id	sid	tid	token	lemma	pos
ejpam-6422	1	1	european	european	PROPN
ejpam-6422	1	2	journal	journal	PROPN
ejpam-6422	1	3	of	of	ADP
ejpam-6422	1	4	pure	pure	ADJ
ejpam-6422	1	5	and	and	CCONJ
ejpam-6422	1	6	applied	applied	ADJ
ejpam-6422	1	7	mathematics	mathematic	NOUN
ejpam-6422	1	8	2025	2025	NUM
ejpam-6422	1	9	,	,	PUNCT
ejpam-6422	1	10	vol	vol	NOUN
ejpam-6422	1	11	.	.	PROPN
ejpam-6422	1	12	18	18	NUM
ejpam-6422	1	13	,	,	PUNCT
ejpam-6422	1	14	issue	issue	NOUN
ejpam-6422	1	15	3	3	NUM
ejpam-6422	1	16	,	,	PUNCT
ejpam-6422	1	17	article	article	NOUN
ejpam-6422	1	18	number	number	NOUN
ejpam-6422	1	19	6422	6422	NUM
ejpam-6422	1	20	issn	issn	PROPN
ejpam-6422	1	21	1307	1307	NUM
ejpam-6422	1	22	-	-	SYM
ejpam-6422	1	23	5543	5543	NUM
ejpam-6422	1	24	–	–	PUNCT
ejpam-6422	1	25	ejpam.com	ejpam.com	X
ejpam-6422	1	26	published	publish	VERB
ejpam-6422	1	27	by	by	ADP
ejpam-6422	1	28	new	new	PROPN
ejpam-6422	1	29	york	york	PROPN
ejpam-6422	1	30	business	business	PROPN
ejpam-6422	1	31	global	global	ADJ
ejpam-6422	1	32	abundant	abundant	ADJ
ejpam-6422	1	33	solitary	solitary	ADJ
ejpam-6422	1	34	solutions	solution	NOUN
ejpam-6422	1	35	for	for	ADP
ejpam-6422	1	36	the	the	DET
ejpam-6422	1	37	fractional	fractional	ADJ
ejpam-6422	1	38	unidirectional	unidirectional	ADJ
ejpam-6422	1	39	wave	wave	NOUN
ejpam-6422	1	40	model	model	NOUN
ejpam-6422	1	41	using	use	VERB
ejpam-6422	1	42	in	in	ADP
ejpam-6422	1	43	oceanography	oceanography	NOUN
ejpam-6422	1	44	,	,	PUNCT
ejpam-6422	1	45	coastal	coastal	ADJ
ejpam-6422	1	46	engineering	engineering	NOUN
ejpam-6422	1	47	,	,	PUNCT
ejpam-6422	1	48	and	and	CCONJ
ejpam-6422	1	49	meteorology	meteorology	NOUN
ejpam-6422	1	50	wael	wael	PROPN
ejpam-6422	1	51	w.	w.	PROPN
ejpam-6422	1	52	mohammed1,∗	mohammed1,∗	PROPN
ejpam-6422	1	53	,	,	PUNCT
ejpam-6422	1	54	monirah	monirah	PROPN
ejpam-6422	1	55	w.	w.	PROPN
ejpam-6422	1	56	alshammary1	alshammary1	PROPN
ejpam-6422	1	57	,	,	PUNCT
ejpam-6422	1	58	ahmed	ahmed	PROPN
ejpam-6422	1	59	e.	e.	PROPN
ejpam-6422	1	60	matouk2,3	matouk2,3	PROPN
ejpam-6422	1	61	,	,	PUNCT
ejpam-6422	1	62	naveed	naveed	PROPN
ejpam-6422	1	63	iqbal1	iqbal1	PROPN
ejpam-6422	2	1	1	1	NUM
ejpam-6422	2	2	department	department	NOUN
ejpam-6422	2	3	of	of	ADP
ejpam-6422	2	4	mathematics	mathematic	NOUN
ejpam-6422	2	5	,	,	PUNCT
ejpam-6422	2	6	college	college	NOUN
ejpam-6422	2	7	of	of	ADP
ejpam-6422	2	8	science	science	NOUN
ejpam-6422	2	9	,	,	PUNCT
ejpam-6422	2	10	university	university	NOUN
ejpam-6422	2	11	of	of	ADP
ejpam-6422	2	12	ha’il	ha’il	PROPN
ejpam-6422	2	13	,	,	PUNCT
ejpam-6422	2	14	ha’il	ha’il	PROPN
ejpam-6422	2	15	2440	2440	NUM
ejpam-6422	2	16	,	,	PUNCT
ejpam-6422	2	17	saudi	saudi	PROPN
ejpam-6422	2	18	arabia	arabia	PROPN
ejpam-6422	2	19	2	2	NUM
ejpam-6422	2	20	department	department	NOUN
ejpam-6422	2	21	of	of	ADP
ejpam-6422	2	22	mathematics	mathematic	NOUN
ejpam-6422	2	23	,	,	PUNCT
ejpam-6422	2	24	college	college	NOUN
ejpam-6422	2	25	of	of	ADP
ejpam-6422	2	26	science	science	PROPN
ejpam-6422	2	27	al	al	PROPN
ejpam-6422	2	28	-	-	PUNCT
ejpam-6422	2	29	zulfi	zulfi	PROPN
ejpam-6422	2	30	,	,	PUNCT
ejpam-6422	2	31	majmaah	majmaah	PROPN
ejpam-6422	2	32	university	university	PROPN
ejpam-6422	2	33	,	,	PUNCT
ejpam-6422	2	34	al	al	PROPN
ejpam-6422	2	35	-	-	PUNCT
ejpam-6422	2	36	majmaah	majmaah	PROPN
ejpam-6422	2	37	11952	11952	NUM
ejpam-6422	2	38	,	,	PUNCT
ejpam-6422	2	39	saudi	saudi	PROPN
ejpam-6422	2	40	arabia	arabia	PROPN
ejpam-6422	2	41	3	3	NUM
ejpam-6422	2	42	college	college	NOUN
ejpam-6422	2	43	of	of	ADP
ejpam-6422	2	44	engineering	engineering	PROPN
ejpam-6422	2	45	,	,	PUNCT
ejpam-6422	2	46	majmaah	majmaah	PROPN
ejpam-6422	2	47	university	university	PROPN
ejpam-6422	2	48	,	,	PUNCT
ejpam-6422	2	49	al	al	PROPN
ejpam-6422	2	50	-	-	PUNCT
ejpam-6422	2	51	majmaah	majmaah	PROPN
ejpam-6422	2	52	11952	11952	NUM
ejpam-6422	2	53	,	,	PUNCT
ejpam-6422	2	54	saudi	saudi	PROPN
ejpam-6422	2	55	arabia	arabia	PROPN
ejpam-6422	2	56	abstract	abstract	NOUN
ejpam-6422	2	57	.	.	PUNCT
ejpam-6422	3	1	in	in	ADP
ejpam-6422	3	2	this	this	DET
ejpam-6422	3	3	paper	paper	NOUN
ejpam-6422	3	4	,	,	PUNCT
ejpam-6422	3	5	we	we	PRON
ejpam-6422	3	6	consider	consider	VERB
ejpam-6422	3	7	the	the	DET
ejpam-6422	3	8	unidirectional	unidirectional	ADJ
ejpam-6422	3	9	wave	wave	NOUN
ejpam-6422	3	10	model	model	NOUN
ejpam-6422	3	11	(	(	PUNCT
ejpam-6422	3	12	uwm	uwm	PROPN
ejpam-6422	3	13	)	)	PUNCT
ejpam-6422	3	14	with	with	ADP
ejpam-6422	3	15	beta	beta	NOUN
ejpam-6422	3	16	-	-	PUNCT
ejpam-6422	3	17	derivative	derivative	NOUN
ejpam-6422	3	18	operator	operator	NOUN
ejpam-6422	3	19	(	(	PUNCT
ejpam-6422	3	20	bdo	bdo	NOUN
ejpam-6422	3	21	)	)	PUNCT
ejpam-6422	3	22	.	.	PUNCT
ejpam-6422	4	1	this	this	DET
ejpam-6422	4	2	model	model	NOUN
ejpam-6422	4	3	simplifies	simplify	VERB
ejpam-6422	4	4	the	the	DET
ejpam-6422	4	5	complexity	complexity	NOUN
ejpam-6422	4	6	of	of	ADP
ejpam-6422	4	7	wave	wave	NOUN
ejpam-6422	4	8	interactions	interaction	NOUN
ejpam-6422	4	9	by	by	ADP
ejpam-6422	4	10	providing	provide	VERB
ejpam-6422	4	11	a	a	DET
ejpam-6422	4	12	onedimensional	onedimensional	ADJ
ejpam-6422	4	13	approach	approach	NOUN
ejpam-6422	4	14	to	to	ADP
ejpam-6422	4	15	understanding	understand	VERB
ejpam-6422	4	16	wave	wave	NOUN
ejpam-6422	4	17	behavior	behavior	NOUN
ejpam-6422	4	18	,	,	PUNCT
ejpam-6422	4	19	particularly	particularly	ADV
ejpam-6422	4	20	under	under	ADP
ejpam-6422	4	21	conditions	condition	NOUN
ejpam-6422	4	22	where	where	SCONJ
ejpam-6422	4	23	wave	wave	NOUN
ejpam-6422	4	24	directionality	directionality	NOUN
ejpam-6422	4	25	plays	play	VERB
ejpam-6422	4	26	a	a	DET
ejpam-6422	4	27	crucial	crucial	ADJ
ejpam-6422	4	28	role	role	NOUN
ejpam-6422	4	29	.	.	PUNCT
ejpam-6422	5	1	its	its	PRON
ejpam-6422	5	2	applications	application	NOUN
ejpam-6422	5	3	are	be	AUX
ejpam-6422	5	4	vital	vital	ADJ
ejpam-6422	5	5	in	in	ADP
ejpam-6422	5	6	different	different	ADJ
ejpam-6422	5	7	area	area	NOUN
ejpam-6422	5	8	,	,	PUNCT
ejpam-6422	5	9	such	such	ADJ
ejpam-6422	5	10	as	as	ADP
ejpam-6422	5	11	oceanography	oceanography	NOUN
ejpam-6422	5	12	,	,	PUNCT
ejpam-6422	5	13	coastal	coastal	ADJ
ejpam-6422	5	14	engineering	engineering	NOUN
ejpam-6422	5	15	,	,	PUNCT
ejpam-6422	5	16	and	and	CCONJ
ejpam-6422	5	17	environmental	environmental	ADJ
ejpam-6422	5	18	science	science	NOUN
ejpam-6422	5	19	,	,	PUNCT
ejpam-6422	5	20	contributing	contribute	VERB
ejpam-6422	5	21	significantly	significantly	ADV
ejpam-6422	5	22	to	to	ADP
ejpam-6422	5	23	our	our	PRON
ejpam-6422	5	24	understanding	understanding	NOUN
ejpam-6422	5	25	of	of	ADP
ejpam-6422	5	26	wave	wave	NOUN
ejpam-6422	5	27	dynamics	dynamic	NOUN
ejpam-6422	5	28	and	and	CCONJ
ejpam-6422	5	29	their	their	PRON
ejpam-6422	5	30	impact	impact	NOUN
ejpam-6422	5	31	on	on	ADP
ejpam-6422	5	32	coastal	coastal	ADJ
ejpam-6422	5	33	and	and	CCONJ
ejpam-6422	5	34	marine	marine	ADJ
ejpam-6422	5	35	environments	environment	NOUN
ejpam-6422	5	36	.	.	PUNCT
ejpam-6422	6	1	therefore	therefore	ADV
ejpam-6422	6	2	,	,	PUNCT
ejpam-6422	6	3	it	it	PRON
ejpam-6422	6	4	is	be	AUX
ejpam-6422	6	5	crucial	crucial	ADJ
ejpam-6422	6	6	to	to	PART
ejpam-6422	6	7	find	find	VERB
ejpam-6422	6	8	the	the	DET
ejpam-6422	6	9	solutions	solution	NOUN
ejpam-6422	6	10	for	for	ADP
ejpam-6422	6	11	this	this	DET
ejpam-6422	6	12	model	model	NOUN
ejpam-6422	6	13	.	.	PUNCT
ejpam-6422	7	1	by	by	ADP
ejpam-6422	7	2	applying	apply	VERB
ejpam-6422	7	3	the	the	DET
ejpam-6422	7	4	f	f	NOUN
ejpam-6422	7	5	-	-	PUNCT
ejpam-6422	7	6	expansion	expansion	NOUN
ejpam-6422	7	7	method	method	NOUN
ejpam-6422	7	8	,	,	PUNCT
ejpam-6422	7	9	we	we	PRON
ejpam-6422	7	10	can	can	AUX
ejpam-6422	7	11	obtain	obtain	VERB
ejpam-6422	7	12	abundant	abundant	ADJ
ejpam-6422	7	13	solutions	solution	NOUN
ejpam-6422	7	14	including	include	VERB
ejpam-6422	7	15	periodic	periodic	ADJ
ejpam-6422	7	16	,	,	PUNCT
ejpam-6422	7	17	bright	bright	ADJ
ejpam-6422	7	18	,	,	PUNCT
ejpam-6422	7	19	kink	kink	PROPN
ejpam-6422	7	20	,	,	PUNCT
ejpam-6422	7	21	anti	anti	ADJ
ejpam-6422	7	22	-	-	ADJ
ejpam-6422	7	23	kink	kink	ADJ
ejpam-6422	7	24	,	,	PUNCT
ejpam-6422	7	25	singular	singular	NOUN
ejpam-6422	7	26	,	,	PUNCT
ejpam-6422	7	27	and	and	CCONJ
ejpam-6422	7	28	dark	dark	ADJ
ejpam-6422	7	29	-	-	PUNCT
ejpam-6422	7	30	bright	bright	ADJ
ejpam-6422	7	31	solitons	soliton	NOUN
ejpam-6422	7	32	.	.	PUNCT
ejpam-6422	8	1	furthermore	furthermore	ADV
ejpam-6422	8	2	,	,	PUNCT
ejpam-6422	8	3	the	the	DET
ejpam-6422	8	4	graphs	graph	NOUN
ejpam-6422	8	5	of	of	ADP
ejpam-6422	8	6	the	the	DET
ejpam-6422	8	7	solutions	solution	NOUN
ejpam-6422	8	8	are	be	AUX
ejpam-6422	8	9	displayed	display	VERB
ejpam-6422	8	10	using	use	VERB
ejpam-6422	8	11	the	the	DET
ejpam-6422	8	12	matlab	matlab	PROPN
ejpam-6422	8	13	software	software	NOUN
ejpam-6422	8	14	to	to	PART
ejpam-6422	8	15	demonstrate	demonstrate	VERB
ejpam-6422	8	16	how	how	SCONJ
ejpam-6422	8	17	the	the	DET
ejpam-6422	8	18	beta	beta	NOUN
ejpam-6422	8	19	-	-	PUNCT
ejpam-6422	8	20	derivative	derivative	NOUN
ejpam-6422	8	21	operator	operator	NOUN
ejpam-6422	8	22	affects	affect	VERB
ejpam-6422	8	23	the	the	DET
ejpam-6422	8	24	obtained	obtain	VERB
ejpam-6422	8	25	solution	solution	NOUN
ejpam-6422	8	26	.	.	PUNCT
ejpam-6422	9	1	2020	2020	NUM
ejpam-6422	9	2	mathematics	mathematic	NOUN
ejpam-6422	9	3	subject	subject	NOUN
ejpam-6422	9	4	classifications	classification	NOUN
ejpam-6422	9	5	:	:	PUNCT
ejpam-6422	9	6	35q51	35q51	NUM
ejpam-6422	9	7	,	,	PUNCT
ejpam-6422	9	8	35q80	35q80	NUM
ejpam-6422	9	9	key	key	ADJ
ejpam-6422	9	10	words	word	NOUN
ejpam-6422	9	11	and	and	CCONJ
ejpam-6422	9	12	phrases	phrase	NOUN
ejpam-6422	9	13	:	:	PUNCT
ejpam-6422	9	14	beta	beta	NOUN
ejpam-6422	9	15	-	-	PUNCT
ejpam-6422	9	16	derivative	derivative	ADJ
ejpam-6422	9	17	,	,	PUNCT
ejpam-6422	9	18	f	f	X
ejpam-6422	9	19	-	-	PUNCT
ejpam-6422	9	20	expansion	expansion	NOUN
ejpam-6422	9	21	method	method	NOUN
ejpam-6422	9	22	,	,	PUNCT
ejpam-6422	9	23	exact	exact	ADJ
ejpam-6422	9	24	solutions	solution	NOUN
ejpam-6422	9	25	,	,	PUNCT
ejpam-6422	9	26	nonlinear	nonlinear	ADJ
ejpam-6422	9	27	evolution	evolution	NOUN
ejpam-6422	9	28	equations	equation	NOUN
ejpam-6422	9	29	1	1	NUM
ejpam-6422	9	30	.	.	PUNCT
ejpam-6422	10	1	introduction	introduction	NOUN
ejpam-6422	10	2	nonlinear	nonlinear	PROPN
ejpam-6422	10	3	evolution	evolution	PROPN
ejpam-6422	10	4	equations	equation	NOUN
ejpam-6422	10	5	(	(	PUNCT
ejpam-6422	10	6	nlees	nlee	NOUN
ejpam-6422	10	7	)	)	PUNCT
ejpam-6422	10	8	provide	provide	VERB
ejpam-6422	10	9	a	a	DET
ejpam-6422	10	10	powerful	powerful	ADJ
ejpam-6422	10	11	mathematical	mathematical	ADJ
ejpam-6422	10	12	framework	framework	NOUN
ejpam-6422	10	13	for	for	ADP
ejpam-6422	10	14	studying	study	VERB
ejpam-6422	10	15	complex	complex	ADJ
ejpam-6422	10	16	systems	system	NOUN
ejpam-6422	10	17	with	with	ADP
ejpam-6422	10	18	memory	memory	NOUN
ejpam-6422	10	19	effects	effect	NOUN
ejpam-6422	10	20	and	and	CCONJ
ejpam-6422	10	21	non	non	ADJ
ejpam-6422	10	22	-	-	ADJ
ejpam-6422	10	23	linear	linear	ADJ
ejpam-6422	10	24	interactions	interaction	NOUN
ejpam-6422	10	25	,	,	PUNCT
ejpam-6422	10	26	leading	lead	VERB
ejpam-6422	10	27	to	to	ADP
ejpam-6422	10	28	novel	novel	ADJ
ejpam-6422	10	29	insights	insight	NOUN
ejpam-6422	10	30	and	and	CCONJ
ejpam-6422	10	31	applications	application	NOUN
ejpam-6422	10	32	in	in	ADP
ejpam-6422	10	33	engineering	engineering	NOUN
ejpam-6422	10	34	and	and	CCONJ
ejpam-6422	10	35	science	science	NOUN
ejpam-6422	10	36	[	[	X
ejpam-6422	10	37	1–5	1–5	X
ejpam-6422	10	38	]	]	X
ejpam-6422	10	39	.	.	PUNCT
ejpam-6422	11	1	the	the	DET
ejpam-6422	11	2	non	non	ADJ
ejpam-6422	11	3	-	-	ADJ
ejpam-6422	11	4	linear	linear	ADJ
ejpam-6422	11	5	nature	nature	NOUN
ejpam-6422	11	6	of	of	ADP
ejpam-6422	11	7	these	these	DET
ejpam-6422	11	8	equations	equation	NOUN
ejpam-6422	11	9	makes	make	VERB
ejpam-6422	11	10	them	they	PRON
ejpam-6422	11	11	suitable	suitable	ADJ
ejpam-6422	11	12	for	for	ADP
ejpam-6422	11	13	modeling	model	VERB
ejpam-6422	11	14	a	a	DET
ejpam-6422	11	15	wide	wide	ADJ
ejpam-6422	11	16	range	range	NOUN
ejpam-6422	11	17	of	of	ADP
ejpam-6422	11	18	phenomena	phenomenon	NOUN
ejpam-6422	11	19	in	in	ADP
ejpam-6422	11	20	engineering	engineering	NOUN
ejpam-6422	11	21	,	,	PUNCT
ejpam-6422	11	22	biology	biology	NOUN
ejpam-6422	11	23	,	,	PUNCT
ejpam-6422	11	24	chemistry	chemistry	NOUN
ejpam-6422	11	25	,	,	PUNCT
ejpam-6422	11	26	and	and	CCONJ
ejpam-6422	11	27	physics	physics	NOUN
ejpam-6422	11	28	.	.	PUNCT
ejpam-6422	12	1	as	as	ADP
ejpam-6422	12	2	a	a	DET
ejpam-6422	12	3	result	result	NOUN
ejpam-6422	12	4	,	,	PUNCT
ejpam-6422	12	5	it	it	PRON
ejpam-6422	12	6	is	be	AUX
ejpam-6422	12	7	important	important	ADJ
ejpam-6422	12	8	to	to	PART
ejpam-6422	12	9	solve	solve	VERB
ejpam-6422	12	10	these	these	DET
ejpam-6422	12	11	nlees	nlee	NOUN
ejpam-6422	12	12	.	.	PUNCT
ejpam-6422	13	1	recently	recently	ADV
ejpam-6422	13	2	,	,	PUNCT
ejpam-6422	13	3	numerous	numerous	ADJ
ejpam-6422	13	4	powerful	powerful	ADJ
ejpam-6422	13	5	approaches	approach	NOUN
ejpam-6422	13	6	for	for	ADP
ejpam-6422	13	7	discovering	discover	VERB
ejpam-6422	13	8	exact	exact	ADJ
ejpam-6422	13	9	solutions	solution	NOUN
ejpam-6422	13	10	to	to	ADP
ejpam-6422	13	11	∗corresponding	∗corresponde	VERB
ejpam-6422	13	12	author	author	NOUN
ejpam-6422	13	13	.	.	PUNCT
ejpam-6422	14	1	doi	doi	NOUN
ejpam-6422	14	2	:	:	PUNCT
ejpam-6422	14	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6422	https://doi.org/10.29020/nybg.ejpam.v18i3.6422	NOUN
ejpam-6422	14	4	email	email	NOUN
ejpam-6422	14	5	addresses	address	NOUN
ejpam-6422	14	6	:	:	PUNCT
ejpam-6422	14	7	w.mohammed@uoh.edu.sa	w.mohammed@uoh.edu.sa	PROPN
ejpam-6422	14	8	(	(	PUNCT
ejpam-6422	14	9	w.	w.	PROPN
ejpam-6422	14	10	w.	w.	PROPN
ejpam-6422	14	11	mohammed	mohammed	PROPN
ejpam-6422	14	12	)	)	PUNCT
ejpam-6422	14	13	,	,	PUNCT
ejpam-6422	14	14	n.iqbal@uoh.edu.sa	n.iqbal@uoh.edu.sa	PROPN
ejpam-6422	15	1	(	(	PUNCT
ejpam-6422	15	2	n.	n.	PROPN
ejpam-6422	15	3	iqbal	iqbal	PROPN
ejpam-6422	15	4	)	)	PUNCT
ejpam-6422	15	5	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6422	16	1	1	1	NUM
ejpam-6422	16	2	copyright	copyright	NOUN
ejpam-6422	16	3	:	:	PUNCT
ejpam-6422	16	4	©	©	PROPN
ejpam-6422	16	5	2025	2025	NUM
ejpam-6422	16	6	the	the	DET
ejpam-6422	16	7	author(s	author(s	NOUN
ejpam-6422	16	8	)	)	PUNCT
ejpam-6422	16	9	.	.	PUNCT
ejpam-6422	17	1	(	(	PUNCT
ejpam-6422	17	2	cc	cc	NOUN
ejpam-6422	17	3	by	by	ADP
ejpam-6422	17	4	-	-	PUNCT
ejpam-6422	17	5	nc	nc	PROPN
ejpam-6422	17	6	4.0	4.0	NUM
ejpam-6422	17	7	)	)	PUNCT
ejpam-6422	17	8	w.	w.	PROPN
ejpam-6422	17	9	w.	w.	PROPN
ejpam-6422	17	10	mohammed	mohammed	PROPN
ejpam-6422	17	11	et	et	PROPN
ejpam-6422	17	12	al	al	PROPN
ejpam-6422	17	13	.	.	PUNCT
ejpam-6422	17	14	/	/	SYM
ejpam-6422	17	15	eur	eur	PROPN
ejpam-6422	17	16	.	.	PUNCT
ejpam-6422	18	1	j.	j.	PROPN
ejpam-6422	18	2	pure	pure	PROPN
ejpam-6422	18	3	appl	appl	PROPN
ejpam-6422	18	4	.	.	PROPN
ejpam-6422	18	5	math	math	PROPN
ejpam-6422	18	6	,	,	PUNCT
ejpam-6422	18	7	18	18	NUM
ejpam-6422	18	8	(	(	PUNCT
ejpam-6422	18	9	3	3	NUM
ejpam-6422	18	10	)	)	PUNCT
ejpam-6422	18	11	(	(	PUNCT
ejpam-6422	18	12	2025	2025	NUM
ejpam-6422	18	13	)	)	PUNCT
ejpam-6422	18	14	,	,	PUNCT
ejpam-6422	18	15	6422	6422	NUM
ejpam-6422	18	16	2	2	NUM
ejpam-6422	18	17	of	of	ADP
ejpam-6422	18	18	13	13	NUM
ejpam-6422	18	19	nlees	nlee	NOUN
ejpam-6422	18	20	have	have	AUX
ejpam-6422	18	21	been	be	AUX
ejpam-6422	18	22	introduced	introduce	VERB
ejpam-6422	18	23	,	,	PUNCT
ejpam-6422	18	24	such	such	ADJ
ejpam-6422	18	25	as	as	ADP
ejpam-6422	18	26	,	,	PUNCT
ejpam-6422	18	27	sine	sine	ADJ
ejpam-6422	18	28	-	-	PUNCT
ejpam-6422	18	29	gordon	gordon	PROPN
ejpam-6422	18	30	expansion	expansion	NOUN
ejpam-6422	18	31	technique	technique	NOUN
ejpam-6422	18	32	[	[	X
ejpam-6422	18	33	6	6	NUM
ejpam-6422	18	34	]	]	PUNCT
ejpam-6422	18	35	,	,	PUNCT
ejpam-6422	18	36	f	f	X
ejpam-6422	18	37	-	-	PUNCT
ejpam-6422	18	38	expansion	expansion	NOUN
ejpam-6422	18	39	method	method	NOUN
ejpam-6422	18	40	[	[	X
ejpam-6422	18	41	7	7	NUM
ejpam-6422	18	42	]	]	PUNCT
ejpam-6422	18	43	,	,	PUNCT
ejpam-6422	18	44	modified	modify	VERB
ejpam-6422	18	45	extended	extended	ADJ
ejpam-6422	18	46	tanh	tanh	NOUN
ejpam-6422	18	47	-	-	PUNCT
ejpam-6422	18	48	function	function	NOUN
ejpam-6422	18	49	method	method	NOUN
ejpam-6422	18	50	[	[	X
ejpam-6422	18	51	8	8	NUM
ejpam-6422	18	52	]	]	PUNCT
ejpam-6422	18	53	,	,	PUNCT
ejpam-6422	18	54	jacobi	jacobi	PROPN
ejpam-6422	18	55	elliptic	elliptic	ADJ
ejpam-6422	18	56	function	function	NOUN
ejpam-6422	18	57	expansion	expansion	NOUN
ejpam-6422	19	1	[	[	X
ejpam-6422	19	2	9	9	NUM
ejpam-6422	19	3	]	]	PUNCT
ejpam-6422	19	4	,	,	PUNCT
ejpam-6422	19	5	exp	exp	NOUN
ejpam-6422	19	6	-	-	PUNCT
ejpam-6422	19	7	function	function	NOUN
ejpam-6422	19	8	method	method	NOUN
ejpam-6422	19	9	[	[	X
ejpam-6422	19	10	10	10	NUM
ejpam-6422	19	11	]	]	PUNCT
ejpam-6422	19	12	,	,	PUNCT
ejpam-6422	19	13	(	(	PUNCT
ejpam-6422	19	14	g′/g)-expansion	g′/g)-expansion	NOUN
ejpam-6422	20	1	[	[	X
ejpam-6422	20	2	11	11	NUM
ejpam-6422	20	3	,	,	PUNCT
ejpam-6422	20	4	12	12	NUM
ejpam-6422	20	5	]	]	PUNCT
ejpam-6422	20	6	,	,	PUNCT
ejpam-6422	20	7	sine	sine	ADJ
ejpam-6422	20	8	-	-	PUNCT
ejpam-6422	20	9	cosine	cosine	NOUN
ejpam-6422	20	10	method	method	NOUN
ejpam-6422	20	11	[	[	X
ejpam-6422	20	12	13	13	NUM
ejpam-6422	20	13	]	]	PUNCT
ejpam-6422	20	14	,	,	PUNCT
ejpam-6422	20	15	exp(−ϕ(ς))-expansion	exp(−ϕ(ς))-expansion	NOUN
ejpam-6422	20	16	method	method	NOUN
ejpam-6422	20	17	[	[	X
ejpam-6422	20	18	14	14	NUM
ejpam-6422	20	19	]	]	PUNCT
ejpam-6422	20	20	,	,	PUNCT
ejpam-6422	20	21	sumudu	sumudu	NOUN
ejpam-6422	20	22	perturbation	perturbation	NOUN
ejpam-6422	20	23	transform	transform	NOUN
ejpam-6422	20	24	method	method	NOUN
ejpam-6422	20	25	[	[	X
ejpam-6422	20	26	15	15	NUM
ejpam-6422	20	27	]	]	X
ejpam-6422	20	28	,	,	PUNCT
ejpam-6422	20	29	unified	unified	ADJ
ejpam-6422	20	30	riccati	riccati	NOUN
ejpam-6422	20	31	equation	equation	NOUN
ejpam-6422	20	32	expansion	expansion	NOUN
ejpam-6422	20	33	technique	technique	NOUN
ejpam-6422	20	34	[	[	X
ejpam-6422	20	35	16	16	NUM
ejpam-6422	20	36	,	,	PUNCT
ejpam-6422	20	37	17	17	NUM
ejpam-6422	20	38	]	]	PUNCT
ejpam-6422	20	39	and	and	CCONJ
ejpam-6422	20	40	etc	etc	X
ejpam-6422	20	41	.	.	X
ejpam-6422	21	1	one	one	NUM
ejpam-6422	21	2	of	of	ADP
ejpam-6422	21	3	these	these	DET
ejpam-6422	21	4	equations	equation	NOUN
ejpam-6422	21	5	is	be	AUX
ejpam-6422	21	6	the	the	DET
ejpam-6422	21	7	unidirectional	unidirectional	ADJ
ejpam-6422	21	8	wave	wave	NOUN
ejpam-6422	21	9	model	model	NOUN
ejpam-6422	21	10	(	(	PUNCT
ejpam-6422	21	11	uwm	uwm	PROPN
ejpam-6422	21	12	)	)	PUNCT
ejpam-6422	21	13	.	.	PUNCT
ejpam-6422	22	1	uwm	uwm	PROPN
ejpam-6422	22	2	is	be	AUX
ejpam-6422	22	3	an	an	DET
ejpam-6422	22	4	essential	essential	ADJ
ejpam-6422	22	5	tool	tool	NOUN
ejpam-6422	22	6	in	in	ADP
ejpam-6422	22	7	understanding	understanding	NOUN
ejpam-6422	22	8	and	and	CCONJ
ejpam-6422	22	9	predicting	predict	VERB
ejpam-6422	22	10	the	the	DET
ejpam-6422	22	11	behavior	behavior	NOUN
ejpam-6422	22	12	of	of	ADP
ejpam-6422	22	13	waves	wave	NOUN
ejpam-6422	22	14	in	in	ADP
ejpam-6422	22	15	various	various	ADJ
ejpam-6422	22	16	natural	natural	ADJ
ejpam-6422	22	17	phenomena	phenomenon	NOUN
ejpam-6422	22	18	.	.	PUNCT
ejpam-6422	23	1	this	this	DET
ejpam-6422	23	2	model	model	NOUN
ejpam-6422	23	3	simplifies	simplify	VERB
ejpam-6422	23	4	the	the	DET
ejpam-6422	23	5	complex	complex	ADJ
ejpam-6422	23	6	interactions	interaction	NOUN
ejpam-6422	23	7	of	of	ADP
ejpam-6422	23	8	waves	wave	NOUN
ejpam-6422	23	9	by	by	ADP
ejpam-6422	23	10	assuming	assume	VERB
ejpam-6422	23	11	that	that	SCONJ
ejpam-6422	23	12	they	they	PRON
ejpam-6422	23	13	propagate	propagate	VERB
ejpam-6422	23	14	in	in	ADP
ejpam-6422	23	15	only	only	ADV
ejpam-6422	23	16	one	one	NUM
ejpam-6422	23	17	direction	direction	NOUN
ejpam-6422	23	18	,	,	PUNCT
ejpam-6422	23	19	making	make	VERB
ejpam-6422	23	20	it	it	PRON
ejpam-6422	23	21	easier	easy	ADJ
ejpam-6422	23	22	to	to	PART
ejpam-6422	23	23	analyze	analyze	VERB
ejpam-6422	23	24	and	and	CCONJ
ejpam-6422	23	25	interpret	interpret	VERB
ejpam-6422	23	26	wave	wave	NOUN
ejpam-6422	23	27	motion	motion	NOUN
ejpam-6422	23	28	.	.	PUNCT
ejpam-6422	24	1	one	one	NUM
ejpam-6422	24	2	of	of	ADP
ejpam-6422	24	3	the	the	DET
ejpam-6422	24	4	major	major	ADJ
ejpam-6422	24	5	fields	field	NOUN
ejpam-6422	24	6	where	where	SCONJ
ejpam-6422	24	7	the	the	DET
ejpam-6422	24	8	unidirectional	unidirectional	ADJ
ejpam-6422	24	9	wave	wave	NOUN
ejpam-6422	24	10	model	model	NOUN
ejpam-6422	24	11	is	be	AUX
ejpam-6422	24	12	crucial	crucial	ADJ
ejpam-6422	24	13	in	in	ADP
ejpam-6422	24	14	oceanography	oceanography	NOUN
ejpam-6422	24	15	.	.	PUNCT
ejpam-6422	25	1	this	this	DET
ejpam-6422	25	2	model	model	NOUN
ejpam-6422	25	3	helps	help	VERB
ejpam-6422	25	4	scientists	scientist	NOUN
ejpam-6422	25	5	and	and	CCONJ
ejpam-6422	25	6	researchers	researcher	NOUN
ejpam-6422	25	7	in	in	ADP
ejpam-6422	25	8	studying	study	VERB
ejpam-6422	25	9	the	the	DET
ejpam-6422	25	10	dynamics	dynamic	NOUN
ejpam-6422	25	11	of	of	ADP
ejpam-6422	25	12	ocean	ocean	NOUN
ejpam-6422	25	13	waves	wave	NOUN
ejpam-6422	25	14	,	,	PUNCT
ejpam-6422	25	15	including	include	VERB
ejpam-6422	25	16	their	their	PRON
ejpam-6422	25	17	formation	formation	NOUN
ejpam-6422	25	18	,	,	PUNCT
ejpam-6422	25	19	propagation	propagation	NOUN
ejpam-6422	25	20	,	,	PUNCT
ejpam-6422	25	21	and	and	CCONJ
ejpam-6422	25	22	interaction	interaction	NOUN
ejpam-6422	25	23	with	with	ADP
ejpam-6422	25	24	other	other	ADJ
ejpam-6422	25	25	components	component	NOUN
ejpam-6422	25	26	of	of	ADP
ejpam-6422	25	27	the	the	DET
ejpam-6422	25	28	ocean	ocean	NOUN
ejpam-6422	25	29	system	system	NOUN
ejpam-6422	25	30	.	.	PUNCT
ejpam-6422	26	1	by	by	ADP
ejpam-6422	26	2	using	use	VERB
ejpam-6422	26	3	this	this	DET
ejpam-6422	26	4	model	model	NOUN
ejpam-6422	26	5	,	,	PUNCT
ejpam-6422	26	6	oceanographers	oceanographer	NOUN
ejpam-6422	26	7	can	can	AUX
ejpam-6422	26	8	accurately	accurately	ADV
ejpam-6422	26	9	predict	predict	VERB
