id	sid	tid	token	lemma	pos
ejpam-5936	1	1	european	european	PROPN
ejpam-5936	1	2	journal	journal	PROPN
ejpam-5936	1	3	of	of	ADP
ejpam-5936	1	4	pure	pure	ADJ
ejpam-5936	1	5	and	and	CCONJ
ejpam-5936	1	6	applied	applied	ADJ
ejpam-5936	1	7	mathematics	mathematic	NOUN
ejpam-5936	1	8	2025	2025	NUM
ejpam-5936	1	9	,	,	PUNCT
ejpam-5936	1	10	vol	vol	NOUN
ejpam-5936	1	11	.	.	PROPN
ejpam-5936	1	12	18	18	NUM
ejpam-5936	1	13	,	,	PUNCT
ejpam-5936	1	14	issue	issue	NOUN
ejpam-5936	1	15	2	2	NUM
ejpam-5936	1	16	,	,	PUNCT
ejpam-5936	1	17	article	article	NOUN
ejpam-5936	1	18	number	number	NOUN
ejpam-5936	1	19	5936	5936	NUM
ejpam-5936	1	20	issn	issn	PROPN
ejpam-5936	1	21	1307	1307	NUM
ejpam-5936	1	22	-	-	SYM
ejpam-5936	1	23	5543	5543	NUM
ejpam-5936	1	24	–	–	PUNCT
ejpam-5936	1	25	ejpam.com	ejpam.com	X
ejpam-5936	1	26	published	publish	VERB
ejpam-5936	1	27	by	by	ADP
ejpam-5936	1	28	new	new	PROPN
ejpam-5936	1	29	york	york	PROPN
ejpam-5936	1	30	business	business	PROPN
ejpam-5936	1	31	global	global	ADJ
ejpam-5936	1	32	novel	novel	ADJ
ejpam-5936	1	33	exact	exact	ADJ
ejpam-5936	1	34	solutions	solution	NOUN
ejpam-5936	1	35	for	for	ADP
ejpam-5936	1	36	a	a	DET
ejpam-5936	1	37	biological	biological	ADJ
ejpam-5936	1	38	population	population	NOUN
ejpam-5936	1	39	model	model	NOUN
ejpam-5936	1	40	using	use	VERB
ejpam-5936	1	41	the	the	DET
ejpam-5936	1	42	power	power	NOUN
ejpam-5936	1	43	index	index	NOUN
ejpam-5936	1	44	method	method	PROPN
ejpam-5936	1	45	zeshan	zeshan	PROPN
ejpam-5936	1	46	haider1,∗	haider1,∗	PROPN
ejpam-5936	1	47	,	,	PUNCT
ejpam-5936	1	48	khalil	khalil	PROPN
ejpam-5936	1	49	ahmad1	ahmad1	PROPN
ejpam-5936	1	50	1	1	NUM
ejpam-5936	1	51	department	department	NOUN
ejpam-5936	1	52	of	of	ADP
ejpam-5936	1	53	mathematics	mathematic	NOUN
ejpam-5936	1	54	,	,	PUNCT
ejpam-5936	1	55	faculty	faculty	NOUN
ejpam-5936	1	56	of	of	ADP
ejpam-5936	1	57	basic	basic	ADJ
ejpam-5936	1	58	and	and	CCONJ
ejpam-5936	1	59	applied	applied	ADJ
ejpam-5936	1	60	sciences	science	NOUN
ejpam-5936	1	61	,	,	PUNCT
ejpam-5936	1	62	air	air	NOUN
ejpam-5936	1	63	university	university	PROPN
ejpam-5936	1	64	,	,	PUNCT
ejpam-5936	1	65	paf	paf	PROPN
ejpam-5936	1	66	complex	complex	PROPN
ejpam-5936	1	67	e-9	e-9	PROPN
ejpam-5936	1	68	,	,	PUNCT
ejpam-5936	1	69	islamabad	islamabad	NOUN
ejpam-5936	1	70	44000	44000	NUM
ejpam-5936	1	71	,	,	PUNCT
ejpam-5936	1	72	pakistan	pakistan	PROPN
ejpam-5936	1	73	abstract	abstract	NOUN
ejpam-5936	1	74	.	.	PUNCT
ejpam-5936	2	1	in	in	ADP
ejpam-5936	2	2	this	this	DET
ejpam-5936	2	3	paper	paper	NOUN
ejpam-5936	2	4	,	,	PUNCT
ejpam-5936	2	5	we	we	PRON
ejpam-5936	2	6	study	study	VERB
ejpam-5936	2	7	a	a	DET
ejpam-5936	2	8	nonlinear	nonlinear	ADJ
ejpam-5936	2	9	biological	biological	ADJ
ejpam-5936	2	10	population	population	NOUN
ejpam-5936	2	11	model	model	NOUN
ejpam-5936	2	12	that	that	PRON
ejpam-5936	2	13	describes	describe	VERB
ejpam-5936	2	14	the	the	DET
ejpam-5936	2	15	spatiotemporal	spatiotemporal	ADJ
ejpam-5936	2	16	evolution	evolution	NOUN
ejpam-5936	2	17	of	of	ADP
ejpam-5936	2	18	population	population	NOUN
ejpam-5936	2	19	density	density	NOUN
ejpam-5936	2	20	,	,	PUNCT
ejpam-5936	2	21	incorporating	incorporate	VERB
ejpam-5936	2	22	nonlinear	nonlinear	ADJ
ejpam-5936	2	23	diffusion	diffusion	NOUN
ejpam-5936	2	24	and	and	CCONJ
ejpam-5936	2	25	reaction	reaction	NOUN
ejpam-5936	2	26	effects	effect	NOUN
ejpam-5936	2	27	.	.	PUNCT
ejpam-5936	3	1	using	use	VERB
ejpam-5936	3	2	the	the	DET
ejpam-5936	3	3	power	power	NOUN
ejpam-5936	3	4	index	index	NOUN
ejpam-5936	3	5	method	method	NOUN
ejpam-5936	3	6	,	,	PUNCT
ejpam-5936	3	7	we	we	PRON
ejpam-5936	3	8	derive	derive	VERB
ejpam-5936	3	9	exact	exact	ADJ
ejpam-5936	3	10	solutions	solution	NOUN
ejpam-5936	3	11	for	for	ADP
ejpam-5936	3	12	this	this	DET
ejpam-5936	3	13	model	model	NOUN
ejpam-5936	3	14	.	.	PUNCT
ejpam-5936	4	1	in	in	ADP
ejpam-5936	4	2	this	this	DET
ejpam-5936	4	3	approach	approach	NOUN
ejpam-5936	4	4	,	,	PUNCT
ejpam-5936	4	5	we	we	PRON
ejpam-5936	4	6	select	select	VERB
ejpam-5936	4	7	appropriate	appropriate	ADJ
ejpam-5936	4	8	indexes	index	NOUN
ejpam-5936	4	9	for	for	ADP
ejpam-5936	4	10	the	the	DET
ejpam-5936	4	11	independent	independent	ADJ
ejpam-5936	4	12	variable	variable	NOUN
ejpam-5936	4	13	in	in	ADP
ejpam-5936	4	14	the	the	DET
ejpam-5936	4	15	similarity	similarity	NOUN
ejpam-5936	4	16	transformation	transformation	NOUN
ejpam-5936	4	17	,	,	PUNCT
ejpam-5936	4	18	allowing	allow	VERB
ejpam-5936	4	19	the	the	DET
ejpam-5936	4	20	unknown	unknown	ADJ
ejpam-5936	4	21	functions	function	NOUN
ejpam-5936	4	22	to	to	PART
ejpam-5936	4	23	take	take	VERB
ejpam-5936	4	24	polynomial	polynomial	ADJ
ejpam-5936	4	25	,	,	PUNCT
ejpam-5936	4	26	rational	rational	ADJ
ejpam-5936	4	27	,	,	PUNCT
ejpam-5936	4	28	or	or	CCONJ
ejpam-5936	4	29	other	other	ADJ
ejpam-5936	4	30	elementary	elementary	ADJ
ejpam-5936	4	31	forms	form	NOUN
ejpam-5936	4	32	.	.	PUNCT
ejpam-5936	5	1	these	these	DET
ejpam-5936	5	2	transformations	transformation	NOUN
ejpam-5936	5	3	reduce	reduce	VERB
ejpam-5936	5	4	the	the	DET
ejpam-5936	5	5	nonlinear	nonlinear	ADJ
ejpam-5936	5	6	partial	partial	ADJ
ejpam-5936	5	7	differential	differential	NOUN
ejpam-5936	5	8	equation	equation	NOUN
ejpam-5936	5	9	(	(	PUNCT
ejpam-5936	5	10	nlpde	nlpde	NOUN
ejpam-5936	5	11	)	)	PUNCT
ejpam-5936	5	12	to	to	PART
ejpam-5936	5	13	nonlinear	nonlinear	VERB
ejpam-5936	5	14	ordinary	ordinary	ADJ
ejpam-5936	5	15	differential	differential	ADJ
ejpam-5936	5	16	equations	equation	NOUN
ejpam-5936	5	17	(	(	PUNCT
ejpam-5936	5	18	nlodes	nlode	NOUN
ejpam-5936	5	19	)	)	PUNCT
ejpam-5936	5	20	.	.	PUNCT
ejpam-5936	6	1	we	we	PRON
ejpam-5936	6	2	then	then	ADV
ejpam-5936	6	3	solve	solve	VERB
ejpam-5936	6	4	the	the	DET
ejpam-5936	6	5	nonlinear	nonlinear	ADJ
ejpam-5936	6	6	ordinary	ordinary	ADJ
ejpam-5936	6	7	differential	differential	ADJ
ejpam-5936	6	8	equations	equation	NOUN
ejpam-5936	6	9	(	(	PUNCT
ejpam-5936	6	10	nlodes	nlode	NOUN
ejpam-5936	6	11	)	)	PUNCT
ejpam-5936	6	12	exactly	exactly	ADV
ejpam-5936	6	13	using	use	VERB
ejpam-5936	6	14	maple	maple	NOUN
ejpam-5936	6	15	.	.	PUNCT
ejpam-5936	7	1	finally	finally	ADV
ejpam-5936	7	2	,	,	PUNCT
ejpam-5936	7	3	by	by	ADP
ejpam-5936	7	4	applying	apply	VERB
ejpam-5936	7	5	the	the	DET
ejpam-5936	7	6	similarity	similarity	NOUN
ejpam-5936	7	7	transformations	transformation	NOUN
ejpam-5936	7	8	and	and	CCONJ
ejpam-5936	7	9	the	the	DET
ejpam-5936	7	10	exact	exact	ADJ
ejpam-5936	7	11	solutions	solution	NOUN
ejpam-5936	7	12	of	of	ADP
ejpam-5936	7	13	the	the	DET
ejpam-5936	7	14	nonlinear	nonlinear	ADJ
ejpam-5936	7	15	ordinary	ordinary	ADJ
ejpam-5936	7	16	differential	differential	ADJ
ejpam-5936	7	17	equations	equation	NOUN
ejpam-5936	7	18	(	(	PUNCT
ejpam-5936	7	19	nlodes	nlode	NOUN
ejpam-5936	7	20	)	)	PUNCT
ejpam-5936	7	21	,	,	PUNCT
ejpam-5936	7	22	we	we	PRON
ejpam-5936	7	23	obtain	obtain	VERB
ejpam-5936	7	24	the	the	DET
ejpam-5936	7	25	exact	exact	ADJ
ejpam-5936	7	26	solutions	solution	NOUN
ejpam-5936	7	27	of	of	ADP
ejpam-5936	7	28	the	the	DET
ejpam-5936	7	29	nonlinear	nonlinear	ADJ
ejpam-5936	7	30	biological	biological	ADJ
ejpam-5936	7	31	population	population	NOUN
ejpam-5936	7	32	model	model	NOUN
ejpam-5936	7	33	.	.	PUNCT
ejpam-5936	8	1	the	the	DET
ejpam-5936	8	2	behavior	behavior	NOUN
ejpam-5936	8	3	of	of	ADP
ejpam-5936	8	4	the	the	DET
ejpam-5936	8	5	solutions	solution	NOUN
ejpam-5936	8	6	is	be	AUX
ejpam-5936	8	7	illustrated	illustrate	VERB
ejpam-5936	8	8	through	through	ADP
ejpam-5936	8	9	3d	3d	NUM
ejpam-5936	8	10	graphs	graph	NOUN
ejpam-5936	8	11	.	.	PUNCT
ejpam-5936	9	1	the	the	DET
ejpam-5936	9	2	results	result	NOUN
ejpam-5936	9	3	demonstrate	demonstrate	VERB
ejpam-5936	9	4	that	that	SCONJ
ejpam-5936	9	5	the	the	DET
ejpam-5936	9	6	proposed	propose	VERB
ejpam-5936	9	7	method	method	NOUN
ejpam-5936	9	8	is	be	AUX
ejpam-5936	9	9	straightforward	straightforward	ADJ
ejpam-5936	9	10	,	,	PUNCT
ejpam-5936	9	11	powerful	powerful	ADJ
ejpam-5936	9	12	,	,	PUNCT
ejpam-5936	9	13	and	and	CCONJ
ejpam-5936	9	14	capable	capable	ADJ
ejpam-5936	9	15	of	of	ADP
ejpam-5936	9	16	yielding	yield	VERB
ejpam-5936	9	17	exact	exact	ADJ
ejpam-5936	9	18	solutions	solution	NOUN
ejpam-5936	9	19	,	,	PUNCT
ejpam-5936	9	20	revealing	reveal	VERB
ejpam-5936	9	21	biological	biological	ADJ
ejpam-5936	9	22	phenomena	phenomenon	NOUN
ejpam-5936	9	23	such	such	ADJ
ejpam-5936	9	24	as	as	ADP
ejpam-5936	9	25	nonlinear	nonlinear	ADJ
ejpam-5936	9	26	diffusion	diffusion	NOUN
ejpam-5936	9	27	,	,	PUNCT
ejpam-5936	9	28	wave	wave	NOUN
ejpam-5936	9	29	propagation	propagation	NOUN
ejpam-5936	9	30	,	,	PUNCT
ejpam-5936	9	31	and	and	CCONJ
ejpam-5936	9	32	decay	decay	NOUN
ejpam-5936	9	33	effects	effect	NOUN
ejpam-5936	9	34	.	.	PUNCT
ejpam-5936	10	1	2020	2020	NUM
ejpam-5936	10	2	mathematics	mathematic	NOUN
ejpam-5936	10	3	subject	subject	NOUN
ejpam-5936	10	4	classifications	classification	NOUN
ejpam-5936	10	5	:	:	PUNCT
ejpam-5936	10	6	35qxx	35qxx	NOUN
ejpam-5936	10	7	,	,	PUNCT
ejpam-5936	10	8	26a33	26a33	NUM
ejpam-5936	10	9	key	key	ADJ
ejpam-5936	10	10	words	word	NOUN
ejpam-5936	10	11	and	and	CCONJ
ejpam-5936	10	12	phrases	phrase	NOUN
ejpam-5936	10	13	:	:	PUNCT
ejpam-5936	10	14	partial	partial	ADJ
ejpam-5936	10	15	differential	differential	NOUN
ejpam-5936	10	16	equation	equation	NOUN
ejpam-5936	10	17	,	,	PUNCT
ejpam-5936	10	18	ordinary	ordinary	ADJ
ejpam-5936	10	19	differential	differential	ADJ
ejpam-5936	10	20	equation	equation	NOUN
ejpam-5936	10	21	,	,	PUNCT
ejpam-5936	10	22	exact	exact	ADJ
ejpam-5936	10	23	solution	solution	NOUN
ejpam-5936	10	24	,	,	PUNCT
ejpam-5936	10	25	power	power	NOUN
ejpam-5936	10	26	index	index	NOUN
ejpam-5936	10	27	method	method	NOUN
ejpam-5936	10	28	,	,	PUNCT
ejpam-5936	10	29	biological	biological	ADJ
ejpam-5936	10	30	population	population	NOUN
ejpam-5936	10	31	model	model	NOUN
ejpam-5936	10	32	1	1	NUM
ejpam-5936	10	33	.	.	PUNCT
ejpam-5936	11	1	introduction	introduction	NOUN
ejpam-5936	11	2	nonlinear	nonlinear	ADJ
ejpam-5936	11	3	partial	partial	ADJ
ejpam-5936	11	4	differential	differential	NOUN
ejpam-5936	11	5	equations	equation	NOUN
ejpam-5936	11	6	(	(	PUNCT
ejpam-5936	11	7	nlpdes	nlpdes	PROPN
ejpam-5936	11	8	)	)	PUNCT
ejpam-5936	11	9	play	play	VERB
ejpam-5936	11	10	a	a	DET
ejpam-5936	11	11	fundamental	fundamental	ADJ
ejpam-5936	11	12	role	role	NOUN
ejpam-5936	11	13	in	in	ADP
ejpam-5936	11	14	modeling	model	VERB
ejpam-5936	11	15	complex	complex	ADJ
ejpam-5936	11	16	phenomena	phenomenon	NOUN
ejpam-5936	11	17	across	across	ADP
ejpam-5936	11	18	various	various	ADJ
ejpam-5936	11	19	scientific	scientific	ADJ
ejpam-5936	11	20	and	and	CCONJ
ejpam-5936	11	21	engineering	engineering	NOUN
ejpam-5936	11	22	disciplines	discipline	NOUN
ejpam-5936	11	23	,	,	PUNCT
ejpam-5936	11	24	including	include	VERB
ejpam-5936	11	25	hydrodynamics	hydrodynamic	NOUN
ejpam-5936	11	26	[	[	X
ejpam-5936	11	27	1	1	NUM
ejpam-5936	11	28	]	]	PUNCT
ejpam-5936	11	29	,	,	PUNCT
ejpam-5936	11	30	[	[	X
ejpam-5936	11	31	2	2	NUM
ejpam-5936	11	32	]	]	PUNCT
ejpam-5936	11	33	,	,	PUNCT
ejpam-5936	11	34	fluid	fluid	ADJ
ejpam-5936	11	35	dynamics	dynamic	NOUN
ejpam-5936	11	36	,	,	PUNCT
ejpam-5936	11	37	plasma	plasma	NOUN
ejpam-5936	11	38	physics	physics	NOUN
ejpam-5936	12	1	[	[	X
ejpam-5936	12	2	3	3	NUM
ejpam-5936	12	3	]	]	PUNCT
ejpam-5936	12	4	,	,	PUNCT
ejpam-5936	12	5	[	[	X
ejpam-5936	12	6	4	4	NUM
ejpam-5936	12	7	]	]	PUNCT
ejpam-5936	12	8	,	,	PUNCT
ejpam-5936	12	9	nonlinear	nonlinear	ADJ
ejpam-5936	12	10	optics	optic	NOUN
ejpam-5936	12	11	[	[	X
ejpam-5936	12	12	5	5	NUM
ejpam-5936	12	13	]	]	PUNCT
ejpam-5936	12	14	,	,	PUNCT
ejpam-5936	12	15	[	[	X
ejpam-5936	12	16	6	6	NUM
ejpam-5936	12	17	]	]	PUNCT
ejpam-5936	12	18	,	,	PUNCT
ejpam-5936	12	19	[	[	X
ejpam-5936	12	20	7	7	NUM
ejpam-5936	12	21	]	]	PUNCT
ejpam-5936	12	22	,	,	PUNCT
ejpam-5936	12	23	[	[	X
ejpam-5936	12	24	8	8	NUM
ejpam-5936	12	25	]	]	PUNCT
ejpam-5936	12	26	,	,	PUNCT
ejpam-5936	12	27	and	and	CCONJ
ejpam-5936	12	28	other	other	ADJ
ejpam-5936	12	29	fields	field	NOUN
ejpam-5936	12	30	[	[	X
ejpam-5936	12	31	9	9	NUM
ejpam-5936	12	32	]	]	PUNCT
ejpam-5936	12	33	,	,	PUNCT
ejpam-5936	12	34	[	[	X
ejpam-5936	12	35	10	10	NUM
ejpam-5936	12	36	]	]	PUNCT
ejpam-5936	12	37	,	,	PUNCT
ejpam-5936	12	38	[	[	X
ejpam-5936	12	39	11	11	NUM
ejpam-5936	12	40	]	]	PUNCT
ejpam-5936	12	41	.	.	PUNCT
ejpam-5936	13	1	the	the	DET
ejpam-5936	13	2	study	study	NOUN
ejpam-5936	13	3	of	of	ADP
ejpam-5936	13	4	exact	exact	ADJ
ejpam-5936	13	5	solutions	solution	NOUN
ejpam-5936	13	6	to	to	PART
ejpam-5936	13	7	nonlinear	nonlinear	VERB
ejpam-5936	13	8	partial	partial	ADJ
ejpam-5936	13	9	differential	differential	NOUN
ejpam-5936	13	10	equations	equation	NOUN
ejpam-5936	13	11	(	(	PUNCT
ejpam-5936	13	12	nlpdes	nlpde	NOUN
ejpam-5936	13	13	)	)	PUNCT
ejpam-5936	13	14	remains	remain	VERB
ejpam-5936	13	15	highly	highly	ADV
ejpam-5936	13	16	relevant	relevant	ADJ
ejpam-5936	13	17	,	,	PUNCT
ejpam-5936	13	18	as	as	SCONJ
ejpam-5936	13	19	it	it	PRON
ejpam-5936	13	20	provides	provide	VERB
ejpam-5936	13	21	deeper	deep	ADJ
ejpam-5936	13	22	insights	insight	NOUN
ejpam-5936	13	23	into	into	ADP
ejpam-5936	13	24	nonlinear	nonlinear	ADJ
ejpam-5936	13	25	wave	wave	NOUN
ejpam-5936	13	26	phenomena	phenomenon	NOUN
ejpam-5936	13	27	and	and	CCONJ
ejpam-5936	13	28	their	their	PRON
ejpam-5936	13	29	inherent	inherent	ADJ
ejpam-5936	13	30	characteristics	characteristic	NOUN
ejpam-5936	13	31	.	.	PUNCT
ejpam-5936	14	1	∗corresponding	∗corresponde	VERB
ejpam-5936	14	2	author	author	NOUN
ejpam-5936	14	3	.	.	PUNCT
ejpam-5936	15	1	doi	doi	NOUN
ejpam-5936	15	2	:	:	PUNCT
ejpam-5936	15	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5936	https://doi.org/10.29020/nybg.ejpam.v18i2.5936	ADP
ejpam-5936	15	4	email	email	NOUN
ejpam-5936	15	5	addresses	address	NOUN
ejpam-5936	15	6	:	:	PUNCT
ejpam-5936	15	7	211904@students.au.edu.pk	211904@students.au.edu.pk	NUM
ejpam-5936	15	8	(	(	PUNCT
ejpam-5936	15	9	z.	z.	PROPN
ejpam-5936	15	10	haider	haider	PROPN
ejpam-5936	15	11	)	)	PUNCT
ejpam-5936	15	12	,	,	PUNCT
ejpam-5936	16	1	khalilmalik@au.edu.pk	khalilmalik@au.edu.pk	PROPN
ejpam-5936	16	2	(	(	PUNCT
ejpam-5936	16	3	k.	k.	PROPN
ejpam-5936	16	4	ahmad	ahmad	PROPN
ejpam-5936	16	5	)	)	PUNCT
ejpam-5936	16	6	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5936	16	7	1	1	NUM
ejpam-5936	16	8	copyright	copyright	NOUN
ejpam-5936	16	9	:	:	PUNCT
ejpam-5936	16	10	©	©	PROPN
ejpam-5936	16	11	2025	2025	NUM
ejpam-5936	16	12	the	the	DET
ejpam-5936	16	13	author(s	author(s	NOUN
ejpam-5936	16	14	)	)	PUNCT
ejpam-5936	16	15	.	.	PUNCT
ejpam-5936	17	1	(	(	PUNCT
ejpam-5936	17	2	cc	cc	NOUN
ejpam-5936	17	3	by	by	ADP
ejpam-5936	17	4	-	-	PUNCT
ejpam-5936	17	5	nc	nc	PROPN
ejpam-5936	17	6	4.0	4.0	NUM
ejpam-5936	17	7	)	)	PUNCT
ejpam-5936	17	8	z.	z.	PROPN
ejpam-5936	17	9	haider	haider	PROPN
ejpam-5936	17	10	,	,	PUNCT
ejpam-5936	17	11	k.	k.	PROPN
ejpam-5936	17	12	ahmad	ahmad	PROPN
ejpam-5936	17	13	/	/	SYM
ejpam-5936	17	14	eur	eur	PROPN
ejpam-5936	17	15	.	.	PUNCT
ejpam-5936	18	1	j.	j.	PROPN
ejpam-5936	18	2	pure	pure	PROPN
ejpam-5936	18	3	appl	appl	PROPN
ejpam-5936	18	4	.	.	PROPN
ejpam-5936	18	5	math	math	PROPN
ejpam-5936	18	6	,	,	PUNCT
ejpam-5936	18	7	18	18	NUM
ejpam-5936	18	8	(	(	PUNCT
ejpam-5936	18	9	2	2	NUM
ejpam-5936	18	10	)	)	PUNCT
ejpam-5936	18	11	(	(	PUNCT
ejpam-5936	18	12	2025	2025	NUM
ejpam-5936	18	13	)	)	PUNCT
ejpam-5936	18	14	,	,	PUNCT
ejpam-5936	18	15	5936	5936	NUM
ejpam-5936	18	16	2	2	NUM
ejpam-5936	18	17	of	of	ADP
ejpam-5936	18	18	18	18	NUM
ejpam-5936	18	19	this	this	DET
ejpam-5936	18	20	article	article	NOUN
ejpam-5936	18	21	examines	examine	VERB
ejpam-5936	18	22	nonlinear	nonlinear	ADJ
ejpam-5936	18	23	degenerate	degenerate	ADJ
ejpam-5936	18	24	parabolic	parabolic	NOUN
ejpam-5936	18	25	equations	equation	NOUN
ejpam-5936	18	26	arising	arise	VERB
ejpam-5936	18	27	in	in	ADP
ejpam-5936	18	28	the	the	DET
ejpam-5936	18	29	spatial	spatial	ADJ
ejpam-5936	18	30	diffusion	diffusion	NOUN
ejpam-5936	18	31	of	of	ADP
ejpam-5936	18	32	biological	biological	ADJ
ejpam-5936	18	33	populations	population	NOUN
ejpam-5936	18	34	.	.	PUNCT
ejpam-5936	19	1	we	we	PRON
ejpam-5936	19	2	consider	consider	VERB
ejpam-5936	19	3	the	the	DET
ejpam-5936	19	4	following	follow	VERB
ejpam-5936	19	5	first	first	ADJ
ejpam-5936	19	6	-	-	PUNCT
ejpam-5936	19	7	order	order	NOUN
ejpam-5936	19	8	time	time	NOUN
ejpam-5936	19	9	-	-	PUNCT
ejpam-5936	19	10	dependent	dependent	ADJ
ejpam-5936	19	11	nonlinear	nonlinear	ADJ
ejpam-5936	19	12	biological	biological	ADJ
ejpam-5936	19	13	population	population	NOUN
ejpam-5936	19	14	model	model	NOUN
ejpam-5936	19	15	:	:	PUNCT
ejpam-5936	19	16	ut	ut	PROPN
ejpam-5936	19	17	−	−	PROPN
ejpam-5936	19	18	2u2x	2u2x	NUM
ejpam-5936	20	1	−	−	ADP
ejpam-5936	20	2	2uuxx	2uuxx	NUM
ejpam-5936	20	3	−	−	NOUN
ejpam-5936	20	4	2u2y	2u2y	NOUN
ejpam-5936	21	1	−	−	NOUN
ejpam-5936	22	1	2uuyy	2uuyy	NUM
ejpam-5936	23	1	−	−	NOUN
ejpam-5936	24	1	u	u	NOUN
ejpam-5936	25	1	=	=	NOUN
ejpam-5936	26	1	0	0	PROPN
ejpam-5936	26	2	.	.	PUNCT
ejpam-5936	27	1	(	(	PUNCT
ejpam-5936	27	2	1	1	X
ejpam-5936	27	3	)	)	PUNCT
ejpam-5936	27	4	in	in	ADP
ejpam-5936	27	5	equation	equation	NOUN
ejpam-5936	27	6	(	(	PUNCT
ejpam-5936	27	7	1	1	NUM
ejpam-5936	27	8	)	)	PUNCT
ejpam-5936	27	9	,	,	PUNCT
ejpam-5936	27	10	u(x	u(x	PROPN
ejpam-5936	27	11	,	,	PUNCT
ejpam-5936	27	12	y	y	PROPN
ejpam-5936	27	13	,	,	PUNCT
ejpam-5936	27	14	t	t	PROPN
ejpam-5936	27	15	)	)	PUNCT
ejpam-5936	27	16	represents	represent	VERB
ejpam-5936	27	17	the	the	DET
ejpam-5936	27	18	population	population	NOUN
ejpam-5936	27	19	density	density	NOUN
ejpam-5936	27	20	,	,	PUNCT
ejpam-5936	27	21	where	where	SCONJ
ejpam-5936	27	22	x	x	X
ejpam-5936	27	23	,	,	PUNCT
ejpam-5936	27	24	y	y	PROPN
ejpam-5936	27	25	,	,	PUNCT
ejpam-5936	27	26	and	and	CCONJ
ejpam-5936	27	27	t	t	PROPN
ejpam-5936	27	28	are	be	AUX
ejpam-5936	27	29	the	the	DET
ejpam-5936	27	30	independent	independent	ADJ
ejpam-5936	27	31	variables	variable	NOUN
ejpam-5936	27	32	.	.	PUNCT
ejpam-5936	28	1	the	the	DET
ejpam-5936	28	2	term	term	NOUN
ejpam-5936	28	3	ut	ut	PROPN
ejpam-5936	28	4	denotes	denote	VERB
ejpam-5936	28	5	the	the	DET
ejpam-5936	28	6	population	population	NOUN
ejpam-5936	28	7	growth	growth	NOUN
ejpam-5936	28	8	rate	rate	NOUN
ejpam-5936	28	9	,	,	PUNCT
ejpam-5936	28	10	while	while	SCONJ
ejpam-5936	28	11	the	the	DET
ejpam-5936	28	12	terms	term	NOUN
ejpam-5936	28	13	−2u2x	−2u2x	PROPN
ejpam-5936	28	14	and	and	CCONJ
ejpam-5936	28	15	−2u2y	−2u2y	PROPN
ejpam-5936	28	16	describe	describe	VERB
ejpam-5936	28	17	population	population	NOUN
ejpam-5936	28	18	movement	movement	NOUN
ejpam-5936	28	19	influenced	influence	VERB
ejpam-5936	28	20	by	by	ADP
ejpam-5936	28	21	local	local	ADJ
ejpam-5936	28	22	density	density	NOUN
ejpam-5936	28	23	gradients	gradient	NOUN
ejpam-5936	28	24	,	,	PUNCT
ejpam-5936	28	25	potentially	potentially	ADV
ejpam-5936	28	26	modeling	model	VERB
ejpam-5936	28	27	phenomena	phenomenon	NOUN
ejpam-5936	28	28	like	like	ADP
ejpam-5936	28	29	density	density	NOUN
ejpam-5936	28	30	-	-	PUNCT
ejpam-5936	28	31	dependent	dependent	ADJ
ejpam-5936	28	32	dispersal	dispersal	NOUN
ejpam-5936	28	33	.	.	PUNCT
ejpam-5936	29	1	the	the	DET
ejpam-5936	29	2	nonlinear	nonlinear	ADJ
ejpam-5936	29	3	diffusion	diffusion	NOUN
ejpam-5936	29	4	terms	term	NOUN
ejpam-5936	29	5	−2uuxx	−2uuxx	PROPN
ejpam-5936	29	6	and	and	CCONJ
ejpam-5936	29	7	−2uuyy	−2uuyy	PROPN
ejpam-5936	29	8	indicate	indicate	VERB
ejpam-5936	29	9	that	that	SCONJ
ejpam-5936	29	10	the	the	DET
ejpam-5936	29	11	rate	rate	NOUN
ejpam-5936	29	12	of	of	ADP
ejpam-5936	29	13	population	population	NOUN
ejpam-5936	29	14	spread	spread	NOUN
ejpam-5936	29	15	depends	depend	VERB
ejpam-5936	29	16	on	on	ADP
ejpam-5936	29	17	the	the	DET
ejpam-5936	29	18	local	local	ADJ
ejpam-5936	29	19	population	population	NOUN
ejpam-5936	29	20	density	density	NOUN
ejpam-5936	29	21	.	.	PUNCT
ejpam-5936	30	1	finally	finally	ADV
ejpam-5936	30	2	,	,	PUNCT
ejpam-5936	30	3	the	the	DET
ejpam-5936	30	4	term	term	NOUN
ejpam-5936	30	5	−u	−u	PRON
ejpam-5936	30	6	represents	represent	VERB
ejpam-5936	30	7	a	a	DET
ejpam-5936	30	8	linear	linear	ADJ
ejpam-5936	30	9	decay	decay	NOUN
ejpam-5936	30	10	in	in	ADP
ejpam-5936	30	11	population	population	NOUN
ejpam-5936	30	12	density	density	NOUN
ejpam-5936	30	13	.	.	PUNCT
ejpam-5936	31	1	many	many	ADJ
ejpam-5936	31	2	researchers	researcher	NOUN
ejpam-5936	31	3	have	have	AUX
ejpam-5936	31	4	analytically	analytically	ADV
ejpam-5936	31	5	and	and	CCONJ
ejpam-5936	31	6	numerically	numerically	ADV
ejpam-5936	31	7	explored	explore	VERB
ejpam-5936	31	8	biological	biological	ADJ
ejpam-5936	31	9	population	population	NOUN
ejpam-5936	31	10	models	model	NOUN
ejpam-5936	31	11	,	,	PUNCT
ejpam-5936	31	12	extensively	extensively	ADV
ejpam-5936	31	13	studying	study	VERB
ejpam-5936	31	14	exact	exact	ADJ
ejpam-5936	31	15	solutions	solution	NOUN
ejpam-5936	31	16	to	to	ADP
ejpam-5936	31	17	these	these	DET
ejpam-5936	31	18	systems	system	NOUN
ejpam-5936	31	19	.	.	PUNCT
ejpam-5936	32	1	bekir	bekir	PROPN
ejpam-5936	32	2	and	and	CCONJ
ejpam-5936	32	3	gunner	gunner	NOUN
ejpam-5936	33	1	[	[	X
ejpam-5936	33	2	12	12	NUM
ejpam-5936	33	3	]	]	PUNCT
ejpam-5936	33	4	investigated	investigate	VERB
ejpam-5936	33	5	a	a	DET
ejpam-5936	33	6	nonlinear	nonlinear	ADJ
ejpam-5936	33	7	fractional	fractional	ADJ
ejpam-5936	33	8	biological	biological	ADJ
ejpam-5936	33	9	population	population	NOUN
ejpam-5936	33	10	model	model	NOUN
ejpam-5936	33	11	using	use	VERB
ejpam-5936	33	12	the	the	DET
ejpam-5936	33	13	(	(	PUNCT
ejpam-5936	33	14	g	g	PROPN
ejpam-5936	33	15	′	′	NUM
ejpam-5936	33	16	/g)-expansion	/g)-expansion	SYM
ejpam-5936	33	17	method	method	NOUN
ejpam-5936	33	18	,	,	PUNCT
ejpam-5936	33	19	obtaining	obtain	VERB
ejpam-5936	33	20	hyperbolic	hyperbolic	ADJ
ejpam-5936	33	21	and	and	CCONJ
ejpam-5936	33	22	trigonometric	trigonometric	ADJ
ejpam-5936	33	23	function	function	NOUN
ejpam-5936	33	24	solutions	solution	NOUN
ejpam-5936	33	25	.	.	PUNCT
ejpam-5936	34	1	hassan	hassan	PROPN
ejpam-5936	34	2	and	and	CCONJ
ejpam-5936	34	3	mohyud	mohyud	NOUN
ejpam-5936	34	4	-	-	PUNCT
ejpam-5936	34	5	din	din	NOUN
ejpam-5936	34	6	[	[	X
ejpam-5936	34	7	13	13	NUM
ejpam-5936	34	8	]	]	PUNCT
ejpam-5936	34	9	employed	employ	VERB
ejpam-5936	34	10	the	the	DET
ejpam-5936	34	11	exp	exp	NOUN
ejpam-5936	34	12	-	-	PUNCT
ejpam-5936	34	13	function	function	NOUN
ejpam-5936	34	14	method	method	NOUN
ejpam-5936	34	15	to	to	PART
ejpam-5936	34	16	derive	derive	VERB
ejpam-5936	34	17	generalized	generalized	ADJ
ejpam-5936	34	18	exact	exact	ADJ
ejpam-5936	34	19	solutions	solution	NOUN
ejpam-5936	34	20	for	for	ADP
ejpam-5936	34	21	fractional	fractional	ADJ
ejpam-5936	34	22	biological	biological	ADJ
ejpam-5936	34	23	population	population	NOUN
ejpam-5936	34	24	models	model	NOUN
ejpam-5936	34	25	.	.	PUNCT
ejpam-5936	35	1	shakeri	shakeri	ADJ
ejpam-5936	35	2	and	and	CCONJ
ejpam-5936	35	3	dehghan	dehghan	PROPN
ejpam-5936	35	4	[	[	X
ejpam-5936	35	5	14	14	NUM
ejpam-5936	35	6	]	]	PUNCT
ejpam-5936	35	7	numerically	numerically	ADV
ejpam-5936	35	8	solved	solve	VERB
ejpam-5936	35	9	the	the	DET
ejpam-5936	35	10	biological	biological	ADJ
ejpam-5936	35	11	population	population	NOUN
ejpam-5936	35	12	model	model	NOUN
ejpam-5936	35	13	using	use	VERB
ejpam-5936	35	14	he	he	PRON
ejpam-5936	35	15	’s	’s	PART
ejpam-5936	35	16	variational	variational	ADJ
ejpam-5936	35	17	iteration	iteration	NOUN
ejpam-5936	35	18	method	method	NOUN
ejpam-5936	35	19	and	and	CCONJ
ejpam-5936	35	20	adomian	adomian	NOUN
ejpam-5936	35	21	’s	’s	PART
ejpam-5936	35	22	decomposition	decomposition	NOUN
ejpam-5936	35	23	method	method	NOUN
ejpam-5936	35	24	.	.	PUNCT
ejpam-5936	36	1	bushnaq	bushnaq	PROPN
ejpam-5936	36	2	et	et	PROPN
ejpam-5936	36	3	al	al	PROPN
ejpam-5936	36	4	.	.	PUNCT
ejpam-5936	37	1	[	[	X
ejpam-5936	37	2	15	15	NUM
ejpam-5936	37	3	]	]	PUNCT
ejpam-5936	37	4	applied	apply	VERB
ejpam-5936	37	5	the	the	DET
ejpam-5936	37	6	optimal	optimal	ADJ
ejpam-5936	37	7	homotopy	homotopy	NOUN
ejpam-5936	37	8	asymptotic	asymptotic	ADJ
ejpam-5936	37	9	method	method	NOUN
ejpam-5936	37	10	to	to	PART
ejpam-5936	37	11	derive	derive	VERB
ejpam-5936	37	12	exact	exact	ADJ
ejpam-5936	37	13	solutions	solution	NOUN
ejpam-5936	37	14	for	for	ADP
ejpam-5936	37	15	the	the	DET
ejpam-5936	37	16	nonlinear	nonlinear	ADJ
ejpam-5936	37	17	fractional	fractional	ADJ
ejpam-5936	37	18	-	-	PUNCT
ejpam-5936	37	19	order	order	NOUN
ejpam-5936	37	20	biological	biological	ADJ
ejpam-5936	37	21	population	population	NOUN
ejpam-5936	37	22	model	model	NOUN
ejpam-5936	37	23	.	.	PUNCT
ejpam-5936	38	1	muhammad	muhammad	PROPN
ejpam-5936	38	2	shakeel	shakeel	PROPN
ejpam-5936	38	3	et	et	PROPN
ejpam-5936	38	4	al	al	PROPN
ejpam-5936	38	5	.	.	PUNCT
ejpam-5936	39	1	[	[	X
ejpam-5936	39	2	16	16	NUM
ejpam-5936	39	3	]	]	PUNCT
ejpam-5936	39	4	obtained	obtain	VERB
ejpam-5936	39	5	closed	closed	ADJ
ejpam-5936	39	6	-	-	PUNCT
ejpam-5936	39	7	form	form	NOUN
ejpam-5936	39	8	solutions	solution	NOUN
ejpam-5936	39	9	via	via	ADP
ejpam-5936	39	10	the	the	DET
ejpam-5936	39	11	modified	modify	VERB
ejpam-5936	39	12	exp	exp	NOUN
ejpam-5936	39	13	-	-	PUNCT
ejpam-5936	39	14	function	function	NOUN
ejpam-5936	39	15	method	method	NOUN
ejpam-5936	39	16	,	,	PUNCT
ejpam-5936	39	17	while	while	SCONJ
ejpam-5936	39	18	mohammad	mohammad	PROPN
ejpam-5936	39	19	ali	ali	PROPN
ejpam-5936	39	20	zirak	zirak	PROPN
ejpam-5936	39	21	and	and	CCONJ
ejpam-5936	39	22	abbas	abbas	PROPN
ejpam-5936	39	23	poya	poya	PROPN
ejpam-5936	40	1	[	[	X
ejpam-5936	40	2	17	17	NUM
ejpam-5936	40	3	]	]	PUNCT
ejpam-5936	40	4	developed	develop	VERB
ejpam-5936	40	5	analytical	analytical	ADJ
ejpam-5936	40	6	solutions	solution	NOUN
ejpam-5936	40	7	for	for	ADP
ejpam-5936	40	8	fractional	fractional	ADJ
ejpam-5936	40	9	biological	biological	ADJ
ejpam-5936	40	10	population	population	NOUN
ejpam-5936	40	11	differential	differential	NOUN
ejpam-5936	40	12	equations	equation	NOUN
ejpam-5936	40	13	using	use	VERB
ejpam-5936	40	14	reconstructed	reconstructed	ADJ
ejpam-5936	40	15	variational	variational	ADJ
ejpam-5936	40	16	iteration	iteration	NOUN
ejpam-5936	40	17	.	.	PUNCT
ejpam-5936	41	1	khater	khater	NOUN
ejpam-5936	41	2	et	et	PROPN
ejpam-5936	41	3	al	al	PROPN
ejpam-5936	41	4	.	.	PUNCT
ejpam-5936	42	1	[	[	X
ejpam-5936	42	2	18	18	NUM
ejpam-5936	42	3	]	]	PUNCT
ejpam-5936	42	4	conducted	conduct	VERB
ejpam-5936	42	5	a	a	DET
ejpam-5936	42	6	comprehensive	comprehensive	ADJ
ejpam-5936	42	7	computational	computational	ADJ
ejpam-5936	42	8	and	and	CCONJ
ejpam-5936	42	9	numerical	numerical	ADJ
ejpam-5936	42	10	study	study	NOUN
ejpam-5936	42	11	of	of	ADP
ejpam-5936	42	12	nonlinear	nonlinear	ADJ
ejpam-5936	42	13	biological	biological	ADJ
ejpam-5936	42	14	population	population	NOUN
ejpam-5936	42	15	models	model	NOUN
ejpam-5936	42	16	,	,	PUNCT
ejpam-5936	42	17	demonstrating	demonstrate	VERB
ejpam-5936	42	18	the	the	DET
ejpam-5936	42	19	efficacy	efficacy	NOUN
ejpam-5936	42	20	of	of	ADP
