id	sid	tid	token	lemma	pos
ejpam-6325	1	1	european	european	PROPN
ejpam-6325	1	2	journal	journal	PROPN
ejpam-6325	1	3	of	of	ADP
ejpam-6325	1	4	pure	pure	ADJ
ejpam-6325	1	5	and	and	CCONJ
ejpam-6325	1	6	applied	applied	ADJ
ejpam-6325	1	7	mathematics	mathematic	NOUN
ejpam-6325	1	8	2025	2025	NUM
ejpam-6325	1	9	,	,	PUNCT
ejpam-6325	1	10	vol	vol	NOUN
ejpam-6325	1	11	.	.	PROPN
ejpam-6325	1	12	18	18	NUM
ejpam-6325	1	13	,	,	PUNCT
ejpam-6325	1	14	issue	issue	NOUN
ejpam-6325	1	15	3	3	NUM
ejpam-6325	1	16	,	,	PUNCT
ejpam-6325	1	17	article	article	NOUN
ejpam-6325	1	18	number	number	NOUN
ejpam-6325	1	19	6235	6235	NUM
ejpam-6325	1	20	issn	issn	PROPN
ejpam-6325	1	21	1307	1307	NUM
ejpam-6325	1	22	-	-	SYM
ejpam-6325	1	23	5543	5543	NUM
ejpam-6325	1	24	–	–	PUNCT
ejpam-6325	1	25	ejpam.com	ejpam.com	X
ejpam-6325	1	26	published	publish	VERB
ejpam-6325	1	27	by	by	ADP
ejpam-6325	1	28	new	new	PROPN
ejpam-6325	1	29	york	york	PROPN
ejpam-6325	1	30	business	business	PROPN
ejpam-6325	1	31	global	global	ADJ
ejpam-6325	1	32	exact	exact	ADJ
ejpam-6325	1	33	solutions	solution	NOUN
ejpam-6325	1	34	of	of	ADP
ejpam-6325	1	35	the	the	DET
ejpam-6325	1	36	damped	damped	PROPN
ejpam-6325	1	37	telegrapher	telegrapher	PROPN
ejpam-6325	1	38	’s	’s	PART
ejpam-6325	1	39	equation	equation	NOUN
ejpam-6325	1	40	with	with	ADP
ejpam-6325	1	41	harmonic	harmonic	ADJ
ejpam-6325	1	42	potential	potential	NOUN
ejpam-6325	1	43	via	via	ADP
ejpam-6325	1	44	the	the	DET
ejpam-6325	1	45	generalized	generalized	ADJ
ejpam-6325	1	46	first	first	ADJ
ejpam-6325	1	47	integral	integral	ADJ
ejpam-6325	1	48	method	method	NOUN
ejpam-6325	1	49	muhammad	muhammad	PROPN
ejpam-6325	1	50	noman	noman	PROPN
ejpam-6325	1	51	qureshi1,∗	qureshi1,∗	PROPN
ejpam-6325	1	52	,	,	PUNCT
ejpam-6325	1	53	atif	atif	PROPN
ejpam-6325	1	54	hassan	hassan	PROPN
ejpam-6325	1	55	soori1	soori1	PROPN
ejpam-6325	1	56	,	,	PUNCT
ejpam-6325	1	57	zeshan	zeshan	PROPN
ejpam-6325	1	58	haider1	haider1	PROPN
ejpam-6325	1	59	,	,	PUNCT
ejpam-6325	1	60	waqar	waqar	PROPN
ejpam-6325	1	61	azeem	azeem	PROPN
ejpam-6325	1	62	khan2	khan2	PROPN
ejpam-6325	1	63	,	,	PUNCT
ejpam-6325	1	64	zohaib	zohaib	PROPN
ejpam-6325	1	65	arshad2	arshad2	PROPN
ejpam-6325	1	66	1	1	NUM
ejpam-6325	1	67	department	department	NOUN
ejpam-6325	1	68	of	of	ADP
ejpam-6325	1	69	mathematics	mathematic	NOUN
ejpam-6325	1	70	,	,	PUNCT
ejpam-6325	1	71	faculty	faculty	NOUN
ejpam-6325	1	72	of	of	ADP
ejpam-6325	1	73	basic	basic	ADJ
ejpam-6325	1	74	and	and	CCONJ
ejpam-6325	1	75	applied	applied	ADJ
ejpam-6325	1	76	sciences	science	NOUN
ejpam-6325	1	77	,	,	PUNCT
ejpam-6325	1	78	air	air	NOUN
ejpam-6325	1	79	university	university	PROPN
ejpam-6325	1	80	,	,	PUNCT
ejpam-6325	1	81	paf	paf	PROPN
ejpam-6325	1	82	complex	complex	PROPN
ejpam-6325	1	83	e-9	e-9	PROPN
ejpam-6325	1	84	,	,	PUNCT
ejpam-6325	1	85	islamabad	islamabad	NOUN
ejpam-6325	1	86	44000	44000	NUM
ejpam-6325	1	87	,	,	PUNCT
ejpam-6325	1	88	pakistan	pakistan	PROPN
ejpam-6325	1	89	4	4	NUM
ejpam-6325	1	90	department	department	NOUN
ejpam-6325	1	91	of	of	ADP
ejpam-6325	1	92	mathematics	mathematic	NOUN
ejpam-6325	1	93	,	,	PUNCT
ejpam-6325	1	94	faculty	faculty	NOUN
ejpam-6325	1	95	of	of	ADP
ejpam-6325	1	96	basic	basic	ADJ
ejpam-6325	1	97	and	and	CCONJ
ejpam-6325	1	98	applied	applied	ADJ
ejpam-6325	1	99	sciences	science	NOUN
ejpam-6325	1	100	,	,	PUNCT
ejpam-6325	1	101	mohi	mohi	AUX
ejpam-6325	1	102	-	-	PUNCT
ejpam-6325	1	103	ud	ud	AUX
ejpam-6325	1	104	-	-	PUNCT
ejpam-6325	1	105	din	din	VERB
ejpam-6325	1	106	islamic	islamic	PROPN
ejpam-6325	1	107	university	university	PROPN
ejpam-6325	1	108	,	,	PUNCT
ejpam-6325	1	109	,	,	PUNCT
ejpam-6325	1	110	ajk	ajk	PROPN
ejpam-6325	1	111	,	,	PUNCT
ejpam-6325	1	112	12010	12010	NUM
ejpam-6325	1	113	,	,	PUNCT
ejpam-6325	1	114	pakistan	pakistan	PROPN
ejpam-6325	1	115	abstract	abstract	NOUN
ejpam-6325	1	116	.	.	PUNCT
ejpam-6325	2	1	this	this	DET
ejpam-6325	2	2	paper	paper	NOUN
ejpam-6325	2	3	aims	aim	VERB
ejpam-6325	2	4	to	to	PART
ejpam-6325	2	5	develop	develop	VERB
ejpam-6325	2	6	exact	exact	ADJ
ejpam-6325	2	7	analytical	analytical	ADJ
ejpam-6325	2	8	solutions	solution	NOUN
ejpam-6325	2	9	for	for	ADP
ejpam-6325	2	10	the	the	DET
ejpam-6325	2	11	telegrapher	telegrapher	PROPN
ejpam-6325	2	12	’s	’s	PART
ejpam-6325	2	13	equation	equation	NOUN
ejpam-6325	2	14	incorporating	incorporate	VERB
ejpam-6325	2	15	both	both	CCONJ
ejpam-6325	2	16	damping	damp	VERB
ejpam-6325	2	17	and	and	CCONJ
ejpam-6325	2	18	harmonic	harmonic	ADJ
ejpam-6325	2	19	potential	potential	NOUN
ejpam-6325	2	20	by	by	ADP
ejpam-6325	2	21	employing	employ	VERB
ejpam-6325	2	22	the	the	DET
ejpam-6325	2	23	generalized	generalized	ADJ
ejpam-6325	2	24	first	first	ADJ
ejpam-6325	2	25	integral	integral	ADJ
ejpam-6325	2	26	method	method	NOUN
ejpam-6325	2	27	.	.	PUNCT
ejpam-6325	3	1	this	this	DET
ejpam-6325	3	2	approach	approach	NOUN
ejpam-6325	3	3	extends	extend	VERB
ejpam-6325	3	4	the	the	DET
ejpam-6325	3	5	classical	classical	ADJ
ejpam-6325	3	6	first	first	ADJ
ejpam-6325	3	7	integral	integral	ADJ
ejpam-6325	3	8	technique	technique	NOUN
ejpam-6325	3	9	through	through	ADP
ejpam-6325	3	10	the	the	DET
ejpam-6325	3	11	use	use	NOUN
ejpam-6325	3	12	of	of	ADP
ejpam-6325	3	13	laurent	laurent	NOUN
ejpam-6325	3	14	polynomials	polynomial	NOUN
ejpam-6325	3	15	,	,	PUNCT
ejpam-6325	3	16	enhancing	enhance	VERB
ejpam-6325	3	17	its	its	PRON
ejpam-6325	3	18	ability	ability	NOUN
ejpam-6325	3	19	to	to	PART
ejpam-6325	3	20	address	address	VERB
ejpam-6325	3	21	complex	complex	ADJ
ejpam-6325	3	22	nonlinear	nonlinear	ADJ
ejpam-6325	3	23	structures	structure	NOUN
ejpam-6325	3	24	.	.	PUNCT
ejpam-6325	4	1	the	the	DET
ejpam-6325	4	2	telegrapher	telegrapher	PROPN
ejpam-6325	4	3	’s	’s	PART
ejpam-6325	4	4	equation	equation	NOUN
ejpam-6325	4	5	,	,	PUNCT
ejpam-6325	4	6	a	a	DET
ejpam-6325	4	7	fundamental	fundamental	ADJ
ejpam-6325	4	8	model	model	NOUN
ejpam-6325	4	9	in	in	ADP
ejpam-6325	4	10	applied	apply	VERB
ejpam-6325	4	11	mathematics	mathematic	NOUN
ejpam-6325	4	12	and	and	CCONJ
ejpam-6325	4	13	physics	physics	NOUN
ejpam-6325	4	14	,	,	PUNCT
ejpam-6325	4	15	describes	describe	VERB
ejpam-6325	4	16	wave	wave	NOUN
ejpam-6325	4	17	propagation	propagation	NOUN
ejpam-6325	4	18	influenced	influence	VERB
ejpam-6325	4	19	by	by	ADP
ejpam-6325	4	20	both	both	DET
ejpam-6325	4	21	dispersive	dispersive	ADJ
ejpam-6325	4	22	and	and	CCONJ
ejpam-6325	4	23	damping	damp	VERB
ejpam-6325	4	24	effects	effect	NOUN
ejpam-6325	4	25	,	,	PUNCT
ejpam-6325	4	26	with	with	ADP
ejpam-6325	4	27	applications	application	NOUN
ejpam-6325	4	28	across	across	ADP
ejpam-6325	4	29	various	various	ADJ
ejpam-6325	4	30	engineering	engineering	NOUN
ejpam-6325	4	31	and	and	CCONJ
ejpam-6325	4	32	physical	physical	ADJ
ejpam-6325	4	33	systems	system	NOUN
ejpam-6325	4	34	.	.	PUNCT
ejpam-6325	5	1	by	by	ADP
ejpam-6325	5	2	applying	apply	VERB
ejpam-6325	5	3	suitable	suitable	ADJ
ejpam-6325	5	4	transformations	transformation	NOUN
ejpam-6325	5	5	,	,	PUNCT
ejpam-6325	5	6	the	the	DET
ejpam-6325	5	7	original	original	ADJ
ejpam-6325	5	8	nonlinear	nonlinear	ADJ
ejpam-6325	5	9	partial	partial	ADJ
ejpam-6325	5	10	differential	differential	NOUN
ejpam-6325	5	11	equation	equation	NOUN
ejpam-6325	5	12	is	be	AUX
ejpam-6325	5	13	reduced	reduce	VERB
ejpam-6325	5	14	to	to	ADP
ejpam-6325	5	15	an	an	DET
ejpam-6325	5	16	ordinary	ordinary	ADJ
ejpam-6325	5	17	differential	differential	ADJ
ejpam-6325	5	18	form	form	NOUN
ejpam-6325	5	19	.	.	PUNCT
ejpam-6325	6	1	the	the	DET
ejpam-6325	6	2	generalized	generalized	ADJ
ejpam-6325	6	3	method	method	NOUN
ejpam-6325	6	4	is	be	AUX
ejpam-6325	6	5	then	then	ADV
ejpam-6325	6	6	utilized	utilize	VERB
ejpam-6325	6	7	to	to	PART
ejpam-6325	6	8	derive	derive	VERB
ejpam-6325	6	9	exact	exact	ADJ
ejpam-6325	6	10	solutions	solution	NOUN
ejpam-6325	6	11	under	under	ADP
ejpam-6325	6	12	different	different	ADJ
ejpam-6325	6	13	parametric	parametric	ADJ
ejpam-6325	6	14	conditions	condition	NOUN
ejpam-6325	6	15	.	.	PUNCT
ejpam-6325	7	1	these	these	DET
ejpam-6325	7	2	solutions	solution	NOUN
ejpam-6325	7	3	offer	offer	VERB
ejpam-6325	7	4	valuable	valuable	ADJ
ejpam-6325	7	5	analytical	analytical	ADJ
ejpam-6325	7	6	insight	insight	NOUN
ejpam-6325	7	7	into	into	ADP
ejpam-6325	7	8	how	how	SCONJ
ejpam-6325	7	9	damping	damp	VERB
ejpam-6325	7	10	influences	influence	NOUN
ejpam-6325	7	11	wave	wave	VERB
ejpam-6325	7	12	amplitude	amplitude	NOUN
ejpam-6325	7	13	,	,	PUNCT
ejpam-6325	7	14	speed	speed	NOUN
ejpam-6325	7	15	,	,	PUNCT
ejpam-6325	7	16	and	and	CCONJ
ejpam-6325	7	17	qualitative	qualitative	ADJ
ejpam-6325	7	18	behavior	behavior	NOUN
ejpam-6325	7	19	.	.	PUNCT
ejpam-6325	8	1	in	in	ADP
ejpam-6325	8	2	particular	particular	ADJ
ejpam-6325	8	3	,	,	PUNCT
ejpam-6325	8	4	the	the	DET
ejpam-6325	8	5	method	method	NOUN
ejpam-6325	8	6	effectively	effectively	ADV
ejpam-6325	8	7	captures	capture	VERB
ejpam-6325	8	8	the	the	DET
ejpam-6325	8	9	modulation	modulation	NOUN
ejpam-6325	8	10	in	in	ADP
ejpam-6325	8	11	wave	wave	NOUN
ejpam-6325	8	12	attenuation	attenuation	NOUN
ejpam-6325	8	13	and	and	CCONJ
ejpam-6325	8	14	propagation	propagation	NOUN
ejpam-6325	8	15	characteristics	characteristic	NOUN
ejpam-6325	8	16	caused	cause	VERB
ejpam-6325	8	17	by	by	ADP
ejpam-6325	8	18	dissipative	dissipative	ADJ
ejpam-6325	8	19	effects	effect	NOUN
ejpam-6325	8	20	.	.	PUNCT
ejpam-6325	9	1	the	the	DET
ejpam-6325	9	2	key	key	ADJ
ejpam-6325	9	3	outcome	outcome	NOUN
ejpam-6325	9	4	of	of	ADP
ejpam-6325	9	5	this	this	DET
ejpam-6325	9	6	study	study	NOUN
ejpam-6325	9	7	is	be	AUX
ejpam-6325	9	8	the	the	DET
ejpam-6325	9	9	demonstration	demonstration	NOUN
ejpam-6325	9	10	that	that	PRON
ejpam-6325	9	11	the	the	DET
ejpam-6325	9	12	generalized	generalized	ADJ
ejpam-6325	9	13	first	first	ADJ
ejpam-6325	9	14	integral	integral	ADJ
ejpam-6325	9	15	method	method	NOUN
ejpam-6325	9	16	serves	serve	VERB
ejpam-6325	9	17	as	as	ADP
ejpam-6325	9	18	a	a	DET
ejpam-6325	9	19	robust	robust	ADJ
ejpam-6325	9	20	and	and	CCONJ
ejpam-6325	9	21	versatile	versatile	ADJ
ejpam-6325	9	22	analytical	analytical	ADJ
ejpam-6325	9	23	tool	tool	NOUN
ejpam-6325	9	24	for	for	ADP
ejpam-6325	9	25	solving	solve	VERB
ejpam-6325	9	26	nonlinear	nonlinear	ADJ
ejpam-6325	9	27	damped	damp	VERB
ejpam-6325	9	28	wave	wave	NOUN
ejpam-6325	9	29	models	model	NOUN
ejpam-6325	9	30	,	,	PUNCT
ejpam-6325	9	31	where	where	SCONJ
ejpam-6325	9	32	conventional	conventional	ADJ
ejpam-6325	9	33	methods	method	NOUN
ejpam-6325	9	34	often	often	ADV
ejpam-6325	9	35	encounter	encounter	VERB
ejpam-6325	9	36	limitations	limitation	NOUN
ejpam-6325	9	37	.	.	PUNCT
ejpam-6325	10	1	its	its	PRON
ejpam-6325	10	2	strength	strength	NOUN
ejpam-6325	10	3	lies	lie	VERB
ejpam-6325	10	4	in	in	ADP
ejpam-6325	10	5	simplifying	simplify	VERB
ejpam-6325	10	6	complex	complex	ADJ
ejpam-6325	10	7	nonlinear	nonlinear	ADJ
ejpam-6325	10	8	systems	system	NOUN
ejpam-6325	10	9	while	while	SCONJ
ejpam-6325	10	10	preserving	preserve	VERB
ejpam-6325	10	11	essential	essential	ADJ
ejpam-6325	10	12	physical	physical	ADJ
ejpam-6325	10	13	effects	effect	NOUN
ejpam-6325	10	14	,	,	PUNCT
ejpam-6325	10	15	providing	provide	VERB
ejpam-6325	10	16	precise	precise	ADJ
ejpam-6325	10	17	analytical	analytical	ADJ
ejpam-6325	10	18	descriptions	description	NOUN
ejpam-6325	10	19	of	of	ADP
ejpam-6325	10	20	wave	wave	NOUN
ejpam-6325	10	21	behavior	behavior	NOUN
ejpam-6325	10	22	.	.	PUNCT
ejpam-6325	11	1	additionally	additionally	ADV
ejpam-6325	11	2	,	,	PUNCT
ejpam-6325	11	3	three	three	NUM
ejpam-6325	11	4	-	-	PUNCT
ejpam-6325	11	5	dimensional	dimensional	ADJ
ejpam-6325	11	6	graphical	graphical	ADJ
ejpam-6325	11	7	visualizations	visualization	NOUN
ejpam-6325	11	8	of	of	ADP
ejpam-6325	11	9	the	the	DET
ejpam-6325	11	10	obtained	obtain	VERB
ejpam-6325	11	11	solutions	solution	NOUN
ejpam-6325	11	12	offer	offer	VERB
ejpam-6325	11	13	a	a	DET
ejpam-6325	11	14	detailed	detailed	ADJ
ejpam-6325	11	15	understanding	understanding	NOUN
ejpam-6325	11	16	of	of	ADP
ejpam-6325	11	17	the	the	DET
ejpam-6325	11	18	system	system	NOUN
ejpam-6325	11	19	’s	’s	PART
ejpam-6325	11	20	spatial	spatial	ADJ
ejpam-6325	11	21	and	and	CCONJ
ejpam-6325	11	22	temporal	temporal	ADJ
ejpam-6325	11	23	dynamics	dynamic	NOUN
ejpam-6325	11	24	.	.	PUNCT
ejpam-6325	12	1	this	this	DET
ejpam-6325	12	2	work	work	NOUN
ejpam-6325	12	3	contributes	contribute	VERB
ejpam-6325	12	4	to	to	ADP
ejpam-6325	12	5	the	the	DET
ejpam-6325	12	6	ongoing	ongoing	ADJ
ejpam-6325	12	7	advancement	advancement	NOUN
ejpam-6325	12	8	of	of	ADP
ejpam-6325	12	9	analytical	analytical	ADJ
ejpam-6325	12	10	techniques	technique	NOUN
ejpam-6325	12	11	for	for	ADP
ejpam-6325	12	12	nonlinear	nonlinear	ADJ
ejpam-6325	12	13	evolution	evolution	NOUN
ejpam-6325	12	14	equations	equation	NOUN
ejpam-6325	12	15	and	and	CCONJ
ejpam-6325	12	16	establishes	establish	VERB
ejpam-6325	12	17	a	a	DET
ejpam-6325	12	18	foundation	foundation	NOUN
ejpam-6325	12	19	for	for	ADP
ejpam-6325	12	20	extending	extend	VERB
ejpam-6325	12	21	this	this	DET
ejpam-6325	12	22	method	method	NOUN
ejpam-6325	12	23	to	to	ADP
ejpam-6325	12	24	other	other	ADJ
ejpam-6325	12	25	complex	complex	ADJ
ejpam-6325	12	26	dynamical	dynamical	ADJ
ejpam-6325	12	27	systems	system	NOUN
ejpam-6325	12	28	involving	involve	VERB
ejpam-6325	12	29	damping	damp	VERB
ejpam-6325	12	30	,	,	PUNCT
ejpam-6325	12	31	dissipation	dissipation	NOUN
ejpam-6325	12	32	,	,	PUNCT
ejpam-6325	12	33	and	and	CCONJ
ejpam-6325	12	34	external	external	ADJ
ejpam-6325	12	35	potentials	potential	NOUN
ejpam-6325	12	36	.	.	PUNCT
ejpam-6325	13	1	2020	2020	NUM
ejpam-6325	13	2	mathematics	mathematic	NOUN
ejpam-6325	13	3	subject	subject	NOUN
ejpam-6325	13	4	classifications	classification	NOUN
ejpam-6325	13	5	:	:	PUNCT
ejpam-6325	13	6	35f20	35f20	NUM
ejpam-6325	13	7	,	,	PUNCT
ejpam-6325	13	8	35a01	35a01	NUM
ejpam-6325	13	9	,	,	PUNCT
ejpam-6325	13	10	35r35	35r35	NUM
ejpam-6325	13	11	,	,	PUNCT
ejpam-6325	13	12	35g20	35g20	NUM
ejpam-6325	13	13	,	,	PUNCT
ejpam-6325	13	14	34a36	34a36	NUM
ejpam-6325	13	15	key	key	ADJ
ejpam-6325	13	16	words	word	NOUN
ejpam-6325	13	17	and	and	CCONJ
ejpam-6325	13	18	phrases	phrase	NOUN
ejpam-6325	13	19	:	:	PUNCT
ejpam-6325	13	20	telegrapher	telegrapher	PROPN
ejpam-6325	13	21	’s	’s	PART
ejpam-6325	13	22	equation	equation	NOUN
ejpam-6325	13	23	,	,	PUNCT
ejpam-6325	13	24	generalized	generalize	VERB
ejpam-6325	13	25	first	first	ADJ
ejpam-6325	13	26	integral	integral	ADJ
ejpam-6325	13	27	method	method	NOUN
ejpam-6325	13	28	,	,	PUNCT
ejpam-6325	13	29	laurent	laurent	NOUN
ejpam-6325	13	30	polynomials	polynomial	NOUN
ejpam-6325	13	31	,	,	PUNCT
ejpam-6325	13	32	wave	wave	NOUN
ejpam-6325	13	33	transformation	transformation	NOUN
ejpam-6325	13	34	,	,	PUNCT
ejpam-6325	13	35	autonomous	autonomous	ADJ
ejpam-6325	13	36	system	system	NOUN
ejpam-6325	13	37	∗corresponding	∗corresponde	VERB
ejpam-6325	13	38	author	author	NOUN
ejpam-6325	13	39	.	.	PUNCT
ejpam-6325	14	1	doi	doi	NOUN
ejpam-6325	14	2	:	:	PUNCT
ejpam-6325	14	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6235	https://doi.org/10.29020/nybg.ejpam.v18i3.6235	DET
ejpam-6325	14	4	email	email	NOUN
ejpam-6325	14	5	addresses	address	VERB
ejpam-6325	14	6	:	:	PUNCT
ejpam-6325	14	7	211900@students.au.edu.pk	211900@students.au.edu.pk	NUM
ejpam-6325	14	8	(	(	PUNCT
ejpam-6325	14	9	m.	m.	PROPN
ejpam-6325	14	10	noman	noman	PROPN
ejpam-6325	14	11	)	)	PUNCT
ejpam-6325	14	12	,	,	PUNCT
ejpam-6325	14	13	atif.soori@au.edu.pk	atif.soori@au.edu.pk	PROPN
ejpam-6325	14	14	(	(	PUNCT
ejpam-6325	14	15	a.	a.	NOUN
ejpam-6325	14	16	soori	soori	PROPN
ejpam-6325	14	17	)	)	PUNCT
ejpam-6325	14	18	211904@students.au.edu.pk	211904@students.au.edu.pk	NUM
ejpam-6325	14	19	,	,	PUNCT
ejpam-6325	14	20	(	(	PUNCT
ejpam-6325	14	21	z.	z.	PROPN
ejpam-6325	14	22	haider	haider	PROPN
ejpam-6325	14	23	)	)	PUNCT
ejpam-6325	14	24	,	,	PUNCT
ejpam-6325	14	25	waqar	waqar	PROPN
ejpam-6325	14	26	qau85@gmail.com	qau85@gmail.com	PROPN
ejpam-6325	14	27	,	,	PUNCT
ejpam-6325	14	28	(	(	PUNCT
ejpam-6325	14	29	w.	w.	PROPN
ejpam-6325	14	30	azeem	azeem	PROPN
ejpam-6325	14	31	)	)	PUNCT
ejpam-6325	14	32	,	,	PUNCT
ejpam-6325	14	33	zohaibsalam.pcs@gmail.com	zohaibsalam.pcs@gmail.com	PROPN
ejpam-6325	14	34	,	,	PUNCT
ejpam-6325	14	35	(	(	PUNCT
ejpam-6325	14	36	z.	z.	PROPN
ejpam-6325	14	37	arshad	arshad	PROPN
ejpam-6325	14	38	)	)	PUNCT
ejpam-6325	14	39	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6325	14	40	1	1	NUM
ejpam-6325	14	41	copyright	copyright	NOUN
ejpam-6325	14	42	:	:	PUNCT
ejpam-6325	15	1	©	©	PROPN
ejpam-6325	15	2	2025	2025	NUM
ejpam-6325	15	3	the	the	DET
ejpam-6325	15	4	author(s	author(s	NOUN
ejpam-6325	15	5	)	)	PUNCT
ejpam-6325	15	6	.	.	PUNCT
ejpam-6325	16	1	(	(	PUNCT
ejpam-6325	16	2	cc	cc	NOUN
ejpam-6325	16	3	by	by	ADP
ejpam-6325	16	4	-	-	PUNCT
ejpam-6325	16	5	nc	nc	PROPN
ejpam-6325	16	6	4.0	4.0	NUM
ejpam-6325	16	7	)	)	PUNCT
ejpam-6325	16	8	m.	m.	NOUN
ejpam-6325	16	9	noman	noman	PROPN
ejpam-6325	16	10	et	et	PROPN
ejpam-6325	16	11	al	al	PROPN
ejpam-6325	16	12	.	.	PUNCT
ejpam-6325	16	13	/	/	SYM
ejpam-6325	16	14	eur	eur	PROPN
ejpam-6325	16	15	.	.	PUNCT
ejpam-6325	17	1	j.	j.	PROPN
ejpam-6325	17	2	pure	pure	PROPN
ejpam-6325	17	3	appl	appl	PROPN
ejpam-6325	17	4	.	.	PROPN
ejpam-6325	17	5	math	math	PROPN
ejpam-6325	17	6	,	,	PUNCT
ejpam-6325	17	7	18	18	NUM
ejpam-6325	17	8	(	(	PUNCT
ejpam-6325	17	9	3	3	NUM
ejpam-6325	17	10	)	)	PUNCT
ejpam-6325	17	11	(	(	PUNCT
ejpam-6325	17	12	2025	2025	NUM
ejpam-6325	17	13	)	)	PUNCT
ejpam-6325	17	14	,	,	PUNCT
ejpam-6325	17	15	6235	6235	NUM
ejpam-6325	17	16	2	2	NUM
ejpam-6325	17	17	of	of	ADP
ejpam-6325	17	18	16	16	NUM
ejpam-6325	17	19	1	1	NUM
ejpam-6325	17	20	.	.	PUNCT
ejpam-6325	18	1	introduction	introduction	NOUN
ejpam-6325	18	2	nonlinear	nonlinear	ADJ
ejpam-6325	18	3	partial	partial	ADJ
ejpam-6325	18	4	differential	differential	NOUN
ejpam-6325	18	5	equations	equation	NOUN
ejpam-6325	18	6	play	play	VERB
ejpam-6325	18	7	a	a	DET
ejpam-6325	18	8	crucial	crucial	ADJ
ejpam-6325	18	9	role	role	NOUN
ejpam-6325	18	10	in	in	ADP