ejpam-6422	26	10	wave	wave	NOUN
ejpam-6422	26	11	height	height	NOUN
ejpam-6422	26	12	,	,	PUNCT
ejpam-6422	26	13	direction	direction	NOUN
ejpam-6422	26	14	,	,	PUNCT
ejpam-6422	26	15	and	and	CCONJ
ejpam-6422	26	16	speed	speed	NOUN
ejpam-6422	26	17	,	,	PUNCT
ejpam-6422	26	18	which	which	PRON
ejpam-6422	26	19	are	be	AUX
ejpam-6422	26	20	essential	essential	ADJ
ejpam-6422	26	21	for	for	ADP
ejpam-6422	26	22	understanding	understand	VERB
ejpam-6422	26	23	the	the	DET
ejpam-6422	26	24	impact	impact	NOUN
ejpam-6422	26	25	of	of	ADP
ejpam-6422	26	26	waves	wave	NOUN
ejpam-6422	26	27	on	on	ADP
ejpam-6422	26	28	coastal	coastal	ADJ
ejpam-6422	26	29	areas	area	NOUN
ejpam-6422	26	30	,	,	PUNCT
ejpam-6422	26	31	marine	marine	ADJ
ejpam-6422	26	32	ecosystems	ecosystem	NOUN
ejpam-6422	26	33	,	,	PUNCT
ejpam-6422	26	34	and	and	CCONJ
ejpam-6422	26	35	human	human	ADJ
ejpam-6422	26	36	activities	activity	NOUN
ejpam-6422	26	37	at	at	ADP
ejpam-6422	26	38	sea	sea	NOUN
ejpam-6422	26	39	.	.	PUNCT
ejpam-6422	27	1	in	in	ADP
ejpam-6422	27	2	coastal	coastal	ADJ
ejpam-6422	27	3	engineering	engineering	NOUN
ejpam-6422	27	4	,	,	PUNCT
ejpam-6422	27	5	the	the	DET
ejpam-6422	27	6	unidirectional	unidirectional	ADJ
ejpam-6422	27	7	wave	wave	NOUN
ejpam-6422	27	8	model	model	NOUN
ejpam-6422	27	9	plays	play	VERB
ejpam-6422	27	10	a	a	DET
ejpam-6422	27	11	vital	vital	ADJ
ejpam-6422	27	12	role	role	NOUN
ejpam-6422	27	13	in	in	ADP
ejpam-6422	27	14	designing	design	VERB
ejpam-6422	27	15	coastal	coastal	ADJ
ejpam-6422	27	16	structures	structure	NOUN
ejpam-6422	27	17	that	that	PRON
ejpam-6422	27	18	can	can	AUX
ejpam-6422	27	19	withstand	withstand	VERB
ejpam-6422	27	20	the	the	DET
ejpam-6422	27	21	forces	force	NOUN
ejpam-6422	27	22	exerted	exert	VERB
ejpam-6422	27	23	by	by	ADP
ejpam-6422	27	24	waves	wave	NOUN
ejpam-6422	27	25	.	.	PUNCT
ejpam-6422	28	1	engineers	engineer	NOUN
ejpam-6422	28	2	use	use	VERB
ejpam-6422	28	3	this	this	DET
ejpam-6422	28	4	model	model	NOUN
ejpam-6422	28	5	to	to	PART
ejpam-6422	28	6	determine	determine	VERB
ejpam-6422	28	7	the	the	DET
ejpam-6422	28	8	wave	wave	NOUN
ejpam-6422	28	9	conditions	condition	NOUN
ejpam-6422	28	10	at	at	ADP
ejpam-6422	28	11	a	a	DET
ejpam-6422	28	12	given	give	VERB
ejpam-6422	28	13	site	site	NOUN
ejpam-6422	28	14	,	,	PUNCT
ejpam-6422	28	15	which	which	PRON
ejpam-6422	28	16	is	be	AUX
ejpam-6422	28	17	crucial	crucial	ADJ
ejpam-6422	28	18	for	for	ADP
ejpam-6422	28	19	designing	design	VERB
ejpam-6422	28	20	breakwaters	breakwater	NOUN
ejpam-6422	28	21	,	,	PUNCT
ejpam-6422	28	22	seawalls	seawall	NOUN
ejpam-6422	28	23	,	,	PUNCT
ejpam-6422	28	24	and	and	CCONJ
ejpam-6422	28	25	other	other	ADJ
ejpam-6422	28	26	coastal	coastal	ADJ
ejpam-6422	28	27	defenses	defense	NOUN
ejpam-6422	28	28	that	that	PRON
ejpam-6422	28	29	protect	protect	VERB
ejpam-6422	28	30	shorelines	shoreline	NOUN
ejpam-6422	28	31	from	from	ADP
ejpam-6422	28	32	erosion	erosion	NOUN
ejpam-6422	28	33	and	and	CCONJ
ejpam-6422	28	34	damage	damage	NOUN
ejpam-6422	28	35	during	during	ADP
ejpam-6422	28	36	storms	storm	NOUN
ejpam-6422	28	37	.	.	PUNCT
ejpam-6422	29	1	by	by	ADP
ejpam-6422	29	2	employing	employ	VERB
ejpam-6422	29	3	the	the	DET
ejpam-6422	29	4	unidirectional	unidirectional	ADJ
ejpam-6422	29	5	wave	wave	NOUN
ejpam-6422	29	6	model	model	NOUN
ejpam-6422	29	7	,	,	PUNCT
ejpam-6422	29	8	engineers	engineer	NOUN
ejpam-6422	29	9	can	can	AUX
ejpam-6422	29	10	make	make	VERB
ejpam-6422	29	11	informed	informed	ADJ
ejpam-6422	29	12	decisions	decision	NOUN
ejpam-6422	29	13	about	about	ADP
ejpam-6422	29	14	the	the	DET
ejpam-6422	29	15	size	size	NOUN
ejpam-6422	29	16	,	,	PUNCT
ejpam-6422	29	17	shape	shape	NOUN
ejpam-6422	29	18	,	,	PUNCT
ejpam-6422	29	19	and	and	CCONJ
ejpam-6422	29	20	placement	placement	NOUN
ejpam-6422	29	21	of	of	ADP
ejpam-6422	29	22	coastal	coastal	ADJ
ejpam-6422	29	23	structures	structure	NOUN
ejpam-6422	29	24	,	,	PUNCT
ejpam-6422	29	25	ensuring	ensure	VERB
ejpam-6422	29	26	their	their	PRON
ejpam-6422	29	27	effectiveness	effectiveness	NOUN
ejpam-6422	29	28	in	in	ADP
ejpam-6422	29	29	minimizing	minimize	VERB
ejpam-6422	29	30	wave	wave	NOUN
ejpam-6422	29	31	impact	impact	NOUN
ejpam-6422	29	32	.	.	PUNCT
ejpam-6422	30	1	meteorologists	meteorologist	NOUN
ejpam-6422	30	2	also	also	ADV
ejpam-6422	30	3	rely	rely	VERB
ejpam-6422	30	4	on	on	ADP
ejpam-6422	30	5	the	the	DET
ejpam-6422	30	6	unidirectional	unidirectional	ADJ
ejpam-6422	30	7	wave	wave	NOUN
ejpam-6422	30	8	model	model	NOUN
ejpam-6422	30	9	to	to	PART
ejpam-6422	30	10	forecast	forecast	VERB
ejpam-6422	30	11	and	and	CCONJ
ejpam-6422	30	12	track	track	VERB
ejpam-6422	30	13	ocean	ocean	NOUN
ejpam-6422	30	14	waves	wave	NOUN
ejpam-6422	30	15	and	and	CCONJ
ejpam-6422	30	16	their	their	PRON
ejpam-6422	30	17	effects	effect	NOUN
ejpam-6422	30	18	on	on	ADP
ejpam-6422	30	19	weather	weather	NOUN
ejpam-6422	30	20	patterns	pattern	NOUN
ejpam-6422	30	21	.	.	PUNCT
ejpam-6422	31	1	by	by	ADP
ejpam-6422	31	2	incorporating	incorporate	VERB
ejpam-6422	31	3	wave	wave	NOUN
ejpam-6422	31	4	data	datum	NOUN
ejpam-6422	31	5	into	into	ADP
ejpam-6422	31	6	their	their	PRON
ejpam-6422	31	7	models	model	NOUN
ejpam-6422	31	8	,	,	PUNCT
ejpam-6422	31	9	meteorologists	meteorologist	NOUN
ejpam-6422	31	10	can	can	AUX
ejpam-6422	31	11	better	well	ADV
ejpam-6422	31	12	predict	predict	VERB
ejpam-6422	31	13	the	the	DET
ejpam-6422	31	14	intensity	intensity	NOUN
ejpam-6422	31	15	and	and	CCONJ
ejpam-6422	31	16	path	path	NOUN
ejpam-6422	31	17	of	of	ADP
ejpam-6422	31	18	storms	storm	NOUN
ejpam-6422	31	19	,	,	PUNCT
ejpam-6422	31	20	hurricanes	hurricane	NOUN
ejpam-6422	31	21	,	,	PUNCT
ejpam-6422	31	22	and	and	CCONJ
ejpam-6422	31	23	other	other	ADJ
ejpam-6422	31	24	extreme	extreme	ADJ
ejpam-6422	31	25	weather	weather	NOUN
ejpam-6422	31	26	events	event	NOUN
ejpam-6422	31	27	that	that	PRON
ejpam-6422	31	28	are	be	AUX
ejpam-6422	31	29	fueled	fuel	VERB
ejpam-6422	31	30	by	by	ADP
ejpam-6422	31	31	ocean	ocean	NOUN
ejpam-6422	31	32	waves	wave	NOUN
ejpam-6422	31	33	.	.	PUNCT
ejpam-6422	32	1	this	this	DET
ejpam-6422	32	2	information	information	NOUN
ejpam-6422	32	3	is	be	AUX
ejpam-6422	32	4	essential	essential	ADJ
ejpam-6422	32	5	for	for	ADP
ejpam-6422	32	6	issuing	issue	VERB
ejpam-6422	32	7	timely	timely	ADJ
ejpam-6422	32	8	warnings	warning	NOUN
ejpam-6422	32	9	and	and	CCONJ
ejpam-6422	32	10	alerts	alert	NOUN
ejpam-6422	32	11	to	to	ADP
ejpam-6422	32	12	coastal	coastal	ADJ
ejpam-6422	32	13	communities	community	NOUN
ejpam-6422	32	14	,	,	PUNCT
ejpam-6422	32	15	helping	help	VERB
ejpam-6422	32	16	to	to	PART
ejpam-6422	32	17	mitigate	mitigate	VERB
ejpam-6422	32	18	the	the	DET
ejpam-6422	32	19	potential	potential	ADJ
ejpam-6422	32	20	damage	damage	NOUN
ejpam-6422	32	21	and	and	CCONJ
ejpam-6422	32	22	loss	loss	NOUN
ejpam-6422	32	23	of	of	ADP
ejpam-6422	32	24	life	life	NOUN
ejpam-6422	32	25	caused	cause	VERB
ejpam-6422	32	26	by	by	ADP
ejpam-6422	32	27	these	these	DET
ejpam-6422	32	28	natural	natural	ADJ
ejpam-6422	32	29	disasters	disaster	NOUN
ejpam-6422	32	30	.	.	PUNCT
ejpam-6422	33	1	the	the	DET
ejpam-6422	33	2	uwm	uwm	PROPN
ejpam-6422	33	3	with	with	ADP
ejpam-6422	33	4	beta	beta	NOUN
ejpam-6422	33	5	-	-	PUNCT
ejpam-6422	33	6	derivative	derivative	NOUN
ejpam-6422	33	7	operator	operator	NOUN
ejpam-6422	33	8	(	(	PUNCT
ejpam-6422	33	9	uwm	uwm	NOUN
ejpam-6422	33	10	-	-	PUNCT
ejpam-6422	33	11	bdo	bdo	NOUN
ejpam-6422	33	12	)	)	PUNCT
ejpam-6422	33	13	takes	take	VERB
ejpam-6422	33	14	the	the	DET
ejpam-6422	33	15	following	follow	VERB
ejpam-6422	33	16	form	form	NOUN
ejpam-6422	33	17	[	[	X
ejpam-6422	33	18	18	18	NUM
ejpam-6422	33	19	]	]	X
ejpam-6422	33	20	:	:	PUNCT
ejpam-6422	33	21	dκ	dκ	PROPN
ejpam-6422	33	22	t	t	PROPN
ejpam-6422	33	23	w	w	PROPN
ejpam-6422	34	1	+	+	NUM
ejpam-6422	34	2	1	1	NUM
ejpam-6422	34	3	6	6	NUM
ejpam-6422	34	4	a1wxxx	a1wxxx	NOUN
ejpam-6422	34	5	+	+	CCONJ
ejpam-6422	34	6	3	3	NUM
ejpam-6422	34	7	2	2	NUM
ejpam-6422	34	8	a2wwx	a2wwx	NOUN
ejpam-6422	34	9	+	+	CCONJ
ejpam-6422	34	10	15	15	NUM
ejpam-6422	34	11	32	32	NUM
ejpam-6422	34	12	a22w2wx	a22w2wx	NOUN
ejpam-6422	34	13	+	+	CCONJ
ejpam-6422	34	14	a3wx	a3wx	NOUN
ejpam-6422	34	15	+	+	CCONJ
ejpam-6422	34	16	a4wy	a4wy	SYM
ejpam-6422	34	17	+	+	CCONJ
ejpam-6422	34	18	a5wz	a5wz	NUM
ejpam-6422	34	19	=	=	SYM
ejpam-6422	34	20	0	0	NUM
ejpam-6422	34	21	,	,	PUNCT
ejpam-6422	34	22	(	(	PUNCT
ejpam-6422	34	23	1	1	X
ejpam-6422	34	24	)	)	PUNCT
ejpam-6422	34	25	where	where	SCONJ
ejpam-6422	34	26	w	w	NOUN
ejpam-6422	34	27	=	=	SYM
ejpam-6422	34	28	w(x	w(x	PROPN
ejpam-6422	34	29	,	,	PUNCT
ejpam-6422	34	30	y	y	PROPN
ejpam-6422	34	31	,	,	PUNCT
ejpam-6422	34	32	z	z	PROPN
ejpam-6422	34	33	,	,	PUNCT
ejpam-6422	34	34	t	t	PROPN
ejpam-6422	34	35	)	)	PUNCT
ejpam-6422	34	36	presents	present	VERB
ejpam-6422	34	37	a	a	DET
ejpam-6422	34	38	wave	wave	NOUN
ejpam-6422	34	39	profile	profile	NOUN
ejpam-6422	34	40	;	;	PUNCT
ejpam-6422	34	41	a1	a1	NOUN
ejpam-6422	34	42	,	,	PUNCT
ejpam-6422	34	43	a2	a2	PROPN
ejpam-6422	34	44	,	,	PUNCT
ejpam-6422	34	45	a3	a3	NOUN
ejpam-6422	34	46	,	,	PUNCT
ejpam-6422	34	47	a4	a4	NOUN
ejpam-6422	34	48	and	and	CCONJ
ejpam-6422	34	49	a5	a5	PROPN
ejpam-6422	34	50	are	be	AUX
ejpam-6422	34	51	constants	constant	NOUN
ejpam-6422	34	52	.	.	PUNCT
ejpam-6422	35	1	dκ	dκ	PROPN
ejpam-6422	35	2	is	be	AUX
ejpam-6422	35	3	the	the	DET
ejpam-6422	35	4	beta	beta	NOUN
ejpam-6422	35	5	-	-	PUNCT
ejpam-6422	35	6	derivative	derivative	NOUN
ejpam-6422	35	7	operator	operator	NOUN
ejpam-6422	35	8	(	(	PUNCT
ejpam-6422	35	9	bdo	bdo	NOUN
ejpam-6422	35	10	)	)	PUNCT
ejpam-6422	35	11	of	of	ADP
ejpam-6422	35	12	order	order	NOUN
ejpam-6422	35	13	κ	κ	NOUN
ejpam-6422	35	14	.	.	PUNCT
ejpam-6422	36	1	the	the	DET
ejpam-6422	36	2	bdo	bdo	NOUN
ejpam-6422	36	3	is	be	AUX
ejpam-6422	36	4	a	a	DET
ejpam-6422	36	5	novel	novel	ADJ
ejpam-6422	36	6	conformable	conformable	ADJ
ejpam-6422	36	7	fractional	fractional	ADJ
ejpam-6422	36	8	derivative	derivative	NOUN
ejpam-6422	36	9	that	that	PRON
ejpam-6422	36	10	was	be	AUX
ejpam-6422	36	11	recently	recently	ADV
ejpam-6422	36	12	proposed	propose	VERB
ejpam-6422	36	13	by	by	ADP
ejpam-6422	36	14	atangana	atangana	PROPN
ejpam-6422	36	15	et	et	PROPN
ejpam-6422	36	16	al	al	PROPN
ejpam-6422	37	1	[	[	X
ejpam-6422	37	2	19	19	NUM
ejpam-6422	37	3	]	]	PUNCT
ejpam-6422	37	4	.	.	PUNCT
ejpam-6422	38	1	now	now	ADV
ejpam-6422	38	2	,	,	PUNCT
ejpam-6422	38	3	let	let	VERB
ejpam-6422	38	4	us	we	PRON
ejpam-6422	38	5	bdo	bdo	VERB
ejpam-6422	38	6	of	of	ADP
ejpam-6422	38	7	order	order	NOUN
ejpam-6422	38	8	κ	κ	X
ejpam-6422	38	9	∈	∈	PROPN
ejpam-6422	38	10	(	(	PUNCT
ejpam-6422	38	11	0	0	NUM
ejpam-6422	38	12	,	,	PUNCT
ejpam-6422	38	13	1	1	NUM
ejpam-6422	38	14	]	]	PUNCT
ejpam-6422	38	15	for	for	ADP
ejpam-6422	38	16	the	the	DET
ejpam-6422	38	17	function	function	NOUN
ejpam-6422	38	18	w	w	PROPN
ejpam-6422	38	19	:	:	PUNCT
ejpam-6422	38	20	(	(	PUNCT
ejpam-6422	38	21	0,∞	0,∞	NOUN
ejpam-6422	38	22	)	)	PUNCT
ejpam-6422	39	1	→	→	SYM
ejpam-6422	39	2	r	r	NOUN
ejpam-6422	39	3	as	as	SCONJ
ejpam-6422	39	4	follows	follow	VERB
ejpam-6422	39	5	:	:	PUNCT
ejpam-6422	39	6	dκ	dκ	PROPN
ejpam-6422	39	7	t	t	PROPN
ejpam-6422	39	8	w(t	w(t	PROPN
ejpam-6422	39	9	)	)	PUNCT
ejpam-6422	40	1	=	=	VERB
ejpam-6422	40	2	lim	lim	PROPN
ejpam-6422	40	3	ϵ→0	ϵ→0	X
ejpam-6422	41	1	w(t+	w(t+	VERB
ejpam-6422	41	2	ϵ(t+	ϵ(t+	ADJ
ejpam-6422	41	3	1	1	NUM
ejpam-6422	41	4	γ(β	γ(β	PROPN
ejpam-6422	41	5	)	)	PUNCT
ejpam-6422	41	6	)	)	PUNCT
ejpam-6422	41	7	1−β)−w(t	1−β)−w(t	NUM
ejpam-6422	41	8	)	)	PUNCT
ejpam-6422	41	9	ϵ	ϵ	X
ejpam-6422	41	10	.	.	PUNCT
ejpam-6422	42	1	for	for	ADP
ejpam-6422	42	2	any	any	DET
ejpam-6422	42	3	constants	constant	NOUN
ejpam-6422	42	4	c1	c1	PROPN
ejpam-6422	42	5	and	and	CCONJ
ejpam-6422	42	6	c2	c2	PROPN
ejpam-6422	42	7	,	,	PUNCT
ejpam-6422	42	8	the	the	DET
ejpam-6422	42	9	bdomeets	bdomeet	NOUN
ejpam-6422	42	10	the	the	DET
ejpam-6422	42	11	following	following	ADJ
ejpam-6422	42	12	characteristics	characteristic	NOUN
ejpam-6422	42	13	[	[	X
ejpam-6422	42	14	19	19	NUM
ejpam-6422	42	15	]	]	X
ejpam-6422	42	16	:	:	PUNCT
ejpam-6422	42	17	(	(	PUNCT
ejpam-6422	42	18	1)dκ	1)dκ	PROPN
ejpam-6422	42	19	t	t	X
ejpam-6422	42	20	[	[	X
ejpam-6422	42	21	c1u(t)+	c1u(t)+	PROPN
ejpam-6422	42	22	c2v(t	c2v(t	PROPN
ejpam-6422	42	23	)	)	PUNCT
ejpam-6422	42	24	]	]	PUNCT
ejpam-6422	43	1	=	=	SYM
ejpam-6422	43	2	c1dκ	c1dκ	PROPN
ejpam-6422	43	3	t	t	PROPN
ejpam-6422	43	4	u(t)+c2dκ	u(t)+c2dκ	PROPN
ejpam-6422	43	5	t	t	PROPN
ejpam-6422	43	6	v(t	v(t	PROPN
ejpam-6422	43	7	)	)	PUNCT
ejpam-6422	43	8	,	,	PUNCT
ejpam-6422	43	9	(	(	PUNCT
ejpam-6422	43	10	2)dκ	2)dκ	PROPN
ejpam-6422	43	11	t	t	PROPN
ejpam-6422	43	12	[	[	X
ejpam-6422	43	13	c1	c1	NOUN
ejpam-6422	43	14	]	]	X
ejpam-6422	43	15	=	=	SYM
ejpam-6422	43	16	0	0	NUM
ejpam-6422	43	17	,	,	PUNCT
ejpam-6422	43	18	(	(	PUNCT
ejpam-6422	43	19	3)dκ	3)dκ	PROPN
ejpam-6422	43	20	t	t	NOUN
ejpam-6422	43	21	u(t	u(t	PROPN
ejpam-6422	43	22	)	)	PUNCT
ejpam-6422	43	23	=	=	SYM
ejpam-6422	43	24	(	(	PUNCT
ejpam-6422	43	25	t+	t+	X
ejpam-6422	43	26	1	1	NUM
ejpam-6422	43	27	γ(κ	γ(κ	PROPN
ejpam-6422	43	28	)	)	PUNCT
ejpam-6422	43	29	)	)	PUNCT
ejpam-6422	44	1	1−κ	1−κ	NUM
ejpam-6422	44	2	du	du	PROPN
ejpam-6422	44	3	dt	dt	NOUN
ejpam-6422	44	4	,	,	PUNCT
ejpam-6422	44	5	(	(	PUNCT
ejpam-6422	44	6	4)d	4)d	NOUN
ejpam-6422	44	7	κ	κ	X
ejpam-6422	44	8	t	t	PROPN
ejpam-6422	44	9	u(v(t	u(v(t	PROPN
ejpam-6422	44	10	)	)	PUNCT
ejpam-6422	44	11	)	)	PUNCT
ejpam-6422	45	1	=	=	PUNCT
ejpam-6422	45	2	(	(	PUNCT
ejpam-6422	45	3	t+	t+	X
ejpam-6422	45	4	1	1	NUM
ejpam-6422	45	5	γ(κ	γ(κ	PROPN
ejpam-6422	45	6	)	)	PUNCT
ejpam-6422	45	7	)	)	PUNCT
ejpam-6422	45	8	1−κv′(t)u′(v(t	1−κv′(t)u′(v(t	NUM
ejpam-6422	45	9	)	)	PUNCT
ejpam-6422	45	10	)	)	PUNCT
ejpam-6422	46	1	(	(	PUNCT
ejpam-6422	46	2	5	5	X
ejpam-6422	46	3	)	)	PUNCT
ejpam-6422	46	4	if	if	SCONJ
ejpam-6422	46	5	θ	θ	PROPN
ejpam-6422	46	6	=	=	SYM
ejpam-6422	46	7	c1	c1	PROPN
ejpam-6422	46	8	κ	κ	PROPN
ejpam-6422	46	9	(	(	PUNCT
ejpam-6422	46	10	t+	t+	NOUN
ejpam-6422	46	11	1	1	NUM
ejpam-6422	46	12	γ(κ	γ(κ	PROPN
ejpam-6422	46	13	)	)	PUNCT
ejpam-6422	46	14	)	)	PUNCT
ejpam-6422	46	15	κ	κ	NOUN
ejpam-6422	46	16	,	,	PUNCT
ejpam-6422	46	17	then	then	ADV
ejpam-6422	46	18	dκ	dκ	PROPN
ejpam-6422	46	19	t	t	PROPN
ejpam-6422	46	20	u(t	u(t	PROPN
ejpam-6422	46	21	)	)	PUNCT
ejpam-6422	46	22	=	=	SYM
ejpam-6422	46	23	c1	c1	PROPN
ejpam-6422	46	24	du	du	PROPN
ejpam-6422	46	25	dt	dt	PROPN
ejpam-6422	46	26	.	.	PUNCT
ejpam-6422	47	1	w.	w.	PROPN
ejpam-6422	47	2	w.	w.	PROPN
ejpam-6422	47	3	mohammed	mohammed	PROPN
ejpam-6422	47	4	et	et	PROPN
ejpam-6422	47	5	al	al	PROPN
ejpam-6422	47	6	.	.	PUNCT
ejpam-6422	47	7	/	/	SYM
ejpam-6422	47	8	eur	eur	PROPN
ejpam-6422	47	9	.	.	PUNCT
ejpam-6422	48	1	j.	j.	PROPN
ejpam-6422	48	2	pure	pure	PROPN
ejpam-6422	48	3	appl	appl	PROPN
ejpam-6422	48	4	.	.	PROPN
ejpam-6422	48	5	math	math	PROPN
ejpam-6422	48	6	,	,	PUNCT
ejpam-6422	48	7	18	18	NUM
ejpam-6422	48	8	(	(	PUNCT
ejpam-6422	48	9	3	3	NUM
ejpam-6422	48	10	)	)	PUNCT
ejpam-6422	48	11	(	(	PUNCT
ejpam-6422	48	12	2025	2025	NUM
ejpam-6422	48	13	)	)	PUNCT
ejpam-6422	48	14	,	,	PUNCT
ejpam-6422	48	15	6422	6422	NUM
ejpam-6422	48	16	3	3	NUM
ejpam-6422	48	17	of	of	ADP
ejpam-6422	48	18	13	13	NUM
ejpam-6422	48	19	the	the	DET
ejpam-6422	48	20	main	main	ADJ
ejpam-6422	48	21	contribution	contribution	NOUN
ejpam-6422	48	22	of	of	ADP
ejpam-6422	48	23	this	this	DET
ejpam-6422	48	24	work	work	NOUN
ejpam-6422	48	25	is	be	AUX
ejpam-6422	48	26	to	to	PART
ejpam-6422	48	27	acquire	acquire	VERB
ejpam-6422	48	28	the	the	DET
ejpam-6422	48	29	exact	exact	ADJ
ejpam-6422	48	30	solutions	solution	NOUN
ejpam-6422	48	31	to	to	ADP
ejpam-6422	48	32	the	the	DET
ejpam-6422	48	33	uwm	uwm	NOUN
ejpam-6422	48	34	-	-	PUNCT
ejpam-6422	48	35	bdo	bdo	NOUN
ejpam-6422	48	36	(	(	PUNCT
ejpam-6422	48	37	1	1	NUM
ejpam-6422	48	38	)	)	PUNCT
ejpam-6422	48	39	.	.	PUNCT
ejpam-6422	49	1	the	the	DET
ejpam-6422	49	2	f	f	NOUN
ejpam-6422	49	3	-	-	PUNCT
ejpam-6422	49	4	expansion	expansion	NOUN
ejpam-6422	49	5	method	method	NOUN
ejpam-6422	49	6	is	be	AUX
ejpam-6422	49	7	used	use	VERB
ejpam-6422	49	8	to	to	PART
ejpam-6422	49	9	create	create	VERB
ejpam-6422	49	10	fractional	fractional	ADJ
ejpam-6422	49	11	solutions	solution	NOUN
ejpam-6422	49	12	in	in	ADP
ejpam-6422	49	13	the	the	DET
ejpam-6422	49	14	form	form	NOUN
ejpam-6422	49	15	of	of	ADP
ejpam-6422	49	16	elliptic	elliptic	ADJ
ejpam-6422	49	17	,	,	PUNCT
ejpam-6422	49	18	trigonometric	trigonometric	ADJ
ejpam-6422	49	19	and	and	CCONJ
ejpam-6422	49	20	hyperbolic	hyperbolic	ADJ
ejpam-6422	49	21	functions	function	NOUN
ejpam-6422	49	22	.	.	PUNCT
ejpam-6422	50	1	numerous	numerous	ADJ
ejpam-6422	50	2	important	important	ADJ
ejpam-6422	50	3	scientific	scientific	ADJ
ejpam-6422	50	4	phenomena	phenomenon	NOUN
ejpam-6422	50	5	may	may	AUX
ejpam-6422	50	6	be	be	AUX
ejpam-6422	50	7	investigated	investigate	VERB
ejpam-6422	50	8	using	use	VERB
ejpam-6422	50	9	the	the	DET
ejpam-6422	50	10	achieved	achieve	VERB
ejpam-6422	50	11	solutions	solution	NOUN
ejpam-6422	50	12	of	of	ADP
ejpam-6422	50	13	the	the	DET
ejpam-6422	50	14	uwm	uwm	NOUN
ejpam-6422	50	15	-	-	PUNCT
ejpam-6422	50	16	bdo	bdo	NOUN
ejpam-6422	50	17	(	(	PUNCT
ejpam-6422	50	18	1	1	NUM
ejpam-6422	50	19	)	)	PUNCT
ejpam-6422	50	20	because	because	SCONJ
ejpam-6422	50	21	this	this	DET
ejpam-6422	50	22	equation	equation	NOUN
ejpam-6422	50	23	has	have	VERB
ejpam-6422	50	24	a	a	DET
ejpam-6422	50	25	significant	significant	ADJ
ejpam-6422	50	26	applications	application	NOUN
ejpam-6422	50	27	in	in	ADP
ejpam-6422	50	28	various	various	ADJ
ejpam-6422	50	29	fields	field	NOUN
ejpam-6422	50	30	such	such	ADJ
ejpam-6422	50	31	as	as	ADP
ejpam-6422	50	32	oceanography	oceanography	NOUN
ejpam-6422	50	33	,	,	PUNCT
ejpam-6422	50	34	coastal	coastal	ADJ
ejpam-6422	50	35	engineering	engineering	NOUN
ejpam-6422	50	36	,	,	PUNCT
ejpam-6422	50	37	and	and	CCONJ
ejpam-6422	50	38	meteorology	meteorology	NOUN
ejpam-6422	50	39	.	.	PUNCT
ejpam-6422	51	1	to	to	PART
ejpam-6422	51	2	analyze	analyze	VERB
ejpam-6422	51	3	the	the	DET
ejpam-6422	51	4	impact	impact	NOUN
ejpam-6422	51	5	of	of	ADP
ejpam-6422	51	6	the	the	DET
ejpam-6422	51	7	bdo	bdo	NOUN
ejpam-6422	51	8	on	on	ADP
ejpam-6422	51	9	the	the	DET
ejpam-6422	51	10	solutions	solution	NOUN
ejpam-6422	51	11	of	of	ADP
ejpam-6422	51	12	uwm	uwm	NOUN
ejpam-6422	51	13	-	-	PUNCT
ejpam-6422	51	14	bdo	bdo	NOUN
ejpam-6422	51	15	(	(	PUNCT
ejpam-6422	51	16	1	1	NUM
ejpam-6422	51	17	)	)	PUNCT
ejpam-6422	51	18	,	,	PUNCT
ejpam-6422	51	19	many	many	ADJ
ejpam-6422	51	20	graphs	graph	NOUN
ejpam-6422	51	21	are	be	AUX
ejpam-6422	51	22	created	create	VERB
ejpam-6422	51	23	with	with	ADP
ejpam-6422	51	24	the	the	DET
ejpam-6422	51	25	matlab	matlab	PROPN
ejpam-6422	51	26	program	program	NOUN
ejpam-6422	51	27	.	.	PUNCT
ejpam-6422	52	1	the	the	DET
ejpam-6422	52	2	following	follow	VERB
ejpam-6422	52	3	is	be	AUX
ejpam-6422	52	4	an	an	DET
ejpam-6422	52	5	outline	outline	NOUN
ejpam-6422	52	6	of	of	ADP
ejpam-6422	52	7	the	the	DET
ejpam-6422	52	8	paper	paper	NOUN
ejpam-6422	52	9	:	:	PUNCT
ejpam-6422	52	10	we	we	PRON
ejpam-6422	52	11	obtain	obtain	VERB
ejpam-6422	52	12	the	the	DET
ejpam-6422	52	13	wave	wave	NOUN
ejpam-6422	52	14	equation	equation	NOUN
ejpam-6422	52	15	for	for	ADP
ejpam-6422	52	16	eq	eq	PROPN
ejpam-6422	52	17	.	.	PUNCT
ejpam-6422	53	1	(	(	PUNCT
ejpam-6422	53	2	1	1	X
ejpam-6422	53	3	)	)	PUNCT
ejpam-6422	53	4	in	in	ADP
ejpam-6422	53	5	section	section	NOUN
ejpam-6422	53	6	2	2	NUM
ejpam-6422	53	7	.	.	PUNCT
ejpam-6422	54	1	the	the	DET
ejpam-6422	54	2	solutions	solution	NOUN
ejpam-6422	54	3	of	of	ADP
ejpam-6422	54	4	uwm	uwm	NOUN
ejpam-6422	54	5	-	-	PUNCT
ejpam-6422	54	6	bdo	bdo	NOUN
ejpam-6422	54	7	(	(	PUNCT
ejpam-6422	54	8	1	1	NUM
ejpam-6422	54	9	)	)	PUNCT
ejpam-6422	54	10	are	be	AUX
ejpam-6422	54	11	obtained	obtain	VERB
ejpam-6422	54	12	in	in	ADP
ejpam-6422	54	13	section	section	NOUN
ejpam-6422	54	14	3	3	NUM
ejpam-6422	54	15	.	.	PUNCT
ejpam-6422	55	1	in	in	ADP
ejpam-6422	55	2	section	section	NOUN
ejpam-6422	55	3	4	4	NUM
ejpam-6422	55	4	,	,	PUNCT
ejpam-6422	55	5	we	we	PRON
ejpam-6422	55	6	discuss	discuss	VERB
ejpam-6422	55	7	the	the	DET
ejpam-6422	55	8	influence	influence	NOUN
ejpam-6422	55	9	of	of	ADP
ejpam-6422	55	10	bdo	bdo	NOUN
ejpam-6422	55	11	on	on	ADP
ejpam-6422	55	12	the	the	DET
ejpam-6422	55	13	solutions	solution	NOUN
ejpam-6422	55	14	of	of	ADP
ejpam-6422	55	15	(	(	PUNCT
ejpam-6422	55	16	1	1	NUM
ejpam-6422	55	17	)	)	PUNCT
ejpam-6422	55	18	.	.	PUNCT
ejpam-6422	56	1	finally	finally	ADV
ejpam-6422	56	2	,	,	PUNCT
ejpam-6422	56	3	the	the	DET
ejpam-6422	56	4	conclusion	conclusion	NOUN
ejpam-6422	56	5	of	of	ADP
ejpam-6422	56	6	the	the	DET
ejpam-6422	56	7	study	study	NOUN
ejpam-6422	56	8	is	be	AUX
ejpam-6422	56	9	stated	state	VERB
ejpam-6422	56	10	.	.	PUNCT
ejpam-6422	57	1	2	2	X
ejpam-6422	57	2	.	.	X
ejpam-6422	57	3	traveling	travel	VERB
ejpam-6422	57	4	wave	wave	NOUN
ejpam-6422	57	5	equation	equation	NOUN
ejpam-6422	57	6	to	to	PART
ejpam-6422	57	7	get	get	VERB
ejpam-6422	57	8	the	the	DET
ejpam-6422	57	9	wave	wave	NOUN
ejpam-6422	57	10	equation	equation	NOUN
ejpam-6422	57	11	for	for	ADP
ejpam-6422	57	12	uwm	uwm	NOUN
ejpam-6422	57	13	-	-	PUNCT
ejpam-6422	57	14	bdo	bdo	NOUN
ejpam-6422	57	15	(	(	PUNCT
ejpam-6422	57	16	1	1	NUM
ejpam-6422	57	17	)	)	PUNCT
ejpam-6422	57	18	,	,	PUNCT
ejpam-6422	57	19	we	we	PRON
ejpam-6422	57	20	apply	apply	VERB
ejpam-6422	57	21	w(x	w(x	PROPN
ejpam-6422	57	22	,	,	PUNCT
ejpam-6422	57	23	y	y	PROPN
ejpam-6422	57	24	,	,	PUNCT
ejpam-6422	57	25	z	z	PROPN
ejpam-6422	57	26	,	,	PUNCT
ejpam-6422	57	27	t	t	PROPN
ejpam-6422	57	28	)	)	PUNCT
ejpam-6422	57	29	=	=	SYM
ejpam-6422	57	30	v(ρ	v(ρ	NOUN
ejpam-6422	57	31	)	)	PUNCT
ejpam-6422	57	32	,	,	PUNCT
ejpam-6422	57	33	ρ	ρ	PROPN
ejpam-6422	57	34	=	=	SYM
ejpam-6422	57	35	ρ1x+	ρ1x+	NOUN
ejpam-6422	57	36	ρ2y	ρ2y	PROPN
ejpam-6422	58	1	+	+	PUNCT
ejpam-6422	59	1	ρ3z	ρ3z	NOUN
ejpam-6422	59	2	+	+	NOUN
ejpam-6422	59	3	λ	λ	X
ejpam-6422	59	4	κ	κ	X
ejpam-6422	59	5	(	(	PUNCT
ejpam-6422	59	6	t+	t+	NOUN
ejpam-6422	59	7	1	1	NUM