ejpam-5936	42	21	advanced	advanced	ADJ
ejpam-5936	42	22	numerical	numerical	ADJ
ejpam-5936	42	23	techniques	technique	NOUN
ejpam-5936	42	24	in	in	ADP
ejpam-5936	42	25	yielding	yield	VERB
ejpam-5936	42	26	accurate	accurate	ADJ
ejpam-5936	42	27	solutions	solution	NOUN
ejpam-5936	42	28	.	.	PUNCT
ejpam-5936	43	1	wang	wang	PROPN
ejpam-5936	43	2	et	et	PROPN
ejpam-5936	43	3	al	al	PROPN
ejpam-5936	43	4	.	.	PUNCT
ejpam-5936	44	1	[	[	X
ejpam-5936	44	2	19	19	NUM
ejpam-5936	44	3	]	]	PUNCT
ejpam-5936	44	4	investigated	investigate	VERB
ejpam-5936	44	5	a	a	DET
ejpam-5936	44	6	generalized	generalized	ADJ
ejpam-5936	44	7	nonlinear	nonlinear	ADJ
ejpam-5936	44	8	evolution	evolution	NOUN
ejpam-5936	44	9	equation	equation	NOUN
ejpam-5936	44	10	relevant	relevant	ADJ
ejpam-5936	44	11	to	to	PART
ejpam-5936	44	12	shallow	shallow	VERB
ejpam-5936	44	13	water	water	NOUN
ejpam-5936	44	14	waves	wave	NOUN
ejpam-5936	44	15	,	,	PUNCT
ejpam-5936	44	16	employing	employ	VERB
ejpam-5936	44	17	the	the	DET
ejpam-5936	44	18	hirota	hirota	NOUN
ejpam-5936	44	19	method	method	NOUN
ejpam-5936	44	20	with	with	ADP
ejpam-5936	44	21	a	a	DET
ejpam-5936	44	22	new	new	ADJ
ejpam-5936	44	23	ansatz	ansatz	ADJ
ejpam-5936	44	24	function	function	NOUN
ejpam-5936	44	25	.	.	PUNCT
ejpam-5936	45	1	their	their	PRON
ejpam-5936	45	2	approach	approach	NOUN
ejpam-5936	45	3	yielded	yield	VERB
ejpam-5936	45	4	novel	novel	ADJ
ejpam-5936	45	5	exact	exact	ADJ
ejpam-5936	45	6	solutions	solution	NOUN
ejpam-5936	45	7	,	,	PUNCT
ejpam-5936	45	8	including	include	VERB
ejpam-5936	45	9	singular	singular	ADJ
ejpam-5936	45	10	and	and	CCONJ
ejpam-5936	45	11	non	non	ADJ
ejpam-5936	45	12	-	-	ADJ
ejpam-5936	45	13	singular	singular	ADJ
ejpam-5936	45	14	complexitons	complexiton	NOUN
ejpam-5936	45	15	,	,	PUNCT
ejpam-5936	45	16	expanding	expand	VERB
ejpam-5936	45	17	the	the	DET
ejpam-5936	45	18	understanding	understanding	NOUN
ejpam-5936	45	19	of	of	ADP
ejpam-5936	45	20	this	this	DET
ejpam-5936	45	21	equation	equation	NOUN
ejpam-5936	45	22	’s	’s	PART
ejpam-5936	45	23	solution	solution	NOUN
ejpam-5936	45	24	space	space	NOUN
ejpam-5936	45	25	.	.	PUNCT
ejpam-5936	46	1	wang	wang	PROPN
ejpam-5936	47	1	[	[	X
ejpam-5936	47	2	20	20	NUM
ejpam-5936	47	3	]	]	PUNCT
ejpam-5936	47	4	explored	explore	VERB
ejpam-5936	47	5	the	the	DET
ejpam-5936	47	6	perturbed	perturb	VERB
ejpam-5936	47	7	chen	chen	PROPN
ejpam-5936	47	8	-	-	PUNCT
ejpam-5936	47	9	lee	lee	PROPN
ejpam-5936	47	10	-	-	PROPN
ejpam-5936	47	11	liu	liu	PROPN
ejpam-5936	47	12	equation	equation	NOUN
ejpam-5936	47	13	,	,	PUNCT
ejpam-5936	47	14	a	a	DET
ejpam-5936	47	15	key	key	ADJ
ejpam-5936	47	16	model	model	NOUN
ejpam-5936	47	17	in	in	ADP
ejpam-5936	47	18	nonlinear	nonlinear	ADJ
ejpam-5936	47	19	optics	optic	NOUN
ejpam-5936	47	20	,	,	PUNCT
ejpam-5936	47	21	obtaining	obtain	VERB
ejpam-5936	47	22	diverse	diverse	ADJ
ejpam-5936	47	23	optical	optical	ADJ
ejpam-5936	47	24	soliton	soliton	NOUN
ejpam-5936	47	25	and	and	CCONJ
ejpam-5936	47	26	other	other	ADJ
ejpam-5936	47	27	wave	wave	NOUN
ejpam-5936	47	28	solutions	solution	NOUN
ejpam-5936	47	29	,	,	PUNCT
ejpam-5936	47	30	contributing	contribute	VERB
ejpam-5936	47	31	significant	significant	ADJ
ejpam-5936	47	32	insights	insight	NOUN
ejpam-5936	47	33	into	into	ADP
ejpam-5936	47	34	the	the	DET
ejpam-5936	47	35	equation	equation	NOUN
ejpam-5936	47	36	’s	’s	PART
ejpam-5936	47	37	dynamics	dynamic	NOUN
ejpam-5936	47	38	.	.	PUNCT
ejpam-5936	48	1	wang	wang	PROPN
ejpam-5936	48	2	et	et	PROPN
ejpam-5936	48	3	al	al	PROPN
ejpam-5936	48	4	.	.	PUNCT
ejpam-5936	49	1	[	[	X
ejpam-5936	49	2	21	21	NUM
ejpam-5936	49	3	]	]	PUNCT
ejpam-5936	49	4	studied	study	VERB
ejpam-5936	49	5	the	the	DET
ejpam-5936	49	6	(	(	PUNCT
ejpam-5936	49	7	2	2	NUM
ejpam-5936	49	8	+	+	NOUN
ejpam-5936	49	9	1)-dimensional	1)-dimensional	ADJ
ejpam-5936	49	10	sawada	sawada	NOUN
ejpam-5936	49	11	–	–	PUNCT
ejpam-5936	49	12	kotera	kotera	PROPN
ejpam-5936	49	13	–	–	PUNCT
ejpam-5936	49	14	kadomtsev	kadomtsev	VERB
ejpam-5936	49	15	petviashvili	petviashvili	NOUN
ejpam-5936	49	16	(	(	PUNCT
ejpam-5936	49	17	skp	skp	PROPN
ejpam-5936	49	18	)	)	PUNCT
ejpam-5936	49	19	equation	equation	NOUN
ejpam-5936	49	20	,	,	PUNCT
ejpam-5936	49	21	obtaining	obtain	VERB
ejpam-5936	49	22	diverse	diverse	ADJ
ejpam-5936	49	23	wave	wave	NOUN
ejpam-5936	49	24	solutions	solution	NOUN
ejpam-5936	49	25	including	include	VERB
ejpam-5936	49	26	lump	lump	NOUN
ejpam-5936	49	27	and	and	CCONJ
ejpam-5936	49	28	breather	breather	NOUN
ejpam-5936	49	29	waves	wave	NOUN
ejpam-5936	49	30	,	,	PUNCT
ejpam-5936	49	31	enhancing	enhance	VERB
ejpam-5936	49	32	understanding	understanding	NOUN
ejpam-5936	49	33	of	of	ADP
ejpam-5936	49	34	nonlinear	nonlinear	ADJ
ejpam-5936	49	35	fluid	fluid	ADJ
ejpam-5936	49	36	dynamics	dynamic	NOUN
ejpam-5936	49	37	.	.	PUNCT
ejpam-5936	50	1	solving	solve	VERB
ejpam-5936	50	2	nonlinear	nonlinear	ADJ
ejpam-5936	50	3	population	population	NOUN
ejpam-5936	50	4	models	model	NOUN
ejpam-5936	50	5	exactly	exactly	ADV
ejpam-5936	50	6	is	be	AUX
ejpam-5936	50	7	often	often	ADV
ejpam-5936	50	8	a	a	DET
ejpam-5936	50	9	formidable	formidable	ADJ
ejpam-5936	50	10	task	task	NOUN
ejpam-5936	50	11	due	due	ADP
ejpam-5936	50	12	to	to	ADP
ejpam-5936	50	13	their	their	PRON
ejpam-5936	50	14	complexity	complexity	NOUN
ejpam-5936	50	15	.	.	PUNCT
ejpam-5936	51	1	traditional	traditional	ADJ
ejpam-5936	51	2	methods	method	NOUN
ejpam-5936	51	3	like	like	ADP
ejpam-5936	51	4	separation	separation	NOUN
ejpam-5936	51	5	of	of	ADP
ejpam-5936	51	6	variables	variable	NOUN
ejpam-5936	51	7	,	,	PUNCT
ejpam-5936	51	8	traveling	travel	VERB
ejpam-5936	51	9	wave	wave	NOUN
ejpam-5936	51	10	reductions	reduction	NOUN
ejpam-5936	51	11	,	,	PUNCT
ejpam-5936	51	12	and	and	CCONJ
ejpam-5936	51	13	perturbation	perturbation	NOUN
ejpam-5936	51	14	techniques	technique	NOUN
ejpam-5936	51	15	have	have	VERB
ejpam-5936	51	16	limitations	limitation	NOUN
ejpam-5936	51	17	in	in	ADP
ejpam-5936	51	18	handling	handle	VERB
ejpam-5936	51	19	strongly	strongly	ADV
ejpam-5936	51	20	nonlinear	nonlinear	ADJ
ejpam-5936	51	21	or	or	CCONJ
ejpam-5936	51	22	high	high	ADJ
ejpam-5936	51	23	-	-	PUNCT
ejpam-5936	51	24	dimensional	dimensional	ADJ
ejpam-5936	51	25	systems	system	NOUN
ejpam-5936	51	26	.	.	PUNCT
ejpam-5936	52	1	this	this	PRON
ejpam-5936	52	2	motivates	motivate	VERB
ejpam-5936	52	3	the	the	DET
ejpam-5936	52	4	exploration	exploration	NOUN
ejpam-5936	52	5	of	of	ADP
ejpam-5936	52	6	alternative	alternative	ADJ
ejpam-5936	52	7	analytical	analytical	ADJ
ejpam-5936	52	8	approaches	approach	NOUN
ejpam-5936	52	9	,	,	PUNCT
ejpam-5936	52	10	such	such	ADJ
ejpam-5936	52	11	as	as	ADP
ejpam-5936	52	12	the	the	DET
ejpam-5936	52	13	power	power	NOUN
ejpam-5936	52	14	index	index	NOUN
ejpam-5936	52	15	method	method	NOUN
ejpam-5936	52	16	,	,	PUNCT
ejpam-5936	52	17	which	which	PRON
ejpam-5936	52	18	can	can	AUX
ejpam-5936	52	19	systematically	systematically	ADV
ejpam-5936	52	20	transform	transform	VERB
ejpam-5936	52	21	and	and	CCONJ
ejpam-5936	52	22	simplify	simplify	VERB
ejpam-5936	52	23	such	such	ADJ
ejpam-5936	52	24	equations	equation	NOUN
ejpam-5936	52	25	into	into	ADP
ejpam-5936	52	26	solvable	solvable	ADJ
ejpam-5936	52	27	forms	form	NOUN
ejpam-5936	52	28	.	.	PUNCT
ejpam-5936	53	1	no	no	DET
ejpam-5936	53	2	previous	previous	ADJ
ejpam-5936	53	3	studies	study	NOUN
ejpam-5936	53	4	have	have	AUX
ejpam-5936	53	5	applied	apply	VERB
ejpam-5936	53	6	the	the	DET
ejpam-5936	53	7	power	power	NOUN
ejpam-5936	53	8	index	index	NOUN
ejpam-5936	53	9	method	method	NOUN
ejpam-5936	53	10	to	to	PART
ejpam-5936	53	11	solve	solve	VERB
ejpam-5936	53	12	this	this	DET
ejpam-5936	53	13	nonlinear	nonlinear	ADJ
ejpam-5936	53	14	biological	biological	ADJ
ejpam-5936	53	15	population	population	NOUN
ejpam-5936	53	16	model	model	NOUN
ejpam-5936	53	17	.	.	PUNCT
ejpam-5936	54	1	in	in	ADP
ejpam-5936	54	2	this	this	DET
ejpam-5936	54	3	work	work	NOUN
ejpam-5936	54	4	,	,	PUNCT
ejpam-5936	54	5	we	we	PRON
ejpam-5936	54	6	present	present	VERB
ejpam-5936	54	7	the	the	DET
ejpam-5936	54	8	first	first	ADJ
ejpam-5936	54	9	successful	successful	ADJ
ejpam-5936	54	10	implez	implez	NOUN
ejpam-5936	54	11	.	.	PUNCT
ejpam-5936	55	1	haider	haider	PROPN
ejpam-5936	55	2	,	,	PUNCT
ejpam-5936	55	3	k.	k.	PROPN
ejpam-5936	55	4	ahmad	ahmad	PROPN
ejpam-5936	55	5	/	/	SYM
ejpam-5936	55	6	eur	eur	PROPN
ejpam-5936	55	7	.	.	PUNCT
ejpam-5936	56	1	j.	j.	PROPN
ejpam-5936	56	2	pure	pure	PROPN
ejpam-5936	56	3	appl	appl	PROPN
ejpam-5936	56	4	.	.	PROPN
ejpam-5936	56	5	math	math	PROPN
ejpam-5936	56	6	,	,	PUNCT
ejpam-5936	56	7	18	18	NUM
ejpam-5936	56	8	(	(	PUNCT
ejpam-5936	56	9	2	2	NUM
ejpam-5936	56	10	)	)	PUNCT
ejpam-5936	56	11	(	(	PUNCT
ejpam-5936	56	12	2025	2025	NUM
ejpam-5936	56	13	)	)	PUNCT
ejpam-5936	56	14	,	,	PUNCT
ejpam-5936	56	15	5936	5936	NUM
ejpam-5936	56	16	3	3	NUM
ejpam-5936	56	17	of	of	ADP
ejpam-5936	56	18	18	18	NUM
ejpam-5936	56	19	mentation	mentation	NOUN
ejpam-5936	56	20	of	of	ADP
ejpam-5936	56	21	this	this	DET
ejpam-5936	56	22	method	method	NOUN
ejpam-5936	56	23	to	to	PART
ejpam-5936	56	24	obtain	obtain	VERB
ejpam-5936	56	25	exact	exact	ADJ
ejpam-5936	56	26	solutions	solution	NOUN
ejpam-5936	56	27	for	for	ADP
ejpam-5936	56	28	the	the	DET
ejpam-5936	56	29	nonlinaer	nonlinaer	ADJ
ejpam-5936	56	30	biological	biological	ADJ
ejpam-5936	56	31	population	population	NOUN
ejpam-5936	56	32	model	model	NOUN
ejpam-5936	56	33	.	.	PUNCT
ejpam-5936	57	1	the	the	DET
ejpam-5936	57	2	power	power	NOUN
ejpam-5936	57	3	index	index	NOUN
ejpam-5936	57	4	method	method	NOUN
ejpam-5936	57	5	represents	represent	VERB
ejpam-5936	57	6	an	an	DET
ejpam-5936	57	7	efficient	efficient	ADJ
ejpam-5936	57	8	analytical	analytical	ADJ
ejpam-5936	57	9	technique	technique	NOUN
ejpam-5936	57	10	for	for	ADP
ejpam-5936	57	11	solving	solve	VERB
ejpam-5936	57	12	nonlinear	nonlinear	ADJ
ejpam-5936	57	13	partial	partial	ADJ
ejpam-5936	57	14	differential	differential	NOUN
ejpam-5936	57	15	equations	equation	NOUN
ejpam-5936	57	16	(	(	PUNCT
ejpam-5936	57	17	nlpdes	nlpde	NOUN
ejpam-5936	57	18	)	)	PUNCT
ejpam-5936	57	19	that	that	PRON
ejpam-5936	57	20	eliminates	eliminate	VERB
ejpam-5936	57	21	the	the	DET
ejpam-5936	57	22	need	need	NOUN
ejpam-5936	57	23	for	for	ADP
ejpam-5936	57	24	series	series	NOUN
ejpam-5936	57	25	expansions	expansion	NOUN
ejpam-5936	57	26	.	.	PUNCT
ejpam-5936	58	1	in	in	ADP
ejpam-5936	58	2	contrast	contrast	NOUN
ejpam-5936	58	3	to	to	ADP
ejpam-5936	58	4	conventional	conventional	ADJ
ejpam-5936	58	5	approaches	approach	NOUN
ejpam-5936	58	6	like	like	ADP
ejpam-5936	58	7	perturbation	perturbation	NOUN
ejpam-5936	58	8	methods	method	NOUN
ejpam-5936	58	9	or	or	CCONJ
ejpam-5936	58	10	homotopy	homotopy	VERB
ejpam-5936	58	11	analysis	analysis	NOUN
ejpam-5936	58	12	that	that	PRON
ejpam-5936	58	13	require	require	VERB
ejpam-5936	58	14	series	series	NOUN
ejpam-5936	58	15	-	-	PUNCT
ejpam-5936	58	16	form	form	NOUN
ejpam-5936	58	17	solutions	solution	NOUN
ejpam-5936	58	18	,	,	PUNCT
ejpam-5936	58	19	this	this	DET
ejpam-5936	58	20	direct	direct	ADJ
ejpam-5936	58	21	method	method	NOUN
ejpam-5936	58	22	utilizes	utilize	VERB
ejpam-5936	58	23	targeted	target	VERB
ejpam-5936	58	24	algebraic	algebraic	ADJ
ejpam-5936	58	25	manipulations	manipulation	NOUN
ejpam-5936	58	26	of	of	ADP
ejpam-5936	58	27	nonlinear	nonlinear	ADJ
ejpam-5936	58	28	terms	term	NOUN
ejpam-5936	58	29	to	to	PART
ejpam-5936	58	30	derive	derive	VERB
ejpam-5936	58	31	exact	exact	ADJ
ejpam-5936	58	32	closed	closed	ADJ
ejpam-5936	58	33	-	-	PUNCT
ejpam-5936	58	34	form	form	NOUN
ejpam-5936	58	35	solutions	solution	NOUN
ejpam-5936	58	36	.	.	PUNCT
ejpam-5936	59	1	novel	novel	ADJ
ejpam-5936	59	2	exact	exact	ADJ
ejpam-5936	59	3	solutions	solution	NOUN
ejpam-5936	59	4	of	of	ADP
ejpam-5936	59	5	nonlinear	nonlinear	ADJ
ejpam-5936	59	6	partial	partial	ADJ
ejpam-5936	59	7	differential	differential	NOUN
ejpam-5936	59	8	equations	equation	NOUN
ejpam-5936	59	9	(	(	PUNCT
ejpam-5936	59	10	nlpdes	nlpde	NOUN
ejpam-5936	59	11	)	)	PUNCT
ejpam-5936	59	12	provide	provide	VERB
ejpam-5936	59	13	both	both	CCONJ
ejpam-5936	59	14	analytical	analytical	ADJ
ejpam-5936	59	15	and	and	CCONJ
ejpam-5936	59	16	graphical	graphical	ADJ
ejpam-5936	59	17	insights	insight	NOUN
ejpam-5936	59	18	into	into	ADP
ejpam-5936	59	19	complex	complex	ADJ
ejpam-5936	59	20	nonlinear	nonlinear	ADJ
ejpam-5936	59	21	phenomena	phenomenon	NOUN
ejpam-5936	59	22	.	.	PUNCT
ejpam-5936	60	1	these	these	DET
ejpam-5936	60	2	solutions	solution	NOUN
ejpam-5936	60	3	significantly	significantly	ADV
ejpam-5936	60	4	enhance	enhance	VERB
ejpam-5936	60	5	our	our	PRON
ejpam-5936	60	6	understanding	understanding	NOUN
ejpam-5936	60	7	of	of	ADP
ejpam-5936	60	8	the	the	DET
ejpam-5936	60	9	qualitative	qualitative	ADJ
ejpam-5936	60	10	structures	structure	NOUN
ejpam-5936	60	11	governing	govern	VERB
ejpam-5936	60	12	natural	natural	ADJ
ejpam-5936	60	13	processes	process	NOUN
ejpam-5936	60	14	across	across	ADP
ejpam-5936	60	15	scientific	scientific	ADJ
ejpam-5936	60	16	and	and	CCONJ
ejpam-5936	60	17	engineering	engineering	NOUN
ejpam-5936	60	18	disciplines	discipline	NOUN
ejpam-5936	60	19	.	.	PUNCT
ejpam-5936	61	1	consequently	consequently	ADV
ejpam-5936	61	2	,	,	PUNCT
ejpam-5936	61	3	researchers	researcher	NOUN
ejpam-5936	61	4	have	have	AUX
ejpam-5936	61	5	extensively	extensively	ADV
ejpam-5936	61	6	investigated	investigate	VERB
ejpam-5936	61	7	exact	exact	ADJ
ejpam-5936	61	8	solutions	solution	NOUN
ejpam-5936	61	9	of	of	ADP
ejpam-5936	61	10	nonlinear	nonlinear	ADJ
ejpam-5936	61	11	partial	partial	ADJ
ejpam-5936	61	12	differential	differential	NOUN
ejpam-5936	61	13	equations	equation	NOUN
ejpam-5936	61	14	(	(	PUNCT
ejpam-5936	61	15	nlpdes	nlpde	NOUN
ejpam-5936	61	16	)	)	PUNCT
ejpam-5936	61	17	,	,	PUNCT
ejpam-5936	61	18	which	which	PRON
ejpam-5936	61	19	arise	arise	VERB
ejpam-5936	61	20	in	in	ADP
ejpam-5936	61	21	diverse	diverse	ADJ
ejpam-5936	61	22	fields	field	NOUN
ejpam-5936	61	23	ranging	range	VERB
ejpam-5936	61	24	from	from	ADP
ejpam-5936	61	25	theoretical	theoretical	ADJ
ejpam-5936	61	26	physics	physics	NOUN
ejpam-5936	61	27	to	to	ADP
ejpam-5936	61	28	applied	apply	VERB
ejpam-5936	61	29	engineering	engineering	NOUN
ejpam-5936	61	30	.	.	PUNCT
ejpam-5936	62	1	in	in	ADP
ejpam-5936	62	2	recent	recent	ADJ
ejpam-5936	62	3	years	year	NOUN
ejpam-5936	62	4	,	,	PUNCT
ejpam-5936	62	5	substantial	substantial	ADJ
ejpam-5936	62	6	progress	progress	NOUN
ejpam-5936	62	7	has	have	AUX
ejpam-5936	62	8	been	be	AUX
ejpam-5936	62	9	made	make	VERB
ejpam-5936	62	10	in	in	ADP
ejpam-5936	62	11	developing	develop	VERB
ejpam-5936	62	12	exact	exact	ADJ
ejpam-5936	62	13	solution	solution	NOUN
ejpam-5936	62	14	methods	method	NOUN
ejpam-5936	62	15	for	for	ADP
ejpam-5936	62	16	nonlinear	nonlinear	ADJ
ejpam-5936	62	17	partial	partial	ADJ
ejpam-5936	62	18	differential	differential	NOUN
ejpam-5936	62	19	equations	equation	NOUN
ejpam-5936	62	20	(	(	PUNCT
ejpam-5936	62	21	nlpdes	nlpde	NOUN
ejpam-5936	62	22	)	)	PUNCT
ejpam-5936	62	23	,	,	PUNCT
ejpam-5936	62	24	with	with	ADP
ejpam-5936	62	25	numerous	numerous	ADJ
ejpam-5936	62	26	powerful	powerful	ADJ
ejpam-5936	62	27	techniques	technique	NOUN
ejpam-5936	62	28	emerging	emerge	VERB
ejpam-5936	62	29	including	include	VERB
ejpam-5936	62	30	,	,	PUNCT
ejpam-5936	62	31	lie	lie	NOUN
ejpam-5936	62	32	symmetry	symmetry	NOUN
ejpam-5936	62	33	analysis	analysis	NOUN
ejpam-5936	62	34	[	[	X
ejpam-5936	62	35	22	22	NUM
ejpam-5936	62	36	]	]	PUNCT
ejpam-5936	62	37	,	,	PUNCT
ejpam-5936	62	38	first	first	ADJ
ejpam-5936	62	39	integral	integral	ADJ
ejpam-5936	62	40	method	method	NOUN
ejpam-5936	62	41	[	[	X
ejpam-5936	62	42	23	23	NUM
ejpam-5936	62	43	]	]	PUNCT
ejpam-5936	62	44	,	,	PUNCT
ejpam-5936	62	45	modified	modify	VERB
ejpam-5936	62	46	exp	exp	NOUN
ejpam-5936	62	47	-	-	PUNCT
ejpam-5936	62	48	function	function	NOUN
ejpam-5936	62	49	method	method	NOUN
ejpam-5936	62	50	[	[	X
ejpam-5936	62	51	24	24	NUM
ejpam-5936	62	52	]	]	PUNCT
ejpam-5936	62	53	,	,	PUNCT
ejpam-5936	62	54	(	(	PUNCT
ejpam-5936	62	55	g	g	NOUN
ejpam-5936	62	56	′	′	NUM
ejpam-5936	62	57	/g)-expansion	/g)-expansion	SYM
ejpam-5936	62	58	method	method	NOUN
ejpam-5936	62	59	[	[	X
ejpam-5936	62	60	25	25	NUM
ejpam-5936	62	61	]	]	PUNCT
ejpam-5936	62	62	,	,	PUNCT
ejpam-5936	62	63	power	power	NOUN
ejpam-5936	62	64	index	index	NOUN
ejpam-5936	62	65	method	method	NOUN
ejpam-5936	62	66	[	[	X
ejpam-5936	62	67	26	26	NUM
ejpam-5936	62	68	]	]	PUNCT
ejpam-5936	62	69	,	,	PUNCT
ejpam-5936	62	70	generalized	generalized	ADJ
ejpam-5936	62	71	expfunction	expfunction	NOUN
ejpam-5936	62	72	method	method	NOUN
ejpam-5936	62	73	[	[	X
ejpam-5936	62	74	27	27	NUM
ejpam-5936	62	75	]	]	PUNCT
ejpam-5936	62	76	,	,	PUNCT
ejpam-5936	62	77	exp(−ϕ(ξ))-expansion	exp(−ϕ(ξ))-expansion	NOUN
ejpam-5936	62	78	method	method	NOUN
ejpam-5936	62	79	[	[	X
ejpam-5936	62	80	28	28	NUM
ejpam-5936	62	81	]	]	X
ejpam-5936	62	82	,	,	PUNCT
ejpam-5936	62	83	simple	simple	ADJ
ejpam-5936	62	84	equations	equation	NOUN
ejpam-5936	62	85	method	method	NOUN
ejpam-5936	62	86	[	[	X
ejpam-5936	62	87	29	29	NUM
ejpam-5936	62	88	]	]	PUNCT
ejpam-5936	62	89	,	,	PUNCT
ejpam-5936	62	90	modified	modify	VERB
ejpam-5936	62	91	extended	extend	VERB
ejpam-5936	62	92	direct	direct	ADJ
ejpam-5936	62	93	algebraic	algebraic	ADJ
ejpam-5936	62	94	method	method	NOUN
ejpam-5936	62	95	[	[	X
ejpam-5936	62	96	30	30	NUM
ejpam-5936	62	97	]	]	PUNCT
ejpam-5936	62	98	to	to	PART
ejpam-5936	62	99	solve	solve	VERB
ejpam-5936	62	100	nonlinear	nonlinear	ADJ
ejpam-5936	62	101	partial	partial	ADJ
ejpam-5936	62	102	differential	differential	NOUN
ejpam-5936	62	103	equations	equation	NOUN
ejpam-5936	62	104	.	.	PUNCT
ejpam-5936	63	1	the	the	DET
ejpam-5936	63	2	effectiveness	effectiveness	NOUN
ejpam-5936	63	3	of	of	ADP
ejpam-5936	63	4	the	the	DET
ejpam-5936	63	5	power	power	NOUN
ejpam-5936	63	6	index	index	NOUN
ejpam-5936	63	7	method	method	NOUN
ejpam-5936	63	8	(	(	PUNCT
ejpam-5936	63	9	pim	pim	PROPN
ejpam-5936	63	10	)	)	PUNCT
ejpam-5936	63	11	for	for	ADP
ejpam-5936	63	12	deriving	derive	VERB
ejpam-5936	63	13	exact	exact	ADJ
ejpam-5936	63	14	solutions	solution	NOUN
ejpam-5936	63	15	to	to	PART
ejpam-5936	63	16	nonlinear	nonlinear	VERB
ejpam-5936	63	17	partial	partial	ADJ
ejpam-5936	63	18	differential	differential	NOUN
ejpam-5936	63	19	equations	equation	NOUN
ejpam-5936	63	20	(	(	PUNCT
ejpam-5936	63	21	nlpdes	nlpde	NOUN
ejpam-5936	63	22	)	)	PUNCT
ejpam-5936	63	23	was	be	AUX
ejpam-5936	63	24	evaluated	evaluate	VERB
ejpam-5936	63	25	through	through	ADP
ejpam-5936	63	26	a	a	DET
ejpam-5936	63	27	systematic	systematic	ADJ
ejpam-5936	63	28	comparison	comparison	NOUN
ejpam-5936	63	29	with	with	ADP
ejpam-5936	63	30	two	two	NUM
ejpam-5936	63	31	established	establish	VERB
ejpam-5936	63	32	analytical	analytical	ADJ
ejpam-5936	63	33	approaches	approach	NOUN
ejpam-5936	63	34	:	:	PUNCT
ejpam-5936	63	35	lie	lie	NOUN
ejpam-5936	63	36	symmetry	symmetry	NOUN
ejpam-5936	63	37	analysis	analysis	NOUN
ejpam-5936	63	38	and	and	CCONJ
ejpam-5936	63	39	the	the	DET
ejpam-5936	63	40	sine	sine	ADJ
ejpam-5936	63	41	-	-	PUNCT
ejpam-5936	63	42	cosine	cosine	NOUN
ejpam-5936	63	43	method	method	NOUN
ejpam-5936	63	44	.	.	PUNCT
ejpam-5936	64	1	as	as	SCONJ
ejpam-5936	64	2	summarized	summarize	VERB
ejpam-5936	64	3	in	in	ADP
ejpam-5936	64	4	table	table	NOUN
ejpam-5936	64	5	1	1	NUM
ejpam-5936	64	6	,	,	PUNCT
ejpam-5936	64	7	these	these	DET
ejpam-5936	64	8	methods	method	NOUN
ejpam-5936	64	9	demonstrate	demonstrate	VERB
ejpam-5936	64	10	distinct	distinct	ADJ
ejpam-5936	64	11	characteristics	characteristic	NOUN
ejpam-5936	64	12	,	,	PUNCT
ejpam-5936	64	13	applicability	applicability	NOUN
ejpam-5936	64	14	ranges	range	NOUN
ejpam-5936	64	15	,	,	PUNCT
ejpam-5936	64	16	and	and	CCONJ
ejpam-5936	64	17	solution	solution	NOUN
ejpam-5936	64	18	strategies	strategy	NOUN
ejpam-5936	64	19	,	,	PUNCT
ejpam-5936	64	20	highlighting	highlight	VERB
ejpam-5936	64	21	their	their	PRON
ejpam-5936	64	22	complementary	complementary	ADJ
ejpam-5936	64	23	strengths	strength	NOUN
ejpam-5936	64	24	and	and	CCONJ
ejpam-5936	64	25	limitations	limitation	NOUN
ejpam-5936	64	26	.	.	PUNCT
ejpam-5936	65	1	the	the	DET
ejpam-5936	65	2	similar	similar	ADJ
ejpam-5936	65	3	function	function	NOUN
ejpam-5936	65	4	transformation	transformation	NOUN
ejpam-5936	65	5	is	be	AUX
ejpam-5936	65	6	a	a	DET
ejpam-5936	65	7	mathematical	mathematical	ADJ
ejpam-5936	65	8	technique	technique	NOUN
ejpam-5936	65	9	that	that	PRON
ejpam-5936	65	10	employs	employ	VERB
ejpam-5936	65	11	specific	specific	ADJ
ejpam-5936	65	12	similarity	similarity	NOUN
ejpam-5936	65	13	transformations	transformation	NOUN
ejpam-5936	65	14	to	to	PART
ejpam-5936	65	15	convert	convert	VERB
ejpam-5936	65	16	nonlinear	nonlinear	ADJ
ejpam-5936	65	17	biological	biological	ADJ
ejpam-5936	65	18	population	population	NOUN
ejpam-5936	65	19	models	model	NOUN
ejpam-5936	65	20	into	into	ADP
ejpam-5936	65	21	more	more	ADJ
ejpam-5936	65	22	z.	z.	PROPN
ejpam-5936	65	23	haider	haider	PROPN
ejpam-5936	65	24	,	,	PUNCT
ejpam-5936	65	25	k.	k.	PROPN
ejpam-5936	65	26	ahmad	ahmad	PROPN
ejpam-5936	65	27	/	/	SYM
ejpam-5936	65	28	eur	eur	PROPN
ejpam-5936	65	29	.	.	PUNCT
ejpam-5936	66	1	j.	j.	PROPN
ejpam-5936	66	2	pure	pure	PROPN
ejpam-5936	66	3	appl	appl	PROPN
ejpam-5936	66	4	.	.	PROPN
ejpam-5936	66	5	math	math	PROPN
ejpam-5936	66	6	,	,	PUNCT
ejpam-5936	66	7	18	18	NUM
ejpam-5936	66	8	(	(	PUNCT
ejpam-5936	66	9	2	2	NUM
ejpam-5936	66	10	)	)	PUNCT
ejpam-5936	66	11	(	(	PUNCT
ejpam-5936	66	12	2025	2025	NUM
ejpam-5936	66	13	)	)	PUNCT
ejpam-5936	66	14	,	,	PUNCT
ejpam-5936	66	15	5936	5936	NUM
ejpam-5936	66	16	4	4	NUM
ejpam-5936	66	17	of	of	ADP
ejpam-5936	66	18	18	18	NUM
ejpam-5936	66	19	tractable	tractable	ADJ
ejpam-5936	66	20	forms	form	NOUN
ejpam-5936	66	21	,	,	PUNCT
ejpam-5936	66	22	enabling	enable	VERB
ejpam-5936	66	23	the	the	DET
ejpam-5936	66	24	derivation	derivation	NOUN
ejpam-5936	66	25	of	of	ADP
ejpam-5936	66	26	novel	novel	ADJ
ejpam-5936	66	27	exact	exact	ADJ
ejpam-5936	66	28	solutions	solution	NOUN
ejpam-5936	66	29	through	through	ADP
ejpam-5936	66	30	methods	method	NOUN
ejpam-5936	66	31	like	like	ADP
ejpam-5936	66	32	the	the	DET
ejpam-5936	66	33	power	power	NOUN
ejpam-5936	66	34	index	index	NOUN
ejpam-5936	66	35	method	method	NOUN
ejpam-5936	66	36	(	(	PUNCT
ejpam-5936	66	37	pim	pim	PROPN
ejpam-5936	66	38	)	)	PUNCT
ejpam-5936	66	39	.	.	PUNCT
ejpam-5936	67	1	the	the	DET
ejpam-5936	67	2	power	power	NOUN
ejpam-5936	67	3	index	index	NOUN
ejpam-5936	67	4	method	method	NOUN
ejpam-5936	67	5	(	(	PUNCT
ejpam-5936	67	6	pim	pim	PROPN
ejpam-5936	67	7	)	)	PUNCT
ejpam-5936	67	8	yields	yield	NOUN
ejpam-5936	67	9	closed	closed	ADJ
ejpam-5936	67	10	-	-	PUNCT
ejpam-5936	67	11	form	form	NOUN
ejpam-5936	67	12	solutions	solution	NOUN
ejpam-5936	67	13	that	that	PRON
ejpam-5936	67	14	are	be	AUX
ejpam-5936	67	15	crucial	crucial	ADJ
ejpam-5936	67	16	for	for	ADP
ejpam-5936	67	17	understanding	understand	VERB
ejpam-5936	67	18	population	population	NOUN
ejpam-5936	67	19	dynamics	dynamic	NOUN
ejpam-5936	67	20	,	,	PUNCT
ejpam-5936	67	21	stability	stability	NOUN
ejpam-5936	67	22	analysis	analysis	NOUN
ejpam-5936	67	23	,	,	PUNCT
ejpam-5936	67	24	and	and	CCONJ
ejpam-5936	67	25	pattern	pattern	NOUN
ejpam-5936	67	26	formation	formation	NOUN
ejpam-5936	67	27	.	.	PUNCT
ejpam-5936	68	1	unlike	unlike	ADP
ejpam-5936	68	2	numerical	numerical	ADJ
ejpam-5936	68	3	methods	method	NOUN
ejpam-5936	68	4	,	,	PUNCT
ejpam-5936	68	5	this	this	DET
ejpam-5936	68	6	analytical	analytical	ADJ
ejpam-5936	68	7	approach	approach	NOUN
ejpam-5936	68	8	provides	provide	VERB
ejpam-5936	68	9	exact	exact	ADJ
ejpam-5936	68	10	solutions	solution	NOUN
ejpam-5936	68	11	without	without	ADP
ejpam-5936	68	12	approximations	approximation	NOUN
ejpam-5936	68	13	,	,	PUNCT
ejpam-5936	68	14	facilitating	facilitate	VERB
ejpam-5936	68	15	the	the	DET
ejpam-5936	68	16	interpretation	interpretation	NOUN
ejpam-5936	68	17	of	of	ADP
ejpam-5936	68	18	biologically	biologically	ADV
ejpam-5936	68	19	meaningful	meaningful	ADJ
ejpam-5936	68	20	parameters	parameter	NOUN
ejpam-5936	68	21	.	.	PUNCT
ejpam-5936	69	1	while	while	SCONJ
ejpam-5936	69	2	the	the	DET
ejpam-5936	69	3	power	power	NOUN
ejpam-5936	69	4	index	index	NOUN
ejpam-5936	69	5	method	method	NOUN
ejpam-5936	69	6	(	(	PUNCT
ejpam-5936	69	7	pim	pim	NOUN
ejpam-5936	69	8	)	)	PUNCT
ejpam-5936	69	9	generates	generate	VERB
ejpam-5936	69	10	exact	exact	ADJ
ejpam-5936	69	11	solutions	solution	NOUN
ejpam-5936	69	12	,	,	PUNCT
ejpam-5936	69	13	which	which	PRON
ejpam-5936	69	14	is	be	AUX
ejpam-5936	69	15	a	a	DET
ejpam-5936	69	16	rare	rare	ADJ
ejpam-5936	69	17	achievement	achievement	NOUN
ejpam-5936	69	18	for	for	ADP
ejpam-5936	69	19	nonlinear	nonlinear	ADJ
ejpam-5936	69	20	models	model	NOUN
ejpam-5936	69	21	,	,	PUNCT
ejpam-5936	69	22	it	it	PRON
ejpam-5936	69	23	is	be	AUX
ejpam-5936	69	24	only	only	ADV
ejpam-5936	69	25	applicable	applicable	ADJ
ejpam-5936	69	26	to	to	ADP
ejpam-5936	69	27	equations	equation	NOUN
ejpam-5936	69	28	admitting	admit	VERB
ejpam-5936	69	29	powerlaw	powerlaw	NOUN
ejpam-5936	69	30	or	or	CCONJ
ejpam-5936	69	31	self	self	NOUN
ejpam-5936	69	32	-	-	PUNCT
ejpam-5936	69	33	similar	similar	ADJ
ejpam-5936	69	34	solutions	solution	NOUN
ejpam-5936	69	35	.	.	PUNCT
ejpam-5936	70	1	the	the	DET
ejpam-5936	70	2	method	method	NOUN
ejpam-5936	70	3	proves	prove	VERB
ejpam-5936	70	4	most	most	ADV
ejpam-5936	70	5	effective	effective	ADJ
ejpam-5936	70	6	for	for	ADP
ejpam-5936	70	7	autonomous	autonomous	ADJ
ejpam-5936	70	8	equations	equation	NOUN
ejpam-5936	70	9	,	,	PUNCT
ejpam-5936	70	10	self	self	NOUN
ejpam-5936	70	11	-	-	PUNCT
ejpam-5936	70	12	similar	similar	ADJ
ejpam-5936	70	13	equations	equation	NOUN
ejpam-5936	70	14	,	,	PUNCT
ejpam-5936	70	15	and	and	CCONJ
ejpam-5936	70	16	equations	equation	NOUN
ejpam-5936	70	17	with	with	ADP
ejpam-5936	70	18	power	power	NOUN
ejpam-5936	70	19	-	-	PUNCT
ejpam-5936	70	20	law	law	NOUN
ejpam-5936	70	21	nonlinearities	nonlinearitie	NOUN
ejpam-5936	70	22	.	.	PUNCT
ejpam-5936	71	1	however	however	ADV
ejpam-5936	71	2	,	,	PUNCT
ejpam-5936	71	3	power	power	NOUN
ejpam-5936	71	4	index	index	NOUN
ejpam-5936	71	5	method	method	NOUN
ejpam-5936	71	6	(	(	PUNCT
ejpam-5936	71	7	pim	pim	PROPN
ejpam-5936	71	8	)	)	PUNCT
ejpam-5936	71	9	is	be	AUX
ejpam-5936	71	10	limited	limit	VERB
ejpam-5936	71	11	to	to	ADP
ejpam-5936	71	12	autonomous	autonomous	ADJ
ejpam-5936	71	13	equations	equation	NOUN
ejpam-5936	71	14	with	with	ADP
ejpam-5936	71	15	specific	specific	ADJ
ejpam-5936	71	16	nonlinearities	nonlinearitie	NOUN
ejpam-5936	71	17	,	,	PUNCT
ejpam-5936	71	18	excluding	exclude	VERB
ejpam-5936	71	19	non	non	ADJ
ejpam-5936	71	20	-	-	ADJ
ejpam-5936	71	21	autonomous	autonomous	ADJ
ejpam-5936	71	22	and	and	CCONJ
ejpam-5936	71	23	fully	fully	ADV
ejpam-5936	71	24	nonlinear	nonlinear	ADJ
ejpam-5936	71	25	polynomial	polynomial	ADJ
ejpam-5936	71	26	cases	case	NOUN