ejpam-6325	18	11	accurately	accurately	ADV
ejpam-6325	18	12	modeling	model	VERB
ejpam-6325	18	13	complex	complex	ADJ
ejpam-6325	18	14	physical	physical	ADJ
ejpam-6325	18	15	,	,	PUNCT
ejpam-6325	18	16	biological	biological	ADJ
ejpam-6325	18	17	,	,	PUNCT
ejpam-6325	18	18	and	and	CCONJ
ejpam-6325	18	19	engineering	engineering	NOUN
ejpam-6325	18	20	systems	system	NOUN
ejpam-6325	18	21	where	where	SCONJ
ejpam-6325	18	22	linear	linear	NOUN
ejpam-6325	18	23	models	model	NOUN
ejpam-6325	18	24	often	often	ADV
ejpam-6325	18	25	fail	fail	VERB
ejpam-6325	18	26	to	to	PART
ejpam-6325	18	27	capture	capture	VERB
ejpam-6325	18	28	intricate	intricate	ADJ
ejpam-6325	18	29	dynamics	dynamic	NOUN
ejpam-6325	18	30	.	.	PUNCT
ejpam-6325	19	1	these	these	DET
ejpam-6325	19	2	equations	equation	NOUN
ejpam-6325	19	3	are	be	AUX
ejpam-6325	19	4	fundamental	fundamental	ADJ
ejpam-6325	19	5	in	in	ADP
ejpam-6325	19	6	describing	describe	VERB
ejpam-6325	19	7	a	a	DET
ejpam-6325	19	8	wide	wide	ADJ
ejpam-6325	19	9	range	range	NOUN
ejpam-6325	19	10	of	of	ADP
ejpam-6325	19	11	phenomena	phenomenon	NOUN
ejpam-6325	19	12	,	,	PUNCT
ejpam-6325	19	13	including	include	VERB
ejpam-6325	19	14	fluid	fluid	ADJ
ejpam-6325	19	15	dynamics	dynamic	NOUN
ejpam-6325	19	16	,	,	PUNCT
ejpam-6325	19	17	heat	heat	NOUN
ejpam-6325	19	18	transfer	transfer	NOUN
ejpam-6325	19	19	,	,	PUNCT
ejpam-6325	19	20	nonlinear	nonlinear	ADJ
ejpam-6325	19	21	optics	optic	NOUN
ejpam-6325	19	22	,	,	PUNCT
ejpam-6325	19	23	population	population	NOUN
ejpam-6325	19	24	dynamics	dynamic	NOUN
ejpam-6325	19	25	,	,	PUNCT
ejpam-6325	19	26	and	and	CCONJ
ejpam-6325	19	27	financial	financial	ADJ
ejpam-6325	19	28	markets	market	NOUN
ejpam-6325	19	29	,	,	PUNCT
ejpam-6325	19	30	where	where	SCONJ
ejpam-6325	19	31	interactions	interaction	NOUN
ejpam-6325	19	32	among	among	ADP
ejpam-6325	19	33	variables	variable	NOUN
ejpam-6325	19	34	are	be	AUX
ejpam-6325	19	35	inherently	inherently	ADV
ejpam-6325	19	36	nonlinear	nonlinear	ADJ
ejpam-6325	19	37	.	.	PUNCT
ejpam-6325	20	1	the	the	DET
ejpam-6325	20	2	importance	importance	NOUN
ejpam-6325	20	3	of	of	ADP
ejpam-6325	20	4	nonlinear	nonlinear	ADJ
ejpam-6325	20	5	pdes	pde	NOUN
ejpam-6325	20	6	is	be	AUX
ejpam-6325	20	7	underscored	underscore	VERB
ejpam-6325	20	8	by	by	ADP
ejpam-6325	20	9	their	their	PRON
ejpam-6325	20	10	ability	ability	NOUN
ejpam-6325	20	11	to	to	PART
ejpam-6325	20	12	describe	describe	VERB
ejpam-6325	20	13	real	real	ADJ
ejpam-6325	20	14	-	-	PUNCT
ejpam-6325	20	15	world	world	NOUN
ejpam-6325	20	16	processes	process	NOUN
ejpam-6325	20	17	with	with	ADP
ejpam-6325	20	18	greater	great	ADJ
ejpam-6325	20	19	fidelity	fidelity	NOUN
ejpam-6325	20	20	,	,	PUNCT
ejpam-6325	20	21	accounting	account	VERB
ejpam-6325	20	22	for	for	ADP
ejpam-6325	20	23	effects	effect	NOUN
ejpam-6325	20	24	such	such	ADJ
ejpam-6325	20	25	as	as	ADP
ejpam-6325	20	26	turbulence	turbulence	NOUN
ejpam-6325	20	27	,	,	PUNCT
ejpam-6325	20	28	shock	shock	NOUN
ejpam-6325	20	29	waves	wave	NOUN
ejpam-6325	20	30	,	,	PUNCT
ejpam-6325	20	31	pattern	pattern	NOUN
ejpam-6325	20	32	formation	formation	NOUN
ejpam-6325	20	33	,	,	PUNCT
ejpam-6325	20	34	and	and	CCONJ
ejpam-6325	20	35	chaotic	chaotic	ADJ
ejpam-6325	20	36	behavior	behavior	NOUN
ejpam-6325	20	37	.	.	PUNCT
ejpam-6325	21	1	in	in	ADP
ejpam-6325	21	2	recent	recent	ADJ
ejpam-6325	21	3	years	year	NOUN
ejpam-6325	21	4	,	,	PUNCT
ejpam-6325	21	5	fractional	fractional	ADJ
ejpam-6325	21	6	calculus	calculus	NOUN
ejpam-6325	21	7	has	have	AUX
ejpam-6325	21	8	emerged	emerge	VERB
ejpam-6325	21	9	as	as	ADP
ejpam-6325	21	10	a	a	DET
ejpam-6325	21	11	powerful	powerful	ADJ
ejpam-6325	21	12	tool	tool	NOUN
ejpam-6325	21	13	in	in	ADP
ejpam-6325	21	14	modeling	model	VERB
ejpam-6325	21	15	complex	complex	ADJ
ejpam-6325	21	16	dynamical	dynamical	ADJ
ejpam-6325	21	17	systems	system	NOUN
ejpam-6325	21	18	,	,	PUNCT
ejpam-6325	21	19	offering	offer	VERB
ejpam-6325	21	20	more	more	ADV
ejpam-6325	21	21	accurate	accurate	ADJ
ejpam-6325	21	22	descriptions	description	NOUN
ejpam-6325	21	23	of	of	ADP
ejpam-6325	21	24	memory	memory	NOUN
ejpam-6325	21	25	and	and	CCONJ
ejpam-6325	21	26	hereditary	hereditary	ADJ
ejpam-6325	21	27	properties	property	NOUN
ejpam-6325	21	28	inherent	inherent	ADJ
ejpam-6325	21	29	in	in	ADP
ejpam-6325	21	30	various	various	ADJ
ejpam-6325	21	31	physical	physical	ADJ
ejpam-6325	21	32	and	and	CCONJ
ejpam-6325	21	33	engineering	engineering	NOUN
ejpam-6325	21	34	processes	process	NOUN
ejpam-6325	21	35	[	[	X
ejpam-6325	21	36	1	1	NUM
ejpam-6325	21	37	]	]	PUNCT
ejpam-6325	21	38	,	,	PUNCT
ejpam-6325	21	39	[	[	X
ejpam-6325	21	40	2	2	NUM
ejpam-6325	21	41	]	]	PUNCT
ejpam-6325	21	42	,	,	PUNCT
ejpam-6325	21	43	[	[	X
ejpam-6325	21	44	3	3	NUM
ejpam-6325	21	45	]	]	PUNCT
ejpam-6325	21	46	.	.	PUNCT
ejpam-6325	22	1	coupled	couple	VERB
ejpam-6325	22	2	with	with	ADP
ejpam-6325	22	3	advances	advance	NOUN
ejpam-6325	22	4	in	in	ADP
ejpam-6325	22	5	numerical	numerical	ADJ
ejpam-6325	22	6	methods	method	NOUN
ejpam-6325	22	7	,	,	PUNCT
ejpam-6325	22	8	including	include	VERB
ejpam-6325	22	9	finite	finite	ADJ
ejpam-6325	22	10	difference	difference	NOUN
ejpam-6325	22	11	schemes	scheme	NOUN
ejpam-6325	22	12	and	and	CCONJ
ejpam-6325	22	13	spectral	spectral	ADJ
ejpam-6325	22	14	techniques	technique	NOUN
ejpam-6325	22	15	,	,	PUNCT
ejpam-6325	22	16	these	these	DET
ejpam-6325	22	17	developments	development	NOUN
ejpam-6325	22	18	have	have	AUX
ejpam-6325	22	19	significantly	significantly	ADV
ejpam-6325	22	20	enhanced	enhance	VERB
ejpam-6325	22	21	the	the	DET
ejpam-6325	22	22	analysis	analysis	NOUN
ejpam-6325	22	23	and	and	CCONJ
ejpam-6325	22	24	solution	solution	NOUN
ejpam-6325	22	25	of	of	ADP
ejpam-6325	22	26	nonlinear	nonlinear	ADJ
ejpam-6325	22	27	partial	partial	ADJ
ejpam-6325	22	28	differential	differential	NOUN
ejpam-6325	22	29	equations	equation	NOUN
ejpam-6325	22	30	[	[	X
ejpam-6325	22	31	4	4	NUM
ejpam-6325	22	32	]	]	PUNCT
ejpam-6325	22	33	,	,	PUNCT
ejpam-6325	22	34	[	[	X
ejpam-6325	22	35	5	5	NUM
ejpam-6325	22	36	]	]	PUNCT
ejpam-6325	22	37	.	.	PUNCT
ejpam-6325	23	1	the	the	DET
ejpam-6325	23	2	incorporation	incorporation	NOUN
ejpam-6325	23	3	of	of	ADP
ejpam-6325	23	4	fractional	fractional	ADJ
ejpam-6325	23	5	derivatives	derivative	NOUN
ejpam-6325	23	6	and	and	CCONJ
ejpam-6325	23	7	novel	novel	ADJ
ejpam-6325	23	8	computational	computational	ADJ
ejpam-6325	23	9	approaches	approach	NOUN
ejpam-6325	23	10	has	have	AUX
ejpam-6325	23	11	expanded	expand	VERB
ejpam-6325	23	12	the	the	DET
ejpam-6325	23	13	capability	capability	NOUN
ejpam-6325	23	14	to	to	PART
ejpam-6325	23	15	capture	capture	VERB
ejpam-6325	23	16	anomalous	anomalous	ADJ
ejpam-6325	23	17	diffusion	diffusion	NOUN
ejpam-6325	23	18	,	,	PUNCT
ejpam-6325	23	19	viscoelasticity	viscoelasticity	NOUN
ejpam-6325	23	20	,	,	PUNCT
ejpam-6325	23	21	and	and	CCONJ
ejpam-6325	23	22	chaotic	chaotic	ADJ
ejpam-6325	23	23	behaviors	behavior	NOUN
ejpam-6325	23	24	across	across	ADP
ejpam-6325	23	25	multiple	multiple	ADJ
ejpam-6325	23	26	scientific	scientific	ADJ
ejpam-6325	23	27	domains	domain	NOUN
ejpam-6325	23	28	.	.	PUNCT
ejpam-6325	24	1	recent	recent	ADJ
ejpam-6325	24	2	studies	study	NOUN
ejpam-6325	24	3	highlight	highlight	VERB
ejpam-6325	24	4	the	the	DET
ejpam-6325	24	5	growing	grow	VERB
ejpam-6325	24	6	interdisciplinary	interdisciplinary	ADJ
ejpam-6325	24	7	interest	interest	NOUN
ejpam-6325	24	8	and	and	CCONJ
ejpam-6325	24	9	provide	provide	VERB
ejpam-6325	24	10	a	a	DET
ejpam-6325	24	11	strong	strong	ADJ
ejpam-6325	24	12	foundation	foundation	NOUN
ejpam-6325	24	13	for	for	ADP
ejpam-6325	24	14	further	further	ADJ
ejpam-6325	24	15	exploration	exploration	NOUN
ejpam-6325	24	16	of	of	ADP
ejpam-6325	24	17	nonlinear	nonlinear	ADJ
ejpam-6325	24	18	wave	wave	NOUN
ejpam-6325	24	19	equations	equation	NOUN
ejpam-6325	24	20	with	with	ADP
ejpam-6325	24	21	damping	damp	VERB
ejpam-6325	24	22	and	and	CCONJ
ejpam-6325	24	23	complex	complex	ADJ
ejpam-6325	24	24	potentials	potential	NOUN
ejpam-6325	24	25	.	.	PUNCT
ejpam-6325	25	1	despite	despite	SCONJ
ejpam-6325	25	2	their	their	PRON
ejpam-6325	25	3	significance	significance	NOUN
ejpam-6325	25	4	,	,	PUNCT
ejpam-6325	25	5	solving	solve	VERB
ejpam-6325	25	6	nonlinear	nonlinear	ADJ
ejpam-6325	25	7	pdes	pde	NOUN
ejpam-6325	25	8	poses	pose	VERB
ejpam-6325	25	9	a	a	DET
ejpam-6325	25	10	substantial	substantial	ADJ
ejpam-6325	25	11	challenge	challenge	NOUN
ejpam-6325	25	12	due	due	ADP
ejpam-6325	25	13	to	to	ADP
ejpam-6325	25	14	the	the	DET
ejpam-6325	25	15	absence	absence	NOUN
ejpam-6325	25	16	of	of	ADP
ejpam-6325	25	17	universal	universal	ADJ
ejpam-6325	25	18	solution	solution	NOUN
ejpam-6325	25	19	methods	method	NOUN
ejpam-6325	25	20	.	.	PUNCT
ejpam-6325	26	1	as	as	ADP
ejpam-6325	26	2	a	a	DET
ejpam-6325	26	3	result	result	NOUN
ejpam-6325	26	4	,	,	PUNCT
ejpam-6325	26	5	various	various	ADJ
ejpam-6325	26	6	analytical	analytical	ADJ
ejpam-6325	26	7	techniques	technique	NOUN
ejpam-6325	26	8	such	such	ADJ
ejpam-6325	26	9	as	as	ADP
ejpam-6325	26	10	perturbation	perturbation	NOUN
ejpam-6325	26	11	methods	method	NOUN
ejpam-6325	26	12	,	,	PUNCT
ejpam-6325	26	13	similarity	similarity	NOUN
ejpam-6325	26	14	transformations	transformation	NOUN
ejpam-6325	26	15	,	,	PUNCT
ejpam-6325	26	16	and	and	CCONJ
ejpam-6325	26	17	variational	variational	ADJ
ejpam-6325	26	18	approaches	approach	NOUN
ejpam-6325	26	19	are	be	AUX
ejpam-6325	26	20	often	often	ADV
ejpam-6325	26	21	employed	employ	VERB
ejpam-6325	26	22	.	.	PUNCT
ejpam-6325	27	1	these	these	PRON
ejpam-6325	27	2	are	be	AUX
ejpam-6325	27	3	complemented	complement	VERB
ejpam-6325	27	4	by	by	ADP
ejpam-6325	27	5	numerical	numerical	ADJ
ejpam-6325	27	6	techniques	technique	NOUN
ejpam-6325	27	7	like	like	ADP
ejpam-6325	27	8	the	the	DET
ejpam-6325	27	9	finite	finite	PROPN
ejpam-6325	27	10	element	element	NOUN
ejpam-6325	27	11	method	method	NOUN
ejpam-6325	27	12	,	,	PUNCT
ejpam-6325	27	13	finite	finite	ADJ
ejpam-6325	27	14	difference	difference	NOUN
ejpam-6325	27	15	schemes	scheme	NOUN
ejpam-6325	27	16	,	,	PUNCT
ejpam-6325	27	17	and	and	CCONJ
ejpam-6325	27	18	spectral	spectral	ADJ
ejpam-6325	27	19	methods	method	NOUN
ejpam-6325	27	20	.	.	PUNCT
ejpam-6325	28	1	however	however	ADV
ejpam-6325	28	2	,	,	PUNCT
ejpam-6325	28	3	many	many	ADJ
ejpam-6325	28	4	traditional	traditional	ADJ
ejpam-6325	28	5	analytical	analytical	ADJ
ejpam-6325	28	6	methods	method	NOUN
ejpam-6325	28	7	suffer	suffer	VERB
ejpam-6325	28	8	from	from	ADP
ejpam-6325	28	9	limitations	limitation	NOUN
ejpam-6325	28	10	such	such	ADJ
ejpam-6325	28	11	as	as	ADP
ejpam-6325	28	12	the	the	DET
ejpam-6325	28	13	requirement	requirement	NOUN
ejpam-6325	28	14	for	for	ADP
ejpam-6325	28	15	small	small	ADJ
ejpam-6325	28	16	parameters	parameter	NOUN
ejpam-6325	28	17	,	,	PUNCT
ejpam-6325	28	18	approximate	approximate	ADJ
ejpam-6325	28	19	series	series	NOUN
ejpam-6325	28	20	expansions	expansion	NOUN
ejpam-6325	28	21	,	,	PUNCT
ejpam-6325	28	22	or	or	CCONJ
ejpam-6325	28	23	difficulties	difficulty	NOUN
ejpam-6325	28	24	in	in	ADP
ejpam-6325	28	25	handling	handle	VERB
ejpam-6325	28	26	damping	damp	VERB
ejpam-6325	28	27	and	and	CCONJ
ejpam-6325	28	28	potential	potential	ADJ
ejpam-6325	28	29	terms	term	NOUN
ejpam-6325	28	30	in	in	ADP
ejpam-6325	28	31	complex	complex	ADJ
ejpam-6325	28	32	equations	equation	NOUN
ejpam-6325	28	33	.	.	PUNCT
ejpam-6325	29	1	utt	utt	NOUN
ejpam-6325	30	1	+	+	CCONJ
ejpam-6325	30	2	(	(	PUNCT
ejpam-6325	30	3	α+	α+	PROPN
ejpam-6325	30	4	β)ut	β)ut	NOUN
ejpam-6325	30	5	+	+	CCONJ
ejpam-6325	30	6	αβ(u	αβ(u	NUM
ejpam-6325	30	7	)	)	PUNCT
ejpam-6325	30	8	=	=	SYM
ejpam-6325	31	1	c2uxx	c2uxx	X
ejpam-6325	31	2	,	,	PUNCT
ejpam-6325	31	3	(	(	PUNCT
ejpam-6325	31	4	1	1	X
ejpam-6325	31	5	)	)	PUNCT
ejpam-6325	31	6	commonly	commonly	ADV
ejpam-6325	31	7	referred	refer	VERB
ejpam-6325	31	8	to	to	ADP
ejpam-6325	31	9	as	as	ADP
ejpam-6325	31	10	the	the	DET
ejpam-6325	31	11	telegrapher	telegrapher	NOUN
ejpam-6325	31	12	’s	’s	PART
ejpam-6325	31	13	equation	equation	NOUN
ejpam-6325	31	14	with	with	ADP
ejpam-6325	31	15	damping	damp	VERB
ejpam-6325	31	16	and	and	CCONJ
ejpam-6325	31	17	harmonic	harmonic	ADJ
ejpam-6325	31	18	potential	potential	NOUN
ejpam-6325	31	19	,	,	PUNCT
ejpam-6325	31	20	describes	describe	VERB
ejpam-6325	31	21	a	a	DET
ejpam-6325	31	22	system	system	NOUN
ejpam-6325	31	23	where	where	SCONJ
ejpam-6325	31	24	wave	wave	NOUN
ejpam-6325	31	25	propagation	propagation	NOUN
ejpam-6325	31	26	is	be	AUX
ejpam-6325	31	27	influenced	influence	VERB
ejpam-6325	31	28	by	by	ADP
ejpam-6325	31	29	both	both	DET
ejpam-6325	31	30	temporal	temporal	ADJ
ejpam-6325	31	31	damping	damp	VERB
ejpam-6325	31	32	and	and	CCONJ
ejpam-6325	31	33	spatial	spatial	ADJ
ejpam-6325	31	34	diffusion	diffusion	NOUN
ejpam-6325	31	35	.	.	PUNCT
ejpam-6325	32	1	here	here	ADV
ejpam-6325	32	2	,	,	PUNCT
ejpam-6325	32	3	utt	utt	PROPN
ejpam-6325	32	4	represents	represent	VERB
ejpam-6325	32	5	the	the	DET
ejpam-6325	32	6	time	time	NOUN
ejpam-6325	32	7	acceleration	acceleration	NOUN
ejpam-6325	32	8	,	,	PUNCT
ejpam-6325	32	9	(	(	PUNCT
ejpam-6325	32	10	α	α	NOUN
ejpam-6325	32	11	+	+	X
ejpam-6325	33	1	β)ut	β)ut	NOUN
ejpam-6325	33	2	is	be	AUX
ejpam-6325	33	3	a	a	DET
ejpam-6325	33	4	damping	damp	VERB
ejpam-6325	33	5	term	term	NOUN
ejpam-6325	33	6	reflecting	reflect	VERB
ejpam-6325	33	7	system	system	NOUN
ejpam-6325	33	8	resistance	resistance	NOUN
ejpam-6325	33	9	or	or	CCONJ
ejpam-6325	33	10	friction	friction	NOUN
ejpam-6325	33	11	,	,	PUNCT
ejpam-6325	33	12	and	and	CCONJ
ejpam-6325	33	13	αβu	αβu	ADV
ejpam-6325	33	14	introduces	introduce	VERB
ejpam-6325	33	15	a	a	DET
ejpam-6325	33	16	harmonic	harmonic	ADJ
ejpam-6325	33	17	potential	potential	NOUN
ejpam-6325	33	18	.	.	PUNCT
ejpam-6325	34	1	the	the	DET
ejpam-6325	34	2	term	term	NOUN
ejpam-6325	34	3	c2uxx	c2uxx	PRON
ejpam-6325	34	4	corresponds	correspond	VERB
ejpam-6325	34	5	to	to	PART
ejpam-6325	34	6	wave	wave	VERB
ejpam-6325	34	7	propagation	propagation	NOUN
ejpam-6325	34	8	,	,	PUNCT
ejpam-6325	34	9	where	where	SCONJ
ejpam-6325	34	10	c	c	PROPN
ejpam-6325	34	11	denotes	denote	VERB
ejpam-6325	34	12	the	the	DET
ejpam-6325	34	13	wave	wave	NOUN
ejpam-6325	34	14	speed	speed	NOUN
ejpam-6325	34	15	.	.	PUNCT
ejpam-6325	35	1	this	this	DET
ejpam-6325	35	2	equation	equation	NOUN
ejpam-6325	35	3	serves	serve	VERB
ejpam-6325	35	4	as	as	ADP
ejpam-6325	35	5	a	a	DET
ejpam-6325	35	6	core	core	NOUN
ejpam-6325	35	7	model	model	NOUN
ejpam-6325	35	8	in	in	ADP
ejpam-6325	35	9	describing	describe	VERB
ejpam-6325	35	10	physical	physical	ADJ
ejpam-6325	35	11	processes	process	NOUN
ejpam-6325	35	12	such	such	ADJ
ejpam-6325	35	13	as	as	ADP
ejpam-6325	35	14	signal	signal	ADJ
ejpam-6325	35	15	transmission	transmission	NOUN
ejpam-6325	35	16	,	,	PUNCT
ejpam-6325	35	17	mechanical	mechanical	ADJ
ejpam-6325	35	18	vibrations	vibration	NOUN
ejpam-6325	35	19	,	,	PUNCT
ejpam-6325	35	20	and	and	CCONJ
ejpam-6325	35	21	heat	heat	NOUN
ejpam-6325	35	22	conduction	conduction	NOUN
ejpam-6325	35	23	,	,	PUNCT
ejpam-6325	35	24	particularly	particularly	ADV
ejpam-6325	35	25	in	in	ADP
ejpam-6325	35	26	contexts	context	NOUN
ejpam-6325	35	27	where	where	SCONJ
ejpam-6325	35	28	both	both	DET
ejpam-6325	35	29	wave	wave	NOUN
ejpam-6325	35	30	-	-	PUNCT
ejpam-6325	35	31	like	like	ADJ
ejpam-6325	35	32	behavior	behavior	NOUN
ejpam-6325	35	33	and	and	CCONJ
ejpam-6325	35	34	energy	energy	NOUN
ejpam-6325	35	35	dissipation	dissipation	NOUN
ejpam-6325	35	36	are	be	AUX
ejpam-6325	35	37	significant	significant	ADJ
ejpam-6325	35	38	[	[	X
ejpam-6325	35	39	6	6	NUM
ejpam-6325	35	40	]	]	PUNCT
ejpam-6325	35	41	,	,	PUNCT
ejpam-6325	35	42	[	[	X
ejpam-6325	35	43	7	7	NUM
ejpam-6325	35	44	]	]	PUNCT
ejpam-6325	35	45	.	.	PUNCT
ejpam-6325	36	1	the	the	DET
ejpam-6325	36	2	parameters	parameter	NOUN
ejpam-6325	36	3	α	α	PRON
ejpam-6325	36	4	,	,	PUNCT
ejpam-6325	36	5	β	β	NOUN
ejpam-6325	36	6	,	,	PUNCT
ejpam-6325	36	7	and	and	CCONJ
ejpam-6325	36	8	c	c	NOUN
ejpam-6325	36	9	have	have	VERB
ejpam-6325	36	10	distinct	distinct	ADJ
ejpam-6325	36	11	physical	physical	ADJ
ejpam-6325	36	12	interpretations	interpretation	NOUN
ejpam-6325	36	13	that	that	PRON
ejpam-6325	36	14	govern	govern	VERB
ejpam-6325	36	15	the	the	DET
ejpam-6325	36	16	dynamics	dynamic	NOUN
ejpam-6325	36	17	of	of	ADP
ejpam-6325	36	18	the	the	DET
ejpam-6325	36	19	system	system	NOUN
ejpam-6325	36	20	:	:	PUNCT
ejpam-6325	36	21	•	•	NUM
ejpam-6325	36	22	damping	damp	VERB
ejpam-6325	36	23	coefficients	coefficient	NOUN
ejpam-6325	36	24	α	α	PROPN
ejpam-6325	36	25	and	and	CCONJ
ejpam-6325	36	26	β	β	X
ejpam-6325	36	27	:	:	PUNCT
ejpam-6325	36	28	these	these	DET
ejpam-6325	36	29	parameters	parameter	NOUN
ejpam-6325	36	30	characterize	characterize	VERB
ejpam-6325	36	31	the	the	DET
ejpam-6325	36	32	dissipative	dissipative	ADJ
ejpam-6325	36	33	effects	effect	NOUN
ejpam-6325	36	34	within	within	ADP
ejpam-6325	36	35	the	the	DET
ejpam-6325	36	36	system	system	NOUN
ejpam-6325	36	37	.	.	PUNCT
ejpam-6325	37	1	the	the	DET
ejpam-6325	37	2	term	term	NOUN
ejpam-6325	37	3	(	(	PUNCT
ejpam-6325	37	4	α+β)ut	α+β)ut	NOUN
ejpam-6325	37	5	models	model	NOUN
ejpam-6325	37	6	damping	damp	VERB
ejpam-6325	37	7	forces	force	NOUN
ejpam-6325	37	8	proportional	proportional	ADJ
ejpam-6325	37	9	to	to	ADP
ejpam-6325	37	10	velocity	velocity	NOUN
ejpam-6325	37	11	,	,	PUNCT
ejpam-6325	37	12	representing	represent	VERB
ejpam-6325	37	13	resistance	resistance	NOUN
ejpam-6325	37	14	or	or	CCONJ
ejpam-6325	37	15	frictional	frictional	ADJ
ejpam-6325	37	16	effects	effect	NOUN
ejpam-6325	37	17	that	that	PRON
ejpam-6325	37	18	gradually	gradually	ADV
ejpam-6325	37	19	reduce	reduce	VERB
ejpam-6325	37	20	the	the	DET
ejpam-6325	37	21	wave	wave	NOUN
ejpam-6325	37	22	amplitude	amplitude	NOUN
ejpam-6325	37	23	over	over	ADP
ejpam-6325	37	24	time	time	NOUN
ejpam-6325	37	25	.	.	PUNCT
ejpam-6325	38	1	meanwhile	meanwhile	ADV
ejpam-6325	38	2	,	,	PUNCT
ejpam-6325	38	3	αβu	αβu	ADV
ejpam-6325	38	4	acts	act	VERB
ejpam-6325	38	5	as	as	ADP
ejpam-6325	38	6	a	a	DET
