id	sid	tid	token	lemma	pos
ejpam-5756	1	1	european	european	PROPN
ejpam-5756	1	2	journal	journal	PROPN
ejpam-5756	1	3	of	of	ADP
ejpam-5756	1	4	pure	pure	ADJ
ejpam-5756	1	5	and	and	CCONJ
ejpam-5756	1	6	applied	applied	ADJ
ejpam-5756	1	7	mathematics	mathematic	NOUN
ejpam-5756	1	8	2025	2025	NUM
ejpam-5756	1	9	,	,	PUNCT
ejpam-5756	1	10	vol	vol	NOUN
ejpam-5756	1	11	.	.	PROPN
ejpam-5756	1	12	18	18	NUM
ejpam-5756	1	13	,	,	PUNCT
ejpam-5756	1	14	issue	issue	NOUN
ejpam-5756	1	15	1	1	NUM
ejpam-5756	1	16	,	,	PUNCT
ejpam-5756	1	17	article	article	NOUN
ejpam-5756	1	18	number	number	NOUN
ejpam-5756	1	19	5756	5756	NUM
ejpam-5756	1	20	issn	issn	VERB
ejpam-5756	1	21	1307	1307	NUM
ejpam-5756	1	22	-	-	SYM
ejpam-5756	1	23	5543	5543	NUM
ejpam-5756	1	24	–	–	PUNCT
ejpam-5756	1	25	ejpam.com	ejpam.com	X
ejpam-5756	1	26	published	publish	VERB
ejpam-5756	1	27	by	by	ADP
ejpam-5756	1	28	new	new	PROPN
ejpam-5756	1	29	york	york	PROPN
ejpam-5756	1	30	business	business	PROPN
ejpam-5756	1	31	global	global	ADJ
ejpam-5756	1	32	analytic	analytic	ADJ
ejpam-5756	1	33	solutions	solution	NOUN
ejpam-5756	1	34	of	of	ADP
ejpam-5756	1	35	the	the	DET
ejpam-5756	1	36	time	time	NOUN
ejpam-5756	1	37	-	-	PUNCT
ejpam-5756	1	38	fractional	fractional	ADJ
ejpam-5756	1	39	date	date	NOUN
ejpam-5756	1	40	-	-	PUNCT
ejpam-5756	1	41	jimbo	jimbo	NOUN
ejpam-5756	1	42	-	-	PUNCT
ejpam-5756	1	43	kashiwara	kashiwara	PROPN
ejpam-5756	1	44	-	-	PUNCT
ejpam-5756	1	45	miwa	miwa	PROPN
ejpam-5756	1	46	equation	equation	NOUN
ejpam-5756	1	47	via	via	ADP
ejpam-5756	1	48	new	new	ADJ
ejpam-5756	1	49	function	function	NOUN
ejpam-5756	1	50	transformations	transformation	NOUN
ejpam-5756	1	51	bushra	bushra	PROPN
ejpam-5756	1	52	yasmeen1,∗	yasmeen1,∗	PROPN
ejpam-5756	1	53	,	,	PUNCT
ejpam-5756	1	54	khalil	khalil	PROPN
ejpam-5756	1	55	ahmad1	ahmad1	PROPN
ejpam-5756	1	56	,	,	PUNCT
ejpam-5756	1	57	nahid	nahid	PROPN
ejpam-5756	1	58	fatima2	fatima2	PROPN
ejpam-5756	1	59	1	1	NUM
ejpam-5756	1	60	department	department	NOUN
ejpam-5756	1	61	of	of	ADP
ejpam-5756	1	62	mathematics	mathematic	NOUN
ejpam-5756	1	63	,	,	PUNCT
ejpam-5756	1	64	faculty	faculty	NOUN
ejpam-5756	1	65	of	of	ADP
ejpam-5756	1	66	basic	basic	ADJ
ejpam-5756	1	67	and	and	CCONJ
ejpam-5756	1	68	applied	applied	ADJ
ejpam-5756	1	69	sciences	science	NOUN
ejpam-5756	1	70	,	,	PUNCT
ejpam-5756	1	71	air	air	NOUN
ejpam-5756	1	72	university	university	PROPN
ejpam-5756	1	73	,	,	PUNCT
ejpam-5756	1	74	paf	paf	PROPN
ejpam-5756	1	75	complex	complex	PROPN
ejpam-5756	1	76	e-9	e-9	PROPN
ejpam-5756	1	77	,	,	PUNCT
ejpam-5756	1	78	islamabad	islamabad	NOUN
ejpam-5756	1	79	44000	44000	NUM
ejpam-5756	1	80	,	,	PUNCT
ejpam-5756	1	81	pakistan	pakistan	PROPN
ejpam-5756	1	82	2	2	NUM
ejpam-5756	1	83	department	department	NOUN
ejpam-5756	1	84	of	of	ADP
ejpam-5756	1	85	mathematics	mathematic	NOUN
ejpam-5756	1	86	and	and	CCONJ
ejpam-5756	1	87	sciences	science	NOUN
ejpam-5756	1	88	,	,	PUNCT
ejpam-5756	1	89	prince	prince	PROPN
ejpam-5756	1	90	sultan	sultan	PROPN
ejpam-5756	1	91	university	university	PROPN
ejpam-5756	1	92	,	,	PUNCT
ejpam-5756	1	93	p.o.box	p.o.box	PROPN
ejpam-5756	1	94	no	no	NOUN
ejpam-5756	1	95	.	.	PUNCT
ejpam-5756	1	96	66833	66833	NUM
ejpam-5756	1	97	,	,	PUNCT
ejpam-5756	1	98	rafha	rafha	PROPN
ejpam-5756	1	99	street	street	PROPN
ejpam-5756	1	100	,	,	PUNCT
ejpam-5756	1	101	riyadh	riyadh	PROPN
ejpam-5756	1	102	11586	11586	NUM
ejpam-5756	1	103	,	,	PUNCT
ejpam-5756	1	104	saudi	saudi	PROPN
ejpam-5756	1	105	arabia	arabia	PROPN
ejpam-5756	1	106	abstract	abstract	NOUN
ejpam-5756	1	107	.	.	PUNCT
ejpam-5756	2	1	in	in	ADP
ejpam-5756	2	2	this	this	DET
ejpam-5756	2	3	paper	paper	NOUN
ejpam-5756	2	4	,	,	PUNCT
ejpam-5756	2	5	a	a	DET
ejpam-5756	2	6	new	new	ADJ
ejpam-5756	2	7	analytical	analytical	ADJ
ejpam-5756	2	8	framework	framework	NOUN
ejpam-5756	2	9	for	for	ADP
ejpam-5756	2	10	solving	solve	VERB
ejpam-5756	2	11	the	the	DET
ejpam-5756	2	12	fundamental	fundamental	ADJ
ejpam-5756	2	13	nonlinear	nonlinear	ADJ
ejpam-5756	2	14	model	model	NOUN
ejpam-5756	2	15	,	,	PUNCT
ejpam-5756	2	16	the	the	DET
ejpam-5756	2	17	time	time	NOUN
ejpam-5756	2	18	-	-	PUNCT
ejpam-5756	2	19	fractional	fractional	ADJ
ejpam-5756	2	20	date	date	NOUN
ejpam-5756	2	21	-	-	PUNCT
ejpam-5756	2	22	jimbo	jimbo	NOUN
ejpam-5756	2	23	-	-	PUNCT
ejpam-5756	2	24	kashiwara	kashiwara	PROPN
ejpam-5756	2	25	-	-	PUNCT
ejpam-5756	2	26	miwa	miwa	PROPN
ejpam-5756	2	27	equation	equation	NOUN
ejpam-5756	2	28	,	,	PUNCT
ejpam-5756	2	29	is	be	AUX
ejpam-5756	2	30	proposed	propose	VERB
ejpam-5756	2	31	.	.	PUNCT
ejpam-5756	3	1	the	the	DET
ejpam-5756	3	2	time	time	NOUN
ejpam-5756	3	3	-	-	PUNCT
ejpam-5756	3	4	fractional	fractional	ADJ
ejpam-5756	3	5	datejimbo	datejimbo	NOUN
ejpam-5756	3	6	-	-	PUNCT
ejpam-5756	3	7	kashiwara	kashiwara	PROPN
ejpam-5756	3	8	-	-	PUNCT
ejpam-5756	3	9	miwa	miwa	PROPN
ejpam-5756	3	10	equation	equation	NOUN
ejpam-5756	3	11	is	be	AUX
ejpam-5756	3	12	made	make	VERB
ejpam-5756	3	13	simpler	simple	ADJ
ejpam-5756	3	14	by	by	ADP
ejpam-5756	3	15	reducing	reduce	VERB
ejpam-5756	3	16	it	it	PRON
ejpam-5756	3	17	to	to	ADP
ejpam-5756	3	18	an	an	DET
ejpam-5756	3	19	ordinary	ordinary	ADJ
ejpam-5756	3	20	differential	differential	ADJ
ejpam-5756	3	21	equation	equation	NOUN
ejpam-5756	3	22	through	through	ADP
ejpam-5756	3	23	the	the	DET
ejpam-5756	3	24	power	power	NOUN
ejpam-5756	3	25	index	index	NOUN
ejpam-5756	3	26	method	method	NOUN
ejpam-5756	3	27	’s	’s	PART
ejpam-5756	3	28	multiplication	multiplication	NOUN
ejpam-5756	3	29	of	of	ADP
ejpam-5756	3	30	variables	variable	NOUN
ejpam-5756	3	31	x	x	PUNCT
ejpam-5756	3	32	and	and	CCONJ
ejpam-5756	3	33	t.	t.	NOUN
ejpam-5756	3	34	because	because	SCONJ
ejpam-5756	3	35	it	it	PRON
ejpam-5756	3	36	permits	permit	VERB
ejpam-5756	3	37	a	a	DET
ejpam-5756	3	38	change	change	NOUN
ejpam-5756	3	39	in	in	ADP
ejpam-5756	3	40	variables	variable	NOUN
ejpam-5756	3	41	,	,	PUNCT
ejpam-5756	3	42	which	which	PRON
ejpam-5756	3	43	can	can	AUX
ejpam-5756	3	44	uncover	uncover	VERB
ejpam-5756	3	45	a	a	DET
ejpam-5756	3	46	hidden	hide	VERB
ejpam-5756	3	47	pattern	pattern	NOUN
ejpam-5756	3	48	in	in	ADP
ejpam-5756	3	49	the	the	DET
ejpam-5756	3	50	equation	equation	NOUN
ejpam-5756	3	51	,	,	PUNCT
ejpam-5756	3	52	multiplying	multiply	VERB
ejpam-5756	3	53	x	x	X
ejpam-5756	3	54	and	and	CCONJ
ejpam-5756	3	55	t	t	PROPN
ejpam-5756	3	56	is	be	AUX
ejpam-5756	3	57	significant	significant	ADJ
ejpam-5756	3	58	.	.	PUNCT
ejpam-5756	4	1	the	the	DET
ejpam-5756	4	2	original	original	ADJ
ejpam-5756	4	3	equation	equation	NOUN
ejpam-5756	4	4	’s	’s	PART
ejpam-5756	4	5	terms	term	NOUN
ejpam-5756	4	6	may	may	AUX
ejpam-5756	4	7	be	be	AUX
ejpam-5756	4	8	removed	remove	VERB
ejpam-5756	4	9	or	or	CCONJ
ejpam-5756	4	10	their	their	PRON
ejpam-5756	4	11	complexity	complexity	NOUN
ejpam-5756	4	12	decreased	decrease	VERB
ejpam-5756	4	13	with	with	ADP
ejpam-5756	4	14	the	the	DET
ejpam-5756	4	15	aid	aid	NOUN
ejpam-5756	4	16	of	of	ADP
ejpam-5756	4	17	this	this	DET
ejpam-5756	4	18	transformation	transformation	NOUN
ejpam-5756	4	19	.	.	PUNCT
ejpam-5756	5	1	the	the	DET
ejpam-5756	5	2	benefits	benefit	NOUN
ejpam-5756	5	3	of	of	ADP
ejpam-5756	5	4	various	various	ADJ
ejpam-5756	5	5	variable	variable	ADJ
ejpam-5756	5	6	transformations	transformation	NOUN
ejpam-5756	5	7	vary	vary	VERB
ejpam-5756	5	8	depending	depend	VERB
ejpam-5756	5	9	on	on	ADP
ejpam-5756	5	10	the	the	DET
ejpam-5756	5	11	particular	particular	ADJ
ejpam-5756	5	12	issue	issue	NOUN
ejpam-5756	5	13	,	,	PUNCT
ejpam-5756	5	14	but	but	CCONJ
ejpam-5756	5	15	this	this	DET
ejpam-5756	5	16	transformation	transformation	NOUN
ejpam-5756	5	17	has	have	VERB
ejpam-5756	5	18	the	the	DET
ejpam-5756	5	19	advantage	advantage	NOUN
ejpam-5756	5	20	of	of	ADP
ejpam-5756	5	21	simplifying	simplify	VERB
ejpam-5756	5	22	the	the	DET
ejpam-5756	5	23	equation	equation	NOUN
ejpam-5756	5	24	,	,	PUNCT
ejpam-5756	5	25	which	which	PRON
ejpam-5756	5	26	makes	make	VERB
ejpam-5756	5	27	it	it	PRON
ejpam-5756	5	28	simpler	simple	ADJ
ejpam-5756	5	29	to	to	PART
ejpam-5756	5	30	solve	solve	VERB
ejpam-5756	5	31	,	,	PUNCT
ejpam-5756	5	32	analyze	analyze	VERB
ejpam-5756	5	33	,	,	PUNCT
ejpam-5756	5	34	and	and	CCONJ
ejpam-5756	5	35	produce	produce	VERB
ejpam-5756	5	36	precise	precise	ADJ
ejpam-5756	5	37	and	and	CCONJ
ejpam-5756	5	38	explicit	explicit	ADJ
ejpam-5756	5	39	solutions	solution	NOUN
ejpam-5756	5	40	.	.	PUNCT
ejpam-5756	6	1	both	both	DET
ejpam-5756	6	2	rational	rational	ADJ
ejpam-5756	6	3	and	and	CCONJ
ejpam-5756	6	4	logarithm	logarithm	NOUN
ejpam-5756	6	5	functions	function	NOUN
ejpam-5756	6	6	are	be	AUX
ejpam-5756	6	7	present	present	ADJ
ejpam-5756	6	8	in	in	ADP
ejpam-5756	6	9	the	the	DET
ejpam-5756	6	10	solutions	solution	NOUN
ejpam-5756	6	11	that	that	PRON
ejpam-5756	6	12	were	be	AUX
ejpam-5756	6	13	obtained	obtain	VERB
ejpam-5756	6	14	.	.	PUNCT
ejpam-5756	7	1	through	through	ADP
ejpam-5756	7	2	3d	3d	PROPN
ejpam-5756	7	3	visualizations	visualization	NOUN
ejpam-5756	7	4	of	of	ADP
ejpam-5756	7	5	the	the	DET
ejpam-5756	7	6	general	general	ADJ
ejpam-5756	7	7	solutions	solution	NOUN
ejpam-5756	7	8	,	,	PUNCT
ejpam-5756	7	9	our	our	PRON
ejpam-5756	7	10	method	method	NOUN
ejpam-5756	7	11	offers	offer	VERB
ejpam-5756	7	12	a	a	DET
ejpam-5756	7	13	deeper	deep	ADJ
ejpam-5756	7	14	comprehension	comprehension	NOUN
ejpam-5756	7	15	of	of	ADP
ejpam-5756	7	16	the	the	DET
ejpam-5756	7	17	dynamics	dynamic	NOUN
ejpam-5756	7	18	of	of	ADP
ejpam-5756	7	19	the	the	DET
ejpam-5756	7	20	equation	equation	NOUN
ejpam-5756	7	21	.	.	PUNCT
ejpam-5756	8	1	the	the	DET
ejpam-5756	8	2	behavior	behavior	NOUN
ejpam-5756	8	3	of	of	ADP
ejpam-5756	8	4	the	the	DET
ejpam-5756	8	5	solution	solution	NOUN
ejpam-5756	8	6	to	to	ADP
ejpam-5756	8	7	the	the	DET
ejpam-5756	8	8	time	time	NOUN
ejpam-5756	8	9	-	-	PUNCT
ejpam-5756	8	10	fractional	fractional	ADJ
ejpam-5756	8	11	date	date	NOUN
ejpam-5756	8	12	-	-	PUNCT
ejpam-5756	8	13	jimbo	jimbo	NOUN
ejpam-5756	8	14	-	-	PUNCT
ejpam-5756	8	15	kashiwara	kashiwara	PROPN
ejpam-5756	8	16	-	-	PUNCT
ejpam-5756	8	17	miwa	miwa	PROPN
ejpam-5756	8	18	equation	equation	NOUN
ejpam-5756	8	19	is	be	AUX
ejpam-5756	8	20	depicted	depict	VERB
ejpam-5756	8	21	in	in	ADP
ejpam-5756	8	22	the	the	DET
ejpam-5756	8	23	paper	paper	NOUN
ejpam-5756	8	24	’s	’s	PART
ejpam-5756	8	25	3d	3d	NUM
ejpam-5756	8	26	visualization	visualization	NOUN
ejpam-5756	8	27	.	.	PUNCT
ejpam-5756	9	1	the	the	DET
ejpam-5756	9	2	solitons	soliton	NOUN
ejpam-5756	9	3	and	and	CCONJ
ejpam-5756	9	4	nonlinear	nonlinear	ADJ
ejpam-5756	9	5	wave	wave	NOUN
ejpam-5756	9	6	solutions	solution	NOUN
ejpam-5756	9	7	are	be	AUX
ejpam-5756	9	8	depicted	depict	VERB
ejpam-5756	9	9	in	in	ADP
ejpam-5756	9	10	each	each	DET
ejpam-5756	9	11	plot	plot	NOUN
ejpam-5756	9	12	.	.	PUNCT
ejpam-5756	10	1	our	our	PRON
ejpam-5756	10	2	findings	finding	NOUN
ejpam-5756	10	3	show	show	VERB
ejpam-5756	10	4	the	the	DET
ejpam-5756	10	5	effectiveness	effectiveness	NOUN
ejpam-5756	10	6	of	of	ADP
ejpam-5756	10	7	the	the	DET
ejpam-5756	10	8	power	power	NOUN
ejpam-5756	10	9	index	index	NOUN
ejpam-5756	10	10	method	method	NOUN
ejpam-5756	10	11	in	in	ADP
ejpam-5756	10	12	this	this	DET
ejpam-5756	10	13	situation	situation	NOUN
ejpam-5756	10	14	and	and	CCONJ
ejpam-5756	10	15	highlight	highlight	VERB
ejpam-5756	10	16	its	its	PRON
ejpam-5756	10	17	capacity	capacity	NOUN
ejpam-5756	10	18	to	to	PART
ejpam-5756	10	19	address	address	VERB
ejpam-5756	10	20	challenging	challenging	ADJ
ejpam-5756	10	21	issues	issue	NOUN
ejpam-5756	10	22	.	.	PUNCT
ejpam-5756	11	1	2020	2020	NUM
ejpam-5756	11	2	mathematics	mathematic	NOUN
ejpam-5756	11	3	subject	subject	NOUN
ejpam-5756	11	4	classifications	classification	NOUN
ejpam-5756	11	5	:	:	PUNCT
ejpam-5756	11	6	35qxx	35qxx	NOUN
ejpam-5756	11	7	,	,	PUNCT
ejpam-5756	11	8	26a33	26a33	NUM
ejpam-5756	11	9	key	key	ADJ
ejpam-5756	11	10	words	word	NOUN
ejpam-5756	11	11	and	and	CCONJ
ejpam-5756	11	12	phrases	phrase	NOUN
ejpam-5756	11	13	:	:	PUNCT
ejpam-5756	11	14	analytic	analytic	ADJ
ejpam-5756	11	15	solution	solution	NOUN
ejpam-5756	11	16	,	,	PUNCT
ejpam-5756	11	17	euler	euler	NOUN
ejpam-5756	11	18	’s	’s	PART
ejpam-5756	11	19	second	second	ADJ
ejpam-5756	11	20	order	order	NOUN
ejpam-5756	11	21	ode	ode	ADJ
ejpam-5756	11	22	,	,	PUNCT
ejpam-5756	11	23	time	time	NOUN
ejpam-5756	11	24	-	-	PUNCT
ejpam-5756	11	25	fractional	fractional	ADJ
ejpam-5756	11	26	derivative	derivative	ADJ
ejpam-5756	11	27	,	,	PUNCT
ejpam-5756	11	28	fractional	fractional	ADJ
ejpam-5756	11	29	calculus	calculus	NOUN
ejpam-5756	11	30	,	,	PUNCT
ejpam-5756	11	31	traveling	travel	VERB
ejpam-5756	11	32	wave	wave	NOUN
ejpam-5756	11	33	transformation	transformation	NOUN
ejpam-5756	11	34	1	1	NUM
ejpam-5756	11	35	.	.	PUNCT
ejpam-5756	11	36	introduction	introduction	NOUN
ejpam-5756	11	37	in	in	ADP
ejpam-5756	11	38	computational	computational	ADJ
ejpam-5756	11	39	chemistry	chemistry	NOUN
ejpam-5756	11	40	,	,	PUNCT
ejpam-5756	11	41	particle	particle	NOUN
ejpam-5756	11	42	physics	physics	PROPN
ejpam-5756	11	43	,	,	PUNCT
ejpam-5756	11	44	plasma	plasma	NOUN
ejpam-5756	11	45	physics	physics	NOUN
ejpam-5756	11	46	,	,	PUNCT
ejpam-5756	11	47	and	and	CCONJ
ejpam-5756	11	48	other	other	ADJ
ejpam-5756	11	49	fields	field	NOUN
ejpam-5756	11	50	,	,	PUNCT
ejpam-5756	11	51	nonlinear	nonlinear	ADJ
ejpam-5756	11	52	partial	partial	ADJ
ejpam-5756	11	53	differential	differential	NOUN
ejpam-5756	11	54	equations	equation	NOUN
ejpam-5756	11	55	(	(	PUNCT
ejpam-5756	11	56	npdes	npde	NOUN
ejpam-5756	11	57	)	)	PUNCT
ejpam-5756	11	58	have	have	AUX
ejpam-5756	11	59	been	be	AUX
ejpam-5756	11	60	used	use	VERB
ejpam-5756	11	61	as	as	ADP
ejpam-5756	11	62	models	model	NOUN
ejpam-5756	11	63	to	to	PART
ejpam-5756	11	64	explain	explain	VERB
ejpam-5756	11	65	nonlinear	nonlinear	ADJ
ejpam-5756	11	66	∗corresponding	∗corresponding	NOUN
ejpam-5756	11	67	author	author	NOUN
ejpam-5756	11	68	.	.	PUNCT
ejpam-5756	12	1	doi	doi	NOUN
ejpam-5756	12	2	:	:	PUNCT
ejpam-5756	12	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5756	https://doi.org/10.29020/nybg.ejpam.v18i1.5756	PROPN
ejpam-5756	12	4	email	email	NOUN
ejpam-5756	12	5	addresses	address	NOUN
ejpam-5756	12	6	:	:	PUNCT
ejpam-5756	12	7	211927@students.au.edu.pk	211927@students.au.edu.pk	NUM
ejpam-5756	12	8	(	(	PUNCT
ejpam-5756	12	9	b.	b.	PROPN
ejpam-5756	12	10	yasmeen	yasmeen	PROPN
ejpam-5756	12	11	)	)	PUNCT
ejpam-5756	12	12	,	,	PUNCT
ejpam-5756	12	13	khalilmalik@au.edu.pk	khalilmalik@au.edu.pk	PROPN
ejpam-5756	12	14	(	(	PUNCT
ejpam-5756	12	15	k.	k.	PROPN
ejpam-5756	12	16	ahmad	ahmad	PROPN
ejpam-5756	12	17	)	)	PUNCT
ejpam-5756	12	18	,	,	PUNCT
ejpam-5756	12	19	drnahidfatima@gmail.com	drnahidfatima@gmail.com	X
ejpam-5756	12	20	(	(	PUNCT
ejpam-5756	12	21	n.	n.	PROPN
ejpam-5756	12	22	fatima	fatima	PROPN
ejpam-5756	12	23	)	)	PUNCT
ejpam-5756	12	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5756	13	1	1	1	NUM
ejpam-5756	13	2	copyright	copyright	NOUN
ejpam-5756	13	3	:	:	PUNCT
ejpam-5756	13	4	©	©	PROPN
ejpam-5756	13	5	2025	2025	NUM
ejpam-5756	13	6	the	the	DET
ejpam-5756	13	7	author(s	author(s	NOUN
ejpam-5756	13	8	)	)	PUNCT
ejpam-5756	13	9	.	.	PUNCT
ejpam-5756	14	1	(	(	PUNCT
ejpam-5756	14	2	cc	cc	NOUN
ejpam-5756	14	3	by	by	ADP
ejpam-5756	14	4	-	-	PUNCT
ejpam-5756	14	5	nc	nc	PROPN
ejpam-5756	14	6	4.0	4.0	NUM
ejpam-5756	14	7	)	)	PUNCT
ejpam-5756	14	8	b.	b.	PROPN
ejpam-5756	14	9	yasmeen	yasmeen	PROPN
ejpam-5756	14	10	,	,	PUNCT
ejpam-5756	14	11	k.	k.	PROPN
ejpam-5756	14	12	ahmad	ahmad	PROPN
ejpam-5756	14	13	,	,	PUNCT
ejpam-5756	14	14	n.	n.	PROPN
ejpam-5756	14	15	fatima	fatima	PROPN
ejpam-5756	14	16	/	/	PUNCT
ejpam-5756	14	17	eur	eur	PROPN
ejpam-5756	14	18	.	.	PUNCT
ejpam-5756	15	1	j.	j.	PROPN
ejpam-5756	15	2	pure	pure	PROPN
ejpam-5756	15	3	appl	appl	PROPN
ejpam-5756	15	4	.	.	PROPN
ejpam-5756	15	5	math	math	PROPN
ejpam-5756	15	6	,	,	PUNCT
ejpam-5756	15	7	18	18	NUM
ejpam-5756	15	8	(	(	PUNCT
ejpam-5756	15	9	1	1	NUM
ejpam-5756	15	10	)	)	PUNCT
ejpam-5756	15	11	(	(	PUNCT
ejpam-5756	15	12	2025	2025	NUM
ejpam-5756	15	13	)	)	PUNCT
ejpam-5756	15	14	,	,	PUNCT
ejpam-5756	15	15	5756	5756	NUM
ejpam-5756	15	16	2	2	NUM
ejpam-5756	15	17	of	of	ADP
ejpam-5756	15	18	17	17	NUM
ejpam-5756	15	19	physical	physical	ADJ
ejpam-5756	15	20	phenomena	phenomenon	NOUN
ejpam-5756	15	21	.	.	PUNCT
ejpam-5756	16	1	the	the	DET
ejpam-5756	16	2	study	study	NOUN
ejpam-5756	16	3	of	of	ADP
ejpam-5756	16	4	exact	exact	ADJ
ejpam-5756	16	5	or	or	CCONJ
ejpam-5756	16	6	analytical	analytical	ADJ
ejpam-5756	16	7	solutions	solution	NOUN
ejpam-5756	16	8	has	have	AUX
ejpam-5756	16	9	received	receive	VERB
ejpam-5756	16	10	a	a	DET
ejpam-5756	16	11	lot	lot	NOUN
ejpam-5756	16	12	of	of	ADP
ejpam-5756	16	13	attention	attention	NOUN
ejpam-5756	16	14	because	because	SCONJ
ejpam-5756	16	15	it	it	PRON
ejpam-5756	16	16	is	be	AUX
ejpam-5756	16	17	crucial	crucial	ADJ
ejpam-5756	16	18	to	to	ADP
ejpam-5756	16	19	the	the	DET
ejpam-5756	16	20	examination	examination	NOUN
ejpam-5756	16	21	of	of	ADP
ejpam-5756	16	22	the	the	DET
ejpam-5756	16	23	model	model	NOUN
ejpam-5756	16	24	physical	physical	ADJ
ejpam-5756	16	25	characteristics	characteristic	NOUN
ejpam-5756	16	26	.	.	PUNCT
ejpam-5756	17	1	different	different	ADJ
ejpam-5756	17	2	wave	wave	NOUN
ejpam-5756	17	3	types	type	NOUN
ejpam-5756	17	4	,	,	PUNCT
ejpam-5756	17	5	such	such	ADJ
ejpam-5756	17	6	as	as	ADP
ejpam-5756	17	7	solitary	solitary	ADJ
ejpam-5756	17	8	waves	wave	NOUN
ejpam-5756	17	9	,	,	PUNCT
ejpam-5756	17	10	optical	optical	ADJ
ejpam-5756	17	11	solutions	solution	NOUN
ejpam-5756	17	12	,	,	PUNCT
ejpam-5756	17	13	singular	singular	ADJ
ejpam-5756	17	14	solutions	solution	NOUN
ejpam-5756	17	15	,	,	PUNCT
ejpam-5756	17	16	periodic	periodic	ADJ
ejpam-5756	17	17	waves	wave	NOUN
ejpam-5756	17	18	,	,	PUNCT
ejpam-5756	17	19	breather	breather	NOUN
ejpam-5756	17	20	waves	wave	NOUN
ejpam-5756	17	21	,	,	PUNCT
ejpam-5756	17	22	rogue	rogue	NOUN
ejpam-5756	17	23	waves	wave	NOUN
ejpam-5756	17	24	,	,	PUNCT
ejpam-5756	17	25	and	and	CCONJ
ejpam-5756	17	26	rational	rational	ADJ
ejpam-5756	17	27	wave	wave	NOUN
ejpam-5756	17	28	solutions	solution	NOUN
ejpam-5756	17	29	,	,	PUNCT
ejpam-5756	17	30	can	can	AUX
ejpam-5756	17	31	be	be	AUX
ejpam-5756	17	32	created	create	VERB
ejpam-5756	17	33	using	use	VERB
ejpam-5756	17	34	analytical	analytical	ADJ
ejpam-5756	17	35	techniques	technique	NOUN
ejpam-5756	17	36	.	.	PUNCT
ejpam-5756	18	1	investigating	investigate	VERB
ejpam-5756	18	2	techniques	technique	NOUN
ejpam-5756	18	3	for	for	ADP
ejpam-5756	18	4	solving	solve	VERB
ejpam-5756	18	5	fractional	fractional	ADJ
ejpam-5756	18	6	nonlinear	nonlinear	ADJ
ejpam-5756	18	7	partial	partial	ADJ
ejpam-5756	18	8	differential	differential	NOUN
ejpam-5756	18	9	equations	equation	NOUN
ejpam-5756	18	10	(	(	PUNCT
ejpam-5756	18	11	pdes	pde	NOUN
ejpam-5756	18	12	)	)	PUNCT
ejpam-5756	18	13	is	be	AUX
ejpam-5756	18	14	necessary	necessary	ADJ
ejpam-5756	18	15	to	to	PART
ejpam-5756	18	16	better	well	ADV
ejpam-5756	18	17	understand	understand	VERB
ejpam-5756	18	18	the	the	DET
ejpam-5756	18	19	dynamics	dynamic	NOUN
ejpam-5756	18	20	of	of	ADP
ejpam-5756	18	21	these	these	DET
ejpam-5756	18	22	real	real	ADJ
ejpam-5756	18	23	-	-	PUNCT
ejpam-5756	18	24	world	world	NOUN
ejpam-5756	18	25	components	component	NOUN
ejpam-5756	18	26	.	.	PUNCT
ejpam-5756	19	1	this	this	DET
ejpam-5756	19	2	investigation	investigation	NOUN
ejpam-5756	19	3	is	be	AUX
ejpam-5756	19	4	necessary	necessary	ADJ
ejpam-5756	19	5	to	to	PART
ejpam-5756	19	6	learn	learn	VERB
ejpam-5756	19	7	more	more	ADV
ejpam-5756	19	8	about	about	ADV
ejpam-5756	19	9	and	and	CCONJ
ejpam-5756	19	10	comprehend	comprehend	VERB
ejpam-5756	19	11	the	the	DET
ejpam-5756	19	12	intricate	intricate	ADJ
ejpam-5756	19	13	behaviors	behavior	NOUN
ejpam-5756	19	14	that	that	PRON
ejpam-5756	19	15	are	be	AUX
ejpam-5756	19	16	present	present	ADJ
ejpam-5756	19	17	in	in	ADP
ejpam-5756	19	18	the	the	DET
ejpam-5756	19	19	systems	system	NOUN
ejpam-5756	19	20	indicated	indicate	VERB
ejpam-5756	19	21	above	above	ADV
ejpam-5756	19	22	.	.	PUNCT
ejpam-5756	20	1	the	the	DET
ejpam-5756	20	2	greater	great	ADJ
ejpam-5756	20	3	richness	richness	NOUN
ejpam-5756	20	4	and	and	CCONJ
ejpam-5756	20	5	generality	generality	NOUN
ejpam-5756	20	6	that	that	PRON
ejpam-5756	20	7	fractional	fractional	ADJ
ejpam-5756	20	8	nonlinear	nonlinear	ADJ
ejpam-5756	20	9	pde	pde	NOUN
ejpam-5756	20	10	solutions	solution	NOUN
ejpam-5756	20	11	offer	offer	NOUN
ejpam-5756	20	12	,	,	PUNCT
ejpam-5756	20	13	which	which	PRON
ejpam-5756	20	14	surpasses	surpass	VERB
ejpam-5756	20	15	classical	classical	ADJ
ejpam-5756	20	16	solutions	solution	NOUN
ejpam-5756	20	17	in	in	ADP
ejpam-5756	20	18	terms	term	NOUN
ejpam-5756	20	19	of	of	ADP
ejpam-5756	20	20	descriptive	descriptive	ADJ
ejpam-5756	20	21	power	power	NOUN
ejpam-5756	20	22	,	,	PUNCT
ejpam-5756	20	23	makes	make	VERB
ejpam-5756	20	24	them	they	PRON
ejpam-5756	20	25	of	of	ADP
ejpam-5756	20	26	academic	academic	ADJ
ejpam-5756	20	27	interest	interest	NOUN
ejpam-5756	21	1	[	[	X
ejpam-5756	21	2	25	25	NUM
ejpam-5756	21	3	]	]	PUNCT
ejpam-5756	21	4	,	,	PUNCT
ejpam-5756	22	1	[	[	X
ejpam-5756	22	2	8	8	NUM
ejpam-5756	22	3	]	]	PUNCT
ejpam-5756	22	4	,	,	PUNCT
ejpam-5756	22	5	[	[	X
ejpam-5756	22	6	9	9	NUM
ejpam-5756	22	7	]	]	PUNCT
ejpam-5756	22	8	,	,	PUNCT
ejpam-5756	22	9	[	[	X
ejpam-5756	22	10	21	21	NUM
ejpam-5756	22	11	]	]	PUNCT
ejpam-5756	22	12	,	,	PUNCT
ejpam-5756	22	13	[	[	X
ejpam-5756	22	14	19	19	NUM
ejpam-5756	22	15	]	]	PUNCT
ejpam-5756	22	16	,	,	PUNCT
ejpam-5756	22	17	[	[	X
ejpam-5756	22	18	18	18	NUM
ejpam-5756	22	19	]	]	PUNCT
ejpam-5756	22	20	.	.	PUNCT
ejpam-5756	23	1	mathematicians	mathematician	NOUN
ejpam-5756	23	2	have	have	AUX
ejpam-5756	23	3	created	create	VERB
ejpam-5756	23	4	and	and	CCONJ
ejpam-5756	23	5	applied	apply	VERB
ejpam-5756	23	6	creative	creative	ADJ
ejpam-5756	23	7	and	and	CCONJ
ejpam-5756	23	8	trustworthy	trustworthy	ADJ
ejpam-5756	23	9	methods	method	NOUN
ejpam-5756	23	10	to	to	PART
ejpam-5756	23	11	explore	explore	VERB
ejpam-5756	23	12	novel	novel	ADJ
ejpam-5756	23	13	discoveries	discovery	NOUN
ejpam-5756	23	14	.	.	PUNCT
ejpam-5756	24	1	the	the	DET
ejpam-5756	24	2	generalized	generalize	VERB
ejpam-5756	24	3	khater	khater	NOUN
ejpam-5756	24	4	method	method	NOUN
ejpam-5756	24	5	,	,	PUNCT
ejpam-5756	24	6	generalized	generalize	VERB
ejpam-5756	24	7	kudryashov	kudryashov	PROPN
ejpam-5756	24	8	method	method	NOUN
ejpam-5756	24	9	,	,	PUNCT
ejpam-5756	24	10	fractional	fractional	ADJ
ejpam-5756	24	11	sub	sub	ADJ
ejpam-5756	24	12	-	-	ADJ
ejpam-5756	24	13	equation	equation	NOUN
ejpam-5756	24	14	method	method	NOUN
ejpam-5756	24	15	,	,	PUNCT
ejpam-5756	24	16	modified	modify	VERB
ejpam-5756	24	17	extended	extend	VERB
ejpam-5756	24	18	direct	direct	ADJ
ejpam-5756	24	19	algebraic	algebraic	ADJ
ejpam-5756	24	20	approach	approach	NOUN
ejpam-5756	24	21	,	,	PUNCT
ejpam-5756	24	22	(	(	PUNCT
ejpam-5756	24	23	g’/g)expansion	g’/g)expansion	NOUN
ejpam-5756	24	24	method	method	NOUN
ejpam-5756	24	25	,	,	PUNCT
ejpam-5756	24	26	and	and	CCONJ
ejpam-5756	24	27	simple	simple	ADJ
ejpam-5756	24	28	equation	equation	NOUN
ejpam-5756	24	29	method	method	NOUN
ejpam-5756	24	30	are	be	AUX
ejpam-5756	24	31	a	a	DET
ejpam-5756	24	32	few	few	ADJ
ejpam-5756	24	33	of	of	ADP
ejpam-5756	24	34	these	these	DET
ejpam-5756	24	35	techniques	technique	NOUN
ejpam-5756	24	36	.	.	PUNCT
ejpam-5756	25	1	numerous	numerous	ADJ
ejpam-5756	25	2	methods	method	NOUN
ejpam-5756	25	3	have	have	AUX
ejpam-5756	25	4	been	be	AUX
ejpam-5756	25	5	employed	employ	VERB
ejpam-5756	25	6	in	in	ADP
ejpam-5756	25	7	recent	recent	ADJ
ejpam-5756	25	8	research	research	NOUN
ejpam-5756	25	9	to	to	PART
ejpam-5756	25	10	look	look	VERB
ejpam-5756	25	11	into	into	ADP
ejpam-5756	25	12	solutions	solution	NOUN
ejpam-5756	25	13	[	[	X
ejpam-5756	25	14	17	17	NUM
ejpam-5756	25	15	]	]	PUNCT
ejpam-5756	25	16	,	,	PUNCT
ejpam-5756	25	17	[	[	X
ejpam-5756	25	18	2	2	NUM
ejpam-5756	25	19	]	]	PUNCT
ejpam-5756	25	20	,	,	PUNCT
ejpam-5756	25	21	[	[	X
ejpam-5756	25	22	20	20	NUM
ejpam-5756	25	23	]	]	PUNCT
ejpam-5756	25	24	,	,	PUNCT
ejpam-5756	25	25	[	[	X
ejpam-5756	25	26	14	14	NUM
ejpam-5756	25	27	]	]	PUNCT
ejpam-5756	25	28	,	,	PUNCT
ejpam-5756	25	29	[	[	X
ejpam-5756	25	30	22	22	NUM
ejpam-5756	25	31	]	]	PUNCT
ejpam-5756	25	32	,	,	PUNCT
ejpam-5756	25	33	[	[	X
ejpam-5756	25	34	16	16	NUM
ejpam-5756	25	35	]	]	PUNCT
ejpam-5756	25	36	.	.	PUNCT
ejpam-5756	26	1	in	in	ADP
ejpam-5756	26	2	mathematics	mathematic	NOUN
ejpam-5756	26	3	,	,	PUNCT
ejpam-5756	26	4	analytic	analytic	ADJ
ejpam-5756	26	5	solutions	solution	NOUN
ejpam-5756	26	6	often	often	ADV
ejpam-5756	26	7	serve	serve	VERB
ejpam-5756	26	8	as	as	ADP
ejpam-5756	26	9	a	a	DET
ejpam-5756	26	10	foundation	foundation	NOUN
ejpam-5756	26	11	for	for	ADP
ejpam-5756	26	12	further	further	ADJ
ejpam-5756	26	13	analysis	analysis	NOUN
ejpam-5756	26	14	.	.	PUNCT
ejpam-5756	27	1	however	however	ADV
ejpam-5756	27	2	,	,	PUNCT
ejpam-5756	27	3	when	when	SCONJ
ejpam-5756	27	4	analytic	analytic	ADJ
ejpam-5756	27	5	solutions	solution	NOUN
ejpam-5756	27	6	are	be	AUX
ejpam-5756	27	7	not	not	PART
ejpam-5756	27	8	feasible	feasible	ADJ
ejpam-5756	27	9	.	.	PUNCT
ejpam-5756	28	1	we	we	PRON
ejpam-5756	28	2	discuss	discuss	VERB
ejpam-5756	28	3	alternative	alternative	ADJ
ejpam-5756	28	4	approaches	approach	NOUN
ejpam-5756	28	5	like	like	ADP
ejpam-5756	28	6	:	:	PUNCT
ejpam-5756	28	7	asymptotic	asymptotic	ADJ
ejpam-5756	28	8	expansions	expansion	NOUN
ejpam-5756	28	9	,	,	PUNCT
ejpam-5756	28	10	perturbation	perturbation	NOUN
ejpam-5756	28	11	theory	theory	NOUN
ejpam-5756	28	12	,	,	PUNCT
ejpam-5756	28	13	bifurcation	bifurcation	NOUN
ejpam-5756	28	14	analysis	analysis	NOUN
ejpam-5756	28	15	,	,	PUNCT
ejpam-5756	28	16	numerical	numerical	ADJ
ejpam-5756	28	17	methods	method	NOUN
ejpam-5756	28	18	(	(	PUNCT
ejpam-5756	28	19	e.g	e.g	PRON
ejpam-5756	28	20	finite	finite	ADJ
ejpam-5756	28	21	element	element	NOUN
ejpam-5756	28	22	,	,	PUNCT
ejpam-5756	28	23	finite	finite	ADJ
ejpam-5756	28	24	difference	difference	NOUN
ejpam-5756	28	25	etc	etc	X
ejpam-5756	28	26	)	)	PUNCT
ejpam-5756	28	27	.	.	PUNCT
ejpam-5756	29	1	these	these	DET
ejpam-5756	29	2	approaches	approach	NOUN
ejpam-5756	29	3	can	can	AUX
ejpam-5756	29	4	provide	provide	VERB
ejpam-5756	29	5	valuable	valuable	ADJ
ejpam-5756	29	6	insights	insight	NOUN
ejpam-5756	29	7	into	into	ADP
ejpam-5756	29	8	solution	solution	NOUN
ejpam-5756	29	9	properties	property	NOUN
ejpam-5756	29	10	,	,	PUNCT
ejpam-5756	29	11	such	such	ADJ
ejpam-5756	29	12	as	as	ADP
ejpam-5756	29	13	:	:	PUNCT
ejpam-5756	29	14	stability	stability	NOUN
ejpam-5756	29	15	and	and	CCONJ
ejpam-5756	29	16	instability	instability	NOUN
ejpam-5756	29	17	,	,	PUNCT
ejpam-5756	29	18	bifurcation	bifurcation	NOUN
ejpam-5756	29	19	and	and	CCONJ
ejpam-5756	29	20	pattern	pattern	NOUN
ejpam-5756	29	21	formation	formation	NOUN
ejpam-5756	29	22	,	,	PUNCT
ejpam-5756	29	23	long	long	ADJ
ejpam-5756	29	24	-	-	PUNCT
ejpam-5756	29	25	time	time	NOUN
ejpam-5756	29	26	behavior	behavior	NOUN
ejpam-5756	29	27	and	and	CCONJ
ejpam-5756	29	28	attraction	attraction	NOUN
ejpam-5756	29	29	,	,	PUNCT
ejpam-5756	29	30	symmetries	symmetry	NOUN
ejpam-5756	29	31	and	and	CCONJ
ejpam-5756	29	32	conservation	conservation	NOUN
ejpam-5756	29	33	law	law	NOUN
ejpam-5756	29	34	.	.	PUNCT
ejpam-5756	30	1	the	the	DET
ejpam-5756	30	2	time	time	NOUN
ejpam-5756	30	3	-	-	PUNCT
ejpam-5756	30	4	fractional	fractional	ADJ
ejpam-5756	30	5	djkm	djkm	NOUN
ejpam-5756	30	6	equation	equation	NOUN
ejpam-5756	30	7	is	be	AUX
ejpam-5756	30	8	a	a	DET
ejpam-5756	30	9	significant	significant	ADJ
ejpam-5756	30	10	extension	extension	NOUN
ejpam-5756	30	11	of	of	ADP
ejpam-5756	30	12	the	the	DET
ejpam-5756	30	13	classical	classical	ADJ
ejpam-5756	30	14	djkm	djkm	NOUN
ejpam-5756	30	15	equation	equation	NOUN
ejpam-5756	30	16	,	,	PUNCT
ejpam-5756	30	17	incorporating	incorporate	VERB
ejpam-5756	30	18	fractional	fractional	ADJ
ejpam-5756	30	19	derivatives	derivative	NOUN
ejpam-5756	30	20	to	to	PART
ejpam-5756	30	21	model	model	VERB
ejpam-5756	30	22	complex	complex	ADJ
ejpam-5756	30	23	phenomena	phenomenon	NOUN
ejpam-5756	30	24	in	in	ADP
ejpam-5756	30	25	physics	physics	NOUN
ejpam-5756	30	26	,	,	PUNCT
ejpam-5756	30	27	mathematics	mathematic	NOUN
ejpam-5756	30	28	and	and	CCONJ
ejpam-5756	30	29	engineering	engineering	NOUN
ejpam-5756	30	30	.	.	PUNCT
ejpam-5756	31	1	despite	despite	SCONJ
ejpam-5756	31	2	the	the	DET
ejpam-5756	31	3	existence	existence	NOUN
ejpam-5756	31	4	of	of	ADP
ejpam-5756	31	5	various	various	ADJ
ejpam-5756	31	6	fractional	fractional	ADJ
ejpam-5756	31	7	derivatives	derivative	NOUN
ejpam-5756	31	8	,	,	PUNCT
ejpam-5756	31	9	our	our	PRON
ejpam-5756	31	10	work	work	NOUN
ejpam-5756	31	11	focuses	focus	VERB
ejpam-5756	31	12	on	on	ADP
ejpam-5756	31	13	the	the	DET
ejpam-5756	31	14	conformable	conformable	ADJ
ejpam-5756	31	15	fractional	fractional	ADJ
ejpam-5756	31	16	derivative	derivative	NOUN
ejpam-5756	31	17	due	due	ADP
ejpam-5756	31	18	to	to	ADP
ejpam-5756	31	19	its	its	PRON
ejpam-5756	31	20	uniqueness	uniqueness	NOUN
ejpam-5756	31	21	.	.	PUNCT
ejpam-5756	32	1	the	the	DET
ejpam-5756	32	2	motivation	motivation	NOUN
ejpam-5756	32	3	for	for	ADP
ejpam-5756	32	4	this	this	DET
ejpam-5756	32	5	work	work	NOUN
ejpam-5756	32	6	is	be	AUX
ejpam-5756	32	7	multifaceted	multifaceted	ADJ
ejpam-5756	32	8	:	:	PUNCT
ejpam-5756	32	9	(	(	PUNCT
ejpam-5756	32	10	1	1	X
ejpam-5756	32	11	)	)	PUNCT
ejpam-5756	32	12	the	the	DET
ejpam-5756	32	13	increasing	increase	VERB
ejpam-5756	32	14	importance	importance	NOUN
ejpam-5756	32	15	of	of	ADP
ejpam-5756	32	16	fractional	fractional	ADJ
ejpam-5756	32	17	derivative	derivative	NOUN
ejpam-5756	32	18	in	in	ADP
ejpam-5756	32	19	modeling	model	VERB
ejpam-5756	32	20	real	real	ADJ
ejpam-5756	32	21	-	-	PUNCT
ejpam-5756	32	22	world	world	NOUN
ejpam-5756	32	23	phenomena	phenomenon	NOUN
ejpam-5756	32	24	(	(	PUNCT
ejpam-5756	32	25	2	2	X
ejpam-5756	32	26	)	)	PUNCT
ejpam-5756	32	27	the	the	DET
ejpam-5756	32	28	need	need	NOUN
ejpam-5756	32	29	for	for	SCONJ
ejpam-5756	32	30	analytic	analytic	ADJ
ejpam-5756	32	31	solutions	solution	NOUN
ejpam-5756	32	32	to	to	PART
ejpam-5756	32	33	understand	understand	VERB
ejpam-5756	32	34	the	the	DET
ejpam-5756	32	35	underlying	underlie	VERB
ejpam-5756	32	36	dynamics	dynamic	NOUN
ejpam-5756	32	37	of	of	ADP
ejpam-5756	32	38	the	the	DET
ejpam-5756	32	39	timefractional	timefractional	ADJ
ejpam-5756	32	40	djkm	djkm	NOUN
ejpam-5756	32	41	equation	equation	NOUN
ejpam-5756	32	42	by	by	ADP
ejpam-5756	32	43	addressing	address	VERB
ejpam-5756	32	44	these	these	DET
ejpam-5756	32	45	motivations	motivation	NOUN
ejpam-5756	32	46	,	,	PUNCT
ejpam-5756	32	47	our	our	PRON
ejpam-5756	32	48	work	work	NOUN
ejpam-5756	32	49	provides	provide	VERB