ejpam-5936	71	27	.	.	PUNCT
ejpam-5936	72	1	the	the	DET
ejpam-5936	72	2	structure	structure	NOUN
ejpam-5936	72	3	of	of	ADP
ejpam-5936	72	4	this	this	DET
ejpam-5936	72	5	paper	paper	NOUN
ejpam-5936	72	6	is	be	AUX
ejpam-5936	72	7	organized	organize	VERB
ejpam-5936	72	8	as	as	SCONJ
ejpam-5936	72	9	follows	follow	VERB
ejpam-5936	72	10	.	.	PUNCT
ejpam-5936	73	1	section	section	NOUN
ejpam-5936	73	2	2	2	NUM
ejpam-5936	73	3	provides	provide	VERB
ejpam-5936	73	4	a	a	DET
ejpam-5936	73	5	brief	brief	ADJ
ejpam-5936	73	6	introduction	introduction	NOUN
ejpam-5936	73	7	to	to	ADP
ejpam-5936	73	8	the	the	DET
ejpam-5936	73	9	power	power	NOUN
ejpam-5936	73	10	index	index	NOUN
ejpam-5936	73	11	method	method	NOUN
ejpam-5936	73	12	.	.	PUNCT
ejpam-5936	74	1	in	in	ADP
ejpam-5936	74	2	section	section	NOUN
ejpam-5936	74	3	3	3	NUM
ejpam-5936	74	4	,	,	PUNCT
ejpam-5936	74	5	we	we	PRON
ejpam-5936	74	6	employ	employ	VERB
ejpam-5936	74	7	this	this	DET
ejpam-5936	74	8	method	method	NOUN
ejpam-5936	74	9	to	to	PART
ejpam-5936	74	10	construct	construct	VERB
ejpam-5936	74	11	exact	exact	ADJ
ejpam-5936	74	12	solutions	solution	NOUN
ejpam-5936	74	13	and	and	CCONJ
ejpam-5936	74	14	visualize	visualize	VERB
ejpam-5936	74	15	their	their	PRON
ejpam-5936	74	16	behaviors	behavior	NOUN
ejpam-5936	74	17	through	through	ADP
ejpam-5936	74	18	3d	3d	NUM
ejpam-5936	74	19	graphical	graphical	ADJ
ejpam-5936	74	20	representations	representation	NOUN
ejpam-5936	74	21	.	.	PUNCT
ejpam-5936	75	1	section	section	NOUN
ejpam-5936	75	2	4	4	NUM
ejpam-5936	75	3	presents	present	VERB
ejpam-5936	75	4	physical	physical	ADJ
ejpam-5936	75	5	interpretations	interpretation	NOUN
ejpam-5936	75	6	of	of	ADP
ejpam-5936	75	7	the	the	DET
ejpam-5936	75	8	obtained	obtain	VERB
ejpam-5936	75	9	solutions	solution	NOUN
ejpam-5936	75	10	.	.	PUNCT
ejpam-5936	76	1	finally	finally	ADV
ejpam-5936	76	2	,	,	PUNCT
ejpam-5936	76	3	section	section	NOUN
ejpam-5936	76	4	5	5	NUM
ejpam-5936	76	5	contains	contain	VERB
ejpam-5936	76	6	concluding	conclude	VERB
ejpam-5936	76	7	remarks	remark	NOUN
ejpam-5936	76	8	.	.	PUNCT
ejpam-5936	77	1	2	2	X
ejpam-5936	77	2	.	.	X
ejpam-5936	77	3	power	power	NOUN
ejpam-5936	77	4	index	index	NOUN
ejpam-5936	77	5	method	method	NOUN
ejpam-5936	77	6	we	we	PRON
ejpam-5936	77	7	define	define	VERB
ejpam-5936	77	8	the	the	DET
ejpam-5936	77	9	new	new	ADJ
ejpam-5936	77	10	wave	wave	NOUN
ejpam-5936	77	11	variable	variable	NOUN
ejpam-5936	77	12	ξ	ξ	PROPN
ejpam-5936	77	13	and	and	CCONJ
ejpam-5936	77	14	the	the	DET
ejpam-5936	77	15	corresponding	corresponding	ADJ
ejpam-5936	77	16	transformation	transformation	NOUN
ejpam-5936	77	17	for	for	ADP
ejpam-5936	77	18	u	u	NOUN
ejpam-5936	77	19	as	as	SCONJ
ejpam-5936	77	20	follows	follow	VERB
ejpam-5936	77	21	:	:	PUNCT
ejpam-5936	77	22	ξ	ξ	X
ejpam-5936	77	23	=	=	SYM
ejpam-5936	77	24	xmz(y	xmz(y	PROPN
ejpam-5936	77	25	)	)	PUNCT
ejpam-5936	77	26	.	.	PUNCT
ejpam-5936	78	1	(	(	PUNCT
ejpam-5936	78	2	2	2	X
ejpam-5936	78	3	)	)	PUNCT
ejpam-5936	78	4	u	u	NOUN
ejpam-5936	78	5	=	=	PROPN
ejpam-5936	78	6	xna(y)etf(ξ	xna(y)etf(ξ	PROPN
ejpam-5936	78	7	)	)	PUNCT
ejpam-5936	78	8	.	.	PUNCT
ejpam-5936	79	1	(	(	PUNCT
ejpam-5936	79	2	3	3	X
ejpam-5936	79	3	)	)	PUNCT
ejpam-5936	79	4	here	here	ADV
ejpam-5936	79	5	,	,	PUNCT
ejpam-5936	79	6	a(y	a(y	PROPN
ejpam-5936	79	7	)	)	PUNCT
ejpam-5936	79	8	and	and	CCONJ
ejpam-5936	79	9	z(y	z(y	PROPN
ejpam-5936	79	10	)	)	PUNCT
ejpam-5936	79	11	are	be	AUX
ejpam-5936	79	12	unknown	unknown	ADJ
ejpam-5936	79	13	functions	function	NOUN
ejpam-5936	79	14	that	that	PRON
ejpam-5936	79	15	can	can	AUX
ejpam-5936	79	16	be	be	AUX
ejpam-5936	79	17	determined	determine	VERB
ejpam-5936	79	18	after	after	ADP
ejpam-5936	79	19	selecting	select	VERB
ejpam-5936	79	20	the	the	DET
ejpam-5936	79	21	indexes	index	NOUN
ejpam-5936	79	22	of	of	ADP
ejpam-5936	79	23	independent	independent	ADJ
ejpam-5936	79	24	variable	variable	ADJ
ejpam-5936	79	25	x.	x.	NOUN
ejpam-5936	80	1	these	these	DET
ejpam-5936	80	2	functions	function	NOUN
ejpam-5936	80	3	may	may	AUX
ejpam-5936	80	4	be	be	AUX
ejpam-5936	80	5	polynomial	polynomial	ADJ
ejpam-5936	80	6	,	,	PUNCT
ejpam-5936	80	7	rational	rational	ADJ
ejpam-5936	80	8	,	,	PUNCT
ejpam-5936	80	9	or	or	CCONJ
ejpam-5936	80	10	other	other	ADJ
ejpam-5936	80	11	elementary	elementary	ADJ
ejpam-5936	80	12	functions	function	NOUN
ejpam-5936	80	13	.	.	PUNCT
ejpam-5936	81	1	now	now	ADV
ejpam-5936	81	2	,	,	PUNCT
ejpam-5936	81	3	differentiate	differentiate	VERB
ejpam-5936	81	4	equations	equation	NOUN
ejpam-5936	81	5	(	(	PUNCT
ejpam-5936	81	6	2	2	NUM
ejpam-5936	81	7	)	)	PUNCT
ejpam-5936	81	8	and	and	CCONJ
ejpam-5936	81	9	(	(	PUNCT
ejpam-5936	81	10	3	3	X
ejpam-5936	81	11	)	)	PUNCT
ejpam-5936	81	12	using	use	VERB
ejpam-5936	81	13	equation	equation	NOUN
ejpam-5936	81	14	(	(	PUNCT
ejpam-5936	81	15	1	1	NUM
ejpam-5936	81	16	)	)	PUNCT
ejpam-5936	81	17	.	.	PUNCT
ejpam-5936	82	1	substituting	substitute	VERB
ejpam-5936	82	2	all	all	DET
ejpam-5936	82	3	derivative	derivative	ADJ
ejpam-5936	82	4	values	value	NOUN
ejpam-5936	82	5	into	into	ADP
ejpam-5936	82	6	equation	equation	NOUN
ejpam-5936	82	7	(	(	PUNCT
ejpam-5936	82	8	1	1	NUM
ejpam-5936	82	9	)	)	PUNCT
ejpam-5936	82	10	,	,	PUNCT
ejpam-5936	82	11	we	we	PRON
ejpam-5936	82	12	can	can	AUX
ejpam-5936	82	13	express	express	VERB
ejpam-5936	82	14	the	the	DET
ejpam-5936	82	15	given	give	VERB
ejpam-5936	82	16	pde	pde	NOUN
ejpam-5936	82	17	(	(	PUNCT
ejpam-5936	82	18	1	1	NUM
ejpam-5936	82	19	)	)	PUNCT
ejpam-5936	82	20	in	in	ADP
ejpam-5936	82	21	terms	term	NOUN
ejpam-5936	82	22	of	of	ADP
ejpam-5936	82	23	the	the	DET
ejpam-5936	82	24	differentials	differential	NOUN
ejpam-5936	82	25	of	of	ADP
ejpam-5936	82	26	the	the	DET
ejpam-5936	82	27	new	new	ADJ
ejpam-5936	82	28	variables	variable	NOUN
ejpam-5936	82	29	as	as	SCONJ
ejpam-5936	82	30	follows	follow	VERB
ejpam-5936	82	31	:	:	PUNCT
ejpam-5936	82	32	x2n+2m(x−2m2z2(y	x2n+2m(x−2m2z2(y	X
ejpam-5936	82	33	)	)	PUNCT
ejpam-5936	83	1	+	+	CCONJ
ejpam-5936	83	2	z	z	X
ejpam-5936	83	3	′2(y))f	′2(y))f	NOUN
ejpam-5936	83	4	′2(ξ	′2(ξ	NUM
ejpam-5936	83	5	)	)	PUNCT
ejpam-5936	83	6	+	+	SYM
ejpam-5936	83	7	x2n+2m(x−2m2z2(y	x2n+2m(x−2m2z2(y	X
ejpam-5936	83	8	)	)	PUNCT
ejpam-5936	84	1	+	+	CCONJ
ejpam-5936	84	2	z	z	NOUN
ejpam-5936	84	3	′2(y	′2(y	NOUN
ejpam-5936	84	4	)	)	PUNCT
ejpam-5936	84	5	)	)	PUNCT
ejpam-5936	85	1	f(ξ)f	f(ξ)f	PROPN
ejpam-5936	85	2	′′(ξ	′′(ξ	PROPN
ejpam-5936	85	3	)	)	PUNCT
ejpam-5936	86	1	+	+	CCONJ
ejpam-5936	86	2	x2n+m(x−2m2z(y)−	x2n+m(x−2m2z(y)−	PROPN
ejpam-5936	86	3	x−2mz(y	x−2mz(y	NOUN
ejpam-5936	86	4	)	)	PUNCT
ejpam-5936	87	1	+	+	CCONJ
ejpam-5936	87	2	4a′(y)z	4a′(y)z	NUM
ejpam-5936	87	3	′(y	′(y	NOUN
ejpam-5936	87	4	)	)	PUNCT
ejpam-5936	87	5	a(y	a(y	PROPN
ejpam-5936	87	6	)	)	PUNCT
ejpam-5936	88	1	+	+	PUNCT
ejpam-5936	88	2	z	z	NOUN
ejpam-5936	88	3	′′(y)+	′′(y)+	PROPN
ejpam-5936	88	4	4x−2nmz(y))f(ξ)f	4x−2nmz(y))f(ξ)f	NUM
ejpam-5936	88	5	′(ξ	′(ξ	NOUN
ejpam-5936	88	6	)	)	PUNCT
ejpam-5936	89	1	+	+	CCONJ
ejpam-5936	89	2	x2n(2x−2n2	x2n(2x−2n2	X
ejpam-5936	89	3	−	−	NOUN
ejpam-5936	89	4	nx−2	nx−2	NOUN
ejpam-5936	89	5	+	+	CCONJ
ejpam-5936	89	6	a′2(y	a′2(y	PROPN
ejpam-5936	89	7	)	)	PUNCT
ejpam-5936	89	8	a2(y	a2(y	NUM
ejpam-5936	89	9	)	)	PUNCT
ejpam-5936	89	10	+	+	CCONJ
ejpam-5936	89	11	a′′(y	a′′(y	X
ejpam-5936	89	12	)	)	PUNCT
ejpam-5936	89	13	a(y	a(y	PROPN
ejpam-5936	89	14	)	)	PUNCT
ejpam-5936	89	15	)	)	PUNCT
ejpam-5936	90	1	f2(ξ	f2(ξ	X
ejpam-5936	90	2	)	)	PUNCT
ejpam-5936	90	3	=	=	NOUN
ejpam-5936	90	4	0	0	X
ejpam-5936	90	5	.	.	PUNCT
ejpam-5936	90	6	(	(	PUNCT
ejpam-5936	90	7	4	4	X
ejpam-5936	90	8	)	)	PUNCT
ejpam-5936	90	9	we	we	PRON
ejpam-5936	90	10	have	have	AUX
ejpam-5936	90	11	selected	select	VERB
ejpam-5936	90	12	those	those	DET
ejpam-5936	90	13	terms	term	NOUN
ejpam-5936	90	14	whose	whose	DET
ejpam-5936	90	15	coefficients	coefficient	NOUN
ejpam-5936	90	16	can	can	AUX
ejpam-5936	90	17	not	not	PART
ejpam-5936	90	18	be	be	AUX
ejpam-5936	90	19	coverted	coverte	VERB
ejpam-5936	90	20	into	into	ADP
ejpam-5936	90	21	the	the	DET
ejpam-5936	90	22	new	new	ADJ
ejpam-5936	90	23	variable	variable	NOUN
ejpam-5936	90	24	ξ	ξ	PROPN
ejpam-5936	90	25	.	.	PUNCT
ejpam-5936	91	1	f1(x	f1(x	PROPN
ejpam-5936	91	2	,	,	PUNCT
ejpam-5936	91	3	y	y	PROPN
ejpam-5936	91	4	,	,	PUNCT
ejpam-5936	91	5	t	t	PROPN
ejpam-5936	91	6	)	)	PUNCT
ejpam-5936	91	7	=	=	SYM
ejpam-5936	92	1	x2m+2z	x2m+2z	PROPN
ejpam-5936	92	2	′2(y)(f	′2(y)(f	NOUN
ejpam-5936	92	3	′2(ξ	′2(ξ	NUM
ejpam-5936	92	4	)	)	PUNCT
ejpam-5936	93	1	+	+	CCONJ
ejpam-5936	93	2	f(ξ)f	f(ξ)f	PROPN
ejpam-5936	93	3	′′(ξ	′′(ξ	PROPN
ejpam-5936	93	4	)	)	PUNCT
ejpam-5936	93	5	)	)	PUNCT
ejpam-5936	93	6	.	.	PUNCT
ejpam-5936	94	1	(	(	PUNCT
ejpam-5936	94	2	5	5	X
ejpam-5936	94	3	)	)	PUNCT
ejpam-5936	94	4	f2(x	f2(x	PROPN
ejpam-5936	94	5	,	,	PUNCT
ejpam-5936	94	6	y	y	PROPN
ejpam-5936	94	7	,	,	PUNCT
ejpam-5936	94	8	t	t	PROPN
ejpam-5936	94	9	)	)	PUNCT
ejpam-5936	95	1	=	=	PUNCT
ejpam-5936	95	2	(	(	PUNCT
ejpam-5936	95	3	4a′(y)z	4a′(y)z	NUM
ejpam-5936	95	4	′(y	′(y	NOUN
ejpam-5936	95	5	)	)	PUNCT
ejpam-5936	95	6	a(y	a(y	PROPN
ejpam-5936	95	7	)	)	PUNCT
ejpam-5936	96	1	+	+	CCONJ
ejpam-5936	96	2	z	z	NOUN
ejpam-5936	96	3	′′(y))xm+2f(ξ)f	′′(y))xm+2f(ξ)f	ADJ
ejpam-5936	96	4	′(ξ	′(ξ	NOUN
ejpam-5936	96	5	)	)	PUNCT
ejpam-5936	96	6	.	.	PUNCT
ejpam-5936	97	1	(	(	PUNCT
ejpam-5936	97	2	6	6	X
ejpam-5936	97	3	)	)	PUNCT
ejpam-5936	97	4	f3(x	f3(x	PROPN
ejpam-5936	97	5	,	,	PUNCT
ejpam-5936	97	6	y	y	PROPN
ejpam-5936	97	7	,	,	PUNCT
ejpam-5936	97	8	t	t	PROPN
ejpam-5936	97	9	)	)	PUNCT
ejpam-5936	97	10	=	=	PUNCT
ejpam-5936	97	11	(	(	PUNCT
ejpam-5936	97	12	2n2	2n2	NUM
ejpam-5936	97	13	+	+	SYM
ejpam-5936	97	14	x2a′2(y	x2a′2(y	NUM
ejpam-5936	97	15	)	)	PUNCT
ejpam-5936	97	16	a2(y	a2(y	X
ejpam-5936	97	17	)	)	PUNCT
ejpam-5936	98	1	+	+	CCONJ
ejpam-5936	98	2	x2a′′(y	x2a′′(y	X
ejpam-5936	98	3	)	)	PUNCT
ejpam-5936	98	4	a(y	a(y	PROPN
ejpam-5936	98	5	)	)	PUNCT
ejpam-5936	98	6	)	)	PUNCT
ejpam-5936	99	1	f2(ξ	f2(ξ	PROPN
ejpam-5936	99	2	)	)	PUNCT
ejpam-5936	99	3	.	.	PUNCT
ejpam-5936	100	1	(	(	PUNCT
ejpam-5936	100	2	7	7	X
ejpam-5936	100	3	)	)	PUNCT
ejpam-5936	100	4	z.	z.	PROPN
ejpam-5936	100	5	haider	haider	PROPN
ejpam-5936	100	6	,	,	PUNCT
ejpam-5936	100	7	k.	k.	PROPN
ejpam-5936	100	8	ahmad	ahmad	PROPN
ejpam-5936	100	9	/	/	SYM
ejpam-5936	100	10	eur	eur	PROPN
ejpam-5936	100	11	.	.	PUNCT
ejpam-5936	101	1	j.	j.	PROPN
ejpam-5936	101	2	pure	pure	PROPN
ejpam-5936	101	3	appl	appl	PROPN
ejpam-5936	101	4	.	.	PROPN
ejpam-5936	101	5	math	math	PROPN
ejpam-5936	101	6	,	,	PUNCT
ejpam-5936	101	7	18	18	NUM
ejpam-5936	101	8	(	(	PUNCT
ejpam-5936	101	9	2	2	NUM
ejpam-5936	101	10	)	)	PUNCT
ejpam-5936	101	11	(	(	PUNCT
ejpam-5936	101	12	2025	2025	NUM
ejpam-5936	101	13	)	)	PUNCT
ejpam-5936	101	14	,	,	PUNCT
ejpam-5936	101	15	5936	5936	NUM
ejpam-5936	101	16	5	5	NUM
ejpam-5936	101	17	of	of	ADP
ejpam-5936	101	18	18	18	NUM
ejpam-5936	101	19	in	in	ADP
ejpam-5936	101	20	equations	equation	NOUN
ejpam-5936	101	21	(	(	PUNCT
ejpam-5936	101	22	5	5	NUM
ejpam-5936	101	23	)	)	PUNCT
ejpam-5936	101	24	,	,	PUNCT
ejpam-5936	101	25	(	(	PUNCT
ejpam-5936	101	26	6	6	NUM
ejpam-5936	101	27	)	)	PUNCT
ejpam-5936	101	28	,	,	PUNCT
ejpam-5936	101	29	and	and	CCONJ
ejpam-5936	101	30	(	(	PUNCT
ejpam-5936	101	31	7	7	NUM
ejpam-5936	101	32	)	)	PUNCT
ejpam-5936	101	33	,	,	PUNCT
ejpam-5936	101	34	we	we	PRON
ejpam-5936	101	35	must	must	AUX
ejpam-5936	101	36	select	select	VERB
ejpam-5936	101	37	the	the	DET
ejpam-5936	101	38	elementary	elementary	ADJ
ejpam-5936	101	39	functions	function	NOUN
ejpam-5936	101	40	a(y	a(y	PROPN
ejpam-5936	101	41	)	)	PUNCT
ejpam-5936	101	42	and	and	CCONJ
ejpam-5936	101	43	z(y	z(y	PROPN
ejpam-5936	101	44	)	)	PUNCT
ejpam-5936	101	45	and	and	CCONJ
ejpam-5936	101	46	the	the	DET
ejpam-5936	101	47	indexes	index	NOUN
ejpam-5936	101	48	m	m	VERB
ejpam-5936	101	49	and	and	CCONJ
ejpam-5936	101	50	n	n	PROPN
ejpam-5936	101	51	of	of	ADP
ejpam-5936	101	52	independent	independent	ADJ
ejpam-5936	101	53	variable	variable	NOUN
ejpam-5936	101	54	x	x	PUNCT
ejpam-5936	101	55	such	such	ADJ
ejpam-5936	101	56	that	that	DET
ejpam-5936	101	57	equation	equation	NOUN
ejpam-5936	101	58	(	(	PUNCT
ejpam-5936	101	59	4	4	X
ejpam-5936	101	60	)	)	PUNCT
ejpam-5936	101	61	transforms	transform	VERB
ejpam-5936	101	62	into	into	ADP
ejpam-5936	101	63	a	a	DET
ejpam-5936	101	64	nonlinear	nonlinear	ADJ
ejpam-5936	101	65	ode	ode	NOUN
ejpam-5936	101	66	.	.	PUNCT
ejpam-5936	102	1	the	the	DET
ejpam-5936	102	2	optimal	optimal	ADJ
ejpam-5936	102	3	choices	choice	NOUN
ejpam-5936	102	4	for	for	ADP
ejpam-5936	102	5	the	the	DET
ejpam-5936	102	6	indexes	index	NOUN
ejpam-5936	102	7	m	m	VERB
ejpam-5936	102	8	and	and	CCONJ
ejpam-5936	102	9	n	n	PROPN
ejpam-5936	102	10	of	of	ADP
ejpam-5936	102	11	the	the	DET
ejpam-5936	102	12	independent	independent	ADJ
ejpam-5936	102	13	variable	variable	NOUN
ejpam-5936	102	14	x	x	PRON
ejpam-5936	102	15	are	be	AUX
ejpam-5936	102	16	as	as	SCONJ
ejpam-5936	102	17	follows	follow	VERB
ejpam-5936	102	18	:	:	PUNCT
ejpam-5936	102	19	table:2	table:2	NOUN
ejpam-5936	102	20	list	list	NOUN
ejpam-5936	102	21	of	of	ADP
ejpam-5936	102	22	optimal	optimal	ADJ
ejpam-5936	102	23	values	value	NOUN
ejpam-5936	102	24	for	for	ADP
ejpam-5936	102	25	the	the	DET
ejpam-5936	102	26	indexes	index	NOUN
ejpam-5936	102	27	of	of	ADP
ejpam-5936	102	28	the	the	DET
ejpam-5936	102	29	independent	independent	ADJ
ejpam-5936	102	30	variable	variable	NOUN
ejpam-5936	102	31	x	x	SYM
ejpam-5936	102	32	2m+	2m+	NUM
ejpam-5936	102	33	2n	2n	NUM
ejpam-5936	103	1	n	n	NOUN
ejpam-5936	103	2	=	=	PUNCT
ejpam-5936	103	3	−m	−m	NOUN
ejpam-5936	103	4	m	m	NOUN
ejpam-5936	103	5	=	=	SYM
ejpam-5936	103	6	−1	−1	NOUN
ejpam-5936	103	7	,	,	PUNCT
ejpam-5936	103	8	n	n	NOUN
ejpam-5936	103	9	=	=	SYM
ejpam-5936	103	10	1	1	NUM
ejpam-5936	103	11	2m+	2m+	NUM
ejpam-5936	103	12	2n	2n	NUM
ejpam-5936	103	13	n	n	NOUN
ejpam-5936	103	14	=	=	PUNCT
ejpam-5936	103	15	−m	−m	NOUN
ejpam-5936	103	16	m	m	NOUN
ejpam-5936	103	17	=	=	SYM
ejpam-5936	103	18	1	1	NUM
ejpam-5936	103	19	,	,	PUNCT
ejpam-5936	103	20	n	n	NOUN
ejpam-5936	103	21	=	=	SYM
ejpam-5936	103	22	−1	−1	NOUN
ejpam-5936	103	23	2n+m	2n+m	PROPN
ejpam-5936	104	1	n	n	NOUN
ejpam-5936	104	2	=	=	SYM
ejpam-5936	104	3	−m	−m	NOUN
ejpam-5936	104	4	2	2	NUM
ejpam-5936	104	5	m	m	NOUN
ejpam-5936	104	6	=	=	SYM
ejpam-5936	104	7	−2	−2	NOUN
ejpam-5936	104	8	,	,	PUNCT
ejpam-5936	104	9	n	n	NOUN
ejpam-5936	104	10	=	=	SYM
ejpam-5936	104	11	1	1	NUM
ejpam-5936	104	12	2n+m−	2n+m−	NUM
ejpam-5936	104	13	2	2	NUM
ejpam-5936	104	14	n	n	NOUN
ejpam-5936	104	15	=	=	SYM
ejpam-5936	104	16	2−m	2−m	NUM
ejpam-5936	104	17	2	2	NUM
ejpam-5936	104	18	m	m	NOUN
ejpam-5936	104	19	=	=	SYM
ejpam-5936	104	20	1	1	NUM
ejpam-5936	104	21	,	,	PUNCT
ejpam-5936	104	22	n	n	NOUN
ejpam-5936	104	23	=	=	SYM
ejpam-5936	104	24	1	1	NUM
ejpam-5936	104	25	2	2	NUM
ejpam-5936	104	26	3	3	NUM
ejpam-5936	104	27	.	.	PUNCT
ejpam-5936	105	1	new	new	ADJ
ejpam-5936	105	2	exact	exact	ADJ
ejpam-5936	105	3	solutions	solution	NOUN
ejpam-5936	105	4	of	of	ADP
ejpam-5936	105	5	biological	biological	ADJ
ejpam-5936	105	6	population	population	NOUN
ejpam-5936	105	7	model	model	NOUN
ejpam-5936	105	8	case:1	case:1	PROPN
ejpam-5936	105	9	(	(	PUNCT
ejpam-5936	105	10	n	n	NOUN
ejpam-5936	105	11	=	=	SYM
ejpam-5936	105	12	1	1	NUM
ejpam-5936	105	13	,	,	PUNCT
ejpam-5936	105	14	m	m	VERB
ejpam-5936	105	15	=	=	SYM
ejpam-5936	105	16	−1	−1	NOUN
ejpam-5936	105	17	)	)	PUNCT
ejpam-5936	105	18	for	for	ADP
ejpam-5936	105	19	n	n	NOUN
ejpam-5936	105	20	=	=	SYM
ejpam-5936	105	21	1	1	NUM
ejpam-5936	105	22	and	and	CCONJ
ejpam-5936	105	23	m	m	PROPN
ejpam-5936	105	24	=	=	SYM
ejpam-5936	105	25	−1	−1	NOUN
ejpam-5936	105	26	,	,	PUNCT
ejpam-5936	105	27	the	the	DET
ejpam-5936	105	28	wave	wave	NOUN
ejpam-5936	105	29	variable	variable	NOUN
ejpam-5936	105	30	ξ	ξ	PROPN
ejpam-5936	105	31	=	=	SYM
ejpam-5936	105	32	xmz(y	xmz(y	PROPN
ejpam-5936	105	33	)	)	PUNCT
ejpam-5936	105	34	becomes	become	VERB
ejpam-5936	105	35	ξ	ξ	NOUN
ejpam-5936	105	36	=	=	SYM
ejpam-5936	105	37	z(y	z(y	PROPN
ejpam-5936	105	38	)	)	PUNCT
ejpam-5936	105	39	x	x	PUNCT
ejpam-5936	105	40	and	and	CCONJ
ejpam-5936	105	41	the	the	DET
ejpam-5936	105	42	transformation	transformation	NOUN
ejpam-5936	105	43	u	u	NOUN
ejpam-5936	105	44	=	=	PROPN
ejpam-5936	105	45	xna(y)etf(ξ	xna(y)etf(ξ	PROPN
ejpam-5936	105	46	)	)	PUNCT
ejpam-5936	105	47	becomes	become	VERB
ejpam-5936	105	48	u	u	NOUN
ejpam-5936	105	49	=	=	PROPN
ejpam-5936	105	50	xa(y)etf(ξ	xa(y)etf(ξ	PROPN
ejpam-5936	105	51	)	)	PUNCT
ejpam-5936	105	52	.	.	PUNCT
ejpam-5936	106	1	substituting	substitute	VERB
ejpam-5936	106	2	the	the	DET
ejpam-5936	106	3	wave	wave	NOUN
ejpam-5936	106	4	variable	variable	NOUN
ejpam-5936	106	5	ξ	ξ	PROPN
ejpam-5936	106	6	=	=	SYM
ejpam-5936	106	7	z(y	z(y	PROPN
ejpam-5936	106	8	)	)	PUNCT
ejpam-5936	106	9	x	x	PUNCT
ejpam-5936	106	10	and	and	CCONJ
ejpam-5936	106	11	the	the	DET
ejpam-5936	106	12	transformation	transformation	NOUN
ejpam-5936	106	13	u	u	NOUN
ejpam-5936	106	14	=	=	PROPN
ejpam-5936	106	15	xa(y)etf(ξ	xa(y)etf(ξ	PROPN
ejpam-5936	106	16	)	)	PUNCT
ejpam-5936	106	17	into	into	ADP
ejpam-5936	106	18	equation	equation	NOUN
ejpam-5936	106	19	(	(	PUNCT
ejpam-5936	106	20	4	4	NUM
ejpam-5936	106	21	)	)	PUNCT
ejpam-5936	106	22	,	,	PUNCT
ejpam-5936	106	23	we	we	PRON
ejpam-5936	106	24	obtain	obtain	AUX
ejpam-5936	106	25	:	:	PUNCT
ejpam-5936	106	26	figure	figure	AUX
ejpam-5936	106	27	1	1	NUM
ejpam-5936	106	28	:	:	PUNCT
ejpam-5936	106	29	3d	3d	NUM
ejpam-5936	106	30	plot	plot	NOUN
ejpam-5936	106	31	of	of	ADP
ejpam-5936	106	32	solution	solution	NOUN
ejpam-5936	106	33	u1	u1	NOUN
ejpam-5936	106	34	given	give	VERB
ejpam-5936	106	35	in	in	ADP
ejpam-5936	106	36	(	(	PUNCT
ejpam-5936	106	37	11	11	NUM
ejpam-5936	106	38	)	)	PUNCT
ejpam-5936	106	39	of	of	ADP
ejpam-5936	106	40	pde	pde	NOUN
ejpam-5936	106	41	(	(	PUNCT
ejpam-5936	106	42	1	1	NUM
ejpam-5936	106	43	)	)	PUNCT
ejpam-5936	106	44	for	for	ADP
ejpam-5936	106	45	c1	c1	NOUN
ejpam-5936	106	46	=	=	SYM
ejpam-5936	106	47	1	1	NUM
ejpam-5936	106	48	,	,	PUNCT
ejpam-5936	106	49	c2	c2	PROPN
ejpam-5936	106	50	=	=	PUNCT
ejpam-5936	106	51	−1	−1	NOUN
ejpam-5936	106	52	and	and	CCONJ
ejpam-5936	106	53	y	y	NOUN
ejpam-5936	106	54	=	=	PUNCT
ejpam-5936	106	55	−3	−3	AUX
ejpam-5936	106	56	.	.	PUNCT
ejpam-5936	107	1	(	(	PUNCT
ejpam-5936	107	2	ξ2	ξ2	NOUN
ejpam-5936	107	3	+	+	CCONJ
ejpam-5936	108	1	z	z	NOUN
ejpam-5936	109	1	′2(y	′2(y	NOUN
ejpam-5936	109	2	)	)	PUNCT
ejpam-5936	110	1	+	+	CCONJ
ejpam-5936	110	2	x2a′2(y	x2a′2(y	PROPN
ejpam-5936	110	3	)	)	PUNCT
ejpam-5936	110	4	a2(y	a2(y	X
ejpam-5936	110	5	)	)	PUNCT
ejpam-5936	110	6	+	+	CCONJ
ejpam-5936	110	7	x2a′′(y	x2a′′(y	X
ejpam-5936	110	8	)	)	PUNCT
ejpam-5936	110	9	a(y	a(y	PROPN
ejpam-5936	110	10	)	)	PUNCT
ejpam-5936	110	11	)	)	PUNCT
ejpam-5936	110	12	f	f	PROPN
ejpam-5936	110	13	′2(ξ	′2(ξ	NUM
ejpam-5936	110	14	)	)	PUNCT
ejpam-5936	111	1	+	+	CCONJ
ejpam-5936	111	2	(	(	PUNCT
ejpam-5936	111	3	ξ2	ξ2	NOUN
ejpam-5936	111	4	+	+	CCONJ
ejpam-5936	111	5	z	z	PROPN
ejpam-5936	111	6	′2(y))f(ξ)f	′2(y))f(ξ)f	ADJ
ejpam-5936	111	7	′′(ξ	′′(ξ	PROPN
ejpam-5936	111	8	)	)	PUNCT
ejpam-5936	112	1	+	+	CCONJ
ejpam-5936	112	2	...	...	PUNCT
ejpam-5936	113	1	(	(	PUNCT
ejpam-5936	113	2	xz′′(y)−	xz′′(y)−	PROPN
ejpam-5936	113	3	2ξ	2ξ	NUM
ejpam-5936	113	4	+	+	CCONJ
ejpam-5936	113	5	4xa′(y)z	4xa′(y)z	PROPN
ejpam-5936	113	6	′(y	′(y	NOUN
ejpam-5936	113	7	)	)	PUNCT
ejpam-5936	113	8	a(y	a(y	PROPN
ejpam-5936	113	9	)	)	PUNCT
ejpam-5936	113	10	)	)	PUNCT
ejpam-5936	113	11	f(ξ)f	f(ξ)f	PROPN
ejpam-5936	113	12	′(ξ	′(ξ	NOUN
ejpam-5936	113	13	)	)	PUNCT
ejpam-5936	113	14	+	+	CCONJ
ejpam-5936	114	1	f2(ξ	f2(ξ	X
ejpam-5936	114	2	)	)	PUNCT
ejpam-5936	114	3	=	=	SYM
ejpam-5936	114	4	0	0	X
ejpam-5936	114	5	.	.	PUNCT
ejpam-5936	115	1	(	(	PUNCT
ejpam-5936	115	2	8)	8)	NUM
ejpam-5936	115	3	z.	z.	PROPN
ejpam-5936	115	4	haider	haider	PROPN
ejpam-5936	115	5	,	,	PUNCT
ejpam-5936	115	6	k.	k.	PROPN
ejpam-5936	115	7	ahmad	ahmad	PROPN
ejpam-5936	115	8	/	/	SYM
ejpam-5936	115	9	eur	eur	PROPN
ejpam-5936	115	10	.	.	PUNCT
ejpam-5936	116	1	j.	j.	PROPN
ejpam-5936	116	2	pure	pure	PROPN
ejpam-5936	116	3	appl	appl	PROPN
ejpam-5936	116	4	.	.	PROPN
ejpam-5936	116	5	math	math	PROPN
ejpam-5936	116	6	,	,	PUNCT
ejpam-5936	116	7	18	18	NUM
ejpam-5936	116	8	(	(	PUNCT
ejpam-5936	116	9	2	2	NUM
ejpam-5936	116	10	)	)	PUNCT
ejpam-5936	116	11	(	(	PUNCT
ejpam-5936	116	12	2025	2025	NUM
ejpam-5936	116	13	)	)	PUNCT
ejpam-5936	116	14	,	,	PUNCT
ejpam-5936	116	15	5936	5936	NUM
ejpam-5936	116	16	6	6	NUM
ejpam-5936	116	17	of	of	ADP
ejpam-5936	116	18	18	18	NUM
ejpam-5936	116	19	figure	figure	NOUN
ejpam-5936	116	20	2	2	NUM
ejpam-5936	116	21	:	:	PUNCT
ejpam-5936	116	22	3d	3d	NUM
ejpam-5936	116	23	plot	plot	NOUN
ejpam-5936	116	24	of	of	ADP
ejpam-5936	116	25	solution	solution	NOUN
ejpam-5936	116	26	u2	u2	NOUN
ejpam-5936	116	27	given	give	VERB
ejpam-5936	116	28	in	in	ADP
ejpam-5936	116	29	(	(	PUNCT
ejpam-5936	116	30	11	11	NUM
ejpam-5936	116	31	)	)	PUNCT
ejpam-5936	116	32	of	of	ADP
ejpam-5936	116	33	pde	pde	NOUN
ejpam-5936	116	34	(	(	PUNCT
ejpam-5936	116	35	1	1	NUM
ejpam-5936	116	36	)	)	PUNCT
ejpam-5936	116	37	for	for	ADP
ejpam-5936	116	38	c1	c1	NOUN
ejpam-5936	116	39	=	=	SYM
ejpam-5936	116	40	1	1	NUM
ejpam-5936	116	41	,	,	PUNCT
ejpam-5936	116	42	c2	c2	PROPN
ejpam-5936	116	43	=	=	PUNCT
ejpam-5936	116	44	−1	−1	NOUN
ejpam-5936	116	45	and	and	CCONJ
ejpam-5936	116	46	x	x	X
ejpam-5936	116	47	=	=	SYM
ejpam-5936	116	48	−1	−1	NOUN
ejpam-5936	116	49	.	.	PUNCT
ejpam-5936	117	1	figure	figure	VERB
ejpam-5936	117	2	3	3	NUM
ejpam-5936	117	3	:	:	PUNCT
ejpam-5936	117	4	3d	3d	NUM
ejpam-5936	117	5	plot	plot	NOUN
ejpam-5936	117	6	of	of	ADP
ejpam-5936	117	7	solution	solution	NOUN
ejpam-5936	117	8	u3	u3	NOUN
ejpam-5936	117	9	given	give	VERB
ejpam-5936	117	10	in	in	ADP
ejpam-5936	117	11	(	(	PUNCT
ejpam-5936	117	12	11	11	NUM
ejpam-5936	117	13	)	)	PUNCT
ejpam-5936	117	14	of	of	ADP
ejpam-5936	117	15	pde	pde	NOUN
ejpam-5936	117	16	(	(	PUNCT
ejpam-5936	117	17	1	1	NUM
ejpam-5936	117	18	)	)	PUNCT
ejpam-5936	117	19	for	for	ADP
ejpam-5936	117	20	c1	c1	NOUN
ejpam-5936	117	21	=	=	PUNCT
ejpam-5936	117	22	−2	−2	PROPN
ejpam-5936	117	23	,	,	PUNCT
ejpam-5936	117	24	c2	c2	PROPN
ejpam-5936	117	25	=	=	SYM
ejpam-5936	117	26	3	3	NUM
ejpam-5936	117	27	and	and	CCONJ
ejpam-5936	117	28	t	t	NOUN
ejpam-5936	117	29	=	=	SYM
ejpam-5936	117	30	1	1	X
ejpam-5936	117	31	.	.	PUNCT
ejpam-5936	117	32	to	to	PART
ejpam-5936	117	33	express	express	VERB
ejpam-5936	117	34	the	the	DET
ejpam-5936	117	35	terms	term	NOUN
ejpam-5936	117	36	in	in	ADP
ejpam-5936	117	37	equation	equation	NOUN
ejpam-5936	117	38	(	(	PUNCT
ejpam-5936	117	39	8)	8)	NUM
ejpam-5936	117	40	in	in	ADP
ejpam-5936	117	41	terms	term	NOUN
ejpam-5936	117	42	of	of	ADP
ejpam-5936	117	43	ξ	ξ	PROPN
ejpam-5936	117	44	,	,	PUNCT
ejpam-5936	117	45	we	we	PRON
ejpam-5936	117	46	set	set	VERB
ejpam-5936	117	47	z	z	NOUN
ejpam-5936	117	48	′(y	′(y	NOUN
ejpam-5936	117	49	)	)	PUNCT
ejpam-5936	118	1	=	=	SYM
ejpam-5936	118	2	1	1	NUM
ejpam-5936	118	3	and	and	CCONJ
ejpam-5936	118	4	a′(y	a′(y	NOUN
ejpam-5936	118	5	)	)	PUNCT
ejpam-5936	118	6	a(y	a(y	PROPN
ejpam-5936	118	7	)	)	PUNCT
ejpam-5936	118	8	=	=	SYM
ejpam-5936	118	9	z′′(y	z′′(y	X
ejpam-5936	118	10	)	)	PUNCT
ejpam-5936	118	11	z′(y	z′(y	PROPN
ejpam-5936	118	12	)	)	PUNCT
ejpam-5936	118	13	.	.	PUNCT
ejpam-5936	119	1	this	this	DET
ejpam-5936	119	2	yields	yield	NOUN
ejpam-5936	119	3	z(y	z(y	PROPN
ejpam-5936	119	4	)	)	PUNCT
ejpam-5936	120	1	=	=	SYM
ejpam-5936	120	2	y	y	PROPN
ejpam-5936	120	3	and	and	CCONJ
ejpam-5936	120	4	a(y	a(y	PROPN
ejpam-5936	120	5	)	)	PUNCT
ejpam-5936	120	6	=	=	SYM
ejpam-5936	121	1	1	1	X
ejpam-5936	121	2	.	.	PUNCT
ejpam-5936	121	3	consequently	consequently	ADV
ejpam-5936	121	4	,	,	PUNCT
ejpam-5936	121	5	the	the	DET
ejpam-5936	121	6	wave	wave	NOUN
ejpam-5936	121	7	variable	variable	NOUN
ejpam-5936	121	8	becomes	become	VERB
ejpam-5936	121	9	ξ	ξ	PROPN
ejpam-5936	121	10	=	=	SYM
ejpam-5936	121	11	y	y	PROPN
ejpam-5936	121	12	x	x	X
ejpam-5936	121	13	and	and	CCONJ
ejpam-5936	121	14	the	the	DET
ejpam-5936	121	15	transformation	transformation	NOUN
ejpam-5936	121	16	takes	take	VERB
ejpam-5936	121	17	the	the	DET
ejpam-5936	121	18	form	form	NOUN
ejpam-5936	121	19	u	u	NOUN
ejpam-5936	121	20	=	=	PROPN
ejpam-5936	121	21	xetf(ξ	xetf(ξ	NUM
ejpam-5936	121	22	)	)	PUNCT
ejpam-5936	121	23	.	.	PUNCT
ejpam-5936	122	1	substituting	substitute	VERB
ejpam-5936	122	2	ξ	ξ	X
ejpam-5936	122	3	=	=	SYM
ejpam-5936	122	4	y	y	PROPN
ejpam-5936	122	5	x	x	X
ejpam-5936	122	6	and	and	CCONJ
ejpam-5936	122	7	u	u	X
ejpam-5936	122	8	=	=	PROPN
ejpam-5936	122	9	xetf(ξ	xetf(ξ	PROPN
ejpam-5936	122	10	)	)	PUNCT
ejpam-5936	122	11	into	into	ADP
ejpam-5936	122	12	equation	equation	NOUN
ejpam-5936	122	13	(	(	PUNCT
ejpam-5936	122	14	8)	8)	NUM
ejpam-5936	122	15	,	,	PUNCT
ejpam-5936	122	16	we	we	PRON
ejpam-5936	122	17	obtain	obtain	VERB
ejpam-5936	122	18	the	the	DET
ejpam-5936	122	19	following	following	ADJ
ejpam-5936	122	20	ode	ode	PROPN
ejpam-5936	122	21	:	:	PUNCT
ejpam-5936	122	22	(	(	PUNCT
ejpam-5936	122	23	ξ2	ξ2	NOUN
ejpam-5936	122	24	+	+	CCONJ
ejpam-5936	122	25	1)f	1)f	NUM
ejpam-5936	122	26	′2(ξ	′2(ξ	NUM
ejpam-5936	122	27	)	)	PUNCT
ejpam-5936	123	1	+	+	CCONJ
ejpam-5936	123	2	(	(	PUNCT
ejpam-5936	123	3	ξ2	ξ2	NOUN
ejpam-5936	123	4	+	+	CCONJ
ejpam-5936	123	5	1)f(ξ)f	1)f(ξ)f	NUM
ejpam-5936	123	6	′′(ξ)−	′′(ξ)−	NOUN
ejpam-5936	123	7	2ξf(ξ)f	2ξf(ξ)f	NUM
ejpam-5936	123	8	′(ξ	′(ξ	NOUN
ejpam-5936	123	9	)	)	PUNCT
ejpam-5936	124	1	+	+	CCONJ
ejpam-5936	125	1	f2(ξ	f2(ξ	X
ejpam-5936	125	2	)	)	PUNCT
ejpam-5936	125	3	=	=	SYM
ejpam-5936	125	4	0	0	X
ejpam-5936	125	5	.	.	PUNCT
ejpam-5936	125	6	(	(	PUNCT
ejpam-5936	125	7	9	9	NUM
ejpam-5936	125	8	)	)	PUNCT
ejpam-5936	126	1	z.	z.	PROPN
ejpam-5936	126	2	haider	haider	PROPN
ejpam-5936	126	3	,	,	PUNCT
ejpam-5936	126	4	k.	k.	PROPN
ejpam-5936	126	5	ahmad	ahmad	PROPN
ejpam-5936	126	6	/	/	SYM
ejpam-5936	126	7	eur	eur	PROPN
ejpam-5936	126	8	.	.	PUNCT
ejpam-5936	127	1	j.	j.	PROPN
ejpam-5936	127	2	pure	pure	PROPN
ejpam-5936	127	3	appl	appl	PROPN
ejpam-5936	127	4	.	.	PROPN
ejpam-5936	127	5	math	math	PROPN
ejpam-5936	127	6	,	,	PUNCT
ejpam-5936	127	7	18	18	NUM
ejpam-5936	127	8	(	(	PUNCT
ejpam-5936	127	9	2	2	NUM
ejpam-5936	127	10	)	)	PUNCT
ejpam-5936	127	11	(	(	PUNCT
ejpam-5936	127	12	2025	2025	NUM
ejpam-5936	127	13	)	)	PUNCT
ejpam-5936	127	14	,	,	PUNCT
ejpam-5936	127	15	5936	5936	NUM
ejpam-5936	127	16	7	7	NUM
ejpam-5936	127	17	of	of	ADP
ejpam-5936	127	18	18	18	NUM
ejpam-5936	127	19	the	the	DET
ejpam-5936	127	20	exact	exact	ADJ
ejpam-5936	127	21	solution	solution	NOUN
ejpam-5936	127	22	of	of	ADP
ejpam-5936	127	23	ode	ode	PROPN
ejpam-5936	127	24	(	(	PUNCT
ejpam-5936	127	25	9	9	NUM
ejpam-5936	127	26	)	)	PUNCT
ejpam-5936	127	27	is	be	AUX
ejpam-5936	127	28	f(ξ	f(ξ	NOUN
ejpam-5936	127	29	)	)	PUNCT
ejpam-5936	127	30	=	=	SYM
ejpam-5936	128	1	√	√	PROPN
ejpam-5936	128	2	−c1	−c1	ADJ
ejpam-5936	128	3	sin(2	sin(2	ADJ
ejpam-5936	128	4	tan−1	tan−1	PROPN