ejpam-6422	59	8	γ(κ	γ(κ	PROPN
ejpam-6422	59	9	)	)	PUNCT
ejpam-6422	59	10	)	)	PUNCT
ejpam-6422	60	1	κ	κ	NOUN
ejpam-6422	60	2	,	,	PUNCT
ejpam-6422	60	3	(	(	PUNCT
ejpam-6422	60	4	2	2	X
ejpam-6422	60	5	)	)	PUNCT
ejpam-6422	60	6	where	where	SCONJ
ejpam-6422	60	7	ρ1	ρ1	NOUN
ejpam-6422	60	8	,	,	PUNCT
ejpam-6422	60	9	ρ2	ρ2	NOUN
ejpam-6422	60	10	,	,	PUNCT
ejpam-6422	60	11	ρ3	ρ3	NOUN
ejpam-6422	60	12	are	be	AUX
ejpam-6422	60	13	non	non	ADJ
ejpam-6422	60	14	-	-	ADJ
ejpam-6422	60	15	zero	zero	NUM
ejpam-6422	60	16	constants	constant	NOUN
ejpam-6422	60	17	and	and	CCONJ
ejpam-6422	60	18	they	they	PRON
ejpam-6422	60	19	represent	represent	VERB
ejpam-6422	60	20	the	the	DET
ejpam-6422	60	21	wave	wave	NOUN
ejpam-6422	60	22	number	number	NOUN
ejpam-6422	60	23	component	component	NOUN
ejpam-6422	60	24	in	in	ADP
ejpam-6422	60	25	the	the	DET
ejpam-6422	60	26	x	x	PROPN
ejpam-6422	60	27	,	,	PUNCT
ejpam-6422	60	28	y	y	PROPN
ejpam-6422	60	29	and	and	CCONJ
ejpam-6422	60	30	z	z	NOUN
ejpam-6422	60	31	directions	direction	NOUN
ejpam-6422	60	32	,	,	PUNCT
ejpam-6422	60	33	respectively	respectively	ADV
ejpam-6422	60	34	;	;	PUNCT
ejpam-6422	60	35	λ	λ	NOUN
ejpam-6422	60	36	is	be	AUX
ejpam-6422	60	37	the	the	DET
ejpam-6422	60	38	wave	wave	NOUN
ejpam-6422	60	39	speed	speed	NOUN
ejpam-6422	60	40	.	.	PUNCT
ejpam-6422	61	1	differentiating	differentiate	VERB
ejpam-6422	61	2	eq	eq	PROPN
ejpam-6422	61	3	.	.	PUNCT
ejpam-6422	62	1	(	(	PUNCT
ejpam-6422	62	2	2	2	NUM
ejpam-6422	62	3	)	)	PUNCT
ejpam-6422	62	4	with	with	ADP
ejpam-6422	62	5	respect	respect	NOUN
ejpam-6422	62	6	to	to	ADP
ejpam-6422	62	7	t	t	PROPN
ejpam-6422	62	8	,	,	PUNCT
ejpam-6422	62	9	x	x	PRON
ejpam-6422	62	10	,	,	PUNCT
ejpam-6422	62	11	y	y	PROPN
ejpam-6422	62	12	and	and	CCONJ
ejpam-6422	62	13	z	z	PROPN
ejpam-6422	62	14	,	,	PUNCT
ejpam-6422	62	15	we	we	PRON
ejpam-6422	62	16	get	get	VERB
ejpam-6422	62	17	dκ	dκ	ADP
ejpam-6422	62	18	t	t	PROPN
ejpam-6422	62	19	w	w	PROPN
ejpam-6422	63	1	=	=	PUNCT
ejpam-6422	63	2	λv	λv	PROPN
ejpam-6422	63	3	′	′	NOUN
ejpam-6422	63	4	,	,	PUNCT
ejpam-6422	63	5	wx	wx	PROPN
ejpam-6422	63	6	=	=	PUNCT
ejpam-6422	64	1	ρ1v	ρ1v	NUM
ejpam-6422	64	2	′	′	NUM
ejpam-6422	64	3	,	,	PUNCT
ejpam-6422	64	4	wy	wy	PROPN
ejpam-6422	64	5	=	=	SYM
ejpam-6422	64	6	ρ2v	ρ2v	PROPN
ejpam-6422	64	7	′	′	NOUN
ejpam-6422	64	8	,	,	PUNCT
ejpam-6422	64	9	wz	wz	ADP
ejpam-6422	64	10	=	=	SYM
ejpam-6422	65	1	ρ3v	ρ3v	PROPN
ejpam-6422	65	2	′	′	NUM
ejpam-6422	65	3	,	,	PUNCT
ejpam-6422	65	4	wxxx	wxxx	NOUN
ejpam-6422	65	5	=	=	SYM
ejpam-6422	65	6	ρ31v	ρ31v	PROPN
ejpam-6422	65	7	′′′.	′′′.	PROPN
ejpam-6422	65	8	(	(	PUNCT
ejpam-6422	65	9	3	3	X
ejpam-6422	65	10	)	)	PUNCT
ejpam-6422	65	11	putting	put	VERB
ejpam-6422	65	12	eqs	eq	NOUN
ejpam-6422	65	13	(	(	PUNCT
ejpam-6422	65	14	2	2	NUM
ejpam-6422	65	15	)	)	PUNCT
ejpam-6422	65	16	and	and	CCONJ
ejpam-6422	65	17	(	(	PUNCT
ejpam-6422	65	18	3	3	X
ejpam-6422	65	19	)	)	PUNCT
ejpam-6422	65	20	into	into	ADP
ejpam-6422	65	21	eq	eq	NOUN
ejpam-6422	65	22	.	.	PUNCT
ejpam-6422	66	1	(	(	PUNCT
ejpam-6422	66	2	1	1	NUM
ejpam-6422	66	3	)	)	PUNCT
ejpam-6422	66	4	,	,	PUNCT
ejpam-6422	66	5	we	we	PRON
ejpam-6422	66	6	get	get	VERB
ejpam-6422	66	7	1	1	NUM
ejpam-6422	66	8	6	6	NUM
ejpam-6422	66	9	a1ρ	a1ρ	ADP
ejpam-6422	66	10	3	3	NUM
ejpam-6422	66	11	1v	1v	NUM
ejpam-6422	66	12	′′′	′′′	ADV
ejpam-6422	67	1	+	+	CCONJ
ejpam-6422	67	2	(	(	PUNCT
ejpam-6422	67	3	λ+	λ+	PUNCT
ejpam-6422	67	4	a3ρ1	a3ρ1	DET
ejpam-6422	67	5	+	+	CCONJ
ejpam-6422	67	6	a4ρ2	a4ρ2	PROPN
ejpam-6422	67	7	+	+	PUNCT
ejpam-6422	67	8	a5ρ3)v	a5ρ3)v	VERB
ejpam-6422	67	9	′	′	NUM
ejpam-6422	68	1	+	+	CCONJ
ejpam-6422	68	2	3	3	NUM
ejpam-6422	68	3	2	2	NUM
ejpam-6422	68	4	a2ρ1vv	a2ρ1vv	NOUN
ejpam-6422	68	5	′	′	NOUN
ejpam-6422	69	1	+	+	CCONJ
ejpam-6422	69	2	15	15	NUM
ejpam-6422	69	3	32	32	NUM
ejpam-6422	69	4	a22ρ1v2v	a22ρ1v2v	NOUN
ejpam-6422	69	5	′	′	NUM
ejpam-6422	70	1	=	=	SYM
ejpam-6422	70	2	0	0	X
ejpam-6422	70	3	.	.	PUNCT
ejpam-6422	71	1	(	(	PUNCT
ejpam-6422	71	2	4	4	X
ejpam-6422	71	3	)	)	PUNCT
ejpam-6422	71	4	integrating	integrate	VERB
ejpam-6422	71	5	eq	eq	NOUN
ejpam-6422	71	6	.	.	PUNCT
ejpam-6422	72	1	(	(	PUNCT
ejpam-6422	72	2	4	4	X
ejpam-6422	72	3	)	)	PUNCT
ejpam-6422	72	4	once	once	ADV
ejpam-6422	72	5	,	,	PUNCT
ejpam-6422	72	6	we	we	PRON
ejpam-6422	72	7	have	have	VERB
ejpam-6422	72	8	v	v	ADP
ejpam-6422	72	9	′′	′′	PROPN
ejpam-6422	72	10	+	+	PROPN
ejpam-6422	72	11	a1v	a1v	PROPN
ejpam-6422	72	12	+	+	ADJ
ejpam-6422	72	13	a2v2	a2v2	PROPN
ejpam-6422	72	14	+	+	ADJ
ejpam-6422	72	15	a3v3	a3v3	NOUN
ejpam-6422	72	16	=	=	SYM
ejpam-6422	72	17	0	0	NUM
ejpam-6422	72	18	,	,	PUNCT
ejpam-6422	72	19	(	(	PUNCT
ejpam-6422	72	20	5	5	NUM
ejpam-6422	72	21	)	)	PUNCT
ejpam-6422	72	22	where	where	SCONJ
ejpam-6422	72	23	a1	a1	NOUN
ejpam-6422	72	24	=	=	PUNCT
ejpam-6422	72	25	6(λ+	6(λ+	NOUN
ejpam-6422	72	26	a3ρ1	a3ρ1	ADP
ejpam-6422	72	27	+	+	CCONJ
ejpam-6422	72	28	a4ρ2	a4ρ2	PROPN
ejpam-6422	72	29	+	+	SYM
ejpam-6422	72	30	a5ρ3	a5ρ3	X
ejpam-6422	72	31	)	)	PUNCT
ejpam-6422	72	32	a1ρ31	a1ρ31	PROPN
ejpam-6422	72	33	,	,	PUNCT
ejpam-6422	72	34	a2	a2	PROPN
ejpam-6422	72	35	=	=	SYM
ejpam-6422	72	36	9a2	9a2	NUM
ejpam-6422	72	37	2a1ρ21	2a1ρ21	NUM
ejpam-6422	72	38	,	,	PUNCT
ejpam-6422	72	39	a3	a3	NOUN
ejpam-6422	72	40	=	=	NOUN
ejpam-6422	72	41	15a22	15a22	NUM
ejpam-6422	72	42	16a1ρ21	16a1ρ21	NUM
ejpam-6422	72	43	.	.	PUNCT
ejpam-6422	73	1	3	3	X
ejpam-6422	73	2	.	.	NOUN
ejpam-6422	73	3	exact	exact	ADJ
ejpam-6422	73	4	solutions	solution	NOUN
ejpam-6422	73	5	of	of	ADP
ejpam-6422	73	6	the	the	DET
ejpam-6422	73	7	uwm	uwm	NOUN
ejpam-6422	73	8	-	-	PUNCT
ejpam-6422	73	9	bdo	bdo	NOUN
ejpam-6422	73	10	let	let	VERB
ejpam-6422	73	11	us	we	PRON
ejpam-6422	73	12	utilize	utilize	VERB
ejpam-6422	73	13	the	the	DET
ejpam-6422	73	14	f	f	NUM
ejpam-6422	73	15	-	-	PUNCT
ejpam-6422	73	16	expansion	expansion	NOUN
ejpam-6422	73	17	method	method	NOUN
ejpam-6422	73	18	(	(	PUNCT
ejpam-6422	73	19	for	for	ADP
ejpam-6422	73	20	more	more	ADJ
ejpam-6422	73	21	information	information	NOUN
ejpam-6422	73	22	see	see	VERB
ejpam-6422	73	23	[	[	X
ejpam-6422	73	24	20–22	20–22	NOUN
ejpam-6422	73	25	]	]	PUNCT
ejpam-6422	73	26	)	)	PUNCT
ejpam-6422	73	27	.	.	PUNCT
ejpam-6422	74	1	assuming	assume	VERB
ejpam-6422	74	2	the	the	DET
ejpam-6422	74	3	solution	solution	NOUN
ejpam-6422	74	4	of	of	ADP
ejpam-6422	74	5	eq	eq	PROPN
ejpam-6422	74	6	.	.	PUNCT
ejpam-6422	75	1	(	(	PUNCT
ejpam-6422	75	2	5	5	NUM
ejpam-6422	75	3	)	)	PUNCT
ejpam-6422	75	4	has	have	VERB
ejpam-6422	75	5	the	the	DET
ejpam-6422	75	6	form	form	NOUN
ejpam-6422	75	7	v(ρ	v(ρ	NOUN
ejpam-6422	75	8	)	)	PUNCT
ejpam-6422	76	1	=	=	SYM
ejpam-6422	76	2	n∑	n∑	PROPN
ejpam-6422	76	3	j=0	j=0	PROPN
ejpam-6422	76	4	ℓjf	ℓjf	PROPN
ejpam-6422	76	5	j(ρ	j(ρ	PROPN
ejpam-6422	76	6	)	)	PUNCT
ejpam-6422	76	7	,	,	PUNCT
ejpam-6422	76	8	ℓn	ℓn	ADV
ejpam-6422	76	9	̸=	̸=	PROPN
ejpam-6422	76	10	0	0	NUM
ejpam-6422	76	11	,	,	PUNCT
ejpam-6422	76	12	(	(	PUNCT
ejpam-6422	76	13	6	6	X
ejpam-6422	76	14	)	)	PUNCT
ejpam-6422	76	15	w.	w.	PROPN
ejpam-6422	76	16	w.	w.	PROPN
ejpam-6422	76	17	mohammed	mohammed	PROPN
ejpam-6422	76	18	et	et	PROPN
ejpam-6422	76	19	al	al	PROPN
ejpam-6422	76	20	.	.	PUNCT
ejpam-6422	76	21	/	/	SYM
ejpam-6422	76	22	eur	eur	PROPN
ejpam-6422	76	23	.	.	PUNCT
ejpam-6422	77	1	j.	j.	PROPN
ejpam-6422	77	2	pure	pure	PROPN
ejpam-6422	77	3	appl	appl	PROPN
ejpam-6422	77	4	.	.	PROPN
ejpam-6422	77	5	math	math	PROPN
ejpam-6422	77	6	,	,	PUNCT
ejpam-6422	77	7	18	18	NUM
ejpam-6422	77	8	(	(	PUNCT
ejpam-6422	77	9	3	3	NUM
ejpam-6422	77	10	)	)	PUNCT
ejpam-6422	77	11	(	(	PUNCT
ejpam-6422	77	12	2025	2025	NUM
ejpam-6422	77	13	)	)	PUNCT
ejpam-6422	77	14	,	,	PUNCT
ejpam-6422	77	15	6422	6422	NUM
ejpam-6422	77	16	4	4	NUM
ejpam-6422	77	17	of	of	ADP
ejpam-6422	77	18	13	13	NUM
ejpam-6422	77	19	where	where	SCONJ
ejpam-6422	77	20	ℓ0	ℓ0	PROPN
ejpam-6422	77	21	,	,	PUNCT
ejpam-6422	77	22	ℓ1	ℓ1	NOUN
ejpam-6422	77	23	,	,	PUNCT
ejpam-6422	77	24	ℓ2	ℓ2	NOUN
ejpam-6422	77	25	,	,	PUNCT
ejpam-6422	77	26	,	,	PUNCT
ejpam-6422	77	27	ℓn−1	ℓn−1	PROPN
ejpam-6422	77	28	and	and	CCONJ
ejpam-6422	77	29	ℓn	ℓn	ADV
ejpam-6422	77	30	are	be	AUX
ejpam-6422	77	31	unknown	unknown	ADJ
ejpam-6422	77	32	constants	constant	NOUN
ejpam-6422	77	33	to	to	PART
ejpam-6422	77	34	be	be	AUX
ejpam-6422	77	35	calculated	calculate	VERB
ejpam-6422	77	36	and	and	CCONJ
ejpam-6422	77	37	f	f	PROPN
ejpam-6422	77	38	solves	solve	VERB
ejpam-6422	77	39	the	the	DET
ejpam-6422	77	40	following	follow	VERB
ejpam-6422	77	41	auxiliary	auxiliary	ADJ
ejpam-6422	77	42	equation	equation	NOUN
ejpam-6422	77	43	:	:	PUNCT
ejpam-6422	77	44	(	(	PUNCT
ejpam-6422	77	45	f	f	PROPN
ejpam-6422	77	46	′)2	′)2	X
ejpam-6422	77	47	=	=	SYM
ejpam-6422	77	48	ℏ1f4	ℏ1f4	PROPN
ejpam-6422	77	49	+	+	CCONJ
ejpam-6422	77	50	ℏ2f2	ℏ2f2	ADJ
ejpam-6422	77	51	+	+	NUM
ejpam-6422	77	52	ℏ3	ℏ3	PROPN
ejpam-6422	77	53	,	,	PUNCT
ejpam-6422	77	54	(	(	PUNCT
ejpam-6422	77	55	7	7	X
ejpam-6422	77	56	)	)	PUNCT
ejpam-6422	77	57	where	where	SCONJ
ejpam-6422	77	58	ℏ1	ℏ1	ADJ
ejpam-6422	77	59	,	,	PUNCT
ejpam-6422	77	60	ℏ2	ℏ2	NOUN
ejpam-6422	77	61	,	,	PUNCT
ejpam-6422	77	62	and	and	CCONJ
ejpam-6422	77	63	ℏ3	ℏ3	PROPN
ejpam-6422	77	64	are	be	AUX
ejpam-6422	77	65	real	real	ADJ
ejpam-6422	77	66	numbers	number	NOUN
ejpam-6422	77	67	.	.	PUNCT
ejpam-6422	78	1	first	first	ADV
ejpam-6422	78	2	,	,	PUNCT
ejpam-6422	78	3	let	let	VERB
ejpam-6422	78	4	us	we	PRON
ejpam-6422	78	5	balance	balance	VERB
ejpam-6422	78	6	v3	v3	PROPN
ejpam-6422	78	7	with	with	ADP
ejpam-6422	78	8	v	v	NUM
ejpam-6422	78	9	′′	′′	PROPN
ejpam-6422	78	10	in	in	ADP
ejpam-6422	78	11	eq	eq	ADP
ejpam-6422	78	12	.	.	PUNCT
ejpam-6422	79	1	(	(	PUNCT
ejpam-6422	79	2	5	5	NUM
ejpam-6422	79	3	)	)	PUNCT
ejpam-6422	79	4	to	to	PART
ejpam-6422	79	5	calculate	calculate	VERB
ejpam-6422	79	6	the	the	DET
ejpam-6422	79	7	parameters	parameter	NOUN
ejpam-6422	79	8	n	n	CCONJ
ejpam-6422	79	9	as	as	ADP
ejpam-6422	79	10	3n	3n	NUM
ejpam-6422	79	11	=	=	SYM
ejpam-6422	79	12	n	n	PROPN
ejpam-6422	79	13	+	+	CCONJ
ejpam-6422	79	14	2	2	NUM
ejpam-6422	79	15	⇒	⇒	NOUN
ejpam-6422	79	16	n	n	NOUN
ejpam-6422	79	17	=	=	SYM
ejpam-6422	79	18	1	1	X
ejpam-6422	79	19	.	.	PUNCT
ejpam-6422	79	20	with	with	ADP
ejpam-6422	79	21	n	n	NOUN
ejpam-6422	79	22	=	=	SYM
ejpam-6422	79	23	1	1	NUM
ejpam-6422	79	24	,	,	PUNCT
ejpam-6422	79	25	eq	eq	NOUN
ejpam-6422	79	26	.	.	PUNCT
ejpam-6422	80	1	(	(	PUNCT
ejpam-6422	80	2	6	6	NUM
ejpam-6422	80	3	)	)	PUNCT
ejpam-6422	80	4	becomes	become	VERB
ejpam-6422	80	5	v(ρ	v(ρ	NOUN
ejpam-6422	80	6	)	)	PUNCT
ejpam-6422	81	1	=	=	PUNCT
ejpam-6422	82	1	ℓ0	ℓ0	ADV
ejpam-6422	82	2	+	+	ADJ
ejpam-6422	82	3	ℓ1f(ρ	ℓ1f(ρ	NOUN
ejpam-6422	82	4	)	)	PUNCT
ejpam-6422	82	5	,	,	PUNCT
ejpam-6422	82	6	(	(	PUNCT
ejpam-6422	82	7	8)	8)	NUM
ejpam-6422	82	8	putting	put	VERB
ejpam-6422	82	9	eq	eq	NOUN
ejpam-6422	82	10	.	.	PUNCT
ejpam-6422	83	1	(	(	PUNCT
ejpam-6422	83	2	8)	8)	NUM
ejpam-6422	83	3	into	into	ADP
ejpam-6422	83	4	eq	eq	NOUN
ejpam-6422	83	5	.	.	PUNCT
ejpam-6422	84	1	(	(	PUNCT
ejpam-6422	84	2	5	5	NUM
ejpam-6422	84	3	)	)	PUNCT
ejpam-6422	84	4	,	,	PUNCT
ejpam-6422	84	5	we	we	PRON
ejpam-6422	84	6	get	get	VERB
ejpam-6422	85	1	+	+	PROPN
ejpam-6422	86	1	[	[	X
ejpam-6422	86	2	2ℏ1ℓ1	2ℏ1ℓ1	NUM
ejpam-6422	86	3	+	+	NOUN
ejpam-6422	86	4	a3ℓ	a3ℓ	PROPN
ejpam-6422	86	5	3	3	NUM
ejpam-6422	86	6	1]f3	1]f3	NUM
ejpam-6422	86	7	+	+	CCONJ
ejpam-6422	87	1	[	[	X
ejpam-6422	87	2	a2ℓ	a2ℓ	NUM
ejpam-6422	87	3	2	2	NUM
ejpam-6422	87	4	1	1	NUM
ejpam-6422	87	5	+	+	CCONJ
ejpam-6422	87	6	3a3ℓ0ℓ	3a3ℓ0ℓ	NUM
ejpam-6422	87	7	2	2	NUM
ejpam-6422	87	8	1]f2	1]f2	NUM
ejpam-6422	87	9	+	+	ADP
ejpam-6422	87	10	[	[	X
ejpam-6422	87	11	ℏ2ℓ1	ℏ2ℓ1	X
ejpam-6422	87	12	+	+	NOUN
ejpam-6422	87	13	a1ℓ1	a1ℓ1	NOUN
ejpam-6422	87	14	+	+	ADJ
ejpam-6422	87	15	2ℓ0ℓ1a2	2ℓ0ℓ1a2	NUM
ejpam-6422	87	16	+	+	CCONJ
ejpam-6422	87	17	3ℓ20ℓ1a3]f	3ℓ20ℓ1a3]f	NUM
ejpam-6422	88	1	+	+	PROPN
ejpam-6422	88	2	[	[	X
ejpam-6422	88	3	a1ℓ0	a1ℓ0	X
ejpam-6422	89	1	+	+	NOUN
ejpam-6422	89	2	a2ℓ	a2ℓ	PROPN
ejpam-6422	89	3	2	2	NUM
ejpam-6422	89	4	0	0	NUM
ejpam-6422	90	1	+	+	ADJ
ejpam-6422	90	2	a3ℓ	a3ℓ	PROPN
ejpam-6422	90	3	3	3	NUM
ejpam-6422	90	4	0	0	NUM
ejpam-6422	90	5	]	]	X
ejpam-6422	90	6	=	=	SYM
ejpam-6422	90	7	0	0	X
ejpam-6422	90	8	.	.	PUNCT
ejpam-6422	91	1	for	for	ADP
ejpam-6422	91	2	j	j	PROPN
ejpam-6422	91	3	=	=	SYM
ejpam-6422	91	4	3	3	NUM
ejpam-6422	91	5	,	,	PUNCT
ejpam-6422	91	6	2	2	NUM
ejpam-6422	91	7	,	,	PUNCT
ejpam-6422	91	8	1	1	NUM
ejpam-6422	91	9	,	,	PUNCT
ejpam-6422	91	10	0	0	NUM
ejpam-6422	91	11	,	,	PUNCT
ejpam-6422	91	12	we	we	PRON
ejpam-6422	91	13	balance	balance	VERB
ejpam-6422	91	14	each	each	DET
ejpam-6422	91	15	coefficient	coefficient	NOUN
ejpam-6422	91	16	of	of	ADP
ejpam-6422	91	17	f	f	PROPN
ejpam-6422	91	18	j	j	PROPN
ejpam-6422	91	19	with	with	ADP
ejpam-6422	91	20	zero	zero	NUM
ejpam-6422	91	21	to	to	PART
ejpam-6422	91	22	have	have	VERB
ejpam-6422	91	23	2ℏ1ℓ1	2ℏ1ℓ1	NOUN
ejpam-6422	92	1	+	+	ADJ
ejpam-6422	92	2	a3ℓ	a3ℓ	PROPN
ejpam-6422	92	3	3	3	NUM
ejpam-6422	92	4	1	1	NUM
ejpam-6422	92	5	=	=	SYM
ejpam-6422	92	6	0	0	NUM
ejpam-6422	92	7	,	,	PUNCT
ejpam-6422	92	8	a2ℓ	a2ℓ	PRON
ejpam-6422	92	9	2	2	NUM
ejpam-6422	92	10	1	1	NUM
ejpam-6422	92	11	+	+	CCONJ
ejpam-6422	92	12	3a3ℓ0ℓ	3a3ℓ0ℓ	NUM
ejpam-6422	92	13	2	2	NUM
ejpam-6422	92	14	1	1	NUM
ejpam-6422	92	15	=	=	SYM
ejpam-6422	92	16	0	0	NUM
ejpam-6422	92	17	,	,	PUNCT
ejpam-6422	92	18	ℏ2ℓ1	ℏ2ℓ1	PUNCT
ejpam-6422	93	1	+	+	NOUN
ejpam-6422	93	2	a1ℓ1	a1ℓ1	NOUN
ejpam-6422	93	3	+	+	ADJ
ejpam-6422	93	4	2ℓ0ℓ1a2	2ℓ0ℓ1a2	NUM
ejpam-6422	93	5	+	+	CCONJ
ejpam-6422	93	6	3ℓ20ℓ1a3	3ℓ20ℓ1a3	NUM
ejpam-6422	93	7	=	=	SYM
ejpam-6422	93	8	0	0	NUM
ejpam-6422	93	9	,	,	PUNCT
ejpam-6422	93	10	and	and	CCONJ
ejpam-6422	93	11	a1ℓ0	a1ℓ0	PROPN
ejpam-6422	94	1	+	+	ADP
ejpam-6422	94	2	a2ℓ	a2ℓ	PROPN
ejpam-6422	94	3	2	2	NUM
ejpam-6422	94	4	0	0	NUM
ejpam-6422	95	1	+	+	NOUN
ejpam-6422	95	2	a3ℓ	a3ℓ	PROPN
ejpam-6422	95	3	3	3	NUM
ejpam-6422	95	4	0	0	NUM
ejpam-6422	95	5	=	=	SYM
ejpam-6422	95	6	0	0	X
ejpam-6422	95	7	.	.	PUNCT
ejpam-6422	95	8	by	by	ADP
ejpam-6422	95	9	solving	solve	VERB
ejpam-6422	95	10	the	the	DET
ejpam-6422	95	11	above	above	ADJ
ejpam-6422	95	12	equations	equation	NOUN
ejpam-6422	95	13	,	,	PUNCT
ejpam-6422	95	14	we	we	PRON
ejpam-6422	95	15	get	get	VERB
ejpam-6422	95	16	ℓ0	ℓ0	ADV
ejpam-6422	95	17	=	=	PROPN
ejpam-6422	95	18	−a2	−a2	PROPN
ejpam-6422	95	19	3a3	3a3	NUM
ejpam-6422	95	20	=	=	PUNCT
ejpam-6422	96	1	−8	−8	X
ejpam-6422	96	2	5a2	5a2	ADV
ejpam-6422	96	3	,	,	PUNCT
ejpam-6422	96	4	ℓ1	ℓ1	NOUN
ejpam-6422	96	5	=	=	SYM
ejpam-6422	96	6	±	±	NUM
ejpam-6422	96	7	√	√	NOUN
ejpam-6422	96	8	−2ℏ1	−2ℏ1	NUM
ejpam-6422	96	9	a3	a3	NOUN
ejpam-6422	96	10	=	=	SYM
ejpam-6422	96	11	±	±	NOUN
ejpam-6422	96	12	√	√	PUNCT
ejpam-6422	97	1	−32a1ρ21ℏ1	−32a1ρ21ℏ1	PROPN
ejpam-6422	97	2	15a22	15a22	NUM
ejpam-6422	97	3	,	,	PUNCT
ejpam-6422	97	4	and	and	CCONJ
ejpam-6422	97	5	ℏ2	ℏ2	NOUN
ejpam-6422	97	6	=	=	SYM
ejpam-6422	97	7	a2	a2	PROPN
ejpam-6422	97	8	2	2	NUM
ejpam-6422	97	9	9a3	9a3	NUM
ejpam-6422	97	10	=	=	SYM
ejpam-6422	97	11	12	12	NUM
ejpam-6422	97	12	5a1ρ21	5a1ρ21	NUM
ejpam-6422	97	13	.	.	PUNCT
ejpam-6422	98	1	(	(	PUNCT
ejpam-6422	98	2	9	9	X
ejpam-6422	98	3	)	)	PUNCT
ejpam-6422	98	4	substituting	substitute	VERB
ejpam-6422	98	5	(	(	PUNCT
ejpam-6422	98	6	9	9	NUM
ejpam-6422	98	7	)	)	PUNCT
ejpam-6422	98	8	into	into	ADP
ejpam-6422	98	9	eq	eq	NOUN
ejpam-6422	98	10	.	.	PUNCT
ejpam-6422	99	1	(	(	PUNCT
ejpam-6422	99	2	8)	8)	NUM
ejpam-6422	99	3	,	,	PUNCT
ejpam-6422	99	4	we	we	PRON
ejpam-6422	99	5	have	have	VERB
ejpam-6422	99	6	the	the	DET
ejpam-6422	99	7	solution	solution	NOUN
ejpam-6422	99	8	of	of	ADP
ejpam-6422	99	9	the	the	DET
ejpam-6422	99	10	traveling	travel	VERB
ejpam-6422	99	11	wave	wave	NOUN
ejpam-6422	99	12	eq	eq	ADP
ejpam-6422	99	13	.	.	PUNCT
ejpam-6422	100	1	(	(	PUNCT
ejpam-6422	100	2	5	5	NUM
ejpam-6422	100	3	)	)	PUNCT
ejpam-6422	100	4	as	as	ADP
ejpam-6422	100	5	:	:	PUNCT
ejpam-6422	100	6	v	v	X
ejpam-6422	100	7	(	(	PUNCT
ejpam-6422	100	8	ρ	ρ	NOUN
ejpam-6422	100	9	)	)	PUNCT
ejpam-6422	100	10	=	=	PUNCT
ejpam-6422	101	1	−8	−8	X
ejpam-6422	101	2	5a2	5a2	NUM
ejpam-6422	101	3	±	±	NUM
ejpam-6422	102	1	√	√	PROPN
ejpam-6422	102	2	−128ℏ1	−128ℏ1	NOUN
ejpam-6422	102	3	25a22ℏ2	25a22ℏ2	PROPN
ejpam-6422	102	4	f	f	X
ejpam-6422	102	5	(	(	PUNCT
ejpam-6422	102	6	ρ	ρ	PROPN
ejpam-6422	102	7	)	)	PUNCT
ejpam-6422	102	8	.	.	PUNCT
ejpam-6422	103	1	(	(	PUNCT
ejpam-6422	103	2	10	10	NUM
ejpam-6422	103	3	)	)	PUNCT
ejpam-6422	103	4	consequently	consequently	ADV
ejpam-6422	103	5	,	,	PUNCT
ejpam-6422	103	6	putting	put	VERB
ejpam-6422	103	7	eq	eq	NOUN
ejpam-6422	103	8	.	.	PUNCT
ejpam-6422	104	1	(	(	PUNCT
ejpam-6422	104	2	10	10	NUM
ejpam-6422	104	3	)	)	PUNCT
ejpam-6422	104	4	into	into	ADP
ejpam-6422	104	5	eq	eq	NOUN
ejpam-6422	104	6	.	.	PUNCT
ejpam-6422	105	1	(	(	PUNCT
ejpam-6422	105	2	2	2	NUM
ejpam-6422	105	3	)	)	PUNCT
ejpam-6422	105	4	,	,	PUNCT
ejpam-6422	105	5	we	we	PRON
ejpam-6422	105	6	get	get	VERB
ejpam-6422	105	7	the	the	DET
ejpam-6422	105	8	next	next	ADJ
ejpam-6422	105	9	solutions	solution	NOUN
ejpam-6422	105	10	for	for	ADP
ejpam-6422	105	11	the	the	DET
ejpam-6422	105	12	uwm	uwm	NOUN
ejpam-6422	105	13	-	-	PUNCT
ejpam-6422	105	14	bdo	bdo	NOUN
ejpam-6422	105	15	(	(	PUNCT
ejpam-6422	105	16	1	1	NUM
ejpam-6422	105	17	):	):	PUNCT
ejpam-6422	105	18	w(x	w(x	PROPN
ejpam-6422	105	19	,	,	PUNCT
ejpam-6422	105	20	y	y	PROPN
ejpam-6422	105	21	,	,	PUNCT
ejpam-6422	105	22	z	z	PROPN
ejpam-6422	105	23	,	,	PUNCT
ejpam-6422	105	24	t	t	PROPN
ejpam-6422	105	25	)	)	PUNCT
ejpam-6422	106	1	=	=	PRON
ejpam-6422	106	2	{	{	PUNCT
ejpam-6422	107	1	−8	−8	X
ejpam-6422	107	2	5a2	5a2	NUM
ejpam-6422	107	3	±	±	NUM
ejpam-6422	108	1	√	√	PROPN
ejpam-6422	108	2	−128ℏ1	−128ℏ1	NOUN
ejpam-6422	108	3	25a22ℏ2	25a22ℏ2	PROPN
ejpam-6422	108	4	f	f	X
ejpam-6422	108	5	(	(	PUNCT
ejpam-6422	108	6	ρ	ρ	PROPN
ejpam-6422	108	7	)	)	PUNCT
ejpam-6422	108	8	}	}	PUNCT
ejpam-6422	108	9	,	,	PUNCT
ejpam-6422	108	10	(	(	PUNCT
ejpam-6422	108	11	11	11	NUM
ejpam-6422	108	12	)	)	PUNCT
ejpam-6422	108	13	where	where	SCONJ
ejpam-6422	108	14	ρ	ρ	PROPN
ejpam-6422	108	15	=	=	SYM
ejpam-6422	108	16	ρ1x+	ρ1x+	PROPN
ejpam-6422	108	17	ρ2y	ρ2y	PROPN
ejpam-6422	108	18	+	+	PUNCT
ejpam-6422	109	1	ρ3z	ρ3z	NOUN
ejpam-6422	109	2	+	+	NOUN
ejpam-6422	109	3	λ	λ	X
ejpam-6422	109	4	κ(t+	κ(t+	ADJ
ejpam-6422	109	5	1	1	NUM
ejpam-6422	109	6	γ(κ	γ(κ	PROPN
ejpam-6422	109	7	)	)	PUNCT
ejpam-6422	109	8	)	)	PUNCT
ejpam-6422	110	1	κ	κ	X
ejpam-6422	110	2	.	.	PUNCT
ejpam-6422	110	3	w.	w.	PROPN
ejpam-6422	110	4	w.	w.	PROPN
ejpam-6422	110	5	mohammed	mohammed	PROPN
ejpam-6422	110	6	et	et	PROPN
ejpam-6422	110	7	al	al	PROPN
ejpam-6422	110	8	.	.	PUNCT
ejpam-6422	110	9	/	/	SYM
ejpam-6422	110	10	eur	eur	PROPN
ejpam-6422	110	11	.	.	PUNCT
ejpam-6422	111	1	j.	j.	PROPN
ejpam-6422	111	2	pure	pure	PROPN
ejpam-6422	111	3	appl	appl	PROPN
ejpam-6422	111	4	.	.	PROPN
ejpam-6422	111	5	math	math	PROPN
ejpam-6422	111	6	,	,	PUNCT
ejpam-6422	111	7	18	18	NUM
ejpam-6422	111	8	(	(	PUNCT
ejpam-6422	111	9	3	3	NUM
ejpam-6422	111	10	)	)	PUNCT
ejpam-6422	111	11	(	(	PUNCT
ejpam-6422	111	12	2025	2025	NUM
ejpam-6422	111	13	)	)	PUNCT
ejpam-6422	111	14	,	,	PUNCT
ejpam-6422	111	15	6422	6422	NUM
ejpam-6422	111	16	5	5	NUM
ejpam-6422	111	17	of	of	ADP
ejpam-6422	111	18	13	13	NUM
ejpam-6422	111	19	there	there	PRON
ejpam-6422	111	20	are	be	VERB
ejpam-6422	111	21	several	several	ADJ
ejpam-6422	111	22	cases	case	NOUN
ejpam-6422	111	23	for	for	ADP
ejpam-6422	111	24	the	the	DET
ejpam-6422	111	25	solutions	solution	NOUN
ejpam-6422	111	26	of	of	ADP
ejpam-6422	111	27	eq	eq	PROPN
ejpam-6422	111	28	.	.	PUNCT
ejpam-6422	112	1	(	(	PUNCT
ejpam-6422	112	2	9	9	NUM
ejpam-6422	112	3	)	)	PUNCT
ejpam-6422	112	4	that	that	SCONJ
ejpam-6422	112	5	depending	depend	VERB
ejpam-6422	112	6	on	on	ADP
ejpam-6422	112	7	ℏ1	ℏ1	ADJ
ejpam-6422	112	8	,	,	PUNCT
ejpam-6422	112	9	ℏ2	ℏ2	NOUN
ejpam-6422	112	10	and	and	CCONJ
ejpam-6422	112	11	ℏ3	ℏ3	PROPN
ejpam-6422	112	12	as	as	SCONJ
ejpam-6422	112	13	follows	follow	VERB
ejpam-6422	112	14	:	:	PUNCT
ejpam-6422	112	15	case	case	NOUN
ejpam-6422	112	16	1	1	NUM
ejpam-6422	112	17	:	:	PUNCT
ejpam-6422	112	18	if	if	SCONJ
ejpam-6422	112	19	ℏ1	ℏ1	PROPN
ejpam-6422	112	20	=	=	SYM
ejpam-6422	112	21	ϖ2	ϖ2	NOUN
ejpam-6422	112	22	,	,	PUNCT
ejpam-6422	112	23	ℏ2	ℏ2	NOUN
ejpam-6422	112	24	=	=	SYM
ejpam-6422	113	1	−	−	PROPN
ejpam-6422	113	2	(	(	PUNCT
ejpam-6422	113	3	1	1	NUM
ejpam-6422	113	4	+	+	NOUN
ejpam-6422	113	5	ϖ2	ϖ2	NOUN
ejpam-6422	113	6	)	)	PUNCT
ejpam-6422	113	7	and	and	CCONJ
ejpam-6422	113	8	ℏ3	ℏ3	PROPN
ejpam-6422	113	9	=	=	SYM
ejpam-6422	113	10	1	1	NUM
ejpam-6422	113	11	,	,	PUNCT
ejpam-6422	113	12	then	then	ADV
ejpam-6422	113	13	f	f	PROPN
ejpam-6422	113	14	(	(	PUNCT
ejpam-6422	113	15	ρ	ρ	PROPN
ejpam-6422	113	16	)	)	PUNCT
ejpam-6422	113	17	=	=	NOUN
ejpam-6422	113	18	sn(ρ	sn(ρ	X
ejpam-6422	113	19	)	)	PUNCT
ejpam-6422	113	20	,	,	PUNCT
ejpam-6422	113	21	and	and	CCONJ
ejpam-6422	113	22	eq	eq	NOUN
ejpam-6422	113	23	.	.	PUNCT
ejpam-6422	114	1	(	(	PUNCT
ejpam-6422	114	2	11	11	NUM
ejpam-6422	114	3	)	)	PUNCT
ejpam-6422	114	4	has	have	VERB
ejpam-6422	114	5	the	the	DET
ejpam-6422	114	6	form	form	NOUN
ejpam-6422	114	7	w(x	w(x	PROPN
ejpam-6422	114	8	,	,	PUNCT
ejpam-6422	114	9	y	y	PROPN
ejpam-6422	114	10	,	,	PUNCT
ejpam-6422	114	11	z	z	PROPN
ejpam-6422	114	12	,	,	PUNCT
ejpam-6422	114	13	t	t	PROPN
ejpam-6422	114	14	)	)	PUNCT
ejpam-6422	114	15	=	=	PRON
ejpam-6422	114	16	{	{	PUNCT
ejpam-6422	115	1	−8	−8	X
ejpam-6422	115	2	5a2	5a2	NUM
ejpam-6422	115	3	±	±	NUM
ejpam-6422	115	4	√	√	PROPN
ejpam-6422	115	5	128ϖ2	128ϖ2	NUM
ejpam-6422	115	6	25a22	25a22	NUM
ejpam-6422	115	7	(	(	PUNCT
ejpam-6422	115	8	1	1	NUM
ejpam-6422	115	9	+	+	NOUN
ejpam-6422	115	10	ϖ2	ϖ2	NOUN
ejpam-6422	115	11	)	)	PUNCT
ejpam-6422	115	12	sn(ρ1x+	sn(ρ1x+	NUM
ejpam-6422	116	1	ρ2y	ρ2y	PROPN
ejpam-6422	117	1	+	+	PUNCT
ejpam-6422	117	2	ρ3z	ρ3z	NOUN
ejpam-6422	117	3	+	+	NOUN
ejpam-6422	117	4	λ	λ	X
ejpam-6422	117	5	κ	κ	X
ejpam-6422	117	6	(	(	PUNCT
ejpam-6422	117	7	t+	t+	NOUN
ejpam-6422	117	8	1	1	NUM
ejpam-6422	117	9	γ(κ	γ(κ	PROPN
ejpam-6422	117	10	)	)	PUNCT
ejpam-6422	117	11	)	)	PUNCT
ejpam-6422	117	12	κ	κ	X