ejpam-5756	32	50	a	a	DET
ejpam-5756	32	51	comprehensive	comprehensive	ADJ
ejpam-5756	32	52	analysis	analysis	NOUN
ejpam-5756	32	53	of	of	ADP
ejpam-5756	32	54	the	the	DET
ejpam-5756	32	55	timefractional	timefractional	ADJ
ejpam-5756	32	56	djkm	djkm	NOUN
ejpam-5756	32	57	equation	equation	NOUN
ejpam-5756	32	58	and	and	CCONJ
ejpam-5756	32	59	contributes	contribute	VERB
ejpam-5756	32	60	to	to	ADP
ejpam-5756	32	61	the	the	DET
ejpam-5756	32	62	growing	grow	VERB
ejpam-5756	32	63	field	field	NOUN
ejpam-5756	32	64	of	of	ADP
ejpam-5756	32	65	fractional	fractional	ADJ
ejpam-5756	32	66	derivatives	derivative	NOUN
ejpam-5756	32	67	djkm	djkm	NOUN
ejpam-5756	32	68	equation	equation	NOUN
ejpam-5756	32	69	was	be	AUX
ejpam-5756	32	70	firstly	firstly	ADV
ejpam-5756	32	71	presented	present	VERB
ejpam-5756	32	72	by	by	ADP
ejpam-5756	32	73	kadomtsev	kadomtsev	NOUN
ejpam-5756	32	74	and	and	CCONJ
ejpam-5756	32	75	petviashvili	petviashvili	NOUN
ejpam-5756	32	76	so	so	SCONJ
ejpam-5756	32	77	as	as	SCONJ
ejpam-5756	32	78	to	to	PART
ejpam-5756	32	79	study	study	VERB
ejpam-5756	32	80	the	the	DET
ejpam-5756	32	81	stability	stability	NOUN
ejpam-5756	32	82	of	of	ADP
ejpam-5756	32	83	the	the	DET
ejpam-5756	32	84	kdv	kdv	NOUN
ejpam-5756	32	85	soliton	soliton	NOUN
ejpam-5756	33	1	[	[	X
ejpam-5756	33	2	13	13	NUM
ejpam-5756	33	3	]	]	PUNCT
ejpam-5756	33	4	.	.	PUNCT
ejpam-5756	34	1	later	later	ADV
ejpam-5756	34	2	,	,	PUNCT
ejpam-5756	34	3	some	some	DET
ejpam-5756	34	4	important	important	ADJ
ejpam-5756	34	5	properties	property	NOUN
ejpam-5756	34	6	of	of	ADP
ejpam-5756	34	7	djkm	djkm	NOUN
ejpam-5756	34	8	have	have	AUX
ejpam-5756	34	9	been	be	AUX
ejpam-5756	34	10	investigated	investigate	VERB
ejpam-5756	34	11	in	in	ADP
ejpam-5756	34	12	[	[	X
ejpam-5756	34	13	5	5	NUM
ejpam-5756	34	14	]	]	PUNCT
ejpam-5756	34	15	,	,	PUNCT
ejpam-5756	34	16	[	[	X
ejpam-5756	34	17	24	24	NUM
ejpam-5756	34	18	]	]	PUNCT
ejpam-5756	34	19	,	,	PUNCT
ejpam-5756	34	20	[	[	X
ejpam-5756	34	21	11	11	NUM
ejpam-5756	34	22	]	]	PUNCT
ejpam-5756	34	23	and	and	CCONJ
ejpam-5756	34	24	[	[	X
ejpam-5756	34	25	15	15	NUM
ejpam-5756	34	26	]	]	PUNCT
ejpam-5756	34	27	.	.	PUNCT
ejpam-5756	35	1	in	in	ADP
ejpam-5756	35	2	2020	2020	NUM
ejpam-5756	35	3	,	,	PUNCT
ejpam-5756	35	4	wazwaz	wazwaz	NOUN
ejpam-5756	35	5	have	have	AUX
ejpam-5756	35	6	observed	observe	VERB
ejpam-5756	35	7	the	the	DET
ejpam-5756	35	8	painleve	painleve	NOUN
ejpam-5756	35	9	integrability	integrability	NOUN
ejpam-5756	35	10	and	and	CCONJ
ejpam-5756	35	11	multiple	multiple	ADJ
ejpam-5756	35	12	soliton	soliton	NOUN
ejpam-5756	35	13	solutions	solution	NOUN
ejpam-5756	35	14	by	by	ADP
ejpam-5756	35	15	getting	get	VERB
ejpam-5756	35	16	variable	variable	ADJ
ejpam-5756	35	17	coefficient	coefficient	NOUN
ejpam-5756	35	18	in	in	ADP
ejpam-5756	35	19	[	[	X
ejpam-5756	35	20	29	29	NUM
ejpam-5756	35	21	]	]	PUNCT
ejpam-5756	35	22	.	.	PUNCT
ejpam-5756	36	1	in	in	ADP
ejpam-5756	36	2	2021	2021	NUM
ejpam-5756	36	3	,	,	PUNCT
ejpam-5756	36	4	khudija	khudija	NOUN
ejpam-5756	36	5	and	and	CCONJ
ejpam-5756	36	6	khalil	khalil	PROPN
ejpam-5756	36	7	applied	apply	VERB
ejpam-5756	36	8	lie	lie	NOUN
ejpam-5756	36	9	symmetry	symmetry	NOUN
ejpam-5756	36	10	transformation	transformation	NOUN
ejpam-5756	36	11	on	on	ADP
ejpam-5756	36	12	djkm	djkm	NOUN
ejpam-5756	36	13	and	and	CCONJ
ejpam-5756	36	14	reduced	reduce	VERB
ejpam-5756	36	15	into	into	ADP
ejpam-5756	36	16	linear	linear	ADJ
ejpam-5756	36	17	pdes	pde	NOUN
ejpam-5756	36	18	[	[	X
ejpam-5756	36	19	3	3	NUM
ejpam-5756	36	20	]	]	PUNCT
ejpam-5756	36	21	.	.	PUNCT
ejpam-5756	37	1	in	in	ADP
ejpam-5756	37	2	paper	paper	NOUN
ejpam-5756	37	3	[	[	X
ejpam-5756	37	4	10	10	NUM
ejpam-5756	37	5	]	]	PUNCT
ejpam-5756	37	6	,	,	PUNCT
ejpam-5756	37	7	the	the	DET
ejpam-5756	37	8	cdjkm	cdjkm	NOUN
ejpam-5756	37	9	equation	equation	NOUN
ejpam-5756	37	10	has	have	VERB
ejpam-5756	37	11	the	the	DET
ejpam-5756	37	12	following	follow	VERB
ejpam-5756	37	13	form	form	NOUN
ejpam-5756	37	14	[	[	X
ejpam-5756	37	15	12	12	NUM
ejpam-5756	37	16	]	]	PUNCT
ejpam-5756	37	17	,	,	PUNCT
ejpam-5756	37	18	[	[	X
ejpam-5756	37	19	7	7	NUM
ejpam-5756	37	20	]	]	PUNCT
ejpam-5756	37	21	.	.	PUNCT
ejpam-5756	38	1	b.	b.	PROPN
ejpam-5756	38	2	yasmeen	yasmeen	PROPN
ejpam-5756	38	3	,	,	PUNCT
ejpam-5756	38	4	k.	k.	PROPN
ejpam-5756	38	5	ahmad	ahmad	PROPN
ejpam-5756	38	6	,	,	PUNCT
ejpam-5756	38	7	n.	n.	PROPN
ejpam-5756	38	8	fatima	fatima	PROPN
ejpam-5756	38	9	/	/	PUNCT
ejpam-5756	38	10	eur	eur	PROPN
ejpam-5756	38	11	.	.	PUNCT
ejpam-5756	39	1	j.	j.	PROPN
ejpam-5756	39	2	pure	pure	PROPN
ejpam-5756	39	3	appl	appl	PROPN
ejpam-5756	39	4	.	.	PROPN
ejpam-5756	39	5	math	math	PROPN
ejpam-5756	39	6	,	,	PUNCT
ejpam-5756	39	7	18	18	NUM
ejpam-5756	39	8	(	(	PUNCT
ejpam-5756	39	9	1	1	NUM
ejpam-5756	39	10	)	)	PUNCT
ejpam-5756	39	11	(	(	PUNCT
ejpam-5756	39	12	2025	2025	NUM
ejpam-5756	39	13	)	)	PUNCT
ejpam-5756	39	14	,	,	PUNCT
ejpam-5756	39	15	5756	5756	NUM
ejpam-5756	39	16	3	3	NUM
ejpam-5756	39	17	of	of	ADP
ejpam-5756	39	18	17	17	NUM
ejpam-5756	39	19	uxxxxy	uxxxxy	NOUN
ejpam-5756	39	20	+	+	CCONJ
ejpam-5756	39	21	4uxxyux	4uxxyux	NUM
ejpam-5756	39	22	+	+	CCONJ
ejpam-5756	39	23	2uxxxuy	2uxxxuy	NUM
ejpam-5756	39	24	+	+	NUM
ejpam-5756	39	25	6uxyuxx	6uxyuxx	NUM
ejpam-5756	39	26	−	−	NOUN
ejpam-5756	39	27	γuyyy	γuyyy	NOUN
ejpam-5756	39	28	−	−	PROPN
ejpam-5756	39	29	2ρ	2ρ	NOUN
ejpam-5756	39	30	∂2	∂2	PROPN
ejpam-5756	39	31	∂x2	∂x2	NOUN
ejpam-5756	39	32	(	(	PUNCT
ejpam-5756	39	33	∂αu	∂αu	PROPN
ejpam-5756	39	34	∂tα	∂tα	PROPN
ejpam-5756	39	35	)	)	PUNCT
ejpam-5756	40	1	=	=	SYM
ejpam-5756	40	2	0	0	PUNCT
ejpam-5756	40	3	(	(	PUNCT
ejpam-5756	40	4	1	1	NUM
ejpam-5756	40	5	)	)	PUNCT
ejpam-5756	40	6	where	where	SCONJ
ejpam-5756	40	7	u	u	NOUN
ejpam-5756	40	8	=	=	SYM
ejpam-5756	40	9	u(x	u(x	PROPN
ejpam-5756	40	10	,	,	PUNCT
ejpam-5756	40	11	y	y	PROPN
ejpam-5756	40	12	,	,	PUNCT
ejpam-5756	40	13	t	t	PROPN
ejpam-5756	40	14	)	)	PUNCT
ejpam-5756	40	15	represents	represent	VERB
ejpam-5756	40	16	the	the	DET
ejpam-5756	40	17	physical	physical	ADJ
ejpam-5756	40	18	quantity	quantity	NOUN
ejpam-5756	40	19	of	of	ADP
ejpam-5756	40	20	wave	wave	NOUN
ejpam-5756	40	21	amplitude	amplitude	NOUN
ejpam-5756	40	22	and	and	CCONJ
ejpam-5756	40	23	the	the	DET
ejpam-5756	40	24	subscripts	subscript	NOUN
ejpam-5756	40	25	indicate	indicate	VERB
ejpam-5756	40	26	partial	partial	ADJ
ejpam-5756	40	27	differentiation	differentiation	NOUN
ejpam-5756	40	28	with	with	ADP
ejpam-5756	40	29	regard	regard	NOUN
ejpam-5756	40	30	to	to	ADP
ejpam-5756	40	31	the	the	DET
ejpam-5756	40	32	specified	specified	ADJ
ejpam-5756	40	33	variables	variable	NOUN
ejpam-5756	40	34	whereas	whereas	SCONJ
ejpam-5756	40	35	γ	γ	PROPN
ejpam-5756	40	36	,	,	PUNCT
ejpam-5756	40	37	ρ	ρ	PROPN
ejpam-5756	40	38	are	be	AUX
ejpam-5756	40	39	constants	constant	NOUN
ejpam-5756	40	40	,	,	PUNCT
ejpam-5756	40	41	and	and	CCONJ
ejpam-5756	40	42	0	0	NUM
ejpam-5756	40	43	<	<	X
ejpam-5756	40	44	α	α	PROPN
ejpam-5756	40	45	≤	≤	ADJ
ejpam-5756	40	46	1	1	NUM
ejpam-5756	40	47	shows	show	VERB
ejpam-5756	40	48	wave	wave	NOUN
ejpam-5756	40	49	behavior	behavior	NOUN
ejpam-5756	40	50	of	of	ADP
ejpam-5756	40	51	the	the	DET
ejpam-5756	40	52	solitions	solition	NOUN
ejpam-5756	40	53	.	.	PUNCT
ejpam-5756	41	1	this	this	DET
ejpam-5756	41	2	definition	definition	NOUN
ejpam-5756	41	3	is	be	AUX
ejpam-5756	41	4	widely	widely	ADV
ejpam-5756	41	5	used	use	VERB
ejpam-5756	41	6	in	in	ADP
ejpam-5756	41	7	different	different	ADJ
ejpam-5756	41	8	fields	field	NOUN
ejpam-5756	41	9	,	,	PUNCT
ejpam-5756	41	10	including	include	VERB
ejpam-5756	41	11	physics	physics	NOUN
ejpam-5756	41	12	,	,	PUNCT
ejpam-5756	41	13	engineering	engineering	NOUN
ejpam-5756	41	14	,	,	PUNCT
ejpam-5756	41	15	and	and	CCONJ
ejpam-5756	41	16	mathematics	mathematic	NOUN
ejpam-5756	41	17	,	,	PUNCT
ejpam-5756	41	18	and	and	CCONJ
ejpam-5756	41	19	has	have	AUX
ejpam-5756	41	20	been	be	AUX
ejpam-5756	41	21	shown	show	VERB
ejpam-5756	41	22	to	to	PART
ejpam-5756	41	23	be	be	AUX
ejpam-5756	41	24	effective	effective	ADJ
ejpam-5756	41	25	in	in	ADP
ejpam-5756	41	26	modeling	model	VERB
ejpam-5756	41	27	complex	complex	ADJ
ejpam-5756	41	28	phenomena	phenomenon	NOUN
ejpam-5756	41	29	.	.	PUNCT
ejpam-5756	42	1	this	this	DET
ejpam-5756	42	2	definition	definition	NOUN
ejpam-5756	42	3	is	be	AUX
ejpam-5756	42	4	chosen	choose	VERB
ejpam-5756	42	5	for	for	ADP
ejpam-5756	42	6	its	its	PRON
ejpam-5756	42	7	simplicity	simplicity	NOUN
ejpam-5756	42	8	and	and	CCONJ
ejpam-5756	42	9	applicability	applicability	NOUN
ejpam-5756	42	10	to	to	ADP
ejpam-5756	42	11	many	many	ADJ
ejpam-5756	42	12	problem	problem	NOUN
ejpam-5756	42	13	.	.	PUNCT
ejpam-5756	43	1	a	a	DET
ejpam-5756	43	2	lot	lot	NOUN
ejpam-5756	43	3	of	of	ADP
ejpam-5756	43	4	studies	study	NOUN
ejpam-5756	43	5	have	have	AUX
ejpam-5756	43	6	been	be	AUX
ejpam-5756	43	7	presented	present	VERB
ejpam-5756	43	8	to	to	PART
ejpam-5756	43	9	seek	seek	VERB
ejpam-5756	43	10	the	the	DET
ejpam-5756	43	11	solutions	solution	NOUN
ejpam-5756	43	12	of	of	ADP
ejpam-5756	43	13	equation	equation	NOUN
ejpam-5756	43	14	(	(	PUNCT
ejpam-5756	43	15	1	1	NUM
ejpam-5756	43	16	)	)	PUNCT
ejpam-5756	43	17	.	.	PUNCT
ejpam-5756	44	1	wang	wang	PROPN
ejpam-5756	44	2	and	and	CCONJ
ejpam-5756	44	3	hu	hu	PROPN
ejpam-5756	45	1	[	[	X
ejpam-5756	45	2	6	6	NUM
ejpam-5756	45	3	]	]	PUNCT
ejpam-5756	45	4	have	have	AUX
ejpam-5756	45	5	derived	derive	VERB
ejpam-5756	45	6	the	the	DET
ejpam-5756	45	7	grammian	grammian	ADJ
ejpam-5756	45	8	solutions	solution	NOUN
ejpam-5756	45	9	of	of	ADP
ejpam-5756	45	10	equation	equation	NOUN
ejpam-5756	45	11	(	(	PUNCT
ejpam-5756	45	12	1	1	NUM
ejpam-5756	45	13	)	)	PUNCT
ejpam-5756	45	14	.	.	PUNCT
ejpam-5756	46	1	guo	guo	PROPN
ejpam-5756	46	2	and	and	CCONJ
ejpam-5756	46	3	lin	lin	PROPN
ejpam-5756	47	1	[	[	X
ejpam-5756	47	2	5	5	NUM
ejpam-5756	47	3	]	]	PUNCT
ejpam-5756	47	4	have	have	AUX
ejpam-5756	47	5	studied	study	VERB
ejpam-5756	47	6	interaction	interaction	NOUN
ejpam-5756	47	7	solutions	solution	NOUN
ejpam-5756	47	8	between	between	ADP
ejpam-5756	47	9	lump	lump	NOUN
ejpam-5756	47	10	and	and	CCONJ
ejpam-5756	47	11	stripe	stripe	NOUN
ejpam-5756	47	12	soliton	soliton	NOUN
ejpam-5756	47	13	solutions	solution	NOUN
ejpam-5756	47	14	via	via	ADP
ejpam-5756	47	15	a	a	DET
ejpam-5756	47	16	quadratic	quadratic	ADJ
ejpam-5756	47	17	function	function	NOUN
ejpam-5756	47	18	.	.	PUNCT
ejpam-5756	48	1	adem	adem	PROPN
ejpam-5756	48	2	et	et	PROPN
ejpam-5756	48	3	al	al	PROPN
ejpam-5756	48	4	.	.	PUNCT
ejpam-5756	49	1	[	[	X
ejpam-5756	49	2	30	30	NUM
ejpam-5756	49	3	]	]	PUNCT
ejpam-5756	49	4	have	have	AUX
ejpam-5756	49	5	used	use	VERB
ejpam-5756	49	6	the	the	DET
ejpam-5756	49	7	extended	extend	VERB
ejpam-5756	49	8	transformed	transform	VERB
ejpam-5756	49	9	rational	rational	ADJ
ejpam-5756	49	10	function	function	NOUN
ejpam-5756	49	11	that	that	PRON
ejpam-5756	49	12	depends	depend	VERB
ejpam-5756	49	13	on	on	ADP
ejpam-5756	49	14	the	the	DET
ejpam-5756	49	15	hirota	hirota	PROPN
ejpam-5756	49	16	bilinear	bilinear	NOUN
ejpam-5756	49	17	form	form	NOUN
ejpam-5756	49	18	to	to	ADP
ejpam-5756	49	19	constructed	construct	VERB
ejpam-5756	49	20	complexion	complexion	NOUN
ejpam-5756	49	21	solutions	solution	NOUN
ejpam-5756	49	22	of	of	ADP
ejpam-5756	49	23	the	the	DET
ejpam-5756	49	24	djkm	djkm	NOUN
ejpam-5756	49	25	equation	equation	NOUN
ejpam-5756	49	26	.	.	PUNCT
ejpam-5756	50	1	yuan	yuan	NOUN
ejpam-5756	50	2	et	et	PROPN
ejpam-5756	50	3	al	al	PROPN
ejpam-5756	50	4	.	.	PUNCT
ejpam-5756	51	1	[	[	X
ejpam-5756	51	2	27	27	NUM
ejpam-5756	51	3	]	]	PUNCT
ejpam-5756	51	4	have	have	AUX
ejpam-5756	51	5	studied	study	VERB
ejpam-5756	51	6	wronskian	wronskian	ADJ
ejpam-5756	51	7	and	and	CCONJ
ejpam-5756	51	8	grammian	grammian	ADJ
ejpam-5756	51	9	solutions	solution	NOUN
ejpam-5756	51	10	to	to	ADP
ejpam-5756	51	11	the	the	DET
ejpam-5756	51	12	djkm	djkm	NOUN
ejpam-5756	51	13	equation	equation	NOUN
ejpam-5756	51	14	.	.	PUNCT
ejpam-5756	52	1	singh	singh	PROPN
ejpam-5756	52	2	and	and	CCONJ
ejpam-5756	52	3	gupta	gupta	PROPN
ejpam-5756	53	1	[	[	X
ejpam-5756	53	2	1	1	X
ejpam-5756	53	3	]	]	PUNCT
ejpam-5756	53	4	have	have	AUX
ejpam-5756	53	5	investigated	investigate	VERB
ejpam-5756	53	6	the	the	DET
ejpam-5756	53	7	painleve	painleve	NOUN
ejpam-5756	53	8	property	property	NOUN
ejpam-5756	53	9	of	of	ADP
ejpam-5756	53	10	the	the	DET
ejpam-5756	53	11	suggested	suggest	VERB
ejpam-5756	53	12	equation	equation	NOUN
ejpam-5756	53	13	and	and	CCONJ
ejpam-5756	53	14	have	have	AUX
ejpam-5756	53	15	revealed	reveal	VERB
ejpam-5756	53	16	some	some	DET
ejpam-5756	53	17	exact	exact	ADJ
ejpam-5756	53	18	solutions	solution	NOUN
ejpam-5756	53	19	to	to	ADP
ejpam-5756	53	20	the	the	DET
ejpam-5756	53	21	studied	study	VERB
ejpam-5756	53	22	equation	equation	NOUN
ejpam-5756	53	23	by	by	ADP
ejpam-5756	53	24	using	use	VERB
ejpam-5756	53	25	the	the	DET
ejpam-5756	53	26	pickering	pickering	NOUN
ejpam-5756	53	27	’s	’s	PART
ejpam-5756	53	28	algorithm	algorithm	NOUN
ejpam-5756	53	29	.	.	PUNCT
ejpam-5756	54	1	sajid	sajid	PROPN
ejpam-5756	54	2	and	and	CCONJ
ejpam-5756	54	3	akram	akram	PROPN
ejpam-5756	55	1	[	[	X
ejpam-5756	55	2	24	24	NUM
ejpam-5756	55	3	]	]	PUNCT
ejpam-5756	55	4	have	have	AUX
ejpam-5756	55	5	utilized	utilize	VERB
ejpam-5756	55	6	exp(ϕ(ξ))-expansion	exp(ϕ(ξ))-expansion	NOUN
ejpam-5756	55	7	method	method	NOUN
ejpam-5756	55	8	to	to	PART
ejpam-5756	55	9	seek	seek	VERB
ejpam-5756	55	10	some	some	DET
ejpam-5756	55	11	exact	exact	ADJ
ejpam-5756	55	12	solutions	solution	NOUN
ejpam-5756	55	13	to	to	ADP
ejpam-5756	55	14	equation	equation	NOUN
ejpam-5756	55	15	(	(	PUNCT
ejpam-5756	55	16	1	1	NUM
ejpam-5756	55	17	)	)	PUNCT
ejpam-5756	55	18	.	.	PUNCT
ejpam-5756	56	1	in	in	ADP
ejpam-5756	56	2	recent	recent	ADJ
ejpam-5756	56	3	years	year	NOUN
ejpam-5756	56	4	,	,	PUNCT
ejpam-5756	56	5	the	the	DET
ejpam-5756	56	6	concept	concept	NOUN
ejpam-5756	56	7	of	of	ADP
ejpam-5756	56	8	fractional	fractional	ADJ
ejpam-5756	56	9	derivatives	derivative	NOUN
ejpam-5756	56	10	has	have	AUX
ejpam-5756	56	11	been	be	AUX
ejpam-5756	56	12	applied	apply	VERB
ejpam-5756	56	13	with	with	ADP
ejpam-5756	56	14	great	great	ADJ
ejpam-5756	56	15	success	success	NOUN
ejpam-5756	56	16	to	to	PART
ejpam-5756	56	17	model	model	VERB
ejpam-5756	56	18	various	various	ADJ
ejpam-5756	56	19	real	real	ADJ
ejpam-5756	56	20	-	-	PUNCT
ejpam-5756	56	21	life	life	NOUN
ejpam-5756	56	22	phenomena	phenomenon	NOUN
ejpam-5756	56	23	in	in	ADP
ejpam-5756	56	24	many	many	ADJ
ejpam-5756	56	25	scientific	scientific	ADJ
ejpam-5756	56	26	fields	field	NOUN
ejpam-5756	56	27	.	.	PUNCT
ejpam-5756	57	1	fractional	fractional	ADJ
ejpam-5756	57	2	order	order	NOUN
ejpam-5756	57	3	operators	operator	NOUN
ejpam-5756	57	4	include	include	VERB
ejpam-5756	57	5	the	the	DET
ejpam-5756	57	6	history	history	NOUN
ejpam-5756	57	7	of	of	ADP
ejpam-5756	57	8	a	a	DET
ejpam-5756	57	9	physical	physical	ADJ
ejpam-5756	57	10	phenomenon	phenomenon	NOUN
ejpam-5756	57	11	from	from	ADP
ejpam-5756	57	12	the	the	DET
ejpam-5756	57	13	initial	initial	ADJ
ejpam-5756	57	14	state	state	NOUN
ejpam-5756	57	15	to	to	ADP
ejpam-5756	57	16	the	the	DET
ejpam-5756	57	17	current	current	ADJ
ejpam-5756	57	18	state	state	NOUN
ejpam-5756	57	19	.	.	PUNCT
ejpam-5756	58	1	therefore	therefore	ADV
ejpam-5756	58	2	,	,	PUNCT
ejpam-5756	58	3	fractional	fractional	ADJ
ejpam-5756	58	4	order	order	NOUN
ejpam-5756	58	5	operators	operator	NOUN
ejpam-5756	58	6	are	be	AUX
ejpam-5756	58	7	often	often	ADV
ejpam-5756	58	8	applied	apply	VERB
ejpam-5756	58	9	to	to	ADP
ejpam-5756	58	10	model	model	NOUN
ejpam-5756	58	11	systems	system	NOUN
ejpam-5756	58	12	that	that	PRON
ejpam-5756	58	13	describe	describe	VERB
ejpam-5756	58	14	the	the	DET
ejpam-5756	58	15	influence	influence	NOUN
ejpam-5756	58	16	of	of	ADP
ejpam-5756	58	17	memory	memory	NOUN
ejpam-5756	58	18	effects	effect	NOUN
ejpam-5756	58	19	in	in	ADP
ejpam-5756	58	20	[	[	X
ejpam-5756	58	21	23	23	NUM
ejpam-5756	58	22	]	]	PUNCT
ejpam-5756	58	23	,	,	PUNCT
ejpam-5756	59	1	[	[	X
ejpam-5756	59	2	26	26	NUM
ejpam-5756	59	3	]	]	PUNCT
ejpam-5756	59	4	,	,	PUNCT
ejpam-5756	59	5	[	[	X
ejpam-5756	59	6	4	4	X
ejpam-5756	59	7	]	]	PUNCT
ejpam-5756	59	8	and	and	CCONJ
ejpam-5756	59	9	[	[	X
ejpam-5756	59	10	28	28	NUM
ejpam-5756	59	11	]	]	PUNCT
ejpam-5756	59	12	.	.	PUNCT
ejpam-5756	60	1	function	function	NOUN
ejpam-5756	60	2	transformation	transformation	NOUN
ejpam-5756	60	3	is	be	AUX
ejpam-5756	60	4	a	a	DET
ejpam-5756	60	5	mathematical	mathematical	ADJ
ejpam-5756	60	6	technique	technique	NOUN
ejpam-5756	60	7	that	that	PRON
ejpam-5756	60	8	uses	use	VERB
ejpam-5756	60	9	a	a	DET
ejpam-5756	60	10	specific	specific	ADJ
ejpam-5756	60	11	transformation	transformation	NOUN
ejpam-5756	60	12	to	to	PART
ejpam-5756	60	13	convert	convert	VERB
ejpam-5756	60	14	the	the	DET
ejpam-5756	60	15	time	time	NOUN
ejpam-5756	60	16	-	-	PUNCT
ejpam-5756	60	17	fractional	fractional	ADJ
ejpam-5756	60	18	djkm	djkm	NOUN
ejpam-5756	60	19	equation	equation	NOUN
ejpam-5756	60	20	into	into	ADP
ejpam-5756	60	21	a	a	DET
ejpam-5756	60	22	more	more	ADV
ejpam-5756	60	23	tractable	tractable	ADJ
ejpam-5756	60	24	form	form	NOUN
ejpam-5756	60	25	,	,	PUNCT
ejpam-5756	60	26	enabling	enable	VERB
ejpam-5756	60	27	us	we	PRON
ejpam-5756	60	28	to	to	PART
ejpam-5756	60	29	derive	derive	VERB
ejpam-5756	60	30	analytical	analytical	ADJ
ejpam-5756	60	31	solutions	solution	NOUN
ejpam-5756	60	32	using	use	VERB
ejpam-5756	60	33	various	various	ADJ
ejpam-5756	60	34	methods	method	NOUN
ejpam-5756	60	35	,	,	PUNCT
ejpam-5756	60	36	such	such	ADJ
ejpam-5756	60	37	as	as	ADP
ejpam-5756	60	38	power	power	NOUN
ejpam-5756	60	39	index	index	NOUN
ejpam-5756	60	40	method	method	NOUN
ejpam-5756	60	41	.	.	PUNCT
ejpam-5756	61	1	we	we	PRON
ejpam-5756	61	2	have	have	AUX
ejpam-5756	61	3	derived	derive	VERB
ejpam-5756	61	4	closed	closed	ADJ
ejpam-5756	61	5	-	-	PUNCT
ejpam-5756	61	6	form	form	NOUN
ejpam-5756	61	7	analytical	analytical	ADJ
ejpam-5756	61	8	solutions	solution	NOUN
ejpam-5756	61	9	for	for	ADP
ejpam-5756	61	10	the	the	DET
ejpam-5756	61	11	time	time	NOUN
ejpam-5756	61	12	-	-	PUNCT
ejpam-5756	61	13	fractional	fractional	ADJ
ejpam-5756	61	14	djkm	djkm	NOUN
ejpam-5756	61	15	equation	equation	NOUN
ejpam-5756	61	16	,	,	PUNCT
ejpam-5756	61	17	which	which	PRON
ejpam-5756	61	18	reveal	reveal	VERB
ejpam-5756	61	19	the	the	DET
ejpam-5756	61	20	dynamics	dynamic	NOUN
ejpam-5756	61	21	of	of	ADP
ejpam-5756	61	22	wave	wave	NOUN
ejpam-5756	61	23	propagation	propagation	NOUN
ejpam-5756	61	24	and	and	CCONJ
ejpam-5756	61	25	dispersion	dispersion	NOUN
ejpam-5756	61	26	in	in	ADP
ejpam-5756	61	27	terms	term	NOUN
ejpam-5756	61	28	of	of	ADP
ejpam-5756	61	29	fractional	fractional	ADJ
ejpam-5756	61	30	derivatives	derivative	NOUN
ejpam-5756	61	31	,	,	PUNCT
ejpam-5756	61	32	providing	provide	VERB
ejpam-5756	61	33	new	new	ADJ
ejpam-5756	61	34	insights	insight	NOUN
ejpam-5756	61	35	into	into	ADP
ejpam-5756	61	36	the	the	DET
ejpam-5756	61	37	behavior	behavior	NOUN
ejpam-5756	61	38	of	of	ADP
ejpam-5756	61	39	complex	complex	ADJ
ejpam-5756	61	40	systems	system	NOUN
ejpam-5756	61	41	.	.	PUNCT
ejpam-5756	62	1	our	our	PRON
ejpam-5756	62	2	results	result	NOUN
ejpam-5756	62	3	can	can	AUX
ejpam-5756	62	4	be	be	AUX
ejpam-5756	62	5	applied	apply	VERB
ejpam-5756	62	6	in	in	ADP
ejpam-5756	62	7	various	various	ADJ
ejpam-5756	62	8	fields	field	NOUN
ejpam-5756	62	9	,	,	PUNCT
ejpam-5756	62	10	such	such	ADJ
ejpam-5756	62	11	as	as	ADP
ejpam-5756	62	12	signal	signal	ADJ
ejpam-5756	62	13	processing	processing	NOUN
ejpam-5756	62	14	,	,	PUNCT
ejpam-5756	62	15	image	image	NOUN
ejpam-5756	62	16	processing	processing	NOUN
ejpam-5756	62	17	,	,	PUNCT
ejpam-5756	62	18	and	and	CCONJ
ejpam-5756	62	19	optical	optical	ADJ
ejpam-5756	62	20	communications	communication	NOUN
ejpam-5756	62	21	,	,	PUNCT
ejpam-5756	62	22	to	to	PART
ejpam-5756	62	23	model	model	VERB
ejpam-5756	62	24	and	and	CCONJ
ejpam-5756	62	25	analyze	analyze	VERB
ejpam-5756	62	26	complex	complex	ADJ
ejpam-5756	62	27	wave	wave	NOUN
ejpam-5756	62	28	phenomena	phenomenon	NOUN
ejpam-5756	62	29	,	,	PUNCT
ejpam-5756	62	30	leading	lead	VERB
ejpam-5756	62	31	to	to	ADP
ejpam-5756	62	32	improved	improved	ADJ
ejpam-5756	62	33	performance	performance	NOUN
ejpam-5756	62	34	and	and	CCONJ
ejpam-5756	62	35	enhanced	enhance	VERB
ejpam-5756	62	36	understanding	understanding	NOUN
ejpam-5756	62	37	of	of	ADP
ejpam-5756	62	38	these	these	DET
ejpam-5756	62	39	systems	system	NOUN
ejpam-5756	62	40	.	.	PUNCT
ejpam-5756	63	1	the	the	DET
ejpam-5756	63	2	purpose	purpose	NOUN
ejpam-5756	63	3	of	of	ADP
ejpam-5756	63	4	the	the	DET
ejpam-5756	63	5	paper	paper	NOUN
ejpam-5756	63	6	is	be	AUX
ejpam-5756	63	7	to	to	PART
ejpam-5756	63	8	develop	develop	VERB
ejpam-5756	63	9	a	a	DET
ejpam-5756	63	10	novel	novel	ADJ
ejpam-5756	63	11	analytical	analytical	ADJ
ejpam-5756	63	12	framework	framework	NOUN
ejpam-5756	63	13	for	for	ADP
ejpam-5756	63	14	solving	solve	VERB
ejpam-5756	63	15	nonlinear	nonlinear	ADJ
ejpam-5756	63	16	partial	partial	ADJ
ejpam-5756	63	17	differential	differential	NOUN
ejpam-5756	63	18	equations	equation	NOUN
ejpam-5756	63	19	using	use	VERB
ejpam-5756	63	20	function	function	NOUN
ejpam-5756	63	21	transformation	transformation	NOUN
ejpam-5756	63	22	,	,	PUNCT
ejpam-5756	63	23	focusing	focus	VERB
ejpam-5756	63	24	on	on	ADP
ejpam-5756	63	25	the	the	DET
ejpam-5756	63	26	timefractional	timefractional	ADJ
ejpam-5756	63	27	djkm	djkm	NOUN
ejpam-5756	63	28	equation	equation	NOUN
ejpam-5756	63	29	.	.	PUNCT
ejpam-5756	64	1	we	we	PRON
ejpam-5756	64	2	address	address	VERB
ejpam-5756	64	3	previously	previously	ADV
ejpam-5756	64	4	unsolved	unsolved	ADJ
ejpam-5756	64	5	problems	problem	NOUN
ejpam-5756	64	6	in	in	ADP
ejpam-5756	64	7	nonlinear	nonlinear	ADJ
ejpam-5756	64	8	pdes	pde	NOUN
ejpam-5756	64	9	,	,	PUNCT
ejpam-5756	64	10	are	be	AUX
ejpam-5756	64	11	deriving	derive	VERB
ejpam-5756	64	12	exact	exact	ADJ
ejpam-5756	64	13	solutions	solution	NOUN
ejpam-5756	64	14	for	for	ADP
ejpam-5756	64	15	nonlinear	nonlinear	ADJ
ejpam-5756	64	16	wave	wave	NOUN
ejpam-5756	64	17	equations	equation	NOUN
ejpam-5756	64	18	with	with	ADP
ejpam-5756	64	19	fractional	fractional	ADJ
ejpam-5756	64	20	time	time	NOUN
ejpam-5756	64	21	derivatives	derivative	NOUN
ejpam-5756	64	22	.	.	PUNCT
ejpam-5756	65	1	overcoming	overcome	VERB
ejpam-5756	65	2	limitations	limitation	NOUN
ejpam-5756	65	3	of	of	ADP
ejpam-5756	65	4	existing	exist	VERB
ejpam-5756	65	5	methods	method	NOUN
ejpam-5756	65	6	in	in	ADP
ejpam-5756	65	7	handling	handle	VERB
ejpam-5756	65	8	nonlinear	nonlinear	ADJ
ejpam-5756	65	9	wave	wave	NOUN
ejpam-5756	65	10	dynamics	dynamic	NOUN
ejpam-5756	65	11	.	.	PUNCT
ejpam-5756	66	1	our	our	PRON
ejpam-5756	66	2	research	research	NOUN
ejpam-5756	66	3	has	have	VERB
ejpam-5756	66	4	significant	significant	ADJ
ejpam-5756	66	5	practical	practical	ADJ
ejpam-5756	66	6	implications	implication	NOUN
ejpam-5756	66	7	for	for	ADP
ejpam-5756	66	8	accurate	accurate	ADJ
ejpam-5756	66	9	modeling	modeling	NOUN
ejpam-5756	66	10	and	and	CCONJ
ejpam-5756	66	11	simulation	simulation	NOUN
ejpam-5756	66	12	of	of	ADP
ejpam-5756	66	13	nonlinear	nonlinear	ADJ
ejpam-5756	66	14	wave	wave	NOUN
ejpam-5756	66	15	phenomena	phenomena	PROPN
ejpam-5756	66	16	in	in	ADP
ejpam-5756	66	17	physics	physics	NOUN
ejpam-5756	66	18	,	,	PUNCT
ejpam-5756	66	19	engineering	engineering	NOUN
ejpam-5756	66	20	and	and	CCONJ
ejpam-5756	66	21	optics	optic	NOUN
ejpam-5756	66	22	.	.	PUNCT
ejpam-5756	67	1	enhanced	enhance	VERB
ejpam-5756	67	2	understanding	understanding	NOUN
ejpam-5756	67	3	of	of	ADP
ejpam-5756	67	4	nonlinear	nonlinear	ADJ
ejpam-5756	67	5	wave	wave	NOUN
ejpam-5756	67	6	interactions	interaction	NOUN
ejpam-5756	67	7	and	and	CCONJ
ejpam-5756	67	8	their	their	PRON
ejpam-5756	67	9	role	role	NOUN
ejpam-5756	67	10	in	in	ADP
ejpam-5756	67	11	complex	complex	ADJ
ejpam-5756	67	12	systems	system	NOUN
ejpam-5756	67	13	.	.	PUNCT
ejpam-5756	68	1	informing	inform	VERB
ejpam-5756	68	2	the	the	DET
ejpam-5756	68	3	development	development	NOUN
ejpam-5756	68	4	of	of	ADP
ejpam-5756	68	5	new	new	ADJ
ejpam-5756	68	6	numerical	numerical	ADJ
ejpam-5756	68	7	methods	method	NOUN
ejpam-5756	68	8	and	and	CCONJ
ejpam-5756	68	9	analytical	analytical	ADJ
ejpam-5756	68	10	tools	tool	NOUN
ejpam-5756	68	11	for	for	ADP
ejpam-5756	68	12	nonlinear	nonlinear	ADJ
ejpam-5756	68	13	pdes	pde	NOUN
ejpam-5756	68	14	.	.	PUNCT
ejpam-5756	69	1	there	there	PRON
ejpam-5756	69	2	are	be	VERB
ejpam-5756	69	3	many	many	ADJ
ejpam-5756	69	4	other	other	ADJ
ejpam-5756	69	5	definitions	definition	NOUN
ejpam-5756	69	6	of	of	ADP
ejpam-5756	69	7	fractional	fractional	ADJ
ejpam-5756	69	8	derivatives	derivative	NOUN
ejpam-5756	69	9	in	in	ADP
ejpam-5756	69	10	different	different	ADJ
ejpam-5756	69	11	ways	way	NOUN
ejpam-5756	69	12	such	such	ADJ
ejpam-5756	69	13	as	as	ADP
ejpam-5756	69	14	caputo	caputo	PROPN
ejpam-5756	69	15	fracb	fracb	PROPN
ejpam-5756	69	16	.	.	PUNCT
ejpam-5756	70	1	yasmeen	yasmeen	PROPN
ejpam-5756	70	2	,	,	PUNCT
ejpam-5756	70	3	k.	k.	PROPN
ejpam-5756	70	4	ahmad	ahmad	PROPN
ejpam-5756	70	5	,	,	PUNCT
ejpam-5756	70	6	n.	n.	PROPN
ejpam-5756	70	7	fatima	fatima	PROPN
ejpam-5756	70	8	/	/	PUNCT
ejpam-5756	70	9	eur	eur	PROPN
ejpam-5756	70	10	.	.	PUNCT
ejpam-5756	71	1	j.	j.	PROPN
ejpam-5756	71	2	pure	pure	PROPN
ejpam-5756	71	3	appl	appl	PROPN
ejpam-5756	71	4	.	.	PROPN
ejpam-5756	71	5	math	math	PROPN
ejpam-5756	71	6	,	,	PUNCT
ejpam-5756	71	7	18	18	NUM
ejpam-5756	71	8	(	(	PUNCT
ejpam-5756	71	9	1	1	NUM
ejpam-5756	71	10	)	)	PUNCT
ejpam-5756	71	11	(	(	PUNCT
ejpam-5756	71	12	2025	2025	NUM
ejpam-5756	71	13	)	)	PUNCT
ejpam-5756	71	14	,	,	PUNCT
ejpam-5756	71	15	5756	5756	NUM
ejpam-5756	71	16	4	4	NUM
ejpam-5756	71	17	of	of	ADP
ejpam-5756	71	18	17	17	NUM
ejpam-5756	71	19	tional	tional	ADJ
ejpam-5756	71	20	derivative	derivative	NOUN
ejpam-5756	71	21	,	,	PUNCT
ejpam-5756	71	22	riemann	riemann	PROPN
ejpam-5756	71	23	liouville	liouville	PROPN
ejpam-5756	71	24	fractional	fractional	PROPN
ejpam-5756	71	25	derivative	derivative	ADJ
ejpam-5756	71	26	and	and	CCONJ
ejpam-5756	71	27	grunwald	grunwald	NOUN
ejpam-5756	71	28	-	-	PUNCT
ejpam-5756	71	29	letnikov	letnikov	NOUN
ejpam-5756	71	30	fractional	fractional	ADJ
ejpam-5756	71	31	derivative	derivative	NOUN
ejpam-5756	71	32	.	.	PUNCT
ejpam-5756	72	1	recently	recently	ADV
ejpam-5756	72	2	,	,	PUNCT
ejpam-5756	72	3	khalil	khalil	PROPN
ejpam-5756	72	4	et	et	PROPN
ejpam-5756	72	5	al	al	PROPN
ejpam-5756	72	6	.	.	PROPN
ejpam-5756	72	7	have	have	AUX
ejpam-5756	72	8	introduced	introduce	VERB
ejpam-5756	72	9	a	a	DET
ejpam-5756	72	10	new	new	ADJ
ejpam-5756	72	11	,	,	PUNCT
ejpam-5756	72	12	straightforward	straightforward	ADJ
ejpam-5756	72	13	definition	definition	NOUN
ejpam-5756	72	14	of	of	ADP
ejpam-5756	72	15	the	the	DET
ejpam-5756	72	16	fractional	fractional	ADJ
ejpam-5756	72	17	derivative	derivative	NOUN
ejpam-5756	72	18	called	call	VERB
ejpam-5756	72	19	the	the	DET
ejpam-5756	72	20	conformable	conformable	ADJ
ejpam-5756	72	21	fractional	fractional	ADJ
ejpam-5756	72	22	derivative	derivative	NOUN
ejpam-5756	72	23	with	with	ADP
ejpam-5756	72	24	the	the	DET
ejpam-5756	72	25	limit	limit	NOUN
ejpam-5756	72	26	operator	operator	NOUN
ejpam-5756	72	27	and	and	CCONJ
ejpam-5756	72	28	he	he	PRON
ejpam-5756	72	29	made	make	VERB
ejpam-5756	72	30	the	the	DET
ejpam-5756	72	31	most	most	ADV
ejpam-5756	72	32	significant	significant	ADJ
ejpam-5756	72	33	contributions	contribution	NOUN
ejpam-5756	72	34	to	to	ADP
ejpam-5756	72	35	fractioanl	fractioanl	PROPN
ejpam-5756	72	36	derivative	derivative	PROPN
ejpam-5756	72	37	.	.	PUNCT
ejpam-5756	73	1	remark	remark	PROPN
ejpam-5756	73	2	1	1	NUM
ejpam-5756	73	3	”	"	PUNCT
ejpam-5756	73	4	we	we	PRON
ejpam-5756	73	5	use	use	VERB
ejpam-5756	73	6	of	of	ADP
ejpam-5756	73	7	polynomial	polynomial	ADJ
ejpam-5756	73	8	fractional	fractional	ADJ
ejpam-5756	73	9	derivatives	derivative	NOUN
ejpam-5756	73	10	as	as	ADP
ejpam-5756	73	11	dα	dα	PROPN
ejpam-5756	73	12	t	t	PROPN
ejpam-5756	73	13	(	(	PUNCT
ejpam-5756	73	14	t	t	PROPN
ejpam-5756	73	15	s	s	PART
ejpam-5756	73	16	)	)	PUNCT
ejpam-5756	73	17	=	=	SYM
ejpam-5756	73	18	γ(s+	γ(s+	ADJ
ejpam-5756	73	19	1	1	X
ejpam-5756	73	20	)	)	PUNCT
ejpam-5756	73	21	γ(s−	γ(s−	NOUN
ejpam-5756	73	22	α+	α+	PUNCT
ejpam-5756	73	23	1	1	NUM
ejpam-5756	73	24	)	)	PUNCT
ejpam-5756	73	25	ts−α	ts−α	NOUN
ejpam-5756	73	26	(	(	PUNCT
ejpam-5756	73	27	2	2	X
ejpam-5756	73	28	)	)	PUNCT
ejpam-5756	73	29	all	all	DET
ejpam-5756	73	30	the	the	DET
ejpam-5756	73	31	fractional	fractional	ADJ
ejpam-5756	73	32	derivatives	derivative	NOUN
ejpam-5756	73	33	applying	apply	VERB
ejpam-5756	73	34	on	on	ADP
ejpam-5756	73	35	polynomial	polynomial	ADJ
ejpam-5756	73	36	have	have	VERB
ejpam-5756	73	37	same	same	ADJ
ejpam-5756	73	38	results	result	NOUN
ejpam-5756	73	39	”	"	PUNCT
ejpam-5756	73	40	.	.	PUNCT
ejpam-5756	74	1	this	this	DET
ejpam-5756	74	2	paper	paper	NOUN
ejpam-5756	74	3	is	be	AUX
ejpam-5756	74	4	divided	divide	VERB
ejpam-5756	74	5	as	as	SCONJ
ejpam-5756	74	6	follows	follow	VERB
ejpam-5756	74	7	:	:	PUNCT
ejpam-5756	74	8	in	in	ADP
ejpam-5756	74	9	section	section	NOUN
ejpam-5756	74	10	2	2	NUM
ejpam-5756	74	11	,	,	PUNCT
ejpam-5756	74	12	power	power	NOUN
ejpam-5756	74	13	index	index	NOUN
ejpam-5756	74	14	method	method	NOUN
ejpam-5756	74	15	(	(	PUNCT
ejpam-5756	74	16	pim	pim	PROPN
ejpam-5756	74	17	)	)	PUNCT
ejpam-5756	74	18	is	be	AUX
ejpam-5756	74	19	introduced	introduce	VERB
ejpam-5756	74	20	.	.	PUNCT
ejpam-5756	75	1	in	in	ADP
ejpam-5756	75	2	section	section	NOUN
ejpam-5756	75	3	3	3	NUM
ejpam-5756	75	4	,	,	PUNCT
ejpam-5756	75	5	new	new	ADJ
ejpam-5756	75	6	function	function	NOUN
ejpam-5756	75	7	transformations	transformation	NOUN
ejpam-5756	75	8	are	be	AUX
ejpam-5756	75	9	applied	apply	VERB
ejpam-5756	75	10	to	to	ADP
ejpam-5756	75	11	the	the	DET
ejpam-5756	75	12	djkm	djkm	NOUN
ejpam-5756	75	13	equation	equation	NOUN
ejpam-5756	75	14	.	.	PUNCT
ejpam-5756	76	1	section	section	NOUN
ejpam-5756	76	2	4	4	NUM
ejpam-5756	76	3	are	be	AUX
ejpam-5756	76	4	devoted	devote	VERB
ejpam-5756	76	5	to	to	ADP
ejpam-5756	76	6	results	result	NOUN
ejpam-5756	76	7	and	and	CCONJ
ejpam-5756	76	8	discussion	discussion	NOUN
ejpam-5756	76	9	.	.	PUNCT
ejpam-5756	77	1	finally	finally	ADV
ejpam-5756	77	2	conclusion	conclusion	NOUN
ejpam-5756	77	3	is	be	AUX
ejpam-5756	77	4	demonstrated	demonstrate	VERB
ejpam-5756	77	5	in	in	ADP
ejpam-5756	77	6	section	section	NOUN
ejpam-5756	77	7	5	5	NUM
ejpam-5756	77	8	.	.	SYM
ejpam-5756	77	9	2	2	NUM
ejpam-5756	77	10	.	.	X
ejpam-5756	77	11	power	power	NOUN
ejpam-5756	77	12	index	index	NOUN
ejpam-5756	77	13	method	method	NOUN
ejpam-5756	77	14	step:-1	step:-1	VERB
ejpam-5756	77	15	considering	consider	VERB
ejpam-5756	77	16	the	the	DET
ejpam-5756	77	17	pde	pde	NOUN