ejpam-5936	128	5	ξ)(ξ2	ξ)(ξ2	NOUN
ejpam-5936	128	6	+	+	CCONJ
ejpam-5936	128	7	1	1	NUM
ejpam-5936	128	8	)	)	PUNCT
ejpam-5936	128	9	+	+	CCONJ
ejpam-5936	128	10	c2	c2	PROPN
ejpam-5936	128	11	cos(2	cos(2	VERB
ejpam-5936	128	12	tan−1	tan−1	PROPN
ejpam-5936	128	13	ξ)(ξ2	ξ)(ξ2	NOUN
ejpam-5936	128	14	+	+	NOUN
ejpam-5936	128	15	1	1	NUM
ejpam-5936	128	16	)	)	PUNCT
ejpam-5936	128	17	)	)	PUNCT
ejpam-5936	128	18	.	.	PUNCT
ejpam-5936	129	1	(	(	PUNCT
ejpam-5936	129	2	10	10	NUM
ejpam-5936	129	3	)	)	PUNCT
ejpam-5936	129	4	the	the	DET
ejpam-5936	129	5	exact	exact	ADJ
ejpam-5936	129	6	solution	solution	NOUN
ejpam-5936	129	7	of	of	ADP
ejpam-5936	129	8	pde	pde	NOUN
ejpam-5936	129	9	(	(	PUNCT
ejpam-5936	129	10	1	1	NUM
ejpam-5936	129	11	)	)	PUNCT
ejpam-5936	129	12	is	be	AUX
ejpam-5936	129	13	u(x	u(x	NOUN
ejpam-5936	129	14	,	,	PUNCT
ejpam-5936	129	15	y	y	PROPN
ejpam-5936	129	16	,	,	PUNCT
ejpam-5936	129	17	t	t	PROPN
ejpam-5936	129	18	)	)	PUNCT
ejpam-5936	130	1	=	=	SYM
ejpam-5936	130	2	et	et	NOUN
ejpam-5936	130	3	√	√	PROPN
ejpam-5936	130	4	−c1	−c1	ADJ
ejpam-5936	130	5	sin(2	sin(2	ADJ
ejpam-5936	130	6	tan−1	tan−1	PROPN
ejpam-5936	130	7	y	y	PROPN
ejpam-5936	130	8	x	x	PROPN
ejpam-5936	130	9	)	)	PUNCT
ejpam-5936	130	10	(	(	PUNCT
ejpam-5936	130	11	y2	y2	PROPN
ejpam-5936	130	12	+	+	CCONJ
ejpam-5936	130	13	x2	x2	NUM
ejpam-5936	130	14	)	)	PUNCT
ejpam-5936	130	15	+	+	CCONJ
ejpam-5936	130	16	c2	c2	PROPN
ejpam-5936	130	17	cos(2	cos(2	VERB
ejpam-5936	130	18	tan−1	tan−1	PROPN
ejpam-5936	130	19	y	y	PROPN
ejpam-5936	130	20	x	x	PROPN
ejpam-5936	130	21	)	)	PUNCT
ejpam-5936	130	22	(	(	PUNCT
ejpam-5936	130	23	y2	y2	PROPN
ejpam-5936	130	24	+	+	CCONJ
ejpam-5936	130	25	x2	x2	ADJ
ejpam-5936	130	26	)	)	PUNCT
ejpam-5936	130	27	.	.	PUNCT
ejpam-5936	131	1	(	(	PUNCT
ejpam-5936	131	2	11	11	NUM
ejpam-5936	131	3	)	)	PUNCT
ejpam-5936	131	4	case:2	case:2	NOUN
ejpam-5936	131	5	(	(	PUNCT
ejpam-5936	131	6	n	n	NOUN
ejpam-5936	131	7	=	=	SYM
ejpam-5936	131	8	1	1	NUM
ejpam-5936	131	9	,	,	PUNCT
ejpam-5936	131	10	m	m	VERB
ejpam-5936	131	11	=	=	SYM
ejpam-5936	131	12	−1	−1	NOUN
ejpam-5936	131	13	)	)	PUNCT
ejpam-5936	131	14	to	to	PART
ejpam-5936	131	15	express	express	VERB
ejpam-5936	131	16	the	the	DET
ejpam-5936	131	17	terms	term	NOUN
ejpam-5936	131	18	in	in	ADP
ejpam-5936	131	19	equation	equation	NOUN
ejpam-5936	131	20	(	(	PUNCT
ejpam-5936	131	21	8)	8)	NUM
ejpam-5936	131	22	in	in	ADP
ejpam-5936	131	23	terms	term	NOUN
ejpam-5936	131	24	of	of	ADP
ejpam-5936	131	25	ξ	ξ	PROPN
ejpam-5936	131	26	,	,	PUNCT
ejpam-5936	131	27	we	we	PRON
ejpam-5936	131	28	set	set	VERB
ejpam-5936	131	29	z	z	NOUN
ejpam-5936	131	30	′(y	′(y	NOUN
ejpam-5936	131	31	)	)	PUNCT
ejpam-5936	132	1	=	=	SYM
ejpam-5936	132	2	1	1	NUM
ejpam-5936	132	3	and	and	CCONJ
ejpam-5936	132	4	a′2(y	a′2(y	PROPN
ejpam-5936	132	5	)	)	PUNCT
ejpam-5936	132	6	a2(y	a2(y	PROPN
ejpam-5936	132	7	)	)	PUNCT
ejpam-5936	132	8	=	=	SYM
ejpam-5936	133	1	−a′′(y	−a′′(y	X
ejpam-5936	133	2	)	)	PUNCT
ejpam-5936	133	3	a(y	a(y	PROPN
ejpam-5936	133	4	)	)	PUNCT
ejpam-5936	133	5	.	.	PUNCT
ejpam-5936	134	1	solving	solve	VERB
ejpam-5936	134	2	these	these	DET
ejpam-5936	134	3	equations	equation	NOUN
ejpam-5936	134	4	yields	yield	VERB
ejpam-5936	134	5	z(y	z(y	PROPN
ejpam-5936	134	6	)	)	PUNCT
ejpam-5936	135	1	=	=	SYM
ejpam-5936	135	2	y	y	PROPN
ejpam-5936	135	3	and	and	CCONJ
ejpam-5936	135	4	a(y	a(y	PROPN
ejpam-5936	135	5	)	)	PUNCT
ejpam-5936	135	6	=	=	PUNCT
ejpam-5936	136	1	√	√	PROPN
ejpam-5936	136	2	y.	y.	NOUN
ejpam-5936	136	3	consequently	consequently	ADV
ejpam-5936	136	4	,	,	PUNCT
ejpam-5936	136	5	the	the	DET
ejpam-5936	136	6	wave	wave	NOUN
ejpam-5936	136	7	variable	variable	NOUN
ejpam-5936	136	8	becomes	become	VERB
ejpam-5936	136	9	ξ	ξ	PROPN
ejpam-5936	136	10	=	=	SYM
ejpam-5936	136	11	y	y	PROPN
ejpam-5936	136	12	x	x	X
ejpam-5936	136	13	and	and	CCONJ
ejpam-5936	136	14	the	the	DET
ejpam-5936	136	15	transformation	transformation	NOUN
ejpam-5936	136	16	takes	take	VERB
ejpam-5936	136	17	the	the	DET
ejpam-5936	136	18	form	form	NOUN
ejpam-5936	136	19	u	u	NOUN
ejpam-5936	136	20	=	=	NOUN
ejpam-5936	136	21	x	x	SYM
ejpam-5936	136	22	√	√	NUM
ejpam-5936	136	23	yetf(ξ	yetf(ξ	NUM
ejpam-5936	136	24	)	)	PUNCT
ejpam-5936	136	25	.	.	PUNCT
ejpam-5936	137	1	substituting	substitute	VERB
ejpam-5936	137	2	ξ	ξ	X
ejpam-5936	137	3	=	=	SYM
ejpam-5936	137	4	y	y	PROPN
ejpam-5936	137	5	x	x	X
ejpam-5936	137	6	and	and	CCONJ
ejpam-5936	137	7	u	u	X
ejpam-5936	137	8	=	=	NOUN
ejpam-5936	137	9	x	x	SYM
ejpam-5936	137	10	√	√	NUM
ejpam-5936	137	11	yetf(ξ	yetf(ξ	NOUN
ejpam-5936	137	12	)	)	PUNCT
ejpam-5936	137	13	into	into	ADP
ejpam-5936	137	14	equation	equation	NOUN
ejpam-5936	137	15	(	(	PUNCT
ejpam-5936	137	16	8)	8)	NUM
ejpam-5936	137	17	,	,	PUNCT
ejpam-5936	137	18	we	we	PRON
ejpam-5936	137	19	derive	derive	VERB
ejpam-5936	137	20	the	the	DET
ejpam-5936	137	21	following	follow	VERB
ejpam-5936	137	22	ode	ode	ADJ
ejpam-5936	137	23	:	:	PUNCT
ejpam-5936	137	24	figure	figure	NOUN
ejpam-5936	137	25	4	4	NUM
ejpam-5936	137	26	:	:	PUNCT
ejpam-5936	137	27	3d	3d	NUM
ejpam-5936	137	28	plot	plot	NOUN
ejpam-5936	137	29	of	of	ADP
ejpam-5936	137	30	solution	solution	NOUN
ejpam-5936	137	31	u4	u4	PROPN
ejpam-5936	137	32	given	give	VERB
ejpam-5936	137	33	in	in	ADP
ejpam-5936	137	34	(	(	PUNCT
ejpam-5936	137	35	14	14	NUM
ejpam-5936	137	36	)	)	PUNCT
ejpam-5936	137	37	of	of	ADP
ejpam-5936	137	38	pde	pde	NOUN
ejpam-5936	137	39	(	(	PUNCT
ejpam-5936	137	40	1	1	NUM
ejpam-5936	137	41	)	)	PUNCT
ejpam-5936	137	42	for	for	ADP
ejpam-5936	137	43	c1	c1	NOUN
ejpam-5936	137	44	=	=	SYM
ejpam-5936	137	45	1	1	NUM
ejpam-5936	137	46	,	,	PUNCT
ejpam-5936	137	47	c2	c2	PROPN
ejpam-5936	137	48	=	=	PUNCT
ejpam-5936	137	49	−1	−1	NOUN
ejpam-5936	137	50	and	and	CCONJ
ejpam-5936	137	51	y	y	NOUN
ejpam-5936	137	52	=	=	NOUN
ejpam-5936	137	53	9	9	X
ejpam-5936	137	54	.	.	PUNCT
ejpam-5936	138	1	(	(	PUNCT
ejpam-5936	138	2	ξ2	ξ2	NOUN
ejpam-5936	138	3	+	+	CCONJ
ejpam-5936	138	4	1)f	1)f	NUM
ejpam-5936	138	5	′2(ξ	′2(ξ	NUM
ejpam-5936	138	6	)	)	PUNCT
ejpam-5936	139	1	+	+	CCONJ
ejpam-5936	139	2	(	(	PUNCT
ejpam-5936	139	3	ξ2	ξ2	NOUN
ejpam-5936	139	4	+	+	CCONJ
ejpam-5936	139	5	1)f(ξ)f	1)f(ξ)f	NUM
ejpam-5936	139	6	′′(ξ	′′(ξ	NUM
ejpam-5936	139	7	)	)	PUNCT
ejpam-5936	140	1	+	+	CCONJ
ejpam-5936	140	2	(	(	PUNCT
ejpam-5936	140	3	2	2	NUM
ejpam-5936	140	4	ξ	ξ	PROPN
ejpam-5936	140	5	−	−	PROPN
ejpam-5936	140	6	2ξ)f(ξ)f	2ξ)f(ξ)f	NUM
ejpam-5936	140	7	′(ξ	′(ξ	NOUN
ejpam-5936	140	8	)	)	PUNCT
ejpam-5936	140	9	+	+	CCONJ
ejpam-5936	141	1	f2(ξ	f2(ξ	X
ejpam-5936	141	2	)	)	PUNCT
ejpam-5936	141	3	=	=	SYM
ejpam-5936	141	4	0	0	X
ejpam-5936	141	5	.	.	PUNCT
ejpam-5936	142	1	(	(	PUNCT
ejpam-5936	142	2	12	12	NUM
ejpam-5936	142	3	)	)	PUNCT
ejpam-5936	142	4	the	the	DET
ejpam-5936	142	5	exact	exact	ADJ
ejpam-5936	142	6	solution	solution	NOUN
ejpam-5936	142	7	of	of	ADP
ejpam-5936	142	8	ode	ode	PROPN
ejpam-5936	142	9	(	(	PUNCT
ejpam-5936	142	10	12	12	NUM
ejpam-5936	142	11	)	)	PUNCT
ejpam-5936	142	12	is	be	AUX
ejpam-5936	142	13	f(ξ	f(ξ	NOUN
ejpam-5936	142	14	)	)	PUNCT
ejpam-5936	142	15	=	=	SYM
ejpam-5936	143	1	√	√	NUM
ejpam-5936	143	2	6ξ(−c2ξ3	6ξ(−c2ξ3	NUM
ejpam-5936	144	1	+	+	CCONJ
ejpam-5936	144	2	3c1ξ2	3c1ξ2	NUM
ejpam-5936	144	3	+	+	CCONJ
ejpam-5936	144	4	3c2ξ	3c2ξ	NUM
ejpam-5936	144	5	−	−	PROPN
ejpam-5936	144	6	c1	c1	NOUN
ejpam-5936	144	7	)	)	PUNCT
ejpam-5936	144	8	3ξ	3ξ	PROPN
ejpam-5936	144	9	.	.	PUNCT
ejpam-5936	145	1	(	(	PUNCT
ejpam-5936	145	2	13	13	NUM
ejpam-5936	145	3	)	)	PUNCT
ejpam-5936	145	4	the	the	DET
ejpam-5936	145	5	exact	exact	ADJ
ejpam-5936	145	6	solution	solution	NOUN
ejpam-5936	145	7	of	of	ADP
ejpam-5936	145	8	pde	pde	NOUN
ejpam-5936	145	9	(	(	PUNCT
ejpam-5936	145	10	1	1	NUM
ejpam-5936	145	11	)	)	PUNCT
ejpam-5936	145	12	is	be	AUX
ejpam-5936	145	13	u(x	u(x	NOUN
ejpam-5936	145	14	,	,	PUNCT
ejpam-5936	145	15	y	y	PROPN
ejpam-5936	145	16	,	,	PUNCT
ejpam-5936	145	17	t	t	PROPN
ejpam-5936	145	18	)	)	PUNCT
ejpam-5936	145	19	=	=	PUNCT
ejpam-5936	146	1	√	√	NUM
ejpam-5936	147	1	6x2et	6x2et	NUM
ejpam-5936	147	2	3	3	NUM
ejpam-5936	147	3	√	√	NUM
ejpam-5936	147	4	y	y	PROPN
ejpam-5936	147	5	√	√	PROPN
ejpam-5936	147	6	−c2	−c2	PROPN
ejpam-5936	147	7	y4	y4	NOUN
ejpam-5936	148	1	x4	x4	PROPN
ejpam-5936	149	1	+	+	CCONJ
ejpam-5936	149	2	3c1	3c1	NUM
ejpam-5936	149	3	y3	y3	NOUN
ejpam-5936	149	4	x3	x3	PROPN
ejpam-5936	149	5	+	+	CCONJ
ejpam-5936	149	6	3c2	3c2	NUM
ejpam-5936	150	1	y2	y2	NOUN
ejpam-5936	150	2	x2	x2	NOUN
ejpam-5936	151	1	−	−	PROPN
ejpam-5936	151	2	c1	c1	PROPN
ejpam-5936	151	3	y	y	PROPN
ejpam-5936	151	4	x	x	PROPN
ejpam-5936	151	5	.	.	PUNCT
ejpam-5936	152	1	(	(	PUNCT
ejpam-5936	152	2	14	14	NUM
ejpam-5936	152	3	)	)	PUNCT
ejpam-5936	152	4	z.	z.	PROPN
ejpam-5936	152	5	haider	haider	PROPN
ejpam-5936	152	6	,	,	PUNCT
ejpam-5936	152	7	k.	k.	PROPN
ejpam-5936	152	8	ahmad	ahmad	PROPN
ejpam-5936	152	9	/	/	SYM
ejpam-5936	152	10	eur	eur	PROPN
ejpam-5936	152	11	.	.	PUNCT
ejpam-5936	153	1	j.	j.	PROPN
ejpam-5936	153	2	pure	pure	PROPN
ejpam-5936	153	3	appl	appl	PROPN
ejpam-5936	153	4	.	.	PROPN
ejpam-5936	153	5	math	math	PROPN
ejpam-5936	153	6	,	,	PUNCT
ejpam-5936	153	7	18	18	NUM
ejpam-5936	153	8	(	(	PUNCT
ejpam-5936	153	9	2	2	NUM
ejpam-5936	153	10	)	)	PUNCT
ejpam-5936	153	11	(	(	PUNCT
ejpam-5936	153	12	2025	2025	NUM
ejpam-5936	153	13	)	)	PUNCT
ejpam-5936	153	14	,	,	PUNCT
ejpam-5936	153	15	5936	5936	NUM
ejpam-5936	153	16	8	8	NUM
ejpam-5936	153	17	of	of	ADP
ejpam-5936	153	18	18	18	NUM
ejpam-5936	153	19	figure	figure	NOUN
ejpam-5936	153	20	5	5	NUM
ejpam-5936	153	21	:	:	PUNCT
ejpam-5936	153	22	3d	3d	NUM
ejpam-5936	153	23	plot	plot	NOUN
ejpam-5936	153	24	of	of	ADP
ejpam-5936	153	25	solution	solution	NOUN
ejpam-5936	153	26	u5	u5	NOUN
ejpam-5936	153	27	given	give	VERB
ejpam-5936	153	28	in	in	ADP
ejpam-5936	153	29	(	(	PUNCT
ejpam-5936	153	30	14	14	NUM
ejpam-5936	153	31	)	)	PUNCT
ejpam-5936	153	32	of	of	ADP
ejpam-5936	153	33	pde	pde	NOUN
ejpam-5936	153	34	(	(	PUNCT
ejpam-5936	153	35	1	1	NUM
ejpam-5936	153	36	)	)	PUNCT
ejpam-5936	153	37	for	for	ADP
ejpam-5936	153	38	c1	c1	NOUN
ejpam-5936	153	39	=	=	SYM
ejpam-5936	153	40	1	1	NUM
ejpam-5936	153	41	,	,	PUNCT
ejpam-5936	153	42	c2	c2	PROPN
ejpam-5936	153	43	=	=	SYM
ejpam-5936	153	44	1	1	NUM
ejpam-5936	153	45	and	and	CCONJ
ejpam-5936	153	46	x	x	SYM
ejpam-5936	153	47	=	=	SYM
ejpam-5936	153	48	−9	−9	PROPN
ejpam-5936	153	49	.	.	PUNCT
ejpam-5936	153	50	figure	figure	NOUN
ejpam-5936	153	51	6	6	NUM
ejpam-5936	153	52	:	:	SYM
ejpam-5936	153	53	3d	3d	NUM
ejpam-5936	153	54	plot	plot	NOUN
ejpam-5936	153	55	of	of	ADP
ejpam-5936	153	56	solution	solution	NOUN
ejpam-5936	153	57	u6	u6	NOUN
ejpam-5936	153	58	given	give	VERB
ejpam-5936	153	59	in	in	ADP
ejpam-5936	153	60	(	(	PUNCT
ejpam-5936	153	61	14	14	NUM
ejpam-5936	153	62	)	)	PUNCT
ejpam-5936	153	63	of	of	ADP
ejpam-5936	153	64	pde	pde	NOUN
ejpam-5936	153	65	(	(	PUNCT
ejpam-5936	153	66	1	1	NUM
ejpam-5936	153	67	)	)	PUNCT
ejpam-5936	153	68	for	for	ADP
ejpam-5936	153	69	c1	c1	NOUN
ejpam-5936	153	70	=	=	SYM
ejpam-5936	153	71	1	1	NUM
ejpam-5936	153	72	,	,	PUNCT
ejpam-5936	153	73	c2	c2	PROPN
ejpam-5936	153	74	=	=	PUNCT
ejpam-5936	154	1	−1	−1	NOUN
ejpam-5936	154	2	and	and	CCONJ
ejpam-5936	154	3	t	t	NOUN
ejpam-5936	154	4	=	=	SYM
ejpam-5936	154	5	1	1	X
ejpam-5936	154	6	.	.	NUM
ejpam-5936	154	7	case:3	case:3	NOUN
ejpam-5936	154	8	(	(	PUNCT
ejpam-5936	154	9	n	n	NOUN
ejpam-5936	154	10	=	=	SYM
ejpam-5936	154	11	1	1	NUM
ejpam-5936	154	12	,	,	PUNCT
ejpam-5936	154	13	m	m	VERB
ejpam-5936	154	14	=	=	ADJ
ejpam-5936	154	15	−2	−2	NOUN
ejpam-5936	154	16	)	)	PUNCT
ejpam-5936	154	17	for	for	ADP
ejpam-5936	154	18	n	n	NOUN
ejpam-5936	154	19	=	=	SYM
ejpam-5936	154	20	1	1	NUM
ejpam-5936	154	21	and	and	CCONJ
ejpam-5936	154	22	m	m	PROPN
ejpam-5936	154	23	=	=	ADJ
ejpam-5936	154	24	−2	−2	NOUN
ejpam-5936	154	25	,	,	PUNCT
ejpam-5936	154	26	the	the	DET
ejpam-5936	154	27	wave	wave	NOUN
ejpam-5936	154	28	variable	variable	NOUN
ejpam-5936	155	1	ξ	ξ	PROPN
ejpam-5936	155	2	=	=	SYM
ejpam-5936	155	3	xmz(y	xmz(y	PROPN
ejpam-5936	155	4	)	)	PUNCT
ejpam-5936	155	5	becomes	become	VERB
ejpam-5936	155	6	ξ	ξ	NOUN
ejpam-5936	155	7	=	=	SYM
ejpam-5936	155	8	z(y	z(y	PROPN
ejpam-5936	155	9	)	)	PUNCT
ejpam-5936	155	10	x2	x2	NOUN
ejpam-5936	155	11	,	,	PUNCT
ejpam-5936	155	12	and	and	CCONJ
ejpam-5936	155	13	the	the	DET
ejpam-5936	155	14	transformation	transformation	NOUN
ejpam-5936	155	15	u	u	NOUN
ejpam-5936	155	16	=	=	PROPN
ejpam-5936	155	17	xna(y)etf(ξ	xna(y)etf(ξ	PROPN
ejpam-5936	155	18	)	)	PUNCT
ejpam-5936	155	19	reduces	reduce	VERB
ejpam-5936	155	20	to	to	ADP
ejpam-5936	155	21	u	u	NOUN
ejpam-5936	155	22	=	=	PUNCT
ejpam-5936	155	23	xa(y)etf(ξ	xa(y)etf(ξ	PROPN
ejpam-5936	155	24	)	)	PUNCT
ejpam-5936	155	25	.	.	PUNCT
ejpam-5936	156	1	substituting	substitute	VERB
ejpam-5936	156	2	ξ	ξ	X
ejpam-5936	156	3	=	=	SYM
ejpam-5936	156	4	z(y	z(y	PROPN
ejpam-5936	156	5	)	)	PUNCT
ejpam-5936	156	6	x2	x2	NOUN
ejpam-5936	156	7	and	and	CCONJ
ejpam-5936	156	8	u	u	X
ejpam-5936	156	9	=	=	PROPN
ejpam-5936	156	10	xa(y)etf(ξ	xa(y)etf(ξ	PROPN
ejpam-5936	156	11	)	)	PUNCT
ejpam-5936	156	12	into	into	ADP
ejpam-5936	156	13	equation	equation	NOUN
ejpam-5936	156	14	(	(	PUNCT
ejpam-5936	156	15	4	4	NUM
ejpam-5936	156	16	)	)	PUNCT
ejpam-5936	156	17	,	,	PUNCT
ejpam-5936	156	18	we	we	PRON
ejpam-5936	156	19	obtain	obtain	VERB
ejpam-5936	156	20	:	:	PUNCT
ejpam-5936	156	21	z.	z.	PROPN
ejpam-5936	156	22	haider	haider	PROPN
ejpam-5936	156	23	,	,	PUNCT
ejpam-5936	156	24	k.	k.	PROPN
ejpam-5936	156	25	ahmad	ahmad	PROPN
ejpam-5936	156	26	/	/	SYM
ejpam-5936	156	27	eur	eur	PROPN
ejpam-5936	156	28	.	.	PUNCT
ejpam-5936	157	1	j.	j.	PROPN
ejpam-5936	157	2	pure	pure	PROPN
ejpam-5936	157	3	appl	appl	PROPN
ejpam-5936	157	4	.	.	PROPN
ejpam-5936	157	5	math	math	PROPN
ejpam-5936	157	6	,	,	PUNCT
ejpam-5936	157	7	18	18	NUM
ejpam-5936	157	8	(	(	PUNCT
ejpam-5936	157	9	2	2	NUM
ejpam-5936	157	10	)	)	PUNCT
ejpam-5936	157	11	(	(	PUNCT
ejpam-5936	157	12	2025	2025	NUM
ejpam-5936	157	13	)	)	PUNCT
ejpam-5936	157	14	,	,	PUNCT
ejpam-5936	157	15	5936	5936	NUM
ejpam-5936	157	16	9	9	NUM
ejpam-5936	157	17	of	of	ADP
ejpam-5936	157	18	18	18	NUM
ejpam-5936	157	19	figure	figure	NOUN
ejpam-5936	157	20	7	7	NUM
ejpam-5936	157	21	:	:	PUNCT
ejpam-5936	157	22	3d	3d	NUM
ejpam-5936	157	23	plot	plot	NOUN
ejpam-5936	157	24	of	of	ADP
ejpam-5936	157	25	solution	solution	NOUN
ejpam-5936	157	26	u7	u7	PROPN
ejpam-5936	157	27	given	give	VERB
ejpam-5936	157	28	in	in	ADP
ejpam-5936	157	29	(	(	PUNCT
ejpam-5936	157	30	18	18	NUM
ejpam-5936	157	31	)	)	PUNCT
ejpam-5936	157	32	od	od	NUM
ejpam-5936	157	33	pde	pde	PROPN
ejpam-5936	157	34	(	(	PUNCT
ejpam-5936	157	35	1	1	NUM
ejpam-5936	157	36	)	)	PUNCT
ejpam-5936	157	37	for	for	ADP
ejpam-5936	157	38	c1	c1	PROPN
ejpam-5936	157	39	=	=	SYM
ejpam-5936	157	40	−1	−1	PROPN
ejpam-5936	157	41	,	,	PUNCT
ejpam-5936	157	42	c2	c2	PROPN
ejpam-5936	157	43	=	=	PUNCT
ejpam-5936	157	44	−2	−2	PROPN
ejpam-5936	157	45	and	and	CCONJ
ejpam-5936	157	46	y	y	NOUN
ejpam-5936	157	47	=	=	SYM
ejpam-5936	157	48	5	5	X
ejpam-5936	157	49	.	.	X
ejpam-5936	157	50	figure	figure	NOUN
ejpam-5936	157	51	8	8	NUM
ejpam-5936	157	52	:	:	PUNCT
ejpam-5936	157	53	3d	3d	NUM
ejpam-5936	157	54	plot	plot	NOUN
ejpam-5936	157	55	of	of	ADP
ejpam-5936	157	56	solution	solution	NOUN
ejpam-5936	157	57	u8	u8	PROPN
ejpam-5936	157	58	given	give	VERB
ejpam-5936	157	59	in	in	ADP
ejpam-5936	157	60	(	(	PUNCT
ejpam-5936	157	61	18	18	NUM
ejpam-5936	157	62	)	)	PUNCT
ejpam-5936	157	63	of	of	ADP
ejpam-5936	157	64	pde	pde	NOUN
ejpam-5936	157	65	(	(	PUNCT
ejpam-5936	157	66	1	1	NUM
ejpam-5936	157	67	)	)	PUNCT
ejpam-5936	157	68	for	for	ADP
ejpam-5936	157	69	c1	c1	PROPN
ejpam-5936	157	70	=	=	SYM
ejpam-5936	157	71	−1	−1	PROPN
ejpam-5936	157	72	,	,	PUNCT
ejpam-5936	157	73	c2	c2	PROPN
ejpam-5936	157	74	=	=	PUNCT
ejpam-5936	157	75	−2	−2	PROPN
ejpam-5936	157	76	and	and	CCONJ
ejpam-5936	157	77	x	x	NOUN
ejpam-5936	157	78	=	=	NOUN
ejpam-5936	157	79	−19	−19	NOUN
ejpam-5936	157	80	.	.	PUNCT
ejpam-5936	158	1	(	(	PUNCT
ejpam-5936	158	2	4ξ2	4ξ2	NUM
ejpam-5936	159	1	+	+	CCONJ
ejpam-5936	159	2	z	z	NOUN
ejpam-5936	159	3	′2(y	′2(y	NOUN
ejpam-5936	159	4	)	)	PUNCT
ejpam-5936	159	5	x2	x2	NOUN
ejpam-5936	159	6	)	)	PUNCT
ejpam-5936	159	7	f	f	PROPN
ejpam-5936	159	8	′2(ξ	′2(ξ	NUM
ejpam-5936	159	9	)	)	PUNCT
ejpam-5936	160	1	+	+	CCONJ
ejpam-5936	161	1	(	(	PUNCT
ejpam-5936	161	2	4ξ2	4ξ2	NUM
ejpam-5936	161	3	+	+	CCONJ
ejpam-5936	161	4	z	z	NOUN
ejpam-5936	161	5	′2(y	′2(y	NOUN
ejpam-5936	161	6	)	)	PUNCT
ejpam-5936	161	7	x2	x2	PROPN
ejpam-5936	161	8	)	)	PUNCT
ejpam-5936	161	9	f(ξ)f	f(ξ)f	PROPN
ejpam-5936	161	10	′′(ξ	′′(ξ	PROPN
ejpam-5936	161	11	)	)	PUNCT
ejpam-5936	161	12	+	+	CCONJ
ejpam-5936	161	13	(	(	PUNCT
ejpam-5936	161	14	4z	4z	X
ejpam-5936	161	15	′(y)a′(y	′(y)a′(y	X
ejpam-5936	161	16	)	)	PUNCT
ejpam-5936	162	1	a(y	a(y	PROPN
ejpam-5936	162	2	)	)	PUNCT
ejpam-5936	163	1	−	−	NOUN
ejpam-5936	163	2	2ξ+	2ξ+	NUM
ejpam-5936	163	3	z	z	NOUN
ejpam-5936	163	4	′′(y))f(ξ)f	′′(y))f(ξ)f	NUM
ejpam-5936	163	5	′(ξ	′(ξ	NOUN
ejpam-5936	163	6	)	)	PUNCT
ejpam-5936	164	1	+	+	CCONJ
ejpam-5936	164	2	(	(	PUNCT
ejpam-5936	164	3	x2a′2(y	x2a′2(y	PROPN
ejpam-5936	164	4	)	)	PUNCT
ejpam-5936	164	5	a(y	a(y	PROPN
ejpam-5936	164	6	)	)	PUNCT
ejpam-5936	165	1	+	+	CCONJ
ejpam-5936	165	2	x2a′′(y	x2a′′(y	X
ejpam-5936	165	3	)	)	PUNCT
ejpam-5936	165	4	a(y	a(y	PROPN
ejpam-5936	165	5	)	)	PUNCT
ejpam-5936	166	1	+	+	NUM
ejpam-5936	166	2	1)f2(ξ	1)f2(ξ	NUM
ejpam-5936	166	3	)	)	PUNCT
ejpam-5936	166	4	=	=	SYM
ejpam-5936	167	1	0	0	X
ejpam-5936	167	2	.	.	PUNCT
ejpam-5936	168	1	(	(	PUNCT
ejpam-5936	168	2	15	15	NUM
ejpam-5936	168	3	)	)	PUNCT
ejpam-5936	168	4	z.	z.	PROPN
ejpam-5936	168	5	haider	haider	PROPN
ejpam-5936	168	6	,	,	PUNCT
ejpam-5936	168	7	k.	k.	PROPN
ejpam-5936	168	8	ahmad	ahmad	PROPN
ejpam-5936	168	9	/	/	SYM
ejpam-5936	168	10	eur	eur	PROPN
ejpam-5936	168	11	.	.	PUNCT
ejpam-5936	169	1	j.	j.	PROPN
ejpam-5936	169	2	pure	pure	PROPN
ejpam-5936	169	3	appl	appl	PROPN
ejpam-5936	169	4	.	.	PROPN
ejpam-5936	169	5	math	math	PROPN
ejpam-5936	169	6	,	,	PUNCT
ejpam-5936	169	7	18	18	NUM
ejpam-5936	169	8	(	(	PUNCT
ejpam-5936	169	9	2	2	NUM
ejpam-5936	169	10	)	)	PUNCT
ejpam-5936	169	11	(	(	PUNCT
ejpam-5936	169	12	2025	2025	NUM
ejpam-5936	169	13	)	)	PUNCT
ejpam-5936	169	14	,	,	PUNCT
ejpam-5936	169	15	5936	5936	NUM
ejpam-5936	169	16	10	10	NUM
ejpam-5936	169	17	of	of	ADP
ejpam-5936	169	18	18	18	NUM
ejpam-5936	169	19	figure	figure	NOUN
ejpam-5936	169	20	9	9	NUM
ejpam-5936	169	21	:	:	PUNCT
ejpam-5936	169	22	3d	3d	NUM
ejpam-5936	169	23	plot	plot	NOUN
ejpam-5936	169	24	of	of	ADP
ejpam-5936	169	25	solution	solution	NOUN
ejpam-5936	169	26	u9	u9	PROPN
ejpam-5936	169	27	given	give	VERB
ejpam-5936	169	28	in	in	ADP
ejpam-5936	169	29	(	(	PUNCT
ejpam-5936	169	30	18	18	NUM
ejpam-5936	169	31	)	)	PUNCT
ejpam-5936	169	32	of	of	ADP
ejpam-5936	169	33	pde	pde	NOUN
ejpam-5936	169	34	(	(	PUNCT
ejpam-5936	169	35	1	1	NUM
ejpam-5936	169	36	)	)	PUNCT
ejpam-5936	169	37	for	for	ADP
ejpam-5936	169	38	c1	c1	PROPN
ejpam-5936	169	39	=	=	SYM
ejpam-5936	169	40	−1	−1	PROPN
ejpam-5936	169	41	,	,	PUNCT
ejpam-5936	169	42	c2	c2	PROPN
ejpam-5936	169	43	=	=	PUNCT
ejpam-5936	169	44	−2	−2	PROPN
ejpam-5936	169	45	and	and	CCONJ
ejpam-5936	169	46	t	t	NOUN
ejpam-5936	169	47	=	=	SYM
ejpam-5936	169	48	1	1	X
ejpam-5936	169	49	.	.	PUNCT
ejpam-5936	169	50	to	to	PART
ejpam-5936	169	51	express	express	VERB
ejpam-5936	169	52	the	the	DET
ejpam-5936	169	53	terms	term	NOUN
ejpam-5936	169	54	in	in	ADP
ejpam-5936	169	55	equation	equation	NOUN
ejpam-5936	169	56	(	(	PUNCT
ejpam-5936	169	57	15	15	NUM
ejpam-5936	169	58	)	)	PUNCT
ejpam-5936	169	59	in	in	ADP
ejpam-5936	169	60	terms	term	NOUN
ejpam-5936	169	61	of	of	ADP
ejpam-5936	169	62	ξ	ξ	PROPN
ejpam-5936	169	63	,	,	PUNCT
ejpam-5936	169	64	we	we	PRON
ejpam-5936	169	65	set	set	VERB
ejpam-5936	169	66	z′2(y	z′2(y	NOUN
ejpam-5936	169	67	)	)	PUNCT
ejpam-5936	169	68	x2	x2	PROPN
ejpam-5936	170	1	=	=	SYM
ejpam-5936	170	2	z(y	z(y	PROPN
ejpam-5936	170	3	)	)	PUNCT
ejpam-5936	171	1	x2	x2	PROPN
ejpam-5936	171	2	and	and	CCONJ
ejpam-5936	171	3	a′2(y	a′2(y	PROPN
ejpam-5936	171	4	)	)	PUNCT
ejpam-5936	171	5	a2(y	a2(y	PROPN
ejpam-5936	171	6	)	)	PUNCT
ejpam-5936	171	7	=	=	SYM
ejpam-5936	172	1	−a′′(y	−a′′(y	X
ejpam-5936	172	2	)	)	PUNCT
ejpam-5936	172	3	a(y	a(y	PROPN
ejpam-5936	172	4	)	)	PUNCT
ejpam-5936	172	5	.	.	PUNCT
ejpam-5936	173	1	solving	solve	VERB
ejpam-5936	173	2	these	these	DET
ejpam-5936	173	3	equations	equation	NOUN
ejpam-5936	173	4	yields	yield	VERB
ejpam-5936	173	5	z(y	z(y	PROPN
ejpam-5936	173	6	)	)	PUNCT
ejpam-5936	174	1	=	=	VERB
ejpam-5936	174	2	y2	y2	PROPN
ejpam-5936	174	3	and	and	CCONJ
ejpam-5936	174	4	a(y	a(y	PROPN
ejpam-5936	174	5	)	)	PUNCT
ejpam-5936	174	6	=	=	PUNCT
ejpam-5936	175	1	√	√	PROPN
ejpam-5936	175	2	y.	y.	NOUN
ejpam-5936	175	3	consequently	consequently	ADV
ejpam-5936	175	4	,	,	PUNCT
ejpam-5936	175	5	the	the	DET
ejpam-5936	175	6	wave	wave	NOUN
ejpam-5936	175	7	variable	variable	NOUN
ejpam-5936	175	8	becomes	become	VERB
ejpam-5936	175	9	ξ	ξ	NOUN
ejpam-5936	175	10	=	=	PUNCT
ejpam-5936	175	11	y2	y2	NOUN
ejpam-5936	175	12	x2	x2	NOUN
ejpam-5936	175	13	,	,	PUNCT
ejpam-5936	175	14	and	and	CCONJ
ejpam-5936	175	15	the	the	DET
ejpam-5936	175	16	transformation	transformation	NOUN
ejpam-5936	175	17	takes	take	VERB
ejpam-5936	175	18	the	the	DET
ejpam-5936	175	19	form	form	NOUN
ejpam-5936	175	20	u	u	NOUN
ejpam-5936	175	21	=	=	NOUN
ejpam-5936	175	22	x	x	SYM
ejpam-5936	175	23	√	√	NUM
ejpam-5936	175	24	yetf(ξ	yetf(ξ	NUM
ejpam-5936	175	25	)	)	PUNCT
ejpam-5936	175	26	.	.	PUNCT
ejpam-5936	176	1	substituting	substitute	VERB
ejpam-5936	176	2	ξ	ξ	X
ejpam-5936	176	3	=	=	SYM
ejpam-5936	176	4	y2	y2	NOUN
ejpam-5936	176	5	x2	x2	NOUN
ejpam-5936	176	6	and	and	CCONJ
ejpam-5936	176	7	u	u	X
ejpam-5936	176	8	=	=	NOUN
ejpam-5936	176	9	x	x	SYM
ejpam-5936	176	10	√	√	NUM
ejpam-5936	176	11	yetf(ξ	yetf(ξ	NOUN
ejpam-5936	176	12	)	)	PUNCT
ejpam-5936	176	13	into	into	ADP
ejpam-5936	176	14	equation	equation	NOUN
ejpam-5936	176	15	(	(	PUNCT
ejpam-5936	176	16	15	15	NUM
ejpam-5936	176	17	)	)	PUNCT
ejpam-5936	176	18	,	,	PUNCT
ejpam-5936	176	19	we	we	PRON
ejpam-5936	176	20	derive	derive	VERB
ejpam-5936	176	21	the	the	DET
ejpam-5936	176	22	following	follow	VERB
ejpam-5936	176	23	ode	ode	ADJ
ejpam-5936	176	24	:	:	PUNCT
ejpam-5936	176	25	4(ξ2	4(ξ2	NUM
ejpam-5936	176	26	+	+	CCONJ
ejpam-5936	176	27	ξ)f	ξ)f	NOUN
ejpam-5936	176	28	′2(ξ	′2(ξ	NUM
ejpam-5936	176	29	)	)	PUNCT
ejpam-5936	177	1	+	+	CCONJ
ejpam-5936	177	2	4(ξ2	4(ξ2	NUM
ejpam-5936	177	3	+	+	CCONJ
ejpam-5936	177	4	ξ)f(ξ)f	ξ)f(ξ)f	PROPN
ejpam-5936	177	5	′′(ξ	′′(ξ	PROPN
ejpam-5936	177	6	)	)	PUNCT
ejpam-5936	178	1	+	+	CCONJ
ejpam-5936	178	2	(	(	PUNCT
ejpam-5936	178	3	6−	6−	NUM
ejpam-5936	178	4	2ξ)f(ξ)f	2ξ)f(ξ)f	NUM
ejpam-5936	178	5	′(ξ	′(ξ	NOUN
ejpam-5936	178	6	)	)	PUNCT
ejpam-5936	179	1	+	+	CCONJ
ejpam-5936	180	1	f2(ξ	f2(ξ	X
ejpam-5936	180	2	)	)	PUNCT
ejpam-5936	180	3	=	=	SYM
ejpam-5936	180	4	0	0	X
ejpam-5936	180	5	.	.	PUNCT
ejpam-5936	181	1	(	(	PUNCT
ejpam-5936	181	2	16	16	NUM
ejpam-5936	181	3	)	)	PUNCT
ejpam-5936	181	4	the	the	DET
ejpam-5936	181	5	analytic	analytic	ADJ
ejpam-5936	181	6	solution	solution	NOUN
ejpam-5936	181	7	of	of	ADP
ejpam-5936	181	8	ode	ode	PROPN
ejpam-5936	181	9	(	(	PUNCT
ejpam-5936	181	10	16	16	NUM
ejpam-5936	181	11	)	)	PUNCT
ejpam-5936	181	12	is	be	AUX
ejpam-5936	181	13	f(ξ	f(ξ	NOUN
ejpam-5936	181	14	)	)	PUNCT
ejpam-5936	181	15	=	=	SYM
ejpam-5936	182	1	2√	2√	PROPN
ejpam-5936	182	2	3ξ	3ξ	NOUN
ejpam-5936	182	3	√	√	ADP
ejpam-5936	183	1	−c2ξ2	−c2ξ2	ADP
ejpam-5936	183	2	+	+	NUM
ejpam-5936	183	3	3c2ξ	3c2ξ	NUM
ejpam-5936	183	4	+	+	CCONJ
ejpam-5936	183	5	3c1ξ	3c1ξ	NOUN
ejpam-5936	183	6	3	3	NUM
ejpam-5936	183	7	2	2	NUM
ejpam-5936	183	8	−	−	NOUN
ejpam-5936	183	9	c1ξ	c1ξ	NOUN
ejpam-5936	183	10	1	1	NUM
ejpam-5936	183	11	2	2	NUM
ejpam-5936	183	12	.	.	PUNCT
ejpam-5936	184	1	(	(	PUNCT
ejpam-5936	184	2	17	17	NUM
ejpam-5936	184	3	)	)	PUNCT
ejpam-5936	184	4	the	the	DET
ejpam-5936	184	5	exact	exact	ADJ
ejpam-5936	184	6	solution	solution	NOUN
ejpam-5936	184	7	of	of	ADP
ejpam-5936	184	8	pde	pde	NOUN
ejpam-5936	184	9	(	(	PUNCT
ejpam-5936	184	10	1	1	NUM
ejpam-5936	184	11	)	)	PUNCT
ejpam-5936	184	12	is	be	AUX
ejpam-5936	184	13	u(x	u(x	NOUN
ejpam-5936	184	14	,	,	PUNCT
ejpam-5936	184	15	y	y	PROPN
ejpam-5936	184	16	,	,	PUNCT
ejpam-5936	184	17	t	t	PROPN
ejpam-5936	184	18	)	)	PUNCT
ejpam-5936	184	19	=	=	SYM
ejpam-5936	184	20	2x2et√	2x2et√	NOUN
ejpam-5936	185	1	3y	3y	NUM
ejpam-5936	185	2	√	√	PROPN
ejpam-5936	185	3	−c2	−c2	PROPN
ejpam-5936	185	4	y4	y4	NOUN
ejpam-5936	186	1	x4	x4	PROPN
ejpam-5936	187	1	+	+	X
ejpam-5936	188	1	3c2	3c2	NUM
ejpam-5936	188	2	y2	y2	NOUN
ejpam-5936	188	3	x2	x2	NOUN
ejpam-5936	189	1	+	+	CCONJ
ejpam-5936	189	2	3c1	3c1	NUM
ejpam-5936	189	3	y3	y3	NOUN
ejpam-5936	189	4	x3	x3	ADJ
ejpam-5936	189	5	−	−	PROPN
ejpam-5936	189	6	c1	c1	PROPN
ejpam-5936	189	7	y	y	PROPN
ejpam-5936	189	8	x	x	PROPN
ejpam-5936	189	9	.	.	PUNCT
ejpam-5936	190	1	(	(	PUNCT
ejpam-5936	190	2	18	18	NUM
ejpam-5936	190	3	)	)	PUNCT
ejpam-5936	190	4	case:4	case:4	NOUN
ejpam-5936	190	5	(	(	PUNCT
ejpam-5936	190	6	n	n	NOUN
ejpam-5936	190	7	=	=	SYM
ejpam-5936	190	8	−1	−1	NOUN
ejpam-5936	190	9	,	,	PUNCT
ejpam-5936	190	10	m	m	VERB
ejpam-5936	190	11	=	=	NOUN
ejpam-5936	190	12	1	1	NUM
ejpam-5936	190	13	)	)	PUNCT
ejpam-5936	190	14	for	for	ADP
ejpam-5936	190	15	n	n	NOUN
ejpam-5936	190	16	=	=	SYM
ejpam-5936	190	17	−1	−1	NOUN
ejpam-5936	190	18	and	and	CCONJ
ejpam-5936	190	19	m	m	NOUN
ejpam-5936	190	20	=	=	ADJ
ejpam-5936	190	21	1	1	NUM
ejpam-5936	190	22	,	,	PUNCT
ejpam-5936	190	23	the	the	DET
ejpam-5936	190	24	wave	wave	NOUN
ejpam-5936	190	25	variable	variable	NOUN
ejpam-5936	190	26	ξ	ξ	PROPN
ejpam-5936	190	27	=	=	SYM
ejpam-5936	190	28	xmz(y	xmz(y	PROPN
ejpam-5936	190	29	)	)	PUNCT
ejpam-5936	190	30	becomes	become	VERB
ejpam-5936	190	31	ξ	ξ	NOUN
ejpam-5936	190	32	=	=	SYM
ejpam-5936	190	33	xz(y	xz(y	X
ejpam-5936	190	34	)	)	PUNCT
ejpam-5936	190	35	,	,	PUNCT
ejpam-5936	190	36	and	and	CCONJ
ejpam-5936	190	37	the	the	DET
ejpam-5936	190	38	transformation	transformation	NOUN
ejpam-5936	190	39	u	u	NOUN
ejpam-5936	190	40	=	=	PROPN
ejpam-5936	190	41	xna(y)etf(ξ	xna(y)etf(ξ	PROPN
ejpam-5936	190	42	)	)	PUNCT
ejpam-5936	190	43	reduces	reduce	VERB
ejpam-5936	190	44	to	to	ADP
ejpam-5936	190	45	u	u	NOUN
ejpam-5936	190	46	=	=	PROPN
ejpam-5936	190	47	a(y)etf(ξ	a(y)etf(ξ	PROPN
ejpam-5936	190	48	)	)	PUNCT
ejpam-5936	190	49	x	x	X
ejpam-5936	190	50	.	.	PUNCT
ejpam-5936	191	1	substituting	substitute	VERB
ejpam-5936	191	2	ξ	ξ	PROPN
ejpam-5936	191	3	=	=	SYM
ejpam-5936	191	4	xz(y	xz(y	X
ejpam-5936	191	5	)	)	PUNCT
ejpam-5936	191	6	and	and	CCONJ
ejpam-5936	191	7	u	u	X
ejpam-5936	191	8	=	=	PROPN
ejpam-5936	191	9	a(y)etf(ξ	a(y)etf(ξ	PROPN
ejpam-5936	191	10	)	)	PUNCT
ejpam-5936	191	11	x	x	PUNCT
ejpam-5936	191	12	into	into	ADP
ejpam-5936	191	13	equation	equation	NOUN
ejpam-5936	191	14	(	(	PUNCT
ejpam-5936	191	15	4	4	NUM
ejpam-5936	191	16	)	)	PUNCT
ejpam-5936	191	17	,	,	PUNCT
ejpam-5936	191	18	we	we	PRON
