id	sid	tid	token	lemma	pos
ejpam-5893	1	1	european	european	PROPN
ejpam-5893	1	2	journal	journal	PROPN
ejpam-5893	1	3	of	of	ADP
ejpam-5893	1	4	pure	pure	ADJ
ejpam-5893	1	5	and	and	CCONJ
ejpam-5893	1	6	applied	applied	ADJ
ejpam-5893	1	7	mathematics	mathematic	NOUN
ejpam-5893	1	8	2025	2025	NUM
ejpam-5893	1	9	,	,	PUNCT
ejpam-5893	1	10	vol	vol	NOUN
ejpam-5893	1	11	.	.	PROPN
ejpam-5893	1	12	18	18	NUM
ejpam-5893	1	13	,	,	PUNCT
ejpam-5893	1	14	issue	issue	NOUN
ejpam-5893	1	15	2	2	NUM
ejpam-5893	1	16	,	,	PUNCT
ejpam-5893	1	17	article	article	NOUN
ejpam-5893	1	18	number	number	NOUN
ejpam-5893	1	19	5893	5893	NUM
ejpam-5893	1	20	issn	issn	PROPN
ejpam-5893	1	21	1307	1307	NUM
ejpam-5893	1	22	-	-	SYM
ejpam-5893	1	23	5543	5543	NUM
ejpam-5893	1	24	–	–	PUNCT
ejpam-5893	1	25	ejpam.com	ejpam.com	X
ejpam-5893	1	26	published	publish	VERB
ejpam-5893	1	27	by	by	ADP
ejpam-5893	1	28	new	new	PROPN
ejpam-5893	1	29	york	york	PROPN
ejpam-5893	1	30	business	business	PROPN
ejpam-5893	1	31	global	global	ADJ
ejpam-5893	1	32	analyzing	analyzing	NOUN
ejpam-5893	1	33	approximate	approximate	ADJ
ejpam-5893	1	34	and	and	CCONJ
ejpam-5893	1	35	exact	exact	ADJ
ejpam-5893	1	36	wave	wave	NOUN
ejpam-5893	1	37	solutions	solution	NOUN
ejpam-5893	1	38	of	of	ADP
ejpam-5893	1	39	optical	optical	ADJ
ejpam-5893	1	40	fibres	fibre	NOUN
ejpam-5893	1	41	in	in	ADP
ejpam-5893	1	42	the	the	DET
ejpam-5893	1	43	time	time	NOUN
ejpam-5893	1	44	-	-	PUNCT
ejpam-5893	1	45	fractional	fractional	ADJ
ejpam-5893	1	46	estevez	estevez	PROPN
ejpam-5893	1	47	-	-	PUNCT
ejpam-5893	1	48	mansfield	mansfield	PROPN
ejpam-5893	1	49	-	-	PUNCT
ejpam-5893	1	50	clarkson	clarkson	PROPN
ejpam-5893	1	51	equation	equation	NOUN
ejpam-5893	1	52	bushra	bushra	PROPN
ejpam-5893	1	53	yasmeen1,∗	yasmeen1,∗	PROPN
ejpam-5893	1	54	,	,	PUNCT
ejpam-5893	1	55	khalil	khalil	PROPN
ejpam-5893	1	56	ahmad1	ahmad1	PROPN
ejpam-5893	1	57	,	,	PUNCT
ejpam-5893	1	58	nahid	nahid	PROPN
ejpam-5893	1	59	fatima2	fatima2	PROPN
ejpam-5893	1	60	1	1	NUM
ejpam-5893	1	61	department	department	NOUN
ejpam-5893	1	62	of	of	ADP
ejpam-5893	1	63	mathematics	mathematic	NOUN
ejpam-5893	1	64	,	,	PUNCT
ejpam-5893	1	65	faculty	faculty	NOUN
ejpam-5893	1	66	of	of	ADP
ejpam-5893	1	67	basic	basic	ADJ
ejpam-5893	1	68	and	and	CCONJ
ejpam-5893	1	69	applied	applied	ADJ
ejpam-5893	1	70	sciences	science	NOUN
ejpam-5893	1	71	,	,	PUNCT
ejpam-5893	1	72	air	air	NOUN
ejpam-5893	1	73	university	university	PROPN
ejpam-5893	1	74	,	,	PUNCT
ejpam-5893	1	75	paf	paf	PROPN
ejpam-5893	1	76	complex	complex	PROPN
ejpam-5893	1	77	e-9	e-9	PROPN
ejpam-5893	1	78	,	,	PUNCT
ejpam-5893	1	79	islamabad	islamabad	NOUN
ejpam-5893	1	80	44000	44000	NUM
ejpam-5893	1	81	,	,	PUNCT
ejpam-5893	1	82	pakistan	pakistan	PROPN
ejpam-5893	1	83	2	2	NUM
ejpam-5893	1	84	department	department	NOUN
ejpam-5893	1	85	of	of	ADP
ejpam-5893	1	86	mathematics	mathematic	NOUN
ejpam-5893	1	87	and	and	CCONJ
ejpam-5893	1	88	sciences	science	NOUN
ejpam-5893	1	89	,	,	PUNCT
ejpam-5893	1	90	prince	prince	PROPN
ejpam-5893	1	91	sultan	sultan	PROPN
ejpam-5893	1	92	university	university	PROPN
ejpam-5893	1	93	,	,	PUNCT
ejpam-5893	1	94	p.o.box	p.o.box	PROPN
ejpam-5893	1	95	no	no	NOUN
ejpam-5893	1	96	.	.	PUNCT
ejpam-5893	1	97	66833	66833	NUM
ejpam-5893	1	98	,	,	PUNCT
ejpam-5893	1	99	rafha	rafha	PROPN
ejpam-5893	1	100	street	street	PROPN
ejpam-5893	1	101	,	,	PUNCT
ejpam-5893	1	102	riyadh	riyadh	PROPN
ejpam-5893	1	103	11586	11586	NUM
ejpam-5893	1	104	,	,	PUNCT
ejpam-5893	1	105	saudi	saudi	PROPN
ejpam-5893	1	106	arabia	arabia	PROPN
ejpam-5893	1	107	abstract	abstract	NOUN
ejpam-5893	1	108	.	.	PUNCT
ejpam-5893	2	1	the	the	DET
ejpam-5893	2	2	study	study	NOUN
ejpam-5893	2	3	aims	aim	VERB
ejpam-5893	2	4	to	to	PART
ejpam-5893	2	5	employ	employ	VERB
ejpam-5893	2	6	the	the	DET
ejpam-5893	2	7	dynamics	dynamic	NOUN
ejpam-5893	2	8	of	of	ADP
ejpam-5893	2	9	hyperbolic	hyperbolic	ADJ
ejpam-5893	2	10	and	and	CCONJ
ejpam-5893	2	11	solitons	soliton	NOUN
ejpam-5893	2	12	wave	wave	NOUN
ejpam-5893	2	13	solutions	solution	NOUN
ejpam-5893	2	14	to	to	ADP
ejpam-5893	2	15	the	the	DET
ejpam-5893	2	16	time	time	NOUN
ejpam-5893	2	17	-	-	PUNCT
ejpam-5893	2	18	fractional	fractional	ADJ
ejpam-5893	2	19	estevez	estevez	PROPN
ejpam-5893	2	20	-	-	PUNCT
ejpam-5893	2	21	mansfield	mansfield	PROPN
ejpam-5893	2	22	-	-	PUNCT
ejpam-5893	2	23	clarkson	clarkson	PROPN
ejpam-5893	2	24	equation	equation	NOUN
ejpam-5893	2	25	,	,	PUNCT
ejpam-5893	2	26	which	which	PRON
ejpam-5893	2	27	is	be	AUX
ejpam-5893	2	28	utilize	utilize	ADJ
ejpam-5893	2	29	to	to	PART
ejpam-5893	2	30	stimulate	stimulate	VERB
ejpam-5893	2	31	the	the	DET
ejpam-5893	2	32	optical	optical	ADJ
ejpam-5893	2	33	fibre	fibre	NOUN
ejpam-5893	2	34	waves	wave	NOUN
ejpam-5893	2	35	in	in	ADP
ejpam-5893	2	36	communication	communication	NOUN
ejpam-5893	2	37	system	system	NOUN
ejpam-5893	2	38	and	and	CCONJ
ejpam-5893	2	39	image	image	NOUN
ejpam-5893	2	40	processing	processing	NOUN
ejpam-5893	2	41	.	.	PUNCT
ejpam-5893	3	1	the	the	DET
ejpam-5893	3	2	proposed	propose	VERB
ejpam-5893	3	3	method	method	NOUN
ejpam-5893	3	4	entails	entail	VERB
ejpam-5893	3	5	transforming	transform	VERB
ejpam-5893	3	6	nonlinear	nonlinear	ADJ
ejpam-5893	3	7	fractional	fractional	ADJ
ejpam-5893	3	8	partial	partial	ADJ
ejpam-5893	3	9	differential	differential	ADJ
ejpam-5893	3	10	equations	equation	NOUN
ejpam-5893	3	11	into	into	ADP
ejpam-5893	3	12	nonlinear	nonlinear	ADJ
ejpam-5893	3	13	ordinary	ordinary	ADJ
ejpam-5893	3	14	differential	differential	ADJ
ejpam-5893	3	15	equations	equation	NOUN
ejpam-5893	3	16	.	.	PUNCT
ejpam-5893	4	1	various	various	ADJ
ejpam-5893	4	2	solutions	solution	NOUN
ejpam-5893	4	3	for	for	ADP
ejpam-5893	4	4	the	the	DET
ejpam-5893	4	5	current	current	ADJ
ejpam-5893	4	6	model	model	NOUN
ejpam-5893	4	7	are	be	AUX
ejpam-5893	4	8	derived	derive	VERB
ejpam-5893	4	9	in	in	ADP
ejpam-5893	4	10	the	the	DET
ejpam-5893	4	11	form	form	NOUN
ejpam-5893	4	12	of	of	ADP
ejpam-5893	4	13	exponential	exponential	ADJ
ejpam-5893	4	14	and	and	CCONJ
ejpam-5893	4	15	trigonometric	trigonometric	ADJ
ejpam-5893	4	16	functions	function	NOUN
ejpam-5893	4	17	.	.	PUNCT
ejpam-5893	5	1	the	the	DET
ejpam-5893	5	2	2d	2d	NOUN
ejpam-5893	5	3	and	and	CCONJ
ejpam-5893	5	4	3d	3d	NUM
ejpam-5893	5	5	under	under	ADP
ejpam-5893	5	6	some	some	DET
ejpam-5893	5	7	suitable	suitable	ADJ
ejpam-5893	5	8	values	value	NOUN
ejpam-5893	5	9	of	of	ADP
ejpam-5893	5	10	parameters	parameter	NOUN
ejpam-5893	5	11	are	be	AUX
ejpam-5893	5	12	also	also	ADV
ejpam-5893	5	13	plotted	plot	VERB
ejpam-5893	5	14	.	.	PUNCT
ejpam-5893	6	1	the	the	DET
ejpam-5893	6	2	accomplished	accomplish	VERB
ejpam-5893	6	3	solutions	solution	NOUN
ejpam-5893	6	4	show	show	VERB
ejpam-5893	6	5	that	that	SCONJ
ejpam-5893	6	6	these	these	PRON
ejpam-5893	6	7	are	be	AUX
ejpam-5893	6	8	reliable	reliable	ADJ
ejpam-5893	6	9	,	,	PUNCT
ejpam-5893	6	10	applicable	applicable	ADJ
ejpam-5893	6	11	,	,	PUNCT
ejpam-5893	6	12	efficient	efficient	ADJ
ejpam-5893	6	13	and	and	CCONJ
ejpam-5893	6	14	intricate	intricate	ADJ
ejpam-5893	6	15	dynamics	dynamic	NOUN
ejpam-5893	6	16	inherent	inherent	ADJ
ejpam-5893	6	17	in	in	ADP
ejpam-5893	6	18	the	the	DET
ejpam-5893	6	19	communication	communication	NOUN
ejpam-5893	6	20	system	system	NOUN
ejpam-5893	6	21	,	,	PUNCT
ejpam-5893	6	22	image	image	NOUN
ejpam-5893	6	23	processing	processing	NOUN
ejpam-5893	6	24	and	and	CCONJ
ejpam-5893	6	25	might	might	AUX
ejpam-5893	6	26	be	be	AUX
ejpam-5893	6	27	used	use	VERB
ejpam-5893	6	28	in	in	ADP
ejpam-5893	6	29	further	further	ADJ
ejpam-5893	6	30	works	work	NOUN
ejpam-5893	6	31	to	to	PART
ejpam-5893	6	32	found	find	VERB
ejpam-5893	6	33	novel	novel	ADJ
ejpam-5893	6	34	solutions	solution	NOUN
ejpam-5893	6	35	for	for	ADP
ejpam-5893	6	36	other	other	ADJ
ejpam-5893	6	37	types	type	NOUN
ejpam-5893	6	38	of	of	ADP
ejpam-5893	6	39	nonlinear	nonlinear	ADJ
ejpam-5893	6	40	evolution	evolution	NOUN
ejpam-5893	6	41	equations	equation	NOUN
ejpam-5893	6	42	ascending	ascend	VERB
ejpam-5893	6	43	in	in	ADP
ejpam-5893	6	44	physical	physical	ADJ
ejpam-5893	6	45	science	science	NOUN
ejpam-5893	6	46	and	and	CCONJ
ejpam-5893	6	47	engineering	engineering	NOUN
ejpam-5893	6	48	.	.	PUNCT
ejpam-5893	7	1	the	the	DET
ejpam-5893	7	2	novelty	novelty	NOUN
ejpam-5893	7	3	of	of	ADP
ejpam-5893	7	4	our	our	PRON
ejpam-5893	7	5	result	result	NOUN
ejpam-5893	7	6	is	be	AUX
ejpam-5893	7	7	to	to	PART
ejpam-5893	7	8	offer	offer	VERB
ejpam-5893	7	9	new	new	ADJ
ejpam-5893	7	10	and	and	CCONJ
ejpam-5893	7	11	critical	critical	ADJ
ejpam-5893	7	12	insights	insight	NOUN
ejpam-5893	7	13	into	into	ADP
ejpam-5893	7	14	the	the	DET
ejpam-5893	7	15	intricate	intricate	ADJ
ejpam-5893	7	16	wave	wave	NOUN
ejpam-5893	7	17	behaviors	behavior	NOUN
ejpam-5893	7	18	of	of	ADP
ejpam-5893	7	19	the	the	DET
ejpam-5893	7	20	time	time	NOUN
ejpam-5893	7	21	-	-	PUNCT
ejpam-5893	7	22	fractional	fractional	ADJ
ejpam-5893	7	23	estevez	estevez	PROPN
ejpam-5893	7	24	-	-	PUNCT
ejpam-5893	7	25	mansfield	mansfield	PROPN
ejpam-5893	7	26	-	-	PUNCT
ejpam-5893	7	27	clarkson	clarkson	PROPN
ejpam-5893	7	28	equation	equation	NOUN
ejpam-5893	7	29	by	by	ADP
ejpam-5893	7	30	illustrating	illustrate	VERB
ejpam-5893	7	31	the	the	DET
ejpam-5893	7	32	basic	basic	ADJ
ejpam-5893	7	33	mechanics	mechanic	NOUN
ejpam-5893	7	34	of	of	ADP
ejpam-5893	7	35	the	the	DET
ejpam-5893	7	36	importance	importance	NOUN
ejpam-5893	7	37	of	of	ADP
ejpam-5893	7	38	waves	wave	NOUN
ejpam-5893	7	39	interaction	interaction	NOUN
ejpam-5893	7	40	and	and	CCONJ
ejpam-5893	7	41	propagation	propagation	NOUN
ejpam-5893	7	42	in	in	ADP
ejpam-5893	7	43	optical	optical	ADJ
ejpam-5893	7	44	fibres	fibre	NOUN
ejpam-5893	7	45	in	in	ADP
ejpam-5893	7	46	deepening	deepen	VERB
ejpam-5893	7	47	our	our	PRON
ejpam-5893	7	48	knowledge	knowledge	NOUN
ejpam-5893	7	49	about	about	ADP
ejpam-5893	7	50	the	the	DET
ejpam-5893	7	51	basic	basic	ADJ
ejpam-5893	7	52	physical	physical	ADJ
ejpam-5893	7	53	model	model	NOUN
ejpam-5893	7	54	.	.	PUNCT
ejpam-5893	8	1	2020	2020	NUM
ejpam-5893	8	2	mathematics	mathematics	PROPN
ejpam-5893	8	3	subject	subject	NOUN
ejpam-5893	8	4	classifications	classification	NOUN
ejpam-5893	8	5	:	:	PUNCT
ejpam-5893	8	6	35qxx	35qxx	NOUN
ejpam-5893	8	7	,	,	PUNCT
ejpam-5893	8	8	26a33	26a33	NUM
ejpam-5893	8	9	key	key	ADJ
ejpam-5893	8	10	words	word	NOUN
ejpam-5893	8	11	and	and	CCONJ
ejpam-5893	8	12	phrases	phrase	NOUN
ejpam-5893	8	13	:	:	PUNCT
ejpam-5893	8	14	nonlinear	nonlinear	ADJ
ejpam-5893	8	15	differential	differential	ADJ
ejpam-5893	8	16	equations	equation	NOUN
ejpam-5893	8	17	,	,	PUNCT
ejpam-5893	8	18	stability	stability	NOUN
ejpam-5893	8	19	analysis	analysis	NOUN
ejpam-5893	8	20	,	,	PUNCT
ejpam-5893	8	21	rescaling	rescaling	NOUN
ejpam-5893	8	22	method	method	NOUN
ejpam-5893	8	23	,	,	PUNCT
ejpam-5893	8	24	fractional	fractional	ADJ
ejpam-5893	8	25	calculus	calculus	NOUN
ejpam-5893	8	26	,	,	PUNCT
ejpam-5893	8	27	traveling	travel	VERB
ejpam-5893	8	28	wave	wave	NOUN
ejpam-5893	8	29	transformation	transformation	NOUN
ejpam-5893	8	30	1	1	NUM
ejpam-5893	8	31	.	.	PUNCT
ejpam-5893	8	32	introduction	introduction	NOUN
ejpam-5893	8	33	in	in	ADP
ejpam-5893	8	34	applied	apply	VERB
ejpam-5893	8	35	science	science	NOUN
ejpam-5893	8	36	,	,	PUNCT
ejpam-5893	8	37	engineering	engineering	NOUN
ejpam-5893	8	38	,	,	PUNCT
ejpam-5893	8	39	and	and	CCONJ
ejpam-5893	8	40	mathematics	mathematic	NOUN
ejpam-5893	8	41	,	,	PUNCT
ejpam-5893	8	42	as	as	ADV
ejpam-5893	8	43	well	well	ADV
ejpam-5893	8	44	as	as	ADP
ejpam-5893	8	45	in	in	ADP
ejpam-5893	8	46	the	the	DET
ejpam-5893	8	47	modeling	modeling	NOUN
ejpam-5893	8	48	of	of	ADP
ejpam-5893	8	49	a	a	DET
ejpam-5893	8	50	variety	variety	NOUN
ejpam-5893	8	51	of	of	ADP
ejpam-5893	8	52	physical	physical	ADJ
ejpam-5893	8	53	nonlinear	nonlinear	ADJ
ejpam-5893	8	54	phenomena	phenomenon	NOUN
ejpam-5893	8	55	,	,	PUNCT
ejpam-5893	8	56	nonlinear	nonlinear	ADJ
ejpam-5893	8	57	fractional	fractional	ADJ
ejpam-5893	8	58	partial	partial	ADJ
ejpam-5893	8	59	differential	differential	NOUN
ejpam-5893	8	60	equations	equation	NOUN
ejpam-5893	8	61	(	(	PUNCT
ejpam-5893	8	62	nfpdes	nfpde	NOUN
ejpam-5893	8	63	)	)	PUNCT
ejpam-5893	8	64	are	be	AUX
ejpam-5893	8	65	essential	essential	ADJ
ejpam-5893	8	66	[	[	X
ejpam-5893	8	67	1	1	NUM
ejpam-5893	8	68	]	]	PUNCT
ejpam-5893	8	69	,	,	PUNCT
ejpam-5893	8	70	[	[	X
ejpam-5893	8	71	2	2	NUM
ejpam-5893	8	72	]	]	PUNCT
ejpam-5893	8	73	.	.	PUNCT
ejpam-5893	9	1	the	the	DET
ejpam-5893	9	2	numerous	numerous	ADJ
ejpam-5893	9	3	fractional	fractional	ADJ
ejpam-5893	9	4	models	model	NOUN
ejpam-5893	9	5	[	[	X
ejpam-5893	9	6	3	3	X
ejpam-5893	9	7	]	]	PUNCT
ejpam-5893	9	8	created	create	VERB
ejpam-5893	9	9	in	in	ADP
ejpam-5893	9	10	[	[	X
ejpam-5893	9	11	4	4	X
ejpam-5893	9	12	]	]	PUNCT
ejpam-5893	9	13	have	have	AUX
ejpam-5893	9	14	attracted	attract	VERB
ejpam-5893	9	15	a	a	DET
ejpam-5893	9	16	lot	lot	NOUN
ejpam-5893	9	17	of	of	ADP
ejpam-5893	9	18	interest	interest	NOUN
ejpam-5893	9	19	in	in	ADP
ejpam-5893	9	20	the	the	DET
ejpam-5893	9	21	domains	domain	NOUN
ejpam-5893	9	22	of	of	ADP
ejpam-5893	9	23	fluid	fluid	NOUN
ejpam-5893	9	24	dynamics	dynamic	NOUN
ejpam-5893	9	25	,	,	PUNCT
ejpam-5893	9	26	fluid	fluid	ADJ
ejpam-5893	9	27	mechanics	mechanic	NOUN
ejpam-5893	9	28	,	,	PUNCT
ejpam-5893	9	29	neurons	neuron	NOUN
ejpam-5893	9	30	,	,	PUNCT
ejpam-5893	9	31	optical	optical	ADJ
ejpam-5893	9	32	fibers	fiber	NOUN
ejpam-5893	9	33	,	,	PUNCT
ejpam-5893	9	34	electric	electric	ADJ
ejpam-5893	9	35	circuits	circuit	NOUN
ejpam-5893	9	36	,	,	PUNCT
ejpam-5893	9	37	water	water	NOUN
ejpam-5893	9	38	waves	wave	NOUN
ejpam-5893	9	39	,	,	PUNCT
ejpam-5893	9	40	plasma	plasma	NOUN
ejpam-5893	9	41	waves	wave	NOUN
ejpam-5893	9	42	,	,	PUNCT
ejpam-5893	9	43	capillary	capillary	ADJ
ejpam-5893	9	44	-	-	PUNCT
ejpam-5893	9	45	gravity	gravity	NOUN
ejpam-5893	9	46	waves	wave	NOUN
ejpam-5893	9	47	,	,	PUNCT
ejpam-5893	9	48	chemical	chemical	NOUN
ejpam-5893	9	49	∗corresponding	∗corresponde	VERB
ejpam-5893	9	50	author	author	NOUN
ejpam-5893	9	51	.	.	PUNCT
ejpam-5893	10	1	doi	doi	NOUN
ejpam-5893	10	2	:	:	PUNCT
ejpam-5893	10	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5893	https://doi.org/10.29020/nybg.ejpam.v18i2.5893	PROPN
ejpam-5893	10	4	email	email	NOUN
ejpam-5893	10	5	addresses	address	NOUN
ejpam-5893	10	6	:	:	PUNCT
ejpam-5893	10	7	211927@students.au.edu.pk	211927@students.au.edu.pk	NUM
ejpam-5893	10	8	(	(	PUNCT
ejpam-5893	10	9	b.	b.	PROPN
ejpam-5893	10	10	yasmeen	yasmeen	PROPN
ejpam-5893	10	11	)	)	PUNCT
ejpam-5893	10	12	,	,	PUNCT
ejpam-5893	10	13	khalilmalik@au.edu.pk	khalilmalik@au.edu.pk	PROPN
ejpam-5893	10	14	(	(	PUNCT
ejpam-5893	10	15	k.	k.	PROPN
ejpam-5893	10	16	ahmad	ahmad	PROPN
ejpam-5893	10	17	)	)	PUNCT
ejpam-5893	10	18	,	,	PUNCT
ejpam-5893	10	19	drnahidfatima@gmail.com	drnahidfatima@gmail.com	X
ejpam-5893	10	20	(	(	PUNCT
ejpam-5893	10	21	n.	n.	PROPN
ejpam-5893	10	22	fatima	fatima	PROPN
ejpam-5893	10	23	)	)	PUNCT
ejpam-5893	10	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5893	11	1	1	1	NUM
ejpam-5893	11	2	copyright	copyright	NOUN
ejpam-5893	11	3	:	:	PUNCT
ejpam-5893	11	4	©	©	PROPN
ejpam-5893	11	5	2025	2025	NUM
ejpam-5893	11	6	the	the	DET
ejpam-5893	11	7	author(s	author(s	NOUN
ejpam-5893	11	8	)	)	PUNCT
ejpam-5893	11	9	.	.	PUNCT
ejpam-5893	12	1	(	(	PUNCT
ejpam-5893	12	2	cc	cc	NOUN
ejpam-5893	12	3	by	by	ADP
ejpam-5893	12	4	-	-	PUNCT
ejpam-5893	12	5	nc	nc	PROPN
ejpam-5893	12	6	4.0	4.0	NUM
ejpam-5893	12	7	)	)	PUNCT
ejpam-5893	12	8	b.	b.	PROPN
ejpam-5893	12	9	yasmeen	yasmeen	PROPN
ejpam-5893	12	10	,	,	PUNCT
ejpam-5893	12	11	k.	k.	PROPN
ejpam-5893	12	12	ahmad	ahmad	PROPN
ejpam-5893	12	13	,	,	PUNCT
ejpam-5893	12	14	n.	n.	PROPN
ejpam-5893	12	15	fatima	fatima	PROPN
ejpam-5893	12	16	/	/	PUNCT
ejpam-5893	12	17	eur	eur	PROPN
ejpam-5893	12	18	.	.	PUNCT
ejpam-5893	13	1	j.	j.	PROPN
ejpam-5893	13	2	pure	pure	PROPN
ejpam-5893	13	3	appl	appl	PROPN
ejpam-5893	13	4	.	.	PROPN
ejpam-5893	13	5	math	math	PROPN
ejpam-5893	13	6	,	,	PUNCT
ejpam-5893	13	7	18	18	NUM
ejpam-5893	13	8	(	(	PUNCT
ejpam-5893	13	9	2	2	NUM
ejpam-5893	13	10	)	)	PUNCT
ejpam-5893	13	11	(	(	PUNCT
ejpam-5893	13	12	2025	2025	NUM
ejpam-5893	13	13	)	)	PUNCT
ejpam-5893	13	14	,	,	PUNCT
ejpam-5893	13	15	5893	5893	NUM
ejpam-5893	13	16	2	2	NUM
ejpam-5893	13	17	of	of	ADP
ejpam-5893	13	18	17	17	NUM
ejpam-5893	13	19	physics	physic	NOUN
ejpam-5893	13	20	,	,	PUNCT
ejpam-5893	13	21	and	and	CCONJ
ejpam-5893	13	22	plasma	plasma	NOUN
ejpam-5893	13	23	physics	physics	NOUN
ejpam-5893	13	24	.	.	PUNCT
ejpam-5893	14	1	it	it	PRON
ejpam-5893	14	2	is	be	AUX
ejpam-5893	14	3	crucial	crucial	ADJ
ejpam-5893	14	4	to	to	PART
ejpam-5893	14	5	comprehend	comprehend	VERB
ejpam-5893	14	6	how	how	SCONJ
ejpam-5893	14	7	different	different	ADJ
ejpam-5893	14	8	elements	element	NOUN
ejpam-5893	14	9	behave	behave	VERB
ejpam-5893	14	10	in	in	ADP
ejpam-5893	14	11	different	different	ADJ
ejpam-5893	14	12	scientific	scientific	ADJ
ejpam-5893	14	13	domains	domain	NOUN
ejpam-5893	14	14	,	,	PUNCT
ejpam-5893	14	15	which	which	PRON
ejpam-5893	14	16	emphasizes	emphasize	VERB
ejpam-5893	14	17	the	the	DET
ejpam-5893	14	18	need	need	NOUN
ejpam-5893	14	19	to	to	PART
ejpam-5893	14	20	investigate	investigate	VERB
ejpam-5893	14	21	methods	method	NOUN
ejpam-5893	14	22	for	for	ADP
ejpam-5893	14	23	solving	solve	VERB
ejpam-5893	14	24	non	non	ADJ
ejpam-5893	14	25	-	-	ADJ
ejpam-5893	14	26	functional	functional	ADJ
ejpam-5893	14	27	partial	partial	ADJ
ejpam-5893	14	28	differential	differential	NOUN
ejpam-5893	14	29	equations	equation	NOUN
ejpam-5893	14	30	(	(	PUNCT
ejpam-5893	14	31	pdes	pde	NOUN
ejpam-5893	14	32	)	)	PUNCT
ejpam-5893	15	1	[	[	X
ejpam-5893	15	2	5	5	NUM
ejpam-5893	15	3	]	]	PUNCT
ejpam-5893	15	4	,	,	PUNCT
ejpam-5893	15	5	[	[	X
ejpam-5893	15	6	6	6	NUM
ejpam-5893	15	7	]	]	PUNCT
ejpam-5893	15	8	and	and	CCONJ
ejpam-5893	15	9	[	[	X
ejpam-5893	15	10	7	7	NUM
ejpam-5893	15	11	]	]	PUNCT
ejpam-5893	15	12	.	.	PUNCT
ejpam-5893	16	1	investigating	investigate	VERB
ejpam-5893	16	2	techniques	technique	NOUN
ejpam-5893	16	3	for	for	ADP
ejpam-5893	16	4	solving	solve	VERB
ejpam-5893	16	5	fractional	fractional	ADJ
ejpam-5893	16	6	nonlinear	nonlinear	ADJ
ejpam-5893	16	7	partial	partial	ADJ
ejpam-5893	16	8	differential	differential	NOUN
ejpam-5893	16	9	equations	equation	NOUN
ejpam-5893	16	10	(	(	PUNCT
ejpam-5893	16	11	pdes	pde	NOUN
ejpam-5893	16	12	)	)	PUNCT
ejpam-5893	16	13	is	be	AUX
ejpam-5893	16	14	necessary	necessary	ADJ
ejpam-5893	16	15	to	to	PART
ejpam-5893	16	16	better	well	ADV
ejpam-5893	16	17	understand	understand	VERB
ejpam-5893	16	18	the	the	DET
ejpam-5893	16	19	dynamics	dynamic	NOUN
ejpam-5893	16	20	of	of	ADP
ejpam-5893	16	21	these	these	DET
ejpam-5893	16	22	real	real	ADJ
ejpam-5893	16	23	-	-	PUNCT
ejpam-5893	16	24	world	world	NOUN
ejpam-5893	16	25	components	component	NOUN
ejpam-5893	16	26	.	.	PUNCT
ejpam-5893	17	1	this	this	DET
ejpam-5893	17	2	investigation	investigation	NOUN
ejpam-5893	17	3	is	be	AUX
ejpam-5893	17	4	necessary	necessary	ADJ
ejpam-5893	17	5	to	to	PART
ejpam-5893	17	6	learn	learn	VERB
ejpam-5893	17	7	more	more	ADV
ejpam-5893	17	8	about	about	ADV
ejpam-5893	17	9	and	and	CCONJ
ejpam-5893	17	10	comprehend	comprehend	VERB
ejpam-5893	17	11	the	the	DET
ejpam-5893	17	12	intricate	intricate	ADJ
ejpam-5893	17	13	behaviors	behavior	NOUN
ejpam-5893	17	14	that	that	PRON
ejpam-5893	17	15	are	be	AUX
ejpam-5893	17	16	present	present	ADJ
ejpam-5893	17	17	in	in	ADP
ejpam-5893	17	18	the	the	DET
ejpam-5893	17	19	systems	system	NOUN
ejpam-5893	17	20	indicated	indicate	VERB
ejpam-5893	17	21	above	above	ADV
ejpam-5893	17	22	.	.	PUNCT
ejpam-5893	18	1	the	the	DET
ejpam-5893	18	2	greater	great	ADJ
ejpam-5893	18	3	richness	richness	NOUN
ejpam-5893	18	4	and	and	CCONJ
ejpam-5893	18	5	generality	generality	NOUN
ejpam-5893	18	6	that	that	PRON
ejpam-5893	18	7	fractional	fractional	ADJ
ejpam-5893	18	8	nonlinear	nonlinear	ADJ
ejpam-5893	18	9	pde	pde	NOUN
ejpam-5893	18	10	solutions	solution	NOUN
ejpam-5893	18	11	offer	offer	NOUN
ejpam-5893	18	12	,	,	PUNCT
ejpam-5893	18	13	which	which	PRON
ejpam-5893	18	14	surpasses	surpass	VERB
ejpam-5893	18	15	classical	classical	ADJ
ejpam-5893	18	16	solutions	solution	NOUN
ejpam-5893	18	17	in	in	ADP
ejpam-5893	18	18	terms	term	NOUN
ejpam-5893	18	19	of	of	ADP
ejpam-5893	18	20	descriptive	descriptive	ADJ
ejpam-5893	18	21	power	power	NOUN
ejpam-5893	18	22	,	,	PUNCT
ejpam-5893	18	23	makes	make	VERB
ejpam-5893	18	24	them	they	PRON
ejpam-5893	18	25	of	of	ADP
ejpam-5893	18	26	scholarly	scholarly	ADJ
ejpam-5893	18	27	interest	interest	NOUN
ejpam-5893	18	28	[	[	X
ejpam-5893	18	29	3	3	NUM
ejpam-5893	18	30	]	]	PUNCT
ejpam-5893	18	31	.	.	PUNCT
ejpam-5893	19	1	to	to	PART
ejpam-5893	19	2	investigate	investigate	VERB
ejpam-5893	19	3	new	new	ADJ
ejpam-5893	19	4	findings	finding	NOUN
ejpam-5893	19	5	,	,	PUNCT
ejpam-5893	19	6	mathematicians	mathematician	NOUN
ejpam-5893	19	7	have	have	AUX
ejpam-5893	19	8	developed	develop	VERB
ejpam-5893	19	9	and	and	CCONJ
ejpam-5893	19	10	implemented	implement	VERB
ejpam-5893	19	11	innovative	innovative	ADJ
ejpam-5893	19	12	and	and	CCONJ
ejpam-5893	19	13	reliable	reliable	ADJ
ejpam-5893	19	14	techniques	technique	NOUN
ejpam-5893	19	15	.	.	PUNCT
ejpam-5893	20	1	some	some	PRON
ejpam-5893	20	2	of	of	ADP
ejpam-5893	20	3	these	these	DET
ejpam-5893	20	4	methods	method	NOUN
ejpam-5893	20	5	are	be	AUX
ejpam-5893	20	6	,	,	PUNCT
ejpam-5893	20	7	generalized	generalized	ADJ
ejpam-5893	20	8	khater	khater	NOUN
ejpam-5893	20	9	method	method	NOUN
ejpam-5893	20	10	,	,	PUNCT
ejpam-5893	20	11	modified	modify	VERB
ejpam-5893	20	12	khater	khater	NOUN
ejpam-5893	20	13	method	method	NOUN
ejpam-5893	20	14	,	,	PUNCT
ejpam-5893	20	15	simple	simple	ADJ
ejpam-5893	20	16	equation	equation	NOUN
ejpam-5893	20	17	method	method	NOUN
ejpam-5893	20	18	,	,	PUNCT
ejpam-5893	20	19	poincare	poincare	PROPN
ejpam-5893	20	20	-	-	PUNCT
ejpam-5893	20	21	lighthill	lighthill	NOUN
ejpam-5893	20	22	-	-	PUNCT
ejpam-5893	20	23	kuo	kuo	PROPN
ejpam-5893	20	24	method	method	NOUN
ejpam-5893	20	25	,	,	PUNCT
ejpam-5893	20	26	generalized	generalize	VERB
ejpam-5893	20	27	kudryashov	kudryashov	PROPN
ejpam-5893	20	28	method	method	NOUN
ejpam-5893	20	29	,	,	PUNCT
ejpam-5893	20	30	fractional	fractional	ADJ
ejpam-5893	20	31	sub	sub	ADJ
ejpam-5893	20	32	-	-	ADJ
ejpam-5893	20	33	equation	equation	NOUN
ejpam-5893	20	34	method	method	NOUN
ejpam-5893	20	35	,	,	PUNCT
ejpam-5893	20	36	modified	modify	VERB
ejpam-5893	20	37	extended	extend	VERB
ejpam-5893	20	38	direct	direct	ADJ
ejpam-5893	20	39	algebraic	algebraic	ADJ
ejpam-5893	20	40	method	method	NOUN
ejpam-5893	20	41	and	and	CCONJ
ejpam-5893	20	42	(	(	PUNCT
ejpam-5893	20	43	g’/g)-expansion	g’/g)-expansion	NOUN
ejpam-5893	20	44	method	method	NOUN
ejpam-5893	20	45	.	.	PUNCT
ejpam-5893	21	1	recent	recent	ADJ
ejpam-5893	21	2	studies	study	NOUN
ejpam-5893	21	3	have	have	AUX
ejpam-5893	21	4	used	use	VERB
ejpam-5893	21	5	a	a	DET
ejpam-5893	21	6	variety	variety	NOUN
ejpam-5893	21	7	of	of	ADP
ejpam-5893	21	8	techniques	technique	NOUN
ejpam-5893	21	9	to	to	PART
ejpam-5893	21	10	investigate	investigate	VERB
ejpam-5893	21	11	solutions	solution	NOUN
ejpam-5893	21	12	for	for	ADP
ejpam-5893	21	13	solitary	solitary	ADJ
ejpam-5893	21	14	waves	wave	NOUN
ejpam-5893	21	15	,	,	PUNCT
ejpam-5893	21	16	revealing	reveal	VERB
ejpam-5893	21	17	a	a	DET
ejpam-5893	21	18	wide	wide	ADJ
ejpam-5893	21	19	range	range	NOUN
ejpam-5893	21	20	of	of	ADP
ejpam-5893	21	21	approaches	approach	NOUN
ejpam-5893	21	22	to	to	ADP
ejpam-5893	21	23	comprehending	comprehend	VERB
ejpam-5893	21	24	intricate	intricate	ADJ
ejpam-5893	21	25	physical	physical	ADJ
ejpam-5893	21	26	phenomena	phenomenon	NOUN
ejpam-5893	21	27	[	[	X
ejpam-5893	21	28	8	8	NUM
ejpam-5893	21	29	]	]	PUNCT
ejpam-5893	21	30	.	.	PUNCT
ejpam-5893	22	1	many	many	ADJ
ejpam-5893	22	2	nonlinear	nonlinear	ADJ
ejpam-5893	22	3	models	model	NOUN
ejpam-5893	22	4	have	have	AUX
ejpam-5893	22	5	been	be	AUX
ejpam-5893	22	6	thoroughly	thoroughly	ADV
ejpam-5893	22	7	examined	examine	VERB
ejpam-5893	22	8	for	for	ADP
ejpam-5893	22	9	their	their	PRON
ejpam-5893	22	10	qualitative	qualitative	ADJ
ejpam-5893	22	11	responses	response	NOUN
ejpam-5893	22	12	in	in	ADP
ejpam-5893	22	13	addition	addition	NOUN
ejpam-5893	22	14	to	to	ADP
ejpam-5893	22	15	their	their	PRON
ejpam-5893	22	16	analytical	analytical	ADJ
ejpam-5893	22	17	solutions	solution	NOUN
ejpam-5893	22	18	,	,	PUNCT
ejpam-5893	22	19	including	include	VERB
ejpam-5893	22	20	stability	stability	NOUN
ejpam-5893	22	21	evaluations	evaluation	NOUN
ejpam-5893	22	22	by	by	ADP
ejpam-5893	22	23	changing	change	VERB
ejpam-5893	22	24	parameters	parameter	NOUN
ejpam-5893	22	25	using	use	VERB
ejpam-5893	22	26	bifurcation	bifurcation	NOUN
ejpam-5893	22	27	theory	theory	NOUN
ejpam-5893	22	28	.	.	PUNCT
ejpam-5893	23	1	moreover	moreover	ADV
ejpam-5893	23	2	,	,	PUNCT
ejpam-5893	23	3	chaos	chaos	NOUN
ejpam-5893	23	4	theory	theory	NOUN
ejpam-5893	23	5	has	have	AUX
ejpam-5893	23	6	been	be	AUX
ejpam-5893	23	7	used	use	VERB
ejpam-5893	23	8	to	to	PART
ejpam-5893	23	9	examine	examine	VERB
ejpam-5893	23	10	their	their	PRON
ejpam-5893	23	11	unexpected	unexpected	ADJ
ejpam-5893	23	12	character	character	NOUN
ejpam-5893	23	13	under	under	ADP
ejpam-5893	23	14	different	different	ADJ
ejpam-5893	23	15	initial	initial	ADJ
ejpam-5893	23	16	conditions	condition	NOUN
ejpam-5893	23	17	.	.	PUNCT
ejpam-5893	24	1	even	even	ADV
ejpam-5893	24	2	in	in	ADP
ejpam-5893	24	3	the	the	DET
ejpam-5893	24	4	most	most	ADV
ejpam-5893	24	5	simple	simple	ADJ
ejpam-5893	24	6	systems	system	NOUN
ejpam-5893	24	7	,	,	PUNCT
ejpam-5893	24	8	chaos	chaos	NOUN
ejpam-5893	24	9	can	can	AUX
ejpam-5893	24	10	appear	appear	VERB
ejpam-5893	24	11	as	as	ADP
ejpam-5893	24	12	erratic	erratic	ADJ
ejpam-5893	24	13	patterns	pattern	NOUN
ejpam-5893	24	14	.	.	PUNCT
ejpam-5893	25	1	a	a	DET
ejpam-5893	25	2	thorough	thorough	ADJ
ejpam-5893	25	3	review	review	NOUN
ejpam-5893	25	4	of	of	ADP
ejpam-5893	25	5	the	the	DET
ejpam-5893	25	6	literature	literature	NOUN
ejpam-5893	25	7	suggests	suggest	VERB
ejpam-5893	25	8	that	that	SCONJ
ejpam-5893	25	9	chaos	chaos	NOUN
ejpam-5893	25	10	seems	seem	VERB
ejpam-5893	25	11	to	to	PART
ejpam-5893	25	12	be	be	AUX
ejpam-5893	25	13	a	a	DET
ejpam-5893	25	14	recurring	recur	VERB
ejpam-5893	25	15	theme	theme	NOUN
ejpam-5893	25	16	in	in	ADP
ejpam-5893	25	17	a	a	DET
ejpam-5893	25	18	number	number	NOUN
ejpam-5893	25	19	of	of	ADP
ejpam-5893	25	20	events	event	NOUN
ejpam-5893	25	21	.	.	PUNCT
ejpam-5893	26	1	smoke	smoke	NOUN
ejpam-5893	26	2	rising	rise	VERB
ejpam-5893	26	3	from	from	ADP
ejpam-5893	26	4	cigarettes	cigarette	NOUN
ejpam-5893	26	5	,	,	PUNCT
ejpam-5893	26	6	for	for	ADP
ejpam-5893	26	7	example	example	NOUN
ejpam-5893	26	8	,	,	PUNCT
ejpam-5893	26	9	becomes	become	VERB
ejpam-5893	26	10	turbulent	turbulent	ADJ
ejpam-5893	26	11	swirls	swirls	NOUN
ejpam-5893	26	12	.	.	PUNCT
ejpam-5893	27	1	additionally	additionally	ADV
ejpam-5893	27	2	,	,	PUNCT
ejpam-5893	27	3	weather	weather	NOUN
ejpam-5893	27	4	patterns	pattern	NOUN
ejpam-5893	27	5	and	and	CCONJ
ejpam-5893	27	6	the	the	DET
ejpam-5893	27	7	movement	movement	NOUN
ejpam-5893	27	8	of	of	ADP
ejpam-5893	27	9	oil	oil	NOUN
ejpam-5893	27	10	through	through	ADP
ejpam-5893	27	11	underground	underground	ADJ
ejpam-5893	27	12	pipelines	pipeline	NOUN
ejpam-5893	27	13	are	be	AUX
ejpam-5893	27	14	examples	example	NOUN
ejpam-5893	27	15	of	of	ADP
ejpam-5893	27	16	disorder	disorder	NOUN
ejpam-5893	27	17	.	.	PUNCT
ejpam-5893	28	1	this	this	DET
ejpam-5893	28	2	study	study	NOUN
ejpam-5893	28	3	focuses	focus	VERB
ejpam-5893	28	4	on	on	ADP