ejpam-5756	77	18	(	(	PUNCT
ejpam-5756	77	19	1	1	NUM
ejpam-5756	77	20	)	)	PUNCT
ejpam-5756	77	21	and	and	CCONJ
ejpam-5756	77	22	we	we	PRON
ejpam-5756	77	23	want	want	VERB
ejpam-5756	77	24	to	to	PART
ejpam-5756	77	25	show	show	VERB
ejpam-5756	77	26	its	its	PRON
ejpam-5756	77	27	exact	exact	ADJ
ejpam-5756	77	28	solution	solution	NOUN
ejpam-5756	77	29	,	,	PUNCT
ejpam-5756	77	30	we	we	PRON
ejpam-5756	77	31	introduce	introduce	VERB
ejpam-5756	77	32	the	the	DET
ejpam-5756	77	33	variable	variable	NOUN
ejpam-5756	77	34	ξ	ξ	PROPN
ejpam-5756	77	35	as	as	ADP
ejpam-5756	77	36	;	;	PUNCT
ejpam-5756	77	37	ξ	ξ	X
ejpam-5756	77	38	=	=	SYM
ejpam-5756	77	39	xmtr	xmtr	NOUN
ejpam-5756	77	40	and	and	CCONJ
ejpam-5756	77	41	transformation	transformation	NOUN
ejpam-5756	77	42	of	of	ADP
ejpam-5756	77	43	general	general	ADJ
ejpam-5756	77	44	form	form	NOUN
ejpam-5756	77	45	is	be	AUX
ejpam-5756	77	46	;	;	PUNCT
ejpam-5756	78	1	u(x	u(x	NOUN
ejpam-5756	78	2	,	,	PUNCT
ejpam-5756	78	3	t	t	NOUN
ejpam-5756	78	4	)	)	PUNCT
ejpam-5756	78	5	=	=	SYM
ejpam-5756	78	6	xntsf(ξ	xntsf(ξ	NOUN
ejpam-5756	78	7	)	)	PUNCT
ejpam-5756	78	8	since	since	SCONJ
ejpam-5756	78	9	ξ	ξ	PROPN
ejpam-5756	78	10	and	and	CCONJ
ejpam-5756	78	11	u	u	NOUN
ejpam-5756	78	12	depend	depend	VERB
ejpam-5756	78	13	only	only	ADV
ejpam-5756	78	14	x	x	SYM
ejpam-5756	78	15	and	and	CCONJ
ejpam-5756	78	16	t	t	PROPN
ejpam-5756	78	17	,	,	PUNCT
ejpam-5756	78	18	so	so	SCONJ
ejpam-5756	78	19	all	all	DET
ejpam-5756	78	20	terms	term	NOUN
ejpam-5756	78	21	vanish	vanish	VERB
ejpam-5756	78	22	except	except	SCONJ
ejpam-5756	78	23	last	last	ADJ
ejpam-5756	78	24	term	term	NOUN
ejpam-5756	78	25	.	.	PUNCT
ejpam-5756	79	1	step:-2	step:-2	ADJ
ejpam-5756	79	2	by	by	ADP
ejpam-5756	79	3	using	use	VERB
ejpam-5756	79	4	fractional	fractional	ADJ
ejpam-5756	79	5	derivatives	derivative	NOUN
ejpam-5756	79	6	of	of	ADP
ejpam-5756	79	7	polynomial	polynomial	ADJ
ejpam-5756	79	8	as	as	ADP
ejpam-5756	79	9	dα	dα	PROPN
ejpam-5756	79	10	t	t	PROPN
ejpam-5756	79	11	(	(	PUNCT
ejpam-5756	79	12	t	t	PROPN
ejpam-5756	79	13	s	s	PART
ejpam-5756	79	14	)	)	PUNCT
ejpam-5756	79	15	=	=	SYM
ejpam-5756	79	16	γ(s+	γ(s+	ADJ
ejpam-5756	79	17	1	1	X
ejpam-5756	79	18	)	)	PUNCT
ejpam-5756	79	19	γ(s−	γ(s−	NOUN
ejpam-5756	79	20	α+	α+	PUNCT
ejpam-5756	79	21	1	1	X
ejpam-5756	79	22	)	)	PUNCT
ejpam-5756	79	23	ts−α	ts−α	NOUN
ejpam-5756	79	24	we	we	PRON
ejpam-5756	79	25	can	can	AUX
ejpam-5756	79	26	find	find	VERB
ejpam-5756	79	27	dα	dα	ADP
ejpam-5756	79	28	t	t	PROPN
ejpam-5756	79	29	u	u	NOUN
ejpam-5756	79	30	=	=	PROPN
ejpam-5756	79	31	dα	dα	PROPN
ejpam-5756	79	32	t	t	PROPN
ejpam-5756	79	33	(	(	PUNCT
ejpam-5756	79	34	x	x	NOUN
ejpam-5756	79	35	ntsf(ξ	ntsf(ξ	NOUN
ejpam-5756	79	36	)	)	PUNCT
ejpam-5756	79	37	)	)	PUNCT
ejpam-5756	80	1	=	=	PUNCT
ejpam-5756	80	2	xn	xn	NUM
ejpam-5756	80	3	γ(s+	γ(s+	NOUN
ejpam-5756	80	4	1	1	NUM
ejpam-5756	80	5	)	)	PUNCT
ejpam-5756	80	6	γ(s−	γ(s−	NOUN
ejpam-5756	80	7	α+	α+	PUNCT
ejpam-5756	80	8	1	1	X
ejpam-5756	80	9	)	)	PUNCT
ejpam-5756	80	10	ts−αf(ξ	ts−αf(ξ	NUM
ejpam-5756	80	11	)	)	PUNCT
ejpam-5756	81	1	+	+	NUM
ejpam-5756	81	2	xntsdα	xntsdα	ADJ
ejpam-5756	81	3	t	t	PROPN
ejpam-5756	81	4	f(ξ	f(ξ	PROPN
ejpam-5756	81	5	)	)	PUNCT
ejpam-5756	82	1	=	=	SYM
ejpam-5756	82	2	xn	xn	NUM
ejpam-5756	82	3	γ(s+	γ(s+	NOUN
ejpam-5756	82	4	1	1	NUM
ejpam-5756	82	5	)	)	PUNCT
ejpam-5756	82	6	γ(s−	γ(s−	NOUN
ejpam-5756	82	7	α+	α+	PUNCT
ejpam-5756	82	8	1	1	X
ejpam-5756	82	9	)	)	PUNCT
ejpam-5756	82	10	ts−αf(ξ	ts−αf(ξ	NUM
ejpam-5756	82	11	)	)	PUNCT
ejpam-5756	83	1	+	+	CCONJ
ejpam-5756	83	2	xm+nts+r−α	xm+nts+r−α	PROPN
ejpam-5756	83	3	γ(r	γ(r	PROPN
ejpam-5756	83	4	+	+	CCONJ
ejpam-5756	83	5	1	1	X
ejpam-5756	83	6	)	)	PUNCT
ejpam-5756	83	7	γ(r	γ(r	NOUN
ejpam-5756	84	1	−	−	PROPN
ejpam-5756	84	2	α+	α+	NOUN
ejpam-5756	84	3	1	1	NUM
ejpam-5756	84	4	)	)	PUNCT
ejpam-5756	84	5	f	f	PROPN
ejpam-5756	84	6	′(ξ	′(ξ	PROPN
ejpam-5756	84	7	)	)	PUNCT
ejpam-5756	84	8	the	the	DET
ejpam-5756	84	9	indexes	index	NOUN
ejpam-5756	84	10	of	of	ADP
ejpam-5756	84	11	x	x	X
ejpam-5756	84	12	and	and	CCONJ
ejpam-5756	84	13	t	t	PROPN
ejpam-5756	84	14	in	in	ADP
ejpam-5756	84	15	every	every	DET
ejpam-5756	84	16	term	term	NOUN
ejpam-5756	84	17	may	may	AUX
ejpam-5756	84	18	be	be	AUX
ejpam-5756	84	19	defined	define	VERB
ejpam-5756	84	20	the	the	DET
ejpam-5756	84	21	following	follow	VERB
ejpam-5756	84	22	form	form	NOUN
ejpam-5756	84	23	px	px	X
ejpam-5756	84	24	=	=	PROPN
ejpam-5756	85	1	a1m+	a1m+	PRON
ejpam-5756	85	2	a2n	a2n	PROPN
ejpam-5756	85	3	pt	pt	X
ejpam-5756	85	4	=	=	PUNCT
ejpam-5756	85	5	b1r	b1r	X
ejpam-5756	85	6	+	+	CCONJ
ejpam-5756	85	7	b2s	b2s	PROPN
ejpam-5756	85	8	where	where	SCONJ
ejpam-5756	85	9	ai	ai	VERB
ejpam-5756	85	10	,	,	PUNCT
ejpam-5756	85	11	bi	bi	NOUN
ejpam-5756	85	12	,	,	PUNCT
ejpam-5756	85	13	i	i	NOUN
ejpam-5756	85	14	=	=	NOUN
ejpam-5756	85	15	1	1	NUM
ejpam-5756	85	16	,	,	PUNCT
ejpam-5756	85	17	2	2	NUM
ejpam-5756	85	18	are	be	AUX
ejpam-5756	85	19	constants	constant	NOUN
ejpam-5756	85	20	that	that	PRON
ejpam-5756	85	21	can	can	AUX
ejpam-5756	85	22	be	be	AUX
ejpam-5756	85	23	come	come	VERB
ejpam-5756	85	24	by	by	ADP
ejpam-5756	85	25	taking	take	VERB
ejpam-5756	85	26	fractional	fractional	ADJ
ejpam-5756	85	27	derivatives	derivative	NOUN
ejpam-5756	85	28	.	.	PUNCT
ejpam-5756	86	1	we	we	PRON
ejpam-5756	86	2	observe	observe	VERB
ejpam-5756	86	3	coefficients	coefficient	NOUN
ejpam-5756	86	4	of	of	ADP
ejpam-5756	86	5	px	px	NOUN
ejpam-5756	86	6	and	and	CCONJ
ejpam-5756	86	7	pt	pt	INTJ
ejpam-5756	86	8	so	so	SCONJ
ejpam-5756	86	9	that	that	SCONJ
ejpam-5756	86	10	the	the	DET
ejpam-5756	86	11	pde	pde	NOUN
ejpam-5756	86	12	may	may	AUX
ejpam-5756	86	13	be	be	AUX
ejpam-5756	86	14	transformed	transform	VERB
ejpam-5756	86	15	to	to	PART
ejpam-5756	86	16	ode	ode	VERB
ejpam-5756	86	17	.	.	PUNCT
ejpam-5756	87	1	the	the	DET
ejpam-5756	87	2	best	well	ADV
ejpam-5756	87	3	optimal	optimal	ADJ
ejpam-5756	87	4	indexes	index	NOUN
ejpam-5756	87	5	of	of	ADP
ejpam-5756	87	6	independent	independent	ADJ
ejpam-5756	87	7	variable	variable	NOUN
ejpam-5756	87	8	x	x	PUNCT
ejpam-5756	87	9	and	and	CCONJ
ejpam-5756	87	10	t	t	PROPN
ejpam-5756	87	11	are	be	AUX
ejpam-5756	87	12	chosen	choose	VERB
ejpam-5756	87	13	in	in	ADP
ejpam-5756	87	14	such	such	ADJ
ejpam-5756	87	15	away	away	ADV
ejpam-5756	87	16	that	that	SCONJ
ejpam-5756	87	17	only	only	ADV
ejpam-5756	87	18	two	two	NUM
ejpam-5756	87	19	indexes	index	NOUN
ejpam-5756	87	20	vary	vary	VERB
ejpam-5756	87	21	at	at	ADP
ejpam-5756	87	22	time	time	NOUN
ejpam-5756	87	23	and	and	CCONJ
ejpam-5756	87	24	others	other	NOUN
ejpam-5756	87	25	are	be	AUX
ejpam-5756	87	26	fixed	fix	VERB
ejpam-5756	87	27	constants	constant	NOUN
ejpam-5756	87	28	.	.	PUNCT
ejpam-5756	88	1	we	we	PRON
ejpam-5756	88	2	continue	continue	VERB
ejpam-5756	88	3	this	this	DET
ejpam-5756	88	4	process	process	NOUN
ejpam-5756	88	5	with	with	ADP
ejpam-5756	88	6	different	different	PROPN
ejpam-5756	88	7	b.	b.	PROPN
ejpam-5756	88	8	yasmeen	yasmeen	PROPN
ejpam-5756	88	9	,	,	PUNCT
ejpam-5756	88	10	k.	k.	PROPN
ejpam-5756	88	11	ahmad	ahmad	PROPN
ejpam-5756	88	12	,	,	PUNCT
ejpam-5756	88	13	n.	n.	PROPN
ejpam-5756	88	14	fatima	fatima	PROPN
ejpam-5756	88	15	/	/	PUNCT
ejpam-5756	88	16	eur	eur	PROPN
ejpam-5756	88	17	.	.	PUNCT
ejpam-5756	89	1	j.	j.	PROPN
ejpam-5756	89	2	pure	pure	PROPN
ejpam-5756	89	3	appl	appl	PROPN
ejpam-5756	89	4	.	.	PROPN
ejpam-5756	89	5	math	math	PROPN
ejpam-5756	89	6	,	,	PUNCT
ejpam-5756	89	7	18	18	NUM
ejpam-5756	89	8	(	(	PUNCT
ejpam-5756	89	9	1	1	NUM
ejpam-5756	89	10	)	)	PUNCT
ejpam-5756	89	11	(	(	PUNCT
ejpam-5756	89	12	2025	2025	NUM
ejpam-5756	89	13	)	)	PUNCT
ejpam-5756	89	14	,	,	PUNCT
ejpam-5756	89	15	5756	5756	NUM
ejpam-5756	89	16	5	5	NUM
ejpam-5756	89	17	of	of	ADP
ejpam-5756	89	18	17	17	NUM
ejpam-5756	89	19	indexes	index	NOUN
ejpam-5756	89	20	of	of	ADP
ejpam-5756	89	21	x	x	X
ejpam-5756	89	22	and	and	CCONJ
ejpam-5756	89	23	t	t	NOUN
ejpam-5756	89	24	so	so	SCONJ
ejpam-5756	89	25	that	that	SCONJ
ejpam-5756	89	26	we	we	PRON
ejpam-5756	89	27	find	find	VERB
ejpam-5756	89	28	all	all	DET
ejpam-5756	89	29	well	well	ADV
ejpam-5756	89	30	-	-	PUNCT
ejpam-5756	89	31	defined	define	VERB
ejpam-5756	89	32	transformations	transformation	NOUN
ejpam-5756	89	33	.	.	PUNCT
ejpam-5756	90	1	step:-3	step:-3	NUM
ejpam-5756	90	2	by	by	ADP
ejpam-5756	90	3	using	use	VERB
ejpam-5756	90	4	the	the	DET
ejpam-5756	90	5	analytic	analytic	ADJ
ejpam-5756	90	6	solution	solution	NOUN
ejpam-5756	90	7	of	of	ADP
ejpam-5756	90	8	ode	ode	PROPN
ejpam-5756	90	9	and	and	CCONJ
ejpam-5756	90	10	transformation	transformation	NOUN
ejpam-5756	90	11	,	,	PUNCT
ejpam-5756	90	12	we	we	PRON
ejpam-5756	90	13	can	can	AUX
ejpam-5756	90	14	easily	easily	ADV
ejpam-5756	90	15	find	find	VERB
ejpam-5756	90	16	the	the	DET
ejpam-5756	90	17	relation	relation	NOUN
ejpam-5756	90	18	between	between	ADP
ejpam-5756	90	19	x	x	PROPN
ejpam-5756	90	20	and	and	CCONJ
ejpam-5756	90	21	ξ	ξ	PROPN
ejpam-5756	90	22	in	in	ADP
ejpam-5756	90	23	each	each	DET
ejpam-5756	90	24	term	term	NOUN
ejpam-5756	90	25	as	as	ADP
ejpam-5756	90	26	;	;	PUNCT
ejpam-5756	90	27	the	the	DET
ejpam-5756	90	28	indexes	index	NOUN
ejpam-5756	90	29	of	of	ADP
ejpam-5756	90	30	x	x	PRON
ejpam-5756	90	31	,	,	PUNCT
ejpam-5756	90	32	t	t	PROPN
ejpam-5756	90	33	in	in	ADP
ejpam-5756	90	34	terms	term	NOUN
ejpam-5756	90	35	containing	contain	VERB
ejpam-5756	90	36	f	f	PROPN
ejpam-5756	90	37	and	and	CCONJ
ejpam-5756	90	38	f	f	PROPN
ejpam-5756	90	39	′	′	NOUN
ejpam-5756	90	40	are	be	AUX
ejpam-5756	90	41	;	;	PUNCT
ejpam-5756	90	42	px(f	px(f	X
ejpam-5756	90	43	)	)	PUNCT
ejpam-5756	90	44	=	=	SYM
ejpam-5756	90	45	n	n	CCONJ
ejpam-5756	90	46	,	,	PUNCT
ejpam-5756	90	47	px(f	px(f	ADJ
ejpam-5756	90	48	′	′	NOUN
ejpam-5756	90	49	)	)	PUNCT
ejpam-5756	91	1	=	=	SYM
ejpam-5756	91	2	m+	m+	NUM
ejpam-5756	91	3	n	n	NOUN
ejpam-5756	91	4	pt(f	pt(f	NOUN
ejpam-5756	91	5	)	)	PUNCT
ejpam-5756	91	6	=	=	SYM
ejpam-5756	91	7	s−	s−	PROPN
ejpam-5756	91	8	α	α	NUM
ejpam-5756	91	9	,	,	PUNCT
ejpam-5756	91	10	pt(f	pt(f	X
ejpam-5756	91	11	′	′	NUM
ejpam-5756	91	12	)	)	PUNCT
ejpam-5756	91	13	=	=	PUNCT
ejpam-5756	91	14	s+	s+	PUNCT
ejpam-5756	91	15	r	r	NOUN
ejpam-5756	91	16	−	−	PROPN
ejpam-5756	91	17	α	α	NOUN
ejpam-5756	91	18	since	since	SCONJ
ejpam-5756	91	19	ξ	ξ	X
ejpam-5756	91	20	=	=	SYM
ejpam-5756	91	21	xmtn	xmtn	PROPN
ejpam-5756	91	22	,	,	PUNCT
ejpam-5756	91	23	so	so	SCONJ
ejpam-5756	91	24	the	the	DET
ejpam-5756	91	25	values	value	NOUN
ejpam-5756	91	26	of	of	ADP
ejpam-5756	91	27	px(f	px(f	NOUN
ejpam-5756	91	28	)	)	PUNCT
ejpam-5756	91	29	and	and	CCONJ
ejpam-5756	91	30	px(f	px(f	PROPN
ejpam-5756	91	31	′	′	NOUN
ejpam-5756	91	32	)	)	PUNCT
ejpam-5756	91	33	must	must	AUX
ejpam-5756	91	34	be	be	AUX
ejpam-5756	91	35	multiplies	multiplie	NOUN
ejpam-5756	91	36	of	of	ADP
ejpam-5756	91	37	m	m	PRON
ejpam-5756	91	38	and	and	CCONJ
ejpam-5756	91	39	similarly	similarly	ADV
ejpam-5756	91	40	,	,	PUNCT
ejpam-5756	91	41	the	the	DET
ejpam-5756	91	42	values	value	NOUN
ejpam-5756	91	43	of	of	ADP
ejpam-5756	91	44	pt(f	pt(f	NOUN
ejpam-5756	91	45	)	)	PUNCT
ejpam-5756	91	46	and	and	CCONJ
ejpam-5756	91	47	pt(f	pt(f	NUM
ejpam-5756	91	48	′	′	NUM
ejpam-5756	91	49	)	)	PUNCT
ejpam-5756	91	50	must	must	AUX
ejpam-5756	91	51	be	be	AUX
ejpam-5756	91	52	multiplies	multiplie	NOUN
ejpam-5756	91	53	of	of	ADP
ejpam-5756	91	54	r.	r.	PROPN
ejpam-5756	91	55	step:-4	step:-4	PROPN
ejpam-5756	91	56	we	we	PRON
ejpam-5756	91	57	select	select	VERB
ejpam-5756	91	58	out	out	ADP
ejpam-5756	91	59	a	a	DET
ejpam-5756	91	60	few	few	ADJ
ejpam-5756	91	61	members	member	NOUN
ejpam-5756	91	62	of	of	ADP
ejpam-5756	91	63	the	the	DET
ejpam-5756	91	64	family	family	NOUN
ejpam-5756	91	65	of	of	ADP
ejpam-5756	91	66	indexes	index	NOUN
ejpam-5756	91	67	of	of	ADP
ejpam-5756	91	68	x	x	X
ejpam-5756	91	69	and	and	CCONJ
ejpam-5756	91	70	ξ	ξ	PROPN
ejpam-5756	91	71	.	.	PUNCT
ejpam-5756	91	72	further	far	ADV
ejpam-5756	91	73	,	,	PUNCT
ejpam-5756	91	74	we	we	PRON
ejpam-5756	91	75	figure	figure	VERB
ejpam-5756	91	76	1	1	NUM
ejpam-5756	91	77	:	:	PUNCT
ejpam-5756	91	78	”	"	PUNCT
ejpam-5756	91	79	flow	flow	VERB
ejpam-5756	91	80	chart	chart	NOUN
ejpam-5756	91	81	of	of	ADP
ejpam-5756	91	82	power	power	NOUN
ejpam-5756	91	83	index	index	NOUN
ejpam-5756	91	84	method	method	NOUN
ejpam-5756	91	85	which	which	PRON
ejpam-5756	91	86	shows	show	VERB
ejpam-5756	91	87	how	how	SCONJ
ejpam-5756	91	88	we	we	PRON
ejpam-5756	91	89	transition	transition	VERB
ejpam-5756	91	90	from	from	ADP
ejpam-5756	91	91	a	a	DET
ejpam-5756	91	92	pde	pde	NOUN
ejpam-5756	91	93	to	to	ADP
ejpam-5756	91	94	an	an	DET
ejpam-5756	91	95	ode	ode	ADJ
ejpam-5756	91	96	,	,	PUNCT
ejpam-5756	91	97	and	and	CCONJ
ejpam-5756	91	98	subsequently	subsequently	ADV
ejpam-5756	91	99	obtain	obtain	VERB
ejpam-5756	91	100	analytical	analytical	ADJ
ejpam-5756	91	101	solutions	solution	NOUN
ejpam-5756	91	102	.	.	PUNCT
ejpam-5756	92	1	furthermore	furthermore	ADV
ejpam-5756	92	2	,	,	PUNCT
ejpam-5756	92	3	when	when	SCONJ
ejpam-5756	92	4	we	we	PRON
ejpam-5756	92	5	substitute	substitute	VERB
ejpam-5756	92	6	the	the	DET
ejpam-5756	92	7	soultion	soultion	NOUN
ejpam-5756	92	8	back	back	ADV
ejpam-5756	92	9	into	into	ADP
ejpam-5756	92	10	the	the	DET
ejpam-5756	92	11	original	original	ADJ
ejpam-5756	92	12	solution	solution	NOUN
ejpam-5756	92	13	pde	pde	NOUN
ejpam-5756	92	14	,	,	PUNCT
ejpam-5756	92	15	it	it	PRON
ejpam-5756	92	16	satisfies	satisfy	VERB
ejpam-5756	92	17	the	the	DET
ejpam-5756	92	18	equation	equation	NOUN
ejpam-5756	92	19	,	,	PUNCT
ejpam-5756	92	20	validating	validate	VERB
ejpam-5756	92	21	our	our	PRON
ejpam-5756	92	22	approach	approach	NOUN
ejpam-5756	92	23	”	"	PUNCT
ejpam-5756	92	24	.	.	PUNCT
ejpam-5756	93	1	get	get	VERB
ejpam-5756	93	2	different	different	ADJ
ejpam-5756	93	3	members	member	NOUN
ejpam-5756	93	4	of	of	ADP
ejpam-5756	93	5	power	power	NOUN
ejpam-5756	93	6	indexes	index	NOUN
ejpam-5756	93	7	in	in	ADP
ejpam-5756	93	8	order	order	NOUN
ejpam-5756	93	9	that	that	SCONJ
ejpam-5756	93	10	we	we	PRON
ejpam-5756	93	11	will	will	AUX
ejpam-5756	93	12	select	select	VERB
ejpam-5756	93	13	unique	unique	ADJ
ejpam-5756	93	14	values	value	NOUN
ejpam-5756	93	15	of	of	ADP
ejpam-5756	93	16	power	power	NOUN
ejpam-5756	93	17	indexed	index	VERB
ejpam-5756	93	18	.	.	PUNCT
ejpam-5756	94	1	we	we	PRON
ejpam-5756	94	2	retain	retain	VERB
ejpam-5756	94	3	the	the	DET
ejpam-5756	94	4	same	same	ADJ
ejpam-5756	94	5	technique	technique	NOUN
ejpam-5756	94	6	for	for	ADP
ejpam-5756	94	7	other	other	ADJ
ejpam-5756	94	8	variables	variable	NOUN
ejpam-5756	94	9	.	.	PUNCT
ejpam-5756	95	1	now	now	ADV
ejpam-5756	95	2	,	,	PUNCT
ejpam-5756	95	3	we	we	PRON
ejpam-5756	95	4	have	have	AUX
ejpam-5756	95	5	got	got	AUX
ejpam-5756	95	6	selected	select	VERB
ejpam-5756	95	7	a	a	DET
ejpam-5756	95	8	new	new	ADJ
ejpam-5756	95	9	variable	variable	NOUN
ejpam-5756	95	10	and	and	CCONJ
ejpam-5756	95	11	transformation	transformation	NOUN
ejpam-5756	95	12	with	with	ADP
ejpam-5756	95	13	changeable	changeable	ADJ
ejpam-5756	95	14	indexes	index	NOUN
ejpam-5756	95	15	.	.	PUNCT
ejpam-5756	96	1	next	next	ADJ
ejpam-5756	96	2	each	each	DET
ejpam-5756	96	3	term	term	NOUN
ejpam-5756	96	4	is	be	AUX
ejpam-5756	96	5	changed	change	VERB
ejpam-5756	96	6	by	by	ADP
ejpam-5756	96	7	using	use	VERB
ejpam-5756	96	8	a	a	DET
ejpam-5756	96	9	new	new	ADJ
ejpam-5756	96	10	variable	variable	NOUN
ejpam-5756	96	11	and	and	CCONJ
ejpam-5756	96	12	transformation	transformation	NOUN
ejpam-5756	96	13	.	.	PUNCT
ejpam-5756	97	1	our	our	PRON
ejpam-5756	97	2	objective	objective	NOUN
ejpam-5756	97	3	is	be	AUX
ejpam-5756	97	4	concentrated	concentrate	VERB
ejpam-5756	97	5	pde	pde	NOUN
ejpam-5756	97	6	into	into	ADP
ejpam-5756	97	7	ode	ode	ADJ
ejpam-5756	97	8	r(ξ	r(ξ	PROPN
ejpam-5756	97	9	,	,	PUNCT
ejpam-5756	97	10	f	f	PROPN
ejpam-5756	97	11	′	′	PROPN
ejpam-5756	97	12	,	,	PUNCT
ejpam-5756	97	13	f	f	PROPN
ejpam-5756	97	14	′′	′′	PROPN
ejpam-5756	97	15	,	,	PUNCT
ejpam-5756	97	16	...	...	PUNCT
ejpam-5756	97	17	)	)	PUNCT
ejpam-5756	98	1	=	=	SYM
ejpam-5756	98	2	0	0	PUNCT
ejpam-5756	98	3	(	(	PUNCT
ejpam-5756	98	4	3	3	NUM
ejpam-5756	98	5	)	)	PUNCT
ejpam-5756	98	6	where	where	SCONJ
ejpam-5756	98	7	r	r	NOUN
ejpam-5756	98	8	is	be	AUX
ejpam-5756	98	9	polynomial	polynomial	ADJ
ejpam-5756	98	10	of	of	ADP
ejpam-5756	98	11	f(ξ	f(ξ	NOUN
ejpam-5756	98	12	)	)	PUNCT
ejpam-5756	98	13	and	and	CCONJ
ejpam-5756	98	14	its	its	PRON
ejpam-5756	98	15	derivatives	derivative	NOUN
ejpam-5756	98	16	.	.	PUNCT
ejpam-5756	99	1	by	by	ADP
ejpam-5756	99	2	using	use	VERB
ejpam-5756	99	3	power	power	NOUN
ejpam-5756	99	4	index	index	NOUN
ejpam-5756	99	5	method	method	NOUN
ejpam-5756	99	6	,	,	PUNCT
ejpam-5756	99	7	we	we	PRON
ejpam-5756	99	8	can	can	AUX
ejpam-5756	99	9	gain	gain	VERB
ejpam-5756	99	10	a	a	DET
ejpam-5756	99	11	deeper	deep	ADJ
ejpam-5756	99	12	understanding	understanding	NOUN
ejpam-5756	99	13	of	of	ADP
ejpam-5756	99	14	power	power	NOUN
ejpam-5756	99	15	and	and	CCONJ
ejpam-5756	99	16	influence	influence	NOUN
ejpam-5756	99	17	within	within	ADP
ejpam-5756	99	18	various	various	ADJ
ejpam-5756	99	19	contexts	contexts	NOUN
ejpam-5756	99	20	,	,	PUNCT
ejpam-5756	99	21	and	and	CCONJ
ejpam-5756	99	22	develop	develop	VERB
ejpam-5756	99	23	more	more	ADV
ejpam-5756	99	24	effective	effective	ADJ
ejpam-5756	99	25	strategies	strategy	NOUN
ejpam-5756	99	26	for	for	ADP
ejpam-5756	99	27	promoting	promote	VERB
ejpam-5756	99	28	positive	positive	ADJ
ejpam-5756	99	29	b.	b.	PROPN
ejpam-5756	99	30	yasmeen	yasmeen	PROPN
ejpam-5756	99	31	,	,	PUNCT
ejpam-5756	99	32	k.	k.	PROPN
ejpam-5756	99	33	ahmad	ahmad	PROPN
ejpam-5756	99	34	,	,	PUNCT
ejpam-5756	99	35	n.	n.	PROPN
ejpam-5756	99	36	fatima	fatima	PROPN
ejpam-5756	99	37	/	/	PUNCT
ejpam-5756	99	38	eur	eur	PROPN
ejpam-5756	99	39	.	.	PUNCT
ejpam-5756	100	1	j.	j.	PROPN
ejpam-5756	100	2	pure	pure	PROPN
ejpam-5756	100	3	appl	appl	PROPN
ejpam-5756	100	4	.	.	PROPN
ejpam-5756	100	5	math	math	PROPN
ejpam-5756	100	6	,	,	PUNCT
ejpam-5756	100	7	18	18	NUM
ejpam-5756	100	8	(	(	PUNCT
ejpam-5756	100	9	1	1	NUM
ejpam-5756	100	10	)	)	PUNCT
ejpam-5756	100	11	(	(	PUNCT
ejpam-5756	100	12	2025	2025	NUM
ejpam-5756	100	13	)	)	PUNCT
ejpam-5756	100	14	,	,	PUNCT
ejpam-5756	100	15	5756	5756	NUM
ejpam-5756	100	16	6	6	NUM
ejpam-5756	100	17	of	of	ADP
ejpam-5756	100	18	17	17	NUM
ejpam-5756	100	19	change	change	NOUN
ejpam-5756	100	20	.	.	PUNCT
ejpam-5756	101	1	step:-5	step:-5	PROPN
ejpam-5756	101	2	solve	solve	VERB
ejpam-5756	101	3	the	the	DET
ejpam-5756	101	4	ode	ode	PROPN
ejpam-5756	101	5	(	(	PUNCT
ejpam-5756	101	6	3	3	NUM
ejpam-5756	101	7	)	)	PUNCT
ejpam-5756	101	8	by	by	ADP
ejpam-5756	101	9	using	use	VERB
ejpam-5756	101	10	computerized	computerized	ADJ
ejpam-5756	101	11	symbolic	symbolic	ADJ
ejpam-5756	101	12	package	package	NOUN
ejpam-5756	101	13	like	like	ADP
ejpam-5756	101	14	maple	maple	NOUN
ejpam-5756	101	15	.	.	PUNCT
ejpam-5756	102	1	if	if	SCONJ
ejpam-5756	102	2	we	we	PRON
ejpam-5756	102	3	get	get	VERB
ejpam-5756	102	4	exact	exact	ADJ
ejpam-5756	102	5	solution	solution	NOUN
ejpam-5756	102	6	of	of	ADP
ejpam-5756	102	7	the	the	DET
ejpam-5756	102	8	ode	ode	NOUN
ejpam-5756	102	9	then	then	ADV
ejpam-5756	102	10	expressing	express	VERB
ejpam-5756	102	11	this	this	DET
ejpam-5756	102	12	solution	solution	NOUN
ejpam-5756	102	13	by	by	ADP
ejpam-5756	102	14	using	use	VERB
ejpam-5756	102	15	new	new	ADJ
ejpam-5756	102	16	variable	variable	NOUN
ejpam-5756	102	17	and	and	CCONJ
ejpam-5756	102	18	transformation	transformation	NOUN
ejpam-5756	102	19	.	.	PUNCT
ejpam-5756	103	1	3	3	X
ejpam-5756	103	2	.	.	X
ejpam-5756	103	3	analytic	analytic	ADJ
ejpam-5756	103	4	solutions	solution	NOUN
ejpam-5756	103	5	of	of	ADP
ejpam-5756	103	6	date	date	NOUN
ejpam-5756	103	7	-	-	PUNCT
ejpam-5756	103	8	jimbo	jimbo	NOUN
ejpam-5756	103	9	-	-	PUNCT
ejpam-5756	103	10	kashiwara	kashiwara	PROPN
ejpam-5756	103	11	-	-	PUNCT
ejpam-5756	103	12	miwa	miwa	PROPN
ejpam-5756	103	13	equation	equation	NOUN
ejpam-5756	103	14	by	by	ADP
ejpam-5756	103	15	using	use	VERB
ejpam-5756	103	16	new	new	ADJ
ejpam-5756	103	17	function	function	NOUN
ejpam-5756	103	18	transformations	transformation	NOUN
ejpam-5756	103	19	case	case	NOUN
ejpam-5756	103	20	1	1	NUM
ejpam-5756	103	21	:	:	PUNCT
ejpam-5756	103	22	we	we	PRON
ejpam-5756	103	23	choose	choose	VERB
ejpam-5756	103	24	function	function	NOUN
ejpam-5756	103	25	transformation	transformation	NOUN
ejpam-5756	103	26	ξ	ξ	X
ejpam-5756	103	27	=	=	SYM
ejpam-5756	103	28	x2rt2n	x2rt2n	PUNCT
ejpam-5756	103	29	(	(	PUNCT
ejpam-5756	103	30	4	4	X
ejpam-5756	103	31	)	)	PUNCT
ejpam-5756	103	32	u	u	NOUN
ejpam-5756	103	33	=	=	SYM
ejpam-5756	103	34	xβf(ξ	xβf(ξ	PROPN
ejpam-5756	103	35	)	)	PUNCT
ejpam-5756	103	36	(	(	PUNCT
ejpam-5756	103	37	5	5	X
ejpam-5756	103	38	)	)	PUNCT
ejpam-5756	103	39	using	use	VERB
ejpam-5756	103	40	time	time	NOUN
ejpam-5756	103	41	-	-	PUNCT
ejpam-5756	103	42	fractional	fractional	ADJ
ejpam-5756	103	43	derivative	derivative	NOUN
ejpam-5756	103	44	,	,	PUNCT
ejpam-5756	103	45	we	we	PRON
ejpam-5756	103	46	have	have	VERB
ejpam-5756	103	47	∂αu	∂αu	PROPN
ejpam-5756	103	48	∂tα	∂tα	PROPN
ejpam-5756	103	49	=	=	SYM
ejpam-5756	103	50	γ(2n+	γ(2n+	PROPN
ejpam-5756	103	51	1	1	NUM
ejpam-5756	103	52	)	)	PUNCT
ejpam-5756	103	53	γ(2n−	γ(2n−	PROPN
ejpam-5756	103	54	α+	α+	PUNCT
ejpam-5756	103	55	1	1	X
ejpam-5756	103	56	)	)	PUNCT
ejpam-5756	103	57	xβ+2rt2n−αf	xβ+2rt2n−αf	PROPN
ejpam-5756	103	58	′(ξ	′(ξ	PROPN
ejpam-5756	103	59	)	)	PUNCT
ejpam-5756	103	60	(	(	PUNCT
ejpam-5756	103	61	6	6	NUM
ejpam-5756	103	62	)	)	PUNCT
ejpam-5756	103	63	∂	∂	NOUN
ejpam-5756	103	64	∂x	∂x	PROPN
ejpam-5756	103	65	(	(	PUNCT
ejpam-5756	103	66	∂αu	∂αu	PROPN
ejpam-5756	103	67	∂tα	∂tα	PROPN
ejpam-5756	103	68	)	)	PUNCT
ejpam-5756	104	1	=	=	PRON
ejpam-5756	104	2	γ(2n+	γ(2n+	NOUN
ejpam-5756	104	3	1	1	NUM
ejpam-5756	104	4	)	)	PUNCT
ejpam-5756	104	5	γ(2n−	γ(2n−	PROPN
ejpam-5756	104	6	α+	α+	PUNCT
ejpam-5756	104	7	1	1	X
ejpam-5756	104	8	)	)	PUNCT
ejpam-5756	104	9	t2n−α	t2n−α	NOUN
ejpam-5756	104	10	(	(	PUNCT
ejpam-5756	104	11	2rt2nxβ+4r−1f	2rt2nxβ+4r−1f	NUM
ejpam-5756	104	12	′′	′′	X
ejpam-5756	104	13	+	+	PROPN
ejpam-5756	104	14	xβ+2r−1(β	xβ+2r−1(β	PROPN
ejpam-5756	105	1	+	+	CCONJ
ejpam-5756	105	2	2r)f	2r)f	NUM
ejpam-5756	105	3	′	′	NUM
ejpam-5756	105	4	)	)	PUNCT
ejpam-5756	106	1	(	(	PUNCT
ejpam-5756	106	2	7	7	X
ejpam-5756	106	3	)	)	PUNCT
ejpam-5756	106	4	∂2	∂2	NOUN
ejpam-5756	106	5	∂x2	∂x2	NOUN
ejpam-5756	106	6	(	(	PUNCT
ejpam-5756	106	7	∂αu	∂αu	PROPN
ejpam-5756	106	8	∂tα	∂tα	PROPN
ejpam-5756	106	9	)	)	PUNCT
ejpam-5756	107	1	=	=	PRON
ejpam-5756	107	2	γ(2n+	γ(2n+	NOUN
ejpam-5756	107	3	1	1	NUM
ejpam-5756	107	4	)	)	PUNCT
ejpam-5756	107	5	γ(2n−	γ(2n−	PROPN
ejpam-5756	107	6	α+	α+	PUNCT
ejpam-5756	107	7	1	1	X
ejpam-5756	107	8	)	)	PUNCT
ejpam-5756	107	9	t2n−α	t2n−α	NOUN
ejpam-5756	107	10	∂	∂	NUM
ejpam-5756	107	11	∂x	∂x	PROPN
ejpam-5756	107	12	(	(	PUNCT
ejpam-5756	107	13	2rt2nxβ+4r−1f	2rt2nxβ+4r−1f	NUM
ejpam-5756	107	14	′′	′′	PROPN
ejpam-5756	107	15	+	+	PROPN
ejpam-5756	107	16	xβ+2r−1(β	xβ+2r−1(β	PROPN
ejpam-5756	108	1	+	+	CCONJ
ejpam-5756	108	2	2r)f	2r)f	NUM
ejpam-5756	108	3	′	′	NUM
ejpam-5756	108	4	)	)	PUNCT
ejpam-5756	109	1	=	=	PRON
ejpam-5756	109	2	γ(2n+	γ(2n+	NOUN
ejpam-5756	109	3	1	1	NUM
ejpam-5756	109	4	)	)	PUNCT
ejpam-5756	109	5	γ(2n−	γ(2n−	PROPN
ejpam-5756	109	6	α+	α+	PUNCT
ejpam-5756	109	7	1	1	X
ejpam-5756	109	8	)	)	PUNCT
ejpam-5756	109	9	t2n−α	t2n−α	NOUN
ejpam-5756	109	10	(	(	PUNCT
ejpam-5756	109	11	4r2t4nxβ+6r−2f	4r2t4nxβ+6r−2f	NUM
ejpam-5756	109	12	′′′	′′′	NOUN
ejpam-5756	110	1	+	+	CCONJ
ejpam-5756	110	2	2rt2nxβ+4r−2(2β	2rt2nxβ+4r−2(2β	NUM
ejpam-5756	110	3	+	+	CCONJ
ejpam-5756	110	4	6r	6r	NUM
ejpam-5756	110	5	−	−	NUM
ejpam-5756	110	6	1)f	1)f	NUM
ejpam-5756	111	1	′′	′′	PROPN
ejpam-5756	111	2	+	+	PROPN
ejpam-5756	111	3	(	(	PUNCT
ejpam-5756	111	4	β	β	NOUN
ejpam-5756	111	5	+	+	NUM
ejpam-5756	111	6	2r)(β	2r)(β	NUM
ejpam-5756	111	7	+	+	NUM
ejpam-5756	111	8	2r	2r	NUM
ejpam-5756	111	9	−	−	NOUN
ejpam-5756	111	10	1)xβ+2r−2f	1)xβ+2r−2f	NUM
ejpam-5756	111	11	′	′	NUM
ejpam-5756	111	12	)	)	PUNCT
ejpam-5756	111	13	(	(	PUNCT
ejpam-5756	111	14	8)	8)	NUM
ejpam-5756	111	15	using	use	VERB
ejpam-5756	111	16	(	(	PUNCT
ejpam-5756	111	17	6	6	NUM
ejpam-5756	111	18	)	)	PUNCT
ejpam-5756	111	19	,	,	PUNCT
ejpam-5756	111	20	(	(	PUNCT
ejpam-5756	111	21	7	7	X
ejpam-5756	111	22	)	)	PUNCT
ejpam-5756	111	23	and	and	CCONJ
ejpam-5756	111	24	(	(	PUNCT
ejpam-5756	111	25	8)	8)	NUM
ejpam-5756	111	26	the	the	DET
ejpam-5756	111	27	pde	pde	NOUN
ejpam-5756	111	28	(	(	PUNCT
ejpam-5756	111	29	1	1	X
ejpam-5756	111	30	)	)	PUNCT
ejpam-5756	111	31	can	can	AUX
ejpam-5756	111	32	be	be	AUX
ejpam-5756	111	33	expressed	express	VERB
ejpam-5756	111	34	in	in	ADP
ejpam-5756	111	35	simplified	simplify	VERB
ejpam-5756	111	36	as	as	ADP
ejpam-5756	111	37	;	;	PUNCT
ejpam-5756	111	38	4r2t4nx4rf	4r2t4nx4rf	NUM
ejpam-5756	111	39	′′′	′′′	NOUN
ejpam-5756	112	1	+	+	CCONJ
ejpam-5756	112	2	2rt2nx2r(3	2rt2nx2r(3	ADJ
ejpam-5756	112	3	+	+	NUM
ejpam-5756	112	4	2r)f	2r)f	NUM
ejpam-5756	112	5	′′	′′	NOUN
ejpam-5756	112	6	+	+	CCONJ
ejpam-5756	112	7	2f	2f	NUM
ejpam-5756	112	8	′	′	NUM
ejpam-5756	112	9	=	=	SYM
ejpam-5756	112	10	0	0	PUNCT
ejpam-5756	113	1	(	(	PUNCT
ejpam-5756	113	2	9	9	NUM
ejpam-5756	113	3	)	)	PUNCT
ejpam-5756	113	4	since	since	SCONJ
ejpam-5756	113	5	ξ	ξ	X
ejpam-5756	113	6	=	=	SYM
ejpam-5756	113	7	x2rt2n	x2rt2n	NUM
ejpam-5756	113	8	,	,	PUNCT
ejpam-5756	113	9	so	so	CCONJ
ejpam-5756	113	10	(	(	PUNCT
ejpam-5756	113	11	9	9	X
ejpam-5756	113	12	)	)	PUNCT
ejpam-5756	113	13	reduces	reduce	VERB
ejpam-5756	113	14	to	to	PART
ejpam-5756	113	15	ode	ode	VERB
ejpam-5756	113	16	.	.	PUNCT
ejpam-5756	114	1	for	for	ADP
ejpam-5756	114	2	simplification	simplification	NOUN
ejpam-5756	114	3	,	,	PUNCT
ejpam-5756	114	4	we	we	PRON
ejpam-5756	114	5	take	take	VERB
ejpam-5756	114	6	v	v	NOUN
ejpam-5756	114	7	=	=	SYM
ejpam-5756	114	8	f	f	NOUN
ejpam-5756	115	1	′	′	NUM
ejpam-5756	115	2	then	then	ADV
ejpam-5756	115	3	(	(	PUNCT
ejpam-5756	115	4	9	9	X
ejpam-5756	115	5	)	)	PUNCT
ejpam-5756	115	6	becomes	become	VERB
ejpam-5756	115	7	ξ2v	ξ2v	PROPN
ejpam-5756	115	8	′′	′′	PROPN
ejpam-5756	115	9	+	+	CCONJ
ejpam-5756	115	10	ξ	ξ	PROPN
ejpam-5756	115	11	(	(	PUNCT
ejpam-5756	115	12	2β	2β	NOUN
ejpam-5756	115	13	+	+	CCONJ
ejpam-5756	115	14	6r	6r	NUM
ejpam-5756	115	15	−	−	NUM
ejpam-5756	115	16	1	1	NUM
ejpam-5756	115	17	2r	2r	NUM
ejpam-5756	115	18	)	)	PUNCT
ejpam-5756	116	1	v	v	NOUN
ejpam-5756	116	2	′	′	NUM
ejpam-5756	117	1	+	+	CCONJ
ejpam-5756	117	2	β2	β2	NOUN
ejpam-5756	117	3	+	+	CCONJ
ejpam-5756	117	4	4βr	4βr	ADJ
ejpam-5756	117	5	+	+	CCONJ
ejpam-5756	117	6	4r2	4r2	NUM
ejpam-5756	118	1	−	−	NOUN
ejpam-5756	118	2	β	β	X
ejpam-5756	118	3	−	−	NOUN
ejpam-5756	118	4	2r	2r	NUM
ejpam-5756	118	5	4r2	4r2	NUM
ejpam-5756	118	6	v	v	NOUN
ejpam-5756	118	7	=	=	SYM
ejpam-5756	118	8	0	0	NUM
ejpam-5756	119	1	(	(	PUNCT
ejpam-5756	119	2	10	10	NUM
ejpam-5756	119	3	)	)	PUNCT
ejpam-5756	119	4	it	it	PRON
ejpam-5756	119	5	is	be	AUX
ejpam-5756	119	6	easy	easy	ADJ
ejpam-5756	119	7	to	to	PART
ejpam-5756	119	8	see	see	VERB
ejpam-5756	119	9	that	that	PRON
ejpam-5756	119	10	(	(	PUNCT
ejpam-5756	119	11	10	10	NUM
ejpam-5756	119	12	)	)	PUNCT
ejpam-5756	119	13	is	be	AUX
ejpam-5756	119	14	euler	euler	NOUN
ejpam-5756	119	15	second	second	ADJ
ejpam-5756	119	16	order	order	NOUN
ejpam-5756	119	17	linear	linear	PROPN
ejpam-5756	119	18	ode	ode	PROPN
ejpam-5756	119	19	.	.	PUNCT
ejpam-5756	120	1	if	if	SCONJ
ejpam-5756	120	2	we	we	PRON
ejpam-5756	120	3	choose	choose	VERB
ejpam-5756	120	4	v	v	NOUN
ejpam-5756	120	5	=	=	SYM
ejpam-5756	120	6	ξk	ξk	PROPN
ejpam-5756	120	7	,	,	PUNCT
ejpam-5756	120	8	v	v	NOUN
ejpam-5756	120	9	′	′	NOUN
ejpam-5756	120	10	=	=	PUNCT
ejpam-5756	121	1	kξk−1	kξk−1	PROPN
ejpam-5756	121	2	and	and	CCONJ
ejpam-5756	121	3	v	v	ADP
ejpam-5756	121	4	′′	′′	PROPN
ejpam-5756	121	5	=	=	PUNCT
ejpam-5756	122	1	k(k	k(k	PROPN
ejpam-5756	122	2	−	−	PROPN
ejpam-5756	122	3	1)ξk−2	1)ξk−2	PROPN
ejpam-5756	122	4	then	then	ADV
ejpam-5756	122	5	the	the	DET
ejpam-5756	122	6	characteristic	characteristic	ADJ
ejpam-5756	122	7	equation	equation	NOUN
ejpam-5756	122	8	of	of	ADP
ejpam-5756	122	9	(	(	PUNCT
ejpam-5756	122	10	10	10	NUM
ejpam-5756	122	11	)	)	PUNCT
ejpam-5756	122	12	is	be	AUX
ejpam-5756	122	13	k(k	k(k	VERB
ejpam-5756	122	14	−	−	PROPN
ejpam-5756	122	15	1	1	NUM
ejpam-5756	122	16	)	)	PUNCT
ejpam-5756	122	17	+	+	CCONJ
ejpam-5756	123	1	k	k	X
ejpam-5756	123	2	(	(	PUNCT
ejpam-5756	123	3	2β	2β	NOUN
ejpam-5756	123	4	+	+	CCONJ
ejpam-5756	123	5	6r	6r	NUM
ejpam-5756	123	6	−	−	NUM
ejpam-5756	123	7	1	1	NUM
ejpam-5756	123	8	2r	2r	NUM
ejpam-5756	123	9	)	)	PUNCT
ejpam-5756	124	1	+	+	CCONJ
ejpam-5756	124	2	β2	β2	ADJ
ejpam-5756	124	3	+	+	CCONJ
ejpam-5756	124	4	4βr	4βr	ADJ
ejpam-5756	124	5	+	+	CCONJ
ejpam-5756	124	6	4r2	4r2	NUM
ejpam-5756	124	7	−	−	NOUN
ejpam-5756	124	8	β	β	X
ejpam-5756	124	9	−	−	NOUN
ejpam-5756	124	10	2r	2r	NUM
ejpam-5756	124	11	4r2	4r2	NUM
ejpam-5756	125	1	=	=	SYM
ejpam-5756	125	2	0	0	PUNCT
ejpam-5756	126	1	(	(	PUNCT
ejpam-5756	126	2	11	11	NUM
ejpam-5756	126	3	)	)	PUNCT
ejpam-5756	126	4	b.	b.	PROPN
ejpam-5756	126	5	yasmeen	yasmeen	PROPN
ejpam-5756	126	6	,	,	PUNCT
ejpam-5756	126	7	k.	k.	PROPN
ejpam-5756	126	8	ahmad	ahmad	PROPN
ejpam-5756	126	9	,	,	PUNCT
ejpam-5756	126	10	n.	n.	PROPN
ejpam-5756	126	11	fatima	fatima	PROPN
ejpam-5756	126	12	/	/	PUNCT
ejpam-5756	126	13	eur	eur	PROPN
ejpam-5756	126	14	.	.	PUNCT
ejpam-5756	127	1	j.	j.	PROPN
ejpam-5756	127	2	pure	pure	PROPN
ejpam-5756	127	3	appl	appl	PROPN
ejpam-5756	127	4	.	.	PROPN
ejpam-5756	127	5	math	math	PROPN
ejpam-5756	127	6	,	,	PUNCT
ejpam-5756	127	7	18	18	NUM
ejpam-5756	127	8	(	(	PUNCT
ejpam-5756	127	9	1	1	NUM
ejpam-5756	127	10	)	)	PUNCT
ejpam-5756	127	11	(	(	PUNCT
ejpam-5756	127	12	2025	2025	NUM
ejpam-5756	127	13	)	)	PUNCT
ejpam-5756	127	14	,	,	PUNCT
ejpam-5756	127	15	5756	5756	NUM
ejpam-5756	127	16	7	7	NUM
ejpam-5756	127	17	of	of	ADP
ejpam-5756	127	18	17	17	NUM
ejpam-5756	127	19	the	the	DET
ejpam-5756	127	20	roots	root	NOUN
ejpam-5756	127	21	of	of	ADP
ejpam-5756	127	22	equation	equation	NOUN
ejpam-5756	127	23	(	(	PUNCT
ejpam-5756	127	24	11	11	NUM
ejpam-5756	127	25	)	)	PUNCT
ejpam-5756	127	26	are	be	AUX
ejpam-5756	127	27	k1	k1	NOUN
ejpam-5756	127	28	=	=	SYM
ejpam-5756	127	29	1−	1−	NUM
ejpam-5756	127	30	2β	2β	NOUN
ejpam-5756	127	31	−	−	PROPN
ejpam-5756	127	32	4r	4r	NUM
ejpam-5756	127	33	2r	2r	NUM
ejpam-5756	127	34	+	+	CCONJ
ejpam-5756	128	1	√	√	INTJ
ejpam-5756	128	2	(	(	PUNCT
ejpam-5756	128	3	2β	2β	NOUN
ejpam-5756	128	4	+	+	CCONJ
ejpam-5756	128	5	4r	4r	NUM
ejpam-5756	128	6	−	−	PROPN
ejpam-5756	128	7	1)2	1)2	NUM
ejpam-5756	128	8	−	−	NUM
ejpam-5756	128	9	4β(β	4β(β	NOUN
ejpam-5756	129	1	+	+	CCONJ
ejpam-5756	129	2	4r	4r	NUM
ejpam-5756	129	3	−	−	NOUN
ejpam-5756	129	4	1	1	NUM
ejpam-5756	129	5	)	)	PUNCT
ejpam-5756	129	6	+	+	CCONJ
ejpam-5756	129	7	2r(2r	2r(2r	NUM