ejpam-6325	38	7	harmonic	harmonic	ADJ
ejpam-6325	38	8	potential	potential	NOUN
ejpam-6325	38	9	,	,	PUNCT
ejpam-6325	38	10	providing	provide	VERB
ejpam-6325	38	11	a	a	DET
ejpam-6325	38	12	m.	m.	NOUN
ejpam-6325	38	13	noman	noman	PROPN
ejpam-6325	38	14	et	et	PROPN
ejpam-6325	38	15	al	al	PROPN
ejpam-6325	38	16	.	.	PUNCT
ejpam-6325	38	17	/	/	SYM
ejpam-6325	38	18	eur	eur	PROPN
ejpam-6325	38	19	.	.	PUNCT
ejpam-6325	39	1	j.	j.	PROPN
ejpam-6325	39	2	pure	pure	PROPN
ejpam-6325	39	3	appl	appl	PROPN
ejpam-6325	39	4	.	.	PROPN
ejpam-6325	39	5	math	math	PROPN
ejpam-6325	39	6	,	,	PUNCT
ejpam-6325	39	7	18	18	NUM
ejpam-6325	39	8	(	(	PUNCT
ejpam-6325	39	9	3	3	NUM
ejpam-6325	39	10	)	)	PUNCT
ejpam-6325	39	11	(	(	PUNCT
ejpam-6325	39	12	2025	2025	NUM
ejpam-6325	39	13	)	)	PUNCT
ejpam-6325	39	14	,	,	PUNCT
ejpam-6325	39	15	6235	6235	NUM
ejpam-6325	39	16	3	3	NUM
ejpam-6325	39	17	of	of	ADP
ejpam-6325	39	18	16	16	NUM
ejpam-6325	39	19	restoring	restore	VERB
ejpam-6325	39	20	force	force	NOUN
ejpam-6325	39	21	proportional	proportional	ADJ
ejpam-6325	39	22	to	to	ADP
ejpam-6325	39	23	the	the	DET
ejpam-6325	39	24	displacement	displacement	NOUN
ejpam-6325	39	25	,	,	PUNCT
ejpam-6325	39	26	which	which	PRON
ejpam-6325	39	27	can	can	AUX
ejpam-6325	39	28	model	model	VERB
ejpam-6325	39	29	elastic	elastic	ADJ
ejpam-6325	39	30	or	or	CCONJ
ejpam-6325	39	31	reactive	reactive	ADJ
ejpam-6325	39	32	effects	effect	NOUN
ejpam-6325	39	33	in	in	ADP
ejpam-6325	39	34	the	the	DET
ejpam-6325	39	35	medium	medium	NOUN
ejpam-6325	39	36	.	.	PUNCT
ejpam-6325	40	1	physically	physically	ADV
ejpam-6325	40	2	,	,	PUNCT
ejpam-6325	40	3	α	α	PROPN
ejpam-6325	40	4	and	and	CCONJ
ejpam-6325	40	5	β	β	X
ejpam-6325	40	6	may	may	AUX
ejpam-6325	40	7	correspond	correspond	VERB
ejpam-6325	40	8	to	to	ADP
ejpam-6325	40	9	different	different	ADJ
ejpam-6325	40	10	mechanisms	mechanism	NOUN
ejpam-6325	40	11	of	of	ADP
ejpam-6325	40	12	energy	energy	NOUN
ejpam-6325	40	13	loss	loss	NOUN
ejpam-6325	40	14	or	or	CCONJ
ejpam-6325	40	15	gain	gain	NOUN
ejpam-6325	40	16	,	,	PUNCT
ejpam-6325	40	17	such	such	ADJ
ejpam-6325	40	18	as	as	ADP
ejpam-6325	40	19	electrical	electrical	ADJ
ejpam-6325	40	20	resistance	resistance	NOUN
ejpam-6325	40	21	in	in	ADP
ejpam-6325	40	22	transmission	transmission	NOUN
ejpam-6325	40	23	lines	line	NOUN
ejpam-6325	40	24	,	,	PUNCT
ejpam-6325	40	25	viscous	viscous	ADJ
ejpam-6325	40	26	damping	damping	NOUN
ejpam-6325	40	27	in	in	ADP
ejpam-6325	40	28	mechanical	mechanical	ADJ
ejpam-6325	40	29	vibrations	vibration	NOUN
ejpam-6325	40	30	,	,	PUNCT
ejpam-6325	40	31	or	or	CCONJ
ejpam-6325	40	32	absorption	absorption	NOUN
ejpam-6325	40	33	effects	effect	NOUN
ejpam-6325	40	34	in	in	ADP
ejpam-6325	40	35	wave	wave	NOUN
ejpam-6325	40	36	propagation	propagation	NOUN
ejpam-6325	40	37	through	through	ADP
ejpam-6325	40	38	lossy	lossy	ADJ
ejpam-6325	40	39	media	medium	NOUN
ejpam-6325	40	40	.	.	PUNCT
ejpam-6325	41	1	•	•	NUM
ejpam-6325	41	2	wave	wave	NOUN
ejpam-6325	41	3	speed	speed	NOUN
ejpam-6325	41	4	c	c	NOUN
ejpam-6325	41	5	:	:	PUNCT
ejpam-6325	41	6	under	under	ADP
ejpam-6325	41	7	the	the	DET
ejpam-6325	41	8	parameter	parameter	NOUN
ejpam-6325	41	9	c	c	PROPN
ejpam-6325	41	10	represents	represent	VERB
ejpam-6325	41	11	the	the	DET
ejpam-6325	41	12	characteristic	characteristic	ADJ
ejpam-6325	41	13	speed	speed	NOUN
ejpam-6325	41	14	of	of	ADP
ejpam-6325	41	15	wave	wave	NOUN
ejpam-6325	41	16	propagation	propagation	NOUN
ejpam-6325	41	17	through	through	ADP
ejpam-6325	41	18	the	the	DET
ejpam-6325	41	19	medium	medium	NOUN
ejpam-6325	41	20	in	in	ADP
ejpam-6325	41	21	the	the	DET
ejpam-6325	41	22	absence	absence	NOUN
ejpam-6325	41	23	of	of	ADP
ejpam-6325	41	24	damping	damp	VERB
ejpam-6325	41	25	and	and	CCONJ
ejpam-6325	41	26	potential	potential	ADJ
ejpam-6325	41	27	effects	effect	NOUN
ejpam-6325	41	28	.	.	PUNCT
ejpam-6325	42	1	it	it	PRON
ejpam-6325	42	2	governs	govern	VERB
ejpam-6325	42	3	the	the	DET
ejpam-6325	42	4	dispersive	dispersive	ADJ
ejpam-6325	42	5	term	term	NOUN
ejpam-6325	42	6	c2uxx	c2uxx	PROPN
ejpam-6325	42	7	,	,	PUNCT
ejpam-6325	42	8	modeling	model	VERB
ejpam-6325	42	9	spatial	spatial	ADJ
ejpam-6325	42	10	diffusion	diffusion	NOUN
ejpam-6325	42	11	or	or	CCONJ
ejpam-6325	42	12	wave	wave	NOUN
ejpam-6325	42	13	transmission	transmission	NOUN
ejpam-6325	42	14	.	.	PUNCT
ejpam-6325	43	1	in	in	ADP
ejpam-6325	43	2	physical	physical	ADJ
ejpam-6325	43	3	contexts	contexts	NOUN
ejpam-6325	43	4	,	,	PUNCT
ejpam-6325	43	5	c	c	PROPN
ejpam-6325	43	6	may	may	AUX
ejpam-6325	43	7	represent	represent	VERB
ejpam-6325	43	8	the	the	DET
ejpam-6325	43	9	speed	speed	NOUN
ejpam-6325	43	10	of	of	ADP
ejpam-6325	43	11	signal	signal	ADJ
ejpam-6325	43	12	transmission	transmission	NOUN
ejpam-6325	43	13	in	in	ADP
ejpam-6325	43	14	telegraph	telegraph	NOUN
ejpam-6325	43	15	lines	line	NOUN
ejpam-6325	43	16	,	,	PUNCT
ejpam-6325	43	17	the	the	DET
ejpam-6325	43	18	speed	speed	NOUN
ejpam-6325	43	19	of	of	ADP
ejpam-6325	43	20	sound	sound	NOUN
ejpam-6325	43	21	in	in	ADP
ejpam-6325	43	22	vibrating	vibrate	VERB
ejpam-6325	43	23	strings	string	NOUN
ejpam-6325	43	24	,	,	PUNCT
ejpam-6325	43	25	or	or	CCONJ
ejpam-6325	43	26	diffusion	diffusion	NOUN
ejpam-6325	43	27	rates	rate	NOUN
ejpam-6325	43	28	in	in	ADP
ejpam-6325	43	29	thermal	thermal	ADJ
ejpam-6325	43	30	and	and	CCONJ
ejpam-6325	43	31	fluid	fluid	ADJ
ejpam-6325	43	32	systems	system	NOUN
ejpam-6325	43	33	.	.	PUNCT
ejpam-6325	44	1	together	together	ADV
ejpam-6325	44	2	,	,	PUNCT
ejpam-6325	44	3	these	these	DET
ejpam-6325	44	4	parameters	parameter	NOUN
ejpam-6325	44	5	control	control	VERB
ejpam-6325	44	6	the	the	DET
ejpam-6325	44	7	interplay	interplay	NOUN
ejpam-6325	44	8	between	between	ADP
ejpam-6325	44	9	wave	wave	NOUN
ejpam-6325	44	10	propagation	propagation	NOUN
ejpam-6325	44	11	,	,	PUNCT
ejpam-6325	44	12	dissipation	dissipation	NOUN
ejpam-6325	44	13	,	,	PUNCT
ejpam-6325	44	14	and	and	CCONJ
ejpam-6325	44	15	restoring	restore	VERB
ejpam-6325	44	16	forces	force	NOUN
ejpam-6325	44	17	,	,	PUNCT
ejpam-6325	44	18	shaping	shape	VERB
ejpam-6325	44	19	solution	solution	NOUN
ejpam-6325	44	20	characteristics	characteristic	NOUN
ejpam-6325	44	21	such	such	ADJ
ejpam-6325	44	22	as	as	ADP
ejpam-6325	44	23	amplitude	amplitude	NOUN
ejpam-6325	44	24	attenuation	attenuation	NOUN
ejpam-6325	44	25	,	,	PUNCT
ejpam-6325	44	26	wave	wave	NOUN
ejpam-6325	44	27	speed	speed	NOUN
ejpam-6325	44	28	modulation	modulation	NOUN
ejpam-6325	44	29	,	,	PUNCT
ejpam-6325	44	30	and	and	CCONJ
ejpam-6325	44	31	oscillatory	oscillatory	ADJ
ejpam-6325	44	32	behavior	behavior	NOUN
ejpam-6325	44	33	.	.	PUNCT
ejpam-6325	45	1	in	in	ADP
ejpam-6325	45	2	recent	recent	ADJ
ejpam-6325	45	3	years	year	NOUN
ejpam-6325	45	4	,	,	PUNCT
ejpam-6325	45	5	there	there	PRON
ejpam-6325	45	6	has	have	AUX
ejpam-6325	45	7	been	be	AUX
ejpam-6325	45	8	considerable	considerable	ADJ
ejpam-6325	45	9	interest	interest	NOUN
ejpam-6325	45	10	in	in	ADP
ejpam-6325	45	11	developing	develop	VERB
ejpam-6325	45	12	both	both	CCONJ
ejpam-6325	45	13	analytical	analytical	ADJ
ejpam-6325	45	14	and	and	CCONJ
ejpam-6325	45	15	numerical	numerical	ADJ
ejpam-6325	45	16	methods	method	NOUN
ejpam-6325	45	17	for	for	ADP
ejpam-6325	45	18	solving	solve	VERB
ejpam-6325	45	19	damped	damped	NOUN
ejpam-6325	45	20	wave	wave	NOUN
ejpam-6325	45	21	equations	equation	NOUN
ejpam-6325	45	22	and	and	CCONJ
ejpam-6325	45	23	related	relate	VERB
ejpam-6325	45	24	nonlinear	nonlinear	ADJ
ejpam-6325	45	25	models	model	NOUN
ejpam-6325	45	26	.	.	PUNCT
ejpam-6325	46	1	techniques	technique	NOUN
ejpam-6325	46	2	such	such	ADJ
ejpam-6325	46	3	as	as	ADP
ejpam-6325	46	4	the	the	DET
ejpam-6325	46	5	exp	exp	NOUN
ejpam-6325	46	6	-	-	PUNCT
ejpam-6325	46	7	function	function	NOUN
ejpam-6325	46	8	method	method	NOUN
ejpam-6325	46	9	,	,	PUNCT
ejpam-6325	46	10	tanh	tanh	NOUN
ejpam-6325	46	11	-	-	PUNCT
ejpam-6325	46	12	coth	coth	NOUN
ejpam-6325	46	13	method	method	NOUN
ejpam-6325	46	14	,	,	PUNCT
ejpam-6325	46	15	sine	sine	ADJ
ejpam-6325	46	16	-	-	PUNCT
ejpam-6325	46	17	gordon	gordon	PROPN
ejpam-6325	46	18	expansion	expansion	NOUN
ejpam-6325	46	19	method	method	NOUN
ejpam-6325	46	20	,	,	PUNCT
ejpam-6325	46	21	and	and	CCONJ
ejpam-6325	46	22	homotopy	homotopy	VERB
ejpam-6325	46	23	analysis	analysis	NOUN
ejpam-6325	46	24	method	method	NOUN
ejpam-6325	46	25	have	have	AUX
ejpam-6325	46	26	been	be	AUX
ejpam-6325	46	27	applied	apply	VERB
ejpam-6325	46	28	to	to	PART
ejpam-6325	46	29	obtain	obtain	VERB
ejpam-6325	46	30	approximate	approximate	ADJ
ejpam-6325	46	31	and	and	CCONJ
ejpam-6325	46	32	exact	exact	ADJ
ejpam-6325	46	33	traveling	traveling	ADJ
ejpam-6325	46	34	wave	wave	NOUN
ejpam-6325	46	35	solutions	solution	NOUN
ejpam-6325	46	36	in	in	ADP
ejpam-6325	46	37	various	various	ADJ
ejpam-6325	46	38	contexts	context	NOUN
ejpam-6325	47	1	[	[	X
ejpam-6325	47	2	8	8	NUM
ejpam-6325	47	3	]	]	PUNCT
ejpam-6325	47	4	,	,	PUNCT
ejpam-6325	48	1	[	[	X
ejpam-6325	48	2	9	9	NUM
ejpam-6325	48	3	]	]	PUNCT
ejpam-6325	48	4	,	,	PUNCT
ejpam-6325	48	5	[	[	X
ejpam-6325	48	6	10	10	NUM
ejpam-6325	48	7	]	]	PUNCT
ejpam-6325	48	8	,	,	PUNCT
ejpam-6325	49	1	[	[	X
ejpam-6325	49	2	11	11	NUM
ejpam-6325	49	3	]	]	PUNCT
ejpam-6325	49	4	.	.	PUNCT
ejpam-6325	50	1	additionally	additionally	ADV
ejpam-6325	50	2	,	,	PUNCT
ejpam-6325	50	3	advanced	advanced	ADJ
ejpam-6325	50	4	numerical	numerical	ADJ
ejpam-6325	50	5	algorithms	algorithm	NOUN
ejpam-6325	50	6	and	and	CCONJ
ejpam-6325	50	7	hybrid	hybrid	ADJ
ejpam-6325	50	8	analyticalnumerical	analyticalnumerical	ADJ
ejpam-6325	50	9	techniques	technique	NOUN
ejpam-6325	50	10	have	have	AUX
ejpam-6325	50	11	been	be	AUX
ejpam-6325	50	12	explored	explore	VERB
ejpam-6325	50	13	to	to	PART
ejpam-6325	50	14	tackle	tackle	VERB
ejpam-6325	50	15	increasingly	increasingly	ADV
ejpam-6325	50	16	complex	complex	ADJ
ejpam-6325	50	17	models	model	NOUN
ejpam-6325	50	18	incorporating	incorporate	VERB
ejpam-6325	50	19	variable	variable	ADJ
ejpam-6325	50	20	coefficients	coefficient	NOUN
ejpam-6325	50	21	,	,	PUNCT
ejpam-6325	50	22	memory	memory	NOUN
ejpam-6325	50	23	effects	effect	NOUN
ejpam-6325	50	24	,	,	PUNCT
ejpam-6325	50	25	and	and	CCONJ
ejpam-6325	50	26	fractional	fractional	ADJ
ejpam-6325	50	27	derivatives	derivative	NOUN
ejpam-6325	50	28	.	.	PUNCT
ejpam-6325	51	1	these	these	DET
ejpam-6325	51	2	developments	development	NOUN
ejpam-6325	51	3	have	have	AUX
ejpam-6325	51	4	significantly	significantly	ADV
ejpam-6325	51	5	broadened	broaden	VERB
ejpam-6325	51	6	the	the	DET
ejpam-6325	51	7	range	range	NOUN
ejpam-6325	51	8	of	of	ADP
ejpam-6325	51	9	solvable	solvable	ADJ
ejpam-6325	51	10	models	model	NOUN
ejpam-6325	51	11	,	,	PUNCT
ejpam-6325	51	12	although	although	SCONJ
ejpam-6325	51	13	challenges	challenge	NOUN
ejpam-6325	51	14	remain	remain	VERB
ejpam-6325	51	15	in	in	ADP
ejpam-6325	51	16	deriving	derive	VERB
ejpam-6325	51	17	exact	exact	ADJ
ejpam-6325	51	18	solutions	solution	NOUN
ejpam-6325	51	19	for	for	ADP
ejpam-6325	51	20	systems	system	NOUN
ejpam-6325	51	21	involving	involve	VERB
ejpam-6325	51	22	both	both	DET
ejpam-6325	51	23	nonlinearities	nonlinearitie	NOUN
ejpam-6325	51	24	and	and	CCONJ
ejpam-6325	51	25	damping	damp	VERB
ejpam-6325	51	26	.	.	PUNCT
ejpam-6325	52	1	traditional	traditional	ADJ
ejpam-6325	52	2	methods	method	NOUN
ejpam-6325	52	3	for	for	ADP
ejpam-6325	52	4	solving	solve	VERB
ejpam-6325	52	5	the	the	DET
ejpam-6325	52	6	telegrapher	telegrapher	NOUN
ejpam-6325	52	7	’s	’s	PART
ejpam-6325	52	8	equation	equation	NOUN
ejpam-6325	52	9	,	,	PUNCT
ejpam-6325	52	10	especially	especially	ADV
ejpam-6325	52	11	in	in	ADP
ejpam-6325	52	12	the	the	DET
ejpam-6325	52	13	presence	presence	NOUN
ejpam-6325	52	14	of	of	ADP
ejpam-6325	52	15	damping	damp	VERB
ejpam-6325	52	16	,	,	PUNCT
ejpam-6325	52	17	often	often	ADV
ejpam-6325	52	18	face	face	VERB
ejpam-6325	52	19	difficulties	difficulty	NOUN
ejpam-6325	52	20	due	due	ADJ
ejpam-6325	52	21	to	to	ADP
ejpam-6325	52	22	their	their	PRON
ejpam-6325	52	23	reliance	reliance	NOUN
ejpam-6325	52	24	on	on	ADP
ejpam-6325	52	25	complex	complex	ADJ
ejpam-6325	52	26	or	or	CCONJ
ejpam-6325	52	27	approximate	approximate	ADJ
ejpam-6325	52	28	procedures	procedure	NOUN
ejpam-6325	52	29	[	[	X
ejpam-6325	52	30	12	12	NUM
ejpam-6325	52	31	]	]	PUNCT
ejpam-6325	52	32	,	,	PUNCT
ejpam-6325	52	33	[	[	X
ejpam-6325	52	34	13	13	NUM
ejpam-6325	52	35	]	]	PUNCT
ejpam-6325	52	36	,	,	PUNCT
ejpam-6325	52	37	[	[	X
ejpam-6325	52	38	14	14	NUM
ejpam-6325	52	39	]	]	PUNCT
ejpam-6325	52	40	,	,	PUNCT
ejpam-6325	52	41	[	[	X
ejpam-6325	52	42	15	15	NUM
ejpam-6325	52	43	]	]	PUNCT
ejpam-6325	52	44	,	,	PUNCT
ejpam-6325	52	45	[	[	X
ejpam-6325	52	46	16	16	NUM
ejpam-6325	52	47	]	]	PUNCT
ejpam-6325	52	48	,	,	PUNCT
ejpam-6325	52	49	[	[	X
ejpam-6325	52	50	17	17	NUM
ejpam-6325	52	51	]	]	PUNCT
ejpam-6325	52	52	,	,	PUNCT
ejpam-6325	52	53	[	[	X
ejpam-6325	52	54	18	18	NUM
ejpam-6325	52	55	]	]	PUNCT
ejpam-6325	52	56	,	,	PUNCT
ejpam-6325	52	57	[	[	X
ejpam-6325	52	58	19	19	NUM
ejpam-6325	52	59	]	]	PUNCT
ejpam-6325	52	60	.	.	PUNCT
ejpam-6325	53	1	many	many	ADJ
ejpam-6325	53	2	of	of	ADP
ejpam-6325	53	3	these	these	DET
ejpam-6325	53	4	techniques	technique	NOUN
ejpam-6325	53	5	are	be	AUX
ejpam-6325	53	6	limited	limit	VERB
ejpam-6325	53	7	in	in	ADP
ejpam-6325	53	8	their	their	PRON
ejpam-6325	53	9	ability	ability	NOUN
ejpam-6325	53	10	to	to	PART
ejpam-6325	53	11	derive	derive	VERB
ejpam-6325	53	12	exact	exact	ADJ
ejpam-6325	53	13	,	,	PUNCT
ejpam-6325	53	14	closed	closed	ADJ
ejpam-6325	53	15	-	-	PUNCT
ejpam-6325	53	16	form	form	NOUN
ejpam-6325	53	17	solutions	solution	NOUN
ejpam-6325	53	18	,	,	PUNCT
ejpam-6325	53	19	especially	especially	ADV
ejpam-6325	53	20	when	when	SCONJ
ejpam-6325	53	21	the	the	DET
ejpam-6325	53	22	equation	equation	NOUN
ejpam-6325	53	23	involves	involve	VERB
ejpam-6325	53	24	nonlinear	nonlinear	ADJ
ejpam-6325	53	25	terms	term	NOUN
ejpam-6325	53	26	and	and	CCONJ
ejpam-6325	53	27	damping	damp	VERB
ejpam-6325	53	28	effects	effect	NOUN
ejpam-6325	53	29	.	.	PUNCT
ejpam-6325	54	1	the	the	DET
ejpam-6325	54	2	generalized	generalized	ADJ
ejpam-6325	54	3	first	first	ADJ
ejpam-6325	54	4	integral	integral	ADJ
ejpam-6325	54	5	method	method	NOUN
ejpam-6325	54	6	provides	provide	VERB
ejpam-6325	54	7	a	a	DET
ejpam-6325	54	8	more	more	ADV
ejpam-6325	54	9	effective	effective	ADJ
ejpam-6325	54	10	approach	approach	NOUN
ejpam-6325	54	11	to	to	ADP
ejpam-6325	54	12	overcoming	overcome	VERB
ejpam-6325	54	13	these	these	DET
ejpam-6325	54	14	limitations	limitation	NOUN
ejpam-6325	54	15	.	.	PUNCT
ejpam-6325	55	1	this	this	DET
ejpam-6325	55	2	method	method	NOUN
ejpam-6325	55	3	extends	extend	VERB
ejpam-6325	55	4	the	the	DET
ejpam-6325	55	5	classical	classical	ADJ
ejpam-6325	55	6	first	first	ADJ
ejpam-6325	55	7	integral	integral	ADJ
ejpam-6325	55	8	technique	technique	NOUN
ejpam-6325	55	9	by	by	ADP
ejpam-6325	55	10	introducing	introduce	VERB
ejpam-6325	55	11	laurent	laurent	NOUN
ejpam-6325	55	12	polynomials	polynomial	NOUN
ejpam-6325	55	13	instead	instead	ADV
ejpam-6325	55	14	of	of	ADP
ejpam-6325	55	15	traditional	traditional	ADJ
ejpam-6325	55	16	polynomials	polynomial	NOUN
ejpam-6325	55	17	,	,	PUNCT
ejpam-6325	55	18	allowing	allow	VERB
ejpam-6325	55	19	for	for	ADP
ejpam-6325	55	20	a	a	DET
ejpam-6325	55	21	broader	broad	ADJ
ejpam-6325	55	22	class	class	NOUN
ejpam-6325	55	23	of	of	ADP
ejpam-6325	55	24	solutions	solution	NOUN
ejpam-6325	55	25	.	.	PUNCT
ejpam-6325	56	1	additionally	additionally	ADV
ejpam-6325	56	2	,	,	PUNCT
ejpam-6325	56	3	it	it	PRON
ejpam-6325	56	4	facilitates	facilitate	VERB
ejpam-6325	56	5	a	a	DET
ejpam-6325	56	6	wave	wave	NOUN
ejpam-6325	56	7	transformation	transformation	NOUN
ejpam-6325	56	8	that	that	PRON
ejpam-6325	56	9	reduces	reduce	VERB
ejpam-6325	56	10	the	the	DET
ejpam-6325	56	11	pde	pde	NOUN
ejpam-6325	56	12	to	to	ADP
ejpam-6325	56	13	an	an	DET
ejpam-6325	56	14	ordinary	ordinary	ADJ
ejpam-6325	56	15	differential	differential	ADJ
ejpam-6325	56	16	equation	equation	NOUN
ejpam-6325	56	17	,	,	PUNCT
ejpam-6325	56	18	significantly	significantly	ADV
ejpam-6325	56	19	simplifying	simplify	VERB
ejpam-6325	56	20	the	the	DET
ejpam-6325	56	21	solution	solution	NOUN
ejpam-6325	56	22	process	process	NOUN
ejpam-6325	56	23	.	.	PUNCT
ejpam-6325	57	1	unlike	unlike	ADP
ejpam-6325	57	2	perturbative	perturbative	ADJ
ejpam-6325	57	3	or	or	CCONJ
ejpam-6325	57	4	numerical	numerical	ADJ
ejpam-6325	57	5	techniques	technique	NOUN
ejpam-6325	57	6	,	,	PUNCT
ejpam-6325	57	7	generalized	generalize	VERB
ejpam-6325	57	8	first	first	ADJ
ejpam-6325	57	9	integral	integral	ADJ
ejpam-6325	57	10	method	method	NOUN
ejpam-6325	57	11	allows	allow	VERB
ejpam-6325	57	12	for	for	ADP
ejpam-6325	57	13	the	the	DET
ejpam-6325	57	14	direct	direct	ADJ
ejpam-6325	57	15	construction	construction	NOUN
ejpam-6325	57	16	of	of	ADP
ejpam-6325	57	17	exact	exact	ADJ
ejpam-6325	57	18	traveling	traveling	ADJ
ejpam-6325	57	19	wave	wave	NOUN
ejpam-6325	57	20	solutions	solution	NOUN
ejpam-6325	57	21	.	.	PUNCT
ejpam-6325	58	1	in	in	ADP
ejpam-6325	58	2	this	this	DET
ejpam-6325	58	3	study	study	NOUN
ejpam-6325	58	4	,	,	PUNCT
ejpam-6325	58	5	we	we	PRON
ejpam-6325	58	6	conduct	conduct	VERB
ejpam-6325	58	7	an	an	DET
ejpam-6325	58	8	analytical	analytical	ADJ
ejpam-6325	58	9	investigation	investigation	NOUN
ejpam-6325	58	10	of	of	ADP
ejpam-6325	58	11	the	the	DET
ejpam-6325	58	12	telegrapher	telegrapher	NOUN
ejpam-6325	58	13	’s	’s	PART
ejpam-6325	58	14	equation	equation	NOUN
ejpam-6325	58	15	with	with	ADP
ejpam-6325	58	16	damping	damp	VERB
ejpam-6325	58	17	and	and	CCONJ
ejpam-6325	58	18	harmonic	harmonic	ADJ
ejpam-6325	58	19	potential	potential	NOUN
ejpam-6325	58	20	using	use	VERB
ejpam-6325	58	21	the	the	DET
ejpam-6325	58	22	generalized	generalized	ADJ
ejpam-6325	58	23	first	first	ADJ
ejpam-6325	58	24	integral	integral	ADJ
ejpam-6325	58	25	method	method	NOUN
ejpam-6325	58	26	.	.	PUNCT
ejpam-6325	59	1	through	through	ADP
ejpam-6325	59	2	an	an	DET
ejpam-6325	59	3	appropriate	appropriate	ADJ
ejpam-6325	59	4	wave	wave	NOUN
