-951	101	23	magnetic	magnetic	ADJ
cana-951	101	24	fields	field	NOUN
cana-951	101	25	,	,	PUNCT
cana-951	101	26	we	we	PRON
cana-951	101	27	specifically	specifically	ADV
cana-951	101	28	consider	consider	VERB
cana-951	101	29	maxwell	maxwell	PROPN
cana-951	101	30	's	's	PART
cana-951	101	31	first	first	ADJ
cana-951	101	32	equation	equation	NOUN
cana-951	101	33	,	,	PUNCT
cana-951	101	34	known	know	VERB
cana-951	101	35	as	as	ADP
cana-951	101	36	the	the	DET
cana-951	101	37	maxwell	maxwell	PROPN
cana-951	101	38	-	-	PUNCT
cana-951	101	39	faraday	faraday	PROPN
cana-951	101	40	equation	equation	NOUN
cana-951	101	41	.	.	PUNCT
cana-951	102	1	this	this	DET
cana-951	102	2	equation	equation	NOUN
cana-951	102	3	elucidates	elucidate	VERB
cana-951	102	4	the	the	DET
cana-951	102	5	phenomenon	phenomenon	NOUN
cana-951	102	6	of	of	ADP
cana-951	102	7	electromagnetic	electromagnetic	ADJ
cana-951	102	8	induction	induction	NOUN
cana-951	102	9	first	first	ADV
cana-951	102	10	discovered	discover	VERB
cana-951	102	11	by	by	ADP
cana-951	102	12	faraday	faraday	PROPN
cana-951	102	13	:	:	PUNCT
cana-951	102	14	∇⃗⃗	∇⃗⃗	PROPN
cana-951	102	15	×	×	NOUN
cana-951	102	16	e⃗⃗	e⃗⃗	NOUN
cana-951	102	17	=	=	PUNCT
cana-951	102	18	−	−	PROPN
cana-951	102	19	∂b⃗⃗	∂b⃗⃗	NOUN
cana-951	102	20	∂t	∂t	PROPN
cana-951	102	21	(	(	PUNCT
cana-951	102	22	14	14	NUM
cana-951	102	23	)	)	PUNCT
cana-951	102	24	as	as	ADP
cana-951	102	25	for	for	ADP
cana-951	102	26	the	the	DET
cana-951	102	27	second	second	ADJ
cana-951	102	28	equation	equation	NOUN
cana-951	102	29	,	,	PUNCT
cana-951	102	30	which	which	PRON
cana-951	102	31	is	be	AUX
cana-951	102	32	the	the	DET
cana-951	102	33	maxwell	maxwell	PROPN
cana-951	102	34	-	-	PUNCT
cana-951	102	35	ampere	ampere	NOUN
cana-951	102	36	equation	equation	NOUN
cana-951	102	37	,	,	PUNCT
cana-951	102	38	and	and	CCONJ
cana-951	102	39	which	which	PRON
cana-951	102	40	stems	stem	VERB
cana-951	102	41	from	from	ADP
cana-951	102	42	ampère	ampère	PROPN
cana-951	102	43	's	's	PART
cana-951	102	44	theorem	theorem	NOUN
cana-951	102	45	,	,	PUNCT
cana-951	102	46	it	it	PRON
cana-951	102	47	links	link	VERB
cana-951	102	48	the	the	DET
cana-951	102	49	evolution	evolution	NOUN
cana-951	102	50	of	of	ADP
cana-951	102	51	the	the	DET
cana-951	102	52	electric	electric	ADJ
cana-951	102	53	field	field	NOUN
cana-951	102	54	as	as	ADP
cana-951	102	55	a	a	DET
cana-951	102	56	function	function	NOUN
cana-951	102	57	of	of	ADP
cana-951	102	58	the	the	DET
cana-951	102	59	magnetic	magnetic	ADJ
cana-951	102	60	field	field	NOUN
cana-951	102	61	.	.	PUNCT
cana-951	103	1	it	it	PRON
cana-951	103	2	is	be	AUX
cana-951	103	3	given	give	VERB
cana-951	103	4	by	by	ADP
cana-951	103	5	:	:	PUNCT
cana-951	103	6	∇⃗⃗	∇⃗⃗	PROPN
cana-951	104	1	×	×	NOUN
cana-951	104	2	h⃗⃗	h⃗⃗	PROPN
cana-951	104	3	=	=	PROPN
cana-951	104	4	∂d⃗⃗	∂d⃗⃗	PROPN
cana-951	104	5	∂t	∂t	PROPN
cana-951	104	6	(	(	PUNCT
cana-951	104	7	15	15	NUM
cana-951	104	8	)	)	PUNCT
cana-951	104	9	what	what	PRON
cana-951	104	10	allowed	allow	VERB
cana-951	104	11	us	we	PRON
cana-951	104	12	to	to	PART
cana-951	104	13	deduce	deduce	VERB
cana-951	104	14	the	the	DET
cana-951	104	15	equation	equation	NOUN
cana-951	104	16	of	of	ADP
cana-951	104	17	propagation	propagation	NOUN
cana-951	104	18	in	in	ADP
cana-951	104	19	a	a	DET
cana-951	104	20	kerr	kerr	NOUN
cana-951	104	21	-	-	PUNCT
cana-951	104	22	biisotropic	biisotropic	NOUN
cana-951	104	23	medium	medium	NOUN
cana-951	104	24	our	our	PRON
cana-951	104	25	result	result	NOUN
cana-951	104	26	is	be	AUX
cana-951	104	27	also	also	ADV
cana-951	104	28	a	a	DET
cana-951	104	29	generalization	generalization	NOUN
cana-951	104	30	:	:	PUNCT
cana-951	104	31	∇⃗⃗	∇⃗⃗	VERB
cana-951	104	32	2	2	NUM
cana-951	104	33	.	.	PUNCT
cana-951	105	1	e⃗⃗	e⃗⃗	PROPN
cana-951	105	2	−	−	PROPN
cana-951	106	1	(	(	PUNCT
cana-951	106	2	με	με	NOUN
cana-951	106	3	−	−	PROPN
cana-951	107	1	μ0ε0|ζeh	μ0ε0|ζeh	NOUN
cana-951	107	2	2	2	NUM
cana-951	107	3	|	|	NOUN
cana-951	107	4	)	)	PUNCT
cana-951	107	5	∂2e⃗⃗	∂2e⃗⃗	PROPN
cana-951	107	6	∂t2	∂t2	NOUN
cana-951	107	7	−√μ0ε0(ζeh	−√μ0ε0(ζeh	PROPN
cana-951	107	8	∗	∗	NOUN
cana-951	107	9	−	−	PROPN
cana-951	107	10	ζeh	ζeh	PROPN
cana-951	107	11	)	)	PUNCT
cana-951	107	12	∂∇⃗⃗	∂∇⃗⃗	NOUN
cana-951	107	13	×e⃗⃗	×e⃗⃗	NOUN
cana-951	108	1	∂t	∂t	PROPN
cana-951	108	2	=	=	SYM
cana-951	108	3	(	(	PUNCT
cana-951	108	4	μεkerr	μεkerr	NOUN
cana-951	108	5	−	−	PROPN
cana-951	108	6	μ0ε0ζehζhe	μ0ε0ζehζhe	PROPN
cana-951	108	7	kerr)|e⃗⃗	kerr)|e⃗⃗	NOUN
cana-951	108	8	|	|	ADV
cana-951	108	9	2	2	NUM
cana-951	108	10	∂2e⃗⃗	∂2e⃗⃗	PROPN
cana-951	108	11	∂t2	∂t2	NOUN
cana-951	108	12	+	+	CCONJ
cana-951	108	13	√μ0ε0ζhe	√μ0ε0ζhe	ADJ
cana-951	108	14	kerr|e⃗⃗	kerr|e⃗⃗	NOUN
cana-951	108	15	|	|	ADV
cana-951	108	16	2	2	NUM
cana-951	108	17	∂∇⃗⃗	∂∇⃗⃗	NOUN
cana-951	108	18	×e⃗⃗	×e⃗⃗	PUNCT
cana-951	108	19	∂t	∂t	PROPN
cana-951	108	20	+	+	CCONJ
cana-951	108	21	μσ	μσ	PROPN
cana-951	108	22	∂e⃗⃗	∂e⃗⃗	NOUN
cana-951	108	23	∂t	∂t	PROPN
cana-951	108	24	(	(	PUNCT
cana-951	108	25	16	16	NUM
cana-951	108	26	)	)	PUNCT
cana-951	108	27	σ	σ	NOUN
cana-951	108	28	is	be	AUX
cana-951	108	29	the	the	DET
cana-951	108	30	absorption	absorption	NOUN
cana-951	108	31	coefficient	coefficient	NOUN
cana-951	108	32	.	.	PUNCT
cana-951	109	1	communications	communication	NOUN
cana-951	109	2	on	on	ADP
cana-951	109	3	applied	apply	VERB
cana-951	109	4	nonlinear	nonlinear	ADJ
cana-951	109	5	analysis	analysis	NOUN
cana-951	109	6	issn	issn	NOUN
cana-951	109	7	:	:	PUNCT
cana-951	109	8	1074	1074	NUM
cana-951	109	9	-	-	PUNCT
cana-951	109	10	133x	133x	NUM
cana-951	109	11	vol	vol	NOUN
cana-951	109	12	31	31	NUM
cana-951	109	13	no	no	NOUN
cana-951	109	14	.	.	PUNCT
cana-951	110	1	4s	4s	NUM
cana-951	110	2	(	(	PUNCT
cana-951	110	3	2024	2024	NUM
cana-951	110	4	)	)	PUNCT
cana-951	110	5	577	577	NUM
cana-951	110	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-951	110	7	the	the	DET
cana-951	110	8	electric	electric	ADJ
cana-951	110	9	field	field	NOUN
cana-951	110	10	in	in	ADP
cana-951	110	11	the	the	DET
cana-951	110	12	bi	bi	ADJ
cana-951	110	13	-	-	ADJ
cana-951	110	14	isotropic	isotropic	ADJ
cana-951	110	15	fiber	fiber	NOUN
cana-951	110	16	can	can	AUX
cana-951	110	17	be	be	AUX
cana-951	110	18	represented	represent	VERB
cana-951	110	19	by	by	ADP
cana-951	110	20	wave	wave	NOUN
cana-951	110	21	propagating	propagate	VERB
cana-951	110	22	in	in	ADP
cana-951	110	23	the	the	DET
cana-951	110	24	z	z	NOUN
cana-951	110	25	direction	direction	NOUN
cana-951	110	26	:	:	PUNCT
cana-951	110	27	e±⃗⃗	e±⃗⃗	NOUN
cana-951	110	28	⃗⃗	⃗⃗	PROPN
cana-951	110	29	=	=	SYM
cana-951	110	30	(	(	PUNCT
cana-951	110	31	ex⃗⃗	ex⃗⃗	PROPN
cana-951	110	32	⃗	⃗	PROPN
cana-951	110	33	±	±	PROPN
cana-951	110	34	iey⃗⃗	iey⃗⃗	ADJ
cana-951	110	35	⃗)ψ±(r	⃗)ψ±(r	PROPN
cana-951	110	36	,	,	PUNCT
cana-951	110	37	t)e	t)e	NOUN
cana-951	110	38	−i(k±z−ω0	−i(k±z−ω0	PROPN
cana-951	110	39	t	t	PROPN
cana-951	110	40	)	)	PUNCT
cana-951	110	41	(	(	PUNCT
cana-951	110	42	17	17	NUM
cana-951	110	43	)	)	PUNCT
cana-951	110	44	e±⃗⃗	e±⃗⃗	NOUN
cana-951	110	45	⃗⃗	⃗⃗	PROPN
cana-951	110	46	=	=	SYM
cana-951	110	47	ψ±⃗⃗	ψ±⃗⃗	PROPN
cana-951	110	48	⃗⃗	⃗⃗	PROPN
cana-951	110	49	⃗(r	⃗(r	PROPN
cana-951	110	50	,	,	PUNCT
cana-951	110	51	t)e	t)e	NOUN
cana-951	110	52	−i(k±z−ω0	−i(k±z−ω0	PROPN
cana-951	110	53	t	t	PROPN
cana-951	110	54	)	)	PUNCT
cana-951	110	55	(	(	PUNCT
cana-951	110	56	18	18	NUM
cana-951	110	57	)	)	PUNCT
cana-951	110	58	where	where	SCONJ
cana-951	110	59	the	the	DET
cana-951	110	60	wave	wave	NOUN
cana-951	110	61	numbers	number	NOUN
cana-951	110	62	k+	k+	X
cana-951	110	63	(	(	PUNCT
cana-951	110	64	rcp	rcp	NOUN
cana-951	110	65	)	)	PUNCT
cana-951	110	66	and	and	CCONJ
cana-951	110	67	k−	k−	PROPN
cana-951	110	68	(	(	PUNCT
cana-951	110	69	lcp	lcp	PROPN
cana-951	110	70	)	)	PUNCT
cana-951	110	71	can	can	AUX
cana-951	110	72	be	be	AUX
cana-951	110	73	written	write	VERB
cana-951	110	74	as	as	ADP
cana-951	110	75	:	:	PUNCT
cana-951	110	76	k+	k+	X
cana-951	110	77	=	=	SYM
cana-951	110	78	k√μ0ε0	k√μ0ε0	PROPN
cana-951	110	79	+	+	PROPN
cana-951	110	80	√με	√με	PROPN
cana-951	110	81	−	−	PROPN
cana-951	110	82	γ2μ0ε0	γ2μ0ε0	PROPN
cana-951	110	83	(	(	PUNCT
cana-951	110	84	19	19	NUM
cana-951	110	85	)	)	PUNCT
cana-951	110	86	k−	k−	NOUN
cana-951	110	87	=	=	PUNCT
cana-951	110	88	−k√μ0ε0	−k√μ0ε0	PUNCT
cana-951	111	1	+	+	ADJ
cana-951	111	2	√με	√με	PROPN
cana-951	111	3	−	−	PROPN
cana-951	111	4	γ2μ0ε0	γ2μ0ε0	PROPN
cana-951	111	5	(	(	PUNCT
cana-951	111	6	20	20	NUM
cana-951	111	7	)	)	PUNCT
cana-951	111	8	the	the	DET
cana-951	111	9	conditions	condition	NOUN
cana-951	111	10	of	of	ADP
cana-951	111	11	slowly	slowly	ADV
cana-951	111	12	variant	variant	ADJ
cana-951	111	13	envelope	envelope	NOUN
cana-951	111	14	are	be	AUX
cana-951	111	15	given	give	VERB
cana-951	111	16	by	by	ADP
cana-951	111	17	[	[	X
cana-951	111	18	12	12	NUM
cana-951	111	19	,	,	PUNCT
cana-951	111	20	13	13	NUM
cana-951	111	21	]	]	NUM
cana-951	111	22	:	:	PUNCT
cana-951	111	23	|	|	ADV
cana-951	111	24	∂2	∂2	PROPN
cana-951	111	25	∂z2	∂z2	PROPN
cana-951	111	26	ψ±|	ψ±|	CCONJ
cana-951	111	27	≪	≪	PROPN
cana-951	111	28	|2ik±|	|2ik±|	X
cana-951	111	29	;	;	PUNCT
cana-951	111	30	|	|	PRON
cana-951	111	31	∂	∂	NUM
cana-951	111	32	∂z	∂z	PROPN
cana-951	111	33	ψ±|	ψ±|	CCONJ
cana-951	111	34	≪	≪	VERB
cana-951	111	35	|iω0ψ±|	|iω0ψ±|	PROPN
cana-951	111	36	(	(	PUNCT
cana-951	111	37	21	21	NUM
cana-951	111	38	)	)	PUNCT
cana-951	112	1	|	|	ADV
cana-951	112	2	∂2	∂2	NUM
cana-951	112	3	∂z2	∂z2	PROPN
cana-951	112	4	|ψ±|	|ψ±|	PROPN
cana-951	112	5	2	2	NUM
cana-951	112	6	ψ±|	ψ±|	NUM
cana-951	112	7	≪	≪	PUNCT
cana-951	112	8	|iω0	|iω0	SYM
cana-951	112	9	∂	∂	NUM
cana-951	112	10	∂t	∂t	PROPN
cana-951	112	11	|ψ±|	|ψ±|	PROPN
cana-951	112	12	2	2	NUM
cana-951	112	13	ψ±|	ψ±|	NUM
cana-951	112	14	≪	≪	PUNCT
cana-951	112	15	|iω0|ψ±|	|iω0|ψ±|	PROPN
cana-951	112	16	2	2	NUM
cana-951	112	17	ψ±|	ψ±|	NUM
cana-951	112	18	(	(	PUNCT
cana-951	112	19	22	22	NUM
cana-951	112	20	)	)	PUNCT
cana-951	112	21	a±(z	a±(z	PROPN
cana-951	112	22	,	,	PUNCT
cana-951	112	23	t	t	PROPN
cana-951	112	24	)	)	PUNCT
cana-951	112	25	2k±	2k±	PROPN
cana-951	112	26	⋅	⋅	PROPN
cana-951	112	27	ez⃗⃗	ez⃗⃗	PROPN
cana-951	112	28	⃗	⃗	PROPN
cana-951	112	29	=	=	SYM
cana-951	112	30	ψ±⃗⃗	ψ±⃗⃗	PROPN
cana-951	112	31	⃗⃗	⃗⃗	PROPN
cana-951	112	32	⃗	⃗	PROPN
cana-951	112	33	(	(	PUNCT
cana-951	112	34	23	23	NUM
cana-951	112	35	)	)	PUNCT
cana-951	112	36	the	the	DET
cana-951	112	37	phenomenon	phenomenon	NOUN
cana-951	112	38	of	of	ADP
cana-951	112	39	dispersion	dispersion	NOUN
cana-951	112	40	is	be	AUX
cana-951	112	41	included	include	VERB
cana-951	112	42	in	in	ADP
cana-951	112	43	heuristic	heuristic	ADJ
cana-951	112	44	form	form	NOUN
cana-951	112	45	through	through	ADP
cana-951	112	46	the	the	DET
cana-951	112	47	relation	relation	NOUN
cana-951	112	48	δk	δk	ADP
cana-951	112	49	=	=	SYM
cana-951	112	50	1	1	NUM
cana-951	112	51	v	v	NOUN
cana-951	112	52	(	(	PUNCT
cana-951	112	53	24	24	NUM
cana-951	112	54	)	)	PUNCT
cana-951	112	55	after	after	ADP
cana-951	112	56	algebraic	algebraic	PROPN
cana-951	112	57	manipulations	manipulation	NOUN
cana-951	112	58	,	,	PUNCT
cana-951	112	59	within	within	ADP
cana-951	112	60	the	the	DET
cana-951	112	61	slowly	slowly	ADV
cana-951	112	62	varying	vary	VERB
cana-951	112	63	amplitude	amplitude	NOUN
cana-951	112	64	approximation	approximation	NOUN
cana-951	112	65	of	of	ADP
cana-951	112	66	maxwell	maxwell	PROPN
cana-951	112	67	’s	’s	PART
cana-951	112	68	equations	equation	NOUN
cana-951	112	69	[	[	X
cana-951	112	70	18	18	NUM
cana-951	112	71	-	-	SYM
cana-951	112	72	23	23	NUM
cana-951	112	73	]	]	PUNCT
cana-951	112	74	,	,	PUNCT
cana-951	112	75	signals	signal	NOUN
cana-951	112	76	’	'	PUNCT
cana-951	112	77	propagating	propagate	VERB
cana-951	112	78	through	through	ADP
cana-951	112	79	bi	bi	ADJ
cana-951	112	80	-	-	ADJ
cana-951	112	81	isotropic	isotropic	ADJ
cana-951	112	82	fiber	fiber	NOUN
cana-951	112	83	is	be	AUX
cana-951	112	84	described	describe	VERB
cana-951	112	85	using	use	VERB
cana-951	112	86	the	the	DET
cana-951	112	87	following	follow	VERB
cana-951	112	88	equation	equation	NOUN
cana-951	112	89	:	:	PUNCT
cana-951	112	90	(	(	PUNCT
cana-951	112	91	∂	∂	X
cana-951	112	92	∂z	∂z	PROPN
cana-951	112	93	a±(z	a±(z	PROPN
cana-951	112	94	,	,	PUNCT
cana-951	112	95	t	t	PROPN
cana-951	112	96	)	)	PUNCT
cana-951	112	97	+	+	CCONJ
cana-951	112	98	(	(	PUNCT
cana-951	112	99	β1	β1	PROPN
cana-951	112	100	∂	∂	NOUN
cana-951	113	1	∂t	∂t	PROPN
cana-951	114	1	+	+	CCONJ
cana-951	114	2	i	i	NOUN
cana-951	114	3	1	1	NUM
cana-951	114	4	2	2	NUM
cana-951	114	5	β2	β2	NOUN
cana-951	114	6	∂2	∂2	NOUN
cana-951	114	7	∂t2	∂t2	NOUN
cana-951	114	8	−	−	ADP
cana-951	114	9	1	1	NUM
cana-951	114	10	6	6	NUM
cana-951	114	11	β3	β3	ADJ
cana-951	114	12	∂3	∂3	NOUN
cana-951	114	13	∂t3	∂t3	ADJ
cana-951	114	14	)	)	PUNCT
cana-951	114	15	a±(z	a±(z	PROPN
cana-951	114	16	,	,	PUNCT
cana-951	114	17	t	t	PROPN
cana-951	114	18	)	)	PUNCT
cana-951	114	19	)	)	PUNCT
cana-951	115	1	=	=	SYM
cana-951	115	2	iδa±(z	iδa±(z	PROPN
cana-951	115	3	,	,	PUNCT
cana-951	115	4	t)iρ|a±(z	t)iρ|a±(z	NOUN
cana-951	115	5	,	,	PUNCT
cana-951	115	6	t)|	t)|	NOUN
cana-951	115	7	2	2	NUM
cana-951	115	8	a±(z	a±(z	PROPN
cana-951	115	9	,	,	PUNCT
cana-951	115	10	t	t	PROPN
cana-951	115	11	)	)	PUNCT
cana-951	115	12	(	(	PUNCT
cana-951	115	13	25	25	NUM
cana-951	115	14	)	)	PUNCT
cana-951	115	15	where	where	SCONJ
cana-951	115	16	the	the	DET
cana-951	115	17	chromatic	chromatic	ADJ
cana-951	115	18	dispersion	dispersion	NOUN
cana-951	115	19	coefficients	coefficient	NOUN
cana-951	115	20	associated	associate	VERB
cana-951	115	21	with	with	ADP
cana-951	115	22	β1	β1	PROPN
cana-951	115	23	,	,	PUNCT
cana-951	115	24	β2	β2	NOUN
cana-951	115	25	and	and	CCONJ
cana-951	115	26	β3	β3	ADJ
cana-951	115	27	,	,	PUNCT
cana-951	115	28	and	and	CCONJ
cana-951	115	29	α	α	PRON
cana-951	115	30	is	be	AUX
cana-951	115	31	the	the	DET
cana-951	115	32	attenuation	attenuation	NOUN
cana-951	115	33	coefficient	coefficient	NOUN
cana-951	115	34	and	and	CCONJ
cana-951	115	35	fiber	fiber	NOUN
cana-951	115	36	nonlinearity	nonlinearity	NOUN
cana-951	115	37	related	relate	VERB
cana-951	115	38	to	to	PART
cana-951	115	39	coefficient	coefficient	NOUN
cana-951	115	40	ρ	ρ	NOUN
cana-951	115	41	.when	.when	ADP
cana-951	115	42	setting	set	VERB
cana-951	115	43	the	the	DET