ejpam-5756	129	8	−	−	NOUN
ejpam-5756	129	9	1	1	NUM
ejpam-5756	129	10	)	)	PUNCT
ejpam-5756	129	11	2r	2r	NUM
ejpam-5756	129	12	k2	k2	PROPN
ejpam-5756	129	13	=	=	SYM
ejpam-5756	129	14	1−	1−	NUM
ejpam-5756	129	15	2β	2β	NOUN
ejpam-5756	129	16	−	−	PROPN
ejpam-5756	129	17	4r	4r	NUM
ejpam-5756	129	18	2r	2r	NUM
ejpam-5756	130	1	−	−	NOUN
ejpam-5756	130	2	√	√	NUM
ejpam-5756	130	3	(	(	PUNCT
ejpam-5756	130	4	2β	2β	NUM
ejpam-5756	130	5	+	+	CCONJ
ejpam-5756	130	6	4r	4r	NUM
ejpam-5756	130	7	−	−	PROPN
ejpam-5756	131	1	1)2	1)2	NUM
ejpam-5756	131	2	−	−	NUM
ejpam-5756	131	3	4β(β	4β(β	NOUN
ejpam-5756	132	1	+	+	CCONJ
ejpam-5756	132	2	4r	4r	NUM
ejpam-5756	132	3	−	−	NOUN
ejpam-5756	132	4	1	1	NUM
ejpam-5756	132	5	)	)	PUNCT
ejpam-5756	132	6	+	+	CCONJ
ejpam-5756	132	7	2r(2r	2r(2r	NUM
ejpam-5756	132	8	−	−	NOUN
ejpam-5756	132	9	1	1	NUM
ejpam-5756	132	10	)	)	PUNCT
ejpam-5756	132	11	2r	2r	NUM
ejpam-5756	132	12	(	(	PUNCT
ejpam-5756	132	13	12	12	NUM
ejpam-5756	132	14	)	)	PUNCT
ejpam-5756	132	15	hence	hence	ADV
ejpam-5756	132	16	the	the	DET
ejpam-5756	132	17	analytic	analytic	ADJ
ejpam-5756	132	18	solution	solution	NOUN
ejpam-5756	132	19	of	of	ADP
ejpam-5756	132	20	ode	ode	PROPN
ejpam-5756	132	21	(	(	PUNCT
ejpam-5756	132	22	10	10	NUM
ejpam-5756	132	23	)	)	PUNCT
ejpam-5756	132	24	is	be	AUX
ejpam-5756	132	25	f	f	NOUN
ejpam-5756	132	26	′	′	NUM
ejpam-5756	132	27	=	=	SYM
ejpam-5756	132	28	v	v	NOUN
ejpam-5756	132	29	=	=	SYM
ejpam-5756	132	30	c1ξ	c1ξ	NOUN
ejpam-5756	132	31	k1	k1	NOUN
ejpam-5756	132	32	+	+	CCONJ
ejpam-5756	132	33	c2ξ	c2ξ	NOUN
ejpam-5756	132	34	k2	k2	NOUN
ejpam-5756	132	35	by	by	ADP
ejpam-5756	132	36	replacing	replace	VERB
ejpam-5756	132	37	v	v	NOUN
ejpam-5756	132	38	=	=	SYM
ejpam-5756	132	39	f	f	NOUN
ejpam-5756	132	40	′	′	NOUN
ejpam-5756	132	41	and	and	CCONJ
ejpam-5756	132	42	taking	take	VERB
ejpam-5756	132	43	integral	integral	ADJ
ejpam-5756	132	44	on	on	ADP
ejpam-5756	132	45	both	both	DET
ejpam-5756	132	46	sides	side	NOUN
ejpam-5756	132	47	,	,	PUNCT
ejpam-5756	132	48	we	we	PRON
ejpam-5756	132	49	get	get	VERB
ejpam-5756	132	50	f(ξ	f(ξ	NOUN
ejpam-5756	132	51	)	)	PUNCT
ejpam-5756	132	52	=	=	SYM
ejpam-5756	132	53	c1	c1	NOUN
ejpam-5756	132	54	ξk1	ξk1	VERB
ejpam-5756	132	55	+	+	PROPN
ejpam-5756	132	56	1	1	NUM
ejpam-5756	132	57	k1	k1	NOUN
ejpam-5756	132	58	+	+	CCONJ
ejpam-5756	132	59	1	1	NUM
ejpam-5756	133	1	+	+	NUM
ejpam-5756	133	2	c2	c2	PROPN
ejpam-5756	133	3	ξk2	ξk2	PROPN
ejpam-5756	133	4	+	+	PROPN
ejpam-5756	133	5	1	1	PROPN
ejpam-5756	133	6	k2	k2	NOUN
ejpam-5756	133	7	+	+	CCONJ
ejpam-5756	133	8	1	1	NUM
ejpam-5756	133	9	+	+	CCONJ
ejpam-5756	133	10	c3	c3	X
ejpam-5756	133	11	(	(	PUNCT
ejpam-5756	133	12	13	13	NUM
ejpam-5756	133	13	)	)	PUNCT
ejpam-5756	133	14	using	use	VERB
ejpam-5756	133	15	transformations	transformation	NOUN
ejpam-5756	133	16	(	(	PUNCT
ejpam-5756	133	17	4	4	NUM
ejpam-5756	133	18	)	)	PUNCT
ejpam-5756	133	19	,	,	PUNCT
ejpam-5756	133	20	(	(	PUNCT
ejpam-5756	133	21	5	5	NUM
ejpam-5756	133	22	)	)	PUNCT
ejpam-5756	133	23	and	and	CCONJ
ejpam-5756	133	24	analytic	analytic	ADJ
ejpam-5756	133	25	solution	solution	NOUN
ejpam-5756	133	26	of	of	ADP
ejpam-5756	133	27	ode	ode	PROPN
ejpam-5756	133	28	(	(	PUNCT
ejpam-5756	133	29	13	13	NUM
ejpam-5756	133	30	)	)	PUNCT
ejpam-5756	133	31	,	,	PUNCT
ejpam-5756	133	32	we	we	PRON
ejpam-5756	133	33	get	get	VERB
ejpam-5756	133	34	exact	exact	ADJ
ejpam-5756	133	35	solution	solution	NOUN
ejpam-5756	133	36	of	of	ADP
ejpam-5756	133	37	pde	pde	NOUN
ejpam-5756	133	38	(	(	PUNCT
ejpam-5756	133	39	1	1	NUM
ejpam-5756	133	40	)	)	PUNCT
ejpam-5756	133	41	which	which	PRON
ejpam-5756	133	42	is	be	AUX
ejpam-5756	133	43	u	u	NOUN
ejpam-5756	133	44	=	=	X
ejpam-5756	133	45	c1x	c1x	X
ejpam-5756	133	46	β	β	X
ejpam-5756	133	47	(	(	PUNCT
ejpam-5756	133	48	x	x	PROPN
ejpam-5756	133	49	2rt2n)k1	2rt2n)k1	NUM
ejpam-5756	133	50	+	+	NOUN
ejpam-5756	133	51	1	1	NUM
ejpam-5756	133	52	k1	k1	NOUN
ejpam-5756	133	53	+	+	CCONJ
ejpam-5756	133	54	1	1	NUM
ejpam-5756	133	55	+	+	CCONJ
ejpam-5756	133	56	c2x	c2x	VERB
ejpam-5756	133	57	β	β	X
ejpam-5756	133	58	(	(	PUNCT
ejpam-5756	133	59	x	x	PROPN
ejpam-5756	133	60	2rt2n)k2	2rt2n)k2	NUM
ejpam-5756	133	61	+	+	ADJ
ejpam-5756	133	62	1	1	NUM
ejpam-5756	133	63	k2	k2	NOUN
ejpam-5756	133	64	+	+	CCONJ
ejpam-5756	133	65	1	1	NUM
ejpam-5756	133	66	+	+	CCONJ
ejpam-5756	133	67	c3x	c3x	PROPN
ejpam-5756	133	68	β	β	X
ejpam-5756	133	69	u	u	NOUN
ejpam-5756	133	70	=	=	PROPN
ejpam-5756	133	71	c1	c1	PROPN
ejpam-5756	133	72	xβ+2rk1	xβ+2rk1	PROPN
ejpam-5756	134	1	+	+	PROPN
ejpam-5756	134	2	2rt2nk1	2rt2nk1	NUM
ejpam-5756	134	3	+	+	SYM
ejpam-5756	134	4	2n	2n	ADJ
ejpam-5756	134	5	k1	k1	NOUN
ejpam-5756	134	6	+	+	CCONJ
ejpam-5756	134	7	1	1	NUM
ejpam-5756	135	1	+	+	NUM
ejpam-5756	135	2	c2	c2	PROPN
ejpam-5756	135	3	xβ+2rk2	xβ+2rk2	NUM
ejpam-5756	136	1	+	+	ADJ
ejpam-5756	136	2	2rt2nk2	2rt2nk2	NUM
ejpam-5756	136	3	+	+	ADJ
ejpam-5756	136	4	2n	2n	ADJ
ejpam-5756	136	5	k2	k2	NOUN
ejpam-5756	136	6	+	+	CCONJ
ejpam-5756	136	7	1	1	NUM
ejpam-5756	136	8	+	+	CCONJ
ejpam-5756	136	9	c3x	c3x	PROPN
ejpam-5756	136	10	β	β	X
ejpam-5756	136	11	(	(	PUNCT
ejpam-5756	136	12	14	14	NUM
ejpam-5756	136	13	)	)	PUNCT
ejpam-5756	136	14	where	where	SCONJ
ejpam-5756	136	15	k1	k1	NOUN
ejpam-5756	136	16	and	and	CCONJ
ejpam-5756	136	17	k2	k2	NOUN
ejpam-5756	136	18	are	be	AUX
ejpam-5756	136	19	given	give	VERB
ejpam-5756	136	20	in	in	ADP
ejpam-5756	136	21	(	(	PUNCT
ejpam-5756	136	22	12	12	NUM
ejpam-5756	136	23	)	)	PUNCT
ejpam-5756	136	24	.	.	PUNCT
ejpam-5756	137	1	when	when	SCONJ
ejpam-5756	137	2	β	β	X
ejpam-5756	137	3	=	=	NOUN
ejpam-5756	137	4	0.5	0.5	NUM
ejpam-5756	137	5	it	it	PRON
ejpam-5756	137	6	become	become	VERB
ejpam-5756	137	7	rapidly	rapidly	ADV
ejpam-5756	137	8	change	change	NOUN
ejpam-5756	137	9	in	in	ADP
ejpam-5756	137	10	the	the	DET
ejpam-5756	137	11	wave	wave	NOUN
ejpam-5756	137	12	amplitude	amplitude	NOUN
ejpam-5756	137	13	.	.	PUNCT
ejpam-5756	138	1	case	case	NOUN
ejpam-5756	138	2	2	2	NUM
ejpam-5756	138	3	:	:	SYM
ejpam-5756	138	4	ξ	ξ	X
ejpam-5756	138	5	=	=	SYM
ejpam-5756	138	6	xtm	xtm	PROPN
ejpam-5756	138	7	(	(	PUNCT
ejpam-5756	138	8	15	15	NUM
ejpam-5756	138	9	)	)	PUNCT
ejpam-5756	138	10	u	u	NOUN
ejpam-5756	138	11	=	=	PROPN
ejpam-5756	138	12	xβtnf(ξ	xβtnf(ξ	PROPN
ejpam-5756	138	13	)	)	PUNCT
ejpam-5756	138	14	(	(	PUNCT
ejpam-5756	138	15	16	16	NUM
ejpam-5756	138	16	)	)	PUNCT
ejpam-5756	138	17	using	use	VERB
ejpam-5756	138	18	time	time	NOUN
ejpam-5756	138	19	-	-	PUNCT
ejpam-5756	138	20	fractional	fractional	ADJ
ejpam-5756	138	21	derivative	derivative	NOUN
ejpam-5756	138	22	,	,	PUNCT
ejpam-5756	138	23	we	we	PRON
ejpam-5756	138	24	have	have	VERB
ejpam-5756	138	25	∂αu	∂αu	PROPN
ejpam-5756	138	26	∂tα	∂tα	PROPN
ejpam-5756	138	27	=	=	SYM
ejpam-5756	138	28	γ(m+	γ(m+	NUM
ejpam-5756	138	29	1	1	NUM
ejpam-5756	138	30	)	)	PUNCT
ejpam-5756	138	31	γ(m−	γ(m−	PROPN
ejpam-5756	138	32	α+	α+	PRON
ejpam-5756	138	33	1	1	NUM
ejpam-5756	138	34	)	)	PUNCT
ejpam-5756	138	35	xβ+1tn+m−αf	xβ+1tn+m−αf	X
ejpam-5756	138	36	′(ξ	′(ξ	PROPN
ejpam-5756	138	37	)	)	PUNCT
ejpam-5756	139	1	+	+	CCONJ
ejpam-5756	139	2	γ(n+	γ(n+	NUM
ejpam-5756	139	3	1	1	NUM
ejpam-5756	139	4	)	)	PUNCT
ejpam-5756	139	5	γ(n−	γ(n−	NOUN
ejpam-5756	139	6	α+	α+	PUNCT
ejpam-5756	139	7	1	1	NUM
ejpam-5756	139	8	)	)	PUNCT
ejpam-5756	139	9	xβtn−αf(ξ	xβtn−αf(ξ	PUNCT
ejpam-5756	139	10	)	)	PUNCT
ejpam-5756	140	1	(	(	PUNCT
ejpam-5756	140	2	17	17	NUM
ejpam-5756	140	3	)	)	PUNCT
ejpam-5756	140	4	∂	∂	NOUN
ejpam-5756	140	5	∂x	∂x	PROPN
ejpam-5756	140	6	(	(	PUNCT
ejpam-5756	140	7	∂αu	∂αu	PROPN
ejpam-5756	140	8	∂tα	∂tα	PROPN
ejpam-5756	140	9	)	)	PUNCT
ejpam-5756	140	10	=	=	PUNCT
ejpam-5756	141	1	γ(m+	γ(m+	NUM
ejpam-5756	141	2	1	1	X
ejpam-5756	141	3	)	)	PUNCT
ejpam-5756	141	4	γ(m−	γ(m−	PROPN
ejpam-5756	141	5	α+	α+	DET
ejpam-5756	141	6	1	1	NUM
ejpam-5756	141	7	)	)	PUNCT
ejpam-5756	141	8	tn+m−α	tn+m−α	PROPN
ejpam-5756	141	9	(	(	PUNCT
ejpam-5756	141	10	tmxβ+1f	tmxβ+1f	ADP
ejpam-5756	141	11	′′	′′	PROPN
ejpam-5756	141	12	+	+	CCONJ
ejpam-5756	141	13	xβ(β	xβ(β	PUNCT
ejpam-5756	142	1	+	+	CCONJ
ejpam-5756	142	2	1)f	1)f	NUM
ejpam-5756	142	3	′	′	NUM
ejpam-5756	142	4	)	)	PUNCT
ejpam-5756	143	1	+	+	CCONJ
ejpam-5756	143	2	γ(n+	γ(n+	NUM
ejpam-5756	143	3	1	1	NUM
ejpam-5756	143	4	)	)	PUNCT
ejpam-5756	143	5	γ(n−	γ(n−	NOUN
ejpam-5756	143	6	α+	α+	PUNCT
ejpam-5756	143	7	1	1	NUM
ejpam-5756	143	8	)	)	PUNCT
ejpam-5756	143	9	tn−α	tn−α	NOUN
ejpam-5756	143	10	(	(	PUNCT
ejpam-5756	143	11	βxβ−1tmf	βxβ−1tmf	INTJ
ejpam-5756	143	12	′	′	NUM
ejpam-5756	144	1	+	+	CCONJ
ejpam-5756	144	2	β(β	β(β	NUM
ejpam-5756	144	3	−	−	NUM
ejpam-5756	144	4	1)f	1)f	NUM
ejpam-5756	145	1	+	+	PUNCT
ejpam-5756	145	2	xβt2mf	xβt2mf	X
ejpam-5756	145	3	′′	′′	PROPN
ejpam-5756	145	4	+	+	CCONJ
ejpam-5756	145	5	βxβ−1tmf	βxβ−1tmf	NUM
ejpam-5756	145	6	′	′	NUM
ejpam-5756	145	7	)	)	PUNCT
ejpam-5756	145	8	(	(	PUNCT
ejpam-5756	145	9	18	18	NUM
ejpam-5756	145	10	)	)	PUNCT
ejpam-5756	145	11	∂2	∂2	NOUN
ejpam-5756	145	12	∂x2	∂x2	NOUN
ejpam-5756	145	13	(	(	PUNCT
ejpam-5756	145	14	∂αu	∂αu	PROPN
ejpam-5756	145	15	∂tα	∂tα	PROPN
ejpam-5756	145	16	)	)	PUNCT
ejpam-5756	146	1	=	=	SYM
ejpam-5756	146	2	m1	m1	PROPN
ejpam-5756	146	3	t	t	PROPN
ejpam-5756	146	4	3mx3f	3mx3f	NUM
ejpam-5756	147	1	′′′	′′′	PROPN
ejpam-5756	148	1	+	+	CCONJ
ejpam-5756	148	2	(	(	PUNCT
ejpam-5756	148	3	2m1(β	2m1(β	NUM
ejpam-5756	148	4	+	+	CCONJ
ejpam-5756	148	5	1	1	NUM
ejpam-5756	148	6	)	)	PUNCT
ejpam-5756	148	7	+	+	CCONJ
ejpam-5756	148	8	n1)t	n1)t	ADJ
ejpam-5756	148	9	2mxβ(2)f	2mxβ(2)f	NUM
ejpam-5756	148	10	′′+	′′+	NOUN
ejpam-5756	149	1	β(m1(β	β(m1(β	PROPN
ejpam-5756	149	2	+	+	CCONJ
ejpam-5756	149	3	1	1	NUM
ejpam-5756	149	4	)	)	PUNCT
ejpam-5756	149	5	+	+	CCONJ
ejpam-5756	149	6	2n1)xt	2n1)xt	NUM
ejpam-5756	149	7	mf	mf	X
ejpam-5756	149	8	′	′	NOUN
ejpam-5756	150	1	+	+	CCONJ
ejpam-5756	151	1	n1β(β	n1β(β	PROPN
ejpam-5756	151	2	−	−	NOUN
ejpam-5756	151	3	1)f	1)f	NUM
ejpam-5756	151	4	=	=	SYM
ejpam-5756	151	5	0	0	PROPN
ejpam-5756	151	6	,	,	PUNCT
ejpam-5756	151	7	(	(	PUNCT
ejpam-5756	151	8	19	19	NUM
ejpam-5756	151	9	)	)	PUNCT
ejpam-5756	151	10	b.	b.	PROPN
ejpam-5756	151	11	yasmeen	yasmeen	PROPN
ejpam-5756	151	12	,	,	PUNCT
ejpam-5756	151	13	k.	k.	PROPN
ejpam-5756	151	14	ahmad	ahmad	PROPN
ejpam-5756	151	15	,	,	PUNCT
ejpam-5756	151	16	n.	n.	PROPN
ejpam-5756	151	17	fatima	fatima	PROPN
ejpam-5756	151	18	/	/	PUNCT
ejpam-5756	151	19	eur	eur	PROPN
ejpam-5756	151	20	.	.	PUNCT
ejpam-5756	152	1	j.	j.	PROPN
ejpam-5756	152	2	pure	pure	PROPN
ejpam-5756	152	3	appl	appl	PROPN
ejpam-5756	152	4	.	.	PROPN
ejpam-5756	152	5	math	math	PROPN
ejpam-5756	152	6	,	,	PUNCT
ejpam-5756	152	7	18	18	NUM
ejpam-5756	152	8	(	(	PUNCT
ejpam-5756	152	9	1	1	NUM
ejpam-5756	152	10	)	)	PUNCT
ejpam-5756	152	11	(	(	PUNCT
ejpam-5756	152	12	2025	2025	NUM
ejpam-5756	152	13	)	)	PUNCT
ejpam-5756	152	14	,	,	PUNCT
ejpam-5756	152	15	5756	5756	NUM
ejpam-5756	152	16	8	8	NUM
ejpam-5756	152	17	of	of	ADP
ejpam-5756	152	18	17	17	NUM
ejpam-5756	152	19	where	where	SCONJ
ejpam-5756	152	20	m1	m1	PROPN
ejpam-5756	152	21	=	=	SYM
ejpam-5756	152	22	γ(m+1	γ(m+1	PUNCT
ejpam-5756	152	23	)	)	PUNCT
ejpam-5756	152	24	γ(m−α+1	γ(m−α+1	NOUN
ejpam-5756	152	25	)	)	PUNCT
ejpam-5756	152	26	and	and	CCONJ
ejpam-5756	152	27	n1	n1	PROPN
ejpam-5756	152	28	=	=	SYM
ejpam-5756	152	29	γ(n+1	γ(n+1	PROPN
ejpam-5756	152	30	)	)	PUNCT
ejpam-5756	152	31	γ(n−α+1	γ(n−α+1	NOUN
ejpam-5756	152	32	)	)	PUNCT
ejpam-5756	152	33	.	.	PUNCT
ejpam-5756	153	1	using	use	VERB
ejpam-5756	153	2	(	(	PUNCT
ejpam-5756	153	3	17	17	NUM
ejpam-5756	153	4	)	)	PUNCT
ejpam-5756	153	5	,	,	PUNCT
ejpam-5756	153	6	(	(	PUNCT
ejpam-5756	153	7	19	19	NUM
ejpam-5756	153	8	)	)	PUNCT
ejpam-5756	153	9	and	and	CCONJ
ejpam-5756	153	10	ξ	ξ	X
ejpam-5756	153	11	=	=	SYM
ejpam-5756	153	12	xtm	xtm	PROPN
ejpam-5756	153	13	,	,	PUNCT
ejpam-5756	153	14	the	the	DET
ejpam-5756	153	15	pde	pde	NOUN
ejpam-5756	153	16	(	(	PUNCT
ejpam-5756	153	17	1	1	X
ejpam-5756	153	18	)	)	PUNCT
ejpam-5756	153	19	can	can	AUX
ejpam-5756	153	20	be	be	AUX
ejpam-5756	153	21	expressed	express	VERB
ejpam-5756	153	22	as	as	ADP
ejpam-5756	153	23	;	;	PUNCT
ejpam-5756	153	24	m1ξ	m1ξ	PROPN
ejpam-5756	153	25	3f	3f	PROPN
ejpam-5756	153	26	′′′	′′′	PROPN
ejpam-5756	154	1	+	+	CCONJ
ejpam-5756	154	2	(	(	PUNCT
ejpam-5756	154	3	2m1(β	2m1(β	NUM
ejpam-5756	154	4	+	+	CCONJ
ejpam-5756	154	5	1	1	NUM
ejpam-5756	154	6	)	)	PUNCT
ejpam-5756	154	7	+	+	CCONJ
ejpam-5756	155	1	n1)ξ	n1)ξ	PROPN
ejpam-5756	155	2	2f	2f	NUM
ejpam-5756	155	3	′′	′′	PROPN
ejpam-5756	155	4	+	+	CCONJ
ejpam-5756	155	5	β(m1(β	β(m1(β	PROPN
ejpam-5756	155	6	+	+	CCONJ
ejpam-5756	155	7	1	1	NUM
ejpam-5756	155	8	)	)	PUNCT
ejpam-5756	155	9	+	+	CCONJ
ejpam-5756	155	10	2n1)ξf	2n1)ξf	NUM
ejpam-5756	155	11	′	′	NUM
ejpam-5756	155	12	+	+	CCONJ
ejpam-5756	155	13	n1β(β	n1β(β	PROPN
ejpam-5756	155	14	−	−	NOUN
ejpam-5756	155	15	1)f	1)f	NUM
ejpam-5756	155	16	=	=	SYM
ejpam-5756	155	17	0	0	NUM
ejpam-5756	156	1	(	(	PUNCT
ejpam-5756	156	2	20	20	NUM
ejpam-5756	156	3	)	)	PUNCT
ejpam-5756	156	4	it	it	PRON
ejpam-5756	156	5	is	be	AUX
ejpam-5756	156	6	easy	easy	ADJ
ejpam-5756	156	7	to	to	PART
ejpam-5756	156	8	see	see	VERB
ejpam-5756	156	9	that	that	PRON
ejpam-5756	156	10	(	(	PUNCT
ejpam-5756	156	11	20	20	NUM
ejpam-5756	156	12	)	)	PUNCT
ejpam-5756	156	13	is	be	AUX
ejpam-5756	156	14	euler	euler	NOUN
ejpam-5756	156	15	second	second	ADJ
ejpam-5756	156	16	order	order	NOUN
ejpam-5756	156	17	linear	linear	PROPN
ejpam-5756	156	18	ode	ode	PROPN
ejpam-5756	156	19	.	.	PUNCT
ejpam-5756	157	1	if	if	SCONJ
ejpam-5756	157	2	we	we	PRON
ejpam-5756	157	3	choose	choose	VERB
ejpam-5756	157	4	f	f	PROPN
ejpam-5756	157	5	=	=	SYM
ejpam-5756	157	6	ξk	ξk	PROPN
ejpam-5756	157	7	,	,	PUNCT
ejpam-5756	157	8	f	f	PROPN
ejpam-5756	157	9	′	′	NUM
ejpam-5756	158	1	=	=	PUNCT
ejpam-5756	158	2	kξk−1	kξk−1	PROPN
ejpam-5756	158	3	,	,	PUNCT
ejpam-5756	158	4	f	f	X
ejpam-5756	158	5	′′	′′	PROPN
ejpam-5756	158	6	=	=	PRON
ejpam-5756	158	7	k(k−	k(k−	PROPN
ejpam-5756	158	8	1)ξk−2	1)ξk−2	PROPN
ejpam-5756	158	9	and	and	CCONJ
ejpam-5756	158	10	f	f	PROPN
ejpam-5756	158	11	′′′	′′′	PROPN
ejpam-5756	159	1	=	=	PUNCT
ejpam-5756	160	1	k(k−	k(k−	PROPN
ejpam-5756	160	2	1)(k−	1)(k−	NUM
ejpam-5756	160	3	2)ξk−3	2)ξk−3	NOUN
ejpam-5756	160	4	then	then	ADV
ejpam-5756	160	5	the	the	DET
ejpam-5756	160	6	characteristic	characteristic	ADJ
ejpam-5756	160	7	equation	equation	NOUN
ejpam-5756	160	8	is	be	AUX
ejpam-5756	160	9	m1k(k−1)(k−2)+k(k−1)(2m1(β+1)+n1)+β(m1(β+1)+2n1)k+n1β(β−1	m1k(k−1)(k−2)+k(k−1)(2m1(β+1)+n1)+β(m1(β+1)+2n1)k+n1β(β−1	ADV
ejpam-5756	160	10	)	)	PUNCT
ejpam-5756	160	11	=	=	SYM
ejpam-5756	160	12	0	0	PUNCT
ejpam-5756	160	13	(	(	PUNCT
ejpam-5756	160	14	21	21	NUM
ejpam-5756	160	15	)	)	PUNCT
ejpam-5756	160	16	the	the	DET
ejpam-5756	160	17	roots	root	NOUN
ejpam-5756	160	18	of	of	ADP
ejpam-5756	160	19	equation	equation	NOUN
ejpam-5756	160	20	(	(	PUNCT
ejpam-5756	160	21	21	21	NUM
ejpam-5756	160	22	)	)	PUNCT
ejpam-5756	160	23	are	be	AUX
ejpam-5756	160	24	k	k	X
ejpam-5756	160	25	=	=	SYM
ejpam-5756	160	26	−β	−β	PROPN
ejpam-5756	160	27	,	,	PUNCT
ejpam-5756	160	28	k	k	PROPN
ejpam-5756	160	29	=	=	SYM
ejpam-5756	160	30	1−	1−	NUM
ejpam-5756	160	31	β	β	X
ejpam-5756	160	32	and	and	CCONJ
ejpam-5756	160	33	k	k	PROPN
ejpam-5756	160	34	=	=	PUNCT
ejpam-5756	161	1	−	−	PROPN
ejpam-5756	161	2	n1	n1	ADJ
ejpam-5756	161	3	m1	m1	NOUN
ejpam-5756	161	4	.	.	PUNCT
ejpam-5756	162	1	hence	hence	ADV
ejpam-5756	162	2	the	the	DET
ejpam-5756	162	3	analytic	analytic	ADJ
ejpam-5756	162	4	solution	solution	NOUN
ejpam-5756	162	5	of	of	ADP
ejpam-5756	162	6	ode	ode	PROPN
ejpam-5756	162	7	(	(	PUNCT
ejpam-5756	162	8	20	20	NUM
ejpam-5756	162	9	)	)	PUNCT
ejpam-5756	162	10	is	be	AUX
ejpam-5756	162	11	f(ξ	f(ξ	NOUN
ejpam-5756	162	12	)	)	PUNCT
ejpam-5756	162	13	=	=	PUNCT
ejpam-5756	162	14	c1ξ	c1ξ	VERB
ejpam-5756	162	15	−β	−β	NOUN
ejpam-5756	162	16	+	+	CCONJ
ejpam-5756	162	17	c2ξ	c2ξ	PROPN
ejpam-5756	162	18	1−β	1−β	NUM
ejpam-5756	163	1	+	+	CCONJ
ejpam-5756	163	2	c3ξ	c3ξ	NOUN
ejpam-5756	163	3	−	−	PROPN
ejpam-5756	163	4	n1	n1	PROPN
ejpam-5756	163	5	m1	m1	NOUN
ejpam-5756	163	6	(	(	PUNCT
ejpam-5756	163	7	22	22	NUM
ejpam-5756	163	8	)	)	PUNCT
ejpam-5756	163	9	using	use	VERB
ejpam-5756	163	10	transformations	transformation	NOUN
ejpam-5756	163	11	(	(	PUNCT
ejpam-5756	163	12	15	15	NUM
ejpam-5756	163	13	)	)	PUNCT
ejpam-5756	163	14	,	,	PUNCT
ejpam-5756	163	15	(	(	PUNCT
ejpam-5756	163	16	16	16	NUM
ejpam-5756	163	17	)	)	PUNCT
ejpam-5756	163	18	and	and	CCONJ
ejpam-5756	163	19	analytic	analytic	ADJ
ejpam-5756	163	20	solution	solution	NOUN
ejpam-5756	163	21	of	of	ADP
ejpam-5756	163	22	ode	ode	PROPN
ejpam-5756	163	23	(	(	PUNCT
ejpam-5756	163	24	22	22	NUM
ejpam-5756	163	25	)	)	PUNCT
ejpam-5756	163	26	,	,	PUNCT
ejpam-5756	163	27	we	we	PRON
ejpam-5756	163	28	get	get	VERB
ejpam-5756	163	29	exact	exact	ADJ
ejpam-5756	163	30	solution	solution	NOUN
ejpam-5756	163	31	of	of	ADP
ejpam-5756	163	32	pde	pde	NOUN
ejpam-5756	163	33	(	(	PUNCT
ejpam-5756	163	34	1	1	NUM
ejpam-5756	163	35	)	)	PUNCT
ejpam-5756	163	36	which	which	PRON
ejpam-5756	163	37	is	be	AUX
ejpam-5756	163	38	u	u	NOUN
ejpam-5756	163	39	=	=	NOUN
ejpam-5756	163	40	xβtn(c1x	xβtn(c1x	PROPN
ejpam-5756	163	41	−βt−βm	−βt−βm	VERB
ejpam-5756	164	1	+	+	CCONJ
ejpam-5756	164	2	c2x	c2x	VERB
ejpam-5756	164	3	−β+1t(1−β)m	−β+1t(1−β)m	X
ejpam-5756	165	1	+	+	CCONJ
ejpam-5756	165	2	c3x	c3x	PROPN
ejpam-5756	165	3	−βn1	−βn1	PROPN
ejpam-5756	165	4	m1	m1	PROPN
ejpam-5756	165	5	t	t	PROPN
ejpam-5756	165	6	−n1	−n1	PROPN
ejpam-5756	165	7	m	m	PROPN
ejpam-5756	165	8	m1	m1	NOUN
ejpam-5756	165	9	)	)	PUNCT
ejpam-5756	165	10	(	(	PUNCT
ejpam-5756	165	11	23	23	NUM
ejpam-5756	165	12	)	)	PUNCT
ejpam-5756	165	13	when	when	SCONJ
ejpam-5756	165	14	β	β	X
ejpam-5756	165	15	becomes	become	VERB
ejpam-5756	165	16	more	more	ADJ
ejpam-5756	165	17	decrease	decrease	NOUN
ejpam-5756	165	18	then	then	ADV
ejpam-5756	165	19	wave	wave	VERB
ejpam-5756	165	20	amplitude	amplitude	NOUN
ejpam-5756	165	21	become	become	VERB
ejpam-5756	165	22	frequent	frequent	ADJ
ejpam-5756	165	23	.	.	PUNCT
ejpam-5756	166	1	case	case	NOUN
ejpam-5756	166	2	3	3	NUM
ejpam-5756	166	3	:	:	PUNCT
ejpam-5756	166	4	if	if	SCONJ
ejpam-5756	166	5	we	we	PRON
ejpam-5756	166	6	choose	choose	VERB
ejpam-5756	166	7	2n	2n	NUM
ejpam-5756	166	8	=	=	SYM
ejpam-5756	166	9	1and	1and	NUM
ejpam-5756	166	10	2r	2r	NUM
ejpam-5756	167	1	=	=	SYM
ejpam-5756	167	2	α	α	NOUN
ejpam-5756	167	3	in	in	ADP
ejpam-5756	167	4	case	case	NOUN
ejpam-5756	167	5	1	1	NUM
ejpam-5756	167	6	ξ	ξ	X
ejpam-5756	167	7	=	=	SYM
ejpam-5756	167	8	xαt	xαt	PROPN
ejpam-5756	167	9	(	(	PUNCT
ejpam-5756	167	10	24	24	NUM
ejpam-5756	167	11	)	)	PUNCT
ejpam-5756	167	12	u	u	NOUN
ejpam-5756	167	13	=	=	SYM
ejpam-5756	167	14	xβf(ξ	xβf(ξ	PROPN
ejpam-5756	167	15	)	)	PUNCT
ejpam-5756	167	16	(	(	PUNCT
ejpam-5756	167	17	25	25	NUM
ejpam-5756	167	18	)	)	PUNCT
ejpam-5756	167	19	using	use	VERB
ejpam-5756	167	20	time	time	NOUN
ejpam-5756	167	21	-	-	PUNCT
ejpam-5756	167	22	fractional	fractional	ADJ
ejpam-5756	167	23	derivative	derivative	NOUN
ejpam-5756	167	24	,	,	PUNCT
ejpam-5756	167	25	we	we	PRON
ejpam-5756	167	26	have	have	VERB
ejpam-5756	167	27	∂αu	∂αu	PROPN
ejpam-5756	167	28	∂tα	∂tα	PROPN
ejpam-5756	167	29	=	=	SYM
ejpam-5756	167	30	γ(2	γ(2	PROPN
ejpam-5756	167	31	)	)	PUNCT
ejpam-5756	167	32	γ(2−	γ(2−	PROPN
ejpam-5756	167	33	α	α	NOUN
ejpam-5756	167	34	)	)	PUNCT
ejpam-5756	167	35	xα+βt1−αf	xα+βt1−αf	X
ejpam-5756	168	1	′	′	NUM
ejpam-5756	168	2	(	(	PUNCT
ejpam-5756	168	3	26	26	NUM
ejpam-5756	168	4	)	)	PUNCT
ejpam-5756	168	5	∂	∂	NOUN
ejpam-5756	168	6	∂x	∂x	PROPN
ejpam-5756	168	7	(	(	PUNCT
ejpam-5756	168	8	∂αu	∂αu	PROPN
ejpam-5756	168	9	∂tα	∂tα	PROPN
ejpam-5756	168	10	)	)	PUNCT
ejpam-5756	168	11	=	=	SYM
ejpam-5756	168	12	γ(2	γ(2	PROPN
ejpam-5756	168	13	)	)	PUNCT
ejpam-5756	168	14	γ(2−	γ(2−	PROPN
ejpam-5756	168	15	α	α	NOUN
ejpam-5756	168	16	)	)	PUNCT
ejpam-5756	168	17	t1−α	t1−α	PROPN
ejpam-5756	168	18	(	(	PUNCT
ejpam-5756	168	19	αtx2α+β−1f	αtx2α+β−1f	X
ejpam-5756	168	20	′′	′′	PROPN
ejpam-5756	168	21	+	+	CCONJ
ejpam-5756	168	22	(	(	PUNCT
ejpam-5756	168	23	α+	α+	NOUN
ejpam-5756	168	24	β)xα+β−1f	β)xα+β−1f	NOUN
ejpam-5756	168	25	′	′	NUM
ejpam-5756	168	26	)	)	PUNCT
ejpam-5756	168	27	(	(	PUNCT
ejpam-5756	168	28	27	27	NUM
ejpam-5756	168	29	)	)	PUNCT
ejpam-5756	168	30	∂2	∂2	NOUN
ejpam-5756	168	31	∂x2	∂x2	NOUN
ejpam-5756	168	32	(	(	PUNCT
ejpam-5756	168	33	∂αu	∂αu	PROPN
ejpam-5756	168	34	∂tα	∂tα	PROPN
ejpam-5756	168	35	)	)	PUNCT
ejpam-5756	168	36	=	=	SYM
ejpam-5756	168	37	γ(2	γ(2	PROPN
ejpam-5756	168	38	)	)	PUNCT
ejpam-5756	168	39	γ(2−	γ(2−	PROPN
ejpam-5756	168	40	α	α	X
ejpam-5756	168	41	)	)	PUNCT
ejpam-5756	168	42	t1−α	t1−α	PROPN
ejpam-5756	168	43	∂	∂	NOUN
ejpam-5756	168	44	∂x	∂x	PROPN
ejpam-5756	168	45	(	(	PUNCT
ejpam-5756	168	46	αtx2α+β−1f	αtx2α+β−1f	X
ejpam-5756	168	47	′′	′′	PROPN
ejpam-5756	168	48	+	+	CCONJ
ejpam-5756	168	49	(	(	PUNCT
ejpam-5756	168	50	α+	α+	NOUN
ejpam-5756	168	51	β)xα+β−1f	β)xα+β−1f	NOUN
ejpam-5756	168	52	′	′	NUM
ejpam-5756	168	53	)	)	PUNCT
ejpam-5756	169	1	=	=	SYM
ejpam-5756	169	2	γ(2	γ(2	PROPN
ejpam-5756	169	3	)	)	PUNCT
ejpam-5756	169	4	γ(2−	γ(2−	PROPN
ejpam-5756	169	5	α	α	NOUN
ejpam-5756	169	6	)	)	PUNCT
ejpam-5756	169	7	t1−α	t1−α	PROPN
ejpam-5756	169	8	(	(	PUNCT
ejpam-5756	169	9	α2tx3α+β−2f	α2tx3α+β−2f	PROPN
ejpam-5756	169	10	′′′	′′′	VERB
ejpam-5756	170	1	+	+	X
ejpam-5756	170	2	α(2α+	α(2α+	ADJ
ejpam-5756	170	3	β	β	NOUN
ejpam-5756	170	4	−	−	NOUN
ejpam-5756	170	5	1)tx2α+β−2f	1)tx2α+β−2f	NUM
ejpam-5756	171	1	′′	′′	PROPN
ejpam-5756	171	2	+	+	CCONJ
ejpam-5756	171	3	α(α+	α(α+	X
ejpam-5756	171	4	β)tx2α+β−2f	β)tx2α+β−2f	ADP
ejpam-5756	172	1	′′	′′	PROPN
ejpam-5756	172	2	+	+	PROPN
ejpam-5756	172	3	(	(	PUNCT
ejpam-5756	172	4	α+	α+	INTJ
ejpam-5756	172	5	β)(α+	β)(α+	NOUN
ejpam-5756	172	6	β	β	NOUN
ejpam-5756	172	7	−	−	PROPN
ejpam-5756	172	8	1)xα+β−2f	1)xα+β−2f	NUM
ejpam-5756	172	9	′	′	NUM
ejpam-5756	172	10	)	)	PUNCT
ejpam-5756	172	11	(	(	PUNCT
ejpam-5756	172	12	28	28	X
ejpam-5756	172	13	)	)	PUNCT
ejpam-5756	172	14	using	use	VERB
ejpam-5756	172	15	(	(	PUNCT
ejpam-5756	172	16	26	26	NUM
ejpam-5756	172	17	)	)	PUNCT
ejpam-5756	172	18	,	,	PUNCT
ejpam-5756	172	19	(	(	PUNCT
ejpam-5756	172	20	27	27	NUM
ejpam-5756	172	21	)	)	PUNCT
ejpam-5756	172	22	and	and	CCONJ
ejpam-5756	172	23	(	(	PUNCT
ejpam-5756	172	24	28	28	NUM
ejpam-5756	172	25	)	)	PUNCT
ejpam-5756	172	26	the	the	DET
ejpam-5756	172	27	pde	pde	NOUN
ejpam-5756	172	28	(	(	PUNCT
ejpam-5756	172	29	1	1	X
ejpam-5756	172	30	)	)	PUNCT
ejpam-5756	172	31	can	can	AUX
ejpam-5756	172	32	be	be	AUX
ejpam-5756	172	33	expressed	express	VERB
ejpam-5756	172	34	as	as	ADP
ejpam-5756	172	35	;	;	PUNCT
ejpam-5756	172	36	α2(xαt)2f	α2(xαt)2f	NOUN
ejpam-5756	172	37	′′′	′′′	NOUN
ejpam-5756	173	1	+	+	CCONJ
ejpam-5756	173	2	α(xαt)(2αβ	α(xαt)(2αβ	NOUN
ejpam-5756	173	3	+	+	CCONJ
ejpam-5756	173	4	3α2	3α2	NUM
ejpam-5756	173	5	−	−	NOUN
ejpam-5756	173	6	α)f	α)f	VERB
ejpam-5756	174	1	′′	′′	PROPN
ejpam-5756	174	2	+	+	CCONJ
ejpam-5756	174	3	(	(	PUNCT
ejpam-5756	174	4	β(β	β(β	NUM
ejpam-5756	174	5	−	−	PROPN
ejpam-5756	174	6	1	1	NUM
ejpam-5756	174	7	)	)	PUNCT
ejpam-5756	174	8	+	+	CCONJ
ejpam-5756	174	9	2αβ	2αβ	ADJ
ejpam-5756	174	10	+	+	CCONJ
ejpam-5756	174	11	α2	α2	ADJ
ejpam-5756	174	12	−	−	NOUN
ejpam-5756	174	13	α)f	α)f	ADJ
ejpam-5756	175	1	′	′	NUM
ejpam-5756	175	2	=	=	SYM
ejpam-5756	175	3	0	0	NUM
ejpam-5756	175	4	(	(	PUNCT
ejpam-5756	175	5	29	29	NUM
ejpam-5756	175	6	)	)	PUNCT
ejpam-5756	175	7	b.	b.	PROPN
ejpam-5756	175	8	yasmeen	yasmeen	PROPN
ejpam-5756	175	9	,	,	PUNCT
ejpam-5756	175	10	k.	k.	PROPN
ejpam-5756	175	11	ahmad	ahmad	PROPN
ejpam-5756	175	12	,	,	PUNCT
ejpam-5756	175	13	n.	n.	PROPN
ejpam-5756	175	14	fatima	fatima	PROPN
ejpam-5756	175	15	/	/	PUNCT
ejpam-5756	175	16	eur	eur	PROPN
ejpam-5756	175	17	.	.	PUNCT
ejpam-5756	176	1	j.	j.	PROPN
ejpam-5756	176	2	pure	pure	PROPN
ejpam-5756	176	3	appl	appl	PROPN
ejpam-5756	176	4	.	.	PROPN
ejpam-5756	176	5	math	math	PROPN
ejpam-5756	176	6	,	,	PUNCT
ejpam-5756	176	7	18	18	NUM
ejpam-5756	176	8	(	(	PUNCT
ejpam-5756	176	9	1	1	NUM
ejpam-5756	176	10	)	)	PUNCT
ejpam-5756	176	11	(	(	PUNCT
ejpam-5756	176	12	2025	2025	NUM
ejpam-5756	176	13	)	)	PUNCT
ejpam-5756	176	14	,	,	PUNCT
ejpam-5756	176	15	5756	5756	NUM
ejpam-5756	176	16	9	9	NUM
ejpam-5756	176	17	of	of	ADP
ejpam-5756	176	18	17	17	NUM
ejpam-5756	176	19	since	since	SCONJ
ejpam-5756	176	20	ξ	ξ	PROPN
ejpam-5756	176	21	=	=	SYM
ejpam-5756	176	22	xαt	xαt	PROPN
ejpam-5756	176	23	,	,	PUNCT
ejpam-5756	176	24	so	so	CCONJ
ejpam-5756	176	25	(	(	PUNCT
ejpam-5756	176	26	29	29	NUM
ejpam-5756	176	27	)	)	PUNCT
ejpam-5756	176	28	reduces	reduce	VERB
ejpam-5756	176	29	to	to	PART
ejpam-5756	176	30	ode	ode	VERB
ejpam-5756	176	31	.	.	PUNCT
ejpam-5756	177	1	for	for	ADP
ejpam-5756	177	2	simplification	simplification	NOUN
ejpam-5756	177	3	,	,	PUNCT
ejpam-5756	177	4	we	we	PRON
ejpam-5756	177	5	take	take	VERB
ejpam-5756	177	6	v	v	NOUN
ejpam-5756	177	7	=	=	SYM
ejpam-5756	177	8	f	f	NOUN
ejpam-5756	178	1	′	′	NUM
ejpam-5756	178	2	then	then	ADV
ejpam-5756	178	3	(	(	PUNCT
ejpam-5756	178	4	29	29	NUM
ejpam-5756	178	5	)	)	PUNCT
ejpam-5756	178	6	becomes	become	VERB
ejpam-5756	178	7	ξ2v	ξ2v	PROPN
ejpam-5756	178	8	′′	′′	PROPN
ejpam-5756	178	9	+	+	CCONJ
ejpam-5756	178	10	ξ	ξ	PROPN
ejpam-5756	178	11	(	(	PUNCT
ejpam-5756	178	12	2β	2β	NOUN
ejpam-5756	179	1	+	+	CCONJ
ejpam-5756	179	2	3α−	3α−	NUM
ejpam-5756	179	3	1	1	NUM
ejpam-5756	179	4	α	α	NOUN
ejpam-5756	179	5	)	)	PUNCT
ejpam-5756	179	6	v	v	ADP
ejpam-5756	179	7	′	′	NUM
ejpam-5756	180	1	+	+	CCONJ
ejpam-5756	180	2	(	(	PUNCT
ejpam-5756	180	3	β(β	β(β	NUM
ejpam-5756	180	4	−	−	PROPN
ejpam-5756	180	5	1	1	NUM
ejpam-5756	180	6	)	)	PUNCT
ejpam-5756	180	7	+	+	CCONJ
ejpam-5756	180	8	2αβ	2αβ	ADJ
ejpam-5756	181	1	+	+	CCONJ
ejpam-5756	181	2	α(α−	α(α−	ADJ
ejpam-5756	181	3	1	1	NUM
ejpam-5756	181	4	)	)	PUNCT
ejpam-5756	181	5	α2	α2	ADJ
ejpam-5756	181	6	)	)	PUNCT
ejpam-5756	181	7	v	v	NOUN
ejpam-5756	181	8	=	=	SYM
ejpam-5756	181	9	0	0	NUM
ejpam-5756	181	10	(	(	PUNCT
ejpam-5756	181	11	30	30	NUM
ejpam-5756	181	12	)	)	PUNCT
ejpam-5756	181	13	it	it	PRON
ejpam-5756	181	14	is	be	AUX
ejpam-5756	181	15	easy	easy	ADJ
ejpam-5756	181	16	to	to	PART
ejpam-5756	181	17	see	see	VERB
ejpam-5756	181	18	that	that	PRON
ejpam-5756	181	19	(	(	PUNCT
ejpam-5756	181	20	30	30	NUM
ejpam-5756	181	21	)	)	PUNCT
ejpam-5756	181	22	is	be	AUX
ejpam-5756	181	23	euler	euler	NOUN
ejpam-5756	181	24	second	second	ADJ
ejpam-5756	181	25	order	order	NOUN
ejpam-5756	181	26	linear	linear	PROPN
ejpam-5756	181	27	ode	ode	PROPN
ejpam-5756	181	28	.	.	PUNCT
ejpam-5756	182	1	if	if	SCONJ
ejpam-5756	182	2	we	we	PRON
ejpam-5756	182	3	choose	choose	VERB
ejpam-5756	182	4	v	v	NOUN
ejpam-5756	182	5	=	=	SYM
ejpam-5756	182	6	ξk	ξk	PROPN
ejpam-5756	182	7	,	,	PUNCT
ejpam-5756	182	8	v	v	NOUN
ejpam-5756	182	9	′	′	NOUN
ejpam-5756	182	10	=	=	PUNCT
ejpam-5756	183	1	kξk−1	kξk−1	PROPN
ejpam-5756	183	2	and	and	CCONJ
ejpam-5756	183	3	v	v	ADP
ejpam-5756	183	4	′′	′′	PROPN
ejpam-5756	183	5	=	=	PUNCT
ejpam-5756	184	1	k(k	k(k	PROPN
ejpam-5756	184	2	−	−	PROPN
ejpam-5756	184	3	1)ξk−2	1)ξk−2	PROPN
ejpam-5756	184	4	then	then	ADV
ejpam-5756	184	5	the	the	DET
ejpam-5756	184	6	characteristic	characteristic	ADJ
ejpam-5756	184	7	equation	equation	NOUN
ejpam-5756	184	8	is	be	AUX
ejpam-5756	184	9	k(k	k(k	ADJ
ejpam-5756	184	10	−	−	PROPN
ejpam-5756	184	11	1	1	NUM
ejpam-5756	184	12	)	)	PUNCT
ejpam-5756	184	13	+	+	CCONJ
ejpam-5756	185	1	k	k	X
ejpam-5756	185	2	(	(	PUNCT
ejpam-5756	185	3	2β	2β	NOUN
ejpam-5756	186	1	+	+	CCONJ
ejpam-5756	186	2	3α−	3α−	NUM
ejpam-5756	186	3	1	1	NUM
ejpam-5756	186	4	α	α	NOUN
ejpam-5756	186	5	)	)	PUNCT
ejpam-5756	187	1	+	+	CCONJ
ejpam-5756	187	2	β(β	β(β	VERB
ejpam-5756	187	3	−	−	NUM
ejpam-5756	187	4	1	1	NUM
ejpam-5756	187	5	)	)	PUNCT
ejpam-5756	187	6	+	+	CCONJ
ejpam-5756	187	7	2αβ	2αβ	ADJ
ejpam-5756	188	1	+	+	CCONJ
ejpam-5756	188	2	α(α−	α(α−	ADJ
ejpam-5756	188	3	1	1	NUM
ejpam-5756	188	4	)	)	PUNCT
ejpam-5756	188	5	α2	α2	NOUN
ejpam-5756	188	6	=	=	SYM
ejpam-5756	188	7	0	0	PUNCT
ejpam-5756	188	8	(	(	PUNCT
ejpam-5756	188	9	31	31	NUM
ejpam-5756	188	10	)	)	PUNCT
ejpam-5756	188	11	the	the	DET
ejpam-5756	188	12	roots	root	NOUN
ejpam-5756	188	13	of	of	ADP
ejpam-5756	188	14	equation	equation	NOUN
ejpam-5756	188	15	(	(	PUNCT
ejpam-5756	188	16	31	31	NUM
ejpam-5756	188	17	)	)	PUNCT
ejpam-5756	188	18	are	be	AUX
ejpam-5756	188	19	k1	k1	NOUN
ejpam-5756	188	20	=	=	SYM
ejpam-5756	188	21	−β+α−1	−β+α−1	ADJ
ejpam-5756	188	22	α	α	NOUN
ejpam-5756	188	23	and	and	CCONJ
ejpam-5756	188	24	k2	k2	PROPN
ejpam-5756	188	25	=	=	SYM
ejpam-5756	188	26	−(β+α	−(β+α	NOUN
ejpam-5756	188	27	α	α	NOUN
ejpam-5756	188	28	)	)	PUNCT
ejpam-5756	188	29	hence	hence	ADV
ejpam-5756	188	30	the	the	DET
ejpam-5756	188	31	analytic	analytic	ADJ
ejpam-5756	188	32	solution	solution	NOUN
ejpam-5756	188	33	of	of	ADP
ejpam-5756	188	34	ode	ode	PROPN
ejpam-5756	188	35	(	(	PUNCT
ejpam-5756	188	36	30	30	NUM
ejpam-5756	188	37	)	)	PUNCT
ejpam-5756	188	38	is	be	AUX
ejpam-5756	188	39	f	f	NOUN
ejpam-5756	188	40	′	′	NUM
ejpam-5756	188	41	=	=	SYM
ejpam-5756	188	42	v	v	NOUN
ejpam-5756	188	43	=	=	SYM
ejpam-5756	188	44	c1ξ	c1ξ	PROPN
ejpam-5756	188	45	−β+α−1	−β+α−1	ADJ
ejpam-5756	188	46	α	α	NOUN
ejpam-5756	188	47	+	+	SYM
ejpam-5756	188	48	c2ξ	c2ξ	PROPN
ejpam-5756	188	49	−(β+α	−(β+α	NOUN
ejpam-5756	188	50	α	α	PROPN
ejpam-5756	188	51	)	)	PUNCT
ejpam-5756	188	52	by	by	ADP
ejpam-5756	188	53	replacing	replace	VERB
ejpam-5756	188	54	v	v	NOUN
ejpam-5756	188	55	=	=	SYM
ejpam-5756	188	56	f	f	NOUN
ejpam-5756	188	57	′	′	NOUN
ejpam-5756	188	58	and	and	CCONJ
ejpam-5756	188	59	taking	take	VERB
ejpam-5756	188	60	integral	integral	ADJ
ejpam-5756	188	61	on	on	ADP
ejpam-5756	188	62	both	both	DET
ejpam-5756	188	63	sides	side	NOUN
ejpam-5756	188	64	,	,	PUNCT
ejpam-5756	188	65	we	we	PRON
ejpam-5756	188	66	get	get	VERB
ejpam-5756	188	67	f(ξ	f(ξ	NOUN
ejpam-5756	188	68	)	)	PUNCT
ejpam-5756	188	69	=	=	SYM
ejpam-5756	188	70	c1	c1	NOUN
ejpam-5756	188	71	ξk1	ξk1	VERB
ejpam-5756	188	72	+	+	PROPN
ejpam-5756	188	73	1	1	NUM
ejpam-5756	188	74	k1	k1	NOUN
ejpam-5756	188	75	+	+	CCONJ
ejpam-5756	188	76	1	1	NUM
ejpam-5756	188	77	+	+	NUM
ejpam-5756	188	78	c2	c2	PROPN
ejpam-5756	188	79	ξk1	ξk1	VERB
ejpam-5756	188	80	+	+	PROPN
ejpam-5756	188	81	1	1	NUM
ejpam-5756	188	82	k2	k2	NOUN
ejpam-5756	188	83	+	+	CCONJ
ejpam-5756	188	84	1	1	NUM
ejpam-5756	188	85	+	+	CCONJ
ejpam-5756	188	86	c3	c3	NOUN
ejpam-5756	188	87	(	(	PUNCT
ejpam-5756	188	88	32	32	NUM
ejpam-5756	188	89	)	)	PUNCT
ejpam-5756	188	90	using	use	VERB
ejpam-5756	188	91	transformations	transformation	NOUN
ejpam-5756	188	92	(	(	PUNCT
ejpam-5756	188	93	24	24	NUM
ejpam-5756	188	94	)	)	PUNCT
ejpam-5756	188	95	,	,	PUNCT
ejpam-5756	188	96	(	(	PUNCT
ejpam-5756	188	97	25	25	NUM
ejpam-5756	188	98	)	)	PUNCT
ejpam-5756	188	99	and	and	CCONJ
ejpam-5756	188	100	analytic	analytic	ADJ
ejpam-5756	188	101	solution	solution	NOUN