ejpam-6325	59	5	transformation	transformation	NOUN
ejpam-6325	59	6	,	,	PUNCT
ejpam-6325	59	7	we	we	PRON
ejpam-6325	59	8	reduce	reduce	VERB
ejpam-6325	59	9	the	the	DET
ejpam-6325	59	10	equation	equation	NOUN
ejpam-6325	59	11	to	to	ADP
ejpam-6325	59	12	an	an	DET
ejpam-6325	59	13	form	form	NOUN
ejpam-6325	59	14	and	and	CCONJ
ejpam-6325	59	15	systematically	systematically	ADV
ejpam-6325	59	16	derive	derive	ADJ
ejpam-6325	59	17	exact	exact	ADJ
ejpam-6325	59	18	solutions	solution	NOUN
ejpam-6325	59	19	under	under	ADP
ejpam-6325	59	20	varying	vary	VERB
ejpam-6325	59	21	conditions	condition	NOUN
ejpam-6325	59	22	.	.	PUNCT
ejpam-6325	60	1	these	these	DET
ejpam-6325	60	2	solutions	solution	NOUN
ejpam-6325	60	3	offer	offer	VERB
ejpam-6325	60	4	insight	insight	NOUN
ejpam-6325	60	5	into	into	ADP
ejpam-6325	60	6	how	how	SCONJ
ejpam-6325	60	7	damping	damp	VERB
ejpam-6325	60	8	influences	influence	NOUN
ejpam-6325	60	9	wave	wave	NOUN
ejpam-6325	60	10	behavior	behavior	NOUN
ejpam-6325	60	11	,	,	PUNCT
ejpam-6325	60	12	including	include	VERB
ejpam-6325	60	13	attenuation	attenuation	NOUN
ejpam-6325	60	14	,	,	PUNCT
ejpam-6325	60	15	distortion	distortion	NOUN
ejpam-6325	60	16	,	,	PUNCT
ejpam-6325	60	17	and	and	CCONJ
ejpam-6325	60	18	propagation	propagation	NOUN
ejpam-6325	60	19	speed	speed	NOUN
ejpam-6325	60	20	variation	variation	NOUN
ejpam-6325	60	21	.	.	PUNCT
ejpam-6325	61	1	the	the	DET
ejpam-6325	61	2	generalized	generalized	ADJ
ejpam-6325	61	3	first	first	ADJ
ejpam-6325	61	4	integral	integral	ADJ
ejpam-6325	61	5	method	method	NOUN
ejpam-6325	61	6	not	not	PART
ejpam-6325	61	7	only	only	ADV
ejpam-6325	61	8	simplifies	simplify	VERB
ejpam-6325	61	9	the	the	DET
ejpam-6325	61	10	analytical	analytical	ADJ
ejpam-6325	61	11	process	process	NOUN
ejpam-6325	61	12	but	but	CCONJ
ejpam-6325	61	13	also	also	ADV
ejpam-6325	61	14	deepens	deepen	VERB
ejpam-6325	61	15	our	our	PRON
ejpam-6325	61	16	understanding	understanding	NOUN
ejpam-6325	61	17	of	of	ADP
ejpam-6325	61	18	dissipative	dissipative	ADJ
ejpam-6325	61	19	wave	wave	NOUN
ejpam-6325	61	20	phenomena	phenomenon	NOUN
ejpam-6325	61	21	.	.	PUNCT
ejpam-6325	62	1	given	give	VERB
ejpam-6325	62	2	its	its	PRON
ejpam-6325	62	3	applicability	applicability	NOUN
ejpam-6325	62	4	to	to	ADP
ejpam-6325	62	5	problems	problem	NOUN
ejpam-6325	62	6	in	in	ADP
ejpam-6325	62	7	signal	signal	ADJ
ejpam-6325	62	8	transmission	transmission	NOUN
ejpam-6325	62	9	,	,	PUNCT
ejpam-6325	62	10	mechanical	mechanical	ADJ
ejpam-6325	62	11	systems	system	NOUN
ejpam-6325	62	12	,	,	PUNCT
ejpam-6325	62	13	and	and	CCONJ
ejpam-6325	62	14	thermal	thermal	ADJ
ejpam-6325	62	15	conm	conm	NOUN
ejpam-6325	62	16	.	.	PUNCT
ejpam-6325	63	1	noman	noman	PROPN
ejpam-6325	63	2	et	et	PROPN
ejpam-6325	63	3	al	al	PROPN
ejpam-6325	63	4	.	.	PUNCT
ejpam-6325	63	5	/	/	SYM
ejpam-6325	63	6	eur	eur	PROPN
ejpam-6325	63	7	.	.	PUNCT
ejpam-6325	64	1	j.	j.	PROPN
ejpam-6325	64	2	pure	pure	PROPN
ejpam-6325	64	3	appl	appl	PROPN
ejpam-6325	64	4	.	.	PROPN
ejpam-6325	64	5	math	math	PROPN
ejpam-6325	64	6	,	,	PUNCT
ejpam-6325	64	7	18	18	NUM
ejpam-6325	64	8	(	(	PUNCT
ejpam-6325	64	9	3	3	NUM
ejpam-6325	64	10	)	)	PUNCT
ejpam-6325	64	11	(	(	PUNCT
ejpam-6325	64	12	2025	2025	NUM
ejpam-6325	64	13	)	)	PUNCT
ejpam-6325	64	14	,	,	PUNCT
ejpam-6325	64	15	6235	6235	NUM
ejpam-6325	64	16	4	4	NUM
ejpam-6325	64	17	of	of	ADP
ejpam-6325	64	18	16	16	NUM
ejpam-6325	64	19	duction	duction	NOUN
ejpam-6325	64	20	,	,	PUNCT
ejpam-6325	64	21	this	this	DET
ejpam-6325	64	22	method	method	NOUN
ejpam-6325	64	23	serves	serve	VERB
ejpam-6325	64	24	as	as	ADP
ejpam-6325	64	25	a	a	DET
ejpam-6325	64	26	valuable	valuable	ADJ
ejpam-6325	64	27	tool	tool	NOUN
ejpam-6325	64	28	in	in	ADP
ejpam-6325	64	29	both	both	CCONJ
ejpam-6325	64	30	theoretical	theoretical	ADJ
ejpam-6325	64	31	research	research	NOUN
ejpam-6325	64	32	and	and	CCONJ
ejpam-6325	64	33	practical	practical	ADJ
ejpam-6325	64	34	modeling	modeling	NOUN
ejpam-6325	64	35	within	within	ADP
ejpam-6325	64	36	applied	applied	ADJ
ejpam-6325	64	37	mathematics	mathematic	NOUN
ejpam-6325	64	38	.	.	PUNCT
ejpam-6325	65	1	the	the	DET
ejpam-6325	65	2	structure	structure	NOUN
ejpam-6325	65	3	of	of	ADP
ejpam-6325	65	4	the	the	DET
ejpam-6325	65	5	paper	paper	NOUN
ejpam-6325	65	6	is	be	AUX
ejpam-6325	65	7	as	as	SCONJ
ejpam-6325	65	8	follows	follow	VERB
ejpam-6325	65	9	.	.	PUNCT
ejpam-6325	66	1	in	in	ADP
ejpam-6325	66	2	section	section	NOUN
ejpam-6325	66	3	2	2	NUM
ejpam-6325	66	4	,	,	PUNCT
ejpam-6325	66	5	we	we	PRON
ejpam-6325	66	6	provide	provide	VERB
ejpam-6325	66	7	a	a	DET
ejpam-6325	66	8	concise	concise	ADJ
ejpam-6325	66	9	overview	overview	NOUN
ejpam-6325	66	10	of	of	ADP
ejpam-6325	66	11	the	the	DET
ejpam-6325	66	12	generalized	generalized	ADJ
ejpam-6325	66	13	first	first	ADJ
ejpam-6325	66	14	integral	integral	ADJ
ejpam-6325	66	15	method	method	NOUN
ejpam-6325	66	16	.	.	PUNCT
ejpam-6325	67	1	section	section	NOUN
ejpam-6325	67	2	3	3	NUM
ejpam-6325	67	3	applies	apply	VERB
ejpam-6325	67	4	this	this	DET
ejpam-6325	67	5	method	method	NOUN
ejpam-6325	67	6	to	to	PART
ejpam-6325	67	7	derive	derive	VERB
ejpam-6325	67	8	exact	exact	ADJ
ejpam-6325	67	9	solutions	solution	NOUN
ejpam-6325	67	10	of	of	ADP
ejpam-6325	67	11	the	the	DET
ejpam-6325	67	12	telegrapher	telegrapher	NOUN
ejpam-6325	67	13	’s	’s	PART
ejpam-6325	67	14	equation	equation	NOUN
ejpam-6325	67	15	with	with	ADP
ejpam-6325	67	16	damping	damp	VERB
ejpam-6325	67	17	and	and	CCONJ
ejpam-6325	67	18	harmonic	harmonic	ADJ
ejpam-6325	67	19	potential	potential	NOUN
ejpam-6325	67	20	.	.	PUNCT
ejpam-6325	68	1	section	section	NOUN
ejpam-6325	68	2	4	4	NUM
ejpam-6325	68	3	presents	present	VERB
ejpam-6325	68	4	a	a	DET
ejpam-6325	68	5	detailed	detailed	ADJ
ejpam-6325	68	6	discussion	discussion	NOUN
ejpam-6325	68	7	of	of	ADP
ejpam-6325	68	8	the	the	DET
ejpam-6325	68	9	results	result	NOUN
ejpam-6325	68	10	,	,	PUNCT
ejpam-6325	68	11	including	include	VERB
ejpam-6325	68	12	physical	physical	ADJ
ejpam-6325	68	13	interpretations	interpretation	NOUN
ejpam-6325	68	14	and	and	CCONJ
ejpam-6325	68	15	stability	stability	NOUN
ejpam-6325	68	16	considerations	consideration	NOUN
ejpam-6325	68	17	.	.	PUNCT
ejpam-6325	69	1	finally	finally	ADV
ejpam-6325	69	2	,	,	PUNCT
ejpam-6325	69	3	section	section	NOUN
ejpam-6325	69	4	5	5	NUM
ejpam-6325	69	5	offers	offer	VERB
ejpam-6325	69	6	graphical	graphical	ADJ
ejpam-6325	69	7	representations	representation	NOUN
ejpam-6325	69	8	of	of	ADP
ejpam-6325	69	9	the	the	DET
ejpam-6325	69	10	obtained	obtain	VERB
ejpam-6325	69	11	solutions	solution	NOUN
ejpam-6325	69	12	to	to	PART
ejpam-6325	69	13	illustrate	illustrate	VERB
ejpam-6325	69	14	their	their	PRON
ejpam-6325	69	15	spatial	spatial	ADJ
ejpam-6325	69	16	and	and	CCONJ
ejpam-6325	69	17	temporal	temporal	ADJ
ejpam-6325	69	18	behaviors	behavior	NOUN
ejpam-6325	69	19	.	.	PUNCT
ejpam-6325	70	1	2	2	X
ejpam-6325	70	2	.	.	X
ejpam-6325	70	3	structural	structural	ADJ
ejpam-6325	70	4	layout	layout	NOUN
ejpam-6325	70	5	of	of	ADP
ejpam-6325	70	6	the	the	DET
ejpam-6325	70	7	generalized	generalized	ADJ
ejpam-6325	70	8	first	first	ADJ
ejpam-6325	70	9	integral	integral	ADJ
ejpam-6325	70	10	method	method	NOUN
ejpam-6325	70	11	step	step	NOUN
ejpam-6325	70	12	1	1	NUM
ejpam-6325	70	13	.	.	PUNCT
ejpam-6325	70	14	consider	consider	VERB
ejpam-6325	70	15	a	a	DET
ejpam-6325	70	16	general	general	ADJ
ejpam-6325	70	17	nonlinear	nonlinear	ADJ
ejpam-6325	70	18	pde	pde	NOUN
ejpam-6325	70	19	in	in	ADP
ejpam-6325	70	20	the	the	DET
ejpam-6325	70	21	form	form	NOUN
ejpam-6325	70	22	f	f	PROPN
ejpam-6325	70	23	(	(	PUNCT
ejpam-6325	70	24	u	u	NOUN
ejpam-6325	70	25	,	,	PUNCT
ejpam-6325	70	26	ux	ux	PROPN
ejpam-6325	70	27	,	,	PUNCT
ejpam-6325	70	28	ut	ut	PROPN
ejpam-6325	70	29	,	,	PUNCT
ejpam-6325	70	30	uxx	uxx	PROPN
ejpam-6325	70	31	,	,	PUNCT
ejpam-6325	70	32	uxt	uxt	NOUN
ejpam-6325	70	33	,	,	PUNCT
ejpam-6325	70	34	...	...	PUNCT
ejpam-6325	70	35	)	)	PUNCT
ejpam-6325	71	1	=	=	SYM
ejpam-6325	71	2	0	0	X
ejpam-6325	71	3	.	.	PUNCT
ejpam-6325	72	1	(	(	PUNCT
ejpam-6325	72	2	2	2	X
ejpam-6325	72	3	)	)	PUNCT
ejpam-6325	72	4	to	to	PART
ejpam-6325	72	5	find	find	VERB
ejpam-6325	72	6	the	the	DET
ejpam-6325	72	7	travelling	travel	VERB
ejpam-6325	72	8	wave	wave	NOUN
ejpam-6325	72	9	solutions	solution	NOUN
ejpam-6325	72	10	to	to	ADP
ejpam-6325	72	11	equation	equation	NOUN
ejpam-6325	72	12	(	(	PUNCT
ejpam-6325	72	13	2	2	NUM
ejpam-6325	72	14	)	)	PUNCT
ejpam-6325	72	15	,	,	PUNCT
ejpam-6325	72	16	we	we	PRON
ejpam-6325	72	17	introduce	introduce	VERB
ejpam-6325	72	18	the	the	DET
ejpam-6325	72	19	wave	wave	NOUN
ejpam-6325	72	20	variable	variable	NOUN
ejpam-6325	72	21	ξ	ξ	PROPN
ejpam-6325	72	22	=	=	SYM
ejpam-6325	72	23	x−	x−	PROPN
ejpam-6325	72	24	ct	ct	PROPN
ejpam-6325	72	25	,	,	PUNCT
ejpam-6325	72	26	(	(	PUNCT
ejpam-6325	72	27	3	3	X
ejpam-6325	72	28	)	)	PUNCT
ejpam-6325	72	29	u(x	u(x	PROPN
ejpam-6325	72	30	,	,	PUNCT
ejpam-6325	72	31	t	t	NOUN
ejpam-6325	72	32	)	)	PUNCT
ejpam-6325	72	33	=	=	SYM
ejpam-6325	72	34	u(ξ	u(ξ	NOUN
ejpam-6325	72	35	)	)	PUNCT
ejpam-6325	72	36	,	,	PUNCT
ejpam-6325	72	37	(	(	PUNCT
ejpam-6325	72	38	4	4	X
ejpam-6325	72	39	)	)	PUNCT
ejpam-6325	72	40	differentiating	differentiate	VERB
ejpam-6325	72	41	equation	equation	NOUN
ejpam-6325	72	42	(	(	PUNCT
ejpam-6325	72	43	3	3	NUM
ejpam-6325	72	44	)	)	PUNCT
ejpam-6325	72	45	and	and	CCONJ
ejpam-6325	72	46	(	(	PUNCT
ejpam-6325	72	47	4	4	NUM
ejpam-6325	72	48	)	)	PUNCT
ejpam-6325	72	49	,	,	PUNCT
ejpam-6325	72	50	according	accord	VERB
ejpam-6325	72	51	to	to	ADP
ejpam-6325	72	52	(	(	PUNCT
ejpam-6325	72	53	2	2	X
ejpam-6325	72	54	)	)	PUNCT
ejpam-6325	72	55	we	we	PRON
ejpam-6325	72	56	have	have	VERB
ejpam-6325	72	57	ux	ux	NOUN
ejpam-6325	72	58	=	=	SYM
ejpam-6325	72	59	u	u	NOUN
ejpam-6325	72	60	′	′	NUM
ejpam-6325	72	61	(	(	PUNCT
ejpam-6325	72	62	ξ	ξ	NOUN
ejpam-6325	72	63	)	)	PUNCT
ejpam-6325	72	64	,	,	PUNCT
ejpam-6325	72	65	(	(	PUNCT
ejpam-6325	72	66	5	5	X
ejpam-6325	72	67	)	)	PUNCT
ejpam-6325	72	68	ut	ut	NOUN
ejpam-6325	73	1	=	=	SYM
ejpam-6325	73	2	−cu′	−cu′	PROPN
ejpam-6325	73	3	(	(	PUNCT
ejpam-6325	73	4	ξ	ξ	NOUN
ejpam-6325	73	5	)	)	PUNCT
ejpam-6325	73	6	,	,	PUNCT
ejpam-6325	73	7	(	(	PUNCT
ejpam-6325	73	8	6	6	NUM
ejpam-6325	73	9	)	)	PUNCT
ejpam-6325	73	10	uxx	uxx	NOUN
ejpam-6325	73	11	=	=	SYM
ejpam-6325	73	12	u	u	PROPN
ejpam-6325	73	13	′′	′′	PROPN
ejpam-6325	73	14	(	(	PUNCT
ejpam-6325	73	15	ξ	ξ	PROPN
ejpam-6325	73	16	)	)	PUNCT
ejpam-6325	73	17	,	,	PUNCT
ejpam-6325	73	18	(	(	PUNCT
ejpam-6325	73	19	7	7	X
ejpam-6325	73	20	)	)	PUNCT
ejpam-6325	73	21	uxt	uxt	NOUN
ejpam-6325	73	22	=	=	SYM
ejpam-6325	73	23	−cu′′	−cu′′	PROPN
ejpam-6325	73	24	(	(	PUNCT
ejpam-6325	73	25	ξ	ξ	NOUN
ejpam-6325	73	26	)	)	PUNCT
ejpam-6325	73	27	,	,	PUNCT
ejpam-6325	73	28	(	(	PUNCT
ejpam-6325	73	29	8)	8)	NUM
ejpam-6325	73	30	and	and	CCONJ
ejpam-6325	73	31	so	so	ADV
ejpam-6325	73	32	on	on	ADV
ejpam-6325	73	33	for	for	ADP
ejpam-6325	73	34	the	the	DET
ejpam-6325	73	35	other	other	ADJ
ejpam-6325	73	36	derivatives	derivative	NOUN
ejpam-6325	73	37	.	.	PUNCT
ejpam-6325	74	1	using	use	VERB
ejpam-6325	74	2	equation	equation	NOUN
ejpam-6325	74	3	(	(	PUNCT
ejpam-6325	74	4	5	5	NUM
ejpam-6325	74	5	-	-	SYM
ejpam-6325	74	6	8)	8)	NUM
ejpam-6325	74	7	the	the	DET
ejpam-6325	74	8	pde	pde	NOUN
ejpam-6325	74	9	(	(	PUNCT
ejpam-6325	74	10	2	2	NUM
ejpam-6325	74	11	)	)	PUNCT
ejpam-6325	74	12	is	be	AUX
ejpam-6325	74	13	converted	convert	VERB
ejpam-6325	74	14	to	to	ADP
ejpam-6325	74	15	an	an	DET
ejpam-6325	74	16	ordinary	ordinary	ADJ
ejpam-6325	74	17	differential	differential	ADJ
ejpam-6325	74	18	equation	equation	NOUN
ejpam-6325	74	19	of	of	ADP
ejpam-6325	74	20	the	the	DET
ejpam-6325	74	21	form	form	NOUN
ejpam-6325	74	22	f	f	PROPN
ejpam-6325	74	23	(	(	PUNCT
ejpam-6325	74	24	u	u	NOUN
ejpam-6325	74	25	,	,	PUNCT
ejpam-6325	74	26	u	u	NOUN
ejpam-6325	74	27	′	′	NOUN
ejpam-6325	74	28	,	,	PUNCT
ejpam-6325	74	29	−cu′	−cu′	PROPN
ejpam-6325	74	30	,	,	PUNCT
ejpam-6325	74	31	u	u	PROPN
ejpam-6325	74	32	′′	′′	PROPN
ejpam-6325	74	33	,	,	PUNCT
ejpam-6325	74	34	−cu′′	−cu′′	PROPN
ejpam-6325	74	35	,	,	PUNCT
ejpam-6325	74	36	...	...	PUNCT
ejpam-6325	74	37	)	)	PUNCT
ejpam-6325	75	1	=	=	SYM
ejpam-6325	75	2	0	0	X
ejpam-6325	75	3	.	.	PUNCT
ejpam-6325	75	4	(	(	PUNCT
ejpam-6325	75	5	9	9	NUM
ejpam-6325	75	6	)	)	PUNCT
ejpam-6325	75	7	where	where	SCONJ
ejpam-6325	75	8	u	u	NOUN
ejpam-6325	75	9	=	=	SYM
ejpam-6325	75	10	u(ξ	u(ξ	NOUN
ejpam-6325	75	11	)	)	PUNCT
ejpam-6325	75	12	is	be	AUX
ejpam-6325	75	13	an	an	DET
ejpam-6325	75	14	unknown	unknown	ADJ
ejpam-6325	75	15	function	function	NOUN
ejpam-6325	75	16	,	,	PUNCT
ejpam-6325	75	17	f	f	PROPN
ejpam-6325	75	18	is	be	AUX
ejpam-6325	75	19	a	a	DET
ejpam-6325	75	20	polynomial	polynomial	NOUN
ejpam-6325	75	21	in	in	ADP
ejpam-6325	75	22	the	the	DET
ejpam-6325	75	23	variable	variable	ADJ
ejpam-6325	75	24	u	u	NOUN
ejpam-6325	75	25	and	and	CCONJ
ejpam-6325	75	26	its	its	PRON
ejpam-6325	75	27	derivatives	derivative	NOUN
ejpam-6325	75	28	.	.	PUNCT
ejpam-6325	76	1	step	step	NOUN
ejpam-6325	76	2	2	2	NUM
ejpam-6325	76	3	.	.	PUNCT
ejpam-6325	76	4	suppose	suppose	VERB
ejpam-6325	76	5	the	the	DET
ejpam-6325	76	6	solution	solution	NOUN
ejpam-6325	76	7	of	of	ADP
ejpam-6325	76	8	ode	ode	PROPN
ejpam-6325	76	9	(	(	PUNCT
ejpam-6325	76	10	9	9	NUM
ejpam-6325	76	11	)	)	PUNCT
ejpam-6325	76	12	can	can	AUX
ejpam-6325	76	13	be	be	AUX
ejpam-6325	76	14	written	write	VERB
ejpam-6325	76	15	as	as	SCONJ
ejpam-6325	76	16	follows	follow	VERB
ejpam-6325	76	17	:	:	PUNCT
ejpam-6325	76	18	u(x	u(x	PROPN
ejpam-6325	76	19	,	,	PUNCT
ejpam-6325	76	20	t	t	NOUN
ejpam-6325	76	21	)	)	PUNCT
ejpam-6325	76	22	=	=	SYM
ejpam-6325	77	1	f(ξ	f(ξ	NOUN
ejpam-6325	77	2	)	)	PUNCT
ejpam-6325	77	3	,	,	PUNCT
ejpam-6325	77	4	(	(	PUNCT
ejpam-6325	77	5	10	10	NUM
ejpam-6325	77	6	)	)	PUNCT
ejpam-6325	77	7	and	and	CCONJ
ejpam-6325	77	8	furthermore	furthermore	ADV
ejpam-6325	77	9	,	,	PUNCT
ejpam-6325	77	10	we	we	PRON
ejpam-6325	77	11	introduce	introduce	VERB
ejpam-6325	77	12	a	a	DET
ejpam-6325	77	13	new	new	ADJ
ejpam-6325	77	14	independent	independent	ADJ
ejpam-6325	77	15	variable	variable	NOUN
ejpam-6325	77	16	{	{	PUNCT
ejpam-6325	77	17	x(ξ	x(ξ	PROPN
ejpam-6325	77	18	)	)	PUNCT
ejpam-6325	77	19	=	=	SYM
ejpam-6325	77	20	f(ξ	f(ξ	X
ejpam-6325	77	21	)	)	PUNCT
ejpam-6325	77	22	y	y	PROPN
ejpam-6325	77	23	(	(	PUNCT
ejpam-6325	77	24	ξ	ξ	PROPN
ejpam-6325	77	25	)	)	PUNCT
ejpam-6325	77	26	=	=	SYM
ejpam-6325	77	27	f	f	PROPN
ejpam-6325	77	28	′(ξ	′(ξ	NOUN
ejpam-6325	77	29	)	)	PUNCT
ejpam-6325	77	30	(	(	PUNCT
ejpam-6325	77	31	11	11	NUM
ejpam-6325	77	32	)	)	PUNCT
ejpam-6325	77	33	m.	m.	NOUN
ejpam-6325	77	34	noman	noman	PROPN
ejpam-6325	77	35	et	et	PROPN
ejpam-6325	77	36	al	al	PROPN
ejpam-6325	77	37	.	.	PUNCT
ejpam-6325	77	38	/	/	SYM
ejpam-6325	77	39	eur	eur	PROPN
ejpam-6325	77	40	.	.	PUNCT
ejpam-6325	78	1	j.	j.	PROPN
ejpam-6325	78	2	pure	pure	PROPN
ejpam-6325	78	3	appl	appl	PROPN
ejpam-6325	78	4	.	.	PROPN
ejpam-6325	78	5	math	math	PROPN
ejpam-6325	78	6	,	,	PUNCT
ejpam-6325	78	7	18	18	NUM
ejpam-6325	78	8	(	(	PUNCT
ejpam-6325	78	9	3	3	NUM
ejpam-6325	78	10	)	)	PUNCT
ejpam-6325	78	11	(	(	PUNCT
ejpam-6325	78	12	2025	2025	NUM
ejpam-6325	78	13	)	)	PUNCT
ejpam-6325	78	14	,	,	PUNCT
ejpam-6325	78	15	6235	6235	NUM
ejpam-6325	78	16	5	5	NUM
ejpam-6325	78	17	of	of	ADP
ejpam-6325	78	18	16	16	NUM
ejpam-6325	78	19	step	step	NOUN
ejpam-6325	78	20	3	3	NUM
ejpam-6325	78	21	.	.	PUNCT
ejpam-6325	79	1	under	under	ADP
ejpam-6325	79	2	the	the	DET
ejpam-6325	79	3	conditions	condition	NOUN
ejpam-6325	79	4	of	of	ADP
ejpam-6325	79	5	step	step	NOUN
ejpam-6325	79	6	2	2	NUM
ejpam-6325	79	7	,	,	PUNCT
ejpam-6325	79	8	equation	equation	NOUN
ejpam-6325	79	9	(	(	PUNCT
ejpam-6325	79	10	9	9	NUM
ejpam-6325	79	11	)	)	PUNCT
ejpam-6325	79	12	can	can	AUX
ejpam-6325	79	13	be	be	AUX
ejpam-6325	79	14	converted	convert	VERB
ejpam-6325	79	15	to	to	ADP
ejpam-6325	79	16	a	a	DET
ejpam-6325	79	17	system	system	NOUN
ejpam-6325	79	18	of	of	ADP
ejpam-6325	79	19	nonlinear	nonlinear	ADJ
ejpam-6325	79	20	odes	ode	NOUN
ejpam-6325	79	21	as	as	SCONJ
ejpam-6325	79	22	follows	follow	VERB
ejpam-6325	79	23	{	{	PUNCT
ejpam-6325	79	24	x	x	NOUN
ejpam-6325	79	25	′(ξ	′(ξ	NOUN
ejpam-6325	79	26	)	)	PUNCT
ejpam-6325	80	1	=	=	SYM
ejpam-6325	80	2	y	y	PROPN
ejpam-6325	80	3	(	(	PUNCT
ejpam-6325	80	4	ξ	ξ	PROPN
ejpam-6325	80	5	)	)	PUNCT
ejpam-6325	80	6	y	y	PROPN
ejpam-6325	80	7	′(ξ	′(ξ	NOUN
ejpam-6325	80	8	)	)	PUNCT
ejpam-6325	80	9	=	=	SYM
ejpam-6325	81	1	f	f	PROPN
ejpam-6325	81	2	(	(	PUNCT
ejpam-6325	81	3	x(ξ	x(ξ	PROPN
ejpam-6325	81	4	)	)	PUNCT
ejpam-6325	81	5	,	,	PUNCT
ejpam-6325	81	6	y	y	PROPN
ejpam-6325	81	7	(	(	PUNCT
ejpam-6325	81	8	ξ	ξ	NOUN
ejpam-6325	81	9	)	)	PUNCT
ejpam-6325	81	10	)	)	PUNCT
ejpam-6325	81	11	(	(	PUNCT
ejpam-6325	81	12	12	12	NUM
ejpam-6325	81	13	)	)	PUNCT
ejpam-6325	81	14	if	if	SCONJ
ejpam-6325	81	15	we	we	PRON
ejpam-6325	81	16	are	be	AUX
ejpam-6325	81	17	able	able	ADJ
ejpam-6325	81	18	to	to	PART
ejpam-6325	81	19	find	find	VERB
ejpam-6325	81	20	the	the	DET
ejpam-6325	81	21	integrals	integral	NOUN
ejpam-6325	81	22	for	for	ADP
ejpam-6325	81	23	equation	equation	NOUN
ejpam-6325	81	24	(	(	PUNCT
ejpam-6325	81	25	12	12	NUM
ejpam-6325	81	26	)	)	PUNCT
ejpam-6325	81	27	,	,	PUNCT
ejpam-6325	81	28	the	the	DET
ejpam-6325	81	29	general	general	ADJ
ejpam-6325	81	30	solutions	solution	NOUN
ejpam-6325	81	31	to	to	ADP
ejpam-6325	81	32	these	these	DET
ejpam-6325	81	33	equations	equation	NOUN
ejpam-6325	81	34	can	can	AUX
ejpam-6325	81	35	be	be	AUX
ejpam-6325	81	36	determined	determine	VERB
ejpam-6325	81	37	directly	directly	ADV
ejpam-6325	81	38	.	.	PUNCT
ejpam-6325	82	1	however	however	ADV
ejpam-6325	82	2	,	,	PUNCT
ejpam-6325	82	3	in	in	ADP
ejpam-6325	82	4	most	most	ADJ
ejpam-6325	82	5	cases	case	NOUN
ejpam-6325	82	6	,	,	PUNCT
ejpam-6325	82	7	even	even	ADV
ejpam-6325	82	8	finding	find	VERB
ejpam-6325	82	9	a	a	DET
ejpam-6325	82	10	single	single	ADJ
ejpam-6325	82	11	first	first	ADJ
ejpam-6325	82	12	integral	integral	ADJ
ejpam-6325	82	13	is	be	AUX