ejpam-6422	117	13	)	)	PUNCT
ejpam-6422	117	14	}	}	PUNCT
ejpam-6422	117	15	.	.	PUNCT
ejpam-6422	118	1	(	(	PUNCT
ejpam-6422	118	2	12	12	NUM
ejpam-6422	118	3	)	)	PUNCT
ejpam-6422	118	4	if	if	SCONJ
ejpam-6422	118	5	ϖ	ϖ	PRON
ejpam-6422	118	6	→	→	SYM
ejpam-6422	118	7	1	1	NUM
ejpam-6422	118	8	,	,	PUNCT
ejpam-6422	118	9	then	then	ADV
ejpam-6422	118	10	eq	eq	ADJ
ejpam-6422	118	11	.	.	PUNCT
ejpam-6422	119	1	(	(	PUNCT
ejpam-6422	119	2	12	12	NUM
ejpam-6422	119	3	)	)	PUNCT
ejpam-6422	119	4	changes	change	NOUN
ejpam-6422	119	5	to	to	ADP
ejpam-6422	119	6	w(x	w(x	PROPN
ejpam-6422	119	7	,	,	PUNCT
ejpam-6422	119	8	y	y	PROPN
ejpam-6422	119	9	,	,	PUNCT
ejpam-6422	119	10	z	z	PROPN
ejpam-6422	119	11	,	,	PUNCT
ejpam-6422	119	12	t	t	PROPN
ejpam-6422	119	13	)	)	PUNCT
ejpam-6422	120	1	=	=	PRON
ejpam-6422	120	2	{	{	PUNCT
ejpam-6422	121	1	−8	−8	X
ejpam-6422	121	2	5a2	5a2	NUM
ejpam-6422	121	3	±	±	NUM
ejpam-6422	121	4	8	8	NUM
ejpam-6422	121	5	5a2	5a2	NOUN
ejpam-6422	121	6	tanh(ρ1x+	tanh(ρ1x+	PROPN
ejpam-6422	121	7	ρ2y	ρ2y	PROPN
ejpam-6422	122	1	+	+	PUNCT
ejpam-6422	123	1	ρ3z	ρ3z	NOUN
ejpam-6422	123	2	+	+	NOUN
ejpam-6422	123	3	λ	λ	X
ejpam-6422	123	4	κ	κ	X
ejpam-6422	123	5	(	(	PUNCT
ejpam-6422	123	6	t+	t+	NOUN
ejpam-6422	123	7	1	1	NUM
ejpam-6422	123	8	γ(κ	γ(κ	PROPN
ejpam-6422	123	9	)	)	PUNCT
ejpam-6422	123	10	)	)	PUNCT
ejpam-6422	123	11	κ	κ	X
ejpam-6422	123	12	)	)	PUNCT
ejpam-6422	123	13	}	}	PUNCT
ejpam-6422	123	14	.	.	PUNCT
ejpam-6422	124	1	(	(	PUNCT
ejpam-6422	124	2	13	13	NUM
ejpam-6422	124	3	)	)	PUNCT
ejpam-6422	124	4	case	case	NOUN
ejpam-6422	124	5	2	2	NUM
ejpam-6422	124	6	:	:	PUNCT
ejpam-6422	124	7	if	if	SCONJ
ejpam-6422	124	8	ℏ1	ℏ1	PROPN
ejpam-6422	124	9	=	=	SYM
ejpam-6422	124	10	ϖ2	ϖ2	NOUN
ejpam-6422	124	11	,	,	PUNCT
ejpam-6422	124	12	ℏ2	ℏ2	NOUN
ejpam-6422	124	13	=	=	SYM
ejpam-6422	125	1	−	−	PROPN
ejpam-6422	125	2	(	(	PUNCT
ejpam-6422	125	3	1	1	NUM
ejpam-6422	125	4	+	+	NOUN
ejpam-6422	125	5	ϖ2	ϖ2	NOUN
ejpam-6422	125	6	)	)	PUNCT
ejpam-6422	125	7	and	and	CCONJ
ejpam-6422	125	8	ℏ3	ℏ3	PROPN
ejpam-6422	125	9	=	=	SYM
ejpam-6422	125	10	1	1	NUM
ejpam-6422	125	11	,	,	PUNCT
ejpam-6422	125	12	then	then	ADV
ejpam-6422	125	13	f	f	PROPN
ejpam-6422	125	14	(	(	PUNCT
ejpam-6422	125	15	ρ	ρ	PROPN
ejpam-6422	125	16	)	)	PUNCT
ejpam-6422	125	17	=	=	SYM
ejpam-6422	125	18	cd(ρ	cd(ρ	NUM
ejpam-6422	125	19	)	)	PUNCT
ejpam-6422	125	20	,	,	PUNCT
ejpam-6422	125	21	and	and	CCONJ
ejpam-6422	125	22	eq	eq	NOUN
ejpam-6422	125	23	.	.	PUNCT
ejpam-6422	126	1	(	(	PUNCT
ejpam-6422	126	2	11	11	NUM
ejpam-6422	126	3	)	)	PUNCT
ejpam-6422	126	4	takes	take	VERB
ejpam-6422	126	5	the	the	DET
ejpam-6422	126	6	form	form	NOUN
ejpam-6422	126	7	w(x	w(x	PROPN
ejpam-6422	126	8	,	,	PUNCT
ejpam-6422	126	9	y	y	PROPN
ejpam-6422	126	10	,	,	PUNCT
ejpam-6422	126	11	z	z	PROPN
ejpam-6422	126	12	,	,	PUNCT
ejpam-6422	126	13	t	t	PROPN
ejpam-6422	126	14	)	)	PUNCT
ejpam-6422	126	15	=	=	PRON
ejpam-6422	126	16	{	{	PUNCT
ejpam-6422	127	1	−8	−8	X
ejpam-6422	127	2	5a2	5a2	NUM
ejpam-6422	127	3	±	±	NUM
ejpam-6422	127	4	√	√	PROPN
ejpam-6422	127	5	128ϖ2	128ϖ2	NUM
ejpam-6422	127	6	25a22	25a22	NUM
ejpam-6422	127	7	(	(	PUNCT
ejpam-6422	127	8	1	1	NUM
ejpam-6422	127	9	+	+	NOUN
ejpam-6422	127	10	ϖ2	ϖ2	NOUN
ejpam-6422	127	11	)	)	PUNCT
ejpam-6422	127	12	cd(ρ1x+	cd(ρ1x+	NOUN
ejpam-6422	127	13	ρ2y	ρ2y	PROPN
ejpam-6422	128	1	+	+	CCONJ
ejpam-6422	128	2	ρ3z	ρ3z	NOUN
ejpam-6422	128	3	+	+	NOUN
ejpam-6422	128	4	λ	λ	X
ejpam-6422	128	5	κ	κ	X
ejpam-6422	128	6	(	(	PUNCT
ejpam-6422	128	7	t+	t+	NOUN
ejpam-6422	128	8	1	1	NUM
ejpam-6422	128	9	γ(κ	γ(κ	PROPN
ejpam-6422	128	10	)	)	PUNCT
ejpam-6422	128	11	)	)	PUNCT
ejpam-6422	128	12	κ	κ	X
ejpam-6422	128	13	)	)	PUNCT
ejpam-6422	128	14	}	}	PUNCT
ejpam-6422	128	15	.	.	PUNCT
ejpam-6422	129	1	(	(	PUNCT
ejpam-6422	129	2	14	14	NUM
ejpam-6422	129	3	)	)	PUNCT
ejpam-6422	129	4	case	case	NOUN
ejpam-6422	129	5	3	3	NUM
ejpam-6422	129	6	:	:	PUNCT
ejpam-6422	129	7	if	if	SCONJ
ejpam-6422	129	8	ℏ1	ℏ1	PROPN
ejpam-6422	129	9	=	=	SYM
ejpam-6422	129	10	−ϖ2	−ϖ2	PROPN
ejpam-6422	129	11	,	,	PUNCT
ejpam-6422	129	12	ℏ2	ℏ2	NOUN
ejpam-6422	129	13	=	=	SYM
ejpam-6422	129	14	2ϖ2	2ϖ2	PROPN
ejpam-6422	130	1	−	−	NOUN
ejpam-6422	130	2	1	1	NUM
ejpam-6422	130	3	and	and	CCONJ
ejpam-6422	130	4	ℏ3	ℏ3	PROPN
ejpam-6422	130	5	=	=	SYM
ejpam-6422	130	6	1−ϖ2	1−ϖ2	NUM
ejpam-6422	130	7	,	,	PUNCT
ejpam-6422	130	8	then	then	ADV
ejpam-6422	130	9	f	f	PROPN
ejpam-6422	130	10	(	(	PUNCT
ejpam-6422	130	11	ρ	ρ	NOUN
ejpam-6422	130	12	)	)	PUNCT
ejpam-6422	130	13	=	=	PUNCT
ejpam-6422	130	14	cn(ρ	cn(ρ	NOUN
ejpam-6422	130	15	)	)	PUNCT
ejpam-6422	130	16	,	,	PUNCT
ejpam-6422	130	17	and	and	CCONJ
ejpam-6422	130	18	eq	eq	NOUN
ejpam-6422	130	19	.	.	PUNCT
ejpam-6422	131	1	(	(	PUNCT
ejpam-6422	131	2	11	11	NUM
ejpam-6422	131	3	)	)	PUNCT
ejpam-6422	131	4	has	have	VERB
ejpam-6422	131	5	the	the	DET
ejpam-6422	131	6	form	form	NOUN
ejpam-6422	131	7	w(x	w(x	PROPN
ejpam-6422	131	8	,	,	PUNCT
ejpam-6422	131	9	y	y	PROPN
ejpam-6422	131	10	,	,	PUNCT
ejpam-6422	131	11	z	z	PROPN
ejpam-6422	131	12	,	,	PUNCT
ejpam-6422	131	13	t	t	PROPN
ejpam-6422	131	14	)	)	PUNCT
ejpam-6422	131	15	=	=	PRON
ejpam-6422	131	16	{	{	PUNCT
ejpam-6422	132	1	−8	−8	X
ejpam-6422	132	2	5a2	5a2	NUM
ejpam-6422	132	3	±	±	NUM
ejpam-6422	132	4	√	√	NOUN
ejpam-6422	132	5	128ϖ2	128ϖ2	NUM
ejpam-6422	132	6	25a22(2ϖ	25a22(2ϖ	NUM
ejpam-6422	132	7	2	2	NUM
ejpam-6422	132	8	−	−	NOUN
ejpam-6422	132	9	1	1	NUM
ejpam-6422	132	10	)	)	PUNCT
ejpam-6422	132	11	cn(ρ1x+	cn(ρ1x+	NOUN
ejpam-6422	132	12	ρ2y	ρ2y	PROPN
ejpam-6422	133	1	+	+	CCONJ
ejpam-6422	134	1	ρ3z	ρ3z	NOUN
ejpam-6422	134	2	+	+	NOUN
ejpam-6422	134	3	λ	λ	X
ejpam-6422	134	4	κ	κ	X
ejpam-6422	134	5	(	(	PUNCT
ejpam-6422	134	6	t+	t+	NOUN
ejpam-6422	134	7	1	1	NUM
ejpam-6422	134	8	γ(κ	γ(κ	PROPN
ejpam-6422	134	9	)	)	PUNCT
ejpam-6422	134	10	)	)	PUNCT
ejpam-6422	134	11	κ	κ	X
ejpam-6422	134	12	)	)	PUNCT
ejpam-6422	134	13	}	}	PUNCT
ejpam-6422	134	14	,	,	PUNCT
ejpam-6422	134	15	(	(	PUNCT
ejpam-6422	134	16	15	15	NUM
ejpam-6422	134	17	)	)	PUNCT
ejpam-6422	134	18	for	for	ADP
ejpam-6422	134	19	1√	1√	PROPN
ejpam-6422	134	20	2	2	NUM
ejpam-6422	134	21	<	<	X
ejpam-6422	134	22	ϖ	ϖ	X
ejpam-6422	134	23	<	<	X
ejpam-6422	134	24	1	1	NUM
ejpam-6422	134	25	.	.	PUNCT
ejpam-6422	135	1	if	if	SCONJ
ejpam-6422	135	2	ϖ	ϖ	PRON
ejpam-6422	135	3	→	→	SYM
ejpam-6422	135	4	1	1	NUM
ejpam-6422	135	5	,	,	PUNCT
ejpam-6422	135	6	then	then	ADV
ejpam-6422	135	7	eq	eq	ADJ
ejpam-6422	135	8	.	.	PUNCT
ejpam-6422	136	1	(	(	PUNCT
ejpam-6422	136	2	15	15	NUM
ejpam-6422	136	3	)	)	PUNCT
ejpam-6422	136	4	becomes	become	VERB
ejpam-6422	136	5	w(x	w(x	PROPN
ejpam-6422	136	6	,	,	PUNCT
ejpam-6422	136	7	y	y	PROPN
ejpam-6422	136	8	,	,	PUNCT
ejpam-6422	136	9	z	z	PROPN
ejpam-6422	136	10	,	,	PUNCT
ejpam-6422	136	11	t	t	PROPN
ejpam-6422	136	12	)	)	PUNCT
ejpam-6422	136	13	=	=	PRON
ejpam-6422	136	14	{	{	PUNCT
ejpam-6422	137	1	−8	−8	X
ejpam-6422	137	2	5a2	5a2	NUM
ejpam-6422	137	3	±	±	NUM
ejpam-6422	137	4	√	√	NUM
ejpam-6422	137	5	128	128	NUM
ejpam-6422	137	6	25a22	25a22	NUM
ejpam-6422	137	7	sech(ρ1x+	sech(ρ1x+	PROPN
ejpam-6422	137	8	ρ2y	ρ2y	PROPN
ejpam-6422	137	9	+	+	PUNCT
ejpam-6422	138	1	ρ3z	ρ3z	PROPN
ejpam-6422	138	2	+	+	NOUN
ejpam-6422	138	3	λ	λ	X
ejpam-6422	138	4	κ	κ	X
ejpam-6422	138	5	(	(	PUNCT
ejpam-6422	138	6	t+	t+	NOUN
ejpam-6422	138	7	1	1	NUM
ejpam-6422	138	8	γ(κ	γ(κ	PROPN
ejpam-6422	138	9	)	)	PUNCT
ejpam-6422	138	10	)	)	PUNCT
ejpam-6422	138	11	κ	κ	X
ejpam-6422	138	12	)	)	PUNCT
ejpam-6422	138	13	}	}	PUNCT
ejpam-6422	138	14	.	.	PUNCT
ejpam-6422	139	1	(	(	PUNCT
ejpam-6422	139	2	16	16	NUM
ejpam-6422	139	3	)	)	PUNCT
ejpam-6422	139	4	case	case	NOUN
ejpam-6422	139	5	4	4	NUM
ejpam-6422	139	6	:	:	PUNCT
ejpam-6422	139	7	if	if	SCONJ
ejpam-6422	139	8	ℏ1	ℏ1	PROPN
ejpam-6422	139	9	=	=	SYM
ejpam-6422	139	10	−1	−1	NOUN
ejpam-6422	139	11	,	,	PUNCT
ejpam-6422	139	12	ℏ2	ℏ2	NOUN
ejpam-6422	139	13	=	=	SYM
ejpam-6422	139	14	2−ϖ2	2−ϖ2	NUM
ejpam-6422	139	15	and	and	CCONJ
ejpam-6422	139	16	ℏ3	ℏ3	PROPN
ejpam-6422	139	17	=	=	SYM
ejpam-6422	139	18	ϖ2	ϖ2	NOUN
ejpam-6422	139	19	−	−	NOUN
ejpam-6422	139	20	1	1	NUM
ejpam-6422	139	21	,	,	PUNCT
ejpam-6422	139	22	then	then	ADV
ejpam-6422	139	23	f	f	PROPN
ejpam-6422	139	24	(	(	PUNCT
ejpam-6422	139	25	ρ	ρ	PROPN
ejpam-6422	139	26	)	)	PUNCT
ejpam-6422	139	27	=	=	PRON
ejpam-6422	139	28	dn(ρ	dn(ρ	PRON
ejpam-6422	139	29	)	)	PUNCT
ejpam-6422	139	30	,	,	PUNCT
ejpam-6422	139	31	and	and	CCONJ
ejpam-6422	139	32	eq	eq	NOUN
ejpam-6422	139	33	.	.	PUNCT
ejpam-6422	140	1	(	(	PUNCT
ejpam-6422	140	2	11	11	NUM
ejpam-6422	140	3	)	)	PUNCT
ejpam-6422	140	4	has	have	VERB
ejpam-6422	140	5	the	the	DET
ejpam-6422	140	6	form	form	NOUN
ejpam-6422	140	7	w(x	w(x	PROPN
ejpam-6422	140	8	,	,	PUNCT
ejpam-6422	140	9	y	y	PROPN
ejpam-6422	140	10	,	,	PUNCT
ejpam-6422	140	11	z	z	PROPN
ejpam-6422	140	12	,	,	PUNCT
ejpam-6422	140	13	t	t	PROPN
ejpam-6422	140	14	)	)	PUNCT
ejpam-6422	140	15	=	=	PRON
ejpam-6422	140	16	{	{	PUNCT
ejpam-6422	141	1	−8	−8	X
ejpam-6422	141	2	5a2	5a2	NUM
ejpam-6422	141	3	±	±	NUM
ejpam-6422	141	4	√	√	NOUN
ejpam-6422	141	5	128	128	NUM
ejpam-6422	141	6	25a22(2−ϖ2	25a22(2−ϖ2	PROPN
ejpam-6422	141	7	)	)	PUNCT
ejpam-6422	142	1	dn(ρ1x+	dn(ρ1x+	NUM
ejpam-6422	142	2	ρ2y	ρ2y	PROPN
ejpam-6422	142	3	+	+	PUNCT
ejpam-6422	143	1	ρ3z	ρ3z	NOUN
ejpam-6422	143	2	+	+	NOUN
ejpam-6422	143	3	λ	λ	X
ejpam-6422	143	4	κ	κ	X
ejpam-6422	143	5	(	(	PUNCT
ejpam-6422	143	6	t+	t+	NOUN
ejpam-6422	143	7	1	1	NUM
ejpam-6422	143	8	γ(κ	γ(κ	PROPN
ejpam-6422	143	9	)	)	PUNCT
ejpam-6422	143	10	)	)	PUNCT
ejpam-6422	143	11	κ	κ	X
ejpam-6422	143	12	)	)	PUNCT
ejpam-6422	143	13	}	}	PUNCT
ejpam-6422	143	14	.	.	PUNCT
ejpam-6422	144	1	(	(	PUNCT
ejpam-6422	144	2	17	17	NUM
ejpam-6422	144	3	)	)	PUNCT
ejpam-6422	144	4	if	if	SCONJ
ejpam-6422	144	5	ϖ	ϖ	PRON
ejpam-6422	144	6	→	→	SYM
ejpam-6422	144	7	1	1	NUM
ejpam-6422	144	8	,	,	PUNCT
ejpam-6422	144	9	then	then	ADV
ejpam-6422	144	10	eq	eq	ADJ
ejpam-6422	144	11	.	.	PUNCT
ejpam-6422	145	1	(	(	PUNCT
ejpam-6422	145	2	17	17	NUM
ejpam-6422	145	3	)	)	PUNCT
ejpam-6422	145	4	becomes	become	VERB
ejpam-6422	145	5	eqs	eqs	X
ejpam-6422	145	6	(	(	PUNCT
ejpam-6422	145	7	16	16	NUM
ejpam-6422	145	8	)	)	PUNCT
ejpam-6422	145	9	.	.	PUNCT
ejpam-6422	146	1	case	case	NOUN
ejpam-6422	146	2	5	5	NUM
ejpam-6422	146	3	:	:	PUNCT
ejpam-6422	146	4	if	if	SCONJ
ejpam-6422	146	5	ℏ1	ℏ1	ADJ
ejpam-6422	146	6	=	=	SYM
ejpam-6422	146	7	1	1	NUM
ejpam-6422	146	8	,	,	PUNCT
ejpam-6422	146	9	ℏ2	ℏ2	NOUN
ejpam-6422	146	10	=	=	SYM
ejpam-6422	147	1	−	−	PROPN
ejpam-6422	147	2	(	(	PUNCT
ejpam-6422	147	3	1	1	NUM
ejpam-6422	147	4	+	+	NOUN
ejpam-6422	147	5	ϖ2	ϖ2	NOUN
ejpam-6422	147	6	)	)	PUNCT
ejpam-6422	147	7	and	and	CCONJ
ejpam-6422	147	8	ℏ3	ℏ3	PROPN
ejpam-6422	147	9	=	=	SYM
ejpam-6422	147	10	ϖ2	ϖ2	PROPN
ejpam-6422	147	11	,	,	PUNCT
ejpam-6422	147	12	then	then	ADV
ejpam-6422	147	13	f	f	PROPN
ejpam-6422	147	14	(	(	PUNCT
ejpam-6422	147	15	ρ	ρ	PROPN
ejpam-6422	147	16	)	)	PUNCT
ejpam-6422	147	17	=	=	SYM
ejpam-6422	147	18	ns(ρ	ns(ρ	ADJ
ejpam-6422	147	19	)	)	PUNCT
ejpam-6422	147	20	,	,	PUNCT
ejpam-6422	147	21	and	and	CCONJ
ejpam-6422	147	22	eq	eq	NOUN
ejpam-6422	147	23	.	.	PUNCT
ejpam-6422	148	1	(	(	PUNCT
ejpam-6422	148	2	11	11	NUM
ejpam-6422	148	3	)	)	PUNCT
ejpam-6422	148	4	has	have	VERB
ejpam-6422	148	5	the	the	DET
ejpam-6422	148	6	form	form	NOUN
ejpam-6422	148	7	w(x	w(x	PROPN
ejpam-6422	148	8	,	,	PUNCT
ejpam-6422	148	9	y	y	PROPN
ejpam-6422	148	10	,	,	PUNCT
ejpam-6422	148	11	z	z	PROPN
ejpam-6422	148	12	,	,	PUNCT
ejpam-6422	148	13	t	t	PROPN
ejpam-6422	148	14	)	)	PUNCT
ejpam-6422	148	15	=	=	PRON
ejpam-6422	148	16	{	{	PUNCT
ejpam-6422	149	1	−8	−8	X
ejpam-6422	149	2	5a2	5a2	NUM
ejpam-6422	149	3	±	±	NUM
ejpam-6422	149	4	√	√	NUM
ejpam-6422	149	5	128	128	NUM
ejpam-6422	149	6	25a22	25a22	NUM
ejpam-6422	149	7	(	(	PUNCT
ejpam-6422	149	8	1	1	NUM
ejpam-6422	149	9	+	+	NOUN
ejpam-6422	149	10	ϖ2	ϖ2	NOUN
ejpam-6422	149	11	)	)	PUNCT
ejpam-6422	149	12	ns(ρ1x+	ns(ρ1x+	NUM
ejpam-6422	149	13	ρ2y	ρ2y	PROPN
ejpam-6422	150	1	+	+	PUNCT
ejpam-6422	150	2	ρ3z	ρ3z	PROPN
ejpam-6422	150	3	+	+	NOUN
ejpam-6422	150	4	λ	λ	X
ejpam-6422	150	5	κ	κ	X
ejpam-6422	150	6	(	(	PUNCT
ejpam-6422	150	7	t+	t+	NOUN
ejpam-6422	150	8	1	1	NUM
ejpam-6422	150	9	γ(κ	γ(κ	PROPN
ejpam-6422	150	10	)	)	PUNCT
ejpam-6422	150	11	)	)	PUNCT
ejpam-6422	150	12	κ	κ	X
ejpam-6422	150	13	)	)	PUNCT
ejpam-6422	150	14	}	}	PUNCT
ejpam-6422	150	15	.	.	PUNCT
ejpam-6422	151	1	(	(	PUNCT
ejpam-6422	151	2	18	18	NUM
ejpam-6422	151	3	)	)	PUNCT
ejpam-6422	151	4	w.	w.	PROPN
ejpam-6422	151	5	w.	w.	PROPN
ejpam-6422	151	6	mohammed	mohammed	PROPN
ejpam-6422	151	7	et	et	PROPN
ejpam-6422	151	8	al	al	PROPN
ejpam-6422	151	9	.	.	PUNCT
ejpam-6422	151	10	/	/	SYM
ejpam-6422	151	11	eur	eur	PROPN
ejpam-6422	151	12	.	.	PUNCT
ejpam-6422	152	1	j.	j.	PROPN
ejpam-6422	152	2	pure	pure	PROPN
ejpam-6422	152	3	appl	appl	PROPN
ejpam-6422	152	4	.	.	PROPN
ejpam-6422	152	5	math	math	PROPN
ejpam-6422	152	6	,	,	PUNCT
ejpam-6422	152	7	18	18	NUM
ejpam-6422	152	8	(	(	PUNCT
ejpam-6422	152	9	3	3	NUM
ejpam-6422	152	10	)	)	PUNCT
ejpam-6422	152	11	(	(	PUNCT
ejpam-6422	152	12	2025	2025	NUM
ejpam-6422	152	13	)	)	PUNCT
ejpam-6422	152	14	,	,	PUNCT
ejpam-6422	152	15	6422	6422	NUM
ejpam-6422	152	16	6	6	NUM
ejpam-6422	152	17	of	of	ADP
ejpam-6422	152	18	13	13	NUM
ejpam-6422	152	19	if	if	SCONJ
ejpam-6422	152	20	ϖ	ϖ	PROPN
ejpam-6422	152	21	→	→	SYM
ejpam-6422	152	22	1	1	NUM
ejpam-6422	152	23	,	,	PUNCT
ejpam-6422	152	24	then	then	ADV
ejpam-6422	152	25	eq	eq	ADJ
ejpam-6422	152	26	.	.	PUNCT
ejpam-6422	153	1	(	(	PUNCT
ejpam-6422	153	2	18	18	NUM
ejpam-6422	153	3	)	)	PUNCT
ejpam-6422	153	4	tends	tend	VERB
ejpam-6422	153	5	to	to	ADP
ejpam-6422	153	6	w(x	w(x	PROPN
ejpam-6422	153	7	,	,	PUNCT
ejpam-6422	153	8	y	y	PROPN
ejpam-6422	153	9	,	,	PUNCT
ejpam-6422	153	10	z	z	PROPN
ejpam-6422	153	11	,	,	PUNCT
ejpam-6422	153	12	t	t	PROPN
ejpam-6422	153	13	)	)	PUNCT
ejpam-6422	154	1	=	=	PRON
ejpam-6422	154	2	{	{	PUNCT
ejpam-6422	155	1	−8	−8	X
ejpam-6422	155	2	5a2	5a2	NUM
ejpam-6422	155	3	±	±	NUM
ejpam-6422	155	4	8	8	NUM
ejpam-6422	155	5	5a2	5a2	NUM
ejpam-6422	155	6	coth(ρ1x+	coth(ρ1x+	NOUN
ejpam-6422	155	7	ρ2y	ρ2y	PROPN
ejpam-6422	155	8	+	+	PUNCT
ejpam-6422	156	1	ρ3z	ρ3z	NOUN
ejpam-6422	156	2	+	+	NOUN
ejpam-6422	156	3	λ	λ	X
ejpam-6422	156	4	κ	κ	X
ejpam-6422	156	5	(	(	PUNCT
ejpam-6422	156	6	t+	t+	NOUN
ejpam-6422	156	7	1	1	NUM
ejpam-6422	156	8	γ(κ	γ(κ	PROPN
ejpam-6422	156	9	)	)	PUNCT
ejpam-6422	156	10	)	)	PUNCT
ejpam-6422	156	11	κ	κ	X
ejpam-6422	156	12	)	)	PUNCT
ejpam-6422	156	13	}	}	PUNCT
ejpam-6422	156	14	.	.	PUNCT
ejpam-6422	157	1	(	(	PUNCT
ejpam-6422	157	2	19	19	NUM
ejpam-6422	157	3	)	)	PUNCT
ejpam-6422	157	4	while	while	SCONJ
ejpam-6422	157	5	if	if	SCONJ
ejpam-6422	157	6	ϖ	ϖ	PRON
ejpam-6422	157	7	→	→	SYM
ejpam-6422	157	8	0	0	NUM
ejpam-6422	157	9	,	,	PUNCT
ejpam-6422	157	10	then	then	ADV
ejpam-6422	157	11	eq	eq	ADJ
ejpam-6422	157	12	.	.	PUNCT
ejpam-6422	158	1	(	(	PUNCT
ejpam-6422	158	2	18	18	NUM
ejpam-6422	158	3	)	)	PUNCT
ejpam-6422	158	4	becomes	become	VERB
ejpam-6422	158	5	w(x	w(x	PROPN
ejpam-6422	158	6	,	,	PUNCT
ejpam-6422	158	7	y	y	PROPN
ejpam-6422	158	8	,	,	PUNCT
ejpam-6422	158	9	z	z	PROPN
ejpam-6422	158	10	,	,	PUNCT
ejpam-6422	158	11	t	t	PROPN
ejpam-6422	158	12	)	)	PUNCT
ejpam-6422	158	13	=	=	PRON
ejpam-6422	158	14	{	{	PUNCT
ejpam-6422	159	1	−8	−8	X
ejpam-6422	159	2	5a2	5a2	NUM
ejpam-6422	159	3	±	±	NUM
ejpam-6422	159	4	√	√	NUM
ejpam-6422	159	5	128	128	NUM
ejpam-6422	159	6	25a22	25a22	NUM
ejpam-6422	159	7	csc(ρ	csc(ρ	PROPN
ejpam-6422	159	8	)	)	PUNCT
ejpam-6422	159	9	}	}	PUNCT
ejpam-6422	159	10	.	.	PUNCT
ejpam-6422	160	1	(	(	PUNCT
ejpam-6422	160	2	20	20	NUM
ejpam-6422	160	3	)	)	PUNCT
ejpam-6422	160	4	case	case	NOUN
ejpam-6422	160	5	6	6	NUM
ejpam-6422	160	6	:	:	PUNCT
ejpam-6422	160	7	if	if	SCONJ
ejpam-6422	160	8	ℏ1	ℏ1	ADJ
ejpam-6422	160	9	=	=	SYM
ejpam-6422	160	10	1	1	NUM
ejpam-6422	160	11	,	,	PUNCT
ejpam-6422	160	12	ℏ2	ℏ2	NOUN
ejpam-6422	160	13	=	=	SYM
ejpam-6422	161	1	−	−	PROPN
ejpam-6422	161	2	(	(	PUNCT
ejpam-6422	161	3	1	1	NUM
ejpam-6422	161	4	+	+	NOUN
ejpam-6422	161	5	ϖ2	ϖ2	NOUN
ejpam-6422	161	6	)	)	PUNCT
ejpam-6422	161	7	and	and	CCONJ
ejpam-6422	161	8	ℏ3	ℏ3	PROPN
ejpam-6422	161	9	=	=	SYM
ejpam-6422	161	10	ϖ2	ϖ2	PROPN
ejpam-6422	161	11	,	,	PUNCT
ejpam-6422	161	12	then	then	ADV
ejpam-6422	161	13	f	f	PROPN
ejpam-6422	161	14	(	(	PUNCT
ejpam-6422	161	15	ρ	ρ	PROPN
ejpam-6422	161	16	)	)	PUNCT
ejpam-6422	161	17	=	=	PUNCT
ejpam-6422	161	18	dc(ρ	dc(ρ	X
ejpam-6422	161	19	)	)	PUNCT
ejpam-6422	161	20	=	=	PRON
ejpam-6422	161	21	dn(ρ	dn(ρ	X
ejpam-6422	161	22	)	)	PUNCT
ejpam-6422	161	23	cn(ρ	cn(ρ	NUM
ejpam-6422	161	24	)	)	PUNCT
ejpam-6422	161	25	,	,	PUNCT
ejpam-6422	161	26	and	and	CCONJ
ejpam-6422	161	27	eq	eq	NOUN
ejpam-6422	161	28	.	.	PUNCT
ejpam-6422	162	1	(	(	PUNCT
ejpam-6422	162	2	11	11	NUM
ejpam-6422	162	3	)	)	PUNCT
ejpam-6422	162	4	has	have	VERB
ejpam-6422	162	5	the	the	DET
ejpam-6422	162	6	form	form	NOUN
ejpam-6422	162	7	w(x	w(x	PROPN
ejpam-6422	162	8	,	,	PUNCT
ejpam-6422	162	9	y	y	PROPN
ejpam-6422	162	10	,	,	PUNCT
ejpam-6422	162	11	z	z	PROPN
ejpam-6422	162	12	,	,	PUNCT
ejpam-6422	162	13	t	t	PROPN
ejpam-6422	162	14	)	)	PUNCT
ejpam-6422	162	15	=	=	PRON
ejpam-6422	162	16	{	{	PUNCT
ejpam-6422	163	1	−8	−8	X
ejpam-6422	163	2	5a2	5a2	NUM
ejpam-6422	163	3	±	±	NUM
ejpam-6422	163	4	√	√	NUM
ejpam-6422	163	5	128	128	NUM
ejpam-6422	163	6	25a22	25a22	NUM
ejpam-6422	163	7	(	(	PUNCT
ejpam-6422	163	8	1	1	NUM
ejpam-6422	163	9	+	+	NOUN
ejpam-6422	163	10	ϖ2	ϖ2	NOUN
ejpam-6422	163	11	)	)	PUNCT
ejpam-6422	163	12	dc(ρ1x+	dc(ρ1x+	NUM
ejpam-6422	163	13	ρ2y	ρ2y	PROPN
ejpam-6422	164	1	+	+	CCONJ
ejpam-6422	164	2	ρ3z	ρ3z	NOUN
ejpam-6422	164	3	+	+	NOUN
ejpam-6422	164	4	λ	λ	X
ejpam-6422	164	5	κ	κ	X
ejpam-6422	164	6	(	(	PUNCT
ejpam-6422	164	7	t+	t+	NOUN
ejpam-6422	164	8	1	1	NUM
ejpam-6422	164	9	γ(κ	γ(κ	PROPN
ejpam-6422	164	10	)	)	PUNCT
ejpam-6422	164	11	)	)	PUNCT
ejpam-6422	164	12	κ	κ	X
ejpam-6422	164	13	)	)	PUNCT
ejpam-6422	164	14	}	}	PUNCT
ejpam-6422	164	15	.	.	PUNCT
ejpam-6422	165	1	(	(	PUNCT
ejpam-6422	165	2	21	21	NUM
ejpam-6422	165	3	)	)	PUNCT
ejpam-6422	165	4	if	if	SCONJ
ejpam-6422	165	5	ϖ	ϖ	PRON
ejpam-6422	165	6	→	→	SYM
ejpam-6422	165	7	0	0	NUM
ejpam-6422	165	8	,	,	PUNCT
ejpam-6422	165	9	then	then	ADV
ejpam-6422	165	10	eq	eq	ADJ
ejpam-6422	165	11	.	.	PUNCT
ejpam-6422	166	1	(	(	PUNCT
ejpam-6422	166	2	21	21	NUM
ejpam-6422	166	3	)	)	PUNCT
ejpam-6422	166	4	becomes	become	VERB
ejpam-6422	166	5	w(x	w(x	PROPN
ejpam-6422	166	6	,	,	PUNCT
ejpam-6422	166	7	y	y	PROPN
ejpam-6422	166	8	,	,	PUNCT
ejpam-6422	166	9	z	z	PROPN
ejpam-6422	166	10	,	,	PUNCT
ejpam-6422	166	11	t	t	PROPN
ejpam-6422	166	12	)	)	PUNCT
ejpam-6422	166	13	=	=	PRON
ejpam-6422	166	14	{	{	PUNCT
ejpam-6422	167	1	−8	−8	X
ejpam-6422	167	2	5a2	5a2	NUM
ejpam-6422	167	3	±	±	NUM
ejpam-6422	167	4	√	√	NUM
ejpam-6422	167	5	128	128	NUM
ejpam-6422	167	6	25a22	25a22	NUM
ejpam-6422	167	7	sec(ρ1x+	sec(ρ1x+	NOUN
ejpam-6422	167	8	ρ2y	ρ2y	PROPN
ejpam-6422	168	1	+	+	CCONJ
ejpam-6422	169	1	ρ3z	ρ3z	NOUN
ejpam-6422	169	2	+	+	NOUN
ejpam-6422	169	3	λ	λ	X
ejpam-6422	169	4	κ	κ	X
ejpam-6422	169	5	(	(	PUNCT
ejpam-6422	169	6	t+	t+	NOUN
ejpam-6422	169	7	1	1	NUM
ejpam-6422	169	8	γ(κ	γ(κ	PROPN
ejpam-6422	169	9	)	)	PUNCT
ejpam-6422	169	10	)	)	PUNCT
ejpam-6422	169	11	κ	κ	X
ejpam-6422	169	12	)	)	PUNCT
ejpam-6422	169	13	}	}	PUNCT
ejpam-6422	169	14	.	.	PUNCT
ejpam-6422	170	1	(	(	PUNCT
ejpam-6422	170	2	22	22	NUM
ejpam-6422	170	3	)	)	PUNCT
ejpam-6422	170	4	case	case	NOUN
ejpam-6422	170	5	7	7	NUM
ejpam-6422	170	6	:	:	PUNCT
ejpam-6422	170	7	if	if	SCONJ
ejpam-6422	170	8	ℏ1	ℏ1	PROPN
ejpam-6422	170	9	=	=	SYM
ejpam-6422	170	10	1−ϖ2	1−ϖ2	NUM
ejpam-6422	170	11	,	,	PUNCT
ejpam-6422	170	12	ℏ2	ℏ2	NOUN
ejpam-6422	170	13	=	=	SYM
ejpam-6422	170	14	2ϖ2	2ϖ2	PROPN
ejpam-6422	170	15	−	−	NOUN
ejpam-6422	170	16	1	1	NUM
ejpam-6422	170	17	and	and	CCONJ
ejpam-6422	170	18	ℏ3	ℏ3	PROPN
ejpam-6422	170	19	=	=	SYM
ejpam-6422	170	20	−ϖ2	−ϖ2	PROPN
ejpam-6422	170	21	,	,	PUNCT
ejpam-6422	170	22	then	then	ADV
ejpam-6422	170	23	f	f	PROPN
ejpam-6422	170	24	(	(	PUNCT
ejpam-6422	170	25	ρ	ρ	PROPN
ejpam-6422	170	26	)	)	PUNCT
ejpam-6422	170	27	=	=	SYM
ejpam-6422	170	28	nc(ρ	nc(ρ	PROPN
ejpam-6422	170	29	)	)	PUNCT
ejpam-6422	170	30	,	,	PUNCT
ejpam-6422	170	31	and	and	CCONJ
ejpam-6422	170	32	eq	eq	NOUN
ejpam-6422	170	33	.	.	PUNCT
ejpam-6422	171	1	(	(	PUNCT
ejpam-6422	171	2	11	11	NUM
ejpam-6422	171	3	)	)	PUNCT
ejpam-6422	171	4	has	have	VERB
ejpam-6422	171	5	the	the	DET
ejpam-6422	171	6	form	form	NOUN
ejpam-6422	171	7	w(x	w(x	PROPN
ejpam-6422	171	8	,	,	PUNCT
ejpam-6422	171	9	y	y	PROPN
ejpam-6422	171	10	,	,	PUNCT
ejpam-6422	171	11	z	z	PROPN
ejpam-6422	171	12	,	,	PUNCT
ejpam-6422	171	13	t	t	PROPN
ejpam-6422	171	14	)	)	PUNCT
ejpam-6422	171	15	=	=	PRON
ejpam-6422	171	16	{	{	PUNCT
ejpam-6422	172	1	−8	−8	X
ejpam-6422	172	2	5a2	5a2	NUM
ejpam-6422	172	3	±	±	NUM
ejpam-6422	172	4	√	√	NUM
ejpam-6422	172	5	128(1−ϖ2	128(1−ϖ2	NUM
ejpam-6422	172	6	)	)	PUNCT
ejpam-6422	172	7	25a22(2ϖ	25a22(2ϖ	NUM
ejpam-6422	172	8	2	2	NUM
ejpam-6422	172	9	−	−	NOUN
ejpam-6422	172	10	1	1	NUM
ejpam-6422	172	11	)	)	PUNCT
ejpam-6422	172	12	nc(ρ1x+	nc(ρ1x+	NUM
ejpam-6422	173	1	ρ2y	ρ2y	PROPN
ejpam-6422	173	2	+	+	PUNCT
ejpam-6422	174	1	ρ3z	ρ3z	NOUN
ejpam-6422	175	1	+	+	NOUN
ejpam-6422	175	2	λ	λ	X
ejpam-6422	175	3	κ	κ	X
ejpam-6422	175	4	(	(	PUNCT
ejpam-6422	175	5	t+	t+	NOUN
ejpam-6422	175	6	1	1	NUM
ejpam-6422	175	7	γ(κ	γ(κ	PROPN
ejpam-6422	175	8	)	)	PUNCT
ejpam-6422	175	9	)	)	PUNCT
ejpam-6422	175	10	κ	κ	X
ejpam-6422	175	11	)	)	PUNCT
ejpam-6422	175	12	}	}	PUNCT
ejpam-6422	175	13	,	,	PUNCT
ejpam-6422	175	14	(	(	PUNCT
ejpam-6422	175	15	23	23	NUM
ejpam-6422	175	16	)	)	PUNCT
ejpam-6422	175	17	for	for	ADP
ejpam-6422	175	18	ϖ	ϖ	INTJ
ejpam-6422	175	19	<	<	X
ejpam-6422	175	20	1√	1√	PROPN
ejpam-6422	175	21	2	2	NUM
ejpam-6422	175	22	.	.	PUNCT
ejpam-6422	176	1	if	if	SCONJ
ejpam-6422	176	2	ϖ	ϖ	PROPN
ejpam-6422	176	3	→	→	SYM
ejpam-6422	176	4	0	0	NUM
ejpam-6422	176	5	,	,	PUNCT
ejpam-6422	176	6	then	then	ADV
ejpam-6422	176	7	eq	eq	ADJ
ejpam-6422	176	8	.	.	PUNCT
ejpam-6422	177	1	(	(	PUNCT
ejpam-6422	177	2	23	23	NUM
ejpam-6422	177	3	)	)	PUNCT