ejpam-5756	188	102	of	of	ADP
ejpam-5756	188	103	ode	ode	PROPN
ejpam-5756	188	104	(	(	PUNCT
ejpam-5756	188	105	32	32	NUM
ejpam-5756	188	106	)	)	PUNCT
ejpam-5756	188	107	,	,	PUNCT
ejpam-5756	188	108	we	we	PRON
ejpam-5756	188	109	get	get	VERB
ejpam-5756	188	110	exact	exact	ADJ
ejpam-5756	188	111	solution	solution	NOUN
ejpam-5756	188	112	of	of	ADP
ejpam-5756	188	113	pde	pde	NOUN
ejpam-5756	188	114	(	(	PUNCT
ejpam-5756	188	115	1	1	NUM
ejpam-5756	188	116	)	)	PUNCT
ejpam-5756	188	117	which	which	PRON
ejpam-5756	188	118	is	be	AUX
ejpam-5756	188	119	u	u	PROPN
ejpam-5756	188	120	=	=	SYM
ejpam-5756	188	121	xβ	xβ	PROPN
ejpam-5756	188	122	(	(	PUNCT
ejpam-5756	188	123	c1	c1	PROPN
ejpam-5756	188	124	(	(	PUNCT
ejpam-5756	188	125	xαt)k1	xαt)k1	PROPN
ejpam-5756	188	126	+	+	ADJ
ejpam-5756	188	127	1	1	NUM
ejpam-5756	188	128	k1	k1	NOUN
ejpam-5756	188	129	+	+	CCONJ
ejpam-5756	188	130	1	1	NUM
ejpam-5756	188	131	+	+	NUM
ejpam-5756	189	1	c2	c2	PROPN
ejpam-5756	190	1	(	(	PUNCT
ejpam-5756	191	1	xαt)k2	xαt)k2	PROPN
ejpam-5756	191	2	+	+	ADJ
ejpam-5756	191	3	1	1	NUM
ejpam-5756	191	4	k2	k2	NOUN
ejpam-5756	191	5	+	+	CCONJ
ejpam-5756	191	6	1	1	NUM
ejpam-5756	191	7	+	+	CCONJ
ejpam-5756	191	8	c3	c3	NOUN
ejpam-5756	191	9	)	)	PUNCT
ejpam-5756	191	10	(	(	PUNCT
ejpam-5756	191	11	33	33	NUM
ejpam-5756	191	12	)	)	PUNCT
ejpam-5756	191	13	when	when	SCONJ
ejpam-5756	191	14	β	β	X
ejpam-5756	191	15	=	=	NOUN
ejpam-5756	191	16	1.5	1.5	NUM
ejpam-5756	191	17	then	then	ADV
ejpam-5756	191	18	small	small	ADJ
ejpam-5756	191	19	oscillation	oscillation	NOUN
ejpam-5756	191	20	in	in	ADP
ejpam-5756	191	21	wave	wave	NOUN
ejpam-5756	191	22	amplitude	amplitude	NOUN
ejpam-5756	191	23	are	be	AUX
ejpam-5756	191	24	observed	observe	VERB
ejpam-5756	191	25	.	.	PUNCT
ejpam-5756	192	1	case	case	NOUN
ejpam-5756	192	2	4	4	NUM
ejpam-5756	192	3	:	:	PUNCT
ejpam-5756	192	4	we	we	PRON
ejpam-5756	192	5	choose	choose	VERB
ejpam-5756	192	6	function	function	NOUN
ejpam-5756	192	7	transformation	transformation	NOUN
ejpam-5756	192	8	ξ	ξ	X
ejpam-5756	192	9	=	=	SYM
ejpam-5756	192	10	xmt	xmt	X
ejpam-5756	192	11	(	(	PUNCT
ejpam-5756	192	12	34	34	NUM
ejpam-5756	192	13	)	)	PUNCT
ejpam-5756	192	14	u	u	NOUN
ejpam-5756	192	15	=	=	PROPN
ejpam-5756	192	16	xnf(ξ)−	xnf(ξ)−	PROPN
ejpam-5756	192	17	xnsint	xnsint	PROPN
ejpam-5756	192	18	(	(	PUNCT
ejpam-5756	192	19	35	35	NUM
ejpam-5756	192	20	)	)	PUNCT
ejpam-5756	192	21	using	use	VERB
ejpam-5756	192	22	time	time	NOUN
ejpam-5756	192	23	-	-	PUNCT
ejpam-5756	192	24	fractional	fractional	ADJ
ejpam-5756	192	25	derivative	derivative	NOUN
ejpam-5756	192	26	,	,	PUNCT
ejpam-5756	192	27	we	we	PRON
ejpam-5756	192	28	have	have	VERB
ejpam-5756	192	29	∂αu	∂αu	PROPN
ejpam-5756	192	30	∂tα	∂tα	PROPN
ejpam-5756	192	31	=	=	SYM
ejpam-5756	192	32	γ(2	γ(2	PROPN
ejpam-5756	192	33	)	)	PUNCT
ejpam-5756	192	34	γ(2−	γ(2−	PROPN
ejpam-5756	192	35	α	α	NOUN
ejpam-5756	192	36	)	)	PUNCT
ejpam-5756	192	37	xm+nt1−αf	xm+nt1−αf	PROPN
ejpam-5756	193	1	′	′	NUM
ejpam-5756	194	1	−	−	PROPN
ejpam-5756	194	2	xnsin	xnsin	NOUN
ejpam-5756	194	3	(	(	PUNCT
ejpam-5756	194	4	t+	t+	NOUN
ejpam-5756	194	5	απ	απ	NOUN
ejpam-5756	194	6	2	2	NUM
ejpam-5756	194	7	)	)	PUNCT
ejpam-5756	194	8	(	(	PUNCT
ejpam-5756	194	9	36	36	NUM
ejpam-5756	194	10	)	)	PUNCT
ejpam-5756	194	11	∂	∂	NOUN
ejpam-5756	194	12	∂x	∂x	PROPN
ejpam-5756	194	13	(	(	PUNCT
ejpam-5756	194	14	∂αu	∂αu	PROPN
ejpam-5756	194	15	∂tα	∂tα	PROPN
ejpam-5756	194	16	)	)	PUNCT
ejpam-5756	194	17	=	=	SYM
ejpam-5756	194	18	γ(2	γ(2	PROPN
ejpam-5756	194	19	)	)	PUNCT
ejpam-5756	194	20	γ(2−	γ(2−	PROPN
ejpam-5756	194	21	α	α	NOUN
ejpam-5756	194	22	)	)	PUNCT
ejpam-5756	194	23	t1−α	t1−α	PROPN
ejpam-5756	194	24	(	(	PUNCT
ejpam-5756	194	25	mtx2m+n−1f	mtx2m+n−1f	NOUN
ejpam-5756	194	26	′′+(m+n)xm+n−1f	′′+(m+n)xm+n−1f	PUNCT
ejpam-5756	194	27	′−nxn−1sin	′−nxn−1sin	PROPN
ejpam-5756	194	28	(	(	PUNCT
ejpam-5756	194	29	t+	t+	NOUN
ejpam-5756	194	30	απ	απ	NOUN
ejpam-5756	194	31	2	2	NUM
ejpam-5756	194	32	)	)	PUNCT
ejpam-5756	194	33	)	)	PUNCT
ejpam-5756	194	34	(	(	PUNCT
ejpam-5756	194	35	37	37	NUM
ejpam-5756	194	36	)	)	PUNCT
ejpam-5756	194	37	∂2	∂2	PROPN
ejpam-5756	194	38	∂x2	∂x2	NOUN
ejpam-5756	194	39	(	(	PUNCT
ejpam-5756	194	40	∂αu	∂αu	PROPN
ejpam-5756	194	41	∂tα	∂tα	PROPN
ejpam-5756	194	42	)	)	PUNCT
ejpam-5756	194	43	=	=	SYM
ejpam-5756	194	44	γ(2	γ(2	PROPN
ejpam-5756	194	45	)	)	PUNCT
ejpam-5756	194	46	γ(2−	γ(2−	PROPN
ejpam-5756	194	47	α	α	X
ejpam-5756	194	48	)	)	PUNCT
ejpam-5756	194	49	t1−α	t1−α	PROPN
ejpam-5756	194	50	∂	∂	NOUN
ejpam-5756	194	51	∂x	∂x	PROPN
ejpam-5756	194	52	(	(	PUNCT
ejpam-5756	194	53	mt2m+n−1f	mt2m+n−1f	PROPN
ejpam-5756	194	54	′′	′′	PROPN
ejpam-5756	194	55	+	+	CCONJ
ejpam-5756	194	56	(	(	PUNCT
ejpam-5756	194	57	m+	m+	NUM
ejpam-5756	194	58	n)xm+n−1f	n)xm+n−1f	NOUN
ejpam-5756	194	59	′	′	PROPN
ejpam-5756	194	60	−	−	PROPN
ejpam-5756	194	61	nxn−1sin	nxn−1sin	PROPN
ejpam-5756	194	62	(	(	PUNCT
ejpam-5756	194	63	t+	t+	NOUN
ejpam-5756	194	64	απ	απ	NOUN
ejpam-5756	194	65	2	2	NUM
ejpam-5756	194	66	)	)	PUNCT
ejpam-5756	194	67	)	)	PUNCT
ejpam-5756	195	1	b.	b.	PROPN
ejpam-5756	195	2	yasmeen	yasmeen	PROPN
ejpam-5756	195	3	,	,	PUNCT
ejpam-5756	195	4	k.	k.	PROPN
ejpam-5756	195	5	ahmad	ahmad	PROPN
ejpam-5756	195	6	,	,	PUNCT
ejpam-5756	195	7	n.	n.	PROPN
ejpam-5756	195	8	fatima	fatima	PROPN
ejpam-5756	195	9	/	/	PUNCT
ejpam-5756	195	10	eur	eur	PROPN
ejpam-5756	195	11	.	.	PUNCT
ejpam-5756	196	1	j.	j.	PROPN
ejpam-5756	196	2	pure	pure	PROPN
ejpam-5756	196	3	appl	appl	PROPN
ejpam-5756	196	4	.	.	PROPN
ejpam-5756	196	5	math	math	PROPN
ejpam-5756	196	6	,	,	PUNCT
ejpam-5756	196	7	18	18	NUM
ejpam-5756	196	8	(	(	PUNCT
ejpam-5756	196	9	1	1	NUM
ejpam-5756	196	10	)	)	PUNCT
ejpam-5756	196	11	(	(	PUNCT
ejpam-5756	196	12	2025	2025	NUM
ejpam-5756	196	13	)	)	PUNCT
ejpam-5756	196	14	,	,	PUNCT
ejpam-5756	196	15	5756	5756	NUM
ejpam-5756	196	16	10	10	NUM
ejpam-5756	196	17	of	of	ADP
ejpam-5756	196	18	17	17	NUM
ejpam-5756	196	19	=	=	SYM
ejpam-5756	196	20	γ(2	γ(2	PROPN
ejpam-5756	196	21	)	)	PUNCT
ejpam-5756	196	22	γ(2−	γ(2−	PROPN
ejpam-5756	196	23	α	α	NOUN
ejpam-5756	196	24	)	)	PUNCT
ejpam-5756	196	25	t1−α	t1−α	NOUN
ejpam-5756	197	1	(	(	PUNCT
ejpam-5756	197	2	m2t2x3m+n−2f	m2t2x3m+n−2f	AUX
ejpam-5756	197	3	′′′	′′′	PROPN
ejpam-5756	198	1	+	+	NUM
ejpam-5756	198	2	m(2m+	m(2m+	ADJ
ejpam-5756	198	3	n−	n−	NOUN
ejpam-5756	198	4	1)tx2m+n−2f	1)tx2m+n−2f	NUM
ejpam-5756	198	5	′′	′′	PROPN
ejpam-5756	198	6	+	+	PROPN
ejpam-5756	198	7	m(m+	m(m+	X
ejpam-5756	198	8	n)tx2m+n−2f	n)tx2m+n−2f	PROPN
ejpam-5756	198	9	′′	′′	PROPN
ejpam-5756	198	10	+	+	PROPN
ejpam-5756	198	11	(	(	PUNCT
ejpam-5756	198	12	m+	m+	NOUN
ejpam-5756	198	13	n)(m+	n)(m+	X
ejpam-5756	198	14	n−	n−	NOUN
ejpam-5756	198	15	1)xm+n−2f	1)xm+n−2f	NUM
ejpam-5756	198	16	′	′	NUM
ejpam-5756	198	17	−	−	NUM
ejpam-5756	199	1	n(n−	n(n−	PROPN
ejpam-5756	199	2	1)xn−2sin	1)xn−2sin	NUM
ejpam-5756	199	3	(	(	PUNCT
ejpam-5756	199	4	t+	t+	NOUN
ejpam-5756	199	5	απ	απ	NOUN
ejpam-5756	199	6	2	2	NUM
ejpam-5756	199	7	)	)	PUNCT
ejpam-5756	199	8	)	)	PUNCT
ejpam-5756	200	1	(	(	PUNCT
ejpam-5756	200	2	38	38	NUM
ejpam-5756	200	3	)	)	PUNCT
ejpam-5756	200	4	using	use	VERB
ejpam-5756	200	5	(	(	PUNCT
ejpam-5756	200	6	36	36	NUM
ejpam-5756	200	7	)	)	PUNCT
ejpam-5756	200	8	,	,	PUNCT
ejpam-5756	200	9	(	(	PUNCT
ejpam-5756	200	10	37	37	NUM
ejpam-5756	200	11	)	)	PUNCT
ejpam-5756	200	12	and	and	CCONJ
ejpam-5756	200	13	(	(	PUNCT
ejpam-5756	200	14	38	38	NUM
ejpam-5756	200	15	)	)	PUNCT
ejpam-5756	200	16	into	into	ADP
ejpam-5756	200	17	the	the	DET
ejpam-5756	200	18	pde	pde	NOUN
ejpam-5756	200	19	(	(	PUNCT
ejpam-5756	200	20	1	1	NUM
ejpam-5756	200	21	)	)	PUNCT
ejpam-5756	200	22	.	.	PUNCT
ejpam-5756	201	1	to	to	PART
ejpam-5756	201	2	convert	convert	VERB
ejpam-5756	201	3	our	our	PRON
ejpam-5756	201	4	equation	equation	NOUN
ejpam-5756	201	5	(	(	PUNCT
ejpam-5756	201	6	38	38	NUM
ejpam-5756	201	7	)	)	PUNCT
ejpam-5756	201	8	into	into	ADP
ejpam-5756	201	9	ode	ode	NOUN
ejpam-5756	201	10	we	we	PRON
ejpam-5756	201	11	have	have	VERB
ejpam-5756	201	12	to	to	PART
ejpam-5756	201	13	take	take	VERB
ejpam-5756	201	14	the	the	DET
ejpam-5756	201	15	only	only	ADJ
ejpam-5756	201	16	value	value	NOUN
ejpam-5756	201	17	n	n	NOUN
ejpam-5756	201	18	=	=	SYM
ejpam-5756	201	19	1	1	NUM
ejpam-5756	201	20	,	,	PUNCT
ejpam-5756	201	21	otherwise	otherwise	ADV
ejpam-5756	201	22	we	we	PRON
ejpam-5756	201	23	are	be	AUX
ejpam-5756	201	24	unable	unable	ADJ
ejpam-5756	201	25	to	to	PART
ejpam-5756	201	26	convert	convert	VERB
ejpam-5756	201	27	ode	ode	PROPN
ejpam-5756	201	28	.	.	PUNCT
ejpam-5756	202	1	m2x2mt2f	m2x2mt2f	PROPN
ejpam-5756	203	1	′′′	′′′	PROPN
ejpam-5756	204	1	+	+	CCONJ
ejpam-5756	204	2	xmt(3m2	xmt(3m2	PROPN
ejpam-5756	204	3	+	+	ADJ
ejpam-5756	204	4	m)f	m)f	ADJ
ejpam-5756	204	5	′′	′′	PROPN
ejpam-5756	204	6	+	+	PROPN
ejpam-5756	204	7	m(m+	m(m+	VERB
ejpam-5756	204	8	1)f	1)f	NUM
ejpam-5756	204	9	′	′	NUM
ejpam-5756	205	1	=	=	SYM
ejpam-5756	205	2	0	0	PUNCT
ejpam-5756	205	3	(	(	PUNCT
ejpam-5756	205	4	39	39	NUM
ejpam-5756	205	5	)	)	PUNCT
ejpam-5756	205	6	since	since	SCONJ
ejpam-5756	205	7	ξ	ξ	X
ejpam-5756	205	8	=	=	SYM
ejpam-5756	205	9	xmt	xmt	X
ejpam-5756	205	10	,	,	PUNCT
ejpam-5756	205	11	so	so	CCONJ
ejpam-5756	205	12	(	(	PUNCT
ejpam-5756	205	13	39	39	NUM
ejpam-5756	205	14	)	)	PUNCT
ejpam-5756	205	15	reduces	reduce	VERB
ejpam-5756	205	16	to	to	PART
ejpam-5756	205	17	ode	ode	VERB
ejpam-5756	205	18	.	.	PUNCT
ejpam-5756	206	1	for	for	ADP
ejpam-5756	206	2	simplification	simplification	NOUN
ejpam-5756	206	3	,	,	PUNCT
ejpam-5756	206	4	we	we	PRON
ejpam-5756	206	5	take	take	VERB
ejpam-5756	206	6	v	v	NOUN
ejpam-5756	206	7	=	=	SYM
ejpam-5756	206	8	f	f	NOUN
ejpam-5756	207	1	′	′	NUM
ejpam-5756	207	2	then	then	ADV
ejpam-5756	207	3	(	(	PUNCT
ejpam-5756	207	4	39	39	NUM
ejpam-5756	207	5	)	)	PUNCT
ejpam-5756	207	6	becomes	become	VERB
ejpam-5756	207	7	ξ2v	ξ2v	PROPN
ejpam-5756	207	8	′′	′′	PROPN
ejpam-5756	207	9	+	+	CCONJ
ejpam-5756	207	10	ξ	ξ	PROPN
ejpam-5756	207	11	(	(	PUNCT
ejpam-5756	207	12	3m+	3m+	NUM
ejpam-5756	207	13	1	1	NUM
ejpam-5756	207	14	m	m	NOUN
ejpam-5756	207	15	)	)	PUNCT
ejpam-5756	207	16	v	v	ADP
ejpam-5756	207	17	′	′	NUM
ejpam-5756	208	1	+	+	CCONJ
ejpam-5756	208	2	(	(	PUNCT
ejpam-5756	208	3	m+	m+	NUM
ejpam-5756	208	4	1	1	NUM
ejpam-5756	208	5	m	m	NOUN
ejpam-5756	208	6	)	)	PUNCT
ejpam-5756	208	7	v	v	NOUN
ejpam-5756	208	8	=	=	SYM
ejpam-5756	208	9	0	0	PUNCT
ejpam-5756	208	10	(	(	PUNCT
ejpam-5756	208	11	40	40	NUM
ejpam-5756	208	12	)	)	PUNCT
ejpam-5756	208	13	it	it	PRON
ejpam-5756	208	14	is	be	AUX
ejpam-5756	208	15	easy	easy	ADJ
ejpam-5756	208	16	to	to	PART
ejpam-5756	208	17	see	see	VERB
ejpam-5756	208	18	that	that	PRON
ejpam-5756	208	19	(	(	PUNCT
ejpam-5756	208	20	40	40	NUM
ejpam-5756	208	21	)	)	PUNCT
ejpam-5756	208	22	is	be	AUX
ejpam-5756	208	23	euler	euler	NOUN
ejpam-5756	208	24	second	second	ADJ
ejpam-5756	208	25	order	order	NOUN
ejpam-5756	208	26	linear	linear	PROPN
ejpam-5756	208	27	ode	ode	PROPN
ejpam-5756	208	28	.	.	PUNCT
ejpam-5756	209	1	if	if	SCONJ
ejpam-5756	209	2	we	we	PRON
ejpam-5756	209	3	choose	choose	VERB
ejpam-5756	209	4	v	v	NOUN
ejpam-5756	209	5	=	=	SYM
ejpam-5756	209	6	ξk	ξk	PROPN
ejpam-5756	209	7	,	,	PUNCT
ejpam-5756	209	8	v	v	NOUN
ejpam-5756	209	9	′	′	NOUN
ejpam-5756	209	10	=	=	PUNCT
ejpam-5756	210	1	kξk−1	kξk−1	PROPN
ejpam-5756	210	2	and	and	CCONJ
ejpam-5756	210	3	v	v	ADP
ejpam-5756	210	4	′′	′′	PROPN
ejpam-5756	210	5	=	=	PUNCT
ejpam-5756	211	1	k(k	k(k	PROPN
ejpam-5756	211	2	−	−	PROPN
ejpam-5756	211	3	1)ξk−2	1)ξk−2	PROPN
ejpam-5756	211	4	then	then	ADV
ejpam-5756	211	5	the	the	DET
ejpam-5756	211	6	characteristic	characteristic	ADJ
ejpam-5756	211	7	equation	equation	NOUN
ejpam-5756	211	8	is	be	AUX
ejpam-5756	211	9	k(k	k(k	ADJ
ejpam-5756	211	10	−	−	PROPN
ejpam-5756	211	11	1	1	NUM
ejpam-5756	211	12	)	)	PUNCT
ejpam-5756	211	13	+	+	CCONJ
ejpam-5756	212	1	k	k	X
ejpam-5756	212	2	(	(	PUNCT
ejpam-5756	212	3	3m+	3m+	NUM
ejpam-5756	212	4	1	1	NUM
ejpam-5756	212	5	m	m	NOUN
ejpam-5756	212	6	)	)	PUNCT
ejpam-5756	213	1	+	+	CCONJ
ejpam-5756	213	2	m+	m+	NUM
ejpam-5756	213	3	1	1	NUM
ejpam-5756	213	4	m	m	NOUN
ejpam-5756	213	5	=	=	SYM
ejpam-5756	213	6	0	0	NUM
ejpam-5756	213	7	(	(	PUNCT
ejpam-5756	213	8	41	41	NUM
ejpam-5756	213	9	)	)	PUNCT
ejpam-5756	213	10	the	the	DET
ejpam-5756	213	11	roots	root	NOUN
ejpam-5756	213	12	of	of	ADP
ejpam-5756	213	13	equation	equation	NOUN
ejpam-5756	213	14	(	(	PUNCT
ejpam-5756	213	15	41	41	NUM
ejpam-5756	213	16	)	)	PUNCT
ejpam-5756	213	17	are	be	AUX
ejpam-5756	213	18	k	k	NOUN
ejpam-5756	213	19	=	=	PUNCT
ejpam-5756	213	20	−1	−1	NOUN
ejpam-5756	213	21	and	and	CCONJ
ejpam-5756	213	22	k	k	PROPN
ejpam-5756	214	1	=	=	SYM
ejpam-5756	214	2	−1−	−1−	PROPN
ejpam-5756	214	3	1	1	NUM
ejpam-5756	214	4	m	m	VERB
ejpam-5756	214	5	hence	hence	ADV
ejpam-5756	214	6	the	the	DET
ejpam-5756	214	7	analytic	analytic	ADJ
ejpam-5756	214	8	solution	solution	NOUN
ejpam-5756	214	9	of	of	ADP
ejpam-5756	214	10	ode	ode	PROPN
ejpam-5756	214	11	(	(	PUNCT
ejpam-5756	214	12	40	40	NUM
ejpam-5756	214	13	)	)	PUNCT
ejpam-5756	214	14	is	be	AUX
ejpam-5756	214	15	f	f	NOUN
ejpam-5756	214	16	′	′	NUM
ejpam-5756	214	17	=	=	SYM
ejpam-5756	214	18	v	v	NOUN
ejpam-5756	214	19	=	=	NOUN
ejpam-5756	214	20	c1ξ	c1ξ	NOUN
ejpam-5756	214	21	−1	−1	NOUN
ejpam-5756	214	22	+	+	CCONJ
ejpam-5756	214	23	c2ξ	c2ξ	PROPN
ejpam-5756	214	24	−1−	−1−	PROPN
ejpam-5756	214	25	1	1	NUM
ejpam-5756	214	26	m	m	NOUN
ejpam-5756	214	27	by	by	ADP
ejpam-5756	214	28	replacing	replace	VERB
ejpam-5756	214	29	v	v	NOUN
ejpam-5756	214	30	=	=	SYM
ejpam-5756	214	31	f	f	NOUN
ejpam-5756	214	32	′	′	NOUN
ejpam-5756	214	33	and	and	CCONJ
ejpam-5756	214	34	taking	take	VERB
ejpam-5756	214	35	integral	integral	ADJ
ejpam-5756	214	36	on	on	ADP
ejpam-5756	214	37	both	both	DET
ejpam-5756	214	38	sides	side	NOUN
ejpam-5756	214	39	,	,	PUNCT
ejpam-5756	214	40	we	we	PRON
ejpam-5756	214	41	get	get	VERB
ejpam-5756	214	42	f(ξ	f(ξ	NOUN
ejpam-5756	214	43	)	)	PUNCT
ejpam-5756	214	44	=	=	PUNCT
ejpam-5756	215	1	c1ln(ξ)−mc2ξ	c1ln(ξ)−mc2ξ	VERB
ejpam-5756	215	2	−	−	NUM
ejpam-5756	215	3	1	1	NUM
ejpam-5756	215	4	m	m	NOUN
ejpam-5756	215	5	+	+	CCONJ
ejpam-5756	215	6	c3	c3	X
ejpam-5756	215	7	(	(	PUNCT
ejpam-5756	215	8	42	42	NUM
ejpam-5756	215	9	)	)	PUNCT
ejpam-5756	215	10	using	use	VERB
ejpam-5756	215	11	transformations	transformation	NOUN
ejpam-5756	215	12	(	(	PUNCT
ejpam-5756	215	13	34	34	NUM
ejpam-5756	215	14	)	)	PUNCT
ejpam-5756	215	15	,	,	PUNCT
ejpam-5756	215	16	(	(	PUNCT
ejpam-5756	215	17	35	35	NUM
ejpam-5756	215	18	)	)	PUNCT
ejpam-5756	215	19	and	and	CCONJ
ejpam-5756	215	20	analytic	analytic	ADJ
ejpam-5756	215	21	solution	solution	NOUN
ejpam-5756	215	22	of	of	ADP
ejpam-5756	215	23	ode	ode	PROPN
ejpam-5756	215	24	(	(	PUNCT
ejpam-5756	215	25	42	42	NUM
ejpam-5756	215	26	)	)	PUNCT
ejpam-5756	215	27	,	,	PUNCT
ejpam-5756	215	28	we	we	PRON
ejpam-5756	215	29	get	get	VERB
ejpam-5756	215	30	exact	exact	ADJ
ejpam-5756	215	31	solution	solution	NOUN
ejpam-5756	215	32	of	of	ADP
ejpam-5756	215	33	pde	pde	NOUN
ejpam-5756	215	34	(	(	PUNCT
ejpam-5756	215	35	1	1	NUM
ejpam-5756	215	36	)	)	PUNCT
ejpam-5756	215	37	which	which	PRON
ejpam-5756	215	38	is	be	AUX
ejpam-5756	215	39	u	u	NOUN
ejpam-5756	215	40	=	=	PROPN
ejpam-5756	215	41	xn	xn	PROPN
ejpam-5756	215	42	(	(	PUNCT
ejpam-5756	215	43	c1ln(x	c1ln(x	PROPN
ejpam-5756	215	44	mt)−	mt)−	PROPN
ejpam-5756	215	45	mc2	mc2	PROPN
ejpam-5756	215	46	t	t	PROPN
ejpam-5756	215	47	−	−	NUM
ejpam-5756	215	48	1	1	NUM
ejpam-5756	215	49	m	m	NOUN
ejpam-5756	215	50	x	x	X
ejpam-5756	216	1	+	+	CCONJ
ejpam-5756	216	2	c3	c3	NOUN
ejpam-5756	216	3	)	)	PUNCT
ejpam-5756	216	4	−	−	PROPN
ejpam-5756	216	5	xnsint	xnsint	NOUN
ejpam-5756	216	6	(	(	PUNCT
ejpam-5756	216	7	43	43	NUM
ejpam-5756	216	8	)	)	PUNCT
ejpam-5756	216	9	when	when	SCONJ
ejpam-5756	216	10	β	β	X
ejpam-5756	216	11	=	=	NOUN
ejpam-5756	216	12	2.5	2.5	NUM
ejpam-5756	216	13	then	then	ADV
ejpam-5756	216	14	it	it	PRON
ejpam-5756	216	15	become	become	AUX
ejpam-5756	216	16	rapidly	rapidly	ADV
ejpam-5756	216	17	changing	change	VERB
ejpam-5756	216	18	in	in	ADP
ejpam-5756	216	19	the	the	DET
ejpam-5756	216	20	wave	wave	NOUN
ejpam-5756	216	21	amplitude	amplitude	NOUN
ejpam-5756	216	22	.	.	PUNCT
ejpam-5756	217	1	case	case	NOUN
ejpam-5756	217	2	5	5	NUM
ejpam-5756	217	3	:	:	PUNCT
ejpam-5756	217	4	we	we	PRON
ejpam-5756	217	5	choose	choose	VERB
ejpam-5756	217	6	function	function	NOUN
ejpam-5756	217	7	transformation	transformation	NOUN
ejpam-5756	217	8	ξ	ξ	X
ejpam-5756	217	9	=	=	NOUN
ejpam-5756	217	10	eaxt	eaxt	NOUN
ejpam-5756	217	11	(	(	PUNCT
ejpam-5756	217	12	44	44	NUM
ejpam-5756	217	13	)	)	PUNCT
ejpam-5756	217	14	u	u	NOUN
ejpam-5756	217	15	=	=	NOUN
ejpam-5756	217	16	e−bxf(ξ	e−bxf(ξ	X
ejpam-5756	217	17	)	)	PUNCT
ejpam-5756	217	18	(	(	PUNCT
ejpam-5756	217	19	45	45	NUM
ejpam-5756	217	20	)	)	PUNCT
ejpam-5756	217	21	using	use	VERB
ejpam-5756	217	22	time	time	NOUN
ejpam-5756	217	23	-	-	PUNCT
ejpam-5756	217	24	fractional	fractional	ADJ
ejpam-5756	217	25	derivative	derivative	NOUN
ejpam-5756	217	26	,	,	PUNCT
ejpam-5756	217	27	we	we	PRON
ejpam-5756	217	28	have	have	VERB
ejpam-5756	217	29	∂αu	∂αu	PROPN
ejpam-5756	217	30	∂tα	∂tα	PROPN
ejpam-5756	217	31	=	=	SYM
ejpam-5756	217	32	γ(2	γ(2	PROPN
ejpam-5756	217	33	)	)	PUNCT
ejpam-5756	217	34	γ(2−	γ(2−	PROPN
ejpam-5756	217	35	α	α	NOUN
ejpam-5756	217	36	)	)	PUNCT
ejpam-5756	217	37	t1−αe(a−b)xf	t1−αe(a−b)xf	NOUN
ejpam-5756	217	38	′	′	NOUN
ejpam-5756	217	39	(	(	PUNCT
ejpam-5756	217	40	46	46	NUM
ejpam-5756	217	41	)	)	PUNCT
ejpam-5756	217	42	b.	b.	PROPN
ejpam-5756	217	43	yasmeen	yasmeen	PROPN
ejpam-5756	217	44	,	,	PUNCT
ejpam-5756	217	45	k.	k.	PROPN
ejpam-5756	217	46	ahmad	ahmad	PROPN
ejpam-5756	217	47	,	,	PUNCT
ejpam-5756	217	48	n.	n.	PROPN
ejpam-5756	217	49	fatima	fatima	PROPN
ejpam-5756	217	50	/	/	PUNCT
ejpam-5756	217	51	eur	eur	PROPN
ejpam-5756	217	52	.	.	PUNCT
ejpam-5756	218	1	j.	j.	PROPN
ejpam-5756	218	2	pure	pure	PROPN
ejpam-5756	218	3	appl	appl	PROPN
ejpam-5756	218	4	.	.	PROPN
ejpam-5756	218	5	math	math	PROPN
ejpam-5756	218	6	,	,	PUNCT
ejpam-5756	218	7	18	18	NUM
ejpam-5756	218	8	(	(	PUNCT
ejpam-5756	218	9	1	1	NUM
ejpam-5756	218	10	)	)	PUNCT
ejpam-5756	218	11	(	(	PUNCT
ejpam-5756	218	12	2025	2025	NUM
ejpam-5756	218	13	)	)	PUNCT
ejpam-5756	218	14	,	,	PUNCT
ejpam-5756	218	15	5756	5756	NUM
ejpam-5756	218	16	11	11	NUM
ejpam-5756	218	17	of	of	ADP
ejpam-5756	218	18	17	17	NUM
ejpam-5756	218	19	∂	∂	NUM
ejpam-5756	218	20	∂x	∂x	PROPN
ejpam-5756	218	21	(	(	PUNCT
ejpam-5756	218	22	∂αu	∂αu	PROPN
ejpam-5756	218	23	∂tα	∂tα	PROPN
ejpam-5756	218	24	)	)	PUNCT
ejpam-5756	218	25	=	=	SYM
ejpam-5756	218	26	γ(2	γ(2	PROPN
ejpam-5756	218	27	)	)	PUNCT
ejpam-5756	218	28	γ(2−	γ(2−	PROPN
ejpam-5756	218	29	α	α	NOUN
ejpam-5756	218	30	)	)	PUNCT
ejpam-5756	218	31	t1−α	t1−α	PROPN
ejpam-5756	218	32	(	(	PUNCT
ejpam-5756	218	33	ate(2a−b)xf	ate(2a−b)xf	NOUN
ejpam-5756	218	34	′′	′′	PROPN
ejpam-5756	218	35	+	+	CCONJ
ejpam-5756	218	36	(	(	PUNCT
ejpam-5756	218	37	a−	a−	PROPN
ejpam-5756	218	38	b)e(a−b)xf	b)e(a−b)xf	NUM
ejpam-5756	218	39	′	′	NUM
ejpam-5756	218	40	)	)	PUNCT
ejpam-5756	218	41	(	(	PUNCT
ejpam-5756	218	42	47	47	NUM
ejpam-5756	218	43	)	)	PUNCT
ejpam-5756	218	44	∂2	∂2	PROPN
ejpam-5756	218	45	∂x2	∂x2	NOUN
ejpam-5756	218	46	(	(	PUNCT
ejpam-5756	218	47	∂αu	∂αu	PROPN
ejpam-5756	218	48	∂tα	∂tα	PROPN
ejpam-5756	218	49	)	)	PUNCT
ejpam-5756	218	50	=	=	SYM
ejpam-5756	218	51	γ(2	γ(2	PROPN
ejpam-5756	218	52	)	)	PUNCT
ejpam-5756	218	53	γ(2−	γ(2−	PROPN
ejpam-5756	218	54	α	α	X
ejpam-5756	218	55	)	)	PUNCT
ejpam-5756	218	56	t1−α	t1−α	PROPN
ejpam-5756	218	57	∂	∂	NOUN
ejpam-5756	218	58	∂x	∂x	PROPN
ejpam-5756	218	59	(	(	PUNCT
ejpam-5756	218	60	ate(2a−b)xf	ate(2a−b)xf	NOUN
ejpam-5756	218	61	′′	′′	PROPN
ejpam-5756	218	62	+	+	CCONJ
ejpam-5756	218	63	(	(	PUNCT
ejpam-5756	218	64	a−	a−	PROPN
ejpam-5756	218	65	b)e(a−b)xf	b)e(a−b)xf	NUM
ejpam-5756	218	66	′	′	NUM
ejpam-5756	218	67	)	)	PUNCT
ejpam-5756	219	1	=	=	SYM
ejpam-5756	219	2	γ(2	γ(2	PROPN
ejpam-5756	219	3	)	)	PUNCT
ejpam-5756	219	4	γ(2−	γ(2−	PROPN
ejpam-5756	219	5	α	α	NOUN
ejpam-5756	219	6	)	)	PUNCT
ejpam-5756	219	7	t1−α	t1−α	PROPN
ejpam-5756	219	8	(	(	PUNCT
ejpam-5756	219	9	a2t2e(3a−b)xf	a2t2e(3a−b)xf	NOUN
ejpam-5756	219	10	′′′	′′′	PROPN
ejpam-5756	220	1	+	+	CCONJ
ejpam-5756	220	2	(	(	PUNCT
ejpam-5756	220	3	3a2	3a2	NUM
ejpam-5756	220	4	−	−	NOUN
ejpam-5756	220	5	2ab)te(2a−b)xf	2ab)te(2a−b)xf	NUM
ejpam-5756	220	6	′′	′′	NOUN
ejpam-5756	220	7	+	+	CCONJ
ejpam-5756	220	8	(	(	PUNCT
ejpam-5756	220	9	a−	a−	PROPN
ejpam-5756	220	10	b)2e(a−b)xf	b)2e(a−b)xf	X
ejpam-5756	220	11	′	′	NUM
ejpam-5756	220	12	)	)	PUNCT
ejpam-5756	221	1	(	(	PUNCT
ejpam-5756	221	2	48	48	NUM
ejpam-5756	221	3	)	)	PUNCT
ejpam-5756	221	4	using	use	VERB
ejpam-5756	221	5	(	(	PUNCT
ejpam-5756	221	6	46	46	NUM
ejpam-5756	221	7	)	)	PUNCT
ejpam-5756	221	8	,	,	PUNCT
ejpam-5756	221	9	(	(	PUNCT
ejpam-5756	221	10	47	47	NUM
ejpam-5756	221	11	)	)	PUNCT
ejpam-5756	221	12	and	and	CCONJ
ejpam-5756	221	13	(	(	PUNCT
ejpam-5756	221	14	48	48	NUM
ejpam-5756	221	15	)	)	PUNCT
ejpam-5756	221	16	into	into	ADP
ejpam-5756	221	17	the	the	DET
ejpam-5756	221	18	pde	pde	NOUN
ejpam-5756	221	19	(	(	PUNCT
ejpam-5756	221	20	1	1	NUM
ejpam-5756	221	21	)	)	PUNCT
ejpam-5756	221	22	.	.	PUNCT
ejpam-5756	222	1	to	to	PART
ejpam-5756	222	2	convert	convert	VERB
ejpam-5756	222	3	our	our	PRON
ejpam-5756	222	4	equation	equation	NOUN
ejpam-5756	222	5	(	(	PUNCT
ejpam-5756	222	6	48	48	NUM
ejpam-5756	222	7	)	)	PUNCT
ejpam-5756	222	8	into	into	ADP
ejpam-5756	222	9	ode	ode	PROPN
ejpam-5756	222	10	we	we	PRON
ejpam-5756	222	11	divide	divide	VERB
ejpam-5756	222	12	a2eax	a2eax	ADJ
ejpam-5756	222	13	a2e2axt2f	a2e2axt2f	NOUN
ejpam-5756	222	14	′′′	′′′	PROPN
ejpam-5756	223	1	+	+	CCONJ
ejpam-5756	223	2	(	(	PUNCT
ejpam-5756	223	3	3a2	3a2	NUM
ejpam-5756	223	4	−	−	NUM
ejpam-5756	223	5	2ab)eaxtf	2ab)eaxtf	NUM
ejpam-5756	223	6	′′	′′	NOUN
ejpam-5756	223	7	+	+	CCONJ
ejpam-5756	223	8	(	(	PUNCT
ejpam-5756	223	9	a−	a−	PROPN
ejpam-5756	223	10	b)2f	b)2f	NOUN
ejpam-5756	223	11	′	′	NUM
ejpam-5756	224	1	=	=	SYM
ejpam-5756	224	2	0	0	PUNCT
ejpam-5756	224	3	(	(	PUNCT
ejpam-5756	224	4	49	49	NUM
ejpam-5756	224	5	)	)	PUNCT
ejpam-5756	224	6	since	since	SCONJ
ejpam-5756	224	7	ξ	ξ	X
ejpam-5756	224	8	=	=	SYM
ejpam-5756	224	9	xmt	xmt	PROPN
ejpam-5756	224	10	,	,	PUNCT
ejpam-5756	224	11	so	so	CCONJ
ejpam-5756	224	12	(	(	PUNCT
ejpam-5756	224	13	49	49	NUM
ejpam-5756	224	14	)	)	PUNCT
ejpam-5756	224	15	reduces	reduce	VERB
ejpam-5756	224	16	to	to	PART
ejpam-5756	224	17	ode	ode	VERB
ejpam-5756	224	18	.	.	PUNCT
ejpam-5756	225	1	for	for	ADP
ejpam-5756	225	2	simplification	simplification	NOUN
ejpam-5756	225	3	,	,	PUNCT
ejpam-5756	225	4	we	we	PRON
ejpam-5756	225	5	take	take	VERB
ejpam-5756	225	6	v	v	NOUN
ejpam-5756	225	7	=	=	SYM
ejpam-5756	225	8	f	f	NOUN
ejpam-5756	226	1	′	′	NUM
ejpam-5756	226	2	then	then	ADV
ejpam-5756	226	3	(	(	PUNCT
ejpam-5756	226	4	49	49	NUM
ejpam-5756	226	5	)	)	PUNCT
ejpam-5756	226	6	becomes	become	VERB
ejpam-5756	226	7	ξ2v	ξ2v	PROPN
ejpam-5756	226	8	′′	′′	PROPN
ejpam-5756	226	9	+	+	CCONJ
ejpam-5756	226	10	(	(	PUNCT
ejpam-5756	226	11	3a−	3a−	PROPN
ejpam-5756	226	12	2b	2b	NUM
ejpam-5756	226	13	a	a	X
ejpam-5756	226	14	)	)	PUNCT
ejpam-5756	226	15	ξv	ξv	PART
ejpam-5756	226	16	′	′	NUM
ejpam-5756	227	1	+	+	CCONJ
ejpam-5756	227	2	(	(	PUNCT
ejpam-5756	227	3	a−	a−	PROPN
ejpam-5756	227	4	b)2	b)2	PROPN
ejpam-5756	227	5	a2	a2	PROPN
ejpam-5756	227	6	v	v	NOUN
ejpam-5756	227	7	=	=	SYM
ejpam-5756	227	8	0	0	NUM
ejpam-5756	227	9	(	(	PUNCT
ejpam-5756	227	10	50	50	NUM
ejpam-5756	227	11	)	)	PUNCT
ejpam-5756	227	12	it	it	PRON
ejpam-5756	227	13	is	be	AUX
ejpam-5756	227	14	easy	easy	ADJ
ejpam-5756	227	15	to	to	PART
ejpam-5756	227	16	see	see	VERB
ejpam-5756	227	17	that	that	SCONJ
ejpam-5756	227	18	(	(	PUNCT
ejpam-5756	227	19	50	50	NUM
ejpam-5756	227	20	)	)	PUNCT
ejpam-5756	227	21	is	be	AUX
ejpam-5756	227	22	euler	euler	NOUN
ejpam-5756	227	23	second	second	ADJ
ejpam-5756	227	24	order	order	NOUN
ejpam-5756	227	25	linear	linear	PROPN
ejpam-5756	227	26	ode	ode	PROPN
ejpam-5756	227	27	.	.	PUNCT
ejpam-5756	228	1	if	if	SCONJ
ejpam-5756	228	2	we	we	PRON
ejpam-5756	228	3	choose	choose	VERB
ejpam-5756	228	4	v	v	NOUN
ejpam-5756	228	5	=	=	SYM
ejpam-5756	228	6	ξk	ξk	PROPN
ejpam-5756	228	7	,	,	PUNCT
ejpam-5756	228	8	v	v	NOUN
ejpam-5756	228	9	′	′	NOUN
ejpam-5756	228	10	=	=	PUNCT
ejpam-5756	229	1	kξk−1	kξk−1	PROPN
ejpam-5756	229	2	and	and	CCONJ
ejpam-5756	229	3	v	v	ADP
ejpam-5756	229	4	′′	′′	PROPN
ejpam-5756	229	5	=	=	PUNCT
ejpam-5756	230	1	k(k	k(k	PROPN
ejpam-5756	230	2	−	−	PROPN
ejpam-5756	230	3	1)ξk−2	1)ξk−2	PROPN
ejpam-5756	230	4	then	then	ADV
ejpam-5756	230	5	the	the	DET
ejpam-5756	230	6	characteristic	characteristic	ADJ
ejpam-5756	230	7	equation	equation	NOUN
ejpam-5756	230	8	is	be	AUX
ejpam-5756	230	9	k(k	k(k	ADJ
ejpam-5756	230	10	−	−	PROPN
ejpam-5756	230	11	1	1	NUM
ejpam-5756	230	12	)	)	PUNCT
ejpam-5756	230	13	+	+	CCONJ
ejpam-5756	231	1	(	(	PUNCT
ejpam-5756	231	2	3a−	3a−	NUM
ejpam-5756	231	3	2b	2b	NUM
ejpam-5756	231	4	a	a	PRON
ejpam-5756	231	5	)	)	PUNCT
ejpam-5756	231	6	k	k	NOUN
ejpam-5756	232	1	+	+	CCONJ
ejpam-5756	232	2	(	(	PUNCT
ejpam-5756	232	3	a−	a−	PROPN
ejpam-5756	232	4	b)2	b)2	PROPN
ejpam-5756	232	5	a2	a2	PROPN
ejpam-5756	232	6	=	=	SYM
ejpam-5756	232	7	0	0	PROPN
ejpam-5756	232	8	(	(	PUNCT
ejpam-5756	232	9	51	51	NUM
ejpam-5756	232	10	)	)	PUNCT
ejpam-5756	232	11	the	the	DET
ejpam-5756	232	12	roots	root	NOUN
ejpam-5756	232	13	of	of	ADP
ejpam-5756	232	14	equation	equation	NOUN
ejpam-5756	232	15	(	(	PUNCT
ejpam-5756	232	16	51	51	NUM
ejpam-5756	232	17	)	)	PUNCT
ejpam-5756	232	18	are	be	AUX
ejpam-5756	232	19	real	real	ADJ
ejpam-5756	232	20	and	and	CCONJ
ejpam-5756	232	21	repeated	repeat	VERB
ejpam-5756	232	22	i	i	PROPN
ejpam-5756	232	23	-	-	PUNCT
ejpam-5756	232	24	e	e	NOUN
ejpam-5756	232	25	k	k	NOUN
ejpam-5756	232	26	=	=	PUNCT
ejpam-5756	232	27	−1	−1	NOUN
ejpam-5756	233	1	+	+	CCONJ
ejpam-5756	233	2	b	b	NOUN
ejpam-5756	233	3	a	a	NOUN
ejpam-5756	233	4	and	and	CCONJ
ejpam-5756	233	5	k	k	NOUN
ejpam-5756	233	6	=	=	PUNCT
ejpam-5756	234	1	−1	−1	NOUN
ejpam-5756	235	1	+	+	CCONJ
ejpam-5756	235	2	b	b	X
ejpam-5756	235	3	a	a	PRON
ejpam-5756	235	4	hence	hence	ADV
ejpam-5756	235	5	the	the	DET
ejpam-5756	235	6	analytic	analytic	ADJ
ejpam-5756	235	7	solution	solution	NOUN
ejpam-5756	235	8	of	of	ADP
ejpam-5756	235	9	ode	ode	PROPN
ejpam-5756	235	10	(	(	PUNCT
ejpam-5756	235	11	50	50	NUM
ejpam-5756	235	12	)	)	PUNCT
ejpam-5756	235	13	is	be	AUX
ejpam-5756	235	14	f	f	NOUN
ejpam-5756	235	15	′	′	NUM
ejpam-5756	235	16	=	=	SYM
ejpam-5756	235	17	v	v	NOUN
ejpam-5756	235	18	=	=	SYM
ejpam-5756	235	19	(	(	PUNCT
ejpam-5756	235	20	c1	c1	NOUN
ejpam-5756	235	21	+	+	CCONJ
ejpam-5756	235	22	c2lnξ)ξ	c2lnξ)ξ	NOUN
ejpam-5756	235	23	−1	−1	NOUN
ejpam-5756	235	24	+	+	CCONJ
ejpam-5756	235	25	b	b	NOUN
ejpam-5756	235	26	a	a	NOUN
ejpam-5756	235	27	by	by	ADP
ejpam-5756	235	28	replacing	replace	VERB
ejpam-5756	235	29	v	v	NOUN
ejpam-5756	235	30	=	=	SYM
ejpam-5756	235	31	f	f	NOUN
ejpam-5756	235	32	′	′	NOUN
ejpam-5756	235	33	and	and	CCONJ
ejpam-5756	235	34	taking	take	VERB
ejpam-5756	235	35	integral	integral	ADJ
ejpam-5756	235	36	on	on	ADP
ejpam-5756	235	37	both	both	DET
ejpam-5756	235	38	sides	side	NOUN
ejpam-5756	235	39	,	,	PUNCT
ejpam-5756	235	40	we	we	PRON
ejpam-5756	235	41	get	get	VERB
ejpam-5756	235	42	f(ξ	f(ξ	NOUN
ejpam-5756	235	43	)	)	PUNCT
ejpam-5756	235	44	=	=	SYM
ejpam-5756	235	45	(	(	PUNCT
ejpam-5756	235	46	c1	c1	PROPN
ejpam-5756	235	47	+	+	CCONJ
ejpam-5756	235	48	c2lnξ)ξ	c2lnξ)ξ	PROPN
ejpam-5756	235	49	b	b	PROPN
ejpam-5756	235	50	a	a	PRON
ejpam-5756	236	1	+	+	X
ejpam-5756	236	2	c3	c3	NOUN
ejpam-5756	236	3	(	(	PUNCT
ejpam-5756	236	4	52	52	NUM
ejpam-5756	236	5	)	)	PUNCT
ejpam-5756	236	6	using	use	VERB
ejpam-5756	236	7	transformations	transformation	NOUN
ejpam-5756	236	8	(	(	PUNCT
ejpam-5756	236	9	44	44	NUM
ejpam-5756	236	10	)	)	PUNCT
ejpam-5756	236	11	,	,	PUNCT
ejpam-5756	236	12	(	(	PUNCT
ejpam-5756	236	13	45	45	NUM
ejpam-5756	236	14	)	)	PUNCT
ejpam-5756	236	15	and	and	CCONJ
ejpam-5756	236	16	analytic	analytic	ADJ
ejpam-5756	236	17	soltuion	soltuion	NOUN
ejpam-5756	236	18	of	of	ADP
ejpam-5756	236	19	ode	ode	PROPN
ejpam-5756	236	20	(	(	PUNCT
ejpam-5756	236	21	52	52	NUM
ejpam-5756	236	22	)	)	PUNCT
ejpam-5756	236	23	,	,	PUNCT
ejpam-5756	236	24	we	we	PRON
ejpam-5756	236	25	get	get	VERB
ejpam-5756	236	26	exact	exact	ADJ
ejpam-5756	236	27	solution	solution	NOUN
ejpam-5756	236	28	of	of	ADP
ejpam-5756	236	29	pde	pde	NOUN
ejpam-5756	236	30	(	(	PUNCT
ejpam-5756	236	31	1	1	NUM
ejpam-5756	236	32	)	)	PUNCT
ejpam-5756	236	33	which	which	PRON
ejpam-5756	236	34	is	be	AUX
ejpam-5756	236	35	u	u	NOUN
ejpam-5756	236	36	=	=	PUNCT
ejpam-5756	236	37	(	(	PUNCT
ejpam-5756	236	38	c1	c1	PROPN
ejpam-5756	236	39	+	+	CCONJ
ejpam-5756	237	1	c2(ax+	c2(ax+	PROPN
ejpam-5756	237	2	ln(t)))t	ln(t)))t	NOUN
ejpam-5756	237	3	b	b	NOUN
ejpam-5756	237	4	a	a	DET
ejpam-5756	237	5	+	+	NOUN
ejpam-5756	237	6	c3e	c3e	ADJ
ejpam-5756	237	7	bx	bx	NOUN
ejpam-5756	237	8	(	(	PUNCT
ejpam-5756	237	9	53	53	NUM
ejpam-5756	237	10	)	)	PUNCT
ejpam-5756	237	11	when	when	SCONJ
ejpam-5756	237	12	a	a	DET
ejpam-5756	237	13	=	=	SYM
ejpam-5756	237	14	1.0	1.0	NUM
ejpam-5756	237	15	and	and	CCONJ
ejpam-5756	237	16	b	b	NOUN
ejpam-5756	237	17	=	=	SYM
ejpam-5756	237	18	1.4	1.4	NUM
ejpam-5756	237	19	amplitude	amplitude	NOUN
ejpam-5756	237	20	of	of	ADP
ejpam-5756	237	21	the	the	DET
ejpam-5756	237	22	wave	wave	NOUN
ejpam-5756	237	23	ocillates	ocillate	NOUN
ejpam-5756	237	24	.	.	PUNCT
ejpam-5756	238	1	case	case	NOUN
ejpam-5756	238	2	6	6	NUM
ejpam-5756	238	3	:	:	PUNCT
ejpam-5756	238	4	we	we	PRON
ejpam-5756	238	5	choose	choose	VERB
ejpam-5756	238	6	function	function	NOUN
ejpam-5756	238	7	transformation	transformation	NOUN
ejpam-5756	238	8	ξ	ξ	X
ejpam-5756	238	9	=	=	SYM
ejpam-5756	238	10	xm	xm	PROPN
ejpam-5756	238	11	1	1	NUM
ejpam-5756	238	12	+	+	NUM
ejpam-5756	238	13	t	t	PROPN
ejpam-5756	238	14	(	(	PUNCT
ejpam-5756	238	15	54	54	NUM
ejpam-5756	238	16	)	)	PUNCT
ejpam-5756	238	17	u	u	NOUN
ejpam-5756	238	18	=	=	PROPN
ejpam-5756	238	19	xnf(ξ	xnf(ξ	PROPN
ejpam-5756	238	20	)	)	PUNCT
ejpam-5756	238	21	(	(	PUNCT
ejpam-5756	238	22	55	55	NUM
ejpam-5756	238	23	)	)	PUNCT
ejpam-5756	238	24	b.	b.	PROPN
ejpam-5756	238	25	yasmeen	yasmeen	PROPN
ejpam-5756	238	26	,	,	PUNCT
ejpam-5756	238	27	k.	k.	PROPN
ejpam-5756	238	28	ahmad	ahmad	PROPN
ejpam-5756	238	29	,	,	PUNCT
ejpam-5756	238	30	n.	n.	PROPN
ejpam-5756	238	31	fatima	fatima	PROPN
ejpam-5756	238	32	/	/	PUNCT
ejpam-5756	238	33	eur	eur	PROPN
ejpam-5756	238	34	.	.	PUNCT
ejpam-5756	239	1	j.	j.	PROPN
ejpam-5756	239	2	pure	pure	PROPN
ejpam-5756	239	3	appl	appl	PROPN
ejpam-5756	239	4	.	.	PROPN
ejpam-5756	239	5	math	math	PROPN
ejpam-5756	239	6	,	,	PUNCT
ejpam-5756	239	7	18	18	NUM
ejpam-5756	239	8	(	(	PUNCT
ejpam-5756	239	9	1	1	NUM
ejpam-5756	239	10	)	)	PUNCT