ejpam-5893	28	5	3	3	NUM
ejpam-5893	28	6	-	-	SYM
ejpam-5893	28	7	d	d	NOUN
ejpam-5893	28	8	and	and	CCONJ
ejpam-5893	28	9	2	2	NUM
ejpam-5893	28	10	-	-	PUNCT
ejpam-5893	28	11	d	d	NOUN
ejpam-5893	28	12	plots	plot	NOUN
ejpam-5893	28	13	,	,	PUNCT
ejpam-5893	28	14	which	which	PRON
ejpam-5893	28	15	are	be	AUX
ejpam-5893	28	16	the	the	DET
ejpam-5893	28	17	most	most	ADV
ejpam-5893	28	18	efficient	efficient	ADJ
ejpam-5893	28	19	ways	way	NOUN
ejpam-5893	28	20	to	to	PART
ejpam-5893	28	21	identify	identify	VERB
ejpam-5893	28	22	irregular	irregular	ADJ
ejpam-5893	28	23	patterns	pattern	NOUN
ejpam-5893	28	24	[	[	X
ejpam-5893	28	25	9	9	NUM
ejpam-5893	28	26	]	]	PUNCT
ejpam-5893	28	27	.	.	PUNCT
ejpam-5893	29	1	in	in	ADP
ejpam-5893	29	2	[	[	X
ejpam-5893	29	3	10	10	NUM
ejpam-5893	29	4	]	]	PUNCT
ejpam-5893	29	5	,	,	PUNCT
ejpam-5893	29	6	the	the	DET
ejpam-5893	29	7	estevez	estevez	PROPN
ejpam-5893	29	8	-	-	PUNCT
ejpam-5893	29	9	mansfield	mansfield	PROPN
ejpam-5893	29	10	-	-	PUNCT
ejpam-5893	29	11	clarkson	clarkson	PROPN
ejpam-5893	29	12	equation	equation	NOUN
ejpam-5893	29	13	,	,	PUNCT
ejpam-5893	29	14	introduced	introduce	VERB
ejpam-5893	29	15	by	by	ADP
ejpam-5893	29	16	pilar	pilar	PROPN
ejpam-5893	29	17	estevez	estevez	PROPN
ejpam-5893	29	18	,	,	PUNCT
ejpam-5893	29	19	elizabeth	elizabeth	PROPN
ejpam-5893	29	20	mansfield	mansfield	PROPN
ejpam-5893	29	21	,	,	PUNCT
ejpam-5893	29	22	and	and	CCONJ
ejpam-5893	29	23	peter	peter	PROPN
ejpam-5893	29	24	clarkson	clarkson	PROPN
ejpam-5893	29	25	in	in	ADP
ejpam-5893	29	26	1997	1997	NUM
ejpam-5893	29	27	,	,	PUNCT
ejpam-5893	29	28	is	be	AUX
ejpam-5893	29	29	a	a	DET
ejpam-5893	29	30	nonlinear	nonlinear	ADJ
ejpam-5893	29	31	partial	partial	ADJ
ejpam-5893	29	32	differential	differential	NOUN
ejpam-5893	29	33	equation	equation	NOUN
ejpam-5893	29	34	[	[	X
ejpam-5893	29	35	11	11	NUM
ejpam-5893	29	36	]	]	PUNCT
ejpam-5893	29	37	,	,	PUNCT
ejpam-5893	29	38	which	which	PRON
ejpam-5893	29	39	is	be	AUX
ejpam-5893	29	40	a	a	DET
ejpam-5893	29	41	nonlinear	nonlinear	ADJ
ejpam-5893	29	42	evolution	evolution	NOUN
ejpam-5893	29	43	equation	equation	NOUN
ejpam-5893	29	44	of	of	ADP
ejpam-5893	29	45	the	the	DET
ejpam-5893	29	46	fourth	fourth	ADJ
ejpam-5893	29	47	order	order	NOUN
ejpam-5893	29	48	.	.	PUNCT
ejpam-5893	30	1	this	this	DET
ejpam-5893	30	2	equation	equation	NOUN
ejpam-5893	30	3	has	have	AUX
ejpam-5893	30	4	proven	prove	VERB
ejpam-5893	30	5	advantageous	advantageous	ADJ
ejpam-5893	30	6	in	in	ADP
ejpam-5893	30	7	examining	examine	VERB
ejpam-5893	30	8	wave	wave	NOUN
ejpam-5893	30	9	dynamics	dynamic	NOUN
ejpam-5893	30	10	in	in	ADP
ejpam-5893	30	11	optical	optical	ADJ
ejpam-5893	30	12	fibre	fibre	NOUN
ejpam-5893	30	13	,	,	PUNCT
ejpam-5893	30	14	as	as	SCONJ
ejpam-5893	30	15	it	it	PRON
ejpam-5893	30	16	was	be	AUX
ejpam-5893	30	17	initially	initially	ADV
ejpam-5893	30	18	employed	employ	VERB
ejpam-5893	30	19	in	in	ADP
ejpam-5893	30	20	their	their	PRON
ejpam-5893	30	21	investigation	investigation	NOUN
ejpam-5893	30	22	of	of	ADP
ejpam-5893	30	23	pattern	pattern	NOUN
ejpam-5893	30	24	dispersion	dispersion	NOUN
ejpam-5893	30	25	in	in	ADP
ejpam-5893	30	26	wave	wave	NOUN
ejpam-5893	30	27	.	.	PUNCT
ejpam-5893	31	1	in	in	ADP
ejpam-5893	31	2	[	[	X
ejpam-5893	31	3	4	4	NUM
ejpam-5893	31	4	]	]	PUNCT
ejpam-5893	31	5	,	,	PUNCT
ejpam-5893	31	6	[	[	X
ejpam-5893	31	7	12	12	NUM
ejpam-5893	31	8	]	]	PUNCT
ejpam-5893	31	9	the	the	DET
ejpam-5893	31	10	model	model	NOUN
ejpam-5893	31	11	under	under	ADP
ejpam-5893	31	12	study	study	NOUN
ejpam-5893	31	13	is	be	AUX
ejpam-5893	31	14	the	the	DET
ejpam-5893	31	15	nonlinear	nonlinear	ADJ
ejpam-5893	31	16	(	(	PUNCT
ejpam-5893	31	17	1	1	NUM
ejpam-5893	31	18	+	+	PROPN
ejpam-5893	31	19	1)-dimensional	1)-dimensional	PROPN
ejpam-5893	31	20	estevez	estevez	PROPN
ejpam-5893	31	21	-	-	PUNCT
ejpam-5893	31	22	mansfield	mansfield	PROPN
ejpam-5893	31	23	-	-	PUNCT
ejpam-5893	31	24	clarkson	clarkson	PROPN
ejpam-5893	31	25	(	(	PUNCT
ejpam-5893	31	26	emc	emc	PROPN
ejpam-5893	31	27	)	)	PUNCT
ejpam-5893	31	28	equation	equation	NOUN
ejpam-5893	31	29	given	give	VERB
ejpam-5893	31	30	as	as	ADP
ejpam-5893	31	31	utxxx	utxxx	PROPN
ejpam-5893	31	32	+	+	NUM
ejpam-5893	31	33	β(uxutx	β(uxutx	NOUN
ejpam-5893	31	34	+	+	NUM
ejpam-5893	31	35	uxxut	uxxut	NOUN
ejpam-5893	31	36	)	)	PUNCT
ejpam-5893	31	37	+	+	NUM
ejpam-5893	31	38	utt	utt	ADJ
ejpam-5893	31	39	=	=	SYM
ejpam-5893	31	40	0	0	NUM
ejpam-5893	31	41	(	(	PUNCT
ejpam-5893	31	42	1	1	NUM
ejpam-5893	31	43	)	)	PUNCT
ejpam-5893	31	44	where	where	SCONJ
ejpam-5893	31	45	u	u	NOUN
ejpam-5893	31	46	=	=	SYM
ejpam-5893	31	47	u(x	u(x	PROPN
ejpam-5893	31	48	,	,	PUNCT
ejpam-5893	31	49	t	t	PROPN
ejpam-5893	31	50	)	)	PUNCT
ejpam-5893	31	51	is	be	AUX
ejpam-5893	31	52	a	a	DET
ejpam-5893	31	53	wave	wave	NOUN
ejpam-5893	31	54	function	function	NOUN
ejpam-5893	31	55	.	.	PUNCT
ejpam-5893	32	1	the	the	DET
ejpam-5893	32	2	parameter	parameter	NOUN
ejpam-5893	32	3	β	β	PROPN
ejpam-5893	32	4	represents	represent	VERB
ejpam-5893	32	5	a	a	DET
ejpam-5893	32	6	non	non	ADJ
ejpam-5893	32	7	-	-	ADJ
ejpam-5893	32	8	zero	zero	NUM
ejpam-5893	32	9	constant	constant	ADJ
ejpam-5893	32	10	.	.	PUNCT
ejpam-5893	33	1	in	in	ADP
ejpam-5893	33	2	the	the	DET
ejpam-5893	33	3	literature	literature	NOUN
ejpam-5893	33	4	,	,	PUNCT
ejpam-5893	33	5	different	different	ADJ
ejpam-5893	33	6	methods	method	NOUN
ejpam-5893	33	7	are	be	AUX
ejpam-5893	33	8	applied	apply	VERB
ejpam-5893	33	9	to	to	PART
ejpam-5893	33	10	solve	solve	VERB
ejpam-5893	33	11	equation	equation	NOUN
ejpam-5893	33	12	(	(	PUNCT
ejpam-5893	33	13	1	1	NUM
ejpam-5893	33	14	)	)	PUNCT
ejpam-5893	33	15	.	.	PUNCT
ejpam-5893	34	1	the	the	DET
ejpam-5893	34	2	time	time	NOUN
ejpam-5893	34	3	-	-	PUNCT
ejpam-5893	34	4	fractional	fractional	ADJ
ejpam-5893	34	5	emc	emc	NOUN
ejpam-5893	34	6	equation	equation	NOUN
ejpam-5893	34	7	is	be	AUX
ejpam-5893	34	8	expressed	express	VERB
ejpam-5893	34	9	in	in	ADP
ejpam-5893	34	10	its	its	PRON
ejpam-5893	34	11	formal	formal	ADJ
ejpam-5893	34	12	form	form	NOUN
ejpam-5893	34	13	as	as	SCONJ
ejpam-5893	34	14	follows	follow	VERB
ejpam-5893	34	15	:	:	PUNCT
ejpam-5893	34	16	dα	dα	PROPN
ejpam-5893	34	17	t	t	PROPN
ejpam-5893	34	18	uxxx	uxxx	PROPN
ejpam-5893	35	1	+	+	CCONJ
ejpam-5893	35	2	β(uxd	β(uxd	PROPN
ejpam-5893	35	3	α	α	X
ejpam-5893	35	4	t	t	NOUN
ejpam-5893	35	5	ux	ux	PROPN
ejpam-5893	36	1	+	+	CCONJ
ejpam-5893	36	2	uxxd	uxxd	PROPN
ejpam-5893	36	3	α	α	PROPN
ejpam-5893	36	4	t	t	PROPN
ejpam-5893	36	5	u	u	NOUN
ejpam-5893	36	6	)	)	PUNCT
ejpam-5893	37	1	+	+	ADJ
ejpam-5893	37	2	d2α	d2α	PROPN
ejpam-5893	37	3	2	2	NUM
ejpam-5893	37	4	t	t	NOUN
ejpam-5893	37	5	u	u	NOUN
ejpam-5893	37	6	=	=	SYM
ejpam-5893	37	7	0	0	NUM
ejpam-5893	37	8	(	(	PUNCT
ejpam-5893	37	9	2	2	NUM
ejpam-5893	37	10	)	)	PUNCT
ejpam-5893	37	11	here	here	ADV
ejpam-5893	37	12	t	t	X
ejpam-5893	37	13	>	>	X
ejpam-5893	37	14	0	0	NUM
ejpam-5893	37	15	,	,	PUNCT
ejpam-5893	37	16	0	0	NUM
ejpam-5893	37	17	<	<	X
ejpam-5893	37	18	α	α	PROPN
ejpam-5893	37	19	≤	≤	NUM
ejpam-5893	37	20	1	1	NUM
ejpam-5893	37	21	.	.	PUNCT
ejpam-5893	38	1	in	in	ADP
ejpam-5893	38	2	the	the	DET
ejpam-5893	38	3	broad	broad	ADJ
ejpam-5893	38	4	field	field	NOUN
ejpam-5893	38	5	of	of	ADP
ejpam-5893	38	6	nonlinear	nonlinear	ADJ
ejpam-5893	38	7	science	science	NOUN
ejpam-5893	38	8	,	,	PUNCT
ejpam-5893	38	9	the	the	DET
ejpam-5893	38	10	emc	emc	PROPN
ejpam-5893	38	11	equation	equation	NOUN
ejpam-5893	38	12	is	be	AUX
ejpam-5893	38	13	a	a	DET
ejpam-5893	38	14	crucial	crucial	ADJ
ejpam-5893	38	15	formula	formula	NOUN
ejpam-5893	38	16	.	.	PUNCT
ejpam-5893	39	1	it	it	PRON
ejpam-5893	39	2	can	can	AUX
ejpam-5893	39	3	be	be	AUX
ejpam-5893	39	4	used	use	VERB
ejpam-5893	39	5	in	in	ADP
ejpam-5893	39	6	image	image	NOUN
ejpam-5893	39	7	processing	processing	NOUN
ejpam-5893	39	8	,	,	PUNCT
ejpam-5893	39	9	fluid	fluid	ADJ
ejpam-5893	39	10	dynamics	dynamic	NOUN
ejpam-5893	39	11	,	,	PUNCT
ejpam-5893	39	12	optics	optic	NOUN
ejpam-5893	39	13	,	,	PUNCT
ejpam-5893	39	14	and	and	CCONJ
ejpam-5893	39	15	plasma	plasma	NOUN
ejpam-5893	39	16	physics	physics	NOUN
ejpam-5893	39	17	and	and	CCONJ
ejpam-5893	39	18	engineering	engineering	NOUN
ejpam-5893	39	19	.	.	PUNCT
ejpam-5893	40	1	recent	recent	ADJ
ejpam-5893	40	2	research	research	NOUN
ejpam-5893	40	3	[	[	X
ejpam-5893	40	4	13	13	NUM
ejpam-5893	40	5	]	]	PUNCT
ejpam-5893	40	6	has	have	AUX
ejpam-5893	40	7	brought	bring	VERB
ejpam-5893	40	8	attention	attention	NOUN
ejpam-5893	40	9	to	to	ADP
ejpam-5893	40	10	the	the	DET
ejpam-5893	40	11	significance	significance	NOUN
ejpam-5893	40	12	of	of	ADP
ejpam-5893	40	13	the	the	DET
ejpam-5893	40	14	emc	emc	PROPN
ejpam-5893	40	15	equation	equation	NOUN
ejpam-5893	40	16	and	and	CCONJ
ejpam-5893	40	17	its	its	PRON
ejpam-5893	40	18	critical	critical	ADJ
ejpam-5893	40	19	role	role	NOUN
ejpam-5893	40	20	in	in	ADP
ejpam-5893	40	21	understanding	understand	VERB
ejpam-5893	40	22	complex	complex	ADJ
ejpam-5893	40	23	physical	physical	ADJ
ejpam-5893	40	24	processes	process	NOUN
ejpam-5893	40	25	.	.	PUNCT
ejpam-5893	41	1	wave	wave	PROPN
ejpam-5893	41	2	b.	b.	PROPN
ejpam-5893	41	3	yasmeen	yasmeen	PROPN
ejpam-5893	41	4	,	,	PUNCT
ejpam-5893	41	5	k.	k.	PROPN
ejpam-5893	41	6	ahmad	ahmad	PROPN
ejpam-5893	41	7	,	,	PUNCT
ejpam-5893	41	8	n.	n.	PROPN
ejpam-5893	41	9	fatima	fatima	PROPN
ejpam-5893	41	10	/	/	PUNCT
ejpam-5893	41	11	eur	eur	PROPN
ejpam-5893	41	12	.	.	PUNCT
ejpam-5893	42	1	j.	j.	PROPN
ejpam-5893	42	2	pure	pure	PROPN
ejpam-5893	42	3	appl	appl	PROPN
ejpam-5893	42	4	.	.	PROPN
ejpam-5893	42	5	math	math	PROPN
ejpam-5893	42	6	,	,	PUNCT
ejpam-5893	42	7	18	18	NUM
ejpam-5893	42	8	(	(	PUNCT
ejpam-5893	42	9	2	2	NUM
ejpam-5893	42	10	)	)	PUNCT
ejpam-5893	42	11	(	(	PUNCT
ejpam-5893	42	12	2025	2025	NUM
ejpam-5893	42	13	)	)	PUNCT
ejpam-5893	42	14	,	,	PUNCT
ejpam-5893	42	15	5893	5893	NUM
ejpam-5893	42	16	3	3	NUM
ejpam-5893	42	17	of	of	ADP
ejpam-5893	42	18	17	17	NUM
ejpam-5893	42	19	behavior	behavior	NOUN
ejpam-5893	42	20	in	in	ADP
ejpam-5893	42	21	shallow	shallow	ADJ
ejpam-5893	42	22	water	water	NOUN
ejpam-5893	42	23	and	and	CCONJ
ejpam-5893	42	24	optical	optical	ADJ
ejpam-5893	42	25	fiber	fiber	NOUN
ejpam-5893	42	26	is	be	AUX
ejpam-5893	42	27	the	the	DET
ejpam-5893	42	28	main	main	ADJ
ejpam-5893	42	29	applications	application	NOUN
ejpam-5893	42	30	for	for	ADP
ejpam-5893	42	31	the	the	DET
ejpam-5893	42	32	emc	emc	PROPN
ejpam-5893	42	33	equation	equation	NOUN
ejpam-5893	42	34	,	,	PUNCT
ejpam-5893	42	35	which	which	PRON
ejpam-5893	42	36	poses	pose	VERB
ejpam-5893	42	37	several	several	ADJ
ejpam-5893	42	38	difficulties	difficulty	NOUN
ejpam-5893	42	39	.	.	PUNCT
ejpam-5893	43	1	researchers	researcher	NOUN
ejpam-5893	43	2	have	have	AUX
ejpam-5893	43	3	used	use	VERB
ejpam-5893	43	4	a	a	DET
ejpam-5893	43	5	variety	variety	NOUN
ejpam-5893	43	6	of	of	ADP
ejpam-5893	43	7	research	research	NOUN
ejpam-5893	43	8	approaches	approach	NOUN
ejpam-5893	43	9	in	in	ADP
ejpam-5893	43	10	their	their	PRON
ejpam-5893	43	11	investigations	investigation	NOUN
ejpam-5893	43	12	.	.	PUNCT
ejpam-5893	44	1	in	in	ADP
ejpam-5893	44	2	[	[	X
ejpam-5893	44	3	13	13	NUM
ejpam-5893	44	4	]	]	PUNCT
ejpam-5893	44	5	,	,	PUNCT
ejpam-5893	44	6	the	the	DET
ejpam-5893	44	7	authors	author	NOUN
ejpam-5893	44	8	used	use	VERB
ejpam-5893	44	9	the	the	DET
ejpam-5893	44	10	sine	sine	NOUN
ejpam-5893	44	11	-	-	PUNCT
ejpam-5893	44	12	gordon	gordon	NOUN
ejpam-5893	44	13	expansion	expansion	NOUN
ejpam-5893	44	14	technique	technique	NOUN
ejpam-5893	44	15	to	to	PART
ejpam-5893	44	16	investigate	investigate	VERB
ejpam-5893	44	17	soliton	soliton	NOUN
ejpam-5893	44	18	solutions	solution	NOUN
ejpam-5893	44	19	of	of	ADP
ejpam-5893	44	20	eq	eq	PROPN
ejpam-5893	44	21	.	.	PUNCT
ejpam-5893	45	1	(	(	PUNCT
ejpam-5893	45	2	2	2	NUM
ejpam-5893	45	3	)	)	PUNCT
ejpam-5893	45	4	and	and	CCONJ
ejpam-5893	45	5	the	the	DET
ejpam-5893	45	6	riemann	riemann	PROPN
ejpam-5893	45	7	model	model	PROPN
ejpam-5893	45	8	.	.	PUNCT
ejpam-5893	46	1	using	use	VERB
ejpam-5893	46	2	a	a	DET
ejpam-5893	46	3	simplified	simplified	ADJ
ejpam-5893	46	4	equation	equation	NOUN
ejpam-5893	46	5	technique	technique	NOUN
ejpam-5893	46	6	,	,	PUNCT
ejpam-5893	46	7	[	[	X
ejpam-5893	46	8	14	14	NUM
ejpam-5893	46	9	]	]	PUNCT
ejpam-5893	46	10	and	and	CCONJ
ejpam-5893	47	1	[	[	X
ejpam-5893	47	2	15	15	NUM
ejpam-5893	47	3	]	]	PUNCT
ejpam-5893	47	4	investigated	investigate	VERB
ejpam-5893	47	5	the	the	DET
ejpam-5893	47	6	emc	emc	PROPN
ejpam-5893	47	7	model	model	NOUN
ejpam-5893	47	8	to	to	PART
ejpam-5893	47	9	determine	determine	VERB
ejpam-5893	47	10	traveling	travel	VERB
ejpam-5893	47	11	wave	wave	NOUN
ejpam-5893	47	12	patterns	pattern	NOUN
ejpam-5893	47	13	.	.	PUNCT
ejpam-5893	48	1	nfpdes	nfpde	NOUN
ejpam-5893	48	2	are	be	AUX
ejpam-5893	48	3	converted	convert	VERB
ejpam-5893	48	4	into	into	ADP
ejpam-5893	48	5	nonlinear	nonlinear	ADJ
ejpam-5893	48	6	ordinary	ordinary	ADJ
ejpam-5893	48	7	differential	differential	ADJ
ejpam-5893	48	8	equations	equation	NOUN
ejpam-5893	48	9	(	(	PUNCT
ejpam-5893	48	10	nodes	node	NOUN
ejpam-5893	48	11	)	)	PUNCT
ejpam-5893	48	12	using	use	VERB
ejpam-5893	48	13	the	the	DET
ejpam-5893	48	14	suggested	suggest	VERB
ejpam-5893	48	15	procedure	procedure	NOUN
ejpam-5893	48	16	[	[	X
ejpam-5893	48	17	16	16	NUM
ejpam-5893	48	18	]	]	PUNCT
ejpam-5893	48	19	,	,	PUNCT
ejpam-5893	48	20	[	[	X
ejpam-5893	48	21	17	17	NUM
ejpam-5893	48	22	]	]	PUNCT
ejpam-5893	48	23	,	,	PUNCT
ejpam-5893	48	24	[	[	X
ejpam-5893	48	25	18	18	NUM
ejpam-5893	48	26	]	]	PUNCT
ejpam-5893	48	27	,	,	PUNCT
ejpam-5893	48	28	[	[	X
ejpam-5893	48	29	19	19	NUM
ejpam-5893	48	30	]	]	PUNCT
ejpam-5893	48	31	,	,	PUNCT
ejpam-5893	48	32	[	[	X
ejpam-5893	48	33	20	20	NUM
ejpam-5893	48	34	]	]	PUNCT
ejpam-5893	48	35	,	,	PUNCT
ejpam-5893	49	1	[	[	X
ejpam-5893	49	2	21	21	NUM
ejpam-5893	49	3	]	]	PUNCT
ejpam-5893	49	4	and	and	CCONJ
ejpam-5893	49	5	[	[	X
ejpam-5893	49	6	22	22	NUM
ejpam-5893	49	7	]	]	PUNCT
ejpam-5893	49	8	.	.	PUNCT
ejpam-5893	50	1	solitons	soliton	NOUN
ejpam-5893	50	2	with	with	ADP
ejpam-5893	50	3	a	a	DET
ejpam-5893	50	4	variety	variety	NOUN
ejpam-5893	50	5	of	of	ADP
ejpam-5893	50	6	mathematical	mathematical	ADJ
ejpam-5893	50	7	structures	structure	NOUN
ejpam-5893	50	8	,	,	PUNCT
ejpam-5893	50	9	such	such	ADJ
ejpam-5893	50	10	as	as	ADP
ejpam-5893	50	11	trigonometric	trigonometric	ADJ
ejpam-5893	50	12	,	,	PUNCT
ejpam-5893	50	13	exponential	exponential	ADJ
ejpam-5893	50	14	,	,	PUNCT
ejpam-5893	50	15	rational	rational	ADJ
ejpam-5893	50	16	,	,	PUNCT
ejpam-5893	50	17	and	and	CCONJ
ejpam-5893	50	18	hyperbolic	hyperbolic	ADJ
ejpam-5893	50	19	functions	function	NOUN
ejpam-5893	50	20	,	,	PUNCT
ejpam-5893	50	21	have	have	AUX
ejpam-5893	50	22	been	be	AUX
ejpam-5893	50	23	found	find	VERB
ejpam-5893	50	24	as	as	ADP
ejpam-5893	50	25	a	a	DET
ejpam-5893	50	26	result	result	NOUN
ejpam-5893	50	27	of	of	ADP
ejpam-5893	50	28	this	this	DET
ejpam-5893	50	29	research	research	NOUN
ejpam-5893	50	30	.	.	PUNCT
ejpam-5893	51	1	their	their	PRON
ejpam-5893	51	2	true	true	ADJ
ejpam-5893	51	3	wave	wave	NOUN
ejpam-5893	51	4	characteristics	characteristic	NOUN
ejpam-5893	51	5	may	may	AUX
ejpam-5893	51	6	be	be	AUX
ejpam-5893	51	7	thoroughly	thoroughly	ADV
ejpam-5893	51	8	examined	examine	VERB
ejpam-5893	51	9	thanks	thank	NOUN
ejpam-5893	51	10	to	to	ADP
ejpam-5893	51	11	these	these	DET
ejpam-5893	51	12	structures	structure	NOUN
ejpam-5893	51	13	.	.	PUNCT
ejpam-5893	52	1	in	in	ADP
ejpam-5893	52	2	particular	particular	ADJ
ejpam-5893	52	3	,	,	PUNCT
ejpam-5893	52	4	the	the	DET
ejpam-5893	52	5	motivation	motivation	NOUN
ejpam-5893	52	6	of	of	ADP
ejpam-5893	52	7	this	this	DET
ejpam-5893	52	8	paper	paper	NOUN
ejpam-5893	52	9	is	be	AUX
ejpam-5893	52	10	to	to	PART
ejpam-5893	52	11	show	show	VERB
ejpam-5893	52	12	that	that	SCONJ
ejpam-5893	52	13	these	these	DET
ejpam-5893	52	14	behaviors	behavior	NOUN
ejpam-5893	52	15	are	be	AUX
ejpam-5893	52	16	different	different	ADJ
ejpam-5893	52	17	kinds	kind	NOUN
ejpam-5893	52	18	of	of	ADP
ejpam-5893	52	19	solitons	soliton	NOUN
ejpam-5893	52	20	.	.	PUNCT
ejpam-5893	53	1	this	this	PRON
ejpam-5893	53	2	is	be	AUX
ejpam-5893	53	3	supported	support	VERB
ejpam-5893	53	4	by	by	ADP
ejpam-5893	53	5	showing	show	VERB
ejpam-5893	53	6	how	how	SCONJ
ejpam-5893	53	7	they	they	PRON
ejpam-5893	53	8	look	look	VERB
ejpam-5893	53	9	in	in	ADP
ejpam-5893	53	10	3d	3d	NUM
ejpam-5893	53	11	,	,	PUNCT
ejpam-5893	53	12	and	and	CCONJ
ejpam-5893	53	13	2d	2d	NUM
ejpam-5893	53	14	graphs	graph	NOUN
ejpam-5893	53	15	.	.	PUNCT
ejpam-5893	54	1	interestingly	interestingly	ADV
ejpam-5893	54	2	,	,	PUNCT
ejpam-5893	54	3	our	our	PRON
ejpam-5893	54	4	results	result	NOUN
ejpam-5893	54	5	produce	produce	VERB
ejpam-5893	54	6	a	a	DET
ejpam-5893	54	7	wider	wide	ADJ
ejpam-5893	54	8	variety	variety	NOUN
ejpam-5893	54	9	of	of	ADP
ejpam-5893	54	10	results	result	NOUN
ejpam-5893	54	11	than	than	ADP
ejpam-5893	54	12	previous	previous	ADJ
ejpam-5893	54	13	solutions	solution	NOUN
ejpam-5893	54	14	,	,	PUNCT
ejpam-5893	54	15	thus	thus	ADV
ejpam-5893	54	16	providing	provide	VERB
ejpam-5893	54	17	new	new	ADJ
ejpam-5893	54	18	and	and	CCONJ
ejpam-5893	54	19	significant	significant	ADJ
ejpam-5893	54	20	insights	insight	NOUN
ejpam-5893	54	21	into	into	ADP
ejpam-5893	54	22	the	the	DET
ejpam-5893	54	23	underlying	underlie	VERB
ejpam-5893	54	24	phenomena	phenomena	NOUN
ejpam-5893	54	25	of	of	ADP
ejpam-5893	54	26	the	the	DET
ejpam-5893	54	27	model	model	NOUN
ejpam-5893	54	28	under	under	ADP
ejpam-5893	54	29	study	study	NOUN
ejpam-5893	54	30	.	.	PUNCT
ejpam-5893	55	1	in	in	ADP
ejpam-5893	55	2	short	short	ADJ
ejpam-5893	55	3	,	,	PUNCT
ejpam-5893	55	4	our	our	PRON
ejpam-5893	55	5	obtained	obtain	VERB
ejpam-5893	55	6	results	result	NOUN
ejpam-5893	55	7	are	be	AUX
ejpam-5893	55	8	newer	new	ADJ
ejpam-5893	55	9	than	than	ADP
ejpam-5893	55	10	the	the	DET
ejpam-5893	55	11	existing	exist	VERB
ejpam-5893	55	12	results	result	NOUN
ejpam-5893	55	13	of	of	ADP
ejpam-5893	55	14	the	the	DET
ejpam-5893	55	15	model	model	NOUN
ejpam-5893	55	16	under	under	ADP
ejpam-5893	55	17	study	study	NOUN
ejpam-5893	55	18	.	.	PUNCT
ejpam-5893	56	1	additionally	additionally	ADV
ejpam-5893	56	2	,	,	PUNCT
ejpam-5893	56	3	graphs	graph	NOUN
ejpam-5893	56	4	representing	represent	VERB
ejpam-5893	56	5	the	the	DET
ejpam-5893	56	6	physical	physical	ADJ
ejpam-5893	56	7	solutions	solution	NOUN
ejpam-5893	56	8	of	of	ADP
ejpam-5893	56	9	various	various	ADJ
ejpam-5893	56	10	fractional	fractional	ADJ
ejpam-5893	56	11	orders	order	NOUN
ejpam-5893	56	12	can	can	AUX
ejpam-5893	56	13	be	be	AUX
ejpam-5893	56	14	compared	compare	VERB
ejpam-5893	56	15	.	.	PUNCT
ejpam-5893	57	1	the	the	DET
ejpam-5893	57	2	rest	rest	NOUN
ejpam-5893	57	3	of	of	ADP
ejpam-5893	57	4	this	this	DET
ejpam-5893	57	5	investigation	investigation	NOUN
ejpam-5893	57	6	is	be	AUX
ejpam-5893	57	7	organized	organize	VERB
ejpam-5893	57	8	in	in	ADP
ejpam-5893	57	9	the	the	DET
ejpam-5893	57	10	following	follow	VERB
ejpam-5893	57	11	sections	section	NOUN
ejpam-5893	57	12	:	:	PUNCT
ejpam-5893	57	13	section	section	NOUN
ejpam-5893	57	14	2	2	NUM
ejpam-5893	57	15	describes	describe	VERB
ejpam-5893	57	16	the	the	DET
ejpam-5893	57	17	main	main	ADJ
ejpam-5893	57	18	points	point	NOUN
ejpam-5893	57	19	of	of	ADP
ejpam-5893	57	20	characteristics	characteristic	NOUN
ejpam-5893	57	21	for	for	ADP
ejpam-5893	57	22	the	the	DET
ejpam-5893	57	23	nonlinear	nonlinear	ADJ
ejpam-5893	57	24	-	-	PUNCT
ejpam-5893	57	25	time	time	NOUN
ejpam-5893	57	26	fractional	fractional	ADJ
ejpam-5893	57	27	emc	emc	PROPN
ejpam-5893	57	28	equation	equation	NOUN
ejpam-5893	57	29	;	;	PUNCT
ejpam-5893	57	30	section	section	NOUN
ejpam-5893	57	31	3	3	NUM
ejpam-5893	57	32	shows	show	VERB
ejpam-5893	57	33	the	the	DET
ejpam-5893	57	34	findings	finding	NOUN
ejpam-5893	57	35	solutions	solution	NOUN
ejpam-5893	57	36	for	for	ADP
ejpam-5893	57	37	the	the	DET
ejpam-5893	57	38	time	time	NOUN
ejpam-5893	57	39	-	-	PUNCT
ejpam-5893	57	40	fractional	fractional	ADJ
ejpam-5893	57	41	emc	emc	NOUN
ejpam-5893	57	42	equation	equation	NOUN
ejpam-5893	57	43	;	;	PUNCT
ejpam-5893	57	44	section	section	NOUN
ejpam-5893	57	45	4	4	NUM
ejpam-5893	57	46	includes	include	VERB
ejpam-5893	57	47	the	the	DET
ejpam-5893	57	48	corresponding	corresponding	ADJ
ejpam-5893	57	49	graphical	graphical	ADJ
ejpam-5893	57	50	representation	representation	NOUN
ejpam-5893	57	51	;	;	PUNCT
ejpam-5893	57	52	section	section	NOUN
ejpam-5893	57	53	5	5	NUM
ejpam-5893	57	54	includes	include	VERB
ejpam-5893	57	55	discussion	discussion	NOUN
ejpam-5893	57	56	and	and	CCONJ
ejpam-5893	57	57	section	section	NOUN
ejpam-5893	57	58	6	6	NUM
ejpam-5893	57	59	,	,	PUNCT
ejpam-5893	57	60	conclusion	conclusion	NOUN
ejpam-5893	57	61	are	be	AUX
ejpam-5893	57	62	summarized	summarize	VERB
ejpam-5893	57	63	in	in	ADP
ejpam-5893	57	64	brief	brief	ADJ
ejpam-5893	57	65	points	point	NOUN
ejpam-5893	57	66	.	.	PUNCT
ejpam-5893	58	1	2	2	X
ejpam-5893	58	2	.	.	X
ejpam-5893	58	3	characteristics	characteristic	NOUN
ejpam-5893	58	4	in	in	ADP
ejpam-5893	58	5	quantum	quantum	ADJ
ejpam-5893	58	6	mechanics	mechanic	NOUN
ejpam-5893	58	7	and	and	CCONJ
ejpam-5893	58	8	field	field	NOUN
ejpam-5893	58	9	theory	theory	NOUN
ejpam-5893	58	10	,	,	PUNCT
ejpam-5893	58	11	this	this	DET
ejpam-5893	58	12	equation	equation	NOUN
ejpam-5893	58	13	is	be	AUX
ejpam-5893	58	14	applicable	applicable	ADJ
ejpam-5893	58	15	in	in	ADP
ejpam-5893	58	16	quantum	quantum	NOUN
ejpam-5893	58	17	systems	system	NOUN
ejpam-5893	58	18	where	where	SCONJ
ejpam-5893	58	19	nonlinearity	nonlinearity	NOUN
ejpam-5893	58	20	and	and	CCONJ
ejpam-5893	58	21	fractional	fractional	ADJ
ejpam-5893	58	22	dynamics	dynamic	NOUN
ejpam-5893	58	23	play	play	VERB
ejpam-5893	58	24	a	a	DET
ejpam-5893	58	25	role	role	NOUN
ejpam-5893	58	26	,	,	PUNCT
ejpam-5893	58	27	such	such	ADJ
ejpam-5893	58	28	as	as	ADP
ejpam-5893	58	29	fractional	fractional	ADJ
ejpam-5893	58	30	quantum	quantum	ADJ
ejpam-5893	58	31	mechanics	mechanic	NOUN
ejpam-5893	58	32	or	or	CCONJ
ejpam-5893	58	33	bose	bose	NOUN
ejpam-5893	58	34	-	-	PUNCT
ejpam-5893	58	35	einstein	einstein	NOUN
ejpam-5893	58	36	condensates	condensate	NOUN
ejpam-5893	58	37	.	.	PUNCT
ejpam-5893	59	1	is	be	AUX
ejpam-5893	59	2	signal	signal	ADJ
ejpam-5893	59	3	processing	processing	NOUN
ejpam-5893	59	4	,	,	PUNCT
ejpam-5893	59	5	this	this	DET
ejpam-5893	59	6	equation	equation	NOUN
ejpam-5893	59	7	is	be	AUX
ejpam-5893	59	8	used	use	VERB
ejpam-5893	59	9	in	in	ADP
ejpam-5893	59	10	signal	signal	NOUN
ejpam-5893	59	11	and	and	CCONJ
ejpam-5893	59	12	image	image	NOUN
ejpam-5893	59	13	processing	processing	NOUN
ejpam-5893	59	14	for	for	ADP
ejpam-5893	59	15	systems	system	NOUN
ejpam-5893	59	16	exhibiting	exhibit	VERB
ejpam-5893	59	17	fractal	fractal	ADJ
ejpam-5893	59	18	or	or	CCONJ
ejpam-5893	59	19	self	self	NOUN
ejpam-5893	59	20	-	-	PUNCT
ejpam-5893	59	21	similar	similar	ADJ
ejpam-5893	59	22	behavior	behavior	NOUN
ejpam-5893	59	23	.	.	PUNCT
ejpam-5893	60	1	in	in	ADP
ejpam-5893	60	2	engineering	engineering	NOUN
ejpam-5893	60	3	,	,	PUNCT
ejpam-5893	60	4	used	use	VERB
ejpam-5893	60	5	in	in	ADP
ejpam-5893	60	6	modeling	modeling	NOUN
ejpam-5893	60	7	and	and	CCONJ
ejpam-5893	60	8	control	control	NOUN
ejpam-5893	60	9	of	of	ADP
ejpam-5893	60	10	nonlinear	nonlinear	ADJ
ejpam-5893	60	11	dynamic	dynamic	ADJ
ejpam-5893	60	12	systems	system	NOUN
ejpam-5893	60	13	where	where	SCONJ
ejpam-5893	60	14	fractional	fractional	ADJ
ejpam-5893	60	15	-	-	PUNCT
ejpam-5893	60	16	order	order	NOUN
ejpam-5893	60	17	dynamics	dynamic	NOUN
ejpam-5893	60	18	are	be	AUX
ejpam-5893	60	19	observed	observe	VERB
ejpam-5893	60	20	,	,	PUNCT
ejpam-5893	60	21	such	such	ADJ
ejpam-5893	60	22	as	as	ADP
ejpam-5893	60	23	robotics	robotic	NOUN
ejpam-5893	60	24	or	or	CCONJ
ejpam-5893	60	25	materials	material	NOUN
ejpam-5893	60	26	with	with	ADP
ejpam-5893	60	27	memory	memory	NOUN
ejpam-5893	60	28	effects	effect	NOUN
ejpam-5893	60	29	.	.	PUNCT
ejpam-5893	61	1	in	in	ADP
ejpam-5893	61	2	nonlinear	nonlinear	ADJ
ejpam-5893	61	3	optics	optic	NOUN
ejpam-5893	61	4	,	,	PUNCT
ejpam-5893	61	5	the	the	DET
ejpam-5893	61	6	time	time	NOUN
ejpam-5893	61	7	-	-	PUNCT
ejpam-5893	61	8	fractional	fractional	ADJ
ejpam-5893	61	9	emc	emc	NOUN
ejpam-5893	61	10	equation	equation	NOUN
ejpam-5893	61	11	is	be	AUX
ejpam-5893	61	12	used	use	VERB
ejpam-5893	61	13	to	to	PART
ejpam-5893	61	14	describe	describe	VERB
ejpam-5893	61	15	light	light	ADJ
ejpam-5893	61	16	propagation	propagation	NOUN
ejpam-5893	61	17	in	in	ADP
ejpam-5893	61	18	nonlinear	nonlinear	ADJ
ejpam-5893	61	19	and	and	CCONJ
ejpam-5893	61	20	dispersive	dispersive	ADJ
ejpam-5893	61	21	media	medium	NOUN
ejpam-5893	61	22	,	,	PUNCT
ejpam-5893	61	23	particularly	particularly	ADV
ejpam-5893	61	24	in	in	ADP
ejpam-5893	61	25	fiber	fiber	NOUN
ejpam-5893	61	26	optics	optic	NOUN
ejpam-5893	61	27	where	where	SCONJ
ejpam-5893	61	28	fractional	fractional	ADJ
ejpam-5893	61	29	effects	effect	NOUN
ejpam-5893	61	30	are	be	AUX
ejpam-5893	61	31	significant	significant	ADJ
ejpam-5893	61	32	.	.	PUNCT
ejpam-5893	62	1	in	in	ADP
ejpam-5893	62	2	fluid	fluid	ADJ
ejpam-5893	62	3	dynamics	dynamic	NOUN
ejpam-5893	62	4	,	,	PUNCT
ejpam-5893	62	5	it	it	PRON
ejpam-5893	62	6	models	model	VERB
ejpam-5893	62	7	the	the	DET
ejpam-5893	62	8	behavior	behavior	NOUN
ejpam-5893	62	9	of	of	ADP
ejpam-5893	62	10	nonlinear	nonlinear	ADJ
ejpam-5893	62	11	waves	wave	NOUN
ejpam-5893	62	12	and	and	CCONJ
ejpam-5893	62	13	instabilities	instability	NOUN
ejpam-5893	62	14	in	in	ADP
ejpam-5893	62	15	fluid	fluid	ADJ
ejpam-5893	62	16	systems	system	NOUN
ejpam-5893	62	17	,	,	PUNCT
ejpam-5893	62	18	especially	especially	ADV
ejpam-5893	62	19	those	those	PRON
ejpam-5893	62	20	with	with	ADP
ejpam-5893	62	21	nonlocal	nonlocal	ADJ
ejpam-5893	62	22	interactions	interaction	NOUN
ejpam-5893	62	23	or	or	CCONJ
ejpam-5893	62	24	anomalous	anomalous	ADJ
ejpam-5893	62	25	flow	flow	NOUN
ejpam-5893	62	26	properties	property	NOUN
ejpam-5893	62	27	.	.	PUNCT
ejpam-5893	63	1	the	the	DET
ejpam-5893	63	2	mathematical	mathematical	ADJ
ejpam-5893	63	3	importance	importance	NOUN
ejpam-5893	63	4	of	of	ADP
ejpam-5893	63	5	nonlinear	nonlinear	ADJ
ejpam-5893	63	6	time	time	NOUN
ejpam-5893	63	7	-	-	PUNCT
ejpam-5893	63	8	fractional	fractional	ADJ
ejpam-5893	63	9	emc	emc	NOUN
ejpam-5893	63	10	is	be	AUX
ejpam-5893	63	11	to	to	ADP
ejpam-5893	63	12	finding	find	VERB
ejpam-5893	63	13	exact	exact	ADJ
ejpam-5893	63	14	or	or	CCONJ
ejpam-5893	63	15	approximate	approximate	ADJ
ejpam-5893	63	16	solutions	solution	NOUN
ejpam-5893	63	17	to	to	ADP
ejpam-5893	63	18	the	the	DET
ejpam-5893	63	19	nonlinear	nonlinear	ADJ
ejpam-5893	63	20	time	time	NOUN
ejpam-5893	63	21	-	-	PUNCT
ejpam-5893	63	22	fractional	fractional	ADJ
ejpam-5893	63	23	emc	emc	NOUN
ejpam-5893	63	24	equation	equation	NOUN
ejpam-5893	63	25	is	be	AUX
ejpam-5893	63	26	a	a	DET
ejpam-5893	63	27	key	key	ADJ
ejpam-5893	63	28	area	area	NOUN
ejpam-5893	63	29	of	of	ADP
ejpam-5893	63	30	research	research	NOUN
ejpam-5893	63	31	,	,	PUNCT
ejpam-5893	63	32	which	which	PRON
ejpam-5893	63	33	helps	help	VERB
ejpam-5893	63	34	in	in	ADP
ejpam-5893	63	35	understanding	understand	VERB
ejpam-5893	63	36	the	the	DET
ejpam-5893	63	37	underlying	underlying	ADJ
ejpam-5893	63	38	physics	physics	NOUN
ejpam-5893	63	39	of	of	ADP
ejpam-5893	63	40	complex	complex	ADJ
ejpam-5893	63	41	systems	system	NOUN
ejpam-5893	63	42	.	.	PUNCT
ejpam-5893	64	1	this	this	DET
ejpam-5893	64	2	equation	equation	NOUN
ejpam-5893	64	3	serves	serve	VERB
ejpam-5893	64	4	as	as	ADP
ejpam-5893	64	5	a	a	DET
ejpam-5893	64	6	platform	platform	NOUN
ejpam-5893	64	7	for	for	ADP