ejpam-6325	82	14	challenging	challenging	ADJ
ejpam-6325	82	15	.	.	PUNCT
ejpam-6325	83	1	this	this	DET
ejpam-6325	83	2	difficulty	difficulty	NOUN
ejpam-6325	83	3	arises	arise	VERB
ejpam-6325	83	4	because	because	SCONJ
ejpam-6325	83	5	,	,	PUNCT
ejpam-6325	83	6	for	for	ADP
ejpam-6325	83	7	a	a	DET
ejpam-6325	83	8	given	give	VERB
ejpam-6325	83	9	autonomous	autonomous	ADJ
ejpam-6325	83	10	system	system	NOUN
ejpam-6325	83	11	,	,	PUNCT
ejpam-6325	83	12	there	there	PRON
ejpam-6325	83	13	is	be	VERB
ejpam-6325	83	14	no	no	DET
ejpam-6325	83	15	systematic	systematic	ADJ
ejpam-6325	83	16	theory	theory	NOUN
ejpam-6325	83	17	that	that	PRON
ejpam-6325	83	18	explicitly	explicitly	ADV
ejpam-6325	83	19	guides	guide	VERB
ejpam-6325	83	20	us	we	PRON
ejpam-6325	83	21	on	on	ADP
ejpam-6325	83	22	how	how	SCONJ
ejpam-6325	83	23	to	to	PART
ejpam-6325	83	24	find	find	VERB
ejpam-6325	83	25	its	its	PRON
ejpam-6325	83	26	first	first	ADJ
ejpam-6325	83	27	integrals	integral	NOUN
ejpam-6325	83	28	,	,	PUNCT
ejpam-6325	83	29	nor	nor	CCONJ
ejpam-6325	83	30	is	be	AUX
ejpam-6325	83	31	there	there	PRON
ejpam-6325	83	32	a	a	DET
ejpam-6325	83	33	clear	clear	ADJ
ejpam-6325	83	34	method	method	NOUN
ejpam-6325	83	35	for	for	ADP
ejpam-6325	83	36	identifying	identify	VERB
ejpam-6325	83	37	what	what	PRON
ejpam-6325	83	38	these	these	DET
ejpam-6325	83	39	first	first	ADJ
ejpam-6325	83	40	integrals	integral	NOUN
ejpam-6325	83	41	are	be	AUX
ejpam-6325	83	42	.	.	PUNCT
ejpam-6325	84	1	to	to	PART
ejpam-6325	84	2	address	address	VERB
ejpam-6325	84	3	this	this	PRON
ejpam-6325	84	4	,	,	PUNCT
ejpam-6325	84	5	we	we	PRON
ejpam-6325	84	6	will	will	AUX
ejpam-6325	84	7	apply	apply	VERB
ejpam-6325	84	8	the	the	DET
ejpam-6325	84	9	division	division	NOUN
ejpam-6325	84	10	theorem	theorem	VERB
ejpam-6325	84	11	for	for	ADP
ejpam-6325	84	12	laurent	laurent	NOUN
ejpam-6325	84	13	polynomials	polynomial	NOUN
ejpam-6325	84	14	to	to	PART
ejpam-6325	84	15	obtain	obtain	VERB
ejpam-6325	84	16	one	one	NUM
ejpam-6325	84	17	first	first	ADJ
ejpam-6325	84	18	integral	integral	ADJ
ejpam-6325	84	19	for	for	ADP
ejpam-6325	84	20	equation	equation	NOUN
ejpam-6325	84	21	(	(	PUNCT
ejpam-6325	84	22	13	13	NUM
ejpam-6325	84	23	)	)	PUNCT
ejpam-6325	84	24	and	and	CCONJ
ejpam-6325	84	25	(	(	PUNCT
ejpam-6325	84	26	14	14	NUM
ejpam-6325	84	27	)	)	PUNCT
ejpam-6325	85	1	[	[	X
ejpam-6325	85	2	20	20	NUM
ejpam-6325	85	3	]	]	PUNCT
ejpam-6325	85	4	,	,	PUNCT
ejpam-6325	85	5	which	which	PRON
ejpam-6325	85	6	will	will	AUX
ejpam-6325	85	7	reduce	reduce	VERB
ejpam-6325	85	8	equation	equation	NOUN
ejpam-6325	85	9	(	(	PUNCT
ejpam-6325	85	10	9	9	NUM
ejpam-6325	85	11	)	)	PUNCT
ejpam-6325	85	12	to	to	ADP
ejpam-6325	85	13	a	a	DET
ejpam-6325	85	14	first	first	ADJ
ejpam-6325	85	15	or	or	CCONJ
ejpam-6325	85	16	second	second	ADJ
ejpam-6325	85	17	order	order	NOUN
ejpam-6325	85	18	,	,	PUNCT
ejpam-6325	85	19	integrable	integrable	ADJ
ejpam-6325	85	20	ordinary	ordinary	ADJ
ejpam-6325	85	21	differential	differential	ADJ
ejpam-6325	85	22	equation	equation	NOUN
ejpam-6325	85	23	(	(	PUNCT
ejpam-6325	85	24	ode	ode	PROPN
ejpam-6325	85	25	)	)	PUNCT
ejpam-6325	85	26	.	.	PUNCT
ejpam-6325	86	1	the	the	DET
ejpam-6325	86	2	exact	exact	ADJ
ejpam-6325	86	3	solution	solution	NOUN
ejpam-6325	86	4	to	to	ADP
ejpam-6325	86	5	equation	equation	NOUN
ejpam-6325	86	6	(	(	PUNCT
ejpam-6325	86	7	9	9	NUM
ejpam-6325	86	8	)	)	PUNCT
ejpam-6325	86	9	can	can	AUX
ejpam-6325	86	10	then	then	ADV
ejpam-6325	86	11	be	be	AUX
ejpam-6325	86	12	obtained	obtain	VERB
ejpam-6325	86	13	by	by	ADP
ejpam-6325	86	14	solving	solve	VERB
ejpam-6325	86	15	this	this	DET
ejpam-6325	86	16	reduced	reduce	VERB
ejpam-6325	86	17	equation	equation	NOUN
ejpam-6325	86	18	.	.	PUNCT
ejpam-6325	87	1	division	division	NOUN
ejpam-6325	87	2	theorem	theorem	VERB
ejpam-6325	87	3	for	for	ADP
ejpam-6325	87	4	laurent	laurent	NOUN
ejpam-6325	87	5	polynomials	polynomial	NOUN
ejpam-6325	87	6	suppose	suppose	VERB
ejpam-6325	87	7	p	p	X
ejpam-6325	87	8	(	(	PUNCT
ejpam-6325	87	9	ω	ω	PROPN
ejpam-6325	87	10	,	,	PUNCT
ejpam-6325	87	11	z	z	NOUN
ejpam-6325	87	12	)	)	PUNCT
ejpam-6325	87	13	and	and	CCONJ
ejpam-6325	87	14	q(ω	q(ω	PROPN
ejpam-6325	87	15	,	,	PUNCT
ejpam-6325	87	16	z	z	NOUN
ejpam-6325	87	17	)	)	PUNCT
ejpam-6325	87	18	are	be	AUX
ejpam-6325	87	19	two	two	NUM
ejpam-6325	87	20	laurent	laurent	NOUN
ejpam-6325	87	21	polynomials	polynomial	NOUN
ejpam-6325	87	22	in	in	ADP
ejpam-6325	87	23	c(ω	c(ω	PROPN
ejpam-6325	87	24	,	,	PUNCT
ejpam-6325	87	25	z	z	NOUN
ejpam-6325	87	26	)	)	PUNCT
ejpam-6325	87	27	and	and	CCONJ
ejpam-6325	87	28	p	p	X
ejpam-6325	87	29	(	(	PUNCT
ejpam-6325	87	30	ω	ω	PROPN
ejpam-6325	87	31	,	,	PUNCT
ejpam-6325	87	32	z	z	NOUN
ejpam-6325	87	33	)	)	PUNCT
ejpam-6325	87	34	is	be	AUX
ejpam-6325	87	35	irreducible	irreducible	ADJ
ejpam-6325	87	36	in	in	ADP
ejpam-6325	87	37	c[ω	c[ω	NOUN
ejpam-6325	87	38	,	,	PUNCT
ejpam-6325	87	39	z	z	X
ejpam-6325	87	40	]	]	X
ejpam-6325	87	41	.	.	PUNCT
ejpam-6325	88	1	if	if	SCONJ
ejpam-6325	88	2	q(ω	q(ω	PROPN
ejpam-6325	88	3	,	,	PUNCT
ejpam-6325	88	4	z	z	NOUN
ejpam-6325	88	5	)	)	PUNCT
ejpam-6325	88	6	vanishes	vanish	VERB
ejpam-6325	88	7	at	at	ADP
ejpam-6325	88	8	any	any	DET
ejpam-6325	88	9	zero	zero	NUM
ejpam-6325	88	10	point	point	NOUN
ejpam-6325	88	11	of	of	ADP
ejpam-6325	88	12	p	p	PROPN
ejpam-6325	88	13	(	(	PUNCT
ejpam-6325	88	14	ω	ω	PROPN
ejpam-6325	88	15	,	,	PUNCT
ejpam-6325	88	16	z	z	PROPN
ejpam-6325	88	17	)	)	PUNCT
ejpam-6325	88	18	then	then	ADV
ejpam-6325	88	19	there	there	PRON
ejpam-6325	88	20	exist	exist	VERB
ejpam-6325	88	21	a	a	DET
ejpam-6325	88	22	laurent	laurent	NOUN
ejpam-6325	88	23	polynomial	polynomial	ADJ
ejpam-6325	88	24	g(ω	g(ω	PROPN
ejpam-6325	88	25	,	,	PUNCT
ejpam-6325	88	26	z	z	NOUN
ejpam-6325	88	27	)	)	PUNCT
ejpam-6325	88	28	in	in	ADP
ejpam-6325	88	29	c[ω	c[ω	NOUN
ejpam-6325	88	30	,	,	PUNCT
ejpam-6325	88	31	z	z	X
ejpam-6325	88	32	]	]	X
ejpam-6325	88	33	such	such	ADJ
ejpam-6325	88	34	that	that	SCONJ
ejpam-6325	88	35	q(ω	q(ω	PROPN
ejpam-6325	88	36	,	,	PUNCT
ejpam-6325	88	37	z)=	z)=	X
ejpam-6325	88	38	p	p	X
ejpam-6325	88	39	(	(	PUNCT
ejpam-6325	88	40	ω	ω	PROPN
ejpam-6325	88	41	,	,	PUNCT
ejpam-6325	88	42	z	z	NOUN
ejpam-6325	88	43	)	)	PUNCT
ejpam-6325	88	44	·	·	PUNCT
ejpam-6325	88	45	g(ω	g(ω	PROPN
ejpam-6325	88	46	,	,	PUNCT
ejpam-6325	88	47	z	z	NOUN
ejpam-6325	88	48	)	)	PUNCT
ejpam-6325	88	49	.	.	PUNCT
ejpam-6325	89	1	3	3	X
ejpam-6325	89	2	.	.	X
ejpam-6325	89	3	employing	employ	VERB
ejpam-6325	89	4	a	a	DET
ejpam-6325	89	5	generalized	generalized	ADJ
ejpam-6325	89	6	first	first	ADJ
ejpam-6325	89	7	integral	integral	ADJ
ejpam-6325	89	8	method	method	NOUN
ejpam-6325	89	9	for	for	ADP
ejpam-6325	89	10	solving	solve	VERB
ejpam-6325	89	11	the	the	DET
ejpam-6325	89	12	telegrapher	telegrapher	NOUN
ejpam-6325	89	13	’s	’s	PART
ejpam-6325	89	14	equation	equation	NOUN
ejpam-6325	89	15	with	with	ADP
ejpam-6325	89	16	damping	damp	VERB
ejpam-6325	89	17	and	and	CCONJ
ejpam-6325	89	18	harmonic	harmonic	ADJ
ejpam-6325	89	19	potential	potential	NOUN
ejpam-6325	89	20	consider	consider	VERB
ejpam-6325	89	21	the	the	DET
ejpam-6325	89	22	wave	wave	NOUN
ejpam-6325	89	23	variable	variable	NOUN
ejpam-6325	89	24	,	,	PUNCT
ejpam-6325	89	25	ξ	ξ	X
ejpam-6325	89	26	=	=	SYM
ejpam-6325	89	27	x+	x+	PROPN
ejpam-6325	89	28	t	t	PROPN
ejpam-6325	89	29	,	,	PUNCT
ejpam-6325	89	30	(	(	PUNCT
ejpam-6325	89	31	13	13	NUM
ejpam-6325	89	32	)	)	PUNCT
ejpam-6325	89	33	and	and	CCONJ
ejpam-6325	89	34	the	the	DET
ejpam-6325	89	35	function	function	NOUN
ejpam-6325	89	36	transformation	transformation	NOUN
ejpam-6325	89	37	as	as	ADP
ejpam-6325	89	38	u(x	u(x	NOUN
ejpam-6325	89	39	,	,	PUNCT
ejpam-6325	89	40	t	t	NOUN
ejpam-6325	89	41	)	)	PUNCT
ejpam-6325	90	1	=	=	SYM
ejpam-6325	90	2	f(ξ	f(ξ	NOUN
ejpam-6325	90	3	)	)	PUNCT
ejpam-6325	90	4	,	,	PUNCT
ejpam-6325	90	5	(	(	PUNCT
ejpam-6325	90	6	14	14	X
ejpam-6325	90	7	)	)	PUNCT
ejpam-6325	90	8	differentiating	differentiate	VERB
ejpam-6325	90	9	equations	equation	NOUN
ejpam-6325	90	10	(	(	PUNCT
ejpam-6325	90	11	13	13	NUM
ejpam-6325	90	12	)	)	PUNCT
ejpam-6325	90	13	and	and	CCONJ
ejpam-6325	90	14	(	(	PUNCT
ejpam-6325	90	15	14	14	NUM
ejpam-6325	90	16	)	)	PUNCT
ejpam-6325	90	17	according	accord	VERB
ejpam-6325	90	18	to	to	ADP
ejpam-6325	90	19	(	(	PUNCT
ejpam-6325	90	20	1	1	NUM
ejpam-6325	90	21	)	)	PUNCT
ejpam-6325	90	22	,	,	PUNCT
ejpam-6325	90	23	we	we	PRON
ejpam-6325	90	24	have	have	VERB
ejpam-6325	90	25	ut	ut	PROPN
ejpam-6325	91	1	=	=	SYM
ejpam-6325	91	2	f	f	X
ejpam-6325	92	1	′	′	NUM
ejpam-6325	92	2	(	(	PUNCT
ejpam-6325	92	3	ξ	ξ	NOUN
ejpam-6325	92	4	)	)	PUNCT
ejpam-6325	92	5	,	,	PUNCT
ejpam-6325	92	6	utt	utt	PROPN
ejpam-6325	92	7	=	=	SYM
ejpam-6325	92	8	f	f	X
ejpam-6325	92	9	′′	′′	PROPN
ejpam-6325	92	10	(	(	PUNCT
ejpam-6325	92	11	ξ	ξ	PROPN
ejpam-6325	92	12	)	)	PUNCT
ejpam-6325	92	13	,	,	PUNCT
ejpam-6325	92	14	ux	ux	PROPN
ejpam-6325	92	15	=	=	SYM
ejpam-6325	92	16	f	f	PROPN
ejpam-6325	93	1	′	′	NUM
ejpam-6325	93	2	(	(	PUNCT
ejpam-6325	93	3	ξ	ξ	NOUN
ejpam-6325	93	4	)	)	PUNCT
ejpam-6325	93	5	,	,	PUNCT
ejpam-6325	93	6	uxx	uxx	X
ejpam-6325	93	7	=	=	SYM
ejpam-6325	94	1	f	f	X
ejpam-6325	94	2	′′	′′	PROPN
ejpam-6325	94	3	(	(	PUNCT
ejpam-6325	94	4	ξ	ξ	PROPN
ejpam-6325	94	5	)	)	PUNCT
ejpam-6325	94	6	,	,	PUNCT
ejpam-6325	94	7	now	now	ADV
ejpam-6325	94	8	,	,	PUNCT
ejpam-6325	94	9	equation(1	equation(1	PROPN
ejpam-6325	94	10	)	)	PUNCT
ejpam-6325	94	11	becomes	become	VERB
ejpam-6325	94	12	f	f	PROPN
ejpam-6325	94	13	′′(ξ	′′(ξ	PROPN
ejpam-6325	94	14	)	)	PUNCT
ejpam-6325	94	15	=	=	PUNCT
ejpam-6325	95	1	(	(	PUNCT
ejpam-6325	95	2	−(α+	−(α+	NUM
ejpam-6325	95	3	β	β	NOUN
ejpam-6325	95	4	)	)	PUNCT
ejpam-6325	95	5	1−	1−	NUM
ejpam-6325	95	6	c2	c2	PROPN
ejpam-6325	95	7	)	)	PUNCT
ejpam-6325	96	1	f	f	PROPN
ejpam-6325	96	2	′(ξ)−	′(ξ)−	PROPN
ejpam-6325	96	3	(	(	PUNCT
ejpam-6325	96	4	αβ	αβ	PROPN
ejpam-6325	96	5	1−	1−	NUM
ejpam-6325	96	6	c2	c2	PROPN
ejpam-6325	96	7	)	)	PUNCT
ejpam-6325	96	8	f(ξ	f(ξ	PROPN
ejpam-6325	96	9	)	)	PUNCT
ejpam-6325	96	10	.	.	PUNCT
ejpam-6325	97	1	(	(	PUNCT
ejpam-6325	97	2	15	15	NUM
ejpam-6325	97	3	)	)	PUNCT
ejpam-6325	97	4	equation	equation	NOUN
ejpam-6325	97	5	(	(	PUNCT
ejpam-6325	97	6	15	15	NUM
ejpam-6325	97	7	)	)	PUNCT
ejpam-6325	97	8	is	be	AUX
ejpam-6325	97	9	the	the	DET
ejpam-6325	97	10	required	require	VERB
ejpam-6325	97	11	ode	ode	NOUN
ejpam-6325	97	12	of	of	ADP
ejpam-6325	97	13	order	order	NOUN
ejpam-6325	97	14	two	two	NUM
ejpam-6325	97	15	,	,	PUNCT
ejpam-6325	97	16	let	let	VERB
ejpam-6325	97	17	{	{	PUNCT
ejpam-6325	97	18	x(ξ	x(ξ	PROPN
ejpam-6325	97	19	)	)	PUNCT
ejpam-6325	97	20	=	=	SYM
ejpam-6325	97	21	f(ξ	f(ξ	X
ejpam-6325	97	22	)	)	PUNCT
ejpam-6325	97	23	y	y	PROPN
ejpam-6325	97	24	(	(	PUNCT
ejpam-6325	97	25	ξ	ξ	PROPN
ejpam-6325	97	26	)	)	PUNCT
ejpam-6325	97	27	=	=	SYM
ejpam-6325	97	28	f	f	PROPN
ejpam-6325	97	29	′(ξ	′(ξ	NOUN
ejpam-6325	97	30	)	)	PUNCT
ejpam-6325	97	31	(	(	PUNCT
ejpam-6325	97	32	16	16	NUM
ejpam-6325	97	33	)	)	PUNCT
ejpam-6325	97	34	{	{	PUNCT
ejpam-6325	97	35	x	x	NOUN
ejpam-6325	97	36	′(ξ	′(ξ	NOUN
ejpam-6325	97	37	)	)	PUNCT
ejpam-6325	97	38	=	=	SYM
ejpam-6325	97	39	f	f	PROPN
ejpam-6325	97	40	′(ξ	′(ξ	PROPN
ejpam-6325	97	41	)	)	PUNCT
ejpam-6325	97	42	y	y	PROPN
ejpam-6325	97	43	′(ξ	′(ξ	NOUN
ejpam-6325	97	44	)	)	PUNCT
ejpam-6325	98	1	=	=	SYM
ejpam-6325	98	2	f	f	X
ejpam-6325	98	3	′′(ξ	′′(ξ	PROPN
ejpam-6325	98	4	)	)	PUNCT
ejpam-6325	98	5	m.	m.	NOUN
ejpam-6325	98	6	noman	noman	PROPN
ejpam-6325	98	7	et	et	PROPN
ejpam-6325	98	8	al	al	PROPN
ejpam-6325	98	9	.	.	PUNCT
ejpam-6325	98	10	/	/	SYM
ejpam-6325	98	11	eur	eur	PROPN
ejpam-6325	98	12	.	.	PUNCT
ejpam-6325	99	1	j.	j.	PROPN
ejpam-6325	99	2	pure	pure	PROPN
ejpam-6325	99	3	appl	appl	PROPN
ejpam-6325	99	4	.	.	PROPN
ejpam-6325	99	5	math	math	PROPN
ejpam-6325	99	6	,	,	PUNCT
ejpam-6325	99	7	18	18	NUM
ejpam-6325	99	8	(	(	PUNCT
ejpam-6325	99	9	3	3	NUM
ejpam-6325	99	10	)	)	PUNCT
ejpam-6325	99	11	(	(	PUNCT
ejpam-6325	99	12	2025	2025	NUM
ejpam-6325	99	13	)	)	PUNCT
ejpam-6325	99	14	,	,	PUNCT
ejpam-6325	99	15	6235	6235	NUM
ejpam-6325	99	16	6	6	NUM
ejpam-6325	99	17	of	of	ADP
ejpam-6325	99	18	16	16	NUM
ejpam-6325	99	19	x	x	SYM
ejpam-6325	99	20	′(ξ	′(ξ	NOUN
ejpam-6325	99	21	)	)	PUNCT
ejpam-6325	100	1	=	=	SYM
ejpam-6325	100	2	y	y	PROPN
ejpam-6325	100	3	(	(	PUNCT
ejpam-6325	100	4	ξ	ξ	PROPN
ejpam-6325	100	5	)	)	PUNCT
ejpam-6325	100	6	y	y	PROPN
ejpam-6325	100	7	′(ξ	′(ξ	NOUN
ejpam-6325	100	8	)	)	PUNCT
ejpam-6325	100	9	=	=	NOUN
ejpam-6325	101	1	(	(	PUNCT
ejpam-6325	101	2	−(α+	−(α+	NUM
ejpam-6325	101	3	β	β	NOUN
ejpam-6325	101	4	)	)	PUNCT
ejpam-6325	101	5	1−	1−	NUM
ejpam-6325	101	6	c2	c2	PROPN
ejpam-6325	101	7	)	)	PUNCT
ejpam-6325	102	1	y	y	PROPN
ejpam-6325	102	2	−	−	PROPN
ejpam-6325	102	3	(	(	PUNCT
ejpam-6325	102	4	αβ	αβ	INTJ
ejpam-6325	102	5	1−	1−	NUM
ejpam-6325	102	6	c2	c2	PROPN
ejpam-6325	102	7	)	)	PUNCT
ejpam-6325	102	8	x	x	PUNCT
ejpam-6325	102	9	thus	thus	ADV
ejpam-6325	102	10	,	,	PUNCT
ejpam-6325	102	11	equation	equation	NOUN
ejpam-6325	102	12	(	(	PUNCT
ejpam-6325	102	13	15	15	NUM
ejpam-6325	102	14	)	)	PUNCT
ejpam-6325	102	15	is	be	AUX
ejpam-6325	102	16	equivalent	equivalent	ADJ
ejpam-6325	102	17	to	to	ADP
ejpam-6325	102	18	the	the	DET
ejpam-6325	102	19	two	two	NUM
ejpam-6325	102	20	dimensional	dimensional	ADJ
ejpam-6325	102	21	autonomous	autonomous	ADJ
ejpam-6325	102	22	system	system	NUM
ejpam-6325	102	23	x	x	SYM
ejpam-6325	102	24	′(ξ	′(ξ	NOUN
ejpam-6325	102	25	)	)	PUNCT
ejpam-6325	103	1	=	=	SYM
ejpam-6325	103	2	y	y	PROPN
ejpam-6325	103	3	(	(	PUNCT
ejpam-6325	103	4	ξ	ξ	PROPN
ejpam-6325	103	5	)	)	PUNCT
ejpam-6325	103	6	y	y	PROPN
ejpam-6325	103	7	′(ξ	′(ξ	NOUN
ejpam-6325	103	8	)	)	PUNCT
ejpam-6325	103	9	=	=	NOUN
ejpam-6325	104	1	(	(	PUNCT
ejpam-6325	104	2	−(α+	−(α+	NUM
ejpam-6325	104	3	β	β	NOUN
ejpam-6325	104	4	)	)	PUNCT
ejpam-6325	104	5	1−	1−	NUM
ejpam-6325	104	6	c2	c2	PROPN
ejpam-6325	104	7	)	)	PUNCT
ejpam-6325	105	1	y	y	PROPN
ejpam-6325	105	2	−	−	PROPN
ejpam-6325	105	3	(	(	PUNCT
ejpam-6325	105	4	αβ	αβ	INTJ
ejpam-6325	105	5	1−	1−	NUM
ejpam-6325	105	6	c2	c2	PROPN
ejpam-6325	105	7	)	)	PUNCT
ejpam-6325	105	8	x	x	X
ejpam-6325	105	9	(	(	PUNCT
ejpam-6325	105	10	17	17	NUM
ejpam-6325	105	11	)	)	PUNCT
ejpam-6325	105	12	let	let	VERB
ejpam-6325	105	13	x(ξ	x(ξ	NOUN
ejpam-6325	105	14	)	)	PUNCT
ejpam-6325	105	15	and	and	CCONJ
ejpam-6325	105	16	y	y	PROPN
ejpam-6325	105	17	(	(	PUNCT
ejpam-6325	105	18	ξ	ξ	PROPN
ejpam-6325	105	19	)	)	PUNCT
ejpam-6325	105	20	be	be	VERB
ejpam-6325	105	21	non	non	ADJ
ejpam-6325	105	22	-	-	ADJ
ejpam-6325	105	23	trivial	trivial	ADJ
ejpam-6325	105	24	solutions	solution	NOUN
ejpam-6325	105	25	of	of	ADP
ejpam-6325	105	26	equation	equation	NOUN
ejpam-6325	105	27	(	(	PUNCT
ejpam-6325	105	28	16	16	NUM
ejpam-6325	105	29	)	)	PUNCT
ejpam-6325	105	30	and	and	CCONJ
ejpam-6325	105	31	let	let	VERB
ejpam-6325	105	32	q(x	q(x	NOUN
ejpam-6325	105	33	,	,	PUNCT
ejpam-6325	105	34	y	y	PROPN
ejpam-6325	105	35	)	)	PUNCT
ejpam-6325	106	1	=	=	PRON
ejpam-6325	106	2	β∑	β∑	PUNCT
ejpam-6325	106	3	k	k	X
ejpam-6325	106	4	=	=	NOUN
ejpam-6325	106	5	α	α	PRON
ejpam-6325	106	6	ak(x)y	ak(x)y	PROPN
ejpam-6325	106	7	k	k	PROPN
ejpam-6325	106	8	is	be	AUX
ejpam-6325	106	9	an	an	DET
ejpam-6325	106	10	irreducible	irreducible	ADJ
ejpam-6325	106	11	laurent	laurent	NOUN
ejpam-6325	106	12	polynomial	polynomial	NOUN
ejpam-6325	106	13	in	in	ADP
ejpam-6325	106	14	c[x(ξ	c[x(ξ	NUM
ejpam-6325	106	15	)	)	PUNCT
ejpam-6325	106	16	,	,	PUNCT
ejpam-6325	106	17	y	y	PROPN
ejpam-6325	106	18	(	(	PUNCT
ejpam-6325	106	19	ξ	ξ	PROPN
ejpam-6325	106	20	)	)	PUNCT
ejpam-6325	106	21	]	]	PUNCT
ejpam-6325	106	22	such	such	ADJ
ejpam-6325	106	23	that	that	SCONJ
ejpam-6325	106	24	q[x(ξ	q[x(ξ	PROPN
ejpam-6325	106	25	)	)	PUNCT
ejpam-6325	106	26	,	,	PUNCT
ejpam-6325	106	27	y	y	PROPN
ejpam-6325	106	28	(	(	PUNCT
ejpam-6325	106	29	ξ	ξ	PROPN
ejpam-6325	106	30	)	)	PUNCT
ejpam-6325	106	31	]	]	PUNCT
ejpam-6325	107	1	=	=	PUNCT
ejpam-6325	107	2	β∑	β∑	PUNCT
ejpam-6325	107	3	k	k	X
ejpam-6325	107	4	=	=	NOUN
ejpam-6325	107	5	α	α	PRON
ejpam-6325	107	6	ak(x)y	ak(x)y	PROPN
ejpam-6325	107	7	k	k	X
ejpam-6325	107	8	=	=	SYM
ejpam-6325	107	9	0	0	PUNCT
ejpam-6325	107	10	(	(	PUNCT
ejpam-6325	107	11	18	18	NUM
ejpam-6325	107	12	)	)	PUNCT
ejpam-6325	107	13	where	where	SCONJ
ejpam-6325	107	14	ak(x)(k	ak(x)(k	NOUN
ejpam-6325	107	15	=	=	SYM
ejpam-6325	107	16	0	0	NUM
ejpam-6325	107	17	,	,	PUNCT
ejpam-6325	107	18	1	1	NUM
ejpam-6325	107	19	,	,	PUNCT
ejpam-6325	107	20	2	2	NUM
ejpam-6325	107	21	,	,	PUNCT
ejpam-6325	107	22	...	...	PUNCT
ejpam-6325	107	23	,	,	PUNCT
ejpam-6325	107	24	)	)	PUNCT
ejpam-6325	107	25	are	be	AUX
ejpam-6325	107	26	laurent	laurent	NOUN
ejpam-6325	107	27	polynomials	polynomial	NOUN
ejpam-6325	107	28	of	of	ADP
ejpam-6325	107	29	x.	x.	NOUN
ejpam-6325	107	30	above	above	ADP
ejpam-6325	107	31	equation	equation	NOUN
ejpam-6325	107	32	is	be	AUX
ejpam-6325	107	33	said	say	VERB
ejpam-6325	107	34	to	to	PART
ejpam-6325	107	35	be	be	AUX
ejpam-6325	107	36	the	the	DET
ejpam-6325	107	37	first	first	ADJ
ejpam-6325	107	38	integral	integral	NOUN
ejpam-6325	107	39	of	of	ADP
ejpam-6325	107	40	eq	eq	NOUN
ejpam-6325	107	41	(	(	PUNCT
ejpam-6325	107	42	16	16	NUM
ejpam-6325	107	43	)	)	PUNCT
ejpam-6325	107	44	.	.	PUNCT
ejpam-6325	108	1	by	by	ADP
ejpam-6325	108	2	applying	apply	VERB
ejpam-6325	108	3	division	division	NOUN
ejpam-6325	108	4	theorem	theorem	VERB
ejpam-6325	108	5	,	,	PUNCT
ejpam-6325	108	6	a	a	DET
ejpam-6325	108	7	laurent	laurent	NOUN
ejpam-6325	108	8	polynomial	polynomial	ADJ
ejpam-6325	108	9	[	[	X
ejpam-6325	108	10	g(x	g(x	NOUN
ejpam-6325	108	11	)	)	PUNCT
ejpam-6325	109	1	+	+	CCONJ
ejpam-6325	109	2	h(x)y	h(x)y	PROPN
ejpam-6325	109	3	]	]	PUNCT
ejpam-6325	109	4	exist	exist	VERB
ejpam-6325	109	5	in	in	ADP
ejpam-6325	109	6	the	the	DET
ejpam-6325	109	7	complex	complex	ADJ
ejpam-6325	109	8	domain	domain	NOUN
ejpam-6325	109	9	c[x	c[x	NOUN
ejpam-6325	109	10	,	,	PUNCT
ejpam-6325	109	11	y	y	PROPN
ejpam-6325	109	12	]	]	PUNCT
ejpam-6325	109	13	such	such	ADJ
ejpam-6325	109	14	that	that	SCONJ
ejpam-6325	109	15	,	,	PUNCT
ejpam-6325	109	16	by	by	ADP