ejpam-5756	239	11	(	(	PUNCT
ejpam-5756	239	12	2025	2025	NUM
ejpam-5756	239	13	)	)	PUNCT
ejpam-5756	239	14	,	,	PUNCT
ejpam-5756	239	15	5756	5756	NUM
ejpam-5756	239	16	12	12	NUM
ejpam-5756	239	17	of	of	ADP
ejpam-5756	239	18	17	17	NUM
ejpam-5756	239	19	using	use	VERB
ejpam-5756	239	20	time	time	NOUN
ejpam-5756	239	21	-	-	PUNCT
ejpam-5756	239	22	fractional	fractional	ADJ
ejpam-5756	239	23	derivative	derivative	NOUN
ejpam-5756	239	24	,	,	PUNCT
ejpam-5756	239	25	we	we	PRON
ejpam-5756	239	26	have	have	VERB
ejpam-5756	239	27	∂αu	∂αu	PROPN
ejpam-5756	239	28	∂tα	∂tα	PROPN
ejpam-5756	239	29	=	=	SYM
ejpam-5756	239	30	γ(3/2	γ(3/2	PROPN
ejpam-5756	239	31	)	)	PUNCT
ejpam-5756	239	32	(	(	PUNCT
ejpam-5756	240	1	1	1	NUM
ejpam-5756	240	2	+	+	NOUN
ejpam-5756	240	3	t)3/2	t)3/2	ADJ
ejpam-5756	240	4	xn+mf	xn+mf	ADJ
ejpam-5756	240	5	′	′	NOUN
ejpam-5756	241	1	(	(	PUNCT
ejpam-5756	241	2	56	56	NUM
ejpam-5756	241	3	)	)	PUNCT
ejpam-5756	241	4	∂	∂	NOUN
ejpam-5756	241	5	∂x	∂x	PROPN
ejpam-5756	241	6	(	(	PUNCT
ejpam-5756	241	7	∂αu	∂αu	PROPN
ejpam-5756	241	8	∂tα	∂tα	PROPN
ejpam-5756	241	9	)	)	PUNCT
ejpam-5756	241	10	=	=	SYM
ejpam-5756	241	11	γ(3/2	γ(3/2	PROPN
ejpam-5756	241	12	)	)	PUNCT
ejpam-5756	241	13	(	(	PUNCT
ejpam-5756	241	14	1	1	NUM
ejpam-5756	241	15	+	+	NUM
ejpam-5756	241	16	t)3/2	t)3/2	PROPN
ejpam-5756	241	17	(	(	PUNCT
ejpam-5756	241	18	m	m	PROPN
ejpam-5756	241	19	xn+2m−1	xn+2m−1	X
ejpam-5756	241	20	(	(	PUNCT
ejpam-5756	241	21	1	1	NUM
ejpam-5756	241	22	+	+	NUM
ejpam-5756	241	23	t	t	PROPN
ejpam-5756	241	24	)	)	PUNCT
ejpam-5756	241	25	f	f	PROPN
ejpam-5756	242	1	′′	′′	PROPN
ejpam-5756	242	2	+	+	CCONJ
ejpam-5756	242	3	(	(	PUNCT
ejpam-5756	242	4	n+m)xn+m−1f	n+m)xn+m−1f	ADV
ejpam-5756	242	5	′	′	NUM
ejpam-5756	242	6	)	)	PUNCT
ejpam-5756	242	7	(	(	PUNCT
ejpam-5756	242	8	57	57	NUM
ejpam-5756	242	9	)	)	PUNCT
ejpam-5756	242	10	∂2	∂2	NOUN
ejpam-5756	242	11	∂x2	∂x2	NOUN
ejpam-5756	242	12	(	(	PUNCT
ejpam-5756	242	13	∂αu	∂αu	PROPN
ejpam-5756	242	14	∂tα	∂tα	PROPN
ejpam-5756	242	15	)	)	PUNCT
ejpam-5756	243	1	=	=	SYM
ejpam-5756	243	2	γ(3/2	γ(3/2	PROPN
ejpam-5756	243	3	)	)	PUNCT
ejpam-5756	243	4	(	(	PUNCT
ejpam-5756	243	5	1	1	NUM
ejpam-5756	243	6	+	+	NUM
ejpam-5756	243	7	t)3/2	t)3/2	ADJ
ejpam-5756	243	8	∂	∂	NOUN
ejpam-5756	243	9	∂x	∂x	PROPN
ejpam-5756	243	10	(	(	PUNCT
ejpam-5756	243	11	m	m	PROPN
ejpam-5756	243	12	xn+2m−1	xn+2m−1	X
ejpam-5756	243	13	(	(	PUNCT
ejpam-5756	243	14	1	1	NUM
ejpam-5756	243	15	+	+	NUM
ejpam-5756	243	16	t	t	PROPN
ejpam-5756	243	17	)	)	PUNCT
ejpam-5756	243	18	f	f	PROPN
ejpam-5756	244	1	′′	′′	PROPN
ejpam-5756	244	2	+	+	CCONJ
ejpam-5756	244	3	(	(	PUNCT
ejpam-5756	244	4	n+m)xn+m−1f	n+m)xn+m−1f	ADV
ejpam-5756	244	5	′	′	NUM
ejpam-5756	244	6	)	)	PUNCT
ejpam-5756	245	1	=	=	SYM
ejpam-5756	245	2	γ(3/2	γ(3/2	PROPN
ejpam-5756	245	3	)	)	PUNCT
ejpam-5756	245	4	(	(	PUNCT
ejpam-5756	245	5	1	1	NUM
ejpam-5756	245	6	+	+	CCONJ
ejpam-5756	245	7	t)3/2	t)3/2	PROPN
ejpam-5756	245	8	(	(	PUNCT
ejpam-5756	245	9	m2x	m2x	PROPN
ejpam-5756	245	10	n+3m−2	n+3m−2	X
ejpam-5756	245	11	(	(	PUNCT
ejpam-5756	245	12	1	1	NUM
ejpam-5756	245	13	+	+	NUM
ejpam-5756	245	14	t)2	t)2	PROPN
ejpam-5756	245	15	f	f	PROPN
ejpam-5756	245	16	′′′	′′′	PROPN
ejpam-5756	246	1	+	+	PROPN
ejpam-5756	246	2	m(2m+	m(2m+	NOUN
ejpam-5756	246	3	n−	n−	NOUN
ejpam-5756	246	4	1	1	NUM
ejpam-5756	246	5	)	)	PUNCT
ejpam-5756	246	6	x2m+n−2	x2m+n−2	NOUN
ejpam-5756	246	7	(	(	PUNCT
ejpam-5756	246	8	1	1	NUM
ejpam-5756	246	9	+	+	NUM
ejpam-5756	246	10	t	t	PROPN
ejpam-5756	246	11	)	)	PUNCT
ejpam-5756	246	12	f	f	PROPN
ejpam-5756	247	1	′′	′′	PROPN
ejpam-5756	247	2	+	+	PROPN
ejpam-5756	247	3	m(m+	m(m+	X
ejpam-5756	247	4	n	n	CCONJ
ejpam-5756	247	5	)	)	PUNCT
ejpam-5756	247	6	x2m+n−2	x2m+n−2	PROPN
ejpam-5756	247	7	(	(	PUNCT
ejpam-5756	247	8	1	1	NUM
ejpam-5756	247	9	+	+	NUM
ejpam-5756	247	10	t	t	PROPN
ejpam-5756	247	11	)	)	PUNCT
ejpam-5756	247	12	f	f	PROPN
ejpam-5756	248	1	′′	′′	PROPN
ejpam-5756	248	2	+	+	CCONJ
ejpam-5756	248	3	(	(	PUNCT
ejpam-5756	248	4	m+	m+	NUM
ejpam-5756	248	5	n)(n+m−	n)(n+m−	NOUN
ejpam-5756	248	6	1)xn+m−2f	1)xn+m−2f	NUM
ejpam-5756	248	7	′	′	NUM
ejpam-5756	248	8	)	)	PUNCT
ejpam-5756	248	9	(	(	PUNCT
ejpam-5756	248	10	58	58	X
ejpam-5756	248	11	)	)	PUNCT
ejpam-5756	248	12	using	use	VERB
ejpam-5756	248	13	(	(	PUNCT
ejpam-5756	248	14	56	56	NUM
ejpam-5756	248	15	)	)	PUNCT
ejpam-5756	248	16	,	,	PUNCT
ejpam-5756	248	17	(	(	PUNCT
ejpam-5756	248	18	57	57	NUM
ejpam-5756	248	19	)	)	PUNCT
ejpam-5756	248	20	and	and	CCONJ
ejpam-5756	248	21	(	(	PUNCT
ejpam-5756	248	22	58	58	NUM
ejpam-5756	248	23	)	)	PUNCT
ejpam-5756	248	24	the	the	DET
ejpam-5756	248	25	pde	pde	NOUN
ejpam-5756	248	26	(	(	PUNCT
ejpam-5756	248	27	1	1	X
ejpam-5756	248	28	)	)	PUNCT
ejpam-5756	248	29	can	can	AUX
ejpam-5756	248	30	be	be	AUX
ejpam-5756	248	31	expressed	express	VERB
ejpam-5756	248	32	as	as	ADP
ejpam-5756	248	33	;	;	PUNCT
ejpam-5756	248	34	m2ξ2f	m2ξ2f	NUM
ejpam-5756	248	35	′′′	′′′	X
ejpam-5756	249	1	+	+	CCONJ
ejpam-5756	249	2	(	(	PUNCT
ejpam-5756	249	3	m2	m2	PROPN
ejpam-5756	249	4	+	+	PROPN
ejpam-5756	249	5	3m)ξf	3m)ξf	NUM
ejpam-5756	249	6	′′	′′	NOUN
ejpam-5756	249	7	+	+	CCONJ
ejpam-5756	249	8	2f	2f	NUM
ejpam-5756	249	9	′	′	NUM
ejpam-5756	250	1	=	=	SYM
ejpam-5756	250	2	0	0	PUNCT
ejpam-5756	251	1	(	(	PUNCT
ejpam-5756	251	2	59	59	NUM
ejpam-5756	251	3	)	)	PUNCT
ejpam-5756	251	4	since	since	SCONJ
ejpam-5756	251	5	ξ	ξ	X
ejpam-5756	251	6	=	=	SYM
ejpam-5756	251	7	xm	xm	PROPN
ejpam-5756	251	8	(	(	PUNCT
ejpam-5756	251	9	1+t	1+t	NUM
ejpam-5756	251	10	)	)	PUNCT
ejpam-5756	251	11	,	,	PUNCT
ejpam-5756	251	12	so	so	CCONJ
ejpam-5756	251	13	(	(	PUNCT
ejpam-5756	251	14	59	59	NUM
ejpam-5756	251	15	)	)	PUNCT
ejpam-5756	251	16	reduces	reduce	VERB
ejpam-5756	251	17	to	to	PART
ejpam-5756	251	18	ode	ode	VERB
ejpam-5756	251	19	.	.	PUNCT
ejpam-5756	252	1	the	the	DET
ejpam-5756	252	2	ode	ode	NOUN
ejpam-5756	252	3	is	be	AUX
ejpam-5756	252	4	same	same	ADJ
ejpam-5756	252	5	as	as	ADP
ejpam-5756	252	6	in	in	ADP
ejpam-5756	252	7	case	case	NOUN
ejpam-5756	252	8	3	3	X
ejpam-5756	252	9	.	.	PUNCT
ejpam-5756	253	1	it	it	PRON
ejpam-5756	253	2	’s	’	VERB
ejpam-5756	253	3	solution	solution	NOUN
ejpam-5756	253	4	will	will	AUX
ejpam-5756	253	5	also	also	ADV
ejpam-5756	253	6	be	be	AUX
ejpam-5756	253	7	same	same	ADJ
ejpam-5756	253	8	.	.	PUNCT
ejpam-5756	254	1	for	for	ADP
ejpam-5756	254	2	simplification	simplification	NOUN
ejpam-5756	254	3	,	,	PUNCT
ejpam-5756	254	4	we	we	PRON
ejpam-5756	254	5	take	take	VERB
ejpam-5756	254	6	v	v	NOUN
ejpam-5756	254	7	=	=	SYM
ejpam-5756	254	8	f	f	NOUN
ejpam-5756	255	1	′	′	NUM
ejpam-5756	255	2	then	then	ADV
ejpam-5756	255	3	(	(	PUNCT
ejpam-5756	255	4	59	59	NUM
ejpam-5756	255	5	)	)	PUNCT
ejpam-5756	255	6	becomes	become	VERB
ejpam-5756	255	7	ξ2v	ξ2v	PROPN
ejpam-5756	255	8	′′	′′	PROPN
ejpam-5756	255	9	+	+	CCONJ
ejpam-5756	255	10	(	(	PUNCT
ejpam-5756	255	11	m2	m2	PROPN
ejpam-5756	255	12	+	+	PROPN
ejpam-5756	255	13	3	3	NUM
ejpam-5756	255	14	m	m	NOUN
ejpam-5756	255	15	m2	m2	PROPN
ejpam-5756	255	16	)	)	PUNCT
ejpam-5756	255	17	ξv	ξv	PROPN
ejpam-5756	255	18	′	′	NOUN
ejpam-5756	256	1	+	+	CCONJ
ejpam-5756	256	2	2	2	NUM
ejpam-5756	256	3	m2	m2	PROPN
ejpam-5756	256	4	v	v	NOUN
ejpam-5756	256	5	=	=	SYM
ejpam-5756	256	6	0	0	NUM
ejpam-5756	256	7	(	(	PUNCT
ejpam-5756	256	8	60	60	NUM
ejpam-5756	256	9	)	)	PUNCT
ejpam-5756	256	10	it	it	PRON
ejpam-5756	256	11	is	be	AUX
ejpam-5756	256	12	easy	easy	ADJ
ejpam-5756	256	13	to	to	PART
ejpam-5756	256	14	see	see	VERB
ejpam-5756	256	15	that	that	PRON
ejpam-5756	256	16	(	(	PUNCT
ejpam-5756	256	17	60	60	NUM
ejpam-5756	256	18	)	)	PUNCT
ejpam-5756	256	19	is	be	AUX
ejpam-5756	256	20	euler	euler	NOUN
ejpam-5756	256	21	second	second	ADJ
ejpam-5756	256	22	order	order	NOUN
ejpam-5756	256	23	linear	linear	PROPN
ejpam-5756	256	24	ode	ode	PROPN
ejpam-5756	256	25	.	.	PUNCT
ejpam-5756	257	1	if	if	SCONJ
ejpam-5756	257	2	we	we	PRON
ejpam-5756	257	3	choose	choose	VERB
ejpam-5756	257	4	v	v	NOUN
ejpam-5756	257	5	=	=	SYM
ejpam-5756	257	6	ξk	ξk	PROPN
ejpam-5756	257	7	,	,	PUNCT
ejpam-5756	257	8	v	v	NOUN
ejpam-5756	257	9	′	′	NOUN
ejpam-5756	257	10	=	=	PUNCT
ejpam-5756	258	1	kξk−1	kξk−1	PROPN
ejpam-5756	258	2	and	and	CCONJ
ejpam-5756	258	3	v	v	ADP
ejpam-5756	258	4	′′	′′	PROPN
ejpam-5756	258	5	=	=	PUNCT
ejpam-5756	259	1	k(k	k(k	ADJ
ejpam-5756	259	2	−	−	PROPN
ejpam-5756	259	3	1)ξk−2	1)ξk−2	PROPN
ejpam-5756	259	4	.	.	PUNCT
ejpam-5756	260	1	then	then	ADV
ejpam-5756	260	2	the	the	DET
ejpam-5756	260	3	characteristic	characteristic	ADJ
ejpam-5756	260	4	equation	equation	NOUN
ejpam-5756	260	5	of	of	ADP
ejpam-5756	260	6	(	(	PUNCT
ejpam-5756	260	7	60	60	NUM
ejpam-5756	260	8	)	)	PUNCT
ejpam-5756	260	9	is	be	AUX
ejpam-5756	260	10	;	;	PUNCT
ejpam-5756	260	11	k(k	k(k	ADJ
ejpam-5756	260	12	−	−	NOUN
ejpam-5756	260	13	1	1	NUM
ejpam-5756	260	14	)	)	PUNCT
ejpam-5756	260	15	+	+	CCONJ
ejpam-5756	260	16	(	(	PUNCT
ejpam-5756	260	17	m+	m+	NUM
ejpam-5756	260	18	3	3	NUM
ejpam-5756	260	19	m	m	NOUN
ejpam-5756	260	20	)	)	PUNCT
ejpam-5756	260	21	k	k	PROPN
ejpam-5756	261	1	+	+	CCONJ
ejpam-5756	261	2	2	2	NUM
ejpam-5756	261	3	m2	m2	PROPN
ejpam-5756	261	4	=	=	SYM
ejpam-5756	261	5	0	0	NUM
ejpam-5756	261	6	(	(	PUNCT
ejpam-5756	261	7	61	61	NUM
ejpam-5756	261	8	)	)	PUNCT
ejpam-5756	261	9	the	the	DET
ejpam-5756	261	10	roots	root	NOUN
ejpam-5756	261	11	of	of	ADP
ejpam-5756	261	12	equation	equation	NOUN
ejpam-5756	261	13	(	(	PUNCT
ejpam-5756	261	14	61	61	NUM
ejpam-5756	261	15	)	)	PUNCT
ejpam-5756	261	16	are	be	AUX
ejpam-5756	261	17	k	k	NOUN
ejpam-5756	261	18	=	=	PUNCT
ejpam-5756	261	19	−1	−1	NOUN
ejpam-5756	261	20	and	and	CCONJ
ejpam-5756	261	21	k	k	NOUN
ejpam-5756	261	22	=	=	PUNCT
ejpam-5756	261	23	−1	−1	NOUN
ejpam-5756	261	24	hence	hence	ADV
ejpam-5756	261	25	the	the	DET
ejpam-5756	261	26	analytic	analytic	ADJ
ejpam-5756	261	27	solution	solution	NOUN
ejpam-5756	261	28	of	of	ADP
ejpam-5756	261	29	ode	ode	PROPN
ejpam-5756	261	30	(	(	PUNCT
ejpam-5756	261	31	60	60	NUM
ejpam-5756	261	32	)	)	PUNCT
ejpam-5756	261	33	is	be	AUX
ejpam-5756	261	34	f	f	NOUN
ejpam-5756	261	35	′	′	NUM
ejpam-5756	261	36	=	=	SYM
ejpam-5756	261	37	v	v	NOUN
ejpam-5756	261	38	=	=	NOUN
ejpam-5756	261	39	c1ξ	c1ξ	NOUN
ejpam-5756	261	40	−	−	NUM
ejpam-5756	261	41	2	2	NUM
ejpam-5756	261	42	m	m	NOUN
ejpam-5756	261	43	+	+	CCONJ
ejpam-5756	261	44	c2ξ	c2ξ	NOUN
ejpam-5756	261	45	−	−	NUM
ejpam-5756	261	46	1	1	NUM
ejpam-5756	261	47	m	m	VERB
ejpam-5756	261	48	by	by	ADP
ejpam-5756	261	49	replacing	replace	VERB
ejpam-5756	261	50	v	v	NOUN
ejpam-5756	261	51	=	=	SYM
ejpam-5756	261	52	f	f	NOUN
ejpam-5756	261	53	′	′	NOUN
ejpam-5756	261	54	and	and	CCONJ
ejpam-5756	261	55	taking	take	VERB
ejpam-5756	261	56	integral	integral	ADJ
ejpam-5756	261	57	on	on	ADP
ejpam-5756	261	58	both	both	DET
ejpam-5756	261	59	sides	side	NOUN
ejpam-5756	261	60	,	,	PUNCT
ejpam-5756	261	61	we	we	PRON
ejpam-5756	261	62	get	get	VERB
ejpam-5756	261	63	f(ξ	f(ξ	NOUN
ejpam-5756	261	64	)	)	PUNCT
ejpam-5756	262	1	=	=	SYM
ejpam-5756	262	2	c1	c1	PROPN
ejpam-5756	262	3	ξ−	ξ−	NOUN
ejpam-5756	262	4	2	2	NUM
ejpam-5756	262	5	m	m	NOUN
ejpam-5756	262	6	+1	+1	ADJ
ejpam-5756	262	7	−	−	NOUN
ejpam-5756	262	8	2	2	NUM
ejpam-5756	262	9	m	m	NOUN
ejpam-5756	262	10	+	+	NOUN
ejpam-5756	262	11	1	1	NUM
ejpam-5756	262	12	+	+	NUM
ejpam-5756	262	13	c2	c2	PROPN
ejpam-5756	262	14	ξ−	ξ−	PROPN
ejpam-5756	262	15	1	1	NUM
ejpam-5756	262	16	m	m	NOUN
ejpam-5756	262	17	+1	+1	ADJ
ejpam-5756	262	18	−	−	NOUN
ejpam-5756	262	19	1	1	NUM
ejpam-5756	262	20	m	m	NOUN
ejpam-5756	262	21	+	+	NUM
ejpam-5756	262	22	1	1	NUM
ejpam-5756	262	23	+	+	CCONJ
ejpam-5756	262	24	c3	c3	X
ejpam-5756	262	25	(	(	PUNCT
ejpam-5756	262	26	62	62	NUM
ejpam-5756	262	27	)	)	PUNCT
ejpam-5756	262	28	using	use	VERB
ejpam-5756	262	29	transformation	transformation	NOUN
ejpam-5756	262	30	(	(	PUNCT
ejpam-5756	262	31	54	54	NUM
ejpam-5756	262	32	)	)	PUNCT
ejpam-5756	262	33	,	,	PUNCT
ejpam-5756	262	34	(	(	PUNCT
ejpam-5756	262	35	55	55	NUM
ejpam-5756	262	36	)	)	PUNCT
ejpam-5756	262	37	and	and	CCONJ
ejpam-5756	262	38	analytic	analytic	ADJ
ejpam-5756	262	39	solution	solution	NOUN
ejpam-5756	262	40	of	of	ADP
ejpam-5756	262	41	ode	ode	PROPN
ejpam-5756	262	42	(	(	PUNCT
ejpam-5756	262	43	62	62	NUM
ejpam-5756	262	44	)	)	PUNCT
ejpam-5756	262	45	,	,	PUNCT
ejpam-5756	262	46	we	we	PRON
ejpam-5756	262	47	get	get	VERB
ejpam-5756	262	48	exact	exact	ADJ
ejpam-5756	262	49	solution	solution	NOUN
ejpam-5756	262	50	of	of	ADP
ejpam-5756	262	51	pde	pde	NOUN
ejpam-5756	262	52	(	(	PUNCT
ejpam-5756	262	53	1	1	NUM
ejpam-5756	262	54	)	)	PUNCT
ejpam-5756	262	55	which	which	PRON
ejpam-5756	262	56	is	be	AUX
ejpam-5756	262	57	u	u	PROPN
ejpam-5756	262	58	=	=	PROPN
ejpam-5756	262	59	xnc1	xnc1	PROPN
ejpam-5756	262	60	(	(	PUNCT
ejpam-5756	262	61	xm	xm	PROPN
ejpam-5756	262	62	1+t	1+t	NUM
ejpam-5756	262	63	)	)	PUNCT
ejpam-5756	262	64	−	−	PROPN
ejpam-5756	263	1	2	2	NUM
ejpam-5756	263	2	m	m	NOUN
ejpam-5756	263	3	+1	+1	INTJ
ejpam-5756	263	4	−	−	NOUN
ejpam-5756	263	5	2	2	NUM
ejpam-5756	263	6	m	m	NOUN
ejpam-5756	263	7	+	+	NOUN
ejpam-5756	263	8	1	1	NUM
ejpam-5756	263	9	+	+	CCONJ
ejpam-5756	263	10	xnc2	xnc2	PROPN
ejpam-5756	263	11	(	(	PUNCT
ejpam-5756	263	12	xm	xm	PROPN
ejpam-5756	263	13	1+t	1+t	NUM
ejpam-5756	263	14	)	)	PUNCT
ejpam-5756	263	15	−	−	PROPN
ejpam-5756	264	1	1	1	NUM
ejpam-5756	264	2	m	m	NOUN
ejpam-5756	264	3	+1	+1	ADJ
ejpam-5756	264	4	−	−	NOUN
ejpam-5756	264	5	1	1	NUM
ejpam-5756	264	6	m	m	NOUN
ejpam-5756	264	7	+	+	NUM
ejpam-5756	264	8	1	1	NUM
ejpam-5756	264	9	+	+	NUM
ejpam-5756	264	10	xnc3	xnc3	PROPN
ejpam-5756	264	11	b.	b.	PROPN
ejpam-5756	264	12	yasmeen	yasmeen	PROPN
ejpam-5756	264	13	,	,	PUNCT
ejpam-5756	264	14	k.	k.	PROPN
ejpam-5756	264	15	ahmad	ahmad	PROPN
ejpam-5756	264	16	,	,	PUNCT
ejpam-5756	264	17	n.	n.	PROPN
ejpam-5756	264	18	fatima	fatima	PROPN
ejpam-5756	264	19	/	/	PUNCT
ejpam-5756	264	20	eur	eur	PROPN
ejpam-5756	264	21	.	.	PUNCT
ejpam-5756	265	1	j.	j.	PROPN
ejpam-5756	265	2	pure	pure	PROPN
ejpam-5756	265	3	appl	appl	PROPN
ejpam-5756	265	4	.	.	PROPN
ejpam-5756	265	5	math	math	PROPN
ejpam-5756	265	6	,	,	PUNCT
ejpam-5756	265	7	18	18	NUM
ejpam-5756	265	8	(	(	PUNCT
ejpam-5756	265	9	1	1	NUM
ejpam-5756	265	10	)	)	PUNCT
ejpam-5756	265	11	(	(	PUNCT
ejpam-5756	265	12	2025	2025	NUM
ejpam-5756	265	13	)	)	PUNCT
ejpam-5756	265	14	,	,	PUNCT
ejpam-5756	265	15	5756	5756	NUM
ejpam-5756	265	16	13	13	NUM
ejpam-5756	265	17	of	of	ADP
ejpam-5756	265	18	17	17	NUM
ejpam-5756	265	19	u	u	NOUN
ejpam-5756	265	20	=	=	PROPN
ejpam-5756	265	21	mc1	mc1	PROPN
ejpam-5756	266	1	xm+n−2	xm+n−2	PROPN
ejpam-5756	266	2	(	(	PUNCT
ejpam-5756	266	3	m−	m−	PROPN
ejpam-5756	266	4	2)(1	2)(1	NUM
ejpam-5756	266	5	+	+	CCONJ
ejpam-5756	266	6	t)−	t)−	PROPN
ejpam-5756	266	7	2	2	NUM
ejpam-5756	266	8	m	m	NOUN
ejpam-5756	266	9	+1	+1	PROPN
ejpam-5756	267	1	+	+	NOUN
ejpam-5756	267	2	mc2	mc2	PROPN
ejpam-5756	267	3	xm+n−1	xm+n−1	PROPN
ejpam-5756	267	4	(	(	PUNCT
ejpam-5756	267	5	m−	m−	PROPN
ejpam-5756	267	6	1)(1	1)(1	NUM
ejpam-5756	267	7	+	+	CCONJ
ejpam-5756	268	1	t)−	t)−	PROPN
ejpam-5756	268	2	1	1	NUM
ejpam-5756	268	3	m	m	NOUN
ejpam-5756	268	4	+1	+1	ADJ
ejpam-5756	268	5	+	+	CCONJ
ejpam-5756	268	6	xnc3	xnc3	PROPN
ejpam-5756	268	7	(	(	PUNCT
ejpam-5756	268	8	63	63	NUM
ejpam-5756	268	9	)	)	PUNCT
ejpam-5756	268	10	when	when	SCONJ
ejpam-5756	268	11	m	m	VERB
ejpam-5756	268	12	=	=	SYM
ejpam-5756	268	13	−0.5	−0.5	PROPN
ejpam-5756	268	14	and	and	CCONJ
ejpam-5756	268	15	n	n	CCONJ
ejpam-5756	268	16	=	=	NOUN
ejpam-5756	268	17	3	3	NUM
ejpam-5756	268	18	there	there	PRON
ejpam-5756	268	19	is	be	VERB
ejpam-5756	268	20	sudden	sudden	ADJ
ejpam-5756	268	21	change	change	NOUN
ejpam-5756	268	22	in	in	ADP
ejpam-5756	268	23	wave	wave	NOUN
ejpam-5756	268	24	amplitude	amplitude	NOUN
ejpam-5756	268	25	.	.	PUNCT
ejpam-5756	269	1	4	4	X
ejpam-5756	269	2	.	.	NUM
ejpam-5756	269	3	figures	figure	NOUN
ejpam-5756	269	4	figure	figure	VERB
ejpam-5756	269	5	2	2	NUM
ejpam-5756	269	6	:	:	PUNCT
ejpam-5756	269	7	3d	3d	NUM
ejpam-5756	269	8	plot	plot	NOUN
ejpam-5756	269	9	of	of	ADP
ejpam-5756	269	10	solution	solution	NOUN
ejpam-5756	269	11	(	(	PUNCT
ejpam-5756	269	12	14	14	NUM
ejpam-5756	269	13	)	)	PUNCT
ejpam-5756	269	14	of	of	ADP
ejpam-5756	269	15	pde	pde	NOUN
ejpam-5756	269	16	(	(	PUNCT
ejpam-5756	269	17	1	1	NUM
ejpam-5756	269	18	)	)	PUNCT
ejpam-5756	269	19	with	with	ADP
ejpam-5756	269	20	r	r	NOUN
ejpam-5756	269	21	=	=	SYM
ejpam-5756	269	22	−1	−1	NOUN
ejpam-5756	269	23	;	;	PUNCT
ejpam-5756	269	24	n	n	NOUN
ejpam-5756	269	25	=	=	SYM
ejpam-5756	269	26	1	1	NUM
ejpam-5756	269	27	and	and	CCONJ
ejpam-5756	269	28	β	β	X
ejpam-5756	269	29	=	=	SYM
ejpam-5756	269	30	0.5	0.5	NUM
ejpam-5756	269	31	shows	show	VERB
ejpam-5756	269	32	more	more	ADJ
ejpam-5756	269	33	rapid	rapid	ADJ
ejpam-5756	269	34	decay	decay	NOUN
ejpam-5756	269	35	in	in	ADP
ejpam-5756	269	36	the	the	DET
ejpam-5756	269	37	wave	wave	NOUN
ejpam-5756	269	38	amplitude	amplitude	NOUN
ejpam-5756	269	39	figure	figure	NOUN
ejpam-5756	269	40	3	3	NUM
ejpam-5756	269	41	:	:	PUNCT
ejpam-5756	269	42	3d	3d	NUM
ejpam-5756	269	43	plot	plot	NOUN
ejpam-5756	269	44	of	of	ADP
ejpam-5756	269	45	solution	solution	NOUN
ejpam-5756	269	46	(	(	PUNCT
ejpam-5756	269	47	23	23	NUM
ejpam-5756	269	48	)	)	PUNCT
ejpam-5756	269	49	of	of	ADP
ejpam-5756	269	50	pde	pde	NOUN
ejpam-5756	269	51	(	(	PUNCT
ejpam-5756	269	52	1	1	NUM
ejpam-5756	269	53	)	)	PUNCT
ejpam-5756	269	54	with	with	ADP
ejpam-5756	269	55	m	m	PROPN
ejpam-5756	269	56	=	=	SYM
ejpam-5756	269	57	8	8	NUM
ejpam-5756	269	58	,	,	PUNCT
ejpam-5756	269	59	β	β	X
ejpam-5756	269	60	=	=	SYM
ejpam-5756	269	61	−10	−10	X
ejpam-5756	269	62	and	and	CCONJ
ejpam-5756	269	63	n	n	CCONJ
ejpam-5756	269	64	=	=	SYM
ejpam-5756	269	65	6	6	NUM
ejpam-5756	269	66	wave	wave	NOUN
ejpam-5756	269	67	amplitude	amplitude	NOUN
ejpam-5756	269	68	become	become	VERB
ejpam-5756	269	69	more	more	ADV
ejpam-5756	269	70	frequent	frequent	ADJ
ejpam-5756	269	71	figure	figure	NOUN
ejpam-5756	269	72	4	4	NUM
ejpam-5756	269	73	:	:	PUNCT
ejpam-5756	269	74	3d	3d	NUM
ejpam-5756	269	75	plot	plot	NOUN
ejpam-5756	269	76	of	of	ADP
ejpam-5756	269	77	solution	solution	NOUN
ejpam-5756	269	78	(	(	PUNCT
ejpam-5756	269	79	33	33	NUM
ejpam-5756	269	80	)	)	PUNCT
ejpam-5756	269	81	of	of	ADP
ejpam-5756	269	82	pde	pde	NOUN
ejpam-5756	269	83	(	(	PUNCT
ejpam-5756	269	84	1	1	NUM
ejpam-5756	269	85	)	)	PUNCT
ejpam-5756	269	86	with	with	ADP
ejpam-5756	269	87	α	α	NOUN
ejpam-5756	269	88	=	=	SYM
ejpam-5756	269	89	1.5	1.5	NUM
ejpam-5756	269	90	;	;	PUNCT
ejpam-5756	269	91	β	β	X
ejpam-5756	269	92	=	=	SYM
ejpam-5756	269	93	1.5	1.5	NUM
ejpam-5756	269	94	wave	wave	NOUN
ejpam-5756	269	95	amplitude	amplitude	NOUN
ejpam-5756	269	96	exhibits	exhibit	VERB
ejpam-5756	269	97	oscillatory	oscillatory	ADJ
ejpam-5756	269	98	behavior	behavior	NOUN
ejpam-5756	269	99	figure	figure	NOUN
ejpam-5756	269	100	5	5	NUM
ejpam-5756	269	101	:	:	PUNCT
ejpam-5756	269	102	3d	3d	NUM
ejpam-5756	269	103	plot	plot	NOUN
ejpam-5756	269	104	of	of	ADP
ejpam-5756	269	105	solution	solution	NOUN
ejpam-5756	269	106	(	(	PUNCT
ejpam-5756	269	107	43	43	NUM
ejpam-5756	269	108	)	)	PUNCT
ejpam-5756	269	109	of	of	ADP
ejpam-5756	269	110	pde	pde	NOUN
ejpam-5756	269	111	(	(	PUNCT
ejpam-5756	269	112	1	1	NUM
ejpam-5756	269	113	)	)	PUNCT
ejpam-5756	269	114	with	with	ADP
ejpam-5756	269	115	α	α	NOUN
ejpam-5756	269	116	=	=	SYM
ejpam-5756	269	117	1.5	1.5	NUM
ejpam-5756	269	118	;	;	PUNCT
ejpam-5756	269	119	β	β	X
ejpam-5756	269	120	=	=	SYM
ejpam-5756	269	121	1.5	1.5	NUM
ejpam-5756	269	122	shows	show	VERB
ejpam-5756	269	123	more	more	ADJ
ejpam-5756	269	124	rapid	rapid	ADJ
ejpam-5756	269	125	decay	decay	NOUN
ejpam-5756	269	126	in	in	ADP
ejpam-5756	269	127	the	the	DET
ejpam-5756	269	128	wave	wave	NOUN
ejpam-5756	269	129	amplitude	amplitude	NOUN
ejpam-5756	269	130	figure	figure	NOUN
ejpam-5756	269	131	6	6	NUM
ejpam-5756	269	132	:	:	PUNCT
ejpam-5756	269	133	3d	3d	NUM
ejpam-5756	269	134	plot	plot	NOUN
ejpam-5756	269	135	of	of	ADP
ejpam-5756	269	136	solution	solution	NOUN
ejpam-5756	269	137	(	(	PUNCT
ejpam-5756	269	138	53	53	NUM
ejpam-5756	269	139	)	)	PUNCT
ejpam-5756	269	140	of	of	ADP
ejpam-5756	269	141	pde	pde	NOUN
ejpam-5756	269	142	(	(	PUNCT
ejpam-5756	269	143	1	1	NUM
ejpam-5756	269	144	)	)	PUNCT
ejpam-5756	269	145	with	with	ADP
ejpam-5756	269	146	a	a	DET
ejpam-5756	269	147	=	=	SYM
ejpam-5756	269	148	1.0	1.0	NUM
ejpam-5756	269	149	and	and	CCONJ
ejpam-5756	269	150	b	b	NOUN
ejpam-5756	269	151	=	=	SYM
ejpam-5756	269	152	1.4	1.4	NUM
ejpam-5756	269	153	wave	wave	NOUN
ejpam-5756	269	154	amplitude	amplitude	NOUN
ejpam-5756	269	155	exhibits	exhibit	VERB
ejpam-5756	269	156	oscillatory	oscillatory	ADJ
ejpam-5756	269	157	behavior	behavior	NOUN
ejpam-5756	269	158	figure	figure	NOUN
ejpam-5756	269	159	7	7	NUM
ejpam-5756	269	160	:	:	PUNCT
ejpam-5756	269	161	3d	3d	NUM
ejpam-5756	269	162	plot	plot	NOUN
ejpam-5756	269	163	of	of	ADP
ejpam-5756	269	164	solution	solution	NOUN
ejpam-5756	269	165	(	(	PUNCT
ejpam-5756	269	166	63	63	NUM
ejpam-5756	269	167	)	)	PUNCT
ejpam-5756	269	168	of	of	ADP
ejpam-5756	269	169	pde	pde	NOUN
ejpam-5756	269	170	(	(	PUNCT
ejpam-5756	269	171	1	1	NUM
ejpam-5756	269	172	)	)	PUNCT
ejpam-5756	269	173	with	with	ADP
ejpam-5756	269	174	m	m	PROPN
ejpam-5756	269	175	=	=	SYM
ejpam-5756	269	176	−0.5	−0.5	PROPN
ejpam-5756	269	177	and	and	CCONJ
ejpam-5756	269	178	n	n	CCONJ
ejpam-5756	269	179	=	=	SYM
ejpam-5756	269	180	3	3	NUM
ejpam-5756	269	181	sudden	sudden	ADJ
ejpam-5756	269	182	change	change	NOUN
ejpam-5756	269	183	in	in	ADP
ejpam-5756	269	184	wave	wave	NOUN
ejpam-5756	269	185	amplitude	amplitude	NOUN
ejpam-5756	269	186	5	5	NUM
ejpam-5756	269	187	.	.	PUNCT
ejpam-5756	269	188	discussion	discussion	NOUN
ejpam-5756	269	189	of	of	ADP
ejpam-5756	269	190	the	the	DET
ejpam-5756	269	191	results	result	NOUN
ejpam-5756	269	192	by	by	ADP
ejpam-5756	269	193	developing	develop	VERB
ejpam-5756	269	194	an	an	DET
ejpam-5756	269	195	analytical	analytical	ADJ
ejpam-5756	269	196	approach	approach	NOUN
ejpam-5756	269	197	to	to	PART
ejpam-5756	269	198	solve	solve	VERB
ejpam-5756	269	199	the	the	DET
ejpam-5756	269	200	time	time	NOUN
ejpam-5756	269	201	-	-	PUNCT
ejpam-5756	269	202	fractional	fractional	ADJ
ejpam-5756	269	203	djkm	djkm	NOUN
ejpam-5756	269	204	equation	equation	NOUN
ejpam-5756	269	205	,	,	PUNCT
ejpam-5756	269	206	this	this	DET
ejpam-5756	269	207	paper	paper	NOUN
ejpam-5756	269	208	significantly	significantly	ADV
ejpam-5756	269	209	advances	advance	VERB
ejpam-5756	269	210	the	the	DET
ejpam-5756	269	211	field	field	NOUN
ejpam-5756	269	212	of	of	ADP
ejpam-5756	269	213	nonlinear	nonlinear	ADJ
ejpam-5756	269	214	science	science	NOUN
ejpam-5756	269	215	.	.	PUNCT
ejpam-5756	270	1	the	the	DET
ejpam-5756	270	2	study	study	NOUN
ejpam-5756	270	3	’s	’s	PART
ejpam-5756	270	4	successful	successful	ADJ
ejpam-5756	270	5	application	application	NOUN
ejpam-5756	270	6	of	of	ADP
ejpam-5756	270	7	the	the	DET
ejpam-5756	270	8	power	power	NOUN
ejpam-5756	270	9	index	index	NOUN
ejpam-5756	270	10	method	method	NOUN
ejpam-5756	270	11	reveals	reveal	VERB
ejpam-5756	270	12	a	a	DET
ejpam-5756	270	13	variety	variety	NOUN
ejpam-5756	270	14	of	of	ADP
ejpam-5756	270	15	solutions	solution	NOUN
ejpam-5756	270	16	with	with	ADP
ejpam-5756	270	17	unique	unique	ADJ
ejpam-5756	270	18	wave	wave	NOUN
ejpam-5756	270	19	structures	structure	NOUN
ejpam-5756	270	20	,	,	PUNCT
ejpam-5756	270	21	demonstrating	demonstrate	VERB
ejpam-5756	270	22	the	the	DET
ejpam-5756	270	23	method	method	NOUN
ejpam-5756	270	24	effectiveness	effectiveness	NOUN
ejpam-5756	270	25	in	in	ADP
ejpam-5756	270	26	solving	solve	VERB
ejpam-5756	270	27	challenging	challenging	ADJ
ejpam-5756	270	28	nonlinear	nonlinear	ADJ
ejpam-5756	270	29	problems	problem	NOUN
ejpam-5756	270	30	.	.	PUNCT
ejpam-5756	271	1	the	the	DET
ejpam-5756	271	2	b.	b.	PROPN
ejpam-5756	271	3	yasmeen	yasmeen	PROPN
ejpam-5756	271	4	,	,	PUNCT
ejpam-5756	271	5	k.	k.	PROPN
ejpam-5756	271	6	ahmad	ahmad	PROPN
ejpam-5756	271	7	,	,	PUNCT
ejpam-5756	271	8	n.	n.	PROPN
ejpam-5756	271	9	fatima	fatima	PROPN
ejpam-5756	271	10	/	/	PUNCT
ejpam-5756	271	11	eur	eur	PROPN
ejpam-5756	271	12	.	.	PUNCT
ejpam-5756	272	1	j.	j.	PROPN
ejpam-5756	272	2	pure	pure	PROPN
ejpam-5756	272	3	appl	appl	PROPN
ejpam-5756	272	4	.	.	PROPN
ejpam-5756	272	5	math	math	PROPN
ejpam-5756	272	6	,	,	PUNCT
ejpam-5756	272	7	18	18	NUM
ejpam-5756	272	8	(	(	PUNCT
ejpam-5756	272	9	1	1	NUM
ejpam-5756	272	10	)	)	PUNCT
ejpam-5756	272	11	(	(	PUNCT
ejpam-5756	272	12	2025	2025	NUM
ejpam-5756	272	13	)	)	PUNCT
ejpam-5756	272	14	,	,	PUNCT
ejpam-5756	272	15	5756	5756	NUM
ejpam-5756	272	16	14	14	NUM
ejpam-5756	272	17	of	of	ADP
ejpam-5756	272	18	17	17	NUM
ejpam-5756	272	19	paper	paper	NOUN
ejpam-5756	272	20	is	be	AUX
ejpam-5756	272	21	a	a	DET
ejpam-5756	272	22	useful	useful	ADJ
ejpam-5756	272	23	tool	tool	NOUN
ejpam-5756	272	24	for	for	ADP
ejpam-5756	272	25	scientists	scientist	NOUN
ejpam-5756	272	26	and	and	CCONJ
ejpam-5756	272	27	researchers	researcher	NOUN
ejpam-5756	272	28	because	because	SCONJ
ejpam-5756	272	29	of	of	ADP
ejpam-5756	272	30	its	its	PRON
ejpam-5756	272	31	thorough	thorough	ADJ
ejpam-5756	272	32	analysis	analysis	NOUN
ejpam-5756	272	33	and	and	CCONJ
ejpam-5756	272	34	graphical	graphical	ADJ
ejpam-5756	272	35	representations	representation	NOUN
ejpam-5756	272	36	,	,	PUNCT
ejpam-5756	272	37	which	which	PRON
ejpam-5756	272	38	provide	provide	VERB
ejpam-5756	272	39	a	a	DET
ejpam-5756	272	40	deeper	deep	ADJ
ejpam-5756	272	41	understanding	understanding	NOUN
ejpam-5756	272	42	of	of	ADP
ejpam-5756	272	43	the	the	DET
ejpam-5756	272	44	equation	equation	NOUN
ejpam-5756	272	45	’s	’s	PART
ejpam-5756	272	46	dynamics	dynamic	NOUN
ejpam-5756	272	47	and	and	CCONJ
ejpam-5756	272	48	physical	physical	ADJ
ejpam-5756	272	49	phenomena	phenomenon	NOUN
ejpam-5756	272	50	.	.	PUNCT
ejpam-5756	273	1	additionally	additionally	ADV
ejpam-5756	273	2	,	,	PUNCT
ejpam-5756	273	3	the	the	DET
ejpam-5756	273	4	study	study	NOUN
ejpam-5756	273	5	opens	open	VERB
ejpam-5756	273	6	up	up	ADP
ejpam-5756	273	7	new	new	ADJ
ejpam-5756	273	8	research	research	NOUN
ejpam-5756	273	9	directions	direction	NOUN
ejpam-5756	273	10	in	in	ADP
ejpam-5756	273	11	a	a	DET
ejpam-5756	273	12	number	number	NOUN
ejpam-5756	273	13	of	of	ADP
ejpam-5756	273	14	scientific	scientific	ADJ
ejpam-5756	273	15	fields	field	NOUN
ejpam-5756	273	16	by	by	ADP
ejpam-5756	273	17	showcasing	showcase	VERB
ejpam-5756	273	18	the	the	DET
ejpam-5756	273	19	power	power	NOUN
ejpam-5756	273	20	index	index	NOUN
ejpam-5756	273	21	method	method	NOUN
ejpam-5756	273	22	capacity	capacity	NOUN
ejpam-5756	273	23	to	to	PART
ejpam-5756	273	24	solve	solve	VERB
ejpam-5756	273	25	fractional	fractional	ADJ
ejpam-5756	273	26	differential	differential	ADJ
ejpam-5756	273	27	equations	equation	NOUN
ejpam-5756	273	28	.	.	PUNCT
ejpam-5756	274	1	all	all	DET
ejpam-5756	274	2	things	thing	NOUN
ejpam-5756	274	3	considered	consider	VERB
ejpam-5756	274	4	,	,	PUNCT
ejpam-5756	274	5	the	the	DET
ejpam-5756	274	6	paper	paper	NOUN
ejpam-5756	274	7	’s	’s	PART
ejpam-5756	274	8	distinctive	distinctive	ADJ
ejpam-5756	274	9	methodology	methodology	NOUN
ejpam-5756	274	10	and	and	CCONJ
ejpam-5756	274	11	conclusions	conclusion	NOUN
ejpam-5756	274	12	make	make	VERB
ejpam-5756	274	13	it	it	PRON
ejpam-5756	274	14	a	a	DET
ejpam-5756	274	15	noteworthy	noteworthy	ADJ
ejpam-5756	274	16	and	and	CCONJ
ejpam-5756	274	17	influential	influential	ADJ
ejpam-5756	274	18	addition	addition	NOUN
ejpam-5756	274	19	to	to	ADP
ejpam-5756	274	20	the	the	DET
ejpam-5756	274	21	field	field	NOUN
ejpam-5756	274	22	.	.	PUNCT
ejpam-5756	275	1	in	in	ADP
ejpam-5756	275	2	this	this	DET
ejpam-5756	275	3	study	study	NOUN
ejpam-5756	275	4	,	,	PUNCT
ejpam-5756	275	5	we	we	PRON
ejpam-5756	275	6	presented	present	VERB
ejpam-5756	275	7	novel	novel	ADJ
ejpam-5756	275	8	solutions	solution	NOUN
ejpam-5756	275	9	known	know	VERB
ejpam-5756	275	10	as	as	ADP
ejpam-5756	275	11	a	a	DET
ejpam-5756	275	12	rational	rational	ADJ
ejpam-5756	275	13	and	and	CCONJ
ejpam-5756	275	14	logarithm	logarithm	NOUN
ejpam-5756	275	15	functions	function	NOUN
ejpam-5756	275	16	.	.	PUNCT
ejpam-5756	276	1	as	as	ADP
ejpam-5756	276	2	a	a	DET
ejpam-5756	276	3	result	result	NOUN
ejpam-5756	276	4	of	of	ADP
ejpam-5756	276	5	the	the	DET
ejpam-5756	276	6	above	above	ADJ
ejpam-5756	276	7	thorough	thorough	ADJ
ejpam-5756	276	8	discussion	discussion	NOUN
ejpam-5756	276	9	and	and	CCONJ
ejpam-5756	276	10	compression	compression	NOUN
ejpam-5756	276	11	,	,	PUNCT
ejpam-5756	276	12	we	we	PRON
ejpam-5756	276	13	are	be	AUX
ejpam-5756	276	14	able	able	ADJ
ejpam-5756	276	15	to	to	PART
ejpam-5756	276	16	produce	produce	VERB
ejpam-5756	276	17	new	new	ADJ
ejpam-5756	276	18	,	,	PUNCT
ejpam-5756	276	19	intriguing	intriguing	ADJ
ejpam-5756	276	20	,	,	PUNCT
ejpam-5756	276	21	and	and	CCONJ
ejpam-5756	276	22	thorough	thorough	ADJ
ejpam-5756	276	23	results	result	NOUN
ejpam-5756	276	24	that	that	PRON
ejpam-5756	276	25	have	have	AUX
ejpam-5756	276	26	not	not	PART
ejpam-5756	276	27	been	be	AUX
ejpam-5756	276	28	addressed	address	VERB
ejpam-5756	276	29	by	by	ADP
ejpam-5756	276	30	other	other	ADJ
ejpam-5756	276	31	approaches	approach	NOUN
ejpam-5756	276	32	in	in	ADP
ejpam-5756	276	33	the	the	DET
ejpam-5756	276	34	prior	prior	ADJ
ejpam-5756	276	35	literature	literature	NOUN
ejpam-5756	276	36	.	.	PUNCT
ejpam-5756	277	1	to	to	PART
ejpam-5756	277	2	solve	solve	VERB
ejpam-5756	277	3	the	the	DET
ejpam-5756	277	4	nonlinear	nonlinear	ADJ
ejpam-5756	277	5	equation	equation	NOUN
ejpam-5756	277	6	,	,	PUNCT
ejpam-5756	277	7	we	we	PRON
ejpam-5756	277	8	employed	employ	VERB
ejpam-5756	277	9	a	a	DET
ejpam-5756	277	10	potent	potent	ADJ
ejpam-5756	277	11	technique	technique	NOUN
ejpam-5756	277	12	.	.	PUNCT
ejpam-5756	278	1	other	other	ADJ
ejpam-5756	278	2	complex	complex	ADJ
ejpam-5756	278	3	equations	equation	NOUN
ejpam-5756	278	4	can	can	AUX
ejpam-5756	278	5	be	be	AUX
ejpam-5756	278	6	studied	study	VERB
ejpam-5756	278	7	using	use	VERB
ejpam-5756	278	8	this	this	DET
ejpam-5756	278	9	method	method	NOUN
ejpam-5756	278	10	.	.	PUNCT
ejpam-5756	279	1	6	6	NUM
ejpam-5756	279	2	.	.	X
ejpam-5756	279	3	conclusions	conclusion	NOUN
ejpam-5756	279	4	this	this	DET
ejpam-5756	279	5	work	work	NOUN
ejpam-5756	279	6	represents	represent	VERB
ejpam-5756	279	7	a	a	DET
ejpam-5756	279	8	major	major	ADJ
ejpam-5756	279	9	advancement	advancement	NOUN
ejpam-5756	279	10	in	in	ADP
ejpam-5756	279	11	the	the	DET
ejpam-5756	279	12	effort	effort	NOUN
ejpam-5756	279	13	to	to	PART
ejpam-5756	279	14	solve	solve	VERB
ejpam-5756	279	15	the	the	DET
ejpam-5756	279	16	time	time	NOUN
ejpam-5756	279	17	-	-	PUNCT
ejpam-5756	279	18	fractional	fractional	ADJ
ejpam-5756	279	19	date	date	NOUN
ejpam-5756	279	20	-	-	PUNCT
ejpam-5756	279	21	jimbo	jimbo	NOUN
ejpam-5756	279	22	-	-	PUNCT
ejpam-5756	279	23	kashiwara	kashiwara	PROPN