cana-951	115	44	variable	variable	ADJ
cana-951	115	45	t̃	t̃	PROPN
cana-951	115	46	=	=	SYM
cana-951	115	47	t	t	PROPN
cana-951	115	48	−	−	PROPN
cana-951	115	49	β1z	β1z	PROPN
cana-951	115	50	,	,	PUNCT
cana-951	115	51	we	we	PRON
cana-951	115	52	obtain	obtain	VERB
cana-951	115	53	the	the	DET
cana-951	115	54	nonlinear	nonlinear	ADJ
cana-951	115	55	schrödinger	schrödinger	ADJ
cana-951	115	56	equation	equation	NOUN
cana-951	115	57	as	as	SCONJ
cana-951	115	58	follows	follow	VERB
cana-951	115	59	:	:	PUNCT
cana-951	115	60	∂	∂	NUM
cana-951	115	61	∂z	∂z	PROPN
cana-951	115	62	a±(z	a±(z	PROPN
cana-951	115	63	,	,	PUNCT
cana-951	115	64	t̃	t̃	PROPN
cana-951	115	65	)	)	PUNCT
cana-951	115	66	+	+	CCONJ
cana-951	116	1	(	(	PUNCT
cana-951	116	2	i	i	NOUN
cana-951	116	3	1	1	NUM
cana-951	116	4	2	2	NUM
cana-951	116	5	β2	β2	NOUN
cana-951	116	6	∂2	∂2	NOUN
cana-951	116	7	∂t̃2	∂t̃2	NOUN
cana-951	117	1	−	−	ADP
cana-951	117	2	1	1	NUM
cana-951	117	3	6	6	NUM
cana-951	117	4	β3	β3	ADJ
cana-951	117	5	∂3	∂3	NOUN
cana-951	117	6	∂t̃3	∂t̃3	ADJ
cana-951	117	7	)	)	PUNCT
cana-951	118	1	a±(z	a±(z	PROPN
cana-951	118	2	,	,	PUNCT
cana-951	118	3	t̃	t̃	PROPN
cana-951	118	4	)	)	PUNCT
cana-951	118	5	=	=	PRON
cana-951	119	1	(	(	PUNCT
cana-951	119	2	−α	−α	NOUN
cana-951	119	3	2	2	NUM
cana-951	119	4	+	+	NUM
cana-951	119	5	iδ	iδ	NOUN
cana-951	119	6	)	)	PUNCT
cana-951	119	7	a±(z	a±(z	PROPN
cana-951	119	8	,	,	PUNCT
cana-951	119	9	t̃	t̃	PROPN
cana-951	119	10	)	)	PUNCT
cana-951	119	11	−	−	PROPN
cana-951	120	1	iρ|a±(z	iρ|a±(z	ADJ
cana-951	120	2	,	,	PUNCT
cana-951	120	3	t̃)|	t̃)|	PROPN
cana-951	120	4	2	2	NUM
cana-951	120	5	a±(z	a±(z	ADJ
cana-951	120	6	,	,	PUNCT
cana-951	120	7	t̃	t̃	PROPN
cana-951	120	8	)	)	PUNCT
cana-951	120	9	(	(	PUNCT
cana-951	120	10	26	26	NUM
cana-951	120	11	)	)	PUNCT
cana-951	120	12	in	in	ADP
cana-951	120	13	this	this	DET
cana-951	120	14	step	step	NOUN
cana-951	120	15	the	the	DET
cana-951	120	16	bi	bi	ADJ
cana-951	120	17	-	-	ADJ
cana-951	120	18	isotropic	isotropic	ADJ
cana-951	120	19	fiber	fiber	NOUN
cana-951	120	20	is	be	AUX
cana-951	120	21	operattin	operattin	NOUN
cana-951	120	22	in	in	ADP
cana-951	120	23	the	the	DET
cana-951	120	24	third	third	ADJ
cana-951	120	25	optical	optical	ADJ
cana-951	120	26	windows	window	NOUN
cana-951	120	27	,	,	PUNCT
cana-951	120	28	where	where	SCONJ
cana-951	120	29	β3	β3	VERB
cana-951	120	30	=	=	SYM
cana-951	120	31	0	0	NUM
cana-951	120	32	and	and	CCONJ
cana-951	120	33	neglecting	neglect	VERB
cana-951	120	34	absorption	absorption	NOUN
cana-951	120	35	α	α	NOUN
cana-951	120	36	=	=	SYM
cana-951	120	37	0	0	PROPN
cana-951	120	38	the	the	DET
cana-951	120	39	eq.(26	eq.(26	NOUN
cana-951	120	40	)	)	PUNCT
cana-951	120	41	becomes	become	VERB
cana-951	120	42	∂	∂	NOUN
cana-951	120	43	∂z	∂z	PROPN
cana-951	120	44	a±(z	a±(z	PROPN
cana-951	120	45	,	,	PUNCT
cana-951	120	46	t̃	t̃	PROPN
cana-951	120	47	)	)	PUNCT
cana-951	121	1	+	+	CCONJ
cana-951	122	1	(	(	PUNCT
cana-951	122	2	i	i	NOUN
cana-951	122	3	1	1	NUM
cana-951	122	4	2	2	NUM
cana-951	122	5	β2	β2	NOUN
cana-951	122	6	∂2	∂2	PROPN
cana-951	122	7	∂t̃2	∂t̃2	NOUN
cana-951	122	8	)	)	PUNCT
cana-951	123	1	a±(z	a±(z	PROPN
cana-951	123	2	,	,	PUNCT
cana-951	123	3	t̃	t̃	PROPN
cana-951	123	4	)	)	PUNCT
cana-951	123	5	=	=	SYM
cana-951	123	6	iδa±(z	iδa±(z	PROPN
cana-951	123	7	,	,	PUNCT
cana-951	123	8	t̃	t̃	PROPN
cana-951	123	9	)	)	PUNCT
cana-951	123	10	−	−	PROPN
cana-951	124	1	iρ|a±(z	iρ|a±(z	ADJ
cana-951	124	2	,	,	PUNCT
cana-951	124	3	t̃)|	t̃)|	PROPN
cana-951	124	4	2	2	NUM
cana-951	124	5	a±(z	a±(z	ADJ
cana-951	124	6	,	,	PUNCT
cana-951	124	7	t̃	t̃	PROPN
cana-951	124	8	)	)	PUNCT
cana-951	124	9	(	(	PUNCT
cana-951	124	10	27	27	NUM
cana-951	124	11	)	)	PUNCT
cana-951	124	12	since	since	SCONJ
cana-951	124	13	a±	a±	PROPN
cana-951	124	14	=	=	SYM
cana-951	124	15	a±(z	a±(z	PROPN
cana-951	124	16	,	,	PUNCT
cana-951	124	17	t̃	t̃	PROPN
cana-951	124	18	)	)	PUNCT
cana-951	124	19	is	be	AUX
cana-951	124	20	a	a	DET
cana-951	124	21	complex	complex	ADJ
cana-951	124	22	function	function	NOUN
cana-951	124	23	,	,	PUNCT
cana-951	124	24	we	we	PRON
cana-951	124	25	assume	assume	VERB
cana-951	124	26	that	that	SCONJ
cana-951	124	27	travelling	travel	VERB
cana-951	124	28	wave	wave	NOUN
cana-951	124	29	transformation	transformation	NOUN
cana-951	124	30	is	be	AUX
cana-951	124	31	in	in	ADP
cana-951	124	32	the	the	DET
cana-951	124	33	form	form	NOUN
cana-951	124	34	a±(z	a±(z	PROPN
cana-951	124	35	,	,	PUNCT
cana-951	124	36	t̃	t̃	PROPN
cana-951	124	37	)	)	PUNCT
cana-951	124	38	=	=	SYM
cana-951	124	39	v±(z	v±(z	PROPN
cana-951	124	40	,	,	PUNCT
cana-951	124	41	t̃)exp(iθ±(z	t̃)exp(iθ±(z	PROPN
cana-951	124	42	,	,	PUNCT
cana-951	124	43	t̃	t̃	PROPN
cana-951	124	44	)	)	PUNCT
cana-951	124	45	)	)	PUNCT
cana-951	125	1	(	(	PUNCT
cana-951	125	2	28	28	NUM
cana-951	125	3	)	)	PUNCT
cana-951	125	4	where	where	SCONJ
cana-951	125	5	v±(z	v±(z	NOUN
cana-951	125	6	,	,	PUNCT
cana-951	125	7	t̃	t̃	PROPN
cana-951	125	8	)	)	PUNCT
cana-951	125	9	and	and	CCONJ
cana-951	125	10	θ±(z	θ±(z	PROPN
cana-951	125	11	,	,	PUNCT
cana-951	125	12	t̃	t̃	PROPN
cana-951	125	13	)	)	PUNCT
cana-951	125	14	are	be	AUX
cana-951	125	15	amplitude	amplitude	NOUN
cana-951	125	16	and	and	CCONJ
cana-951	125	17	phase	phase	NOUN
cana-951	125	18	functions	function	NOUN
cana-951	125	19	respectively.substituting	respectively.substitute	VERB
cana-951	125	20	the	the	DET
cana-951	125	21	wave	wave	NOUN
cana-951	125	22	transformation	transformation	NOUN
cana-951	125	23	eq.(17	eq.(17	NOUN
cana-951	125	24	)	)	PUNCT
cana-951	125	25	into	into	ADP
cana-951	125	26	eq.(18	eq.(18	NOUN
cana-951	125	27	)	)	PUNCT
cana-951	125	28	and	and	CCONJ
cana-951	125	29	separating	separate	VERB
cana-951	125	30	the	the	DET
cana-951	125	31	real	real	ADJ
cana-951	125	32	and	and	CCONJ
cana-951	125	33	imaginary	imaginary	ADJ
cana-951	125	34	parts	part	NOUN
cana-951	125	35	,	,	PUNCT
cana-951	125	36	we	we	PRON
cana-951	125	37	have	have	VERB
cana-951	125	38	communications	communication	NOUN
cana-951	125	39	on	on	ADP
cana-951	125	40	applied	apply	VERB
cana-951	125	41	nonlinear	nonlinear	ADJ
cana-951	125	42	analysis	analysis	NOUN
cana-951	125	43	issn	issn	NOUN
cana-951	125	44	:	:	PUNCT
cana-951	125	45	1074	1074	NUM
cana-951	125	46	-	-	PUNCT
cana-951	125	47	133x	133x	NUM
cana-951	125	48	vol	vol	NOUN
cana-951	125	49	31	31	NUM
cana-951	125	50	no	no	NOUN
cana-951	125	51	.	.	PUNCT
cana-951	126	1	4s	4s	NUM
cana-951	126	2	(	(	PUNCT
cana-951	126	3	2024	2024	NUM
cana-951	126	4	)	)	PUNCT
cana-951	126	5	578	578	NUM
cana-951	126	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-951	126	7	−v±θ±z	−v±θ±z	X
cana-951	126	8	−	−	NUM
cana-951	126	9	1	1	NUM
cana-951	126	10	2	2	NUM
cana-951	126	11	β2(z)(v±t̃t̃	β2(z)(v±t̃t̃	NOUN
cana-951	126	12	−	−	X
cana-951	126	13	v±θ±z	v±θ±z	INTJ
cana-951	126	14	2	2	NUM
cana-951	126	15	)	)	PUNCT
cana-951	126	16	−	−	PROPN
cana-951	126	17	ρ±v±	ρ±v±	PROPN
cana-951	126	18	3	3	NUM
cana-951	126	19	=	=	SYM
cana-951	126	20	0	0	NUM
cana-951	127	1	(	(	PUNCT
cana-951	127	2	29	29	NUM
cana-951	127	3	)	)	PUNCT
cana-951	127	4	v±z	v±z	PROPN
cana-951	127	5	−	−	NOUN
cana-951	127	6	β2(z)(2θ±zv±z	β2(z)(2θ±zv±z	PUNCT
cana-951	128	1	+	+	CCONJ
cana-951	128	2	v±θ±zz	v±θ±zz	NOUN
cana-951	128	3	)	)	PUNCT
cana-951	128	4	−	−	PROPN
cana-951	128	5	v±	v±	NOUN
cana-951	128	6	=	=	SYM
cana-951	128	7	0	0	NUM
cana-951	128	8	(	(	PUNCT
cana-951	128	9	30	30	NUM
cana-951	128	10	)	)	PUNCT
cana-951	128	11	where	where	SCONJ
cana-951	128	12	θ±z	θ±z	X
cana-951	128	13	=	=	SYM
cana-951	128	14	dθ±	dθ±	ADV
cana-951	128	15	dz	dz	NOUN
cana-951	128	16	,	,	PUNCT
cana-951	128	17	θ±zz	θ±zz	NOUN
cana-951	128	18	=	=	PUNCT
cana-951	128	19	d2θ±	d2θ±	NOUN
cana-951	128	20	dz2	dz2	NOUN
cana-951	128	21	and	and	CCONJ
cana-951	128	22	v±z	v±z	PROPN
cana-951	128	23	=	=	NOUN
cana-951	128	24	dv±	dv±	X
cana-951	128	25	dz	dz	NOUN
cana-951	128	26	,	,	PUNCT
cana-951	128	27	v±t̃	v±t̃	NOUN
cana-951	128	28	=	=	SYM
cana-951	128	29	dv±	dv±	NOUN
cana-951	128	30	dt̃	dt̃	NOUN
cana-951	128	31	considering	consider	VERB
cana-951	128	32	the	the	DET
cana-951	128	33	homogenous	homogenous	ADJ
cana-951	128	34	balance	balance	NOUN
cana-951	128	35	in	in	ADP
cana-951	128	36	eq.(29	eq.(29	PROPN
cana-951	128	37	)	)	PUNCT
cana-951	128	38	and	and	CCONJ
cana-951	128	39	eq.(30	eq.(30	NOUN
cana-951	128	40	)	)	PUNCT
cana-951	128	41	,	,	PUNCT
cana-951	128	42	we	we	PRON
cana-951	128	43	assume	assume	VERB
cana-951	128	44	that	that	SCONJ
cana-951	128	45	eq.(29	eq.(29	NOUN
cana-951	128	46	)	)	PUNCT
cana-951	128	47	and	and	CCONJ
cana-951	128	48	eq.(30	eq.(30	NOUN
cana-951	128	49	)	)	PUNCT
cana-951	128	50	have	have	VERB
cana-951	128	51	the	the	DET
cana-951	128	52	following	follow	VERB
cana-951	128	53	solutions	solution	NOUN
cana-951	128	54	form	form	NOUN
cana-951	128	55	{	{	PUNCT
cana-951	128	56	v±(z	v±(z	PROPN
cana-951	128	57	,	,	PUNCT
cana-951	128	58	t̃	t̃	PROPN
cana-951	128	59	)	)	PUNCT
cana-951	128	60	=	=	PUNCT
cana-951	129	1	v±(ξ	v±(ξ	PROPN
cana-951	129	2	)	)	PUNCT
cana-951	129	3	=	=	PROPN
cana-951	129	4	a0	a0	PROPN
cana-951	129	5	+	+	CCONJ
cana-951	129	6	a1	a1	NOUN
cana-951	129	7	(	(	PUNCT
cana-951	129	8	g±	g±	ADJ
cana-951	129	9	′	′	NOUN
cana-951	129	10	g±	g±	NOUN
cana-951	129	11	)	)	PUNCT
cana-951	130	1	+	+	CCONJ
cana-951	130	2	b1√1	b1√1	NOUN
cana-951	130	3	+	+	CCONJ
cana-951	130	4	1	1	NUM
cana-951	130	5	μ	μ	NOUN
cana-951	130	6	(	(	PUNCT
cana-951	130	7	g±	g±	ADJ
cana-951	130	8	′	′	NOUN
cana-951	130	9	g±	g±	NOUN
cana-951	130	10	)	)	PUNCT
cana-951	130	11	2	2	NUM
cana-951	130	12	ξ±	ξ±	NOUN
cana-951	130	13	=	=	SYM
cana-951	130	14	p±(z)t̃	p±(z)t̃	PROPN
cana-951	130	15	+	+	CCONJ
cana-951	130	16	q±(z	q±(z	PROPN
cana-951	130	17	)	)	PUNCT
cana-951	130	18	(	(	PUNCT
cana-951	130	19	31	31	NUM
cana-951	130	20	)	)	PUNCT
cana-951	130	21	θ±(z	θ±(z	PROPN
cana-951	130	22	,	,	PUNCT
cana-951	130	23	t̃	t̃	PROPN
cana-951	130	24	)	)	PUNCT
cana-951	130	25	=	=	PRON
cana-951	130	26	a±(z)t̃	a±(z)t̃	PROPN
cana-951	130	27	2	2	NUM
cana-951	131	1	+	+	CCONJ
cana-951	131	2	b±(z)t̃	b±(z)t̃	PROPN
cana-951	131	3	+	+	CCONJ
cana-951	131	4	c±(z	c±(z	PROPN
cana-951	131	5	)	)	PUNCT
cana-951	131	6	(	(	PUNCT
cana-951	131	7	32	32	NUM
cana-951	131	8	)	)	PUNCT
cana-951	131	9	where	where	SCONJ
cana-951	131	10	g±	g±	PROPN
cana-951	131	11	=	=	SYM
cana-951	131	12	g±(ξ	g±(ξ	NOUN
cana-951	131	13	)	)	PUNCT
cana-951	131	14	satifies	satifie	NOUN
cana-951	131	15	{	{	PUNCT
cana-951	131	16	−a0a±	−a0a±	NUM
cana-951	131	17	′(z	′(z	NOUN
cana-951	131	18	)	)	PUNCT
cana-951	131	19	+	+	CCONJ
cana-951	131	20	2a0a±	2a0a±	PROPN
cana-951	131	21	2(z)β±2(z	2(z)β±2(z	NUM
cana-951	131	22	)	)	PUNCT
cana-951	131	23	=	=	SYM
cana-951	132	1	0	0	NUM
cana-951	132	2	−a1a±	−a1a±	PROPN
cana-951	132	3	′(z	′(z	NOUN
cana-951	132	4	)	)	PUNCT
cana-951	133	1	+	+	CCONJ
cana-951	133	2	2a1a±	2a1a±	NUM
cana-951	133	3	2(z)β±2(z	2(z)β±2(z	NUM
cana-951	133	4	)	)	PUNCT
cana-951	134	1	=	=	SYM
cana-951	134	2	0	0	NUM
cana-951	134	3	−b1a±	−b1a±	PROPN
cana-951	134	4	′(z	′(z	NOUN
cana-951	134	5	)	)	PUNCT
cana-951	135	1	+	+	CCONJ
cana-951	135	2	2b1a±	2b1a±	NUM
cana-951	135	3	2(z)β±2(z	2(z)β±2(z	NUM
cana-951	135	4	)	)	PUNCT
cana-951	135	5	=	=	SYM
cana-951	135	6	0	0	NUM
cana-951	135	7	b1b±	b1b±	NOUN
cana-951	135	8	′(z	′(z	NOUN
cana-951	135	9	)	)	PUNCT
cana-951	136	1	+	+	CCONJ
cana-951	136	2	2b1a±	2b1a±	NUM
cana-951	136	3	2(z)b±(z)β±2(z	2(z)b±(z)β±2(z	NUM
cana-951	136	4	)	)	PUNCT
cana-951	136	5	=	=	SYM
cana-951	136	6	0	0	NUM
cana-951	136	7	−a1β±2(z	−a1β±2(z	NUM
cana-951	136	8	)	)	PUNCT
cana-951	136	9	−	−	PROPN
cana-951	136	10	a1	a1	NOUN
cana-951	136	11	3ρ±	3ρ±	NUM
cana-951	136	12	−	−	NOUN
cana-951	136	13	3a1b1	3a1b1	NUM
cana-951	137	1	2ρ±	2ρ±	NUM
cana-951	137	2	μ	μ	NOUN
cana-951	137	3	=	=	SYM
cana-951	137	4	0	0	NUM
cana-951	137	5	3a0a1	3a0a1	NUM
cana-951	137	6	2	2	NUM
cana-951	137	7	+	+	CCONJ
cana-951	137	8	3a0b1	3a0b1	NUM
cana-951	137	9	2	2	NUM
cana-951	137	10	μ	μ	NOUN
cana-951	137	11	=	=	SYM
cana-951	137	12	0	0	NUM
cana-951	137	13	−	−	NOUN
cana-951	137	14	1	1	NUM
cana-951	137	15	2	2	NUM
cana-951	137	16	μb1β±2(z)p	μb1β±2(z)p	NOUN
cana-951	137	17	2(z	2(z	NUM
cana-951	137	18	)	)	PUNCT
cana-951	137	19	−	−	PROPN
cana-951	137	20	ρ±b1	ρ±b1	PROPN
cana-951	137	21	3	3	NUM
cana-951	137	22	−	−	PROPN
cana-951	137	23	b1c±	b1c±	PROPN
cana-951	137	24	′(z	′(z	NOUN
cana-951	137	25	)	)	PUNCT
cana-951	138	1	−	−	PROPN
cana-951	139	1	3a0b1ρ±	3a0b1ρ±	NUM
cana-951	139	2	+	+	CCONJ
cana-951	139	3	1	1	NUM
cana-951	139	4	2	2	NUM
cana-951	139	5	b1β±2(z)b	b1β±2(z)b	NOUN
cana-951	139	6	2	2	NUM
cana-951	139	7	=	=	SYM
cana-951	139	8	0	0	NUM
cana-951	139	9	−a1c±	−a1c±	NUM
cana-951	139	10	′(z	′(z	NOUN
cana-951	139	11	)	)	PUNCT
cana-951	140	1	−	−	ADP
cana-951	140	2	a1μβ±2(z)p±	a1μβ±2(z)p±	PROPN
cana-951	140	3	2(z	2(z	NUM
cana-951	140	4	)	)	PUNCT
cana-951	140	5	−	−	PROPN
cana-951	140	6	3ρ±a0	3ρ±a0	NUM
cana-951	140	7	2a1	2a1	NUM
cana-951	140	8	−	−	NUM
cana-951	140	9	3a1b1	3a1b1	NUM
cana-951	141	1	2ρ±	2ρ±	NUM
cana-951	141	2	+	+	NOUN
cana-951	141	3	1	1	NUM
cana-951	141	4	2	2	NUM
cana-951	141	5	a1b	a1b	NOUN
cana-951	141	6	2β±2(z	2β±2(z	NUM
cana-951	141	7	)	)	PUNCT
cana-951	141	8	=	=	SYM
cana-951	141	9	0	0	NUM
cana-951	141	10	p±	p±	NOUN
cana-951	141	11	′(z	′(z	NOUN
cana-951	141	12	)	)	PUNCT
cana-951	141	13	−	−	ADP
cana-951	141	14	2p±(z)ρ±β±2(z	2p±(z)ρ±β±2(z	NUM
cana-951	141	15	)	)	PUNCT
cana-951	141	16	q±	q±	PROPN
cana-951	141	17	′(z	′(z	NOUN
cana-951	141	18	)	)	PUNCT
cana-951	142	1	+	+	CCONJ
cana-951	142	2	p±(z)β±2(z)b	p±(z)β±2(z)b	PUNCT
cana-951	142	3	=	=	SYM
cana-951	142	4	0	0	NUM
cana-951	142	5	−ρ±β±2(z	−ρ±β±2(z	NOUN
cana-951	142	6	)	)	PUNCT
cana-951	142	7	=	=	SYM
cana-951	142	8	1	1	NUM
cana-951	142	9	(	(	PUNCT
cana-951	142	10	33	33	NUM
cana-951	142	11	)	)	PUNCT
cana-951	142	12	solving	solve	VERB
cana-951	142	13	the	the	DET
cana-951	142	14	algebric	algebric	ADJ
cana-951	142	15	system	system	NOUN
cana-951	142	16	with	with	ADP
cana-951	142	17	the	the	DET
cana-951	142	18	help	help	NOUN
cana-951	142	19	of	of	ADP
cana-951	142	20	mathematica	mathematica	PROPN
cana-951	142	21	,	,	PUNCT
cana-951	142	22	we	we	PRON
cana-951	142	23	get	get	VERB
cana-951	142	24	the	the	DET
cana-951	142	25	following	follow	VERB
cana-951	142	26	cases	case	NOUN
cana-951	142	27	.	.	PUNCT
cana-951	143	1	case	case	NOUN
cana-951	143	2	1	1	NUM