ejpam-6422	177	4	becomes	become	VERB
ejpam-6422	177	5	eqs	eqs	X
ejpam-6422	177	6	(	(	PUNCT
ejpam-6422	177	7	22	22	NUM
ejpam-6422	177	8	)	)	PUNCT
ejpam-6422	177	9	.	.	PUNCT
ejpam-6422	178	1	case	case	NOUN
ejpam-6422	178	2	8	8	NUM
ejpam-6422	178	3	:	:	PUNCT
ejpam-6422	178	4	if	if	SCONJ
ejpam-6422	178	5	ℏ1	ℏ1	PROPN
ejpam-6422	178	6	=	=	SYM
ejpam-6422	178	7	ϖ2	ϖ2	NOUN
ejpam-6422	178	8	−	−	NOUN
ejpam-6422	178	9	1	1	NUM
ejpam-6422	178	10	,	,	PUNCT
ejpam-6422	179	1	ℏ2	ℏ2	NOUN
ejpam-6422	179	2	=	=	SYM
ejpam-6422	179	3	2−ϖ2	2−ϖ2	NUM
ejpam-6422	179	4	and	and	CCONJ
ejpam-6422	179	5	ℏ3	ℏ3	PROPN
ejpam-6422	179	6	=	=	SYM
ejpam-6422	179	7	−1	−1	NOUN
ejpam-6422	179	8	,	,	PUNCT
ejpam-6422	179	9	then	then	ADV
ejpam-6422	179	10	f	f	PROPN
ejpam-6422	179	11	(	(	PUNCT
ejpam-6422	179	12	ρ	ρ	PROPN
ejpam-6422	179	13	)	)	PUNCT
ejpam-6422	179	14	=	=	SYM
ejpam-6422	179	15	nd(ρ	nd(ρ	NUM
ejpam-6422	179	16	)	)	PUNCT
ejpam-6422	179	17	,	,	PUNCT
ejpam-6422	179	18	and	and	CCONJ
ejpam-6422	179	19	eq	eq	NOUN
ejpam-6422	179	20	.	.	PUNCT
ejpam-6422	180	1	(	(	PUNCT
ejpam-6422	180	2	11	11	NUM
ejpam-6422	180	3	)	)	PUNCT
ejpam-6422	180	4	takes	take	VERB
ejpam-6422	180	5	the	the	DET
ejpam-6422	180	6	form	form	NOUN
ejpam-6422	180	7	w(x	w(x	PROPN
ejpam-6422	180	8	,	,	PUNCT
ejpam-6422	180	9	y	y	PROPN
ejpam-6422	180	10	,	,	PUNCT
ejpam-6422	180	11	z	z	PROPN
ejpam-6422	180	12	,	,	PUNCT
ejpam-6422	180	13	t	t	PROPN
ejpam-6422	180	14	)	)	PUNCT
ejpam-6422	180	15	=	=	PRON
ejpam-6422	180	16	{	{	PUNCT
ejpam-6422	181	1	−8	−8	X
ejpam-6422	181	2	5a2	5a2	NUM
ejpam-6422	181	3	±	±	NUM
ejpam-6422	181	4	√	√	NUM
ejpam-6422	181	5	128(1−ϖ2	128(1−ϖ2	NUM
ejpam-6422	181	6	)	)	PUNCT
ejpam-6422	181	7	25a22(2−ϖ2	25a22(2−ϖ2	PROPN
ejpam-6422	181	8	)	)	PUNCT
ejpam-6422	181	9	nd(ρ1x+	nd(ρ1x+	NUM
ejpam-6422	181	10	ρ2y	ρ2y	PROPN
ejpam-6422	182	1	+	+	CCONJ
ejpam-6422	182	2	ρ3z	ρ3z	PROPN
ejpam-6422	182	3	+	+	NOUN
ejpam-6422	182	4	λ	λ	X
ejpam-6422	182	5	κ	κ	X
ejpam-6422	182	6	(	(	PUNCT
ejpam-6422	182	7	t+	t+	NOUN
ejpam-6422	182	8	1	1	NUM
ejpam-6422	182	9	γ(κ	γ(κ	PROPN
ejpam-6422	182	10	)	)	PUNCT
ejpam-6422	182	11	)	)	PUNCT
ejpam-6422	182	12	κ	κ	X
ejpam-6422	182	13	)	)	PUNCT
ejpam-6422	182	14	}	}	PUNCT
ejpam-6422	182	15	.	.	PUNCT
ejpam-6422	183	1	(	(	PUNCT
ejpam-6422	183	2	24	24	NUM
ejpam-6422	183	3	)	)	PUNCT
ejpam-6422	183	4	case	case	NOUN
ejpam-6422	183	5	9	9	NUM
ejpam-6422	183	6	:	:	PUNCT
ejpam-6422	183	7	if	if	SCONJ
ejpam-6422	183	8	ℏ1	ℏ1	PROPN
ejpam-6422	183	9	=	=	SYM
ejpam-6422	183	10	−ϖ2(1	−ϖ2(1	NOUN
ejpam-6422	183	11	−	−	NOUN
ejpam-6422	183	12	ϖ2	ϖ2	NOUN
ejpam-6422	183	13	)	)	PUNCT
ejpam-6422	183	14	,	,	PUNCT
ejpam-6422	183	15	ℏ2	ℏ2	NOUN
ejpam-6422	183	16	=	=	SYM
ejpam-6422	183	17	2ϖ2	2ϖ2	PROPN
ejpam-6422	184	1	−	−	NOUN
ejpam-6422	184	2	1	1	NUM
ejpam-6422	184	3	and	and	CCONJ
ejpam-6422	184	4	ℏ3	ℏ3	PROPN
ejpam-6422	184	5	=	=	SYM
ejpam-6422	184	6	1	1	NUM
ejpam-6422	184	7	,	,	PUNCT
ejpam-6422	184	8	then	then	ADV
ejpam-6422	184	9	f	f	PROPN
ejpam-6422	184	10	(	(	PUNCT
ejpam-6422	184	11	ρ	ρ	PROPN
ejpam-6422	184	12	)	)	PUNCT
ejpam-6422	184	13	=	=	SYM
ejpam-6422	184	14	sd(ρ	sd(ρ	NOUN
ejpam-6422	184	15	)	)	PUNCT
ejpam-6422	184	16	,	,	PUNCT
ejpam-6422	184	17	and	and	CCONJ
ejpam-6422	184	18	eq	eq	NOUN
ejpam-6422	184	19	.	.	PUNCT
ejpam-6422	185	1	(	(	PUNCT
ejpam-6422	185	2	11	11	NUM
ejpam-6422	185	3	)	)	PUNCT
ejpam-6422	185	4	takes	take	VERB
ejpam-6422	185	5	the	the	DET
ejpam-6422	185	6	form	form	NOUN
ejpam-6422	185	7	w(x	w(x	PROPN
ejpam-6422	185	8	,	,	PUNCT
ejpam-6422	185	9	y	y	PROPN
ejpam-6422	185	10	,	,	PUNCT
ejpam-6422	185	11	z	z	PROPN
ejpam-6422	185	12	,	,	PUNCT
ejpam-6422	185	13	t	t	PROPN
ejpam-6422	185	14	)	)	PUNCT
ejpam-6422	185	15	=	=	PRON
ejpam-6422	185	16	{	{	PUNCT
ejpam-6422	186	1	−8	−8	X
ejpam-6422	186	2	5a2	5a2	NUM
ejpam-6422	186	3	±	±	NUM
ejpam-6422	186	4	√	√	NUM
ejpam-6422	186	5	128ϖ2(1−ϖ2	128ϖ2(1−ϖ2	NUM
ejpam-6422	186	6	)	)	PUNCT
ejpam-6422	186	7	25a22(1−	25a22(1−	NUM
ejpam-6422	186	8	2ϖ2	2ϖ2	NUM
ejpam-6422	186	9	)	)	PUNCT
ejpam-6422	186	10	sd(ρ1x+	sd(ρ1x+	NUM
ejpam-6422	186	11	ρ2y	ρ2y	PROPN
ejpam-6422	187	1	+	+	PUNCT
ejpam-6422	188	1	ρ3z	ρ3z	NOUN
ejpam-6422	189	1	+	+	NOUN
ejpam-6422	189	2	λ	λ	X
ejpam-6422	189	3	κ	κ	X
ejpam-6422	189	4	(	(	PUNCT
ejpam-6422	189	5	t+	t+	NOUN
ejpam-6422	189	6	1	1	NUM
ejpam-6422	189	7	γ(κ	γ(κ	PROPN
ejpam-6422	189	8	)	)	PUNCT
ejpam-6422	189	9	)	)	PUNCT
ejpam-6422	189	10	κ	κ	X
ejpam-6422	189	11	)	)	PUNCT
ejpam-6422	189	12	}	}	PUNCT
ejpam-6422	189	13	,	,	PUNCT
ejpam-6422	189	14	(	(	PUNCT
ejpam-6422	189	15	25	25	NUM
ejpam-6422	189	16	)	)	PUNCT
ejpam-6422	189	17	for	for	ADP
ejpam-6422	189	18	ϖ	ϖ	INTJ
ejpam-6422	189	19	>	>	X
ejpam-6422	189	20	1√	1√	PROPN
ejpam-6422	189	21	2	2	NUM
ejpam-6422	189	22	.	.	PUNCT
ejpam-6422	189	23	case	case	NOUN
ejpam-6422	189	24	10	10	NUM
ejpam-6422	189	25	:	:	PUNCT
ejpam-6422	189	26	if	if	SCONJ
ejpam-6422	189	27	ℏ1	ℏ1	ADJ
ejpam-6422	189	28	=	=	SYM
ejpam-6422	189	29	1	1	NUM
ejpam-6422	189	30	,	,	PUNCT
ejpam-6422	189	31	ℏ2	ℏ2	NOUN
ejpam-6422	189	32	=	=	SYM
ejpam-6422	189	33	2ϖ2	2ϖ2	PROPN
ejpam-6422	189	34	−	−	NOUN
ejpam-6422	189	35	1	1	NUM
ejpam-6422	189	36	and	and	CCONJ
ejpam-6422	189	37	ℏ3	ℏ3	PROPN
ejpam-6422	189	38	=	=	SYM
ejpam-6422	189	39	−ϖ2(1	−ϖ2(1	PROPN
ejpam-6422	189	40	−ϖ2	−ϖ2	PROPN
ejpam-6422	189	41	)	)	PUNCT
ejpam-6422	189	42	,	,	PUNCT
ejpam-6422	189	43	then	then	ADV
ejpam-6422	189	44	f	f	PROPN
ejpam-6422	189	45	(	(	PUNCT
ejpam-6422	189	46	ρ	ρ	PROPN
ejpam-6422	189	47	)	)	PUNCT
ejpam-6422	189	48	=	=	SYM
ejpam-6422	189	49	ds(ρ	ds(ρ	X
ejpam-6422	189	50	)	)	PUNCT
ejpam-6422	189	51	,	,	PUNCT
ejpam-6422	189	52	and	and	CCONJ
ejpam-6422	189	53	eq	eq	NOUN
ejpam-6422	189	54	.	.	PUNCT
ejpam-6422	190	1	(	(	PUNCT
ejpam-6422	190	2	11	11	NUM
ejpam-6422	190	3	)	)	PUNCT
ejpam-6422	190	4	takes	take	VERB
ejpam-6422	190	5	the	the	DET
ejpam-6422	190	6	form	form	NOUN
ejpam-6422	190	7	w(x	w(x	PROPN
ejpam-6422	190	8	,	,	PUNCT
ejpam-6422	190	9	y	y	PROPN
ejpam-6422	190	10	,	,	PUNCT
ejpam-6422	190	11	z	z	PROPN
ejpam-6422	190	12	,	,	PUNCT
ejpam-6422	190	13	t	t	PROPN
ejpam-6422	190	14	)	)	PUNCT
ejpam-6422	190	15	=	=	PRON
ejpam-6422	190	16	{	{	PUNCT
ejpam-6422	191	1	−8	−8	X
ejpam-6422	191	2	5a2	5a2	NUM
ejpam-6422	191	3	±	±	NUM
ejpam-6422	192	1	√	√	PROPN
ejpam-6422	192	2	−128ℏ1	−128ℏ1	NOUN
ejpam-6422	192	3	25a22ℏ2	25a22ℏ2	PROPN
ejpam-6422	192	4	ds(ρ1x+	ds(ρ1x+	NUM
ejpam-6422	192	5	ρ2y	ρ2y	PROPN
ejpam-6422	192	6	+	+	PUNCT
ejpam-6422	193	1	ρ3z	ρ3z	NOUN
ejpam-6422	194	1	+	+	NOUN
ejpam-6422	194	2	λ	λ	X
ejpam-6422	194	3	κ	κ	X
ejpam-6422	194	4	(	(	PUNCT
ejpam-6422	194	5	t+	t+	NOUN
ejpam-6422	194	6	1	1	NUM
ejpam-6422	194	7	γ(κ	γ(κ	PROPN
ejpam-6422	194	8	)	)	PUNCT
ejpam-6422	194	9	)	)	PUNCT
ejpam-6422	194	10	κ	κ	X
ejpam-6422	194	11	)	)	PUNCT
ejpam-6422	194	12	}	}	PUNCT
ejpam-6422	194	13	,	,	PUNCT
ejpam-6422	194	14	(	(	PUNCT
ejpam-6422	194	15	26	26	NUM
ejpam-6422	194	16	)	)	PUNCT
ejpam-6422	194	17	w.	w.	PROPN
ejpam-6422	194	18	w.	w.	PROPN
ejpam-6422	194	19	mohammed	mohammed	PROPN
ejpam-6422	194	20	et	et	PROPN
ejpam-6422	194	21	al	al	PROPN
ejpam-6422	194	22	.	.	PUNCT
ejpam-6422	194	23	/	/	SYM
ejpam-6422	194	24	eur	eur	PROPN
ejpam-6422	194	25	.	.	PUNCT
ejpam-6422	195	1	j.	j.	PROPN
ejpam-6422	195	2	pure	pure	PROPN
ejpam-6422	195	3	appl	appl	PROPN
ejpam-6422	195	4	.	.	PROPN
ejpam-6422	195	5	math	math	PROPN
ejpam-6422	195	6	,	,	PUNCT
ejpam-6422	195	7	18	18	NUM
ejpam-6422	195	8	(	(	PUNCT
ejpam-6422	195	9	3	3	NUM
ejpam-6422	195	10	)	)	PUNCT
ejpam-6422	195	11	(	(	PUNCT
ejpam-6422	195	12	2025	2025	NUM
ejpam-6422	195	13	)	)	PUNCT
ejpam-6422	195	14	,	,	PUNCT
ejpam-6422	195	15	6422	6422	NUM
ejpam-6422	195	16	7	7	NUM
ejpam-6422	195	17	of	of	ADP
ejpam-6422	195	18	13	13	NUM
ejpam-6422	195	19	for	for	ADP
ejpam-6422	195	20	ϖ	ϖ	INTJ
ejpam-6422	195	21	<	<	X
ejpam-6422	195	22	1√	1√	PROPN
ejpam-6422	195	23	2	2	NUM
ejpam-6422	195	24	.	.	PUNCT
ejpam-6422	196	1	case	case	NOUN
ejpam-6422	196	2	12	12	NUM
ejpam-6422	196	3	:	:	PUNCT
ejpam-6422	196	4	if	if	SCONJ
ejpam-6422	196	5	ℏ1	ℏ1	PROPN
ejpam-6422	196	6	=	=	SYM
ejpam-6422	196	7	1	1	NUM
ejpam-6422	196	8	4	4	NUM
ejpam-6422	196	9	,	,	PUNCT
ejpam-6422	196	10	ℏ2	ℏ2	NOUN
ejpam-6422	196	11	=	=	SYM
ejpam-6422	196	12	ϖ2−2	ϖ2−2	SYM
ejpam-6422	196	13	2	2	NUM
ejpam-6422	196	14	and	and	CCONJ
ejpam-6422	196	15	ℏ3	ℏ3	PROPN
ejpam-6422	196	16	=	=	SYM
ejpam-6422	197	1	ϖ2	ϖ2	PROPN
ejpam-6422	197	2	4	4	NUM
ejpam-6422	197	3	,	,	PUNCT
ejpam-6422	197	4	then	then	ADV
ejpam-6422	197	5	f	f	PROPN
ejpam-6422	197	6	(	(	PUNCT
ejpam-6422	197	7	ρ	ρ	PROPN
ejpam-6422	197	8	)	)	PUNCT
ejpam-6422	197	9	=	=	SYM
ejpam-6422	197	10	ns(ρ	ns(ρ	X
ejpam-6422	197	11	)	)	PUNCT
ejpam-6422	197	12	±	±	NOUN
ejpam-6422	197	13	ds(ρ	ds(ρ	NOUN
ejpam-6422	197	14	)	)	PUNCT
ejpam-6422	197	15	,	,	PUNCT
ejpam-6422	197	16	and	and	CCONJ
ejpam-6422	197	17	eq	eq	NOUN
ejpam-6422	197	18	.	.	PUNCT
ejpam-6422	198	1	(	(	PUNCT
ejpam-6422	198	2	11	11	NUM
ejpam-6422	198	3	)	)	PUNCT
ejpam-6422	198	4	takes	take	VERB
ejpam-6422	198	5	the	the	DET
ejpam-6422	198	6	form	form	NOUN
ejpam-6422	198	7	w(x	w(x	PROPN
ejpam-6422	198	8	,	,	PUNCT
ejpam-6422	198	9	y	y	PROPN
ejpam-6422	198	10	,	,	PUNCT
ejpam-6422	198	11	z	z	PROPN
ejpam-6422	198	12	,	,	PUNCT
ejpam-6422	198	13	t	t	PROPN
ejpam-6422	198	14	)	)	PUNCT
ejpam-6422	198	15	=	=	PUNCT
ejpam-6422	199	1	−8	−8	X
ejpam-6422	199	2	5a2	5a2	NUM
ejpam-6422	199	3	±	±	NUM
ejpam-6422	199	4	√	√	PROPN
ejpam-6422	199	5	−128ℏ1	−128ℏ1	PROPN
ejpam-6422	199	6	25a22ℏ2	25a22ℏ2	PROPN
ejpam-6422	199	7	(	(	PUNCT
ejpam-6422	199	8	ns(ρ1x+	ns(ρ1x+	NUM
ejpam-6422	199	9	ρ2y	ρ2y	PROPN
ejpam-6422	199	10	+	+	PUNCT
ejpam-6422	200	1	ρ3z	ρ3z	PROPN
ejpam-6422	200	2	+	+	NOUN
ejpam-6422	200	3	λ	λ	X
ejpam-6422	200	4	κ	κ	X
ejpam-6422	200	5	(	(	PUNCT
ejpam-6422	200	6	t+	t+	NOUN
ejpam-6422	200	7	1	1	NUM
ejpam-6422	200	8	γ(κ	γ(κ	PROPN
ejpam-6422	200	9	)	)	PUNCT
ejpam-6422	200	10	)	)	PUNCT
ejpam-6422	200	11	κ	κ	X
ejpam-6422	200	12	)	)	PUNCT
ejpam-6422	200	13	±	±	NOUN
ejpam-6422	200	14	ds(ρ1x+	ds(ρ1x+	NUM
ejpam-6422	200	15	ρ2y	ρ2y	PROPN
ejpam-6422	200	16	+	+	PUNCT
ejpam-6422	201	1	ρ3z	ρ3z	NOUN
ejpam-6422	201	2	+	+	NOUN
ejpam-6422	201	3	λ	λ	X
ejpam-6422	201	4	κ	κ	X
ejpam-6422	201	5	(	(	PUNCT
ejpam-6422	201	6	t+	t+	NOUN
ejpam-6422	201	7	1	1	NUM
ejpam-6422	201	8	γ(κ	γ(κ	PROPN
ejpam-6422	201	9	)	)	PUNCT
ejpam-6422	201	10	)	)	PUNCT
ejpam-6422	201	11	κ	κ	X
ejpam-6422	201	12	)	)	PUNCT
ejpam-6422	201	13	)	)	PUNCT
ejpam-6422	201	14	.	.	PUNCT
ejpam-6422	202	1	(	(	PUNCT
ejpam-6422	202	2	27	27	NUM
ejpam-6422	202	3	)	)	PUNCT
ejpam-6422	202	4	if	if	SCONJ
ejpam-6422	202	5	ϖ	ϖ	PRON
ejpam-6422	202	6	→	→	SYM
ejpam-6422	202	7	1	1	NUM
ejpam-6422	202	8	,	,	PUNCT
ejpam-6422	202	9	then	then	ADV
ejpam-6422	202	10	eq	eq	ADJ
ejpam-6422	202	11	.	.	PUNCT
ejpam-6422	203	1	(	(	PUNCT
ejpam-6422	203	2	27	27	NUM
ejpam-6422	203	3	)	)	PUNCT
ejpam-6422	203	4	changes	change	NOUN
ejpam-6422	203	5	to	to	ADP
ejpam-6422	203	6	w(x	w(x	PROPN
ejpam-6422	203	7	,	,	PUNCT
ejpam-6422	203	8	y	y	PROPN
ejpam-6422	203	9	,	,	PUNCT
ejpam-6422	203	10	z	z	PROPN
ejpam-6422	203	11	,	,	PUNCT
ejpam-6422	203	12	t	t	PROPN
ejpam-6422	203	13	)	)	PUNCT
ejpam-6422	203	14	=	=	PUNCT
ejpam-6422	204	1	−8	−8	X
ejpam-6422	204	2	5a2	5a2	NUM
ejpam-6422	204	3	±	±	NUM
ejpam-6422	205	1	√	√	ADV
ejpam-6422	205	2	1	1	NUM
ejpam-6422	205	3	9a23	9a23	NOUN
ejpam-6422	205	4	(	(	PUNCT
ejpam-6422	205	5	coth(ρ1x+	coth(ρ1x+	NOUN
ejpam-6422	205	6	ρ2y	ρ2y	PROPN
ejpam-6422	206	1	+	+	PUNCT
ejpam-6422	207	1	ρ3z	ρ3z	PROPN
ejpam-6422	207	2	+	+	NOUN
ejpam-6422	207	3	λ	λ	X
ejpam-6422	207	4	κ	κ	X
ejpam-6422	207	5	(	(	PUNCT
ejpam-6422	207	6	t+	t+	NOUN
ejpam-6422	207	7	1	1	NUM
ejpam-6422	207	8	γ(κ	γ(κ	PROPN
ejpam-6422	207	9	)	)	PUNCT
ejpam-6422	207	10	)	)	PUNCT
ejpam-6422	207	11	κ	κ	X
ejpam-6422	207	12	)	)	PUNCT
ejpam-6422	207	13	±	±	NUM
ejpam-6422	207	14	csch(ρ1x+	csch(ρ1x+	NOUN
ejpam-6422	207	15	ρ2y	ρ2y	PROPN
ejpam-6422	208	1	+	+	CCONJ
ejpam-6422	209	1	ρ3z	ρ3z	PROPN
ejpam-6422	209	2	+	+	NOUN
ejpam-6422	209	3	λ	λ	X
ejpam-6422	209	4	κ	κ	X
ejpam-6422	209	5	(	(	PUNCT
ejpam-6422	209	6	t+	t+	NOUN
ejpam-6422	209	7	1	1	NUM
ejpam-6422	209	8	γ(κ	γ(κ	PROPN
ejpam-6422	209	9	)	)	PUNCT
ejpam-6422	209	10	)	)	PUNCT
ejpam-6422	209	11	κ	κ	X
ejpam-6422	209	12	)	)	PUNCT
ejpam-6422	209	13	)	)	PUNCT
ejpam-6422	209	14	.	.	PUNCT
ejpam-6422	210	1	(	(	PUNCT
ejpam-6422	210	2	28	28	NUM
ejpam-6422	210	3	)	)	PUNCT
ejpam-6422	210	4	while	while	SCONJ
ejpam-6422	210	5	,	,	PUNCT
ejpam-6422	210	6	if	if	SCONJ
ejpam-6422	210	7	ϖ	ϖ	PRON
ejpam-6422	210	8	→	→	SYM
ejpam-6422	210	9	0	0	NUM
ejpam-6422	210	10	,	,	PUNCT
ejpam-6422	210	11	then	then	ADV
ejpam-6422	210	12	eq	eq	ADJ
ejpam-6422	210	13	.	.	PUNCT
ejpam-6422	211	1	(	(	PUNCT
ejpam-6422	211	2	27	27	NUM
ejpam-6422	211	3	)	)	PUNCT
ejpam-6422	211	4	tends	tend	VERB
ejpam-6422	211	5	to	to	ADP
ejpam-6422	211	6	w(x	w(x	PROPN
ejpam-6422	211	7	,	,	PUNCT
ejpam-6422	211	8	y	y	PROPN
ejpam-6422	211	9	,	,	PUNCT
ejpam-6422	211	10	z	z	PROPN
ejpam-6422	211	11	,	,	PUNCT
ejpam-6422	211	12	t	t	PROPN
ejpam-6422	211	13	)	)	PUNCT
ejpam-6422	211	14	=	=	PUNCT
ejpam-6422	212	1	−8	−8	X
ejpam-6422	212	2	5a2	5a2	NUM
ejpam-6422	212	3	±	±	NUM
ejpam-6422	212	4	√	√	PROPN
ejpam-6422	212	5	−128ℏ1	−128ℏ1	NOUN
ejpam-6422	212	6	25a22ℏ2	25a22ℏ2	PROPN
ejpam-6422	212	7	(	(	PUNCT
ejpam-6422	212	8	csc(ρ1x+	csc(ρ1x+	NOUN
ejpam-6422	212	9	ρ2y	ρ2y	PROPN
ejpam-6422	213	1	+	+	CCONJ
ejpam-6422	213	2	ρ3z	ρ3z	PROPN
ejpam-6422	213	3	+	+	NOUN
ejpam-6422	213	4	λ	λ	X
ejpam-6422	213	5	κ	κ	X
ejpam-6422	213	6	(	(	PUNCT
ejpam-6422	213	7	t+	t+	NOUN
ejpam-6422	213	8	1	1	NUM
ejpam-6422	213	9	γ(κ	γ(κ	PROPN
ejpam-6422	213	10	)	)	PUNCT
ejpam-6422	213	11	)	)	PUNCT
ejpam-6422	213	12	κ	κ	X
ejpam-6422	213	13	)	)	PUNCT
ejpam-6422	213	14	±	±	PROPN
ejpam-6422	213	15	cot(ρ1x+	cot(ρ1x+	NOUN
ejpam-6422	213	16	ρ2y	ρ2y	PROPN
ejpam-6422	213	17	+	+	PROPN
ejpam-6422	214	1	ρ3z	ρ3z	NOUN
ejpam-6422	214	2	+	+	NOUN
ejpam-6422	214	3	λ	λ	X
ejpam-6422	214	4	κ	κ	X
ejpam-6422	214	5	(	(	PUNCT
ejpam-6422	214	6	t+	t+	NOUN
ejpam-6422	214	7	1	1	NUM
ejpam-6422	214	8	γ(κ	γ(κ	PROPN
ejpam-6422	214	9	)	)	PUNCT
ejpam-6422	214	10	)	)	PUNCT
ejpam-6422	214	11	κ	κ	X
ejpam-6422	214	12	)	)	PUNCT
ejpam-6422	214	13	)	)	PUNCT
ejpam-6422	214	14	.	.	PUNCT
ejpam-6422	215	1	(	(	PUNCT
ejpam-6422	215	2	29	29	NUM
ejpam-6422	215	3	)	)	PUNCT
ejpam-6422	215	4	case	case	NOUN
ejpam-6422	215	5	13	13	NUM
ejpam-6422	215	6	:	:	PUNCT
ejpam-6422	215	7	if	if	SCONJ
ejpam-6422	215	8	ℏ1	ℏ1	PROPN
ejpam-6422	215	9	=	=	SYM
ejpam-6422	215	10	ϖ2	ϖ2	NOUN
ejpam-6422	215	11	4	4	NUM
ejpam-6422	215	12	,	,	PUNCT
ejpam-6422	215	13	ℏ2	ℏ2	NOUN
ejpam-6422	215	14	=	=	SYM
ejpam-6422	215	15	ϖ2−2	ϖ2−2	SYM
ejpam-6422	215	16	2	2	NUM
ejpam-6422	215	17	and	and	CCONJ
ejpam-6422	215	18	ℏ3	ℏ3	PROPN
ejpam-6422	215	19	=	=	SYM
ejpam-6422	216	1	ϖ2	ϖ2	PROPN
ejpam-6422	216	2	4	4	NUM
ejpam-6422	216	3	,	,	PUNCT
ejpam-6422	216	4	then	then	ADV
ejpam-6422	216	5	f	f	PROPN
ejpam-6422	216	6	(	(	PUNCT
ejpam-6422	216	7	ρ	ρ	PROPN
ejpam-6422	216	8	)	)	PUNCT
ejpam-6422	216	9	=	=	SYM
ejpam-6422	217	1	√	√	NUM
ejpam-6422	217	2	1−ϖ2	1−ϖ2	NUM
ejpam-6422	217	3	(	(	PUNCT
ejpam-6422	217	4	sd(ρ)±	sd(ρ)±	NOUN
ejpam-6422	217	5	cd(ρ	cd(ρ	NUM
ejpam-6422	217	6	)	)	PUNCT
ejpam-6422	217	7	)	)	PUNCT
ejpam-6422	217	8	,	,	PUNCT
ejpam-6422	217	9	and	and	CCONJ
ejpam-6422	217	10	eq	eq	NOUN
ejpam-6422	217	11	.	.	PUNCT
ejpam-6422	218	1	(	(	PUNCT
ejpam-6422	218	2	11	11	NUM
ejpam-6422	218	3	)	)	PUNCT
ejpam-6422	218	4	takes	take	VERB
ejpam-6422	218	5	the	the	DET
ejpam-6422	218	6	form	form	NOUN
ejpam-6422	218	7	w(x	w(x	PROPN
ejpam-6422	218	8	,	,	PUNCT
ejpam-6422	218	9	y	y	PROPN
ejpam-6422	218	10	,	,	PUNCT
ejpam-6422	218	11	z	z	PROPN
ejpam-6422	218	12	,	,	PUNCT
ejpam-6422	218	13	t	t	PROPN
ejpam-6422	218	14	)	)	PUNCT
ejpam-6422	218	15	=	=	PUNCT
ejpam-6422	219	1	−8	−8	X
ejpam-6422	219	2	5a2	5a2	NUM
ejpam-6422	219	3	±	±	NUM
ejpam-6422	219	4	√	√	PROPN
ejpam-6422	219	5	−128ℏ1	−128ℏ1	NOUN
ejpam-6422	219	6	25a22ℏ2	25a22ℏ2	PROPN
ejpam-6422	219	7	(	(	PUNCT
ejpam-6422	219	8	sd(ρ1x+	sd(ρ1x+	NUM
ejpam-6422	219	9	ρ2y	ρ2y	PROPN
ejpam-6422	219	10	+	+	PUNCT
ejpam-6422	220	1	ρ3z	ρ3z	NOUN
ejpam-6422	221	1	+	+	NOUN
ejpam-6422	221	2	λ	λ	X
ejpam-6422	221	3	κ	κ	X
ejpam-6422	221	4	(	(	PUNCT
ejpam-6422	221	5	t+	t+	NOUN
ejpam-6422	221	6	1	1	NUM
ejpam-6422	221	7	γ(κ	γ(κ	PROPN
ejpam-6422	221	8	)	)	PUNCT
ejpam-6422	221	9	)	)	PUNCT
ejpam-6422	221	10	κ	κ	X
ejpam-6422	221	11	)	)	PUNCT
ejpam-6422	221	12	±	±	NOUN
ejpam-6422	221	13	cd(ρ1x+	cd(ρ1x+	NOUN
ejpam-6422	221	14	ρ2y	ρ2y	PROPN
ejpam-6422	222	1	+	+	CCONJ
ejpam-6422	222	2	ρ3z	ρ3z	PROPN
ejpam-6422	222	3	+	+	NOUN
ejpam-6422	222	4	λ	λ	X
ejpam-6422	222	5	κ	κ	X
ejpam-6422	222	6	(	(	PUNCT
ejpam-6422	222	7	t+	t+	NOUN
ejpam-6422	222	8	1	1	NUM
ejpam-6422	222	9	γ(κ	γ(κ	PROPN
ejpam-6422	222	10	)	)	PUNCT
ejpam-6422	222	11	)	)	PUNCT
ejpam-6422	222	12	κ	κ	X
ejpam-6422	222	13	)	)	PUNCT
ejpam-6422	222	14	)	)	PUNCT
ejpam-6422	222	15	.	.	PUNCT
ejpam-6422	223	1	(	(	PUNCT
ejpam-6422	223	2	30	30	X
ejpam-6422	223	3	)	)	PUNCT
ejpam-6422	223	4	case	case	NOUN
ejpam-6422	223	5	14	14	NUM
ejpam-6422	223	6	:	:	PUNCT
ejpam-6422	223	7	if	if	SCONJ
ejpam-6422	223	8	ℏ1	ℏ1	ADJ
ejpam-6422	223	9	=	=	NOUN
ejpam-6422	223	10	ϖ2−1	ϖ2−1	ADP
ejpam-6422	223	11	4	4	NUM
ejpam-6422	223	12	,	,	PUNCT
ejpam-6422	223	13	ℏ2	ℏ2	NOUN
ejpam-6422	223	14	=	=	SYM
ejpam-6422	223	15	ϖ2	ϖ2	PROPN
ejpam-6422	223	16	+	+	PROPN
ejpam-6422	223	17	1	1	NUM
ejpam-6422	223	18	2	2	NUM
ejpam-6422	223	19	and	and	CCONJ
ejpam-6422	223	20	ℏ3	ℏ3	PROPN
ejpam-6422	223	21	=	=	PRON
ejpam-6422	224	1	ϖ2−1	ϖ2−1	ADP
ejpam-6422	224	2	4	4	NUM
ejpam-6422	224	3	,	,	PUNCT
ejpam-6422	224	4	then	then	ADV
ejpam-6422	224	5	f	f	PROPN
ejpam-6422	224	6	(	(	PUNCT
ejpam-6422	224	7	ρ	ρ	PROPN
ejpam-6422	224	8	)	)	PUNCT
ejpam-6422	224	9	=	=	SYM
ejpam-6422	224	10	ϖsd(ρ	ϖsd(ρ	X
ejpam-6422	224	11	)	)	PUNCT
ejpam-6422	224	12	±	±	NOUN
ejpam-6422	224	13	nd(ρ	nd(ρ	NUM
ejpam-6422	224	14	)	)	PUNCT
ejpam-6422	224	15	,	,	PUNCT
ejpam-6422	224	16	and	and	CCONJ
ejpam-6422	224	17	eq	eq	NOUN
ejpam-6422	224	18	.	.	PUNCT
ejpam-6422	225	1	(	(	PUNCT
ejpam-6422	225	2	11	11	NUM
ejpam-6422	225	3	)	)	PUNCT
ejpam-6422	225	4	has	have	VERB
ejpam-6422	225	5	the	the	DET
ejpam-6422	225	6	form	form	NOUN
ejpam-6422	225	7	w(x	w(x	PROPN
ejpam-6422	225	8	,	,	PUNCT
ejpam-6422	225	9	y	y	PROPN
ejpam-6422	225	10	,	,	PUNCT
ejpam-6422	225	11	z	z	PROPN
ejpam-6422	225	12	,	,	PUNCT
ejpam-6422	225	13	t	t	PROPN
ejpam-6422	225	14	)	)	PUNCT
ejpam-6422	225	15	=	=	PUNCT
ejpam-6422	226	1	−8	−8	X
ejpam-6422	226	2	5a2	5a2	NUM
ejpam-6422	226	3	±	±	NUM
ejpam-6422	226	4	√	√	PROPN
ejpam-6422	226	5	−128ℏ1	−128ℏ1	PROPN
ejpam-6422	226	6	25a22ℏ2	25a22ℏ2	PROPN
ejpam-6422	226	7	(	(	PUNCT
ejpam-6422	226	8	ϖsd(ρ1x+	ϖsd(ρ1x+	X
ejpam-6422	226	9	ρ2y	ρ2y	PROPN
ejpam-6422	227	1	+	+	PUNCT
ejpam-6422	228	1	ρ3z	ρ3z	PROPN
ejpam-6422	228	2	+	+	NOUN
ejpam-6422	228	3	λ	λ	X
ejpam-6422	228	4	κ	κ	X
ejpam-6422	228	5	(	(	PUNCT
ejpam-6422	228	6	t+	t+	NOUN
ejpam-6422	228	7	1	1	NUM
ejpam-6422	228	8	γ(κ	γ(κ	PROPN
ejpam-6422	228	9	)	)	PUNCT
ejpam-6422	228	10	)	)	PUNCT
ejpam-6422	228	11	κ	κ	X
ejpam-6422	228	12	)	)	PUNCT
ejpam-6422	228	13	±	±	NOUN
ejpam-6422	228	14	nd(ρ1x+	nd(ρ1x+	PRON
ejpam-6422	228	15	ρ2y	ρ2y	PROPN
ejpam-6422	228	16	+	+	CCONJ
ejpam-6422	229	1	ρ3z	ρ3z	PROPN
ejpam-6422	229	2	+	+	NOUN
ejpam-6422	229	3	λ	λ	X
ejpam-6422	229	4	κ	κ	X
ejpam-6422	229	5	(	(	PUNCT
ejpam-6422	229	6	t+	t+	NOUN
ejpam-6422	229	7	1	1	NUM
ejpam-6422	229	8	γ(κ	γ(κ	PROPN
ejpam-6422	229	9	)	)	PUNCT
ejpam-6422	229	10	)	)	PUNCT
ejpam-6422	229	11	κ	κ	X
ejpam-6422	229	12	)	)	PUNCT
ejpam-6422	229	13	)	)	PUNCT
ejpam-6422	229	14	.	.	PUNCT
ejpam-6422	230	1	(	(	PUNCT
ejpam-6422	230	2	31	31	NUM
ejpam-6422	230	3	)	)	PUNCT
ejpam-6422	230	4	case	case	NOUN
ejpam-6422	230	5	15	15	NUM
ejpam-6422	230	6	:	:	PUNCT
ejpam-6422	230	7	if	if	SCONJ
ejpam-6422	230	8	ℏ1	ℏ1	PROPN
ejpam-6422	230	9	=	=	SYM
ejpam-6422	230	10	ϖ2	ϖ2	NOUN
ejpam-6422	230	11	4	4	NUM
ejpam-6422	230	12	,	,	PUNCT
ejpam-6422	230	13	ℏ2	ℏ2	NOUN
ejpam-6422	230	14	=	=	SYM
ejpam-6422	230	15	ϖ2−2	ϖ2−2	SYM
ejpam-6422	230	16	2	2	NUM
ejpam-6422	230	17	and	and	CCONJ
ejpam-6422	230	18	ℏ3	ℏ3	PROPN
ejpam-6422	230	19	=	=	SYM
ejpam-6422	230	20	1	1	NUM
ejpam-6422	230	21	4	4	NUM
ejpam-6422	230	22	,	,	PUNCT
ejpam-6422	230	23	then	then	ADV
ejpam-6422	230	24	f	f	PROPN
ejpam-6422	230	25	(	(	PUNCT
ejpam-6422	230	26	ρ	ρ	PROPN
ejpam-6422	230	27	)	)	PUNCT
ejpam-6422	230	28	=	=	NOUN
ejpam-6422	230	29	sn(ρ	sn(ρ	X
ejpam-6422	230	30	)	)	PUNCT
ejpam-6422	230	31	1±dn	1±dn	NUM
ejpam-6422	230	32	,	,	PUNCT
ejpam-6422	230	33	and	and	CCONJ
ejpam-6422	230	34	eq	eq	NOUN
ejpam-6422	230	35	.	.	PUNCT
ejpam-6422	231	1	(	(	PUNCT
ejpam-6422	231	2	11	11	NUM
ejpam-6422	231	3	)	)	PUNCT
ejpam-6422	231	4	takes	take	VERB
ejpam-6422	231	5	the	the	DET
ejpam-6422	231	6	form	form	NOUN
ejpam-6422	231	7	w(x	w(x	PROPN
ejpam-6422	231	8	,	,	PUNCT
ejpam-6422	231	9	y	y	PROPN
ejpam-6422	231	10	,	,	PUNCT
ejpam-6422	231	11	z	z	PROPN
ejpam-6422	231	12	,	,	PUNCT
ejpam-6422	231	13	t	t	PROPN
ejpam-6422	231	14	)	)	PUNCT
ejpam-6422	231	15	=	=	PUNCT
ejpam-6422	232	1	−8	−8	X
ejpam-6422	232	2	5a2	5a2	NUM
ejpam-6422	232	3	±	±	NUM
ejpam-6422	232	4	√	√	PROPN
ejpam-6422	232	5	−128ℏ1	−128ℏ1	PROPN
ejpam-6422	232	6	25a22ℏ2	25a22ℏ2	PROPN
ejpam-6422	232	7	(	(	PUNCT
ejpam-6422	232	8	sn(ρ1x+	sn(ρ1x+	NUM
ejpam-6422	232	9	ρ2y	ρ2y	PROPN
ejpam-6422	233	1	+	+	CCONJ
ejpam-6422	233	2	ρ3z	ρ3z	NOUN
ejpam-6422	233	3	+	+	NOUN
ejpam-6422	233	4	λ	λ	X
ejpam-6422	233	5	κ(t+	κ(t+	ADJ
ejpam-6422	233	6	1	1	NUM
ejpam-6422	233	7	γ(κ	γ(κ	PROPN
ejpam-6422	233	8	)	)	PUNCT
ejpam-6422	233	9	)	)	PUNCT
ejpam-6422	234	1	κ	κ	X
ejpam-6422	234	2	)	)	PUNCT
ejpam-6422	234	3	1±	1±	NUM
ejpam-6422	234	4	dn(ρ1x+	dn(ρ1x+	NUM
ejpam-6422	234	5	ρ2y	ρ2y	PROPN
ejpam-6422	234	6	+	+	PUNCT
ejpam-6422	235	1	ρ3z	ρ3z	NOUN
ejpam-6422	235	2	+	+	NOUN
ejpam-6422	235	3	λ	λ	X
ejpam-6422	235	4	κ(t+	κ(t+	ADJ
ejpam-6422	235	5	1	1	NUM
ejpam-6422	235	6	γ(κ	γ(κ	PROPN
ejpam-6422	235	7	)	)	PUNCT
ejpam-6422	235	8	)	)	PUNCT
ejpam-6422	236	1	κ	κ	NOUN
ejpam-6422	236	2	)	)	PUNCT
ejpam-6422	236	3	)	)	PUNCT
ejpam-6422	236	4	.	.	PUNCT