ejpam-5893	64	8	analyzing	analyze	VERB
ejpam-5893	64	9	fractional	fractional	ADJ
ejpam-5893	64	10	solitons	soliton	NOUN
ejpam-5893	64	11	and	and	CCONJ
ejpam-5893	64	12	their	their	PRON
ejpam-5893	64	13	interactions	interaction	NOUN
ejpam-5893	64	14	.	.	PUNCT
ejpam-5893	65	1	by	by	ADP
ejpam-5893	65	2	incorporating	incorporate	VERB
ejpam-5893	65	3	fractional	fractional	ADJ
ejpam-5893	65	4	calculus	calculus	NOUN
ejpam-5893	65	5	,	,	PUNCT
ejpam-5893	65	6	the	the	DET
ejpam-5893	65	7	emc	emc	PROPN
ejpam-5893	65	8	equation	equation	NOUN
ejpam-5893	65	9	becomes	become	VERB
ejpam-5893	65	10	a	a	DET
ejpam-5893	65	11	powerful	powerful	ADJ
ejpam-5893	65	12	tool	tool	NOUN
ejpam-5893	65	13	to	to	PART
ejpam-5893	65	14	model	model	VERB
ejpam-5893	65	15	a	a	DET
ejpam-5893	65	16	wide	wide	ADJ
ejpam-5893	65	17	range	range	NOUN
ejpam-5893	65	18	of	of	ADP
ejpam-5893	65	19	phenomena	phenomenon	NOUN
ejpam-5893	65	20	that	that	SCONJ
ejpam-5893	65	21	traditional	traditional	ADJ
ejpam-5893	65	22	integer	integer	NOUN
ejpam-5893	65	23	-	-	PUNCT
ejpam-5893	65	24	order	order	NOUN
ejpam-5893	65	25	models	model	NOUN
ejpam-5893	65	26	can	can	AUX
ejpam-5893	65	27	not	not	PART
ejpam-5893	65	28	handle	handle	VERB
ejpam-5893	65	29	,	,	PUNCT
ejpam-5893	65	30	making	make	VERB
ejpam-5893	65	31	it	it	PRON
ejpam-5893	65	32	valuable	valuable	ADJ
ejpam-5893	65	33	across	across	ADP
ejpam-5893	65	34	multiple	multiple	ADJ
ejpam-5893	65	35	scientific	scientific	ADJ
ejpam-5893	65	36	and	and	CCONJ
ejpam-5893	65	37	engineering	engineering	NOUN
ejpam-5893	65	38	disciplines	discipline	NOUN
ejpam-5893	65	39	.	.	PUNCT
ejpam-5893	66	1	the	the	DET
ejpam-5893	66	2	robustness	robustness	NOUN
ejpam-5893	66	3	of	of	ADP
ejpam-5893	66	4	the	the	DET
ejpam-5893	66	5	propose	propose	ADJ
ejpam-5893	66	6	method	method	NOUN
ejpam-5893	66	7	refers	refer	VERB
ejpam-5893	66	8	to	to	ADP
ejpam-5893	66	9	its	its	PRON
ejpam-5893	66	10	ability	ability	NOUN
ejpam-5893	66	11	to	to	PART
ejpam-5893	66	12	understand	understand	VERB
ejpam-5893	66	13	numerical	numerical	ADJ
ejpam-5893	66	14	stability	stability	NOUN
ejpam-5893	66	15	,	,	PUNCT
ejpam-5893	66	16	handling	handling	NOUN
ejpam-5893	66	17	of	of	ADP
ejpam-5893	66	18	singub	singub	PROPN
ejpam-5893	66	19	.	.	PUNCT
ejpam-5893	67	1	yasmeen	yasmeen	PROPN
ejpam-5893	67	2	,	,	PUNCT
ejpam-5893	67	3	k.	k.	PROPN
ejpam-5893	67	4	ahmad	ahmad	PROPN
ejpam-5893	67	5	,	,	PUNCT
ejpam-5893	67	6	n.	n.	PROPN
ejpam-5893	67	7	fatima	fatima	PROPN
ejpam-5893	67	8	/	/	PUNCT
ejpam-5893	67	9	eur	eur	PROPN
ejpam-5893	67	10	.	.	PUNCT
ejpam-5893	68	1	j.	j.	PROPN
ejpam-5893	68	2	pure	pure	PROPN
ejpam-5893	68	3	appl	appl	PROPN
ejpam-5893	68	4	.	.	PROPN
ejpam-5893	68	5	math	math	PROPN
ejpam-5893	68	6	,	,	PUNCT
ejpam-5893	68	7	18	18	NUM
ejpam-5893	68	8	(	(	PUNCT
ejpam-5893	68	9	2	2	NUM
ejpam-5893	68	10	)	)	PUNCT
ejpam-5893	68	11	(	(	PUNCT
ejpam-5893	68	12	2025	2025	NUM
ejpam-5893	68	13	)	)	PUNCT
ejpam-5893	68	14	,	,	PUNCT
ejpam-5893	68	15	5893	5893	NUM
ejpam-5893	68	16	4	4	NUM
ejpam-5893	68	17	of	of	ADP
ejpam-5893	68	18	17	17	NUM
ejpam-5893	68	19	larities	laritie	NOUN
ejpam-5893	68	20	and	and	CCONJ
ejpam-5893	68	21	computational	computational	ADJ
ejpam-5893	68	22	efficiency	efficiency	NOUN
ejpam-5893	68	23	.	.	PUNCT
ejpam-5893	69	1	the	the	DET
ejpam-5893	69	2	role	role	NOUN
ejpam-5893	69	3	of	of	ADP
ejpam-5893	69	4	the	the	DET
ejpam-5893	69	5	nonlinear	nonlinear	ADJ
ejpam-5893	69	6	time	time	NOUN
ejpam-5893	69	7	-	-	PUNCT
ejpam-5893	69	8	fractional	fractional	ADJ
ejpam-5893	69	9	emc	emc	NOUN
ejpam-5893	69	10	equation	equation	NOUN
ejpam-5893	69	11	is	be	AUX
ejpam-5893	69	12	to	to	PART
ejpam-5893	69	13	extends	extend	VERB
ejpam-5893	69	14	the	the	DET
ejpam-5893	69	15	classical	classical	ADJ
ejpam-5893	69	16	emc	emc	NOUN
ejpam-5893	69	17	equation	equation	NOUN
ejpam-5893	69	18	to	to	PART
ejpam-5893	69	19	accommodate	accommodate	VERB
ejpam-5893	69	20	fractional	fractional	ADJ
ejpam-5893	69	21	-	-	PUNCT
ejpam-5893	69	22	order	order	NOUN
ejpam-5893	69	23	derivatives	derivative	NOUN
ejpam-5893	69	24	,	,	PUNCT
ejpam-5893	69	25	making	make	VERB
ejpam-5893	69	26	it	it	PRON
ejpam-5893	69	27	applicable	applicable	ADJ
ejpam-5893	69	28	to	to	ADP
ejpam-5893	69	29	systems	system	NOUN
ejpam-5893	69	30	with	with	ADP
ejpam-5893	69	31	nonlocal	nonlocal	ADJ
ejpam-5893	69	32	and	and	CCONJ
ejpam-5893	69	33	memory	memory	NOUN
ejpam-5893	69	34	-	-	PUNCT
ejpam-5893	69	35	dependent	dependent	ADJ
ejpam-5893	69	36	behavior	behavior	NOUN
ejpam-5893	69	37	.	.	PUNCT
ejpam-5893	70	1	it	it	PRON
ejpam-5893	70	2	plays	play	VERB
ejpam-5893	70	3	a	a	DET
ejpam-5893	70	4	critical	critical	ADJ
ejpam-5893	70	5	role	role	NOUN
ejpam-5893	70	6	in	in	ADP
ejpam-5893	70	7	modeling	model	VERB
ejpam-5893	70	8	nonlinear	nonlinear	ADJ
ejpam-5893	70	9	wave	wave	NOUN
ejpam-5893	70	10	propagation	propagation	NOUN
ejpam-5893	70	11	in	in	ADP
ejpam-5893	70	12	complex	complex	ADJ
ejpam-5893	70	13	media	medium	NOUN
ejpam-5893	70	14	.	.	PUNCT
ejpam-5893	71	1	this	this	DET
ejpam-5893	71	2	equation	equation	NOUN
ejpam-5893	71	3	bridges	bridge	NOUN
ejpam-5893	71	4	linear	linear	VERB
ejpam-5893	71	5	fractional	fractional	ADJ
ejpam-5893	71	6	dynamics	dynamic	NOUN
ejpam-5893	71	7	with	with	ADP
ejpam-5893	71	8	nonlinear	nonlinear	ADJ
ejpam-5893	71	9	effects	effect	NOUN
ejpam-5893	71	10	,	,	PUNCT
ejpam-5893	71	11	enabling	enable	VERB
ejpam-5893	71	12	the	the	DET
ejpam-5893	71	13	modeling	modeling	NOUN
ejpam-5893	71	14	of	of	ADP
ejpam-5893	71	15	phenomena	phenomenon	NOUN
ejpam-5893	71	16	such	such	ADJ
ejpam-5893	71	17	as	as	ADP
ejpam-5893	71	18	solitons	soliton	NOUN
ejpam-5893	71	19	,	,	PUNCT
ejpam-5893	71	20	rogue	rogue	NOUN
ejpam-5893	71	21	waves	wave	NOUN
ejpam-5893	71	22	,	,	PUNCT
ejpam-5893	71	23	and	and	CCONJ
ejpam-5893	71	24	bifurcations	bifurcation	NOUN
ejpam-5893	71	25	.	.	PUNCT
ejpam-5893	72	1	physical	physical	ADJ
ejpam-5893	72	2	interpretation	interpretation	NOUN
ejpam-5893	72	3	of	of	ADP
ejpam-5893	72	4	the	the	DET
ejpam-5893	72	5	nonlinear	nonlinear	ADJ
ejpam-5893	72	6	time	time	NOUN
ejpam-5893	72	7	-	-	PUNCT
ejpam-5893	72	8	fractional	fractional	ADJ
ejpam-5893	72	9	emc	emc	NOUN
ejpam-5893	72	10	equation	equation	NOUN
ejpam-5893	72	11	lies	lie	VERB
ejpam-5893	72	12	in	in	ADP
ejpam-5893	72	13	its	its	PRON
ejpam-5893	72	14	ability	ability	NOUN
ejpam-5893	72	15	to	to	PART
ejpam-5893	72	16	describe	describe	VERB
ejpam-5893	72	17	phenomena	phenomenon	NOUN
ejpam-5893	72	18	governed	govern	VERB
ejpam-5893	72	19	by	by	ADP
ejpam-5893	72	20	fractional	fractional	ADJ
ejpam-5893	72	21	dynamics	dynamic	NOUN
ejpam-5893	72	22	and	and	CCONJ
ejpam-5893	72	23	nonlinear	nonlinear	ADJ
ejpam-5893	72	24	interactions	interaction	NOUN
ejpam-5893	72	25	.	.	PUNCT
ejpam-5893	73	1	the	the	DET
ejpam-5893	73	2	time	time	NOUN
ejpam-5893	73	3	-	-	PUNCT
ejpam-5893	73	4	fractional	fractional	ADJ
ejpam-5893	73	5	derivative	derivative	NOUN
ejpam-5893	73	6	reflects	reflect	VERB
ejpam-5893	73	7	a	a	DET
ejpam-5893	73	8	nonlocal	nonlocal	ADJ
ejpam-5893	73	9	memory	memory	NOUN
ejpam-5893	73	10	effect	effect	NOUN
ejpam-5893	73	11	,	,	PUNCT
ejpam-5893	73	12	meaning	mean	VERB
ejpam-5893	73	13	the	the	DET
ejpam-5893	73	14	system	system	NOUN
ejpam-5893	73	15	’s	’s	PART
ejpam-5893	73	16	present	present	ADJ
ejpam-5893	73	17	state	state	NOUN
ejpam-5893	73	18	is	be	AUX
ejpam-5893	73	19	influenced	influence	VERB
ejpam-5893	73	20	by	by	ADP
ejpam-5893	73	21	its	its	PRON
ejpam-5893	73	22	past	past	ADJ
ejpam-5893	73	23	states	state	NOUN
ejpam-5893	73	24	in	in	ADP
ejpam-5893	73	25	a	a	DET
ejpam-5893	73	26	weighted	weighted	ADJ
ejpam-5893	73	27	manner	manner	NOUN
ejpam-5893	73	28	.	.	PUNCT
ejpam-5893	74	1	the	the	DET
ejpam-5893	74	2	fractional	fractional	ADJ
ejpam-5893	74	3	nature	nature	NOUN
ejpam-5893	74	4	implies	imply	VERB
ejpam-5893	74	5	that	that	SCONJ
ejpam-5893	74	6	energy	energy	NOUN
ejpam-5893	74	7	dissipation	dissipation	NOUN
ejpam-5893	74	8	or	or	CCONJ
ejpam-5893	74	9	storage	storage	NOUN
ejpam-5893	74	10	is	be	AUX
ejpam-5893	74	11	distributed	distribute	VERB
ejpam-5893	74	12	over	over	ADP
ejpam-5893	74	13	time	time	NOUN
ejpam-5893	74	14	in	in	ADP
ejpam-5893	74	15	a	a	DET
ejpam-5893	74	16	non	non	ADJ
ejpam-5893	74	17	-	-	ADJ
ejpam-5893	74	18	exponential	exponential	ADJ
ejpam-5893	74	19	manner	manner	NOUN
ejpam-5893	74	20	,	,	PUNCT
ejpam-5893	74	21	aligning	align	VERB
ejpam-5893	74	22	with	with	ADP
ejpam-5893	74	23	real	real	ADJ
ejpam-5893	74	24	-	-	PUNCT
ejpam-5893	74	25	world	world	NOUN
ejpam-5893	74	26	observations	observation	NOUN
ejpam-5893	74	27	in	in	ADP
ejpam-5893	74	28	complex	complex	ADJ
ejpam-5893	74	29	systems	system	NOUN
ejpam-5893	74	30	.	.	PUNCT
ejpam-5893	75	1	this	this	PRON
ejpam-5893	75	2	is	be	AUX
ejpam-5893	75	3	seen	see	VERB
ejpam-5893	75	4	in	in	ADP
ejpam-5893	75	5	materials	material	NOUN
ejpam-5893	75	6	with	with	ADP
ejpam-5893	75	7	viscoelastic	viscoelastic	ADJ
ejpam-5893	75	8	properties	property	NOUN
ejpam-5893	75	9	,	,	PUNCT
ejpam-5893	75	10	where	where	SCONJ
ejpam-5893	75	11	the	the	DET
ejpam-5893	75	12	stress	stress	NOUN
ejpam-5893	75	13	-	-	PUNCT
ejpam-5893	75	14	strain	strain	NOUN
ejpam-5893	75	15	relationship	relationship	NOUN
ejpam-5893	75	16	depends	depend	VERB
ejpam-5893	75	17	on	on	ADP
ejpam-5893	75	18	the	the	DET
ejpam-5893	75	19	entire	entire	ADJ
ejpam-5893	75	20	deformation	deformation	NOUN
ejpam-5893	75	21	history	history	NOUN
ejpam-5893	75	22	.	.	PUNCT
ejpam-5893	76	1	3	3	X
ejpam-5893	76	2	.	.	X
ejpam-5893	76	3	methodology	methodology	NOUN
ejpam-5893	76	4	in	in	ADP
ejpam-5893	76	5	this	this	DET
ejpam-5893	76	6	paragraph	paragraph	NOUN
ejpam-5893	76	7	,	,	PUNCT
ejpam-5893	76	8	we	we	PRON
ejpam-5893	76	9	have	have	AUX
ejpam-5893	76	10	applied	apply	VERB
ejpam-5893	76	11	stability	stability	NOUN
ejpam-5893	76	12	analysis	analysis	NOUN
ejpam-5893	76	13	and	and	CCONJ
ejpam-5893	76	14	rescaling	rescaling	NOUN
ejpam-5893	76	15	method	method	NOUN
ejpam-5893	76	16	for	for	ADP
ejpam-5893	76	17	finding	find	VERB
ejpam-5893	76	18	exact	exact	ADJ
ejpam-5893	76	19	and	and	CCONJ
ejpam-5893	76	20	approximate	approximate	ADJ
ejpam-5893	76	21	solutions	solution	NOUN
ejpam-5893	76	22	to	to	ADP
ejpam-5893	76	23	the	the	DET
ejpam-5893	76	24	time	time	NOUN
ejpam-5893	76	25	-	-	PUNCT
ejpam-5893	76	26	fractional	fractional	ADJ
ejpam-5893	76	27	emc	emc	NOUN
ejpam-5893	76	28	equation	equation	NOUN
ejpam-5893	76	29	.	.	PUNCT
ejpam-5893	77	1	step	step	NOUN
ejpam-5893	77	2	1	1	NUM
ejpam-5893	77	3	:	:	PUNCT
ejpam-5893	77	4	first	first	ADV
ejpam-5893	77	5	,	,	PUNCT
ejpam-5893	77	6	a	a	DET
ejpam-5893	77	7	general	general	ADJ
ejpam-5893	77	8	form	form	NOUN
ejpam-5893	77	9	of	of	ADP
ejpam-5893	77	10	a	a	DET
ejpam-5893	77	11	time	time	NOUN
ejpam-5893	77	12	-	-	PUNCT
ejpam-5893	77	13	fractional	fractional	ADJ
ejpam-5893	77	14	differential	differential	NOUN
ejpam-5893	77	15	equation	equation	NOUN
ejpam-5893	77	16	is	be	AUX
ejpam-5893	77	17	examined	examine	VERB
ejpam-5893	77	18	p	p	X
ejpam-5893	77	19	(	(	PUNCT
ejpam-5893	77	20	dα	dα	PROPN
ejpam-5893	77	21	t	t	PROPN
ejpam-5893	77	22	u	u	PROPN
ejpam-5893	77	23	,	,	PUNCT
ejpam-5893	77	24	ux	ux	PROPN
ejpam-5893	77	25	,	,	PUNCT
ejpam-5893	78	1	d	d	PROPN
ejpam-5893	78	2	2α	2α	NOUN
ejpam-5893	78	3	2	2	NUM
ejpam-5893	78	4	t	t	NOUN
ejpam-5893	78	5	u	u	NOUN
ejpam-5893	78	6	,	,	PUNCT
ejpam-5893	78	7	uxx	uxx	PROPN
ejpam-5893	78	8	,	,	PUNCT
ejpam-5893	78	9	...	...	PUNCT
ejpam-5893	78	10	)	)	PUNCT
ejpam-5893	79	1	=	=	SYM
ejpam-5893	79	2	0	0	PUNCT
ejpam-5893	79	3	(	(	PUNCT
ejpam-5893	79	4	3	3	NUM
ejpam-5893	79	5	)	)	PUNCT
ejpam-5893	79	6	where	where	SCONJ
ejpam-5893	79	7	p	p	NOUN
ejpam-5893	79	8	is	be	AUX
ejpam-5893	79	9	the	the	DET
ejpam-5893	79	10	polynomial	polynomial	ADJ
ejpam-5893	79	11	in	in	ADP
ejpam-5893	79	12	the	the	DET
ejpam-5893	79	13	function	function	NOUN
ejpam-5893	79	14	u(x	u(x	NOUN
ejpam-5893	79	15	,	,	PUNCT
ejpam-5893	79	16	t	t	PROPN
ejpam-5893	79	17	)	)	PUNCT
ejpam-5893	79	18	and	and	CCONJ
ejpam-5893	79	19	its	its	PRON
ejpam-5893	79	20	various	various	ADJ
ejpam-5893	79	21	partial	partial	ADJ
ejpam-5893	79	22	derivatives	derivative	NOUN
ejpam-5893	79	23	and	and	CCONJ
ejpam-5893	79	24	d2α	d2α	NOUN
ejpam-5893	79	25	2	2	NUM
ejpam-5893	79	26	t	t	NOUN
ejpam-5893	79	27	u	u	NOUN
ejpam-5893	79	28	indicates	indicate	VERB
ejpam-5893	79	29	two	two	NUM
ejpam-5893	79	30	times	time	NOUN
ejpam-5893	79	31	sequential	sequential	ADJ
ejpam-5893	79	32	conformable	conformable	ADJ
ejpam-5893	79	33	fractional	fractional	ADJ
ejpam-5893	79	34	derivatives	derivative	NOUN
ejpam-5893	79	35	of	of	ADP
ejpam-5893	79	36	the	the	DET
ejpam-5893	79	37	function	function	NOUN
ejpam-5893	79	38	u(x	u(x	NOUN
ejpam-5893	79	39	,	,	PUNCT
ejpam-5893	79	40	t	t	PROPN
ejpam-5893	79	41	)	)	PUNCT
ejpam-5893	79	42	.	.	PUNCT
ejpam-5893	80	1	step	step	NOUN
ejpam-5893	80	2	2	2	NUM
ejpam-5893	80	3	:	:	PUNCT
ejpam-5893	80	4	applying	apply	VERB
ejpam-5893	80	5	the	the	DET
ejpam-5893	80	6	transformation	transformation	NOUN
ejpam-5893	80	7	u(x	u(x	NOUN
ejpam-5893	80	8	,	,	PUNCT
ejpam-5893	80	9	t	t	NOUN
ejpam-5893	80	10	)	)	PUNCT
ejpam-5893	80	11	=	=	SYM
ejpam-5893	81	1	f(ξ	f(ξ	NOUN
ejpam-5893	81	2	)	)	PUNCT
ejpam-5893	81	3	,	,	PUNCT
ejpam-5893	81	4	ξ	ξ	X
ejpam-5893	81	5	=	=	PUNCT
ejpam-5893	81	6	√	√	PROPN
ejpam-5893	81	7	k	k	NOUN
ejpam-5893	81	8	(	(	PUNCT
ejpam-5893	81	9	x−	x−	PROPN
ejpam-5893	81	10	wtα	wtα	PROPN
ejpam-5893	82	1	γ(1	γ(1	PROPN
ejpam-5893	82	2	+	+	CCONJ
ejpam-5893	82	3	α	α	NOUN
ejpam-5893	82	4	)	)	PUNCT
ejpam-5893	82	5	)	)	PUNCT
ejpam-5893	83	1	(	(	PUNCT
ejpam-5893	83	2	4	4	X
ejpam-5893	83	3	)	)	PUNCT
ejpam-5893	83	4	using	use	VERB
ejpam-5893	83	5	(	(	PUNCT
ejpam-5893	83	6	4	4	NUM
ejpam-5893	83	7	)	)	PUNCT
ejpam-5893	83	8	,	,	PUNCT
ejpam-5893	83	9	we	we	PRON
ejpam-5893	83	10	can	can	AUX
ejpam-5893	83	11	write	write	VERB
ejpam-5893	83	12	(	(	PUNCT
ejpam-5893	83	13	3	3	NUM
ejpam-5893	83	14	)	)	PUNCT
ejpam-5893	83	15	in	in	ADP
ejpam-5893	83	16	the	the	DET
ejpam-5893	83	17	following	follow	VERB
ejpam-5893	83	18	integer	integer	NOUN
ejpam-5893	83	19	order	order	NOUN
ejpam-5893	83	20	nonlinear	nonlinear	ADJ
ejpam-5893	83	21	ordinary	ordinary	ADJ
ejpam-5893	83	22	differential	differential	ADJ
ejpam-5893	83	23	equation	equation	NOUN
ejpam-5893	83	24	(	(	PUNCT
ejpam-5893	83	25	ode	ode	PROPN
ejpam-5893	83	26	):	):	PUNCT
ejpam-5893	83	27	q(f	q(f	PROPN
ejpam-5893	83	28	′	′	NUM
ejpam-5893	83	29	,	,	PUNCT
ejpam-5893	83	30	f	f	PROPN
ejpam-5893	83	31	′′	′′	PROPN
ejpam-5893	83	32	,	,	PUNCT
ejpam-5893	83	33	f	f	PROPN
ejpam-5893	83	34	′′′	′′′	PROPN
ejpam-5893	83	35	,	,	PUNCT
ejpam-5893	83	36	...	...	PUNCT
ejpam-5893	83	37	)	)	PUNCT
ejpam-5893	84	1	=	=	SYM
ejpam-5893	84	2	0	0	PUNCT
ejpam-5893	84	3	(	(	PUNCT
ejpam-5893	84	4	5	5	NUM
ejpam-5893	84	5	)	)	PUNCT
ejpam-5893	85	1	where	where	SCONJ
ejpam-5893	85	2	f	f	X
ejpam-5893	85	3	′	′	NOUN
ejpam-5893	85	4	=	=	PUNCT
ejpam-5893	85	5	df	df	PROPN
ejpam-5893	85	6	dξ	dξ	PROPN
ejpam-5893	85	7	,	,	PUNCT
ejpam-5893	85	8	f	f	PROPN
ejpam-5893	85	9	′′	′′	PROPN
ejpam-5893	85	10	=	=	PUNCT
ejpam-5893	85	11	d2f	d2f	PROPN
ejpam-5893	85	12	dξ2	dξ2	NOUN
ejpam-5893	85	13	,	,	PUNCT
ejpam-5893	85	14	etc	etc	X
ejpam-5893	85	15	and	and	CCONJ
ejpam-5893	85	16	q	q	NOUN
ejpam-5893	85	17	is	be	AUX
ejpam-5893	85	18	the	the	DET
ejpam-5893	85	19	polynomial	polynomial	NOUN
ejpam-5893	85	20	in	in	ADP
ejpam-5893	85	21	f	f	PROPN
ejpam-5893	85	22	and	and	CCONJ
ejpam-5893	85	23	its	its	PRON
ejpam-5893	85	24	derivatives	derivative	NOUN
ejpam-5893	85	25	.	.	PUNCT
ejpam-5893	86	1	step	step	NOUN
ejpam-5893	86	2	3	3	NUM
ejpam-5893	86	3	:	:	PUNCT
ejpam-5893	86	4	now	now	ADV
ejpam-5893	86	5	,	,	PUNCT
ejpam-5893	86	6	we	we	PRON
ejpam-5893	86	7	take	take	VERB
ejpam-5893	86	8	a	a	DET
ejpam-5893	86	9	new	new	ADJ
ejpam-5893	86	10	independent	independent	ADJ
ejpam-5893	86	11	variable	variable	NOUN
ejpam-5893	86	12	x	x	X
ejpam-5893	86	13	=	=	SYM
ejpam-5893	86	14	x(ξ	x(ξ	PROPN
ejpam-5893	86	15	)	)	PUNCT
ejpam-5893	86	16	,	,	PUNCT
ejpam-5893	87	1	y	y	PROPN
ejpam-5893	87	2	=	=	SYM
ejpam-5893	87	3	y	y	PROPN
ejpam-5893	87	4	(	(	PUNCT
ejpam-5893	87	5	ξ	ξ	NOUN
ejpam-5893	87	6	)	)	PUNCT
ejpam-5893	87	7	such	such	ADJ
ejpam-5893	87	8	that	that	SCONJ
ejpam-5893	87	9	x(ξ	x(ξ	PROPN
ejpam-5893	87	10	)	)	PUNCT
ejpam-5893	87	11	=	=	SYM
ejpam-5893	87	12	f(ξ	f(ξ	NOUN
ejpam-5893	87	13	)	)	PUNCT
ejpam-5893	87	14	,	,	PUNCT
ejpam-5893	87	15	y	y	PROPN
ejpam-5893	87	16	(	(	PUNCT
ejpam-5893	87	17	ξ	ξ	PROPN
ejpam-5893	87	18	)	)	PUNCT
ejpam-5893	87	19	=	=	SYM
ejpam-5893	87	20	df	df	PROPN
ejpam-5893	87	21	dξ	dξ	PROPN
ejpam-5893	87	22	thus	thus	ADV
ejpam-5893	87	23	,	,	PUNCT
ejpam-5893	87	24	(	(	PUNCT
ejpam-5893	87	25	5	5	X
ejpam-5893	87	26	)	)	PUNCT
ejpam-5893	87	27	reduces	reduce	VERB
ejpam-5893	87	28	to	to	ADP
ejpam-5893	87	29	a	a	DET
ejpam-5893	87	30	new	new	ADJ
ejpam-5893	87	31	system	system	NOUN
ejpam-5893	87	32	of	of	ADP
ejpam-5893	87	33	odes	ode	NOUN
ejpam-5893	87	34	for	for	ADP
ejpam-5893	87	35	stability	stability	NOUN
ejpam-5893	87	36	analysis	analysis	NOUN
ejpam-5893	87	37	x	x	SYM
ejpam-5893	87	38	′(ξ	′(ξ	NOUN
ejpam-5893	87	39	)	)	PUNCT
ejpam-5893	87	40	=	=	SYM
ejpam-5893	87	41	f(x	f(x	PROPN
ejpam-5893	87	42	,	,	PUNCT
ejpam-5893	87	43	y	y	PROPN
ejpam-5893	87	44	)	)	PUNCT
ejpam-5893	88	1	=	=	PUNCT
ejpam-5893	88	2	y	y	PROPN
ejpam-5893	88	3	y	y	PROPN
ejpam-5893	88	4	′(ξ	′(ξ	PROPN
ejpam-5893	88	5	)	)	PUNCT
ejpam-5893	88	6	=	=	SYM
ejpam-5893	89	1	g(x	g(x	NOUN
ejpam-5893	89	2	,	,	PUNCT
ejpam-5893	89	3	y	y	NOUN
ejpam-5893	89	4	)	)	PUNCT
ejpam-5893	89	5	=	=	PUNCT
ejpam-5893	90	1	x	x	X
ejpam-5893	90	2	′′	′′	PROPN
ejpam-5893	90	3	b.	b.	PROPN
ejpam-5893	90	4	yasmeen	yasmeen	PROPN
ejpam-5893	90	5	,	,	PUNCT
ejpam-5893	90	6	k.	k.	PROPN
ejpam-5893	90	7	ahmad	ahmad	PROPN
ejpam-5893	90	8	,	,	PUNCT
ejpam-5893	90	9	n.	n.	PROPN
ejpam-5893	90	10	fatima	fatima	PROPN
ejpam-5893	90	11	/	/	PUNCT
ejpam-5893	90	12	eur	eur	PROPN
ejpam-5893	90	13	.	.	PUNCT
ejpam-5893	91	1	j.	j.	PROPN
ejpam-5893	91	2	pure	pure	PROPN
ejpam-5893	91	3	appl	appl	PROPN
ejpam-5893	91	4	.	.	PROPN
ejpam-5893	91	5	math	math	PROPN
ejpam-5893	91	6	,	,	PUNCT
ejpam-5893	91	7	18	18	NUM
ejpam-5893	91	8	(	(	PUNCT
ejpam-5893	91	9	2	2	NUM
ejpam-5893	91	10	)	)	PUNCT
ejpam-5893	91	11	(	(	PUNCT
ejpam-5893	91	12	2025	2025	NUM
ejpam-5893	91	13	)	)	PUNCT
ejpam-5893	91	14	,	,	PUNCT
ejpam-5893	91	15	5893	5893	NUM
ejpam-5893	91	16	5	5	NUM
ejpam-5893	91	17	of	of	ADP
ejpam-5893	91	18	17	17	NUM
ejpam-5893	91	19	3.1	3.1	NUM
ejpam-5893	91	20	.	.	PUNCT
ejpam-5893	92	1	determination	determination	NOUN
ejpam-5893	92	2	of	of	ADP
ejpam-5893	92	3	approximate	approximate	ADJ
ejpam-5893	92	4	solution	solution	NOUN
ejpam-5893	92	5	by	by	ADP
ejpam-5893	92	6	using	use	VERB
ejpam-5893	92	7	stability	stability	NOUN
ejpam-5893	92	8	analysis	analysis	NOUN
ejpam-5893	92	9	in	in	ADP
ejpam-5893	92	10	this	this	DET
ejpam-5893	92	11	section	section	NOUN
ejpam-5893	92	12	,	,	PUNCT
ejpam-5893	92	13	to	to	PART
ejpam-5893	92	14	study	study	VERB
ejpam-5893	92	15	the	the	DET
ejpam-5893	92	16	stability	stability	NOUN
ejpam-5893	92	17	of	of	ADP
ejpam-5893	92	18	the	the	DET
ejpam-5893	92	19	system	system	NOUN
ejpam-5893	92	20	,	,	PUNCT
ejpam-5893	92	21	we	we	PRON
ejpam-5893	92	22	first	first	ADV
ejpam-5893	92	23	found	find	VERB
ejpam-5893	92	24	the	the	DET
ejpam-5893	92	25	fixed	fix	VERB
ejpam-5893	92	26	points	point	NOUN
ejpam-5893	92	27	by	by	ADP
ejpam-5893	92	28	solving	solve	VERB
ejpam-5893	92	29	the	the	DET
ejpam-5893	92	30	equations	equation	NOUN
ejpam-5893	92	31	where	where	SCONJ
ejpam-5893	92	32	all	all	DET
ejpam-5893	92	33	changes	change	NOUN
ejpam-5893	92	34	in	in	ADP
ejpam-5893	92	35	the	the	DET
ejpam-5893	92	36	system	system	NOUN
ejpam-5893	92	37	(	(	PUNCT
ejpam-5893	92	38	time	time	NOUN
ejpam-5893	92	39	derivatives	derivative	NOUN
ejpam-5893	92	40	)	)	PUNCT
ejpam-5893	92	41	become	become	VERB
ejpam-5893	92	42	zero	zero	NUM
ejpam-5893	92	43	.	.	PUNCT
ejpam-5893	93	1	after	after	ADP
ejpam-5893	93	2	identifying	identify	VERB
ejpam-5893	93	3	the	the	DET
ejpam-5893	93	4	fixed	fix	VERB
ejpam-5893	93	5	points	point	NOUN
ejpam-5893	93	6	,	,	PUNCT
ejpam-5893	93	7	we	we	PRON
ejpam-5893	93	8	calculated	calculate	VERB
ejpam-5893	93	9	the	the	DET
ejpam-5893	93	10	jacobian	jacobian	ADJ
ejpam-5893	93	11	matrix	matrix	NOUN
ejpam-5893	93	12	,	,	PUNCT
ejpam-5893	93	13	which	which	PRON
ejpam-5893	93	14	is	be	AUX
ejpam-5893	93	15	made	make	VERB
ejpam-5893	93	16	up	up	ADP
ejpam-5893	93	17	of	of	ADP
ejpam-5893	93	18	partial	partial	ADJ
ejpam-5893	93	19	derivatives	derivative	NOUN
ejpam-5893	93	20	of	of	ADP
ejpam-5893	93	21	the	the	DET
ejpam-5893	93	22	system	system	NOUN
ejpam-5893	93	23	’s	’s	PART
ejpam-5893	93	24	equations	equation	NOUN
ejpam-5893	93	25	.	.	PUNCT
ejpam-5893	94	1	j(x	j(x	PROPN
ejpam-5893	94	2	,	,	PUNCT
ejpam-5893	94	3	y	y	PROPN
ejpam-5893	94	4	)	)	PUNCT
ejpam-5893	95	1	=	=	PUNCT
ejpam-5893	96	1	[	[	PUNCT
ejpam-5893	96	2	∂f	∂f	PROPN
ejpam-5893	96	3	∂x	∂x	PROPN
ejpam-5893	96	4	∂f	∂f	PROPN
ejpam-5893	96	5	∂y	∂y	PROPN
ejpam-5893	96	6	∂g	∂g	PROPN
ejpam-5893	96	7	∂x	∂x	PROPN
ejpam-5893	96	8	∂g	∂g	PROPN
ejpam-5893	96	9	∂y	∂y	PROPN
ejpam-5893	96	10	]	]	PUNCT
ejpam-5893	96	11	to	to	PART
ejpam-5893	96	12	check	check	VERB
ejpam-5893	96	13	the	the	DET
ejpam-5893	96	14	stability	stability	NOUN
ejpam-5893	96	15	of	of	ADP
ejpam-5893	96	16	these	these	DET
ejpam-5893	96	17	fixed	fix	VERB
ejpam-5893	96	18	points	point	NOUN
ejpam-5893	96	19	,	,	PUNCT
ejpam-5893	96	20	we	we	PRON
ejpam-5893	96	21	calculated	calculate	VERB
ejpam-5893	96	22	the	the	DET
ejpam-5893	96	23	eigenvalues	eigenvalue	NOUN
ejpam-5893	96	24	and	and	CCONJ
ejpam-5893	96	25	eigenvectors	eigenvector	NOUN
ejpam-5893	96	26	of	of	ADP
ejpam-5893	96	27	the	the	DET
ejpam-5893	96	28	jacobian	jacobian	ADJ
ejpam-5893	96	29	matrix	matrix	NOUN
ejpam-5893	96	30	.	.	PUNCT
ejpam-5893	97	1	if	if	SCONJ
ejpam-5893	97	2	all	all	DET
ejpam-5893	97	3	eigenvalues	eigenvalue	NOUN
ejpam-5893	97	4	had	have	VERB
ejpam-5893	97	5	negative	negative	ADJ
ejpam-5893	97	6	real	real	ADJ
ejpam-5893	97	7	parts	part	NOUN
ejpam-5893	97	8	,	,	PUNCT
ejpam-5893	97	9	the	the	DET
ejpam-5893	97	10	fixed	fix	VERB
ejpam-5893	97	11	point	point	NOUN
ejpam-5893	97	12	was	be	AUX
ejpam-5893	97	13	stable	stable	ADJ
ejpam-5893	97	14	,	,	PUNCT
ejpam-5893	97	15	meaning	mean	VERB
ejpam-5893	97	16	the	the	DET
ejpam-5893	97	17	system	system	NOUN
ejpam-5893	97	18	would	would	AUX
ejpam-5893	97	19	return	return	VERB
ejpam-5893	97	20	to	to	ADP
ejpam-5893	97	21	it	it	PRON
ejpam-5893	97	22	after	after	ADP
ejpam-5893	97	23	small	small	ADJ
ejpam-5893	97	24	disturbances	disturbance	NOUN
ejpam-5893	97	25	.	.	PUNCT
ejpam-5893	98	1	if	if	SCONJ
ejpam-5893	98	2	any	any	DET
ejpam-5893	98	3	eigenvalue	eigenvalue	NOUN
ejpam-5893	98	4	had	have	VERB
ejpam-5893	98	5	a	a	DET
ejpam-5893	98	6	positive	positive	ADJ
ejpam-5893	98	7	real	real	ADJ
ejpam-5893	98	8	part	part	NOUN
ejpam-5893	98	9	,	,	PUNCT
ejpam-5893	98	10	the	the	DET
ejpam-5893	98	11	fixed	fix	VERB
ejpam-5893	98	12	point	point	NOUN
ejpam-5893	98	13	was	be	AUX
ejpam-5893	98	14	unstable	unstable	ADJ
ejpam-5893	98	15	.	.	PUNCT
ejpam-5893	99	1	complex	complex	ADJ
ejpam-5893	99	2	eigenvalues	eigenvalue	NOUN
ejpam-5893	99	3	with	with	ADP
ejpam-5893	99	4	imaginary	imaginary	ADJ
ejpam-5893	99	5	parts	part	NOUN
ejpam-5893	99	6	indicated	indicate	VERB
ejpam-5893	99	7	oscillatory	oscillatory	ADJ
ejpam-5893	99	8	behavior	behavior	NOUN
ejpam-5893	99	9	.	.	PUNCT
ejpam-5893	100	1	eigenvectors	eigenvector	NOUN
ejpam-5893	100	2	helped	help	VERB
ejpam-5893	100	3	us	we	PRON
ejpam-5893	100	4	understand	understand	VERB
ejpam-5893	100	5	the	the	DET
ejpam-5893	100	6	directions	direction	NOUN
ejpam-5893	100	7	in	in	ADP
ejpam-5893	100	8	which	which	PRON
ejpam-5893	100	9	the	the	DET
ejpam-5893	100	10	system	system	NOUN
ejpam-5893	100	11	grows	grow	VERB
ejpam-5893	100	12	or	or	CCONJ
ejpam-5893	100	13	shrinks	shrink	VERB
ejpam-5893	100	14	around	around	ADP
ejpam-5893	100	15	the	the	DET
ejpam-5893	100	16	fixed	fix	VERB
ejpam-5893	100	17	points	point	NOUN
ejpam-5893	100	18	,	,	PUNCT
ejpam-5893	100	19	providing	provide	VERB
ejpam-5893	100	20	a	a	DET
ejpam-5893	100	21	clearer	clear	ADJ
ejpam-5893	100	22	picture	picture	NOUN
ejpam-5893	100	23	of	of	ADP
ejpam-5893	100	24	stability	stability	NOUN
ejpam-5893	100	25	or	or	CCONJ
ejpam-5893	100	26	phase	phase	NOUN
ejpam-5893	100	27	space	space	NOUN
ejpam-5893	100	28	.	.	PUNCT
ejpam-5893	101	1	the	the	DET
ejpam-5893	101	2	phase	phase	NOUN
ejpam-5893	101	3	space	space	NOUN
ejpam-5893	101	4	is	be	AUX
ejpam-5893	101	5	a	a	DET
ejpam-5893	101	6	graph	graph	NOUN
ejpam-5893	101	7	where	where	SCONJ
ejpam-5893	101	8	we	we	PRON
ejpam-5893	101	9	plot	plot	VERB
ejpam-5893	101	10	the	the	DET
ejpam-5893	101	11	variables	variable	NOUN
ejpam-5893	101	12	of	of	ADP
ejpam-5893	101	13	the	the	DET
ejpam-5893	101	14	system	system	NOUN
ejpam-5893	101	15	against	against	ADP
ejpam-5893	101	16	each	each	DET
ejpam-5893	101	17	other	other	ADJ
ejpam-5893	101	18	to	to	PART
ejpam-5893	101	19	see	see	VERB
ejpam-5893	101	20	how	how	SCONJ
ejpam-5893	101	21	the	the	DET
ejpam-5893	101	22	system	system	NOUN
ejpam-5893	101	23	changes	change	VERB
ejpam-5893	101	24	over	over	ADP
ejpam-5893	101	25	time	time	NOUN
ejpam-5893	101	26	.	.	PUNCT
ejpam-5893	102	1	analyze	analyze	VERB
ejpam-5893	102	2	the	the	DET
ejpam-5893	102	3	trajectory	trajectory	NOUN
ejpam-5893	102	4	to	to	PART
ejpam-5893	102	5	understand	understand	VERB
ejpam-5893	102	6	how	how	SCONJ
ejpam-5893	102	7	the	the	DET
ejpam-5893	102	8	system	system	NOUN
ejpam-5893	102	9	behaves	behave	VERB
ejpam-5893	102	10	overall	overall	ADV
ejpam-5893	102	11	.	.	PUNCT
ejpam-5893	103	1	we	we	PRON
ejpam-5893	103	2	used	use	VERB
ejpam-5893	103	3	numerical	numerical	ADJ
ejpam-5893	103	4	simulations	simulation	NOUN
ejpam-5893	103	5	to	to	PART
ejpam-5893	103	6	plot	plot	VERB
ejpam-5893	103	7	trajectories	trajectory	NOUN
ejpam-5893	103	8	starting	start	VERB
ejpam-5893	103	9	from	from	ADP
ejpam-5893	103	10	different	different	ADJ
ejpam-5893	103	11	initial	initial	ADJ
ejpam-5893	103	12	conditions	condition	NOUN
ejpam-5893	103	13	.	.	PUNCT
ejpam-5893	104	1	these	these	DET
ejpam-5893	104	2	trajectories	trajectory	NOUN
ejpam-5893	104	3	showed	show	VERB
ejpam-5893	104	4	how	how	SCONJ
ejpam-5893	104	5	the	the	DET
ejpam-5893	104	6	system	system	NOUN
ejpam-5893	104	7	moves	move	VERB
ejpam-5893	104	8	toward	toward	ADP
ejpam-5893	104	9	fixed	fix	VERB
ejpam-5893	104	10	points	point	NOUN
ejpam-5893	104	11	,	,	PUNCT
ejpam-5893	104	12	cycles	cycle	NOUN
ejpam-5893	104	13	,	,	PUNCT
ejpam-5893	104	14	or	or	CCONJ
ejpam-5893	104	15	more	more	ADJ
ejpam-5893	104	16	complex	complex	ADJ
ejpam-5893	104	17	behaviors	behavior	NOUN
ejpam-5893	104	18	like	like	ADP
ejpam-5893	104	19	chaos	chaos	NOUN
ejpam-5893	104	20	.	.	PUNCT
ejpam-5893	105	1	the	the	DET
ejpam-5893	105	2	eigenvectors	eigenvector	NOUN
ejpam-5893	105	3	helped	help	VERB
ejpam-5893	105	4	us	we	PRON
ejpam-5893	105	5	identify	identify	VERB
ejpam-5893	105	6	stable	stable	ADJ
ejpam-5893	105	7	and	and	CCONJ
ejpam-5893	105	8	unstable	unstable	ADJ
ejpam-5893	105	9	directions	direction	NOUN
ejpam-5893	105	10	near	near	ADP
ejpam-5893	105	11	the	the	DET
ejpam-5893	105	12	fixed	fix	VERB
ejpam-5893	105	13	points	point	NOUN
ejpam-5893	105	14	,	,	PUNCT
ejpam-5893	105	15	which	which	PRON
ejpam-5893	105	16	guided	guide	VERB
ejpam-5893	105	17	how	how	SCONJ
ejpam-5893	105	18	the	the	DET
ejpam-5893	105	19	trajectories	trajectory	NOUN
ejpam-5893	105	20	flowed	flow	VERB
ejpam-5893	105	21	.	.	PUNCT
ejpam-5893	106	1	this	this	DET