ejpam-5936	191	19	obtain	obtain	VERB
ejpam-5936	191	20	:	:	PUNCT
ejpam-5936	191	21	(	(	PUNCT
ejpam-5936	191	22	ξ2	ξ2	NOUN
ejpam-5936	191	23	+	+	CCONJ
ejpam-5936	192	1	x4z	x4z	PROPN
ejpam-5936	192	2	′2(y))f(ξ)f	′2(y))f(ξ)f	ADJ
ejpam-5936	192	3	′′(ξ	′′(ξ	PROPN
ejpam-5936	192	4	)	)	PUNCT
ejpam-5936	193	1	+	+	CCONJ
ejpam-5936	193	2	(	(	PUNCT
ejpam-5936	193	3	ξ2	ξ2	NOUN
ejpam-5936	193	4	+	+	CCONJ
ejpam-5936	193	5	x4z	x4z	PROPN
ejpam-5936	193	6	′2(y))f	′2(y))f	NOUN
ejpam-5936	193	7	′2(ξ	′2(ξ	NUM
ejpam-5936	193	8	)	)	PUNCT
ejpam-5936	194	1	+	+	CCONJ
ejpam-5936	195	1	(	(	PUNCT
ejpam-5936	195	2	x3z	x3z	X
ejpam-5936	195	3	′′(y)+	′′(y)+	VERB
ejpam-5936	195	4	4x3z	4x3z	NUM
ejpam-5936	195	5	′(y)a′(y	′(y)a′(y	NOUN
ejpam-5936	195	6	)	)	PUNCT
ejpam-5936	195	7	a(y	a(y	PROPN
ejpam-5936	195	8	)	)	PUNCT
ejpam-5936	195	9	−	−	PROPN
ejpam-5936	195	10	4ξ)f(ξ)f	4ξ)f(ξ)f	NUM
ejpam-5936	195	11	′(ξ	′(ξ	NOUN
ejpam-5936	195	12	)	)	PUNCT
ejpam-5936	195	13	+	+	CCONJ
ejpam-5936	195	14	(	(	PUNCT
ejpam-5936	195	15	x2a′′(y	x2a′′(y	X
ejpam-5936	195	16	)	)	PUNCT
ejpam-5936	195	17	a(y	a(y	PROPN
ejpam-5936	195	18	)	)	PUNCT
ejpam-5936	196	1	+	+	CCONJ
ejpam-5936	196	2	3	3	NUM
ejpam-5936	196	3	+	+	NUM
ejpam-5936	196	4	x2a′2(y	x2a′2(y	PROPN
ejpam-5936	196	5	)	)	PUNCT
ejpam-5936	196	6	a2(y	a2(y	NUM
ejpam-5936	196	7	)	)	PUNCT
ejpam-5936	196	8	)	)	PUNCT
ejpam-5936	197	1	f2(ξ	f2(ξ	X
ejpam-5936	197	2	)	)	PUNCT
ejpam-5936	197	3	=	=	NOUN
ejpam-5936	197	4	0	0	X
ejpam-5936	197	5	.	.	PUNCT
ejpam-5936	198	1	(	(	PUNCT
ejpam-5936	198	2	19	19	NUM
ejpam-5936	198	3	)	)	PUNCT
ejpam-5936	198	4	z.	z.	PROPN
ejpam-5936	198	5	haider	haider	PROPN
ejpam-5936	198	6	,	,	PUNCT
ejpam-5936	198	7	k.	k.	PROPN
ejpam-5936	198	8	ahmad	ahmad	PROPN
ejpam-5936	198	9	/	/	SYM
ejpam-5936	198	10	eur	eur	PROPN
ejpam-5936	198	11	.	.	PUNCT
ejpam-5936	199	1	j.	j.	PROPN
ejpam-5936	199	2	pure	pure	PROPN
ejpam-5936	199	3	appl	appl	PROPN
ejpam-5936	199	4	.	.	PROPN
ejpam-5936	199	5	math	math	PROPN
ejpam-5936	199	6	,	,	PUNCT
ejpam-5936	199	7	18	18	NUM
ejpam-5936	199	8	(	(	PUNCT
ejpam-5936	199	9	2	2	NUM
ejpam-5936	199	10	)	)	PUNCT
ejpam-5936	199	11	(	(	PUNCT
ejpam-5936	199	12	2025	2025	NUM
ejpam-5936	199	13	)	)	PUNCT
ejpam-5936	199	14	,	,	PUNCT
ejpam-5936	199	15	5936	5936	NUM
ejpam-5936	199	16	11	11	NUM
ejpam-5936	199	17	of	of	ADP
ejpam-5936	199	18	18	18	NUM
ejpam-5936	199	19	figure	figure	NOUN
ejpam-5936	199	20	10	10	NUM
ejpam-5936	199	21	:	:	PUNCT
ejpam-5936	199	22	3d	3d	NUM
ejpam-5936	199	23	plot	plot	NOUN
ejpam-5936	199	24	of	of	ADP
ejpam-5936	199	25	solution	solution	NOUN
ejpam-5936	199	26	u10	u10	NOUN
ejpam-5936	199	27	given	give	VERB
ejpam-5936	199	28	in	in	ADP
ejpam-5936	199	29	(	(	PUNCT
ejpam-5936	199	30	22	22	NUM
ejpam-5936	199	31	)	)	PUNCT
ejpam-5936	199	32	of	of	ADP
ejpam-5936	199	33	pde	pde	NOUN
ejpam-5936	199	34	(	(	PUNCT
ejpam-5936	199	35	1	1	NUM
ejpam-5936	199	36	)	)	PUNCT
ejpam-5936	199	37	for	for	ADP
ejpam-5936	199	38	c1	c1	NOUN
ejpam-5936	199	39	=	=	SYM
ejpam-5936	199	40	1	1	NUM
ejpam-5936	199	41	,	,	PUNCT
ejpam-5936	199	42	c2	c2	PROPN
ejpam-5936	199	43	=	=	PUNCT
ejpam-5936	199	44	−1	−1	NOUN
ejpam-5936	199	45	and	and	CCONJ
ejpam-5936	199	46	y	y	PROPN
ejpam-5936	199	47	=	=	SYM
ejpam-5936	199	48	3	3	X
ejpam-5936	199	49	.	.	X
ejpam-5936	199	50	figure	figure	NOUN
ejpam-5936	199	51	11	11	NUM
ejpam-5936	199	52	:	:	PUNCT
ejpam-5936	199	53	3d	3d	NUM
ejpam-5936	199	54	plot	plot	NOUN
ejpam-5936	199	55	of	of	ADP
ejpam-5936	199	56	solution	solution	NOUN
ejpam-5936	199	57	u11	u11	PROPN
ejpam-5936	199	58	given	give	VERB
ejpam-5936	199	59	in	in	ADP
ejpam-5936	199	60	(	(	PUNCT
ejpam-5936	199	61	22	22	NUM
ejpam-5936	199	62	)	)	PUNCT
ejpam-5936	199	63	of	of	ADP
ejpam-5936	199	64	pde	pde	NOUN
ejpam-5936	199	65	(	(	PUNCT
ejpam-5936	199	66	1	1	NUM
ejpam-5936	199	67	)	)	PUNCT
ejpam-5936	199	68	for	for	ADP
ejpam-5936	199	69	c1	c1	NOUN
ejpam-5936	199	70	=	=	SYM
ejpam-5936	199	71	1	1	NUM
ejpam-5936	199	72	,	,	PUNCT
ejpam-5936	199	73	c2	c2	PROPN
ejpam-5936	199	74	=	=	SYM
ejpam-5936	199	75	1	1	NUM
ejpam-5936	199	76	and	and	CCONJ
ejpam-5936	199	77	x	x	SYM
ejpam-5936	199	78	=	=	SYM
ejpam-5936	199	79	3	3	X
ejpam-5936	199	80	.	.	PUNCT
ejpam-5936	199	81	to	to	PART
ejpam-5936	199	82	express	express	VERB
ejpam-5936	199	83	the	the	DET
ejpam-5936	199	84	terms	term	NOUN
ejpam-5936	199	85	in	in	ADP
ejpam-5936	199	86	equation	equation	NOUN
ejpam-5936	199	87	(	(	PUNCT
ejpam-5936	199	88	19	19	NUM
ejpam-5936	199	89	)	)	PUNCT
ejpam-5936	199	90	in	in	ADP
ejpam-5936	199	91	terms	term	NOUN
ejpam-5936	199	92	of	of	ADP
ejpam-5936	199	93	ξ	ξ	PROPN
ejpam-5936	199	94	,	,	PUNCT
ejpam-5936	199	95	we	we	PRON
ejpam-5936	199	96	set	set	VERB
ejpam-5936	199	97	x4z	x4z	PROPN
ejpam-5936	199	98	′2(y	′2(y	PROPN
ejpam-5936	199	99	)	)	PUNCT
ejpam-5936	199	100	=	=	PUNCT
ejpam-5936	200	1	x4z4(y	x4z4(y	PROPN
ejpam-5936	200	2	)	)	PUNCT
ejpam-5936	200	3	and	and	CCONJ
ejpam-5936	200	4	a′′(y	a′′(y	ADJ
ejpam-5936	200	5	)	)	PUNCT
ejpam-5936	200	6	a′(y	a′(y	PROPN
ejpam-5936	200	7	)	)	PUNCT
ejpam-5936	200	8	=	=	SYM
ejpam-5936	200	9	−a′2(y	−a′2(y	X
ejpam-5936	200	10	)	)	PUNCT
ejpam-5936	200	11	a(y	a(y	PROPN
ejpam-5936	200	12	)	)	PUNCT
ejpam-5936	200	13	.	.	PUNCT
ejpam-5936	201	1	solving	solve	VERB
ejpam-5936	201	2	these	these	DET
ejpam-5936	201	3	equations	equation	NOUN
ejpam-5936	201	4	yields	yield	VERB
ejpam-5936	201	5	z(y	z(y	PROPN
ejpam-5936	201	6	)	)	PUNCT
ejpam-5936	202	1	=	=	SYM
ejpam-5936	202	2	1	1	NUM
ejpam-5936	202	3	y	y	PROPN
ejpam-5936	202	4	and	and	CCONJ
ejpam-5936	202	5	a(y	a(y	PROPN
ejpam-5936	202	6	)	)	PUNCT
ejpam-5936	202	7	=	=	PUNCT
ejpam-5936	203	1	√	√	PROPN
ejpam-5936	203	2	y.	y.	NOUN
ejpam-5936	203	3	consequently	consequently	ADV
ejpam-5936	203	4	,	,	PUNCT
ejpam-5936	203	5	the	the	DET
ejpam-5936	203	6	wave	wave	NOUN
ejpam-5936	203	7	variable	variable	NOUN
ejpam-5936	203	8	becomes	become	VERB
ejpam-5936	203	9	ξ	ξ	NOUN
ejpam-5936	203	10	=	=	SYM
ejpam-5936	203	11	x	x	SYM
ejpam-5936	203	12	y	y	PROPN
ejpam-5936	203	13	and	and	CCONJ
ejpam-5936	203	14	,	,	PUNCT
ejpam-5936	203	15	the	the	DET
ejpam-5936	203	16	transformation	transformation	NOUN
ejpam-5936	203	17	takes	take	VERB
ejpam-5936	203	18	the	the	DET
ejpam-5936	203	19	form	form	NOUN
ejpam-5936	203	20	u	u	NOUN
ejpam-5936	203	21	=	=	NOUN
ejpam-5936	203	22	√	√	NUM
ejpam-5936	203	23	yetf(ξ	yetf(ξ	NUM
ejpam-5936	203	24	)	)	PUNCT
ejpam-5936	203	25	x	x	X
ejpam-5936	203	26	.	.	PUNCT
ejpam-5936	204	1	z.	z.	PROPN
ejpam-5936	204	2	haider	haider	PROPN
ejpam-5936	204	3	,	,	PUNCT
ejpam-5936	204	4	k.	k.	PROPN
ejpam-5936	204	5	ahmad	ahmad	PROPN
ejpam-5936	204	6	/	/	SYM
ejpam-5936	204	7	eur	eur	PROPN
ejpam-5936	204	8	.	.	PUNCT
ejpam-5936	205	1	j.	j.	PROPN
ejpam-5936	205	2	pure	pure	PROPN
ejpam-5936	205	3	appl	appl	PROPN
ejpam-5936	205	4	.	.	PROPN
ejpam-5936	205	5	math	math	PROPN
ejpam-5936	205	6	,	,	PUNCT
ejpam-5936	205	7	18	18	NUM
ejpam-5936	205	8	(	(	PUNCT
ejpam-5936	205	9	2	2	NUM
ejpam-5936	205	10	)	)	PUNCT
ejpam-5936	205	11	(	(	PUNCT
ejpam-5936	205	12	2025	2025	NUM
ejpam-5936	205	13	)	)	PUNCT
ejpam-5936	205	14	,	,	PUNCT
ejpam-5936	205	15	5936	5936	NUM
ejpam-5936	205	16	12	12	NUM
ejpam-5936	205	17	of	of	ADP
ejpam-5936	205	18	18	18	NUM
ejpam-5936	205	19	figure	figure	NOUN
ejpam-5936	205	20	12	12	NUM
ejpam-5936	205	21	:	:	PUNCT
ejpam-5936	205	22	3d	3d	NUM
ejpam-5936	205	23	plot	plot	NOUN
ejpam-5936	205	24	of	of	ADP
ejpam-5936	205	25	solution	solution	NOUN
ejpam-5936	205	26	u12	u12	NOUN
ejpam-5936	205	27	given	give	VERB
ejpam-5936	205	28	in	in	ADP
ejpam-5936	205	29	(	(	PUNCT
ejpam-5936	205	30	22	22	NUM
ejpam-5936	205	31	)	)	PUNCT
ejpam-5936	205	32	of	of	ADP
ejpam-5936	205	33	pde	pde	NOUN
ejpam-5936	205	34	(	(	PUNCT
ejpam-5936	205	35	1	1	NUM
ejpam-5936	205	36	)	)	PUNCT
ejpam-5936	205	37	for	for	ADP
ejpam-5936	205	38	c1	c1	NOUN
ejpam-5936	205	39	=	=	SYM
ejpam-5936	205	40	1	1	NUM
ejpam-5936	205	41	,	,	PUNCT
ejpam-5936	205	42	c2	c2	PROPN
ejpam-5936	205	43	=	=	PUNCT
ejpam-5936	205	44	−1	−1	NOUN
ejpam-5936	205	45	and	and	CCONJ
ejpam-5936	205	46	t	t	NOUN
ejpam-5936	205	47	=	=	SYM
ejpam-5936	205	48	3	3	X
ejpam-5936	205	49	.	.	PUNCT
ejpam-5936	205	50	substituting	substitute	VERB
ejpam-5936	205	51	these	these	DET
ejpam-5936	205	52	expressions	expression	NOUN
ejpam-5936	205	53	into	into	ADP
ejpam-5936	205	54	equation	equation	NOUN
ejpam-5936	205	55	(	(	PUNCT
ejpam-5936	205	56	19	19	NUM
ejpam-5936	205	57	)	)	PUNCT
ejpam-5936	205	58	,	,	PUNCT
ejpam-5936	205	59	we	we	PRON
ejpam-5936	205	60	obtain	obtain	VERB
ejpam-5936	205	61	the	the	DET
ejpam-5936	205	62	following	following	ADJ
ejpam-5936	205	63	ode	ode	PROPN
ejpam-5936	205	64	:	:	PUNCT
ejpam-5936	205	65	(	(	PUNCT
ejpam-5936	205	66	ξ4	ξ4	NOUN
ejpam-5936	205	67	+	+	CCONJ
ejpam-5936	205	68	ξ2)f(ξ)f	ξ2)f(ξ)f	NUM
ejpam-5936	205	69	′′(ξ	′′(ξ	NUM
ejpam-5936	205	70	)	)	PUNCT
ejpam-5936	206	1	+	+	CCONJ
ejpam-5936	206	2	(	(	PUNCT
ejpam-5936	206	3	ξ4	ξ4	NOUN
ejpam-5936	206	4	+	+	CCONJ
ejpam-5936	206	5	ξ2)f	ξ2)f	PROPN
ejpam-5936	206	6	′2(ξ)−	′2(ξ)−	PROPN
ejpam-5936	206	7	4ξf(ξ)f	4ξf(ξ)f	PROPN
ejpam-5936	206	8	′(ξ	′(ξ	NOUN
ejpam-5936	206	9	)	)	PUNCT
ejpam-5936	207	1	+	+	NUM
ejpam-5936	207	2	3f2(ξ	3f2(ξ	X
ejpam-5936	207	3	)	)	PUNCT
ejpam-5936	207	4	=	=	SYM
ejpam-5936	208	1	0	0	X
ejpam-5936	208	2	.	.	PUNCT
ejpam-5936	209	1	(	(	PUNCT
ejpam-5936	209	2	20	20	NUM
ejpam-5936	209	3	)	)	PUNCT
ejpam-5936	209	4	the	the	DET
ejpam-5936	209	5	analytic	analytic	ADJ
ejpam-5936	209	6	solution	solution	NOUN
ejpam-5936	209	7	of	of	ADP
ejpam-5936	209	8	ode	ode	PROPN
ejpam-5936	209	9	(	(	PUNCT
ejpam-5936	209	10	20	20	NUM
ejpam-5936	209	11	)	)	PUNCT
ejpam-5936	209	12	is	be	AUX
ejpam-5936	209	13	f(ξ	f(ξ	NOUN
ejpam-5936	209	14	)	)	PUNCT
ejpam-5936	209	15	=	=	PUNCT
ejpam-5936	210	1	√	√	ADV
ejpam-5936	210	2	2	2	NUM
ejpam-5936	210	3	√	√	ADP
ejpam-5936	210	4	−c2ξ5	−c2ξ5	PROPN
ejpam-5936	210	5	+	+	CCONJ
ejpam-5936	210	6	c1ξ4	c1ξ4	NOUN
ejpam-5936	210	7	−	−	NOUN
ejpam-5936	211	1	c2ξ3	c2ξ3	NOUN
ejpam-5936	211	2	+	+	CCONJ
ejpam-5936	211	3	c1ξ2	c1ξ2	AUX
ejpam-5936	211	4	ξ2	ξ2	NOUN
ejpam-5936	211	5	+	+	CCONJ
ejpam-5936	211	6	1	1	NUM
ejpam-5936	211	7	.	.	PUNCT
ejpam-5936	212	1	(	(	PUNCT
ejpam-5936	212	2	21	21	NUM
ejpam-5936	212	3	)	)	PUNCT
ejpam-5936	212	4	the	the	DET
ejpam-5936	212	5	exact	exact	ADJ
ejpam-5936	212	6	solution	solution	NOUN
ejpam-5936	212	7	of	of	ADP
ejpam-5936	212	8	pde	pde	NOUN
ejpam-5936	212	9	(	(	PUNCT
ejpam-5936	212	10	1	1	NUM
ejpam-5936	212	11	)	)	PUNCT
ejpam-5936	212	12	is	be	AUX
ejpam-5936	212	13	u(x	u(x	NOUN
ejpam-5936	212	14	,	,	PUNCT
ejpam-5936	212	15	y	y	PROPN
ejpam-5936	212	16	,	,	PUNCT
ejpam-5936	212	17	t	t	PROPN
ejpam-5936	212	18	)	)	PUNCT
ejpam-5936	212	19	=	=	SYM
ejpam-5936	213	1	√	√	PROPN
ejpam-5936	213	2	2et	2et	NOUN
ejpam-5936	213	3	√	√	NUM
ejpam-5936	213	4	−c2x5	−c2x5	PROPN
ejpam-5936	213	5	+	+	NOUN
ejpam-5936	213	6	c1x4y	c1x4y	PART
ejpam-5936	213	7	−	−	NOUN
ejpam-5936	213	8	c2x3y2	c2x3y2	NOUN
ejpam-5936	213	9	+	+	CCONJ
ejpam-5936	213	10	c1x2y3	c1x2y3	PROPN
ejpam-5936	213	11	x3	x3	PROPN
ejpam-5936	213	12	+	+	CCONJ
ejpam-5936	213	13	xy2	xy2	PROPN
ejpam-5936	213	14	.	.	PUNCT
ejpam-5936	214	1	(	(	PUNCT
ejpam-5936	214	2	22	22	NUM
ejpam-5936	214	3	)	)	PUNCT
ejpam-5936	214	4	case:5	case:5	NOUN
ejpam-5936	214	5	(	(	PUNCT
ejpam-5936	214	6	n	n	NOUN
ejpam-5936	214	7	=	=	SYM
ejpam-5936	214	8	1	1	NUM
ejpam-5936	214	9	2	2	NUM
ejpam-5936	214	10	,	,	PUNCT
ejpam-5936	214	11	m	m	VERB
ejpam-5936	214	12	=	=	NOUN
ejpam-5936	214	13	1	1	NUM
ejpam-5936	214	14	)	)	PUNCT
ejpam-5936	214	15	for	for	ADP
ejpam-5936	214	16	n	n	NOUN
ejpam-5936	214	17	=	=	SYM
ejpam-5936	214	18	1	1	NUM
ejpam-5936	214	19	2	2	NUM
ejpam-5936	214	20	and	and	CCONJ
ejpam-5936	214	21	m	m	NOUN
ejpam-5936	214	22	=	=	ADJ
ejpam-5936	214	23	1	1	NUM
ejpam-5936	214	24	,	,	PUNCT
ejpam-5936	214	25	the	the	DET
ejpam-5936	214	26	wave	wave	NOUN
ejpam-5936	214	27	variable	variable	NOUN
ejpam-5936	214	28	ξ	ξ	PROPN
ejpam-5936	214	29	=	=	SYM
ejpam-5936	214	30	xmz(y	xmz(y	PROPN
ejpam-5936	214	31	)	)	PUNCT
ejpam-5936	214	32	becomes	become	VERB
ejpam-5936	214	33	ξ	ξ	NOUN
ejpam-5936	214	34	=	=	SYM
ejpam-5936	214	35	xz(y	xz(y	X
ejpam-5936	214	36	)	)	PUNCT
ejpam-5936	214	37	and	and	CCONJ
ejpam-5936	214	38	the	the	DET
ejpam-5936	214	39	transformation	transformation	NOUN
ejpam-5936	214	40	u	u	NOUN
ejpam-5936	214	41	=	=	SYM
ejpam-5936	214	42	xna(t)etf(ξ	xna(t)etf(ξ	X
ejpam-5936	214	43	)	)	PUNCT
ejpam-5936	214	44	reduces	reduce	VERB
ejpam-5936	214	45	to	to	ADP
ejpam-5936	214	46	u	u	NOUN
ejpam-5936	214	47	=	=	NOUN
ejpam-5936	214	48	√	√	PROPN
ejpam-5936	214	49	xa(y)etf(ξ	xa(y)etf(ξ	NUM
ejpam-5936	214	50	)	)	PUNCT
ejpam-5936	214	51	.	.	PUNCT
ejpam-5936	215	1	substituting	substitute	VERB
ejpam-5936	215	2	ξ	ξ	PROPN
ejpam-5936	215	3	=	=	SYM
ejpam-5936	215	4	xz(y	xz(y	X
ejpam-5936	215	5	)	)	PUNCT
ejpam-5936	215	6	and	and	CCONJ
ejpam-5936	215	7	u	u	X
ejpam-5936	215	8	=	=	NOUN
ejpam-5936	215	9	√	√	PROPN
ejpam-5936	215	10	xa(y)etf(ξ	xa(y)etf(ξ	NUM
ejpam-5936	215	11	)	)	PUNCT
ejpam-5936	215	12	into	into	ADP
ejpam-5936	215	13	equation	equation	NOUN
ejpam-5936	215	14	(	(	PUNCT
ejpam-5936	215	15	4	4	X
ejpam-5936	215	16	)	)	PUNCT
ejpam-5936	215	17	yields	yield	NOUN
ejpam-5936	215	18	:	:	PUNCT
ejpam-5936	215	19	(	(	PUNCT
ejpam-5936	215	20	ξ2	ξ2	NOUN
ejpam-5936	215	21	+	+	CCONJ
ejpam-5936	215	22	x4z	x4z	PROPN
ejpam-5936	215	23	′2(y))f(ξ)f	′2(y))f(ξ)f	ADJ
ejpam-5936	215	24	′′(ξ	′′(ξ	PROPN
ejpam-5936	215	25	)	)	PUNCT
ejpam-5936	216	1	+	+	CCONJ
ejpam-5936	216	2	(	(	PUNCT
ejpam-5936	216	3	ξ2	ξ2	NOUN
ejpam-5936	216	4	+	+	CCONJ
ejpam-5936	216	5	x4z	x4z	PROPN
ejpam-5936	216	6	′2(y))f	′2(y))f	NOUN
ejpam-5936	216	7	′2(ξ	′2(ξ	NUM
ejpam-5936	216	8	)	)	PUNCT
ejpam-5936	217	1	+	+	CCONJ
ejpam-5936	217	2	(	(	PUNCT
ejpam-5936	217	3	2ξ	2ξ	NUM
ejpam-5936	218	1	+	+	CCONJ
ejpam-5936	218	2	x3z	x3z	PROPN
ejpam-5936	218	3	′′(y)+	′′(y)+	VERB
ejpam-5936	218	4	4x3z	4x3z	NUM
ejpam-5936	218	5	′(y)a′(y	′(y)a′(y	NOUN
ejpam-5936	218	6	)	)	PUNCT
ejpam-5936	219	1	a(y	a(y	PROPN
ejpam-5936	219	2	)	)	PUNCT
ejpam-5936	219	3	)	)	PUNCT
ejpam-5936	219	4	f(ξ)f	f(ξ)f	PROPN
ejpam-5936	219	5	′(ξ	′(ξ	NOUN
ejpam-5936	219	6	)	)	PUNCT
ejpam-5936	219	7	+	+	CCONJ
ejpam-5936	219	8	(	(	PUNCT
ejpam-5936	219	9	x2a′′(y	x2a′′(y	X
ejpam-5936	219	10	)	)	PUNCT
ejpam-5936	219	11	a(y	a(y	PROPN
ejpam-5936	219	12	)	)	PUNCT
ejpam-5936	219	13	+	+	SYM
ejpam-5936	219	14	x2a′2(y	x2a′2(y	NUM
ejpam-5936	219	15	)	)	PUNCT
ejpam-5936	219	16	a2(y	a2(y	NUM
ejpam-5936	219	17	)	)	PUNCT
ejpam-5936	219	18	)	)	PUNCT
ejpam-5936	220	1	f2(ξ	f2(ξ	X
ejpam-5936	220	2	)	)	PUNCT
ejpam-5936	220	3	=	=	NOUN
ejpam-5936	220	4	0	0	X
ejpam-5936	220	5	.	.	PUNCT
ejpam-5936	221	1	(	(	PUNCT
ejpam-5936	221	2	23	23	NUM
ejpam-5936	221	3	)	)	PUNCT
ejpam-5936	221	4	to	to	PART
ejpam-5936	221	5	express	express	VERB
ejpam-5936	221	6	the	the	DET
ejpam-5936	221	7	terms	term	NOUN
ejpam-5936	221	8	in	in	ADP
ejpam-5936	221	9	equation	equation	NOUN
ejpam-5936	221	10	(	(	PUNCT
ejpam-5936	221	11	23	23	NUM
ejpam-5936	221	12	)	)	PUNCT
ejpam-5936	221	13	in	in	ADP
ejpam-5936	221	14	terms	term	NOUN
ejpam-5936	221	15	of	of	ADP
ejpam-5936	221	16	ξ	ξ	PROPN
ejpam-5936	221	17	,	,	PUNCT
ejpam-5936	221	18	we	we	PRON
ejpam-5936	221	19	set	set	VERB
ejpam-5936	221	20	x4z	x4z	PROPN
ejpam-5936	221	21	′2(y	′2(y	PROPN
ejpam-5936	221	22	)	)	PUNCT
ejpam-5936	221	23	=	=	PUNCT
ejpam-5936	222	1	x4z4(y	x4z4(y	PROPN
ejpam-5936	222	2	)	)	PUNCT
ejpam-5936	222	3	and	and	CCONJ
ejpam-5936	222	4	a′′(y	a′′(y	ADJ
ejpam-5936	222	5	)	)	PUNCT
ejpam-5936	222	6	a′(y	a′(y	PROPN
ejpam-5936	222	7	)	)	PUNCT
ejpam-5936	222	8	=	=	SYM
ejpam-5936	222	9	−a′(y	−a′(y	PROPN
ejpam-5936	222	10	)	)	PUNCT
ejpam-5936	222	11	a(y	a(y	PROPN
ejpam-5936	222	12	)	)	PUNCT
ejpam-5936	222	13	.	.	PUNCT
ejpam-5936	223	1	solving	solve	VERB
ejpam-5936	223	2	these	these	DET
ejpam-5936	223	3	equations	equation	NOUN
ejpam-5936	223	4	yields	yield	VERB
ejpam-5936	223	5	z(y	z(y	PROPN
ejpam-5936	223	6	)	)	PUNCT
ejpam-5936	224	1	=	=	SYM
ejpam-5936	224	2	1	1	NUM
ejpam-5936	224	3	y	y	PROPN
ejpam-5936	224	4	and	and	CCONJ
ejpam-5936	224	5	a(y	a(y	PROPN
ejpam-5936	224	6	)	)	PUNCT
ejpam-5936	224	7	=	=	PUNCT
ejpam-5936	225	1	√	√	PROPN
ejpam-5936	225	2	y.	y.	NOUN
ejpam-5936	225	3	consequently	consequently	ADV
ejpam-5936	225	4	,	,	PUNCT
ejpam-5936	225	5	z.	z.	PROPN
ejpam-5936	225	6	haider	haider	PROPN
ejpam-5936	225	7	,	,	PUNCT
ejpam-5936	225	8	k.	k.	PROPN
ejpam-5936	225	9	ahmad	ahmad	PROPN
ejpam-5936	225	10	/	/	SYM
ejpam-5936	225	11	eur	eur	PROPN
ejpam-5936	225	12	.	.	PUNCT
ejpam-5936	226	1	j.	j.	PROPN
ejpam-5936	226	2	pure	pure	PROPN
ejpam-5936	226	3	appl	appl	PROPN
ejpam-5936	226	4	.	.	PROPN
ejpam-5936	226	5	math	math	PROPN
ejpam-5936	226	6	,	,	PUNCT
ejpam-5936	226	7	18	18	NUM
ejpam-5936	226	8	(	(	PUNCT
ejpam-5936	226	9	2	2	NUM
ejpam-5936	226	10	)	)	PUNCT
ejpam-5936	226	11	(	(	PUNCT
ejpam-5936	226	12	2025	2025	NUM
ejpam-5936	226	13	)	)	PUNCT
ejpam-5936	226	14	,	,	PUNCT
ejpam-5936	226	15	5936	5936	NUM
ejpam-5936	226	16	13	13	NUM
ejpam-5936	226	17	of	of	ADP
ejpam-5936	226	18	18	18	NUM
ejpam-5936	226	19	figure	figure	NOUN
ejpam-5936	226	20	13	13	NUM
ejpam-5936	226	21	:	:	PUNCT
ejpam-5936	226	22	3d	3d	NUM
ejpam-5936	226	23	plot	plot	NOUN
ejpam-5936	226	24	of	of	ADP
ejpam-5936	226	25	solution	solution	NOUN
ejpam-5936	226	26	u13	u13	NOUN
ejpam-5936	226	27	given	give	VERB
ejpam-5936	226	28	in	in	ADP
ejpam-5936	226	29	(	(	PUNCT
ejpam-5936	226	30	26	26	NUM
ejpam-5936	226	31	)	)	PUNCT
ejpam-5936	226	32	of	of	ADP
ejpam-5936	226	33	pde	pde	NOUN
ejpam-5936	226	34	(	(	PUNCT
ejpam-5936	226	35	1	1	NUM
ejpam-5936	226	36	)	)	PUNCT
ejpam-5936	226	37	for	for	ADP
ejpam-5936	226	38	c1	c1	NOUN
ejpam-5936	226	39	=	=	PUNCT
ejpam-5936	226	40	−3	−3	PROPN
ejpam-5936	226	41	,	,	PUNCT
ejpam-5936	226	42	c2	c2	PROPN
ejpam-5936	226	43	=	=	PUNCT
ejpam-5936	226	44	−1	−1	NOUN
ejpam-5936	226	45	and	and	CCONJ
ejpam-5936	226	46	y	y	PROPN
ejpam-5936	226	47	=	=	PUNCT
ejpam-5936	226	48	−1	−1	PROPN
ejpam-5936	226	49	.	.	PUNCT
ejpam-5936	227	1	figure	figure	NOUN
ejpam-5936	227	2	14	14	NUM
ejpam-5936	227	3	:	:	PUNCT
ejpam-5936	227	4	3d	3d	NUM
ejpam-5936	227	5	plot	plot	NOUN
ejpam-5936	227	6	of	of	ADP
ejpam-5936	227	7	solution	solution	NOUN
ejpam-5936	227	8	u14	u14	NOUN
ejpam-5936	227	9	given	give	VERB
ejpam-5936	227	10	in	in	ADP
ejpam-5936	227	11	(	(	PUNCT
ejpam-5936	227	12	26	26	NUM
ejpam-5936	227	13	)	)	PUNCT
ejpam-5936	227	14	of	of	ADP
ejpam-5936	227	15	pde	pde	NOUN
ejpam-5936	227	16	(	(	PUNCT
ejpam-5936	227	17	1	1	NUM
ejpam-5936	227	18	)	)	PUNCT
ejpam-5936	227	19	for	for	ADP
ejpam-5936	227	20	c1	c1	NOUN
ejpam-5936	227	21	=	=	PUNCT
ejpam-5936	227	22	−3	−3	PROPN
ejpam-5936	227	23	,	,	PUNCT
ejpam-5936	227	24	c2	c2	PROPN
ejpam-5936	227	25	=	=	PUNCT
ejpam-5936	227	26	1	1	NUM
ejpam-5936	227	27	and	and	CCONJ
ejpam-5936	227	28	x	x	SYM
ejpam-5936	227	29	=	=	SYM
ejpam-5936	227	30	2	2	X
ejpam-5936	227	31	.	.	PUNCT
ejpam-5936	228	1	the	the	DET
ejpam-5936	228	2	wave	wave	NOUN
ejpam-5936	228	3	variable	variable	NOUN
ejpam-5936	228	4	becomes	become	VERB
ejpam-5936	228	5	ξ	ξ	NOUN
ejpam-5936	228	6	=	=	SYM
ejpam-5936	228	7	x	x	SYM
ejpam-5936	228	8	y	y	PROPN
ejpam-5936	228	9	and	and	CCONJ
ejpam-5936	228	10	the	the	DET
ejpam-5936	228	11	transformation	transformation	NOUN
ejpam-5936	228	12	takes	take	VERB
ejpam-5936	228	13	the	the	DET
ejpam-5936	228	14	form	form	NOUN
ejpam-5936	228	15	u	u	NOUN
ejpam-5936	228	16	=	=	NOUN
ejpam-5936	228	17	√	√	PROPN
ejpam-5936	228	18	xyetf(ξ	xyetf(ξ	PROPN
ejpam-5936	228	19	)	)	PUNCT
ejpam-5936	228	20	.	.	PUNCT
ejpam-5936	229	1	substituting	substitute	VERB
ejpam-5936	229	2	these	these	DET
ejpam-5936	229	3	expressions	expression	NOUN
ejpam-5936	229	4	into	into	ADP
ejpam-5936	229	5	equation	equation	NOUN
ejpam-5936	229	6	(	(	PUNCT
ejpam-5936	229	7	23	23	NUM
ejpam-5936	229	8	)	)	PUNCT
ejpam-5936	229	9	,	,	PUNCT
ejpam-5936	229	10	we	we	PRON
ejpam-5936	229	11	derive	derive	VERB
ejpam-5936	229	12	the	the	DET
ejpam-5936	229	13	following	follow	VERB
ejpam-5936	229	14	ode	ode	PROPN
ejpam-5936	229	15	:	:	PUNCT
ejpam-5936	229	16	(	(	PUNCT
ejpam-5936	229	17	ξ4	ξ4	NOUN
ejpam-5936	229	18	+	+	CCONJ
ejpam-5936	229	19	ξ2)f(ξ)f	ξ2)f(ξ)f	NUM
ejpam-5936	229	20	′′(ξ	′′(ξ	NUM
ejpam-5936	229	21	)	)	PUNCT
ejpam-5936	229	22	+	+	NUM
ejpam-5936	229	23	2ξf(ξ)f	2ξf(ξ)f	NUM
ejpam-5936	229	24	′(ξ	′(ξ	NOUN
ejpam-5936	229	25	)	)	PUNCT
ejpam-5936	229	26	+	+	CCONJ
ejpam-5936	229	27	(	(	PUNCT
ejpam-5936	229	28	ξ4	ξ4	ADJ
ejpam-5936	229	29	+	+	CCONJ
ejpam-5936	229	30	ξ2)f	ξ2)f	NOUN
ejpam-5936	229	31	′2(ξ	′2(ξ	NUM
ejpam-5936	229	32	)	)	PUNCT
ejpam-5936	229	33	=	=	SYM
ejpam-5936	230	1	0	0	X
ejpam-5936	230	2	.	.	PUNCT
ejpam-5936	231	1	(	(	PUNCT
ejpam-5936	231	2	24	24	NUM
ejpam-5936	231	3	)	)	PUNCT
ejpam-5936	231	4	z.	z.	PROPN
ejpam-5936	231	5	haider	haider	PROPN
ejpam-5936	231	6	,	,	PUNCT
ejpam-5936	231	7	k.	k.	PROPN
ejpam-5936	231	8	ahmad	ahmad	PROPN
ejpam-5936	231	9	/	/	SYM
ejpam-5936	231	10	eur	eur	PROPN
ejpam-5936	231	11	.	.	PUNCT
ejpam-5936	232	1	j.	j.	PROPN
ejpam-5936	232	2	pure	pure	PROPN
ejpam-5936	232	3	appl	appl	PROPN
ejpam-5936	232	4	.	.	PROPN
ejpam-5936	232	5	math	math	PROPN
ejpam-5936	232	6	,	,	PUNCT
ejpam-5936	232	7	18	18	NUM
ejpam-5936	232	8	(	(	PUNCT
ejpam-5936	232	9	2	2	NUM
ejpam-5936	232	10	)	)	PUNCT
ejpam-5936	232	11	(	(	PUNCT
ejpam-5936	232	12	2025	2025	NUM
ejpam-5936	232	13	)	)	PUNCT
ejpam-5936	232	14	,	,	PUNCT
ejpam-5936	232	15	5936	5936	NUM
ejpam-5936	232	16	14	14	NUM
ejpam-5936	232	17	of	of	ADP
ejpam-5936	232	18	18	18	NUM
ejpam-5936	232	19	figure	figure	NOUN
ejpam-5936	232	20	15	15	NUM
ejpam-5936	232	21	:	:	PUNCT
ejpam-5936	232	22	3d	3d	NUM
ejpam-5936	232	23	plot	plot	NOUN
ejpam-5936	232	24	of	of	ADP
ejpam-5936	232	25	solution	solution	NOUN
ejpam-5936	232	26	u15	u15	NOUN
ejpam-5936	232	27	given	give	VERB
ejpam-5936	232	28	in	in	ADP
ejpam-5936	232	29	(	(	PUNCT
ejpam-5936	232	30	26	26	NUM
ejpam-5936	232	31	)	)	PUNCT
ejpam-5936	232	32	of	of	ADP
ejpam-5936	232	33	pde	pde	NOUN
ejpam-5936	232	34	(	(	PUNCT
ejpam-5936	232	35	1	1	NUM
ejpam-5936	232	36	)	)	PUNCT
ejpam-5936	232	37	for	for	ADP
ejpam-5936	232	38	c1	c1	PROPN
ejpam-5936	232	39	=	=	SYM
ejpam-5936	232	40	−1	−1	PROPN
ejpam-5936	232	41	,	,	PUNCT
ejpam-5936	232	42	c2	c2	PROPN
ejpam-5936	232	43	=	=	PUNCT
ejpam-5936	232	44	1	1	NUM
ejpam-5936	232	45	and	and	CCONJ
ejpam-5936	232	46	t	t	NOUN
ejpam-5936	232	47	=	=	SYM
ejpam-5936	232	48	1	1	X
ejpam-5936	232	49	.	.	PUNCT
ejpam-5936	233	1	the	the	DET
ejpam-5936	233	2	analytic	analytic	ADJ
ejpam-5936	233	3	solution	solution	NOUN
ejpam-5936	233	4	of	of	ADP
ejpam-5936	233	5	ode	ode	PROPN
ejpam-5936	233	6	(	(	PUNCT
ejpam-5936	233	7	24	24	NUM
ejpam-5936	233	8	)	)	PUNCT
ejpam-5936	233	9	is	be	AUX
ejpam-5936	233	10	f(ξ	f(ξ	NOUN
ejpam-5936	233	11	)	)	PUNCT
ejpam-5936	233	12	=	=	SYM
ejpam-5936	234	1	√	√	NUM
ejpam-5936	234	2	2c1ξ	2c1ξ	NOUN
ejpam-5936	235	1	+	+	CCONJ
ejpam-5936	235	2	2c2	2c2	NUM
ejpam-5936	235	3	−	−	NOUN
ejpam-5936	235	4	2c1	2c1	NUM
ejpam-5936	236	1	ξ	ξ	X
ejpam-5936	236	2	.	.	PUNCT
ejpam-5936	237	1	(	(	PUNCT
ejpam-5936	237	2	25	25	NUM
ejpam-5936	237	3	)	)	PUNCT
ejpam-5936	237	4	the	the	DET
ejpam-5936	237	5	exact	exact	ADJ
ejpam-5936	237	6	solution	solution	NOUN
ejpam-5936	237	7	of	of	ADP
ejpam-5936	237	8	pde	pde	NOUN
ejpam-5936	237	9	(	(	PUNCT
ejpam-5936	237	10	1	1	NUM
ejpam-5936	237	11	)	)	PUNCT
ejpam-5936	237	12	is	be	AUX
ejpam-5936	237	13	u(x	u(x	NOUN
ejpam-5936	237	14	,	,	PUNCT
ejpam-5936	237	15	y	y	PROPN
ejpam-5936	237	16	,	,	PUNCT
ejpam-5936	237	17	t	t	PROPN
ejpam-5936	237	18	)	)	PUNCT
ejpam-5936	237	19	=	=	SYM
ejpam-5936	237	20	et	et	NOUN
ejpam-5936	237	21	√	√	NOUN
ejpam-5936	237	22	2c1x2	2c1x2	NUM
ejpam-5936	238	1	+	+	CCONJ
ejpam-5936	238	2	2c2xy	2c2xy	NUM
ejpam-5936	238	3	−	−	NOUN
ejpam-5936	238	4	2c1y2	2c1y2	NUM
ejpam-5936	238	5	.	.	PUNCT
ejpam-5936	239	1	(	(	PUNCT
ejpam-5936	239	2	26	26	NUM
ejpam-5936	239	3	)	)	PUNCT
ejpam-5936	239	4	4	4	NUM
ejpam-5936	239	5	.	.	NOUN
ejpam-5936	239	6	results	result	NOUN
ejpam-5936	239	7	and	and	CCONJ
ejpam-5936	239	8	discussion	discussion	NOUN
ejpam-5936	239	9	by	by	ADP
ejpam-5936	239	10	developing	develop	VERB
ejpam-5936	239	11	an	an	DET
ejpam-5936	239	12	analytical	analytical	ADJ
ejpam-5936	239	13	approach	approach	NOUN
ejpam-5936	239	14	to	to	ADP
ejpam-5936	239	15	solving	solve	VERB
ejpam-5936	239	16	the	the	DET
ejpam-5936	239	17	nonlinear	nonlinear	ADJ
ejpam-5936	239	18	biological	biological	ADJ
ejpam-5936	239	19	population	population	NOUN
ejpam-5936	239	20	model	model	NOUN
ejpam-5936	240	1	,	,	PUNCT
ejpam-5936	240	2	this	this	DET
ejpam-5936	240	3	paper	paper	NOUN
ejpam-5936	240	4	makes	make	VERB
ejpam-5936	240	5	a	a	DET
ejpam-5936	240	6	significant	significant	ADJ
ejpam-5936	240	7	contribution	contribution	NOUN
ejpam-5936	240	8	to	to	ADP
ejpam-5936	240	9	the	the	DET
ejpam-5936	240	10	field	field	NOUN
ejpam-5936	240	11	of	of	ADP
ejpam-5936	240	12	nonlinear	nonlinear	ADJ
ejpam-5936	240	13	science	science	NOUN
ejpam-5936	240	14	.	.	PUNCT
ejpam-5936	241	1	the	the	DET
ejpam-5936	241	2	successful	successful	ADJ
ejpam-5936	241	3	applications	application	NOUN
ejpam-5936	241	4	of	of	ADP
ejpam-5936	241	5	the	the	DET
ejpam-5936	241	6	power	power	NOUN
ejpam-5936	241	7	index	index	NOUN
ejpam-5936	241	8	method	method	NOUN
ejpam-5936	241	9	reveal	reveal	VERB
ejpam-5936	241	10	a	a	DET
ejpam-5936	241	11	variety	variety	NOUN
ejpam-5936	241	12	of	of	ADP
ejpam-5936	241	13	solutions	solution	NOUN
ejpam-5936	241	14	with	with	ADP
ejpam-5936	241	15	unique	unique	ADJ
ejpam-5936	241	16	wave	wave	NOUN
ejpam-5936	241	17	structures	structure	NOUN
ejpam-5936	241	18	,	,	PUNCT
ejpam-5936	241	19	demonstrating	demonstrate	VERB
ejpam-5936	241	20	its	its	PRON
ejpam-5936	241	21	effectiveness	effectiveness	NOUN
ejpam-5936	241	22	in	in	ADP
ejpam-5936	241	23	solving	solve	VERB
ejpam-5936	241	24	complex	complex	ADJ
ejpam-5936	241	25	nonlinear	nonlinear	ADJ
ejpam-5936	241	26	problems	problem	NOUN
ejpam-5936	241	27	.	.	PUNCT
ejpam-5936	242	1	the	the	DET
ejpam-5936	242	2	paper	paper	NOUN
ejpam-5936	242	3	serves	serve	VERB
ejpam-5936	242	4	as	as	ADP
ejpam-5936	242	5	a	a	DET
ejpam-5936	242	6	valuable	valuable	ADJ
ejpam-5936	242	7	resource	resource	NOUN
ejpam-5936	242	8	for	for	ADP
ejpam-5936	242	9	scientists	scientist	NOUN
ejpam-5936	242	10	and	and	CCONJ
ejpam-5936	242	11	researchers	researcher	NOUN
ejpam-5936	242	12	due	due	ADP
ejpam-5936	242	13	to	to	ADP
ejpam-5936	242	14	its	its	PRON
ejpam-5936	242	15	comprehensive	comprehensive	ADJ
ejpam-5936	242	16	analysis	analysis	NOUN
ejpam-5936	242	17	and	and	CCONJ
ejpam-5936	242	18	graphical	graphical	ADJ
ejpam-5936	242	19	representations	representation	NOUN
ejpam-5936	242	20	,	,	PUNCT
ejpam-5936	242	21	which	which	PRON
ejpam-5936	242	22	provide	provide	VERB
ejpam-5936	242	23	deeper	deep	ADJ
ejpam-5936	242	24	insights	insight	NOUN
ejpam-5936	242	25	into	into	ADP
ejpam-5936	242	26	the	the	DET
ejpam-5936	242	27	equation	equation	NOUN
ejpam-5936	242	28	’s	’s	PART