cana-951	143	3	a0	a0	NOUN
cana-951	143	4	=	=	SYM
cana-951	143	5	0	0	NUM
cana-951	143	6	,	,	PUNCT
cana-951	143	7	b1	b1	NOUN
cana-951	143	8	=	=	SYM
cana-951	143	9	0	0	NUM
cana-951	143	10	,	,	PUNCT
cana-951	143	11	a1	a1	NOUN
cana-951	143	12	=	=	PUNCT
cana-951	143	13	a1	a1	PROPN
cana-951	143	14	,	,	PUNCT
cana-951	143	15	p±(z	p±(z	NOUN
cana-951	143	16	)	)	PUNCT
cana-951	143	17	=	=	SYM
cana-951	143	18	c2a±(z	c2a±(z	NOUN
cana-951	143	19	)	)	PUNCT
cana-951	143	20	,	,	PUNCT
cana-951	143	21	q±(z	q±(z	PROPN
cana-951	143	22	)	)	PUNCT
cana-951	143	23	=	=	SYM
cana-951	143	24	1	1	NUM
cana-951	143	25	2	2	NUM
cana-951	143	26	c1c2a±(z	c1c2a±(z	NOUN
cana-951	143	27	)	)	PUNCT
cana-951	144	1	+	+	CCONJ
cana-951	144	2	c3	c3	PROPN
cana-951	144	3	(	(	PUNCT
cana-951	144	4	34	34	NUM
cana-951	144	5	)	)	PUNCT
cana-951	144	6	b±(z	b±(z	PROPN
cana-951	144	7	)	)	PUNCT
cana-951	144	8	=	=	SYM
cana-951	144	9	c1a±(z	c1a±(z	PROPN
cana-951	144	10	)	)	PUNCT
cana-951	144	11	,	,	PUNCT
cana-951	144	12	c±(z	c±(z	PROPN
cana-951	144	13	)	)	PUNCT
cana-951	144	14	=	=	SYM
cana-951	144	15	1	1	NUM
cana-951	144	16	4	4	NUM
cana-951	144	17	(	(	PUNCT
cana-951	144	18	c1	c1	NOUN
cana-951	144	19	2	2	NUM
cana-951	144	20	−	−	PROPN
cana-951	144	21	2μc2	2μc2	NUM
cana-951	144	22	2)a±(z	2)a±(z	NOUN
cana-951	144	23	)	)	PUNCT
cana-951	144	24	+	+	CCONJ
cana-951	144	25	c4	c4	NOUN
cana-951	144	26	(	(	PUNCT
cana-951	144	27	35	35	NUM
cana-951	144	28	)	)	PUNCT
cana-951	144	29	ρ±(z	ρ±(z	PROPN
cana-951	144	30	)	)	PUNCT
cana-951	144	31	=	=	SYM
cana-951	145	1	c2	c2	PROPN
cana-951	145	2	2β±(z)a±	2β±(z)a±	NUM
cana-951	145	3	2(z	2(z	NUM
cana-951	145	4	)	)	PUNCT
cana-951	145	5	a1	a1	NOUN
cana-951	145	6	2	2	NUM
cana-951	145	7	(	(	PUNCT
cana-951	145	8	36	36	NUM
cana-951	145	9	)	)	PUNCT
cana-951	145	10	where	where	SCONJ
cana-951	145	11	ci(i	ci(i	PUNCT
cana-951	145	12	=	=	SYM
cana-951	145	13	1,2	1,2	NUM
cana-951	145	14	,	,	PUNCT
cana-951	145	15	…	…	PUNCT
cana-951	145	16	,	,	PUNCT
cana-951	145	17	5	5	X
cana-951	145	18	)	)	PUNCT
cana-951	145	19	are	be	AUX
cana-951	145	20	arbitry	arbitry	NOUN
cana-951	145	21	constants	constant	NOUN
cana-951	145	22	and	and	CCONJ
cana-951	145	23	a±(z	a±(z	PROPN
cana-951	145	24	)	)	PUNCT
cana-951	145	25	is	be	AUX
cana-951	145	26	given	give	VERB
cana-951	145	27	by	by	ADP
cana-951	145	28	a±(z)[−2∫	a±(z)[−2∫	NOUN
cana-951	145	29	β±2(z)dz	β±2(z)dz	NOUN
cana-951	145	30	+	+	CCONJ
cana-951	145	31	c5	c5	PROPN
cana-951	145	32	]	]	X
cana-951	145	33	=	=	SYM
cana-951	145	34	1	1	NUM
cana-951	145	35	(	(	PUNCT
cana-951	145	36	37	37	NUM
cana-951	145	37	)	)	PUNCT
cana-951	145	38	the	the	DET
cana-951	145	39	exact	exact	ADJ
cana-951	145	40	solution	solution	NOUN
cana-951	145	41	of	of	ADP
cana-951	145	42	eq.(26	eq.(26	NOUN
cana-951	145	43	)	)	PUNCT
cana-951	145	44	is	be	AUX
cana-951	145	45	given	give	VERB
cana-951	145	46	by	by	ADP
cana-951	145	47	,	,	PUNCT
cana-951	145	48	communications	communication	NOUN
cana-951	145	49	on	on	ADP
cana-951	145	50	applied	apply	VERB
cana-951	145	51	nonlinear	nonlinear	ADJ
cana-951	145	52	analysis	analysis	NOUN
cana-951	145	53	issn	issn	NOUN
cana-951	145	54	:	:	PUNCT
cana-951	145	55	1074	1074	NUM
cana-951	145	56	-	-	PUNCT
cana-951	145	57	133x	133x	NUM
cana-951	145	58	vol	vol	NOUN
cana-951	145	59	31	31	NUM
cana-951	145	60	no	no	NOUN
cana-951	145	61	.	.	PUNCT
cana-951	146	1	4s	4s	NUM
cana-951	146	2	(	(	PUNCT
cana-951	146	3	2024	2024	NUM
cana-951	146	4	)	)	PUNCT
cana-951	146	5	579	579	NUM
cana-951	146	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-951	146	7	a±(z	a±(z	PROPN
cana-951	146	8	,	,	PUNCT
cana-951	146	9	t̃	t̃	PROPN
cana-951	146	10	)	)	PUNCT
cana-951	146	11	=	=	PRON
cana-951	146	12	{	{	PUNCT
cana-951	147	1	√−μa1	√−μa1	ADV
cana-951	147	2	(	(	PUNCT
cana-951	147	3	a1sinh√−μξ+a2cosh√−μξ	a1sinh√−μξ+a2cosh√−μξ	NOUN
cana-951	147	4	a1cosh√−μξ+a2sinh√−μξ	a1cosh√−μξ+a2sinh√−μξ	PROPN
cana-951	147	5	)	)	PUNCT
cana-951	147	6	.	.	PUNCT
cana-951	148	1	exp(iθ±(z	exp(iθ±(z	ADJ
cana-951	148	2	,	,	PUNCT
cana-951	148	3	t̃	t̃	PROPN
cana-951	148	4	)	)	PUNCT
cana-951	148	5	)	)	PUNCT
cana-951	148	6	;	;	PUNCT
cana-951	148	7	μ	μ	PROPN
cana-951	148	8	<	<	X
cana-951	148	9	0	0	PUNCT
cana-951	148	10	√μa1	√μa1	NOUN
cana-951	148	11	(	(	PUNCT
cana-951	148	12	a1sin√μξ+a2cos√μξ	a1sin√μξ+a2cos√μξ	PROPN
cana-951	148	13	a2sin√μξ−a1cos√μξ	a2sin√μξ−a1cos√μξ	PROPN
cana-951	148	14	)	)	PUNCT
cana-951	148	15	.	.	PUNCT
cana-951	149	1	exp(iθ±(z	exp(iθ±(z	ADJ
cana-951	149	2	,	,	PUNCT
cana-951	149	3	t̃	t̃	PROPN
cana-951	149	4	)	)	PUNCT
cana-951	149	5	)	)	PUNCT
cana-951	149	6	;	;	PUNCT
cana-951	149	7	μ	μ	PROPN
cana-951	149	8	>	>	SYM
cana-951	149	9	0	0	PUNCT
cana-951	149	10	a2	a2	PROPN
cana-951	149	11	a1+a2	a1+a2	PROPN
cana-951	149	12	;	;	PUNCT
cana-951	149	13	μ	μ	PROPN
cana-951	149	14	=	=	SYM
cana-951	149	15	0	0	NUM
cana-951	150	1	(	(	PUNCT
cana-951	150	2	38	38	NUM
cana-951	150	3	)	)	PUNCT
cana-951	150	4	the	the	DET
cana-951	150	5	dark	dark	ADJ
cana-951	150	6	solitary	solitary	NOUN
cana-951	150	7	of	of	ADP
cana-951	150	8	eq.(27	eq.(27	PROPN
cana-951	150	9	)	)	PUNCT
cana-951	150	10	are	be	AUX
cana-951	150	11	given	give	VERB
cana-951	150	12	in	in	ADP
cana-951	150	13	the	the	DET
cana-951	150	14	form	form	NOUN
cana-951	150	15	a±1(z	a±1(z	NOUN
cana-951	150	16	,	,	PUNCT
cana-951	150	17	t̃	t̃	PROPN
cana-951	150	18	)	)	PUNCT
cana-951	150	19	=	=	SYM
cana-951	150	20	√−μa1tanh(√−μξ	√−μa1tanh(√−μξ	NOUN
cana-951	150	21	+	+	CCONJ
cana-951	150	22	ξ0	ξ0	PROPN
cana-951	150	23	)	)	PUNCT
cana-951	150	24	⋅	⋅	PROPN
cana-951	150	25	exp{ia±(z	exp{ia±(z	PROPN
cana-951	150	26	,	,	PUNCT
cana-951	150	27	t)[t̃	t)[t̃	X
cana-951	150	28	2	2	NUM
cana-951	150	29	+	+	CCONJ
cana-951	150	30	c1t̃	c1t̃	NOUN
cana-951	150	31	+	+	CCONJ
cana-951	150	32	(	(	PUNCT
cana-951	150	33	c1	c1	PROPN
cana-951	150	34	2	2	NUM
cana-951	150	35	−	−	NOUN
cana-951	150	36	2μc2	2μc2	NUM
cana-951	150	37	2	2	NUM
cana-951	150	38	]	]	PUNCT
cana-951	150	39	}	}	PUNCT
cana-951	150	40	(	(	PUNCT
cana-951	150	41	39	39	NUM
cana-951	150	42	)	)	PUNCT
cana-951	150	43	the	the	DET
cana-951	150	44	hyperbolic	hyperbolic	ADJ
cana-951	150	45	function	function	NOUN
cana-951	150	46	solution	solution	NOUN
cana-951	150	47	of	of	ADP
cana-951	150	48	eq.(27	eq.(27	PROPN
cana-951	150	49	)	)	PUNCT
cana-951	150	50	are	be	AUX
cana-951	150	51	written	write	VERB
cana-951	150	52	as	as	ADP
cana-951	150	53	a±2(z	a±2(z	NOUN
cana-951	150	54	,	,	PUNCT
cana-951	150	55	t̃	t̃	PROPN
cana-951	150	56	)	)	PUNCT
cana-951	150	57	=	=	NOUN
cana-951	150	58	√−μa1coth(√−μξ	√−μa1coth(√−μξ	X
cana-951	150	59	+	+	X
cana-951	150	60	ξ0	ξ0	ADJ
cana-951	150	61	)	)	PUNCT
cana-951	150	62	⋅	⋅	PROPN
cana-951	150	63	exp{ia±(z	exp{ia±(z	PROPN
cana-951	150	64	,	,	PUNCT
cana-951	150	65	t)[t̃	t)[t̃	X
cana-951	150	66	2	2	NUM
cana-951	150	67	+	+	CCONJ
cana-951	150	68	c1t̃	c1t̃	NOUN
cana-951	150	69	+	+	CCONJ
cana-951	150	70	(	(	PUNCT
cana-951	150	71	c1	c1	PROPN
cana-951	150	72	2	2	NUM
cana-951	150	73	−	−	NOUN
cana-951	150	74	2μc2	2μc2	NUM
cana-951	150	75	2	2	NUM
cana-951	150	76	]	]	PUNCT
cana-951	150	77	}	}	PUNCT
cana-951	150	78	(	(	PUNCT
cana-951	150	79	40	40	NUM
cana-951	150	80	)	)	PUNCT
cana-951	150	81	and	and	CCONJ
cana-951	150	82	the	the	DET
cana-951	150	83	triangular	triangular	NOUN
cana-951	150	84	periodic	periodic	ADJ
cana-951	150	85	wave	wave	NOUN
cana-951	150	86	solution	solution	NOUN
cana-951	150	87	of	of	ADP
cana-951	150	88	eq.(27	eq.(27	PROPN
cana-951	150	89	)	)	PUNCT
cana-951	150	90	are	be	AUX
cana-951	150	91	written	write	VERB
cana-951	150	92	as	as	ADP
cana-951	150	93	a±3(z	a±3(z	PROPN
cana-951	150	94	,	,	PUNCT
cana-951	150	95	t̃	t̃	PROPN
cana-951	150	96	)	)	PUNCT
cana-951	151	1	=	=	SYM
cana-951	151	2	√−μa1cot(√−μξ	√−μa1cot(√−μξ	NOUN
cana-951	151	3	+	+	CCONJ
cana-951	151	4	ξ0	ξ0	PROPN
cana-951	151	5	)	)	PUNCT
cana-951	151	6	⋅	⋅	PROPN
cana-951	151	7	exp{ia±(z	exp{ia±(z	PROPN
cana-951	151	8	,	,	PUNCT
cana-951	151	9	t)[t̃	t)[t̃	X
cana-951	151	10	2	2	NUM
cana-951	151	11	+	+	CCONJ
cana-951	151	12	c1t̃	c1t̃	NOUN
cana-951	151	13	+	+	CCONJ
cana-951	151	14	(	(	PUNCT
cana-951	151	15	c1	c1	PROPN
cana-951	151	16	2	2	NUM
cana-951	151	17	−	−	NOUN
cana-951	151	18	2μc2	2μc2	NUM
cana-951	151	19	2	2	NUM
cana-951	151	20	]	]	PUNCT
cana-951	151	21	}	}	PUNCT
cana-951	151	22	(	(	PUNCT
cana-951	151	23	41	41	NUM
cana-951	151	24	)	)	PUNCT
cana-951	151	25	fig.1	fig.1	PROPN
cana-951	151	26	.	.	PUNCT
cana-951	152	1	numerical	numerical	PROPN
cana-951	152	2	simulation	simulation	PROPN
cana-951	152	3	of	of	ADP
cana-951	152	4	rcp	rcp	NOUN
cana-951	152	5	amplitude	amplitude	NOUN
cana-951	152	6	a+1(z	a+1(z	PROPN
cana-951	152	7	,	,	PUNCT
cana-951	152	8	t̃	t̃	PROPN
cana-951	152	9	)	)	PUNCT
cana-951	152	10	for	for	ADP
cana-951	152	11	the	the	DET
cana-951	152	12	first	first	ADJ
cana-951	152	13	case	case	NOUN
cana-951	152	14	of	of	ADP
cana-951	152	15	solutions	solution	NOUN
cana-951	152	16	where	where	SCONJ
cana-951	152	17	:	:	PUNCT
cana-951	152	18	c1=3	c1=3	PROPN
cana-951	152	19	,	,	PUNCT
cana-951	152	20	c2=4	c2=4	PROPN
cana-951	152	21	,	,	PUNCT
cana-951	152	22	c3=5	c3=5	PROPN
cana-951	152	23	ξ0	ξ0	PROPN
cana-951	152	24	=	=	NOUN
cana-951	152	25	1	1	NUM
cana-951	152	26	;	;	PUNCT
cana-951	152	27	μ=-1/2	μ=-1/2	NOUN
cana-951	152	28	,	,	PUNCT
cana-951	152	29	a1	a1	PROPN
cana-951	152	30	=3	=3	PROPN
cana-951	152	31	,	,	PUNCT
cana-951	152	32	b1=3	b1=3	PROPN
cana-951	152	33	,	,	PUNCT
cana-951	152	34	μr	μr	NOUN
cana-951	152	35	=	=	SYM
cana-951	152	36	1.4	1.4	NUM
cana-951	152	37	,	,	PUNCT
cana-951	152	38	εr	εr	AUX
cana-951	152	39	=	=	SYM
cana-951	152	40	5.2	5.2	NUM
cana-951	152	41	,	,	PUNCT
cana-951	152	42	γ	γ	X
cana-951	152	43	=	=	SYM
cana-951	152	44	0.5	0.5	NUM
cana-951	152	45	,	,	PUNCT
cana-951	152	46	κ	κ	X
cana-951	152	47	=	=	NOUN
cana-951	152	48	0.5,γkerr	0.5,γkerr	NUM
cana-951	152	49	=	=	SYM
cana-951	152	50	2.58	2.58	NUM
cana-951	152	51	×	×	NOUN
cana-951	152	52	10−17	10−17	NUM
cana-951	152	53	κkerr	κkerr	NOUN
cana-951	152	54	=	=	PUNCT
cana-951	152	55	3.58	3.58	NUM
cana-951	152	56	×	×	NOUN
cana-951	152	57	10−17	10−17	NUM
cana-951	152	58	.	.	PUNCT
cana-951	153	1	communications	communication	NOUN
cana-951	153	2	on	on	ADP
cana-951	153	3	applied	apply	VERB
cana-951	153	4	nonlinear	nonlinear	ADJ
cana-951	153	5	analysis	analysis	NOUN
cana-951	153	6	issn	issn	NOUN
cana-951	153	7	:	:	PUNCT
cana-951	153	8	1074	1074	NUM
cana-951	153	9	-	-	PUNCT
cana-951	153	10	133x	133x	NUM
cana-951	153	11	vol	vol	NOUN
cana-951	153	12	31	31	NUM
cana-951	153	13	no	no	NOUN
cana-951	153	14	.	.	PUNCT
cana-951	154	1	4s	4s	NUM
cana-951	154	2	(	(	PUNCT
cana-951	154	3	2024	2024	NUM
cana-951	154	4	)	)	PUNCT
cana-951	155	1	580	580	NUM
cana-951	155	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-951	155	3	fig.2	fig.2	PROPN
cana-951	155	4	.	.	PUNCT
cana-951	156	1	numerical	numerical	PROPN
cana-951	156	2	simulation	simulation	PROPN
cana-951	156	3	of	of	ADP
cana-951	156	4	lcp	lcp	PROPN
cana-951	156	5	amplitude	amplitude	NOUN
cana-951	156	6	a−1(z	a−1(z	PROPN
cana-951	156	7	,	,	PUNCT
cana-951	156	8	t̃	t̃	PROPN
cana-951	156	9	)	)	PUNCT
cana-951	156	10	for	for	ADP
cana-951	156	11	the	the	DET
cana-951	156	12	first	first	ADJ
cana-951	156	13	case	case	NOUN
cana-951	156	14	of	of	ADP
cana-951	156	15	solutions	solution	NOUN
cana-951	156	16	where	where	SCONJ
cana-951	156	17	:	:	PUNCT
cana-951	156	18	c1=3	c1=3	PROPN
cana-951	156	19	,	,	PUNCT
cana-951	156	20	c2=4	c2=4	PROPN
cana-951	156	21	,	,	PUNCT
cana-951	156	22	c3=5	c3=5	PROPN
cana-951	156	23	ξ0	ξ0	PROPN
cana-951	156	24	=	=	NOUN
cana-951	156	25	1	1	NUM
cana-951	156	26	;	;	PUNCT
cana-951	156	27	μ=-1/2	μ=-1/2	NOUN
cana-951	156	28	,	,	PUNCT
cana-951	156	29	a1	a1	PROPN
cana-951	156	30	=3	=3	PROPN
cana-951	156	31	,	,	PUNCT
cana-951	156	32	b1=3	b1=3	PROPN
cana-951	156	33	,	,	PUNCT
cana-951	156	34	μr	μr	NOUN
cana-951	156	35	=	=	SYM
cana-951	156	36	1.4	1.4	NUM
cana-951	156	37	,	,	PUNCT
cana-951	156	38	εr	εr	NOUN
cana-951	156	39	=	=	SYM
cana-951	156	40	5.2	5.2	NUM
cana-951	156	41	,	,	PUNCT
cana-951	156	42	γ	γ	X
cana-951	156	43	=	=	SYM
cana-951	156	44	0.5	0.5	NUM
cana-951	156	45	,	,	PUNCT
cana-951	156	46	κ	κ	X
cana-951	156	47	=	=	NOUN
cana-951	156	48	0.5,γkerr	0.5,γkerr	NUM
cana-951	156	49	=	=	SYM
cana-951	156	50	2.58	2.58	NUM
cana-951	156	51	×	×	NOUN
cana-951	156	52	10−17	10−17	NUM
cana-951	156	53	κkerr	κkerr	NOUN
cana-951	156	54	=	=	PUNCT
cana-951	156	55	3.58	3.58	NUM
cana-951	156	56	×	×	NOUN
cana-951	156	57	10−17	10−17	NUM
cana-951	156	58	.	.	PUNCT
cana-951	156	59	case	case	NOUN
cana-951	156	60	2	2	NUM
cana-951	156	61	a0	a0	NOUN
cana-951	156	62	=	=	SYM
cana-951	156	63	0	0	NUM
cana-951	156	64	;	;	PUNCT
cana-951	156	65	a1	a1	NOUN
cana-951	156	66	=	=	SYM
cana-951	156	67	0	0	NUM
cana-951	156	68	,	,	PUNCT
cana-951	156	69	b1	b1	NOUN
cana-951	156	70	=	=	SYM
cana-951	156	71	b1	b1	PROPN
cana-951	156	72	,	,	PUNCT
cana-951	156	73	p±(z	p±(z	NOUN
cana-951	156	74	)	)	PUNCT
cana-951	156	75	=	=	SYM
cana-951	156	76	c2a(z	c2a(z	PROPN
cana-951	156	77	)	)	PUNCT
cana-951	156	78	,	,	PUNCT
cana-951	156	79	b±(z	b±(z	PROPN
cana-951	156	80	)	)	PUNCT
cana-951	156	81	=	=	SYM
cana-951	156	82	c1a±(z	c1a±(z	PROPN
cana-951	156	83	)	)	PUNCT
cana-951	156	84	(	(	PUNCT
cana-951	156	85	42	42	NUM
cana-951	156	86	)	)	PUNCT
cana-951	156	87	q±(z	q±(z	PROPN
cana-951	156	88	)	)	PUNCT
cana-951	156	89	=	=	SYM
cana-951	156	90	1	1	NUM
cana-951	156	91	2	2	NUM
cana-951	156	92	c1c2a±(z	c1c2a±(z	NOUN
cana-951	156	93	)	)	PUNCT
cana-951	157	1	+	+	CCONJ
cana-951	157	2	c3	c3	NOUN
cana-951	157	3	;	;	PUNCT
cana-951	157	4	−a±(z)β±(z	−a±(z)β±(z	NUM
cana-951	157	5	)	)	PUNCT
cana-951	157	6	=	=	SYM
cana-951	157	7	1	1	NUM
cana-951	157	8	(	(	PUNCT
cana-951	157	9	43	43	NUM
cana-951	157	10	)	)	PUNCT
cana-951	157	11	c±(z	c±(z	PROPN
cana-951	157	12	)	)	PUNCT
cana-951	157	13	=	=	SYM
cana-951	157	14	1	1	NUM
cana-951	157	15	4	4	NUM
cana-951	157	16	(	(	PUNCT
cana-951	157	17	c1	c1	NOUN
cana-951	157	18	2	2	NUM
cana-951	157	19	+	+	CCONJ
cana-951	157	20	μc2	μc2	PROPN
cana-951	157	21	2)a±(z	2)a±(z	NUM
cana-951	157	22	)	)	PUNCT
cana-951	158	1	+	+	CCONJ
cana-951	158	2	c4	c4	NOUN
cana-951	158	3	(	(	PUNCT
cana-951	158	4	44	44	NUM
cana-951	158	5	)	)	PUNCT
cana-951	158	6	a±(z)[−2∫	a±(z)[−2∫	PUNCT
cana-951	158	7	β±2(z)dz	β±2(z)dz	NOUN
cana-951	158	8	+	+	CCONJ
cana-951	158	9	c5	c5	PROPN
cana-951	158	10	]	]	X