ejpam-5893	106	2	analysis	analysis	NOUN
ejpam-5893	106	3	gave	give	VERB
ejpam-5893	106	4	us	we	PRON
ejpam-5893	106	5	a	a	DET
ejpam-5893	106	6	complete	complete	ADJ
ejpam-5893	106	7	picture	picture	NOUN
ejpam-5893	106	8	of	of	ADP
ejpam-5893	106	9	both	both	CCONJ
ejpam-5893	106	10	the	the	DET
ejpam-5893	106	11	local	local	ADJ
ejpam-5893	106	12	and	and	CCONJ
ejpam-5893	106	13	global	global	ADJ
ejpam-5893	106	14	behavior	behavior	NOUN
ejpam-5893	106	15	of	of	ADP
ejpam-5893	106	16	the	the	DET
ejpam-5893	106	17	system	system	NOUN
ejpam-5893	106	18	.	.	PUNCT
ejpam-5893	107	1	3.2	3.2	NUM
ejpam-5893	107	2	.	.	PUNCT
ejpam-5893	107	3	determination	determination	NOUN
ejpam-5893	107	4	of	of	ADP
ejpam-5893	107	5	exact	exact	ADJ
ejpam-5893	107	6	solution	solution	NOUN
ejpam-5893	107	7	by	by	ADP
ejpam-5893	107	8	using	use	VERB
ejpam-5893	107	9	rescaling	rescale	VERB
ejpam-5893	107	10	the	the	DET
ejpam-5893	107	11	determination	determination	NOUN
ejpam-5893	107	12	of	of	ADP
ejpam-5893	107	13	an	an	DET
ejpam-5893	107	14	exact	exact	ADJ
ejpam-5893	107	15	solution	solution	NOUN
ejpam-5893	107	16	by	by	ADP
ejpam-5893	107	17	rescaling	rescale	VERB
ejpam-5893	107	18	into	into	ADP
ejpam-5893	107	19	its	its	PRON
ejpam-5893	107	20	simplest	simple	ADJ
ejpam-5893	107	21	form	form	NOUN
ejpam-5893	107	22	and	and	CCONJ
ejpam-5893	107	23	then	then	ADV
ejpam-5893	107	24	integrating	integrate	VERB
ejpam-5893	107	25	involves	involve	VERB
ejpam-5893	107	26	a	a	DET
ejpam-5893	107	27	structured	structured	ADJ
ejpam-5893	107	28	methodology	methodology	NOUN
ejpam-5893	107	29	.	.	PUNCT
ejpam-5893	108	1	first	first	ADV
ejpam-5893	108	2	,	,	PUNCT
ejpam-5893	108	3	the	the	DET
ejpam-5893	108	4	problem	problem	NOUN
ejpam-5893	108	5	is	be	AUX
ejpam-5893	108	6	analyzed	analyze	VERB
ejpam-5893	108	7	to	to	PART
ejpam-5893	108	8	identify	identify	VERB
ejpam-5893	108	9	the	the	DET
ejpam-5893	108	10	governing	govern	VERB
ejpam-5893	108	11	equation	equation	NOUN
ejpam-5893	108	12	,	,	PUNCT
ejpam-5893	108	13	variables	variable	NOUN
ejpam-5893	108	14	,	,	PUNCT
ejpam-5893	108	15	and	and	CCONJ
ejpam-5893	108	16	parameters	parameter	NOUN
ejpam-5893	108	17	.	.	PUNCT
ejpam-5893	109	1	the	the	DET
ejpam-5893	109	2	equation	equation	NOUN
ejpam-5893	109	3	is	be	AUX
ejpam-5893	109	4	examined	examine	VERB
ejpam-5893	109	5	for	for	ADP
ejpam-5893	109	6	scaling	scale	VERB
ejpam-5893	109	7	laws	law	NOUN
ejpam-5893	109	8	to	to	PART
ejpam-5893	109	9	guide	guide	VERB
ejpam-5893	109	10	the	the	DET
ejpam-5893	109	11	rescaling	rescaling	NOUN
ejpam-5893	109	12	process	process	NOUN
ejpam-5893	109	13	.	.	PUNCT
ejpam-5893	110	1	next	next	ADJ
ejpam-5893	110	2	,	,	PUNCT
ejpam-5893	110	3	dimensionless	dimensionless	ADJ
ejpam-5893	110	4	variables	variable	NOUN
ejpam-5893	110	5	are	be	AUX
ejpam-5893	110	6	introduced	introduce	VERB
ejpam-5893	110	7	to	to	PART
ejpam-5893	110	8	reduce	reduce	VERB
ejpam-5893	110	9	complexity	complexity	NOUN
ejpam-5893	110	10	,	,	PUNCT
ejpam-5893	110	11	typically	typically	ADV
ejpam-5893	110	12	by	by	ADP
ejpam-5893	110	13	substituting	substitute	VERB
ejpam-5893	110	14	scaled	scale	VERB
ejpam-5893	110	15	variables	variable	NOUN
ejpam-5893	110	16	like	like	ADP
ejpam-5893	110	17	z	z	NOUN
ejpam-5893	110	18	=	=	SYM
ejpam-5893	110	19	h1(w	h1(w	NOUN
ejpam-5893	110	20	,	,	PUNCT
ejpam-5893	110	21	k	k	NOUN
ejpam-5893	110	22	)	)	PUNCT
ejpam-5893	110	23	,	,	PUNCT
ejpam-5893	110	24	v	v	X
ejpam-5893	110	25	=	=	SYM
ejpam-5893	110	26	h2(w	h2(w	PROPN
ejpam-5893	110	27	,	,	PUNCT
ejpam-5893	110	28	k	k	NOUN
ejpam-5893	110	29	,	,	PUNCT
ejpam-5893	110	30	β	β	NOUN
ejpam-5893	110	31	)	)	PUNCT
ejpam-5893	110	32	where	where	SCONJ
ejpam-5893	110	33	α	α	X
ejpam-5893	110	34	,	,	PUNCT
ejpam-5893	110	35	β	β	X
ejpam-5893	110	36	are	be	AUX
ejpam-5893	110	37	scaling	scale	VERB
ejpam-5893	110	38	factors	factor	NOUN
ejpam-5893	110	39	.	.	PUNCT
ejpam-5893	111	1	these	these	DET
ejpam-5893	111	2	substitutions	substitution	NOUN
ejpam-5893	111	3	simplify	simplify	VERB
ejpam-5893	111	4	the	the	DET
ejpam-5893	111	5	original	original	ADJ
ejpam-5893	111	6	equation	equation	NOUN
ejpam-5893	111	7	by	by	ADP
ejpam-5893	111	8	reducing	reduce	VERB
ejpam-5893	111	9	the	the	DET
ejpam-5893	111	10	number	number	NOUN
ejpam-5893	111	11	of	of	ADP
ejpam-5893	111	12	parameters	parameter	NOUN
ejpam-5893	111	13	or	or	CCONJ
ejpam-5893	111	14	their	their	PRON
ejpam-5893	111	15	interaction	interaction	NOUN
ejpam-5893	111	16	.	.	PUNCT
ejpam-5893	112	1	after	after	ADP
ejpam-5893	112	2	rescaling	rescale	VERB
ejpam-5893	112	3	,	,	PUNCT
ejpam-5893	112	4	the	the	DET
ejpam-5893	112	5	equation	equation	NOUN
ejpam-5893	112	6	is	be	AUX
ejpam-5893	112	7	rewritten	rewrite	VERB
ejpam-5893	112	8	in	in	ADP
ejpam-5893	112	9	terms	term	NOUN
ejpam-5893	112	10	of	of	ADP
ejpam-5893	112	11	the	the	DET
ejpam-5893	112	12	new	new	ADJ
ejpam-5893	112	13	variables	variable	NOUN
ejpam-5893	112	14	,	,	PUNCT
ejpam-5893	112	15	often	often	ADV
ejpam-5893	112	16	resulting	result	VERB
ejpam-5893	112	17	in	in	ADP
ejpam-5893	112	18	a	a	DET
ejpam-5893	112	19	simpler	simple	ADJ
ejpam-5893	112	20	or	or	CCONJ
ejpam-5893	112	21	standard	standard	ADJ
ejpam-5893	112	22	form	form	NOUN
ejpam-5893	112	23	,	,	PUNCT
ejpam-5893	112	24	such	such	ADJ
ejpam-5893	112	25	as	as	ADP
ejpam-5893	112	26	a	a	DET
ejpam-5893	112	27	separable	separable	ADJ
ejpam-5893	112	28	equation	equation	NOUN
ejpam-5893	112	29	or	or	CCONJ
ejpam-5893	112	30	a	a	DET
ejpam-5893	112	31	known	know	VERB
ejpam-5893	112	32	ordinary	ordinary	ADJ
ejpam-5893	112	33	differential	differential	ADJ
ejpam-5893	112	34	equation	equation	NOUN
ejpam-5893	112	35	(	(	PUNCT
ejpam-5893	112	36	ode	ode	PROPN
ejpam-5893	112	37	)	)	PUNCT
ejpam-5893	112	38	.	.	PUNCT
ejpam-5893	113	1	once	once	ADV
ejpam-5893	113	2	simplified	simplify	VERB
ejpam-5893	113	3	,	,	PUNCT
ejpam-5893	113	4	the	the	DET
ejpam-5893	113	5	equation	equation	NOUN
ejpam-5893	113	6	is	be	AUX
ejpam-5893	113	7	solved	solve	VERB
ejpam-5893	113	8	analytically	analytically	ADV
ejpam-5893	113	9	.	.	PUNCT
ejpam-5893	114	1	if	if	SCONJ
ejpam-5893	114	2	the	the	DET
ejpam-5893	114	3	equation	equation	NOUN
ejpam-5893	114	4	is	be	AUX
ejpam-5893	114	5	separable	separable	ADJ
ejpam-5893	114	6	,	,	PUNCT
ejpam-5893	114	7	direct	direct	ADJ
ejpam-5893	114	8	integration	integration	NOUN
ejpam-5893	114	9	is	be	AUX
ejpam-5893	114	10	performed	perform	VERB
ejpam-5893	114	11	.	.	PUNCT
ejpam-5893	115	1	finally	finally	ADV
ejpam-5893	115	2	,	,	PUNCT
ejpam-5893	115	3	the	the	DET
ejpam-5893	115	4	solution	solution	NOUN
ejpam-5893	115	5	is	be	AUX
ejpam-5893	115	6	rescaled	rescale	VERB
ejpam-5893	115	7	back	back	ADV
ejpam-5893	115	8	to	to	ADP
ejpam-5893	115	9	the	the	DET
ejpam-5893	115	10	original	original	ADJ
ejpam-5893	115	11	variables	variable	NOUN
ejpam-5893	115	12	to	to	PART
ejpam-5893	115	13	ensure	ensure	VERB
ejpam-5893	115	14	dimensional	dimensional	ADJ
ejpam-5893	115	15	consistency	consistency	NOUN
ejpam-5893	115	16	and	and	CCONJ
ejpam-5893	115	17	physical	physical	ADJ
ejpam-5893	115	18	applicability	applicability	NOUN
ejpam-5893	115	19	.	.	PUNCT
ejpam-5893	116	1	the	the	DET
ejpam-5893	116	2	obtained	obtain	VERB
ejpam-5893	116	3	solution	solution	NOUN
ejpam-5893	116	4	is	be	AUX
ejpam-5893	116	5	verified	verify	VERB
ejpam-5893	116	6	by	by	ADP
ejpam-5893	116	7	substituting	substitute	VERB
ejpam-5893	116	8	it	it	PRON
ejpam-5893	116	9	into	into	ADP
ejpam-5893	116	10	the	the	DET
ejpam-5893	116	11	original	original	ADJ
ejpam-5893	116	12	equation	equation	NOUN
ejpam-5893	116	13	and	and	CCONJ
ejpam-5893	116	14	ensuring	ensure	VERB
ejpam-5893	116	15	consistency	consistency	NOUN
ejpam-5893	116	16	with	with	ADP
ejpam-5893	116	17	the	the	DET
ejpam-5893	116	18	problem	problem	NOUN
ejpam-5893	116	19	’s	’s	PART
ejpam-5893	116	20	constraints	constraint	NOUN
ejpam-5893	116	21	.	.	PUNCT
ejpam-5893	117	1	this	this	DET
ejpam-5893	117	2	systematic	systematic	ADJ
ejpam-5893	117	3	approach	approach	NOUN
ejpam-5893	117	4	simplifies	simplifie	NOUN
ejpam-5893	117	5	complex	complex	ADJ
ejpam-5893	117	6	equations	equation	NOUN
ejpam-5893	117	7	into	into	ADP
ejpam-5893	117	8	solvable	solvable	ADJ
ejpam-5893	117	9	forms	form	NOUN
ejpam-5893	117	10	and	and	CCONJ
ejpam-5893	117	11	provides	provide	VERB
ejpam-5893	117	12	exact	exact	ADJ
ejpam-5893	117	13	solutions	solution	NOUN
ejpam-5893	117	14	with	with	ADP
ejpam-5893	117	15	clarity	clarity	NOUN
ejpam-5893	117	16	and	and	CCONJ
ejpam-5893	117	17	precision	precision	NOUN
ejpam-5893	117	18	.	.	PUNCT
ejpam-5893	118	1	sometimes	sometimes	ADV
ejpam-5893	118	2	to	to	PART
ejpam-5893	118	3	handle	handle	VERB
ejpam-5893	118	4	b.	b.	PROPN
ejpam-5893	118	5	yasmeen	yasmeen	PROPN
ejpam-5893	118	6	,	,	PUNCT
ejpam-5893	118	7	k.	k.	PROPN
ejpam-5893	118	8	ahmad	ahmad	PROPN
ejpam-5893	118	9	,	,	PUNCT
ejpam-5893	118	10	n.	n.	PROPN
ejpam-5893	118	11	fatima	fatima	PROPN
ejpam-5893	118	12	/	/	PUNCT
ejpam-5893	118	13	eur	eur	PROPN
ejpam-5893	118	14	.	.	PUNCT
ejpam-5893	119	1	j.	j.	PROPN
ejpam-5893	119	2	pure	pure	PROPN
ejpam-5893	119	3	appl	appl	PROPN
ejpam-5893	119	4	.	.	PROPN
ejpam-5893	119	5	math	math	PROPN
ejpam-5893	119	6	,	,	PUNCT
ejpam-5893	119	7	18	18	NUM
ejpam-5893	119	8	(	(	PUNCT
ejpam-5893	119	9	2	2	NUM
ejpam-5893	119	10	)	)	PUNCT
ejpam-5893	119	11	(	(	PUNCT
ejpam-5893	119	12	2025	2025	NUM
ejpam-5893	119	13	)	)	PUNCT
ejpam-5893	119	14	,	,	PUNCT
ejpam-5893	119	15	5893	5893	NUM
ejpam-5893	119	16	6	6	NUM
ejpam-5893	119	17	of	of	ADP
ejpam-5893	119	18	17	17	NUM
ejpam-5893	119	19	ode	ode	ADJ
ejpam-5893	119	20	by	by	ADP
ejpam-5893	119	21	using	use	VERB
ejpam-5893	119	22	elementary	elementary	ADJ
ejpam-5893	119	23	techniques	technique	NOUN
ejpam-5893	119	24	and	and	CCONJ
ejpam-5893	119	25	our	our	PRON
ejpam-5893	119	26	system	system	NOUN
ejpam-5893	119	27	not	not	PART
ejpam-5893	119	28	give	give	VERB
ejpam-5893	119	29	exact	exact	ADJ
ejpam-5893	119	30	answers	answer	NOUN
ejpam-5893	119	31	that	that	PRON
ejpam-5893	119	32	’s	’	VERB
ejpam-5893	119	33	why	why	SCONJ
ejpam-5893	119	34	we	we	PRON
ejpam-5893	119	35	use	use	VERB
ejpam-5893	119	36	rescaling	rescaling	NOUN
ejpam-5893	119	37	method	method	NOUN
ejpam-5893	119	38	.	.	PUNCT
ejpam-5893	120	1	4	4	X
ejpam-5893	120	2	.	.	X
ejpam-5893	120	3	applications	application	NOUN
ejpam-5893	120	4	the	the	DET
ejpam-5893	120	5	purpose	purpose	NOUN
ejpam-5893	120	6	of	of	ADP
ejpam-5893	120	7	this	this	DET
ejpam-5893	120	8	section	section	NOUN
ejpam-5893	120	9	is	be	AUX
ejpam-5893	120	10	to	to	PART
ejpam-5893	120	11	provide	provide	VERB
ejpam-5893	120	12	approximate	approximate	NOUN
ejpam-5893	120	13	for	for	ADP
ejpam-5893	120	14	case	case	NOUN
ejpam-5893	120	15	1	1	NUM
ejpam-5893	120	16	by	by	ADP
ejpam-5893	120	17	applying	apply	VERB
ejpam-5893	120	18	stability	stability	NOUN
ejpam-5893	120	19	analysis	analysis	NOUN
ejpam-5893	120	20	and	and	CCONJ
ejpam-5893	120	21	case	case	NOUN
ejpam-5893	120	22	2	2	NUM
ejpam-5893	120	23	is	be	AUX
ejpam-5893	120	24	for	for	ADP
ejpam-5893	120	25	exact	exact	ADJ
ejpam-5893	120	26	solutions	solution	NOUN
ejpam-5893	120	27	by	by	ADP
ejpam-5893	120	28	using	use	VERB
ejpam-5893	120	29	rescaling	rescaling	NOUN
ejpam-5893	120	30	to	to	ADP
ejpam-5893	120	31	time	time	NOUN
ejpam-5893	120	32	-	-	PUNCT
ejpam-5893	120	33	fractional	fractional	ADJ
ejpam-5893	120	34	emc	emc	NOUN
ejpam-5893	120	35	equation	equation	NOUN
ejpam-5893	120	36	with	with	ADP
ejpam-5893	120	37	nonlinearity	nonlinearity	NOUN
ejpam-5893	120	38	.	.	PUNCT
ejpam-5893	121	1	case	case	NOUN
ejpam-5893	121	2	1	1	NUM
ejpam-5893	121	3	we	we	PRON
ejpam-5893	121	4	take	take	VERB
ejpam-5893	121	5	traveling	travel	VERB
ejpam-5893	121	6	wave	wave	NOUN
ejpam-5893	121	7	transformation	transformation	NOUN
ejpam-5893	121	8	for	for	ADP
ejpam-5893	121	9	our	our	PRON
ejpam-5893	121	10	purpose	purpose	NOUN
ejpam-5893	121	11	.	.	PUNCT
ejpam-5893	122	1	u(x	u(x	PROPN
ejpam-5893	122	2	,	,	PUNCT
ejpam-5893	122	3	t	t	NOUN
ejpam-5893	122	4	)	)	PUNCT
ejpam-5893	122	5	=	=	SYM
ejpam-5893	122	6	u(ξ	u(ξ	NOUN
ejpam-5893	122	7	)	)	PUNCT
ejpam-5893	122	8	,	,	PUNCT
ejpam-5893	122	9	ξ	ξ	X
ejpam-5893	122	10	=	=	PUNCT
ejpam-5893	122	11	√	√	PROPN
ejpam-5893	122	12	k	k	NOUN
ejpam-5893	122	13	(	(	PUNCT
ejpam-5893	122	14	x−	x−	PROPN
ejpam-5893	122	15	wtα	wtα	PROPN
ejpam-5893	123	1	γ(1	γ(1	PROPN
ejpam-5893	123	2	+	+	CCONJ
ejpam-5893	123	3	α	α	NOUN
ejpam-5893	123	4	)	)	PUNCT
ejpam-5893	123	5	)	)	PUNCT
ejpam-5893	124	1	(	(	PUNCT
ejpam-5893	124	2	6	6	X
ejpam-5893	124	3	)	)	PUNCT
ejpam-5893	124	4	where	where	SCONJ
ejpam-5893	124	5	k	k	PROPN
ejpam-5893	124	6	is	be	AUX
ejpam-5893	124	7	a	a	DET
ejpam-5893	124	8	wavelength	wavelength	NOUN
ejpam-5893	124	9	,	,	PUNCT
ejpam-5893	124	10	w	w	PROPN
ejpam-5893	124	11	γ(1+α	γ(1+α	PROPN
ejpam-5893	124	12	)	)	PUNCT
ejpam-5893	124	13	is	be	AUX
ejpam-5893	124	14	angular	angular	ADJ
ejpam-5893	124	15	frequency	frequency	NOUN
ejpam-5893	124	16	and	and	CCONJ
ejpam-5893	124	17	α	α	NOUN
ejpam-5893	124	18	is	be	AUX
ejpam-5893	124	19	a	a	DET
ejpam-5893	124	20	fractional	fractional	ADJ
ejpam-5893	124	21	order	order	NOUN
ejpam-5893	124	22	.	.	PUNCT
ejpam-5893	125	1	by	by	ADP
ejpam-5893	125	2	means	mean	NOUN
ejpam-5893	125	3	of	of	ADP
ejpam-5893	125	4	the	the	DET
ejpam-5893	125	5	wave	wave	NOUN
ejpam-5893	125	6	transformation	transformation	NOUN
ejpam-5893	125	7	(	(	PUNCT
ejpam-5893	125	8	6	6	NUM
ejpam-5893	125	9	)	)	PUNCT
ejpam-5893	125	10	,	,	PUNCT
ejpam-5893	125	11	equation	equation	NOUN
ejpam-5893	125	12	(	(	PUNCT
ejpam-5893	125	13	2	2	X
ejpam-5893	125	14	)	)	PUNCT
ejpam-5893	125	15	converts	convert	NOUN
ejpam-5893	125	16	into	into	ADP
ejpam-5893	125	17	the	the	DET
ejpam-5893	125	18	under	under	NOUN
ejpam-5893	125	19	mentioned	mention	VERB
ejpam-5893	125	20	node	node	NOUN
ejpam-5893	125	21	−k2wu	−k2wu	NUM
ejpam-5893	125	22	′′′′	′′′′	PROPN
ejpam-5893	125	23	+	+	CCONJ
ejpam-5893	125	24	β(−wk	β(−wk	PROPN
ejpam-5893	125	25	√	√	PROPN
ejpam-5893	125	26	ku	ku	PROPN
ejpam-5893	125	27	′u	′u	VERB
ejpam-5893	125	28	′′	′′	PROPN
ejpam-5893	125	29	−	−	PROPN
ejpam-5893	125	30	wk	wk	INTJ
ejpam-5893	125	31	√	√	PROPN
ejpam-5893	125	32	ku	ku	PROPN
ejpam-5893	125	33	′u	′u	PROPN
ejpam-5893	125	34	′′	′′	PROPN
ejpam-5893	125	35	)	)	PUNCT
ejpam-5893	125	36	+	+	CCONJ
ejpam-5893	125	37	kw2u	kw2u	PROPN
ejpam-5893	125	38	′′	′′	NOUN
ejpam-5893	125	39	=	=	SYM
ejpam-5893	125	40	0	0	PUNCT
ejpam-5893	125	41	(	(	PUNCT
ejpam-5893	125	42	7	7	NUM
ejpam-5893	125	43	)	)	PUNCT
ejpam-5893	125	44	further	far	ADV
ejpam-5893	125	45	simplifying	simplify	VERB
ejpam-5893	125	46	(	(	PUNCT
ejpam-5893	125	47	7	7	NUM
ejpam-5893	125	48	)	)	PUNCT
ejpam-5893	125	49	and	and	CCONJ
ejpam-5893	125	50	canceling	cancel	VERB
ejpam-5893	125	51	w	w	PROPN
ejpam-5893	125	52	and	and	CCONJ
ejpam-5893	125	53	k	k	X
ejpam-5893	125	54	from	from	ADP
ejpam-5893	125	55	(	(	PUNCT
ejpam-5893	125	56	7	7	NUM
ejpam-5893	125	57	)	)	PUNCT
ejpam-5893	125	58	ku	ku	PROPN
ejpam-5893	125	59	′′′′	′′′′	PROPN
ejpam-5893	125	60	+	+	CCONJ
ejpam-5893	125	61	2β	2β	NOUN
ejpam-5893	125	62	√	√	NUM
ejpam-5893	125	63	ku	ku	PROPN
ejpam-5893	125	64	′u	′u	PROPN
ejpam-5893	125	65	′′	′′	PROPN
ejpam-5893	125	66	−	−	PROPN
ejpam-5893	125	67	wu	wu	PROPN
ejpam-5893	126	1	′′	′′	PROPN
ejpam-5893	126	2	=	=	NOUN
ejpam-5893	126	3	0	0	PUNCT
ejpam-5893	127	1	(	(	PUNCT
ejpam-5893	127	2	8)	8)	NUM
ejpam-5893	127	3	by	by	ADP
ejpam-5893	127	4	once	once	ADV
ejpam-5893	127	5	integrating	integrate	VERB
ejpam-5893	127	6	(	(	PUNCT
ejpam-5893	127	7	8)	8)	NUM
ejpam-5893	127	8	and	and	CCONJ
ejpam-5893	127	9	ignoring	ignore	VERB
ejpam-5893	127	10	the	the	DET
ejpam-5893	127	11	integral	integral	ADJ
ejpam-5893	127	12	constant	constant	ADJ
ejpam-5893	127	13	,	,	PUNCT
ejpam-5893	127	14	we	we	PRON
ejpam-5893	127	15	can	can	AUX
ejpam-5893	127	16	determine	determine	VERB
ejpam-5893	127	17	ku	ku	PROPN
ejpam-5893	127	18	′′′	′′′	PROPN
ejpam-5893	128	1	+	+	CCONJ
ejpam-5893	128	2	2β	2β	NOUN
ejpam-5893	128	3	√	√	NUM
ejpam-5893	128	4	k(u	k(u	PROPN
ejpam-5893	128	5	′)2	′)2	PROPN
ejpam-5893	128	6	−	−	PROPN
ejpam-5893	128	7	wu	wu	NOUN
ejpam-5893	129	1	′	′	NUM
ejpam-5893	129	2	=	=	SYM
ejpam-5893	129	3	0	0	PUNCT
ejpam-5893	130	1	(	(	PUNCT
ejpam-5893	130	2	9	9	NUM
ejpam-5893	130	3	)	)	PUNCT
ejpam-5893	130	4	if	if	SCONJ
ejpam-5893	130	5	we	we	PRON
ejpam-5893	130	6	set	set	VERB
ejpam-5893	130	7	u	u	PRON
ejpam-5893	130	8	′	′	NOUN
ejpam-5893	130	9	=	=	SYM
ejpam-5893	130	10	v	v	NOUN
ejpam-5893	130	11	,	,	PUNCT
ejpam-5893	130	12	then	then	ADV
ejpam-5893	130	13	(	(	PUNCT
ejpam-5893	130	14	9	9	X
ejpam-5893	130	15	)	)	PUNCT
ejpam-5893	130	16	becomes	become	VERB
ejpam-5893	130	17	kv	kv	PROPN
ejpam-5893	130	18	′′	′′	PROPN
ejpam-5893	130	19	+	+	CCONJ
ejpam-5893	130	20	2β	2β	NUM
ejpam-5893	130	21	√	√	NUM
ejpam-5893	130	22	kv	kv	PROPN
ejpam-5893	130	23	2	2	NUM
ejpam-5893	130	24	−	−	PROPN
ejpam-5893	130	25	wv	wv	PROPN
ejpam-5893	130	26	=	=	SYM
ejpam-5893	130	27	0	0	NUM
ejpam-5893	130	28	(	(	PUNCT
ejpam-5893	130	29	10	10	NUM
ejpam-5893	130	30	)	)	PUNCT
ejpam-5893	131	1	where	where	SCONJ
ejpam-5893	131	2	v	v	ADP
ejpam-5893	131	3	′	′	NOUN
ejpam-5893	131	4	=	=	PUNCT
ejpam-5893	132	1	dv	dv	PROPN
ejpam-5893	132	2	dξ	dξ	PROPN
ejpam-5893	132	3	.	.	PUNCT
ejpam-5893	133	1	let	let	VERB
ejpam-5893	133	2	’s	’s	PRON
ejpam-5893	133	3	take	take	VERB
ejpam-5893	133	4	r	r	NOUN
ejpam-5893	133	5	=	=	SYM
ejpam-5893	133	6	2β	2β	NOUN
ejpam-5893	133	7	√	√	NUM
ejpam-5893	133	8	k	k	PROPN
ejpam-5893	133	9	and	and	CCONJ
ejpam-5893	133	10	s	s	NOUN
ejpam-5893	133	11	=	=	PROPN
ejpam-5893	133	12	w	w	PROPN
ejpam-5893	133	13	k	k	PROPN
ejpam-5893	133	14	after	after	ADP
ejpam-5893	133	15	simplification	simplification	NOUN
ejpam-5893	133	16	,	,	PUNCT
ejpam-5893	133	17	we	we	PRON
ejpam-5893	133	18	get	get	VERB
ejpam-5893	133	19	v	v	ADP
ejpam-5893	134	1	′′	′′	PROPN
ejpam-5893	134	2	=	=	PUNCT
ejpam-5893	134	3	sv	sv	PROPN
ejpam-5893	134	4	−	−	PROPN
ejpam-5893	134	5	rv	rv	PROPN
ejpam-5893	134	6	2	2	NUM
ejpam-5893	134	7	(	(	PUNCT
ejpam-5893	134	8	11	11	NUM
ejpam-5893	134	9	)	)	PUNCT
ejpam-5893	134	10	introducing	introduce	VERB
ejpam-5893	134	11	x	x	X
ejpam-5893	134	12	=	=	SYM
ejpam-5893	134	13	v	v	PART
ejpam-5893	134	14	(	(	PUNCT
ejpam-5893	134	15	ξ	ξ	NOUN
ejpam-5893	134	16	)	)	PUNCT
ejpam-5893	134	17	and	and	CCONJ
ejpam-5893	134	18	y	y	PROPN
ejpam-5893	134	19	=	=	PROPN
ejpam-5893	134	20	v	v	NUM
ejpam-5893	134	21	′(ξ	′(ξ	NOUN
ejpam-5893	134	22	)	)	PUNCT
ejpam-5893	134	23	as	as	ADP
ejpam-5893	134	24	new	new	ADJ
ejpam-5893	134	25	variables	variable	NOUN
ejpam-5893	134	26	,	,	PUNCT
ejpam-5893	134	27	then	then	ADV
ejpam-5893	134	28	equation	equation	NOUN
ejpam-5893	134	29	(	(	PUNCT
ejpam-5893	134	30	11	11	NUM
ejpam-5893	134	31	)	)	PUNCT
ejpam-5893	134	32	is	be	AUX
ejpam-5893	134	33	equivalent	equivalent	ADJ
ejpam-5893	134	34	to	to	ADP
ejpam-5893	134	35	2	2	NUM
ejpam-5893	134	36	-	-	PUNCT
ejpam-5893	134	37	d	d	NOUN
ejpam-5893	134	38	autonomous	autonomous	ADJ
ejpam-5893	134	39	system	system	NOUN
ejpam-5893	135	1	dx	dx	PROPN
ejpam-5893	135	2	dξ	dξ	PROPN
ejpam-5893	136	1	=	=	SYM
ejpam-5893	136	2	y	y	PROPN
ejpam-5893	136	3	,	,	PUNCT
ejpam-5893	136	4	dy	dy	X
ejpam-5893	136	5	dξ	dξ	PROPN
ejpam-5893	137	1	=	=	PUNCT
ejpam-5893	137	2	y	y	PROPN
ejpam-5893	137	3	′	′	NUM
ejpam-5893	138	1	=	=	PUNCT
ejpam-5893	138	2	sv	sv	PROPN
ejpam-5893	138	3	−	−	PROPN
ejpam-5893	138	4	rv	rv	PROPN
ejpam-5893	138	5	2	2	NUM
ejpam-5893	138	6	(	(	PUNCT
ejpam-5893	138	7	12	12	NUM
ejpam-5893	138	8	)	)	PUNCT
ejpam-5893	138	9	as	as	ADP
ejpam-5893	138	10	a	a	DET
ejpam-5893	138	11	result	result	NOUN
ejpam-5893	138	12	,	,	PUNCT
ejpam-5893	138	13	we	we	PRON
ejpam-5893	138	14	obtain	obtain	VERB
ejpam-5893	138	15	this	this	DET
ejpam-5893	138	16	form	form	NOUN
ejpam-5893	138	17	x	x	NOUN
ejpam-5893	138	18	′	′	NUM
ejpam-5893	138	19	=	=	SYM
ejpam-5893	138	20	f(x	f(x	PROPN
ejpam-5893	138	21	,	,	PUNCT
ejpam-5893	138	22	y	y	PROPN
ejpam-5893	138	23	)	)	PUNCT
ejpam-5893	139	1	=	=	SYM
ejpam-5893	139	2	y	y	PROPN
ejpam-5893	139	3	(	(	PUNCT
ejpam-5893	139	4	13	13	NUM
ejpam-5893	139	5	)	)	PUNCT
ejpam-5893	139	6	y	y	NOUN
ejpam-5893	139	7	′	′	NUM
ejpam-5893	140	1	=	=	PUNCT
ejpam-5893	140	2	g(x	g(x	NOUN
ejpam-5893	140	3	,	,	PUNCT
ejpam-5893	140	4	y	y	PROPN
ejpam-5893	140	5	)	)	PUNCT
ejpam-5893	141	1	=	=	PUNCT
ejpam-5893	141	2	sv	sv	INTJ
ejpam-5893	141	3	−	−	PROPN
ejpam-5893	141	4	rv	rv	PROPN
ejpam-5893	141	5	2	2	NUM
ejpam-5893	141	6	(	(	PUNCT
ejpam-5893	141	7	14	14	NUM
ejpam-5893	141	8	)	)	PUNCT
ejpam-5893	141	9	b.	b.	PROPN
ejpam-5893	141	10	yasmeen	yasmeen	PROPN
ejpam-5893	141	11	,	,	PUNCT
ejpam-5893	141	12	k.	k.	PROPN
ejpam-5893	141	13	ahmad	ahmad	PROPN
ejpam-5893	141	14	,	,	PUNCT
ejpam-5893	141	15	n.	n.	PROPN
ejpam-5893	141	16	fatima	fatima	PROPN
ejpam-5893	141	17	/	/	PUNCT
ejpam-5893	141	18	eur	eur	PROPN
ejpam-5893	141	19	.	.	PUNCT
ejpam-5893	142	1	j.	j.	PROPN
ejpam-5893	142	2	pure	pure	PROPN
ejpam-5893	142	3	appl	appl	PROPN
ejpam-5893	142	4	.	.	PROPN
ejpam-5893	142	5	math	math	PROPN
ejpam-5893	142	6	,	,	PUNCT
ejpam-5893	142	7	18	18	NUM
ejpam-5893	142	8	(	(	PUNCT
ejpam-5893	142	9	2	2	NUM
ejpam-5893	142	10	)	)	PUNCT
ejpam-5893	142	11	(	(	PUNCT
ejpam-5893	142	12	2025	2025	NUM
ejpam-5893	142	13	)	)	PUNCT
ejpam-5893	142	14	,	,	PUNCT
ejpam-5893	142	15	5893	5893	NUM
ejpam-5893	142	16	7	7	NUM
ejpam-5893	142	17	of	of	ADP
ejpam-5893	142	18	17	17	NUM
ejpam-5893	142	19	to	to	PART
ejpam-5893	142	20	find	find	VERB
ejpam-5893	142	21	the	the	DET
ejpam-5893	142	22	fixed	fix	VERB
ejpam-5893	142	23	points	point	NOUN
ejpam-5893	142	24	of	of	ADP
ejpam-5893	142	25	the	the	DET
ejpam-5893	142	26	system	system	NOUN
ejpam-5893	142	27	,	,	PUNCT
ejpam-5893	142	28	the	the	DET
ejpam-5893	142	29	smooth	smooth	ADJ
ejpam-5893	142	30	functions	function	NOUN
ejpam-5893	142	31	can	can	AUX
ejpam-5893	142	32	be	be	AUX
ejpam-5893	142	33	written	write	VERB
ejpam-5893	142	34	in	in	ADP
ejpam-5893	142	35	the	the	DET
ejpam-5893	142	36	following	follow	VERB
ejpam-5893	142	37	equations	equation	NOUN
ejpam-5893	142	38	fixed	fix	VERB
ejpam-5893	142	39	points	point	NOUN
ejpam-5893	142	40	:	:	PUNCT
ejpam-5893	143	1	f(x	f(x	PROPN
ejpam-5893	143	2	,	,	PUNCT
ejpam-5893	143	3	y	y	PROPN
ejpam-5893	143	4	)	)	PUNCT
ejpam-5893	143	5	=	=	SYM
ejpam-5893	143	6	0	0	NUM
ejpam-5893	143	7	,	,	PUNCT
ejpam-5893	143	8	=	=	PRON
ejpam-5893	143	9	⇒	⇒	NOUN
ejpam-5893	143	10	y	y	PROPN
ejpam-5893	143	11	=	=	SYM
ejpam-5893	143	12	0	0	PUNCT
ejpam-5893	144	1	g(x	g(x	NOUN
ejpam-5893	144	2	,	,	PUNCT
ejpam-5893	144	3	y	y	PROPN
ejpam-5893	144	4	)	)	PUNCT
ejpam-5893	144	5	=	=	SYM
ejpam-5893	144	6	0	0	NUM
ejpam-5893	144	7	,	,	PUNCT
ejpam-5893	144	8	=	=	PRON
ejpam-5893	144	9	⇒	⇒	VERB
ejpam-5893	144	10	sx	sx	PROPN
ejpam-5893	144	11	−	−	PROPN
ejpam-5893	144	12	rx2	rx2	X
ejpam-5893	144	13	=	=	SYM
ejpam-5893	144	14	0	0	PROPN
ejpam-5893	144	15	,	,	PUNCT
ejpam-5893	144	16	=	=	PRON
ejpam-5893	144	17	⇒	⇒	NOUN
ejpam-5893	144	18	x	x	PUNCT
ejpam-5893	145	1	=	=	SYM
ejpam-5893	145	2	0	0	NUM
ejpam-5893	145	3	,	,	PUNCT
ejpam-5893	145	4	s	s	AUX
ejpam-5893	145	5	r	r	NOUN
ejpam-5893	145	6	the	the	DET
ejpam-5893	145	7	fixed	fix	VERB
ejpam-5893	145	8	points	point	NOUN
ejpam-5893	145	9	for	for	ADP
ejpam-5893	145	10	the	the	DET
ejpam-5893	145	11	system	system	NOUN
ejpam-5893	145	12	are	be	AUX
ejpam-5893	145	13	(	(	PUNCT
ejpam-5893	145	14	x	x	X
ejpam-5893	145	15	,	,	PUNCT
ejpam-5893	145	16	y	y	PROPN
ejpam-5893	145	17	)	)	PUNCT
ejpam-5893	145	18	=	=	PUNCT
ejpam-5893	146	1	(	(	PUNCT
ejpam-5893	146	2	0	0	NUM
ejpam-5893	146	3	,	,	PUNCT
ejpam-5893	146	4	0	0	NUM
ejpam-5893	146	5	)	)	PUNCT
ejpam-5893	146	6	,	,	PUNCT
ejpam-5893	146	7	(	(	PUNCT
ejpam-5893	146	8	s	s	NOUN
ejpam-5893	146	9	r	r	NOUN
ejpam-5893	146	10	,	,	PUNCT
ejpam-5893	146	11	0	0	NUM
ejpam-5893	146	12	)	)	PUNCT
ejpam-5893	146	13	jacobian	jacobian	ADJ
ejpam-5893	146	14	matrix	matrix	NOUN
ejpam-5893	146	15	:	:	PUNCT
ejpam-5893	146	16	to	to	PART
ejpam-5893	146	17	find	find	VERB
ejpam-5893	146	18	the	the	DET
ejpam-5893	146	19	jacobian	jacobian	ADJ
ejpam-5893	146	20	matrix	matrix	NOUN
ejpam-5893	146	21	of	of	ADP
ejpam-5893	146	22	the	the	DET
ejpam-5893	146	23	system	system	NOUN
ejpam-5893	146	24	,	,	PUNCT
ejpam-5893	146	25	we	we	PRON
ejpam-5893	146	26	have	have	VERB
ejpam-5893	146	27	j(x	j(x	PROPN
ejpam-5893	146	28	,	,	PUNCT
ejpam-5893	146	29	y	y	PROPN
ejpam-5893	146	30	)	)	PUNCT
ejpam-5893	147	1	=	=	PUNCT
ejpam-5893	148	1	[	[	PUNCT
ejpam-5893	148	2	∂f	∂f	PROPN
ejpam-5893	148	3	∂x	∂x	PROPN
ejpam-5893	148	4	∂f	∂f	PROPN
ejpam-5893	148	5	∂y	∂y	PROPN
ejpam-5893	148	6	∂g	∂g	PROPN
ejpam-5893	148	7	∂x	∂x	PROPN
ejpam-5893	148	8	∂g	∂g	PROPN
ejpam-5893	148	9	∂y	∂y	X
ejpam-5893	148	10	]	]	PUNCT
ejpam-5893	148	11	=	=	PUNCT
ejpam-5893	149	1	[	[	PUNCT
ejpam-5893	149	2	0	0	NUM
ejpam-5893	149	3	1	1	NUM
ejpam-5893	149	4	s−	s−	NOUN
ejpam-5893	149	5	2rx	2rx	ADV
ejpam-5893	149	6	0	0	PUNCT
ejpam-5893	149	7	]	]	X
ejpam-5893	150	1	j(0	j(0	PROPN
ejpam-5893	150	2	,	,	PUNCT
ejpam-5893	150	3	0	0	NUM
ejpam-5893	150	4	)	)	PUNCT
ejpam-5893	150	5	=	=	NOUN
ejpam-5893	151	1	[	[	PUNCT
ejpam-5893	151	2	0	0	NUM
ejpam-5893	151	3	1	1	NUM
ejpam-5893	151	4	s	s	NOUN
ejpam-5893	151	5	0	0	NUM
ejpam-5893	151	6	]	]	PUNCT
ejpam-5893	151	7	j	j	PROPN
ejpam-5893	151	8	(	(	PUNCT
ejpam-5893	151	9	s	s	NOUN
ejpam-5893	151	10	r	r	NOUN
ejpam-5893	151	11	,	,	PUNCT
ejpam-5893	151	12	0	0	NUM
ejpam-5893	151	13	)	)	PUNCT
ejpam-5893	151	14	=	=	NOUN
ejpam-5893	152	1	[	[	PUNCT
ejpam-5893	152	2	0	0	NUM
ejpam-5893	152	3	1	1	NUM
ejpam-5893	152	4	−s	−s	NOUN
ejpam-5893	152	5	0	0	NUM
ejpam-5893	152	6	]	]	PUNCT
ejpam-5893	152	7	eigenvalues	eigenvalue	VERB
ejpam-5893	152	8	at	at	ADP
ejpam-5893	152	9	fixed	fix	VERB
ejpam-5893	152	10	points	point	NOUN
ejpam-5893	152	11	:	:	PUNCT
ejpam-5893	152	12	eigenvalues	eigenvalue	NOUN
ejpam-5893	152	13	of	of	ADP
ejpam-5893	152	14	jacobian	jacobian	ADJ
ejpam-5893	152	15	matrix	matrix	NOUN
ejpam-5893	152	16	j	j	PROPN
ejpam-5893	152	17	,	,	PUNCT
ejpam-5893	152	18	can	can	AUX
ejpam-5893	152	19	be	be	AUX
ejpam-5893	152	20	found	find	VERB
ejpam-5893	152	21	by	by	ADP
ejpam-5893	152	22	following	follow	VERB
ejpam-5893	152	23	characteristics	characteristic	NOUN
ejpam-5893	152	24	equation	equation	NOUN
ejpam-5893	152	25	det(j	det(j	PROPN
ejpam-5893	152	26	−	−	PROPN
ejpam-5893	152	27	λi	λi	NOUN
ejpam-5893	152	28	)	)	PUNCT
ejpam-5893	152	29	=	=	SYM
ejpam-5893	152	30	0	0	NUM
ejpam-5893	152	31	•	•	NUM
ejpam-5893	152	32	case	case	NOUN
ejpam-5893	152	33	1(a	1(a	NUM
ejpam-5893	152	34	)	)	PUNCT
ejpam-5893	152	35	at	at	ADP
ejpam-5893	152	36	fixed	fix	VERB
ejpam-5893	152	37	point	point	NOUN
ejpam-5893	152	38	j(0	j(0	PROPN
ejpam-5893	152	39	,	,	PUNCT
ejpam-5893	152	40	0	0	NUM
ejpam-5893	152	41	)	)	PUNCT
ejpam-5893	152	42	|j(0	|j(0	NOUN
ejpam-5893	152	43	,	,	PUNCT
ejpam-5893	152	44	0)−	0)−	PUNCT
ejpam-5893	153	1	λi|	λi|	NOUN
ejpam-5893	153	2	=	=	SYM
ejpam-5893	153	3	∣∣∣∣−λ	∣∣∣∣−λ	SYM
ejpam-5893	153	4	1	1	NUM
ejpam-5893	153	5	s	s	NOUN
ejpam-5893	153	6	−λ	−λ	NOUN
ejpam-5893	153	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5893	153	8	=	=	NOUN
ejpam-5893	153	9	0	0	NUM
ejpam-5893	153	10	where	where	SCONJ
ejpam-5893	153	11	s	s	VERB
ejpam-5893	153	12	=	=	PROPN
ejpam-5893	153	13	w	w	PROPN
ejpam-5893	153	14	k	k	PROPN
ejpam-5893	153	15	the	the	DET
ejpam-5893	153	16	eigenvalue	eigenvalue	PROPN
ejpam-5893	153	17	can	can	AUX
ejpam-5893	153	18	be	be	AUX
ejpam-5893	153	19	written	write	VERB
ejpam-5893	153	20	as	as	ADP
ejpam-5893	153	21	λ	λ	PROPN
ejpam-5893	153	22	=	=	SYM
ejpam-5893	153	23	±	±	NUM
ejpam-5893	153	24	√	√	PROPN
ejpam-5893	153	25	w	w	PROPN
ejpam-5893	153	26	k	k	PROPN
ejpam-5893	154	1	=	=	AUX
ejpam-5893	154	2	⇒	⇒	VERB