ejpam-5936	242	29	dynamics	dynamic	NOUN
ejpam-5936	242	30	and	and	CCONJ
ejpam-5936	242	31	related	relate	VERB
ejpam-5936	242	32	physical	physical	ADJ
ejpam-5936	242	33	phenomena	phenomenon	NOUN
ejpam-5936	242	34	.	.	PUNCT
ejpam-5936	243	1	moreover	moreover	ADV
ejpam-5936	243	2	,	,	PUNCT
ejpam-5936	243	3	this	this	DET
ejpam-5936	243	4	study	study	NOUN
ejpam-5936	243	5	opens	open	VERB
ejpam-5936	243	6	new	new	ADJ
ejpam-5936	243	7	research	research	NOUN
ejpam-5936	243	8	avenues	avenue	NOUN
ejpam-5936	243	9	across	across	ADP
ejpam-5936	243	10	multiple	multiple	ADJ
ejpam-5936	243	11	scientific	scientific	ADJ
ejpam-5936	243	12	disciplines	discipline	NOUN
ejpam-5936	243	13	by	by	ADP
ejpam-5936	243	14	showcasing	showcase	VERB
ejpam-5936	243	15	the	the	DET
ejpam-5936	243	16	power	power	NOUN
ejpam-5936	243	17	index	index	NOUN
ejpam-5936	243	18	method	method	NOUN
ejpam-5936	243	19	capability	capability	NOUN
ejpam-5936	243	20	to	to	PART
ejpam-5936	243	21	solve	solve	VERB
ejpam-5936	243	22	nonlinear	nonlinear	ADJ
ejpam-5936	243	23	differential	differential	ADJ
ejpam-5936	243	24	equations	equation	NOUN
ejpam-5936	243	25	.	.	PUNCT
ejpam-5936	244	1	overall	overall	ADV
ejpam-5936	244	2	,	,	PUNCT
ejpam-5936	244	3	the	the	DET
ejpam-5936	244	4	paper	paper	NOUN
ejpam-5936	244	5	’s	’s	PART
ejpam-5936	244	6	unique	unique	ADJ
ejpam-5936	244	7	methodology	methodology	NOUN
ejpam-5936	244	8	and	and	CCONJ
ejpam-5936	244	9	findings	finding	NOUN
ejpam-5936	244	10	make	make	VERB
ejpam-5936	244	11	it	it	PRON
ejpam-5936	244	12	a	a	DET
ejpam-5936	244	13	significant	significant	ADJ
ejpam-5936	244	14	and	and	CCONJ
ejpam-5936	244	15	influential	influential	ADJ
ejpam-5936	244	16	contribution	contribution	NOUN
ejpam-5936	244	17	to	to	ADP
ejpam-5936	244	18	the	the	DET
ejpam-5936	244	19	field	field	NOUN
ejpam-5936	244	20	.	.	PUNCT
ejpam-5936	245	1	a	a	DET
ejpam-5936	245	2	variety	variety	NOUN
ejpam-5936	245	3	of	of	ADP
ejpam-5936	245	4	graphs	graph	NOUN
ejpam-5936	245	5	from	from	ADP
ejpam-5936	245	6	fig	fig	NOUN
ejpam-5936	245	7	.	.	PUNCT
ejpam-5936	246	1	1	1	NUM
ejpam-5936	246	2	to	to	ADP
ejpam-5936	246	3	fig	fig	NOUN
ejpam-5936	246	4	.	.	PUNCT
ejpam-5936	247	1	15	15	NUM
ejpam-5936	247	2	presented	present	VERB
ejpam-5936	247	3	illustrates	illustrate	VERB
ejpam-5936	247	4	a	a	DET
ejpam-5936	247	5	range	range	NOUN
ejpam-5936	247	6	of	of	ADP
ejpam-5936	247	7	behaviors	behavior	NOUN
ejpam-5936	247	8	typical	typical	ADJ
ejpam-5936	247	9	of	of	ADP
ejpam-5936	247	10	solutions	solution	NOUN
ejpam-5936	247	11	to	to	ADP
ejpam-5936	247	12	nonlinear	nonlinear	ADJ
ejpam-5936	247	13	pdes	pde	NOUN
ejpam-5936	247	14	,	,	PUNCT
ejpam-5936	247	15	including	include	VERB
ejpam-5936	247	16	growth	growth	NOUN
ejpam-5936	247	17	,	,	PUNCT
ejpam-5936	247	18	decay	decay	NOUN
ejpam-5936	247	19	,	,	PUNCT
ejpam-5936	247	20	diffusion	diffusion	NOUN
ejpam-5936	247	21	,	,	PUNCT
ejpam-5936	247	22	wave	wave	NOUN
ejpam-5936	247	23	propagation	propagation	NOUN
ejpam-5936	247	24	,	,	PUNCT
ejpam-5936	247	25	and	and	CCONJ
ejpam-5936	247	26	singularities	singularity	NOUN
ejpam-5936	247	27	.	.	PUNCT
ejpam-5936	248	1	these	these	DET
ejpam-5936	248	2	behaviors	behavior	NOUN
ejpam-5936	248	3	are	be	AUX
ejpam-5936	248	4	commonly	commonly	ADV
ejpam-5936	248	5	observed	observe	VERB
ejpam-5936	248	6	in	in	ADP
ejpam-5936	248	7	models	model	NOUN
ejpam-5936	248	8	across	across	ADP
ejpam-5936	248	9	biological	biological	ADJ
ejpam-5936	248	10	,	,	PUNCT
ejpam-5936	248	11	physical	physical	ADJ
ejpam-5936	248	12	,	,	PUNCT
ejpam-5936	248	13	and	and	CCONJ
ejpam-5936	248	14	engineering	engineering	NOUN
ejpam-5936	248	15	systems	system	NOUN
ejpam-5936	248	16	.	.	PUNCT
ejpam-5936	249	1	the	the	DET
ejpam-5936	249	2	graphical	graphical	ADJ
ejpam-5936	249	3	examination	examination	NOUN
ejpam-5936	249	4	presented	present	VERB
ejpam-5936	249	5	showcases	showcase	VERB
ejpam-5936	249	6	a	a	DET
ejpam-5936	249	7	variety	variety	NOUN
ejpam-5936	249	8	of	of	ADP
ejpam-5936	249	9	z.	z.	PROPN
ejpam-5936	249	10	haider	haider	PROPN
ejpam-5936	249	11	,	,	PUNCT
ejpam-5936	249	12	k.	k.	PROPN
ejpam-5936	249	13	ahmad	ahmad	PROPN
ejpam-5936	249	14	/	/	SYM
ejpam-5936	249	15	eur	eur	PROPN
ejpam-5936	249	16	.	.	PUNCT
ejpam-5936	250	1	j.	j.	PROPN
ejpam-5936	250	2	pure	pure	PROPN
ejpam-5936	250	3	appl	appl	PROPN
ejpam-5936	250	4	.	.	PROPN
ejpam-5936	250	5	math	math	PROPN
ejpam-5936	250	6	,	,	PUNCT
ejpam-5936	250	7	18	18	NUM
ejpam-5936	250	8	(	(	PUNCT
ejpam-5936	250	9	2	2	NUM
ejpam-5936	250	10	)	)	PUNCT
ejpam-5936	250	11	(	(	PUNCT
ejpam-5936	250	12	2025	2025	NUM
ejpam-5936	250	13	)	)	PUNCT
ejpam-5936	250	14	,	,	PUNCT
ejpam-5936	250	15	5936	5936	NUM
ejpam-5936	250	16	15	15	NUM
ejpam-5936	250	17	of	of	ADP
ejpam-5936	250	18	18	18	NUM
ejpam-5936	250	19	how	how	SCONJ
ejpam-5936	250	20	the	the	DET
ejpam-5936	250	21	solutions	solution	NOUN
ejpam-5936	250	22	evolve	evolve	VERB
ejpam-5936	250	23	in	in	ADP
ejpam-5936	250	24	both	both	DET
ejpam-5936	250	25	space	space	NOUN
ejpam-5936	250	26	and	and	CCONJ
ejpam-5936	250	27	time	time	NOUN
ejpam-5936	250	28	,	,	PUNCT
ejpam-5936	250	29	contingent	contingent	NOUN
ejpam-5936	250	30	on	on	ADP
ejpam-5936	250	31	the	the	DET
ejpam-5936	250	32	specific	specific	ADJ
ejpam-5936	250	33	equations	equation	NOUN
ejpam-5936	250	34	and	and	CCONJ
ejpam-5936	250	35	parameter	parameter	NOUN
ejpam-5936	250	36	values	value	NOUN
ejpam-5936	250	37	employed	employ	VERB
ejpam-5936	250	38	.	.	PUNCT
ejpam-5936	251	1	the	the	DET
ejpam-5936	251	2	plots	plot	NOUN
ejpam-5936	251	3	for	for	ADP
ejpam-5936	251	4	u1(x	u1(x	PROPN
ejpam-5936	251	5	,	,	PUNCT
ejpam-5936	251	6	t	t	PROPN
ejpam-5936	251	7	)	)	PUNCT
ejpam-5936	251	8	,	,	PUNCT
ejpam-5936	251	9	u2(y	u2(y	PROPN
ejpam-5936	251	10	,	,	PUNCT
ejpam-5936	251	11	t	t	PROPN
ejpam-5936	251	12	)	)	PUNCT
ejpam-5936	251	13	,	,	PUNCT
ejpam-5936	251	14	u4(x	u4(x	PROPN
ejpam-5936	251	15	,	,	PUNCT
ejpam-5936	251	16	t	t	PROPN
ejpam-5936	251	17	)	)	PUNCT
ejpam-5936	251	18	,	,	PUNCT
ejpam-5936	251	19	u5(y	u5(y	PROPN
ejpam-5936	251	20	,	,	PUNCT
ejpam-5936	251	21	t	t	PROPN
ejpam-5936	251	22	)	)	PUNCT
ejpam-5936	251	23	,	,	PUNCT
ejpam-5936	251	24	u7(x	u7(x	PROPN
ejpam-5936	251	25	,	,	PUNCT
ejpam-5936	251	26	t	t	PROPN
ejpam-5936	251	27	)	)	PUNCT
ejpam-5936	251	28	,	,	PUNCT
ejpam-5936	251	29	and	and	CCONJ
ejpam-5936	251	30	u8(y	u8(y	PROPN
ejpam-5936	251	31	,	,	PUNCT
ejpam-5936	251	32	t	t	PROPN
ejpam-5936	251	33	)	)	PUNCT
ejpam-5936	251	34	consistently	consistently	ADV
ejpam-5936	251	35	highlight	highlight	VERB
ejpam-5936	251	36	a	a	DET
ejpam-5936	251	37	significant	significant	ADJ
ejpam-5936	251	38	increase	increase	NOUN
ejpam-5936	251	39	in	in	ADP
ejpam-5936	251	40	the	the	DET
ejpam-5936	251	41	solution	solution	NOUN
ejpam-5936	251	42	’s	’s	PART
ejpam-5936	251	43	magnitude	magnitude	NOUN
ejpam-5936	251	44	over	over	ADP
ejpam-5936	251	45	time	time	NOUN
ejpam-5936	251	46	across	across	ADP
ejpam-5936	251	47	their	their	PRON
ejpam-5936	251	48	respective	respective	ADJ
ejpam-5936	251	49	spatial	spatial	ADJ
ejpam-5936	251	50	extents	extent	NOUN
ejpam-5936	251	51	,	,	PUNCT
ejpam-5936	251	52	without	without	ADP
ejpam-5936	251	53	displaying	display	VERB
ejpam-5936	251	54	typical	typical	ADJ
ejpam-5936	251	55	wave	wave	NOUN
ejpam-5936	251	56	-	-	PUNCT
ejpam-5936	251	57	like	like	ADJ
ejpam-5936	251	58	movement	movement	NOUN
ejpam-5936	251	59	.	.	PUNCT
ejpam-5936	252	1	in	in	ADP
ejpam-5936	252	2	these	these	DET
ejpam-5936	252	3	instances	instance	NOUN
ejpam-5936	252	4	,	,	PUNCT
ejpam-5936	252	5	the	the	DET
ejpam-5936	252	6	spatial	spatial	ADJ
ejpam-5936	252	7	patterns	pattern	NOUN
ejpam-5936	252	8	remain	remain	VERB
ejpam-5936	252	9	largely	largely	ADV
ejpam-5936	252	10	stationary	stationary	ADJ
ejpam-5936	252	11	,	,	PUNCT
ejpam-5936	252	12	with	with	ADP
ejpam-5936	252	13	their	their	PRON
ejpam-5936	252	14	amplitudes	amplitude	NOUN
ejpam-5936	252	15	scaling	scale	VERB
ejpam-5936	252	16	uniformly	uniformly	ADV
ejpam-5936	252	17	as	as	SCONJ
ejpam-5936	252	18	time	time	NOUN
ejpam-5936	252	19	progresses	progress	NOUN
ejpam-5936	252	20	.	.	PUNCT
ejpam-5936	253	1	conversely	conversely	ADV
ejpam-5936	253	2	,	,	PUNCT
ejpam-5936	253	3	the	the	DET
ejpam-5936	253	4	spatial	spatial	ADJ
ejpam-5936	253	5	distributions	distribution	NOUN
ejpam-5936	253	6	captured	capture	VERB
ejpam-5936	253	7	at	at	ADP
ejpam-5936	253	8	single	single	ADJ
ejpam-5936	253	9	moments	moment	NOUN
ejpam-5936	253	10	in	in	ADP
ejpam-5936	253	11	time	time	NOUN
ejpam-5936	253	12	for	for	ADP
ejpam-5936	253	13	u3(x	u3(x	PROPN
ejpam-5936	253	14	,	,	PUNCT
ejpam-5936	253	15	y	y	PROPN
ejpam-5936	253	16	)	)	PUNCT
ejpam-5936	253	17	,	,	PUNCT
ejpam-5936	253	18	u6(x	u6(x	PROPN
ejpam-5936	253	19	,	,	PUNCT
ejpam-5936	253	20	y	y	PROPN
ejpam-5936	253	21	)	)	PUNCT
ejpam-5936	253	22	,	,	PUNCT
ejpam-5936	253	23	u9(x	u9(x	PROPN
ejpam-5936	253	24	,	,	PUNCT
ejpam-5936	253	25	y	y	NOUN
ejpam-5936	253	26	)	)	PUNCT
ejpam-5936	253	27	,	,	PUNCT
ejpam-5936	253	28	and	and	CCONJ
ejpam-5936	253	29	u15(x	u15(x	NOUN
ejpam-5936	253	30	,	,	PUNCT
ejpam-5936	253	31	y	y	NOUN
ejpam-5936	253	32	)	)	PUNCT
ejpam-5936	253	33	reveal	reveal	VERB
ejpam-5936	253	34	intricate	intricate	ADJ
ejpam-5936	253	35	and	and	CCONJ
ejpam-5936	253	36	spatially	spatially	ADV
ejpam-5936	253	37	varying	vary	VERB
ejpam-5936	253	38	amplitudes	amplitude	NOUN
ejpam-5936	253	39	,	,	PUNCT
ejpam-5936	253	40	suggesting	suggest	VERB
ejpam-5936	253	41	intrinsic	intrinsic	ADJ
ejpam-5936	253	42	spatial	spatial	ADJ
ejpam-5936	253	43	frameworks	framework	NOUN
ejpam-5936	253	44	that	that	PRON
ejpam-5936	253	45	could	could	AUX
ejpam-5936	253	46	impact	impact	VERB
ejpam-5936	253	47	the	the	DET
ejpam-5936	253	48	temporal	temporal	ADJ
ejpam-5936	253	49	development	development	NOUN
ejpam-5936	253	50	of	of	ADP
ejpam-5936	253	51	the	the	DET
ejpam-5936	253	52	complete	complete	ADJ
ejpam-5936	253	53	solutions	solution	NOUN
ejpam-5936	253	54	.	.	PUNCT
ejpam-5936	254	1	notably	notably	ADV
ejpam-5936	254	2	,	,	PUNCT
ejpam-5936	254	3	the	the	DET
ejpam-5936	254	4	snapshot	snapshot	NOUN
ejpam-5936	254	5	of	of	ADP
ejpam-5936	254	6	u12(x	u12(x	PROPN
ejpam-5936	254	7	,	,	PUNCT
ejpam-5936	254	8	y	y	PROPN
ejpam-5936	254	9	)	)	PUNCT
ejpam-5936	254	10	at	at	ADP
ejpam-5936	254	11	a	a	DET
ejpam-5936	254	12	particular	particular	ADJ
ejpam-5936	254	13	time	time	NOUN
ejpam-5936	254	14	point	point	NOUN
ejpam-5936	254	15	shows	show	VERB
ejpam-5936	254	16	a	a	DET
ejpam-5936	254	17	highly	highly	ADV
ejpam-5936	254	18	concentrated	concentrated	ADJ
ejpam-5936	254	19	and	and	CCONJ
ejpam-5936	254	20	potentially	potentially	ADV
ejpam-5936	254	21	problematic	problematic	ADJ
ejpam-5936	254	22	behavior	behavior	NOUN
ejpam-5936	254	23	near	near	ADP
ejpam-5936	254	24	the	the	DET
ejpam-5936	254	25	center	center	NOUN
ejpam-5936	254	26	.	.	PUNCT
ejpam-5936	255	1	lastly	lastly	ADV
ejpam-5936	255	2	,	,	PUNCT
ejpam-5936	255	3	the	the	DET
ejpam-5936	255	4	behaviors	behavior	NOUN
ejpam-5936	255	5	depicted	depict	VERB
ejpam-5936	255	6	in	in	ADP
ejpam-5936	255	7	u10(x	u10(x	NOUN
ejpam-5936	255	8	,	,	PUNCT
ejpam-5936	255	9	t	t	PROPN
ejpam-5936	255	10	)	)	PUNCT
ejpam-5936	255	11	,	,	PUNCT
ejpam-5936	255	12	u13(x	u13(x	PROPN
ejpam-5936	255	13	,	,	PUNCT
ejpam-5936	255	14	t	t	PROPN
ejpam-5936	255	15	)	)	PUNCT
ejpam-5936	255	16	,	,	PUNCT
ejpam-5936	255	17	and	and	CCONJ
ejpam-5936	255	18	u14(y	u14(y	PROPN
ejpam-5936	255	19	,	,	PUNCT
ejpam-5936	255	20	t	t	PROPN
ejpam-5936	255	21	)	)	PUNCT
ejpam-5936	255	22	demonstrate	demonstrate	VERB
ejpam-5936	255	23	a	a	DET
ejpam-5936	255	24	more	more	ADV
ejpam-5936	255	25	complex	complex	ADJ
ejpam-5936	255	26	interaction	interaction	NOUN
ejpam-5936	255	27	between	between	ADP
ejpam-5936	255	28	temporal	temporal	ADJ
ejpam-5936	255	29	growth	growth	NOUN
ejpam-5936	255	30	and	and	CCONJ
ejpam-5936	255	31	specific	specific	ADJ
ejpam-5936	255	32	spatial	spatial	ADJ
ejpam-5936	255	33	curvatures	curvature	NOUN
ejpam-5936	255	34	,	,	PUNCT
ejpam-5936	255	35	indicating	indicate	VERB
ejpam-5936	255	36	an	an	DET
ejpam-5936	255	37	amplification	amplification	NOUN
ejpam-5936	255	38	that	that	PRON
ejpam-5936	255	39	differs	differ	VERB
ejpam-5936	255	40	depending	depend	VERB
ejpam-5936	255	41	on	on	ADP
ejpam-5936	255	42	location	location	NOUN
ejpam-5936	255	43	rather	rather	ADV
ejpam-5936	255	44	than	than	ADP
ejpam-5936	255	45	straightforward	straightforward	ADJ
ejpam-5936	255	46	wave	wave	NOUN
ejpam-5936	255	47	propagation	propagation	NOUN
ejpam-5936	255	48	.	.	PUNCT
ejpam-5936	256	1	in	in	ADP
ejpam-5936	256	2	summary	summary	NOUN
ejpam-5936	256	3	,	,	PUNCT
ejpam-5936	256	4	the	the	DET
ejpam-5936	256	5	analysis	analysis	NOUN
ejpam-5936	256	6	underscores	underscore	VERB
ejpam-5936	256	7	a	a	DET
ejpam-5936	256	8	spectrum	spectrum	NOUN
ejpam-5936	256	9	of	of	ADP
ejpam-5936	256	10	solution	solution	NOUN
ejpam-5936	256	11	behaviors	behavior	NOUN
ejpam-5936	256	12	,	,	PUNCT
ejpam-5936	256	13	ranging	range	VERB
ejpam-5936	256	14	from	from	ADP
ejpam-5936	256	15	predominant	predominant	ADJ
ejpam-5936	256	16	temporal	temporal	ADJ
ejpam-5936	256	17	growth	growth	NOUN
ejpam-5936	256	18	to	to	ADP
ejpam-5936	256	19	intricate	intricate	ADJ
ejpam-5936	256	20	static	static	ADJ
ejpam-5936	256	21	spatial	spatial	ADJ
ejpam-5936	256	22	configurations	configuration	NOUN
ejpam-5936	256	23	and	and	CCONJ
ejpam-5936	256	24	dynamic	dynamic	ADJ
ejpam-5936	256	25	evolutions	evolution	NOUN
ejpam-5936	256	26	in	in	ADP
ejpam-5936	256	27	both	both	DET
ejpam-5936	256	28	space	space	NOUN
ejpam-5936	256	29	and	and	CCONJ
ejpam-5936	256	30	time	time	NOUN
ejpam-5936	256	31	,	,	PUNCT
ejpam-5936	256	32	emphasizing	emphasize	VERB
ejpam-5936	256	33	the	the	DET
ejpam-5936	256	34	crucial	crucial	ADJ
ejpam-5936	256	35	role	role	NOUN
ejpam-5936	256	36	of	of	ADP
ejpam-5936	256	37	parameter	parameter	NOUN
ejpam-5936	256	38	selection	selection	NOUN
ejpam-5936	256	39	and	and	CCONJ
ejpam-5936	256	40	variable	variable	ADJ
ejpam-5936	256	41	fixation	fixation	NOUN
ejpam-5936	256	42	.	.	PUNCT
ejpam-5936	257	1	further	further	ADJ
ejpam-5936	257	2	exploration	exploration	NOUN
ejpam-5936	257	3	of	of	ADP
ejpam-5936	257	4	the	the	DET
ejpam-5936	257	5	fundamental	fundamental	ADJ
ejpam-5936	257	6	mathematical	mathematical	ADJ
ejpam-5936	257	7	forms	form	NOUN
ejpam-5936	257	8	is	be	AUX
ejpam-5936	257	9	necessary	necessary	ADJ
ejpam-5936	257	10	to	to	PART
ejpam-5936	257	11	comprehensively	comprehensively	ADV
ejpam-5936	257	12	categorize	categorize	VERB
ejpam-5936	257	13	and	and	CCONJ
ejpam-5936	257	14	elucidate	elucidate	VERB
ejpam-5936	257	15	the	the	DET
ejpam-5936	257	16	potential	potential	NOUN
ejpam-5936	257	17	for	for	ADP
ejpam-5936	257	18	wave	wave	NOUN
ejpam-5936	257	19	-	-	PUNCT
ejpam-5936	257	20	like	like	ADJ
ejpam-5936	257	21	characteristics	characteristic	NOUN
ejpam-5936	257	22	within	within	ADP
ejpam-5936	257	23	these	these	DET
ejpam-5936	257	24	solution	solution	NOUN
ejpam-5936	257	25	sets	set	NOUN
ejpam-5936	257	26	.	.	PUNCT
ejpam-5936	258	1	5	5	X
ejpam-5936	258	2	.	.	X
ejpam-5936	258	3	conclusions	conclusion	NOUN
ejpam-5936	258	4	this	this	DET
ejpam-5936	258	5	study	study	NOUN
ejpam-5936	258	6	successfully	successfully	ADV
ejpam-5936	258	7	derived	derive	VERB
ejpam-5936	258	8	novel	novel	ADJ
ejpam-5936	258	9	exact	exact	ADJ
ejpam-5936	258	10	solutions	solution	NOUN
ejpam-5936	258	11	for	for	ADP
ejpam-5936	258	12	a	a	DET
ejpam-5936	258	13	nonlinear	nonlinear	ADJ
ejpam-5936	258	14	biological	biological	ADJ
ejpam-5936	258	15	population	population	NOUN
ejpam-5936	258	16	model	model	NOUN
ejpam-5936	258	17	using	use	VERB
ejpam-5936	258	18	the	the	DET
ejpam-5936	258	19	power	power	NOUN
ejpam-5936	258	20	index	index	NOUN
ejpam-5936	258	21	method	method	NOUN
ejpam-5936	258	22	(	(	PUNCT
ejpam-5936	258	23	pim	pim	PROPN
ejpam-5936	258	24	)	)	PUNCT
ejpam-5936	258	25	,	,	PUNCT
ejpam-5936	258	26	demonstrating	demonstrate	VERB
ejpam-5936	258	27	its	its	PRON
ejpam-5936	258	28	effectiveness	effectiveness	NOUN
ejpam-5936	258	29	for	for	ADP
ejpam-5936	258	30	degenerate	degenerate	ADJ
ejpam-5936	258	31	parabolic	parabolic	ADJ
ejpam-5936	258	32	equations	equation	NOUN
ejpam-5936	258	33	with	with	ADP
ejpam-5936	258	34	power	power	NOUN
ejpam-5936	258	35	-	-	PUNCT
ejpam-5936	258	36	law	law	NOUN
ejpam-5936	258	37	nonlinearities	nonlinearitie	NOUN
ejpam-5936	258	38	.	.	PUNCT
ejpam-5936	259	1	the	the	DET
ejpam-5936	259	2	closed	close	VERB
ejpam-5936	259	3	-	-	PUNCT
ejpam-5936	259	4	form	form	NOUN
ejpam-5936	259	5	solutions	solution	NOUN
ejpam-5936	259	6	provide	provide	VERB
ejpam-5936	259	7	explicit	explicit	ADJ
ejpam-5936	259	8	descriptions	description	NOUN
ejpam-5936	259	9	of	of	ADP
ejpam-5936	259	10	population	population	NOUN
ejpam-5936	259	11	density	density	NOUN
ejpam-5936	259	12	dynamics	dynamic	NOUN
ejpam-5936	259	13	,	,	PUNCT
ejpam-5936	259	14	capturing	capture	VERB
ejpam-5936	259	15	essential	essential	ADJ
ejpam-5936	259	16	features	feature	NOUN
ejpam-5936	259	17	like	like	ADP
ejpam-5936	259	18	finite	finite	ADJ
ejpam-5936	259	19	-	-	ADJ
ejpam-5936	259	20	speed	speed	NOUN
ejpam-5936	259	21	propagation	propagation	NOUN
ejpam-5936	259	22	and	and	CCONJ
ejpam-5936	259	23	density	density	NOUN
ejpam-5936	259	24	-	-	PUNCT
ejpam-5936	259	25	dependent	dependent	ADJ
ejpam-5936	259	26	dispersal	dispersal	NOUN
ejpam-5936	259	27	.	.	PUNCT
ejpam-5936	260	1	graphical	graphical	ADJ
ejpam-5936	260	2	analysis	analysis	NOUN
ejpam-5936	260	3	of	of	ADP
ejpam-5936	260	4	these	these	DET
ejpam-5936	260	5	solutions	solution	NOUN
ejpam-5936	260	6	(	(	PUNCT
ejpam-5936	260	7	figures	figure	NOUN
ejpam-5936	260	8	1	1	NUM
ejpam-5936	260	9	-	-	SYM
ejpam-5936	260	10	15	15	NUM
ejpam-5936	260	11	)	)	PUNCT
ejpam-5936	260	12	revealed	reveal	VERB
ejpam-5936	260	13	distinct	distinct	ADJ
ejpam-5936	260	14	spatial	spatial	ADJ
ejpam-5936	260	15	-	-	PUNCT
ejpam-5936	260	16	temporal	temporal	ADJ
ejpam-5936	260	17	patterns	pattern	NOUN
ejpam-5936	260	18	,	,	PUNCT
ejpam-5936	260	19	offering	offer	VERB
ejpam-5936	260	20	valuable	valuable	ADJ
ejpam-5936	260	21	insights	insight	NOUN
ejpam-5936	260	22	into	into	ADP
ejpam-5936	260	23	how	how	SCONJ
ejpam-5936	260	24	nonlinear	nonlinear	ADJ
ejpam-5936	260	25	diffusion	diffusion	NOUN
ejpam-5936	260	26	interacts	interact	VERB
ejpam-5936	260	27	with	with	ADP
ejpam-5936	260	28	population	population	NOUN
ejpam-5936	260	29	growth	growth	NOUN
ejpam-5936	260	30	processes	process	NOUN
ejpam-5936	260	31	.	.	PUNCT
ejpam-5936	261	1	compared	compare	VERB
ejpam-5936	261	2	to	to	ADP
ejpam-5936	261	3	numerical	numerical	ADJ
ejpam-5936	261	4	or	or	CCONJ
ejpam-5936	261	5	perturbation	perturbation	NOUN
ejpam-5936	261	6	approaches	approach	NOUN
ejpam-5936	261	7	,	,	PUNCT
ejpam-5936	261	8	the	the	DET
ejpam-5936	261	9	pim	pim	PROPN
ejpam-5936	261	10	’s	’s	PART
ejpam-5936	261	11	strength	strength	NOUN
ejpam-5936	261	12	lies	lie	VERB
ejpam-5936	261	13	in	in	ADP
ejpam-5936	261	14	delivering	deliver	VERB
ejpam-5936	261	15	exact	exact	ADJ
ejpam-5936	261	16	analytical	analytical	ADJ
ejpam-5936	261	17	solutions	solution	NOUN
ejpam-5936	261	18	while	while	SCONJ
ejpam-5936	261	19	preserving	preserve	VERB
ejpam-5936	261	20	the	the	DET
ejpam-5936	261	21	system	system	NOUN
ejpam-5936	261	22	’s	’s	PART
ejpam-5936	261	23	inherent	inherent	ADJ
ejpam-5936	261	24	scaling	scale	VERB
ejpam-5936	261	25	properties	property	NOUN
ejpam-5936	261	26	.	.	PUNCT
ejpam-5936	262	1	while	while	SCONJ
ejpam-5936	262	2	the	the	DET
ejpam-5936	262	3	pim	pim	PROPN
ejpam-5936	262	4	proves	prove	VERB
ejpam-5936	262	5	powerful	powerful	ADJ
ejpam-5936	262	6	for	for	ADP
ejpam-5936	262	7	autonomous	autonomous	ADJ
ejpam-5936	262	8	equations	equation	NOUN
ejpam-5936	262	9	with	with	ADP
ejpam-5936	262	10	specific	specific	ADJ
ejpam-5936	262	11	nonlinearities	nonlinearitie	NOUN
ejpam-5936	262	12	,	,	PUNCT
ejpam-5936	262	13	its	its	PRON
ejpam-5936	262	14	limitations	limitation	NOUN
ejpam-5936	262	15	motivate	motivate	VERB
ejpam-5936	262	16	important	important	ADJ
ejpam-5936	262	17	future	future	ADJ
ejpam-5936	262	18	research	research	NOUN
ejpam-5936	262	19	directions	direction	NOUN
ejpam-5936	262	20	.	.	PUNCT
ejpam-5936	263	1	the	the	DET
ejpam-5936	263	2	method	method	NOUN
ejpam-5936	263	3	can	can	AUX
ejpam-5936	263	4	not	not	PART
ejpam-5936	263	5	currently	currently	ADV
ejpam-5936	263	6	handle	handle	VERB
ejpam-5936	263	7	non	non	ADJ
ejpam-5936	263	8	-	-	ADJ
ejpam-5936	263	9	autonomous	autonomous	ADJ
ejpam-5936	263	10	systems	system	NOUN
ejpam-5936	263	11	or	or	CCONJ
ejpam-5936	263	12	fully	fully	ADV
ejpam-5936	263	13	nonlinear	nonlinear	ADJ
ejpam-5936	263	14	polynomial	polynomial	ADJ
ejpam-5936	263	15	equations	equation	NOUN
ejpam-5936	263	16	,	,	PUNCT
ejpam-5936	263	17	suggesting	suggest	VERB
ejpam-5936	263	18	the	the	DET
ejpam-5936	263	19	need	need	NOUN
ejpam-5936	263	20	for	for	ADP
ejpam-5936	263	21	hybrid	hybrid	ADJ
ejpam-5936	263	22	analytical	analytical	ADJ
ejpam-5936	263	23	-	-	PUNCT
ejpam-5936	263	24	numerical	numerical	ADJ
ejpam-5936	263	25	approaches	approach	NOUN
ejpam-5936	263	26	.	.	PUNCT
ejpam-5936	264	1	further	further	ADJ
ejpam-5936	264	2	work	work	NOUN
ejpam-5936	264	3	should	should	AUX
ejpam-5936	264	4	focus	focus	VERB
ejpam-5936	264	5	on	on	ADP
ejpam-5936	264	6	empirical	empirical	ADJ
ejpam-5936	264	7	validation	validation	NOUN
ejpam-5936	264	8	against	against	ADP
ejpam-5936	264	9	ecological	ecological	ADJ
ejpam-5936	264	10	data	datum	NOUN
ejpam-5936	264	11	,	,	PUNCT
ejpam-5936	264	12	extensions	extension	NOUN
ejpam-5936	264	13	to	to	ADP
ejpam-5936	264	14	multi	multi	ADJ
ejpam-5936	264	15	-	-	ADJ
ejpam-5936	264	16	species	species	ADJ
ejpam-5936	264	17	interactions	interaction	NOUN
ejpam-5936	264	18	,	,	PUNCT
ejpam-5936	264	19	and	and	CCONJ
ejpam-5936	264	20	adaptations	adaptation	NOUN
ejpam-5936	264	21	for	for	ADP
ejpam-5936	264	22	stochastic	stochastic	ADJ
ejpam-5936	264	23	environments	environment	NOUN
ejpam-5936	264	24	.	.	PUNCT
ejpam-5936	265	1	these	these	DET
ejpam-5936	265	2	advancements	advancement	NOUN
ejpam-5936	265	3	would	would	AUX
ejpam-5936	265	4	strengthen	strengthen	VERB
ejpam-5936	265	5	the	the	DET
ejpam-5936	265	6	method	method	NOUN
ejpam-5936	265	7	’s	’s	PART
ejpam-5936	265	8	practical	practical	ADJ
ejpam-5936	265	9	utility	utility	NOUN
ejpam-5936	265	10	while	while	SCONJ
ejpam-5936	265	11	maintaining	maintain	VERB
ejpam-5936	265	12	its	its	PRON
ejpam-5936	265	13	mathematical	mathematical	ADJ
ejpam-5936	265	14	rigor	rigor	NOUN
ejpam-5936	265	15	,	,	PUNCT
ejpam-5936	265	16	potentially	potentially	ADV
ejpam-5936	265	17	expanding	expand	VERB
ejpam-5936	265	18	its	its	PRON
ejpam-5936	265	19	applications	application	NOUN
ejpam-5936	265	20	to	to	ADP
ejpam-5936	265	21	other	other	ADJ
ejpam-5936	265	22	biological	biological	ADJ
ejpam-5936	265	23	and	and	CCONJ
ejpam-5936	265	24	physical	physical	ADJ
ejpam-5936	265	25	systems	system	NOUN
ejpam-5936	265	26	governed	govern	VERB
ejpam-5936	265	27	by	by	ADP
ejpam-5936	265	28	nonlinear	nonlinear	ADJ
ejpam-5936	265	29	diffusion	diffusion	NOUN
ejpam-5936	265	30	processes	process	NOUN
ejpam-5936	265	31	.	.	PUNCT
ejpam-5936	266	1	the	the	DET
ejpam-5936	266	2	power	power	NOUN
ejpam-5936	266	3	index	index	NOUN
ejpam-5936	266	4	method	method	NOUN
ejpam-5936	266	5	has	have	AUX
ejpam-5936	266	6	proven	prove	VERB
ejpam-5936	266	7	to	to	PART
ejpam-5936	266	8	be	be	AUX
ejpam-5936	266	9	an	an	DET
ejpam-5936	266	10	effective	effective	ADJ
ejpam-5936	266	11	analytical	analytical	ADJ
ejpam-5936	266	12	tool	tool	NOUN
ejpam-5936	266	13	for	for	ADP
ejpam-5936	266	14	deriving	derive	VERB
ejpam-5936	266	15	novel	novel	ADJ
ejpam-5936	266	16	exact	exact	ADJ
ejpam-5936	266	17	solutions	solution	NOUN
ejpam-5936	266	18	to	to	ADP
ejpam-5936	266	19	biological	biological	ADJ
ejpam-5936	266	20	population	population	NOUN
ejpam-5936	266	21	models	model	NOUN
ejpam-5936	266	22	,	,	PUNCT
ejpam-5936	266	23	offering	offer	VERB
ejpam-5936	266	24	deeper	deep	ADJ
ejpam-5936	266	25	insights	insight	NOUN
ejpam-5936	266	26	into	into	ADP
ejpam-5936	266	27	the	the	DET
ejpam-5936	266	28	dynamics	dynamic	NOUN
ejpam-5936	266	29	of	of	ADP
ejpam-5936	266	30	species	species	NOUN
ejpam-5936	266	31	interactions	interaction	NOUN
ejpam-5936	266	32	,	,	PUNCT
ejpam-5936	266	33	diffusion	diffusion	NOUN
ejpam-5936	266	34	processes	process	NOUN
ejpam-5936	266	35	,	,	PUNCT
ejpam-5936	266	36	and	and	CCONJ
ejpam-5936	266	37	growth	growth	NOUN
ejpam-5936	266	38	patterns	pattern	NOUN
ejpam-5936	266	39	.	.	PUNCT
ejpam-5936	267	1	by	by	ADP
ejpam-5936	267	2	transforming	transform	VERB
ejpam-5936	267	3	nonlinear	nonlinear	ADJ
ejpam-5936	267	4	z.	z.	PROPN
ejpam-5936	267	5	haider	haider	PROPN
ejpam-5936	267	6	,	,	PUNCT
ejpam-5936	267	7	k.	k.	PROPN
ejpam-5936	267	8	ahmad	ahmad	PROPN
ejpam-5936	267	9	/	/	SYM
ejpam-5936	267	10	eur	eur	PROPN
ejpam-5936	267	11	.	.	PUNCT
ejpam-5936	268	1	j.	j.	PROPN
ejpam-5936	268	2	pure	pure	PROPN
ejpam-5936	268	3	appl	appl	PROPN
ejpam-5936	268	4	.	.	PROPN
ejpam-5936	268	5	math	math	PROPN
ejpam-5936	268	6	,	,	PUNCT
ejpam-5936	268	7	18	18	NUM
ejpam-5936	268	8	(	(	PUNCT
ejpam-5936	268	9	2	2	NUM
ejpam-5936	268	10	)	)	PUNCT
ejpam-5936	268	11	(	(	PUNCT
ejpam-5936	268	12	2025	2025	NUM
ejpam-5936	268	13	)	)	PUNCT
ejpam-5936	268	14	,	,	PUNCT
ejpam-5936	268	15	5936	5936	NUM
ejpam-5936	268	16	16	16	NUM
ejpam-5936	268	17	of	of	ADP
ejpam-5936	268	18	18	18	NUM
ejpam-5936	268	19	partial	partial	ADJ
ejpam-5936	268	20	differential	differential	NOUN
ejpam-5936	268	21	equations	equation	NOUN
ejpam-5936	268	22	(	(	PUNCT
ejpam-5936	268	23	pdes	pde	NOUN
ejpam-5936	268	24	)	)	PUNCT
ejpam-5936	268	25	into	into	ADP
ejpam-5936	268	26	solvable	solvable	ADJ
ejpam-5936	268	27	forms	form	NOUN
ejpam-5936	268	28	,	,	PUNCT
ejpam-5936	268	29	this	this	DET
ejpam-5936	268	30	method	method	NOUN
ejpam-5936	268	31	provides	provide	VERB
ejpam-5936	268	32	closed	closed	ADJ
ejpam-5936	268	33	-	-	PUNCT
ejpam-5936	268	34	form	form	NOUN
ejpam-5936	268	35	solutions	solution	NOUN
ejpam-5936	268	36	that	that	PRON
ejpam-5936	268	37	are	be	AUX
ejpam-5936	268	38	crucial	crucial	ADJ
ejpam-5936	268	39	for	for	ADP
ejpam-5936	268	40	understanding	understand	VERB
ejpam-5936	268	41	complex	complex	ADJ
ejpam-5936	268	42	ecological	ecological	ADJ
ejpam-5936	268	43	behaviors	behavior	NOUN
ejpam-5936	268	44	,	,	PUNCT
ejpam-5936	268	45	such	such	ADJ
ejpam-5936	268	46	as	as	ADP
ejpam-5936	268	47	wave	wave	NOUN
ejpam-5936	268	48	propagation	propagation	NOUN
ejpam-5936	268	49	,	,	PUNCT
ejpam-5936	268	50	spatial	spatial	ADJ
ejpam-5936	268	51	patterning	patterning	NOUN
ejpam-5936	268	52	,	,	PUNCT
ejpam-5936	268	53	and	and	CCONJ
ejpam-5936	268	54	stability	stability	NOUN
ejpam-5936	268	55	regimes	regime	NOUN
ejpam-5936	268	56	.	.	PUNCT
ejpam-5936	269	1	however	however	ADV
ejpam-5936	269	2	,	,	PUNCT
ejpam-5936	269	3	the	the	DET
ejpam-5936	269	4	true	true	ADJ