cana-951	158	11	=	=	SYM
cana-951	158	12	1	1	NUM
cana-951	158	13	(	(	PUNCT
cana-951	158	14	45	45	NUM
cana-951	158	15	)	)	PUNCT
cana-951	158	16	in	in	ADP
cana-951	158	17	this	this	DET
cana-951	158	18	case	case	NOUN
cana-951	158	19	,	,	PUNCT
cana-951	158	20	we	we	PRON
cana-951	158	21	have	have	VERB
cana-951	158	22	the	the	DET
cana-951	158	23	exact	exact	ADJ
cana-951	158	24	solution	solution	NOUN
cana-951	158	25	of	of	ADP
cana-951	158	26	eq.(27	eq.(27	PROPN
cana-951	158	27	)	)	PUNCT
cana-951	158	28	as	as	SCONJ
cana-951	158	29	follows	follow	VERB
cana-951	158	30	a±(z	a±(z	PROPN
cana-951	158	31	,	,	PUNCT
cana-951	158	32	t̃	t̃	PROPN
cana-951	158	33	)	)	PUNCT
cana-951	158	34	=	=	PRON
cana-951	158	35	{	{	PUNCT
cana-951	158	36	b1√1	b1√1	NOUN
cana-951	158	37	−	−	PROPN
cana-951	159	1	(	(	PUNCT
cana-951	159	2	a1sinh√−μξ+a2cosh√−μξ	a1sinh√−μξ+a2cosh√−μξ	NOUN
cana-951	159	3	a1cosh√−μξ+a2sinh√−μξ	a1cosh√−μξ+a2sinh√−μξ	PROPN
cana-951	159	4	)	)	PUNCT
cana-951	159	5	2	2	NUM
cana-951	159	6	.	.	PUNCT
cana-951	160	1	exp(iθ±(z	exp(iθ±(z	ADJ
cana-951	160	2	,	,	PUNCT
cana-951	160	3	t̃	t̃	PROPN
cana-951	160	4	)	)	PUNCT
cana-951	160	5	)	)	PUNCT
cana-951	160	6	;	;	PUNCT
cana-951	160	7	μ	μ	PROPN
cana-951	160	8	<	<	X
cana-951	160	9	0	0	PUNCT
cana-951	161	1	b1√1	b1√1	NOUN
cana-951	161	2	+	+	CCONJ
cana-951	161	3	(	(	PUNCT
cana-951	161	4	a1sin√μξ+a2cos√μξ	a1sin√μξ+a2cos√μξ	PROPN
cana-951	161	5	a2sin√μξ−a1cos√μξ	a2sin√μξ−a1cos√μξ	PROPN
cana-951	161	6	)	)	PUNCT
cana-951	161	7	2	2	X
cana-951	161	8	.	.	PUNCT
cana-951	162	1	exp(iθ±(z	exp(iθ±(z	ADJ
cana-951	162	2	,	,	PUNCT
cana-951	162	3	t̃	t̃	PROPN
cana-951	162	4	)	)	PUNCT
cana-951	162	5	)	)	PUNCT
cana-951	162	6	;	;	PUNCT
cana-951	162	7	μ	μ	PROPN
cana-951	162	8	>	>	X
cana-951	162	9	0	0	PUNCT
cana-951	162	10	(	(	PUNCT
cana-951	162	11	46	46	NUM
cana-951	162	12	)	)	PUNCT
cana-951	162	13	the	the	DET
cana-951	162	14	bright	bright	ADJ
cana-951	162	15	solitary	solitary	ADJ
cana-951	162	16	wave	wave	NOUN
cana-951	162	17	solution	solution	NOUN
cana-951	162	18	of	of	ADP
cana-951	162	19	eq.(27	eq.(27	PROPN
cana-951	162	20	)	)	PUNCT
cana-951	162	21	are	be	AUX
cana-951	162	22	given	give	VERB
cana-951	162	23	by	by	ADP
cana-951	162	24	a±4(z	a±4(z	PROPN
cana-951	162	25	,	,	PUNCT
cana-951	162	26	t̃	t̃	PROPN
cana-951	162	27	)	)	PUNCT
cana-951	162	28	=	=	SYM
cana-951	162	29	b1sec(√−μξ	b1sec(√−μξ	X
cana-951	162	30	+	+	X
cana-951	162	31	ξ0	ξ0	NUM
cana-951	162	32	)	)	PUNCT
cana-951	162	33	.	.	PUNCT
cana-951	163	1	exp{ia±(z	exp{ia±(z	PROPN
cana-951	163	2	,	,	PUNCT
cana-951	163	3	t̃)[t̃	t̃)[t̃	PROPN
cana-951	163	4	2	2	NUM
cana-951	163	5	+	+	NOUN
cana-951	163	6	c1t̃	c1t̃	NOUN
cana-951	163	7	+	+	CCONJ
cana-951	163	8	(	(	PUNCT
cana-951	163	9	c1	c1	PROPN
cana-951	163	10	2	2	NUM
cana-951	163	11	−	−	NOUN
cana-951	163	12	2μc2	2μc2	NUM
cana-951	163	13	2	2	NUM
cana-951	163	14	]	]	PUNCT
cana-951	163	15	}	}	PUNCT
cana-951	163	16	(	(	PUNCT
cana-951	163	17	47	47	NUM
cana-951	163	18	)	)	PUNCT
cana-951	163	19	the	the	DET
cana-951	163	20	singular	singular	ADJ
cana-951	163	21	solution	solution	NOUN
cana-951	163	22	of	of	ADP
cana-951	163	23	eq.(27	eq.(27	PROPN
cana-951	163	24	)	)	PUNCT
cana-951	163	25	are	be	AUX
cana-951	163	26	given	give	VERB
cana-951	163	27	by	by	ADP
cana-951	163	28	a±5(z	a±5(z	PROPN
cana-951	163	29	,	,	PUNCT
cana-951	163	30	t̃	t̃	PROPN
cana-951	163	31	)	)	PUNCT
cana-951	163	32	=	=	NOUN
cana-951	163	33	b1csch(√−μξ	b1csch(√−μξ	VERB
cana-951	163	34	+	+	X
cana-951	163	35	ξ0	ξ0	NUM
cana-951	163	36	)	)	PUNCT
cana-951	163	37	.	.	PUNCT
cana-951	164	1	exp{ia±(z	exp{ia±(z	PROPN
cana-951	164	2	,	,	PUNCT
cana-951	164	3	t̃)[t̃	t̃)[t̃	PROPN
cana-951	164	4	2	2	NUM
cana-951	164	5	+	+	NOUN
cana-951	164	6	c1t̃	c1t̃	NOUN
cana-951	164	7	+	+	CCONJ
cana-951	164	8	(	(	PUNCT
cana-951	164	9	c1	c1	PROPN
cana-951	164	10	2	2	NUM
cana-951	164	11	−	−	NOUN
cana-951	164	12	2μc2	2μc2	NUM
cana-951	164	13	2	2	NUM
cana-951	164	14	]	]	PUNCT
cana-951	164	15	}	}	PUNCT
cana-951	164	16	(	(	PUNCT
cana-951	164	17	48	48	NUM
cana-951	164	18	)	)	PUNCT
cana-951	164	19	the	the	DET
cana-951	164	20	triangular	triangular	NOUN
cana-951	164	21	periodic	periodic	ADJ
cana-951	164	22	solution	solution	NOUN
cana-951	164	23	of	of	ADP
cana-951	164	24	eq.(27	eq.(27	PROPN
cana-951	164	25	)	)	PUNCT
cana-951	164	26	are	be	AUX
cana-951	164	27	given	give	VERB
cana-951	164	28	by	by	ADP
cana-951	164	29	communications	communication	NOUN
cana-951	164	30	on	on	ADP
cana-951	164	31	applied	apply	VERB
cana-951	164	32	nonlinear	nonlinear	ADJ
cana-951	164	33	analysis	analysis	NOUN
cana-951	164	34	issn	issn	NOUN
cana-951	164	35	:	:	PUNCT
cana-951	164	36	1074	1074	NUM
cana-951	164	37	-	-	PUNCT
cana-951	164	38	133x	133x	NUM
cana-951	164	39	vol	vol	NOUN
cana-951	164	40	31	31	NUM
cana-951	164	41	no	no	NOUN
cana-951	164	42	.	.	PUNCT
cana-951	165	1	4s	4s	NUM
cana-951	165	2	(	(	PUNCT
cana-951	165	3	2024	2024	NUM
cana-951	165	4	)	)	PUNCT
cana-951	165	5	581	581	NUM
cana-951	165	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-951	165	7	a±6(z	a±6(z	PROPN
cana-951	165	8	,	,	PUNCT
cana-951	165	9	t̃	t̃	PROPN
cana-951	165	10	)	)	PUNCT
cana-951	165	11	=	=	NOUN
cana-951	165	12	b1csch(√−μξ	b1csch(√−μξ	VERB
cana-951	165	13	+	+	X
cana-951	165	14	ξ0	ξ0	ADJ
cana-951	165	15	)	)	PUNCT
cana-951	165	16	⋅	⋅	PROPN
cana-951	165	17	exp{ia±(z	exp{ia±(z	PROPN
cana-951	165	18	,	,	PUNCT
cana-951	165	19	t̃)[t̃	t̃)[t̃	PROPN
cana-951	165	20	2	2	NUM
cana-951	165	21	+	+	NOUN
cana-951	165	22	c1t̃	c1t̃	NOUN
cana-951	165	23	+	+	CCONJ
cana-951	165	24	(	(	PUNCT
cana-951	165	25	c1	c1	PROPN
cana-951	165	26	2	2	NUM
cana-951	165	27	−	−	NOUN
cana-951	165	28	2μc2	2μc2	NUM
cana-951	165	29	2	2	NUM
cana-951	165	30	]	]	PUNCT
cana-951	165	31	}	}	PUNCT
cana-951	165	32	(	(	PUNCT
cana-951	165	33	49	49	NUM
cana-951	165	34	)	)	PUNCT
cana-951	165	35	fig.3	fig.3	PROPN
cana-951	165	36	.	.	PROPN
cana-951	166	1	numerical	numerical	PROPN
cana-951	166	2	simulation	simulation	PROPN
cana-951	166	3	of	of	ADP
cana-951	166	4	rcp	rcp	PROPN
cana-951	166	5	amplitude	amplitude	NOUN
cana-951	166	6	a+4(z	a+4(z	PROPN
cana-951	166	7	,	,	PUNCT
cana-951	166	8	t̃	t̃	PROPN
cana-951	166	9	)	)	PUNCT
cana-951	166	10	for	for	ADP
cana-951	166	11	the	the	DET
cana-951	166	12	first	first	ADJ
cana-951	166	13	case	case	NOUN
cana-951	166	14	of	of	ADP
cana-951	166	15	solutions	solution	NOUN
cana-951	166	16	where	where	SCONJ
cana-951	166	17	:	:	PUNCT
cana-951	166	18	c1=3	c1=3	PROPN
cana-951	166	19	,	,	PUNCT
cana-951	166	20	c2=4	c2=4	PROPN
cana-951	166	21	,	,	PUNCT
cana-951	166	22	c3=5	c3=5	PROPN
cana-951	166	23	ξ0	ξ0	PROPN
cana-951	166	24	=	=	NOUN
cana-951	166	25	1	1	NUM
cana-951	166	26	;	;	PUNCT
cana-951	166	27	μ=-1/2	μ=-1/2	NOUN
cana-951	166	28	,	,	PUNCT
cana-951	166	29	a1	a1	PROPN
cana-951	166	30	=3	=3	PROPN
cana-951	166	31	,	,	PUNCT
cana-951	166	32	b1=3	b1=3	PROPN
cana-951	166	33	,	,	PUNCT
cana-951	166	34	μr	μr	NOUN
cana-951	166	35	=	=	SYM
cana-951	166	36	1.4	1.4	NUM
cana-951	166	37	,	,	PUNCT
cana-951	166	38	εr	εr	AUX
cana-951	166	39	=	=	SYM
cana-951	166	40	5.2	5.2	NUM
cana-951	166	41	,	,	PUNCT
cana-951	166	42	γ	γ	X
cana-951	166	43	=	=	SYM
cana-951	166	44	0.5	0.5	NUM
cana-951	166	45	,	,	PUNCT
cana-951	166	46	κ	κ	X
cana-951	166	47	=	=	NOUN
cana-951	166	48	0.5,γkerr	0.5,γkerr	NUM
cana-951	166	49	=	=	SYM
cana-951	166	50	2.58	2.58	NUM
cana-951	166	51	×	×	NOUN
cana-951	166	52	10−17	10−17	NUM
cana-951	166	53	κkerr	κkerr	NOUN
cana-951	166	54	=	=	PUNCT
cana-951	166	55	3.58	3.58	NUM
cana-951	166	56	×	×	NOUN
cana-951	166	57	10−17	10−17	NUM
cana-951	166	58	.	.	PUNCT
cana-951	166	59	.	.	PUNCT
cana-951	167	1	fig.4	fig.4	PROPN
cana-951	167	2	.	.	PROPN
cana-951	167	3	numerical	numerical	PROPN
cana-951	167	4	simulation	simulation	PROPN
cana-951	167	5	of	of	ADP
cana-951	167	6	lcp	lcp	PROPN
cana-951	167	7	amplitude	amplitude	NOUN
cana-951	167	8	a−4(z	a−4(z	PROPN
cana-951	167	9	,	,	PUNCT
cana-951	167	10	t̃	t̃	PROPN
cana-951	167	11	)	)	PUNCT
cana-951	167	12	for	for	ADP
cana-951	167	13	the	the	DET
cana-951	167	14	first	first	ADJ
cana-951	167	15	case	case	NOUN
cana-951	167	16	of	of	ADP
cana-951	167	17	solutions	solution	NOUN
cana-951	167	18	where	where	SCONJ
cana-951	167	19	:	:	PUNCT
cana-951	167	20	c1=3	c1=3	PROPN
cana-951	167	21	,	,	PUNCT
cana-951	167	22	c2=4	c2=4	PROPN
cana-951	167	23	,	,	PUNCT
cana-951	167	24	c3=5	c3=5	PROPN
cana-951	167	25	ξ0	ξ0	PROPN
cana-951	167	26	=	=	NOUN
cana-951	167	27	1	1	NUM
cana-951	167	28	;	;	PUNCT
cana-951	167	29	μ=-1/2	μ=-1/2	NOUN
cana-951	167	30	,	,	PUNCT
cana-951	167	31	a1	a1	PROPN
cana-951	167	32	=3	=3	PROPN
cana-951	167	33	,	,	PUNCT
cana-951	167	34	b1=3	b1=3	PROPN
cana-951	167	35	,	,	PUNCT
cana-951	167	36	μr	μr	NOUN
cana-951	167	37	=	=	SYM
cana-951	167	38	1.4	1.4	NUM
cana-951	167	39	,	,	PUNCT
cana-951	167	40	εr	εr	NOUN
cana-951	167	41	=	=	SYM
cana-951	167	42	5.2	5.2	NUM
cana-951	167	43	,	,	PUNCT
cana-951	167	44	γ	γ	X
cana-951	167	45	=	=	SYM
cana-951	167	46	0.5	0.5	NUM
cana-951	167	47	,	,	PUNCT
cana-951	167	48	κ	κ	X
cana-951	167	49	=	=	NOUN
cana-951	167	50	0.5,γkerr	0.5,γkerr	NUM
cana-951	167	51	=	=	SYM
cana-951	167	52	2.58	2.58	NUM
cana-951	167	53	×	×	NOUN
cana-951	167	54	10−17	10−17	NUM
cana-951	167	55	κkerr	κkerr	NOUN
cana-951	167	56	=	=	PUNCT
cana-951	167	57	3.58	3.58	NUM
cana-951	167	58	×	×	NOUN
cana-951	167	59	10−17	10−17	NUM
cana-951	167	60	.	.	PUNCT
cana-951	168	1	communications	communication	NOUN
cana-951	168	2	on	on	ADP
cana-951	168	3	applied	apply	VERB
cana-951	168	4	nonlinear	nonlinear	ADJ
cana-951	168	5	analysis	analysis	NOUN
cana-951	168	6	issn	issn	NOUN
cana-951	168	7	:	:	PUNCT
cana-951	168	8	1074	1074	NUM
cana-951	168	9	-	-	PUNCT
cana-951	168	10	133x	133x	NUM
cana-951	168	11	vol	vol	NOUN
cana-951	168	12	31	31	NUM
cana-951	168	13	no	no	NOUN
cana-951	168	14	.	.	PUNCT
cana-951	169	1	4s	4s	NUM
cana-951	169	2	(	(	PUNCT
cana-951	169	3	2024	2024	NUM
cana-951	169	4	)	)	PUNCT
cana-951	169	5	582	582	NUM
cana-951	169	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-951	169	7	case	case	NOUN
cana-951	169	8	3	3	NUM
cana-951	169	9	a0	a0	NOUN
cana-951	169	10	=	=	SYM
cana-951	169	11	0	0	PROPN
cana-951	169	12	,	,	PUNCT
cana-951	169	13	a1	a1	NOUN
cana-951	169	14	=	=	SYM
cana-951	169	15	a1	a1	NOUN
cana-951	169	16	,	,	PUNCT
cana-951	169	17	b1	b1	NOUN
cana-951	169	18	=	=	SYM
cana-951	169	19	b1	b1	PROPN
cana-951	169	20	,	,	PUNCT
cana-951	169	21	p±(z	p±(z	NOUN
cana-951	169	22	)	)	PUNCT
cana-951	169	23	=	=	SYM
cana-951	169	24	c2a±(z	c2a±(z	NOUN
cana-951	169	25	)	)	PUNCT
cana-951	169	26	(	(	PUNCT
cana-951	169	27	50	50	NUM
cana-951	169	28	)	)	PUNCT
cana-951	169	29	q±(z	q±(z	PROPN
cana-951	169	30	)	)	PUNCT
cana-951	169	31	=	=	SYM
cana-951	169	32	1	1	NUM
cana-951	169	33	2	2	NUM
cana-951	169	34	c1c2a±(z	c1c2a±(z	NOUN
cana-951	169	35	)	)	PUNCT
cana-951	169	36	+	+	CCONJ
cana-951	169	37	c3	c3	PROPN
cana-951	169	38	;	;	PUNCT
cana-951	169	39	b±(z	b±(z	PROPN
cana-951	169	40	)	)	PUNCT
cana-951	169	41	=	=	SYM
cana-951	169	42	c1a±(z	c1a±(z	PROPN
cana-951	169	43	)	)	PUNCT
cana-951	169	44	(	(	PUNCT
cana-951	169	45	51	51	NUM
cana-951	169	46	)	)	PUNCT
cana-951	169	47	c±(z	c±(z	PROPN
cana-951	169	48	)	)	PUNCT
cana-951	169	49	=	=	SYM
cana-951	169	50	1	1	NUM
cana-951	169	51	8	8	NUM
cana-951	169	52	(	(	PUNCT
cana-951	169	53	c1	c1	NOUN
cana-951	169	54	2	2	NUM
cana-951	169	55	−	−	PROPN
cana-951	169	56	2μc2	2μc2	NUM
cana-951	169	57	2)a±(z	2)a±(z	NOUN
cana-951	169	58	)	)	PUNCT
cana-951	169	59	+	+	CCONJ
cana-951	169	60	c1	c1	NOUN
cana-951	169	61	(	(	PUNCT
cana-951	169	62	52	52	NUM
cana-951	169	63	)	)	PUNCT
cana-951	169	64	−a±(z)β±2(z	−a±(z)β±2(z	NUM
cana-951	169	65	)	)	PUNCT
cana-951	169	66	=	=	SYM
cana-951	169	67	1	1	NUM
cana-951	169	68	;	;	PUNCT
cana-951	169	69	ρ±(z	ρ±(z	PROPN
cana-951	169	70	)	)	PUNCT
cana-951	169	71	=	=	SYM
cana-951	169	72	c1	c1	PROPN
cana-951	169	73	2β±2(z)a±	2β±2(z)a±	NUM
cana-951	169	74	2(z	2(z	NUM
cana-951	169	75	)	)	PUNCT
cana-951	169	76	4b1	4b1	NUM
cana-951	169	77	2	2	NUM
cana-951	169	78	(	(	PUNCT
cana-951	169	79	53	53	NUM
cana-951	169	80	)	)	PUNCT
cana-951	169	81	where	where	SCONJ
cana-951	169	82	a±(z	a±(z	NOUN
cana-951	169	83	)	)	PUNCT
cana-951	169	84	satisfies	satisfy	VERB
cana-951	169	85	the	the	DET
cana-951	169	86	following	follow	VERB
cana-951	169	87	condition	condition	NOUN
cana-951	169	88	a±(z)[−2∫	a±(z)[−2∫	X
cana-951	169	89	β±2(z)dz	β±2(z)dz	NOUN
cana-951	169	90	+	+	CCONJ
cana-951	169	91	c5	c5	PROPN
cana-951	169	92	]	]	X
cana-951	169	93	=	=	SYM
cana-951	169	94	1	1	NUM
cana-951	169	95	(	(	PUNCT
cana-951	169	96	54	54	NUM
cana-951	169	97	)	)	PUNCT
cana-951	169	98	in	in	ADP
cana-951	169	99	this	this	DET
cana-951	169	100	case	case	NOUN
cana-951	169	101	we	we	PRON
cana-951	169	102	have	have	VERB
cana-951	169	103	to	to	PART
cana-951	169	104	type	type	VERB
cana-951	169	105	of	of	ADP
cana-951	169	106	exact	exact	ADJ
cana-951	169	107	solutions	solution	NOUN
cana-951	169	108	for	for	ADP
cana-951	169	109	the	the	DET
cana-951	169	110	eq.(27	eq.(27	PROPN
cana-951	169	111	)	)	PUNCT
cana-951	170	1	•	•	ADP
cana-951	170	2	μ	μ	PROPN
cana-951	170	3	<	<	X
cana-951	170	4	0	0	NUM
cana-951	170	5	,	,	PUNCT
cana-951	170	6	the	the	DET
cana-951	170	7	hyperbolic	hyperbolic	ADJ
cana-951	170	8	solutions	solution	NOUN
cana-951	170	9	are	be	AUX
cana-951	170	10	defined	define	VERB
cana-951	170	11	by	by	ADP
cana-951	170	12	a±7(z	a±7(z	NOUN
cana-951	170	13	,	,	PUNCT
cana-951	170	14	t̃	t̃	PROPN
cana-951	170	15	)	)	PUNCT
cana-951	170	16	=	=	SYM
cana-951	171	1	√−μa1	√−μa1	CCONJ
cana-951	171	2	[	[	PUNCT
cana-951	171	3	a1sinh√−μξ+a2cosh√−μξ	a1sinh√−μξ+a2cosh√−μξ	NOUN
cana-951	171	4	a1cosh√−μξ+a2sinh√−μξ	a1cosh√−μξ+a2sinh√−μξ	VERB
cana-951	171	5	∓	∓	PROPN
cana-951	171	6	i√	i√	PROPN
cana-951	171	7	(	(	PUNCT
cana-951	171	8	a1sinh√−μξ+a2cosh√−μξ	a1sinh√−μξ+a2cosh√−μξ	NOUN
cana-951	171	9	a1cosh√−μξ+a2sinh√−μξ	a1cosh√−μξ+a2sinh√−μξ	NOUN
cana-951	171	10	)	)	PUNCT
cana-951	171	11	2	2	NUM
cana-951	171	12	]	]	PUNCT
cana-951	171	13	.	.	PUNCT
cana-951	172	1	exp[iθ±(z	exp[iθ±(z	PROPN
cana-951	172	2	,	,	PUNCT
cana-951	172	3	t̃	t̃	PROPN
cana-951	172	4	)	)	PUNCT
cana-951	172	5	]	]	PUNCT
cana-951	172	6	(	(	PUNCT
cana-951	172	7	55	55	NUM
cana-951	172	8	)	)	PUNCT
cana-951	172	9	•	•	NOUN
cana-951	172	10	if	if	SCONJ
cana-951	172	11	μ	μ	PROPN
cana-951	172	12	<	<	X
cana-951	172	13	0	0	NUM