ejpam-6422	237	1	(	(	PUNCT
ejpam-6422	237	2	32	32	NUM
ejpam-6422	237	3	)	)	PUNCT
ejpam-6422	237	4	w.	w.	PROPN
ejpam-6422	237	5	w.	w.	PROPN
ejpam-6422	237	6	mohammed	mohammed	PROPN
ejpam-6422	237	7	et	et	PROPN
ejpam-6422	237	8	al	al	PROPN
ejpam-6422	237	9	.	.	PUNCT
ejpam-6422	237	10	/	/	SYM
ejpam-6422	237	11	eur	eur	PROPN
ejpam-6422	237	12	.	.	PUNCT
ejpam-6422	238	1	j.	j.	PROPN
ejpam-6422	238	2	pure	pure	PROPN
ejpam-6422	238	3	appl	appl	PROPN
ejpam-6422	238	4	.	.	PROPN
ejpam-6422	238	5	math	math	PROPN
ejpam-6422	238	6	,	,	PUNCT
ejpam-6422	238	7	18	18	NUM
ejpam-6422	238	8	(	(	PUNCT
ejpam-6422	238	9	3	3	NUM
ejpam-6422	238	10	)	)	PUNCT
ejpam-6422	238	11	(	(	PUNCT
ejpam-6422	238	12	2025	2025	NUM
ejpam-6422	238	13	)	)	PUNCT
ejpam-6422	238	14	,	,	PUNCT
ejpam-6422	238	15	6422	6422	NUM
ejpam-6422	238	16	8	8	NUM
ejpam-6422	238	17	of	of	ADP
ejpam-6422	238	18	13	13	NUM
ejpam-6422	238	19	if	if	SCONJ
ejpam-6422	238	20	ϖ	ϖ	PROPN
ejpam-6422	238	21	→	→	SYM
ejpam-6422	238	22	1	1	NUM
ejpam-6422	238	23	,	,	PUNCT
ejpam-6422	238	24	then	then	ADV
ejpam-6422	238	25	eq	eq	ADJ
ejpam-6422	238	26	.	.	PUNCT
ejpam-6422	239	1	(	(	PUNCT
ejpam-6422	239	2	32	32	NUM
ejpam-6422	239	3	)	)	PUNCT
ejpam-6422	239	4	becomes	become	VERB
ejpam-6422	239	5	w(x	w(x	PROPN
ejpam-6422	239	6	,	,	PUNCT
ejpam-6422	239	7	y	y	PROPN
ejpam-6422	239	8	,	,	PUNCT
ejpam-6422	239	9	z	z	PROPN
ejpam-6422	239	10	,	,	PUNCT
ejpam-6422	239	11	t	t	PROPN
ejpam-6422	239	12	)	)	PUNCT
ejpam-6422	239	13	=	=	PUNCT
ejpam-6422	240	1	−8	−8	X
ejpam-6422	240	2	5a2	5a2	NUM
ejpam-6422	240	3	±	±	NUM
ejpam-6422	241	1	√	√	ADV
ejpam-6422	241	2	1	1	NUM
ejpam-6422	241	3	9a23	9a23	NOUN
ejpam-6422	241	4	(	(	PUNCT
ejpam-6422	241	5	tanh(ρ1x+	tanh(ρ1x+	PROPN
ejpam-6422	241	6	ρ2y	ρ2y	PROPN
ejpam-6422	241	7	+	+	PUNCT
ejpam-6422	242	1	ρ3z	ρ3z	NOUN
ejpam-6422	242	2	+	+	NOUN
ejpam-6422	242	3	λ	λ	X
ejpam-6422	242	4	κ(t+	κ(t+	ADJ
ejpam-6422	242	5	1	1	NUM
ejpam-6422	242	6	γ(κ	γ(κ	PROPN
ejpam-6422	242	7	)	)	PUNCT
ejpam-6422	242	8	)	)	PUNCT
ejpam-6422	243	1	κ	κ	X
ejpam-6422	243	2	)	)	PUNCT
ejpam-6422	243	3	1±	1±	NUM
ejpam-6422	243	4	sech(ρ1x+	sech(ρ1x+	NOUN
ejpam-6422	243	5	ρ2y	ρ2y	PROPN
ejpam-6422	243	6	+	+	PUNCT
ejpam-6422	243	7	ρ3z	ρ3z	PROPN
ejpam-6422	244	1	+	+	NOUN
ejpam-6422	244	2	λ	λ	X
ejpam-6422	244	3	κ(t+	κ(t+	ADJ
ejpam-6422	244	4	1	1	NUM
ejpam-6422	244	5	γ(κ	γ(κ	PROPN
ejpam-6422	244	6	)	)	PUNCT
ejpam-6422	244	7	)	)	PUNCT
ejpam-6422	245	1	κ	κ	NOUN
ejpam-6422	245	2	)	)	PUNCT
ejpam-6422	245	3	)	)	PUNCT
ejpam-6422	245	4	.	.	PUNCT
ejpam-6422	246	1	(	(	PUNCT
ejpam-6422	246	2	33	33	NUM
ejpam-6422	246	3	)	)	PUNCT
ejpam-6422	246	4	case	case	NOUN
ejpam-6422	246	5	16	16	NUM
ejpam-6422	246	6	:	:	PUNCT
ejpam-6422	246	7	if	if	SCONJ
ejpam-6422	246	8	ℏ1	ℏ1	PROPN
ejpam-6422	246	9	=	=	SYM
ejpam-6422	246	10	−1	−1	NOUN
ejpam-6422	246	11	4	4	NUM
ejpam-6422	246	12	,	,	PUNCT
ejpam-6422	246	13	ℏ2	ℏ2	NOUN
ejpam-6422	246	14	=	=	PUNCT
ejpam-6422	246	15	ϖ2	ϖ2	PROPN
ejpam-6422	246	16	+	+	PROPN
ejpam-6422	246	17	1	1	NUM
ejpam-6422	246	18	2	2	NUM
ejpam-6422	246	19	and	and	CCONJ
ejpam-6422	246	20	ℏ3	ℏ3	PROPN
ejpam-6422	246	21	=	=	SYM
ejpam-6422	246	22	(	(	PUNCT
ejpam-6422	246	23	1−ϖ2	1−ϖ2	NUM
ejpam-6422	246	24	)	)	PUNCT
ejpam-6422	246	25	2	2	NUM
ejpam-6422	246	26	4	4	NUM
ejpam-6422	246	27	,	,	PUNCT
ejpam-6422	246	28	then	then	ADV
ejpam-6422	246	29	f	f	PROPN
ejpam-6422	246	30	(	(	PUNCT
ejpam-6422	246	31	ρ	ρ	NOUN
ejpam-6422	246	32	)	)	PUNCT
ejpam-6422	246	33	=	=	SYM
ejpam-6422	246	34	ϖcn(ρ	ϖcn(ρ	X
ejpam-6422	246	35	)	)	PUNCT
ejpam-6422	246	36	±	±	NOUN
ejpam-6422	246	37	dn(ρ	dn(ρ	PUNCT
ejpam-6422	246	38	)	)	PUNCT
ejpam-6422	246	39	,	,	PUNCT
ejpam-6422	246	40	and	and	CCONJ
ejpam-6422	246	41	eq	eq	NOUN
ejpam-6422	246	42	.	.	PUNCT
ejpam-6422	247	1	(	(	PUNCT
ejpam-6422	247	2	11	11	NUM
ejpam-6422	247	3	)	)	PUNCT
ejpam-6422	247	4	takes	take	VERB
ejpam-6422	247	5	the	the	DET
ejpam-6422	247	6	form	form	NOUN
ejpam-6422	247	7	w(x	w(x	PROPN
ejpam-6422	247	8	,	,	PUNCT
ejpam-6422	247	9	y	y	PROPN
ejpam-6422	247	10	,	,	PUNCT
ejpam-6422	247	11	z	z	PROPN
ejpam-6422	247	12	,	,	PUNCT
ejpam-6422	247	13	t	t	PROPN
ejpam-6422	247	14	)	)	PUNCT
ejpam-6422	247	15	=	=	PUNCT
ejpam-6422	248	1	−8	−8	X
ejpam-6422	248	2	5a2	5a2	NUM
ejpam-6422	248	3	±	±	NUM
ejpam-6422	248	4	√	√	NOUN
ejpam-6422	248	5	64ℏ1	64ℏ1	NUM
ejpam-6422	248	6	25a22(ϖ	25a22(ϖ	NUM
ejpam-6422	248	7	2	2	NUM
ejpam-6422	248	8	+	+	NUM
ejpam-6422	248	9	1	1	NUM
ejpam-6422	248	10	)	)	PUNCT
ejpam-6422	248	11	(	(	PUNCT
ejpam-6422	248	12	ϖcn(ρ1x+	ϖcn(ρ1x+	X
ejpam-6422	248	13	ρ2y	ρ2y	PROPN
ejpam-6422	249	1	+	+	PUNCT
ejpam-6422	250	1	ρ3z	ρ3z	NOUN
ejpam-6422	250	2	+	+	NOUN
ejpam-6422	250	3	λ	λ	X
ejpam-6422	250	4	κ	κ	X
ejpam-6422	250	5	(	(	PUNCT
ejpam-6422	250	6	t+	t+	NOUN
ejpam-6422	250	7	1	1	NUM
ejpam-6422	250	8	γ(κ	γ(κ	PROPN
ejpam-6422	250	9	)	)	PUNCT
ejpam-6422	250	10	)	)	PUNCT
ejpam-6422	250	11	κ	κ	X
ejpam-6422	250	12	)	)	PUNCT
ejpam-6422	250	13	±	±	NOUN
ejpam-6422	250	14	dn(ρ1x+	dn(ρ1x+	NUM
ejpam-6422	250	15	ρ2y	ρ2y	PROPN
ejpam-6422	250	16	+	+	PUNCT
ejpam-6422	251	1	ρ3z	ρ3z	NOUN
ejpam-6422	252	1	+	+	NOUN
ejpam-6422	252	2	λ	λ	X
ejpam-6422	252	3	κ	κ	X
ejpam-6422	252	4	(	(	PUNCT
ejpam-6422	252	5	t+	t+	NOUN
ejpam-6422	252	6	1	1	NUM
ejpam-6422	252	7	γ(κ	γ(κ	PROPN
ejpam-6422	252	8	)	)	PUNCT
ejpam-6422	252	9	)	)	PUNCT
ejpam-6422	252	10	κ	κ	X
ejpam-6422	252	11	)	)	PUNCT
ejpam-6422	252	12	)	)	PUNCT
ejpam-6422	252	13	.	.	PUNCT
ejpam-6422	253	1	(	(	PUNCT
ejpam-6422	253	2	34	34	NUM
ejpam-6422	253	3	)	)	PUNCT
ejpam-6422	253	4	case	case	NOUN
ejpam-6422	253	5	17	17	NUM
ejpam-6422	253	6	:	:	PUNCT
ejpam-6422	253	7	if	if	SCONJ
ejpam-6422	253	8	ℏ1	ℏ1	PROPN
ejpam-6422	253	9	=	=	NOUN
ejpam-6422	253	10	1	1	NUM
ejpam-6422	253	11	4	4	NUM
ejpam-6422	253	12	,	,	PUNCT
ejpam-6422	253	13	ℏ2	ℏ2	NOUN
ejpam-6422	253	14	=	=	SYM
ejpam-6422	253	15	1−2ϖ2	1−2ϖ2	NUM
ejpam-6422	253	16	2	2	NUM
ejpam-6422	253	17	and	and	CCONJ
ejpam-6422	253	18	ℏ3	ℏ3	PROPN
ejpam-6422	253	19	=	=	SYM
ejpam-6422	253	20	1	1	NUM
ejpam-6422	253	21	4	4	NUM
ejpam-6422	253	22	,	,	PUNCT
ejpam-6422	253	23	then	then	ADV
ejpam-6422	253	24	f	f	PROPN
ejpam-6422	253	25	(	(	PUNCT
ejpam-6422	253	26	ρ	ρ	PROPN
ejpam-6422	253	27	)	)	PUNCT
ejpam-6422	253	28	=	=	PRON
ejpam-6422	253	29	sn(ρ	sn(ρ	X
ejpam-6422	253	30	)	)	PUNCT
ejpam-6422	253	31	1±cn(ρ	1±cn(ρ	NUM
ejpam-6422	253	32	)	)	PUNCT
ejpam-6422	253	33	,	,	PUNCT
ejpam-6422	253	34	and	and	CCONJ
ejpam-6422	253	35	eq	eq	NOUN
ejpam-6422	253	36	.	.	PUNCT
ejpam-6422	254	1	(	(	PUNCT
ejpam-6422	254	2	11	11	NUM
ejpam-6422	254	3	)	)	PUNCT
ejpam-6422	254	4	has	have	VERB
ejpam-6422	254	5	the	the	DET
ejpam-6422	254	6	form	form	NOUN
ejpam-6422	254	7	w(x	w(x	PROPN
ejpam-6422	254	8	,	,	PUNCT
ejpam-6422	254	9	y	y	PROPN
ejpam-6422	254	10	,	,	PUNCT
ejpam-6422	254	11	z	z	PROPN
ejpam-6422	254	12	,	,	PUNCT
ejpam-6422	254	13	t	t	PROPN
ejpam-6422	254	14	)	)	PUNCT
ejpam-6422	254	15	=	=	PUNCT
ejpam-6422	255	1	−8	−8	X
ejpam-6422	255	2	5a2	5a2	NUM
ejpam-6422	255	3	±	±	NUM
ejpam-6422	255	4	√	√	NOUN
ejpam-6422	255	5	64ℏ1	64ℏ1	NUM
ejpam-6422	255	6	25a22(2ϖ	25a22(2ϖ	NUM
ejpam-6422	255	7	2	2	NUM
ejpam-6422	255	8	−	−	NOUN
ejpam-6422	255	9	1	1	NUM
ejpam-6422	255	10	)	)	PUNCT
ejpam-6422	255	11	sn(ρ1x+	sn(ρ1x+	NUM
ejpam-6422	255	12	ρ2y	ρ2y	PROPN
ejpam-6422	256	1	+	+	CCONJ
ejpam-6422	256	2	ρ3z	ρ3z	NOUN
ejpam-6422	256	3	+	+	NOUN
ejpam-6422	256	4	λ	λ	X
ejpam-6422	256	5	κ(t+	κ(t+	ADJ
ejpam-6422	256	6	1	1	NUM
ejpam-6422	256	7	γ(κ	γ(κ	PROPN
ejpam-6422	256	8	)	)	PUNCT
ejpam-6422	256	9	)	)	PUNCT
ejpam-6422	257	1	κ	κ	X
ejpam-6422	257	2	)	)	PUNCT
ejpam-6422	257	3	1±	1±	NUM
ejpam-6422	257	4	cn(ρ1x+	cn(ρ1x+	NUM
ejpam-6422	257	5	ρ2y	ρ2y	PROPN
ejpam-6422	258	1	+	+	CCONJ
ejpam-6422	259	1	ρ3z	ρ3z	NOUN
ejpam-6422	259	2	+	+	NOUN
ejpam-6422	259	3	λ	λ	X
ejpam-6422	259	4	κ(t+	κ(t+	ADJ
ejpam-6422	259	5	1	1	NUM
ejpam-6422	259	6	γ(κ	γ(κ	PROPN
ejpam-6422	259	7	)	)	PUNCT
ejpam-6422	259	8	)	)	PUNCT
ejpam-6422	260	1	κ	κ	NOUN
ejpam-6422	260	2	)	)	PUNCT
ejpam-6422	260	3	,	,	PUNCT
ejpam-6422	260	4	(	(	PUNCT
ejpam-6422	260	5	35	35	NUM
ejpam-6422	260	6	)	)	PUNCT
ejpam-6422	260	7	for	for	ADP
ejpam-6422	260	8	1√	1√	PROPN
ejpam-6422	260	9	2	2	NUM
ejpam-6422	260	10	<	<	X
ejpam-6422	260	11	ϖ	ϖ	X
ejpam-6422	260	12	<	<	X
ejpam-6422	260	13	1	1	NUM
ejpam-6422	260	14	.	.	PUNCT
ejpam-6422	261	1	where	where	SCONJ
ejpam-6422	261	2	cn(ρ	cn(ρ	NOUN
ejpam-6422	261	3	)	)	PUNCT
ejpam-6422	261	4	=	=	SYM
ejpam-6422	261	5	cn(ρ,ϖ	cn(ρ,ϖ	NOUN
ejpam-6422	261	6	)	)	PUNCT
ejpam-6422	261	7	,	,	PUNCT
ejpam-6422	261	8	dn(ρ	dn(ρ	PUNCT
ejpam-6422	261	9	)	)	PUNCT
ejpam-6422	261	10	=	=	PUNCT
ejpam-6422	261	11	dn(ρ,ϖ	dn(ρ,ϖ	NOUN
ejpam-6422	261	12	)	)	PUNCT
ejpam-6422	261	13	,	,	PUNCT
ejpam-6422	261	14	sn(ρ	sn(ρ	X
ejpam-6422	261	15	)	)	PUNCT
ejpam-6422	262	1	=	=	SYM
ejpam-6422	262	2	sn(ρ,ϖ	sn(ρ,ϖ	NOUN
ejpam-6422	262	3	)	)	PUNCT
ejpam-6422	262	4	,	,	PUNCT
ejpam-6422	262	5	sc(ρ	sc(ρ	NUM
ejpam-6422	262	6	)	)	PUNCT
ejpam-6422	262	7	=	=	SYM
ejpam-6422	262	8	sc(ρ,ϖ	sc(ρ,ϖ	NOUN
ejpam-6422	262	9	)	)	PUNCT
ejpam-6422	262	10	,	,	PUNCT
ejpam-6422	262	11	ds(ρ	ds(ρ	X
ejpam-6422	262	12	)	)	PUNCT
ejpam-6422	262	13	=	=	SYM
ejpam-6422	262	14	ds(ρ,ϖ	ds(ρ,ϖ	NOUN
ejpam-6422	262	15	)	)	PUNCT
ejpam-6422	262	16	,	,	PUNCT
ejpam-6422	262	17	are	be	AUX
ejpam-6422	262	18	the	the	DET
ejpam-6422	262	19	jacobi	jacobi	PROPN
ejpam-6422	262	20	elliptic	elliptic	ADJ
ejpam-6422	262	21	functions	function	NOUN
ejpam-6422	262	22	(	(	PUNCT
ejpam-6422	262	23	jefs	jef	NOUN
ejpam-6422	262	24	)	)	PUNCT
ejpam-6422	262	25	for	for	ADP
ejpam-6422	262	26	0	0	NUM
ejpam-6422	262	27	<	<	X
ejpam-6422	262	28	ϖ	ϖ	X
ejpam-6422	262	29	<	<	X
ejpam-6422	262	30	1	1	NUM
ejpam-6422	262	31	and	and	CCONJ
ejpam-6422	262	32	ϖ	ϖ	PROPN
ejpam-6422	262	33	is	be	AUX
ejpam-6422	262	34	the	the	DET
ejpam-6422	262	35	elliptic	elliptic	ADJ
ejpam-6422	262	36	modulus	modulus	NOUN
ejpam-6422	262	37	.	.	PUNCT
ejpam-6422	263	1	we	we	PRON
ejpam-6422	263	2	note	note	VERB
ejpam-6422	263	3	that	that	SCONJ
ejpam-6422	263	4	jefs	jef	VERB
ejpam-6422	263	5	ϖ	ϖ	PROPN
ejpam-6422	263	6	→	→	SYM
ejpam-6422	263	7	0	0	NUM
ejpam-6422	263	8	ϖ	ϖ	NOUN
ejpam-6422	263	9	→	→	SYM
ejpam-6422	263	10	1	1	NUM
ejpam-6422	263	11	sn(ρ	sn(ρ	X
ejpam-6422	263	12	)	)	PUNCT
ejpam-6422	263	13	sin(ρ	sin(ρ	PROPN
ejpam-6422	263	14	)	)	PUNCT
ejpam-6422	263	15	tanh(ρ	tanh(ρ	NOUN
ejpam-6422	263	16	)	)	PUNCT
ejpam-6422	263	17	cs(ρ	cs(ρ	PUNCT
ejpam-6422	263	18	)	)	PUNCT
ejpam-6422	263	19	cot(ρ	cot(ρ	PROPN
ejpam-6422	263	20	)	)	PUNCT
ejpam-6422	263	21	csch(ρ	csch(ρ	NOUN
ejpam-6422	263	22	)	)	PUNCT
ejpam-6422	263	23	cn(ρ	cn(ρ	PUNCT
ejpam-6422	263	24	)	)	PUNCT
ejpam-6422	263	25	cos(ρ	cos(ρ	NOUN
ejpam-6422	263	26	)	)	PUNCT
ejpam-6422	263	27	sech(ρ	sech(ρ	NOUN
ejpam-6422	263	28	)	)	PUNCT
ejpam-6422	263	29	ds(ρ	ds(ρ	X
ejpam-6422	263	30	)	)	PUNCT
ejpam-6422	263	31	csc(ρ	csc(ρ	PROPN
ejpam-6422	263	32	)	)	PUNCT
ejpam-6422	263	33	csch(ρ	csch(ρ	NOUN
ejpam-6422	263	34	)	)	PUNCT
ejpam-6422	263	35	dn(ρ	dn(ρ	PUNCT
ejpam-6422	263	36	)	)	PUNCT
ejpam-6422	263	37	1	1	NUM
ejpam-6422	263	38	sech(ρ	sech(ρ	NOUN
ejpam-6422	263	39	)	)	PUNCT
ejpam-6422	263	40	sc(ρ	sc(ρ	NOUN
ejpam-6422	263	41	)	)	PUNCT
ejpam-6422	263	42	tan(ρ	tan(ρ	NUM
ejpam-6422	263	43	)	)	PUNCT
ejpam-6422	263	44	sinh(ρ	sinh(ρ	NOUN
ejpam-6422	263	45	)	)	PUNCT
ejpam-6422	263	46	ns(ρ	ns(ρ	ADJ
ejpam-6422	263	47	)	)	PUNCT
ejpam-6422	263	48	csc(ρ	csc(ρ	PROPN
ejpam-6422	263	49	)	)	PUNCT
ejpam-6422	263	50	coth(ρ	coth(ρ	NOUN
ejpam-6422	263	51	)	)	PUNCT
ejpam-6422	263	52	4	4	NUM
ejpam-6422	263	53	.	.	PUNCT
ejpam-6422	263	54	discussion	discussion	NOUN
ejpam-6422	263	55	and	and	CCONJ
ejpam-6422	263	56	effect	effect	NOUN
ejpam-6422	263	57	of	of	ADP
ejpam-6422	263	58	bdo	bdo	NOUN
ejpam-6422	263	59	the	the	DET
ejpam-6422	263	60	uwm	uwm	NOUN
ejpam-6422	263	61	-	-	PUNCT
ejpam-6422	263	62	bdo	bdo	NOUN
ejpam-6422	263	63	provides	provide	VERB
ejpam-6422	263	64	a	a	DET
ejpam-6422	263	65	powerful	powerful	ADJ
ejpam-6422	263	66	tool	tool	NOUN
ejpam-6422	263	67	for	for	ADP
ejpam-6422	263	68	modeling	model	VERB
ejpam-6422	263	69	wave	wave	NOUN
ejpam-6422	263	70	propagation	propagation	NOUN
ejpam-6422	263	71	in	in	ADP
ejpam-6422	263	72	a	a	DET
ejpam-6422	263	73	wide	wide	ADJ
ejpam-6422	263	74	range	range	NOUN
ejpam-6422	263	75	of	of	ADP
ejpam-6422	263	76	physical	physical	ADJ
ejpam-6422	263	77	systems	system	NOUN
ejpam-6422	263	78	.	.	PUNCT
ejpam-6422	264	1	by	by	ADP
ejpam-6422	264	2	capturing	capture	VERB
ejpam-6422	264	3	non	non	ADJ
ejpam-6422	264	4	-	-	ADJ
ejpam-6422	264	5	local	local	ADJ
ejpam-6422	264	6	effects	effect	NOUN
ejpam-6422	264	7	and	and	CCONJ
ejpam-6422	264	8	memory	memory	NOUN
ejpam-6422	264	9	effects	effect	NOUN
ejpam-6422	264	10	,	,	PUNCT
ejpam-6422	264	11	this	this	DET
ejpam-6422	264	12	mathematical	mathematical	ADJ
ejpam-6422	264	13	model	model	NOUN
ejpam-6422	264	14	offers	offer	VERB
ejpam-6422	264	15	a	a	DET
ejpam-6422	264	16	more	more	ADV
ejpam-6422	264	17	comprehensive	comprehensive	ADJ
ejpam-6422	264	18	understanding	understanding	NOUN
ejpam-6422	264	19	of	of	ADP
ejpam-6422	264	20	complex	complex	ADJ
ejpam-6422	264	21	wave	wave	NOUN
ejpam-6422	264	22	phenomena	phenomenon	NOUN
ejpam-6422	264	23	in	in	ADP
ejpam-6422	264	24	heterogeneous	heterogeneous	ADJ
ejpam-6422	264	25	media	medium	NOUN
ejpam-6422	264	26	.	.	PUNCT
ejpam-6422	265	1	the	the	DET
ejpam-6422	265	2	incorporation	incorporation	NOUN
ejpam-6422	265	3	of	of	ADP
ejpam-6422	265	4	fractional	fractional	ADJ
ejpam-6422	265	5	derivatives	derivative	NOUN
ejpam-6422	265	6	into	into	ADP
ejpam-6422	265	7	the	the	DET
ejpam-6422	265	8	wave	wave	NOUN
ejpam-6422	265	9	equation	equation	NOUN
ejpam-6422	265	10	opens	open	VERB
ejpam-6422	265	11	up	up	ADP
ejpam-6422	265	12	new	new	ADJ
ejpam-6422	265	13	avenues	avenue	NOUN
ejpam-6422	265	14	for	for	ADP
ejpam-6422	265	15	research	research	NOUN
ejpam-6422	265	16	and	and	CCONJ
ejpam-6422	265	17	applications	application	NOUN
ejpam-6422	265	18	in	in	ADP
ejpam-6422	265	19	areas	area	NOUN
ejpam-6422	265	20	such	such	ADJ
ejpam-6422	265	21	as	as	ADP
ejpam-6422	265	22	acoustics	acoustic	NOUN
ejpam-6422	265	23	,	,	PUNCT
ejpam-6422	265	24	electromagnetics	electromagnetic	NOUN
ejpam-6422	265	25	,	,	PUNCT
ejpam-6422	265	26	and	and	CCONJ
ejpam-6422	265	27	geophysics	geophysic	NOUN
ejpam-6422	265	28	,	,	PUNCT
ejpam-6422	265	29	where	where	SCONJ
ejpam-6422	265	30	accurate	accurate	ADJ
ejpam-6422	265	31	and	and	CCONJ
ejpam-6422	265	32	efficient	efficient	ADJ
ejpam-6422	265	33	wave	wave	NOUN
ejpam-6422	265	34	modeling	modeling	NOUN
ejpam-6422	265	35	is	be	AUX
ejpam-6422	265	36	essential	essential	ADJ
ejpam-6422	265	37	.	.	PUNCT
ejpam-6422	266	1	we	we	PRON
ejpam-6422	266	2	discuss	discuss	VERB
ejpam-6422	266	3	the	the	DET
ejpam-6422	266	4	impact	impact	NOUN
ejpam-6422	266	5	of	of	ADP
ejpam-6422	266	6	the	the	DET
ejpam-6422	266	7	beta	beta	NOUN
ejpam-6422	266	8	-	-	PUNCT
ejpam-6422	266	9	derivative	derivative	NOUN
ejpam-6422	266	10	operator	operator	NOUN
ejpam-6422	266	11	on	on	ADP
ejpam-6422	266	12	the	the	DET
ejpam-6422	266	13	obtained	obtain	VERB
ejpam-6422	266	14	solutions	solution	NOUN
ejpam-6422	266	15	of	of	ADP
ejpam-6422	266	16	uwm	uwm	NOUN
ejpam-6422	266	17	-	-	PUNCT
ejpam-6422	266	18	bdo	bdo	NOUN
ejpam-6422	266	19	(	(	PUNCT
ejpam-6422	266	20	1	1	NUM
ejpam-6422	266	21	)	)	PUNCT
ejpam-6422	266	22	.	.	PUNCT
ejpam-6422	267	1	to	to	PART
ejpam-6422	267	2	show	show	VERB
ejpam-6422	267	3	how	how	SCONJ
ejpam-6422	267	4	these	these	DET
ejpam-6422	267	5	solutions	solution	NOUN
ejpam-6422	267	6	behave	behave	VERB
ejpam-6422	267	7	,	,	PUNCT
ejpam-6422	267	8	various	various	ADJ
ejpam-6422	267	9	graphical	graphical	ADJ
ejpam-6422	267	10	representations	representation	NOUN
ejpam-6422	267	11	w.	w.	PROPN
ejpam-6422	267	12	w.	w.	PROPN
ejpam-6422	267	13	mohammed	mohammed	PROPN
ejpam-6422	267	14	et	et	PROPN
ejpam-6422	267	15	al	al	PROPN
ejpam-6422	267	16	.	.	PUNCT
ejpam-6422	267	17	/	/	SYM
ejpam-6422	267	18	eur	eur	PROPN
ejpam-6422	267	19	.	.	PUNCT
ejpam-6422	268	1	j.	j.	PROPN
ejpam-6422	268	2	pure	pure	PROPN
ejpam-6422	268	3	appl	appl	PROPN
ejpam-6422	268	4	.	.	PROPN
ejpam-6422	268	5	math	math	PROPN
ejpam-6422	268	6	,	,	PUNCT
ejpam-6422	268	7	18	18	NUM
ejpam-6422	268	8	(	(	PUNCT
ejpam-6422	268	9	3	3	NUM
ejpam-6422	268	10	)	)	PUNCT
ejpam-6422	268	11	(	(	PUNCT
ejpam-6422	268	12	2025	2025	NUM
ejpam-6422	268	13	)	)	PUNCT
ejpam-6422	268	14	,	,	PUNCT
ejpam-6422	268	15	6422	6422	NUM
ejpam-6422	268	16	9	9	NUM
ejpam-6422	268	17	of	of	ADP
ejpam-6422	268	18	13	13	NUM
ejpam-6422	268	19	are	be	AUX
ejpam-6422	268	20	offered	offer	VERB
ejpam-6422	268	21	.	.	PUNCT
ejpam-6422	269	1	for	for	ADP
ejpam-6422	269	2	some	some	DET
ejpam-6422	269	3	obtained	obtain	VERB
ejpam-6422	269	4	solutions	solution	NOUN
ejpam-6422	269	5	,	,	PUNCT
ejpam-6422	269	6	such	such	ADJ
ejpam-6422	269	7	as	as	ADP
ejpam-6422	269	8	eqs	eqs	PROPN
ejpam-6422	269	9	.	.	PUNCT
ejpam-6422	270	1	(	(	PUNCT
ejpam-6422	270	2	12	12	NUM
ejpam-6422	270	3	)	)	PUNCT
ejpam-6422	270	4	,	,	PUNCT
ejpam-6422	270	5	(	(	PUNCT
ejpam-6422	270	6	13	13	NUM
ejpam-6422	270	7	)	)	PUNCT
ejpam-6422	270	8	and	and	CCONJ
ejpam-6422	270	9	(	(	PUNCT
ejpam-6422	270	10	16	16	NUM
ejpam-6422	270	11	)	)	PUNCT
ejpam-6422	270	12	,	,	PUNCT
ejpam-6422	270	13	we	we	PRON
ejpam-6422	270	14	simulate	simulate	VERB
ejpam-6422	270	15	the	the	DET
ejpam-6422	270	16	graphical	graphical	ADJ
ejpam-6422	270	17	representations	representation	NOUN
ejpam-6422	270	18	for	for	ADP
ejpam-6422	270	19	ρ1	ρ1	NOUN
ejpam-6422	270	20	=	=	SYM
ejpam-6422	270	21	ρ2	ρ2	NOUN
ejpam-6422	270	22	=	=	SYM
ejpam-6422	270	23	ρ3	ρ3	NOUN
ejpam-6422	270	24	=	=	SYM
ejpam-6422	270	25	1	1	NUM
ejpam-6422	270	26	,	,	PUNCT
ejpam-6422	270	27	a2	a2	NOUN
ejpam-6422	270	28	=	=	SYM
ejpam-6422	270	29	1	1	NUM
ejpam-6422	270	30	and	and	CCONJ
ejpam-6422	270	31	for	for	ADP
ejpam-6422	270	32	varying	vary	VERB
ejpam-6422	270	33	values	value	NOUN
ejpam-6422	270	34	of	of	ADP
ejpam-6422	270	35	κ	κ	NOUN
ejpam-6422	270	36	.	.	PUNCT
ejpam-6422	271	1	we	we	PRON
ejpam-6422	271	2	deduce	deduce	VERB
ejpam-6422	271	3	from	from	ADP
ejpam-6422	271	4	these	these	DET
ejpam-6422	271	5	figures	figure	NOUN
ejpam-6422	271	6	that	that	SCONJ
ejpam-6422	271	7	when	when	SCONJ
ejpam-6422	271	8	the	the	DET
ejpam-6422	271	9	fractional	fractional	ADJ
ejpam-6422	271	10	order	order	NOUN
ejpam-6422	271	11	decreases	decrease	VERB
ejpam-6422	271	12	,	,	PUNCT
ejpam-6422	271	13	the	the	DET
ejpam-6422	271	14	surface	surface	NOUN
ejpam-6422	271	15	moves	move	VERB
ejpam-6422	271	16	into	into	ADP
ejpam-6422	271	17	the	the	DET
ejpam-6422	271	18	right	right	NOUN
ejpam-6422	271	19	as	as	SCONJ
ejpam-6422	271	20	follows	follow	VERB
ejpam-6422	271	21	:	:	PUNCT
ejpam-6422	271	22	(	(	PUNCT
ejpam-6422	271	23	a	a	X
ejpam-6422	271	24	)	)	PUNCT
ejpam-6422	271	25	κ	κ	NOUN
ejpam-6422	271	26	=	=	SYM
ejpam-6422	271	27	1	1	NUM
ejpam-6422	271	28	(	(	PUNCT
ejpam-6422	271	29	b	b	NOUN
ejpam-6422	271	30	)	)	PUNCT
ejpam-6422	271	31	κ	κ	NOUN
ejpam-6422	272	1	=	=	NOUN
ejpam-6422	272	2	0.8	0.8	NUM
ejpam-6422	272	3	(	(	PUNCT
ejpam-6422	272	4	c	c	NOUN
ejpam-6422	272	5	)	)	PUNCT
ejpam-6422	272	6	κ	κ	NOUN
ejpam-6422	272	7	=	=	SYM
ejpam-6422	272	8	0.6	0.6	NUM
ejpam-6422	272	9	(	(	PUNCT
ejpam-6422	272	10	d	d	NOUN
ejpam-6422	272	11	)	)	PUNCT
ejpam-6422	272	12	κ	κ	NOUN
ejpam-6422	272	13	=	=	SYM
ejpam-6422	272	14	0.5	0.5	NUM
ejpam-6422	272	15	(	(	PUNCT
ejpam-6422	272	16	e	e	NOUN
ejpam-6422	272	17	)	)	PUNCT
ejpam-6422	272	18	κ	κ	NOUN
ejpam-6422	272	19	=	=	SYM
ejpam-6422	272	20	0.4	0.4	NUM
ejpam-6422	272	21	(	(	PUNCT
ejpam-6422	272	22	f	f	X
ejpam-6422	272	23	)	)	PUNCT
ejpam-6422	272	24	κ	κ	NOUN
ejpam-6422	273	1	=	=	SYM
ejpam-6422	273	2	1	1	NUM
ejpam-6422	273	3	,	,	PUNCT
ejpam-6422	273	4	0.8	0.8	NUM
ejpam-6422	273	5	,	,	PUNCT
ejpam-6422	273	6	0.6	0.6	NUM
ejpam-6422	273	7	,	,	PUNCT
ejpam-6422	273	8	0.5	0.5	NUM
ejpam-6422	273	9	,	,	PUNCT
ejpam-6422	273	10	0.4	0.4	NUM
ejpam-6422	273	11	figure	figure	NOUN
ejpam-6422	273	12	1	1	NUM
ejpam-6422	273	13	.	.	PUNCT
ejpam-6422	274	1	(	(	PUNCT
ejpam-6422	274	2	a	a	DET
ejpam-6422	274	3	-	-	PUNCT
ejpam-6422	274	4	e	e	NOUN
ejpam-6422	274	5	)	)	PUNCT
ejpam-6422	274	6	describe	describe	VERB
ejpam-6422	274	7	3d	3d	NUM
ejpam-6422	274	8	-	-	PUNCT
ejpam-6422	274	9	profile	profile	NOUN
ejpam-6422	274	10	of	of	ADP
ejpam-6422	274	11	solution	solution	NOUN
ejpam-6422	274	12	w(x	w(x	PROPN
ejpam-6422	274	13	,	,	PUNCT
ejpam-6422	274	14	y	y	PROPN
ejpam-6422	274	15	,	,	PUNCT
ejpam-6422	274	16	z	z	PROPN
ejpam-6422	274	17	,	,	PUNCT
ejpam-6422	274	18	t	t	PROPN
ejpam-6422	274	19	)	)	PUNCT
ejpam-6422	274	20	in	in	ADP
ejpam-6422	274	21	eq	eq	NOUN
ejpam-6422	274	22	(	(	PUNCT
ejpam-6422	274	23	12	12	NUM
ejpam-6422	274	24	)	)	PUNCT
ejpam-6422	274	25	with	with	ADP
ejpam-6422	274	26	ϖ	ϖ	PROPN
ejpam-6422	274	27	=	=	SYM
ejpam-6422	274	28	0.5	0.5	NUM
ejpam-6422	274	29	,	,	PUNCT
ejpam-6422	274	30	a2	a2	NOUN
ejpam-6422	274	31	=	=	SYM
ejpam-6422	274	32	1	1	NUM
ejpam-6422	274	33	,	,	PUNCT
ejpam-6422	274	34	y	y	NOUN
ejpam-6422	274	35	=	=	PUNCT
ejpam-6422	274	36	z	z	NOUN
ejpam-6422	274	37	=	=	SYM
ejpam-6422	274	38	0	0	NUM
ejpam-6422	274	39	,	,	PUNCT
ejpam-6422	274	40	ρ1	ρ1	NOUN
ejpam-6422	274	41	=	=	SYM
ejpam-6422	274	42	ρ2	ρ2	NOUN
ejpam-6422	274	43	=	=	SYM
ejpam-6422	274	44	ρ3	ρ3	NOUN
ejpam-6422	274	45	=	=	SYM
ejpam-6422	274	46	1	1	NUM
ejpam-6422	274	47	,	,	PUNCT
ejpam-6422	274	48	x	x	SYM
ejpam-6422	274	49	∈	∈	PROPN
ejpam-6422	275	1	[	[	X
ejpam-6422	275	2	−4	−4	X
ejpam-6422	275	3	,	,	PUNCT
ejpam-6422	275	4	4	4	NUM
ejpam-6422	275	5	]	]	PUNCT
ejpam-6422	275	6	,	,	PUNCT
ejpam-6422	275	7	and	and	CCONJ
ejpam-6422	275	8	t	t	X
ejpam-6422	275	9	∈	∈	PROPN
ejpam-6422	276	1	[	[	X
ejpam-6422	276	2	0	0	NUM
ejpam-6422	276	3	,	,	PUNCT
ejpam-6422	276	4	3	3	NUM
ejpam-6422	276	5	]	]	PUNCT
ejpam-6422	276	6	(	(	PUNCT
ejpam-6422	276	7	f	f	X
ejpam-6422	276	8	)	)	PUNCT
ejpam-6422	276	9	display	display	VERB
ejpam-6422	276	10	2d	2d	NOUN
ejpam-6422	276	11	-	-	PUNCT
ejpam-6422	276	12	profile	profile	NOUN
ejpam-6422	276	13	of	of	ADP
ejpam-6422	276	14	eq	eq	NOUN
ejpam-6422	276	15	.	.	PUNCT