ejpam-5756	279	24	-	-	PUNCT
ejpam-5756	279	25	miwa	miwa	PROPN
ejpam-5756	279	26	equation	equation	NOUN
ejpam-5756	279	27	,	,	PUNCT
ejpam-5756	279	28	a	a	DET
ejpam-5756	279	29	basic	basic	ADJ
ejpam-5756	279	30	nonlinear	nonlinear	ADJ
ejpam-5756	279	31	model	model	NOUN
ejpam-5756	279	32	with	with	ADP
ejpam-5756	279	33	broad	broad	ADJ
ejpam-5756	279	34	applications	application	NOUN
ejpam-5756	279	35	in	in	ADP
ejpam-5756	279	36	many	many	ADJ
ejpam-5756	279	37	scientific	scientific	ADJ
ejpam-5756	279	38	fields	field	NOUN
ejpam-5756	279	39	.	.	PUNCT
ejpam-5756	280	1	we	we	PRON
ejpam-5756	280	2	have	have	AUX
ejpam-5756	280	3	effectively	effectively	ADV
ejpam-5756	280	4	derived	derive	VERB
ejpam-5756	280	5	a	a	DET
ejpam-5756	280	6	wide	wide	ADJ
ejpam-5756	280	7	range	range	NOUN
ejpam-5756	280	8	of	of	ADP
ejpam-5756	280	9	solutions	solution	NOUN
ejpam-5756	280	10	by	by	ADP
ejpam-5756	280	11	utilizing	utilize	VERB
ejpam-5756	280	12	the	the	DET
ejpam-5756	280	13	power	power	NOUN
ejpam-5756	280	14	index	index	NOUN
ejpam-5756	280	15	method	method	NOUN
ejpam-5756	280	16	,	,	PUNCT
ejpam-5756	280	17	demonstrating	demonstrate	VERB
ejpam-5756	280	18	the	the	DET
ejpam-5756	280	19	method	method	NOUN
ejpam-5756	280	20	’s	’s	PART
ejpam-5756	280	21	potential	potential	NOUN
ejpam-5756	280	22	for	for	ADP
ejpam-5756	280	23	modeling	model	VERB
ejpam-5756	280	24	intricate	intricate	ADJ
ejpam-5756	280	25	wave	wave	NOUN
ejpam-5756	280	26	structures	structure	NOUN
ejpam-5756	280	27	.	.	PUNCT
ejpam-5756	281	1	various	various	ADJ
ejpam-5756	281	2	solutions	solution	NOUN
ejpam-5756	281	3	for	for	ADP
ejpam-5756	281	4	the	the	DET
ejpam-5756	281	5	current	current	ADJ
ejpam-5756	281	6	model	model	NOUN
ejpam-5756	281	7	are	be	AUX
ejpam-5756	281	8	derived	derive	VERB
ejpam-5756	281	9	in	in	ADP
ejpam-5756	281	10	the	the	DET
ejpam-5756	281	11	form	form	NOUN
ejpam-5756	281	12	of	of	ADP
ejpam-5756	281	13	rational	rational	ADJ
ejpam-5756	281	14	and	and	CCONJ
ejpam-5756	281	15	logarithm	logarithm	NOUN
ejpam-5756	281	16	functions	function	NOUN
ejpam-5756	281	17	.	.	PUNCT
ejpam-5756	282	1	every	every	DET
ejpam-5756	282	2	result	result	NOUN
ejpam-5756	282	3	found	find	VERB
ejpam-5756	282	4	in	in	ADP
ejpam-5756	282	5	this	this	DET
ejpam-5756	282	6	paper	paper	NOUN
ejpam-5756	282	7	is	be	AUX
ejpam-5756	282	8	fresh	fresh	ADJ
ejpam-5756	282	9	and	and	CCONJ
ejpam-5756	282	10	original	original	ADJ
ejpam-5756	282	11	.	.	PUNCT
ejpam-5756	283	1	the	the	DET
ejpam-5756	283	2	3d	3d	NOUN
ejpam-5756	283	3	under	under	ADP
ejpam-5756	283	4	some	some	DET
ejpam-5756	283	5	suitable	suitable	ADJ
ejpam-5756	283	6	values	value	NOUN
ejpam-5756	283	7	of	of	ADP
ejpam-5756	283	8	parameters	parameter	NOUN
ejpam-5756	283	9	are	be	AUX
ejpam-5756	283	10	also	also	ADV
ejpam-5756	283	11	plotted	plot	VERB
ejpam-5756	283	12	.	.	PUNCT
ejpam-5756	284	1	these	these	DET
ejpam-5756	284	2	solutions	solution	NOUN
ejpam-5756	284	3	provide	provide	VERB
ejpam-5756	284	4	important	important	ADJ
ejpam-5756	284	5	insights	insight	NOUN
ejpam-5756	284	6	into	into	ADP
ejpam-5756	284	7	the	the	DET
ejpam-5756	284	8	complex	complex	ADJ
ejpam-5756	284	9	dynamics	dynamic	NOUN
ejpam-5756	284	10	of	of	ADP
ejpam-5756	284	11	nonlinear	nonlinear	ADJ
ejpam-5756	284	12	phenomena	phenomenon	NOUN
ejpam-5756	284	13	and	and	CCONJ
ejpam-5756	284	14	have	have	VERB
ejpam-5756	284	15	important	important	ADJ
ejpam-5756	284	16	applications	application	NOUN
ejpam-5756	284	17	in	in	ADP
ejpam-5756	284	18	contemporary	contemporary	ADJ
ejpam-5756	284	19	science	science	NOUN
ejpam-5756	284	20	and	and	CCONJ
ejpam-5756	284	21	engineering	engineering	NOUN
ejpam-5756	284	22	.	.	PUNCT
ejpam-5756	285	1	it	it	PRON
ejpam-5756	285	2	provides	provide	VERB
ejpam-5756	285	3	a	a	DET
ejpam-5756	285	4	versatile	versatile	ADJ
ejpam-5756	285	5	and	and	CCONJ
ejpam-5756	285	6	flexible	flexible	ADJ
ejpam-5756	285	7	method	method	NOUN
ejpam-5756	285	8	for	for	ADP
ejpam-5756	285	9	solving	solve	VERB
ejpam-5756	285	10	challenging	challenging	ADJ
ejpam-5756	285	11	equations	equation	NOUN
ejpam-5756	285	12	.	.	PUNCT
ejpam-5756	286	1	it	it	PRON
ejpam-5756	286	2	can	can	AUX
ejpam-5756	286	3	be	be	AUX
ejpam-5756	286	4	used	use	VERB
ejpam-5756	286	5	with	with	ADP
ejpam-5756	286	6	a	a	DET
ejpam-5756	286	7	variety	variety	NOUN
ejpam-5756	286	8	of	of	ADP
ejpam-5756	286	9	physical	physical	ADJ
ejpam-5756	286	10	models	model	NOUN
ejpam-5756	286	11	and	and	CCONJ
ejpam-5756	286	12	systems	system	NOUN
ejpam-5756	286	13	.	.	PUNCT
ejpam-5756	287	1	further	further	ADJ
ejpam-5756	287	2	investigation	investigation	NOUN
ejpam-5756	287	3	into	into	ADP
ejpam-5756	287	4	the	the	DET
ejpam-5756	287	5	use	use	NOUN
ejpam-5756	287	6	of	of	ADP
ejpam-5756	287	7	fractional	fractional	ADJ
ejpam-5756	287	8	calculus	calculus	NOUN
ejpam-5756	287	9	in	in	ADP
ejpam-5756	287	10	nonlinear	nonlinear	ADJ
ejpam-5756	287	11	dynamics	dynamic	NOUN
ejpam-5756	287	12	is	be	AUX
ejpam-5756	287	13	made	make	VERB
ejpam-5756	287	14	possible	possible	ADJ
ejpam-5756	287	15	by	by	ADP
ejpam-5756	287	16	the	the	DET
ejpam-5756	287	17	efficacy	efficacy	NOUN
ejpam-5756	287	18	of	of	ADP
ejpam-5756	287	19	the	the	DET
ejpam-5756	287	20	power	power	NOUN
ejpam-5756	287	21	index	index	NOUN
ejpam-5756	287	22	method	method	NOUN
ejpam-5756	287	23	as	as	SCONJ
ejpam-5756	287	24	shown	show	VERB
ejpam-5756	287	25	in	in	ADP
ejpam-5756	287	26	this	this	DET
ejpam-5756	287	27	work	work	NOUN
ejpam-5756	287	28	.	.	PUNCT
ejpam-5756	288	1	determining	determine	VERB
ejpam-5756	288	2	precise	precise	ADJ
ejpam-5756	288	3	solutions	solution	NOUN
ejpam-5756	288	4	for	for	ADP
ejpam-5756	288	5	such	such	ADJ
ejpam-5756	288	6	intricate	intricate	ADJ
ejpam-5756	288	7	equations	equation	NOUN
ejpam-5756	288	8	creates	create	VERB
ejpam-5756	288	9	new	new	ADJ
ejpam-5756	288	10	opportunities	opportunity	NOUN
ejpam-5756	288	11	to	to	PART
ejpam-5756	288	12	investigate	investigate	VERB
ejpam-5756	288	13	the	the	DET
ejpam-5756	288	14	complex	complex	ADJ
ejpam-5756	288	15	behavior	behavior	NOUN
ejpam-5756	288	16	of	of	ADP
ejpam-5756	288	17	nonlinear	nonlinear	ADJ
ejpam-5756	288	18	systems	system	NOUN
ejpam-5756	288	19	,	,	PUNCT
ejpam-5756	288	20	which	which	PRON
ejpam-5756	288	21	is	be	AUX
ejpam-5756	288	22	crucial	crucial	ADJ
ejpam-5756	288	23	for	for	ADP
ejpam-5756	288	24	improving	improve	VERB
ejpam-5756	288	25	our	our	PRON
ejpam-5756	288	26	comprehension	comprehension	NOUN
ejpam-5756	288	27	of	of	ADP
ejpam-5756	288	28	a	a	DET
ejpam-5756	288	29	range	range	NOUN
ejpam-5756	288	30	of	of	ADP
ejpam-5756	288	31	physical	physical	ADJ
ejpam-5756	288	32	and	and	CCONJ
ejpam-5756	288	33	natural	natural	ADJ
ejpam-5756	288	34	phenomena	phenomenon	NOUN
ejpam-5756	288	35	.	.	PUNCT
ejpam-5756	289	1	furthermore	furthermore	ADV
ejpam-5756	289	2	,	,	PUNCT
ejpam-5756	289	3	the	the	DET
ejpam-5756	289	4	solutions	solution	NOUN
ejpam-5756	289	5	graphical	graphical	ADJ
ejpam-5756	289	6	representations	representation	NOUN
ejpam-5756	289	7	offer	offer	VERB
ejpam-5756	289	8	a	a	DET
ejpam-5756	289	9	visual	visual	ADJ
ejpam-5756	289	10	depiction	depiction	NOUN
ejpam-5756	289	11	of	of	ADP
ejpam-5756	289	12	the	the	DET
ejpam-5756	289	13	underlying	underlie	VERB
ejpam-5756	289	14	dynamics	dynamic	NOUN
ejpam-5756	289	15	,	,	PUNCT
ejpam-5756	289	16	promoting	promote	VERB
ejpam-5756	289	17	a	a	DET
ejpam-5756	289	18	better	well	ADJ
ejpam-5756	289	19	understanding	understanding	NOUN
ejpam-5756	289	20	of	of	ADP
ejpam-5756	289	21	the	the	DET
ejpam-5756	289	22	complex	complex	ADJ
ejpam-5756	289	23	interactions	interaction	NOUN
ejpam-5756	289	24	among	among	ADP
ejpam-5756	289	25	the	the	DET
ejpam-5756	289	26	different	different	ADJ
ejpam-5756	289	27	parameters	parameter	NOUN
ejpam-5756	289	28	.	.	PUNCT
ejpam-5756	290	1	the	the	DET
ejpam-5756	290	2	obtained	obtain	VERB
ejpam-5756	290	3	solutions	solution	NOUN
ejpam-5756	290	4	are	be	AUX
ejpam-5756	290	5	verified	verify	VERB
ejpam-5756	290	6	using	use	VERB
ejpam-5756	290	7	maple	maple	NOUN
ejpam-5756	290	8	software	software	NOUN
ejpam-5756	290	9	by	by	ADP
ejpam-5756	290	10	substituting	substitute	VERB
ejpam-5756	290	11	the	the	DET
ejpam-5756	290	12	solutions	solution	NOUN
ejpam-5756	290	13	back	back	ADV
ejpam-5756	290	14	into	into	ADP
ejpam-5756	290	15	the	the	DET
ejpam-5756	290	16	equation	equation	NOUN
ejpam-5756	290	17	.	.	PUNCT
ejpam-5756	291	1	7	7	X
ejpam-5756	291	2	.	.	X
ejpam-5756	291	3	future	future	ADJ
ejpam-5756	291	4	recommendations	recommendation	NOUN
ejpam-5756	291	5	future	future	ADJ
ejpam-5756	291	6	studies	study	NOUN
ejpam-5756	291	7	could	could	AUX
ejpam-5756	291	8	focus	focus	VERB
ejpam-5756	291	9	on	on	ADP
ejpam-5756	291	10	applying	apply	VERB
ejpam-5756	291	11	this	this	DET
ejpam-5756	291	12	methodology	methodology	NOUN
ejpam-5756	291	13	to	to	ADP
ejpam-5756	291	14	more	more	ADV
ejpam-5756	291	15	complex	complex	ADJ
ejpam-5756	291	16	issues	issue	NOUN
ejpam-5756	291	17	,	,	PUNCT
ejpam-5756	291	18	like	like	ADP
ejpam-5756	291	19	coupled	couple	VERB
ejpam-5756	291	20	nonlinear	nonlinear	ADJ
ejpam-5756	291	21	time	time	NOUN
ejpam-5756	291	22	-	-	PUNCT
ejpam-5756	291	23	fractional	fractional	ADJ
ejpam-5756	291	24	date	date	NOUN
ejpam-5756	291	25	-	-	PUNCT
ejpam-5756	291	26	jimbo	jimbo	NOUN
ejpam-5756	291	27	-	-	PUNCT
ejpam-5756	291	28	kashiwara	kashiwara	PROPN
ejpam-5756	291	29	-	-	PUNCT
ejpam-5756	291	30	miwa	miwa	PROPN
ejpam-5756	291	31	equations	equation	NOUN
ejpam-5756	291	32	and	and	CCONJ
ejpam-5756	291	33	systems	system	NOUN
ejpam-5756	291	34	of	of	ADP
ejpam-5756	291	35	nonlinear	nonlinear	ADJ
ejpam-5756	291	36	pdes	pde	NOUN
ejpam-5756	291	37	,	,	PUNCT
ejpam-5756	291	38	which	which	PRON
ejpam-5756	291	39	are	be	AUX
ejpam-5756	291	40	essential	essential	ADJ
ejpam-5756	291	41	for	for	ADP
ejpam-5756	291	42	simulating	simulate	VERB
ejpam-5756	291	43	intricate	intricate	ADJ
ejpam-5756	291	44	physics	physics	NOUN
ejpam-5756	291	45	and	and	CCONJ
ejpam-5756	291	46	engineering	engineering	NOUN
ejpam-5756	291	47	phenomena	phenomenon	NOUN
ejpam-5756	291	48	.	.	PUNCT
ejpam-5756	292	1	additionally	additionally	ADV
ejpam-5756	292	2	,	,	PUNCT
ejpam-5756	292	3	this	this	DET
ejpam-5756	292	4	study	study	NOUN
ejpam-5756	292	5	will	will	AUX
ejpam-5756	292	6	be	be	AUX
ejpam-5756	292	7	expanded	expand	VERB
ejpam-5756	292	8	upon	upon	SCONJ
ejpam-5756	292	9	to	to	PART
ejpam-5756	292	10	create	create	VERB
ejpam-5756	292	11	a	a	DET
ejpam-5756	292	12	new	new	ADJ
ejpam-5756	292	13	technique	technique	NOUN
ejpam-5756	292	14	for	for	ADP
ejpam-5756	292	15	exact	exact	ADJ
ejpam-5756	292	16	solutions	solution	NOUN
ejpam-5756	292	17	with	with	ADP
ejpam-5756	292	18	a	a	DET
ejpam-5756	292	19	variety	variety	NOUN
ejpam-5756	292	20	of	of	ADP
ejpam-5756	292	21	behaviors	behavior	NOUN
ejpam-5756	292	22	,	,	PUNCT
ejpam-5756	292	23	especially	especially	ADV
ejpam-5756	292	24	in	in	ADP
ejpam-5756	292	25	the	the	DET
ejpam-5756	292	26	fields	field	NOUN
ejpam-5756	292	27	of	of	ADP
ejpam-5756	292	28	neuroscience	neuroscience	NOUN
ejpam-5756	292	29	,	,	PUNCT
ejpam-5756	292	30	machine	machine	NOUN
ejpam-5756	292	31	b.	b.	PROPN
ejpam-5756	292	32	yasmeen	yasmeen	PROPN
ejpam-5756	292	33	,	,	PUNCT
ejpam-5756	292	34	k.	k.	PROPN
ejpam-5756	292	35	ahmad	ahmad	PROPN
ejpam-5756	292	36	,	,	PUNCT
ejpam-5756	292	37	n.	n.	PROPN
ejpam-5756	292	38	fatima	fatima	PROPN
ejpam-5756	292	39	/	/	PUNCT
ejpam-5756	292	40	eur	eur	PROPN
ejpam-5756	292	41	.	.	PUNCT
ejpam-5756	293	1	j.	j.	PROPN
ejpam-5756	293	2	pure	pure	PROPN
ejpam-5756	293	3	appl	appl	PROPN
ejpam-5756	293	4	.	.	PROPN
ejpam-5756	293	5	math	math	PROPN
ejpam-5756	293	6	,	,	PUNCT
ejpam-5756	293	7	18	18	NUM
ejpam-5756	293	8	(	(	PUNCT
ejpam-5756	293	9	1	1	NUM
ejpam-5756	293	10	)	)	PUNCT
ejpam-5756	293	11	(	(	PUNCT
ejpam-5756	293	12	2025	2025	NUM
ejpam-5756	293	13	)	)	PUNCT
ejpam-5756	293	14	,	,	PUNCT
ejpam-5756	293	15	5756	5756	NUM
ejpam-5756	293	16	15	15	NUM
ejpam-5756	293	17	of	of	ADP
ejpam-5756	293	18	17	17	NUM
ejpam-5756	293	19	learning	learn	VERB
ejpam-5756	293	20	for	for	ADP
ejpam-5756	293	21	flow	flow	NOUN
ejpam-5756	293	22	,	,	PUNCT
ejpam-5756	293	23	and	and	CCONJ
ejpam-5756	293	24	power	power	NOUN
ejpam-5756	293	25	electronics	electronic	NOUN
ejpam-5756	293	26	,	,	PUNCT
ejpam-5756	293	27	where	where	SCONJ
ejpam-5756	293	28	nonlinear	nonlinear	ADJ
ejpam-5756	293	29	oscillators	oscillator	NOUN
ejpam-5756	293	30	are	be	AUX
ejpam-5756	293	31	crucial	crucial	ADJ
ejpam-5756	293	32	.	.	PUNCT
ejpam-5756	294	1	the	the	DET
ejpam-5756	294	2	world	world	NOUN
ejpam-5756	294	3	will	will	AUX
ejpam-5756	294	4	transform	transform	VERB
ejpam-5756	294	5	in	in	ADP
ejpam-5756	294	6	a	a	DET
ejpam-5756	294	7	new	new	ADJ
ejpam-5756	294	8	way	way	NOUN
ejpam-5756	294	9	as	as	ADP
ejpam-5756	294	10	a	a	DET
ejpam-5756	294	11	result	result	NOUN
ejpam-5756	294	12	of	of	ADP
ejpam-5756	294	13	our	our	PRON
ejpam-5756	294	14	research	research	NOUN
ejpam-5756	294	15	.	.	PUNCT
ejpam-5756	295	1	acknowledgements	acknowledgement	VERB
ejpam-5756	295	2	the	the	DET
ejpam-5756	295	3	author	author	NOUN
ejpam-5756	295	4	dr	dr	PROPN
ejpam-5756	295	5	.	.	PROPN
ejpam-5756	295	6	nahid	nahid	PROPN
ejpam-5756	295	7	fatima	fatima	PROPN
ejpam-5756	295	8	would	would	AUX
ejpam-5756	295	9	like	like	VERB
ejpam-5756	295	10	to	to	PART
ejpam-5756	295	11	acknowledge	acknowledge	VERB
ejpam-5756	295	12	the	the	DET
ejpam-5756	295	13	support	support	NOUN
ejpam-5756	295	14	of	of	ADP
ejpam-5756	295	15	prince	prince	PROPN
ejpam-5756	295	16	sultan	sultan	PROPN
ejpam-5756	295	17	university	university	PROPN
ejpam-5756	295	18	,	,	PUNCT
ejpam-5756	295	19	riyadh	riyadh	PROPN
ejpam-5756	295	20	,	,	PUNCT
ejpam-5756	295	21	saudi	saudi	PROPN
ejpam-5756	295	22	arabia	arabia	PROPN
ejpam-5756	295	23	for	for	ADP
ejpam-5756	295	24	paying	pay	VERB
ejpam-5756	295	25	the	the	DET
ejpam-5756	295	26	article	article	NOUN
ejpam-5756	295	27	processing	processing	NOUN
ejpam-5756	295	28	charges	charge	NOUN
ejpam-5756	295	29	(	(	PUNCT
ejpam-5756	295	30	apc	apc	PROPN
ejpam-5756	295	31	)	)	PUNCT
ejpam-5756	295	32	for	for	ADP
ejpam-5756	295	33	this	this	DET
ejpam-5756	295	34	outstanding	outstanding	ADJ
ejpam-5756	295	35	publication	publication	NOUN
ejpam-5756	295	36	.	.	PUNCT
ejpam-5756	296	1	the	the	DET
ejpam-5756	296	2	authors	author	NOUN
ejpam-5756	296	3	bushra	bushra	PROPN
ejpam-5756	296	4	yasmeen	yasmeen	PROPN
ejpam-5756	296	5	and	and	CCONJ
ejpam-5756	296	6	dr	dr	PROPN
ejpam-5756	296	7	.	.	PROPN
ejpam-5756	296	8	khalil	khalil	PROPN
ejpam-5756	296	9	ahmad	ahmad	PROPN
ejpam-5756	296	10	would	would	AUX
ejpam-5756	296	11	like	like	VERB
ejpam-5756	296	12	to	to	PART
ejpam-5756	296	13	thankful	thankful	VERB
ejpam-5756	296	14	the	the	DET
ejpam-5756	296	15	air	air	NOUN
ejpam-5756	296	16	marshal	marshal	NOUN
ejpam-5756	296	17	abdul	abdul	PROPN
ejpam-5756	296	18	moeed	moeed	PROPN
ejpam-5756	296	19	khan	khan	PROPN
ejpam-5756	296	20	,	,	PUNCT
ejpam-5756	296	21	hi(m	hi(m	NOUN
ejpam-5756	296	22	)	)	PUNCT
ejpam-5756	296	23	,	,	PUNCT
ejpam-5756	296	24	vice	vice	NOUN
ejpam-5756	296	25	chancellor	chancellor	NOUN
ejpam-5756	296	26	,	,	PUNCT
ejpam-5756	296	27	air	air	NOUN
ejpam-5756	296	28	university	university	PROPN
ejpam-5756	296	29	,	,	PUNCT
ejpam-5756	296	30	islamabad	islamabad	PROPN
ejpam-5756	296	31	,	,	PUNCT
ejpam-5756	296	32	pakistan	pakistan	PROPN
ejpam-5756	296	33	.	.	PUNCT
ejpam-5756	297	1	competing	compete	VERB
ejpam-5756	297	2	interests	interest	NOUN
ejpam-5756	297	3	the	the	DET
ejpam-5756	297	4	authors	author	NOUN
ejpam-5756	297	5	declare	declare	VERB
ejpam-5756	297	6	that	that	SCONJ
ejpam-5756	297	7	they	they	PRON
ejpam-5756	297	8	have	have	VERB
ejpam-5756	297	9	no	no	DET
ejpam-5756	297	10	competing	compete	VERB
ejpam-5756	297	11	interests	interest	NOUN
ejpam-5756	297	12	.	.	PUNCT
ejpam-5756	298	1	data	datum	NOUN
ejpam-5756	298	2	availability	availability	NOUN
ejpam-5756	298	3	statement	statement	NOUN
ejpam-5756	298	4	please	please	INTJ
ejpam-5756	298	5	contact	contact	VERB
ejpam-5756	298	6	the	the	DET
ejpam-5756	298	7	authors	author	NOUN
ejpam-5756	298	8	for	for	ADP
ejpam-5756	298	9	data	datum	NOUN
ejpam-5756	298	10	requests	request	NOUN
ejpam-5756	298	11	.	.	PUNCT
ejpam-5756	299	1	references	reference	NOUN
ejpam-5756	299	2	[	[	X
ejpam-5756	299	3	1	1	NUM
ejpam-5756	299	4	]	]	PUNCT
ejpam-5756	299	5	a.	a.	PROPN
ejpam-5756	299	6	r.	r.	PROPN
ejpam-5756	299	7	adem	adem	PROPN
ejpam-5756	299	8	,	,	PUNCT
ejpam-5756	299	9	y.	y.	PROPN
ejpam-5756	299	10	yildirim	yildirim	PROPN
ejpam-5756	299	11	,	,	PUNCT
ejpam-5756	299	12	and	and	CCONJ
ejpam-5756	299	13	e.	e.	PROPN
ejpam-5756	299	14	yaşar	yaşar	PROPN
ejpam-5756	299	15	.	.	PUNCT
ejpam-5756	300	1	complexiton	complexiton	NOUN
ejpam-5756	300	2	solutions	solution	NOUN
ejpam-5756	300	3	and	and	CCONJ
ejpam-5756	300	4	soliton	soliton	NOUN
ejpam-5756	300	5	solutions:(2	solutions:(2	PROPN
ejpam-5756	300	6	+	+	CCONJ
ejpam-5756	300	7	1)(2	1)(2	NUM
ejpam-5756	300	8	+	+	NUM
ejpam-5756	300	9	1)-dimensional	1)-dimensional	NUM
ejpam-5756	300	10	date	date	NOUN
ejpam-5756	300	11	-	-	PUNCT
ejpam-5756	300	12	jimbo	jimbo	NOUN
ejpam-5756	300	13	-	-	PUNCT
ejpam-5756	300	14	kashiwara	kashiwara	PROPN
ejpam-5756	300	15	-	-	PUNCT
ejpam-5756	300	16	miwa	miwa	PROPN
ejpam-5756	300	17	equation	equation	NOUN
ejpam-5756	300	18	.	.	PUNCT
ejpam-5756	301	1	pramana	pramana	PROPN
ejpam-5756	301	2	,	,	PUNCT
ejpam-5756	301	3	92:1–12	92:1–12	NUM
ejpam-5756	301	4	,	,	PUNCT
ejpam-5756	301	5	2019	2019	NUM
ejpam-5756	301	6	.	.	PUNCT
ejpam-5756	302	1	[	[	X
ejpam-5756	302	2	2	2	NUM
ejpam-5756	302	3	]	]	X
ejpam-5756	302	4	l.	l.	PROPN
ejpam-5756	302	5	akinyemi	akinyemi	PROPN
ejpam-5756	302	6	,	,	PUNCT
ejpam-5756	302	7	a.	a.	NOUN
ejpam-5756	302	8	houwe	houwe	NOUN
ejpam-5756	302	9	,	,	PUNCT
ejpam-5756	302	10	s.	s.	PROPN
ejpam-5756	302	11	abbagari	abbagari	PROPN
ejpam-5756	302	12	,	,	PUNCT
ejpam-5756	302	13	a.	a.	NOUN
ejpam-5756	302	14	m.	m.	NOUN
ejpam-5756	302	15	wazwaz	wazwaz	PROPN
ejpam-5756	302	16	,	,	PUNCT
ejpam-5756	302	17	h.	h.	PROPN
ejpam-5756	302	18	m.	m.	PROPN
ejpam-5756	302	19	alshehri	alshehri	PROPN
ejpam-5756	302	20	,	,	PUNCT
ejpam-5756	302	21	and	and	CCONJ
ejpam-5756	302	22	m.	m.	PROPN
ejpam-5756	302	23	s.	s.	PROPN
ejpam-5756	302	24	osman	osman	PROPN
ejpam-5756	302	25	.	.	PUNCT
ejpam-5756	303	1	effects	effect	NOUN
ejpam-5756	303	2	of	of	ADP
ejpam-5756	303	3	the	the	DET
ejpam-5756	303	4	higher	high	ADJ
ejpam-5756	303	5	-	-	PUNCT
ejpam-5756	303	6	order	order	NOUN
ejpam-5756	303	7	dispersion	dispersion	NOUN
ejpam-5756	303	8	on	on	ADP
ejpam-5756	303	9	solitary	solitary	ADJ
ejpam-5756	303	10	waves	wave	NOUN
ejpam-5756	303	11	and	and	CCONJ
ejpam-5756	303	12	modulation	modulation	NOUN
ejpam-5756	303	13	instability	instability	NOUN
ejpam-5756	303	14	in	in	ADP
ejpam-5756	303	15	a	a	DET
ejpam-5756	303	16	monomode	monomode	ADJ
ejpam-5756	303	17	fiber	fiber	NOUN
ejpam-5756	303	18	.	.	PUNCT
ejpam-5756	304	1	optik	optik	PROPN
ejpam-5756	304	2	,	,	PUNCT
ejpam-5756	304	3	288:171202	288:171202	NOUN
ejpam-5756	304	4	,	,	PUNCT
ejpam-5756	304	5	2023	2023	NUM
ejpam-5756	304	6	.	.	PUNCT
ejpam-5756	305	1	[	[	X
ejpam-5756	305	2	3	3	X
ejpam-5756	305	3	]	]	PUNCT
ejpam-5756	305	4	k.	k.	PROPN
ejpam-5756	305	5	bibi	bibi	PROPN
ejpam-5756	305	6	and	and	CCONJ
ejpam-5756	305	7	k.	k.	PROPN
ejpam-5756	305	8	ahmad	ahmad	PROPN
ejpam-5756	305	9	.	.	PUNCT
ejpam-5756	306	1	exact	exact	ADJ
ejpam-5756	306	2	solutions	solution	NOUN
ejpam-5756	306	3	of	of	ADP
ejpam-5756	306	4	newell	newell	PROPN
ejpam-5756	306	5	-	-	PUNCT
ejpam-5756	306	6	whitehead	whitehead	PROPN
ejpam-5756	306	7	-	-	PUNCT
ejpam-5756	306	8	segel	segel	NOUN
ejpam-5756	306	9	equations	equation	NOUN
ejpam-5756	306	10	using	use	VERB
ejpam-5756	306	11	symmetry	symmetry	NOUN
ejpam-5756	306	12	transformations	transformation	NOUN
ejpam-5756	306	13	.	.	PUNCT
ejpam-5756	307	1	journal	journal	NOUN
ejpam-5756	307	2	of	of	ADP
ejpam-5756	307	3	function	function	NOUN
ejpam-5756	307	4	spaces	space	NOUN
ejpam-5756	307	5	,	,	PUNCT
ejpam-5756	307	6	2021(1):6658081	2021(1):6658081	NUM
ejpam-5756	307	7	,	,	PUNCT
ejpam-5756	307	8	2021	2021	NUM
ejpam-5756	307	9	.	.	PUNCT
ejpam-5756	308	1	[	[	X
ejpam-5756	308	2	4	4	NUM
ejpam-5756	308	3	]	]	PUNCT
ejpam-5756	308	4	m.	m.	NOUN
ejpam-5756	308	5	bilal	bilal	PROPN
ejpam-5756	308	6	,	,	PUNCT
ejpam-5756	308	7	j.	j.	PROPN
ejpam-5756	308	8	iqbal	iqbal	PROPN
ejpam-5756	308	9	,	,	PUNCT
ejpam-5756	308	10	k.	k.	PROPN
ejpam-5756	308	11	shah	shah	PROPN
ejpam-5756	308	12	,	,	PUNCT
ejpam-5756	308	13	b.	b.	PROPN
ejpam-5756	308	14	abdalla	abdalla	PROPN
ejpam-5756	308	15	,	,	PUNCT
ejpam-5756	308	16	t.	t.	NOUN
ejpam-5756	308	17	abdeljawad	abdeljawad	NOUN
ejpam-5756	308	18	,	,	PUNCT
ejpam-5756	308	19	and	and	CCONJ
ejpam-5756	308	20	i.	i.	PROPN
ejpam-5756	308	21	ullah	ullah	PROPN
ejpam-5756	308	22	.	.	PUNCT
ejpam-5756	309	1	analytical	analytical	ADJ
ejpam-5756	309	2	solutions	solution	NOUN
ejpam-5756	309	3	of	of	ADP
ejpam-5756	309	4	the	the	DET
ejpam-5756	309	5	space	space	NOUN
ejpam-5756	309	6	-	-	PUNCT
ejpam-5756	309	7	time	time	NOUN
ejpam-5756	309	8	fractional	fractional	ADJ
ejpam-5756	309	9	kundu	kundu	NOUN
ejpam-5756	309	10	-	-	PUNCT
ejpam-5756	309	11	eckhaus	eckhaus	NOUN
ejpam-5756	309	12	equation	equation	NOUN
ejpam-5756	309	13	by	by	ADP
ejpam-5756	309	14	using	use	VERB
ejpam-5756	309	15	modified	modify	VERB
ejpam-5756	309	16	extended	extend	VERB
ejpam-5756	309	17	direct	direct	ADJ
ejpam-5756	309	18	algebraic	algebraic	ADJ
ejpam-5756	309	19	method	method	NOUN
ejpam-5756	309	20	.	.	PUNCT
ejpam-5756	310	1	partial	partial	ADJ
ejpam-5756	310	2	differential	differential	ADJ
ejpam-5756	310	3	equations	equation	NOUN
ejpam-5756	310	4	in	in	ADP
ejpam-5756	310	5	applied	applied	ADJ
ejpam-5756	310	6	mathematics	mathematic	NOUN
ejpam-5756	310	7	,	,	PUNCT
ejpam-5756	310	8	11:100832	11:100832	NUM
ejpam-5756	310	9	,	,	PUNCT
ejpam-5756	310	10	2024	2024	NUM
ejpam-5756	310	11	.	.	PUNCT
ejpam-5756	311	1	[	[	X
ejpam-5756	311	2	5	5	X
ejpam-5756	311	3	]	]	PUNCT
ejpam-5756	311	4	e.	e.	PROPN
ejpam-5756	311	5	date	date	PROPN
ejpam-5756	311	6	,	,	PUNCT
ejpam-5756	311	7	m.	m.	NOUN
ejpam-5756	311	8	jimbo	jimbo	PROPN
ejpam-5756	311	9	,	,	PUNCT
ejpam-5756	311	10	m.	m.	NOUN
ejpam-5756	311	11	kashiwara	kashiwara	PROPN
ejpam-5756	311	12	,	,	PUNCT
ejpam-5756	311	13	and	and	CCONJ
ejpam-5756	311	14	t.	t.	PROPN
ejpam-5756	311	15	miwa	miwa	PROPN
ejpam-5756	311	16	.	.	PUNCT
ejpam-5756	312	1	transformation	transformation	NOUN
ejpam-5756	312	2	groups	group	NOUN
ejpam-5756	312	3	for	for	ADP
ejpam-5756	312	4	soliton	soliton	NOUN
ejpam-5756	312	5	equations	equation	NOUN
ejpam-5756	312	6	:	:	PUNCT
ejpam-5756	312	7	iv	iv	X
ejpam-5756	312	8	.	.	PUNCT
ejpam-5756	313	1	a	a	DET
ejpam-5756	313	2	new	new	ADJ
ejpam-5756	313	3	hierarchy	hierarchy	NOUN
ejpam-5756	313	4	of	of	ADP
ejpam-5756	313	5	soliton	soliton	NOUN
ejpam-5756	313	6	equations	equation	NOUN
ejpam-5756	313	7	of	of	ADP
ejpam-5756	313	8	kp	kp	PROPN
ejpam-5756	313	9	-	-	NOUN
ejpam-5756	313	10	type	type	NOUN
ejpam-5756	313	11	.	.	PUNCT
ejpam-5756	314	1	physica	physica	NOUN
ejpam-5756	314	2	d	d	NOUN
ejpam-5756	314	3	:	:	PUNCT
ejpam-5756	314	4	nonlinear	nonlinear	ADJ
ejpam-5756	314	5	phenomena	phenomenon	NOUN
ejpam-5756	314	6	,	,	PUNCT
ejpam-5756	314	7	4(3):343–365	4(3):343–365	PROPN
ejpam-5756	314	8	,	,	PUNCT
ejpam-5756	314	9	1982	1982	NUM
ejpam-5756	314	10	.	.	PUNCT
ejpam-5756	315	1	[	[	X
ejpam-5756	315	2	6	6	NUM
ejpam-5756	315	3	]	]	PUNCT
ejpam-5756	315	4	b.	b.	PROPN
ejpam-5756	315	5	dorizzi	dorizzi	PROPN
ejpam-5756	315	6	,	,	PUNCT
ejpam-5756	315	7	b.	b.	PROPN
ejpam-5756	315	8	grammaticos	grammaticos	PROPN
ejpam-5756	315	9	,	,	PUNCT
ejpam-5756	315	10	a.	a.	NOUN
ejpam-5756	315	11	ramani	ramani	PROPN
ejpam-5756	315	12	,	,	PUNCT
ejpam-5756	315	13	and	and	CCONJ
ejpam-5756	315	14	p.	p.	PROPN
ejpam-5756	315	15	winternitz	winternitz	PROPN
ejpam-5756	315	16	.	.	PUNCT
ejpam-5756	315	17	are	be	AUX
ejpam-5756	315	18	all	all	DET
ejpam-5756	315	19	the	the	DET
ejpam-5756	315	20	equations	equation	NOUN
ejpam-5756	315	21	of	of	ADP
ejpam-5756	315	22	the	the	DET
ejpam-5756	315	23	kadomtsev	kadomtsev	PROPN
ejpam-5756	315	24	–	–	PUNCT
ejpam-5756	315	25	petviashvili	petviashvili	ADJ
ejpam-5756	315	26	hierarchy	hierarchy	NOUN
ejpam-5756	315	27	integrable	integrable	ADJ
ejpam-5756	315	28	?	?	PUNCT
ejpam-5756	316	1	journal	journal	PROPN
ejpam-5756	316	2	of	of	ADP
ejpam-5756	316	3	mathematical	mathematical	ADJ
ejpam-5756	316	4	physics	physics	NOUN
ejpam-5756	316	5	,	,	PUNCT
ejpam-5756	316	6	27(12):2848–2852	27(12):2848–2852	PROPN
ejpam-5756	316	7	,	,	PUNCT
ejpam-5756	316	8	1986	1986	NUM
ejpam-5756	316	9	.	.	PUNCT
ejpam-5756	317	1	[	[	X
ejpam-5756	317	2	7	7	X
ejpam-5756	317	3	]	]	X
ejpam-5756	317	4	f.	f.	PROPN
ejpam-5756	317	5	guo	guo	PROPN
ejpam-5756	317	6	and	and	CCONJ
ejpam-5756	317	7	j.	j.	PROPN
ejpam-5756	317	8	lin	lin	PROPN
ejpam-5756	317	9	.	.	PUNCT
ejpam-5756	318	1	interaction	interaction	NOUN
ejpam-5756	318	2	solutions	solution	NOUN
ejpam-5756	318	3	between	between	ADP
ejpam-5756	318	4	lump	lump	NOUN
ejpam-5756	318	5	and	and	CCONJ
ejpam-5756	318	6	stripe	stripe	NOUN
ejpam-5756	318	7	soliton	soliton	NOUN
ejpam-5756	318	8	to	to	ADP
ejpam-5756	318	9	the	the	DET
ejpam-5756	318	10	(	(	PUNCT
ejpam-5756	318	11	2	2	NUM
ejpam-5756	318	12	+	+	SYM
ejpam-5756	318	13	1)dimensional	1)dimensional	NUM
ejpam-5756	318	14	date	date	NOUN
ejpam-5756	318	15	–	–	PUNCT
ejpam-5756	318	16	jimbo	jimbo	PROPN
ejpam-5756	318	17	–	–	PUNCT
ejpam-5756	318	18	kashiwara	kashiwara	PROPN
ejpam-5756	318	19	–	–	PUNCT
ejpam-5756	318	20	miwa	miwa	PROPN
ejpam-5756	318	21	equation	equation	NOUN
ejpam-5756	318	22	.	.	PUNCT
ejpam-5756	319	1	nonlinear	nonlinear	ADJ
ejpam-5756	319	2	dynamics	dynamic	NOUN
ejpam-5756	319	3	,	,	PUNCT
ejpam-5756	319	4	96(2):1233	96(2):1233	NUM
ejpam-5756	319	5	–	–	PUNCT
ejpam-5756	319	6	1241	1241	NUM
ejpam-5756	319	7	,	,	PUNCT
ejpam-5756	319	8	2019	2019	NUM
ejpam-5756	319	9	.	.	PUNCT
ejpam-5756	320	1	[	[	X
ejpam-5756	320	2	8	8	NUM
ejpam-5756	320	3	]	]	PUNCT
ejpam-5756	320	4	k.	k.	PROPN
ejpam-5756	320	5	hosseini	hosseini	PROPN
ejpam-5756	320	6	,	,	PUNCT
ejpam-5756	320	7	e.	e.	PROPN
ejpam-5756	320	8	hinçal	hinçal	PROPN
ejpam-5756	320	9	,	,	PUNCT
ejpam-5756	320	10	f.	f.	PROPN
ejpam-5756	320	11	alizadeh	alizadeh	PROPN
ejpam-5756	320	12	,	,	PUNCT
ejpam-5756	320	13	d.	d.	PROPN
ejpam-5756	320	14	baleanu	baleanu	PROPN
ejpam-5756	320	15	,	,	PUNCT
ejpam-5756	320	16	and	and	CCONJ
ejpam-5756	320	17	m.	m.	PROPN
ejpam-5756	320	18	s.	s.	PROPN
ejpam-5756	320	19	osman	osman	PROPN
ejpam-5756	320	20	.	.	PUNCT
ejpam-5756	321	1	bifurcation	bifurcation	NOUN
ejpam-5756	321	2	analysis	analysis	NOUN
ejpam-5756	321	3	,	,	PUNCT
ejpam-5756	321	4	sensitivity	sensitivity	NOUN
ejpam-5756	321	5	analysis	analysis	NOUN
ejpam-5756	321	6	,	,	PUNCT
ejpam-5756	321	7	and	and	CCONJ
ejpam-5756	321	8	jacobi	jacobi	PROPN
ejpam-5756	321	9	elliptic	elliptic	ADJ
ejpam-5756	321	10	function	function	NOUN
ejpam-5756	321	11	structures	structure	NOUN
ejpam-5756	321	12	to	to	ADP
ejpam-5756	321	13	a	a	DET
ejpam-5756	321	14	generalized	generalized	ADJ
ejpam-5756	321	15	nonlinear	nonlinear	NOUN
ejpam-5756	321	16	schrödinger	schrödinger	NOUN
ejpam-5756	321	17	equation	equation	NOUN
ejpam-5756	321	18	.	.	PUNCT
ejpam-5756	322	1	international	international	ADJ
ejpam-5756	322	2	journal	journal	PROPN
ejpam-5756	322	3	of	of	ADP
ejpam-5756	322	4	theoretical	theoretical	ADJ
ejpam-5756	322	5	physics	physics	NOUN
ejpam-5756	322	6	,	,	PUNCT
ejpam-5756	322	7	63(12):1–12	63(12):1–12	NUM
ejpam-5756	322	8	,	,	PUNCT
ejpam-5756	322	9	2024	2024	NUM
ejpam-5756	322	10	.	.	PUNCT
ejpam-5756	323	1	[	[	X
ejpam-5756	323	2	9	9	NUM
ejpam-5756	323	3	]	]	PUNCT
ejpam-5756	323	4	m.	m.	NOUN
ejpam-5756	323	5	a.	a.	PROPN
ejpam-5756	323	6	iqbal	iqbal	PROPN
ejpam-5756	323	7	,	,	PUNCT
ejpam-5756	323	8	k.	k.	PROPN
ejpam-5756	323	9	a.	a.	PROPN
ejpam-5756	323	10	gepreel	gepreel	PROPN
ejpam-5756	323	11	,	,	PUNCT
ejpam-5756	323	12	m.	m.	NOUN
ejpam-5756	323	13	ali	ali	PROPN
ejpam-5756	323	14	akbar	akbar	PROPN
ejpam-5756	323	15	,	,	PUNCT
ejpam-5756	323	16	and	and	CCONJ
ejpam-5756	323	17	m.	m.	PROPN
ejpam-5756	323	18	s.	s.	PROPN
ejpam-5756	323	19	osman	osman	PROPN
ejpam-5756	323	20	.	.	PUNCT
ejpam-5756	324	1	the	the	DET
ejpam-5756	324	2	compatibility	compatibility	NOUN
ejpam-5756	324	3	and	and	CCONJ
ejpam-5756	324	4	dynamics	dynamic	NOUN
ejpam-5756	324	5	of	of	ADP
ejpam-5756	324	6	optical	optical	ADJ
ejpam-5756	324	7	soliton	soliton	NOUN
ejpam-5756	324	8	solutions	solution	NOUN
ejpam-5756	324	9	for	for	ADP
ejpam-5756	324	10	higher	high	ADJ
ejpam-5756	324	11	-	-	PUNCT
ejpam-5756	324	12	order	order	NOUN
ejpam-5756	324	13	nonlinear	nonlinear	ADJ
ejpam-5756	324	14	schrödinger	schrödinger	NOUN
ejpam-5756	324	15	model	model	NOUN
ejpam-5756	324	16	.	.	PUNCT
ejpam-5756	325	1	modern	modern	ADJ
ejpam-5756	325	2	physics	physics	PROPN
ejpam-5756	325	3	letters	letters	PROPN
ejpam-5756	325	4	b	b	NOUN
ejpam-5756	325	5	,	,	PUNCT
ejpam-5756	325	6	page	page	NOUN
ejpam-5756	325	7	2550086	2550086	NUM
ejpam-5756	325	8	,	,	PUNCT
ejpam-5756	325	9	2024	2024	NUM
ejpam-5756	325	10	.	.	PUNCT
ejpam-5756	326	1	b.	b.	PROPN
ejpam-5756	326	2	yasmeen	yasmeen	PROPN
ejpam-5756	326	3	,	,	PUNCT
ejpam-5756	326	4	k.	k.	PROPN
ejpam-5756	326	5	ahmad	ahmad	PROPN
ejpam-5756	326	6	,	,	PUNCT
ejpam-5756	326	7	n.	n.	PROPN
ejpam-5756	326	8	fatima	fatima	PROPN
ejpam-5756	326	9	/	/	PUNCT
ejpam-5756	326	10	eur	eur	PROPN
ejpam-5756	326	11	.	.	PUNCT
ejpam-5756	327	1	j.	j.	PROPN
ejpam-5756	327	2	pure	pure	PROPN
ejpam-5756	327	3	appl	appl	PROPN
ejpam-5756	327	4	.	.	PROPN
ejpam-5756	327	5	math	math	PROPN
ejpam-5756	327	6	,	,	PUNCT
ejpam-5756	327	7	18	18	NUM
ejpam-5756	327	8	(	(	PUNCT
ejpam-5756	327	9	1	1	NUM
ejpam-5756	327	10	)	)	PUNCT
ejpam-5756	327	11	(	(	PUNCT
ejpam-5756	327	12	2025	2025	NUM
ejpam-5756	327	13	)	)	PUNCT
ejpam-5756	327	14	,	,	PUNCT
ejpam-5756	327	15	5756	5756	NUM
ejpam-5756	327	16	16	16	NUM
ejpam-5756	327	17	of	of	ADP
ejpam-5756	327	18	17	17	NUM
ejpam-5756	327	19	[	[	SYM
ejpam-5756	327	20	10	10	NUM
ejpam-5756	327	21	]	]	PUNCT
ejpam-5756	327	22	m.	m.	NOUN
ejpam-5756	327	23	a.	a.	PROPN
ejpam-5756	327	24	iqbal	iqbal	PROPN
ejpam-5756	327	25	,	,	PUNCT
ejpam-5756	327	26	y.	y.	PROPN
ejpam-5756	327	27	wang	wang	PROPN
ejpam-5756	327	28	,	,	PUNCT
ejpam-5756	327	29	m.	m.	NOUN
ejpam-5756	327	30	m.	m.	PROPN
ejpam-5756	327	31	miah	miah	PROPN
ejpam-5756	327	32	,	,	PUNCT
ejpam-5756	327	33	and	and	CCONJ
ejpam-5756	327	34	m.	m.	PROPN
ejpam-5756	327	35	s.	s.	PROPN
ejpam-5756	327	36	osman	osman	PROPN
ejpam-5756	327	37	.	.	PUNCT
ejpam-5756	328	1	study	study	NOUN
ejpam-5756	328	2	on	on	ADP
ejpam-5756	328	3	date	date	NOUN
ejpam-5756	328	4	–	–	PUNCT
ejpam-5756	328	5	jimbo	jimbo	PROPN