cana-951	172	14	,	,	PUNCT
cana-951	172	15	cothξ0	cothξ0	NOUN
cana-951	172	16	=	=	SYM
cana-951	172	17	a2	a2	PROPN
cana-951	172	18	a1	a1	NOUN
cana-951	172	19	,	,	PUNCT
cana-951	172	20	|	|	ADV
cana-951	172	21	a1	a1	NOUN
cana-951	172	22	a2	a2	PROPN
cana-951	172	23	|	|	ADV
cana-951	172	24	>	>	X
cana-951	172	25	1,then	1,then	NUM
cana-951	172	26	the	the	DET
cana-951	172	27	bright	bright	ADJ
cana-951	172	28	-	-	PUNCT
cana-951	172	29	dark	dark	NOUN
cana-951	172	30	soliton	soliton	NOUN
cana-951	172	31	of	of	ADP
cana-951	172	32	eq.(27	eq.(27	PROPN
cana-951	172	33	)	)	PUNCT
cana-951	172	34	are	be	AUX
cana-951	172	35	derived	derive	VERB
cana-951	172	36	as	as	ADP
cana-951	172	37	,	,	PUNCT
cana-951	172	38	a±7,1(z	a±7,1(z	PROPN
cana-951	172	39	,	,	PUNCT
cana-951	172	40	t̃	t̃	PROPN
cana-951	172	41	)	)	PUNCT
cana-951	173	1	=	=	NOUN
cana-951	173	2	√−μa1[tanh√−μξ	√−μa1[tanh√−μξ	NOUN
cana-951	173	3	+	+	X
cana-951	173	4	ξ0	ξ0	NOUN
cana-951	173	5	]	]	X
cana-951	173	6	=	=	PUNCT
cana-951	173	7	∓isec(√−μξ	∓isec(√−μξ	PROPN
cana-951	174	1	+	+	CCONJ
cana-951	174	2	ξ0	ξ0	PROPN
cana-951	174	3	)	)	PUNCT
cana-951	174	4	.	.	PUNCT
cana-951	175	1	exp[iθ±(z	exp[iθ±(z	PROPN
cana-951	175	2	,	,	PUNCT
cana-951	175	3	t̃	t̃	PROPN
cana-951	175	4	)	)	PUNCT
cana-951	175	5	]	]	PUNCT
cana-951	175	6	(	(	PUNCT
cana-951	175	7	56	56	NUM
cana-951	175	8	)	)	PUNCT
cana-951	175	9	•	•	NOUN
cana-951	175	10	if	if	SCONJ
cana-951	175	11	μ	μ	PROPN
cana-951	175	12	<	<	X
cana-951	175	13	0	0	NUM
cana-951	175	14	,	,	PUNCT
cana-951	175	15	cothξ0	cothξ0	NOUN
cana-951	175	16	=	=	SYM
cana-951	175	17	a2	a2	PROPN
cana-951	175	18	a1	a1	NOUN
cana-951	175	19	,	,	PUNCT
cana-951	175	20	|	|	ADV
cana-951	175	21	a1	a1	NOUN
cana-951	175	22	a2	a2	NOUN
cana-951	175	23	|	|	ADV
cana-951	175	24	<	<	X
cana-951	175	25	1,then	1,then	NUM
cana-951	175	26	the	the	DET
cana-951	175	27	solution	solution	NOUN
cana-951	175	28	of	of	ADP
cana-951	175	29	eq.(27	eq.(27	PROPN
cana-951	175	30	)	)	PUNCT
cana-951	175	31	becomes	become	VERB
cana-951	175	32	a±7,2(z	a±7,2(z	NOUN
cana-951	175	33	,	,	PUNCT
cana-951	175	34	t̃	t̃	PROPN
cana-951	175	35	)	)	PUNCT
cana-951	175	36	=	=	NOUN
cana-951	175	37	√−μa1[coth√−μξ	√−μa1[coth√−μξ	NOUN
cana-951	175	38	+	+	CCONJ
cana-951	175	39	ξ0	ξ0	ADJ
cana-951	175	40	]	]	X
cana-951	175	41	=	=	SYM
cana-951	175	42	±csch(√−μξ	±csch(√−μξ	PROPN
cana-951	175	43	+	+	CCONJ
cana-951	175	44	ξ0	ξ0	PROPN
cana-951	175	45	)	)	PUNCT
cana-951	175	46	.	.	PUNCT
cana-951	176	1	exp[iθ±(z	exp[iθ±(z	PROPN
cana-951	176	2	,	,	PUNCT
cana-951	176	3	t̃	t̃	PROPN
cana-951	176	4	)	)	PUNCT
cana-951	176	5	]	]	PUNCT
cana-951	176	6	(	(	PUNCT
cana-951	176	7	57	57	NUM
cana-951	176	8	)	)	PUNCT
cana-951	176	9	•	•	NUM
cana-951	176	10	μ	μ	PROPN
cana-951	176	11	>	>	X
cana-951	176	12	0	0	PUNCT
cana-951	177	1	the	the	DET
cana-951	177	2	triangular	triangular	ADJ
cana-951	177	3	periodic	periodic	ADJ
cana-951	177	4	sulution	sulution	NOUN
cana-951	177	5	are	be	AUX
cana-951	177	6	given	give	VERB
cana-951	177	7	by	by	ADP
cana-951	177	8	a±8(z	a±8(z	PROPN
cana-951	177	9	,	,	PUNCT
cana-951	177	10	t̃	t̃	PROPN
cana-951	177	11	)	)	PUNCT
cana-951	177	12	=	=	SYM
cana-951	178	1	√−μa1	√−μa1	CCONJ
cana-951	178	2	[	[	PUNCT
cana-951	178	3	a1cos√−μξ+a2sin√−μξ	a1cos√−μξ+a2sin√−μξ	VERB
cana-951	178	4	a1cos√−μξ+a2sin√−μξ	a1cos√−μξ+a2sin√−μξ	PROPN
cana-951	178	5	∓	∓	NOUN
cana-951	178	6	i√	i√	ADV
cana-951	178	7	(	(	PUNCT
cana-951	178	8	a1cos√−μξ+a2sin√−μξ	a1cos√−μξ+a2sin√−μξ	PART
cana-951	178	9	a1cos√−μξ+a2sin√−μξ	a1cos√−μξ+a2sin√−μξ	PROPN
cana-951	178	10	)	)	PUNCT
cana-951	178	11	2	2	NUM
cana-951	178	12	]	]	PUNCT
cana-951	178	13	.	.	PUNCT
cana-951	179	1	exp[iθ±(z	exp[iθ±(z	PROPN
cana-951	179	2	,	,	PUNCT
cana-951	179	3	t̃	t̃	PROPN
cana-951	179	4	)	)	PUNCT
cana-951	179	5	]	]	PUNCT
cana-951	180	1	(	(	PUNCT
cana-951	180	2	58	58	NUM
cana-951	180	3	)	)	PUNCT
cana-951	180	4	•	•	NOUN
cana-951	180	5	if	if	SCONJ
cana-951	180	6	μ	μ	PROPN
cana-951	180	7	>	>	X
cana-951	180	8	0	0	NUM
cana-951	180	9	,	,	PUNCT
cana-951	180	10	tanξ0	tanξ0	ADJ
cana-951	180	11	=	=	SYM
cana-951	180	12	a2	a2	NOUN
cana-951	180	13	a1	a1	NOUN
cana-951	180	14	,	,	PUNCT
cana-951	180	15	hen	hen	VERB
cana-951	180	16	the	the	DET
cana-951	180	17	solution	solution	NOUN
cana-951	180	18	of	of	ADP
cana-951	180	19	eq.(27	eq.(27	PROPN
cana-951	180	20	)	)	PUNCT
cana-951	180	21	becomes	become	VERB
cana-951	180	22	as	as	ADP
cana-951	180	23	follow	follow	VERB
cana-951	180	24	a±8,1(z	a±8,1(z	PROPN
cana-951	180	25	,	,	PUNCT
cana-951	180	26	t̃	t̃	PROPN
cana-951	180	27	)	)	PUNCT
cana-951	180	28	=	=	SYM
cana-951	180	29	√μa1[cot√μξ	√μa1[cot√μξ	NOUN
cana-951	180	30	+	+	X
cana-951	180	31	ξ0	ξ0	ADJ
cana-951	180	32	]	]	X
cana-951	180	33	=	=	PUNCT
cana-951	180	34	±csch(√μξ	±csch(√μξ	NOUN
cana-951	180	35	+	+	CCONJ
cana-951	180	36	ξ0	ξ0	ADJ
cana-951	180	37	)	)	PUNCT
cana-951	180	38	.	.	PUNCT
cana-951	181	1	exp[iθ±(z	exp[iθ±(z	PROPN
cana-951	181	2	,	,	PUNCT
cana-951	181	3	t̃	t̃	PROPN
cana-951	181	4	)	)	PUNCT
cana-951	181	5	]	]	PUNCT
cana-951	181	6	(	(	PUNCT
cana-951	181	7	59	59	NUM
cana-951	181	8	)	)	PUNCT
cana-951	181	9	where	where	SCONJ
cana-951	181	10	θ±(z	θ±(z	PROPN
cana-951	181	11	,	,	PUNCT
cana-951	181	12	t̃	t̃	PROPN
cana-951	181	13	)	)	PUNCT
cana-951	181	14	=	=	SYM
cana-951	181	15	a±(z	a±(z	PROPN
cana-951	181	16	)	)	PUNCT
cana-951	182	1	[	[	X
cana-951	182	2	t̃	t̃	PROPN
cana-951	182	3	2	2	NUM
cana-951	182	4	+	+	NOUN
cana-951	182	5	c1t̃	c1t̃	NOUN
cana-951	182	6	+	+	CCONJ
cana-951	182	7	c1	c1	PROPN
cana-951	182	8	2−2μc2	2−2μc2	NUM
cana-951	182	9	2	2	NUM
cana-951	182	10	8	8	NUM
cana-951	182	11	a±(z	a±(z	ADJ
cana-951	182	12	)	)	PUNCT
cana-951	182	13	+	+	CCONJ
cana-951	182	14	c4	c4	NOUN
cana-951	182	15	]	]	PUNCT
cana-951	182	16	(	(	PUNCT
cana-951	182	17	60	60	NUM
cana-951	182	18	)	)	PUNCT
cana-951	182	19	ξ±	ξ±	PROPN
cana-951	182	20	=	=	NOUN
cana-951	182	21	c2a±(z)t̃	c2a±(z)t̃	NOUN
cana-951	182	22	+	+	CCONJ
cana-951	182	23	1	1	NUM
cana-951	182	24	2	2	NUM
cana-951	182	25	c1c2a±(z	c1c2a±(z	NOUN
cana-951	182	26	)	)	PUNCT
cana-951	183	1	+	+	CCONJ
cana-951	183	2	c3	c3	PROPN
cana-951	183	3	(	(	PUNCT
cana-951	183	4	61	61	NUM
cana-951	183	5	)	)	PUNCT
cana-951	183	6	communications	communication	NOUN
cana-951	183	7	on	on	ADP
cana-951	183	8	applied	apply	VERB
cana-951	183	9	nonlinear	nonlinear	ADJ
cana-951	183	10	analysis	analysis	NOUN
cana-951	183	11	issn	issn	NOUN
cana-951	183	12	:	:	PUNCT
cana-951	183	13	1074	1074	NUM
cana-951	183	14	-	-	PUNCT
cana-951	183	15	133x	133x	NUM
cana-951	183	16	vol	vol	NOUN
cana-951	183	17	31	31	NUM
cana-951	183	18	no	no	NOUN
cana-951	183	19	.	.	PUNCT
cana-951	184	1	4s	4s	NUM
cana-951	184	2	(	(	PUNCT
cana-951	184	3	2024	2024	NUM
cana-951	184	4	)	)	PUNCT
cana-951	185	1	583	583	NUM
cana-951	185	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-951	185	3	fig.5	fig.5	PROPN
cana-951	185	4	.	.	PUNCT
cana-951	185	5	numerical	numerical	PROPN
cana-951	185	6	simulation	simulation	PROPN
cana-951	185	7	of	of	ADP
cana-951	185	8	rcp	rcp	VERB
cana-951	185	9	amplitude	amplitude	NOUN
cana-951	185	10	a+7(z	a+7(z	NOUN
cana-951	185	11	,	,	PUNCT
cana-951	185	12	t̃	t̃	PROPN
cana-951	185	13	)	)	PUNCT
cana-951	185	14	for	for	ADP
cana-951	185	15	the	the	DET
cana-951	185	16	first	first	ADJ
cana-951	185	17	case	case	NOUN
cana-951	185	18	of	of	ADP
cana-951	185	19	solutions	solution	NOUN
cana-951	185	20	where	where	SCONJ
cana-951	185	21	:	:	PUNCT
cana-951	185	22	c1=3	c1=3	PROPN
cana-951	185	23	,	,	PUNCT
cana-951	185	24	c2=4	c2=4	PROPN
cana-951	185	25	,	,	PUNCT
cana-951	185	26	c3=5	c3=5	PROPN
cana-951	185	27	ξ0	ξ0	PROPN
cana-951	185	28	=	=	NOUN
cana-951	185	29	1	1	NUM
cana-951	185	30	;	;	PUNCT
cana-951	185	31	μ=-1/2	μ=-1/2	NOUN
cana-951	185	32	,	,	PUNCT
cana-951	185	33	a1	a1	PROPN
cana-951	185	34	=3	=3	PROPN
cana-951	185	35	,	,	PUNCT
cana-951	185	36	b1=3	b1=3	PROPN
cana-951	185	37	,	,	PUNCT
cana-951	185	38	μr	μr	NOUN
cana-951	185	39	=	=	SYM
cana-951	185	40	1.4	1.4	NUM
cana-951	185	41	,	,	PUNCT
cana-951	185	42	εr	εr	NOUN
cana-951	185	43	=	=	SYM
cana-951	185	44	5.2	5.2	NUM
cana-951	185	45	,	,	PUNCT
cana-951	185	46	γ	γ	X
cana-951	185	47	=	=	SYM
cana-951	185	48	0.5	0.5	NUM
cana-951	185	49	,	,	PUNCT
cana-951	185	50	κ	κ	X
cana-951	185	51	=	=	NOUN
cana-951	185	52	0.5,γkerr	0.5,γkerr	NUM
cana-951	185	53	=	=	SYM
cana-951	185	54	2.58	2.58	NUM
cana-951	185	55	×	×	NOUN
cana-951	185	56	10−17	10−17	NUM
cana-951	185	57	κkerr	κkerr	NOUN
cana-951	185	58	=	=	PUNCT
cana-951	185	59	3.58	3.58	NUM
cana-951	185	60	×	×	NOUN
cana-951	185	61	10−17	10−17	NUM
cana-951	185	62	.	.	PUNCT
cana-951	186	1	fig.5	fig.5	PROPN
cana-951	186	2	.	.	PUNCT
cana-951	186	3	numerical	numerical	PROPN
cana-951	186	4	simulation	simulation	PROPN
cana-951	186	5	of	of	ADP
cana-951	186	6	lcp	lcp	PROPN
cana-951	186	7	amplitude	amplitude	NOUN
cana-951	186	8	a−7(z	a−7(z	NOUN
cana-951	186	9	,	,	PUNCT
cana-951	186	10	t̃	t̃	PROPN
cana-951	186	11	)	)	PUNCT
cana-951	186	12	for	for	ADP
cana-951	186	13	the	the	DET
cana-951	186	14	first	first	ADJ
cana-951	186	15	case	case	NOUN
cana-951	186	16	of	of	ADP
cana-951	186	17	solutions	solution	NOUN
cana-951	186	18	where	where	SCONJ
cana-951	186	19	:	:	PUNCT
cana-951	186	20	c1=3	c1=3	PROPN
cana-951	186	21	,	,	PUNCT
cana-951	186	22	c2=4	c2=4	PROPN
cana-951	186	23	,	,	PUNCT
cana-951	186	24	c3=5	c3=5	PROPN
cana-951	186	25	ξ0	ξ0	PROPN
cana-951	186	26	=	=	NOUN
cana-951	186	27	1	1	NUM
cana-951	186	28	;	;	PUNCT
cana-951	186	29	μ=-1/2	μ=-1/2	NOUN
cana-951	186	30	,	,	PUNCT
cana-951	186	31	a1	a1	PROPN
cana-951	186	32	=3	=3	PROPN
cana-951	186	33	,	,	PUNCT
cana-951	186	34	b1=3	b1=3	PROPN
cana-951	186	35	,	,	PUNCT
cana-951	186	36	μr	μr	NOUN
cana-951	186	37	=	=	SYM
cana-951	186	38	1.4	1.4	NUM
cana-951	186	39	,	,	PUNCT
cana-951	186	40	εr	εr	NOUN
cana-951	186	41	=	=	SYM
cana-951	186	42	5.2	5.2	NUM
cana-951	186	43	,	,	PUNCT
cana-951	186	44	γ	γ	X
cana-951	186	45	=	=	SYM
cana-951	186	46	0.5	0.5	NUM
cana-951	186	47	,	,	PUNCT
cana-951	186	48	κ	κ	X
cana-951	186	49	=	=	NOUN
cana-951	186	50	0.5,γkerr	0.5,γkerr	NUM
cana-951	186	51	=	=	SYM
cana-951	186	52	2.58	2.58	NUM
cana-951	186	53	×	×	NOUN
cana-951	186	54	10−17	10−17	NUM
cana-951	186	55	κkerr	κkerr	NOUN
cana-951	186	56	=	=	PUNCT
cana-951	186	57	3.58	3.58	NUM
cana-951	186	58	×	×	NOUN
cana-951	186	59	10−17	10−17	NUM
cana-951	186	60	.	.	PUNCT
cana-951	187	1	in	in	ADP
cana-951	187	2	the	the	DET
cana-951	187	3	following	follow	VERB
cana-951	187	4	figures	figure	NOUN
cana-951	187	5	1	1	NUM
cana-951	187	6	-	-	SYM
cana-951	187	7	6	6	NUM
cana-951	187	8	,	,	PUNCT
cana-951	187	9	the	the	DET
cana-951	187	10	different	different	ADJ
cana-951	187	11	exact	exact	ADJ
cana-951	187	12	families	family	NOUN
cana-951	187	13	of	of	ADP
cana-951	187	14	solutions	solution	NOUN
cana-951	187	15	were	be	AUX
cana-951	187	16	obtained	obtain	VERB
cana-951	187	17	and	and	CCONJ
cana-951	187	18	we	we	PRON
cana-951	187	19	take	take	VERB
cana-951	187	20	as	as	ADP
cana-951	187	21	an	an	DET
cana-951	187	22	example	example	NOUN
cana-951	187	23	some	some	DET
cana-951	187	24	graphs	graph	NOUN
cana-951	187	25	for	for	ADP
cana-951	187	26	the	the	DET
cana-951	187	27	solutions	solution	NOUN
cana-951	187	28	of	of	ADP
cana-951	187	29	case	case	NOUN
cana-951	187	30	1	1	NUM
cana-951	187	31	,	,	PUNCT
cana-951	187	32	case	case	NOUN
cana-951	187	33	2	2	NUM
cana-951	187	34	,	,	PUNCT
cana-951	187	35	and	and	CCONJ
cana-951	187	36	case	case	NOUN
cana-951	187	37	3	3	NUM
cana-951	187	38	with	with	ADP
cana-951	187	39	two	two	NUM
cana-951	187	40	modes	mode	NOUN
cana-951	187	41	of	of	ADP
cana-951	187	42	communications	communication	NOUN
cana-951	187	43	on	on	ADP
cana-951	187	44	applied	apply	VERB
cana-951	187	45	nonlinear	nonlinear	ADJ
cana-951	187	46	analysis	analysis	NOUN
cana-951	187	47	issn	issn	NOUN
cana-951	187	48	:	:	PUNCT
cana-951	187	49	1074	1074	NUM
cana-951	187	50	-	-	PUNCT
cana-951	187	51	133x	133x	NUM
cana-951	187	52	vol	vol	NOUN
cana-951	187	53	31	31	NUM
cana-951	187	54	no	no	NOUN
cana-951	187	55	.	.	PUNCT
cana-951	188	1	4s	4s	NUM
cana-951	188	2	(	(	PUNCT
cana-951	188	3	2024	2024	NUM
cana-951	188	4	)	)	PUNCT
cana-951	188	5	584	584	NUM
cana-951	188	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-951	188	7	propagation	propagation	NOUN
cana-951	188	8	(	(	PUNCT
cana-951	188	9	rcp	rcp	PROPN
cana-951	188	10	)	)	PUNCT
cana-951	188	11	and	and	CCONJ
cana-951	188	12	(	(	PUNCT
cana-951	188	13	lcp	lcp	PROPN
cana-951	188	14	)	)	PUNCT
cana-951	188	15	.	.	PUNCT
cana-951	189	1	the	the	DET
cana-951	189	2	extended	extended	ADJ
cana-951	189	3	g'/g	g'/g	ADJ
cana-951	189	4	-	-	PUNCT
cana-951	189	5	expansion	expansion	NOUN
cana-951	189	6	method	method	NOUN
cana-951	189	7	has	have	AUX
cana-951	189	8	been	be	AUX
cana-951	189	9	used	use	VERB
cana-951	189	10	to	to	PART
cana-951	189	11	present	present	VERB
cana-951	189	12	an	an	DET
cana-951	189	13	analytic	analytic	ADJ
cana-951	189	14	study	study	NOUN
cana-951	189	15	of	of	ADP
cana-951	189	16	the	the	DET
cana-951	189	17	generalized	generalized	ADJ
cana-951	189	18	nonlinear	nonlinear	ADJ
cana-951	189	19	schrödinger	schrödinger	ADJ
cana-951	189	20	equation	equation	NOUN
cana-951	189	21	in	in	ADP
cana-951	189	22	bi	bi	ADJ
cana-951	189	23	-	-	ADJ
cana-951	189	24	isotropic	isotropic	ADJ
cana-951	189	25	(	(	PUNCT
cana-951	189	26	chiral	chiral	ADJ
cana-951	189	27	and	and	CCONJ
cana-951	189	28	nonreciprocal	nonreciprocal	ADJ
cana-951	189	29	)	)	PUNCT
cana-951	189	30	.	.	PUNCT
cana-951	190	1	optical	optical	ADJ
cana-951	190	2	fibers	fiber	NOUN
cana-951	190	3	.	.	PUNCT
cana-951	191	1	the	the	DET
cana-951	191	2	method	method	NOUN
cana-951	191	3	is	be	AUX
cana-951	191	4	constructed	construct	VERB
cana-951	191	5	on	on	ADP
cana-951	191	6	a	a	DET
cana-951	191	7	perturbation	perturbation	NOUN
cana-951	191	8	expansion	expansion	NOUN
cana-951	191	9	in	in	ADP
cana-951	191	10	powers	power	NOUN
cana-951	191	11	of	of	ADP
cana-951	191	12	a	a	DET
cana-951	191	13	dimensionless	dimensionless	NOUN
cana-951	191	14	parameter	parameter	NOUN
cana-951	191	15	,	,	PUNCT
cana-951	191	16	which	which	PRON
cana-951	191	17	allows	allow	VERB
cana-951	191	18	for	for	ADP
cana-951	191	19	the	the	DET
cana-951	191	20	inclusion	inclusion	NOUN
cana-951	191	21	of	of	ADP
cana-951	191	22	varying	vary	VERB
cana-951	191	23	dispersion	dispersion	NOUN