ejpam-6422	277	1	(	(	PUNCT
ejpam-6422	277	2	12	12	NUM
ejpam-6422	277	3	)	)	PUNCT
ejpam-6422	277	4	with	with	ADP
ejpam-6422	277	5	various	various	ADJ
ejpam-6422	277	6	κ	κ	PROPN
ejpam-6422	277	7	w.	w.	PROPN
ejpam-6422	277	8	w.	w.	PROPN
ejpam-6422	277	9	mohammed	mohammed	PROPN
ejpam-6422	277	10	et	et	PROPN
ejpam-6422	277	11	al	al	PROPN
ejpam-6422	277	12	.	.	PUNCT
ejpam-6422	277	13	/	/	SYM
ejpam-6422	277	14	eur	eur	PROPN
ejpam-6422	277	15	.	.	PUNCT
ejpam-6422	278	1	j.	j.	PROPN
ejpam-6422	278	2	pure	pure	PROPN
ejpam-6422	278	3	appl	appl	PROPN
ejpam-6422	278	4	.	.	PROPN
ejpam-6422	278	5	math	math	PROPN
ejpam-6422	278	6	,	,	PUNCT
ejpam-6422	278	7	18	18	NUM
ejpam-6422	278	8	(	(	PUNCT
ejpam-6422	278	9	3	3	NUM
ejpam-6422	278	10	)	)	PUNCT
ejpam-6422	278	11	(	(	PUNCT
ejpam-6422	278	12	2025	2025	NUM
ejpam-6422	278	13	)	)	PUNCT
ejpam-6422	278	14	,	,	PUNCT
ejpam-6422	278	15	6422	6422	NUM
ejpam-6422	278	16	10	10	NUM
ejpam-6422	278	17	of	of	ADP
ejpam-6422	278	18	13	13	NUM
ejpam-6422	278	19	(	(	PUNCT
ejpam-6422	278	20	a	a	NOUN
ejpam-6422	278	21	)	)	PUNCT
ejpam-6422	278	22	κ	κ	NOUN
ejpam-6422	278	23	=	=	SYM
ejpam-6422	278	24	1	1	NUM
ejpam-6422	278	25	(	(	PUNCT
ejpam-6422	278	26	b	b	NOUN
ejpam-6422	278	27	)	)	PUNCT
ejpam-6422	278	28	κ	κ	NOUN
ejpam-6422	279	1	=	=	NOUN
ejpam-6422	279	2	0.8	0.8	NUM
ejpam-6422	279	3	(	(	PUNCT
ejpam-6422	279	4	c	c	NOUN
ejpam-6422	279	5	)	)	PUNCT
ejpam-6422	279	6	κ	κ	NOUN
ejpam-6422	279	7	=	=	SYM
ejpam-6422	279	8	0.6	0.6	NUM
ejpam-6422	279	9	(	(	PUNCT
ejpam-6422	279	10	d	d	NOUN
ejpam-6422	279	11	)	)	PUNCT
ejpam-6422	279	12	κ	κ	NOUN
ejpam-6422	279	13	=	=	SYM
ejpam-6422	279	14	0.5	0.5	NUM
ejpam-6422	279	15	(	(	PUNCT
ejpam-6422	279	16	e	e	NOUN
ejpam-6422	279	17	)	)	PUNCT
ejpam-6422	279	18	κ	κ	NOUN
ejpam-6422	279	19	=	=	SYM
ejpam-6422	279	20	0.4	0.4	NUM
ejpam-6422	279	21	(	(	PUNCT
ejpam-6422	279	22	f	f	X
ejpam-6422	279	23	)	)	PUNCT
ejpam-6422	279	24	κ	κ	NOUN
ejpam-6422	280	1	=	=	SYM
ejpam-6422	280	2	1	1	NUM
ejpam-6422	280	3	,	,	PUNCT
ejpam-6422	280	4	0.8	0.8	NUM
ejpam-6422	280	5	,	,	PUNCT
ejpam-6422	280	6	0.6	0.6	NUM
ejpam-6422	280	7	,	,	PUNCT
ejpam-6422	280	8	0.5	0.5	NUM
ejpam-6422	280	9	,	,	PUNCT
ejpam-6422	280	10	0.4	0.4	NUM
ejpam-6422	280	11	figure	figure	NOUN
ejpam-6422	280	12	2	2	NUM
ejpam-6422	280	13	.	.	PUNCT
ejpam-6422	281	1	(	(	PUNCT
ejpam-6422	281	2	a	a	DET
ejpam-6422	281	3	-	-	PUNCT
ejpam-6422	281	4	e	e	NOUN
ejpam-6422	281	5	)	)	PUNCT
ejpam-6422	281	6	describe	describe	VERB
ejpam-6422	281	7	3d	3d	NUM
ejpam-6422	281	8	-	-	PUNCT
ejpam-6422	281	9	profile	profile	NOUN
ejpam-6422	281	10	of	of	ADP
ejpam-6422	281	11	solution	solution	NOUN
ejpam-6422	281	12	w(x	w(x	PROPN
ejpam-6422	281	13	,	,	PUNCT
ejpam-6422	281	14	y	y	PROPN
ejpam-6422	281	15	,	,	PUNCT
ejpam-6422	281	16	z	z	PROPN
ejpam-6422	281	17	,	,	PUNCT
ejpam-6422	281	18	t	t	PROPN
ejpam-6422	281	19	)	)	PUNCT
ejpam-6422	281	20	in	in	ADP
ejpam-6422	281	21	eq	eq	NOUN
ejpam-6422	281	22	(	(	PUNCT
ejpam-6422	281	23	13	13	NUM
ejpam-6422	281	24	)	)	PUNCT
ejpam-6422	281	25	with	with	ADP
ejpam-6422	281	26	a2	a2	PROPN
ejpam-6422	281	27	=	=	SYM
ejpam-6422	281	28	1	1	NUM
ejpam-6422	281	29	,	,	PUNCT
ejpam-6422	281	30	y	y	NOUN
ejpam-6422	281	31	=	=	PUNCT
ejpam-6422	281	32	z	z	NOUN
ejpam-6422	281	33	=	=	SYM
ejpam-6422	281	34	0	0	NUM
ejpam-6422	281	35	,	,	PUNCT
ejpam-6422	281	36	ρ1	ρ1	NOUN
ejpam-6422	281	37	=	=	SYM
ejpam-6422	281	38	ρ2	ρ2	NOUN
ejpam-6422	281	39	=	=	SYM
ejpam-6422	281	40	ρ3	ρ3	NOUN
ejpam-6422	281	41	=	=	SYM
ejpam-6422	281	42	1	1	NUM
ejpam-6422	281	43	,	,	PUNCT
ejpam-6422	282	1	x	x	SYM
ejpam-6422	282	2	∈	∈	PROPN
ejpam-6422	283	1	[	[	X
ejpam-6422	283	2	−4	−4	X
ejpam-6422	283	3	,	,	PUNCT
ejpam-6422	283	4	4	4	NUM
ejpam-6422	283	5	]	]	PUNCT
ejpam-6422	283	6	,	,	PUNCT
ejpam-6422	283	7	and	and	CCONJ
ejpam-6422	283	8	t	t	X
ejpam-6422	283	9	∈	∈	PROPN
ejpam-6422	284	1	[	[	X
ejpam-6422	284	2	0	0	NUM
ejpam-6422	284	3	,	,	PUNCT
ejpam-6422	284	4	3	3	NUM
ejpam-6422	284	5	]	]	PUNCT
ejpam-6422	284	6	(	(	PUNCT
ejpam-6422	284	7	f	f	X
ejpam-6422	284	8	)	)	PUNCT
ejpam-6422	284	9	display	display	VERB
ejpam-6422	284	10	2d	2d	NOUN
ejpam-6422	284	11	-	-	PUNCT
ejpam-6422	284	12	profile	profile	NOUN
ejpam-6422	284	13	of	of	ADP
ejpam-6422	284	14	eq	eq	NOUN
ejpam-6422	284	15	.	.	PUNCT
ejpam-6422	285	1	(	(	PUNCT
ejpam-6422	285	2	13	13	NUM
ejpam-6422	285	3	)	)	PUNCT
ejpam-6422	285	4	with	with	ADP
ejpam-6422	285	5	various	various	ADJ
ejpam-6422	285	6	κ	κ	PROPN
ejpam-6422	285	7	w.	w.	PROPN
ejpam-6422	285	8	w.	w.	PROPN
ejpam-6422	285	9	mohammed	mohammed	PROPN
ejpam-6422	285	10	et	et	PROPN
ejpam-6422	285	11	al	al	PROPN
ejpam-6422	285	12	.	.	PUNCT
ejpam-6422	285	13	/	/	SYM
ejpam-6422	285	14	eur	eur	PROPN
ejpam-6422	285	15	.	.	PUNCT
ejpam-6422	286	1	j.	j.	PROPN
ejpam-6422	286	2	pure	pure	PROPN
ejpam-6422	286	3	appl	appl	PROPN
ejpam-6422	286	4	.	.	PROPN
ejpam-6422	286	5	math	math	PROPN
ejpam-6422	286	6	,	,	PUNCT
ejpam-6422	286	7	18	18	NUM
ejpam-6422	286	8	(	(	PUNCT
ejpam-6422	286	9	3	3	NUM
ejpam-6422	286	10	)	)	PUNCT
ejpam-6422	286	11	(	(	PUNCT
ejpam-6422	286	12	2025	2025	NUM
ejpam-6422	286	13	)	)	PUNCT
ejpam-6422	286	14	,	,	PUNCT
ejpam-6422	286	15	6422	6422	NUM
ejpam-6422	286	16	11	11	NUM
ejpam-6422	286	17	of	of	ADP
ejpam-6422	286	18	13	13	NUM
ejpam-6422	286	19	(	(	PUNCT
ejpam-6422	286	20	a	a	NOUN
ejpam-6422	286	21	)	)	PUNCT
ejpam-6422	286	22	κ	κ	NOUN
ejpam-6422	286	23	=	=	SYM
ejpam-6422	286	24	1	1	NUM
ejpam-6422	286	25	(	(	PUNCT
ejpam-6422	286	26	b	b	NOUN
ejpam-6422	286	27	)	)	PUNCT
ejpam-6422	286	28	κ	κ	NOUN
ejpam-6422	287	1	=	=	NOUN
ejpam-6422	287	2	0.8	0.8	NUM
ejpam-6422	287	3	(	(	PUNCT
ejpam-6422	287	4	c	c	NOUN
ejpam-6422	287	5	)	)	PUNCT
ejpam-6422	287	6	κ	κ	NOUN
ejpam-6422	287	7	=	=	SYM
ejpam-6422	287	8	0.6	0.6	NUM
ejpam-6422	287	9	(	(	PUNCT
ejpam-6422	287	10	d	d	NOUN
ejpam-6422	287	11	)	)	PUNCT
ejpam-6422	287	12	κ	κ	NOUN
ejpam-6422	287	13	=	=	SYM
ejpam-6422	287	14	0.5	0.5	NUM
ejpam-6422	287	15	(	(	PUNCT
ejpam-6422	287	16	e	e	NOUN
ejpam-6422	287	17	)	)	PUNCT
ejpam-6422	287	18	κ	κ	NOUN
ejpam-6422	287	19	=	=	SYM
ejpam-6422	287	20	0.4	0.4	NUM
ejpam-6422	287	21	(	(	PUNCT
ejpam-6422	287	22	f	f	X
ejpam-6422	287	23	)	)	PUNCT
ejpam-6422	287	24	κ	κ	NOUN
ejpam-6422	288	1	=	=	SYM
ejpam-6422	288	2	1	1	NUM
ejpam-6422	288	3	,	,	PUNCT
ejpam-6422	288	4	0.8	0.8	NUM
ejpam-6422	288	5	,	,	PUNCT
ejpam-6422	288	6	0.6	0.6	NUM
ejpam-6422	288	7	,	,	PUNCT
ejpam-6422	288	8	0.5	0.5	NUM
ejpam-6422	288	9	,	,	PUNCT
ejpam-6422	288	10	0.4	0.4	NUM
ejpam-6422	288	11	figure	figure	NOUN
ejpam-6422	288	12	3	3	NUM
ejpam-6422	288	13	.	.	PUNCT
ejpam-6422	289	1	(	(	PUNCT
ejpam-6422	289	2	a	a	DET
ejpam-6422	289	3	-	-	PUNCT
ejpam-6422	289	4	e	e	NOUN
ejpam-6422	289	5	)	)	PUNCT
ejpam-6422	289	6	describe	describe	VERB
ejpam-6422	289	7	3d	3d	NUM
ejpam-6422	289	8	-	-	PUNCT
ejpam-6422	289	9	profile	profile	NOUN
ejpam-6422	289	10	of	of	ADP
ejpam-6422	289	11	solution	solution	NOUN
ejpam-6422	289	12	w(x	w(x	PROPN
ejpam-6422	289	13	,	,	PUNCT
ejpam-6422	289	14	y	y	PROPN
ejpam-6422	289	15	,	,	PUNCT
ejpam-6422	289	16	z	z	PROPN
ejpam-6422	289	17	,	,	PUNCT
ejpam-6422	289	18	t	t	PROPN
ejpam-6422	289	19	)	)	PUNCT
ejpam-6422	289	20	in	in	ADP
ejpam-6422	289	21	eq	eq	NOUN
ejpam-6422	289	22	(	(	PUNCT
ejpam-6422	289	23	33	33	NUM
ejpam-6422	289	24	)	)	PUNCT
ejpam-6422	289	25	with	with	ADP
ejpam-6422	289	26	a2	a2	PROPN
ejpam-6422	289	27	=	=	SYM
ejpam-6422	289	28	1	1	NUM
ejpam-6422	289	29	,	,	PUNCT
ejpam-6422	289	30	y	y	NOUN
ejpam-6422	289	31	=	=	PUNCT
ejpam-6422	289	32	z	z	NOUN
ejpam-6422	289	33	=	=	SYM
ejpam-6422	289	34	0	0	NUM
ejpam-6422	289	35	,	,	PUNCT
ejpam-6422	289	36	ρ1	ρ1	NOUN
ejpam-6422	289	37	=	=	SYM
ejpam-6422	289	38	ρ2	ρ2	NOUN
ejpam-6422	289	39	=	=	SYM
ejpam-6422	289	40	ρ3	ρ3	NOUN
ejpam-6422	289	41	=	=	SYM
ejpam-6422	289	42	1	1	NUM
ejpam-6422	289	43	,	,	PUNCT
ejpam-6422	290	1	x	x	SYM
ejpam-6422	290	2	∈	∈	PROPN
ejpam-6422	291	1	[	[	X
ejpam-6422	291	2	−4	−4	X
ejpam-6422	291	3	,	,	PUNCT
ejpam-6422	291	4	4	4	NUM
ejpam-6422	291	5	]	]	PUNCT
ejpam-6422	291	6	,	,	PUNCT
ejpam-6422	291	7	and	and	CCONJ
ejpam-6422	291	8	t	t	X
ejpam-6422	291	9	∈	∈	PROPN
ejpam-6422	292	1	[	[	X
ejpam-6422	292	2	0	0	NUM
ejpam-6422	292	3	,	,	PUNCT
ejpam-6422	292	4	3	3	NUM
ejpam-6422	292	5	]	]	PUNCT
ejpam-6422	292	6	(	(	PUNCT
ejpam-6422	292	7	f	f	X
ejpam-6422	292	8	)	)	PUNCT
ejpam-6422	292	9	display	display	VERB
ejpam-6422	292	10	2d	2d	NOUN
ejpam-6422	292	11	-	-	PUNCT
ejpam-6422	292	12	profile	profile	NOUN
ejpam-6422	292	13	of	of	ADP
ejpam-6422	292	14	eq	eq	NOUN
ejpam-6422	292	15	.	.	PUNCT
ejpam-6422	293	1	(	(	PUNCT
ejpam-6422	293	2	33	33	NUM
ejpam-6422	293	3	)	)	PUNCT
ejpam-6422	293	4	with	with	ADP
ejpam-6422	293	5	various	various	ADJ
ejpam-6422	293	6	κ	κ	PROPN
ejpam-6422	293	7	w.	w.	PROPN
ejpam-6422	293	8	w.	w.	PROPN
ejpam-6422	293	9	mohammed	mohammed	PROPN
ejpam-6422	293	10	et	et	PROPN
ejpam-6422	293	11	al	al	PROPN
ejpam-6422	293	12	.	.	PUNCT
ejpam-6422	293	13	/	/	SYM
ejpam-6422	293	14	eur	eur	PROPN
ejpam-6422	293	15	.	.	PUNCT
ejpam-6422	294	1	j.	j.	PROPN
ejpam-6422	294	2	pure	pure	PROPN
ejpam-6422	294	3	appl	appl	PROPN
ejpam-6422	294	4	.	.	PROPN
ejpam-6422	294	5	math	math	PROPN
ejpam-6422	294	6	,	,	PUNCT
ejpam-6422	294	7	18	18	NUM
ejpam-6422	294	8	(	(	PUNCT
ejpam-6422	294	9	3	3	NUM
ejpam-6422	294	10	)	)	PUNCT
ejpam-6422	294	11	(	(	PUNCT
ejpam-6422	294	12	2025	2025	NUM
ejpam-6422	294	13	)	)	PUNCT
ejpam-6422	294	14	,	,	PUNCT
ejpam-6422	294	15	6422	6422	NUM
ejpam-6422	294	16	12	12	NUM
ejpam-6422	294	17	of	of	ADP
ejpam-6422	294	18	13	13	NUM
ejpam-6422	294	19	5	5	NUM
ejpam-6422	294	20	.	.	PUNCT
ejpam-6422	295	1	conclusions	conclusion	NOUN
ejpam-6422	295	2	in	in	ADP
ejpam-6422	295	3	this	this	DET
ejpam-6422	295	4	paper	paper	NOUN
ejpam-6422	295	5	,	,	PUNCT
ejpam-6422	295	6	the	the	DET
ejpam-6422	295	7	unidirectional	unidirectional	ADJ
ejpam-6422	295	8	wave	wave	NOUN
ejpam-6422	295	9	model	model	NOUN
ejpam-6422	295	10	(	(	PUNCT
ejpam-6422	295	11	uwm	uwm	PROPN
ejpam-6422	295	12	)	)	PUNCT
ejpam-6422	295	13	(	(	PUNCT
ejpam-6422	295	14	1	1	X
ejpam-6422	295	15	)	)	PUNCT
ejpam-6422	295	16	with	with	ADP
ejpam-6422	295	17	beta	beta	NOUN
ejpam-6422	295	18	-	-	PUNCT
ejpam-6422	295	19	derivative	derivative	NOUN
ejpam-6422	295	20	operator	operator	NOUN
ejpam-6422	295	21	(	(	PUNCT
ejpam-6422	295	22	bdo	bdo	NOUN
ejpam-6422	295	23	)	)	PUNCT
ejpam-6422	295	24	was	be	AUX
ejpam-6422	295	25	considered	consider	VERB
ejpam-6422	295	26	.	.	PUNCT
ejpam-6422	296	1	we	we	PRON
ejpam-6422	296	2	obtained	obtain	VERB
ejpam-6422	296	3	many	many	ADJ
ejpam-6422	296	4	various	various	ADJ
ejpam-6422	296	5	kind	kind	NOUN
ejpam-6422	296	6	of	of	ADP
ejpam-6422	296	7	solutions	solution	NOUN
ejpam-6422	296	8	including	include	VERB
ejpam-6422	296	9	periodic	periodic	ADJ
ejpam-6422	296	10	soliton	soliton	NOUN
ejpam-6422	296	11	,	,	PUNCT
ejpam-6422	296	12	bright	bright	ADJ
ejpam-6422	296	13	soliton	soliton	NOUN
ejpam-6422	296	14	,	,	PUNCT
ejpam-6422	296	15	kink	kink	NOUN
ejpam-6422	296	16	soliton	soliton	NOUN
ejpam-6422	296	17	,	,	PUNCT
ejpam-6422	296	18	anti	anti	ADJ
ejpam-6422	296	19	-	-	ADJ
ejpam-6422	296	20	kink	kink	ADJ
ejpam-6422	296	21	soliton	soliton	NOUN
ejpam-6422	296	22	,	,	PUNCT
ejpam-6422	296	23	singular	singular	NOUN
ejpam-6422	296	24	soliton	soliton	NOUN
ejpam-6422	296	25	,	,	PUNCT
ejpam-6422	296	26	and	and	CCONJ
ejpam-6422	296	27	dark	dark	ADV
ejpam-6422	296	28	-	-	PUNCT
ejpam-6422	296	29	bright	bright	ADJ
ejpam-6422	296	30	soliton	soliton	NOUN
ejpam-6422	296	31	by	by	ADP
ejpam-6422	296	32	using	use	VERB
ejpam-6422	296	33	the	the	DET
ejpam-6422	296	34	f	f	ADJ
ejpam-6422	296	35	-	-	PUNCT
ejpam-6422	296	36	expansion	expansion	NOUN
ejpam-6422	296	37	method	method	NOUN
ejpam-6422	296	38	.	.	PUNCT
ejpam-6422	297	1	the	the	DET
ejpam-6422	297	2	uwm	uwm	NOUN
ejpam-6422	297	3	-	-	PUNCT
ejpam-6422	297	4	bdo	bdo	NOUN
ejpam-6422	297	5	(	(	PUNCT
ejpam-6422	297	6	1	1	NUM
ejpam-6422	297	7	)	)	PUNCT
ejpam-6422	297	8	has	have	VERB
ejpam-6422	297	9	a	a	DET
ejpam-6422	297	10	significant	significant	ADJ
ejpam-6422	297	11	applications	application	NOUN
ejpam-6422	297	12	in	in	ADP
ejpam-6422	297	13	many	many	ADJ
ejpam-6422	297	14	fields	field	NOUN
ejpam-6422	297	15	such	such	ADJ
ejpam-6422	297	16	as	as	ADP
ejpam-6422	297	17	oceanography	oceanography	NOUN
ejpam-6422	297	18	,	,	PUNCT
ejpam-6422	297	19	coastal	coastal	ADJ
ejpam-6422	297	20	engineering	engineering	NOUN
ejpam-6422	297	21	,	,	PUNCT
ejpam-6422	297	22	and	and	CCONJ
ejpam-6422	297	23	meteorology	meteorology	NOUN
ejpam-6422	297	24	,	,	PUNCT
ejpam-6422	297	25	allowing	allow	VERB
ejpam-6422	297	26	for	for	ADP
ejpam-6422	297	27	an	an	DET
ejpam-6422	297	28	examination	examination	NOUN
ejpam-6422	297	29	of	of	ADP
ejpam-6422	297	30	a	a	DET
ejpam-6422	297	31	variety	variety	NOUN
ejpam-6422	297	32	of	of	ADP
ejpam-6422	297	33	scientific	scientific	ADJ
ejpam-6422	297	34	phenomena	phenomenon	NOUN
ejpam-6422	297	35	.	.	PUNCT
ejpam-6422	298	1	to	to	PART
ejpam-6422	298	2	study	study	VERB
ejpam-6422	298	3	the	the	DET
ejpam-6422	298	4	effect	effect	NOUN
ejpam-6422	298	5	of	of	ADP
ejpam-6422	298	6	the	the	DET
ejpam-6422	298	7	beta	beta	NOUN
ejpam-6422	298	8	-	-	PUNCT
ejpam-6422	298	9	derivative	derivative	NOUN
ejpam-6422	298	10	operator	operator	NOUN
ejpam-6422	298	11	on	on	ADP
ejpam-6422	298	12	the	the	DET
ejpam-6422	298	13	solutions	solution	NOUN
ejpam-6422	298	14	of	of	ADP
ejpam-6422	298	15	eq	eq	PROPN
ejpam-6422	298	16	.	.	PUNCT
ejpam-6422	299	1	(	(	PUNCT
ejpam-6422	299	2	1	1	NUM
ejpam-6422	299	3	)	)	PUNCT
ejpam-6422	299	4	,	,	PUNCT
ejpam-6422	299	5	many	many	ADJ
ejpam-6422	299	6	figures	figure	NOUN
ejpam-6422	299	7	(	(	PUNCT
ejpam-6422	299	8	see	see	VERB
ejpam-6422	299	9	figures	figure	NOUN
ejpam-6422	299	10	1	1	NUM
ejpam-6422	299	11	,	,	PUNCT
ejpam-6422	299	12	2	2	NUM
ejpam-6422	299	13	and	and	CCONJ
ejpam-6422	299	14	3	3	NUM
ejpam-6422	299	15	)	)	PUNCT
ejpam-6422	299	16	are	be	AUX
ejpam-6422	299	17	produced	produce	VERB
ejpam-6422	299	18	by	by	ADP
ejpam-6422	299	19	utilizing	utilize	VERB
ejpam-6422	299	20	the	the	DET
ejpam-6422	299	21	matlab	matlab	PROPN
ejpam-6422	299	22	program	program	NOUN
ejpam-6422	299	23	.	.	PUNCT
ejpam-6422	300	1	we	we	PRON
ejpam-6422	300	2	deduced	deduce	VERB
ejpam-6422	300	3	that	that	SCONJ
ejpam-6422	300	4	when	when	SCONJ
ejpam-6422	300	5	the	the	DET
ejpam-6422	300	6	order	order	NOUN
ejpam-6422	300	7	of	of	ADP
ejpam-6422	300	8	the	the	DET
ejpam-6422	300	9	bdo	bdo	NOUN
ejpam-6422	300	10	decreases	decrease	VERB
ejpam-6422	300	11	,	,	PUNCT
ejpam-6422	300	12	the	the	DET
ejpam-6422	300	13	surface	surface	NOUN
ejpam-6422	300	14	of	of	ADP
ejpam-6422	300	15	the	the	DET
ejpam-6422	300	16	solutions	solution	NOUN
ejpam-6422	300	17	moves	move	NOUN
ejpam-6422	300	18	to	to	ADP
ejpam-6422	300	19	the	the	DET
ejpam-6422	300	20	right	right	NOUN
ejpam-6422	300	21	.	.	PUNCT
ejpam-6422	301	1	in	in	ADP
ejpam-6422	301	2	the	the	DET
ejpam-6422	301	3	future	future	ADJ
ejpam-6422	301	4	work	work	NOUN
ejpam-6422	301	5	,	,	PUNCT
ejpam-6422	301	6	we	we	PRON
ejpam-6422	301	7	can	can	AUX
ejpam-6422	301	8	get	get	VERB
ejpam-6422	301	9	the	the	DET
ejpam-6422	301	10	exact	exact	ADJ
ejpam-6422	301	11	solutions	solution	NOUN
ejpam-6422	301	12	for	for	ADP
ejpam-6422	301	13	the	the	DET
ejpam-6422	301	14	uwm	uwm	PROPN
ejpam-6422	301	15	with	with	ADP
ejpam-6422	301	16	stochastic	stochastic	ADJ
ejpam-6422	301	17	process	process	NOUN
ejpam-6422	301	18	.	.	PUNCT
ejpam-6422	302	1	acknowledgements	acknowledgement	NOUN
ejpam-6422	302	2	this	this	DET
ejpam-6422	302	3	research	research	NOUN
ejpam-6422	302	4	has	have	AUX
ejpam-6422	302	5	been	be	AUX
ejpam-6422	302	6	funded	fund	VERB
ejpam-6422	302	7	by	by	ADP
ejpam-6422	302	8	scientific	scientific	ADJ
ejpam-6422	302	9	research	research	NOUN
ejpam-6422	302	10	deanship	deanship	NOUN
ejpam-6422	302	11	at	at	ADP
ejpam-6422	302	12	the	the	DET
ejpam-6422	302	13	university	university	NOUN
ejpam-6422	302	14	of	of	ADP
ejpam-6422	302	15	ha’il	ha’il	PROPN
ejpam-6422	302	16	-	-	PUNCT
ejpam-6422	302	17	saudi	saudi	PROPN
ejpam-6422	302	18	arabia	arabia	PROPN
ejpam-6422	302	19	through	through	ADP
ejpam-6422	302	20	project	project	NOUN
ejpam-6422	302	21	number	number	NOUN
ejpam-6422	302	22	rg-25004	rg-25004	NOUN
ejpam-6422	302	23	.	.	PUNCT
ejpam-6422	303	1	references	reference	NOUN
ejpam-6422	303	2	[	[	X
ejpam-6422	303	3	1	1	NUM
ejpam-6422	303	4	]	]	PUNCT
ejpam-6422	303	5	k.	k.	PROPN
ejpam-6422	303	6	b.	b.	PROPN
ejpam-6422	303	7	oldham	oldham	PROPN
ejpam-6422	303	8	and	and	CCONJ
ejpam-6422	303	9	j.	j.	PROPN
ejpam-6422	303	10	spanier	spanier	PROPN
ejpam-6422	303	11	.	.	PUNCT
ejpam-6422	304	1	the	the	DET
ejpam-6422	304	2	fractional	fractional	ADJ
ejpam-6422	304	3	calculus	calculus	NOUN
ejpam-6422	304	4	:	:	PUNCT
ejpam-6422	304	5	theory	theory	NOUN
ejpam-6422	304	6	and	and	CCONJ
ejpam-6422	304	7	applications	application	NOUN
ejpam-6422	304	8	of	of	ADP
ejpam-6422	304	9	differentiation	differentiation	NOUN
ejpam-6422	304	10	and	and	CCONJ
ejpam-6422	304	11	integration	integration	NOUN
ejpam-6422	304	12	to	to	ADP
ejpam-6422	304	13	arbitrary	arbitrary	ADJ
ejpam-6422	304	14	order	order	NOUN
ejpam-6422	304	15	.	.	PUNCT
ejpam-6422	305	1	academic	academic	ADJ
ejpam-6422	305	2	press	press	NOUN
ejpam-6422	305	3	,	,	PUNCT
ejpam-6422	305	4	new	new	PROPN
ejpam-6422	305	5	york	york	PROPN
ejpam-6422	305	6	,	,	PUNCT
ejpam-6422	305	7	ny	ny	PROPN
ejpam-6422	305	8	,	,	PUNCT
ejpam-6422	305	9	usa	usa	PROPN
ejpam-6422	305	10	,	,	PUNCT
ejpam-6422	305	11	1974	1974	NUM
ejpam-6422	305	12	.	.	PUNCT
ejpam-6422	306	1	[	[	X
ejpam-6422	306	2	2	2	X
ejpam-6422	306	3	]	]	PUNCT
ejpam-6422	306	4	k.	k.	PROPN
ejpam-6422	306	5	s.	s.	PROPN
ejpam-6422	306	6	miller	miller	PROPN
ejpam-6422	306	7	and	and	CCONJ
ejpam-6422	306	8	b.	b.	PROPN
ejpam-6422	306	9	ross	ross	PROPN
ejpam-6422	306	10	.	.	PUNCT
ejpam-6422	307	1	an	an	DET
ejpam-6422	307	2	introduction	introduction	NOUN
ejpam-6422	307	3	to	to	ADP
ejpam-6422	307	4	the	the	DET
ejpam-6422	307	5	fractional	fractional	ADJ
ejpam-6422	307	6	calculus	calculus	NOUN
ejpam-6422	307	7	and	and	CCONJ
ejpam-6422	307	8	fractional	fractional	ADJ
ejpam-6422	307	9	differential	differential	ADJ
ejpam-6422	307	10	equations	equation	NOUN
ejpam-6422	307	11	.	.	PUNCT
ejpam-6422	308	1	a	a	DET
ejpam-6422	308	2	wiley	wiley	NOUN
ejpam-6422	308	3	-	-	PUNCT
ejpam-6422	308	4	interscience	interscience	NOUN
ejpam-6422	308	5	publication	publication	NOUN
ejpam-6422	308	6	,	,	PUNCT
ejpam-6422	308	7	john	john	PROPN
ejpam-6422	308	8	wiley	wiley	PROPN
ejpam-6422	308	9	&	&	CCONJ
ejpam-6422	308	10	sons	son	NOUN
ejpam-6422	308	11	,	,	PUNCT
ejpam-6422	308	12	new	new	PROPN
ejpam-6422	308	13	york	york	PROPN
ejpam-6422	308	14	,	,	PUNCT
ejpam-6422	308	15	ny	ny	PROPN
ejpam-6422	308	16	,	,	PUNCT
ejpam-6422	308	17	usa	usa	PROPN
ejpam-6422	308	18	,	,	PUNCT
ejpam-6422	308	19	1993	1993	NUM
ejpam-6422	308	20	.	.	PUNCT
ejpam-6422	309	1	[	[	X
ejpam-6422	309	2	3	3	NUM
ejpam-6422	309	3	]	]	X
ejpam-6422	309	4	i.	i.	NOUN
ejpam-6422	309	5	podlubny	podlubny	PROPN
ejpam-6422	309	6	.	.	PUNCT
ejpam-6422	310	1	fractional	fractional	ADJ
ejpam-6422	310	2	differential	differential	ADJ
ejpam-6422	310	3	equations	equation	NOUN
ejpam-6422	310	4	,	,	PUNCT
ejpam-6422	310	5	volume	volume	NOUN
ejpam-6422	310	6	198	198	NUM
ejpam-6422	310	7	of	of	ADP
ejpam-6422	310	8	mathematics	mathematic	NOUN
ejpam-6422	310	9	in	in	ADP
ejpam-6422	310	10	science	science	NOUN
ejpam-6422	310	11	and	and	CCONJ
ejpam-6422	310	12	engineering	engineering	NOUN
ejpam-6422	310	13	.	.	PUNCT
ejpam-6422	311	1	academic	academic	ADJ
ejpam-6422	311	2	press	press	NOUN
ejpam-6422	311	3	,	,	PUNCT
ejpam-6422	311	4	san	san	PROPN
ejpam-6422	311	5	diego	diego	PROPN
ejpam-6422	311	6	,	,	PUNCT
ejpam-6422	311	7	ca	ca	PROPN
ejpam-6422	311	8	,	,	PUNCT
ejpam-6422	311	9	usa	usa	PROPN
ejpam-6422	311	10	,	,	PUNCT
ejpam-6422	311	11	1999	1999	NUM
ejpam-6422	311	12	.	.	PUNCT
ejpam-6422	312	1	[	[	X
ejpam-6422	312	2	4	4	NUM
ejpam-6422	312	3	]	]	PUNCT
ejpam-6422	312	4	f.	f.	PROPN
ejpam-6422	312	5	m.	m.	PROPN
ejpam-6422	312	6	al	al	PROPN
ejpam-6422	312	7	-	-	PUNCT
ejpam-6422	312	8	askar	askar	PROPN
ejpam-6422	312	9	,	,	PUNCT
ejpam-6422	312	10	c.	c.	PROPN
ejpam-6422	312	11	cesarano	cesarano	PROPN
ejpam-6422	312	12	,	,	PUNCT
ejpam-6422	312	13	and	and	CCONJ
ejpam-6422	312	14	w.	w.	PROPN
ejpam-6422	312	15	w.	w.	PROPN
ejpam-6422	312	16	mohammed	mohammed	PROPN
ejpam-6422	312	17	.	.	PUNCT
ejpam-6422	313	1	abundant	abundant	ADJ
ejpam-6422	313	2	solitary	solitary	ADJ
ejpam-6422	313	3	wave	wave	NOUN
ejpam-6422	313	4	solutions	solution	NOUN
ejpam-6422	313	5	for	for	ADP
ejpam-6422	313	6	the	the	DET
ejpam-6422	313	7	boiti	boiti	PROPN
ejpam-6422	313	8	–	–	PUNCT
ejpam-6422	313	9	leon	leon	PROPN
ejpam-6422	313	10	–	–	PUNCT
ejpam-6422	313	11	manna	manna	NOUN
ejpam-6422	313	12	–	–	PUNCT
ejpam-6422	313	13	pempinelli	pempinelli	ADJ
ejpam-6422	313	14	equation	equation	NOUN
ejpam-6422	313	15	with	with	ADP
ejpam-6422	313	16	m	m	ADJ
ejpam-6422	313	17	-	-	PUNCT
ejpam-6422	313	18	truncated	truncate	VERB
ejpam-6422	313	19	derivative	derivative	NOUN
ejpam-6422	313	20	.	.	PUNCT
ejpam-6422	314	1	axioms	axiom	NOUN
ejpam-6422	314	2	,	,	PUNCT
ejpam-6422	314	3	12:466	12:466	NUM
ejpam-6422	314	4	,	,	PUNCT
ejpam-6422	314	5	2023	2023	NUM
ejpam-6422	314	6	.	.	PUNCT
ejpam-6422	315	1	[	[	X
ejpam-6422	315	2	5	5	X
ejpam-6422	315	3	]	]	PUNCT
ejpam-6422	315	4	m.	m.	NOUN
ejpam-6422	315	5	mouy	mouy	PROPN
ejpam-6422	315	6	,	,	PUNCT
ejpam-6422	315	7	h.	h.	PROPN
ejpam-6422	315	8	boulares	boulares	PROPN
ejpam-6422	315	9	,	,	PUNCT
ejpam-6422	315	10	s.	s.	PROPN
ejpam-6422	315	11	alshammari	alshammari	PROPN
ejpam-6422	315	12	,	,	PUNCT
ejpam-6422	315	13	m.	m.	NOUN
ejpam-6422	315	14	alshammari	alshammari	PROPN
ejpam-6422	315	15	,	,	PUNCT
ejpam-6422	315	16	y.	y.	PROPN
ejpam-6422	315	17	laskri	laskri	PROPN
ejpam-6422	315	18	,	,	PUNCT
ejpam-6422	315	19	and	and	CCONJ
ejpam-6422	315	20	w.	w.	PROPN
ejpam-6422	315	21	w.	w.	PROPN
ejpam-6422	315	22	mohammed	mohammed	PROPN
ejpam-6422	315	23	.	.	PUNCT