ejpam-5756	328	6	–	–	PUNCT
ejpam-5756	328	7	kashiwara	kashiwara	PROPN
ejpam-5756	328	8	–	–	PUNCT
ejpam-5756	328	9	miwa	miwa	PROPN
ejpam-5756	328	10	equation	equation	NOUN
ejpam-5756	328	11	with	with	ADP
ejpam-5756	328	12	conformable	conformable	ADJ
ejpam-5756	328	13	derivative	derivative	ADJ
ejpam-5756	328	14	dependent	dependent	NOUN
ejpam-5756	328	15	on	on	ADP
ejpam-5756	328	16	time	time	NOUN
ejpam-5756	328	17	parameter	parameter	NOUN
ejpam-5756	328	18	to	to	PART
ejpam-5756	328	19	find	find	VERB
ejpam-5756	328	20	the	the	DET
ejpam-5756	328	21	exact	exact	ADJ
ejpam-5756	328	22	dynamic	dynamic	ADJ
ejpam-5756	328	23	wave	wave	NOUN
ejpam-5756	328	24	solutions	solution	NOUN
ejpam-5756	328	25	.	.	PUNCT
ejpam-5756	329	1	fractal	fractal	ADJ
ejpam-5756	329	2	and	and	CCONJ
ejpam-5756	329	3	fractional	fractional	ADJ
ejpam-5756	329	4	,	,	PUNCT
ejpam-5756	329	5	6(1):4	6(1):4	NOUN
ejpam-5756	329	6	,	,	PUNCT
ejpam-5756	329	7	2021	2021	NUM
ejpam-5756	329	8	.	.	PUNCT
ejpam-5756	330	1	[	[	X
ejpam-5756	330	2	11	11	NUM
ejpam-5756	330	3	]	]	PUNCT
ejpam-5756	330	4	h.	h.	PROPN
ejpam-5756	330	5	f.	f.	PROPN
ejpam-5756	330	6	ismael	ismael	PROPN
ejpam-5756	330	7	,	,	PUNCT
ejpam-5756	330	8	h.	h.	PROPN
ejpam-5756	330	9	bulut	bulut	PROPN
ejpam-5756	330	10	,	,	PUNCT
ejpam-5756	330	11	c.	c.	PROPN
ejpam-5756	330	12	park	park	PROPN
ejpam-5756	330	13	,	,	PUNCT
ejpam-5756	330	14	and	and	CCONJ
ejpam-5756	330	15	m.	m.	PROPN
ejpam-5756	330	16	s.	s.	PROPN
ejpam-5756	330	17	osman	osman	PROPN
ejpam-5756	330	18	.	.	PUNCT
ejpam-5756	331	1	m	m	PROPN
ejpam-5756	331	2	-	-	NOUN
ejpam-5756	331	3	lump	lump	NOUN
ejpam-5756	331	4	,	,	PUNCT
ejpam-5756	331	5	n	n	CCONJ
ejpam-5756	331	6	-	-	PUNCT
ejpam-5756	331	7	soliton	soliton	NOUN
ejpam-5756	331	8	solutions	solution	NOUN
ejpam-5756	331	9	,	,	PUNCT
ejpam-5756	331	10	and	and	CCONJ
ejpam-5756	331	11	the	the	DET
ejpam-5756	331	12	collision	collision	NOUN
ejpam-5756	331	13	phenomena	phenomena	NOUN
ejpam-5756	331	14	for	for	ADP
ejpam-5756	331	15	the	the	DET
ejpam-5756	331	16	(	(	PUNCT
ejpam-5756	331	17	2	2	NUM
ejpam-5756	331	18	+	+	NUM
ejpam-5756	331	19	1)-dimensional	1)-dimensional	NUM
ejpam-5756	331	20	date	date	NOUN
ejpam-5756	331	21	-	-	PUNCT
ejpam-5756	331	22	jimbo	jimbo	NOUN
ejpam-5756	331	23	-	-	PUNCT
ejpam-5756	331	24	kashiwara	kashiwara	PROPN
ejpam-5756	331	25	-	-	PUNCT
ejpam-5756	331	26	miwa	miwa	PROPN
ejpam-5756	331	27	equation	equation	NOUN
ejpam-5756	331	28	.	.	PUNCT
ejpam-5756	332	1	results	result	NOUN
ejpam-5756	332	2	in	in	ADP
ejpam-5756	332	3	physics	physics	NOUN
ejpam-5756	332	4	,	,	PUNCT
ejpam-5756	332	5	19:103329	19:103329	NUM
ejpam-5756	332	6	,	,	PUNCT
ejpam-5756	332	7	2020	2020	NUM
ejpam-5756	332	8	.	.	PUNCT
ejpam-5756	333	1	[	[	X
ejpam-5756	333	2	12	12	NUM
ejpam-5756	333	3	]	]	PUNCT
ejpam-5756	333	4	h.	h.	PROPN
ejpam-5756	333	5	f.	f.	PROPN
ejpam-5756	333	6	ismael	ismael	PROPN
ejpam-5756	333	7	,	,	PUNCT
ejpam-5756	333	8	a.	a.	PROPN
ejpam-5756	333	9	seadawy	seadawy	PROPN
ejpam-5756	333	10	,	,	PUNCT
ejpam-5756	333	11	and	and	CCONJ
ejpam-5756	333	12	h.	h.	PROPN
ejpam-5756	333	13	bulut	bulut	PROPN
ejpam-5756	333	14	.	.	PUNCT
ejpam-5756	334	1	rational	rational	ADJ
ejpam-5756	334	2	solutions	solution	NOUN
ejpam-5756	334	3	,	,	PUNCT
ejpam-5756	334	4	and	and	CCONJ
ejpam-5756	334	5	the	the	DET
ejpam-5756	334	6	interaction	interaction	NOUN
ejpam-5756	334	7	solutions	solution	NOUN
ejpam-5756	334	8	to	to	ADP
ejpam-5756	334	9	the	the	DET
ejpam-5756	334	10	(	(	PUNCT
ejpam-5756	334	11	2	2	NUM
ejpam-5756	334	12	+	+	NUM
ejpam-5756	334	13	1)-dimensional	1)-dimensional	NUM
ejpam-5756	334	14	time	time	NOUN
ejpam-5756	334	15	-	-	PUNCT
ejpam-5756	334	16	dependent	dependent	ADJ
ejpam-5756	334	17	date	date	NOUN
ejpam-5756	334	18	–	–	PUNCT
ejpam-5756	334	19	jimbo	jimbo	PROPN
ejpam-5756	334	20	–	–	PUNCT
ejpam-5756	334	21	kashiwara	kashiwara	PROPN
ejpam-5756	334	22	–	–	PUNCT
ejpam-5756	334	23	miwa	miwa	PROPN
ejpam-5756	334	24	equation	equation	NOUN
ejpam-5756	334	25	.	.	PUNCT
ejpam-5756	335	1	international	international	ADJ
ejpam-5756	335	2	journal	journal	PROPN
ejpam-5756	335	3	of	of	ADP
ejpam-5756	335	4	computer	computer	NOUN
ejpam-5756	335	5	mathematics	mathematic	NOUN
ejpam-5756	335	6	,	,	PUNCT
ejpam-5756	335	7	98(12):2369–2377	98(12):2369–2377	NOUN
ejpam-5756	335	8	,	,	PUNCT
ejpam-5756	335	9	2021	2021	NUM
ejpam-5756	335	10	.	.	PUNCT
ejpam-5756	336	1	[	[	X
ejpam-5756	336	2	13	13	NUM
ejpam-5756	336	3	]	]	X
ejpam-5756	336	4	b.	b.	PROPN
ejpam-5756	336	5	b.	b.	PROPN
ejpam-5756	336	6	kadomtsev	kadomtsev	PROPN
ejpam-5756	336	7	and	and	CCONJ
ejpam-5756	336	8	v.	v.	ADP
ejpam-5756	336	9	i.	i.	PROPN
ejpam-5756	336	10	petviashvili	petviashvili	PROPN
ejpam-5756	336	11	.	.	PUNCT
ejpam-5756	337	1	on	on	ADP
ejpam-5756	337	2	the	the	DET
ejpam-5756	337	3	stability	stability	NOUN
ejpam-5756	337	4	of	of	ADP
ejpam-5756	337	5	solitary	solitary	ADJ
ejpam-5756	337	6	waves	wave	NOUN
ejpam-5756	337	7	in	in	ADP
ejpam-5756	337	8	weakly	weakly	ADJ
ejpam-5756	337	9	dispersing	dispersing	NOUN
ejpam-5756	337	10	media	medium	NOUN
ejpam-5756	337	11	.	.	PUNCT
ejpam-5756	338	1	doklady	doklady	PROPN
ejpam-5756	338	2	akademii	akademii	PROPN
ejpam-5756	338	3	nauk	nauk	PROPN
ejpam-5756	338	4	,	,	PUNCT
ejpam-5756	338	5	192(4):753–756	192(4):753–756	NUM
ejpam-5756	338	6	,	,	PUNCT
ejpam-5756	338	7	1970	1970	NUM
ejpam-5756	338	8	.	.	PUNCT
ejpam-5756	339	1	[	[	X
ejpam-5756	339	2	14	14	NUM
ejpam-5756	339	3	]	]	PUNCT
ejpam-5756	339	4	s.	s.	PROPN
ejpam-5756	339	5	s.	s.	PROPN
ejpam-5756	339	6	s.	s.	PROPN
ejpam-5756	339	7	kilic	kilic	PROPN
ejpam-5756	339	8	and	and	CCONJ
ejpam-5756	339	9	e.	e.	PROPN
ejpam-5756	339	10	çelik	çelik	PROPN
ejpam-5756	339	11	.	.	PUNCT
ejpam-5756	340	1	complex	complex	ADJ
ejpam-5756	340	2	solutions	solution	NOUN
ejpam-5756	340	3	to	to	ADP
ejpam-5756	340	4	the	the	DET
ejpam-5756	340	5	higher	high	ADJ
ejpam-5756	340	6	-	-	PUNCT
ejpam-5756	340	7	order	order	NOUN
ejpam-5756	340	8	nonlinear	nonlinear	ADJ
ejpam-5756	340	9	boussinesq	boussinesq	ADJ
ejpam-5756	340	10	type	type	NOUN
ejpam-5756	340	11	wave	wave	NOUN
ejpam-5756	340	12	equation	equation	NOUN
ejpam-5756	340	13	transform	transform	NOUN
ejpam-5756	340	14	.	.	PUNCT
ejpam-5756	341	1	ricerche	ricerche	PROPN
ejpam-5756	341	2	di	di	PROPN
ejpam-5756	341	3	matematica	matematica	PROPN
ejpam-5756	341	4	,	,	PUNCT
ejpam-5756	341	5	73(4):1793–1800	73(4):1793–1800	PROPN
ejpam-5756	341	6	,	,	PUNCT
ejpam-5756	341	7	2024	2024	NUM
ejpam-5756	341	8	.	.	PUNCT
ejpam-5756	342	1	[	[	X
ejpam-5756	342	2	15	15	NUM
ejpam-5756	342	3	]	]	X
ejpam-5756	342	4	j.	j.	PROPN
ejpam-5756	342	5	g.	g.	PROPN
ejpam-5756	342	6	liu	liu	PROPN
ejpam-5756	342	7	,	,	PUNCT
ejpam-5756	342	8	w.	w.	PROPN
ejpam-5756	342	9	h.	h.	PROPN
ejpam-5756	342	10	zhu	zhu	PROPN
ejpam-5756	342	11	,	,	PUNCT
ejpam-5756	342	12	m.	m.	PROPN
ejpam-5756	342	13	s.	s.	PROPN
ejpam-5756	342	14	osman	osman	PROPN
ejpam-5756	342	15	,	,	PUNCT
ejpam-5756	342	16	and	and	CCONJ
ejpam-5756	342	17	w.	w.	PROPN
ejpam-5756	342	18	x.	x.	PROPN
ejpam-5756	342	19	ma	ma	PROPN
ejpam-5756	342	20	.	.	PROPN
ejpam-5756	343	1	an	an	DET
ejpam-5756	343	2	explicit	explicit	ADJ
ejpam-5756	343	3	plethora	plethora	NOUN
ejpam-5756	343	4	of	of	ADP
ejpam-5756	343	5	different	different	ADJ
ejpam-5756	343	6	classes	class	NOUN
ejpam-5756	343	7	of	of	ADP
ejpam-5756	343	8	interactive	interactive	ADJ
ejpam-5756	343	9	lump	lump	NOUN
ejpam-5756	343	10	solutions	solution	NOUN
ejpam-5756	343	11	for	for	ADP
ejpam-5756	343	12	an	an	DET
ejpam-5756	343	13	extension	extension	NOUN
ejpam-5756	343	14	form	form	NOUN
ejpam-5756	343	15	of	of	ADP
ejpam-5756	343	16	3d	3d	PROPN
ejpam-5756	343	17	-	-	PUNCT
ejpam-5756	343	18	jimbo	jimbo	PROPN
ejpam-5756	343	19	–	–	PUNCT
ejpam-5756	343	20	miwa	miwa	PROPN
ejpam-5756	343	21	model	model	NOUN
ejpam-5756	343	22	.	.	PUNCT
ejpam-5756	344	1	the	the	DET
ejpam-5756	344	2	european	european	PROPN
ejpam-5756	344	3	physical	physical	PROPN
ejpam-5756	344	4	journal	journal	PROPN
ejpam-5756	344	5	plus	plus	CCONJ
ejpam-5756	344	6	,	,	PUNCT
ejpam-5756	344	7	135(5):1–9	135(5):1–9	NUM
ejpam-5756	344	8	,	,	PUNCT
ejpam-5756	344	9	2020	2020	NUM
ejpam-5756	344	10	.	.	PUNCT
ejpam-5756	345	1	[	[	X
ejpam-5756	345	2	16	16	NUM
ejpam-5756	345	3	]	]	PUNCT
ejpam-5756	345	4	j.	j.	PROPN
ejpam-5756	345	5	r.	r.	PROPN
ejpam-5756	345	6	liu	liu	PROPN
ejpam-5756	345	7	.	.	PUNCT
ejpam-5756	346	1	a	a	DET
ejpam-5756	346	2	class	class	NOUN
ejpam-5756	346	3	of	of	ADP
ejpam-5756	346	4	nonlinear	nonlinear	ADJ
ejpam-5756	346	5	heat	heat	NOUN
ejpam-5756	346	6	-	-	PUNCT
ejpam-5756	346	7	type	type	NOUN
ejpam-5756	346	8	equations	equation	NOUN
ejpam-5756	346	9	and	and	CCONJ
ejpam-5756	346	10	their	their	PRON
ejpam-5756	346	11	multi	multi	ADJ
ejpam-5756	346	12	-	-	ADJ
ejpam-5756	346	13	wave	wave	ADJ
ejpam-5756	346	14	solutions	solution	NOUN
ejpam-5756	346	15	by	by	ADP
ejpam-5756	346	16	a	a	DET
ejpam-5756	346	17	generalized	generalized	ADJ
ejpam-5756	346	18	bilinear	bilinear	NOUN
ejpam-5756	346	19	technique	technique	NOUN
ejpam-5756	346	20	.	.	PUNCT
ejpam-5756	347	1	modern	modern	ADJ
ejpam-5756	347	2	physics	physics	NOUN
ejpam-5756	347	3	letters	letters	PROPN
ejpam-5756	347	4	b	b	PROPN
ejpam-5756	347	5	,	,	PUNCT
ejpam-5756	347	6	30(06):1650067	30(06):1650067	NUM
ejpam-5756	347	7	,	,	PUNCT
ejpam-5756	347	8	2016	2016	NUM
ejpam-5756	347	9	.	.	PUNCT
ejpam-5756	348	1	[	[	X
ejpam-5756	348	2	17	17	NUM
ejpam-5756	348	3	]	]	PUNCT
ejpam-5756	348	4	m.	m.	NOUN
ejpam-5756	348	5	s.	s.	PROPN
ejpam-5756	348	6	osman	osman	PROPN
ejpam-5756	348	7	.	.	PUNCT
ejpam-5756	349	1	on	on	ADP
ejpam-5756	349	2	complex	complex	ADJ
ejpam-5756	349	3	wave	wave	NOUN
ejpam-5756	349	4	solutions	solution	NOUN
ejpam-5756	349	5	governed	govern	VERB
ejpam-5756	349	6	by	by	ADP
ejpam-5756	349	7	the	the	DET
ejpam-5756	349	8	2d	2d	PROPN
ejpam-5756	349	9	ginzburg	ginzburg	NOUN
ejpam-5756	349	10	–	–	PUNCT
ejpam-5756	349	11	landau	landau	VERB
ejpam-5756	349	12	equation	equation	NOUN
ejpam-5756	349	13	with	with	ADP
ejpam-5756	349	14	variable	variable	ADJ
ejpam-5756	349	15	coefficients	coefficient	NOUN
ejpam-5756	349	16	.	.	PUNCT
ejpam-5756	350	1	optik	optik	PROPN
ejpam-5756	350	2	,	,	PUNCT
ejpam-5756	350	3	156:169–174	156:169–174	NUM
ejpam-5756	350	4	,	,	PUNCT
ejpam-5756	350	5	2018	2018	NUM
ejpam-5756	350	6	.	.	PUNCT
ejpam-5756	351	1	[	[	X
ejpam-5756	351	2	18	18	NUM
ejpam-5756	351	3	]	]	PUNCT
ejpam-5756	351	4	m.	m.	NOUN
ejpam-5756	351	5	s.	s.	PROPN
ejpam-5756	351	6	osman	osman	PROPN
ejpam-5756	351	7	,	,	PUNCT
ejpam-5756	351	8	h.	h.	PROPN
ejpam-5756	351	9	i.	i.	PROPN
ejpam-5756	351	10	abdel	abdel	PROPN
ejpam-5756	351	11	-	-	PUNCT
ejpam-5756	351	12	gawad	gawad	PROPN
ejpam-5756	351	13	,	,	PUNCT
ejpam-5756	351	14	and	and	CCONJ
ejpam-5756	351	15	m.	m.	NOUN
ejpam-5756	351	16	a.	a.	PROPN
ejpam-5756	351	17	el	el	PROPN
ejpam-5756	351	18	mahdy	mahdy	PROPN
ejpam-5756	351	19	.	.	PUNCT
ejpam-5756	352	1	two	two	NUM
ejpam-5756	352	2	-	-	PUNCT
ejpam-5756	352	3	layer	layer	NOUN
ejpam-5756	352	4	-	-	PUNCT
ejpam-5756	352	5	atmospheric	atmospheric	NOUN
ejpam-5756	352	6	blocking	blocking	NOUN
ejpam-5756	352	7	in	in	ADP
ejpam-5756	352	8	a	a	DET
ejpam-5756	352	9	medium	medium	NOUN
ejpam-5756	352	10	with	with	ADP
ejpam-5756	352	11	high	high	ADJ
ejpam-5756	352	12	nonlinearity	nonlinearity	NOUN
ejpam-5756	352	13	and	and	CCONJ
ejpam-5756	352	14	lateral	lateral	ADJ
ejpam-5756	352	15	dispersion	dispersion	NOUN
ejpam-5756	352	16	.	.	PUNCT
ejpam-5756	353	1	results	result	NOUN
ejpam-5756	353	2	in	in	ADP
ejpam-5756	353	3	physics	physics	NOUN
ejpam-5756	353	4	,	,	PUNCT
ejpam-5756	353	5	8:1054–1060	8:1054–1060	NUM
ejpam-5756	353	6	,	,	PUNCT
ejpam-5756	353	7	2018	2018	NUM
ejpam-5756	353	8	.	.	PUNCT
ejpam-5756	354	1	[	[	X
ejpam-5756	354	2	19	19	NUM
ejpam-5756	354	3	]	]	X
ejpam-5756	354	4	n.	n.	PROPN
ejpam-5756	354	5	raza	raza	PROPN
ejpam-5756	354	6	,	,	PUNCT
ejpam-5756	354	7	m.	m.	NOUN
ejpam-5756	354	8	s.	s.	PROPN
ejpam-5756	354	9	osman	osman	PROPN
ejpam-5756	354	10	,	,	PUNCT
ejpam-5756	354	11	a.	a.	PROPN
ejpam-5756	354	12	h.	h.	PROPN
ejpam-5756	354	13	abdel	abdel	PROPN
ejpam-5756	354	14	-	-	PUNCT
ejpam-5756	354	15	aty	aty	PROPN
ejpam-5756	354	16	,	,	PUNCT
ejpam-5756	354	17	s.	s.	PROPN
ejpam-5756	354	18	abdel	abdel	PROPN
ejpam-5756	354	19	-	-	PUNCT
ejpam-5756	354	20	khalek	khalek	PROPN
ejpam-5756	354	21	,	,	PUNCT
ejpam-5756	354	22	and	and	CCONJ
ejpam-5756	354	23	h.	h.	PROPN
ejpam-5756	354	24	r.	r.	PROPN
ejpam-5756	354	25	besbes	besbes	PROPN
ejpam-5756	354	26	.	.	PUNCT
ejpam-5756	355	1	optical	optical	ADJ
ejpam-5756	355	2	solitons	soliton	NOUN
ejpam-5756	355	3	of	of	ADP
ejpam-5756	355	4	space	space	NOUN
ejpam-5756	355	5	-	-	PUNCT
ejpam-5756	355	6	time	time	NOUN
ejpam-5756	355	7	fractional	fractional	ADJ
ejpam-5756	355	8	fokas	fokas	ADJ
ejpam-5756	355	9	–	–	PUNCT
ejpam-5756	355	10	lenells	lenell	NOUN
ejpam-5756	355	11	equation	equation	NOUN
ejpam-5756	355	12	with	with	ADP
ejpam-5756	355	13	two	two	NUM
ejpam-5756	355	14	versatile	versatile	ADJ
ejpam-5756	355	15	integration	integration	NOUN
ejpam-5756	355	16	architectures	architecture	NOUN
ejpam-5756	355	17	.	.	PUNCT
ejpam-5756	356	1	advances	advance	NOUN
ejpam-5756	356	2	in	in	ADP
ejpam-5756	356	3	difference	difference	NOUN
ejpam-5756	356	4	equations	equation	NOUN
ejpam-5756	356	5	,	,	PUNCT
ejpam-5756	356	6	pages	page	NOUN
ejpam-5756	356	7	1–15	1–15	NUM
ejpam-5756	356	8	,	,	PUNCT
ejpam-5756	356	9	2020	2020	NUM
ejpam-5756	356	10	.	.	PUNCT
ejpam-5756	357	1	[	[	X
ejpam-5756	357	2	20	20	NUM
ejpam-5756	357	3	]	]	PUNCT
ejpam-5756	357	4	h.	h.	PROPN
ejpam-5756	357	5	u.	u.	PROPN
ejpam-5756	357	6	rehman	rehman	PROPN
ejpam-5756	357	7	,	,	PUNCT
ejpam-5756	357	8	r.	r.	PROPN
ejpam-5756	357	9	akber	akber	PROPN
ejpam-5756	357	10	,	,	PUNCT
ejpam-5756	357	11	a.	a.	NOUN
ejpam-5756	357	12	m.	m.	PROPN
ejpam-5756	357	13	wazwaz	wazwaz	PROPN
ejpam-5756	357	14	,	,	PUNCT
ejpam-5756	357	15	h.	h.	PROPN
ejpam-5756	357	16	m.	m.	PROPN
ejpam-5756	357	17	alshehri	alshehri	PROPN
ejpam-5756	357	18	,	,	PUNCT
ejpam-5756	357	19	and	and	CCONJ
ejpam-5756	357	20	m.	m.	PROPN
ejpam-5756	357	21	s.	s.	PROPN
ejpam-5756	357	22	osman	osman	PROPN
ejpam-5756	357	23	.	.	PUNCT
ejpam-5756	358	1	analysis	analysis	NOUN
ejpam-5756	358	2	of	of	ADP
ejpam-5756	358	3	brownian	brownian	ADJ
ejpam-5756	358	4	motion	motion	NOUN
ejpam-5756	358	5	in	in	ADP
ejpam-5756	358	6	stochastic	stochastic	ADJ
ejpam-5756	358	7	schrödinger	schrödinger	NOUN
ejpam-5756	358	8	wave	wave	NOUN
ejpam-5756	358	9	equation	equation	NOUN
ejpam-5756	358	10	using	use	VERB
ejpam-5756	358	11	sardar	sardar	PROPN
ejpam-5756	358	12	sub	sub	ADJ
ejpam-5756	358	13	-	-	ADJ
ejpam-5756	358	14	equation	equation	NOUN
ejpam-5756	358	15	method	method	NOUN
ejpam-5756	358	16	.	.	PUNCT
ejpam-5756	359	1	optik	optik	PROPN
ejpam-5756	359	2	,	,	PUNCT
ejpam-5756	359	3	289:171305	289:171305	NUM
ejpam-5756	359	4	,	,	PUNCT
ejpam-5756	359	5	2023	2023	NUM
ejpam-5756	359	6	.	.	PUNCT
ejpam-5756	360	1	[	[	X
ejpam-5756	360	2	21	21	NUM
ejpam-5756	360	3	]	]	X
ejpam-5756	360	4	m.	m.	NOUN
ejpam-5756	360	5	m.	m.	NOUN
ejpam-5756	360	6	roshid	roshid	VERB
ejpam-5756	360	7	,	,	PUNCT
ejpam-5756	360	8	m.	m.	NOUN
ejpam-5756	360	9	uddin	uddin	PROPN
ejpam-5756	360	10	,	,	PUNCT
ejpam-5756	360	11	s.	s.	PROPN
ejpam-5756	360	12	boulaaras	boulaaras	PROPN
ejpam-5756	360	13	,	,	PUNCT
ejpam-5756	360	14	and	and	CCONJ
ejpam-5756	360	15	m.	m.	PROPN
ejpam-5756	360	16	s.	s.	PROPN
ejpam-5756	360	17	osman	osman	PROPN
ejpam-5756	360	18	.	.	PUNCT
ejpam-5756	361	1	dynamic	dynamic	ADJ
ejpam-5756	361	2	optical	optical	ADJ
ejpam-5756	361	3	soliton	soliton	NOUN
ejpam-5756	361	4	solutions	solution	NOUN
ejpam-5756	361	5	of	of	ADP
ejpam-5756	361	6	m	m	NOUN
ejpam-5756	361	7	-	-	PUNCT
ejpam-5756	361	8	fractional	fractional	ADJ
ejpam-5756	361	9	modify	modify	VERB
ejpam-5756	361	10	unstable	unstable	ADJ
ejpam-5756	361	11	nonlinear	nonlinear	NOUN
ejpam-5756	361	12	schrödinger	schrödinger	NOUN
ejpam-5756	361	13	equation	equation	NOUN
ejpam-5756	361	14	via	via	ADP
ejpam-5756	361	15	two	two	NUM
ejpam-5756	361	16	analytic	analytic	ADJ
ejpam-5756	361	17	methods	method	NOUN
ejpam-5756	361	18	.	.	PUNCT
ejpam-5756	362	1	results	result	NOUN
ejpam-5756	362	2	in	in	ADP
ejpam-5756	362	3	engineering	engineering	NOUN
ejpam-5756	362	4	,	,	PUNCT
ejpam-5756	362	5	25:103757	25:103757	NOUN
ejpam-5756	362	6	,	,	PUNCT
ejpam-5756	362	7	2025	2025	NUM
ejpam-5756	362	8	.	.	PUNCT
ejpam-5756	363	1	[	[	X
ejpam-5756	363	2	22	22	NUM
ejpam-5756	363	3	]	]	PUNCT
ejpam-5756	363	4	s.	s.	PROPN
ejpam-5756	363	5	s.	s.	PROPN
ejpam-5756	363	6	sener	sener	PROPN
ejpam-5756	363	7	.	.	PUNCT
ejpam-5756	364	1	new	new	ADJ
ejpam-5756	364	2	wave	wave	NOUN
ejpam-5756	364	3	behaviors	behavior	NOUN
ejpam-5756	364	4	of	of	ADP
ejpam-5756	364	5	the	the	DET
ejpam-5756	364	6	(	(	PUNCT
ejpam-5756	364	7	3	3	NUM
ejpam-5756	364	8	+	+	NUM
ejpam-5756	364	9	1)-dimensional	1)-dimensional	NUM
ejpam-5756	364	10	date	date	NOUN
ejpam-5756	364	11	-	-	PUNCT
ejpam-5756	364	12	jimbo	jimbo	NOUN
ejpam-5756	364	13	-	-	PUNCT
ejpam-5756	364	14	kashiwaramiwa	kashiwaramiwa	PROPN
ejpam-5756	364	15	equation	equation	NOUN
ejpam-5756	364	16	.	.	PUNCT
ejpam-5756	365	1	journal	journal	PROPN
ejpam-5756	365	2	of	of	ADP
ejpam-5756	365	3	mathematical	mathematical	ADJ
ejpam-5756	365	4	sciences	science	NOUN
ejpam-5756	365	5	and	and	CCONJ
ejpam-5756	365	6	modelling	modelling	NOUN
ejpam-5756	365	7	,	,	PUNCT
ejpam-5756	365	8	4(3):126–132	4(3):126–132	NOUN
ejpam-5756	365	9	,	,	PUNCT
ejpam-5756	365	10	2021	2021	NUM
ejpam-5756	365	11	.	.	PUNCT
ejpam-5756	366	1	[	[	X
ejpam-5756	366	2	23	23	NUM
ejpam-5756	366	3	]	]	X
ejpam-5756	366	4	f.	f.	PROPN
ejpam-5756	366	5	ali	ali	PROPN
ejpam-5756	366	6	shah	shah	PROPN
ejpam-5756	366	7	,	,	PUNCT
ejpam-5756	366	8	b.	b.	PROPN
ejpam-5756	366	9	kamran	kamran	PROPN
ejpam-5756	366	10	,	,	PUNCT
ejpam-5756	366	11	w.	w.	PROPN
ejpam-5756	366	12	boulila	boulila	PROPN
ejpam-5756	366	13	,	,	PUNCT
ejpam-5756	366	14	a.	a.	NOUN
ejpam-5756	366	15	koubaa	koubaa	PROPN
ejpam-5756	366	16	,	,	PUNCT
ejpam-5756	366	17	and	and	CCONJ
ejpam-5756	366	18	n.	n.	PROPN
ejpam-5756	366	19	mlaiki	mlaiki	PROPN
ejpam-5756	366	20	.	.	PUNCT
ejpam-5756	367	1	numerical	numerical	ADJ
ejpam-5756	367	2	solution	solution	NOUN
ejpam-5756	367	3	of	of	ADP
ejpam-5756	367	4	advection	advection	NOUN
ejpam-5756	367	5	-	-	PUNCT
ejpam-5756	367	6	diffusion	diffusion	NOUN
ejpam-5756	367	7	equation	equation	NOUN
ejpam-5756	367	8	of	of	ADP
ejpam-5756	367	9	fractional	fractional	ADJ
ejpam-5756	367	10	order	order	NOUN
ejpam-5756	367	11	using	use	VERB
ejpam-5756	367	12	chebyshev	chebyshev	NOUN
ejpam-5756	367	13	collocation	collocation	NOUN
ejpam-5756	367	14	method	method	NOUN
ejpam-5756	367	15	.	.	PUNCT
ejpam-5756	368	1	fractal	fractal	ADJ
ejpam-5756	368	2	and	and	CCONJ
ejpam-5756	368	3	fractional	fractional	ADJ
ejpam-5756	368	4	,	,	PUNCT
ejpam-5756	368	5	7(10):762	7(10):762	NUM
ejpam-5756	368	6	,	,	PUNCT
ejpam-5756	368	7	2023	2023	NUM
ejpam-5756	368	8	.	.	PUNCT
ejpam-5756	369	1	[	[	X
ejpam-5756	369	2	24	24	NUM
ejpam-5756	369	3	]	]	PUNCT
ejpam-5756	369	4	m.	m.	NOUN
ejpam-5756	369	5	singh	singh	PROPN
ejpam-5756	369	6	and	and	CCONJ
ejpam-5756	369	7	r.	r.	PROPN
ejpam-5756	369	8	k.	k.	PROPN
ejpam-5756	369	9	gupta	gupta	PROPN
ejpam-5756	369	10	.	.	PUNCT
ejpam-5756	370	1	on	on	ADP
ejpam-5756	370	2	painlevé	painlevé	NOUN
ejpam-5756	370	3	analysis	analysis	NOUN
ejpam-5756	370	4	,	,	PUNCT
ejpam-5756	370	5	symmetry	symmetry	NOUN
ejpam-5756	370	6	group	group	NOUN
ejpam-5756	370	7	and	and	CCONJ
ejpam-5756	370	8	conservation	conservation	NOUN
ejpam-5756	370	9	laws	law	NOUN
ejpam-5756	370	10	of	of	ADP
ejpam-5756	370	11	date	date	NOUN
ejpam-5756	370	12	–	–	PUNCT
ejpam-5756	370	13	jimbo	jimbo	PROPN
ejpam-5756	370	14	–	–	PUNCT
ejpam-5756	370	15	kashiwara	kashiwara	PROPN
ejpam-5756	370	16	–	–	PUNCT
ejpam-5756	370	17	miwa	miwa	PROPN
ejpam-5756	370	18	equation	equation	NOUN
ejpam-5756	370	19	.	.	PUNCT
ejpam-5756	371	1	international	international	ADJ
ejpam-5756	371	2	journal	journal	PROPN
ejpam-5756	371	3	of	of	ADP
ejpam-5756	371	4	applied	applied	ADJ
ejpam-5756	371	5	and	and	CCONJ
ejpam-5756	371	6	computational	computational	ADJ
ejpam-5756	371	7	mathematics	mathematic	NOUN
ejpam-5756	371	8	,	,	PUNCT
ejpam-5756	371	9	4(3):1–15	4(3):1–15	NUM
ejpam-5756	371	10	,	,	PUNCT
ejpam-5756	371	11	2018	2018	NUM
ejpam-5756	371	12	.	.	PUNCT
ejpam-5756	372	1	[	[	X
ejpam-5756	372	2	25	25	NUM
ejpam-5756	372	3	]	]	X
ejpam-5756	372	4	s.	s.	PROPN
ejpam-5756	372	5	tarla	tarla	PROPN
ejpam-5756	372	6	,	,	PUNCT
ejpam-5756	372	7	k.	k.	PROPN
ejpam-5756	372	8	k.	k.	PROPN
ejpam-5756	372	9	ali	ali	PROPN
ejpam-5756	372	10	,	,	PUNCT
ejpam-5756	372	11	r.	r.	PROPN
ejpam-5756	372	12	yilmazer	yilmazer	PROPN
ejpam-5756	372	13	,	,	PUNCT
ejpam-5756	372	14	and	and	CCONJ
ejpam-5756	372	15	m.	m.	PROPN
ejpam-5756	372	16	s.	s.	PROPN
ejpam-5756	372	17	osman	osman	PROPN
ejpam-5756	372	18	.	.	PUNCT
ejpam-5756	373	1	new	new	ADJ
ejpam-5756	373	2	optical	optical	ADJ
ejpam-5756	373	3	solitons	soliton	NOUN
ejpam-5756	373	4	based	base	VERB
ejpam-5756	373	5	on	on	ADP
ejpam-5756	373	6	the	the	DET
ejpam-5756	373	7	perturbed	perturb	VERB
ejpam-5756	373	8	chen	chen	PROPN
ejpam-5756	373	9	-	-	PUNCT
ejpam-5756	373	10	lee	lee	PROPN
ejpam-5756	373	11	-	-	PUNCT
ejpam-5756	373	12	liu	liu	PROPN
ejpam-5756	373	13	model	model	PROPN
ejpam-5756	373	14	through	through	ADP
ejpam-5756	373	15	jacobi	jacobi	PROPN
ejpam-5756	373	16	elliptic	elliptic	ADJ
ejpam-5756	373	17	function	function	NOUN
ejpam-5756	373	18	method	method	NOUN
ejpam-5756	373	19	.	.	PUNCT
ejpam-5756	374	1	optical	optical	ADJ
ejpam-5756	374	2	and	and	CCONJ
ejpam-5756	374	3	b.	b.	PROPN
ejpam-5756	374	4	yasmeen	yasmeen	PROPN
ejpam-5756	374	5	,	,	PUNCT
ejpam-5756	374	6	k.	k.	PROPN
ejpam-5756	374	7	ahmad	ahmad	PROPN
ejpam-5756	374	8	,	,	PUNCT
ejpam-5756	374	9	n.	n.	PROPN
ejpam-5756	374	10	fatima	fatima	PROPN
ejpam-5756	374	11	/	/	PUNCT
ejpam-5756	374	12	eur	eur	PROPN
ejpam-5756	374	13	.	.	PUNCT
ejpam-5756	375	1	j.	j.	PROPN
ejpam-5756	375	2	pure	pure	PROPN
ejpam-5756	375	3	appl	appl	PROPN
ejpam-5756	375	4	.	.	PROPN
ejpam-5756	375	5	math	math	PROPN
ejpam-5756	375	6	,	,	PUNCT
ejpam-5756	375	7	18	18	NUM
ejpam-5756	375	8	(	(	PUNCT
ejpam-5756	375	9	1	1	NUM
ejpam-5756	375	10	)	)	PUNCT
ejpam-5756	375	11	(	(	PUNCT
ejpam-5756	375	12	2025	2025	NUM
ejpam-5756	375	13	)	)	PUNCT
ejpam-5756	375	14	,	,	PUNCT
ejpam-5756	375	15	5756	5756	NUM
ejpam-5756	375	16	17	17	NUM
ejpam-5756	375	17	of	of	ADP
ejpam-5756	375	18	17	17	NUM
ejpam-5756	375	19	quantum	quantum	ADJ
ejpam-5756	375	20	electronics	electronic	NOUN
ejpam-5756	375	21	,	,	PUNCT
ejpam-5756	375	22	54(2):131	54(2):131	NUM
ejpam-5756	375	23	,	,	PUNCT
ejpam-5756	375	24	2022	2022	NUM
ejpam-5756	375	25	.	.	PUNCT
ejpam-5756	376	1	[	[	X
ejpam-5756	376	2	26	26	NUM
ejpam-5756	376	3	]	]	PUNCT
ejpam-5756	376	4	a.	a.	NOUN
ejpam-5756	376	5	umer	umer	PROPN
ejpam-5756	376	6	,	,	PUNCT
ejpam-5756	376	7	m.	m.	NOUN
ejpam-5756	376	8	abbas	abbas	PROPN
ejpam-5756	376	9	,	,	PUNCT
ejpam-5756	376	10	m.	m.	PROPN
ejpam-5756	376	11	shafiq	shafiq	PROPN
ejpam-5756	376	12	,	,	PUNCT
ejpam-5756	376	13	f.	f.	PROPN
ejpam-5756	376	14	a.	a.	PROPN
ejpam-5756	376	15	abdullah	abdullah	PROPN
ejpam-5756	376	16	,	,	PUNCT
ejpam-5756	376	17	m.	m.	PROPN
ejpam-5756	376	18	de	de	PROPN
ejpam-5756	376	19	la	la	X
ejpam-5756	376	20	sen	sen	PROPN
ejpam-5756	376	21	,	,	PUNCT
ejpam-5756	376	22	and	and	CCONJ
ejpam-5756	376	23	t.	t.	PROPN
ejpam-5756	376	24	abdeljawad	abdeljawad	PROPN
ejpam-5756	376	25	.	.	PUNCT
ejpam-5756	377	1	numerical	numerical	ADJ
ejpam-5756	377	2	solutions	solution	NOUN
ejpam-5756	377	3	of	of	ADP
ejpam-5756	377	4	atangana	atangana	PROPN
ejpam-5756	377	5	-	-	PUNCT
ejpam-5756	377	6	baleanu	baleanu	PROPN
ejpam-5756	377	7	time	time	NOUN
ejpam-5756	377	8	-	-	PUNCT
ejpam-5756	377	9	fractional	fractional	ADJ
ejpam-5756	377	10	advection	advection	NOUN
ejpam-5756	377	11	diffusion	diffusion	NOUN
ejpam-5756	377	12	equation	equation	NOUN
ejpam-5756	377	13	via	via	ADP
ejpam-5756	377	14	an	an	DET
ejpam-5756	377	15	extended	extend	VERB
ejpam-5756	377	16	cubic	cubic	ADJ
ejpam-5756	377	17	b	b	NOUN
ejpam-5756	377	18	-	-	PUNCT
ejpam-5756	377	19	spline	spline	NOUN
ejpam-5756	377	20	technique	technique	NOUN
ejpam-5756	377	21	.	.	PUNCT
ejpam-5756	378	1	alexandria	alexandria	PROPN
ejpam-5756	378	2	engineering	engineering	PROPN
ejpam-5756	378	3	journal	journal	PROPN
ejpam-5756	378	4	,	,	PUNCT
ejpam-5756	378	5	74:285	74:285	NUM
ejpam-5756	378	6	–	–	PUNCT
ejpam-5756	378	7	300	300	NUM
ejpam-5756	378	8	,	,	PUNCT
ejpam-5756	378	9	2023	2023	NUM
ejpam-5756	378	10	.	.	PUNCT
ejpam-5756	379	1	[	[	X
ejpam-5756	379	2	27	27	NUM
ejpam-5756	379	3	]	]	PUNCT
ejpam-5756	379	4	s.	s.	PROPN
ejpam-5756	379	5	n.	n.	PROPN
ejpam-5756	379	6	wang	wang	PROPN
ejpam-5756	379	7	and	and	CCONJ
ejpam-5756	379	8	j.	j.	PROPN
ejpam-5756	379	9	hu	hu	PROPN
ejpam-5756	379	10	.	.	PUNCT
ejpam-5756	380	1	grammian	grammian	ADJ
ejpam-5756	380	2	solutions	solution	NOUN
ejpam-5756	380	3	for	for	ADP
ejpam-5756	380	4	a	a	DET
ejpam-5756	380	5	(	(	PUNCT
ejpam-5756	380	6	2	2	NUM
ejpam-5756	380	7	+	+	NUM
ejpam-5756	380	8	1)-dimensional	1)-dimensional	NUM
ejpam-5756	380	9	integrable	integrable	ADJ
ejpam-5756	380	10	coupled	couple	VERB
ejpam-5756	380	11	modified	modify	VERB
ejpam-5756	380	12	date	date	NOUN
ejpam-5756	380	13	–	–	PUNCT
ejpam-5756	380	14	jimbo	jimbo	PROPN
ejpam-5756	380	15	–	–	PUNCT
ejpam-5756	380	16	kashiwara	kashiwara	PROPN
ejpam-5756	380	17	–	–	PUNCT
ejpam-5756	380	18	miwa	miwa	PROPN
ejpam-5756	380	19	equation	equation	NOUN
ejpam-5756	380	20	.	.	PUNCT
ejpam-5756	381	1	modern	modern	ADJ
ejpam-5756	381	2	physics	physics	PROPN
ejpam-5756	381	3	letters	letters	PROPN
ejpam-5756	381	4	b	b	PROPN
ejpam-5756	381	5	,	,	PUNCT
ejpam-5756	381	6	33(10):1950119	33(10):1950119	NUM
ejpam-5756	381	7	,	,	PUNCT
ejpam-5756	381	8	2019	2019	NUM
ejpam-5756	381	9	.	.	PUNCT
ejpam-5756	382	1	[	[	X
ejpam-5756	382	2	28	28	NUM
ejpam-5756	382	3	]	]	PUNCT
ejpam-5756	382	4	x.	x.	PROPN
ejpam-5756	382	5	wang	wang	PROPN
ejpam-5756	382	6	,	,	PUNCT
ejpam-5756	382	7	h.	h.	PROPN
ejpam-5756	382	8	ehsan	ehsan	PROPN
ejpam-5756	382	9	,	,	PUNCT
ejpam-5756	382	10	m.	m.	NOUN
ejpam-5756	382	11	abbas	abbas	PROPN
ejpam-5756	382	12	,	,	PUNCT
ejpam-5756	382	13	g.	g.	PROPN
ejpam-5756	382	14	akram	akram	PROPN
ejpam-5756	382	15	,	,	PUNCT
ejpam-5756	382	16	m.	m.	NOUN
ejpam-5756	382	17	sadaf	sadaf	NOUN
ejpam-5756	382	18	,	,	PUNCT
ejpam-5756	382	19	and	and	CCONJ
ejpam-5756	382	20	t.	t.	PROPN
ejpam-5756	382	21	abdeljawad	abdeljawad	NOUN
ejpam-5756	382	22	.	.	PUNCT
ejpam-5756	383	1	analytical	analytical	ADJ
ejpam-5756	383	2	solitary	solitary	ADJ
ejpam-5756	383	3	wave	wave	NOUN
ejpam-5756	383	4	solutions	solution	NOUN
ejpam-5756	383	5	of	of	ADP
ejpam-5756	383	6	a	a	DET
ejpam-5756	383	7	time	time	NOUN
ejpam-5756	383	8	-	-	PUNCT
ejpam-5756	383	9	fractional	fractional	ADJ
ejpam-5756	383	10	thin	thin	ADJ
ejpam-5756	383	11	-	-	PUNCT
ejpam-5756	383	12	film	film	NOUN
ejpam-5756	383	13	ferroelectric	ferroelectric	ADJ
ejpam-5756	383	14	material	material	NOUN
ejpam-5756	383	15	equation	equation	NOUN
ejpam-5756	383	16	involving	involve	VERB
ejpam-5756	383	17	beta	beta	NOUN
ejpam-5756	383	18	-	-	PUNCT
ejpam-5756	383	19	derivative	derivative	NOUN
ejpam-5756	383	20	using	use	VERB
ejpam-5756	383	21	modified	modify	VERB
ejpam-5756	383	22	auxiliary	auxiliary	ADJ
ejpam-5756	383	23	equation	equation	NOUN
ejpam-5756	383	24	method	method	NOUN
ejpam-5756	383	25	.	.	PUNCT
ejpam-5756	384	1	results	result	NOUN
ejpam-5756	384	2	in	in	ADP
ejpam-5756	384	3	physics	physics	NOUN
ejpam-5756	384	4	,	,	PUNCT
ejpam-5756	384	5	48:106411	48:106411	NUM
ejpam-5756	384	6	,	,	PUNCT
ejpam-5756	384	7	2023	2023	NUM
ejpam-5756	384	8	.	.	PUNCT
ejpam-5756	385	1	[	[	X
ejpam-5756	385	2	29	29	NUM
ejpam-5756	385	3	]	]	PUNCT
ejpam-5756	385	4	a.	a.	NOUN
ejpam-5756	385	5	m.	m.	NOUN
ejpam-5756	385	6	wazwaz	wazwaz	PROPN
ejpam-5756	385	7	.	.	PUNCT
ejpam-5756	386	1	a	a	DET
ejpam-5756	386	2	(	(	PUNCT
ejpam-5756	386	3	2	2	NUM
ejpam-5756	386	4	+	+	NUM
ejpam-5756	386	5	1)-dimensional	1)-dimensional	NUM
ejpam-5756	386	6	time	time	NOUN
ejpam-5756	386	7	-	-	PUNCT
ejpam-5756	386	8	dependent	dependent	ADJ
ejpam-5756	386	9	date	date	NOUN
ejpam-5756	386	10	–	–	PUNCT
ejpam-5756	386	11	jimbo	jimbo	PROPN
ejpam-5756	386	12	–	–	PUNCT
ejpam-5756	386	13	kashiwara	kashiwara	PROPN
ejpam-5756	386	14	–	–	PUNCT
ejpam-5756	386	15	miwa	miwa	PROPN
ejpam-5756	386	16	equation	equation	NOUN
ejpam-5756	386	17	:	:	PUNCT
ejpam-5756	386	18	painlevé	painlevé	VERB
ejpam-5756	386	19	integrability	integrability	NOUN
ejpam-5756	386	20	and	and	CCONJ
ejpam-5756	386	21	multiple	multiple	ADJ
ejpam-5756	386	22	soliton	soliton	NOUN
ejpam-5756	386	23	solutions	solution	NOUN
ejpam-5756	386	24	.	.	PUNCT
ejpam-5756	387	1	computers	computer	NOUN
ejpam-5756	387	2	&	&	CCONJ
ejpam-5756	387	3	mathematics	mathematics	PROPN
ejpam-5756	387	4	with	with	ADP
ejpam-5756	387	5	applications	application	NOUN
ejpam-5756	387	6	,	,	PUNCT
ejpam-5756	387	7	79(4):1145–1149	79(4):1145–1149	NUM
ejpam-5756	387	8	,	,	PUNCT
ejpam-5756	387	9	2020	2020	NUM
ejpam-5756	387	10	.	.	PUNCT
ejpam-5756	388	1	[	[	X
ejpam-5756	388	2	30	30	NUM
ejpam-5756	388	3	]	]	X
ejpam-5756	388	4	y.	y.	PROPN
ejpam-5756	388	5	q.	q.	PROPN
ejpam-5756	388	6	yuan	yuan	PROPN
ejpam-5756	388	7	,	,	PUNCT
ejpam-5756	388	8	b.	b.	PROPN
ejpam-5756	388	9	tian	tian	PROPN
ejpam-5756	388	10	,	,	PUNCT
ejpam-5756	388	11	w.	w.	PROPN
ejpam-5756	388	12	r.	r.	PROPN
ejpam-5756	388	13	sun	sun	PROPN
ejpam-5756	388	14	,	,	PUNCT
ejpam-5756	388	15	j.	j.	PROPN
ejpam-5756	388	16	chai	chai	PROPN
ejpam-5756	388	17	,	,	PUNCT
ejpam-5756	388	18	and	and	CCONJ
ejpam-5756	388	19	l.	l.	PROPN
ejpam-5756	388	20	liu	liu	PROPN
ejpam-5756	388	21	.	.	PROPN
ejpam-5756	389	1	wronskian	wronskian	PROPN
ejpam-5756	389	2	and	and	CCONJ
ejpam-5756	389	3	grammian	grammian	ADJ
ejpam-5756	389	4	solutions	solution	NOUN
ejpam-5756	389	5	for	for	ADP
ejpam-5756	389	6	a	a	DET
ejpam-5756	389	7	(	(	PUNCT
ejpam-5756	389	8	2	2	NUM
ejpam-5756	389	9	+	+	NUM
ejpam-5756	389	10	1)-dimensional	1)-dimensional	NUM
ejpam-5756	389	11	date	date	NOUN
ejpam-5756	389	12	–	–	PUNCT
ejpam-5756	389	13	jimbo	jimbo	PROPN
ejpam-5756	389	14	–	–	PUNCT
ejpam-5756	389	15	kashiwara	kashiwara	PROPN
ejpam-5756	389	16	–	–	PUNCT
ejpam-5756	389	17	miwa	miwa	PROPN
ejpam-5756	389	18	equation	equation	NOUN
ejpam-5756	389	19	.	.	PUNCT
ejpam-5756	390	1	computers	computer	NOUN
ejpam-5756	390	2	&	&	CCONJ
ejpam-5756	390	3	mathematics	mathematics	PROPN
ejpam-5756	390	4	with	with	ADP
ejpam-5756	390	5	applications	application	NOUN
ejpam-5756	390	6	,	,	PUNCT
ejpam-5756	390	7	74(4):873–879	74(4):873–879	NUM
ejpam-5756	390	8	,	,	PUNCT
ejpam-5756	390	9	2017	2017	NUM
ejpam-5756	390	10	.	.	PUNCT