ejpam-6325	109	17	chain	chain	NOUN
ejpam-6325	109	18	rule	rule	NOUN
ejpam-6325	109	19	dq	dq	PROPN
ejpam-6325	109	20	dξ	dξ	PROPN
ejpam-6325	110	1	=	=	PRON
ejpam-6325	110	2	β∑	β∑	PUNCT
ejpam-6325	111	1	k	k	X
ejpam-6325	111	2	=	=	NOUN
ejpam-6325	111	3	α	α	X
ejpam-6325	111	4	a′k(x)y	a′k(x)y	NUM
ejpam-6325	111	5	k+1	k+1	NOUN
ejpam-6325	112	1	+	+	CCONJ
ejpam-6325	112	2	β∑	β∑	PUNCT
ejpam-6325	112	3	k	k	X
ejpam-6325	112	4	=	=	NOUN
ejpam-6325	112	5	α	α	NOUN
ejpam-6325	112	6	kak(x)y	kak(x)y	NOUN
ejpam-6325	112	7	k	k	X
ejpam-6325	112	8	·	·	PUNCT
ejpam-6325	112	9	(	(	PUNCT
ejpam-6325	112	10	−(α+	−(α+	NUM
ejpam-6325	112	11	β	β	NOUN
ejpam-6325	112	12	)	)	PUNCT
ejpam-6325	112	13	1−	1−	NUM
ejpam-6325	112	14	c2	c2	PROPN
ejpam-6325	112	15	)	)	PUNCT
ejpam-6325	113	1	+	+	CCONJ
ejpam-6325	113	2	β∑	β∑	PUNCT
ejpam-6325	113	3	k	k	X
ejpam-6325	113	4	=	=	NOUN
ejpam-6325	113	5	α	α	NOUN
ejpam-6325	113	6	kak(x)y	kak(x)y	NOUN
ejpam-6325	113	7	k−1	k−1	PROPN
ejpam-6325	113	8	·	·	PUNCT
ejpam-6325	113	9	(	(	PUNCT
ejpam-6325	113	10	−αβ	−αβ	PROPN
ejpam-6325	113	11	1−	1−	NUM
ejpam-6325	113	12	c2	c2	PROPN
ejpam-6325	113	13	x	x	PUNCT
ejpam-6325	113	14	)	)	PUNCT
ejpam-6325	113	15	(	(	PUNCT
ejpam-6325	113	16	19	19	NUM
ejpam-6325	113	17	)	)	PUNCT
ejpam-6325	114	1	[	[	X
ejpam-6325	114	2	g(x	g(x	NOUN
ejpam-6325	114	3	)	)	PUNCT
ejpam-6325	115	1	+	+	CCONJ
ejpam-6325	115	2	h(x)y	h(x)y	PROPN
ejpam-6325	115	3	]	]	PUNCT
ejpam-6325	116	1	[	[	PUNCT
ejpam-6325	116	2	β∑	β∑	X
ejpam-6325	116	3	k	k	X
ejpam-6325	116	4	=	=	NOUN
ejpam-6325	116	5	α	α	PRON
ejpam-6325	116	6	ak(x)y	ak(x)y	PROPN
ejpam-6325	116	7	k	k	X
ejpam-6325	116	8	]	]	PUNCT
ejpam-6325	116	9	=	=	PUNCT
ejpam-6325	116	10	[	[	PUNCT
ejpam-6325	116	11	β∑	β∑	INTJ
ejpam-6325	116	12	k	k	X
ejpam-6325	116	13	=	=	NOUN
ejpam-6325	116	14	α	α	X
ejpam-6325	116	15	a′k(x)y	a′k(x)y	PUNCT
ejpam-6325	116	16	k+1	k+1	X
ejpam-6325	116	17	]	]	PUNCT
ejpam-6325	117	1	+	+	CCONJ
ejpam-6325	117	2	[	[	PUNCT
ejpam-6325	117	3	β∑	β∑	INTJ
ejpam-6325	117	4	k	k	X
ejpam-6325	117	5	=	=	NOUN
ejpam-6325	117	6	α	α	NOUN
ejpam-6325	117	7	kak(x)y	kak(x)y	NOUN
ejpam-6325	117	8	k	k	X
ejpam-6325	117	9	]	]	X
ejpam-6325	117	10	·	·	PUNCT
ejpam-6325	117	11	(	(	PUNCT
ejpam-6325	117	12	−(α+	−(α+	NUM
ejpam-6325	117	13	β	β	NOUN
ejpam-6325	117	14	)	)	PUNCT
ejpam-6325	117	15	1−	1−	NUM
ejpam-6325	117	16	c2	c2	PROPN
ejpam-6325	117	17	)	)	PUNCT
ejpam-6325	118	1	+	+	CCONJ
ejpam-6325	118	2	[	[	PUNCT
ejpam-6325	118	3	β∑	β∑	INTJ
ejpam-6325	118	4	k	k	X
ejpam-6325	118	5	=	=	NOUN
ejpam-6325	118	6	α	α	NOUN
ejpam-6325	118	7	kak(x)y	kak(x)y	NOUN
ejpam-6325	118	8	k−1	k−1	PROPN
ejpam-6325	118	9	]	]	PUNCT
ejpam-6325	118	10	·	·	PUNCT
ejpam-6325	118	11	(	(	PUNCT
ejpam-6325	118	12	−αβ	−αβ	PROPN
ejpam-6325	118	13	1−	1−	NUM
ejpam-6325	118	14	c2	c2	PROPN
ejpam-6325	118	15	x	x	PUNCT
ejpam-6325	118	16	)	)	PUNCT
ejpam-6325	118	17	(	(	PUNCT
ejpam-6325	118	18	20	20	NUM
ejpam-6325	118	19	)	)	PUNCT
ejpam-6325	118	20	now	now	ADV
ejpam-6325	118	21	for	for	ADP
ejpam-6325	118	22	α	α	NOUN
ejpam-6325	118	23	=	=	SYM
ejpam-6325	118	24	0	0	PROPN
ejpam-6325	118	25	and	and	CCONJ
ejpam-6325	118	26	β	β	X
ejpam-6325	118	27	=	=	SYM
ejpam-6325	118	28	1	1	NUM
ejpam-6325	118	29	equation	equation	NOUN
ejpam-6325	118	30	(	(	PUNCT
ejpam-6325	118	31	17	17	NUM
ejpam-6325	118	32	)	)	PUNCT
ejpam-6325	118	33	becomes	become	VERB
ejpam-6325	118	34	[	[	X
ejpam-6325	118	35	g(x	g(x	NOUN
ejpam-6325	118	36	)	)	PUNCT
ejpam-6325	119	1	+	+	CCONJ
ejpam-6325	120	1	h(x)y	h(x)y	PROPN
ejpam-6325	120	2	]	]	PUNCT
ejpam-6325	120	3	{	{	PUNCT
ejpam-6325	120	4	a0(x)y	a0(x)y	NUM
ejpam-6325	120	5	0	0	NUM
ejpam-6325	121	1	+	+	CCONJ
ejpam-6325	121	2	a1(x)y	a1(x)y	NUM
ejpam-6325	121	3	1	1	NUM
ejpam-6325	121	4	}	}	PUNCT
ejpam-6325	121	5	=	=	PRON
ejpam-6325	121	6	{	{	PUNCT
ejpam-6325	121	7	a′0(x)y	a′0(x)y	PROPN
ejpam-6325	121	8	1	1	NUM
ejpam-6325	121	9	+	+	CCONJ
ejpam-6325	121	10	a′1(x)y	a′1(x)y	NOUN
ejpam-6325	121	11	2	2	NUM
ejpam-6325	121	12	}	}	PUNCT
ejpam-6325	121	13	+	+	CCONJ
ejpam-6325	121	14	{	{	PUNCT
ejpam-6325	121	15	a1(x)y	a1(x)y	PROPN
ejpam-6325	121	16	1	1	NUM
ejpam-6325	121	17	}	}	PUNCT
ejpam-6325	121	18	·	·	PUNCT
ejpam-6325	121	19	(	(	PUNCT
ejpam-6325	121	20	−(α+	−(α+	NUM
ejpam-6325	121	21	β	β	NOUN
ejpam-6325	121	22	)	)	PUNCT
ejpam-6325	121	23	1−	1−	NUM
ejpam-6325	121	24	c2	c2	PROPN
ejpam-6325	121	25	)	)	PUNCT
ejpam-6325	122	1	+	+	CCONJ
ejpam-6325	122	2	{	{	PUNCT
ejpam-6325	122	3	a1(x)y	a1(x)y	NOUN
ejpam-6325	122	4	0	0	NUM
ejpam-6325	122	5	}	}	PUNCT
ejpam-6325	122	6	·	·	PUNCT
ejpam-6325	122	7	(	(	PUNCT
ejpam-6325	122	8	−αβ	−αβ	PROPN
ejpam-6325	122	9	1−	1−	NUM
ejpam-6325	122	10	c2	c2	PROPN
ejpam-6325	122	11	x	x	PUNCT
ejpam-6325	122	12	)	)	PUNCT
ejpam-6325	122	13	(	(	PUNCT
ejpam-6325	122	14	21	21	NUM
ejpam-6325	122	15	)	)	PUNCT
ejpam-6325	122	16	m.	m.	NOUN
ejpam-6325	122	17	noman	noman	PROPN
ejpam-6325	122	18	et	et	PROPN
ejpam-6325	122	19	al	al	PROPN
ejpam-6325	122	20	.	.	PUNCT
ejpam-6325	122	21	/	/	SYM
ejpam-6325	122	22	eur	eur	PROPN
ejpam-6325	122	23	.	.	PUNCT
ejpam-6325	123	1	j.	j.	PROPN
ejpam-6325	123	2	pure	pure	PROPN
ejpam-6325	123	3	appl	appl	PROPN
ejpam-6325	123	4	.	.	PROPN
ejpam-6325	123	5	math	math	PROPN
ejpam-6325	123	6	,	,	PUNCT
ejpam-6325	123	7	18	18	NUM
ejpam-6325	123	8	(	(	PUNCT
ejpam-6325	123	9	3	3	NUM
ejpam-6325	123	10	)	)	PUNCT
ejpam-6325	123	11	(	(	PUNCT
ejpam-6325	123	12	2025	2025	NUM
ejpam-6325	123	13	)	)	PUNCT
ejpam-6325	123	14	,	,	PUNCT
ejpam-6325	123	15	6235	6235	NUM
ejpam-6325	123	16	7	7	NUM
ejpam-6325	123	17	of	of	ADP
ejpam-6325	123	18	16	16	NUM
ejpam-6325	123	19	comparing	compare	VERB
ejpam-6325	123	20	coefficients	coefficient	NOUN
ejpam-6325	123	21	of	of	ADP
ejpam-6325	123	22	y	y	PROPN
ejpam-6325	123	23	2	2	NUM
ejpam-6325	123	24	,	,	PUNCT
ejpam-6325	123	25	y	y	PROPN
ejpam-6325	123	26	1	1	NUM
ejpam-6325	123	27	,	,	PUNCT
ejpam-6325	123	28	y	y	PROPN
ejpam-6325	123	29	0	0	NUM
ejpam-6325	124	1	y	y	PROPN
ejpam-6325	124	2	2	2	NUM
ejpam-6325	124	3	;	;	PUNCT
ejpam-6325	124	4	h(x)a1(x	h(x)a1(x	X
ejpam-6325	124	5	)	)	PUNCT
ejpam-6325	124	6	=	=	PUNCT
ejpam-6325	124	7	a	a	DET
ejpam-6325	124	8	′	′	NUM
ejpam-6325	124	9	1(x	1(x	NUM
ejpam-6325	124	10	)	)	PUNCT
ejpam-6325	124	11	.	.	PUNCT
ejpam-6325	125	1	(	(	PUNCT
ejpam-6325	125	2	22	22	X
ejpam-6325	125	3	)	)	PUNCT
ejpam-6325	125	4	y	y	PROPN
ejpam-6325	125	5	1	1	NUM
ejpam-6325	125	6	;	;	PUNCT
ejpam-6325	125	7	h(x)ao(x	h(x)ao(x	X
ejpam-6325	125	8	)	)	PUNCT
ejpam-6325	125	9	+	+	CCONJ
ejpam-6325	125	10	g(x)a1(x	g(x)a1(x	NOUN
ejpam-6325	125	11	)	)	PUNCT
ejpam-6325	125	12	=	=	PUNCT
ejpam-6325	126	1	a	a	DET
ejpam-6325	126	2	′	′	NUM
ejpam-6325	126	3	(	(	PUNCT
ejpam-6325	126	4	0)(x)−	0)(x)−	NOUN
ejpam-6325	126	5	a1(x	a1(x	NOUN
ejpam-6325	126	6	)	)	PUNCT
ejpam-6325	126	7	α+	α+	X
ejpam-6325	126	8	β	β	PROPN
ejpam-6325	126	9	1−	1−	NUM
ejpam-6325	126	10	c2	c2	PROPN
ejpam-6325	126	11	.	.	PUNCT
ejpam-6325	127	1	(	(	PUNCT
ejpam-6325	127	2	23	23	NUM
ejpam-6325	127	3	)	)	PUNCT
ejpam-6325	127	4	y	y	PROPN
ejpam-6325	127	5	0	0	NUM
ejpam-6325	127	6	;	;	PUNCT
ejpam-6325	127	7	g(x)ao(x	g(x)ao(x	X
ejpam-6325	127	8	)	)	PUNCT
ejpam-6325	127	9	=	=	SYM
ejpam-6325	127	10	−a1(x	−a1(x	NOUN
ejpam-6325	127	11	)	)	PUNCT
ejpam-6325	127	12	(	(	PUNCT
ejpam-6325	127	13	αβ	αβ	INTJ
ejpam-6325	127	14	1−	1−	NUM
ejpam-6325	127	15	c2	c2	PROPN
ejpam-6325	127	16	x	x	PUNCT
ejpam-6325	127	17	)	)	PUNCT
ejpam-6325	127	18	.	.	PUNCT
ejpam-6325	128	1	(	(	PUNCT
ejpam-6325	128	2	24	24	NUM
ejpam-6325	128	3	)	)	PUNCT
ejpam-6325	128	4	from	from	ADP
ejpam-6325	128	5	equation	equation	NOUN
ejpam-6325	128	6	(	(	PUNCT
ejpam-6325	128	7	21	21	NUM
ejpam-6325	128	8	)	)	PUNCT
ejpam-6325	128	9	we	we	PRON
ejpam-6325	128	10	suppose	suppose	VERB
ejpam-6325	128	11	a	a	DET
ejpam-6325	128	12	laurent	laurent	ADJ
ejpam-6325	128	13	polynomial	polynomial	ADJ
ejpam-6325	128	14	h(x	h(x	PROPN
ejpam-6325	128	15	)	)	PUNCT
ejpam-6325	129	1	=	=	SYM
ejpam-6325	129	2	1	1	NUM
ejpam-6325	129	3	x	x	NOUN
ejpam-6325	129	4	,	,	PUNCT
ejpam-6325	129	5	so	so	CCONJ
ejpam-6325	129	6	equation	equation	NOUN
ejpam-6325	129	7	(	(	PUNCT
ejpam-6325	129	8	21	21	NUM
ejpam-6325	129	9	)	)	PUNCT
ejpam-6325	129	10	=	=	NOUN
ejpam-6325	129	11	⇒	⇒	NOUN
ejpam-6325	129	12	1	1	NUM
ejpam-6325	129	13	x	x	X
ejpam-6325	129	14	=	=	PUNCT
ejpam-6325	129	15	a	a	DET
ejpam-6325	129	16	′	′	NUM
ejpam-6325	129	17	o(x	o(x	PROPN
ejpam-6325	129	18	)	)	PUNCT
ejpam-6325	129	19	ao(x	ao(x	PUNCT
ejpam-6325	129	20	)	)	PUNCT
ejpam-6325	129	21	,	,	PUNCT
ejpam-6325	129	22	integration	integration	NOUN
ejpam-6325	129	23	gives	give	VERB
ejpam-6325	129	24	ao(x	ao(x	PUNCT
ejpam-6325	129	25	)	)	PUNCT
ejpam-6325	129	26	=	=	SYM
ejpam-6325	129	27	c1(x	c1(x	NOUN
ejpam-6325	129	28	)	)	PUNCT
ejpam-6325	129	29	.	.	PUNCT
ejpam-6325	130	1	(	(	PUNCT
ejpam-6325	130	2	25	25	NUM
ejpam-6325	130	3	)	)	PUNCT
ejpam-6325	130	4	equation	equation	NOUN
ejpam-6325	130	5	(	(	PUNCT
ejpam-6325	130	6	22	22	NUM
ejpam-6325	130	7	)	)	PUNCT
ejpam-6325	131	1	=	=	NOUN
ejpam-6325	131	2	⇒	⇒	NOUN
ejpam-6325	131	3	a0(x	a0(x	NOUN
ejpam-6325	131	4	)	)	PUNCT
ejpam-6325	131	5	x	x	PUNCT
ejpam-6325	132	1	+	+	PUNCT
ejpam-6325	132	2	c1xg(x	c1xg(x	NUM
ejpam-6325	132	3	)	)	PUNCT
ejpam-6325	132	4	=	=	SYM
ejpam-6325	132	5	a′0(x)−	a′0(x)−	NOUN
ejpam-6325	132	6	c1x	c1x	NOUN
ejpam-6325	132	7	·	·	PUNCT
ejpam-6325	132	8	[	[	PUNCT
ejpam-6325	132	9	α+	α+	X
ejpam-6325	132	10	β	β	X
ejpam-6325	132	11	1−	1−	NUM
ejpam-6325	132	12	c2	c2	PROPN
ejpam-6325	132	13	]	]	PUNCT
ejpam-6325	132	14	.	.	PUNCT
ejpam-6325	133	1	(	(	PUNCT
ejpam-6325	133	2	26	26	NUM
ejpam-6325	133	3	)	)	PUNCT
ejpam-6325	133	4	c1xg(x	c1xg(x	PROPN
ejpam-6325	133	5	)	)	PUNCT
ejpam-6325	134	1	+	+	CCONJ
ejpam-6325	134	2	c1x	c1x	NOUN
ejpam-6325	134	3	·	·	PUNCT
ejpam-6325	134	4	[	[	PUNCT
ejpam-6325	134	5	α+	α+	X
ejpam-6325	134	6	β	β	X
ejpam-6325	134	7	1−	1−	NUM
ejpam-6325	134	8	c2	c2	PROPN
ejpam-6325	134	9	]	]	PUNCT
ejpam-6325	135	1	=	=	PUNCT
ejpam-6325	136	1	a′0(x)−	a′0(x)−	PROPN
ejpam-6325	136	2	a0(x	a0(x	NOUN
ejpam-6325	136	3	)	)	PUNCT
ejpam-6325	136	4	x	x	X
ejpam-6325	136	5	.	.	PUNCT
ejpam-6325	137	1	(	(	PUNCT
ejpam-6325	137	2	27	27	NUM
ejpam-6325	137	3	)	)	PUNCT
ejpam-6325	137	4	c1g(x	c1g(x	NUM
ejpam-6325	137	5	)	)	PUNCT
ejpam-6325	138	1	+	+	CCONJ
ejpam-6325	138	2	c1	c1	NOUN
ejpam-6325	138	3	·	·	PUNCT
ejpam-6325	138	4	[	[	PUNCT
ejpam-6325	138	5	α+	α+	X
ejpam-6325	138	6	β	β	X
ejpam-6325	138	7	1−	1−	NUM
ejpam-6325	138	8	c2	c2	PROPN
ejpam-6325	138	9	]	]	PUNCT
ejpam-6325	139	1	=	=	PUNCT
ejpam-6325	139	2	d	d	X
ejpam-6325	139	3	dx	dx	PROPN
ejpam-6325	139	4	(	(	PUNCT
ejpam-6325	139	5	a0(x	a0(x	NOUN
ejpam-6325	139	6	)	)	PUNCT
ejpam-6325	139	7	x	x	SYM
ejpam-6325	139	8	)	)	PUNCT
ejpam-6325	139	9	.	.	PUNCT
ejpam-6325	140	1	(	(	PUNCT
ejpam-6325	140	2	28	28	X
ejpam-6325	140	3	)	)	PUNCT
ejpam-6325	140	4	integrating	integrating	NOUN
ejpam-6325	140	5	(	(	PUNCT
ejpam-6325	140	6	27	27	NUM
ejpam-6325	140	7	)	)	PUNCT
ejpam-6325	140	8	c1	c1	PROPN
ejpam-6325	140	9	∫	∫	PROPN
ejpam-6325	140	10	g(x)dx	g(x)dx	VERB
ejpam-6325	140	11	+	+	CCONJ
ejpam-6325	140	12	c1x	c1x	PROPN
ejpam-6325	140	13	·	·	PUNCT
ejpam-6325	140	14	α+	α+	X
ejpam-6325	140	15	β	β	X
ejpam-6325	140	16	1−	1−	NUM
ejpam-6325	140	17	c2	c2	PROPN
ejpam-6325	140	18	+	+	CCONJ
ejpam-6325	140	19	c2	c2	PROPN
ejpam-6325	140	20	=	=	SYM
ejpam-6325	140	21	a0(x	a0(x	PROPN
ejpam-6325	140	22	)	)	PUNCT
ejpam-6325	140	23	x	x	X
ejpam-6325	140	24	,	,	PUNCT
ejpam-6325	140	25	c1x	c1x	PROPN
ejpam-6325	140	26	∫	∫	PROPN
ejpam-6325	140	27	g(x)dx	g(x)dx	PART
ejpam-6325	140	28	+	+	CCONJ
ejpam-6325	140	29	c1x	c1x	PROPN
ejpam-6325	140	30	2	2	NUM
ejpam-6325	140	31	·	·	PUNCT
ejpam-6325	141	1	α+	α+	X
ejpam-6325	141	2	β	β	X
ejpam-6325	141	3	1−	1−	NUM
ejpam-6325	141	4	c2	c2	PROPN
ejpam-6325	141	5	+	+	CCONJ
ejpam-6325	141	6	c2x	c2x	PROPN
ejpam-6325	141	7	=	=	SYM
ejpam-6325	141	8	a0(x	a0(x	PROPN
ejpam-6325	141	9	)	)	PUNCT
ejpam-6325	141	10	.	.	PUNCT
ejpam-6325	142	1	(	(	PUNCT
ejpam-6325	142	2	29	29	NUM
ejpam-6325	142	3	)	)	PUNCT
ejpam-6325	142	4	for	for	ADP
ejpam-6325	142	5	equation	equation	NOUN
ejpam-6325	142	6	(	(	PUNCT
ejpam-6325	142	7	21	21	NUM
ejpam-6325	142	8	)	)	PUNCT
ejpam-6325	142	9	and	and	CCONJ
ejpam-6325	142	10	(	(	PUNCT
ejpam-6325	142	11	22	22	NUM
ejpam-6325	142	12	)	)	PUNCT
ejpam-6325	142	13	,	,	PUNCT
ejpam-6325	142	14	equation	equation	NOUN
ejpam-6325	142	15	(	(	PUNCT
ejpam-6325	142	16	23	23	NUM
ejpam-6325	142	17	)	)	PUNCT
ejpam-6325	143	1	=	=	NOUN
ejpam-6325	143	2	⇒	⇒	NOUN
ejpam-6325	143	3	[	[	PUNCT
ejpam-6325	143	4	c1x	c1x	PROPN
ejpam-6325	143	5	∫	∫	PROPN
ejpam-6325	143	6	g(x	g(x	PROPN
ejpam-6325	143	7	)	)	PUNCT
ejpam-6325	143	8	dx	dx	PROPN
ejpam-6325	144	1	+	+	CCONJ
ejpam-6325	144	2	c1x	c1x	VERB
ejpam-6325	144	3	2	2	NUM
ejpam-6325	144	4	·	·	PUNCT
ejpam-6325	144	5	α+	α+	X
ejpam-6325	144	6	β	β	X
ejpam-6325	144	7	1−	1−	NUM
ejpam-6325	144	8	c2	c2	PROPN
ejpam-6325	144	9	+	+	CCONJ
ejpam-6325	144	10	c2x	c2x	NOUN
ejpam-6325	144	11	]	]	X
ejpam-6325	144	12	g(x	g(x	X
ejpam-6325	144	13	)	)	PUNCT
ejpam-6325	145	1	=	=	SYM
ejpam-6325	145	2	−c1x	−c1x	PROPN
ejpam-6325	145	3	2	2	NUM
ejpam-6325	145	4	(	(	PUNCT
ejpam-6325	145	5	αβ	αβ	PROPN
ejpam-6325	145	6	1−	1−	NUM
ejpam-6325	145	7	c2	c2	PROPN
ejpam-6325	145	8	)	)	PUNCT
ejpam-6325	146	1	[	[	PUNCT
ejpam-6325	146	2	g(x	g(x	NOUN
ejpam-6325	146	3	)	)	PUNCT
ejpam-6325	146	4	∫	∫	NOUN
ejpam-6325	146	5	g(x	g(x	NOUN
ejpam-6325	146	6	)	)	PUNCT
ejpam-6325	147	1	dx	dx	PROPN
ejpam-6325	148	1	+	+	NOUN
ejpam-6325	148	2	xg(x	xg(x	PUNCT
ejpam-6325	148	3	)	)	PUNCT
ejpam-6325	148	4	·	·	PUNCT
ejpam-6325	149	1	α+	α+	X
ejpam-6325	149	2	β	β	NOUN
ejpam-6325	149	3	1−	1−	NUM
ejpam-6325	149	4	c2	c2	PROPN
ejpam-6325	149	5	+	+	NOUN
ejpam-6325	149	6	ag(x	ag(x	X
ejpam-6325	149	7	)	)	PUNCT
ejpam-6325	149	8	]	]	PUNCT
ejpam-6325	150	1	=	=	PUNCT
ejpam-6325	150	2	−x	−x	NOUN
ejpam-6325	150	3	·	·	PUNCT
ejpam-6325	150	4	αβ	αβ	PRON
ejpam-6325	150	5	1−	1−	NUM
ejpam-6325	150	6	c2	c2	PROPN
ejpam-6325	150	7	(	(	PUNCT
ejpam-6325	150	8	30	30	NUM
ejpam-6325	150	9	)	)	PUNCT
ejpam-6325	150	10	m.	m.	NOUN
ejpam-6325	150	11	noman	noman	PROPN
ejpam-6325	150	12	et	et	PROPN
ejpam-6325	150	13	al	al	PROPN
ejpam-6325	150	14	.	.	PUNCT
ejpam-6325	150	15	/	/	SYM
ejpam-6325	150	16	eur	eur	PROPN
ejpam-6325	150	17	.	.	PUNCT
ejpam-6325	151	1	j.	j.	PROPN
ejpam-6325	151	2	pure	pure	PROPN
ejpam-6325	151	3	appl	appl	PROPN
ejpam-6325	151	4	.	.	PROPN
ejpam-6325	151	5	math	math	PROPN
ejpam-6325	151	6	,	,	PUNCT
ejpam-6325	151	7	18	18	NUM
ejpam-6325	151	8	(	(	PUNCT
ejpam-6325	151	9	3	3	NUM
ejpam-6325	151	10	)	)	PUNCT
ejpam-6325	151	11	(	(	PUNCT
ejpam-6325	151	12	2025	2025	NUM
ejpam-6325	151	13	)	)	PUNCT
ejpam-6325	151	14	,	,	PUNCT
ejpam-6325	151	15	6235	6235	NUM
ejpam-6325	151	16	8	8	NUM
ejpam-6325	151	17	of	of	ADP
ejpam-6325	151	18	16	16	NUM
ejpam-6325	151	19	where	where	SCONJ
ejpam-6325	151	20	a	a	DET
ejpam-6325	151	21	=	=	PROPN
ejpam-6325	151	22	c2	c2	PROPN
ejpam-6325	151	23	c1	c1	PROPN
ejpam-6325	151	24	in	in	ADP
ejpam-6325	151	25	applying	apply	VERB
ejpam-6325	151	26	the	the	DET
ejpam-6325	151	27	generalized	generalize	VERB
ejpam-6325	151	28	first	first	ADJ
ejpam-6325	151	29	integral	integral	ADJ
ejpam-6325	151	30	method	method	NOUN
ejpam-6325	151	31	,	,	PUNCT
ejpam-6325	151	32	the	the	DET
ejpam-6325	151	33	function	function	NOUN
ejpam-6325	151	34	g(x	g(x	NOUN
ejpam-6325	151	35	)	)	PUNCT
ejpam-6325	151	36	is	be	AUX
ejpam-6325	151	37	assumed	assume	VERB
ejpam-6325	151	38	as	as	ADP
ejpam-6325	151	39	a	a	DET
ejpam-6325	151	40	constant	constant	ADJ
ejpam-6325	151	41	b	b	NOUN
ejpam-6325	151	42	to	to	PART
ejpam-6325	151	43	simplify	simplify	VERB
ejpam-6325	151	44	the	the	DET
ejpam-6325	151	45	integration	integration	NOUN
ejpam-6325	151	46	process	process	NOUN
ejpam-6325	151	47	,	,	PUNCT
ejpam-6325	151	48	with	with	SCONJ
ejpam-6325	151	49	its	its	PRON
ejpam-6325	151	50	value	value	NOUN
ejpam-6325	151	51	subsequently	subsequently	ADV
ejpam-6325	151	52	determined	determine	VERB
ejpam-6325	151	53	from	from	ADP
ejpam-6325	151	54	the	the	DET
ejpam-6325	151	55	consistency	consistency	NOUN
ejpam-6325	151	56	condition	condition	NOUN
ejpam-6325	151	57	of	of	ADP
ejpam-6325	151	58	the	the	DET
ejpam-6325	151	59	reduced	reduce	VERB
ejpam-6325	151	60	equation	equation	NOUN
ejpam-6325	151	61	,	,	PUNCT
ejpam-6325	151	62	expressed	express	VERB
ejpam-6325	151	63	in	in	ADP
ejpam-6325	151	64	terms	term	NOUN
ejpam-6325	151	65	of	of	ADP
ejpam-6325	151	66	the	the	DET
ejpam-6325	151	67	system	system	NOUN
ejpam-6325	151	68	parameters	parameter	NOUN
ejpam-6325	151	69	α	α	PRON
ejpam-6325	151	70	,	,	PUNCT
ejpam-6325	151	71	β	β	NOUN
ejpam-6325	151	72	,	,	PUNCT
ejpam-6325	151	73	and	and	CCONJ
ejpam-6325	151	74	c	c	X
ejpam-6325	151	75	,	,	PUNCT
ejpam-6325	151	76	so	so	ADV
ejpam-6325	151	77	equation(29	equation(29	NOUN
ejpam-6325	151	78	)	)	PUNCT
ejpam-6325	152	1	=	=	VERB
ejpam-6325	152	2	⇒	⇒	NOUN
ejpam-6325	152	3	b2x	b2x	NOUN
ejpam-6325	152	4	+	+	ADV
ejpam-6325	152	5	bx	bx	X
ejpam-6325	152	6	·	·	PUNCT
ejpam-6325	153	1	[	[	X
ejpam-6325	153	2	α+	α+	X
ejpam-6325	153	3	β	β	X
ejpam-6325	153	4	1−	1−	NUM
ejpam-6325	153	5	c2	c2	PROPN
ejpam-6325	153	6	]	]	PUNCT
ejpam-6325	154	1	+	+	PUNCT
ejpam-6325	154	2	ba	ba	NOUN
ejpam-6325	154	3	=	=	SYM
ejpam-6325	154	4	−x	−x	NOUN
ejpam-6325	154	5	[	[	PUNCT
ejpam-6325	154	6	αβ	αβ	NOUN
ejpam-6325	154	7	1−	1−	NUM
ejpam-6325	154	8	c2	c2	PROPN
ejpam-6325	154	9	]	]	PUNCT
ejpam-6325	154	10	.	.	PUNCT
ejpam-6325	155	1	(	(	PUNCT
ejpam-6325	155	2	31	31	NUM
ejpam-6325	155	3	)	)	PUNCT
ejpam-6325	155	4	compairing	compaire	VERB
ejpam-6325	155	5	power	power	NOUN
ejpam-6325	155	6	of	of	ADP
ejpam-6325	155	7	x	x	PUNCT
ejpam-6325	155	8	on	on	ADP
ejpam-6325	155	9	both	both	DET
ejpam-6325	155	10	sides	side	NOUN
ejpam-6325	155	11	of	of	ADP
ejpam-6325	155	12	(	(	PUNCT
ejpam-6325	155	13	30	30	NUM
ejpam-6325	155	14	)	)	PUNCT
ejpam-6325	155	15	x1	x1	PROPN
ejpam-6325	155	16	;	;	PUNCT
ejpam-6325	155	17	b2	b2	NOUN
ejpam-6325	155	18	+	+	PROPN
ejpam-6325	155	19	b	b	NOUN
ejpam-6325	155	20	·	·	PUNCT
ejpam-6325	155	21	[	[	PUNCT
ejpam-6325	155	22	α+β	α+β	NUM