cana-951	191	24	and	and	CCONJ
cana-951	191	25	nonlinearity	nonlinearity	NOUN
cana-951	191	26	.	.	PUNCT
cana-951	192	1	this	this	DET
cana-951	192	2	types	type	NOUN
cana-951	192	3	the	the	DET
cana-951	192	4	method	method	NOUN
cana-951	192	5	well	well	ADV
cana-951	192	6	-	-	PUNCT
cana-951	192	7	suited	suited	ADJ
cana-951	192	8	for	for	ADP
cana-951	192	9	modeling	model	VERB
cana-951	192	10	a	a	DET
cana-951	192	11	wide	wide	ADJ
cana-951	192	12	range	range	NOUN
cana-951	192	13	of	of	ADP
cana-951	192	14	optical	optical	ADJ
cana-951	192	15	fibres	fibre	NOUN
cana-951	192	16	,	,	PUNCT
cana-951	192	17	including	include	VERB
cana-951	192	18	those	those	PRON
cana-951	192	19	with	with	ADP
cana-951	192	20	complex	complex	ADJ
cana-951	192	21	dispersion	dispersion	NOUN
cana-951	192	22	and	and	CCONJ
cana-951	192	23	nonlinearity	nonlinearity	NOUN
cana-951	192	24	profiles	profile	NOUN
cana-951	192	25	.	.	PUNCT
cana-951	193	1	the	the	DET
cana-951	193	2	method	method	NOUN
cana-951	193	3	was	be	AUX
cana-951	193	4	used	use	VERB
cana-951	193	5	to	to	PART
cana-951	193	6	find	find	VERB
cana-951	193	7	exact	exact	ADJ
cana-951	193	8	different	different	ADJ
cana-951	193	9	families	family	NOUN
cana-951	193	10	of	of	ADP
cana-951	193	11	solutions	solution	NOUN
cana-951	193	12	of	of	ADP
cana-951	193	13	the	the	DET
cana-951	193	14	nonlinear	nonlinear	ADJ
cana-951	193	15	schrödinger	schrödinger	ADJ
cana-951	193	16	equation	equation	NOUN
cana-951	193	17	for	for	ADP
cana-951	193	18	a	a	DET
cana-951	193	19	bi	bi	ADJ
cana-951	193	20	-	-	ADJ
cana-951	193	21	isotropic	isotropic	ADJ
cana-951	193	22	optical	optical	ADJ
cana-951	193	23	fiber	fiber	NOUN
cana-951	193	24	.	.	PUNCT
cana-951	194	1	the	the	DET
cana-951	194	2	method	method	NOUN
cana-951	194	3	was	be	AUX
cana-951	194	4	able	able	ADJ
cana-951	194	5	to	to	PART
cana-951	194	6	accurately	accurately	ADV
cana-951	194	7	describe	describe	VERB
cana-951	194	8	the	the	DET
cana-951	194	9	propagation	propagation	NOUN
cana-951	194	10	of	of	ADP
cana-951	194	11	optical	optical	ADJ
cana-951	194	12	pulses	pulse	NOUN
cana-951	194	13	in	in	ADP
cana-951	194	14	bi	bi	ADJ
cana-951	194	15	-	-	ADJ
cana-951	194	16	isotropic	isotropic	ADJ
cana-951	194	17	(	(	PUNCT
cana-951	194	18	chiral	chiral	ADJ
cana-951	194	19	and	and	CCONJ
cana-951	194	20	non	non	ADJ
cana-951	194	21	-	-	ADJ
cana-951	194	22	reciprocal	reciprocal	ADJ
cana-951	194	23	)	)	PUNCT
cana-951	194	24	.	.	PUNCT
cana-951	195	1	fibers	fiber	NOUN
cana-951	195	2	and	and	CCONJ
cana-951	195	3	can	can	AUX
cana-951	195	4	be	be	AUX
cana-951	195	5	used	use	VERB
cana-951	195	6	to	to	PART
cana-951	195	7	predict	predict	VERB
cana-951	195	8	the	the	DET
cana-951	195	9	behavior	behavior	NOUN
cana-951	195	10	of	of	ADP
cana-951	195	11	these	these	DET
cana-951	195	12	pulses	pulse	NOUN
cana-951	195	13	under	under	ADP
cana-951	195	14	different	different	ADJ
cana-951	195	15	conditions	condition	NOUN
cana-951	195	16	.	.	PUNCT
cana-951	196	1	the	the	DET
cana-951	196	2	method	method	NOUN
cana-951	196	3	can	can	AUX
cana-951	196	4	also	also	ADV
cana-951	196	5	be	be	AUX
cana-951	196	6	used	use	VERB
cana-951	196	7	to	to	PART
cana-951	196	8	study	study	VERB
cana-951	196	9	the	the	DET
cana-951	196	10	dynamics	dynamic	NOUN
cana-951	196	11	of	of	ADP
cana-951	196	12	solitons	soliton	NOUN
cana-951	196	13	,	,	PUNCT
cana-951	196	14	including	include	VERB
cana-951	196	15	the	the	DET
cana-951	196	16	stability	stability	NOUN
cana-951	196	17	and	and	CCONJ
cana-951	196	18	interactions	interaction	NOUN
cana-951	196	19	of	of	ADP
cana-951	196	20	these	these	DET
cana-951	196	21	localized	localize	VERB
cana-951	196	22	structures	structure	NOUN
cana-951	196	23	.	.	PUNCT
cana-951	197	1	5	5	X
cana-951	197	2	.	.	X
cana-951	197	3	results	result	NOUN
cana-951	197	4	this	this	DET
cana-951	197	5	investigate	investigate	NOUN
cana-951	197	6	is	be	AUX
cana-951	197	7	concerned	concern	VERB
cana-951	197	8	with	with	ADP
cana-951	197	9	a	a	DET
cana-951	197	10	new	new	ADJ
cana-951	197	11	formulation	formulation	NOUN
cana-951	197	12	of	of	ADP
cana-951	197	13	constitutive	constitutive	ADJ
cana-951	197	14	relation	relation	NOUN
cana-951	197	15	linking	link	VERB
cana-951	197	16	to	to	ADP
cana-951	197	17	the	the	DET
cana-951	197	18	magnetic	magnetic	ADJ
cana-951	197	19	effect	effect	NOUN
cana-951	197	20	,	,	PUNCT
cana-951	197	21	to	to	PART
cana-951	197	22	understand	understand	VERB
cana-951	197	23	rigorously	rigorously	ADV
cana-951	197	24	the	the	DET
cana-951	197	25	physical	physical	ADJ
cana-951	197	26	nature	nature	NOUN
cana-951	197	27	of	of	ADP
cana-951	197	28	biisotropic	biisotropic	ADJ
cana-951	197	29	effects	effect	NOUN
cana-951	197	30	and	and	CCONJ
cana-951	197	31	to	to	PART
cana-951	197	32	generalize	generalize	VERB
cana-951	197	33	the	the	DET
cana-951	197	34	main	main	ADJ
cana-951	197	35	macroscopic	macroscopic	ADJ
cana-951	197	36	models	model	NOUN
cana-951	197	37	.	.	PUNCT
cana-951	198	1	we	we	PRON
cana-951	198	2	inferred	infer	VERB
cana-951	198	3	the	the	DET
cana-951	198	4	nonlinear	nonlinear	ADJ
cana-951	198	5	schrodinger	schrodinger	PROPN
cana-951	198	6	equation	equation	NOUN
cana-951	198	7	for	for	ADP
cana-951	198	8	a	a	DET
cana-951	198	9	bi	bi	ADJ
cana-951	198	10	-	-	ADJ
cana-951	198	11	isotropic	isotropic	ADJ
cana-951	198	12	medium	medium	ADJ
cana-951	198	13	term	term	NOUN
cana-951	198	14	with	with	ADP
cana-951	198	15	a	a	DET
cana-951	198	16	nonlinear	nonlinear	ADJ
cana-951	198	17	term	term	NOUN
cana-951	198	18	of	of	ADP
cana-951	198	19	magnetizing	magnetize	VERB
cana-951	198	20	.	.	PUNCT
cana-951	199	1	in	in	ADP
cana-951	199	2	this	this	DET
cana-951	199	3	article	article	NOUN
cana-951	199	4	,	,	PUNCT
cana-951	199	5	the	the	DET
cana-951	199	6	extended	extended	ADJ
cana-951	199	7	(	(	PUNCT
cana-951	199	8	g'/g)-expansion	g'/g)-expansion	NOUN
cana-951	199	9	method	method	NOUN
cana-951	199	10	is	be	AUX
cana-951	199	11	a	a	DET
cana-951	199	12	powerful	powerful	ADJ
cana-951	199	13	technique	technique	NOUN
cana-951	199	14	for	for	ADP
cana-951	199	15	determining	determine	VERB
cana-951	199	16	a	a	DET
cana-951	199	17	family	family	NOUN
cana-951	199	18	of	of	ADP
cana-951	199	19	solutions	solution	NOUN
cana-951	199	20	of	of	ADP
cana-951	199	21	the	the	DET
cana-951	199	22	nonlinear	nonlinear	ADJ
cana-951	199	23	schrödinger	schrödinger	ADJ
cana-951	199	24	equation	equation	NOUN
cana-951	199	25	in	in	ADP
cana-951	199	26	biisotropic	biisotropic	ADJ
cana-951	199	27	optical	optical	ADJ
cana-951	199	28	fibers	fiber	NOUN
cana-951	199	29	.	.	PUNCT
cana-951	200	1	this	this	DET
cana-951	200	2	method	method	NOUN
cana-951	200	3	is	be	AUX
cana-951	200	4	based	base	VERB
cana-951	200	5	on	on	ADP
cana-951	200	6	the	the	DET
cana-951	200	7	use	use	NOUN
cana-951	200	8	of	of	ADP
cana-951	200	9	a	a	DET
cana-951	200	10	perturbation	perturbation	NOUN
cana-951	200	11	expansion	expansion	NOUN
cana-951	200	12	in	in	ADP
cana-951	200	13	powers	power	NOUN
cana-951	200	14	of	of	ADP
cana-951	200	15	the	the	DET
cana-951	200	16	dimensionless	dimensionless	NOUN
cana-951	200	17	parameter	parameter	NOUN
cana-951	200	18	,	,	PUNCT
cana-951	200	19	and	and	CCONJ
cana-951	200	20	it	it	PRON
cana-951	200	21	is	be	AUX
cana-951	200	22	valid	valid	ADJ
cana-951	200	23	for	for	ADP
cana-951	200	24	both	both	CCONJ
cana-951	200	25	weak	weak	ADJ
cana-951	200	26	and	and	CCONJ
cana-951	200	27	strong	strong	ADJ
cana-951	200	28	nonlinearities	nonlinearitie	NOUN
cana-951	200	29	.	.	PUNCT
cana-951	201	1	the	the	DET
cana-951	201	2	method	method	NOUN
cana-951	201	3	allows	allow	VERB
cana-951	201	4	for	for	ADP
cana-951	201	5	the	the	DET
cana-951	201	6	inclusion	inclusion	NOUN
cana-951	201	7	of	of	ADP
cana-951	201	8	varying	vary	VERB
cana-951	201	9	dispersion	dispersion	NOUN
cana-951	201	10	and	and	CCONJ
cana-951	201	11	nonlinearity	nonlinearity	NOUN
cana-951	201	12	,	,	PUNCT
cana-951	201	13	making	make	VERB
cana-951	201	14	it	it	PRON
cana-951	201	15	well	well	ADV
cana-951	201	16	-	-	PUNCT
cana-951	201	17	suited	suited	ADJ
cana-951	201	18	for	for	ADP
cana-951	201	19	modeling	model	VERB
cana-951	201	20	a	a	DET
cana-951	201	21	wide	wide	ADJ
cana-951	201	22	range	range	NOUN
cana-951	201	23	of	of	ADP
cana-951	201	24	optical	optical	ADJ
cana-951	201	25	fibres	fibre	NOUN
cana-951	201	26	.	.	PUNCT
cana-951	202	1	overall	overall	ADV
cana-951	202	2	,	,	PUNCT
cana-951	202	3	the	the	DET
cana-951	202	4	extended	extended	ADJ
cana-951	202	5	(	(	PUNCT
cana-951	202	6	g'/g)-expansion	g'/g)-expansion	NOUN
cana-951	202	7	method	method	NOUN
cana-951	202	8	is	be	AUX
cana-951	202	9	a	a	DET
cana-951	202	10	valuable	valuable	ADJ
cana-951	202	11	tool	tool	NOUN
cana-951	202	12	for	for	ADP
cana-951	202	13	understanding	understand	VERB
cana-951	202	14	the	the	DET
cana-951	202	15	dynamics	dynamic	NOUN
cana-951	202	16	of	of	ADP
cana-951	202	17	nonlinear	nonlinear	ADJ
cana-951	202	18	optical	optical	ADJ
cana-951	202	19	systems	system	NOUN
cana-951	202	20	,	,	PUNCT
cana-951	202	21	and	and	CCONJ
cana-951	202	22	it	it	PRON
cana-951	202	23	is	be	AUX
cana-951	202	24	expected	expect	VERB
cana-951	202	25	to	to	PART
cana-951	202	26	have	have	VERB
cana-951	202	27	a	a	DET
cana-951	202	28	wide	wide	ADJ
cana-951	202	29	range	range	NOUN
cana-951	202	30	of	of	ADP
cana-951	202	31	applications	application	NOUN
cana-951	202	32	in	in	ADP
cana-951	202	33	the	the	DET
cana-951	202	34	field	field	NOUN
cana-951	202	35	of	of	ADP
cana-951	202	36	nonlinear	nonlinear	ADJ
cana-951	202	37	optics	optic	NOUN
cana-951	202	38	.	.	PUNCT
cana-951	203	1	refrences	refrence	NOUN
cana-951	204	1	[	[	X
cana-951	204	2	1	1	X
cana-951	204	3	]	]	X
cana-951	204	4	gao	gao	PROPN
cana-951	204	5	,	,	PUNCT
cana-951	204	6	x.	x.	NOUN
cana-951	204	7	:	:	PUNCT
cana-951	204	8	variety	variety	NOUN
cana-951	204	9	of	of	ADP
cana-951	204	10	the	the	DET
cana-951	204	11	cosmic	cosmic	ADJ
cana-951	204	12	plasmas	plasma	NOUN
cana-951	204	13	:	:	PUNCT
cana-951	204	14	general	general	ADJ
cana-951	204	15	variable	variable	ADJ
cana-951	204	16	-	-	PUNCT
cana-951	204	17	coefficient	coefficient	NOUN
cana-951	204	18	korteweg	korteweg	NOUN
cana-951	204	19	-	-	PUNCT
cana-951	204	20	de	de	NOUN
cana-951	204	21	vries	vries	PROPN
cana-951	204	22	–	–	PUNCT
cana-951	204	23	burgers	burger	NOUN
cana-951	204	24	equation	equation	NOUN
cana-951	204	25	with	with	ADP
cana-951	204	26	experimental	experimental	ADJ
cana-951	204	27	/	/	SYM
cana-951	204	28	observational	observational	ADJ
cana-951	204	29	support	support	NOUN
cana-951	204	30	.	.	PUNCT
cana-951	205	1	europhys	europhy	NOUN
cana-951	205	2	.	.	PUNCT
cana-951	206	1	lett.110	lett.110	PROPN
cana-951	206	2	,	,	PUNCT
cana-951	206	3	15002	15002	NUM
cana-951	206	4	(	(	PUNCT
cana-951	206	5	2015	2015	NUM
cana-951	206	6	)	)	PUNCT
cana-951	206	7	.	.	PUNCT
cana-951	207	1	[	[	X
cana-951	207	2	2	2	NUM
cana-951	207	3	]	]	X
cana-951	207	4	zhen	zhen	PROPN
cana-951	207	5	,	,	PUNCT
cana-951	207	6	h.-l	h.-l	PROPN
cana-951	207	7	.	.	PUNCT
cana-951	207	8	,	,	PUNCT
cana-951	207	9	tian	tian	PROPN
cana-951	207	10	,	,	PUNCT
cana-951	207	11	b.	b.	PROPN
cana-951	207	12	,	,	PUNCT
cana-951	207	13	wang	wang	PROPN
cana-951	207	14	,	,	PUNCT
cana-951	207	15	y.-f	y.-f	PROPN
cana-951	207	16	.	.	PUNCT
cana-951	207	17	:	:	PUNCT
cana-951	207	18	soliton	soliton	NOUN
cana-951	207	19	solution	solution	NOUN
cana-951	207	20	and	and	CCONJ
cana-951	207	21	chaotic	chaotic	ADJ
cana-951	207	22	motions	motion	NOUN
cana-951	207	23	of	of	ADP
cana-951	207	24	the	the	DET
cana-951	207	25	zakharov	zakharov	ADJ
cana-951	207	26	equation	equation	NOUN
cana-951	207	27	for	for	ADP
cana-951	207	28	the	the	DET
cana-951	207	29	langmuir	langmuir	PROPN
cana-951	207	30	wave	wave	NOUN
cana-951	207	31	in	in	ADP
cana-951	207	32	the	the	DET
cana-951	207	33	plasma	plasma	NOUN
cana-951	207	34	.	.	PUNCT
cana-951	208	1	phys	phy	NOUN
cana-951	208	2	.	.	PUNCT
cana-951	209	1	plasmas	plasma	NOUN
cana-951	209	2	22	22	NUM
cana-951	209	3	,	,	PUNCT
cana-951	209	4	1–9	1–9	NUM
cana-951	209	5	(	(	PUNCT
cana-951	209	6	2015	2015	NUM
cana-951	209	7	)	)	PUNCT
cana-951	209	8	.	.	PUNCT
cana-951	210	1	[	[	X
cana-951	210	2	3	3	X
cana-951	210	3	]	]	X
cana-951	210	4	sun	sun	NOUN
cana-951	210	5	,	,	PUNCT
cana-951	210	6	w.-r	w.-r	PROPN
cana-951	210	7	.	.	PUNCT
cana-951	210	8	,	,	PUNCT
cana-951	210	9	tian	tian	PROPN
cana-951	210	10	,	,	PUNCT
cana-951	210	11	b.	b.	PROPN
cana-951	210	12	,	,	PUNCT
cana-951	210	13	jiang	jiang	PROPN
cana-951	210	14	,	,	PUNCT
cana-951	210	15	y.	y.	PROPN
cana-951	210	16	optical	optical	ADJ
cana-951	210	17	rogue	rogue	NOUN
cana-951	210	18	waves	wave	NOUN
cana-951	210	19	associated	associate	VERB
cana-951	210	20	with	with	ADP
cana-951	210	21	the	the	DET
cana-951	210	22	negative	negative	ADJ
cana-951	210	23	coherent	coherent	ADJ
cana-951	210	24	coupling	coupling	NOUN
cana-951	210	25	in	in	ADP
cana-951	210	26	an	an	DET
cana-951	210	27	isotropic	isotropic	ADJ
cana-951	210	28	medium	medium	NOUN
cana-951	210	29	.	.	PUNCT
cana-951	211	1	phys	phy	NOUN
cana-951	211	2	.	.	PUNCT
cana-951	212	1	rev	rev	PROPN
cana-951	212	2	.	.	PUNCT
cana-951	213	1	e	e	PROPN
cana-951	213	2	91	91	NUM
cana-951	213	3	,	,	PUNCT
cana-951	213	4	023205	023205	NUM
cana-951	213	5	(	(	PUNCT
cana-951	213	6	2015	2015	NUM
cana-951	213	7	)	)	PUNCT
cana-951	213	8	.	.	PUNCT
cana-951	214	1	[	[	X
cana-951	214	2	4	4	NUM
cana-951	214	3	]	]	X
cana-951	214	4	wang	wang	PROPN
cana-951	214	5	,	,	PUNCT
cana-951	214	6	y.-f	y.-f	PROPN
cana-951	214	7	.	.	PUNCT
cana-951	214	8	,	,	PUNCT
cana-951	214	9	tian	tian	PROPN
cana-951	214	10	,	,	PUNCT
cana-951	214	11	b.	b.	PROPN
cana-951	214	12	,	,	PUNCT
cana-951	214	13	wang	wang	PROPN
cana-951	214	14	,	,	PUNCT
cana-951	214	15	m.	m.	NOUN
cana-951	214	16	solitons	soliton	NOUN
cana-951	214	17	via	via	ADP
cana-951	214	18	an	an	DET
cana-951	214	19	auxiliary	auxiliary	ADJ
cana-951	214	20	function	function	NOUN
cana-951	214	21	for	for	ADP
cana-951	214	22	an	an	DET
cana-951	214	23	inhomogeneous	inhomogeneous	ADJ
cana-951	214	24	higher	high	ADJ
cana-951	214	25	-	-	PUNCT
cana-951	214	26	order	order	NOUN
cana-951	214	27	nonlinear	nonlinear	ADJ
cana-951	214	28	schrödinger	schrödinger	ADJ
cana-951	214	29	equation	equation	NOUN
cana-951	214	30	in	in	ADP
cana-951	214	31	optical	optical	ADJ