ejpam-5893	154	3	λ11	λ11	NOUN
ejpam-5893	154	4	=	=	PUNCT
ejpam-5893	154	5	√	√	PROPN
ejpam-5893	155	1	w	w	PROPN
ejpam-5893	155	2	k	k	PROPN
ejpam-5893	155	3	,	,	PUNCT
ejpam-5893	155	4	λ12	λ12	PROPN
ejpam-5893	155	5	=	=	PUNCT
ejpam-5893	155	6	−	−	PROPN
ejpam-5893	156	1	√	√	NUM
ejpam-5893	156	2	w	w	PROPN
ejpam-5893	156	3	k	k	PROPN
ejpam-5893	156	4	if	if	SCONJ
ejpam-5893	156	5	we	we	PRON
ejpam-5893	156	6	choose	choose	VERB
ejpam-5893	156	7	the	the	DET
ejpam-5893	156	8	values	value	NOUN
ejpam-5893	156	9	of	of	ADP
ejpam-5893	156	10	parameters	parameter	NOUN
ejpam-5893	156	11	β	β	X
ejpam-5893	156	12	=	=	SYM
ejpam-5893	156	13	1	1	NUM
ejpam-5893	156	14	,	,	PUNCT
ejpam-5893	156	15	w	w	NOUN
ejpam-5893	156	16	=	=	NOUN
ejpam-5893	156	17	16	16	NUM
ejpam-5893	156	18	,	,	PUNCT
ejpam-5893	156	19	k	k	NOUN
ejpam-5893	156	20	=	=	SYM
ejpam-5893	156	21	4	4	NUM
ejpam-5893	156	22	,	,	PUNCT
ejpam-5893	156	23	r	r	NOUN
ejpam-5893	156	24	=	=	SYM
ejpam-5893	156	25	1	1	NUM
ejpam-5893	156	26	we	we	PRON
ejpam-5893	156	27	get	get	VERB
ejpam-5893	156	28	λ11	λ11	ADJ
ejpam-5893	156	29	=	=	SYM
ejpam-5893	156	30	2	2	NUM
ejpam-5893	156	31	,	,	PUNCT
ejpam-5893	156	32	λ12	λ12	NOUN
ejpam-5893	156	33	=	=	NOUN
ejpam-5893	156	34	−2	−2	NOUN
ejpam-5893	156	35	the	the	PRON
ejpam-5893	156	36	eigenvalues	eigenvalue	VERB
ejpam-5893	156	37	λ11	λ11	NOUN
ejpam-5893	156	38	=	=	SYM
ejpam-5893	156	39	2	2	NUM
ejpam-5893	156	40	and	and	CCONJ
ejpam-5893	156	41	λ12	λ12	ADJ
ejpam-5893	156	42	=	=	ADJ
ejpam-5893	156	43	−2	−2	NOUN
ejpam-5893	156	44	indicates	indicate	VERB
ejpam-5893	156	45	that	that	SCONJ
ejpam-5893	156	46	the	the	DET
ejpam-5893	156	47	fixed	fix	VERB
ejpam-5893	156	48	points	point	NOUN
ejpam-5893	156	49	(	(	PUNCT
ejpam-5893	156	50	0,0	0,0	NOUN
ejpam-5893	156	51	)	)	PUNCT
ejpam-5893	156	52	is	be	AUX
ejpam-5893	156	53	saddle	saddle	VERB
ejpam-5893	156	54	.	.	PUNCT
ejpam-5893	157	1	with	with	ADP
ejpam-5893	157	2	these	these	DET
ejpam-5893	157	3	parameteric	parameteric	ADJ
ejpam-5893	157	4	values	value	NOUN
ejpam-5893	157	5	,	,	PUNCT
ejpam-5893	157	6	the	the	DET
ejpam-5893	157	7	system	system	NOUN
ejpam-5893	157	8	of	of	ADP
ejpam-5893	157	9	odes	ode	NOUN
ejpam-5893	157	10	simplifies	simplifie	NOUN
ejpam-5893	157	11	to	to	ADP
ejpam-5893	157	12	x	x	SYM
ejpam-5893	157	13	′	′	NUM
ejpam-5893	157	14	=	=	SYM
ejpam-5893	157	15	y	y	PROPN
ejpam-5893	157	16	,	,	PUNCT
ejpam-5893	157	17	y	y	PROPN
ejpam-5893	157	18	′	′	NUM
ejpam-5893	158	1	=	=	NOUN
ejpam-5893	158	2	4x	4x	NUM
ejpam-5893	158	3	−x2	−x2	PROPN
ejpam-5893	158	4	(	(	PUNCT
ejpam-5893	158	5	15	15	NUM
ejpam-5893	158	6	)	)	PUNCT
ejpam-5893	158	7	b.	b.	PROPN
ejpam-5893	158	8	yasmeen	yasmeen	PROPN
ejpam-5893	158	9	,	,	PUNCT
ejpam-5893	158	10	k.	k.	PROPN
ejpam-5893	158	11	ahmad	ahmad	PROPN
ejpam-5893	158	12	,	,	PUNCT
ejpam-5893	158	13	n.	n.	PROPN
ejpam-5893	158	14	fatima	fatima	PROPN
ejpam-5893	158	15	/	/	PUNCT
ejpam-5893	158	16	eur	eur	PROPN
ejpam-5893	158	17	.	.	PUNCT
ejpam-5893	159	1	j.	j.	PROPN
ejpam-5893	159	2	pure	pure	PROPN
ejpam-5893	159	3	appl	appl	PROPN
ejpam-5893	159	4	.	.	PROPN
ejpam-5893	159	5	math	math	PROPN
ejpam-5893	159	6	,	,	PUNCT
ejpam-5893	159	7	18	18	NUM
ejpam-5893	159	8	(	(	PUNCT
ejpam-5893	159	9	2	2	NUM
ejpam-5893	159	10	)	)	PUNCT
ejpam-5893	159	11	(	(	PUNCT
ejpam-5893	159	12	2025	2025	NUM
ejpam-5893	159	13	)	)	PUNCT
ejpam-5893	159	14	,	,	PUNCT
ejpam-5893	159	15	5893	5893	NUM
ejpam-5893	159	16	8	8	NUM
ejpam-5893	159	17	of	of	ADP
ejpam-5893	159	18	17	17	NUM
ejpam-5893	159	19	eigenvector	eigenvector	NOUN
ejpam-5893	159	20	at	at	ADP
ejpam-5893	159	21	λ	λ	X
ejpam-5893	159	22	=	=	SYM
ejpam-5893	159	23	±	±	PROPN
ejpam-5893	159	24	√	√	PROPN
ejpam-5893	159	25	w	w	PROPN
ejpam-5893	160	1	k	k	X
ejpam-5893	160	2	:	:	PUNCT
ejpam-5893	160	3	for	for	ADP
ejpam-5893	160	4	each	each	DET
ejpam-5893	160	5	eigenvalue	eigenvalue	ADJ
ejpam-5893	160	6	λ11	λ11	NOUN
ejpam-5893	160	7	and	and	CCONJ
ejpam-5893	160	8	λ12	λ12	ADJ
ejpam-5893	160	9	,	,	PUNCT
ejpam-5893	160	10	the	the	DET
ejpam-5893	160	11	eigenvectors	eigenvector	NOUN
ejpam-5893	160	12	are	be	AUX
ejpam-5893	160	13	v11	v11	NOUN
ejpam-5893	160	14	=	=	PUNCT
ejpam-5893	160	15	[	[	PUNCT
ejpam-5893	160	16	1	1	NUM
ejpam-5893	160	17	λ11	λ11	NOUN
ejpam-5893	160	18	]	]	PUNCT
ejpam-5893	160	19	,	,	PUNCT
ejpam-5893	160	20	v12	v12	VERB
ejpam-5893	160	21	=	=	PUNCT
ejpam-5893	160	22	[	[	PUNCT
ejpam-5893	160	23	1	1	NUM
ejpam-5893	160	24	λ12	λ12	ADJ
ejpam-5893	160	25	]	]	X
ejpam-5893	160	26	=	=	NOUN
ejpam-5893	160	27	⇒	⇒	NOUN
ejpam-5893	160	28	v11	v11	NOUN
ejpam-5893	160	29	=	=	PUNCT
ejpam-5893	160	30	[	[	PUNCT
ejpam-5893	160	31	1√	1√	PROPN
ejpam-5893	160	32	w	w	PROPN
ejpam-5893	160	33	k	k	X
ejpam-5893	160	34	]	]	PUNCT
ejpam-5893	160	35	,	,	PUNCT
ejpam-5893	160	36	v12	v12	VERB
ejpam-5893	160	37	=	=	PUNCT
ejpam-5893	160	38	[	[	PUNCT
ejpam-5893	160	39	1	1	NUM
ejpam-5893	160	40	−	−	NOUN
ejpam-5893	160	41	√	√	NUM
ejpam-5893	160	42	w	w	PROPN
ejpam-5893	160	43	k	k	X
ejpam-5893	160	44	]	]	PUNCT
ejpam-5893	160	45	trajectory	trajectory	NOUN
ejpam-5893	160	46	for	for	ADP
ejpam-5893	160	47	the	the	DET
ejpam-5893	160	48	system	system	NOUN
ejpam-5893	160	49	,	,	PUNCT
ejpam-5893	160	50	the	the	DET
ejpam-5893	160	51	general	general	ADJ
ejpam-5893	160	52	form	form	NOUN
ejpam-5893	160	53	is	be	AUX
ejpam-5893	160	54	[	[	PUNCT
ejpam-5893	160	55	x1	x1	ADJ
ejpam-5893	160	56	y1	y1	NOUN
ejpam-5893	160	57	]	]	PUNCT
ejpam-5893	160	58	=	=	PUNCT
ejpam-5893	161	1	c1v11e	c1v11e	NOUN
ejpam-5893	161	2	λ11ξ	λ11ξ	PUNCT
ejpam-5893	161	3	+	+	CCONJ
ejpam-5893	161	4	c2v12e	c2v12e	PROPN
ejpam-5893	161	5	λ12ξ	λ12ξ	PROPN
ejpam-5893	161	6	=	=	SYM
ejpam-5893	161	7	c1	c1	PROPN
ejpam-5893	161	8	[	[	PUNCT
ejpam-5893	161	9	1√	1√	PROPN
ejpam-5893	161	10	w	w	PROPN
ejpam-5893	161	11	k	k	X
ejpam-5893	161	12	]	]	PUNCT
ejpam-5893	161	13	eλ11ξ	eλ11ξ	X
ejpam-5893	161	14	+	+	CCONJ
ejpam-5893	161	15	c2	c2	PROPN
ejpam-5893	161	16	[	[	PUNCT
ejpam-5893	161	17	1	1	NUM
ejpam-5893	161	18	−	−	NOUN
ejpam-5893	161	19	√	√	NUM
ejpam-5893	161	20	w	w	PROPN
ejpam-5893	161	21	k	k	X
ejpam-5893	161	22	]	]	PUNCT
ejpam-5893	161	23	eλ12ξ	eλ12ξ	VERB
ejpam-5893	161	24	u	u	NOUN
ejpam-5893	161	25	′(ξ	′(ξ	NOUN
ejpam-5893	161	26	)	)	PUNCT
ejpam-5893	161	27	=	=	NOUN
ejpam-5893	161	28	v	v	X
ejpam-5893	161	29	(	(	PUNCT
ejpam-5893	161	30	ξ	ξ	NOUN
ejpam-5893	161	31	)	)	PUNCT
ejpam-5893	161	32	=	=	SYM
ejpam-5893	161	33	x(ξ	x(ξ	PROPN
ejpam-5893	161	34	)	)	PUNCT
ejpam-5893	162	1	=	=	SYM
ejpam-5893	162	2	c1exp	c1exp	NOUN
ejpam-5893	162	3	(	(	PUNCT
ejpam-5893	162	4	√	√	PROPN
ejpam-5893	162	5	w	w	PROPN
ejpam-5893	162	6	k	k	PROPN
ejpam-5893	162	7	ξ	ξ	PROPN
ejpam-5893	162	8	)	)	PUNCT
ejpam-5893	163	1	+	+	CCONJ
ejpam-5893	163	2	c2exp	c2exp	PROPN
ejpam-5893	163	3	(	(	PUNCT
ejpam-5893	163	4	−	−	PROPN
ejpam-5893	163	5	√	√	PROPN
ejpam-5893	163	6	w	w	PROPN
ejpam-5893	163	7	k	k	PROPN
ejpam-5893	163	8	ξ	ξ	PROPN
ejpam-5893	163	9	)	)	PUNCT
ejpam-5893	163	10	after	after	ADP
ejpam-5893	163	11	integration	integration	NOUN
ejpam-5893	163	12	u(ξ	u(ξ	NOUN
ejpam-5893	163	13	)	)	PUNCT
ejpam-5893	163	14	=	=	SYM
ejpam-5893	163	15	√	√	PROPN
ejpam-5893	163	16	w	w	X
ejpam-5893	164	1	k	k	ADJ
ejpam-5893	164	2	c1exp	c1exp	NOUN
ejpam-5893	164	3	(	(	PUNCT
ejpam-5893	164	4	√	√	PROPN
ejpam-5893	164	5	w	w	PROPN
ejpam-5893	164	6	k	k	PROPN
ejpam-5893	164	7	ξ	ξ	PROPN
ejpam-5893	164	8	)	)	PUNCT
ejpam-5893	165	1	−	−	PROPN
ejpam-5893	166	1	√	√	NUM
ejpam-5893	166	2	w	w	PROPN
ejpam-5893	167	1	k	k	PROPN
ejpam-5893	167	2	c2exp	c2exp	PROPN
ejpam-5893	167	3	(	(	PUNCT
ejpam-5893	167	4	−	−	PROPN
ejpam-5893	167	5	√	√	PROPN
ejpam-5893	167	6	w	w	PROPN
ejpam-5893	167	7	k	k	PROPN
ejpam-5893	167	8	ξ	ξ	PROPN
ejpam-5893	167	9	)	)	PUNCT
ejpam-5893	168	1	+	+	CCONJ
ejpam-5893	168	2	c3	c3	PROPN
ejpam-5893	168	3	(	(	PUNCT
ejpam-5893	168	4	16	16	NUM
ejpam-5893	168	5	)	)	PUNCT
ejpam-5893	168	6	u11(x	u11(x	NOUN
ejpam-5893	168	7	,	,	PUNCT
ejpam-5893	168	8	t	t	PROPN
ejpam-5893	168	9	)	)	PUNCT
ejpam-5893	168	10	=	=	PUNCT
ejpam-5893	169	1	√	√	PROPN
ejpam-5893	169	2	w	w	NOUN
ejpam-5893	170	1	k	k	X
ejpam-5893	170	2	c1exp	c1exp	PROPN
ejpam-5893	171	1	[	[	X
ejpam-5893	172	1	√	√	X
ejpam-5893	172	2	w	w	PROPN
ejpam-5893	172	3	k	k	PROPN
ejpam-5893	173	1	√	√	PROPN
ejpam-5893	173	2	k	k	PROPN
ejpam-5893	174	1	(	(	PUNCT
ejpam-5893	174	2	x−	x−	PROPN
ejpam-5893	174	3	wtα	wtα	PROPN
ejpam-5893	174	4	γ(1	γ(1	PROPN
ejpam-5893	174	5	+	+	CCONJ
ejpam-5893	174	6	α	α	NOUN
ejpam-5893	174	7	)	)	PUNCT
ejpam-5893	174	8	)	)	PUNCT
ejpam-5893	174	9	]	]	PUNCT
ejpam-5893	175	1	−	−	PROPN
ejpam-5893	175	2	√	√	NUM
ejpam-5893	176	1	w	w	PROPN
ejpam-5893	176	2	k	k	PROPN
ejpam-5893	176	3	c2exp	c2exp	PROPN
ejpam-5893	176	4	[	[	PUNCT
ejpam-5893	176	5	−	−	PROPN
ejpam-5893	176	6	√	√	PROPN
ejpam-5893	176	7	w	w	PROPN
ejpam-5893	176	8	k	k	PROPN
ejpam-5893	177	1	√	√	PROPN
ejpam-5893	177	2	k	k	PROPN
ejpam-5893	177	3	(	(	PUNCT
ejpam-5893	177	4	x−	x−	PROPN
ejpam-5893	177	5	wtα	wtα	PROPN
ejpam-5893	178	1	γ(1	γ(1	PROPN
ejpam-5893	178	2	+	+	CCONJ
ejpam-5893	178	3	α	α	NOUN
ejpam-5893	178	4	)	)	PUNCT
ejpam-5893	178	5	)	)	PUNCT
ejpam-5893	178	6	]	]	PUNCT
ejpam-5893	179	1	+	+	PUNCT
ejpam-5893	179	2	c3	c3	PROPN
ejpam-5893	179	3	u11(x	u11(x	NOUN
ejpam-5893	179	4	,	,	PUNCT
ejpam-5893	179	5	t	t	PROPN
ejpam-5893	179	6	)	)	PUNCT
ejpam-5893	179	7	=	=	PUNCT
ejpam-5893	180	1	√	√	PROPN
ejpam-5893	180	2	w	w	NOUN
ejpam-5893	181	1	k	k	X
ejpam-5893	181	2	c1exp	c1exp	PROPN
ejpam-5893	182	1	[	[	X
ejpam-5893	182	2	√	√	NUM
ejpam-5893	182	3	w	w	NOUN
ejpam-5893	182	4	(	(	PUNCT
ejpam-5893	182	5	x−	x−	PROPN
ejpam-5893	182	6	wtα	wtα	PROPN
ejpam-5893	182	7	γ(1	γ(1	PROPN
ejpam-5893	182	8	+	+	CCONJ
ejpam-5893	182	9	α	α	NOUN
ejpam-5893	182	10	)	)	PUNCT
ejpam-5893	182	11	)	)	PUNCT
ejpam-5893	182	12	]	]	PUNCT
ejpam-5893	183	1	−	−	PROPN
ejpam-5893	183	2	√	√	NUM
ejpam-5893	184	1	w	w	PROPN
ejpam-5893	184	2	k	k	PROPN
ejpam-5893	184	3	c2exp	c2exp	PROPN
ejpam-5893	184	4	[	[	PUNCT
ejpam-5893	184	5	−	−	PROPN
ejpam-5893	184	6	√	√	NUM
ejpam-5893	184	7	w	w	PROPN
ejpam-5893	184	8	(	(	PUNCT
ejpam-5893	184	9	x−	x−	PROPN
ejpam-5893	184	10	wtα	wtα	PROPN
ejpam-5893	185	1	γ(1	γ(1	PROPN
ejpam-5893	185	2	+	+	CCONJ
ejpam-5893	185	3	α	α	NOUN
ejpam-5893	185	4	)	)	PUNCT
ejpam-5893	185	5	)	)	PUNCT
ejpam-5893	185	6	]	]	PUNCT
ejpam-5893	186	1	+	+	PUNCT
ejpam-5893	186	2	c3	c3	X
ejpam-5893	186	3	(	(	PUNCT
ejpam-5893	186	4	17	17	NUM
ejpam-5893	186	5	)	)	PUNCT
ejpam-5893	186	6	•	•	NUM
ejpam-5893	186	7	case	case	NOUN
ejpam-5893	186	8	1(b	1(b	NUM
ejpam-5893	186	9	)	)	PUNCT
ejpam-5893	186	10	at	at	ADP
ejpam-5893	186	11	fixed	fix	VERB
ejpam-5893	186	12	point	point	NOUN
ejpam-5893	186	13	j	j	PROPN
ejpam-5893	186	14	(	(	PUNCT
ejpam-5893	186	15	sr	sr	PROPN
ejpam-5893	186	16	,	,	PUNCT
ejpam-5893	186	17	0	0	NUM
ejpam-5893	186	18	)	)	PUNCT
ejpam-5893	186	19	|j(s	|j(s	NOUN
ejpam-5893	186	20	r	r	NOUN
ejpam-5893	186	21	,	,	PUNCT
ejpam-5893	186	22	0)−	0)−	PUNCT
ejpam-5893	187	1	λi|	λi|	NOUN
ejpam-5893	187	2	=	=	SYM
ejpam-5893	187	3	∣∣∣∣−λ	∣∣∣∣−λ	SYM
ejpam-5893	187	4	1	1	NUM
ejpam-5893	187	5	−s	−s	NOUN
ejpam-5893	187	6	−λ	−λ	NOUN
ejpam-5893	187	7	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5893	187	8	=	=	SYM
ejpam-5893	187	9	0	0	NUM
ejpam-5893	188	1	the	the	DET
ejpam-5893	188	2	eigenvalue	eigenvalue	NOUN
ejpam-5893	188	3	can	can	AUX
ejpam-5893	188	4	be	be	AUX
ejpam-5893	188	5	written	write	VERB
ejpam-5893	188	6	as	as	ADP
ejpam-5893	188	7	λ	λ	X
ejpam-5893	188	8	=	=	PUNCT
ejpam-5893	188	9	±i	±i	PROPN
ejpam-5893	188	10	√	√	PROPN
ejpam-5893	188	11	w	w	NOUN
ejpam-5893	188	12	k	k	X
ejpam-5893	189	1	=	=	VERB
ejpam-5893	189	2	⇒	⇒	NOUN
ejpam-5893	189	3	λ13	λ13	X
ejpam-5893	190	1	=	=	PUNCT
ejpam-5893	190	2	i	i	PRON
ejpam-5893	190	3	√	√	VERB
ejpam-5893	191	1	w	w	VERB
ejpam-5893	191	2	k	k	PROPN
ejpam-5893	191	3	,	,	PUNCT
ejpam-5893	191	4	λ14	λ14	PROPN
ejpam-5893	191	5	=	=	PUNCT
ejpam-5893	191	6	−i	−i	PROPN
ejpam-5893	192	1	√	√	INTJ
ejpam-5893	192	2	w	w	PROPN
ejpam-5893	192	3	k	k	PROPN
ejpam-5893	193	1	if	if	SCONJ
ejpam-5893	193	2	we	we	PRON
ejpam-5893	193	3	choose	choose	VERB
ejpam-5893	193	4	the	the	DET
ejpam-5893	193	5	values	value	NOUN
ejpam-5893	193	6	of	of	ADP
ejpam-5893	193	7	parameters	parameter	NOUN
ejpam-5893	193	8	β	β	X
ejpam-5893	193	9	=	=	SYM
ejpam-5893	193	10	1	1	NUM
ejpam-5893	193	11	2	2	NUM
ejpam-5893	193	12	,	,	PUNCT
ejpam-5893	193	13	w	w	NOUN
ejpam-5893	193	14	=	=	SYM
ejpam-5893	193	15	32	32	NUM
ejpam-5893	193	16	,	,	PUNCT
ejpam-5893	193	17	k	k	NOUN
ejpam-5893	193	18	=	=	SYM
ejpam-5893	193	19	2	2	NUM
ejpam-5893	193	20	,	,	PUNCT
ejpam-5893	193	21	r	r	NOUN
ejpam-5893	193	22	=	=	SYM
ejpam-5893	193	23	1√	1√	NUM
ejpam-5893	193	24	2	2	NUM
ejpam-5893	193	25	we	we	PRON
ejpam-5893	193	26	get	get	VERB
ejpam-5893	193	27	λ13	λ13	NOUN
ejpam-5893	193	28	=	=	SYM
ejpam-5893	193	29	4i	4i	NOUN
ejpam-5893	193	30	,	,	PUNCT
ejpam-5893	193	31	λ14	λ14	NOUN
ejpam-5893	193	32	=	=	SYM
ejpam-5893	193	33	−4i	−4i	PROPN
ejpam-5893	193	34	b.	b.	PROPN
ejpam-5893	193	35	yasmeen	yasmeen	PROPN
ejpam-5893	193	36	,	,	PUNCT
ejpam-5893	193	37	k.	k.	PROPN
ejpam-5893	193	38	ahmad	ahmad	PROPN
ejpam-5893	193	39	,	,	PUNCT
ejpam-5893	193	40	n.	n.	PROPN
ejpam-5893	193	41	fatima	fatima	PROPN
ejpam-5893	193	42	/	/	PUNCT
ejpam-5893	193	43	eur	eur	PROPN
ejpam-5893	193	44	.	.	PUNCT
ejpam-5893	194	1	j.	j.	PROPN
ejpam-5893	194	2	pure	pure	PROPN
ejpam-5893	194	3	appl	appl	PROPN
ejpam-5893	194	4	.	.	PROPN
ejpam-5893	194	5	math	math	PROPN
ejpam-5893	194	6	,	,	PUNCT
ejpam-5893	194	7	18	18	NUM
ejpam-5893	194	8	(	(	PUNCT
ejpam-5893	194	9	2	2	NUM
ejpam-5893	194	10	)	)	PUNCT
ejpam-5893	194	11	(	(	PUNCT
ejpam-5893	194	12	2025	2025	NUM
ejpam-5893	194	13	)	)	PUNCT
ejpam-5893	194	14	,	,	PUNCT
ejpam-5893	194	15	5893	5893	NUM
ejpam-5893	194	16	9	9	NUM
ejpam-5893	194	17	of	of	ADP
ejpam-5893	194	18	17	17	NUM
ejpam-5893	194	19	the	the	DET
ejpam-5893	194	20	eigenvalues	eigenvalue	NOUN
ejpam-5893	194	21	λ13	λ13	NOUN
ejpam-5893	194	22	=	=	SYM
ejpam-5893	194	23	4i	4i	NOUN
ejpam-5893	194	24	and	and	CCONJ
ejpam-5893	194	25	λ14	λ14	NOUN
ejpam-5893	194	26	=	=	SYM
ejpam-5893	194	27	−4i	−4i	NOUN
ejpam-5893	194	28	show	show	VERB
ejpam-5893	194	29	that	that	SCONJ
ejpam-5893	194	30	the	the	DET
ejpam-5893	194	31	fixed	fix	VERB
ejpam-5893	194	32	points	point	NOUN
ejpam-5893	194	33	(	(	PUNCT
ejpam-5893	194	34	sr	sr	PROPN
ejpam-5893	194	35	,	,	PUNCT
ejpam-5893	194	36	0	0	NUM
ejpam-5893	194	37	)	)	PUNCT
ejpam-5893	194	38	is	be	AUX
ejpam-5893	194	39	centre	centre	NOUN
ejpam-5893	194	40	and	and	CCONJ
ejpam-5893	194	41	the	the	DET
ejpam-5893	194	42	system	system	NOUN
ejpam-5893	194	43	of	of	ADP
ejpam-5893	194	44	odes	ode	NOUN
ejpam-5893	194	45	simplifies	simplifie	NOUN
ejpam-5893	194	46	under	under	ADP
ejpam-5893	194	47	these	these	DET
ejpam-5893	194	48	parameters	parameter	NOUN
ejpam-5893	194	49	.	.	PUNCT
ejpam-5893	195	1	x	x	X
ejpam-5893	196	1	′	′	NUM
ejpam-5893	196	2	=	=	SYM
ejpam-5893	196	3	y	y	PROPN
ejpam-5893	196	4	,	,	PUNCT
ejpam-5893	196	5	y	y	PROPN
ejpam-5893	196	6	′	′	NUM
ejpam-5893	196	7	=	=	NOUN
ejpam-5893	196	8	16x	16x	NOUN
ejpam-5893	196	9	−	−	PROPN
ejpam-5893	196	10	1√	1√	PROPN
ejpam-5893	196	11	2	2	NUM
ejpam-5893	196	12	x2	x2	NOUN
ejpam-5893	196	13	(	(	PUNCT
ejpam-5893	196	14	18	18	NUM
ejpam-5893	196	15	)	)	PUNCT
ejpam-5893	196	16	eigenvector	eigenvector	NOUN
ejpam-5893	196	17	at	at	ADP
ejpam-5893	196	18	λ	λ	PROPN
ejpam-5893	196	19	=	=	PUNCT
ejpam-5893	196	20	±i	±i	PROPN
ejpam-5893	196	21	√	√	PROPN
ejpam-5893	196	22	w	w	SYM
ejpam-5893	196	23	k	k	NOUN
ejpam-5893	196	24	:	:	PUNCT
ejpam-5893	196	25	for	for	ADP
ejpam-5893	196	26	each	each	DET
ejpam-5893	196	27	eigenvalue	eigenvalue	NOUN
ejpam-5893	196	28	λ13	λ13	PROPN
ejpam-5893	196	29	and	and	CCONJ
ejpam-5893	196	30	λ14	λ14	PROPN
ejpam-5893	196	31	,	,	PUNCT
ejpam-5893	196	32	the	the	DET
ejpam-5893	196	33	eigenvectors	eigenvector	NOUN
ejpam-5893	196	34	are	be	AUX
ejpam-5893	196	35	v13	v13	NOUN
ejpam-5893	196	36	=	=	PUNCT
ejpam-5893	196	37	[	[	PUNCT
ejpam-5893	196	38	1	1	NUM
ejpam-5893	196	39	λ13	λ13	NOUN
ejpam-5893	196	40	]	]	PUNCT
ejpam-5893	196	41	,	,	PUNCT
ejpam-5893	196	42	v14	v14	X
ejpam-5893	196	43	=	=	PUNCT
ejpam-5893	197	1	[	[	PUNCT
ejpam-5893	197	2	1	1	NUM
ejpam-5893	197	3	λ14	λ14	NOUN
ejpam-5893	197	4	]	]	PUNCT
ejpam-5893	197	5	=	=	NOUN
ejpam-5893	197	6	⇒	⇒	NOUN
ejpam-5893	197	7	v13	v13	NOUN
ejpam-5893	198	1	=	=	PUNCT
ejpam-5893	198	2	[	[	PUNCT
ejpam-5893	198	3	1	1	NUM
ejpam-5893	198	4	i	i	NOUN
ejpam-5893	198	5	√	√	VERB
ejpam-5893	198	6	w	w	VERB
ejpam-5893	198	7	k	k	X
ejpam-5893	198	8	]	]	PUNCT
ejpam-5893	198	9	,	,	PUNCT
ejpam-5893	198	10	v14	v14	X
ejpam-5893	198	11	=	=	PUNCT
ejpam-5893	198	12	[	[	PUNCT
ejpam-5893	198	13	1	1	NUM
ejpam-5893	198	14	−i	−i	NOUN
ejpam-5893	198	15	√	√	PROPN
ejpam-5893	199	1	w	w	PROPN
ejpam-5893	200	1	k	k	X
ejpam-5893	200	2	]	]	PUNCT
ejpam-5893	200	3	trajectory	trajectory	NOUN
ejpam-5893	200	4	[	[	PUNCT
ejpam-5893	200	5	x2	x2	NOUN
ejpam-5893	200	6	y2	y2	NOUN
ejpam-5893	200	7	]	]	PUNCT
ejpam-5893	201	1	=	=	PUNCT
ejpam-5893	201	2	c4v13e	c4v13e	PROPN
ejpam-5893	201	3	λ13ξ	λ13ξ	X
ejpam-5893	202	1	+	+	CCONJ
ejpam-5893	202	2	c5v14e	c5v14e	PROPN
ejpam-5893	202	3	λ14ξ	λ14ξ	NOUN
ejpam-5893	202	4	=	=	SYM
ejpam-5893	202	5	c4	c4	NOUN
ejpam-5893	202	6	[	[	PUNCT
ejpam-5893	202	7	1	1	NUM
ejpam-5893	202	8	i	i	NOUN
ejpam-5893	202	9	√	√	VERB
ejpam-5893	202	10	w	w	VERB
ejpam-5893	202	11	k	k	X
ejpam-5893	202	12	]	]	PUNCT
ejpam-5893	202	13	eλ13ξ	eλ13ξ	VERB
ejpam-5893	203	1	+	+	CCONJ
ejpam-5893	203	2	c5	c5	PROPN
ejpam-5893	203	3	[	[	PUNCT
ejpam-5893	203	4	1	1	NUM
ejpam-5893	203	5	−i	−i	NOUN
ejpam-5893	203	6	√	√	PROPN
ejpam-5893	203	7	w	w	PROPN
ejpam-5893	203	8	k	k	X
ejpam-5893	203	9	]	]	PUNCT
ejpam-5893	203	10	eλ14ξ	eλ14ξ	X
ejpam-5893	203	11	u	u	NOUN
ejpam-5893	203	12	′(ξ	′(ξ	NOUN
ejpam-5893	203	13	)	)	PUNCT
ejpam-5893	203	14	=	=	NOUN
ejpam-5893	203	15	v	v	X
ejpam-5893	203	16	(	(	PUNCT
ejpam-5893	203	17	ξ	ξ	NOUN
ejpam-5893	203	18	)	)	PUNCT
ejpam-5893	203	19	=	=	SYM
ejpam-5893	203	20	x(ξ	x(ξ	PROPN
ejpam-5893	203	21	)	)	PUNCT
ejpam-5893	203	22	=	=	SYM
ejpam-5893	204	1	c4exp	c4exp	PROPN
ejpam-5893	204	2	(	(	PUNCT
ejpam-5893	204	3	i	i	PRON
ejpam-5893	204	4	√	√	VERB
ejpam-5893	204	5	w	w	VERB
ejpam-5893	204	6	k	k	PROPN
ejpam-5893	204	7	ξ	ξ	PROPN
ejpam-5893	204	8	)	)	PUNCT
ejpam-5893	205	1	+	+	CCONJ
ejpam-5893	205	2	c5exp	c5exp	PROPN
ejpam-5893	205	3	(	(	PUNCT
ejpam-5893	205	4	−	−	PROPN
ejpam-5893	205	5	i	i	PRON
ejpam-5893	205	6	√	√	VERB
ejpam-5893	205	7	w	w	VERB
ejpam-5893	205	8	k	k	PROPN
ejpam-5893	205	9	ξ	ξ	PROPN
ejpam-5893	205	10	)	)	PUNCT
ejpam-5893	205	11	after	after	ADP
ejpam-5893	205	12	integration	integration	NOUN
ejpam-5893	205	13	u(ξ	u(ξ	NOUN
ejpam-5893	205	14	)	)	PUNCT
ejpam-5893	205	15	=	=	SYM
ejpam-5893	205	16	c4	c4	NOUN
ejpam-5893	205	17	(	(	PUNCT
ejpam-5893	205	18	cos	cos	INTJ
ejpam-5893	205	19	√	√	PROPN
ejpam-5893	205	20	w	w	VERB
ejpam-5893	205	21	k	k	PROPN
ejpam-5893	205	22	ξ	ξ	PROPN
ejpam-5893	206	1	+	+	CCONJ
ejpam-5893	206	2	isin	isin	VERB
ejpam-5893	206	3	√	√	PROPN
ejpam-5893	206	4	w	w	PROPN
ejpam-5893	206	5	k	k	PROPN
ejpam-5893	206	6	ξ	ξ	PROPN
ejpam-5893	206	7	)	)	PUNCT
ejpam-5893	207	1	+	+	CCONJ
ejpam-5893	207	2	c5	c5	PROPN
ejpam-5893	207	3	(	(	PUNCT
ejpam-5893	207	4	cos	cos	INTJ
ejpam-5893	207	5	√	√	PROPN
ejpam-5893	207	6	w	w	PROPN
ejpam-5893	208	1	k	k	PROPN
ejpam-5893	208	2	ξ	ξ	PRON
ejpam-5893	208	3	−	−	PROPN
ejpam-5893	208	4	isin	isin	NOUN
ejpam-5893	208	5	√	√	PROPN
ejpam-5893	208	6	w	w	PROPN
ejpam-5893	208	7	k	k	PROPN
ejpam-5893	208	8	ξ	ξ	PROPN
ejpam-5893	208	9	)	)	PUNCT
ejpam-5893	209	1	+	+	CCONJ
ejpam-5893	209	2	c6	c6	NOUN
ejpam-5893	209	3	(	(	PUNCT
ejpam-5893	209	4	19	19	NUM
ejpam-5893	209	5	)	)	PUNCT
ejpam-5893	209	6	u(ξ	u(ξ	NOUN
ejpam-5893	209	7	)	)	PUNCT
ejpam-5893	209	8	=	=	SYM
ejpam-5893	209	9	c4	c4	NOUN
ejpam-5893	209	10	+	+	CCONJ
ejpam-5893	209	11	c5	c5	PROPN
ejpam-5893	209	12	(	(	PUNCT
ejpam-5893	209	13	cos	cos	INTJ
ejpam-5893	209	14	√	√	PROPN
ejpam-5893	209	15	w	w	PROPN
ejpam-5893	209	16	k	k	PROPN
ejpam-5893	209	17	ξ	ξ	PROPN
ejpam-5893	209	18	)	)	PUNCT
ejpam-5893	210	1	+	+	NUM
ejpam-5893	210	2	i(c4	i(c4	VERB
ejpam-5893	210	3	−	−	PROPN
ejpam-5893	210	4	c5	c5	PROPN
ejpam-5893	210	5	)	)	PUNCT
ejpam-5893	210	6	(	(	PUNCT
ejpam-5893	210	7	sin	sin	NOUN
ejpam-5893	210	8	√	√	PROPN
ejpam-5893	210	9	w	w	PROPN
ejpam-5893	210	10	k	k	PROPN
ejpam-5893	210	11	ξ	ξ	PROPN
ejpam-5893	210	12	)	)	PUNCT
ejpam-5893	211	1	+	+	CCONJ
ejpam-5893	211	2	c6	c6	NOUN
ejpam-5893	211	3	if	if	SCONJ
ejpam-5893	211	4	we	we	PRON
ejpam-5893	211	5	take	take	VERB
ejpam-5893	211	6	c4	c4	NOUN
ejpam-5893	211	7	+	+	CCONJ
ejpam-5893	211	8	c5	c5	PROPN
ejpam-5893	211	9	=	=	PUNCT
ejpam-5893	211	10	a	a	PRON
ejpam-5893	211	11	and	and	CCONJ
ejpam-5893	211	12	i(c4	i(c4	ADJ
ejpam-5893	211	13	−	−	PROPN
ejpam-5893	211	14	c5	c5	PROPN
ejpam-5893	211	15	)	)	PUNCT
ejpam-5893	212	1	=	=	SYM
ejpam-5893	212	2	b	b	PROPN
ejpam-5893	212	3	u12(x	u12(x	PROPN
ejpam-5893	212	4	,	,	PUNCT
ejpam-5893	212	5	t	t	PROPN
ejpam-5893	212	6	)	)	PUNCT
ejpam-5893	212	7	=	=	SYM
ejpam-5893	213	1	acos	acos	PROPN
ejpam-5893	214	1	[	[	X
ejpam-5893	214	2	√	√	X
ejpam-5893	214	3	w	w	PROPN
ejpam-5893	214	4	(	(	PUNCT
ejpam-5893	214	5	x−	x−	PROPN
ejpam-5893	214	6	wtα	wtα	PROPN
ejpam-5893	214	7	γ(1	γ(1	PROPN
ejpam-5893	214	8	+	+	CCONJ
ejpam-5893	214	9	α	α	NOUN
ejpam-5893	214	10	)	)	PUNCT
ejpam-5893	214	11	)	)	PUNCT
ejpam-5893	214	12	]	]	PUNCT
ejpam-5893	215	1	+	+	PUNCT
ejpam-5893	215	2	bsin	bsin	NOUN
ejpam-5893	215	3	[	[	X
ejpam-5893	215	4	√	√	X
ejpam-5893	215	5	w	w	NOUN
ejpam-5893	215	6	(	(	PUNCT
ejpam-5893	215	7	x−	x−	PROPN
ejpam-5893	215	8	wtα	wtα	PROPN
ejpam-5893	215	9	γ(1	γ(1	PROPN
ejpam-5893	215	10	+	+	CCONJ
ejpam-5893	215	11	α	α	NOUN
ejpam-5893	215	12	)	)	PUNCT
ejpam-5893	215	13	)	)	PUNCT
ejpam-5893	215	14	]	]	PUNCT
ejpam-5893	216	1	+	+	CCONJ
ejpam-5893	216	2	c6	c6	NOUN
ejpam-5893	216	3	(	(	PUNCT
ejpam-5893	216	4	20	20	NUM
ejpam-5893	216	5	)	)	PUNCT
ejpam-5893	216	6	case	case	NOUN
ejpam-5893	216	7	2	2	NUM
ejpam-5893	216	8	to	to	PART
ejpam-5893	216	9	find	find	VERB
ejpam-5893	216	10	the	the	DET
ejpam-5893	216	11	exact	exact	ADJ
ejpam-5893	216	12	solution	solution	NOUN
ejpam-5893	216	13	of	of	ADP
ejpam-5893	216	14	ode	ode	PROPN
ejpam-5893	216	15	(	(	PUNCT
ejpam-5893	216	16	10	10	NUM
ejpam-5893	216	17	)	)	PUNCT
ejpam-5893	216	18	using	use	VERB
ejpam-5893	216	19	traveling	travel	VERB
ejpam-5893	216	20	wave	wave	NOUN
ejpam-5893	216	21	transformation	transformation	NOUN
ejpam-5893	216	22	(	(	PUNCT
ejpam-5893	216	23	6	6	NUM
ejpam-5893	216	24	)	)	PUNCT
ejpam-5893	216	25	,	,	PUNCT
ejpam-5893	216	26	first	first	ADV
ejpam-5893	216	27	rescaling	rescale	VERB
ejpam-5893	216	28	it	it	PRON
ejpam-5893	216	29	by	by	ADP
ejpam-5893	216	30	using	use	VERB
ejpam-5893	216	31	new	new	ADJ
ejpam-5893	216	32	variables	variable	NOUN
ejpam-5893	216	33	z	z	NOUN
ejpam-5893	216	34	=	=	PUNCT
ejpam-5893	217	1	√	√	PROPN
ejpam-5893	217	2	w	w	PROPN
ejpam-5893	217	3	k	k	PROPN
ejpam-5893	217	4	ξ	ξ	PROPN
ejpam-5893	217	5	,	,	PUNCT
ejpam-5893	217	6	v	v	NOUN
ejpam-5893	217	7	=	=	X
ejpam-5893	217	8	w	w	PROPN
ejpam-5893	217	9	β	β	NOUN
ejpam-5893	217	10	√	√	PROPN
ejpam-5893	217	11	k	k	PROPN
ejpam-5893	217	12	w	w	PROPN
ejpam-5893	217	13	(	(	PUNCT
ejpam-5893	217	14	z	z	NOUN
ejpam-5893	217	15	)	)	PUNCT
ejpam-5893	217	16	(	(	PUNCT
ejpam-5893	217	17	21	21	NUM
ejpam-5893	217	18	)	)	PUNCT
ejpam-5893	218	1	dv	dv	PROPN
ejpam-5893	218	2	dz	dz	PROPN
ejpam-5893	218	3	=	=	PUNCT
ejpam-5893	218	4	w	w	PROPN
ejpam-5893	218	5	β	β	NOUN
ejpam-5893	218	6	√	√	PROPN
ejpam-5893	218	7	k	k	PROPN
ejpam-5893	218	8	w	w	NOUN
ejpam-5893	218	9	′(z	′(z	NOUN
ejpam-5893	218	10	)	)	PUNCT
ejpam-5893	218	11	,	,	PUNCT
ejpam-5893	218	12	d2v	d2v	VERB
ejpam-5893	218	13	dz2	dz2	NOUN
ejpam-5893	218	14	=	=	PUNCT
ejpam-5893	218	15	w	w	PROPN
ejpam-5893	218	16	β	β	NOUN
ejpam-5893	218	17	√	√	PROPN
ejpam-5893	218	18	k	k	PROPN
ejpam-5893	218	19	w	w	PROPN
ejpam-5893	218	20	′′(z	′′(z	PROPN
ejpam-5893	218	21	)	)	PUNCT
ejpam-5893	218	22	b.	b.	PROPN
ejpam-5893	218	23	yasmeen	yasmeen	PROPN
ejpam-5893	218	24	,	,	PUNCT
ejpam-5893	218	25	k.	k.	PROPN
ejpam-5893	218	26	ahmad	ahmad	PROPN
ejpam-5893	218	27	,	,	PUNCT
ejpam-5893	218	28	n.	n.	PROPN
ejpam-5893	218	29	fatima	fatima	PROPN
ejpam-5893	218	30	/	/	PUNCT
ejpam-5893	218	31	eur	eur	PROPN
ejpam-5893	218	32	.	.	PUNCT
ejpam-5893	219	1	j.	j.	PROPN
ejpam-5893	219	2	pure	pure	PROPN
ejpam-5893	219	3	appl	appl	PROPN
ejpam-5893	219	4	.	.	PROPN
ejpam-5893	219	5	math	math	PROPN
ejpam-5893	219	6	,	,	PUNCT
ejpam-5893	219	7	18	18	NUM
ejpam-5893	219	8	(	(	PUNCT
ejpam-5893	219	9	2	2	NUM
ejpam-5893	219	10	)	)	PUNCT
ejpam-5893	219	11	(	(	PUNCT
ejpam-5893	219	12	2025	2025	NUM
ejpam-5893	219	13	)	)	PUNCT
ejpam-5893	219	14	,	,	PUNCT
ejpam-5893	219	15	5893	5893	NUM
ejpam-5893	219	16	10	10	NUM
ejpam-5893	219	17	of	of	ADP
ejpam-5893	219	18	17	17	NUM
ejpam-5893	219	19	substitute	substitute	NOUN
ejpam-5893	219	20	these	these	DET
ejpam-5893	219	21	relations	relation	NOUN
ejpam-5893	219	22	into	into	ADP
ejpam-5893	219	23	ode	ode	PROPN
ejpam-5893	219	24	(	(	PUNCT
ejpam-5893	219	25	10	10	NUM
ejpam-5893	219	26	)	)	PUNCT
ejpam-5893	219	27	,	,	PUNCT
ejpam-5893	219	28	we	we	PRON
ejpam-5893	219	29	get	get	VERB
ejpam-5893	219	30	k	k	PROPN
ejpam-5893	219	31	(	(	PUNCT
ejpam-5893	219	32	w	w	PROPN
ejpam-5893	219	33	β	β	NOUN
ejpam-5893	219	34	√	√	PROPN
ejpam-5893	219	35	k	k	PROPN
ejpam-5893	219	36	w	w	PROPN
ejpam-5893	219	37	′′(z	′′(z	PROPN
ejpam-5893	219	38	)	)	PUNCT
ejpam-5893	219	39	)	)	PUNCT
ejpam-5893	220	1	+	+	CCONJ
ejpam-5893	220	2	2β	2β	NOUN
ejpam-5893	220	3	√	√	NUM
ejpam-5893	220	4	k	k	PROPN
ejpam-5893	221	1	(	(	PUNCT
ejpam-5893	221	2	w	w	PROPN
ejpam-5893	221	3	β	β	NOUN
ejpam-5893	221	4	√	√	PROPN
ejpam-5893	222	1	k	k	PROPN
ejpam-5893	222	2	w	w	PROPN
ejpam-5893	222	3	(	(	PUNCT
ejpam-5893	222	4	z	z	NOUN
ejpam-5893	222	5	)	)	PUNCT
ejpam-5893	222	6	)	)	PUNCT
ejpam-5893	222	7	2	2	NUM
ejpam-5893	222	8	−	−	NOUN
ejpam-5893	223	1	w	w	NOUN
ejpam-5893	224	1	(	(	PUNCT
ejpam-5893	224	2	w	w	PROPN
ejpam-5893	224	3	β	β	NOUN
ejpam-5893	224	4	√	√	PROPN
ejpam-5893	225	1	k	k	PROPN
ejpam-5893	225	2	w	w	PROPN
ejpam-5893	225	3	(	(	PUNCT
ejpam-5893	225	4	z	z	NOUN
ejpam-5893	225	5	)	)	PUNCT
ejpam-5893	225	6	)	)	PUNCT
ejpam-5893	226	1	=	=	PUNCT
ejpam-5893	226	2	0	0	NUM
ejpam-5893	227	1	w	w	NOUN
ejpam-5893	227	2	√	√	PUNCT
ejpam-5893	227	3	k	k	PROPN
ejpam-5893	227	4	β	β	PROPN
ejpam-5893	227	5	w	w	PROPN
ejpam-5893	227	6	′′(z	′′(z	PROPN
ejpam-5893	227	7	)	)	PUNCT
ejpam-5893	227	8	+	+	SYM
ejpam-5893	228	1	2	2	NUM
ejpam-5893	228	2	w2	w2	NOUN
ejpam-5893	228	3	β	β	NOUN
ejpam-5893	228	4	√	√	PROPN
ejpam-5893	228	5	k	k	PROPN
ejpam-5893	228	6	w	w	PROPN
ejpam-5893	228	7	2(z)−	2(z)−	NUM
ejpam-5893	228	8	w2	w2	NOUN
ejpam-5893	228	9	β	β	NOUN
ejpam-5893	228	10	√	√	PROPN
ejpam-5893	228	11	k	k	PROPN
ejpam-5893	228	12	w	w	PROPN
ejpam-5893	228	13	(	(	PUNCT
ejpam-5893	228	14	z	z	NOUN
ejpam-5893	228	15	)	)	PUNCT
ejpam-5893	228	16	=	=	SYM
ejpam-5893	228	17	0	0	NUM
ejpam-5893	228	18	(	(	PUNCT
ejpam-5893	228	19	22	22	NUM
ejpam-5893	228	20	)	)	PUNCT
ejpam-5893	228	21	multiply	multiply	ADP
ejpam-5893	228	22	β	β	X
ejpam-5893	228	23	and	and	CCONJ
ejpam-5893	228	24	divide	divide	VERB
ejpam-5893	228	25	by	by	ADP
ejpam-5893	228	26	w	w	PROPN
ejpam-5893	228	27	and	and	CCONJ
ejpam-5893	228	28	√	√	PROPN
ejpam-5893	228	29	k	k	PROPN
ejpam-5893	228	30	through	through	ADP
ejpam-5893	228	31	(	(	PUNCT
ejpam-5893	228	32	22	22	NUM
ejpam-5893	228	33	)	)	PUNCT
ejpam-5893	228	34	,	,	PUNCT
ejpam-5893	228	35	we	we	PRON
ejpam-5893	228	36	have	have	VERB
ejpam-5893	228	37	w	w	PROPN
ejpam-5893	228	38	′′(z	′′(z	NOUN
ejpam-5893	228	39	)	)	PUNCT