ejpam-6325	155	23	1−c2	1−c2	NUM
ejpam-6325	155	24	]	]	PUNCT
ejpam-6325	156	1	=	=	PUNCT
ejpam-6325	156	2	−αβ	−αβ	PROPN
ejpam-6325	156	3	1−c2	1−c2	NUM
ejpam-6325	156	4	.	.	PUNCT
ejpam-6325	157	1	x0	x0	PROPN
ejpam-6325	157	2	;	;	PUNCT
ejpam-6325	157	3	ab	ab	PROPN
ejpam-6325	157	4	=	=	PROPN
ejpam-6325	157	5	0	0	PROPN
ejpam-6325	157	6	.	.	PUNCT
ejpam-6325	158	1	here	here	ADV
ejpam-6325	158	2	a	a	DET
ejpam-6325	158	3	=	=	NOUN
ejpam-6325	158	4	0	0	PUNCT
ejpam-6325	158	5	because	because	SCONJ
ejpam-6325	158	6	b	b	PROPN
ejpam-6325	158	7	̸=	̸=	PROPN
ejpam-6325	158	8	0	0	PUNCT
ejpam-6325	158	9	now	now	ADV
ejpam-6325	158	10	,	,	PUNCT
ejpam-6325	158	11	=	=	SYM
ejpam-6325	158	12	⇒	⇒	NOUN
ejpam-6325	158	13	b2	b2	NOUN
ejpam-6325	158	14	+	+	PROPN
ejpam-6325	158	15	b	b	NOUN
ejpam-6325	158	16	·	·	PUNCT
ejpam-6325	158	17	[	[	PUNCT
ejpam-6325	158	18	α+β	α+β	NUM
ejpam-6325	158	19	1−c2	1−c2	NUM
ejpam-6325	158	20	]	]	PUNCT
ejpam-6325	158	21	=	=	PUNCT
ejpam-6325	158	22	−αβ	−αβ	PROPN
ejpam-6325	158	23	1−c2	1−c2	NUM
ejpam-6325	158	24	,	,	PUNCT
ejpam-6325	158	25	quadratic	quadratic	ADJ
ejpam-6325	158	26	in	in	ADP
ejpam-6325	158	27	b	b	PROPN
ejpam-6325	158	28	b	b	X
ejpam-6325	158	29	=	=	SYM
ejpam-6325	158	30	−(α+β	−(α+β	PROPN
ejpam-6325	158	31	)	)	PUNCT
ejpam-6325	158	32	1−c2	1−c2	NUM
ejpam-6325	158	33	±	±	NUM
ejpam-6325	158	34	√	√	PUNCT
ejpam-6325	158	35	(	(	PUNCT
ejpam-6325	158	36	α+β)2−4(αβ)(1−c2	α+β)2−4(αβ)(1−c2	NUM
ejpam-6325	158	37	)	)	PUNCT
ejpam-6325	158	38	(	(	PUNCT
ejpam-6325	158	39	1−c2)2	1−c2)2	NUM
ejpam-6325	158	40	2	2	NUM
ejpam-6325	158	41	.	.	PUNCT
ejpam-6325	159	1	(	(	PUNCT
ejpam-6325	159	2	32	32	NUM
ejpam-6325	159	3	)	)	PUNCT
ejpam-6325	159	4	g(x	g(x	NOUN
ejpam-6325	159	5	)	)	PUNCT
ejpam-6325	160	1	=	=	SYM
ejpam-6325	161	1	b	b	X
ejpam-6325	161	2	where	where	SCONJ
ejpam-6325	161	3	b	b	NOUN
ejpam-6325	161	4	is	be	AUX
ejpam-6325	161	5	the	the	DET
ejpam-6325	161	6	solution	solution	NOUN
ejpam-6325	161	7	of	of	ADP
ejpam-6325	161	8	above	above	ADP
ejpam-6325	161	9	quadratic	quadratic	ADJ
ejpam-6325	161	10	equation	equation	NOUN
ejpam-6325	161	11	.	.	PUNCT
ejpam-6325	162	1	now	now	ADV
ejpam-6325	162	2	equation	equation	NOUN
ejpam-6325	162	3	(	(	PUNCT
ejpam-6325	162	4	23	23	NUM
ejpam-6325	162	5	)	)	PUNCT
ejpam-6325	162	6	=	=	NOUN
ejpam-6325	162	7	⇒	⇒	NOUN
ejpam-6325	162	8	a0(x)g(x	a0(x)g(x	NOUN
ejpam-6325	162	9	)	)	PUNCT
ejpam-6325	162	10	=	=	SYM
ejpam-6325	163	1	−c1x	−c1x	PROPN
ejpam-6325	163	2	(	(	PUNCT
ejpam-6325	163	3	αβ	αβ	INTJ
ejpam-6325	163	4	1−	1−	NUM
ejpam-6325	163	5	c2	c2	PROPN
ejpam-6325	163	6	)	)	PUNCT
ejpam-6325	163	7	x	x	PUNCT
ejpam-6325	163	8	a0(x	a0(x	NOUN
ejpam-6325	163	9	)	)	PUNCT
ejpam-6325	163	10	=	=	SYM
ejpam-6325	164	1	−c1x	−c1x	PROPN
ejpam-6325	164	2	2	2	NUM
ejpam-6325	164	3	(	(	PUNCT
ejpam-6325	164	4	αβ	αβ	NOUN
ejpam-6325	164	5	1−c2	1−c2	NUM
ejpam-6325	164	6	)	)	PUNCT
ejpam-6325	164	7	b	b	NOUN
ejpam-6325	164	8	,	,	PUNCT
ejpam-6325	164	9	now	now	ADV
ejpam-6325	164	10	,	,	PUNCT
ejpam-6325	164	11	for	for	ADP
ejpam-6325	164	12	α	α	NOUN
ejpam-6325	164	13	=	=	SYM
ejpam-6325	164	14	0	0	PROPN
ejpam-6325	164	15	,	,	PUNCT
ejpam-6325	164	16	β	β	NOUN
ejpam-6325	164	17	=	=	SYM
ejpam-6325	164	18	1	1	NUM
ejpam-6325	164	19	equation	equation	NOUN
ejpam-6325	164	20	(	(	PUNCT
ejpam-6325	164	21	17	17	NUM
ejpam-6325	164	22	)	)	PUNCT
ejpam-6325	165	1	=	=	NOUN
ejpam-6325	165	2	⇒	⇒	NOUN
ejpam-6325	165	3	a0(x	a0(x	NOUN
ejpam-6325	165	4	)	)	PUNCT
ejpam-6325	165	5	+	+	CCONJ
ejpam-6325	165	6	a1(x)y	a1(x)y	NUM
ejpam-6325	165	7	=	=	SYM
ejpam-6325	165	8	0	0	NUM
ejpam-6325	165	9	,	,	PUNCT
ejpam-6325	165	10	y	y	PROPN
ejpam-6325	165	11	=	=	PUNCT
ejpam-6325	165	12	−a0(x	−a0(x	PROPN
ejpam-6325	165	13	)	)	PUNCT
ejpam-6325	165	14	a1(x	a1(x	NOUN
ejpam-6325	165	15	)	)	PUNCT
ejpam-6325	165	16	,	,	PUNCT
ejpam-6325	165	17	y	y	PROPN
ejpam-6325	165	18	=	=	SYM
ejpam-6325	165	19	(	(	PUNCT
ejpam-6325	165	20	αβ)x	αβ)x	NOUN
ejpam-6325	165	21	b(1−	b(1−	PROPN
ejpam-6325	165	22	c2	c2	PROPN
ejpam-6325	165	23	)	)	PUNCT
ejpam-6325	165	24	,	,	PUNCT
ejpam-6325	165	25	dξ	dξ	PROPN
ejpam-6325	165	26	dx	dx	PROPN
ejpam-6325	166	1	=	=	SYM
ejpam-6325	166	2	1	1	NUM
ejpam-6325	166	3	(	(	PUNCT
ejpam-6325	166	4	αβ)x	αβ)x	NOUN
ejpam-6325	166	5	b(1−	b(1−	PROPN
ejpam-6325	166	6	c2	c2	PROPN
ejpam-6325	166	7	)	)	PUNCT
ejpam-6325	166	8	,	,	PUNCT
ejpam-6325	166	9	m.	m.	NOUN
ejpam-6325	166	10	noman	noman	PROPN
ejpam-6325	166	11	et	et	PROPN
ejpam-6325	166	12	al	al	PROPN
ejpam-6325	166	13	.	.	PUNCT
ejpam-6325	166	14	/	/	SYM
ejpam-6325	166	15	eur	eur	PROPN
ejpam-6325	166	16	.	.	PUNCT
ejpam-6325	167	1	j.	j.	PROPN
ejpam-6325	167	2	pure	pure	PROPN
ejpam-6325	167	3	appl	appl	PROPN
ejpam-6325	167	4	.	.	PROPN
ejpam-6325	167	5	math	math	PROPN
ejpam-6325	167	6	,	,	PUNCT
ejpam-6325	167	7	18	18	NUM
ejpam-6325	167	8	(	(	PUNCT
ejpam-6325	167	9	3	3	NUM
ejpam-6325	167	10	)	)	PUNCT
ejpam-6325	167	11	(	(	PUNCT
ejpam-6325	167	12	2025	2025	NUM
ejpam-6325	167	13	)	)	PUNCT
ejpam-6325	167	14	,	,	PUNCT
ejpam-6325	167	15	6235	6235	NUM
ejpam-6325	167	16	9	9	NUM
ejpam-6325	167	17	of	of	ADP
ejpam-6325	167	18	16	16	NUM
ejpam-6325	167	19	integration	integration	NOUN
ejpam-6325	167	20	gives	give	VERB
ejpam-6325	167	21	ξ	ξ	PROPN
ejpam-6325	167	22	=	=	SYM
ejpam-6325	167	23	b(1−	b(1−	PROPN
ejpam-6325	167	24	c2	c2	PROPN
ejpam-6325	167	25	)	)	PUNCT
ejpam-6325	168	1	αβ	αβ	VERB
ejpam-6325	169	1	lnx	lnx	PROPN
ejpam-6325	169	2	+	+	PROPN
ejpam-6325	169	3	k	k	PROPN
ejpam-6325	169	4	,	,	PUNCT
ejpam-6325	169	5	ξ	ξ	PROPN
ejpam-6325	169	6	−k	−k	PROPN
ejpam-6325	169	7	=	=	SYM
ejpam-6325	169	8	b(1−	b(1−	PROPN
ejpam-6325	169	9	c2	c2	PROPN
ejpam-6325	169	10	)	)	PUNCT
ejpam-6325	169	11	αβ	αβ	PRON
ejpam-6325	169	12	lnx	lnx	PROPN
ejpam-6325	169	13	,	,	PUNCT
ejpam-6325	169	14	αβ(ξ	αβ(ξ	X
ejpam-6325	169	15	−k	−k	NOUN
ejpam-6325	169	16	)	)	PUNCT
ejpam-6325	169	17	b(1−	b(1−	PROPN
ejpam-6325	169	18	c2	c2	PROPN
ejpam-6325	169	19	)	)	PUNCT
ejpam-6325	170	1	=	=	SYM
ejpam-6325	170	2	lnx	lnx	PROPN
ejpam-6325	170	3	=	=	PRON
ejpam-6325	170	4	⇒	⇒	VERB
ejpam-6325	170	5	x	x	PUNCT
ejpam-6325	170	6	=	=	SYM
ejpam-6325	170	7	f(ξ	f(ξ	X
ejpam-6325	170	8	)	)	PUNCT
ejpam-6325	170	9	=	=	SYM
ejpam-6325	170	10	u	u	NOUN
ejpam-6325	170	11	=	=	NOUN
ejpam-6325	170	12	exp	exp	X
ejpam-6325	170	13	(	(	PUNCT
ejpam-6325	170	14	αβ(ξ	αβ(ξ	NUM
ejpam-6325	170	15	−k	−k	NOUN
ejpam-6325	170	16	)	)	PUNCT
ejpam-6325	170	17	b(1−	b(1−	PROPN
ejpam-6325	170	18	c2	c2	PROPN
ejpam-6325	170	19	)	)	PUNCT
ejpam-6325	170	20	)	)	PUNCT
ejpam-6325	170	21	.	.	PUNCT
ejpam-6325	171	1	(	(	PUNCT
ejpam-6325	171	2	33	33	NUM
ejpam-6325	171	3	)	)	PUNCT
ejpam-6325	171	4	where	where	SCONJ
ejpam-6325	171	5	ξ	ξ	X
ejpam-6325	171	6	=	=	SYM
ejpam-6325	171	7	x+	x+	PROPN
ejpam-6325	171	8	t	t	PROPN
ejpam-6325	171	9	and	and	CCONJ
ejpam-6325	171	10	b	b	X
ejpam-6325	172	1	=	=	SYM
ejpam-6325	172	2	−(α+	−(α+	NUM
ejpam-6325	172	3	β	β	NOUN
ejpam-6325	172	4	)	)	PUNCT
ejpam-6325	172	5	1−	1−	NUM
ejpam-6325	172	6	c2	c2	PROPN
ejpam-6325	172	7	±	±	PROPN
ejpam-6325	172	8	√√√√(α+	√√√√(α+	NOUN
ejpam-6325	172	9	β)2	β)2	ADV
ejpam-6325	172	10	−	−	PROPN
ejpam-6325	172	11	4αβ(1−	4αβ(1−	PROPN
ejpam-6325	172	12	c2	c2	PROPN
ejpam-6325	172	13	)	)	PUNCT
ejpam-6325	172	14	(	(	PUNCT
ejpam-6325	172	15	1−	1−	NUM
ejpam-6325	172	16	c2)2	c2)2	DET
ejpam-6325	172	17	2	2	NUM
ejpam-6325	172	18	.	.	PUNCT
ejpam-6325	173	1	equation	equation	NOUN
ejpam-6325	173	2	(	(	PUNCT
ejpam-6325	173	3	32	32	NUM
ejpam-6325	173	4	)	)	PUNCT
ejpam-6325	173	5	is	be	AUX
ejpam-6325	173	6	the	the	DET
ejpam-6325	173	7	required	require	VERB
ejpam-6325	173	8	solution	solution	NOUN
ejpam-6325	173	9	of	of	ADP
ejpam-6325	173	10	telegrapher	telegrapher	PROPN
ejpam-6325	173	11	’s	’s	PART
ejpam-6325	173	12	equation	equation	NOUN
ejpam-6325	173	13	with	with	ADP
ejpam-6325	173	14	damping	damp	VERB
ejpam-6325	173	15	and	and	CCONJ
ejpam-6325	173	16	harmonic	harmonic	ADJ
ejpam-6325	173	17	potential	potential	NOUN
ejpam-6325	173	18	.	.	PUNCT
ejpam-6325	174	1	this	this	DET
ejpam-6325	174	2	solution	solution	NOUN
ejpam-6325	174	3	best	well	ADV
ejpam-6325	174	4	describes	describe	VERB
ejpam-6325	174	5	underdamped	underdamped	ADJ
ejpam-6325	174	6	or	or	CCONJ
ejpam-6325	174	7	overdamped	overdampe	VERB
ejpam-6325	174	8	wave	wave	NOUN
ejpam-6325	174	9	propagation	propagation	NOUN
ejpam-6325	174	10	depending	depend	VERB
ejpam-6325	174	11	on	on	ADP
ejpam-6325	174	12	the	the	DET
ejpam-6325	174	13	discriminant	discriminant	NOUN
ejpam-6325	174	14	(	(	PUNCT
ejpam-6325	174	15	α+	α+	X
ejpam-6325	174	16	β)2	β)2	NOUN
ejpam-6325	174	17	−	−	PROPN
ejpam-6325	174	18	4αβ(1−	4αβ(1−	PROPN
ejpam-6325	174	19	c2	c2	PROPN
ejpam-6325	174	20	):	):	PUNCT
ejpam-6325	174	21	•	•	ADP
ejpam-6325	174	22	if	if	SCONJ
ejpam-6325	174	23	the	the	DET
ejpam-6325	174	24	discriminant	discriminant	NOUN
ejpam-6325	174	25	is	be	AUX
ejpam-6325	174	26	positive	positive	ADJ
ejpam-6325	174	27	,	,	PUNCT
ejpam-6325	174	28	the	the	DET
ejpam-6325	174	29	system	system	NOUN
ejpam-6325	174	30	is	be	AUX
ejpam-6325	174	31	overdamped	overdampe	VERB
ejpam-6325	174	32	,	,	PUNCT
ejpam-6325	174	33	leading	lead	VERB
ejpam-6325	174	34	to	to	ADP
ejpam-6325	174	35	non	non	ADJ
ejpam-6325	174	36	-	-	ADJ
ejpam-6325	174	37	oscillatory	oscillatory	ADJ
ejpam-6325	174	38	exponential	exponential	ADJ
ejpam-6325	174	39	decay	decay	NOUN
ejpam-6325	174	40	.	.	PUNCT
ejpam-6325	175	1	•	•	NUM
ejpam-6325	175	2	if	if	SCONJ
ejpam-6325	175	3	the	the	DET
ejpam-6325	175	4	discriminant	discriminant	NOUN
ejpam-6325	175	5	is	be	AUX
ejpam-6325	175	6	zero	zero	NUM
ejpam-6325	175	7	,	,	PUNCT
ejpam-6325	175	8	the	the	DET
ejpam-6325	175	9	system	system	NOUN
ejpam-6325	175	10	is	be	AUX
ejpam-6325	175	11	critically	critically	ADV
ejpam-6325	175	12	damped	damp	VERB
ejpam-6325	175	13	.	.	PUNCT
ejpam-6325	176	1	•	•	INTJ
ejpam-6325	176	2	if	if	SCONJ
ejpam-6325	176	3	the	the	DET
ejpam-6325	176	4	discriminant	discriminant	NOUN
ejpam-6325	176	5	is	be	AUX
ejpam-6325	176	6	negative	negative	ADJ
ejpam-6325	176	7	,	,	PUNCT
ejpam-6325	176	8	the	the	DET
ejpam-6325	176	9	system	system	NOUN
ejpam-6325	176	10	exhibits	exhibit	VERB
ejpam-6325	176	11	underdamped	underdamped	ADJ
ejpam-6325	176	12	oscillations	oscillation	NOUN
ejpam-6325	176	13	,	,	PUNCT
ejpam-6325	176	14	where	where	SCONJ
ejpam-6325	176	15	waves	wave	NOUN
ejpam-6325	176	16	persist	persist	VERB
ejpam-6325	176	17	but	but	CCONJ
ejpam-6325	176	18	are	be	AUX
ejpam-6325	176	19	modulated	modulate	VERB
ejpam-6325	176	20	by	by	ADP
ejpam-6325	176	21	exponential	exponential	ADJ
ejpam-6325	176	22	decay	decay	NOUN
ejpam-6325	176	23	.	.	PUNCT
ejpam-6325	177	1	m.	m.	PROPN
ejpam-6325	177	2	noman	noman	PROPN
ejpam-6325	177	3	et	et	PROPN
ejpam-6325	177	4	al	al	PROPN
ejpam-6325	177	5	.	.	PUNCT
ejpam-6325	177	6	/	/	SYM
ejpam-6325	177	7	eur	eur	PROPN
ejpam-6325	177	8	.	.	PUNCT
ejpam-6325	178	1	j.	j.	PROPN
ejpam-6325	178	2	pure	pure	PROPN
ejpam-6325	178	3	appl	appl	PROPN
ejpam-6325	178	4	.	.	PROPN
ejpam-6325	178	5	math	math	PROPN
ejpam-6325	178	6	,	,	PUNCT
ejpam-6325	178	7	18	18	NUM
ejpam-6325	178	8	(	(	PUNCT
ejpam-6325	178	9	3	3	NUM
ejpam-6325	178	10	)	)	PUNCT
ejpam-6325	178	11	(	(	PUNCT
ejpam-6325	178	12	2025	2025	NUM
ejpam-6325	178	13	)	)	PUNCT
ejpam-6325	178	14	,	,	PUNCT
ejpam-6325	178	15	6235	6235	NUM
ejpam-6325	178	16	10	10	NUM
ejpam-6325	178	17	of	of	ADP
ejpam-6325	178	18	16	16	NUM
ejpam-6325	178	19	figure	figure	NOUN
ejpam-6325	178	20	1	1	NUM
ejpam-6325	178	21	:	:	PUNCT
ejpam-6325	178	22	three	three	NUM
ejpam-6325	178	23	-	-	PUNCT
ejpam-6325	178	24	dimensional	dimensional	ADJ
ejpam-6325	178	25	plot	plot	NOUN
ejpam-6325	178	26	of	of	ADP
ejpam-6325	178	27	the	the	DET
ejpam-6325	178	28	exact	exact	ADJ
ejpam-6325	178	29	solution	solution	NOUN
ejpam-6325	178	30	u1(x	u1(x	PROPN
ejpam-6325	178	31	,	,	PUNCT
ejpam-6325	178	32	t	t	PROPN
ejpam-6325	178	33	)	)	PUNCT
ejpam-6325	178	34	showing	show	VERB
ejpam-6325	178	35	rapid	rapid	ADJ
ejpam-6325	178	36	exponential	exponential	ADJ
ejpam-6325	178	37	growth	growth	NOUN
ejpam-6325	178	38	as	as	ADP
ejpam-6325	178	39	t	t	PROPN
ejpam-6325	178	40	→	→	SYM
ejpam-6325	178	41	0	0	NUM
ejpam-6325	178	42	+	+	NUM
ejpam-6325	178	43	and	and	CCONJ
ejpam-6325	178	44	x	x	SYM
ejpam-6325	178	45	→	→	SYM
ejpam-6325	178	46	0	0	NUM
ejpam-6325	178	47	.	.	PUNCT
ejpam-6325	179	1	the	the	DET
ejpam-6325	179	2	solution	solution	NOUN
ejpam-6325	179	3	represents	represent	VERB
ejpam-6325	179	4	a	a	DET
ejpam-6325	179	5	highly	highly	ADV
ejpam-6325	179	6	localized	localized	ADJ
ejpam-6325	179	7	pulse	pulse	NOUN
ejpam-6325	179	8	that	that	PRON
ejpam-6325	179	9	sharply	sharply	ADV
ejpam-6325	179	10	increases	increase	VERB
ejpam-6325	179	11	in	in	ADP
ejpam-6325	179	12	amplitude	amplitude	NOUN
ejpam-6325	179	13	.	.	PUNCT
ejpam-6325	180	1	physically	physically	ADV
ejpam-6325	180	2	,	,	PUNCT
ejpam-6325	180	3	this	this	PRON
ejpam-6325	180	4	may	may	AUX
ejpam-6325	180	5	correspond	correspond	VERB
ejpam-6325	180	6	to	to	ADP
ejpam-6325	180	7	a	a	DET
ejpam-6325	180	8	resonance	resonance	NOUN
ejpam-6325	180	9	or	or	CCONJ
ejpam-6325	180	10	instability	instability	NOUN
ejpam-6325	180	11	triggered	trigger	VERB
ejpam-6325	180	12	by	by	ADP
ejpam-6325	180	13	specific	specific	ADJ
ejpam-6325	180	14	combinations	combination	NOUN
ejpam-6325	180	15	of	of	ADP
ejpam-6325	180	16	damping	damp	VERB
ejpam-6325	180	17	parameters	parameter	NOUN
ejpam-6325	180	18	α	α	NOUN
ejpam-6325	180	19	and	and	CCONJ
ejpam-6325	180	20	β	β	NOUN
ejpam-6325	180	21	,	,	PUNCT
ejpam-6325	180	22	where	where	SCONJ
ejpam-6325	180	23	energy	energy	NOUN
ejpam-6325	180	24	is	be	AUX
ejpam-6325	180	25	not	not	PART
ejpam-6325	180	26	dissipated	dissipate	VERB
ejpam-6325	180	27	fast	fast	ADV
ejpam-6325	180	28	enough	enough	ADV
ejpam-6325	180	29	to	to	PART
ejpam-6325	180	30	suppress	suppress	VERB
ejpam-6325	180	31	the	the	DET
ejpam-6325	180	32	growth	growth	NOUN
ejpam-6325	180	33	.	.	PUNCT
ejpam-6325	181	1	figure	figure	VERB
ejpam-6325	181	2	2	2	NUM
ejpam-6325	181	3	:	:	PUNCT
ejpam-6325	181	4	plot	plot	NOUN
ejpam-6325	181	5	of	of	ADP
ejpam-6325	181	6	the	the	DET
ejpam-6325	181	7	exact	exact	ADJ
ejpam-6325	181	8	solution	solution	NOUN
ejpam-6325	181	9	u2(x	u2(x	PROPN
ejpam-6325	181	10	,	,	PUNCT
ejpam-6325	181	11	t	t	NOUN
ejpam-6325	181	12	)	)	PUNCT
ejpam-6325	181	13	demonstrating	demonstrate	VERB
ejpam-6325	181	14	smooth	smooth	ADJ
ejpam-6325	181	15	exponential	exponential	ADJ
ejpam-6325	181	16	growth	growth	NOUN
ejpam-6325	181	17	as	as	ADP
ejpam-6325	181	18	t	t	PROPN
ejpam-6325	181	19	→	→	SYM
ejpam-6325	181	20	0	0	NUM
ejpam-6325	181	21	,	,	PUNCT
ejpam-6325	181	22	with	with	ADP
ejpam-6325	181	23	wave	wave	NOUN
ejpam-6325	181	24	attenuation	attenuation	NOUN
ejpam-6325	181	25	visible	visible	ADJ
ejpam-6325	181	26	along	along	ADP
ejpam-6325	181	27	the	the	DET
ejpam-6325	181	28	spatial	spatial	ADJ
ejpam-6325	181	29	axis	axis	NOUN
ejpam-6325	181	30	.	.	PUNCT
ejpam-6325	182	1	this	this	DET
ejpam-6325	182	2	solution	solution	NOUN
ejpam-6325	182	3	reflects	reflect	VERB
ejpam-6325	182	4	a	a	DET
ejpam-6325	182	5	scenario	scenario	NOUN
ejpam-6325	182	6	where	where	SCONJ
ejpam-6325	182	7	the	the	DET
ejpam-6325	182	8	damping	damping	NOUN
ejpam-6325	182	9	can	can	AUX
ejpam-6325	182	10	not	not	PART
ejpam-6325	182	11	fully	fully	ADV
ejpam-6325	182	12	prevent	prevent	VERB
ejpam-6325	182	13	energy	energy	NOUN
ejpam-6325	182	14	concentration	concentration	NOUN
ejpam-6325	182	15	near	near	ADP
ejpam-6325	182	16	the	the	DET
ejpam-6325	182	17	origin	origin	NOUN
ejpam-6325	182	18	.	.	PUNCT
ejpam-6325	183	1	the	the	DET
ejpam-6325	183	2	result	result	NOUN
ejpam-6325	183	3	can	can	AUX
ejpam-6325	183	4	model	model	VERB
ejpam-6325	183	5	physical	physical	ADJ
ejpam-6325	183	6	systems	system	NOUN
ejpam-6325	183	7	with	with	ADP
ejpam-6325	183	8	weak	weak	ADJ
ejpam-6325	183	9	dissipation	dissipation	NOUN
ejpam-6325	183	10	or	or	CCONJ
ejpam-6325	183	11	external	external	ADJ
ejpam-6325	183	12	energy	energy	NOUN
ejpam-6325	183	13	input	input	NOUN
ejpam-6325	183	14	,	,	PUNCT
ejpam-6325	183	15	such	such	ADJ
ejpam-6325	183	16	as	as	ADP
ejpam-6325	183	17	electrical	electrical	ADJ
ejpam-6325	183	18	pulses	pulse	NOUN
ejpam-6325	183	19	or	or	CCONJ
ejpam-6325	183	20	signals	signal	NOUN
ejpam-6325	183	21	in	in	ADP
ejpam-6325	183	22	low	low	ADJ
ejpam-6325	183	23	-	-	PUNCT
ejpam-6325	183	24	resistance	resistance	NOUN
ejpam-6325	183	25	media	medium	NOUN
ejpam-6325	183	26	.	.	PUNCT
ejpam-6325	184	1	m.	m.	PROPN
ejpam-6325	184	2	noman	noman	PROPN
ejpam-6325	184	3	et	et	PROPN
ejpam-6325	184	4	al	al	PROPN
ejpam-6325	184	5	.	.	PUNCT
ejpam-6325	184	6	/	/	SYM
ejpam-6325	184	7	eur	eur	PROPN
ejpam-6325	184	8	.	.	PUNCT
ejpam-6325	185	1	j.	j.	PROPN
ejpam-6325	185	2	pure	pure	PROPN
ejpam-6325	185	3	appl	appl	PROPN
ejpam-6325	185	4	.	.	PROPN
ejpam-6325	185	5	math	math	PROPN
ejpam-6325	185	6	,	,	PUNCT
ejpam-6325	185	7	18	18	NUM
ejpam-6325	185	8	(	(	PUNCT
ejpam-6325	185	9	3	3	NUM
ejpam-6325	185	10	)	)	PUNCT
ejpam-6325	185	11	(	(	PUNCT
ejpam-6325	185	12	2025	2025	NUM
ejpam-6325	185	13	)	)	PUNCT
ejpam-6325	185	14	,	,	PUNCT
ejpam-6325	185	15	6235	6235	NUM
ejpam-6325	185	16	11	11	NUM
ejpam-6325	185	17	of	of	ADP
ejpam-6325	185	18	16	16	NUM
ejpam-6325	185	19	figure	figure	NOUN
ejpam-6325	185	20	3	3	NUM
ejpam-6325	185	21	:	:	PUNCT
ejpam-6325	185	22	plot	plot	NOUN
ejpam-6325	185	23	of	of	ADP
ejpam-6325	185	24	u3(x	u3(x	PROPN
ejpam-6325	185	25	,	,	PUNCT
ejpam-6325	185	26	t	t	PROPN
ejpam-6325	185	27	)	)	PUNCT
ejpam-6325	185	28	,	,	PUNCT
ejpam-6325	185	29	exhibiting	exhibit	VERB
ejpam-6325	185	30	rapid	rapid	ADJ
ejpam-6325	185	31	spatial	spatial	ADJ
ejpam-6325	185	32	decay	decay	NOUN
ejpam-6325	185	33	with	with	ADP
ejpam-6325	185	34	increasing	increase	VERB
ejpam-6325	185	35	x	x	PUNCT
ejpam-6325	185	36	and	and	CCONJ
ejpam-6325	185	37	temporal	temporal	ADJ
ejpam-6325	185	38	flattening	flattening	NOUN
ejpam-6325	185	39	as	as	ADP
ejpam-6325	185	40	t	t	NOUN
ejpam-6325	185	41	increases	increase	NOUN
ejpam-6325	185	42	.	.	PUNCT
ejpam-6325	186	1	the	the	DET
ejpam-6325	186	2	solution	solution	NOUN