ejpam-5936	269	5	potential	potential	NOUN
ejpam-5936	269	6	of	of	ADP
ejpam-5936	269	7	this	this	DET
ejpam-5936	269	8	approach	approach	NOUN
ejpam-5936	269	9	extends	extend	VERB
ejpam-5936	269	10	beyond	beyond	ADP
ejpam-5936	269	11	the	the	DET
ejpam-5936	269	12	current	current	ADJ
ejpam-5936	269	13	findings	finding	NOUN
ejpam-5936	269	14	.	.	PUNCT
ejpam-5936	270	1	future	future	ADJ
ejpam-5936	270	2	research	research	NOUN
ejpam-5936	270	3	should	should	AUX
ejpam-5936	270	4	focus	focus	VERB
ejpam-5936	270	5	on	on	ADP
ejpam-5936	270	6	bridging	bridge	VERB
ejpam-5936	270	7	the	the	DET
ejpam-5936	270	8	gap	gap	NOUN
ejpam-5936	270	9	between	between	ADP
ejpam-5936	270	10	theoretical	theoretical	ADJ
ejpam-5936	270	11	solutions	solution	NOUN
ejpam-5936	270	12	and	and	CCONJ
ejpam-5936	270	13	real	real	ADJ
ejpam-5936	270	14	-	-	PUNCT
ejpam-5936	270	15	world	world	NOUN
ejpam-5936	270	16	biological	biological	ADJ
ejpam-5936	270	17	systems	system	NOUN
ejpam-5936	270	18	by	by	ADP
ejpam-5936	270	19	incorporating	incorporate	VERB
ejpam-5936	270	20	data	datum	NOUN
ejpam-5936	270	21	-	-	PUNCT
ejpam-5936	270	22	driven	drive	VERB
ejpam-5936	270	23	parameter	parameter	NOUN
ejpam-5936	270	24	estimation	estimation	NOUN
ejpam-5936	270	25	,	,	PUNCT
ejpam-5936	270	26	stochastic	stochastic	ADJ
ejpam-5936	270	27	influences	influence	NOUN
ejpam-5936	270	28	,	,	PUNCT
ejpam-5936	270	29	and	and	CCONJ
ejpam-5936	270	30	multi	multi	ADJ
ejpam-5936	270	31	-	-	ADJ
ejpam-5936	270	32	scale	scale	ADJ
ejpam-5936	270	33	interactions	interaction	NOUN
ejpam-5936	270	34	.	.	PUNCT
ejpam-5936	271	1	additionally	additionally	ADV
ejpam-5936	271	2	,	,	PUNCT
ejpam-5936	271	3	integrating	integrate	VERB
ejpam-5936	271	4	machine	machine	NOUN
ejpam-5936	271	5	learning	learning	NOUN
ejpam-5936	271	6	and	and	CCONJ
ejpam-5936	271	7	hybrid	hybrid	ADJ
ejpam-5936	271	8	numerical	numerical	ADJ
ejpam-5936	271	9	-	-	PUNCT
ejpam-5936	271	10	analytical	analytical	ADJ
ejpam-5936	271	11	techniques	technique	NOUN
ejpam-5936	271	12	could	could	AUX
ejpam-5936	271	13	further	far	ADV
ejpam-5936	271	14	enhance	enhance	VERB
ejpam-5936	271	15	the	the	DET
ejpam-5936	271	16	method	method	NOUN
ejpam-5936	271	17	’s	’s	PART
ejpam-5936	271	18	efficiency	efficiency	NOUN
ejpam-5936	271	19	in	in	ADP
ejpam-5936	271	20	handling	handle	VERB
ejpam-5936	271	21	more	more	ADJ
ejpam-5936	271	22	intricate	intricate	ADJ
ejpam-5936	271	23	models	model	NOUN
ejpam-5936	271	24	,	,	PUNCT
ejpam-5936	271	25	such	such	ADJ
ejpam-5936	271	26	as	as	ADP
ejpam-5936	271	27	those	those	PRON
ejpam-5936	271	28	involving	involve	VERB
ejpam-5936	271	29	cross	cross	NOUN
ejpam-5936	271	30	-	-	NOUN
ejpam-5936	271	31	diffusion	diffusion	NOUN
ejpam-5936	271	32	,	,	PUNCT
ejpam-5936	271	33	fractional	fractional	ADJ
ejpam-5936	271	34	dynamics	dynamic	NOUN
ejpam-5936	271	35	,	,	PUNCT
ejpam-5936	271	36	or	or	CCONJ
ejpam-5936	271	37	time	time	NOUN
ejpam-5936	271	38	-	-	PUNCT
ejpam-5936	271	39	dependent	dependent	ADJ
ejpam-5936	271	40	environmental	environmental	ADJ
ejpam-5936	271	41	factors	factor	NOUN
ejpam-5936	271	42	.	.	PUNCT
ejpam-5936	272	1	moreover	moreover	ADV
ejpam-5936	272	2	,	,	PUNCT
ejpam-5936	272	3	the	the	DET
ejpam-5936	272	4	mathematical	mathematical	ADJ
ejpam-5936	272	5	rigor	rigor	NOUN
ejpam-5936	272	6	of	of	ADP
ejpam-5936	272	7	the	the	DET
ejpam-5936	272	8	power	power	NOUN
ejpam-5936	272	9	index	index	NOUN
ejpam-5936	272	10	method	method	NOUN
ejpam-5936	272	11	should	should	AUX
ejpam-5936	272	12	be	be	AUX
ejpam-5936	272	13	complemented	complement	VERB
ejpam-5936	272	14	by	by	ADP
ejpam-5936	272	15	dynamical	dynamical	ADJ
ejpam-5936	272	16	systems	system	NOUN
ejpam-5936	272	17	analysis	analysis	NOUN
ejpam-5936	272	18	,	,	PUNCT
ejpam-5936	272	19	including	include	VERB
ejpam-5936	272	20	stability	stability	NOUN
ejpam-5936	272	21	studies	study	NOUN
ejpam-5936	272	22	,	,	PUNCT
ejpam-5936	272	23	bifurcation	bifurcation	NOUN
ejpam-5936	272	24	theory	theory	NOUN
ejpam-5936	272	25	,	,	PUNCT
ejpam-5936	272	26	and	and	CCONJ
ejpam-5936	272	27	phase	phase	NOUN
ejpam-5936	272	28	-	-	PUNCT
ejpam-5936	272	29	space	space	NOUN
ejpam-5936	272	30	exploration	exploration	NOUN
ejpam-5936	272	31	,	,	PUNCT
ejpam-5936	272	32	to	to	PART
ejpam-5936	272	33	ensure	ensure	VERB
ejpam-5936	272	34	that	that	SCONJ
ejpam-5936	272	35	the	the	DET
ejpam-5936	272	36	derived	derive	VERB
ejpam-5936	272	37	solutions	solution	NOUN
ejpam-5936	272	38	are	be	AUX
ejpam-5936	272	39	not	not	PART
ejpam-5936	272	40	only	only	ADV
ejpam-5936	272	41	exact	exact	ADJ
ejpam-5936	272	42	but	but	CCONJ
ejpam-5936	272	43	also	also	ADV
ejpam-5936	272	44	biologically	biologically	ADV
ejpam-5936	272	45	meaningful	meaningful	ADJ
ejpam-5936	272	46	.	.	PUNCT
ejpam-5936	273	1	collaboration	collaboration	NOUN
ejpam-5936	273	2	between	between	ADP
ejpam-5936	273	3	mathematicians	mathematician	NOUN
ejpam-5936	273	4	,	,	PUNCT
ejpam-5936	273	5	ecologists	ecologist	NOUN
ejpam-5936	273	6	,	,	PUNCT
ejpam-5936	273	7	and	and	CCONJ
ejpam-5936	273	8	computational	computational	ADJ
ejpam-5936	273	9	scientists	scientist	NOUN
ejpam-5936	273	10	will	will	AUX
ejpam-5936	273	11	be	be	AUX
ejpam-5936	273	12	key	key	ADJ
ejpam-5936	273	13	in	in	ADP
ejpam-5936	273	14	validating	validate	VERB
ejpam-5936	273	15	these	these	DET
ejpam-5936	273	16	solutions	solution	NOUN
ejpam-5936	273	17	against	against	ADP
ejpam-5936	273	18	experimental	experimental	ADJ
ejpam-5936	273	19	and	and	CCONJ
ejpam-5936	273	20	field	field	NOUN
ejpam-5936	273	21	data	datum	NOUN
ejpam-5936	273	22	,	,	PUNCT
ejpam-5936	273	23	ensuring	ensure	VERB
ejpam-5936	273	24	their	their	PRON
ejpam-5936	273	25	applicability	applicability	NOUN
ejpam-5936	273	26	.	.	PUNCT
ejpam-5936	274	1	acknowledgements	acknowledgement	NOUN
ejpam-5936	274	2	the	the	DET
ejpam-5936	274	3	authors	author	NOUN
ejpam-5936	274	4	zeshan	zeshan	PROPN
ejpam-5936	274	5	haider	haider	PROPN
ejpam-5936	274	6	and	and	CCONJ
ejpam-5936	274	7	dr	dr	PROPN
ejpam-5936	274	8	.	.	PROPN
ejpam-5936	274	9	khalil	khalil	PROPN
ejpam-5936	274	10	ahmad	ahmad	PROPN
ejpam-5936	274	11	would	would	AUX
ejpam-5936	274	12	like	like	VERB
ejpam-5936	274	13	to	to	PART
ejpam-5936	274	14	thankful	thankful	VERB
ejpam-5936	274	15	the	the	DET
ejpam-5936	274	16	air	air	NOUN
ejpam-5936	274	17	marshal	marshal	NOUN
ejpam-5936	274	18	abdul	abdul	PROPN
ejpam-5936	274	19	moeed	moeed	PROPN
ejpam-5936	274	20	khan	khan	PROPN
ejpam-5936	274	21	,	,	PUNCT
ejpam-5936	274	22	hi(m	hi(m	NOUN
ejpam-5936	274	23	)	)	PUNCT
ejpam-5936	274	24	,	,	PUNCT
ejpam-5936	274	25	vice	vice	NOUN
ejpam-5936	274	26	chancellor	chancellor	NOUN
ejpam-5936	274	27	,	,	PUNCT
ejpam-5936	274	28	air	air	NOUN
ejpam-5936	274	29	university	university	PROPN
ejpam-5936	274	30	,	,	PUNCT
ejpam-5936	274	31	islamabad	islamabad	PROPN
ejpam-5936	274	32	,	,	PUNCT
ejpam-5936	274	33	pakistan	pakistan	PROPN
ejpam-5936	274	34	.	.	PUNCT
ejpam-5936	275	1	competing	compete	VERB
ejpam-5936	275	2	interests	interest	NOUN
ejpam-5936	275	3	the	the	DET
ejpam-5936	275	4	authors	author	NOUN
ejpam-5936	275	5	declare	declare	VERB
ejpam-5936	275	6	that	that	SCONJ
ejpam-5936	275	7	they	they	PRON
ejpam-5936	275	8	have	have	VERB
ejpam-5936	275	9	no	no	DET
ejpam-5936	275	10	competing	compete	VERB
ejpam-5936	275	11	interests	interest	NOUN
ejpam-5936	275	12	.	.	PUNCT
ejpam-5936	276	1	data	datum	NOUN
ejpam-5936	276	2	availability	availability	NOUN
ejpam-5936	276	3	statement	statement	NOUN
ejpam-5936	276	4	please	please	INTJ
ejpam-5936	276	5	contact	contact	VERB
ejpam-5936	276	6	the	the	DET
ejpam-5936	276	7	authors	author	NOUN
ejpam-5936	276	8	for	for	ADP
ejpam-5936	276	9	data	datum	NOUN
ejpam-5936	276	10	requests	request	NOUN
ejpam-5936	276	11	.	.	PUNCT
ejpam-5936	277	1	references	reference	NOUN
ejpam-5936	277	2	[	[	X
ejpam-5936	277	3	1	1	NUM
ejpam-5936	277	4	]	]	PUNCT
ejpam-5936	277	5	k.	k.	PROPN
ejpam-5936	277	6	j.	j.	PROPN
ejpam-5936	277	7	wang	wang	PROPN
ejpam-5936	277	8	,	,	PUNCT
ejpam-5936	277	9	g.	g.	PROPN
ejpam-5936	277	10	d.	d.	PROPN
ejpam-5936	277	11	wang	wang	PROPN
ejpam-5936	277	12	,	,	PUNCT
ejpam-5936	277	13	and	and	CCONJ
ejpam-5936	277	14	h.	h.	PROPN
ejpam-5936	277	15	w.	w.	PROPN
ejpam-5936	277	16	zhu	zhu	PROPN
ejpam-5936	277	17	,	,	PUNCT
ejpam-5936	277	18	a	a	DET
ejpam-5936	277	19	new	new	ADJ
ejpam-5936	277	20	perspective	perspective	NOUN
ejpam-5936	277	21	on	on	ADP
ejpam-5936	277	22	the	the	DET
ejpam-5936	277	23	study	study	NOUN
ejpam-5936	277	24	of	of	ADP
ejpam-5936	277	25	the	the	DET
ejpam-5936	277	26	fractal	fractal	ADJ
ejpam-5936	277	27	coupled	couple	VERB
ejpam-5936	277	28	boussinesq	boussinesq	ADJ
ejpam-5936	277	29	–	–	PUNCT
ejpam-5936	277	30	burger	burger	NOUN
ejpam-5936	277	31	equation	equation	NOUN
ejpam-5936	277	32	in	in	ADP
ejpam-5936	277	33	shallow	shallow	ADJ
ejpam-5936	277	34	water	water	NOUN
ejpam-5936	277	35	,	,	PUNCT
ejpam-5936	277	36	fractals	fractal	VERB
ejpam-5936	277	37	29	29	NUM
ejpam-5936	277	38	(	(	PUNCT
ejpam-5936	277	39	05	05	NUM
ejpam-5936	277	40	)	)	PUNCT
ejpam-5936	277	41	(	(	PUNCT
ejpam-5936	277	42	2021	2021	NUM
ejpam-5936	277	43	)	)	PUNCT
ejpam-5936	277	44	,	,	PUNCT
ejpam-5936	277	45	2150122	2150122	NUM
ejpam-5936	277	46	.	.	PUNCT
ejpam-5936	278	1	[	[	X
ejpam-5936	278	2	2	2	NUM
ejpam-5936	278	3	]	]	PUNCT
ejpam-5936	278	4	m.	m.	NOUN
ejpam-5936	278	5	sohail	sohail	PROPN
ejpam-5936	278	6	,	,	PUNCT
ejpam-5936	278	7	y.	y.	PROPN
ejpam-5936	278	8	m.	m.	PROPN
ejpam-5936	278	9	chu	chu	PROPN
ejpam-5936	278	10	,	,	PUNCT
ejpam-5936	278	11	e.	e.	PROPN
ejpam-5936	278	12	r.	r.	PROPN
ejpam-5936	278	13	el	el	PROPN
ejpam-5936	278	14	-	-	PUNCT
ejpam-5936	278	15	zahar	zahar	PROPN
ejpam-5936	278	16	,	,	PUNCT
ejpam-5936	278	17	u.	u.	PROPN
ejpam-5936	278	18	nazir	nazir	PROPN
ejpam-5936	278	19	,	,	PUNCT
ejpam-5936	278	20	and	and	CCONJ
ejpam-5936	278	21	t.	t.	PROPN
ejpam-5936	278	22	naseem	naseem	PROPN
ejpam-5936	278	23	,	,	PUNCT
ejpam-5936	278	24	contribution	contribution	NOUN
ejpam-5936	278	25	of	of	ADP
ejpam-5936	278	26	joule	joule	NOUN
ejpam-5936	278	27	heating	heating	NOUN
ejpam-5936	278	28	and	and	CCONJ
ejpam-5936	278	29	viscous	viscous	ADJ
ejpam-5936	278	30	dissipation	dissipation	NOUN
ejpam-5936	278	31	on	on	ADP
ejpam-5936	278	32	three	three	NUM
ejpam-5936	278	33	dimensional	dimensional	ADJ
ejpam-5936	278	34	flow	flow	NOUN
ejpam-5936	278	35	of	of	ADP
ejpam-5936	278	36	casson	casson	PROPN
ejpam-5936	278	37	model	model	NOUN
ejpam-5936	278	38	comprising	comprise	VERB
ejpam-5936	278	39	temperature	temperature	NOUN
ejpam-5936	278	40	dependent	dependent	ADJ
ejpam-5936	278	41	conductance	conductance	NOUN
ejpam-5936	278	42	utilizing	utilize	VERB
ejpam-5936	278	43	shooting	shooting	NOUN
ejpam-5936	278	44	method	method	NOUN
ejpam-5936	278	45	,	,	PUNCT
ejpam-5936	278	46	physica	physica	NOUN
ejpam-5936	278	47	scripta	scripta	NOUN
ejpam-5936	278	48	96	96	NUM
ejpam-5936	278	49	(	(	PUNCT
ejpam-5936	278	50	8)	8)	NUM
ejpam-5936	278	51	(	(	PUNCT
ejpam-5936	278	52	2021	2021	NUM
ejpam-5936	278	53	)	)	PUNCT
ejpam-5936	278	54	,	,	PUNCT
ejpam-5936	278	55	085208	085208	NUM
ejpam-5936	278	56	.	.	PUNCT
ejpam-5936	279	1	[	[	X
ejpam-5936	279	2	3	3	X
ejpam-5936	279	3	]	]	PUNCT
ejpam-5936	279	4	k.	k.	PROPN
ejpam-5936	279	5	j.	j.	PROPN
ejpam-5936	279	6	wang	wang	PROPN
ejpam-5936	279	7	and	and	CCONJ
ejpam-5936	279	8	g.	g.	PROPN
ejpam-5936	279	9	d.	d.	PROPN
ejpam-5936	279	10	wang	wang	PROPN
ejpam-5936	279	11	,	,	PUNCT
ejpam-5936	279	12	variational	variational	ADJ
ejpam-5936	279	13	principle	principle	NOUN
ejpam-5936	279	14	,	,	PUNCT
ejpam-5936	279	15	solitary	solitary	ADJ
ejpam-5936	279	16	and	and	CCONJ
ejpam-5936	279	17	periodic	periodic	ADJ
ejpam-5936	279	18	wave	wave	NOUN
ejpam-5936	279	19	solutions	solution	NOUN
ejpam-5936	279	20	of	of	ADP
ejpam-5936	279	21	the	the	DET
ejpam-5936	279	22	fractal	fractal	ADJ
ejpam-5936	279	23	modified	modify	VERB
ejpam-5936	279	24	equal	equal	ADJ
ejpam-5936	279	25	width	width	ADJ
ejpam-5936	279	26	equation	equation	NOUN
ejpam-5936	279	27	in	in	ADP
ejpam-5936	279	28	plasma	plasma	NOUN
ejpam-5936	279	29	physics	physic	NOUN
ejpam-5936	279	30	,	,	PUNCT
ejpam-5936	279	31	fractals	fractal	VERB
ejpam-5936	279	32	29	29	NUM
ejpam-5936	279	33	(	(	PUNCT
ejpam-5936	279	34	05	05	NUM
ejpam-5936	279	35	)	)	PUNCT
ejpam-5936	279	36	(	(	PUNCT
ejpam-5936	279	37	2021	2021	NUM
ejpam-5936	279	38	)	)	PUNCT
ejpam-5936	279	39	,	,	PUNCT
ejpam-5936	279	40	2150115	2150115	NUM
ejpam-5936	279	41	.	.	PUNCT
ejpam-5936	280	1	[	[	X
ejpam-5936	280	2	4	4	X
ejpam-5936	280	3	]	]	PUNCT
ejpam-5936	280	4	k.	k.	PROPN
ejpam-5936	280	5	k.	k.	PROPN
ejpam-5936	280	6	ali	ali	PROPN
ejpam-5936	280	7	,	,	PUNCT
ejpam-5936	280	8	r.	r.	PROPN
ejpam-5936	280	9	yilmazer	yilmazer	PROPN
ejpam-5936	280	10	,	,	PUNCT
ejpam-5936	280	11	h.	h.	PROPN
ejpam-5936	280	12	m.	m.	PROPN
ejpam-5936	280	13	baskonus	baskonus	PROPN
ejpam-5936	280	14	,	,	PUNCT
ejpam-5936	280	15	and	and	CCONJ
ejpam-5936	280	16	h.	h.	PROPN
ejpam-5936	280	17	bulut	bulut	PROPN
ejpam-5936	280	18	,	,	PUNCT
ejpam-5936	280	19	new	new	ADJ
ejpam-5936	280	20	wave	wave	NOUN
ejpam-5936	280	21	behaviors	behavior	NOUN
ejpam-5936	280	22	and	and	CCONJ
ejpam-5936	280	23	stability	stability	NOUN
ejpam-5936	280	24	analysis	analysis	NOUN
ejpam-5936	280	25	of	of	ADP
ejpam-5936	280	26	the	the	DET
ejpam-5936	280	27	gilson	gilson	NOUN
ejpam-5936	280	28	–	–	PUNCT
ejpam-5936	280	29	pickering	pickere	VERB
ejpam-5936	280	30	equation	equation	NOUN
ejpam-5936	280	31	in	in	ADP
ejpam-5936	280	32	plasma	plasma	NOUN
ejpam-5936	280	33	physics	physics	PROPN
ejpam-5936	280	34	,	,	PUNCT
ejpam-5936	280	35	indian	indian	PROPN
ejpam-5936	280	36	journal	journal	PROPN
ejpam-5936	280	37	of	of	ADP
ejpam-5936	280	38	physics	physics	PROPN
ejpam-5936	280	39	95	95	NUM
ejpam-5936	280	40	(	(	PUNCT
ejpam-5936	280	41	2021	2021	NUM
ejpam-5936	280	42	)	)	PUNCT
ejpam-5936	280	43	,	,	PUNCT
ejpam-5936	280	44	1003–1008	1003–1008	NUM
ejpam-5936	280	45	.	.	PUNCT
ejpam-5936	281	1	[	[	X
ejpam-5936	281	2	5	5	NUM
ejpam-5936	281	3	]	]	PUNCT
ejpam-5936	281	4	b.	b.	PROPN
ejpam-5936	281	5	q.	q.	PROPN
ejpam-5936	281	6	li	li	PROPN
ejpam-5936	281	7	and	and	CCONJ
ejpam-5936	281	8	y.	y.	PROPN
ejpam-5936	281	9	l.	l.	PROPN
ejpam-5936	281	10	ma	ma	PROPN
ejpam-5936	281	11	,	,	PUNCT
ejpam-5936	281	12	n	n	X
ejpam-5936	281	13	-order	-order	NOUN
ejpam-5936	281	14	rogue	rogue	NOUN
ejpam-5936	281	15	waves	wave	NOUN
ejpam-5936	281	16	and	and	CCONJ
ejpam-5936	281	17	their	their	PRON
ejpam-5936	281	18	novel	novel	ADJ
ejpam-5936	281	19	colliding	collide	VERB
ejpam-5936	281	20	dynamics	dynamic	NOUN
ejpam-5936	281	21	z.	z.	PROPN
ejpam-5936	281	22	haider	haider	PROPN
ejpam-5936	281	23	,	,	PUNCT
ejpam-5936	281	24	k.	k.	PROPN
ejpam-5936	281	25	ahmad	ahmad	PROPN
ejpam-5936	281	26	/	/	SYM
ejpam-5936	281	27	eur	eur	PROPN
ejpam-5936	281	28	.	.	PUNCT
ejpam-5936	282	1	j.	j.	PROPN
ejpam-5936	282	2	pure	pure	PROPN
ejpam-5936	282	3	appl	appl	PROPN
ejpam-5936	282	4	.	.	PROPN
ejpam-5936	282	5	math	math	PROPN
ejpam-5936	282	6	,	,	PUNCT
ejpam-5936	282	7	18	18	NUM
ejpam-5936	282	8	(	(	PUNCT
ejpam-5936	282	9	2	2	NUM
ejpam-5936	282	10	)	)	PUNCT
ejpam-5936	282	11	(	(	PUNCT
ejpam-5936	282	12	2025	2025	NUM
ejpam-5936	282	13	)	)	PUNCT
ejpam-5936	282	14	,	,	PUNCT
ejpam-5936	282	15	5936	5936	NUM
ejpam-5936	282	16	17	17	NUM
ejpam-5936	282	17	of	of	ADP
ejpam-5936	282	18	18	18	NUM
ejpam-5936	282	19	for	for	ADP
ejpam-5936	282	20	a	a	DET
ejpam-5936	282	21	transient	transient	ADJ
ejpam-5936	282	22	stimulated	stimulated	ADJ
ejpam-5936	282	23	raman	raman	NOUN
ejpam-5936	282	24	scattering	scatter	VERB
ejpam-5936	282	25	system	system	NOUN
ejpam-5936	282	26	arising	arise	VERB
ejpam-5936	282	27	from	from	ADP
ejpam-5936	282	28	nonlinear	nonlinear	ADJ
ejpam-5936	282	29	optics	optic	NOUN
ejpam-5936	282	30	,	,	PUNCT
ejpam-5936	282	31	nonlinear	nonlinear	ADJ
ejpam-5936	282	32	dynamics	dynamic	NOUN
ejpam-5936	282	33	101	101	NUM
ejpam-5936	282	34	(	(	PUNCT
ejpam-5936	282	35	4	4	NUM
ejpam-5936	282	36	)	)	PUNCT
ejpam-5936	282	37	(	(	PUNCT
ejpam-5936	282	38	2020	2020	NUM
ejpam-5936	282	39	)	)	PUNCT
ejpam-5936	282	40	,	,	PUNCT
ejpam-5936	282	41	2449–2461	2449–2461	NUM
ejpam-5936	282	42	.	.	PUNCT
ejpam-5936	283	1	[	[	X
ejpam-5936	283	2	6	6	NUM
ejpam-5936	283	3	]	]	PUNCT
ejpam-5936	283	4	m.	m.	NOUN
ejpam-5936	283	5	wang	wang	PROPN
ejpam-5936	283	6	,	,	PUNCT
ejpam-5936	283	7	b.	b.	PROPN
ejpam-5936	283	8	tian	tian	PROPN
ejpam-5936	283	9	,	,	PUNCT
ejpam-5936	283	10	c.	c.	PROPN
ejpam-5936	283	11	c.	c.	PROPN
ejpam-5936	283	12	hu	hu	PROPN
ejpam-5936	283	13	,	,	PUNCT
ejpam-5936	283	14	and	and	CCONJ
ejpam-5936	283	15	s.	s.	PROPN
ejpam-5936	283	16	h.	h.	PROPN
ejpam-5936	283	17	liu	liu	PROPN
ejpam-5936	283	18	,	,	PUNCT
ejpam-5936	283	19	generalized	generalize	VERB
ejpam-5936	283	20	darboux	darboux	VERB
ejpam-5936	283	21	transformation	transformation	NOUN
ejpam-5936	283	22	,	,	PUNCT
ejpam-5936	283	23	solitonic	solitonic	ADJ
ejpam-5936	283	24	interactions	interaction	NOUN
ejpam-5936	283	25	and	and	CCONJ
ejpam-5936	283	26	bound	bind	VERB
ejpam-5936	283	27	states	state	NOUN
ejpam-5936	283	28	for	for	ADP
ejpam-5936	283	29	a	a	DET
ejpam-5936	283	30	coupled	couple	VERB
ejpam-5936	283	31	fourth	fourth	ADJ
ejpam-5936	283	32	-	-	PUNCT
ejpam-5936	283	33	order	order	NOUN
ejpam-5936	283	34	nonlinear	nonlinear	NOUN
ejpam-5936	283	35	schrödinger	schrödinger	NOUN
ejpam-5936	283	36	system	system	NOUN
ejpam-5936	283	37	in	in	ADP
ejpam-5936	283	38	a	a	DET
ejpam-5936	283	39	birefringent	birefringent	NOUN
ejpam-5936	283	40	optical	optical	ADJ
ejpam-5936	283	41	fiber	fiber	NOUN
ejpam-5936	283	42	,	,	PUNCT
ejpam-5936	283	43	applied	apply	VERB
ejpam-5936	283	44	mathematics	mathematics	NOUN
ejpam-5936	283	45	letters	letter	NOUN
ejpam-5936	283	46	119	119	NUM
ejpam-5936	283	47	(	(	PUNCT
ejpam-5936	283	48	2021	2021	NUM
ejpam-5936	283	49	)	)	PUNCT
ejpam-5936	283	50	,	,	PUNCT
ejpam-5936	283	51	106936	106936	NUM
ejpam-5936	283	52	.	.	PUNCT
ejpam-5936	284	1	[	[	X
ejpam-5936	284	2	7	7	X
ejpam-5936	284	3	]	]	PUNCT
ejpam-5936	284	4	k.	k.	PROPN
ejpam-5936	284	5	j.	j.	PROPN
ejpam-5936	284	6	wang	wang	PROPN
ejpam-5936	284	7	,	,	PUNCT
ejpam-5936	284	8	periodic	periodic	ADJ
ejpam-5936	284	9	solution	solution	NOUN
ejpam-5936	284	10	of	of	ADP
ejpam-5936	284	11	the	the	DET
ejpam-5936	284	12	time	time	NOUN
ejpam-5936	284	13	-	-	PUNCT
ejpam-5936	284	14	space	space	NOUN
ejpam-5936	284	15	fractional	fractional	ADJ
ejpam-5936	284	16	complex	complex	ADJ
ejpam-5936	284	17	nonlinear	nonlinear	ADJ
ejpam-5936	284	18	fokaslenells	fokaslenell	NOUN
ejpam-5936	284	19	equation	equation	NOUN
ejpam-5936	284	20	by	by	ADP
ejpam-5936	284	21	an	an	DET
ejpam-5936	284	22	ancient	ancient	ADJ
ejpam-5936	284	23	chinese	chinese	ADJ
ejpam-5936	284	24	algorithm	algorithm	NOUN
ejpam-5936	284	25	,	,	PUNCT
ejpam-5936	284	26	optik	optik	PROPN
ejpam-5936	284	27	243	243	NUM
ejpam-5936	284	28	(	(	PUNCT
ejpam-5936	284	29	2021	2021	NUM
ejpam-5936	284	30	)	)	PUNCT
ejpam-5936	284	31	,	,	PUNCT
ejpam-5936	284	32	167461	167461	NUM
ejpam-5936	284	33	.	.	PUNCT
ejpam-5936	285	1	[	[	X
ejpam-5936	285	2	8	8	NUM
ejpam-5936	285	3	]	]	PUNCT
ejpam-5936	285	4	x.	x.	NOUN
ejpam-5936	285	5	y.	y.	PROPN
ejpam-5936	285	6	gao	gao	PROPN
ejpam-5936	285	7	,	,	PUNCT
ejpam-5936	285	8	y.	y.	PROPN
ejpam-5936	285	9	j.	j.	PROPN
ejpam-5936	285	10	guo	guo	PROPN
ejpam-5936	285	11	,	,	PUNCT
ejpam-5936	285	12	and	and	CCONJ
ejpam-5936	285	13	w.	w.	PROPN
ejpam-5936	285	14	r.	r.	PROPN
ejpam-5936	285	15	shan	shan	PROPN
ejpam-5936	285	16	,	,	PUNCT
ejpam-5936	285	17	optical	optical	ADJ
ejpam-5936	285	18	waves	wave	NOUN
ejpam-5936	285	19	/	/	SYM
ejpam-5936	285	20	modes	mode	NOUN
ejpam-5936	285	21	in	in	ADP
ejpam-5936	285	22	a	a	DET
ejpam-5936	285	23	multicomponent	multicomponent	ADJ
ejpam-5936	285	24	inhomogeneous	inhomogeneous	ADJ
ejpam-5936	285	25	optical	optical	ADJ
ejpam-5936	285	26	fiber	fiber	NOUN
ejpam-5936	285	27	via	via	ADP
ejpam-5936	285	28	a	a	DET
ejpam-5936	285	29	three	three	NUM
ejpam-5936	285	30	-	-	PUNCT
ejpam-5936	285	31	coupled	couple	VERB
ejpam-5936	285	32	variable	variable	ADJ
ejpam-5936	285	33	-	-	PUNCT
ejpam-5936	285	34	coefficient	coefficient	NOUN
ejpam-5936	285	35	nonlinear	nonlinear	PROPN
ejpam-5936	285	36	schrödinger	schrödinger	NOUN
ejpam-5936	285	37	system	system	NOUN
ejpam-5936	285	38	,	,	PUNCT
ejpam-5936	285	39	applied	apply	VERB
ejpam-5936	285	40	mathematics	mathematics	NOUN
ejpam-5936	285	41	letters	letter	NOUN
ejpam-5936	285	42	120	120	NUM
ejpam-5936	285	43	(	(	PUNCT
ejpam-5936	285	44	2021	2021	NUM
ejpam-5936	285	45	)	)	PUNCT
ejpam-5936	285	46	,	,	PUNCT
ejpam-5936	285	47	107161	107161	NUM
ejpam-5936	285	48	.	.	PUNCT
ejpam-5936	286	1	[	[	X
ejpam-5936	286	2	9	9	NUM
ejpam-5936	286	3	]	]	PUNCT
ejpam-5936	286	4	w.	w.	PROPN
ejpam-5936	286	5	x.	x.	PROPN
ejpam-5936	286	6	ma	ma	PROPN
ejpam-5936	286	7	,	,	PUNCT
ejpam-5936	286	8	n	n	NUM
ejpam-5936	286	9	-soliton	-soliton	PROPN
ejpam-5936	286	10	solutions	solution	NOUN
ejpam-5936	286	11	and	and	CCONJ
ejpam-5936	286	12	the	the	DET
ejpam-5936	286	13	hirota	hirota	NOUN
ejpam-5936	286	14	conditions	condition	NOUN
ejpam-5936	286	15	in	in	ADP
ejpam-5936	286	16	(	(	PUNCT
ejpam-5936	286	17	2	2	NUM
ejpam-5936	286	18	+	+	NOUN
ejpam-5936	286	19	1)-dimensions	1)-dimensions	NUM
ejpam-5936	286	20	,	,	PUNCT
ejpam-5936	286	21	optical	optical	ADJ
ejpam-5936	286	22	and	and	CCONJ
ejpam-5936	286	23	quantum	quantum	ADJ
ejpam-5936	286	24	electronics	electronic	NOUN
ejpam-5936	286	25	52	52	NUM
ejpam-5936	286	26	(	(	PUNCT
ejpam-5936	286	27	12	12	NUM
ejpam-5936	286	28	)	)	PUNCT
ejpam-5936	286	29	(	(	PUNCT
ejpam-5936	286	30	2020	2020	NUM
ejpam-5936	286	31	)	)	PUNCT
ejpam-5936	286	32	,	,	PUNCT
ejpam-5936	286	33	511	511	NUM
ejpam-5936	286	34	.	.	PUNCT
ejpam-5936	287	1	[	[	X
ejpam-5936	287	2	10	10	NUM
ejpam-5936	287	3	]	]	X
ejpam-5936	287	4	w.	w.	PROPN
ejpam-5936	287	5	x.	x.	PROPN
ejpam-5936	287	6	ma	ma	PROPN
ejpam-5936	287	7	,	,	PUNCT
ejpam-5936	287	8	n	n	NUM
ejpam-5936	287	9	-soliton	-soliton	PROPN
ejpam-5936	287	10	solutions	solution	NOUN
ejpam-5936	287	11	and	and	CCONJ
ejpam-5936	287	12	the	the	DET
ejpam-5936	287	13	hirota	hirota	NOUN
ejpam-5936	287	14	conditions	condition	NOUN
ejpam-5936	287	15	in	in	ADP
ejpam-5936	287	16	(	(	PUNCT
ejpam-5936	287	17	1	1	NUM
ejpam-5936	287	18	+	+	NOUN
ejpam-5936	287	19	1)-dimensions	1)-dimensions	NUM
ejpam-5936	287	20	,	,	PUNCT
ejpam-5936	287	21	international	international	ADJ
ejpam-5936	287	22	journal	journal	NOUN
ejpam-5936	287	23	of	of	ADP
ejpam-5936	287	24	nonlinear	nonlinear	PROPN
ejpam-5936	287	25	sciences	sciences	PROPN
ejpam-5936	287	26	and	and	CCONJ
ejpam-5936	287	27	numerical	numerical	PROPN
ejpam-5936	287	28	simulation	simulation	NOUN
ejpam-5936	287	29	23	23	NUM
ejpam-5936	287	30	(	(	PUNCT
ejpam-5936	287	31	1	1	NUM
ejpam-5936	287	32	)	)	PUNCT
ejpam-5936	287	33	(	(	PUNCT
ejpam-5936	287	34	2022	2022	NUM
ejpam-5936	287	35	)	)	PUNCT
ejpam-5936	287	36	,	,	PUNCT
ejpam-5936	287	37	123–133	123–133	NUM
ejpam-5936	287	38	.	.	PUNCT
ejpam-5936	288	1	[	[	X
ejpam-5936	288	2	11	11	NUM
ejpam-5936	288	3	]	]	PUNCT
ejpam-5936	288	4	x.	x.	NOUN
ejpam-5936	288	5	y.	y.	PROPN
ejpam-5936	288	6	gao	gao	PROPN
ejpam-5936	288	7	,	,	PUNCT
ejpam-5936	288	8	y.	y.	PROPN
ejpam-5936	288	9	j.	j.	PROPN
ejpam-5936	288	10	guo	guo	PROPN
ejpam-5936	288	11	,	,	PUNCT
ejpam-5936	288	12	and	and	CCONJ
ejpam-5936	288	13	w.	w.	PROPN
ejpam-5936	288	14	r.	r.	PROPN
ejpam-5936	288	15	shan	shan	PROPN
ejpam-5936	288	16	,	,	PUNCT
ejpam-5936	288	17	beholding	behold	VERB
ejpam-5936	288	18	the	the	DET
ejpam-5936	288	19	shallow	shallow	ADJ
ejpam-5936	288	20	water	water	NOUN
ejpam-5936	288	21	waves	wave	NOUN
ejpam-5936	288	22	near	near	ADP
ejpam-5936	288	23	an	an	DET
ejpam-5936	288	24	ocean	ocean	NOUN
ejpam-5936	288	25	beach	beach	NOUN
ejpam-5936	288	26	or	or	CCONJ
ejpam-5936	288	27	in	in	ADP
ejpam-5936	288	28	a	a	DET
ejpam-5936	288	29	lake	lake	NOUN
ejpam-5936	288	30	via	via	ADP
ejpam-5936	288	31	a	a	DET
ejpam-5936	288	32	boussinesq	boussinesq	ADJ
ejpam-5936	288	33	-	-	PUNCT
ejpam-5936	288	34	burgers	burger	NOUN
ejpam-5936	288	35	system	system	NOUN
ejpam-5936	288	36	,	,	PUNCT
ejpam-5936	288	37	chaos	chaos	NOUN
ejpam-5936	288	38	,	,	PUNCT
ejpam-5936	288	39	solitons	soliton	NOUN
ejpam-5936	288	40	&	&	CCONJ
ejpam-5936	288	41	fractals	fractal	NOUN
ejpam-5936	288	42	147	147	NUM
ejpam-5936	288	43	(	(	PUNCT
ejpam-5936	288	44	2021	2021	NUM
ejpam-5936	288	45	)	)	PUNCT
ejpam-5936	288	46	,	,	PUNCT
ejpam-5936	288	47	110875	110875	NUM
ejpam-5936	288	48	.	.	PUNCT
ejpam-5936	289	1	[	[	X
ejpam-5936	289	2	12	12	NUM
ejpam-5936	289	3	]	]	PUNCT
ejpam-5936	289	4	a.	a.	NOUN
ejpam-5936	289	5	bekir	bekir	NOUN
ejpam-5936	289	6	and	and	CCONJ
ejpam-5936	289	7	ö.	ö.	PROPN
ejpam-5936	289	8	güner	güner	NOUN
ejpam-5936	289	9	,	,	PUNCT
ejpam-5936	289	10	exact	exact	ADJ
ejpam-5936	289	11	solutions	solution	NOUN
ejpam-5936	289	12	of	of	ADP
ejpam-5936	289	13	nonlinear	nonlinear	ADJ
ejpam-5936	289	14	fractional	fractional	ADJ
ejpam-5936	289	15	differential	differential	NOUN
ejpam-5936	289	16	equations	equation	NOUN
ejpam-5936	289	17	by	by	ADP
ejpam-5936	289	18	(	(	PUNCT
ejpam-5936	289	19	g	g	PROPN
ejpam-5936	289	20	′	′	NUM
ejpam-5936	289	21	g	g	NOUN
ejpam-5936	289	22	)	)	PUNCT
ejpam-5936	289	23	-expansion	-expansion	PROPN
ejpam-5936	289	24	method	method	NOUN
ejpam-5936	289	25	,	,	PUNCT
ejpam-5936	289	26	chinese	chinese	PROPN
ejpam-5936	289	27	physics	physics	PROPN
ejpam-5936	289	28	b	b	PROPN
ejpam-5936	289	29	22	22	NUM
ejpam-5936	289	30	(	(	PUNCT
ejpam-5936	289	31	11	11	NUM
ejpam-5936	289	32	)	)	PUNCT
ejpam-5936	289	33	(	(	PUNCT
ejpam-5936	289	34	2013	2013	NUM
ejpam-5936	289	35	)	)	PUNCT
ejpam-5936	289	36	,	,	PUNCT
ejpam-5936	289	37	110202	110202	NUM
ejpam-5936	289	38	.	.	PUNCT
ejpam-5936	290	1	[	[	X
ejpam-5936	290	2	13	13	NUM
ejpam-5936	290	3	]	]	PUNCT
ejpam-5936	290	4	q.	q.	PROPN
ejpam-5936	290	5	m.	m.	PROPN
ejpam-5936	290	6	ul	ul	PROPN
ejpam-5936	290	7	hassan	hassan	PROPN
ejpam-5936	290	8	and	and	CCONJ
ejpam-5936	290	9	s.	s.	PROPN
ejpam-5936	290	10	t.	t.	PROPN
ejpam-5936	290	11	mohyud	mohyud	PROPN
ejpam-5936	290	12	-	-	PUNCT
ejpam-5936	290	13	din	din	NOUN
ejpam-5936	290	14	,	,	PUNCT
ejpam-5936	290	15	investigating	investigate	VERB
ejpam-5936	290	16	biological	biological	ADJ
ejpam-5936	290	17	population	population	NOUN
ejpam-5936	290	18	model	model	NOUN
ejpam-5936	290	19	using	use	VERB
ejpam-5936	290	20	exp	exp	NOUN
ejpam-5936	290	21	-	-	PUNCT
ejpam-5936	290	22	function	function	NOUN
ejpam-5936	290	23	method	method	NOUN
ejpam-5936	290	24	,	,	PUNCT
ejpam-5936	290	25	international	international	ADJ
ejpam-5936	290	26	journal	journal	NOUN
ejpam-5936	290	27	of	of	ADP
ejpam-5936	290	28	biomathematics	biomathematic	NOUN
ejpam-5936	290	29	9	9	NUM
ejpam-5936	290	30	(	(	PUNCT
ejpam-5936	290	31	02	02	NUM
ejpam-5936	290	32	)	)	PUNCT
ejpam-5936	290	33	(	(	PUNCT
ejpam-5936	290	34	2016	2016	NUM
ejpam-5936	290	35	)	)	PUNCT
ejpam-5936	290	36	,	,	PUNCT