ejpam-5893	229	1	+	+	CCONJ
ejpam-5893	229	2	2	2	NUM
ejpam-5893	229	3	w	w	NOUN
ejpam-5893	229	4	k	k	PROPN
ejpam-5893	229	5	w	w	PROPN
ejpam-5893	229	6	2(z)−	2(z)−	NUM
ejpam-5893	229	7	w	w	NOUN
ejpam-5893	229	8	k	k	PROPN
ejpam-5893	229	9	w	w	PROPN
ejpam-5893	229	10	(	(	PUNCT
ejpam-5893	229	11	z	z	NOUN
ejpam-5893	229	12	)	)	PUNCT
ejpam-5893	229	13	=	=	SYM
ejpam-5893	229	14	0	0	NUM
ejpam-5893	229	15	(	(	PUNCT
ejpam-5893	229	16	23	23	NUM
ejpam-5893	229	17	)	)	PUNCT
ejpam-5893	229	18	let	let	VERB
ejpam-5893	229	19	m	m	VERB
ejpam-5893	229	20	=	=	VERB
ejpam-5893	229	21	w	w	PROPN
ejpam-5893	229	22	k	k	PROPN
ejpam-5893	229	23	.	.	PUNCT
ejpam-5893	230	1	then	then	ADV
ejpam-5893	230	2	(	(	PUNCT
ejpam-5893	230	3	22	22	NUM
ejpam-5893	230	4	)	)	PUNCT
ejpam-5893	230	5	becomes	become	VERB
ejpam-5893	230	6	w	w	PROPN
ejpam-5893	230	7	′′(z	′′(z	PROPN
ejpam-5893	230	8	)	)	PUNCT
ejpam-5893	231	1	+	+	CCONJ
ejpam-5893	232	1	2mw	2mw	ADJ
ejpam-5893	232	2	2(z)−mw	2(z)−mw	NUM
ejpam-5893	232	3	(	(	PUNCT
ejpam-5893	232	4	z	z	NOUN
ejpam-5893	232	5	)	)	PUNCT
ejpam-5893	232	6	=	=	SYM
ejpam-5893	232	7	0	0	NUM
ejpam-5893	232	8	(	(	PUNCT
ejpam-5893	232	9	24	24	NUM
ejpam-5893	232	10	)	)	PUNCT
ejpam-5893	232	11	reduce	reduce	VERB
ejpam-5893	232	12	the	the	DET
ejpam-5893	232	13	order	order	NOUN
ejpam-5893	232	14	multiply	multiply	VERB
ejpam-5893	232	15	through	through	ADP
ejpam-5893	232	16	by	by	ADP
ejpam-5893	232	17	w	w	PROPN
ejpam-5893	232	18	′(z	′(z	NOUN
ejpam-5893	232	19	)	)	PUNCT
ejpam-5893	232	20	,	,	PUNCT
ejpam-5893	232	21	which	which	PRON
ejpam-5893	232	22	allows	allow	VERB
ejpam-5893	232	23	us	we	PRON
ejpam-5893	232	24	to	to	PART
ejpam-5893	232	25	integrate	integrate	VERB
ejpam-5893	232	26	directly	directly	ADV
ejpam-5893	232	27	w	w	ADP
ejpam-5893	232	28	′(z)w	′(z)w	PROPN
ejpam-5893	232	29	′′(z	′′(z	NOUN
ejpam-5893	232	30	)	)	PUNCT
ejpam-5893	233	1	+	+	CCONJ
ejpam-5893	233	2	2mw	2mw	ADJ
ejpam-5893	233	3	2(z)w	2(z)w	NOUN
ejpam-5893	233	4	′(z)−mw	′(z)−mw	NOUN
ejpam-5893	233	5	(	(	PUNCT
ejpam-5893	233	6	z)w	z)w	NUM
ejpam-5893	233	7	′(z	′(z	NOUN
ejpam-5893	233	8	)	)	PUNCT
ejpam-5893	233	9	=	=	SYM
ejpam-5893	233	10	0	0	PUNCT
ejpam-5893	233	11	(	(	PUNCT
ejpam-5893	233	12	25	25	NUM
ejpam-5893	233	13	)	)	PUNCT
ejpam-5893	233	14	for	for	ADP
ejpam-5893	233	15	simplicity	simplicity	NOUN
ejpam-5893	233	16	w	w	PROPN
ejpam-5893	233	17	′(z)w	′(z)w	PROPN
ejpam-5893	233	18	′′(z	′′(z	NOUN
ejpam-5893	233	19	)	)	PUNCT
ejpam-5893	233	20	=	=	SYM
ejpam-5893	233	21	1	1	NUM
ejpam-5893	233	22	2	2	NUM
ejpam-5893	233	23	d	d	NOUN
ejpam-5893	233	24	dz	dz	X
ejpam-5893	233	25	(	(	PUNCT
ejpam-5893	233	26	w	w	NOUN
ejpam-5893	233	27	′(z))2	′(z))2	PUNCT
ejpam-5893	233	28	1	1	NUM
ejpam-5893	233	29	2	2	NUM
ejpam-5893	233	30	d	d	NOUN
ejpam-5893	233	31	dz	dz	X
ejpam-5893	233	32	(	(	PUNCT
ejpam-5893	233	33	w	w	NOUN
ejpam-5893	233	34	′(z))2	′(z))2	X
ejpam-5893	234	1	+	+	NOUN
ejpam-5893	234	2	m	m	PROPN
ejpam-5893	234	3	d	d	X
ejpam-5893	234	4	dz	dz	X
ejpam-5893	234	5	(	(	PUNCT
ejpam-5893	234	6	w	w	NOUN
ejpam-5893	234	7	3(z)−	3(z)−	NUM
ejpam-5893	234	8	1	1	NUM
ejpam-5893	234	9	2	2	NUM
ejpam-5893	234	10	w	w	NOUN
ejpam-5893	234	11	2(z	2(z	NUM
ejpam-5893	234	12	)	)	PUNCT
ejpam-5893	234	13	)	)	PUNCT
ejpam-5893	235	1	=	=	SYM
ejpam-5893	235	2	0	0	PUNCT
ejpam-5893	235	3	integrate	integrate	VERB
ejpam-5893	235	4	with	with	ADP
ejpam-5893	235	5	respect	respect	NOUN
ejpam-5893	235	6	to	to	ADP
ejpam-5893	235	7	”	"	PUNCT
ejpam-5893	235	8	z	z	NOUN
ejpam-5893	235	9	”	"	PUNCT
ejpam-5893	235	10	and	and	CCONJ
ejpam-5893	235	11	setting	set	VERB
ejpam-5893	235	12	constant	constant	ADJ
ejpam-5893	235	13	of	of	ADP
ejpam-5893	235	14	integration	integration	NOUN
ejpam-5893	235	15	is	be	AUX
ejpam-5893	235	16	zero	zero	NUM
ejpam-5893	235	17	.	.	PUNCT
ejpam-5893	236	1	1	1	NUM
ejpam-5893	236	2	2	2	NUM
ejpam-5893	236	3	(	(	PUNCT
ejpam-5893	236	4	w	w	NOUN
ejpam-5893	236	5	′(z))2	′(z))2	X
ejpam-5893	236	6	+	+	NOUN
ejpam-5893	236	7	m	m	PROPN
ejpam-5893	236	8	(	(	PUNCT
ejpam-5893	236	9	w	w	NOUN
ejpam-5893	236	10	3(z)−	3(z)−	NUM
ejpam-5893	236	11	1	1	NUM
ejpam-5893	236	12	2	2	NUM
ejpam-5893	236	13	w	w	NOUN
ejpam-5893	236	14	2(z	2(z	NUM
ejpam-5893	236	15	)	)	PUNCT
ejpam-5893	236	16	)	)	PUNCT
ejpam-5893	237	1	=	=	SYM
ejpam-5893	237	2	0	0	PUNCT
ejpam-5893	238	1	(	(	PUNCT
ejpam-5893	238	2	w	w	NOUN
ejpam-5893	238	3	′(z))2	′(z))2	NOUN
ejpam-5893	238	4	+	+	CCONJ
ejpam-5893	239	1	2	2	NUM
ejpam-5893	239	2	m	m	VERB
ejpam-5893	239	3	(	(	PUNCT
ejpam-5893	239	4	w	w	NOUN
ejpam-5893	239	5	3(z)−	3(z)−	NUM
ejpam-5893	239	6	1	1	NUM
ejpam-5893	239	7	2	2	NUM
ejpam-5893	239	8	w	w	NOUN
ejpam-5893	239	9	2(z	2(z	NUM
ejpam-5893	239	10	)	)	PUNCT
ejpam-5893	239	11	)	)	PUNCT
ejpam-5893	240	1	=	=	SYM
ejpam-5893	240	2	0	0	PUNCT
ejpam-5893	241	1	(	(	PUNCT
ejpam-5893	241	2	w	w	NOUN
ejpam-5893	241	3	′(z))2	′(z))2	PROPN
ejpam-5893	241	4	=	=	SYM
ejpam-5893	241	5	mw	mw	AUX
ejpam-5893	241	6	2(z)−	2(z)−	NUM
ejpam-5893	241	7	2mw	2mw	NOUN
ejpam-5893	241	8	3(z	3(z	NUM
ejpam-5893	241	9	)	)	PUNCT
ejpam-5893	241	10	taking	take	VERB
ejpam-5893	241	11	square	square	ADJ
ejpam-5893	241	12	root	root	NOUN
ejpam-5893	241	13	of	of	ADP
ejpam-5893	241	14	both	both	DET
ejpam-5893	241	15	sides	side	NOUN
ejpam-5893	241	16	w	w	ADP
ejpam-5893	241	17	′(z	′(z	NOUN
ejpam-5893	241	18	)	)	PUNCT
ejpam-5893	241	19	=	=	SYM
ejpam-5893	241	20	±	±	PROPN
ejpam-5893	241	21	√	√	NOUN
ejpam-5893	241	22	mw	mw	VERB
ejpam-5893	241	23	2(z)−	2(z)−	NUM
ejpam-5893	241	24	2mw	2mw	NOUN
ejpam-5893	241	25	3(z	3(z	NUM
ejpam-5893	241	26	)	)	PUNCT
ejpam-5893	241	27	after	after	ADP
ejpam-5893	241	28	integration	integration	NOUN
ejpam-5893	241	29	,	,	PUNCT
ejpam-5893	241	30	w	w	PROPN
ejpam-5893	241	31	(	(	PUNCT
ejpam-5893	241	32	z	z	NOUN
ejpam-5893	241	33	)	)	PUNCT
ejpam-5893	241	34	=	=	SYM
ejpam-5893	241	35	1	1	NUM
ejpam-5893	241	36	2	2	NUM
ejpam-5893	241	37	tan2	tan2	NOUN
ejpam-5893	241	38	(	(	PUNCT
ejpam-5893	241	39	c7	c7	PROPN
ejpam-5893	241	40	2	2	NUM
ejpam-5893	241	41	√	√	PROPN
ejpam-5893	241	42	m−	m−	PROPN
ejpam-5893	241	43	1	1	NUM
ejpam-5893	241	44	2	2	NUM
ejpam-5893	241	45	z	z	NOUN
ejpam-5893	241	46	√	√	NOUN
ejpam-5893	241	47	m	m	VERB
ejpam-5893	241	48	)	)	PUNCT
ejpam-5893	242	1	+	+	CCONJ
ejpam-5893	242	2	1	1	NUM
ejpam-5893	242	3	2	2	NUM
ejpam-5893	242	4	(	(	PUNCT
ejpam-5893	242	5	26	26	NUM
ejpam-5893	242	6	)	)	PUNCT
ejpam-5893	242	7	where	where	SCONJ
ejpam-5893	242	8	c7	c7	PROPN
ejpam-5893	242	9	is	be	AUX
ejpam-5893	242	10	constant	constant	ADJ
ejpam-5893	242	11	of	of	ADP
ejpam-5893	242	12	integration	integration	NOUN
ejpam-5893	242	13	.	.	PUNCT
ejpam-5893	243	1	w	w	NOUN
ejpam-5893	243	2	(	(	PUNCT
ejpam-5893	243	3	z	z	NOUN
ejpam-5893	243	4	)	)	PUNCT
ejpam-5893	243	5	=	=	SYM
ejpam-5893	243	6	1	1	NUM
ejpam-5893	243	7	2	2	NUM
ejpam-5893	243	8	tan2	tan2	NOUN
ejpam-5893	243	9	(	(	PUNCT
ejpam-5893	243	10	c7	c7	PROPN
ejpam-5893	243	11	2	2	NUM
ejpam-5893	243	12	√	√	PROPN
ejpam-5893	243	13	w	w	PROPN
ejpam-5893	244	1	k	k	NOUN
ejpam-5893	245	1	−	−	PROPN
ejpam-5893	245	2	1	1	NUM
ejpam-5893	245	3	2	2	NUM
ejpam-5893	245	4	√	√	PROPN
ejpam-5893	245	5	w	w	PROPN
ejpam-5893	245	6	k	k	PROPN
ejpam-5893	245	7	ξ	ξ	PROPN
ejpam-5893	245	8	√	√	PROPN
ejpam-5893	245	9	w	w	PROPN
ejpam-5893	245	10	k	k	PROPN
ejpam-5893	245	11	)	)	PUNCT
ejpam-5893	246	1	+	+	CCONJ
ejpam-5893	246	2	1	1	NUM
ejpam-5893	246	3	2	2	NUM
ejpam-5893	246	4	b.	b.	PROPN
ejpam-5893	246	5	yasmeen	yasmeen	PROPN
ejpam-5893	246	6	,	,	PUNCT
ejpam-5893	246	7	k.	k.	PROPN
ejpam-5893	246	8	ahmad	ahmad	PROPN
ejpam-5893	246	9	,	,	PUNCT
ejpam-5893	246	10	n.	n.	PROPN
ejpam-5893	246	11	fatima	fatima	PROPN
ejpam-5893	246	12	/	/	PUNCT
ejpam-5893	246	13	eur	eur	PROPN
ejpam-5893	246	14	.	.	PUNCT
ejpam-5893	247	1	j.	j.	PROPN
ejpam-5893	247	2	pure	pure	PROPN
ejpam-5893	247	3	appl	appl	PROPN
ejpam-5893	247	4	.	.	PROPN
ejpam-5893	247	5	math	math	PROPN
ejpam-5893	247	6	,	,	PUNCT
ejpam-5893	247	7	18	18	NUM
ejpam-5893	247	8	(	(	PUNCT
ejpam-5893	247	9	2	2	NUM
ejpam-5893	247	10	)	)	PUNCT
ejpam-5893	247	11	(	(	PUNCT
ejpam-5893	247	12	2025	2025	NUM
ejpam-5893	247	13	)	)	PUNCT
ejpam-5893	247	14	,	,	PUNCT
ejpam-5893	247	15	5893	5893	NUM
ejpam-5893	247	16	11	11	NUM
ejpam-5893	247	17	of	of	ADP
ejpam-5893	247	18	17	17	NUM
ejpam-5893	247	19	w	w	NOUN
ejpam-5893	247	20	(	(	PUNCT
ejpam-5893	247	21	z	z	NOUN
ejpam-5893	247	22	)	)	PUNCT
ejpam-5893	247	23	=	=	SYM
ejpam-5893	247	24	1	1	NUM
ejpam-5893	247	25	2	2	NUM
ejpam-5893	247	26	tan2	tan2	NOUN
ejpam-5893	247	27	(	(	PUNCT
ejpam-5893	247	28	c7	c7	PROPN
ejpam-5893	247	29	2	2	NUM
ejpam-5893	247	30	√	√	PROPN
ejpam-5893	247	31	w	w	PROPN
ejpam-5893	248	1	k	k	NOUN
ejpam-5893	248	2	−	−	PROPN
ejpam-5893	248	3	1	1	NUM
ejpam-5893	248	4	2	2	NUM
ejpam-5893	248	5	w	w	PROPN
ejpam-5893	248	6	k	k	PROPN
ejpam-5893	248	7	ξ	ξ	PROPN
ejpam-5893	248	8	)	)	PUNCT
ejpam-5893	249	1	+	+	CCONJ
ejpam-5893	249	2	1	1	NUM
ejpam-5893	249	3	2	2	NUM
ejpam-5893	249	4	(	(	PUNCT
ejpam-5893	249	5	27	27	NUM
ejpam-5893	249	6	)	)	PUNCT
ejpam-5893	249	7	as	as	ADP
ejpam-5893	249	8	above	above	ADP
ejpam-5893	249	9	v	v	NOUN
ejpam-5893	249	10	=	=	SYM
ejpam-5893	249	11	w	w	PROPN
ejpam-5893	249	12	β	β	NOUN
ejpam-5893	249	13	√	√	PROPN
ejpam-5893	249	14	k	k	PROPN
ejpam-5893	249	15	w	w	PROPN
ejpam-5893	249	16	(	(	PUNCT
ejpam-5893	249	17	z	z	NOUN
ejpam-5893	249	18	)	)	PUNCT
ejpam-5893	249	19	=	=	NOUN
ejpam-5893	249	20	⇒	⇒	NOUN
ejpam-5893	249	21	w	w	PROPN
ejpam-5893	249	22	(	(	PUNCT
ejpam-5893	249	23	z	z	NOUN
ejpam-5893	249	24	)	)	PUNCT
ejpam-5893	249	25	=	=	NOUN
ejpam-5893	250	1	β	β	NOUN
ejpam-5893	250	2	√	√	NUM
ejpam-5893	250	3	k	k	PROPN
ejpam-5893	250	4	w	w	NOUN
ejpam-5893	250	5	v	v	INTJ
ejpam-5893	250	6	,	,	PUNCT
ejpam-5893	250	7	then	then	ADV
ejpam-5893	250	8	(	(	PUNCT
ejpam-5893	250	9	27	27	NUM
ejpam-5893	250	10	)	)	PUNCT
ejpam-5893	250	11	becomes	become	VERB
ejpam-5893	250	12	v	v	ADP
ejpam-5893	250	13	=	=	SYM
ejpam-5893	250	14	w	w	NOUN
ejpam-5893	250	15	2β	2β	NOUN
ejpam-5893	250	16	√	√	PROPN
ejpam-5893	250	17	k	k	PROPN
ejpam-5893	250	18	tan2	tan2	PROPN
ejpam-5893	250	19	(	(	PUNCT
ejpam-5893	250	20	c7	c7	PROPN
ejpam-5893	250	21	2	2	NUM
ejpam-5893	251	1	√	√	PROPN
ejpam-5893	251	2	w	w	PROPN
ejpam-5893	252	1	k	k	NOUN
ejpam-5893	252	2	−	−	PROPN
ejpam-5893	252	3	1	1	NUM
ejpam-5893	252	4	2	2	NUM
ejpam-5893	252	5	w	w	PROPN
ejpam-5893	252	6	k	k	PROPN
ejpam-5893	252	7	ξ	ξ	PROPN
ejpam-5893	252	8	)	)	PUNCT
ejpam-5893	253	1	+	+	CCONJ
ejpam-5893	253	2	1	1	NUM
ejpam-5893	253	3	2	2	NUM
ejpam-5893	253	4	from	from	ADP
ejpam-5893	253	5	u	u	NOUN
ejpam-5893	253	6	′	′	NUM
ejpam-5893	253	7	=	=	SYM
ejpam-5893	253	8	v	v	NOUN
ejpam-5893	253	9	and	and	CCONJ
ejpam-5893	253	10	after	after	ADP
ejpam-5893	253	11	integration	integration	NOUN
ejpam-5893	253	12	,	,	PUNCT
ejpam-5893	253	13	we	we	PRON
ejpam-5893	253	14	get	get	VERB
ejpam-5893	253	15	u(ξ	u(ξ	NOUN
ejpam-5893	253	16	)	)	PUNCT
ejpam-5893	253	17	=	=	SYM
ejpam-5893	253	18	−	−	PROPN
ejpam-5893	253	19	√	√	PROPN
ejpam-5893	253	20	ktan	ktan	PROPN
ejpam-5893	253	21	(	(	PUNCT
ejpam-5893	253	22	c7	c7	PROPN
ejpam-5893	253	23	√	√	PROPN
ejpam-5893	253	24	w	w	PROPN
ejpam-5893	253	25	k	k	PROPN
ejpam-5893	253	26	k−2wξ	k−2wξ	PROPN
ejpam-5893	253	27	2k	2k	NOUN
ejpam-5893	253	28	)	)	PUNCT
ejpam-5893	254	1	2β	2β	NOUN
ejpam-5893	254	2	+	+	CCONJ
ejpam-5893	254	3	√	√	PUNCT
ejpam-5893	254	4	karctan	karctan	PROPN
ejpam-5893	254	5	(	(	PUNCT
ejpam-5893	254	6	tan	tan	PROPN
ejpam-5893	254	7	(	(	PUNCT
ejpam-5893	254	8	c7	c7	PROPN
ejpam-5893	254	9	√	√	PROPN
ejpam-5893	254	10	w	w	PROPN
ejpam-5893	254	11	k	k	PROPN
ejpam-5893	254	12	k−2wξ	k−2wξ	PROPN
ejpam-5893	254	13	2k	2k	NUM
ejpam-5893	254	14	)	)	PUNCT
ejpam-5893	254	15	)	)	PUNCT
ejpam-5893	255	1	2β	2β	NOUN
ejpam-5893	256	1	+	+	CCONJ
ejpam-5893	256	2	1	1	NUM
ejpam-5893	256	3	2	2	NUM
ejpam-5893	256	4	ξ	ξ	X
ejpam-5893	256	5	+	+	CCONJ
ejpam-5893	256	6	c8	c8	PROPN
ejpam-5893	256	7	u(x	u(x	PROPN
ejpam-5893	256	8	,	,	PUNCT
ejpam-5893	256	9	t	t	PROPN
ejpam-5893	256	10	)	)	PUNCT
ejpam-5893	256	11	=	=	SYM
ejpam-5893	257	1	−	−	PROPN
ejpam-5893	257	2	√	√	NUM
ejpam-5893	257	3	ktan(θ	ktan(θ	PROPN
ejpam-5893	257	4	)	)	PUNCT
ejpam-5893	257	5	2β	2β	NOUN
ejpam-5893	257	6	+	+	CCONJ
ejpam-5893	257	7	√	√	ADJ
ejpam-5893	257	8	karctan[tan(θ	karctan[tan(θ	PROPN
ejpam-5893	257	9	)	)	PUNCT
ejpam-5893	257	10	]	]	PUNCT
ejpam-5893	258	1	2β	2β	NOUN
ejpam-5893	258	2	+	+	CCONJ
ejpam-5893	258	3	1	1	NUM
ejpam-5893	258	4	2	2	NUM
ejpam-5893	258	5	√	√	NOUN
ejpam-5893	258	6	k	k	PROPN
ejpam-5893	258	7	(	(	PUNCT
ejpam-5893	258	8	x−	x−	PROPN
ejpam-5893	258	9	wtα	wtα	PROPN
ejpam-5893	259	1	γ(1	γ(1	PROPN
ejpam-5893	259	2	+	+	CCONJ
ejpam-5893	259	3	α	α	NOUN
ejpam-5893	259	4	)	)	PUNCT
ejpam-5893	259	5	)	)	PUNCT
ejpam-5893	260	1	+	+	CCONJ
ejpam-5893	260	2	c8	c8	PROPN
ejpam-5893	260	3	(	(	PUNCT
ejpam-5893	260	4	28	28	NUM
ejpam-5893	260	5	)	)	PUNCT
ejpam-5893	260	6	where	where	SCONJ
ejpam-5893	260	7	θ	θ	PROPN
ejpam-5893	260	8	=	=	SYM
ejpam-5893	260	9	c7	c7	PROPN
ejpam-5893	260	10	√	√	PROPN
ejpam-5893	260	11	w	w	PROPN
ejpam-5893	260	12	k	k	PROPN
ejpam-5893	260	13	k−2w	k−2w	NOUN
ejpam-5893	260	14	√	√	PROPN
ejpam-5893	261	1	k	k	PROPN
ejpam-5893	262	1	(	(	PUNCT
ejpam-5893	262	2	x−	x−	PROPN
ejpam-5893	262	3	wtα	wtα	PROPN
ejpam-5893	262	4	γ(1+α	γ(1+α	PROPN
ejpam-5893	262	5	)	)	PUNCT
ejpam-5893	262	6	)	)	PUNCT
ejpam-5893	263	1	2k	2k	NOUN
ejpam-5893	263	2	and	and	CCONJ
ejpam-5893	263	3	c8	c8	PROPN
ejpam-5893	263	4	is	be	AUX
ejpam-5893	263	5	constant	constant	ADJ
ejpam-5893	263	6	of	of	ADP
ejpam-5893	263	7	integration	integration	NOUN
ejpam-5893	263	8	.	.	PUNCT
ejpam-5893	264	1	the	the	DET
ejpam-5893	264	2	exact	exact	ADJ
ejpam-5893	264	3	solution	solution	NOUN
ejpam-5893	264	4	u(x	u(x	NOUN
ejpam-5893	264	5	,	,	PUNCT
ejpam-5893	264	6	t	t	NOUN
ejpam-5893	264	7	)	)	PUNCT
ejpam-5893	264	8	in	in	ADP
ejpam-5893	264	9	(	(	PUNCT
ejpam-5893	264	10	28	28	NUM
ejpam-5893	264	11	)	)	PUNCT
ejpam-5893	264	12	shown	show	VERB
ejpam-5893	264	13	in	in	ADP
ejpam-5893	264	14	figure	figure	NOUN
ejpam-5893	264	15	(	(	PUNCT
ejpam-5893	264	16	7	7	NUM
ejpam-5893	264	17	)	)	PUNCT
ejpam-5893	264	18	and	and	CCONJ
ejpam-5893	264	19	figure	figure	NOUN
ejpam-5893	264	20	(	(	PUNCT
ejpam-5893	264	21	8)	8)	NUM
ejpam-5893	264	22	whereas	whereas	SCONJ
ejpam-5893	264	23	w	w	PROPN
ejpam-5893	264	24	γ(1+α	γ(1+α	PROPN
ejpam-5893	264	25	)	)	PUNCT
ejpam-5893	264	26	indicates	indicate	VERB
ejpam-5893	264	27	sudden	sudden	ADJ
ejpam-5893	264	28	change	change	NOUN
ejpam-5893	264	29	in	in	ADP
ejpam-5893	264	30	the	the	DET
ejpam-5893	264	31	angular	angular	ADJ
ejpam-5893	264	32	frequency	frequency	NOUN
ejpam-5893	264	33	.	.	PUNCT
ejpam-5893	265	1	5	5	X
ejpam-5893	265	2	.	.	X
ejpam-5893	265	3	graphical	graphical	ADJ
ejpam-5893	265	4	representation	representation	NOUN
ejpam-5893	265	5	the	the	DET
ejpam-5893	265	6	physical	physical	ADJ
ejpam-5893	265	7	structure	structure	NOUN
ejpam-5893	265	8	of	of	ADP
ejpam-5893	265	9	applied	apply	VERB
ejpam-5893	265	10	phenomena	phenomenon	NOUN
ejpam-5893	265	11	in	in	ADP
ejpam-5893	265	12	the	the	DET
ejpam-5893	265	13	real	real	ADJ
ejpam-5893	265	14	world	world	NOUN
ejpam-5893	265	15	can	can	AUX
ejpam-5893	265	16	only	only	ADV
ejpam-5893	265	17	be	be	AUX
ejpam-5893	265	18	depicted	depict	VERB
ejpam-5893	265	19	through	through	ADP
ejpam-5893	265	20	the	the	DET
ejpam-5893	265	21	use	use	NOUN
ejpam-5893	265	22	of	of	ADP
ejpam-5893	265	23	graphic	graphic	ADJ
ejpam-5893	265	24	representations	representation	NOUN
ejpam-5893	265	25	.	.	PUNCT
ejpam-5893	266	1	the	the	DET
ejpam-5893	266	2	evaluated	evaluated	ADJ
ejpam-5893	266	3	soliton	soliton	NOUN
ejpam-5893	266	4	solutions	solution	NOUN
ejpam-5893	266	5	in	in	ADP
ejpam-5893	266	6	equations	equation	NOUN
ejpam-5893	266	7	(	(	PUNCT
ejpam-5893	266	8	15	15	NUM
ejpam-5893	266	9	)	)	PUNCT
ejpam-5893	266	10	,	,	PUNCT
ejpam-5893	266	11	(	(	PUNCT
ejpam-5893	266	12	18	18	NUM
ejpam-5893	266	13	)	)	PUNCT
ejpam-5893	266	14	,	,	PUNCT
ejpam-5893	266	15	given	give	VERB
ejpam-5893	266	16	the	the	DET
ejpam-5893	266	17	supplied	supply	VERB
ejpam-5893	266	18	values	value	NOUN
ejpam-5893	266	19	for	for	ADP
ejpam-5893	266	20	the	the	DET
ejpam-5893	266	21	free	free	ADJ
ejpam-5893	266	22	parameters	parameter	NOUN
ejpam-5893	266	23	,	,	PUNCT
ejpam-5893	266	24	give	give	VERB
ejpam-5893	266	25	a	a	DET
ejpam-5893	266	26	range	range	NOUN
ejpam-5893	266	27	of	of	ADP
ejpam-5893	266	28	geometrical	geometrical	ADJ
ejpam-5893	266	29	shapes	shape	NOUN
ejpam-5893	266	30	that	that	PRON
ejpam-5893	266	31	represent	represent	VERB
ejpam-5893	266	32	the	the	DET
ejpam-5893	266	33	hyperbolic	hyperbolic	ADJ
ejpam-5893	266	34	phase	phase	NOUN
ejpam-5893	266	35	space	space	NOUN
ejpam-5893	266	36	in	in	ADP
ejpam-5893	266	37	figure	figure	NOUN
ejpam-5893	266	38	(	(	PUNCT
ejpam-5893	266	39	1	1	NUM
ejpam-5893	266	40	)	)	PUNCT
ejpam-5893	266	41	and	and	CCONJ
ejpam-5893	266	42	figure	figure	NOUN
ejpam-5893	266	43	(	(	PUNCT
ejpam-5893	266	44	4	4	NUM
ejpam-5893	266	45	)	)	PUNCT
ejpam-5893	266	46	.	.	PUNCT
ejpam-5893	267	1	the	the	DET
ejpam-5893	267	2	results	result	NOUN
ejpam-5893	267	3	in	in	ADP
ejpam-5893	267	4	(	(	PUNCT
ejpam-5893	267	5	17	17	NUM
ejpam-5893	267	6	)	)	PUNCT
ejpam-5893	267	7	,	,	PUNCT
ejpam-5893	267	8	(	(	PUNCT
ejpam-5893	267	9	20	20	NUM
ejpam-5893	267	10	)	)	PUNCT
ejpam-5893	267	11	and	and	CCONJ
ejpam-5893	267	12	(	(	PUNCT
ejpam-5893	267	13	28	28	NUM
ejpam-5893	267	14	)	)	PUNCT
ejpam-5893	267	15	can	can	AUX
ejpam-5893	267	16	understand	understand	VERB
ejpam-5893	267	17	the	the	DET
ejpam-5893	267	18	waves	wave	NOUN
ejpam-5893	267	19	propagating	propagate	VERB
ejpam-5893	267	20	to	to	ADP
ejpam-5893	267	21	the	the	DET
ejpam-5893	267	22	optical	optical	ADJ
ejpam-5893	267	23	fibres	fibre	NOUN
ejpam-5893	267	24	when	when	SCONJ
ejpam-5893	267	25	we	we	PRON
ejpam-5893	267	26	set	set	VERB
ejpam-5893	267	27	α	α	NOUN
ejpam-5893	267	28	=	=	SYM
ejpam-5893	267	29	0.5	0.5	NUM
ejpam-5893	267	30	in	in	ADP
ejpam-5893	267	31	figure	figure	NOUN
ejpam-5893	267	32	(	(	PUNCT
ejpam-5893	267	33	3	3	NUM
ejpam-5893	267	34	)	)	PUNCT
ejpam-5893	267	35	and	and	CCONJ
ejpam-5893	267	36	figure	figure	NOUN
ejpam-5893	267	37	(	(	PUNCT
ejpam-5893	267	38	5	5	NUM
ejpam-5893	267	39	)	)	PUNCT
ejpam-5893	267	40	,	,	PUNCT
ejpam-5893	267	41	when	when	SCONJ
ejpam-5893	267	42	we	we	PRON
ejpam-5893	267	43	set	set	VERB
ejpam-5893	267	44	α	α	NOUN
ejpam-5893	267	45	=	=	NOUN
ejpam-5893	267	46	0.9	0.9	NUM
ejpam-5893	267	47	in	in	ADP
ejpam-5893	267	48	figure	figure	NOUN
ejpam-5893	267	49	(	(	PUNCT
ejpam-5893	267	50	8)	8)	NUM
ejpam-5893	267	51	and	and	CCONJ
ejpam-5893	267	52	when	when	SCONJ
ejpam-5893	267	53	we	we	PRON
ejpam-5893	267	54	set	set	VERB
ejpam-5893	267	55	α	α	NOUN
ejpam-5893	267	56	=	=	SYM
ejpam-5893	267	57	1	1	NUM
ejpam-5893	267	58	in	in	ADP
ejpam-5893	267	59	figure	figure	NOUN
ejpam-5893	267	60	(	(	PUNCT
ejpam-5893	267	61	2	2	NUM
ejpam-5893	267	62	)	)	PUNCT
ejpam-5893	267	63	,	,	PUNCT
ejpam-5893	267	64	figure	figure	NOUN
ejpam-5893	267	65	(	(	PUNCT
ejpam-5893	267	66	6	6	NUM
ejpam-5893	267	67	)	)	PUNCT
ejpam-5893	267	68	and	and	CCONJ
ejpam-5893	267	69	figure	figure	NOUN
ejpam-5893	267	70	(	(	PUNCT
ejpam-5893	267	71	7	7	NUM
ejpam-5893	267	72	)	)	PUNCT
ejpam-5893	267	73	.	.	PUNCT
ejpam-5893	268	1	b.	b.	PROPN
ejpam-5893	268	2	yasmeen	yasmeen	PROPN
ejpam-5893	268	3	,	,	PUNCT
ejpam-5893	268	4	k.	k.	PROPN
ejpam-5893	268	5	ahmad	ahmad	PROPN
ejpam-5893	268	6	,	,	PUNCT
ejpam-5893	268	7	n.	n.	PROPN
ejpam-5893	268	8	fatima	fatima	PROPN
ejpam-5893	268	9	/	/	PUNCT
ejpam-5893	268	10	eur	eur	PROPN
ejpam-5893	268	11	.	.	PUNCT
ejpam-5893	269	1	j.	j.	PROPN
ejpam-5893	269	2	pure	pure	PROPN
ejpam-5893	269	3	appl	appl	PROPN
ejpam-5893	269	4	.	.	PROPN
ejpam-5893	269	5	math	math	PROPN
ejpam-5893	269	6	,	,	PUNCT
ejpam-5893	269	7	18	18	NUM
ejpam-5893	269	8	(	(	PUNCT
ejpam-5893	269	9	2	2	NUM
ejpam-5893	269	10	)	)	PUNCT
ejpam-5893	269	11	(	(	PUNCT
ejpam-5893	269	12	2025	2025	NUM
ejpam-5893	269	13	)	)	PUNCT
ejpam-5893	269	14	,	,	PUNCT
ejpam-5893	269	15	5893	5893	NUM
ejpam-5893	269	16	12	12	NUM
ejpam-5893	269	17	of	of	ADP
ejpam-5893	269	18	17	17	NUM
ejpam-5893	269	19	figure	figure	NOUN
ejpam-5893	269	20	1	1	NUM
ejpam-5893	269	21	:	:	PUNCT
ejpam-5893	269	22	hyperbolic	hyperbolic	ADJ
ejpam-5893	269	23	phase	phase	NOUN
ejpam-5893	269	24	space	space	NOUN
ejpam-5893	269	25	for	for	ADP
ejpam-5893	269	26	solution	solution	NOUN
ejpam-5893	269	27	of	of	ADP
ejpam-5893	269	28	(	(	PUNCT
ejpam-5893	269	29	15	15	NUM
ejpam-5893	269	30	)	)	PUNCT
ejpam-5893	269	31	when	when	SCONJ
ejpam-5893	269	32	β	β	X
ejpam-5893	269	33	=	=	SYM
ejpam-5893	269	34	1	1	NUM
ejpam-5893	269	35	,	,	PUNCT
ejpam-5893	269	36	w	w	NOUN
ejpam-5893	269	37	=	=	NOUN
ejpam-5893	269	38	16	16	NUM
ejpam-5893	269	39	,	,	PUNCT
ejpam-5893	269	40	k	k	NOUN
ejpam-5893	270	1	=	=	SYM
ejpam-5893	270	2	4	4	NUM
ejpam-5893	270	3	,	,	PUNCT
ejpam-5893	270	4	r	r	NOUN
ejpam-5893	270	5	=	=	SYM
ejpam-5893	270	6	1	1	NUM
ejpam-5893	270	7	figure	figure	NOUN
ejpam-5893	270	8	2	2	NUM
ejpam-5893	270	9	:	:	PUNCT
ejpam-5893	270	10	3d	3d	NOUN
ejpam-5893	270	11	for	for	ADP
ejpam-5893	270	12	solution	solution	NOUN
ejpam-5893	270	13	of	of	ADP
ejpam-5893	270	14	(	(	PUNCT
ejpam-5893	270	15	17	17	NUM
ejpam-5893	270	16	)	)	PUNCT
ejpam-5893	270	17	when	when	SCONJ
ejpam-5893	270	18	α	α	PROPN
ejpam-5893	270	19	=	=	SYM
ejpam-5893	270	20	1	1	NUM
ejpam-5893	270	21	figure	figure	NOUN
ejpam-5893	270	22	3	3	NUM
ejpam-5893	270	23	:	:	PUNCT
ejpam-5893	270	24	3d	3d	NOUN
ejpam-5893	270	25	for	for	ADP
ejpam-5893	270	26	solution	solution	NOUN
ejpam-5893	270	27	of	of	ADP
ejpam-5893	270	28	(	(	PUNCT
ejpam-5893	270	29	17	17	NUM
ejpam-5893	270	30	)	)	PUNCT
ejpam-5893	270	31	when	when	SCONJ
ejpam-5893	270	32	α	α	NOUN
ejpam-5893	270	33	=	=	NOUN
ejpam-5893	270	34	1	1	NUM
ejpam-5893	270	35	2	2	NUM
ejpam-5893	270	36	b.	b.	PROPN
ejpam-5893	270	37	yasmeen	yasmeen	PROPN
ejpam-5893	270	38	,	,	PUNCT
ejpam-5893	270	39	k.	k.	PROPN
ejpam-5893	270	40	ahmad	ahmad	PROPN
ejpam-5893	270	41	,	,	PUNCT
ejpam-5893	270	42	n.	n.	PROPN
ejpam-5893	270	43	fatima	fatima	PROPN
ejpam-5893	270	44	/	/	PUNCT
ejpam-5893	270	45	eur	eur	PROPN
ejpam-5893	270	46	.	.	PUNCT
ejpam-5893	271	1	j.	j.	PROPN
ejpam-5893	271	2	pure	pure	PROPN
ejpam-5893	271	3	appl	appl	PROPN
ejpam-5893	271	4	.	.	PROPN
ejpam-5893	271	5	math	math	PROPN
ejpam-5893	271	6	,	,	PUNCT
ejpam-5893	271	7	18	18	NUM
ejpam-5893	271	8	(	(	PUNCT
ejpam-5893	271	9	2	2	NUM
ejpam-5893	271	10	)	)	PUNCT
ejpam-5893	271	11	(	(	PUNCT
ejpam-5893	271	12	2025	2025	NUM
ejpam-5893	271	13	)	)	PUNCT
ejpam-5893	271	14	,	,	PUNCT
ejpam-5893	271	15	5893	5893	NUM
ejpam-5893	271	16	13	13	NUM
ejpam-5893	271	17	of	of	ADP
ejpam-5893	271	18	17	17	NUM
ejpam-5893	271	19	figure	figure	NOUN
ejpam-5893	271	20	4	4	NUM
ejpam-5893	271	21	:	:	PUNCT
ejpam-5893	271	22	hyperbolic	hyperbolic	ADJ
ejpam-5893	271	23	phase	phase	NOUN
ejpam-5893	271	24	space	space	NOUN
ejpam-5893	271	25	for	for	ADP
ejpam-5893	271	26	solution	solution	NOUN
ejpam-5893	271	27	of	of	ADP
ejpam-5893	271	28	(	(	PUNCT
ejpam-5893	271	29	18	18	NUM
ejpam-5893	271	30	)	)	PUNCT
ejpam-5893	271	31	when	when	SCONJ
ejpam-5893	271	32	β	β	X
ejpam-5893	271	33	=	=	NOUN
ejpam-5893	271	34	1	1	NUM
ejpam-5893	271	35	2	2	NUM
ejpam-5893	271	36	,	,	PUNCT
ejpam-5893	271	37	w	w	NOUN
ejpam-5893	271	38	=	=	SYM
ejpam-5893	271	39	32	32	NUM
ejpam-5893	271	40	,	,	PUNCT
ejpam-5893	271	41	k	k	NOUN
ejpam-5893	272	1	=	=	SYM
ejpam-5893	272	2	2	2	NUM
ejpam-5893	272	3	,	,	PUNCT
ejpam-5893	272	4	r	r	NOUN
ejpam-5893	272	5	=	=	SYM
ejpam-5893	272	6	1√	1√	NUM
ejpam-5893	272	7	2	2	NUM
ejpam-5893	272	8	figure	figure	NOUN
ejpam-5893	272	9	5	5	NUM
ejpam-5893	272	10	:	:	PUNCT
ejpam-5893	272	11	3d	3d	NOUN
ejpam-5893	272	12	for	for	ADP
ejpam-5893	272	13	solution	solution	NOUN
ejpam-5893	272	14	of	of	ADP
ejpam-5893	272	15	(	(	PUNCT
ejpam-5893	272	16	20	20	NUM
ejpam-5893	272	17	)	)	PUNCT
ejpam-5893	272	18	when	when	SCONJ
ejpam-5893	272	19	α	α	NOUN
ejpam-5893	272	20	=	=	NOUN
ejpam-5893	272	21	1	1	NUM
ejpam-5893	272	22	2	2	NUM
ejpam-5893	272	23	figure	figure	NOUN
ejpam-5893	272	24	6	6	NUM
ejpam-5893	272	25	:	:	SYM
ejpam-5893	272	26	3d	3d	NOUN
ejpam-5893	272	27	for	for	ADP
ejpam-5893	272	28	solution	solution	NOUN
ejpam-5893	272	29	of	of	ADP
ejpam-5893	272	30	(	(	PUNCT
ejpam-5893	272	31	20	20	NUM
ejpam-5893	272	32	)	)	PUNCT
ejpam-5893	272	33	when	when	SCONJ
ejpam-5893	272	34	α	α	PROPN
ejpam-5893	272	35	=	=	SYM
ejpam-5893	272	36	1	1	NUM
ejpam-5893	272	37	b.	b.	PROPN
ejpam-5893	272	38	yasmeen	yasmeen	PROPN
ejpam-5893	272	39	,	,	PUNCT
ejpam-5893	272	40	k.	k.	PROPN
ejpam-5893	272	41	ahmad	ahmad	PROPN
ejpam-5893	272	42	,	,	PUNCT
ejpam-5893	272	43	n.	n.	PROPN
ejpam-5893	272	44	fatima	fatima	PROPN
ejpam-5893	272	45	/	/	PUNCT
ejpam-5893	272	46	eur	eur	PROPN
ejpam-5893	272	47	.	.	PUNCT
ejpam-5893	273	1	j.	j.	PROPN
ejpam-5893	273	2	pure	pure	PROPN
ejpam-5893	273	3	appl	appl	PROPN
ejpam-5893	273	4	.	.	PROPN
ejpam-5893	273	5	math	math	PROPN
ejpam-5893	273	6	,	,	PUNCT
ejpam-5893	273	7	18	18	NUM
ejpam-5893	273	8	(	(	PUNCT
ejpam-5893	273	9	2	2	NUM
ejpam-5893	273	10	)	)	PUNCT
ejpam-5893	273	11	(	(	PUNCT
ejpam-5893	273	12	2025	2025	NUM
ejpam-5893	273	13	)	)	PUNCT
ejpam-5893	273	14	,	,	PUNCT
ejpam-5893	273	15	5893	5893	NUM
ejpam-5893	273	16	14	14	NUM
ejpam-5893	273	17	of	of	ADP
ejpam-5893	273	18	17	17	NUM
ejpam-5893	273	19	figure	figure	NOUN
ejpam-5893	273	20	7	7	NUM
ejpam-5893	273	21	:	:	SYM
ejpam-5893	273	22	3d	3d	NOUN
ejpam-5893	273	23	for	for	ADP
ejpam-5893	273	24	solution	solution	NOUN
ejpam-5893	273	25	of	of	ADP
ejpam-5893	273	26	(	(	PUNCT
ejpam-5893	273	27	28	28	NUM
ejpam-5893	273	28	)	)	PUNCT
ejpam-5893	273	29	when	when	SCONJ
ejpam-5893	273	30	α	α	PROPN
ejpam-5893	273	31	=	=	SYM
ejpam-5893	273	32	1	1	NUM
ejpam-5893	273	33	figure	figure	NOUN
ejpam-5893	273	34	8	8	NUM
ejpam-5893	273	35	:	:	PUNCT
ejpam-5893	273	36	3d	3d	NOUN
ejpam-5893	273	37	for	for	ADP
ejpam-5893	273	38	solution	solution	NOUN
ejpam-5893	273	39	of	of	ADP
ejpam-5893	273	40	(	(	PUNCT
ejpam-5893	273	41	28	28	NUM
ejpam-5893	273	42	)	)	PUNCT
ejpam-5893	273	43	when	when	SCONJ
ejpam-5893	273	44	α	α	NOUN
ejpam-5893	273	45	=	=	NOUN
ejpam-5893	273	46	0.9	0.9	NUM
ejpam-5893	273	47	6	6	NUM
ejpam-5893	273	48	.	.	PUNCT
ejpam-5893	274	1	discussion	discussion	NOUN
ejpam-5893	274	2	the	the	DET
ejpam-5893	274	3	stability	stability	NOUN
ejpam-5893	274	4	analysis	analysis	NOUN
ejpam-5893	274	5	method	method	NOUN
ejpam-5893	274	6	has	have	AUX
ejpam-5893	274	7	been	be	AUX
ejpam-5893	274	8	utilized	utilize	VERB
ejpam-5893	274	9	to	to	PART
ejpam-5893	274	10	study	study	VERB
ejpam-5893	274	11	and	and	CCONJ
ejpam-5893	274	12	solve	solve	VERB
ejpam-5893	274	13	the	the	DET
ejpam-5893	274	14	nonlinear	nonlinear	ADJ
ejpam-5893	274	15	timefractional	timefractional	ADJ
ejpam-5893	274	16	emc	emc	PROPN
ejpam-5893	274	17	equation	equation	NOUN
ejpam-5893	274	18	.	.	PUNCT
ejpam-5893	275	1	this	this	DET
ejpam-5893	275	2	approach	approach	NOUN
ejpam-5893	275	3	used	use	VERB
ejpam-5893	275	4	methodology	methodology	NOUN
ejpam-5893	275	5	to	to	PART
ejpam-5893	275	6	transform	transform	VERB
ejpam-5893	275	7	nfpdes	nfpde	NOUN
ejpam-5893	275	8	into	into	ADP
ejpam-5893	275	9	nodes	node	NOUN
ejpam-5893	275	10	.	.	PUNCT
ejpam-5893	276	1	different	different	ADJ
ejpam-5893	276	2	answers	answer	NOUN
ejpam-5893	276	3	in	in	ADP
ejpam-5893	276	4	the	the	DET
ejpam-5893	276	5	form	form	NOUN
ejpam-5893	276	6	of	of	ADP
ejpam-5893	276	7	exponential	exponential	ADJ
ejpam-5893	276	8	and	and	CCONJ
ejpam-5893	276	9	trigonometric	trigonometric	ADJ
ejpam-5893	276	10	functions	function	NOUN
ejpam-5893	276	11	were	be	AUX
ejpam-5893	276	12	obtained	obtain	VERB