cana-951	214	32	fiber	fiber	NOUN
cana-951	214	33	communications	communication	NOUN
cana-951	214	34	.	.	PUNCT
cana-951	215	1	nonlinear	nonlinear	ADJ
cana-951	215	2	dyn	dyn	PROPN
cana-951	215	3	.	.	PUNCT
cana-951	216	1	79	79	NUM
cana-951	216	2	,	,	PUNCT
cana-951	216	3	721–729	721–729	NUM
cana-951	216	4	(	(	PUNCT
cana-951	216	5	2015	2015	NUM
cana-951	216	6	)	)	PUNCT
cana-951	216	7	.	.	PUNCT
cana-951	217	1	[	[	X
cana-951	217	2	5	5	NUM
cana-951	217	3	]	]	X
cana-951	217	4	gao	gao	PROPN
cana-951	217	5	,	,	PUNCT
cana-951	217	6	x.-y.bäcklund	x.-y.bäcklund	ADP
cana-951	217	7	transformation	transformation	NOUN
cana-951	217	8	and	and	CCONJ
cana-951	217	9	shock	shock	NOUN
cana-951	217	10	-	-	PUNCT
cana-951	217	11	wave	wave	NOUN
cana-951	217	12	-	-	PUNCT
cana-951	217	13	type	type	NOUN
cana-951	217	14	solutions	solution	NOUN
cana-951	217	15	for	for	ADP
cana-951	217	16	a	a	DET
cana-951	217	17	generalized	generalize	VERB
cana-951	217	18	(	(	PUNCT
cana-951	217	19	3	3	NUM
cana-951	217	20	+	+	NOUN
cana-951	217	21	1)-dimensional	1)-dimensional	ADJ
cana-951	217	22	variablecoefficient	variablecoefficient	ADJ
cana-951	217	23	b	b	X
cana-951	217	24	-	-	PUNCT
cana-951	217	25	type	type	NOUN
cana-951	217	26	kadomtsev	kadomtsev	ADJ
cana-951	217	27	-	-	PUNCT
cana-951	217	28	petviashvili	petviashvili	NOUN
cana-951	217	29	equation	equation	NOUN
cana-951	217	30	in	in	ADP
cana-951	217	31	fluid	fluid	ADJ
cana-951	217	32	mechanics	mechanic	NOUN
cana-951	217	33	.	.	PUNCT
cana-951	218	1	ocean	ocean	PROPN
cana-951	218	2	eng	eng	PROPN
cana-951	218	3	.	.	PROPN
cana-951	219	1	96	96	NUM
cana-951	219	2	,	,	PUNCT
cana-951	219	3	245–247	245–247	NUM
cana-951	219	4	(	(	PUNCT
cana-951	219	5	2015	2015	NUM
cana-951	219	6	)	)	PUNCT
cana-951	219	7	.	.	PUNCT
cana-951	220	1	[	[	X
cana-951	220	2	6	6	NUM
cana-951	220	3	]	]	PUNCT
cana-951	220	4	ao	ao	PROPN
cana-951	220	5	,	,	PUNCT
cana-951	220	6	x.-y	x.-y	NOUN
cana-951	220	7	.	.	PUNCT
cana-951	221	1	incompressible	incompressible	ADJ
cana-951	221	2	-	-	PUNCT
cana-951	221	3	fluid	fluid	ADJ
cana-951	221	4	symbolic	symbolic	ADJ
cana-951	221	5	computation	computation	NOUN
cana-951	221	6	and	and	CCONJ
cana-951	221	7	bäcklund	bäcklund	NOUN
cana-951	221	8	transformation	transformation	NOUN
cana-951	221	9	:	:	PUNCT
cana-951	221	10	(	(	PUNCT
cana-951	221	11	3	3	NUM
cana-951	221	12	+	+	SYM
cana-951	221	13	1)-dimensional	1)-dimensional	NUM
cana-951	221	14	variablecoefficient	variablecoefficient	ADJ
cana-951	221	15	boiti	boiti	PROPN
cana-951	221	16	-	-	PUNCT
cana-951	221	17	leon	leon	PROPN
cana-951	221	18	-	-	PUNCT
cana-951	221	19	manna	manna	NOUN
cana-951	221	20	-	-	PUNCT
cana-951	221	21	pempinelli	pempinelli	NOUN
cana-951	221	22	model	model	NOUN
cana-951	221	23	.	.	PUNCT
cana-951	222	1	z.	z.	PROPN
cana-951	222	2	naturforsch	naturforsch	PROPN
cana-951	222	3	.	.	PUNCT
cana-951	223	1	a.	a.	PROPN
cana-951	223	2	70	70	NUM
cana-951	223	3	,	,	PUNCT
cana-951	223	4	59–61	59–61	NUM
cana-951	223	5	(	(	PUNCT
cana-951	223	6	2015	2015	NUM
cana-951	223	7	)	)	PUNCT
cana-951	223	8	.	.	PUNCT
cana-951	224	1	[	[	X
cana-951	224	2	7	7	NUM
cana-951	224	3	]	]	X
cana-951	224	4	biswas	biswas	PROPN
cana-951	224	5	,	,	PUNCT
cana-951	224	6	a.	a.	PROPN
cana-951	224	7	,	,	PUNCT
cana-951	224	8	mirzazadeh	mirzazadeh	PROPN
cana-951	224	9	,	,	PUNCT
cana-951	224	10	m.	m.	NOUN
cana-951	224	11	,	,	PUNCT
cana-951	224	12	savescu	savescu	NOUN
cana-951	224	13	,	,	PUNCT
cana-951	224	14	m.	m.	NOUN
cana-951	224	15	,	,	PUNCT
cana-951	224	16	milovic	milovic	ADJ
cana-951	224	17	,	,	PUNCT
cana-951	224	18	d	d	PROPN
cana-951	224	19	,	,	PUNCT
cana-951	224	20	khan	khan	PROPN
cana-951	224	21	,	,	PUNCT
cana-951	224	22	k.r	k.r	PROPN
cana-951	224	23	.	.	PROPN
cana-951	224	24	,	,	PUNCT
cana-951	224	25	mahmood	mahmood	PROPN
cana-951	224	26	,	,	PUNCT
cana-951	224	27	m.f	m.f	PROPN
cana-951	224	28	.	.	PROPN
cana-951	224	29	,	,	PUNCT
cana-951	224	30	belic	belic	ADJ
cana-951	224	31	,	,	PUNCT
cana-951	224	32	m.	m.	NOUN
cana-951	224	33	:	:	PUNCT
cana-951	224	34	singular	singular	PROPN
cana-951	224	35	solitons	soliton	NOUN
cana-951	224	36	in	in	ADP
cana-951	224	37	optical	optical	ADJ
cana-951	224	38	metamaterials	metamaterial	NOUN
cana-951	224	39	by	by	ADP
cana-951	224	40	ansatz	ansatz	ADJ
cana-951	224	41	method	method	NOUN
cana-951	224	42	and	and	CCONJ
cana-951	224	43	simplest	simple	ADJ
cana-951	224	44	equation	equation	NOUN
cana-951	224	45	approach	approach	NOUN
cana-951	224	46	.	.	PUNCT
cana-951	225	1	j.	j.	PROPN
cana-951	225	2	mod	mod	PROPN
cana-951	225	3	.	.	PROPN
cana-951	225	4	opt	opt	PROPN
cana-951	225	5	.	.	PROPN
cana-951	226	1	61	61	NUM
cana-951	226	2	,	,	PUNCT
cana-951	226	3	1550–1555	1550–1555	NUM
cana-951	226	4	(	(	PUNCT
cana-951	226	5	2014	2014	NUM
cana-951	226	6	)	)	PUNCT
cana-951	226	7	.	.	PUNCT
cana-951	227	1	[	[	X
cana-951	227	2	8	8	NUM
cana-951	227	3	]	]	X
cana-951	227	4	mirzazadeh	mirzazadeh	PROPN
cana-951	227	5	,	,	PUNCT
cana-951	227	6	m.	m.	PROPN
cana-951	227	7	arnous	arnous	PROPN
cana-951	227	8	,	,	PUNCT
cana-951	227	9	a.h	a.h	PROPN
cana-951	227	10	.	.	PROPN
cana-951	227	11	,	,	PUNCT
cana-951	227	12	mahmood	mahmood	PROPN
cana-951	227	13	,	,	PUNCT
cana-951	227	14	m.f	m.f	PROPN
cana-951	227	15	.	.	PROPN
cana-951	227	16	,	,	PUNCT
cana-951	227	17	zerrad	zerrad	PROPN
cana-951	227	18	,	,	PUNCT
cana-951	227	19	e.	e.	PROPN
cana-951	227	20	,	,	PUNCT
cana-951	227	21	biswas	biswas	PROPN
cana-951	227	22	,	,	PUNCT
cana-951	227	23	a.	a.	NOUN
cana-951	227	24	:	:	PUNCT
cana-951	227	25	soliton	soliton	NOUN
cana-951	227	26	solutions	solution	NOUN
cana-951	227	27	to	to	PART
cana-951	227	28	resonant	resonant	VERB
cana-951	227	29	nonlinear	nonlinear	ADJ
cana-951	227	30	schrödinger	schrödinger	NOUN
cana-951	227	31	’s	’s	PART
cana-951	227	32	equation	equation	NOUN
cana-951	227	33	with	with	ADP
cana-951	227	34	time	time	NOUN
cana-951	227	35	-	-	PUNCT
cana-951	227	36	dependent	dependent	ADJ
cana-951	227	37	coefficients	coefficient	NOUN
cana-951	227	38	by	by	ADP
cana-951	227	39	trial	trial	NOUN
cana-951	227	40	solution	solution	NOUN
cana-951	227	41	approach	approach	NOUN
cana-951	227	42	.	.	PUNCT
cana-951	228	1	nonlinear	nonlinear	ADJ
cana-951	228	2	dyn	dyn	PROPN
cana-951	228	3	.	.	PUNCT
cana-951	229	1	81(1–2	81(1–2	PROPN
cana-951	229	2	)	)	PUNCT
cana-951	229	3	,	,	PUNCT
cana-951	229	4	277282	277282	NUM
cana-951	229	5	(	(	PUNCT
cana-951	229	6	2015	2015	NUM
cana-951	229	7	)	)	PUNCT
cana-951	229	8	.	.	PUNCT
cana-951	230	1	[	[	X
cana-951	230	2	9	9	NUM
cana-951	230	3	]	]	SYM
cana-951	230	4	mirzazadeh	mirzazadeh	PROPN
cana-951	230	5	,	,	PUNCT
cana-951	230	6	m.	m.	NOUN
cana-951	230	7	,	,	PUNCT
cana-951	230	8	zhou	zhou	PROPN
cana-951	230	9	,	,	PUNCT
cana-951	230	10	q.	q.	PROPN
cana-951	230	11	,	,	PUNCT
cana-951	230	12	bhrawy	bhrawy	PROPN
cana-951	230	13	,	,	PUNCT
cana-951	230	14	a.h	a.h	PROPN
cana-951	230	15	.	.	PROPN
cana-951	230	16	,	,	PUNCT
cana-951	230	17	biswas	biswas	PROPN
cana-951	230	18	,	,	PUNCT
cana-951	230	19	a.	a.	NOUN
cana-951	230	20	,	,	PUNCT
cana-951	230	21	belic	belic	ADJ
cana-951	230	22	,	,	PUNCT
cana-951	230	23	m.	m.	NOUN
cana-951	230	24	:	:	PUNCT
cana-951	230	25	optical	optical	ADJ
cana-951	230	26	solitons	soliton	NOUN
cana-951	230	27	in	in	ADP
cana-951	230	28	cascaded	cascade	VERB
cana-951	230	29	system	system	NOUN
cana-951	230	30	with	with	ADP
cana-951	230	31	three	three	NUM
cana-951	230	32	integration	integration	NOUN
cana-951	230	33	schemes	scheme	NOUN
cana-951	230	34	.	.	PUNCT
cana-951	231	1	j.	j.	PROPN
cana-951	231	2	optoelectron	optoelectron	PROPN
cana-951	231	3	.	.	PUNCT
cana-951	232	1	adv	adv	PROPN
cana-951	232	2	.	.	PUNCT
cana-951	232	3	mater	mater	PROPN
cana-951	232	4	.	.	PUNCT
cana-951	233	1	17(1–2	17(1–2	NOUN
cana-951	233	2	)	)	PUNCT
cana-951	233	3	,	,	PUNCT
cana-951	233	4	74–81	74–81	NUM
cana-951	233	5	(	(	PUNCT
cana-951	233	6	2015	2015	NUM
cana-951	233	7	)	)	PUNCT
cana-951	233	8	.	.	PUNCT
cana-951	234	1	communications	communication	NOUN
cana-951	234	2	on	on	ADP
cana-951	234	3	applied	apply	VERB
cana-951	234	4	nonlinear	nonlinear	ADJ
cana-951	234	5	analysis	analysis	NOUN
cana-951	234	6	issn	issn	NOUN
cana-951	234	7	:	:	PUNCT
cana-951	234	8	1074	1074	NUM
cana-951	234	9	-	-	PUNCT
cana-951	234	10	133x	133x	NUM
cana-951	234	11	vol	vol	NOUN
cana-951	234	12	31	31	NUM
cana-951	234	13	no	no	NOUN
cana-951	234	14	.	.	PUNCT
cana-951	235	1	4s	4s	NUM
cana-951	235	2	(	(	PUNCT
cana-951	235	3	2024	2024	NUM
cana-951	235	4	)	)	PUNCT
cana-951	235	5	585	585	NUM
cana-951	235	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-951	236	1	[	[	X
cana-951	236	2	10	10	NUM
cana-951	236	3	]	]	X
cana-951	236	4	eslami	eslami	NOUN
cana-951	236	5	,	,	PUNCT
cana-951	236	6	m.	m.	NOUN
cana-951	236	7	,	,	PUNCT
cana-951	236	8	mirzazadeh	mirzazadeh	PROPN
cana-951	236	9	,	,	PUNCT
cana-951	236	10	m.	m.	NOUN
cana-951	236	11	,	,	PUNCT
cana-951	236	12	vajargah	vajargah	PROPN
cana-951	236	13	,	,	PUNCT
cana-951	236	14	b.f	b.f	PROPN
cana-951	236	15	.	.	PROPN
cana-951	236	16	,	,	PUNCT
cana-951	236	17	biswas	biswas	PROPN
cana-951	236	18	,	,	PUNCT
cana-951	236	19	a.:optical	a.:optical	ADJ
cana-951	236	20	solitons	soliton	NOUN
cana-951	236	21	for	for	ADP
cana-951	236	22	the	the	DET
cana-951	236	23	resonant	resonant	ADJ
cana-951	236	24	nonlinear	nonlinear	ADJ
cana-951	236	25	schrödinger	schrödinger	NOUN
cana-951	236	26	’s	’s	PART
cana-951	236	27	equation	equation	NOUN
cana-951	236	28	with	with	ADP
cana-951	236	29	time	time	NOUN
cana-951	236	30	-	-	PUNCT
cana-951	236	31	dependent	dependent	ADJ
cana-951	236	32	coefficients	coefficient	NOUN
cana-951	236	33	by	by	ADP
cana-951	236	34	the	the	DET
cana-951	236	35	first	first	ADJ
cana-951	236	36	integralmethod	integralmethod	NOUN
cana-951	236	37	.	.	PUNCT
cana-951	237	1	optikint	optikint	PROPN
cana-951	237	2	.	.	PUNCT
cana-951	238	1	j.	j.	PROPN
cana-951	238	2	light	light	PROPN
cana-951	238	3	electron	electron	PROPN
cana-951	238	4	opt	opt	PROPN
cana-951	238	5	.	.	PUNCT
cana-951	239	1	125(13	125(13	NUM
cana-951	239	2	)	)	PUNCT
cana-951	239	3	,	,	PUNCT
cana-951	239	4	3107–3116	3107–3116	NUM
cana-951	239	5	(	(	PUNCT
cana-951	239	6	2014	2014	NUM
cana-951	239	7	)	)	PUNCT
cana-951	239	8	.	.	PUNCT
cana-951	240	1	[	[	X
cana-951	240	2	11	11	NUM
cana-951	240	3	]	]	X
cana-951	240	4	mirzazadeh	mirzazadeh	PROPN
cana-951	240	5	,	,	PUNCT
cana-951	240	6	m.	m.	NOUN
cana-951	240	7	,	,	PUNCT
cana-951	240	8	biswas	biswas	PROPN
cana-951	240	9	,	,	PUNCT
cana-951	240	10	a.	a.	NOUN
cana-951	240	11	:	:	PUNCT
cana-951	240	12	optical	optical	ADJ
cana-951	240	13	solitons	soliton	NOUN
cana-951	240	14	with	with	ADP
cana-951	240	15	spatiotemporal	spatiotemporal	ADJ
cana-951	240	16	dispersion	dispersion	NOUN
cana-951	240	17	by	by	ADP
cana-951	240	18	first	first	ADJ
cana-951	240	19	integral	integral	ADJ
cana-951	240	20	approach	approach	NOUN
cana-951	240	21	and	and	CCONJ
cana-951	240	22	functional	functional	ADJ
cana-951	240	23	variable	variable	ADJ
cana-951	240	24	method	method	NOUN
cana-951	240	25	.	.	PUNCT
cana-951	241	1	optik	optik	PROPN
cana-951	241	2	int	int	PROPN
cana-951	241	3	.	.	PUNCT
cana-951	242	1	j.	j.	PROPN
cana-951	242	2	light	light	PROPN
cana-951	242	3	electron	electron	PROPN
cana-951	242	4	opt	opt	PROPN
cana-951	242	5	.	.	PUNCT
cana-951	243	1	125(19	125(19	NUM
cana-951	243	2	)	)	PUNCT
cana-951	243	3	,	,	PUNCT
cana-951	243	4	5467–5475	5467–5475	NUM
cana-951	243	5	(	(	PUNCT
cana-951	243	6	2014	2014	NUM
cana-951	243	7	)	)	PUNCT
cana-951	243	8	.	.	PUNCT
cana-951	244	1	[	[	X
cana-951	244	2	12	12	NUM
cana-951	244	3	]	]	X
cana-951	244	4	mirzazadeh	mirzazadeh	PROPN
cana-951	244	5	,	,	PUNCT
cana-951	244	6	m.	m.	NOUN
cana-951	244	7	,	,	PUNCT
cana-951	244	8	zhou	zhou	PROPN
cana-951	244	9	,	,	PUNCT
cana-951	244	10	q	q	NOUN
cana-951	244	11	,	,	PUNCT
cana-951	244	12	zerrad	zerrad	PROPN
cana-951	244	13	,	,	PUNCT
cana-951	244	14	e.	e.	PROPN
cana-951	244	15	,	,	PUNCT
cana-951	244	16	mahmood	mahmood	PROPN
cana-951	244	17	,	,	PUNCT
cana-951	244	18	m.f	m.f	PROPN
cana-951	244	19	.	.	PROPN
cana-951	244	20	,biswas	,biswas	PROPN
cana-951	244	21	,	,	PUNCT
cana-951	244	22	a.	a.	NOUN
cana-951	244	23	,	,	PUNCT
cana-951	244	24	belic	belic	ADJ
cana-951	244	25	,	,	PUNCT
cana-951	244	26	m.	m.	NOUN
cana-951	244	27	:	:	PUNCT
cana-951	244	28	bifurcation	bifurcation	NOUN
cana-951	244	29	analysis	analysis	NOUN
cana-951	244	30	and	and	CCONJ
cana-951	244	31	bright	bright	ADJ
cana-951	244	32	soliton	soliton	NOUN
cana-951	244	33	of	of	ADP
cana-951	244	34	generalized	generalized	ADJ
cana-951	244	35	resonant	resonant	ADJ
cana-951	244	36	dispersive	dispersive	ADJ
cana-951	244	37	nonlinear	nonlinear	PROPN
cana-951	244	38	schrodinger	schrodinger	PROPN
cana-951	244	39	’s	’s	PART
cana-951	244	40	equation	equation	NOUN
cana-951	244	41	.	.	PUNCT
cana-951	245	1	optoelectron	optoelectron	PROPN
cana-951	245	2	.	.	PUNCT
cana-951	246	1	adv	adv	PROPN
cana-951	246	2	.	.	PUNCT
cana-951	246	3	mater	mater	PROPN
cana-951	246	4	.	.	PUNCT
cana-951	246	5	9(11–12	9(11–12	NUM
cana-951	246	6	)	)	PUNCT
cana-951	246	7	,	,	PUNCT
cana-951	246	8	1342–1346	1342–1346	NUM
cana-951	246	9	(	(	PUNCT
cana-951	246	10	2015	2015	NUM
cana-951	246	11	)	)	PUNCT
cana-951	246	12	.	.	PUNCT
cana-951	247	1	[	[	X
cana-951	247	2	13	13	NUM
cana-951	247	3	]	]	SYM
cana-951	247	4	mirzazadeh	mirzazadeh	PROPN
cana-951	247	5	,	,	PUNCT
cana-951	247	6	m	m	PROPN
cana-951	247	7	,	,	PUNCT
cana-951	247	8	mahmood	mahmood	PROPN
cana-951	247	9	,	,	PUNCT
cana-951	247	10	m.f	m.f	PROPN
cana-951	247	11	.	.	PROPN
cana-951	247	12	,	,	PUNCT
cana-951	247	13	majid	majid	PROPN
cana-951	247	14	,	,	PUNCT
cana-951	247	15	f.b	f.b	PROPN
cana-951	247	16	.	.	PROPN
cana-951	247	17	,	,	PUNCT
cana-951	247	18	biswas	biswas	PROPN
cana-951	247	19	,	,	PUNCT
cana-951	247	20	a.	a.	PROPN
cana-951	247	21	,belic	,belic	PUNCT
cana-951	247	22	,	,	PUNCT
cana-951	247	23	m.	m.	NOUN
cana-951	247	24	:	:	PUNCT
cana-951	247	25	optical	optical	ADJ
cana-951	247	26	solitons	soliton	NOUN
cana-951	247	27	in	in	ADP
cana-951	247	28	birefringent	birefringent	NOUN
cana-951	247	29	fibers	fiber	NOUN
cana-951	247	30	with	with	ADP
cana-951	247	31	riccati	riccati	NOUN
cana-951	247	32	equation	equation	NOUN
cana-951	247	33	method	method	NOUN
cana-951	247	34	.	.	PUNCT
cana-951	248	1	optoelectron	optoelectron	PROPN
cana-951	248	2	.	.	PUNCT