ejpam-6422	316	1	on	on	ADP
ejpam-6422	316	2	averaging	average	VERB
ejpam-6422	316	3	principle	principle	NOUN
ejpam-6422	316	4	for	for	ADP
ejpam-6422	316	5	caputo	caputo	PROPN
ejpam-6422	316	6	–	–	PUNCT
ejpam-6422	316	7	hadamard	hadamard	ADJ
ejpam-6422	316	8	fractional	fractional	ADJ
ejpam-6422	316	9	stochastic	stochastic	ADJ
ejpam-6422	316	10	differential	differential	ADJ
ejpam-6422	316	11	pantograph	pantograph	NOUN
ejpam-6422	316	12	equation	equation	NOUN
ejpam-6422	316	13	.	.	PUNCT
ejpam-6422	317	1	fractal	fractal	ADJ
ejpam-6422	317	2	and	and	CCONJ
ejpam-6422	317	3	fractional	fractional	ADJ
ejpam-6422	317	4	,	,	PUNCT
ejpam-6422	317	5	7:31	7:31	NUM
ejpam-6422	317	6	,	,	PUNCT
ejpam-6422	317	7	2022	2022	NUM
ejpam-6422	317	8	.	.	PUNCT
ejpam-6422	318	1	[	[	X
ejpam-6422	318	2	6	6	NUM
ejpam-6422	318	3	]	]	X
ejpam-6422	318	4	h.	h.	PROPN
ejpam-6422	318	5	m.	m.	PROPN
ejpam-6422	318	6	baskonus	baskonus	PROPN
ejpam-6422	318	7	,	,	PUNCT
ejpam-6422	318	8	h.	h.	PROPN
ejpam-6422	318	9	bulut	bulut	PROPN
ejpam-6422	318	10	,	,	PUNCT
ejpam-6422	318	11	and	and	CCONJ
ejpam-6422	318	12	t.	t.	PROPN
ejpam-6422	318	13	a.	a.	PROPN
ejpam-6422	318	14	sulaiman	sulaiman	PROPN
ejpam-6422	318	15	.	.	PUNCT
ejpam-6422	319	1	new	new	ADJ
ejpam-6422	319	2	complex	complex	ADJ
ejpam-6422	319	3	hyperbolic	hyperbolic	ADJ
ejpam-6422	319	4	structures	structure	NOUN
ejpam-6422	319	5	to	to	ADP
ejpam-6422	319	6	the	the	DET
ejpam-6422	319	7	lonngren	lonngren	NOUN
ejpam-6422	319	8	-	-	PUNCT
ejpam-6422	319	9	wave	wave	NOUN
ejpam-6422	319	10	equation	equation	NOUN
ejpam-6422	319	11	by	by	ADP
ejpam-6422	319	12	using	use	VERB
ejpam-6422	319	13	sine	sine	NOUN
ejpam-6422	319	14	-	-	PUNCT
ejpam-6422	319	15	gordon	gordon	PROPN
ejpam-6422	319	16	expansion	expansion	NOUN
ejpam-6422	319	17	method	method	NOUN
ejpam-6422	319	18	.	.	PUNCT
ejpam-6422	320	1	applied	apply	VERB
ejpam-6422	320	2	mathematics	mathematic	NOUN
ejpam-6422	320	3	and	and	CCONJ
ejpam-6422	320	4	nonlinear	nonlinear	ADJ
ejpam-6422	320	5	sciences	sciences	PROPN
ejpam-6422	320	6	,	,	PUNCT
ejpam-6422	320	7	4:129–138	4:129–138	NUM
ejpam-6422	320	8	,	,	PUNCT
ejpam-6422	320	9	2019	2019	NUM
ejpam-6422	320	10	.	.	PUNCT
ejpam-6422	321	1	[	[	X
ejpam-6422	321	2	7	7	X
ejpam-6422	321	3	]	]	PUNCT
ejpam-6422	321	4	b.	b.	PROPN
ejpam-6422	321	5	lu	lu	PROPN
ejpam-6422	321	6	.	.	PUNCT
ejpam-6422	322	1	the	the	DET
ejpam-6422	322	2	first	first	ADJ
ejpam-6422	322	3	integral	integral	ADJ
ejpam-6422	322	4	method	method	NOUN
ejpam-6422	322	5	for	for	ADP
ejpam-6422	322	6	some	some	DET
ejpam-6422	322	7	time	time	NOUN
ejpam-6422	322	8	fractional	fractional	ADJ
ejpam-6422	322	9	differential	differential	ADJ
ejpam-6422	322	10	equations	equation	NOUN
ejpam-6422	322	11	.	.	PUNCT
ejpam-6422	323	1	journal	journal	PROPN
ejpam-6422	323	2	of	of	ADP
ejpam-6422	323	3	mathematical	mathematical	ADJ
ejpam-6422	323	4	analysis	analysis	NOUN
ejpam-6422	323	5	and	and	CCONJ
ejpam-6422	323	6	applications	application	NOUN
ejpam-6422	323	7	,	,	PUNCT
ejpam-6422	323	8	395:684–693	395:684–693	NUM
ejpam-6422	323	9	,	,	PUNCT
ejpam-6422	323	10	2012	2012	NUM
ejpam-6422	323	11	.	.	PUNCT
ejpam-6422	324	1	[	[	X
ejpam-6422	324	2	8	8	NUM
ejpam-6422	324	3	]	]	PUNCT
ejpam-6422	324	4	a.	a.	PROPN
ejpam-6422	324	5	e.	e.	PROPN
ejpam-6422	324	6	hamza	hamza	PROPN
ejpam-6422	324	7	,	,	PUNCT
ejpam-6422	324	8	m.	m.	NOUN
ejpam-6422	324	9	alshammari	alshammari	PROPN
ejpam-6422	324	10	,	,	PUNCT
ejpam-6422	324	11	d.	d.	PROPN
ejpam-6422	324	12	atta	atta	PROPN
ejpam-6422	324	13	,	,	PUNCT
ejpam-6422	324	14	and	and	CCONJ
ejpam-6422	324	15	w.	w.	PROPN
ejpam-6422	324	16	w.	w.	PROPN
ejpam-6422	324	17	mohammed	mohammed	PROPN
ejpam-6422	324	18	.	.	PUNCT
ejpam-6422	325	1	fractional	fractional	ADJ
ejpam-6422	325	2	-	-	PUNCT
ejpam-6422	325	3	stochastic	stochastic	NOUN
ejpam-6422	325	4	shallow	shallow	ADJ
ejpam-6422	325	5	water	water	NOUN
ejpam-6422	325	6	equations	equation	NOUN
ejpam-6422	325	7	and	and	CCONJ
ejpam-6422	325	8	its	its	PRON
ejpam-6422	325	9	analytical	analytical	ADJ
ejpam-6422	325	10	solutions	solution	NOUN
ejpam-6422	325	11	.	.	PUNCT
ejpam-6422	326	1	results	result	NOUN
ejpam-6422	326	2	in	in	ADP
ejpam-6422	326	3	physics	physics	NOUN
ejpam-6422	326	4	,	,	PUNCT
ejpam-6422	326	5	53:106953	53:106953	NUM
ejpam-6422	326	6	,	,	PUNCT
ejpam-6422	326	7	2023	2023	NUM
ejpam-6422	326	8	.	.	PUNCT
ejpam-6422	327	1	w.	w.	PROPN
ejpam-6422	327	2	w.	w.	PROPN
ejpam-6422	327	3	mohammed	mohammed	PROPN
ejpam-6422	327	4	et	et	PROPN
ejpam-6422	327	5	al	al	PROPN
ejpam-6422	327	6	.	.	PUNCT
ejpam-6422	327	7	/	/	SYM
ejpam-6422	327	8	eur	eur	PROPN
ejpam-6422	327	9	.	.	PUNCT
ejpam-6422	328	1	j.	j.	PROPN
ejpam-6422	328	2	pure	pure	PROPN
ejpam-6422	328	3	appl	appl	PROPN
ejpam-6422	328	4	.	.	PROPN
ejpam-6422	328	5	math	math	PROPN
ejpam-6422	328	6	,	,	PUNCT
ejpam-6422	328	7	18	18	NUM
ejpam-6422	328	8	(	(	PUNCT
ejpam-6422	328	9	3	3	NUM
ejpam-6422	328	10	)	)	PUNCT
ejpam-6422	328	11	(	(	PUNCT
ejpam-6422	328	12	2025	2025	NUM
ejpam-6422	328	13	)	)	PUNCT
ejpam-6422	328	14	,	,	PUNCT
ejpam-6422	328	15	6422	6422	NUM
ejpam-6422	328	16	13	13	NUM
ejpam-6422	328	17	of	of	ADP
ejpam-6422	328	18	13	13	NUM
ejpam-6422	329	1	[	[	X
ejpam-6422	329	2	9	9	NUM
ejpam-6422	329	3	]	]	PUNCT
ejpam-6422	329	4	z.	z.	PROPN
ejpam-6422	329	5	l.	l.	PROPN
ejpam-6422	329	6	yan	yan	PROPN
ejpam-6422	329	7	.	.	PUNCT
ejpam-6422	330	1	abundant	abundant	ADJ
ejpam-6422	330	2	families	family	NOUN
ejpam-6422	330	3	of	of	ADP
ejpam-6422	330	4	jacobi	jacobi	PROPN
ejpam-6422	330	5	elliptic	elliptic	ADJ
ejpam-6422	330	6	function	function	NOUN
ejpam-6422	330	7	solutions	solution	NOUN
ejpam-6422	330	8	of	of	ADP
ejpam-6422	330	9	the	the	DET
ejpam-6422	330	10	dimensional	dimensional	ADJ
ejpam-6422	330	11	integrable	integrable	ADJ
ejpam-6422	330	12	davey	davey	NOUN
ejpam-6422	330	13	-	-	PUNCT
ejpam-6422	330	14	stewartson	stewartson	NOUN
ejpam-6422	330	15	-	-	PUNCT
ejpam-6422	330	16	type	type	NOUN
ejpam-6422	330	17	equation	equation	NOUN
ejpam-6422	330	18	via	via	ADP
ejpam-6422	330	19	a	a	DET
ejpam-6422	330	20	new	new	ADJ
ejpam-6422	330	21	method	method	NOUN
ejpam-6422	330	22	.	.	PUNCT
ejpam-6422	331	1	chaos	chaos	NOUN
ejpam-6422	331	2	,	,	PUNCT
ejpam-6422	331	3	solitons	soliton	NOUN
ejpam-6422	331	4	&	&	CCONJ
ejpam-6422	331	5	fractals	fractal	NOUN
ejpam-6422	331	6	,	,	PUNCT
ejpam-6422	331	7	18:299–309	18:299–309	NUM
ejpam-6422	331	8	,	,	PUNCT
ejpam-6422	331	9	2003	2003	NUM
ejpam-6422	331	10	.	.	PUNCT
ejpam-6422	332	1	[	[	X
ejpam-6422	332	2	10	10	NUM
ejpam-6422	332	3	]	]	PUNCT
ejpam-6422	333	1	j.	j.	PROPN
ejpam-6422	333	2	h.	h.	PROPN
ejpam-6422	333	3	he	he	PRON
ejpam-6422	333	4	and	and	CCONJ
ejpam-6422	333	5	x.	x.	PROPN
ejpam-6422	333	6	h.	h.	PROPN
ejpam-6422	333	7	wu	wu	PROPN
ejpam-6422	333	8	.	.	PUNCT
ejpam-6422	334	1	exp	exp	NOUN
ejpam-6422	334	2	-	-	PUNCT
ejpam-6422	334	3	function	function	NOUN
ejpam-6422	334	4	method	method	NOUN
ejpam-6422	334	5	for	for	ADP
ejpam-6422	334	6	nonlinear	nonlinear	ADJ
ejpam-6422	334	7	wave	wave	NOUN
ejpam-6422	334	8	equations	equation	NOUN
ejpam-6422	334	9	.	.	PUNCT
ejpam-6422	335	1	chaos	chaos	NOUN
ejpam-6422	335	2	,	,	PUNCT
ejpam-6422	335	3	solitons	soliton	NOUN
ejpam-6422	335	4	&	&	CCONJ
ejpam-6422	335	5	fractals	fractal	NOUN
ejpam-6422	335	6	,	,	PUNCT
ejpam-6422	335	7	30:700–708	30:700–708	NUM
ejpam-6422	335	8	,	,	PUNCT
ejpam-6422	335	9	2006	2006	NUM
ejpam-6422	335	10	.	.	PUNCT
ejpam-6422	336	1	[	[	X
ejpam-6422	336	2	11	11	NUM
ejpam-6422	336	3	]	]	PUNCT
ejpam-6422	336	4	m.	m.	PROPN
ejpam-6422	336	5	l.	l.	PROPN
ejpam-6422	336	6	wang	wang	PROPN
ejpam-6422	336	7	,	,	PUNCT
ejpam-6422	336	8	x.	x.	PROPN
ejpam-6422	336	9	z.	z.	PROPN
ejpam-6422	336	10	li	li	PROPN
ejpam-6422	336	11	,	,	PUNCT
ejpam-6422	336	12	and	and	CCONJ
ejpam-6422	336	13	j.	j.	PROPN
ejpam-6422	336	14	l.	l.	PROPN
ejpam-6422	336	15	zhang	zhang	PROPN
ejpam-6422	336	16	.	.	PUNCT
ejpam-6422	337	1	the	the	DET
ejpam-6422	337	2	(	(	PUNCT
ejpam-6422	337	3	g′/g)-expansion	g′/g)-expansion	PROPN
ejpam-6422	337	4	method	method	NOUN
ejpam-6422	337	5	and	and	CCONJ
ejpam-6422	337	6	travelling	travel	VERB
ejpam-6422	337	7	wave	wave	NOUN
ejpam-6422	337	8	solutions	solution	NOUN
ejpam-6422	337	9	of	of	ADP
ejpam-6422	337	10	nonlinear	nonlinear	ADJ
ejpam-6422	337	11	evolution	evolution	NOUN
ejpam-6422	337	12	equations	equation	NOUN
ejpam-6422	337	13	in	in	ADP
ejpam-6422	337	14	mathematical	mathematical	ADJ
ejpam-6422	337	15	physics	physic	NOUN
ejpam-6422	337	16	.	.	PUNCT
ejpam-6422	338	1	physics	physics	PROPN
ejpam-6422	338	2	letters	letter	NOUN
ejpam-6422	338	3	a	a	PRON
ejpam-6422	338	4	,	,	PUNCT
ejpam-6422	338	5	372:417–423	372:417–423	NUM
ejpam-6422	338	6	,	,	PUNCT
ejpam-6422	338	7	2008	2008	NUM
ejpam-6422	338	8	.	.	PUNCT
ejpam-6422	339	1	[	[	X
ejpam-6422	339	2	12	12	NUM
ejpam-6422	339	3	]	]	PUNCT
ejpam-6422	339	4	h.	h.	PROPN
ejpam-6422	339	5	zhang	zhang	PROPN
ejpam-6422	339	6	.	.	PUNCT
ejpam-6422	340	1	new	new	ADJ
ejpam-6422	340	2	application	application	NOUN
ejpam-6422	340	3	of	of	ADP
ejpam-6422	340	4	the	the	DET
ejpam-6422	340	5	(	(	PUNCT
ejpam-6422	340	6	g′/g)-expansion	g′/g)-expansion	PROPN
ejpam-6422	340	7	method	method	NOUN
ejpam-6422	340	8	.	.	PUNCT
ejpam-6422	341	1	communications	communication	NOUN
ejpam-6422	341	2	in	in	ADP
ejpam-6422	341	3	nonlinear	nonlinear	ADJ
ejpam-6422	341	4	science	science	NOUN
ejpam-6422	341	5	and	and	CCONJ
ejpam-6422	341	6	numerical	numerical	PROPN
ejpam-6422	341	7	simulation	simulation	PROPN
ejpam-6422	341	8	,	,	PUNCT
ejpam-6422	341	9	14:3220–3225	14:3220–3225	NUM
ejpam-6422	341	10	,	,	PUNCT
ejpam-6422	341	11	2009	2009	NUM
ejpam-6422	341	12	.	.	PUNCT
ejpam-6422	342	1	[	[	X
ejpam-6422	342	2	13	13	NUM
ejpam-6422	342	3	]	]	PUNCT
ejpam-6422	342	4	a.	a.	NOUN
ejpam-6422	342	5	m.	m.	NOUN
ejpam-6422	342	6	wazwaz	wazwaz	PROPN
ejpam-6422	342	7	.	.	PUNCT
ejpam-6422	343	1	the	the	DET
ejpam-6422	343	2	sine	sine	ADJ
ejpam-6422	343	3	-	-	PUNCT
ejpam-6422	343	4	cosine	cosine	NOUN
ejpam-6422	343	5	method	method	NOUN
ejpam-6422	343	6	for	for	ADP
ejpam-6422	343	7	obtaining	obtain	VERB
ejpam-6422	343	8	solutions	solution	NOUN
ejpam-6422	343	9	with	with	ADP
ejpam-6422	343	10	compact	compact	ADJ
ejpam-6422	343	11	and	and	CCONJ
ejpam-6422	343	12	noncompact	noncompact	ADJ
ejpam-6422	343	13	structures	structure	NOUN
ejpam-6422	343	14	.	.	PUNCT
ejpam-6422	344	1	applied	apply	VERB
ejpam-6422	344	2	mathematics	mathematic	NOUN
ejpam-6422	344	3	and	and	CCONJ
ejpam-6422	344	4	computation	computation	NOUN
ejpam-6422	344	5	,	,	PUNCT
ejpam-6422	344	6	159:559–576	159:559–576	NUM
ejpam-6422	344	7	,	,	PUNCT
ejpam-6422	344	8	2004	2004	NUM
ejpam-6422	344	9	.	.	PUNCT
ejpam-6422	345	1	[	[	X
ejpam-6422	345	2	14	14	NUM
ejpam-6422	345	3	]	]	X
ejpam-6422	345	4	k.	k.	PROPN
ejpam-6422	345	5	khan	khan	PROPN
ejpam-6422	345	6	and	and	CCONJ
ejpam-6422	345	7	m.	m.	NOUN
ejpam-6422	345	8	a.	a.	NOUN
ejpam-6422	345	9	akbar	akbar	NOUN
ejpam-6422	345	10	.	.	PUNCT
ejpam-6422	346	1	the	the	DET
ejpam-6422	346	2	exp(−ϕ(ς))-expansion	exp(−ϕ(ς))-expansion	NOUN
ejpam-6422	346	3	method	method	NOUN
ejpam-6422	346	4	for	for	ADP
ejpam-6422	346	5	finding	find	VERB
ejpam-6422	346	6	travelling	travel	VERB
ejpam-6422	346	7	wave	wave	NOUN
ejpam-6422	346	8	solutions	solution	NOUN
ejpam-6422	346	9	of	of	ADP
ejpam-6422	346	10	vakhnenko	vakhnenko	NOUN
ejpam-6422	346	11	-	-	PUNCT
ejpam-6422	346	12	parkes	parke	NOUN
ejpam-6422	346	13	equation	equation	NOUN
ejpam-6422	346	14	.	.	PUNCT
ejpam-6422	347	1	international	international	ADJ
ejpam-6422	347	2	journal	journal	NOUN
ejpam-6422	347	3	of	of	ADP
ejpam-6422	347	4	dynamical	dynamical	ADJ
ejpam-6422	347	5	systems	system	NOUN
ejpam-6422	347	6	and	and	CCONJ
ejpam-6422	347	7	differential	differential	ADJ
ejpam-6422	347	8	equations	equation	NOUN
ejpam-6422	347	9	,	,	PUNCT
ejpam-6422	347	10	5:72–83	5:72–83	NUM
ejpam-6422	347	11	,	,	PUNCT
ejpam-6422	347	12	2014	2014	NUM
ejpam-6422	347	13	.	.	PUNCT
ejpam-6422	348	1	[	[	X
ejpam-6422	348	2	15	15	NUM
ejpam-6422	348	3	]	]	X
ejpam-6422	348	4	m.	m.	NOUN
ejpam-6422	348	5	nadeem	nadeem	PROPN
ejpam-6422	348	6	,	,	PUNCT
ejpam-6422	348	7	o.	o.	PROPN
ejpam-6422	348	8	a.	a.	NOUN
ejpam-6422	348	9	arqub	arqub	PROPN
ejpam-6422	348	10	,	,	PUNCT
ejpam-6422	348	11	m.	m.	NOUN
ejpam-6422	348	12	a.	a.	PROPN
ejpam-6422	348	13	el	el	PROPN
ejpam-6422	348	14	-	-	PUNCT
ejpam-6422	348	15	meligy	meligy	PROPN
ejpam-6422	348	16	,	,	PUNCT
ejpam-6422	348	17	and	and	CCONJ
ejpam-6422	348	18	a.	a.	NOUN
ejpam-6422	348	19	a.	a.	PROPN
ejpam-6422	348	20	ibrahim	ibrahim	PROPN
ejpam-6422	348	21	.	.	PUNCT
ejpam-6422	349	1	fractional	fractional	ADJ
ejpam-6422	349	2	analysis	analysis	NOUN
ejpam-6422	349	3	of	of	ADP
ejpam-6422	349	4	time	time	NOUN
ejpam-6422	349	5	-	-	PUNCT
ejpam-6422	349	6	fractional	fractional	ADJ
ejpam-6422	349	7	emden	emden	NOUN
ejpam-6422	349	8	–	–	PUNCT
ejpam-6422	349	9	fowler	fowler	PROPN
ejpam-6422	349	10	model	model	NOUN
ejpam-6422	349	11	arising	arise	VERB
ejpam-6422	349	12	in	in	ADP
ejpam-6422	349	13	fluid	fluid	ADJ
ejpam-6422	349	14	flow	flow	NOUN
ejpam-6422	349	15	of	of	ADP
ejpam-6422	349	16	porous	porous	ADJ
ejpam-6422	349	17	media	medium	NOUN
ejpam-6422	349	18	and	and	CCONJ
ejpam-6422	349	19	physical	physical	ADJ
ejpam-6422	349	20	sciences	science	NOUN
ejpam-6422	349	21	.	.	PUNCT
ejpam-6422	350	1	international	international	ADJ
ejpam-6422	350	2	journal	journal	PROPN
ejpam-6422	350	3	of	of	ADP
ejpam-6422	350	4	geometric	geometric	ADJ
ejpam-6422	350	5	methods	method	NOUN
ejpam-6422	350	6	in	in	ADP
ejpam-6422	350	7	modern	modern	ADJ
ejpam-6422	350	8	physics	physic	NOUN
ejpam-6422	350	9	,	,	PUNCT
ejpam-6422	350	10	2025	2025	NUM
ejpam-6422	350	11	.	.	PUNCT
ejpam-6422	351	1	[	[	X
ejpam-6422	351	2	16	16	NUM
ejpam-6422	351	3	]	]	PUNCT
ejpam-6422	351	4	m.	m.	NOUN
ejpam-6422	351	5	nadeem	nadeem	PROPN
ejpam-6422	351	6	,	,	PUNCT
ejpam-6422	351	7	o.	o.	PROPN
ejpam-6422	351	8	a.	a.	NOUN
ejpam-6422	351	9	arqub	arqub	PROPN
ejpam-6422	351	10	,	,	PUNCT
ejpam-6422	351	11	h.	h.	PROPN
ejpam-6422	351	12	m.	m.	PROPN
ejpam-6422	351	13	hazaimeh	hazaimeh	PROPN
ejpam-6422	351	14	,	,	PUNCT
ejpam-6422	351	15	and	and	CCONJ
ejpam-6422	351	16	a.	a.	NOUN
ejpam-6422	351	17	a.	a.	PROPN
ejpam-6422	351	18	ibrahim	ibrahim	PROPN
ejpam-6422	351	19	.	.	PUNCT
ejpam-6422	352	1	bifurcation	bifurcation	NOUN
ejpam-6422	352	2	,	,	PUNCT
ejpam-6422	352	3	chaos	chaos	NOUN
ejpam-6422	352	4	,	,	PUNCT
ejpam-6422	352	5	and	and	CCONJ
ejpam-6422	352	6	time	time	NOUN
ejpam-6422	352	7	series	series	NOUN
ejpam-6422	352	8	analysis	analysis	NOUN
ejpam-6422	352	9	of	of	ADP
ejpam-6422	352	10	the	the	DET
ejpam-6422	352	11	manakov	manakov	NOUN
ejpam-6422	352	12	model	model	NOUN
ejpam-6422	352	13	utilizing	utilize	VERB
ejpam-6422	352	14	the	the	DET
ejpam-6422	352	15	unified	unified	ADJ
ejpam-6422	352	16	riccati	riccati	NOUN
ejpam-6422	352	17	equation	equation	NOUN
ejpam-6422	352	18	expansion	expansion	NOUN
ejpam-6422	352	19	technique	technique	NOUN
ejpam-6422	352	20	.	.	PUNCT
ejpam-6422	353	1	modern	modern	ADJ
ejpam-6422	353	2	physics	physics	NOUN
ejpam-6422	353	3	letters	letter	NOUN
ejpam-6422	353	4	a	a	PRON
ejpam-6422	353	5	,	,	PUNCT
ejpam-6422	353	6	40:2550074	40:2550074	NUM
ejpam-6422	353	7	,	,	PUNCT
ejpam-6422	353	8	2025	2025	NUM
ejpam-6422	353	9	.	.	PUNCT
ejpam-6422	354	1	[	[	X
ejpam-6422	354	2	17	17	NUM
ejpam-6422	354	3	]	]	PUNCT
ejpam-6422	354	4	m.	m.	NOUN
ejpam-6422	354	5	nadeem	nadeem	PROPN
ejpam-6422	354	6	and	and	CCONJ
ejpam-6422	354	7	o.	o.	NOUN
ejpam-6422	354	8	a.	a.	NOUN
ejpam-6422	354	9	arqub	arqub	PROPN
ejpam-6422	354	10	.	.	PUNCT
ejpam-6422	355	1	soliton	soliton	NOUN
ejpam-6422	355	2	solutions	solution	NOUN
ejpam-6422	355	3	and	and	CCONJ
ejpam-6422	355	4	stability	stability	NOUN
ejpam-6422	355	5	analysis	analysis	NOUN
ejpam-6422	355	6	to	to	ADP
ejpam-6422	355	7	the	the	DET
ejpam-6422	355	8	hirotabilinear	hirotabilinear	ADJ
ejpam-6422	355	9	-	-	PUNCT
ejpam-6422	355	10	like	like	ADJ
ejpam-6422	355	11	model	model	NOUN
ejpam-6422	355	12	using	use	VERB
ejpam-6422	355	13	the	the	DET
ejpam-6422	355	14	unified	unified	ADJ
ejpam-6422	355	15	riccati	riccati	NOUN
ejpam-6422	355	16	equation	equation	NOUN
ejpam-6422	355	17	expansion	expansion	NOUN
ejpam-6422	355	18	approach	approach	NOUN
ejpam-6422	355	19	.	.	PUNCT
ejpam-6422	356	1	modern	modern	ADJ
ejpam-6422	356	2	physics	physics	NOUN
ejpam-6422	356	3	letters	letter	NOUN
ejpam-6422	356	4	a	a	DET
ejpam-6422	356	5	,	,	PUNCT
ejpam-6422	356	6	39:2550138	39:2550138	NUM
ejpam-6422	356	7	,	,	PUNCT
ejpam-6422	356	8	2025	2025	NUM
ejpam-6422	356	9	.	.	PUNCT
ejpam-6422	357	1	[	[	X
ejpam-6422	357	2	18	18	NUM
ejpam-6422	357	3	]	]	PUNCT
ejpam-6422	357	4	a.	a.	NOUN
ejpam-6422	357	5	m.	m.	NOUN
ejpam-6422	357	6	wazwaz	wazwaz	PROPN
ejpam-6422	357	7	.	.	PUNCT
ejpam-6422	358	1	a	a	DET
ejpam-6422	358	2	hamiltonian	hamiltonian	ADJ
ejpam-6422	358	3	equation	equation	NOUN
ejpam-6422	358	4	produces	produce	VERB
ejpam-6422	358	5	a	a	DET
ejpam-6422	358	6	variety	variety	NOUN
ejpam-6422	358	7	of	of	ADP
ejpam-6422	358	8	painlevé	painlevé	NOUN
ejpam-6422	358	9	integrable	integrable	ADJ
ejpam-6422	358	10	equations	equation	NOUN
ejpam-6422	358	11	:	:	PUNCT
ejpam-6422	358	12	solutions	solution	NOUN
ejpam-6422	358	13	of	of	ADP
ejpam-6422	358	14	distinct	distinct	ADJ
ejpam-6422	358	15	physical	physical	ADJ
ejpam-6422	358	16	structures	structure	NOUN
ejpam-6422	358	17	.	.	PUNCT
ejpam-6422	359	1	international	international	ADJ
ejpam-6422	359	2	journal	journal	PROPN
ejpam-6422	359	3	of	of	ADP
ejpam-6422	359	4	numerical	numerical	ADJ
ejpam-6422	359	5	methods	method	NOUN
ejpam-6422	359	6	for	for	ADP
ejpam-6422	359	7	heat	heat	NOUN
ejpam-6422	359	8	&	&	CCONJ
ejpam-6422	359	9	fluid	fluid	ADJ
ejpam-6422	359	10	flow	flow	NOUN
ejpam-6422	359	11	,	,	PUNCT
ejpam-6422	359	12	34:1730–1751	34:1730–1751	NUM
ejpam-6422	359	13	,	,	PUNCT
ejpam-6422	359	14	2024	2024	NUM
ejpam-6422	359	15	.	.	PUNCT
ejpam-6422	360	1	[	[	X
ejpam-6422	360	2	19	19	NUM
ejpam-6422	360	3	]	]	PUNCT
ejpam-6422	360	4	a.	a.	NOUN
ejpam-6422	360	5	atangana	atangana	PROPN
ejpam-6422	360	6	and	and	CCONJ
ejpam-6422	360	7	e.	e.	PROPN
ejpam-6422	360	8	f.	f.	PROPN
ejpam-6422	360	9	d.	d.	PROPN
ejpam-6422	360	10	goufo	goufo	PROPN
ejpam-6422	360	11	.	.	PUNCT
ejpam-6422	361	1	extension	extension	NOUN
ejpam-6422	361	2	of	of	ADP
ejpam-6422	361	3	matched	match	VERB
ejpam-6422	361	4	asymptotic	asymptotic	ADJ
ejpam-6422	361	5	method	method	NOUN
ejpam-6422	361	6	to	to	ADP
ejpam-6422	361	7	fractional	fractional	VERB
ejpam-6422	361	8	boundary	boundary	ADJ
ejpam-6422	361	9	layers	layer	NOUN
ejpam-6422	361	10	problems	problem	NOUN
ejpam-6422	361	11	.	.	PUNCT
ejpam-6422	362	1	mathematical	mathematical	ADJ
ejpam-6422	362	2	problems	problem	NOUN
ejpam-6422	362	3	in	in	ADP
ejpam-6422	362	4	engineering	engineering	NOUN
ejpam-6422	362	5	,	,	PUNCT
ejpam-6422	362	6	2014:107535	2014:107535	NUM
ejpam-6422	362	7	,	,	PUNCT
ejpam-6422	362	8	2014	2014	NUM
ejpam-6422	362	9	.	.	PUNCT
ejpam-6422	363	1	[	[	X
ejpam-6422	363	2	20	20	NUM
ejpam-6422	363	3	]	]	X
ejpam-6422	363	4	y.	y.	PROPN
ejpam-6422	363	5	z.	z.	PROPN
ejpam-6422	363	6	peng	peng	PROPN
ejpam-6422	363	7	.	.	PUNCT
ejpam-6422	364	1	exact	exact	ADJ
ejpam-6422	364	2	periodic	periodic	ADJ
ejpam-6422	364	3	wave	wave	NOUN
ejpam-6422	364	4	solutions	solution	NOUN
ejpam-6422	364	5	to	to	ADP
ejpam-6422	364	6	the	the	DET
ejpam-6422	364	7	coupled	couple	VERB
ejpam-6422	364	8	schrödinger	schrödinger	NOUN
ejpam-6422	364	9	-	-	PUNCT
ejpam-6422	364	10	kdv	kdv	NOUN
ejpam-6422	364	11	equation	equation	NOUN
ejpam-6422	364	12	and	and	CCONJ
ejpam-6422	364	13	ds	ds	ADJ
ejpam-6422	364	14	equations	equation	NOUN
ejpam-6422	364	15	.	.	PUNCT
ejpam-6422	365	1	pramana	pramana	PROPN
ejpam-6422	365	2	journal	journal	PROPN
ejpam-6422	365	3	of	of	ADP
ejpam-6422	365	4	physics	physics	PROPN
ejpam-6422	365	5	,	,	PUNCT
ejpam-6422	365	6	62:933–941	62:933–941	PROPN
ejpam-6422	365	7	,	,	PUNCT
ejpam-6422	365	8	2004	2004	NUM
ejpam-6422	365	9	.	.	PUNCT
ejpam-6422	366	1	[	[	X
ejpam-6422	366	2	21	21	NUM
ejpam-6422	366	3	]	]	X
ejpam-6422	366	4	d.	d.	PROPN
ejpam-6422	366	5	zhang	zhang	PROPN
ejpam-6422	366	6	.	.	PUNCT
ejpam-6422	367	1	doubly	doubly	ADV
ejpam-6422	367	2	periodic	periodic	ADJ
ejpam-6422	367	3	solutions	solution	NOUN
ejpam-6422	367	4	of	of	ADP
ejpam-6422	367	5	the	the	DET
ejpam-6422	367	6	modified	modify	VERB
ejpam-6422	367	7	kawahara	kawahara	NOUN
ejpam-6422	367	8	equation	equation	NOUN
ejpam-6422	367	9	.	.	PUNCT
ejpam-6422	368	1	chaos	chaos	NOUN
ejpam-6422	368	2	,	,	PUNCT
ejpam-6422	368	3	solitons	soliton	NOUN
ejpam-6422	368	4	&	&	CCONJ
ejpam-6422	368	5	fractals	fractal	NOUN
ejpam-6422	368	6	,	,	PUNCT
ejpam-6422	368	7	25:1155–1160	25:1155–1160	NUM
ejpam-6422	368	8	,	,	PUNCT
ejpam-6422	368	9	2005	2005	NUM
ejpam-6422	368	10	.	.	PUNCT
ejpam-6422	369	1	[	[	X
ejpam-6422	369	2	22	22	NUM
ejpam-6422	369	3	]	]	PUNCT
ejpam-6422	369	4	q.	q.	PROPN
ejpam-6422	369	5	liu	liu	PROPN
ejpam-6422	369	6	and	and	CCONJ
ejpam-6422	369	7	j.	j.	PROPN
ejpam-6422	369	8	m.	m.	PROPN
ejpam-6422	369	9	zhu	zhu	PROPN
ejpam-6422	369	10	.	.	PUNCT
ejpam-6422	370	1	exact	exact	ADJ
ejpam-6422	370	2	jacobian	jacobian	PROPN
ejpam-6422	370	3	elliptic	elliptic	ADJ
ejpam-6422	370	4	function	function	NOUN
ejpam-6422	370	5	solutions	solution	NOUN
ejpam-6422	370	6	and	and	CCONJ
ejpam-6422	370	7	hyperbolic	hyperbolic	ADJ
ejpam-6422	370	8	function	function	NOUN
ejpam-6422	370	9	solutions	solution	NOUN
ejpam-6422	370	10	for	for	ADP
ejpam-6422	370	11	sawada	sawada	NOUN
ejpam-6422	370	12	-	-	PUNCT
ejpam-6422	370	13	kotera	kotera	PROPN
ejpam-6422	370	14	equation	equation	NOUN
ejpam-6422	370	15	with	with	ADP
ejpam-6422	370	16	variable	variable	ADJ
ejpam-6422	370	17	coefficient	coefficient	NOUN
ejpam-6422	370	18	.	.	PUNCT
ejpam-6422	371	1	physics	physics	NOUN
ejpam-6422	371	2	letters	letter	NOUN
ejpam-6422	371	3	a	a	PRON
ejpam-6422	371	4	,	,	PUNCT
ejpam-6422	371	5	352:233–238	352:233–238	NUM
ejpam-6422	371	6	,	,	PUNCT
ejpam-6422	371	7	2006	2006	NUM
ejpam-6422	371	8	.	.	PUNCT