ejpam-5893	276	13	by	by	ADP
ejpam-5893	276	14	solving	solve	VERB
ejpam-5893	276	15	the	the	DET
ejpam-5893	276	16	resulting	result	VERB
ejpam-5893	276	17	problem	problem	NOUN
ejpam-5893	276	18	.	.	PUNCT
ejpam-5893	277	1	using	use	VERB
ejpam-5893	277	2	appropriate	appropriate	ADJ
ejpam-5893	277	3	values	value	NOUN
ejpam-5893	277	4	for	for	ADP
ejpam-5893	277	5	the	the	DET
ejpam-5893	277	6	associated	associated	ADJ
ejpam-5893	277	7	parameters	parameter	NOUN
ejpam-5893	277	8	,	,	PUNCT
ejpam-5893	277	9	we	we	PRON
ejpam-5893	277	10	successfully	successfully	ADV
ejpam-5893	277	11	examined	examine	VERB
ejpam-5893	277	12	a	a	DET
ejpam-5893	277	13	few	few	ADJ
ejpam-5893	277	14	generated	generate	VERB
ejpam-5893	277	15	solutions	solution	NOUN
ejpam-5893	277	16	of	of	ADP
ejpam-5893	277	17	exact	exact	ADJ
ejpam-5893	277	18	and	and	CCONJ
ejpam-5893	277	19	approximate	approximate	ADJ
ejpam-5893	277	20	.	.	PUNCT
ejpam-5893	278	1	our	our	PRON
ejpam-5893	278	2	analysis	analysis	NOUN
ejpam-5893	278	3	revealed	reveal	VERB
ejpam-5893	278	4	that	that	SCONJ
ejpam-5893	278	5	the	the	DET
ejpam-5893	278	6	solution	solution	NOUN
ejpam-5893	278	7	of	of	ADP
ejpam-5893	278	8	case	case	NOUN
ejpam-5893	278	9	1	1	NUM
ejpam-5893	278	10	shows	show	VERB
ejpam-5893	278	11	the	the	DET
ejpam-5893	278	12	behavior	behavior	NOUN
ejpam-5893	278	13	i	i	PRON
ejpam-5893	278	14	-	-	PUNCT
ejpam-5893	278	15	e	e	VERB
ejpam-5893	278	16	saddle	saddle	NOUN
ejpam-5893	278	17	and	and	CCONJ
ejpam-5893	278	18	centre	centre	NOUN
ejpam-5893	278	19	and	and	CCONJ
ejpam-5893	278	20	case	case	NOUN
ejpam-5893	278	21	2	2	NUM
ejpam-5893	278	22	shows	show	VERB
ejpam-5893	278	23	exact	exact	ADJ
ejpam-5893	278	24	solution	solution	NOUN
ejpam-5893	278	25	.	.	PUNCT
ejpam-5893	279	1	solutions	solution	NOUN
ejpam-5893	279	2	derived	derive	VERB
ejpam-5893	279	3	from	from	ADP
ejpam-5893	279	4	the	the	DET
ejpam-5893	279	5	soliton	soliton	NOUN
ejpam-5893	279	6	simulations	simulation	NOUN
ejpam-5893	279	7	illustrated	illustrate	VERB
ejpam-5893	279	8	the	the	DET
ejpam-5893	279	9	fundamental	fundamental	ADJ
ejpam-5893	279	10	ideas	idea	NOUN
ejpam-5893	279	11	that	that	PRON
ejpam-5893	279	12	controlled	control	VERB
ejpam-5893	279	13	the	the	DET
ejpam-5893	279	14	wave	wave	NOUN
ejpam-5893	279	15	’s	’s	PART
ejpam-5893	279	16	interaction	interaction	NOUN
ejpam-5893	279	17	and	and	CCONJ
ejpam-5893	279	18	propagation	propagation	NOUN
ejpam-5893	279	19	.	.	PUNCT
ejpam-5893	280	1	the	the	DET
ejpam-5893	280	2	complex	complex	ADJ
ejpam-5893	280	3	dynamics	dynamic	NOUN
ejpam-5893	280	4	of	of	ADP
ejpam-5893	280	5	the	the	DET
ejpam-5893	280	6	emc	emc	PROPN
ejpam-5893	280	7	equation	equation	NOUN
ejpam-5893	280	8	can	can	AUX
ejpam-5893	280	9	be	be	AUX
ejpam-5893	280	10	better	well	ADV
ejpam-5893	280	11	understood	understand	VERB
ejpam-5893	280	12	thanks	thank	NOUN
ejpam-5893	280	13	to	to	ADP
ejpam-5893	280	14	these	these	DET
ejpam-5893	280	15	answers	answer	NOUN
ejpam-5893	280	16	.	.	PUNCT
ejpam-5893	281	1	researchers	researcher	NOUN
ejpam-5893	281	2	may	may	AUX
ejpam-5893	281	3	better	well	ADV
ejpam-5893	281	4	grasp	grasp	VERB
ejpam-5893	281	5	how	how	SCONJ
ejpam-5893	281	6	the	the	DET
ejpam-5893	281	7	model	model	NOUN
ejpam-5893	281	8	behaves	behave	VERB
ejpam-5893	281	9	in	in	ADP
ejpam-5893	281	10	different	different	ADJ
ejpam-5893	281	11	contexts	context	NOUN
ejpam-5893	281	12	by	by	ADP
ejpam-5893	281	13	looking	look	VERB
ejpam-5893	281	14	at	at	ADP
ejpam-5893	281	15	these	these	DET
ejpam-5893	281	16	solutions	solution	NOUN
ejpam-5893	281	17	,	,	PUNCT
ejpam-5893	281	18	which	which	PRON
ejpam-5893	281	19	will	will	AUX
ejpam-5893	281	20	help	help	VERB
ejpam-5893	281	21	them	they	PRON
ejpam-5893	281	22	comprehend	comprehend	VERB
ejpam-5893	281	23	problems	problem	NOUN
ejpam-5893	281	24	like	like	ADP
ejpam-5893	281	25	wave	wave	NOUN
ejpam-5893	281	26	dynamics	dynamic	NOUN
ejpam-5893	281	27	in	in	ADP
ejpam-5893	281	28	optical	optical	ADJ
ejpam-5893	281	29	fiber	fiber	NOUN
ejpam-5893	281	30	.	.	PUNCT
ejpam-5893	282	1	as	as	ADP
ejpam-5893	282	2	a	a	DET
ejpam-5893	282	3	result	result	NOUN
ejpam-5893	282	4	,	,	PUNCT
ejpam-5893	282	5	the	the	DET
ejpam-5893	282	6	findings	finding	NOUN
ejpam-5893	282	7	of	of	ADP
ejpam-5893	282	8	our	our	PRON
ejpam-5893	282	9	research	research	NOUN
ejpam-5893	282	10	are	be	AUX
ejpam-5893	282	11	crucial	crucial	ADJ
ejpam-5893	282	12	for	for	ADP
ejpam-5893	282	13	tackling	tackle	VERB
ejpam-5893	282	14	the	the	DET
ejpam-5893	282	15	real	real	ADJ
ejpam-5893	282	16	-	-	PUNCT
ejpam-5893	282	17	world	world	NOUN
ejpam-5893	282	18	difficulties	difficulty	NOUN
ejpam-5893	282	19	associated	associate	VERB
ejpam-5893	282	20	with	with	ADP
ejpam-5893	282	21	examining	examine	VERB
ejpam-5893	282	22	various	various	ADJ
ejpam-5893	282	23	nonlinear	nonlinear	ADJ
ejpam-5893	282	24	structures	structure	NOUN
ejpam-5893	282	25	that	that	PRON
ejpam-5893	282	26	arise	arise	VERB
ejpam-5893	282	27	in	in	ADP
ejpam-5893	282	28	shallow	shallow	ADJ
ejpam-5893	282	29	water	water	NOUN
ejpam-5893	282	30	.	.	PUNCT
ejpam-5893	283	1	in	in	ADP
ejpam-5893	283	2	addition	addition	NOUN
ejpam-5893	283	3	to	to	ADP
ejpam-5893	283	4	helping	help	VERB
ejpam-5893	283	5	us	we	PRON
ejpam-5893	283	6	understand	understand	VERB
ejpam-5893	283	7	the	the	DET
ejpam-5893	283	8	dynamics	dynamic	NOUN
ejpam-5893	283	9	in	in	ADP
ejpam-5893	283	10	these	these	DET
ejpam-5893	283	11	environments	environment	NOUN
ejpam-5893	283	12	,	,	PUNCT
ejpam-5893	283	13	they	they	PRON
ejpam-5893	283	14	may	may	AUX
ejpam-5893	283	15	be	be	AUX
ejpam-5893	283	16	used	use	VERB
ejpam-5893	283	17	to	to	PART
ejpam-5893	283	18	forecast	forecast	VERB
ejpam-5893	283	19	and	and	CCONJ
ejpam-5893	283	20	control	control	VERB
ejpam-5893	283	21	fundamental	fundamental	ADJ
ejpam-5893	283	22	fluid	fluid	ADJ
ejpam-5893	283	23	mechanics	mechanic	NOUN
ejpam-5893	283	24	events	event	NOUN
ejpam-5893	283	25	.	.	PUNCT
ejpam-5893	284	1	7	7	X
ejpam-5893	284	2	.	.	X
ejpam-5893	284	3	conclusion	conclusion	NOUN
ejpam-5893	284	4	and	and	CCONJ
ejpam-5893	284	5	future	future	ADJ
ejpam-5893	284	6	work	work	NOUN
ejpam-5893	284	7	we	we	PRON
ejpam-5893	284	8	successfully	successfully	ADV
ejpam-5893	284	9	obtained	obtain	VERB
ejpam-5893	284	10	two	two	NUM
ejpam-5893	284	11	cases	case	NOUN
ejpam-5893	284	12	of	of	ADP
ejpam-5893	284	13	wave	wave	NOUN
ejpam-5893	284	14	solutions	solution	NOUN
ejpam-5893	284	15	to	to	PART
ejpam-5893	284	16	solved	solve	VERB
ejpam-5893	284	17	fractional	fractional	ADJ
ejpam-5893	284	18	optical	optical	ADJ
ejpam-5893	284	19	fiber	fiber	NOUN
ejpam-5893	284	20	equation	equation	NOUN
ejpam-5893	284	21	which	which	PRON
ejpam-5893	284	22	are	be	AUX
ejpam-5893	284	23	the	the	DET
ejpam-5893	284	24	nonlinear	nonlinear	ADJ
ejpam-5893	284	25	space	space	NOUN
ejpam-5893	284	26	-	-	PUNCT
ejpam-5893	284	27	time	time	NOUN
ejpam-5893	284	28	fractional	fractional	ADJ
ejpam-5893	284	29	emc	emc	PROPN
ejpam-5893	284	30	equation	equation	NOUN
ejpam-5893	284	31	.	.	PUNCT
ejpam-5893	285	1	we	we	PRON
ejpam-5893	285	2	obtained	obtain	VERB
ejpam-5893	285	3	different	different	ADJ
ejpam-5893	285	4	kinds	kind	NOUN
ejpam-5893	285	5	of	of	ADP
ejpam-5893	285	6	hyperbolic	hyperbolic	ADJ
ejpam-5893	285	7	and	and	CCONJ
ejpam-5893	285	8	soliton	soliton	NOUN
ejpam-5893	285	9	wave	wave	NOUN
ejpam-5893	285	10	solutions	solution	NOUN
ejpam-5893	285	11	,	,	PUNCT
ejpam-5893	285	12	using	use	VERB
ejpam-5893	285	13	stability	stability	NOUN
ejpam-5893	285	14	analysis	analysis	NOUN
ejpam-5893	285	15	method	method	NOUN
ejpam-5893	285	16	to	to	PART
ejpam-5893	285	17	describe	describe	VERB
ejpam-5893	285	18	stable	stable	ADJ
ejpam-5893	285	19	,	,	PUNCT
ejpam-5893	285	20	unstable	unstable	ADJ
ejpam-5893	285	21	or	or	CCONJ
ejpam-5893	285	22	saddle	saddle	NOUN
ejpam-5893	285	23	point	point	NOUN
ejpam-5893	285	24	and	and	CCONJ
ejpam-5893	285	25	rescaling	rescaling	NOUN
ejpam-5893	285	26	method	method	NOUN
ejpam-5893	285	27	to	to	PART
ejpam-5893	285	28	reduce	reduce	VERB
ejpam-5893	285	29	the	the	DET
ejpam-5893	285	30	equation	equation	NOUN
ejpam-5893	285	31	to	to	PART
ejpam-5893	285	32	get	get	VERB
ejpam-5893	285	33	exact	exact	ADJ
ejpam-5893	285	34	solution	solution	NOUN
ejpam-5893	285	35	.	.	PUNCT
ejpam-5893	286	1	using	use	VERB
ejpam-5893	286	2	mathematica	mathematica	PROPN
ejpam-5893	286	3	software	software	PROPN
ejpam-5893	286	4	,	,	PUNCT
ejpam-5893	286	5	the	the	DET
ejpam-5893	286	6	derived	derive	VERB
ejpam-5893	286	7	solutions	solution	NOUN
ejpam-5893	286	8	are	be	AUX
ejpam-5893	286	9	validated	validate	VERB
ejpam-5893	286	10	by	by	ADP
ejpam-5893	286	11	substituting	substitute	VERB
ejpam-5893	286	12	into	into	ADP
ejpam-5893	286	13	the	the	DET
ejpam-5893	286	14	equation	equation	NOUN
ejpam-5893	286	15	.	.	PUNCT
ejpam-5893	287	1	both	both	DET
ejpam-5893	287	2	cases	case	NOUN
ejpam-5893	287	3	of	of	ADP
ejpam-5893	287	4	the	the	DET
ejpam-5893	287	5	new	new	ADJ
ejpam-5893	287	6	analytical	analytical	ADJ
ejpam-5893	287	7	and	and	CCONJ
ejpam-5893	287	8	approximate	approximate	VERB
ejpam-5893	287	9	the	the	DET
ejpam-5893	287	10	nonlinear	nonlinear	ADJ
ejpam-5893	287	11	space	space	NOUN
ejpam-5893	287	12	-	-	PUNCT
ejpam-5893	287	13	time	time	NOUN
ejpam-5893	287	14	fractional	fractional	ADJ
ejpam-5893	287	15	emc	emc	PROPN
ejpam-5893	287	16	equation	equation	NOUN
ejpam-5893	287	17	appeared	appear	VERB
ejpam-5893	287	18	in	in	ADP
ejpam-5893	287	19	equations	equation	NOUN
ejpam-5893	287	20	(	(	PUNCT
ejpam-5893	287	21	17	17	NUM
ejpam-5893	287	22	)	)	PUNCT
ejpam-5893	287	23	,	,	PUNCT
ejpam-5893	287	24	(	(	PUNCT
ejpam-5893	287	25	20	20	NUM
ejpam-5893	287	26	)	)	PUNCT
ejpam-5893	287	27	and	and	CCONJ
ejpam-5893	287	28	(	(	PUNCT
ejpam-5893	287	29	28	28	NUM
ejpam-5893	287	30	)	)	PUNCT
ejpam-5893	287	31	.	.	PUNCT
ejpam-5893	288	1	these	these	DET
ejpam-5893	288	2	solutions	solution	NOUN
ejpam-5893	288	3	might	might	AUX
ejpam-5893	288	4	also	also	ADV
ejpam-5893	288	5	be	be	AUX
ejpam-5893	288	6	helpful	helpful	ADJ
ejpam-5893	288	7	for	for	ADP
ejpam-5893	288	8	optical	optical	ADJ
ejpam-5893	288	9	fibre	fibre	NOUN
ejpam-5893	288	10	in	in	ADP
ejpam-5893	288	11	engineering	engineering	NOUN
ejpam-5893	288	12	and	and	CCONJ
ejpam-5893	288	13	scientific	scientific	ADJ
ejpam-5893	288	14	domains	domain	NOUN
ejpam-5893	288	15	.	.	PUNCT
ejpam-5893	289	1	both	both	DET
ejpam-5893	289	2	two	two	NUM
ejpam-5893	289	3	and	and	CCONJ
ejpam-5893	289	4	three	three	NUM
ejpam-5893	289	5	-	-	PUNCT
ejpam-5893	289	6	dimensional	dimensional	ADJ
ejpam-5893	289	7	graphs	graph	NOUN
ejpam-5893	289	8	are	be	AUX
ejpam-5893	289	9	used	use	VERB
ejpam-5893	289	10	to	to	PART
ejpam-5893	289	11	illustrate	illustrate	VERB
ejpam-5893	289	12	the	the	DET
ejpam-5893	289	13	results	result	NOUN
ejpam-5893	289	14	,	,	PUNCT
ejpam-5893	289	15	about	about	ADP
ejpam-5893	289	16	b.	b.	PROPN
ejpam-5893	289	17	yasmeen	yasmeen	PROPN
ejpam-5893	289	18	,	,	PUNCT
ejpam-5893	289	19	k.	k.	PROPN
ejpam-5893	289	20	ahmad	ahmad	PROPN
ejpam-5893	289	21	,	,	PUNCT
ejpam-5893	289	22	n.	n.	PROPN
ejpam-5893	289	23	fatima	fatima	PROPN
ejpam-5893	289	24	/	/	PUNCT
ejpam-5893	289	25	eur	eur	PROPN
ejpam-5893	289	26	.	.	PUNCT
ejpam-5893	290	1	j.	j.	PROPN
ejpam-5893	290	2	pure	pure	PROPN
ejpam-5893	290	3	appl	appl	PROPN
ejpam-5893	290	4	.	.	PROPN
ejpam-5893	290	5	math	math	PROPN
ejpam-5893	290	6	,	,	PUNCT
ejpam-5893	290	7	18	18	NUM
ejpam-5893	290	8	(	(	PUNCT
ejpam-5893	290	9	2	2	NUM
ejpam-5893	290	10	)	)	PUNCT
ejpam-5893	290	11	(	(	PUNCT
ejpam-5893	290	12	2025	2025	NUM
ejpam-5893	290	13	)	)	PUNCT
ejpam-5893	290	14	,	,	PUNCT
ejpam-5893	290	15	5893	5893	NUM
ejpam-5893	290	16	15	15	NUM
ejpam-5893	290	17	of	of	ADP
ejpam-5893	290	18	17	17	NUM
ejpam-5893	290	19	how	how	SCONJ
ejpam-5893	290	20	sudden	sudden	ADJ
ejpam-5893	290	21	change	change	NOUN
ejpam-5893	290	22	in	in	ADP
ejpam-5893	290	23	angular	angular	ADJ
ejpam-5893	290	24	frequency	frequency	NOUN
ejpam-5893	290	25	.	.	PUNCT
ejpam-5893	291	1	stability	stability	NOUN
ejpam-5893	291	2	analysis	analysis	NOUN
ejpam-5893	291	3	is	be	AUX
ejpam-5893	291	4	performed	perform	VERB
ejpam-5893	291	5	to	to	PART
ejpam-5893	291	6	ensure	ensure	VERB
ejpam-5893	291	7	that	that	SCONJ
ejpam-5893	291	8	the	the	DET
ejpam-5893	291	9	solutions	solution	NOUN
ejpam-5893	291	10	are	be	AUX
ejpam-5893	291	11	approximate	approximate	ADJ
ejpam-5893	291	12	while	while	SCONJ
ejpam-5893	291	13	rescaling	rescale	VERB
ejpam-5893	291	14	ensure	ensure	VERB
ejpam-5893	291	15	that	that	SCONJ
ejpam-5893	291	16	the	the	DET
ejpam-5893	291	17	solution	solution	NOUN
ejpam-5893	291	18	are	be	AUX
ejpam-5893	291	19	exact	exact	ADJ
ejpam-5893	291	20	and	and	CCONJ
ejpam-5893	291	21	accurate	accurate	ADJ
ejpam-5893	291	22	.	.	PUNCT
ejpam-5893	292	1	the	the	DET
ejpam-5893	292	2	findings	finding	NOUN
ejpam-5893	292	3	will	will	AUX
ejpam-5893	292	4	be	be	AUX
ejpam-5893	292	5	useful	useful	ADJ
ejpam-5893	292	6	for	for	ADP
ejpam-5893	292	7	further	further	ADJ
ejpam-5893	292	8	research	research	NOUN
ejpam-5893	292	9	on	on	ADP
ejpam-5893	292	10	the	the	DET
ejpam-5893	292	11	related	relate	VERB
ejpam-5893	292	12	system	system	NOUN
ejpam-5893	292	13	.	.	PUNCT
ejpam-5893	293	1	the	the	DET
ejpam-5893	293	2	techniques	technique	NOUN
ejpam-5893	293	3	employed	employ	VERB
ejpam-5893	293	4	are	be	AUX
ejpam-5893	293	5	readily	readily	ADV
ejpam-5893	293	6	applicable	applicable	ADJ
ejpam-5893	293	7	to	to	ADP
ejpam-5893	293	8	other	other	ADJ
ejpam-5893	293	9	fractional	fractional	ADJ
ejpam-5893	293	10	partial	partial	ADJ
ejpam-5893	293	11	differential	differential	NOUN
ejpam-5893	293	12	equations	equation	NOUN
ejpam-5893	293	13	that	that	PRON
ejpam-5893	293	14	are	be	AUX
ejpam-5893	293	15	nonlinear	nonlinear	ADJ
ejpam-5893	293	16	.	.	PUNCT
ejpam-5893	294	1	future	future	ADJ
ejpam-5893	294	2	studies	study	NOUN
ejpam-5893	294	3	could	could	AUX
ejpam-5893	294	4	concentrate	concentrate	VERB
ejpam-5893	294	5	on	on	ADP
ejpam-5893	294	6	examining	examine	VERB
ejpam-5893	294	7	different	different	ADJ
ejpam-5893	294	8	approaches	approach	NOUN
ejpam-5893	294	9	to	to	ADP
ejpam-5893	294	10	solving	solve	VERB
ejpam-5893	294	11	the	the	DET
ejpam-5893	294	12	problem	problem	NOUN
ejpam-5893	294	13	,	,	PUNCT
ejpam-5893	294	14	like	like	ADP
ejpam-5893	294	15	numerical	numerical	ADJ
ejpam-5893	294	16	simulations	simulation	NOUN
ejpam-5893	294	17	or	or	CCONJ
ejpam-5893	294	18	other	other	ADJ
ejpam-5893	294	19	analytical	analytical	ADJ
ejpam-5893	294	20	methods	method	NOUN
ejpam-5893	294	21	like	like	ADP
ejpam-5893	294	22	the	the	DET
ejpam-5893	294	23	inverse	inverse	NOUN
ejpam-5893	294	24	scattering	scattering	NOUN
ejpam-5893	294	25	transform	transform	NOUN
ejpam-5893	294	26	,	,	PUNCT
ejpam-5893	294	27	as	as	ADV
ejpam-5893	294	28	well	well	ADV
ejpam-5893	294	29	as	as	ADP
ejpam-5893	294	30	how	how	SCONJ
ejpam-5893	294	31	the	the	DET
ejpam-5893	294	32	emc	emc	PROPN
ejpam-5893	294	33	equation	equation	NOUN
ejpam-5893	294	34	behaves	behave	VERB
ejpam-5893	294	35	under	under	ADP
ejpam-5893	294	36	various	various	ADJ
ejpam-5893	294	37	perturbations	perturbation	NOUN
ejpam-5893	294	38	and	and	CCONJ
ejpam-5893	294	39	boundary	boundary	ADJ
ejpam-5893	294	40	conditions	condition	NOUN
ejpam-5893	294	41	to	to	PART
ejpam-5893	294	42	better	well	ADV
ejpam-5893	294	43	understand	understand	VERB
ejpam-5893	294	44	its	its	PRON
ejpam-5893	294	45	physical	physical	ADJ
ejpam-5893	294	46	implications	implication	NOUN
ejpam-5893	294	47	and	and	CCONJ
ejpam-5893	294	48	possible	possible	ADJ
ejpam-5893	294	49	uses	use	NOUN
ejpam-5893	294	50	.	.	PUNCT
ejpam-5893	295	1	acknowledgements	acknowledgement	VERB
ejpam-5893	295	2	the	the	DET
ejpam-5893	295	3	author	author	NOUN
ejpam-5893	295	4	dr	dr	PROPN
ejpam-5893	295	5	.	.	PROPN
ejpam-5893	295	6	nahid	nahid	PROPN
ejpam-5893	295	7	fatima	fatima	PROPN
ejpam-5893	295	8	would	would	AUX
ejpam-5893	295	9	like	like	VERB
ejpam-5893	295	10	to	to	PART
ejpam-5893	295	11	acknowledge	acknowledge	VERB
ejpam-5893	295	12	the	the	DET
ejpam-5893	295	13	support	support	NOUN
ejpam-5893	295	14	of	of	ADP
ejpam-5893	295	15	prince	prince	PROPN
ejpam-5893	295	16	sultan	sultan	PROPN
ejpam-5893	295	17	university	university	PROPN
ejpam-5893	295	18	,	,	PUNCT
ejpam-5893	295	19	riyadh	riyadh	PROPN
ejpam-5893	295	20	,	,	PUNCT
ejpam-5893	295	21	saudi	saudi	PROPN
ejpam-5893	295	22	arabia	arabia	PROPN
ejpam-5893	295	23	for	for	ADP
ejpam-5893	295	24	paying	pay	VERB
ejpam-5893	295	25	the	the	DET
ejpam-5893	295	26	article	article	NOUN
ejpam-5893	295	27	processing	processing	NOUN
ejpam-5893	295	28	charges	charge	NOUN
ejpam-5893	295	29	(	(	PUNCT
ejpam-5893	295	30	apc	apc	PROPN
ejpam-5893	295	31	)	)	PUNCT
ejpam-5893	295	32	for	for	ADP
ejpam-5893	295	33	this	this	DET
ejpam-5893	295	34	publication	publication	NOUN
ejpam-5893	295	35	.	.	PUNCT
ejpam-5893	296	1	the	the	DET
ejpam-5893	296	2	authors	author	NOUN
ejpam-5893	296	3	bushra	bushra	PROPN
ejpam-5893	296	4	yasmeen	yasmeen	PROPN
ejpam-5893	296	5	and	and	CCONJ
ejpam-5893	296	6	dr	dr	PROPN
ejpam-5893	296	7	.	.	PROPN
ejpam-5893	296	8	khalil	khalil	PROPN
ejpam-5893	296	9	ahmad	ahmad	PROPN
ejpam-5893	296	10	would	would	AUX
ejpam-5893	296	11	like	like	VERB
ejpam-5893	296	12	to	to	PART
ejpam-5893	296	13	thankful	thankful	VERB
ejpam-5893	296	14	the	the	DET
ejpam-5893	296	15	air	air	NOUN
ejpam-5893	296	16	marshal	marshal	NOUN
ejpam-5893	296	17	abdul	abdul	PROPN
ejpam-5893	296	18	moeed	moeed	PROPN
ejpam-5893	296	19	khan	khan	PROPN
ejpam-5893	296	20	,	,	PUNCT
ejpam-5893	296	21	hi(m	hi(m	NOUN
ejpam-5893	296	22	)	)	PUNCT
ejpam-5893	296	23	,	,	PUNCT
ejpam-5893	296	24	vice	vice	NOUN
ejpam-5893	296	25	chancellor	chancellor	NOUN
ejpam-5893	296	26	,	,	PUNCT
ejpam-5893	296	27	air	air	NOUN
ejpam-5893	296	28	university	university	PROPN
ejpam-5893	296	29	,	,	PUNCT
ejpam-5893	296	30	islamabad	islamabad	PROPN
ejpam-5893	296	31	,	,	PUNCT
ejpam-5893	296	32	pakistan	pakistan	PROPN
ejpam-5893	296	33	.	.	PUNCT
ejpam-5893	297	1	competing	compete	VERB
ejpam-5893	297	2	interests	interest	NOUN
ejpam-5893	297	3	the	the	DET
ejpam-5893	297	4	authors	author	NOUN
ejpam-5893	297	5	declare	declare	VERB
ejpam-5893	297	6	that	that	SCONJ
ejpam-5893	297	7	they	they	PRON
ejpam-5893	297	8	have	have	VERB
ejpam-5893	297	9	no	no	DET
ejpam-5893	297	10	competing	compete	VERB
ejpam-5893	297	11	interests	interest	NOUN
ejpam-5893	297	12	.	.	PUNCT
ejpam-5893	298	1	data	datum	NOUN
ejpam-5893	298	2	availability	availability	NOUN
ejpam-5893	298	3	statement	statement	NOUN
ejpam-5893	298	4	please	please	INTJ
ejpam-5893	298	5	contact	contact	VERB
ejpam-5893	298	6	the	the	DET
ejpam-5893	298	7	authors	author	NOUN
ejpam-5893	298	8	for	for	ADP
ejpam-5893	298	9	data	datum	NOUN
ejpam-5893	298	10	requests	request	NOUN
ejpam-5893	298	11	.	.	PUNCT
ejpam-5893	299	1	authors	author	NOUN
ejpam-5893	299	2	’	'	PUNCT
ejpam-5893	299	3	contributions	contribution	NOUN
ejpam-5893	299	4	all	all	DET
ejpam-5893	299	5	authors	author	NOUN
ejpam-5893	299	6	contributed	contribute	VERB
ejpam-5893	299	7	equally	equally	ADV
ejpam-5893	299	8	to	to	ADP
ejpam-5893	299	9	finishing	finish	VERB
ejpam-5893	299	10	the	the	DET
ejpam-5893	299	11	manuscripts	manuscript	NOUN
ejpam-5893	299	12	.	.	PUNCT
ejpam-5893	300	1	all	all	DET
ejpam-5893	300	2	authors	author	NOUN
ejpam-5893	300	3	read	read	VERB
ejpam-5893	300	4	and	and	CCONJ
ejpam-5893	300	5	approved	approve	VERB
ejpam-5893	300	6	the	the	DET
ejpam-5893	300	7	final	final	ADJ
ejpam-5893	300	8	manuscript	manuscript	NOUN
ejpam-5893	300	9	.	.	PUNCT
ejpam-5893	301	1	references	reference	NOUN
ejpam-5893	301	2	[	[	X
ejpam-5893	301	3	1	1	X
ejpam-5893	301	4	]	]	PUNCT
ejpam-5893	301	5	muhammad	muhammad	PROPN
ejpam-5893	301	6	bilal	bilal	PROPN
ejpam-5893	301	7	,	,	PUNCT
ejpam-5893	301	8	javed	javed	PROPN
ejpam-5893	301	9	iqbal	iqbal	PROPN
ejpam-5893	301	10	,	,	PUNCT
ejpam-5893	301	11	rashid	rashid	PROPN
ejpam-5893	301	12	ali	ali	PROPN
ejpam-5893	301	13	,	,	PUNCT
ejpam-5893	301	14	fuad	fuad	PROPN
ejpam-5893	301	15	a	a	DET
ejpam-5893	301	16	awwad	awwad	NOUN
ejpam-5893	301	17	,	,	PUNCT
ejpam-5893	301	18	and	and	CCONJ
ejpam-5893	301	19	emad	emad	PROPN
ejpam-5893	301	20	aa	aa	PROPN
ejpam-5893	301	21	ismail	ismail	PROPN
ejpam-5893	301	22	.	.	PUNCT
ejpam-5893	302	1	establishing	establish	VERB
ejpam-5893	302	2	breather	breather	NOUN
ejpam-5893	302	3	and	and	CCONJ
ejpam-5893	302	4	n	n	CCONJ
ejpam-5893	302	5	-	-	PUNCT
ejpam-5893	302	6	soliton	soliton	NOUN
ejpam-5893	302	7	solutions	solution	NOUN
ejpam-5893	302	8	for	for	ADP
ejpam-5893	302	9	conformable	conformable	ADJ
ejpam-5893	302	10	klein	klein	PROPN
ejpam-5893	302	11	–	–	PUNCT
ejpam-5893	302	12	gordon	gordon	PROPN
ejpam-5893	302	13	equation	equation	NOUN
ejpam-5893	302	14	.	.	PUNCT
ejpam-5893	303	1	open	open	ADJ
ejpam-5893	303	2	physics	physics	PROPN
ejpam-5893	303	3	,	,	PUNCT
ejpam-5893	303	4	22(1):20240044	22(1):20240044	NUM
ejpam-5893	303	5	,	,	PUNCT
ejpam-5893	303	6	2024	2024	NUM
ejpam-5893	303	7	.	.	PUNCT
ejpam-5893	304	1	[	[	X
ejpam-5893	304	2	2	2	X
ejpam-5893	304	3	]	]	PUNCT
ejpam-5893	304	4	muhammad	muhammad	PROPN
ejpam-5893	304	5	bilal	bilal	PROPN
ejpam-5893	304	6	,	,	PUNCT
ejpam-5893	304	7	javed	javed	PROPN
ejpam-5893	304	8	iqbal	iqbal	PROPN
ejpam-5893	304	9	,	,	PUNCT
ejpam-5893	304	10	rashid	rashid	PROPN
ejpam-5893	304	11	ali	ali	PROPN
ejpam-5893	304	12	,	,	PUNCT
ejpam-5893	304	13	fuad	fuad	PROPN
ejpam-5893	304	14	a	a	DET
ejpam-5893	304	15	awwad	awwad	NOUN
ejpam-5893	304	16	,	,	PUNCT
ejpam-5893	304	17	and	and	CCONJ
ejpam-5893	304	18	emad	emad	NOUN
ejpam-5893	304	19	a	a	DET
ejpam-5893	304	20	a.	a.	NOUN
ejpam-5893	304	21	ismail	ismail	PROPN
ejpam-5893	304	22	.	.	PUNCT
ejpam-5893	305	1	exploring	explore	VERB
ejpam-5893	305	2	families	family	NOUN
ejpam-5893	305	3	of	of	ADP
ejpam-5893	305	4	solitary	solitary	ADJ
ejpam-5893	305	5	wave	wave	NOUN
ejpam-5893	305	6	solutions	solution	NOUN
ejpam-5893	305	7	for	for	ADP
ejpam-5893	305	8	the	the	DET
ejpam-5893	305	9	fractional	fractional	ADJ
ejpam-5893	305	10	coupled	couple	VERB
ejpam-5893	305	11	higgs	higgs	NOUN
ejpam-5893	305	12	system	system	NOUN
ejpam-5893	305	13	using	use	VERB
ejpam-5893	305	14	modified	modify	VERB
ejpam-5893	305	15	extended	extend	VERB
ejpam-5893	305	16	direct	direct	ADJ
ejpam-5893	305	17	algebraic	algebraic	ADJ
ejpam-5893	305	18	method	method	NOUN
ejpam-5893	305	19	.	.	PUNCT
ejpam-5893	306	1	fractal	fractal	ADJ
ejpam-5893	306	2	and	and	CCONJ
ejpam-5893	306	3	fractional	fractional	ADJ
ejpam-5893	306	4	,	,	PUNCT
ejpam-5893	306	5	7(9):653	7(9):653	NUM
ejpam-5893	306	6	,	,	PUNCT
ejpam-5893	306	7	2023	2023	NUM
ejpam-5893	306	8	.	.	PUNCT
ejpam-5893	307	1	[	[	X
ejpam-5893	307	2	3	3	X
ejpam-5893	307	3	]	]	X
ejpam-5893	307	4	m	m	PROPN
ejpam-5893	307	5	mossa	mossa	PROPN
ejpam-5893	307	6	al	al	PROPN
ejpam-5893	307	7	-	-	PUNCT
ejpam-5893	307	8	sawalha	sawalha	NOUN
ejpam-5893	307	9	,	,	PUNCT
ejpam-5893	307	10	saima	saima	PROPN
ejpam-5893	307	11	noor	noor	PROPN
ejpam-5893	307	12	,	,	PUNCT
ejpam-5893	307	13	saleh	saleh	PROPN
ejpam-5893	307	14	alshammari	alshammari	PROPN
ejpam-5893	307	15	,	,	PUNCT
ejpam-5893	307	16	abdul	abdul	PROPN
ejpam-5893	307	17	hamid	hamid	PROPN
ejpam-5893	307	18	ganie	ganie	PROPN
ejpam-5893	307	19	,	,	PUNCT
ejpam-5893	307	20	and	and	CCONJ
ejpam-5893	307	21	ahmad	ahmad	PROPN
ejpam-5893	307	22	shafee	shafee	PROPN
ejpam-5893	307	23	.	.	PUNCT
ejpam-5893	308	1	analytical	analytical	ADJ
ejpam-5893	308	2	insights	insight	NOUN
ejpam-5893	308	3	into	into	ADP
ejpam-5893	308	4	solitary	solitary	ADJ
ejpam-5893	308	5	wave	wave	NOUN
ejpam-5893	308	6	solutions	solution	NOUN
ejpam-5893	308	7	of	of	ADP
ejpam-5893	308	8	the	the	DET
ejpam-5893	308	9	fractional	fractional	ADJ
ejpam-5893	308	10	estevezmansfield	estevezmansfield	ADJ
ejpam-5893	308	11	-	-	PUNCT
ejpam-5893	308	12	clarkson	clarkson	NOUN
ejpam-5893	308	13	equation	equation	NOUN
ejpam-5893	308	14	.	.	PUNCT
ejpam-5893	309	1	aims	aim	VERB
ejpam-5893	309	2	mathematics	mathematic	NOUN
ejpam-5893	309	3	,	,	PUNCT
ejpam-5893	309	4	9(6):13589–13606	9(6):13589–13606	NUM
ejpam-5893	309	5	,	,	PUNCT
ejpam-5893	309	6	2024	2024	NUM
ejpam-5893	309	7	.	.	PUNCT
ejpam-5893	310	1	[	[	X
ejpam-5893	310	2	4	4	NUM
ejpam-5893	310	3	]	]	X
ejpam-5893	310	4	mohammad	mohammad	PROPN
ejpam-5893	310	5	alqudah	alqudah	PROPN
ejpam-5893	310	6	,	,	PUNCT
ejpam-5893	310	7	safyan	safyan	PROPN
ejpam-5893	310	8	mukhtar	mukhtar	PROPN
ejpam-5893	310	9	,	,	PUNCT
ejpam-5893	310	10	haifa	haifa	PROPN
ejpam-5893	310	11	a	a	DET
ejpam-5893	310	12	alyousef	alyousef	NOUN
ejpam-5893	310	13	,	,	PUNCT
ejpam-5893	310	14	sherif	sherif	VERB
ejpam-5893	310	15	me	i	PRON
ejpam-5893	310	16	ismaeel	ismaeel	PROPN
ejpam-5893	310	17	,	,	PUNCT
ejpam-5893	310	18	sa	sa	PROPN
ejpam-5893	310	19	eltantawy	eltantawy	PROPN
ejpam-5893	310	20	,	,	PUNCT
ejpam-5893	310	21	and	and	CCONJ
ejpam-5893	310	22	fazal	fazal	PROPN
ejpam-5893	310	23	ghani	ghani	PROPN
ejpam-5893	310	24	.	.	PUNCT
ejpam-5893	311	1	probing	probe	VERB
ejpam-5893	311	2	the	the	DET
ejpam-5893	311	3	diversity	diversity	NOUN
ejpam-5893	311	4	of	of	ADP
ejpam-5893	311	5	soliton	soliton	NOUN
ejpam-5893	311	6	phenomena	phenomenon	NOUN
ejpam-5893	311	7	within	within	ADP
ejpam-5893	311	8	conformable	conformable	ADJ
ejpam-5893	311	9	estevez	estevez	PROPN
ejpam-5893	311	10	-	-	PUNCT
ejpam-5893	311	11	mansfield	mansfield	PROPN
ejpam-5893	311	12	-	-	PUNCT
ejpam-5893	311	13	clarkson	clarkson	PROPN
ejpam-5893	311	14	equation	equation	NOUN
ejpam-5893	311	15	in	in	ADP
ejpam-5893	311	16	shallow	shallow	ADJ
ejpam-5893	311	17	water	water	NOUN
ejpam-5893	311	18	.	.	PUNCT
ejpam-5893	312	1	aims	aim	VERB
ejpam-5893	312	2	mathematics	mathematic	NOUN
ejpam-5893	312	3	,	,	PUNCT
ejpam-5893	312	4	9(8):21212–21238	9(8):21212–21238	PROPN
ejpam-5893	312	5	,	,	PUNCT
ejpam-5893	312	6	2024	2024	NUM
ejpam-5893	312	7	.	.	PUNCT
ejpam-5893	313	1	[	[	X
ejpam-5893	313	2	5	5	NUM
ejpam-5893	313	3	]	]	X
ejpam-5893	313	4	chaoyang	chaoyang	PROPN
ejpam-5893	313	5	zhu	zhu	PROPN
ejpam-5893	313	6	,	,	PUNCT
ejpam-5893	313	7	mawaheb	mawaheb	PROPN
ejpam-5893	313	8	al	al	PROPN
ejpam-5893	313	9	-	-	PUNCT
ejpam-5893	313	10	dossari	dossari	PROPN
ejpam-5893	313	11	,	,	PUNCT
ejpam-5893	313	12	s	s	NOUN
ejpam-5893	313	13	rezapour	rezapour	NOUN
ejpam-5893	313	14	,	,	PUNCT
ejpam-5893	313	15	and	and	CCONJ
ejpam-5893	313	16	stanford	stanford	PROPN
ejpam-5893	313	17	shateyi	shateyi	PROPN
ejpam-5893	313	18	.	.	PUNCT
ejpam-5893	314	1	on	on	ADP
ejpam-5893	314	2	the	the	DET
ejpam-5893	314	3	exact	exact	ADJ
ejpam-5893	314	4	soliton	soliton	NOUN
ejpam-5893	314	5	solutions	solution	NOUN
ejpam-5893	314	6	and	and	CCONJ
ejpam-5893	314	7	different	different	ADJ
ejpam-5893	314	8	wave	wave	NOUN
ejpam-5893	314	9	structures	structure	NOUN
ejpam-5893	314	10	to	to	ADP
ejpam-5893	314	11	the	the	DET
ejpam-5893	314	12	modified	modify	VERB
ejpam-5893	314	13	schrödinger	schrödinger	NOUN
ejpam-5893	314	14	’s	’s	PART
ejpam-5893	314	15	equation	equation	NOUN
ejpam-5893	314	16	.	.	PUNCT
ejpam-5893	315	1	results	result	NOUN
ejpam-5893	315	2	in	in	ADP
ejpam-5893	315	3	physics	physics	NOUN
ejpam-5893	315	4	,	,	PUNCT
ejpam-5893	315	5	54:107037	54:107037	NUM
ejpam-5893	315	6	,	,	PUNCT
ejpam-5893	315	7	2023	2023	NUM
ejpam-5893	315	8	.	.	PUNCT
ejpam-5893	316	1	b.	b.	PROPN
ejpam-5893	316	2	yasmeen	yasmeen	PROPN
ejpam-5893	316	3	,	,	PUNCT
ejpam-5893	316	4	k.	k.	PROPN
ejpam-5893	316	5	ahmad	ahmad	PROPN
ejpam-5893	316	6	,	,	PUNCT
ejpam-5893	316	7	n.	n.	PROPN
ejpam-5893	316	8	fatima	fatima	PROPN
ejpam-5893	316	9	/	/	PUNCT
ejpam-5893	316	10	eur	eur	PROPN
ejpam-5893	316	11	.	.	PUNCT