cana-951	249	1	adv	adv	PROPN
cana-951	249	2	.	.	PUNCT
cana-951	249	3	mater	mater	PROPN
cana-951	249	4	.	.	PUNCT
cana-951	250	1	7–8	7–8	X
cana-951	250	2	,	,	PUNCT
cana-951	250	3	1032–1036	1032–1036	NUM
cana-951	250	4	(	(	PUNCT
cana-951	250	5	2015	2015	NUM
cana-951	250	6	)	)	PUNCT
cana-951	250	7	.	.	PUNCT
cana-951	251	1	[	[	X
cana-951	251	2	14	14	NUM
cana-951	251	3	]	]	X
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cana-951	251	5	m	m	PROPN
cana-951	251	6	,	,	PUNCT
cana-951	251	7	li	li	PROPN
cana-951	251	8	x	x	PROPN
cana-951	251	9	,	,	PUNCT
cana-951	251	10	zhang	zhang	PROPN
cana-951	251	11	j.	j.	PROPN
cana-951	251	12	the	the	PRON
cana-951	251	13	(	(	PUNCT
cana-951	251	14	g′/g)-expansion	g′/g)-expansion	PROPN
cana-951	251	15	method	method	NOUN
cana-951	251	16	and	and	CCONJ
cana-951	251	17	travelling	travel	VERB
cana-951	251	18	wave	wave	NOUN
cana-951	251	19	solutions	solution	NOUN
cana-951	251	20	of	of	ADP
cana-951	251	21	nonlinear	nonlinear	ADJ
cana-951	251	22	evolution	evolution	NOUN
cana-951	251	23	equations	equation	NOUN
cana-951	251	24	in	in	ADP
cana-951	251	25	mathematical	mathematical	ADJ
cana-951	251	26	physics	physic	NOUN
cana-951	251	27	.	.	PUNCT
cana-951	252	1	phys	phy	NOUN
cana-951	252	2	lett	lett	PROPN
cana-951	252	3	a.	a.	PROPN
cana-951	252	4	2008;372	2008;372	NUM
cana-951	252	5	:	:	PUNCT
cana-951	252	6	417–423	417–423	NUM
cana-951	252	7	.	.	PUNCT
cana-951	253	1	[	[	X
cana-951	253	2	15	15	NUM
cana-951	253	3	]	]	X
cana-951	253	4	zayed	zayed	PROPN
cana-951	253	5	em	em	PRON
cana-951	253	6	,	,	PUNCT
cana-951	253	7	alurrfi	alurrfi	PROPN
cana-951	253	8	ka	ka	PROPN
cana-951	253	9	.	.	PROPN
cana-951	254	1	on	on	ADP
cana-951	254	2	solving	solve	VERB
cana-951	254	3	two	two	NUM
cana-951	254	4	higher	high	ADJ
cana-951	254	5	-	-	PUNCT
cana-951	254	6	order	order	NOUN
cana-951	254	7	nonlinear	nonlinear	ADJ
cana-951	254	8	pdes	pde	NOUN
cana-951	254	9	describing	describe	VERB
cana-951	254	10	the	the	DET
cana-951	254	11	propagation	propagation	NOUN
cana-951	254	12	of	of	ADP
cana-951	254	13	optical	optical	ADJ
cana-951	254	14	pulses	pulse	NOUN
cana-951	254	15	in	in	ADP
cana-951	254	16	optic	optic	ADJ
cana-951	254	17	fibers	fiber	NOUN
cana-951	254	18	using	use	VERB
cana-951	254	19	the	the	DET
cana-951	254	20	(	(	PUNCT
cana-951	254	21	(	(	PUNCT
cana-951	254	22	g′/g),(1	g′/g),(1	NOUN
cana-951	254	23	/	/	SYM
cana-951	254	24	g))-expansion	g))-expansion	NOUN
cana-951	254	25	method	method	NOUN
cana-951	254	26	.	.	PUNCT
cana-951	255	1	ricerche	ricerche	PROPN
cana-951	255	2	mat	mat	PROPN
cana-951	255	3	.	.	PUNCT
cana-951	256	1	2015;64:164–194	2015;64:164–194	NOUN
cana-951	256	2	.	.	PUNCT
cana-951	257	1	[	[	X
cana-951	257	2	16	16	NUM
cana-951	257	3	]	]	PUNCT
cana-951	257	4	zayed	zayed	PROPN
cana-951	257	5	em	em	PRON
cana-951	257	6	,	,	PUNCT
cana-951	257	7	shahoot	shahoot	PROPN
cana-951	257	8	am	am	PROPN
cana-951	257	9	,	,	PUNCT
cana-951	257	10	alurrfi	alurrfi	PROPN
cana-951	257	11	ka	ka	PROPN
cana-951	257	12	.	.	PUNCT
cana-951	258	1	the	the	DET
cana-951	258	2	(	(	PUNCT
cana-951	258	3	(	(	PUNCT
cana-951	258	4	g′/g),(1	g′/g),(1	NOUN
cana-951	258	5	/	/	SYM
cana-951	258	6	g))expansion	g))expansion	NOUN
cana-951	258	7	method	method	NOUN
cana-951	258	8	and	and	CCONJ
cana-951	258	9	its	its	PRON
cana-951	258	10	applications	application	NOUN
cana-951	258	11	for	for	ADP
cana-951	258	12	constructing	construct	VERB
cana-951	258	13	many	many	ADJ
cana-951	258	14	new	new	ADJ
cana-951	258	15	exact	exact	ADJ
cana-951	258	16	solutions	solution	NOUN
cana-951	258	17	of	of	ADP
cana-951	258	18	the	the	DET
cana-951	258	19	higher	high	ADJ
cana-951	258	20	-	-	PUNCT
cana-951	258	21	order	order	NOUN
cana-951	258	22	nonlinear	nonlinear	ADJ
cana-951	258	23	schrödinger	schrödinger	ADJ
cana-951	258	24	equation	equation	NOUN
cana-951	258	25	and	and	CCONJ
cana-951	258	26	the	the	DET
cana-951	258	27	quantum	quantum	ADJ
cana-951	258	28	zakharov	zakharov	ADJ
cana-951	258	29	kuznetsov	kuznetsov	PROPN
cana-951	258	30	equation	equation	NOUN
cana-951	258	31	.	.	PUNCT
cana-951	259	1	opt	opt	PROPN
cana-951	259	2	.	.	PUNCT
cana-951	260	1	quant	quant	PROPN
cana-951	260	2	.	.	PUNCT
cana-951	261	1	electron	electron	PROPN
cana-951	261	2	.	.	PUNCT
cana-951	262	1	2018;50.doi:10.1007	2018;50.doi:10.1007	NUM
cana-951	262	2	/	/	SYM
cana-951	262	3	s11082	s11082	PROPN
cana-951	262	4	-	-	PUNCT
cana-951	262	5	018	018	NUM
cana-951	262	6	-	-	PUNCT
cana-951	262	7	1337	1337	NUM
cana-951	262	8	.	.	PUNCT
cana-951	263	1	[	[	X
cana-951	263	2	17	17	NUM
cana-951	263	3	]	]	X
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cana-951	263	6	sandeep	sandeep	PROPN
cana-951	263	7	,	,	PUNCT
cana-951	263	8	kumar	kumar	PROPN
cana-951	263	9	,	,	PUNCT
cana-951	263	10	sachin	sachin	PROPN
cana-951	263	11	,	,	PUNCT
cana-951	263	12	and	and	CCONJ
cana-951	263	13	nisar	nisar	PROPN
cana-951	263	14	,	,	PUNCT
cana-951	263	15	kottakkaran	kottakkaran	VERB
cana-951	263	16	sooppy	sooppy	ADJ
cana-951	263	17	.	.	PUNCT
cana-951	264	1	invariant	invariant	ADJ
cana-951	264	2	soliton	soliton	NOUN
cana-951	264	3	solutions	solution	NOUN
cana-951	264	4	for	for	ADP
cana-951	264	5	the	the	DET
cana-951	264	6	coupled	couple	VERB
cana-951	264	7	nonlinear	nonlinear	ADJ
cana-951	264	8	schrödinger	schrödinger	ADJ
cana-951	264	9	type	type	NOUN
cana-951	264	10	equation	equation	NOUN
cana-951	264	11	.	.	PUNCT
cana-951	265	1	alexandria	alexandria	PROPN
cana-951	265	2	engineering	engineering	PROPN
cana-951	265	3	journal	journal	PROPN
cana-951	265	4	,	,	PUNCT
cana-951	265	5	2023	2023	NUM
cana-951	265	6	,	,	PUNCT
cana-951	265	7	vol	vol	NOUN
cana-951	265	8	.	.	PROPN
cana-951	265	9	66	66	NUM
cana-951	265	10	,	,	PUNCT
cana-951	265	11	p.	p.	NOUN
cana-951	265	12	97	97	NUM
cana-951	265	13	-	-	SYM
cana-951	265	14	105	105	NUM
cana-951	265	15	.	.	PUNCT
cana-951	266	1	[	[	X
cana-951	266	2	18	18	NUM
cana-951	266	3	]	]	X
cana-951	266	4	yan	yan	PROPN
cana-951	266	5	zy	zy	PROPN
cana-951	266	6	.	.	PROPN
cana-951	266	7	generalized	generalize	VERB
cana-951	266	8	method	method	NOUN
cana-951	266	9	and	and	CCONJ
cana-951	266	10	its	its	PRON
cana-951	266	11	application	application	NOUN
cana-951	266	12	in	in	ADP
cana-951	266	13	the	the	DET
cana-951	266	14	higher	high	ADJ
cana-951	266	15	-	-	PUNCT
cana-951	266	16	order	order	NOUN
cana-951	266	17	nonlinear	nonlinear	ADJ
cana-951	266	18	schrodinger	schrodinger	PROPN
cana-951	266	19	equation	equation	NOUN
cana-951	266	20	in	in	ADP
cana-951	266	21	nonlinear	nonlinear	ADJ
cana-951	266	22	optical	optical	ADJ
cana-951	266	23	fibres	fibre	NOUN
cana-951	266	24	.	.	PUNCT
cana-951	267	1	chaos	chaos	NOUN
cana-951	267	2	solitons	soliton	NOUN
cana-951	267	3	fractals	fractal	NOUN
cana-951	267	4	.	.	PUNCT
cana-951	268	1	2003;16	2003;16	NUM
cana-951	268	2	:	:	PUNCT
cana-951	269	1	759–766	759–766	X
cana-951	269	2	.	.	PUNCT
cana-951	270	1	[	[	X
cana-951	270	2	19	19	NUM
cana-951	270	3	]	]	PUNCT
cana-951	270	4	z.	z.	PROPN
cana-951	270	5	mezache	mezache	PROPN
cana-951	270	6	and	and	CCONJ
cana-951	270	7	f.	f.	PROPN
cana-951	270	8	benabdelaziz	benabdelaziz	PROPN
cana-951	270	9	,	,	PUNCT
cana-951	270	10	study	study	NOUN
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cana-951	270	12	chiroptical	chiroptical	ADJ
cana-951	270	13	fiber	fiber	NOUN
cana-951	270	14	nonlinearities	nonlinearitie	NOUN
cana-951	270	15	with	with	ADP
cana-951	270	16	new	new	ADJ
cana-951	270	17	formulation	formulation	NOUN
cana-951	270	18	of	of	ADP
cana-951	270	19	constitutive	constitutive	ADJ
cana-951	270	20	equations	equation	NOUN
cana-951	270	21	,	,	PUNCT
cana-951	270	22	j.	j.	PROPN
cana-951	270	23	electromagn	electromagn	PROPN
cana-951	270	24	.	.	PUNCT
cana-951	271	1	waves	wave	NOUN
cana-951	271	2	appl	appl	PROPN
cana-951	271	3	.	.	PUNCT
cana-951	272	1	29	29	NUM
cana-951	272	2	(	(	PUNCT
cana-951	272	3	2015	2015	NUM
cana-951	272	4	)	)	PUNCT
cana-951	272	5	,	,	PUNCT
cana-951	272	6	2257–2268	2257–2268	NUM
cana-951	272	7	.	.	PUNCT
cana-951	273	1	[	[	X
cana-951	273	2	20	20	NUM
cana-951	273	3	]	]	PUNCT
cana-951	273	4	z.	z.	PROPN
cana-951	273	5	mezache	mezache	PROPN
cana-951	273	6	and	and	CCONJ
cana-951	273	7	f.	f.	PROPN
cana-951	273	8	benabdelaziz	benabdelaziz	PROPN
cana-951	273	9	,	,	PUNCT
cana-951	273	10	rigorous	rigorous	ADJ
cana-951	273	11	approach	approach	NOUN
cana-951	273	12	of	of	ADP
cana-951	273	13	the	the	DET
cana-951	273	14	constitutive	constitutive	ADJ
cana-951	273	15	relations	relation	NOUN
cana-951	273	16	for	for	ADP
cana-951	273	17	nonlinear	nonlinear	ADJ
cana-951	273	18	chiral	chiral	ADJ
cana-951	273	19	media	medium	NOUN
cana-951	273	20	,	,	PUNCT
cana-951	273	21	prog	prog	NOUN
cana-951	273	22	.	.	PUNCT
cana-951	274	1	electromagn	electromagn	PROPN
cana-951	274	2	.	.	PUNCT
cana-951	275	1	res	re	NOUN
cana-951	275	2	.	.	PUNCT
cana-951	276	1	lett	lett	PROPN
cana-951	276	2	.	.	PUNCT
cana-951	277	1	52	52	NUM
cana-951	277	2	(	(	PUNCT
cana-951	277	3	2015	2015	NUM
cana-951	277	4	)	)	PUNCT
cana-951	277	5	,	,	PUNCT
cana-951	277	6	57–62	57–62	NUM
cana-951	277	7	.	.	PUNCT
cana-951	278	1	[	[	X
cana-951	278	2	21	21	NUM
cana-951	278	3	]	]	X
cana-951	278	4	mezache	mezache	PROPN
cana-951	278	5	,	,	PUNCT
cana-951	278	6	s.	s.	PROPN
cana-951	278	7	aib	aib	PROPN
cana-951	278	8	,	,	PUNCT
cana-951	278	9	f.	f.	PROPN
cana-951	278	10	benabdelaziz	benabdelaziz	PROPN
cana-951	278	11	and	and	CCONJ
cana-951	278	12	c.	c.	PROPN
cana-951	278	13	zebiri	zebiri	PROPN
cana-951	278	14	,	,	PUNCT
cana-951	278	15	modeling	modeling	NOUN
cana-951	278	16	of	of	ADP
cana-951	278	17	a	a	DET
cana-951	278	18	light	light	ADJ
cana-951	278	19	pulse	pulse	NOUN
cana-951	278	20	in	in	ADP
cana-951	278	21	bi	bi	ADJ
cana-951	278	22	-	-	ADJ
cana-951	278	23	isotropic	isotropic	ADJ
cana-951	278	24	optical	optical	ADJ
cana-951	278	25	fiber	fiber	NOUN
cana-951	278	26	with	with	ADP
cana-951	278	27	kerr	kerr	PROPN
cana-951	278	28	effect	effect	PROPN
cana-951	278	29	:	:	PUNCT
cana-951	278	30	case	case	NOUN
cana-951	278	31	of	of	ADP
cana-951	278	32	tellegen	tellegen	ADJ
cana-951	278	33	media	medium	NOUN
cana-951	278	34	,	,	PUNCT
cana-951	278	35	nonlinear	nonlinear	ADJ
cana-951	278	36	dyn	dyn	NOUN
cana-951	278	37	.	.	PUNCT
cana-951	279	1	86	86	NUM
cana-951	279	2	(	(	PUNCT
cana-951	279	3	2	2	NUM
cana-951	279	4	)	)	PUNCT
cana-951	279	5	(	(	PUNCT
cana-951	279	6	2016	2016	NUM
cana-951	279	7	)	)	PUNCT
cana-951	279	8	,	,	PUNCT
cana-951	280	1	789–794	789–794	NUM
cana-951	280	2	.	.	PUNCT
cana-951	281	1	[	[	X
cana-951	281	2	22	22	NUM
cana-951	281	3	]	]	X
cana-951	281	4	zinelabiddine	zinelabiddine	NOUN
cana-951	281	5	,	,	PUNCT
cana-951	281	6	mezache	mezache	PROPN
cana-951	281	7	,	,	PUNCT
cana-951	281	8	and	and	CCONJ
cana-951	281	9	benabdelaziz	benabdelaziz	ADJ
cana-951	281	10	fatiha	fatiha	PROPN
cana-951	281	11	.	.	PUNCT
cana-951	282	1	"	"	PUNCT
cana-951	282	2	effect	effect	NOUN
cana-951	282	3	of	of	ADP
cana-951	282	4	the	the	DET
cana-951	282	5	nonlinear	nonlinear	ADJ
cana-951	282	6	parameters	parameter	NOUN
cana-951	282	7	on	on	ADP
cana-951	282	8	the	the	DET
cana-951	282	9	propagation	propagation	NOUN
cana-951	282	10	in	in	ADP
cana-951	282	11	biisotropic	biisotropic	ADJ
cana-951	282	12	media	medium	NOUN
cana-951	282	13	.	.	PUNCT
cana-951	282	14	"	"	PUNCT
cana-951	283	1	international	international	ADJ
cana-951	283	2	journal	journal	NOUN
cana-951	283	3	of	of	ADP
cana-951	283	4	nonlinear	nonlinear	PROPN
cana-951	283	5	sciences	sciences	PROPN
cana-951	283	6	and	and	CCONJ
cana-951	283	7	numerical	numerical	PROPN
cana-951	283	8	simulation	simulation	PROPN
cana-951	283	9	18.6	18.6	NUM
cana-951	283	10	(	(	PUNCT
cana-951	283	11	2017	2017	NUM
cana-951	283	12	):	):	PUNCT
cana-951	283	13	541	541	NUM
cana-951	283	14	-	-	SYM
cana-951	283	15	547	547	NUM
cana-951	283	16	.	.	PUNCT
cana-951	284	1	[	[	X
cana-951	284	2	23	23	NUM
cana-951	284	3	]	]	X
cana-951	284	4	mezache	mezache	PROPN
cana-951	284	5	,	,	PUNCT
cana-951	284	6	zinelabiddine	zinelabiddine	NOUN
cana-951	284	7	,	,	PUNCT
cana-951	284	8	and	and	CCONJ
cana-951	284	9	fatiha	fatiha	PROPN
cana-951	284	10	benabdelaziz	benabdelaziz	PROPN
cana-951	284	11	.	.	PUNCT
cana-951	285	1	"	"	PUNCT
cana-951	285	2	nonlinear	nonlinear	ADJ
cana-951	285	3	effects	effect	NOUN
cana-951	285	4	in	in	ADP
cana-951	285	5	chiral	chiral	ADJ
cana-951	285	6	nihility	nihility	NOUN
cana-951	285	7	metamaterial	metamaterial	NOUN
cana-951	285	8	.	.	PUNCT
cana-951	285	9	"	"	PUNCT
cana-951	286	1	optical	optical	ADJ
cana-951	286	2	and	and	CCONJ
cana-951	286	3	quantum	quantum	ADJ
cana-951	286	4	electronics	electronic	NOUN
cana-951	286	5	50.8	50.8	NUM
cana-951	286	6	(	(	PUNCT
cana-951	286	7	2018	2018	NUM
cana-951	286	8	):	):	PUNCT
cana-951	286	9	1	1	NUM
cana-951	286	10	-	-	SYM
cana-951	286	11	10	10	NUM
cana-951	286	12	.	.	PUNCT
cana-951	287	1	[	[	X
cana-951	287	2	24	24	NUM
cana-951	287	3	]	]	PUNCT
cana-951	287	4	ameen	ameen	NOUN
cana-951	287	5	,	,	PUNCT
cana-951	287	6	ismail	ismail	PROPN
cana-951	287	7	gad	gad	PROPN
cana-951	287	8	,	,	PUNCT
cana-951	287	9	taie	taie	PROPN
cana-951	287	10	,	,	PUNCT
cana-951	287	11	rasha	rasha	PROPN
cana-951	287	12	osman	osman	PROPN
cana-951	287	13	ahmed	ahmed	PROPN
cana-951	287	14	,	,	PUNCT
cana-951	287	15	and	and	CCONJ
cana-951	287	16	ali	ali	PROPN
cana-951	287	17	,	,	PUNCT
cana-951	287	18	hegagi	hegagi	PROPN
cana-951	287	19	mohamed	mohamed	PROPN
cana-951	287	20	.	.	PUNCT
cana-951	288	1	two	two	NUM
cana-951	288	2	effective	effective	ADJ
cana-951	288	3	methods	method	NOUN
cana-951	288	4	for	for	ADP
cana-951	288	5	solving	solve	VERB
cana-951	288	6	nonlinear	nonlinear	NOUN
cana-951	288	7	coupled	couple	VERB
cana-951	288	8	time	time	NOUN
cana-951	288	9	-	-	PUNCT
cana-951	288	10	fractional	fractional	ADJ
cana-951	288	11	schrödinger	schrödinger	ADJ
cana-951	288	12	equations	equation	NOUN
cana-951	288	13	.	.	PUNCT
cana-951	289	1	alexandria	alexandria	PROPN
cana-951	289	2	engineering	engineering	PROPN
cana-951	289	3	journal	journal	PROPN
cana-951	289	4	,	,	PUNCT
cana-951	289	5	2023	2023	NUM
cana-951	289	6	,	,	PUNCT
cana-951	289	7	vol	vol	NOUN
cana-951	289	8	.	.	PROPN
cana-951	289	9	70	70	NUM
cana-951	289	10	,	,	PUNCT
cana-951	289	11	p.	p.	NOUN
cana-951	289	12	331	331	NUM
cana-951	289	13	-	-	SYM
cana-951	289	14	347	347	NUM
cana-951	289	15	.	.	PUNCT