ejpam-5936	290	37	1650026	1650026	NUM
ejpam-5936	290	38	.	.	PUNCT
ejpam-5936	291	1	[	[	X
ejpam-5936	291	2	14	14	NUM
ejpam-5936	291	3	]	]	X
ejpam-5936	291	4	f.	f.	PROPN
ejpam-5936	291	5	shakeri	shakeri	PROPN
ejpam-5936	291	6	and	and	CCONJ
ejpam-5936	291	7	m.	m.	NOUN
ejpam-5936	291	8	dehghan	dehghan	PROPN
ejpam-5936	291	9	,	,	PUNCT
ejpam-5936	291	10	numerical	numerical	ADJ
ejpam-5936	291	11	solution	solution	NOUN
ejpam-5936	291	12	of	of	ADP
ejpam-5936	291	13	a	a	DET
ejpam-5936	291	14	biological	biological	ADJ
ejpam-5936	291	15	population	population	NOUN
ejpam-5936	291	16	model	model	NOUN
ejpam-5936	291	17	using	use	VERB
ejpam-5936	291	18	he	he	PRON
ejpam-5936	291	19	’s	’s	PART
ejpam-5936	291	20	variational	variational	ADJ
ejpam-5936	291	21	iteration	iteration	NOUN
ejpam-5936	291	22	method	method	NOUN
ejpam-5936	291	23	,	,	PUNCT
ejpam-5936	291	24	computers	computer	NOUN
ejpam-5936	291	25	&	&	CCONJ
ejpam-5936	291	26	mathematics	mathematic	NOUN
ejpam-5936	291	27	with	with	ADP
ejpam-5936	291	28	applications	application	NOUN
ejpam-5936	291	29	54	54	NUM
ejpam-5936	291	30	(	(	PUNCT
ejpam-5936	291	31	7	7	NUM
ejpam-5936	291	32	-	-	SYM
ejpam-5936	291	33	8)	8)	NUM
ejpam-5936	291	34	(	(	PUNCT
ejpam-5936	291	35	2007	2007	NUM
ejpam-5936	291	36	)	)	PUNCT
ejpam-5936	291	37	,	,	PUNCT
ejpam-5936	291	38	1197–1209	1197–1209	NUM
ejpam-5936	291	39	.	.	PUNCT
ejpam-5936	292	1	[	[	X
ejpam-5936	292	2	15	15	NUM
ejpam-5936	292	3	]	]	X
ejpam-5936	292	4	s.	s.	PROPN
ejpam-5936	292	5	bushnaq	bushnaq	PROPN
ejpam-5936	292	6	,	,	PUNCT
ejpam-5936	292	7	s.	s.	PROPN
ejpam-5936	292	8	ali	ali	PROPN
ejpam-5936	292	9	,	,	PUNCT
ejpam-5936	292	10	k.	k.	PROPN
ejpam-5936	292	11	shah	shah	PROPN
ejpam-5936	292	12	,	,	PUNCT
ejpam-5936	292	13	and	and	CCONJ
ejpam-5936	292	14	m.	m.	PROPN
ejpam-5936	292	15	arif	arif	PROPN
ejpam-5936	292	16	,	,	PUNCT
ejpam-5936	292	17	exact	exact	ADJ
ejpam-5936	292	18	solution	solution	NOUN
ejpam-5936	292	19	to	to	ADP
ejpam-5936	292	20	non	non	ADJ
ejpam-5936	292	21	-	-	ADJ
ejpam-5936	292	22	linear	linear	ADJ
ejpam-5936	292	23	biological	biological	ADJ
ejpam-5936	292	24	population	population	NOUN
ejpam-5936	292	25	model	model	NOUN
ejpam-5936	292	26	with	with	ADP
ejpam-5936	292	27	fractional	fractional	ADJ
ejpam-5936	292	28	order	order	NOUN
ejpam-5936	292	29	,	,	PUNCT
ejpam-5936	292	30	thermal	thermal	ADJ
ejpam-5936	292	31	science	science	NOUN
ejpam-5936	292	32	22	22	NUM
ejpam-5936	292	33	(	(	PUNCT
ejpam-5936	292	34	suppl	suppl	ADJ
ejpam-5936	292	35	.	.	PROPN
ejpam-5936	292	36	1	1	NUM
ejpam-5936	292	37	)	)	PUNCT
ejpam-5936	292	38	(	(	PUNCT
ejpam-5936	292	39	2018	2018	NUM
ejpam-5936	292	40	)	)	PUNCT
ejpam-5936	292	41	,	,	PUNCT
ejpam-5936	292	42	317	317	NUM
ejpam-5936	292	43	–	–	PUNCT
ejpam-5936	292	44	327	327	NUM
ejpam-5936	292	45	.	.	PUNCT
ejpam-5936	293	1	[	[	X
ejpam-5936	293	2	16	16	NUM
ejpam-5936	293	3	]	]	X
ejpam-5936	293	4	m.	m.	PROPN
ejpam-5936	293	5	shakeel	shakeel	PROPN
ejpam-5936	293	6	,	,	PUNCT
ejpam-5936	293	7	m.	m.	PROPN
ejpam-5936	293	8	a.	a.	PROPN
ejpam-5936	293	9	iqbal	iqbal	PROPN
ejpam-5936	293	10	,	,	PUNCT
ejpam-5936	293	11	and	and	CCONJ
ejpam-5936	293	12	s.	s.	PROPN
ejpam-5936	293	13	t.	t.	PROPN
ejpam-5936	293	14	mohyud	mohyud	PROPN
ejpam-5936	293	15	-	-	PUNCT
ejpam-5936	293	16	din	din	NOUN
ejpam-5936	293	17	,	,	PUNCT
ejpam-5936	293	18	closed	close	VERB
ejpam-5936	293	19	form	form	NOUN
ejpam-5936	293	20	solutions	solution	NOUN
ejpam-5936	293	21	for	for	ADP
ejpam-5936	293	22	nonlinear	nonlinear	ADJ
ejpam-5936	293	23	biological	biological	ADJ
ejpam-5936	293	24	population	population	NOUN
ejpam-5936	293	25	model	model	NOUN
ejpam-5936	293	26	,	,	PUNCT
ejpam-5936	293	27	journal	journal	NOUN
ejpam-5936	293	28	of	of	ADP
ejpam-5936	293	29	biological	biological	ADJ
ejpam-5936	293	30	systems	system	NOUN
ejpam-5936	293	31	26	26	NUM
ejpam-5936	293	32	(	(	PUNCT
ejpam-5936	293	33	01	01	NUM
ejpam-5936	293	34	)	)	PUNCT
ejpam-5936	293	35	(	(	PUNCT
ejpam-5936	293	36	2018	2018	NUM
ejpam-5936	293	37	)	)	PUNCT
ejpam-5936	293	38	,	,	PUNCT
ejpam-5936	293	39	207–223	207–223	NUM
ejpam-5936	293	40	.	.	PUNCT
ejpam-5936	294	1	[	[	X
ejpam-5936	294	2	17	17	NUM
ejpam-5936	294	3	]	]	PUNCT
ejpam-5936	294	4	m.	m.	NOUN
ejpam-5936	294	5	a.	a.	PROPN
ejpam-5936	294	6	zirak	zirak	PROPN
ejpam-5936	294	7	and	and	CCONJ
ejpam-5936	294	8	a.	a.	NOUN
ejpam-5936	294	9	poya	poya	PROPN
ejpam-5936	294	10	,	,	PUNCT
ejpam-5936	294	11	analytical	analytical	ADJ
ejpam-5936	294	12	solution	solution	NOUN
ejpam-5936	294	13	of	of	ADP
ejpam-5936	294	14	biological	biological	ADJ
ejpam-5936	294	15	population	population	NOUN
ejpam-5936	294	16	of	of	ADP
ejpam-5936	294	17	fractional	fractional	ADJ
ejpam-5936	294	18	differential	differential	ADJ
ejpam-5936	294	19	equations	equation	NOUN
ejpam-5936	294	20	by	by	ADP
ejpam-5936	294	21	reconstruction	reconstruction	NOUN
ejpam-5936	294	22	of	of	ADP
ejpam-5936	294	23	variational	variational	ADJ
ejpam-5936	294	24	iteration	iteration	NOUN
ejpam-5936	294	25	method	method	NOUN
ejpam-5936	294	26	,	,	PUNCT
ejpam-5936	294	27	journal	journal	NOUN
ejpam-5936	294	28	for	for	ADP
ejpam-5936	294	29	research	research	NOUN
ejpam-5936	294	30	in	in	ADP
ejpam-5936	294	31	applied	apply	VERB
ejpam-5936	294	32	sciences	science	NOUN
ejpam-5936	294	33	and	and	CCONJ
ejpam-5936	294	34	biotechnology	biotechnology	NOUN
ejpam-5936	294	35	2	2	NUM
ejpam-5936	294	36	(	(	PUNCT
ejpam-5936	294	37	3	3	NUM
ejpam-5936	294	38	)	)	PUNCT
ejpam-5936	294	39	(	(	PUNCT
ejpam-5936	294	40	2023	2023	NUM
ejpam-5936	294	41	)	)	PUNCT
ejpam-5936	294	42	,	,	PUNCT
ejpam-5936	294	43	158–162	158–162	NUM
ejpam-5936	294	44	.	.	PUNCT
ejpam-5936	295	1	[	[	X
ejpam-5936	295	2	18	18	NUM
ejpam-5936	295	3	]	]	PUNCT
ejpam-5936	295	4	m.	m.	NOUN
ejpam-5936	295	5	m.	m.	NOUN
ejpam-5936	295	6	khater	khater	PROPN
ejpam-5936	295	7	,	,	PUNCT
ejpam-5936	295	8	nonlinear	nonlinear	ADJ
ejpam-5936	295	9	biological	biological	ADJ
ejpam-5936	295	10	population	population	NOUN
ejpam-5936	295	11	model	model	NOUN
ejpam-5936	295	12	;	;	PUNCT
ejpam-5936	295	13	computational	computational	ADJ
ejpam-5936	295	14	and	and	CCONJ
ejpam-5936	295	15	numerical	numerical	ADJ
ejpam-5936	295	16	investigations	investigation	NOUN
ejpam-5936	295	17	,	,	PUNCT
ejpam-5936	295	18	chaos	chaos	NOUN
ejpam-5936	295	19	,	,	PUNCT
ejpam-5936	295	20	solitons	soliton	NOUN
ejpam-5936	295	21	&	&	CCONJ
ejpam-5936	295	22	fractals	fractal	NOUN
ejpam-5936	295	23	162	162	NUM
ejpam-5936	295	24	(	(	PUNCT
ejpam-5936	295	25	2022	2022	NUM
ejpam-5936	295	26	)	)	PUNCT
ejpam-5936	295	27	,	,	PUNCT
ejpam-5936	295	28	112388	112388	NUM
ejpam-5936	295	29	.	.	PUNCT
ejpam-5936	296	1	[	[	X
ejpam-5936	296	2	19	19	NUM
ejpam-5936	296	3	]	]	PUNCT
ejpam-5936	296	4	k.	k.	PROPN
ejpam-5936	296	5	j.	j.	PROPN
ejpam-5936	296	6	wang	wang	PROPN
ejpam-5936	296	7	,	,	PUNCT
ejpam-5936	296	8	x.	x.	PROPN
ejpam-5936	296	9	l.	l.	PROPN
ejpam-5936	296	10	liu	liu	PROPN
ejpam-5936	296	11	,	,	PUNCT
ejpam-5936	296	12	w.	w.	PROPN
ejpam-5936	296	13	d.	d.	PROPN
ejpam-5936	296	14	wang	wang	PROPN
ejpam-5936	296	15	,	,	PUNCT
ejpam-5936	296	16	s.	s.	PROPN
ejpam-5936	296	17	li	li	PROPN
ejpam-5936	296	18	,	,	PUNCT
ejpam-5936	296	19	and	and	CCONJ
ejpam-5936	296	20	h.	h.	PROPN
ejpam-5936	296	21	w.	w.	PROPN
ejpam-5936	296	22	zhu	zhu	PROPN
ejpam-5936	296	23	,	,	PUNCT
ejpam-5936	296	24	novel	novel	ADJ
ejpam-5936	296	25	singular	singular	NOUN
ejpam-5936	296	26	and	and	CCONJ
ejpam-5936	296	27	nonsingular	nonsingular	ADJ
ejpam-5936	296	28	complexiton	complexiton	PROPN
ejpam-5936	296	29	,	,	PUNCT
ejpam-5936	296	30	interaction	interaction	NOUN
ejpam-5936	296	31	wave	wave	NOUN
ejpam-5936	296	32	and	and	CCONJ
ejpam-5936	296	33	the	the	DET
ejpam-5936	296	34	complex	complex	ADJ
ejpam-5936	296	35	multi	multi	ADJ
ejpam-5936	296	36	-	-	ADJ
ejpam-5936	296	37	soliton	soliton	ADJ
ejpam-5936	296	38	solutions	solution	NOUN
ejpam-5936	296	39	to	to	ADP
ejpam-5936	296	40	the	the	DET
ejpam-5936	296	41	generalized	generalize	VERB
ejpam-5936	296	42	nonlinear	nonlinear	ADJ
ejpam-5936	296	43	evolution	evolution	NOUN
ejpam-5936	296	44	equation	equation	NOUN
ejpam-5936	296	45	,	,	PUNCT
ejpam-5936	296	46	modern	modern	ADJ
ejpam-5936	296	47	physics	physics	NOUN
ejpam-5936	296	48	letters	letters	PROPN
ejpam-5936	296	49	b	b	PROPN
ejpam-5936	296	50	(	(	PUNCT
ejpam-5936	296	51	2025	2025	NUM
ejpam-5936	296	52	)	)	PUNCT
ejpam-5936	296	53	,	,	PUNCT
ejpam-5936	296	54	2550135	2550135	NUM
ejpam-5936	296	55	.	.	PUNCT
ejpam-5936	297	1	[	[	X
ejpam-5936	297	2	20	20	NUM
ejpam-5936	297	3	]	]	PUNCT
ejpam-5936	297	4	k.	k.	PROPN
ejpam-5936	297	5	j.	j.	PROPN
ejpam-5936	297	6	wang	wang	PROPN
ejpam-5936	297	7	,	,	PUNCT
ejpam-5936	297	8	the	the	DET
ejpam-5936	297	9	perturbed	perturb	VERB
ejpam-5936	297	10	chen	chen	PROPN
ejpam-5936	297	11	–	–	PUNCT
ejpam-5936	297	12	lee	lee	PROPN
ejpam-5936	297	13	–	–	PUNCT
ejpam-5936	297	14	liu	liu	PROPN
ejpam-5936	297	15	equation	equation	NOUN
ejpam-5936	297	16	:	:	PUNCT
ejpam-5936	297	17	diverse	diverse	ADJ
ejpam-5936	297	18	optical	optical	ADJ
ejpam-5936	297	19	soliton	soliton	NOUN
ejpam-5936	297	20	solutions	solution	NOUN
ejpam-5936	297	21	and	and	CCONJ
ejpam-5936	297	22	other	other	ADJ
ejpam-5936	297	23	wave	wave	NOUN
ejpam-5936	297	24	solutions	solution	NOUN
ejpam-5936	297	25	,	,	PUNCT
ejpam-5936	297	26	advances	advance	NOUN
ejpam-5936	297	27	in	in	ADP
ejpam-5936	297	28	mathematical	mathematical	ADJ
ejpam-5936	297	29	physics	physics	NOUN
ejpam-5936	297	30	2024	2024	NUM
ejpam-5936	297	31	(	(	PUNCT
ejpam-5936	297	32	1	1	NUM
ejpam-5936	297	33	)	)	PUNCT
ejpam-5936	297	34	(	(	PUNCT
ejpam-5936	297	35	2024	2024	NUM
ejpam-5936	297	36	)	)	PUNCT
ejpam-5936	297	37	,	,	PUNCT
ejpam-5936	297	38	4990396	4990396	NUM
ejpam-5936	297	39	.	.	PUNCT
ejpam-5936	298	1	z.	z.	PROPN
ejpam-5936	298	2	haider	haider	PROPN
ejpam-5936	298	3	,	,	PUNCT
ejpam-5936	298	4	k.	k.	PROPN
ejpam-5936	298	5	ahmad	ahmad	PROPN
ejpam-5936	298	6	/	/	SYM
ejpam-5936	298	7	eur	eur	PROPN
ejpam-5936	298	8	.	.	PUNCT
ejpam-5936	299	1	j.	j.	PROPN
ejpam-5936	299	2	pure	pure	PROPN
ejpam-5936	299	3	appl	appl	PROPN
ejpam-5936	299	4	.	.	PROPN
ejpam-5936	299	5	math	math	PROPN
ejpam-5936	299	6	,	,	PUNCT
ejpam-5936	299	7	18	18	NUM
ejpam-5936	299	8	(	(	PUNCT
ejpam-5936	299	9	2	2	NUM
ejpam-5936	299	10	)	)	PUNCT
ejpam-5936	299	11	(	(	PUNCT
ejpam-5936	299	12	2025	2025	NUM
ejpam-5936	299	13	)	)	PUNCT
ejpam-5936	299	14	,	,	PUNCT
ejpam-5936	299	15	5936	5936	NUM
ejpam-5936	299	16	18	18	NUM
ejpam-5936	299	17	of	of	ADP
ejpam-5936	299	18	18	18	NUM
ejpam-5936	299	19	[	[	X
ejpam-5936	299	20	21	21	NUM
ejpam-5936	299	21	]	]	PUNCT
ejpam-5936	299	22	k.	k.	PROPN
ejpam-5936	299	23	j.	j.	PROPN
ejpam-5936	299	24	wang	wang	PROPN
ejpam-5936	299	25	,	,	PUNCT
ejpam-5936	299	26	h.	h.	PROPN
ejpam-5936	299	27	w.	w.	PROPN
ejpam-5936	299	28	zhu	zhu	PROPN
ejpam-5936	299	29	,	,	PUNCT
ejpam-5936	299	30	f.	f.	PROPN
ejpam-5936	299	31	shi	shi	PROPN
ejpam-5936	299	32	,	,	PUNCT
ejpam-5936	299	33	x.	x.	PROPN
ejpam-5936	299	34	l.	l.	PROPN
ejpam-5936	299	35	liu	liu	PROPN
ejpam-5936	299	36	,	,	PUNCT
ejpam-5936	299	37	g.	g.	PROPN
ejpam-5936	299	38	d.	d.	PROPN
ejpam-5936	299	39	wang	wang	PROPN
ejpam-5936	299	40	,	,	PUNCT
ejpam-5936	299	41	and	and	CCONJ
ejpam-5936	299	42	g.	g.	PROPN
ejpam-5936	299	43	li	li	PROPN
ejpam-5936	299	44	,	,	PUNCT
ejpam-5936	299	45	lump	lump	NOUN
ejpam-5936	299	46	wave	wave	NOUN
ejpam-5936	299	47	,	,	PUNCT
ejpam-5936	299	48	breather	breather	NOUN
ejpam-5936	299	49	wave	wave	NOUN
ejpam-5936	299	50	and	and	CCONJ
ejpam-5936	299	51	other	other	ADJ
ejpam-5936	299	52	abundant	abundant	ADJ
ejpam-5936	299	53	wave	wave	NOUN
ejpam-5936	299	54	solutions	solution	NOUN
ejpam-5936	299	55	to	to	ADP
ejpam-5936	299	56	the	the	DET
ejpam-5936	299	57	(	(	PUNCT
ejpam-5936	299	58	2	2	NUM
ejpam-5936	299	59	+	+	NOUN
ejpam-5936	299	60	1)-dimensional	1)-dimensional	ADJ
ejpam-5936	299	61	sawada	sawada	NOUN
ejpam-5936	299	62	–	–	PUNCT
ejpam-5936	299	63	kotera	kotera	PROPN
ejpam-5936	299	64	–	–	PUNCT
ejpam-5936	299	65	kadomtsev	kadomtsev	VERB
ejpam-5936	299	66	petviashvili	petviashvili	ADJ
ejpam-5936	299	67	equation	equation	NOUN
ejpam-5936	299	68	of	of	ADP
ejpam-5936	299	69	fluid	fluid	ADJ
ejpam-5936	299	70	mechanics	mechanic	NOUN
ejpam-5936	299	71	,	,	PUNCT
ejpam-5936	299	72	pramana	pramana	NOUN
ejpam-5936	299	73	99	99	NUM
ejpam-5936	299	74	(	(	PUNCT
ejpam-5936	299	75	1	1	NUM
ejpam-5936	299	76	)	)	PUNCT
ejpam-5936	299	77	(	(	PUNCT
ejpam-5936	299	78	2025	2025	NUM
ejpam-5936	299	79	)	)	PUNCT
ejpam-5936	299	80	,	,	PUNCT
ejpam-5936	299	81	1–12	1–12	NOUN
ejpam-5936	299	82	.	.	PUNCT
ejpam-5936	300	1	[	[	X
ejpam-5936	300	2	22	22	NUM
ejpam-5936	300	3	]	]	PUNCT
ejpam-5936	300	4	s.	s.	PROPN
ejpam-5936	300	5	kumar	kumar	PROPN
ejpam-5936	300	6	,	,	PUNCT
ejpam-5936	300	7	i.	i.	PROPN
ejpam-5936	300	8	khan	khan	PROPN
ejpam-5936	300	9	,	,	PUNCT
ejpam-5936	300	10	s.	s.	PROPN
ejpam-5936	300	11	rani	rani	PROPN
ejpam-5936	300	12	,	,	PUNCT
ejpam-5936	300	13	and	and	CCONJ
ejpam-5936	300	14	b.	b.	PROPN
ejpam-5936	300	15	ghanbari	ghanbari	PROPN
ejpam-5936	300	16	,	,	PUNCT
ejpam-5936	300	17	lie	lie	NOUN
ejpam-5936	300	18	symmetry	symmetry	NOUN
ejpam-5936	300	19	analysis	analysis	NOUN
ejpam-5936	300	20	and	and	CCONJ
ejpam-5936	300	21	dynamics	dynamic	NOUN
ejpam-5936	300	22	of	of	ADP
ejpam-5936	300	23	exact	exact	ADJ
ejpam-5936	300	24	solutions	solution	NOUN
ejpam-5936	300	25	of	of	ADP
ejpam-5936	300	26	the	the	DET
ejpam-5936	300	27	(	(	PUNCT
ejpam-5936	300	28	2	2	NUM
ejpam-5936	300	29	+	+	NOUN
ejpam-5936	300	30	1)-dimensional	1)-dimensional	PROPN
ejpam-5936	300	31	nonlinear	nonlinear	ADJ
ejpam-5936	300	32	sharma	sharma	PROPN
ejpam-5936	300	33	–	–	PUNCT
ejpam-5936	300	34	tasso	tasso	ADJ
ejpam-5936	300	35	–	–	PUNCT
ejpam-5936	300	36	olver	olver	NOUN
ejpam-5936	300	37	equation	equation	NOUN
ejpam-5936	300	38	,	,	PUNCT
ejpam-5936	300	39	mathematical	mathematical	ADJ
ejpam-5936	300	40	problems	problem	NOUN
ejpam-5936	300	41	in	in	ADP
ejpam-5936	300	42	engineering	engineer	VERB
ejpam-5936	300	43	2021	2021	NUM
ejpam-5936	300	44	(	(	PUNCT
ejpam-5936	300	45	1	1	NUM
ejpam-5936	300	46	)	)	PUNCT
ejpam-5936	300	47	(	(	PUNCT
ejpam-5936	300	48	2021	2021	NUM
ejpam-5936	300	49	)	)	PUNCT
ejpam-5936	300	50	,	,	PUNCT
ejpam-5936	300	51	9961764	9961764	NUM
ejpam-5936	300	52	.	.	PUNCT
ejpam-5936	301	1	[	[	X
ejpam-5936	301	2	23	23	NUM
ejpam-5936	301	3	]	]	PUNCT
ejpam-5936	301	4	q.	q.	PROPN
ejpam-5936	301	5	zhang	zhang	PROPN
ejpam-5936	301	6	,	,	PUNCT
ejpam-5936	301	7	m.	m.	PROPN
ejpam-5936	301	8	xiong	xiong	PROPN
ejpam-5936	301	9	,	,	PUNCT
ejpam-5936	301	10	and	and	CCONJ
ejpam-5936	301	11	l.	l.	PROPN
ejpam-5936	301	12	chen	chen	PROPN
ejpam-5936	301	13	,	,	PUNCT
ejpam-5936	301	14	exact	exact	ADJ
ejpam-5936	301	15	solutions	solution	NOUN
ejpam-5936	301	16	of	of	ADP
ejpam-5936	301	17	two	two	NUM
ejpam-5936	301	18	nonlinear	nonlinear	ADJ
ejpam-5936	301	19	partial	partial	ADJ
ejpam-5936	301	20	differential	differential	NOUN
ejpam-5936	301	21	equations	equation	NOUN
ejpam-5936	301	22	by	by	ADP
ejpam-5936	301	23	the	the	DET
ejpam-5936	301	24	first	first	ADJ
ejpam-5936	301	25	integral	integral	ADJ
ejpam-5936	301	26	method	method	NOUN
ejpam-5936	301	27	,	,	PUNCT
ejpam-5936	301	28	advances	advance	NOUN
ejpam-5936	301	29	in	in	ADP
ejpam-5936	301	30	pure	pure	ADJ
ejpam-5936	301	31	mathematics	mathematic	NOUN
ejpam-5936	301	32	10	10	NUM
ejpam-5936	301	33	(	(	PUNCT
ejpam-5936	301	34	01	01	NUM
ejpam-5936	301	35	)	)	PUNCT
ejpam-5936	301	36	(	(	PUNCT
ejpam-5936	301	37	2020	2020	NUM
ejpam-5936	301	38	)	)	PUNCT
ejpam-5936	301	39	,	,	PUNCT
ejpam-5936	301	40	12–20	12–20	NUM
ejpam-5936	301	41	.	.	PUNCT
ejpam-5936	302	1	[	[	X
ejpam-5936	302	2	24	24	NUM
ejpam-5936	302	3	]	]	PUNCT
ejpam-5936	302	4	m.	m.	NOUN
ejpam-5936	302	5	shakeel	shakeel	PROPN
ejpam-5936	302	6	,	,	PUNCT
ejpam-5936	302	7	attaullah	attaullah	PROPN
ejpam-5936	302	8	,	,	PUNCT
ejpam-5936	302	9	n.	n.	NOUN
ejpam-5936	302	10	a.	a.	NOUN
ejpam-5936	302	11	shah	shah	PROPN
ejpam-5936	302	12	,	,	PUNCT
ejpam-5936	302	13	and	and	CCONJ
ejpam-5936	302	14	j.	j.	PROPN
ejpam-5936	302	15	d.	d.	PROPN
ejpam-5936	302	16	chung	chung	PROPN
ejpam-5936	302	17	,	,	PUNCT
ejpam-5936	302	18	modified	modify	VERB
ejpam-5936	302	19	exp	exp	NOUN
ejpam-5936	302	20	-	-	PUNCT
ejpam-5936	302	21	function	function	NOUN
ejpam-5936	302	22	method	method	NOUN
ejpam-5936	302	23	to	to	PART
ejpam-5936	302	24	find	find	VERB
ejpam-5936	302	25	exact	exact	ADJ
ejpam-5936	302	26	solutions	solution	NOUN
ejpam-5936	302	27	of	of	ADP
ejpam-5936	302	28	microtubules	microtubule	NOUN
ejpam-5936	302	29	nonlinear	nonlinear	ADJ
ejpam-5936	302	30	dynamics	dynamic	NOUN
ejpam-5936	302	31	models	model	NOUN
ejpam-5936	302	32	,	,	PUNCT
ejpam-5936	302	33	symmetry	symmetry	NOUN
ejpam-5936	302	34	15	15	NUM
ejpam-5936	302	35	(	(	PUNCT
ejpam-5936	302	36	2	2	NUM
ejpam-5936	302	37	)	)	PUNCT
ejpam-5936	302	38	(	(	PUNCT
ejpam-5936	302	39	2023	2023	NUM
ejpam-5936	302	40	)	)	PUNCT
ejpam-5936	302	41	,	,	PUNCT
ejpam-5936	302	42	360	360	NUM
ejpam-5936	302	43	.	.	PUNCT
ejpam-5936	303	1	[	[	X
ejpam-5936	303	2	25	25	NUM
ejpam-5936	303	3	]	]	PUNCT
ejpam-5936	303	4	m.	m.	PROPN
ejpam-5936	303	5	shakeel	shakeel	PROPN
ejpam-5936	303	6	,	,	PUNCT
ejpam-5936	303	7	q.	q.	PROPN
ejpam-5936	303	8	m.	m.	PROPN
ejpam-5936	303	9	ul	ul	PROPN
ejpam-5936	303	10	-	-	PROPN
ejpam-5936	303	11	hassan	hassan	PROPN
ejpam-5936	303	12	,	,	PUNCT
ejpam-5936	303	13	j.	j.	PROPN
ejpam-5936	303	14	ahmad	ahmad	PROPN
ejpam-5936	303	15	,	,	PUNCT
ejpam-5936	303	16	and	and	CCONJ
ejpam-5936	303	17	t.	t.	NOUN
ejpam-5936	303	18	naqvi	naqvi	NOUN
ejpam-5936	303	19	,	,	PUNCT
ejpam-5936	303	20	exact	exact	ADJ
ejpam-5936	303	21	solutions	solution	NOUN
ejpam-5936	303	22	of	of	ADP
ejpam-5936	303	23	the	the	DET
ejpam-5936	303	24	time	time	NOUN
ejpam-5936	303	25	fractional	fractional	PROPN
ejpam-5936	303	26	bbm	bbm	PROPN
ejpam-5936	303	27	–	–	PUNCT
ejpam-5936	303	28	burger	burger	NOUN
ejpam-5936	303	29	equation	equation	NOUN
ejpam-5936	303	30	by	by	ADP
ejpam-5936	303	31	novel	novel	NOUN
ejpam-5936	303	32	(	(	PUNCT
ejpam-5936	303	33	g	g	NOUN
ejpam-5936	303	34	′	′	NUM
ejpam-5936	303	35	g	g	NOUN
ejpam-5936	303	36	)	)	PUNCT
ejpam-5936	303	37	-expansion	-expansion	PROPN
ejpam-5936	303	38	method	method	NOUN
ejpam-5936	303	39	,	,	PUNCT
ejpam-5936	303	40	advances	advance	NOUN
ejpam-5936	303	41	in	in	ADP
ejpam-5936	303	42	mathematical	mathematical	ADJ
ejpam-5936	303	43	physics	physics	NOUN
ejpam-5936	303	44	2014	2014	NUM
ejpam-5936	303	45	(	(	PUNCT
ejpam-5936	303	46	1	1	NUM
ejpam-5936	303	47	)	)	PUNCT
ejpam-5936	303	48	(	(	PUNCT
ejpam-5936	303	49	2014	2014	NUM
ejpam-5936	303	50	)	)	PUNCT
ejpam-5936	303	51	,	,	PUNCT
ejpam-5936	303	52	181594	181594	NUM
ejpam-5936	303	53	.	.	PUNCT
ejpam-5936	304	1	[	[	X
ejpam-5936	304	2	26	26	NUM
ejpam-5936	304	3	]	]	PUNCT
ejpam-5936	304	4	k.	k.	PROPN
ejpam-5936	304	5	ahmad	ahmad	PROPN
ejpam-5936	304	6	and	and	CCONJ
ejpam-5936	304	7	k.	k.	PROPN
ejpam-5936	304	8	bibi	bibi	PROPN
ejpam-5936	304	9	,	,	PUNCT
ejpam-5936	304	10	new	new	ADJ
ejpam-5936	304	11	function	function	NOUN
ejpam-5936	304	12	solutions	solution	NOUN
ejpam-5936	304	13	of	of	ADP
ejpam-5936	304	14	ablowitz	ablowitz	NOUN
ejpam-5936	304	15	-	-	PUNCT
ejpam-5936	304	16	kaup	kaup	PROPN
ejpam-5936	304	17	-	-	PUNCT
ejpam-5936	304	18	newell	newell	PROPN
ejpam-5936	304	19	-	-	PUNCT
ejpam-5936	304	20	segur	segur	NOUN
ejpam-5936	304	21	water	water	NOUN
ejpam-5936	304	22	wave	wave	NOUN
ejpam-5936	304	23	equation	equation	NOUN
ejpam-5936	304	24	via	via	ADP
ejpam-5936	304	25	power	power	NOUN
ejpam-5936	304	26	index	index	NOUN
ejpam-5936	304	27	method	method	NOUN
ejpam-5936	304	28	,	,	PUNCT
ejpam-5936	304	29	journal	journal	NOUN
ejpam-5936	304	30	of	of	ADP
ejpam-5936	304	31	function	function	NOUN
ejpam-5936	304	32	spaces	space	VERB
ejpam-5936	304	33	2022	2022	NUM
ejpam-5936	304	34	(	(	PUNCT
ejpam-5936	304	35	1	1	NUM
ejpam-5936	304	36	)	)	PUNCT
ejpam-5936	304	37	(	(	PUNCT
ejpam-5936	304	38	2022	2022	NUM
ejpam-5936	304	39	)	)	PUNCT
ejpam-5936	304	40	,	,	PUNCT
ejpam-5936	304	41	9405644	9405644	NUM
ejpam-5936	304	42	.	.	PUNCT
ejpam-5936	305	1	[	[	X
ejpam-5936	305	2	27	27	NUM
ejpam-5936	305	3	]	]	X
ejpam-5936	305	4	m.	m.	PROPN
ejpam-5936	305	5	shakeel	shakeel	PROPN
ejpam-5936	305	6	,	,	PUNCT
ejpam-5936	305	7	attaullah	attaullah	PROPN
ejpam-5936	305	8	,	,	PUNCT
ejpam-5936	305	9	m.	m.	NOUN
ejpam-5936	305	10	kbiri	kbiri	PROPN
ejpam-5936	305	11	alaoui	alaoui	PROPN
ejpam-5936	305	12	,	,	PUNCT
ejpam-5936	305	13	a.	a.	PROPN
ejpam-5936	305	14	m.	m.	PROPN
ejpam-5936	305	15	zidan	zidan	PROPN
ejpam-5936	305	16	,	,	PUNCT
ejpam-5936	305	17	n.	n.	NOUN
ejpam-5936	305	18	a.	a.	NOUN
ejpam-5936	305	19	shah	shah	PROPN
ejpam-5936	305	20	,	,	PUNCT
ejpam-5936	305	21	and	and	CCONJ
ejpam-5936	305	22	w.	w.	PROPN
ejpam-5936	305	23	weera	weera	PROPN
ejpam-5936	305	24	,	,	PUNCT
ejpam-5936	305	25	closed	closed	ADJ
ejpam-5936	305	26	-	-	PUNCT
ejpam-5936	305	27	form	form	NOUN
ejpam-5936	305	28	solutions	solution	NOUN
ejpam-5936	305	29	in	in	ADP
ejpam-5936	305	30	a	a	DET
ejpam-5936	305	31	magneto	magneto	NOUN
ejpam-5936	305	32	-	-	PUNCT
ejpam-5936	305	33	electro	electro	ADJ
ejpam-5936	305	34	-	-	PUNCT
ejpam-5936	305	35	elastic	elastic	ADJ
ejpam-5936	305	36	circular	circular	ADJ
ejpam-5936	305	37	rod	rod	NOUN
ejpam-5936	305	38	via	via	ADP
ejpam-5936	305	39	generalized	generalized	ADJ
ejpam-5936	305	40	expfunction	expfunction	NOUN
ejpam-5936	305	41	method	method	NOUN
ejpam-5936	305	42	,	,	PUNCT
ejpam-5936	305	43	mathematics	mathematics	NOUN
ejpam-5936	305	44	10	10	NUM
ejpam-5936	305	45	(	(	PUNCT
ejpam-5936	305	46	18	18	NUM
ejpam-5936	305	47	)	)	PUNCT
ejpam-5936	305	48	(	(	PUNCT
ejpam-5936	305	49	2022	2022	NUM
ejpam-5936	305	50	)	)	PUNCT
ejpam-5936	305	51	,	,	PUNCT
ejpam-5936	305	52	3400	3400	NUM
ejpam-5936	305	53	.	.	PUNCT
ejpam-5936	306	1	[	[	X
ejpam-5936	306	2	28	28	NUM
ejpam-5936	306	3	]	]	X
ejpam-5936	306	4	a.	a.	NOUN
ejpam-5936	306	5	rani	rani	PROPN
ejpam-5936	306	6	,	,	PUNCT
ejpam-5936	306	7	m.	m.	PROPN
ejpam-5936	306	8	shakeel	shakeel	PROPN
ejpam-5936	306	9	,	,	PUNCT
ejpam-5936	306	10	m.	m.	PROPN
ejpam-5936	306	11	kbiri	kbiri	PROPN
ejpam-5936	306	12	alaoui	alaoui	PROPN
ejpam-5936	306	13	,	,	PUNCT
ejpam-5936	306	14	a.	a.	PROPN
ejpam-5936	306	15	m.	m.	PROPN
ejpam-5936	306	16	zidan	zidan	PROPN
ejpam-5936	306	17	,	,	PUNCT
ejpam-5936	306	18	n.	n.	NOUN
ejpam-5936	306	19	a.	a.	NOUN
ejpam-5936	306	20	shah	shah	PROPN
ejpam-5936	306	21	,	,	PUNCT
ejpam-5936	306	22	and	and	CCONJ
ejpam-5936	306	23	p.	p.	PROPN
ejpam-5936	306	24	junsawang	junsawang	PROPN
ejpam-5936	306	25	,	,	PUNCT
ejpam-5936	306	26	application	application	NOUN
ejpam-5936	306	27	of	of	ADP
ejpam-5936	306	28	the	the	DET
ejpam-5936	306	29	exp(−ϕ(ξ))-expansion	exp(−ϕ(ξ))-expansion	NOUN
ejpam-5936	306	30	method	method	NOUN
ejpam-5936	306	31	to	to	PART
ejpam-5936	306	32	find	find	VERB
ejpam-5936	306	33	the	the	DET
ejpam-5936	306	34	soliton	soliton	NOUN
ejpam-5936	306	35	solutions	solution	NOUN
ejpam-5936	306	36	in	in	ADP
ejpam-5936	306	37	biomembranes	biomembrane	NOUN
ejpam-5936	306	38	and	and	CCONJ
ejpam-5936	306	39	nerves	nerve	NOUN
ejpam-5936	306	40	,	,	PUNCT
ejpam-5936	306	41	mathematics	mathematics	PROPN
ejpam-5936	306	42	10	10	NUM
ejpam-5936	306	43	(	(	PUNCT
ejpam-5936	306	44	18	18	NUM
ejpam-5936	306	45	)	)	PUNCT
ejpam-5936	306	46	(	(	PUNCT
ejpam-5936	306	47	2022	2022	NUM
ejpam-5936	306	48	)	)	PUNCT
ejpam-5936	306	49	,	,	PUNCT
ejpam-5936	306	50	3372	3372	NUM
ejpam-5936	306	51	.	.	PUNCT
ejpam-5936	307	1	[	[	X
ejpam-5936	307	2	29	29	NUM
ejpam-5936	307	3	]	]	X
ejpam-5936	307	4	n.	n.	PROPN
ejpam-5936	307	5	k.	k.	PROPN
ejpam-5936	307	6	vitanov	vitanov	PROPN
ejpam-5936	307	7	,	,	PUNCT
ejpam-5936	307	8	z.	z.	PROPN
ejpam-5936	307	9	i.	i.	PROPN
ejpam-5936	307	10	dimitrova	dimitrova	PROPN
ejpam-5936	307	11	,	,	PUNCT
ejpam-5936	307	12	and	and	CCONJ
ejpam-5936	307	13	k.	k.	PROPN
ejpam-5936	307	14	n.	n.	PROPN
ejpam-5936	307	15	vitanov	vitanov	PROPN
ejpam-5936	307	16	,	,	PUNCT
ejpam-5936	307	17	on	on	ADP
ejpam-5936	307	18	the	the	DET
ejpam-5936	307	19	use	use	NOUN
ejpam-5936	307	20	of	of	ADP
ejpam-5936	307	21	composite	composite	ADJ
ejpam-5936	307	22	functions	function	NOUN
ejpam-5936	307	23	in	in	ADP
ejpam-5936	307	24	the	the	DET
ejpam-5936	307	25	simple	simple	ADJ
ejpam-5936	307	26	equations	equation	NOUN
ejpam-5936	307	27	method	method	VERB
ejpam-5936	307	28	to	to	PART
ejpam-5936	307	29	obtain	obtain	VERB
ejpam-5936	307	30	exact	exact	ADJ
ejpam-5936	307	31	solutions	solution	NOUN
ejpam-5936	307	32	of	of	ADP
ejpam-5936	307	33	nonlinear	nonlinear	ADJ
ejpam-5936	307	34	differential	differential	ADJ
ejpam-5936	307	35	equations	equation	NOUN
ejpam-5936	307	36	,	,	PUNCT
ejpam-5936	307	37	computation	computation	NOUN
ejpam-5936	307	38	9	9	NUM
ejpam-5936	307	39	(	(	PUNCT
ejpam-5936	307	40	10	10	NUM
ejpam-5936	307	41	)	)	PUNCT
ejpam-5936	307	42	(	(	PUNCT
ejpam-5936	307	43	2021	2021	NUM
ejpam-5936	307	44	)	)	PUNCT
ejpam-5936	307	45	,	,	PUNCT
ejpam-5936	307	46	104	104	NUM
ejpam-5936	307	47	.	.	PUNCT
ejpam-5936	308	1	[	[	X
ejpam-5936	308	2	30	30	NUM
ejpam-5936	308	3	]	]	PUNCT
ejpam-5936	308	4	m.	m.	NOUN
ejpam-5936	308	5	bilal	bilal	PROPN
ejpam-5936	308	6	,	,	PUNCT
ejpam-5936	308	7	j.	j.	PROPN
ejpam-5936	308	8	iqbal	iqbal	PROPN
ejpam-5936	308	9	,	,	PUNCT
ejpam-5936	308	10	k.	k.	PROPN
ejpam-5936	308	11	shah	shah	PROPN
ejpam-5936	308	12	,	,	PUNCT
ejpam-5936	308	13	b.	b.	PROPN
ejpam-5936	308	14	abdalla	abdalla	PROPN
ejpam-5936	308	15	,	,	PUNCT
ejpam-5936	308	16	t.	t.	NOUN
ejpam-5936	308	17	abdeljawad	abdeljawad	NOUN
ejpam-5936	308	18	,	,	PUNCT
ejpam-5936	308	19	and	and	CCONJ
ejpam-5936	308	20	i.	i.	PROPN
ejpam-5936	308	21	ullah	ullah	PROPN
ejpam-5936	308	22	,	,	PUNCT
ejpam-5936	308	23	analytical	analytical	ADJ
ejpam-5936	308	24	solutions	solution	NOUN
ejpam-5936	308	25	of	of	ADP
ejpam-5936	308	26	the	the	DET
ejpam-5936	308	27	space	space	NOUN
ejpam-5936	308	28	–	–	PUNCT
ejpam-5936	308	29	time	time	NOUN
ejpam-5936	308	30	fractional	fractional	ADJ
ejpam-5936	308	31	kundu	kundu	NOUN
ejpam-5936	308	32	–	–	PUNCT
ejpam-5936	308	33	eckhaus	eckhaus	NOUN
ejpam-5936	308	34	equation	equation	NOUN
ejpam-5936	308	35	by	by	ADP
ejpam-5936	308	36	using	use	VERB
ejpam-5936	308	37	modified	modify	VERB
ejpam-5936	308	38	extended	extend	VERB
ejpam-5936	308	39	direct	direct	ADJ
ejpam-5936	308	40	algebraic	algebraic	ADJ
ejpam-5936	308	41	method	method	NOUN
ejpam-5936	308	42	,	,	PUNCT
ejpam-5936	308	43	partial	partial	ADJ
ejpam-5936	308	44	differential	differential	ADJ
ejpam-5936	308	45	equations	equation	NOUN
ejpam-5936	308	46	in	in	ADP
ejpam-5936	308	47	applied	applied	ADJ
ejpam-5936	308	48	mathematics	mathematic	NOUN
ejpam-5936	308	49	11	11	NUM
ejpam-5936	308	50	(	(	PUNCT
ejpam-5936	308	51	2024	2024	NUM
ejpam-5936	308	52	)	)	PUNCT
ejpam-5936	308	53	,	,	PUNCT
ejpam-5936	308	54	100832	100832	NUM
ejpam-5936	308	55	.	.	PUNCT