ejpam-5893	317	1	j.	j.	PROPN
ejpam-5893	317	2	pure	pure	PROPN
ejpam-5893	317	3	appl	appl	PROPN
ejpam-5893	317	4	.	.	PROPN
ejpam-5893	317	5	math	math	PROPN
ejpam-5893	317	6	,	,	PUNCT
ejpam-5893	317	7	18	18	NUM
ejpam-5893	317	8	(	(	PUNCT
ejpam-5893	317	9	2	2	NUM
ejpam-5893	317	10	)	)	PUNCT
ejpam-5893	317	11	(	(	PUNCT
ejpam-5893	317	12	2025	2025	NUM
ejpam-5893	317	13	)	)	PUNCT
ejpam-5893	317	14	,	,	PUNCT
ejpam-5893	317	15	5893	5893	NUM
ejpam-5893	317	16	16	16	NUM
ejpam-5893	317	17	of	of	ADP
ejpam-5893	317	18	17	17	NUM
ejpam-5893	317	19	[	[	SYM
ejpam-5893	317	20	6	6	NUM
ejpam-5893	317	21	]	]	SYM
ejpam-5893	317	22	c	c	PROPN
ejpam-5893	317	23	zhu	zhu	PROPN
ejpam-5893	317	24	,	,	PUNCT
ejpam-5893	317	25	m	m	PROPN
ejpam-5893	317	26	al	al	PROPN
ejpam-5893	317	27	-	-	PUNCT
ejpam-5893	317	28	dossari	dossari	PROPN
ejpam-5893	317	29	,	,	PUNCT
ejpam-5893	317	30	nsa	nsa	PROPN
ejpam-5893	317	31	el	el	PROPN
ejpam-5893	317	32	-	-	PUNCT
ejpam-5893	317	33	gawaad	gawaad	NOUN
ejpam-5893	317	34	,	,	PUNCT
ejpam-5893	317	35	sam	sam	PROPN
ejpam-5893	317	36	alsallami	alsallami	PROPN
ejpam-5893	317	37	,	,	PUNCT
ejpam-5893	317	38	and	and	CCONJ
ejpam-5893	317	39	s	s	VERB
ejpam-5893	317	40	shateyi	shateyi	NOUN
ejpam-5893	317	41	.	.	PUNCT
ejpam-5893	318	1	uncovering	uncover	VERB
ejpam-5893	318	2	diverse	diverse	ADJ
ejpam-5893	318	3	soliton	soliton	NOUN
ejpam-5893	318	4	solutions	solution	NOUN
ejpam-5893	318	5	in	in	ADP
ejpam-5893	318	6	the	the	DET
ejpam-5893	318	7	modified	modify	VERB
ejpam-5893	318	8	schrödinger	schrödinger	NOUN
ejpam-5893	318	9	’s	’s	PART
ejpam-5893	318	10	equation	equation	NOUN
ejpam-5893	318	11	via	via	ADP
ejpam-5893	318	12	innovative	innovative	ADJ
ejpam-5893	318	13	approaches	approach	NOUN
ejpam-5893	318	14	.	.	PUNCT
ejpam-5893	319	1	results	result	NOUN
ejpam-5893	319	2	in	in	ADP
ejpam-5893	319	3	physics	physics	PROPN
ejpam-5893	319	4	,	,	PUNCT
ejpam-5893	319	5	54:107100	54:107100	NUM
ejpam-5893	319	6	,	,	PUNCT
ejpam-5893	319	7	2023	2023	NUM
ejpam-5893	319	8	.	.	PUNCT
ejpam-5893	320	1	[	[	X
ejpam-5893	320	2	7	7	X
ejpam-5893	320	3	]	]	X
ejpam-5893	320	4	chaoyang	chaoyang	PROPN
ejpam-5893	320	5	zhu	zhu	PROPN
ejpam-5893	320	6	,	,	PUNCT
ejpam-5893	320	7	suhad	suhad	PROPN
ejpam-5893	320	8	ali	ali	PROPN
ejpam-5893	320	9	osman	osman	PROPN
ejpam-5893	320	10	abdallah	abdallah	PROPN
ejpam-5893	320	11	,	,	PUNCT
ejpam-5893	320	12	s	s	NOUN
ejpam-5893	320	13	rezapour	rezapour	NOUN
ejpam-5893	320	14	,	,	PUNCT
ejpam-5893	320	15	and	and	CCONJ
ejpam-5893	320	16	stanford	stanford	PROPN
ejpam-5893	320	17	shateyi	shateyi	PROPN
ejpam-5893	320	18	.	.	PUNCT
ejpam-5893	321	1	on	on	ADP
ejpam-5893	321	2	new	new	ADJ
ejpam-5893	321	3	diverse	diverse	ADJ
ejpam-5893	321	4	variety	variety	NOUN
ejpam-5893	321	5	analytical	analytical	ADJ
ejpam-5893	321	6	optical	optical	ADJ
ejpam-5893	321	7	soliton	soliton	NOUN
ejpam-5893	321	8	solutions	solution	NOUN
ejpam-5893	321	9	to	to	ADP
ejpam-5893	321	10	the	the	DET
ejpam-5893	321	11	perturbed	perturb	VERB
ejpam-5893	321	12	nonlinear	nonlinear	PROPN
ejpam-5893	321	13	schrödinger	schrödinger	NOUN
ejpam-5893	321	14	equation	equation	NOUN
ejpam-5893	321	15	.	.	PUNCT
ejpam-5893	322	1	results	result	NOUN
ejpam-5893	322	2	in	in	ADP
ejpam-5893	322	3	physics	physics	NOUN
ejpam-5893	322	4	,	,	PUNCT
ejpam-5893	322	5	54:107046	54:107046	NUM
ejpam-5893	322	6	,	,	PUNCT
ejpam-5893	322	7	2023	2023	NUM
ejpam-5893	322	8	.	.	PUNCT
ejpam-5893	323	1	[	[	X
ejpam-5893	323	2	8	8	NUM
ejpam-5893	323	3	]	]	X
ejpam-5893	323	4	ahmed	ahmed	PROPN
ejpam-5893	323	5	h	h	PROPN
ejpam-5893	323	6	arnous	arnous	PROPN
ejpam-5893	323	7	,	,	PUNCT
ejpam-5893	323	8	mohammad	mohammad	PROPN
ejpam-5893	323	9	mirzazadeh	mirzazadeh	PROPN
ejpam-5893	323	10	,	,	PUNCT
ejpam-5893	323	11	lanre	lanre	NOUN
ejpam-5893	323	12	akinyemi	akinyemi	NOUN
ejpam-5893	323	13	,	,	PUNCT
ejpam-5893	323	14	and	and	CCONJ
ejpam-5893	323	15	arzu	arzu	NOUN
ejpam-5893	323	16	akbulut	akbulut	PROPN
ejpam-5893	323	17	.	.	PUNCT
ejpam-5893	324	1	new	new	ADJ
ejpam-5893	324	2	solitary	solitary	ADJ
ejpam-5893	324	3	waves	wave	NOUN
ejpam-5893	324	4	and	and	CCONJ
ejpam-5893	324	5	exact	exact	ADJ
ejpam-5893	324	6	solutions	solution	NOUN
ejpam-5893	324	7	for	for	ADP
ejpam-5893	324	8	the	the	DET
ejpam-5893	324	9	fifth	fifth	ADJ
ejpam-5893	324	10	-	-	PUNCT
ejpam-5893	324	11	order	order	NOUN
ejpam-5893	324	12	nonlinear	nonlinear	ADJ
ejpam-5893	324	13	wave	wave	NOUN
ejpam-5893	324	14	equation	equation	NOUN
ejpam-5893	324	15	using	use	VERB
ejpam-5893	324	16	two	two	NUM
ejpam-5893	324	17	integration	integration	NOUN
ejpam-5893	324	18	techniques	technique	NOUN
ejpam-5893	324	19	.	.	PUNCT
ejpam-5893	325	1	journal	journal	PROPN
ejpam-5893	325	2	of	of	ADP
ejpam-5893	325	3	ocean	ocean	PROPN
ejpam-5893	325	4	engineering	engineering	NOUN
ejpam-5893	325	5	and	and	CCONJ
ejpam-5893	325	6	science	science	NOUN
ejpam-5893	325	7	,	,	PUNCT
ejpam-5893	325	8	8(5):475–480	8(5):475–480	NOUN
ejpam-5893	325	9	,	,	PUNCT
ejpam-5893	325	10	2023	2023	NUM
ejpam-5893	325	11	.	.	PUNCT
ejpam-5893	326	1	[	[	X
ejpam-5893	326	2	9	9	NUM
ejpam-5893	326	3	]	]	X
ejpam-5893	326	4	syeda	syeda	NOUN
ejpam-5893	326	5	sarwat	sarwat	PROPN
ejpam-5893	326	6	kazmi	kazmi	PROPN
ejpam-5893	326	7	,	,	PUNCT
ejpam-5893	326	8	adil	adil	PROPN
ejpam-5893	326	9	jhangeer	jhangeer	NOUN
ejpam-5893	326	10	,	,	PUNCT
ejpam-5893	326	11	and	and	CCONJ
ejpam-5893	326	12	muhammad	muhammad	PROPN
ejpam-5893	326	13	bilal	bilal	PROPN
ejpam-5893	326	14	riaz	riaz	PROPN
ejpam-5893	326	15	.	.	PUNCT
ejpam-5893	327	1	analyzing	analyze	VERB
ejpam-5893	327	2	sensitivity	sensitivity	NOUN
ejpam-5893	327	3	and	and	CCONJ
ejpam-5893	327	4	multi	multi	ADJ
ejpam-5893	327	5	-	-	ADJ
ejpam-5893	327	6	soliton	soliton	ADJ
ejpam-5893	327	7	solutions	solution	NOUN
ejpam-5893	327	8	in	in	ADP
ejpam-5893	327	9	the	the	DET
ejpam-5893	327	10	estevez	estevez	NOUN
ejpam-5893	327	11	–	–	PUNCT
ejpam-5893	327	12	mansfield	mansfield	PROPN
ejpam-5893	327	13	–	–	PUNCT
ejpam-5893	327	14	clarkson	clarkson	PROPN
ejpam-5893	327	15	equation	equation	NOUN
ejpam-5893	327	16	:	:	PUNCT
ejpam-5893	327	17	insights	insight	NOUN
ejpam-5893	327	18	into	into	ADP
ejpam-5893	327	19	dynamics	dynamic	NOUN
ejpam-5893	327	20	of	of	ADP
ejpam-5893	327	21	bifurcation	bifurcation	NOUN
ejpam-5893	327	22	and	and	CCONJ
ejpam-5893	327	23	chaos	chaos	NOUN
ejpam-5893	327	24	.	.	PUNCT
ejpam-5893	328	1	partial	partial	ADJ
ejpam-5893	328	2	differential	differential	ADJ
ejpam-5893	328	3	equations	equation	NOUN
ejpam-5893	328	4	in	in	ADP
ejpam-5893	328	5	applied	applied	ADJ
ejpam-5893	328	6	mathematics	mathematic	NOUN
ejpam-5893	328	7	,	,	PUNCT
ejpam-5893	328	8	11:100826	11:100826	NUM
ejpam-5893	328	9	,	,	PUNCT
ejpam-5893	328	10	2024	2024	NUM
ejpam-5893	328	11	.	.	PUNCT
ejpam-5893	329	1	[	[	X
ejpam-5893	329	2	10	10	NUM
ejpam-5893	329	3	]	]	X
ejpam-5893	329	4	aliyu	aliyu	NOUN
ejpam-5893	329	5	isa	isa	PROPN
ejpam-5893	329	6	aliyu	aliyu	PROPN
ejpam-5893	329	7	,	,	PUNCT
ejpam-5893	329	8	jibrin	jibrin	NOUN
ejpam-5893	329	9	sale	sale	NOUN
ejpam-5893	329	10	yusuf	yusuf	PROPN
ejpam-5893	329	11	,	,	PUNCT
ejpam-5893	329	12	malik	malik	PROPN
ejpam-5893	329	13	muhammad	muhammad	PROPN
ejpam-5893	329	14	nauman	nauman	PROPN
ejpam-5893	329	15	,	,	PUNCT
ejpam-5893	329	16	dilber	dilber	PROPN
ejpam-5893	329	17	uzun	uzun	PROPN
ejpam-5893	329	18	ozsahin	ozsahin	PROPN
ejpam-5893	329	19	,	,	PUNCT
ejpam-5893	329	20	baba	baba	PROPN
ejpam-5893	329	21	galadima	galadima	PROPN
ejpam-5893	329	22	agaie	agaie	PROPN
ejpam-5893	329	23	,	,	PUNCT
ejpam-5893	329	24	juliana	juliana	PROPN
ejpam-5893	329	25	haji	haji	PROPN
ejpam-5893	329	26	zaini	zaini	PROPN
ejpam-5893	329	27	,	,	PUNCT
ejpam-5893	329	28	and	and	CCONJ
ejpam-5893	329	29	huzaifa	huzaifa	PROPN
ejpam-5893	329	30	umar	umar	PROPN
ejpam-5893	329	31	.	.	PROPN
ejpam-5893	329	32	lie	lie	PROPN
ejpam-5893	329	33	symmetry	symmetry	NOUN
ejpam-5893	329	34	analysis	analysis	NOUN
ejpam-5893	329	35	and	and	CCONJ
ejpam-5893	329	36	explicit	explicit	ADJ
ejpam-5893	329	37	solutions	solution	NOUN
ejpam-5893	329	38	to	to	ADP
ejpam-5893	329	39	the	the	DET
ejpam-5893	329	40	estevez	estevez	NOUN
ejpam-5893	329	41	–	–	PUNCT
ejpam-5893	329	42	mansfield	mansfield	PROPN
ejpam-5893	329	43	–	–	PUNCT
ejpam-5893	329	44	clarkson	clarkson	PROPN
ejpam-5893	329	45	equation	equation	NOUN
ejpam-5893	329	46	.	.	PUNCT
ejpam-5893	330	1	symmetry	symmetry	PROPN
ejpam-5893	330	2	,	,	PUNCT
ejpam-5893	330	3	16(9):1194	16(9):1194	NUM
ejpam-5893	330	4	,	,	PUNCT
ejpam-5893	330	5	2024	2024	NUM
ejpam-5893	330	6	.	.	PUNCT
ejpam-5893	331	1	[	[	X
ejpam-5893	331	2	11	11	NUM
ejpam-5893	331	3	]	]	PUNCT
ejpam-5893	331	4	haitham	haitham	PROPN
ejpam-5893	331	5	qawaqneh	qawaqneh	PROPN
ejpam-5893	331	6	and	and	CCONJ
ejpam-5893	331	7	yasser	yasser	PROPN
ejpam-5893	331	8	alrashedi	alrashedi	PROPN
ejpam-5893	331	9	.	.	PUNCT
ejpam-5893	332	1	mathematical	mathematical	ADJ
ejpam-5893	332	2	and	and	CCONJ
ejpam-5893	332	3	physical	physical	ADJ
ejpam-5893	332	4	analysis	analysis	NOUN
ejpam-5893	332	5	of	of	ADP
ejpam-5893	332	6	fractional	fractional	ADJ
ejpam-5893	332	7	estevez	estevez	PROPN
ejpam-5893	332	8	–	–	PUNCT
ejpam-5893	332	9	mansfield	mansfield	PROPN
ejpam-5893	332	10	–	–	PUNCT
ejpam-5893	332	11	clarkson	clarkson	PROPN
ejpam-5893	332	12	equation	equation	NOUN
ejpam-5893	332	13	.	.	PUNCT
ejpam-5893	333	1	fractal	fractal	PROPN
ejpam-5893	333	2	and	and	CCONJ
ejpam-5893	333	3	fractional	fractional	ADJ
ejpam-5893	333	4	,	,	PUNCT
ejpam-5893	333	5	8(8):467	8(8):467	NUM
ejpam-5893	333	6	,	,	PUNCT
ejpam-5893	333	7	2024	2024	NUM
ejpam-5893	333	8	.	.	PUNCT
ejpam-5893	334	1	[	[	X
ejpam-5893	334	2	12	12	NUM
ejpam-5893	334	3	]	]	X
ejpam-5893	334	4	yan	yan	PROPN
ejpam-5893	334	5	zhen	zhen	PROPN
ejpam-5893	334	6	-	-	PUNCT
ejpam-5893	334	7	ya	ya	PROPN
ejpam-5893	334	8	.	.	PUNCT
ejpam-5893	335	1	abundant	abundant	ADJ
ejpam-5893	335	2	symmetries	symmetry	NOUN
ejpam-5893	335	3	and	and	CCONJ
ejpam-5893	335	4	exact	exact	ADJ
ejpam-5893	335	5	compacton	compacton	NOUN
ejpam-5893	335	6	-	-	PUNCT
ejpam-5893	335	7	like	like	ADJ
ejpam-5893	335	8	structures	structure	NOUN
ejpam-5893	335	9	in	in	ADP
ejpam-5893	335	10	the	the	DET
ejpam-5893	335	11	twoparameter	twoparameter	ADJ
ejpam-5893	335	12	family	family	NOUN
ejpam-5893	335	13	of	of	ADP
ejpam-5893	335	14	the	the	DET
ejpam-5893	335	15	estevez	estevez	PROPN
ejpam-5893	335	16	–	–	PUNCT
ejpam-5893	335	17	mansfield	mansfield	PROPN
ejpam-5893	335	18	–	–	PUNCT
ejpam-5893	335	19	clarkson	clarkson	PROPN
ejpam-5893	335	20	equations	equation	NOUN
ejpam-5893	335	21	.	.	PUNCT
ejpam-5893	336	1	communications	communication	NOUN
ejpam-5893	336	2	in	in	ADP
ejpam-5893	336	3	theoretical	theoretical	ADJ
ejpam-5893	336	4	physics	physics	NOUN
ejpam-5893	336	5	,	,	PUNCT
ejpam-5893	336	6	37(1):27	37(1):27	NUM
ejpam-5893	336	7	,	,	PUNCT
ejpam-5893	336	8	2002	2002	NUM
ejpam-5893	336	9	.	.	PUNCT
ejpam-5893	337	1	[	[	X
ejpam-5893	337	2	13	13	NUM
ejpam-5893	337	3	]	]	PUNCT
ejpam-5893	337	4	purobi	purobi	PROPN
ejpam-5893	337	5	rani	rani	PROPN
ejpam-5893	337	6	kundu	kundu	PROPN
ejpam-5893	337	7	,	,	PUNCT
ejpam-5893	337	8	md	md	PROPN
ejpam-5893	337	9	rezwan	rezwan	PROPN
ejpam-5893	337	10	ahamed	ahamed	PROPN
ejpam-5893	337	11	fahim	fahim	PROPN
ejpam-5893	337	12	,	,	PUNCT
ejpam-5893	337	13	md	md	PROPN
ejpam-5893	337	14	ekramul	ekramul	PROPN
ejpam-5893	337	15	islam	islam	PROPN
ejpam-5893	337	16	,	,	PUNCT
ejpam-5893	337	17	and	and	CCONJ
ejpam-5893	337	18	m	m	PROPN
ejpam-5893	337	19	ali	ali	PROPN
ejpam-5893	337	20	akbar	akbar	NOUN
ejpam-5893	337	21	.	.	PUNCT
ejpam-5893	338	1	the	the	DET
ejpam-5893	338	2	sine	sine	NOUN
ejpam-5893	338	3	-	-	PUNCT
ejpam-5893	338	4	gordon	gordon	PROPN
ejpam-5893	338	5	expansion	expansion	NOUN
ejpam-5893	338	6	method	method	NOUN
ejpam-5893	338	7	for	for	ADP
ejpam-5893	338	8	higher	high	ADJ
ejpam-5893	338	9	-	-	PUNCT
ejpam-5893	338	10	dimensional	dimensional	ADJ
ejpam-5893	338	11	nlees	nlee	NOUN
ejpam-5893	338	12	and	and	CCONJ
ejpam-5893	338	13	parametric	parametric	ADJ
ejpam-5893	338	14	analysis	analysis	NOUN
ejpam-5893	338	15	.	.	PUNCT
ejpam-5893	339	1	heliyon	heliyon	NOUN
ejpam-5893	339	2	,	,	PUNCT
ejpam-5893	339	3	7(3	7(3	NUM
ejpam-5893	339	4	)	)	PUNCT
ejpam-5893	339	5	,	,	PUNCT
ejpam-5893	339	6	2021	2021	NUM
ejpam-5893	339	7	.	.	PUNCT
ejpam-5893	340	1	[	[	X
ejpam-5893	340	2	14	14	NUM
ejpam-5893	340	3	]	]	X
ejpam-5893	340	4	muhammad	muhammad	PROPN
ejpam-5893	340	5	akbar	akbar	PROPN
ejpam-5893	340	6	,	,	PUNCT
ejpam-5893	340	7	rashid	rashid	PROPN
ejpam-5893	340	8	nawaz	nawaz	PROPN
ejpam-5893	340	9	,	,	PUNCT
ejpam-5893	340	10	sumbal	sumbal	PROPN
ejpam-5893	340	11	ahsan	ahsan	PROPN
ejpam-5893	340	12	,	,	PUNCT
ejpam-5893	340	13	kottakkaran	kottakkaran	VERB
ejpam-5893	340	14	sooppy	sooppy	ADJ
ejpam-5893	340	15	nisar	nisar	PROPN
ejpam-5893	340	16	,	,	PUNCT
ejpam-5893	340	17	kamal	kamal	PROPN
ejpam-5893	340	18	shah	shah	PROPN
ejpam-5893	340	19	,	,	PUNCT
ejpam-5893	340	20	emad	emad	PROPN
ejpam-5893	340	21	e	e	PROPN
ejpam-5893	340	22	mahmoud	mahmoud	PROPN
ejpam-5893	340	23	,	,	PUNCT
ejpam-5893	340	24	and	and	CCONJ
ejpam-5893	340	25	mm	mm	PROPN
ejpam-5893	340	26	alqarni	alqarni	PROPN
ejpam-5893	340	27	.	.	PUNCT
ejpam-5893	341	1	fractional	fractional	ADJ
ejpam-5893	341	2	power	power	NOUN
ejpam-5893	341	3	series	series	PROPN
ejpam-5893	341	4	approach	approach	NOUN
ejpam-5893	341	5	for	for	ADP
ejpam-5893	341	6	the	the	DET
ejpam-5893	341	7	solution	solution	NOUN
ejpam-5893	341	8	of	of	ADP
ejpam-5893	341	9	fractional	fractional	ADJ
ejpam-5893	341	10	-	-	PUNCT
ejpam-5893	341	11	order	order	NOUN
ejpam-5893	341	12	integro	integro	ADJ
ejpam-5893	341	13	-	-	PUNCT
ejpam-5893	341	14	differential	differential	NOUN
ejpam-5893	341	15	equations	equation	NOUN
ejpam-5893	341	16	.	.	PUNCT
ejpam-5893	342	1	fractals	fractal	NOUN
ejpam-5893	342	2	,	,	PUNCT
ejpam-5893	342	3	30(01):2240016	30(01):2240016	NUM
ejpam-5893	342	4	,	,	PUNCT
ejpam-5893	342	5	2022	2022	NUM
ejpam-5893	342	6	.	.	PUNCT
ejpam-5893	343	1	[	[	X
ejpam-5893	343	2	15	15	NUM
ejpam-5893	343	3	]	]	X
ejpam-5893	343	4	hikmet	hikmet	X
ejpam-5893	343	5	koyunbakan	koyunbakan	X
ejpam-5893	343	6	,	,	PUNCT
ejpam-5893	343	7	kamal	kamal	PROPN
ejpam-5893	343	8	shah	shah	NOUN
ejpam-5893	343	9	,	,	PUNCT
ejpam-5893	343	10	and	and	CCONJ
ejpam-5893	343	11	thabet	thabet	ADJ
ejpam-5893	343	12	abdeljawad	abdeljawad	NOUN
ejpam-5893	343	13	.	.	PUNCT
ejpam-5893	344	1	well	well	ADJ
ejpam-5893	344	2	-	-	PUNCT
ejpam-5893	344	3	posedness	posedness	NOUN
ejpam-5893	344	4	of	of	ADP
ejpam-5893	344	5	inverse	inverse	NOUN
ejpam-5893	344	6	sturm	sturm	PROPN
ejpam-5893	344	7	–	–	PUNCT
ejpam-5893	344	8	liouville	liouville	NOUN
ejpam-5893	344	9	problem	problem	NOUN
ejpam-5893	344	10	with	with	ADP
ejpam-5893	344	11	fractional	fractional	ADJ
ejpam-5893	344	12	derivative	derivative	ADJ
ejpam-5893	344	13	.	.	PUNCT
ejpam-5893	345	1	qualitative	qualitative	ADJ
ejpam-5893	345	2	theory	theory	NOUN
ejpam-5893	345	3	of	of	ADP
ejpam-5893	345	4	dynamical	dynamical	ADJ
ejpam-5893	345	5	systems	system	NOUN
ejpam-5893	345	6	,	,	PUNCT
ejpam-5893	345	7	22(1):23	22(1):23	NUM
ejpam-5893	345	8	,	,	PUNCT
ejpam-5893	345	9	2023	2023	NUM
ejpam-5893	345	10	.	.	PUNCT
ejpam-5893	346	1	[	[	X
ejpam-5893	346	2	16	16	NUM
ejpam-5893	346	3	]	]	X
ejpam-5893	346	4	farman	farman	PROPN
ejpam-5893	346	5	ali	ali	PROPN
ejpam-5893	346	6	shah	shah	PROPN
ejpam-5893	346	7	,	,	PUNCT
ejpam-5893	346	8	kamran	kamran	PROPN
ejpam-5893	346	9	,	,	PUNCT
ejpam-5893	346	10	wadii	wadii	NOUN
ejpam-5893	346	11	boulila	boulila	PROPN
ejpam-5893	346	12	,	,	PUNCT
ejpam-5893	346	13	anis	anis	PROPN
ejpam-5893	346	14	koubaa	koubaa	PROPN
ejpam-5893	346	15	,	,	PUNCT
ejpam-5893	346	16	and	and	CCONJ
ejpam-5893	346	17	nabil	nabil	PROPN
ejpam-5893	346	18	mlaiki	mlaiki	PROPN
ejpam-5893	346	19	.	.	PUNCT
ejpam-5893	347	1	numerical	numerical	ADJ
ejpam-5893	347	2	solution	solution	NOUN
ejpam-5893	347	3	of	of	ADP
ejpam-5893	347	4	advection	advection	NOUN
ejpam-5893	347	5	–	–	PUNCT
ejpam-5893	347	6	diffusion	diffusion	NOUN
ejpam-5893	347	7	equation	equation	NOUN
ejpam-5893	347	8	of	of	ADP
ejpam-5893	347	9	fractional	fractional	ADJ
ejpam-5893	347	10	order	order	NOUN
ejpam-5893	347	11	using	use	VERB
ejpam-5893	347	12	chebyshev	chebyshev	NOUN
ejpam-5893	347	13	collocation	collocation	NOUN
ejpam-5893	347	14	method	method	NOUN
ejpam-5893	347	15	.	.	PUNCT
ejpam-5893	348	1	fractal	fractal	ADJ
ejpam-5893	348	2	and	and	CCONJ
ejpam-5893	348	3	fractional	fractional	ADJ
ejpam-5893	348	4	,	,	PUNCT
ejpam-5893	348	5	7(10):762	7(10):762	NUM
ejpam-5893	348	6	,	,	PUNCT
ejpam-5893	348	7	2023	2023	NUM
ejpam-5893	348	8	.	.	PUNCT
ejpam-5893	349	1	[	[	X
ejpam-5893	349	2	17	17	NUM
ejpam-5893	349	3	]	]	X
ejpam-5893	349	4	aqsa	aqsa	PROPN
ejpam-5893	349	5	umer	umer	PROPN
ejpam-5893	349	6	,	,	PUNCT
ejpam-5893	349	7	muhammad	muhammad	PROPN
ejpam-5893	349	8	abbas	abbas	PROPN
ejpam-5893	349	9	,	,	PUNCT
ejpam-5893	349	10	madiha	madiha	PROPN
ejpam-5893	349	11	shafiq	shafiq	PROPN
ejpam-5893	349	12	,	,	PUNCT
ejpam-5893	349	13	farah	farah	PROPN
ejpam-5893	349	14	aini	aini	PROPN
ejpam-5893	349	15	abdullah	abdullah	PROPN
ejpam-5893	349	16	,	,	PUNCT
ejpam-5893	349	17	manuel	manuel	PROPN
ejpam-5893	349	18	de	de	PROPN
ejpam-5893	349	19	la	la	PROPN
ejpam-5893	349	20	sen	sen	PROPN
ejpam-5893	349	21	,	,	PUNCT
ejpam-5893	349	22	and	and	CCONJ
ejpam-5893	349	23	thabet	thabet	ADJ
ejpam-5893	349	24	abdeljawad	abdeljawad	NOUN
ejpam-5893	349	25	.	.	PUNCT
ejpam-5893	350	1	numerical	numerical	ADJ
ejpam-5893	350	2	solutions	solution	NOUN
ejpam-5893	350	3	of	of	ADP
ejpam-5893	350	4	atangana	atangana	PROPN
ejpam-5893	350	5	-	-	PUNCT
ejpam-5893	350	6	baleanu	baleanu	ADJ
ejpam-5893	350	7	timefractional	timefractional	ADJ
ejpam-5893	350	8	advection	advection	NOUN
ejpam-5893	350	9	diffusion	diffusion	NOUN
ejpam-5893	350	10	equation	equation	NOUN
ejpam-5893	350	11	via	via	ADP
ejpam-5893	350	12	an	an	DET
ejpam-5893	350	13	extended	extend	VERB
ejpam-5893	350	14	cubic	cubic	ADJ
ejpam-5893	350	15	b	b	NOUN
ejpam-5893	350	16	-	-	PUNCT
ejpam-5893	350	17	spline	spline	NOUN
ejpam-5893	350	18	technique	technique	NOUN
ejpam-5893	350	19	.	.	PUNCT
ejpam-5893	351	1	alexandria	alexandria	PROPN
ejpam-5893	351	2	engineering	engineering	PROPN
ejpam-5893	351	3	journal	journal	PROPN
ejpam-5893	351	4	,	,	PUNCT
ejpam-5893	351	5	74:285–300	74:285–300	PROPN
ejpam-5893	351	6	,	,	PUNCT
ejpam-5893	351	7	2023	2023	NUM
ejpam-5893	351	8	.	.	PUNCT
ejpam-5893	352	1	[	[	X
ejpam-5893	352	2	18	18	NUM
ejpam-5893	352	3	]	]	X
ejpam-5893	352	4	muhammad	muhammad	PROPN
ejpam-5893	352	5	bilal	bilal	PROPN
ejpam-5893	352	6	,	,	PUNCT
ejpam-5893	352	7	javed	javed	PROPN
ejpam-5893	352	8	iqbal	iqbal	PROPN
ejpam-5893	352	9	,	,	PUNCT
ejpam-5893	352	10	kamal	kamal	PROPN
ejpam-5893	352	11	shah	shah	PROPN
ejpam-5893	352	12	,	,	PUNCT
ejpam-5893	352	13	bahaaeldin	bahaaeldin	VERB
ejpam-5893	352	14	abdalla	abdalla	PROPN
ejpam-5893	352	15	,	,	PUNCT
ejpam-5893	352	16	thabet	thabet	ADJ
ejpam-5893	352	17	abdeljawad	abdeljawad	NOUN
ejpam-5893	352	18	,	,	PUNCT
ejpam-5893	352	19	and	and	CCONJ
ejpam-5893	352	20	ikram	ikram	PROPN
ejpam-5893	352	21	ullah	ullah	PROPN
ejpam-5893	352	22	.	.	PUNCT
ejpam-5893	353	1	analytical	analytical	ADJ
ejpam-5893	353	2	solutions	solution	NOUN
ejpam-5893	353	3	of	of	ADP
ejpam-5893	353	4	the	the	DET
ejpam-5893	353	5	space	space	NOUN
ejpam-5893	353	6	–	–	PUNCT
ejpam-5893	353	7	time	time	NOUN
ejpam-5893	353	8	fractional	fractional	ADJ
ejpam-5893	353	9	kundu	kundu	NOUN
ejpam-5893	353	10	–	–	PUNCT
ejpam-5893	353	11	eckhaus	eckhaus	NOUN
ejpam-5893	353	12	equation	equation	NOUN
ejpam-5893	353	13	by	by	ADP
ejpam-5893	353	14	using	use	VERB
ejpam-5893	353	15	modified	modify	VERB
ejpam-5893	353	16	extended	extend	VERB
ejpam-5893	353	17	direct	direct	ADJ
ejpam-5893	353	18	algebraic	algebraic	ADJ
ejpam-5893	353	19	method	method	NOUN
ejpam-5893	353	20	.	.	PUNCT
ejpam-5893	354	1	partial	partial	ADJ
ejpam-5893	354	2	difb	difb	NOUN
ejpam-5893	354	3	.	.	PUNCT
ejpam-5893	355	1	yasmeen	yasmeen	PROPN
ejpam-5893	355	2	,	,	PUNCT
ejpam-5893	355	3	k.	k.	PROPN
ejpam-5893	355	4	ahmad	ahmad	PROPN
ejpam-5893	355	5	,	,	PUNCT
ejpam-5893	355	6	n.	n.	PROPN
ejpam-5893	355	7	fatima	fatima	PROPN
ejpam-5893	355	8	/	/	PUNCT
ejpam-5893	355	9	eur	eur	PROPN
ejpam-5893	355	10	.	.	PUNCT
ejpam-5893	356	1	j.	j.	PROPN
ejpam-5893	356	2	pure	pure	PROPN
ejpam-5893	356	3	appl	appl	PROPN
ejpam-5893	356	4	.	.	PROPN
ejpam-5893	356	5	math	math	PROPN
ejpam-5893	356	6	,	,	PUNCT
ejpam-5893	356	7	18	18	NUM
ejpam-5893	356	8	(	(	PUNCT
ejpam-5893	356	9	2	2	NUM
ejpam-5893	356	10	)	)	PUNCT
ejpam-5893	356	11	(	(	PUNCT
ejpam-5893	356	12	2025	2025	NUM
ejpam-5893	356	13	)	)	PUNCT
ejpam-5893	356	14	,	,	PUNCT
ejpam-5893	356	15	5893	5893	NUM
ejpam-5893	356	16	17	17	NUM
ejpam-5893	356	17	of	of	ADP
ejpam-5893	356	18	17	17	NUM
ejpam-5893	356	19	ferential	ferential	ADJ
ejpam-5893	356	20	equations	equation	NOUN
ejpam-5893	356	21	in	in	ADP
ejpam-5893	356	22	applied	applied	ADJ
ejpam-5893	356	23	mathematics	mathematic	NOUN
ejpam-5893	356	24	,	,	PUNCT
ejpam-5893	356	25	11:100832	11:100832	NUM
ejpam-5893	356	26	,	,	PUNCT
ejpam-5893	356	27	2024	2024	NUM
ejpam-5893	356	28	.	.	PUNCT
ejpam-5893	357	1	[	[	X
ejpam-5893	357	2	19	19	NUM
ejpam-5893	357	3	]	]	PUNCT
ejpam-5893	357	4	xiaoming	xiaoming	PROPN
ejpam-5893	357	5	wang	wang	PROPN
ejpam-5893	357	6	,	,	PUNCT
ejpam-5893	357	7	haiqa	haiqa	PROPN
ejpam-5893	357	8	ehsan	ehsan	PROPN
ejpam-5893	357	9	,	,	PUNCT
ejpam-5893	357	10	muhammad	muhammad	PROPN
ejpam-5893	357	11	abbas	abbas	PROPN
ejpam-5893	357	12	,	,	PUNCT
ejpam-5893	357	13	ghazala	ghazala	PROPN
ejpam-5893	357	14	akram	akram	PROPN
ejpam-5893	357	15	,	,	PUNCT
ejpam-5893	357	16	maasoomah	maasoomah	NOUN
ejpam-5893	357	17	sadaf	sadaf	NOUN
ejpam-5893	357	18	,	,	PUNCT
ejpam-5893	357	19	and	and	CCONJ
ejpam-5893	357	20	thabet	thabet	ADJ
ejpam-5893	357	21	abdeljawad	abdeljawad	NOUN
ejpam-5893	357	22	.	.	PUNCT
ejpam-5893	358	1	analytical	analytical	ADJ
ejpam-5893	358	2	solitary	solitary	ADJ
ejpam-5893	358	3	wave	wave	NOUN
ejpam-5893	358	4	solutions	solution	NOUN
ejpam-5893	358	5	of	of	ADP
ejpam-5893	358	6	a	a	DET
ejpam-5893	358	7	time	time	NOUN
ejpam-5893	358	8	-	-	PUNCT
ejpam-5893	358	9	fractional	fractional	ADJ
ejpam-5893	358	10	thin	thin	ADJ
ejpam-5893	358	11	-	-	PUNCT
ejpam-5893	358	12	film	film	NOUN
ejpam-5893	358	13	ferroelectric	ferroelectric	ADJ
ejpam-5893	358	14	material	material	NOUN
ejpam-5893	358	15	equation	equation	NOUN
ejpam-5893	358	16	involving	involve	VERB
ejpam-5893	358	17	beta	beta	NOUN
ejpam-5893	358	18	-	-	PUNCT
ejpam-5893	358	19	derivative	derivative	NOUN
ejpam-5893	358	20	using	use	VERB
ejpam-5893	358	21	modified	modify	VERB
ejpam-5893	358	22	auxiliary	auxiliary	ADJ
ejpam-5893	358	23	equation	equation	NOUN
ejpam-5893	358	24	method	method	NOUN
ejpam-5893	358	25	.	.	PUNCT
ejpam-5893	359	1	results	result	NOUN
ejpam-5893	359	2	in	in	ADP
ejpam-5893	359	3	physics	physics	NOUN
ejpam-5893	359	4	,	,	PUNCT
ejpam-5893	359	5	48:106411	48:106411	NUM
ejpam-5893	359	6	,	,	PUNCT
ejpam-5893	359	7	2023	2023	NUM
ejpam-5893	359	8	.	.	PUNCT
ejpam-5893	360	1	[	[	X
ejpam-5893	360	2	20	20	NUM
ejpam-5893	360	3	]	]	PUNCT
ejpam-5893	360	4	muhammad	muhammad	PROPN
ejpam-5893	360	5	arfan	arfan	PROPN
ejpam-5893	360	6	,	,	PUNCT
ejpam-5893	360	7	kamal	kamal	PROPN
ejpam-5893	360	8	shah	shah	PROPN
ejpam-5893	360	9	,	,	PUNCT
ejpam-5893	360	10	aman	aman	PROPN
ejpam-5893	360	11	ullah	ullah	PROPN
ejpam-5893	360	12	,	,	PUNCT
ejpam-5893	360	13	and	and	CCONJ
ejpam-5893	360	14	thabet	thabet	ADJ
ejpam-5893	360	15	abdeljawad	abdeljawad	NOUN
ejpam-5893	360	16	.	.	PUNCT
ejpam-5893	361	1	study	study	NOUN
ejpam-5893	361	2	of	of	ADP
ejpam-5893	361	3	fuzzy	fuzzy	ADJ
ejpam-5893	361	4	fractional	fractional	ADJ
ejpam-5893	361	5	order	order	NOUN
ejpam-5893	361	6	diffusion	diffusion	NOUN
ejpam-5893	361	7	problem	problem	NOUN
ejpam-5893	361	8	under	under	ADP
ejpam-5893	361	9	the	the	DET
ejpam-5893	361	10	mittag	mittag	ADJ
ejpam-5893	361	11	-	-	PUNCT
ejpam-5893	361	12	leffler	leffler	NOUN
ejpam-5893	361	13	kernel	kernel	PROPN
ejpam-5893	361	14	law	law	NOUN
ejpam-5893	361	15	.	.	PUNCT
ejpam-5893	362	1	physica	physica	PROPN
ejpam-5893	362	2	scripta	scripta	PROPN
ejpam-5893	362	3	,	,	PUNCT
ejpam-5893	362	4	96(7):074002	96(7):074002	NUM
ejpam-5893	362	5	,	,	PUNCT
ejpam-5893	362	6	2021	2021	NUM
ejpam-5893	362	7	.	.	PUNCT
ejpam-5893	363	1	[	[	X
ejpam-5893	363	2	21	21	NUM
ejpam-5893	363	3	]	]	X
ejpam-5893	363	4	rohul	rohul	PROPN
ejpam-5893	363	5	amin	amin	PROPN
ejpam-5893	363	6	,	,	PUNCT
ejpam-5893	363	7	kamal	kamal	PROPN
ejpam-5893	363	8	shah	shah	PROPN
ejpam-5893	363	9	,	,	PUNCT
ejpam-5893	363	10	qasem	qasem	PROPN
ejpam-5893	363	11	m	m	PROPN
ejpam-5893	363	12	al	al	PROPN
ejpam-5893	363	13	-	-	PUNCT
ejpam-5893	363	14	mdallal	mdallal	PROPN
ejpam-5893	363	15	,	,	PUNCT
ejpam-5893	363	16	imran	imran	PROPN
ejpam-5893	363	17	khan	khan	PROPN
ejpam-5893	363	18	,	,	PUNCT
ejpam-5893	363	19	and	and	CCONJ
ejpam-5893	363	20	muhammad	muhammad	PROPN
ejpam-5893	363	21	asif	asif	PROPN
ejpam-5893	363	22	.	.	PUNCT
ejpam-5893	363	23	efficient	efficient	ADJ
ejpam-5893	363	24	numerical	numerical	ADJ
ejpam-5893	363	25	algorithm	algorithm	NOUN
ejpam-5893	363	26	for	for	ADP
ejpam-5893	363	27	the	the	DET
ejpam-5893	363	28	solution	solution	NOUN
ejpam-5893	363	29	of	of	ADP
ejpam-5893	363	30	eight	eight	NUM
ejpam-5893	363	31	order	order	NOUN
ejpam-5893	363	32	boundary	boundary	ADJ
ejpam-5893	363	33	value	value	NOUN
ejpam-5893	363	34	problems	problem	NOUN
ejpam-5893	363	35	by	by	ADP
ejpam-5893	363	36	haar	haar	PROPN
ejpam-5893	363	37	wavelet	wavelet	NOUN
ejpam-5893	363	38	method	method	NOUN
ejpam-5893	363	39	.	.	PUNCT
ejpam-5893	364	1	international	international	ADJ
ejpam-5893	364	2	journal	journal	PROPN
ejpam-5893	364	3	of	of	ADP
ejpam-5893	364	4	applied	applied	ADJ
ejpam-5893	364	5	and	and	CCONJ
ejpam-5893	364	6	computational	computational	ADJ
ejpam-5893	364	7	mathematics	mathematic	NOUN
ejpam-5893	364	8	,	,	PUNCT
ejpam-5893	364	9	7:1–18	7:1–18	NUM
ejpam-5893	364	10	,	,	PUNCT
ejpam-5893	364	11	2021	2021	NUM
ejpam-5893	364	12	.	.	PUNCT
ejpam-5893	365	1	[	[	X
ejpam-5893	365	2	22	22	NUM
ejpam-5893	365	3	]	]	X
ejpam-5893	365	4	bushra	bushra	PROPN
ejpam-5893	365	5	yasmeen	yasmeen	PROPN
ejpam-5893	365	6	,	,	PUNCT
ejpam-5893	365	7	khalil	khalil	PROPN
ejpam-5893	365	8	ahmad	ahmad	PROPN
ejpam-5893	365	9	,	,	PUNCT
ejpam-5893	365	10	and	and	CCONJ
ejpam-5893	365	11	nahid	nahid	PROPN
ejpam-5893	365	12	fatima	fatima	PROPN
ejpam-5893	365	13	.	.	PUNCT
ejpam-5893	366	1	analytic	analytic	ADJ
ejpam-5893	366	2	solutions	solution	NOUN
ejpam-5893	366	3	of	of	ADP
ejpam-5893	366	4	the	the	DET
ejpam-5893	366	5	timefractional	timefractional	ADJ
ejpam-5893	366	6	date	date	NOUN
ejpam-5893	366	7	-	-	PUNCT
ejpam-5893	366	8	jimbo	jimbo	NOUN
ejpam-5893	366	9	-	-	PUNCT
ejpam-5893	366	10	kashiwara	kashiwara	PROPN
ejpam-5893	366	11	-	-	PUNCT
ejpam-5893	366	12	miwa	miwa	PROPN
ejpam-5893	366	13	equation	equation	NOUN
ejpam-5893	366	14	via	via	ADP
ejpam-5893	366	15	new	new	ADJ
ejpam-5893	366	16	function	function	NOUN
ejpam-5893	366	17	transformations	transformation	NOUN
ejpam-5893	366	18	.	.	PUNCT
ejpam-5893	367	1	european	european	ADJ
ejpam-5893	367	2	journal	journal	PROPN
ejpam-5893	367	3	of	of	ADP
ejpam-5893	367	4	pure	pure	ADJ
ejpam-5893	367	5	and	and	CCONJ
ejpam-5893	367	6	applied	applied	ADJ
ejpam-5893	367	7	mathematics	mathematic	NOUN
ejpam-5893	367	8	,	,	PUNCT
ejpam-5893	367	9	18(1):5756–5756	18(1):5756–5756	NUM
ejpam-5893	367	10	,	,	PUNCT
ejpam-5893	367	11	2025	2025	NUM
ejpam-5893	367	12	.	.	PUNCT