ejpam-6325	186	3	characterizes	characterize	VERB
ejpam-6325	186	4	a	a	DET
ejpam-6325	186	5	strongly	strongly	ADV
ejpam-6325	186	6	damped	damp	VERB
ejpam-6325	186	7	wave	wave	NOUN
ejpam-6325	186	8	where	where	SCONJ
ejpam-6325	186	9	energy	energy	NOUN
ejpam-6325	186	10	dissipates	dissipate	VERB
ejpam-6325	186	11	quickly	quickly	ADV
ejpam-6325	186	12	in	in	ADP
ejpam-6325	186	13	both	both	DET
ejpam-6325	186	14	time	time	NOUN
ejpam-6325	186	15	and	and	CCONJ
ejpam-6325	186	16	space	space	NOUN
ejpam-6325	186	17	.	.	PUNCT
ejpam-6325	187	1	such	such	ADJ
ejpam-6325	187	2	behavior	behavior	NOUN
ejpam-6325	187	3	is	be	AUX
ejpam-6325	187	4	typical	typical	ADJ
ejpam-6325	187	5	in	in	ADP
ejpam-6325	187	6	overdamped	overdampe	VERB
ejpam-6325	187	7	electrical	electrical	ADJ
ejpam-6325	187	8	or	or	CCONJ
ejpam-6325	187	9	thermal	thermal	ADJ
ejpam-6325	187	10	systems	system	NOUN
ejpam-6325	187	11	,	,	PUNCT
ejpam-6325	187	12	where	where	SCONJ
ejpam-6325	187	13	signals	signal	NOUN
ejpam-6325	187	14	are	be	AUX
ejpam-6325	187	15	quickly	quickly	ADV
ejpam-6325	187	16	attenuated	attenuate	VERB
ejpam-6325	187	17	.	.	PUNCT
ejpam-6325	188	1	figure	figure	VERB
ejpam-6325	188	2	4	4	NUM
ejpam-6325	188	3	:	:	SYM
ejpam-6325	188	4	three	three	NUM
ejpam-6325	188	5	-	-	PUNCT
ejpam-6325	188	6	dimensional	dimensional	ADJ
ejpam-6325	188	7	surface	surface	NOUN
ejpam-6325	188	8	plot	plot	NOUN
ejpam-6325	188	9	of	of	ADP
ejpam-6325	188	10	the	the	DET
ejpam-6325	188	11	approximate	approximate	ADJ
ejpam-6325	188	12	solution	solution	NOUN
ejpam-6325	188	13	u4(x	u4(x	PROPN
ejpam-6325	188	14	,	,	PUNCT
ejpam-6325	188	15	t	t	PROPN
ejpam-6325	188	16	)	)	PUNCT
ejpam-6325	188	17	to	to	ADP
ejpam-6325	188	18	the	the	DET
ejpam-6325	188	19	damped	damp	VERB
ejpam-6325	188	20	wave	wave	NOUN
ejpam-6325	188	21	equation	equation	NOUN
ejpam-6325	188	22	utt	utt	NOUN
ejpam-6325	189	1	+	+	CCONJ
ejpam-6325	189	2	(	(	PUNCT
ejpam-6325	189	3	α	α	NOUN
ejpam-6325	189	4	+	+	X
ejpam-6325	189	5	β)ut	β)ut	ADJ
ejpam-6325	189	6	+	+	PUNCT
ejpam-6325	189	7	αβu	αβu	ADV
ejpam-6325	189	8	=	=	NOUN
ejpam-6325	189	9	c2uxx	c2uxx	PROPN
ejpam-6325	189	10	.	.	PUNCT
ejpam-6325	190	1	the	the	DET
ejpam-6325	190	2	plot	plot	NOUN
ejpam-6325	190	3	illustrates	illustrate	VERB
ejpam-6325	190	4	the	the	DET
ejpam-6325	190	5	temporal	temporal	ADJ
ejpam-6325	190	6	and	and	CCONJ
ejpam-6325	190	7	spatial	spatial	ADJ
ejpam-6325	190	8	evolution	evolution	NOUN
ejpam-6325	190	9	of	of	ADP
ejpam-6325	190	10	the	the	DET
ejpam-6325	190	11	solution	solution	NOUN
ejpam-6325	190	12	.	.	PUNCT
ejpam-6325	191	1	the	the	DET
ejpam-6325	191	2	exponential	exponential	ADJ
ejpam-6325	191	3	growth	growth	NOUN
ejpam-6325	191	4	in	in	ADP
ejpam-6325	191	5	u4(x	u4(x	PROPN
ejpam-6325	191	6	,	,	PUNCT
ejpam-6325	191	7	t	t	PROPN
ejpam-6325	191	8	)	)	PUNCT
ejpam-6325	191	9	over	over	ADP
ejpam-6325	191	10	time	time	NOUN
ejpam-6325	191	11	,	,	PUNCT
ejpam-6325	191	12	visible	visible	ADJ
ejpam-6325	191	13	from	from	ADP
ejpam-6325	191	14	the	the	DET
ejpam-6325	191	15	surface	surface	NOUN
ejpam-6325	191	16	,	,	PUNCT
ejpam-6325	191	17	indicates	indicate	VERB
ejpam-6325	191	18	a	a	DET
ejpam-6325	191	19	scenario	scenario	NOUN
ejpam-6325	191	20	where	where	SCONJ
ejpam-6325	191	21	the	the	DET
ejpam-6325	191	22	damping	damp	VERB
ejpam-6325	191	23	effect	effect	NOUN
ejpam-6325	191	24	is	be	AUX
ejpam-6325	191	25	insufficient	insufficient	ADJ
ejpam-6325	191	26	to	to	PART
ejpam-6325	191	27	counteract	counteract	VERB
ejpam-6325	191	28	the	the	DET
ejpam-6325	191	29	restoring	restore	VERB
ejpam-6325	191	30	and	and	CCONJ
ejpam-6325	191	31	wave	wave	NOUN
ejpam-6325	191	32	propagation	propagation	NOUN
ejpam-6325	191	33	forces	force	NOUN
ejpam-6325	191	34	.	.	PUNCT
ejpam-6325	192	1	the	the	DET
ejpam-6325	192	2	parameters	parameter	NOUN
ejpam-6325	192	3	α	α	PRON
ejpam-6325	192	4	,	,	PUNCT
ejpam-6325	192	5	β	β	NOUN
ejpam-6325	192	6	,	,	PUNCT
ejpam-6325	192	7	and	and	CCONJ
ejpam-6325	192	8	c	c	PROPN
ejpam-6325	192	9	significantly	significantly	ADV
ejpam-6325	192	10	influence	influence	VERB
ejpam-6325	192	11	the	the	DET
ejpam-6325	192	12	system	system	NOUN
ejpam-6325	192	13	’s	’s	PART
ejpam-6325	192	14	dynamic	dynamic	ADJ
ejpam-6325	192	15	response	response	NOUN
ejpam-6325	192	16	.	.	PUNCT
ejpam-6325	193	1	m.	m.	PROPN
ejpam-6325	193	2	noman	noman	PROPN
ejpam-6325	193	3	et	et	PROPN
ejpam-6325	193	4	al	al	PROPN
ejpam-6325	193	5	.	.	PUNCT
ejpam-6325	193	6	/	/	SYM
ejpam-6325	193	7	eur	eur	PROPN
ejpam-6325	193	8	.	.	PUNCT
ejpam-6325	194	1	j.	j.	PROPN
ejpam-6325	194	2	pure	pure	PROPN
ejpam-6325	194	3	appl	appl	PROPN
ejpam-6325	194	4	.	.	PROPN
ejpam-6325	194	5	math	math	PROPN
ejpam-6325	194	6	,	,	PUNCT
ejpam-6325	194	7	18	18	NUM
ejpam-6325	194	8	(	(	PUNCT
ejpam-6325	194	9	3	3	NUM
ejpam-6325	194	10	)	)	PUNCT
ejpam-6325	194	11	(	(	PUNCT
ejpam-6325	194	12	2025	2025	NUM
ejpam-6325	194	13	)	)	PUNCT
ejpam-6325	194	14	,	,	PUNCT
ejpam-6325	194	15	6235	6235	NUM
ejpam-6325	194	16	12	12	NUM
ejpam-6325	194	17	of	of	ADP
ejpam-6325	194	18	16	16	NUM
ejpam-6325	194	19	4	4	NUM
ejpam-6325	194	20	.	.	PUNCT
ejpam-6325	194	21	results	result	NOUN
ejpam-6325	194	22	and	and	CCONJ
ejpam-6325	194	23	discussion	discussion	NOUN
ejpam-6325	194	24	the	the	DET
ejpam-6325	194	25	provided	provide	VERB
ejpam-6325	194	26	graphs	graph	NOUN
ejpam-6325	194	27	represent	represent	VERB
ejpam-6325	194	28	the	the	DET
ejpam-6325	194	29	explicit	explicit	ADJ
ejpam-6325	194	30	solutions	solution	NOUN
ejpam-6325	194	31	to	to	ADP
ejpam-6325	194	32	the	the	DET
ejpam-6325	194	33	telegrapher	telegrapher	PROPN
ejpam-6325	194	34	’s	’s	PART
ejpam-6325	194	35	equation	equation	NOUN
ejpam-6325	194	36	utt	utt	NOUN
ejpam-6325	195	1	+	+	CCONJ
ejpam-6325	195	2	(	(	PUNCT
ejpam-6325	195	3	α+	α+	PROPN
ejpam-6325	195	4	β)ut	β)ut	NOUN
ejpam-6325	195	5	+	+	CCONJ
ejpam-6325	195	6	(	(	PUNCT
ejpam-6325	195	7	αβ)u	αβ)u	PROPN
ejpam-6325	195	8	=	=	SYM
ejpam-6325	195	9	c2uxx	c2uxx	PROPN
ejpam-6325	195	10	,	,	PUNCT
ejpam-6325	195	11	with	with	ADP
ejpam-6325	195	12	the	the	DET
ejpam-6325	195	13	solution	solution	NOUN
ejpam-6325	195	14	expressed	express	VERB
ejpam-6325	195	15	as	as	ADP
ejpam-6325	195	16	x	x	X
ejpam-6325	195	17	=	=	SYM
ejpam-6325	195	18	f(ξ	f(ξ	X
ejpam-6325	195	19	)	)	PUNCT
ejpam-6325	195	20	=	=	SYM
ejpam-6325	195	21	u	u	NOUN
ejpam-6325	195	22	=	=	NOUN
ejpam-6325	195	23	exp	exp	X
ejpam-6325	195	24	(	(	PUNCT
ejpam-6325	195	25	αβ(ξ−k	αβ(ξ−k	NOUN
ejpam-6325	195	26	)	)	PUNCT
ejpam-6325	195	27	b(1−c2	b(1−c2	PROPN
ejpam-6325	195	28	)	)	PUNCT
ejpam-6325	195	29	)	)	PUNCT
ejpam-6325	195	30	,	,	PUNCT
ejpam-6325	195	31	and	and	CCONJ
ejpam-6325	195	32	b	b	X
ejpam-6325	195	33	is	be	AUX
ejpam-6325	195	34	the	the	DET
ejpam-6325	195	35	perimeter	perimeter	NOUN
ejpam-6325	195	36	depending	depend	VERB
ejpam-6325	195	37	on	on	ADP
ejpam-6325	195	38	α	α	PROPN
ejpam-6325	195	39	,	,	PUNCT
ejpam-6325	195	40	β	β	X
ejpam-6325	195	41	and	and	CCONJ
ejpam-6325	195	42	c	c	PROPN
ejpam-6325	195	43	defined	define	VERB
ejpam-6325	195	44	by	by	ADP
ejpam-6325	195	45	b	b	NOUN
ejpam-6325	195	46	=	=	SYM
ejpam-6325	195	47	−(α+	−(α+	NUM
ejpam-6325	195	48	β	β	NOUN
ejpam-6325	195	49	)	)	PUNCT
ejpam-6325	195	50	1−	1−	NUM
ejpam-6325	195	51	c2	c2	PROPN
ejpam-6325	195	52	±	±	PROPN
ejpam-6325	195	53	√√√√(α+	√√√√(α+	NOUN
ejpam-6325	195	54	β)2	β)2	ADV
ejpam-6325	195	55	−	−	PROPN
ejpam-6325	195	56	4αβ(1−	4αβ(1−	PROPN
ejpam-6325	195	57	c2	c2	PROPN
ejpam-6325	195	58	)	)	PUNCT
ejpam-6325	195	59	(	(	PUNCT
ejpam-6325	195	60	1−	1−	NUM
ejpam-6325	195	61	c2)2	c2)2	DET
ejpam-6325	195	62	2	2	NUM
ejpam-6325	195	63	,	,	PUNCT
ejpam-6325	195	64	each	each	PRON
ejpam-6325	195	65	of	of	ADP
ejpam-6325	195	66	the	the	DET
ejpam-6325	195	67	four	four	NUM
ejpam-6325	195	68	3d	3d	PROPN
ejpam-6325	195	69	surface	surface	NOUN
ejpam-6325	195	70	plots	plot	NOUN
ejpam-6325	195	71	corresponds	correspond	VERB
ejpam-6325	195	72	to	to	ADP
ejpam-6325	195	73	different	different	ADJ
ejpam-6325	195	74	choices	choice	NOUN
ejpam-6325	195	75	of	of	ADP
ejpam-6325	195	76	the	the	DET
ejpam-6325	195	77	parameters	parameter	NOUN
ejpam-6325	195	78	α	α	NOUN
ejpam-6325	195	79	,	,	PUNCT
ejpam-6325	195	80	β	β	X
ejpam-6325	195	81	,	,	PUNCT
ejpam-6325	195	82	c	c	PROPN
ejpam-6325	195	83	and	and	CCONJ
ejpam-6325	195	84	k	k	PROPN
ejpam-6325	195	85	highlighting	highlight	VERB
ejpam-6325	195	86	the	the	DET
ejpam-6325	195	87	diverse	diverse	ADJ
ejpam-6325	195	88	behaviors	behavior	NOUN
ejpam-6325	195	89	this	this	DET
ejpam-6325	195	90	solution	solution	NOUN
ejpam-6325	195	91	can	can	AUX
ejpam-6325	195	92	capture	capture	VERB
ejpam-6325	195	93	.	.	PUNCT
ejpam-6325	196	1	figure	figure	VERB
ejpam-6325	196	2	1	1	NUM
ejpam-6325	196	3	(	(	PUNCT
ejpam-6325	196	4	graph	graph	NOUN
ejpam-6325	196	5	of	of	ADP
ejpam-6325	196	6	u1(x	u1(x	PROPN
ejpam-6325	196	7	,	,	PUNCT
ejpam-6325	196	8	t	t	PROPN
ejpam-6325	196	9	)	)	PUNCT
ejpam-6325	196	10	displays	display	VERB
ejpam-6325	196	11	a	a	DET
ejpam-6325	196	12	highly	highly	ADV
ejpam-6325	196	13	singular	singular	ADJ
ejpam-6325	196	14	behavior	behavior	NOUN
ejpam-6325	196	15	centered	center	VERB
ejpam-6325	196	16	near	near	ADP
ejpam-6325	196	17	x	x	X
ejpam-6325	197	1	=	=	SYM
ejpam-6325	197	2	0	0	NUM
ejpam-6325	197	3	t	t	NOUN
ejpam-6325	197	4	=	=	SYM
ejpam-6325	197	5	0	0	X
ejpam-6325	197	6	.	.	PUNCT
ejpam-6325	198	1	the	the	DET
ejpam-6325	198	2	solution	solution	NOUN
ejpam-6325	198	3	grows	grow	VERB
ejpam-6325	198	4	extremely	extremely	ADV
ejpam-6325	198	5	large	large	ADJ
ejpam-6325	198	6	in	in	ADP
ejpam-6325	198	7	a	a	DET
ejpam-6325	198	8	very	very	ADV
ejpam-6325	198	9	narrow	narrow	ADJ
ejpam-6325	198	10	region	region	NOUN
ejpam-6325	198	11	,	,	PUNCT
ejpam-6325	198	12	suggesting	suggest	VERB
ejpam-6325	198	13	that	that	SCONJ
ejpam-6325	198	14	for	for	ADP
ejpam-6325	198	15	specific	specific	ADJ
ejpam-6325	198	16	parameter	parameter	NOUN
ejpam-6325	198	17	values	value	NOUN
ejpam-6325	198	18	,	,	PUNCT
ejpam-6325	198	19	the	the	DET
ejpam-6325	198	20	system	system	NOUN
ejpam-6325	198	21	experiences	experience	VERB
ejpam-6325	198	22	rapid	rapid	ADJ
ejpam-6325	198	23	and	and	CCONJ
ejpam-6325	198	24	significant	significant	ADJ
ejpam-6325	198	25	amplification	amplification	NOUN
ejpam-6325	198	26	.	.	PUNCT
ejpam-6325	199	1	this	this	DET
ejpam-6325	199	2	behavior	behavior	NOUN
ejpam-6325	199	3	models	model	VERB
ejpam-6325	199	4	real	real	ADJ
ejpam-6325	199	5	-	-	PUNCT
ejpam-6325	199	6	world	world	NOUN
ejpam-6325	199	7	phenomena	phenomenon	NOUN
ejpam-6325	199	8	where	where	SCONJ
ejpam-6325	199	9	initial	initial	ADJ
ejpam-6325	199	10	conditions	condition	NOUN
ejpam-6325	199	11	or	or	CCONJ
ejpam-6325	199	12	parameter	parameter	NOUN
ejpam-6325	199	13	choices	choice	NOUN
ejpam-6325	199	14	lead	lead	VERB
ejpam-6325	199	15	to	to	ADP
ejpam-6325	199	16	instability	instability	NOUN
ejpam-6325	199	17	or	or	CCONJ
ejpam-6325	199	18	catastrophic	catastrophic	ADJ
ejpam-6325	199	19	failure	failure	NOUN
ejpam-6325	199	20	,	,	PUNCT
ejpam-6325	199	21	such	such	ADJ
ejpam-6325	199	22	as	as	ADP
ejpam-6325	199	23	resonance	resonance	NOUN
ejpam-6325	199	24	in	in	ADP
ejpam-6325	199	25	mechanical	mechanical	ADJ
ejpam-6325	199	26	systems	system	NOUN
ejpam-6325	199	27	or	or	CCONJ
ejpam-6325	199	28	blow	blow	NOUN
ejpam-6325	199	29	-	-	PUNCT
ejpam-6325	199	30	up	up	NOUN
ejpam-6325	199	31	in	in	ADP
ejpam-6325	199	32	nonlinear	nonlinear	ADJ
ejpam-6325	199	33	media	medium	NOUN
ejpam-6325	199	34	.	.	PUNCT
ejpam-6325	200	1	figure	figure	NOUN
ejpam-6325	200	2	2	2	NUM
ejpam-6325	200	3	(	(	PUNCT
ejpam-6325	200	4	graph	graph	NOUN
ejpam-6325	200	5	of	of	ADP
ejpam-6325	200	6	u2(x	u2(x	NOUN
ejpam-6325	200	7	,	,	PUNCT
ejpam-6325	200	8	t	t	PROPN
ejpam-6325	200	9	)	)	PUNCT
ejpam-6325	200	10	shows	show	VERB
ejpam-6325	200	11	rapid	rapid	ADJ
ejpam-6325	200	12	growth	growth	NOUN
ejpam-6325	200	13	along	along	ADP
ejpam-6325	200	14	the	the	DET
ejpam-6325	200	15	time	time	NOUN
ejpam-6325	200	16	axis	axis	NOUN
ejpam-6325	200	17	while	while	SCONJ
ejpam-6325	200	18	remaining	remain	VERB
ejpam-6325	200	19	relatively	relatively	ADV
ejpam-6325	200	20	flat	flat	ADJ
ejpam-6325	200	21	along	along	ADP
ejpam-6325	200	22	the	the	DET
ejpam-6325	200	23	spatial	spatial	ADJ
ejpam-6325	200	24	direction	direction	NOUN
ejpam-6325	200	25	.	.	PUNCT
ejpam-6325	201	1	this	this	PRON
ejpam-6325	201	2	indicates	indicate	VERB
ejpam-6325	201	3	that	that	SCONJ
ejpam-6325	201	4	the	the	DET
ejpam-6325	201	5	temporal	temporal	ADJ
ejpam-6325	201	6	damping	damping	NOUN
ejpam-6325	201	7	is	be	AUX
ejpam-6325	201	8	not	not	PART
ejpam-6325	201	9	sufficient	sufficient	ADJ
ejpam-6325	201	10	to	to	PART
ejpam-6325	201	11	counteract	counteract	VERB
ejpam-6325	201	12	the	the	DET
ejpam-6325	201	13	intrinsic	intrinsic	ADJ
ejpam-6325	201	14	growth	growth	NOUN
ejpam-6325	201	15	,	,	PUNCT
ejpam-6325	201	16	making	make	VERB
ejpam-6325	201	17	this	this	DET
ejpam-6325	201	18	solution	solution	NOUN
ejpam-6325	201	19	appropriate	appropriate	ADJ
ejpam-6325	201	20	to	to	ADP
ejpam-6325	201	21	model	model	NOUN
ejpam-6325	201	22	systems	system	NOUN
ejpam-6325	201	23	where	where	SCONJ
ejpam-6325	201	24	energy	energy	NOUN
ejpam-6325	201	25	input	input	NOUN
ejpam-6325	201	26	over	over	ADP
ejpam-6325	201	27	time	time	NOUN
ejpam-6325	201	28	leads	lead	VERB
ejpam-6325	201	29	to	to	ADP
ejpam-6325	201	30	an	an	DET
ejpam-6325	201	31	unstable	unstable	ADJ
ejpam-6325	201	32	build	build	NOUN
ejpam-6325	201	33	-	-	PUNCT
ejpam-6325	201	34	up	up	NOUN
ejpam-6325	201	35	,	,	PUNCT
ejpam-6325	201	36	such	such	ADJ
ejpam-6325	201	37	as	as	ADP
ejpam-6325	201	38	certain	certain	ADJ
ejpam-6325	201	39	electrical	electrical	ADJ
ejpam-6325	201	40	circuits	circuit	NOUN
ejpam-6325	201	41	or	or	CCONJ
ejpam-6325	201	42	unstable	unstable	ADJ
ejpam-6325	201	43	feedback	feedback	NOUN
ejpam-6325	201	44	systems	system	NOUN
ejpam-6325	201	45	.	.	PUNCT
ejpam-6325	202	1	figure	figure	VERB
ejpam-6325	202	2	3	3	NUM
ejpam-6325	202	3	(	(	PUNCT
ejpam-6325	202	4	graph	graph	NOUN
ejpam-6325	202	5	of	of	ADP
ejpam-6325	202	6	u3(x	u3(x	PROPN
ejpam-6325	202	7	,	,	PUNCT
ejpam-6325	202	8	t	t	PROPN
ejpam-6325	202	9	)	)	PUNCT
ejpam-6325	202	10	portrays	portray	VERB
ejpam-6325	202	11	a	a	DET
ejpam-6325	202	12	localized	localize	VERB
ejpam-6325	202	13	sharp	sharp	ADJ
ejpam-6325	202	14	peak	peak	NOUN
ejpam-6325	202	15	at	at	ADP
ejpam-6325	202	16	an	an	DET
ejpam-6325	202	17	early	early	ADJ
ejpam-6325	202	18	time	time	NOUN
ejpam-6325	202	19	that	that	PRON
ejpam-6325	202	20	dissipates	dissipate	VERB
ejpam-6325	202	21	as	as	ADP
ejpam-6325	202	22	time	time	NOUN
ejpam-6325	202	23	progresses	progress	NOUN
ejpam-6325	202	24	.	.	PUNCT
ejpam-6325	203	1	this	this	PRON
ejpam-6325	203	2	suggests	suggest	VERB
ejpam-6325	203	3	a	a	DET
ejpam-6325	203	4	pulse	pulse	NOUN
ejpam-6325	203	5	-	-	PUNCT
ejpam-6325	203	6	like	like	NOUN
ejpam-6325	203	7	or	or	CCONJ
ejpam-6325	203	8	shock	shock	NOUN
ejpam-6325	203	9	-	-	PUNCT
ejpam-6325	203	10	like	like	ADJ
ejpam-6325	203	11	solution	solution	NOUN
ejpam-6325	203	12	that	that	PRON
ejpam-6325	203	13	decays	decay	VERB
ejpam-6325	203	14	naturally	naturally	ADV
ejpam-6325	203	15	due	due	ADP
ejpam-6325	203	16	to	to	ADP
ejpam-6325	203	17	the	the	DET
ejpam-6325	203	18	damping	damp	VERB
ejpam-6325	203	19	effects	effect	NOUN
ejpam-6325	203	20	.	.	PUNCT
ejpam-6325	204	1	it	it	PRON
ejpam-6325	204	2	captures	capture	VERB
ejpam-6325	204	3	scenarios	scenario	NOUN
ejpam-6325	204	4	like	like	ADP
ejpam-6325	204	5	dissipative	dissipative	ADJ
ejpam-6325	204	6	wave	wave	NOUN
ejpam-6325	204	7	propagation	propagation	NOUN
ejpam-6325	204	8	,	,	PUNCT
ejpam-6325	204	9	where	where	SCONJ
ejpam-6325	204	10	an	an	DET
ejpam-6325	204	11	initial	initial	ADJ
ejpam-6325	204	12	disturbance	disturbance	NOUN
ejpam-6325	204	13	gradually	gradually	ADV
ejpam-6325	204	14	loses	lose	VERB
ejpam-6325	204	15	energy	energy	NOUN
ejpam-6325	204	16	as	as	SCONJ
ejpam-6325	204	17	it	it	PRON
ejpam-6325	204	18	travels	travel	VERB
ejpam-6325	204	19	,	,	PUNCT
ejpam-6325	204	20	which	which	PRON
ejpam-6325	204	21	is	be	AUX
ejpam-6325	204	22	crucial	crucial	ADJ
ejpam-6325	204	23	in	in	ADP
ejpam-6325	204	24	fields	field	NOUN
ejpam-6325	204	25	like	like	ADP
ejpam-6325	204	26	seismology	seismology	NOUN
ejpam-6325	204	27	,	,	PUNCT
ejpam-6325	204	28	material	material	NOUN
ejpam-6325	204	29	sciences	science	NOUN
ejpam-6325	204	30	,	,	PUNCT
ejpam-6325	204	31	and	and	CCONJ
ejpam-6325	204	32	acoustic	acoustic	ADJ
ejpam-6325	204	33	wave	wave	NOUN
ejpam-6325	204	34	modeling	modeling	NOUN
ejpam-6325	204	35	.	.	PUNCT
ejpam-6325	205	1	figure	figure	NOUN
ejpam-6325	205	2	4	4	NUM
ejpam-6325	205	3	(	(	PUNCT
ejpam-6325	205	4	graph	graph	NOUN
ejpam-6325	205	5	of	of	ADP
ejpam-6325	205	6	u4(x	u4(x	PROPN
ejpam-6325	205	7	,	,	PUNCT
ejpam-6325	205	8	t	t	PROPN
ejpam-6325	205	9	)	)	PUNCT
ejpam-6325	205	10	differs	differ	VERB
ejpam-6325	205	11	significantly	significantly	ADV
ejpam-6325	205	12	by	by	ADP
ejpam-6325	205	13	exhibiting	exhibit	VERB
ejpam-6325	205	14	a	a	DET
ejpam-6325	205	15	smooth	smooth	ADJ
ejpam-6325	205	16	,	,	PUNCT
ejpam-6325	205	17	controlled	control	VERB
ejpam-6325	205	18	increase	increase	NOUN
ejpam-6325	205	19	in	in	ADP
ejpam-6325	205	20	amplitude	amplitude	NOUN
ejpam-6325	205	21	without	without	ADP
ejpam-6325	205	22	any	any	DET
ejpam-6325	205	23	signs	sign	NOUN
ejpam-6325	205	24	of	of	ADP
ejpam-6325	205	25	instability	instability	NOUN
ejpam-6325	205	26	.	.	PUNCT
ejpam-6325	206	1	here	here	ADV
ejpam-6325	206	2	,	,	PUNCT
ejpam-6325	206	3	the	the	DET
ejpam-6325	206	4	solution	solution	NOUN
ejpam-6325	206	5	remains	remain	VERB
ejpam-6325	206	6	bounded	bound	VERB
ejpam-6325	206	7	and	and	CCONJ
ejpam-6325	206	8	grows	grow	VERB
ejpam-6325	206	9	predictably	predictably	ADV
ejpam-6325	206	10	,	,	PUNCT
ejpam-6325	206	11	which	which	PRON
ejpam-6325	206	12	corresponds	correspond	VERB
ejpam-6325	206	13	to	to	ADP
ejpam-6325	206	14	stable	stable	ADJ
ejpam-6325	206	15	regimes	regime	NOUN
ejpam-6325	206	16	where	where	SCONJ
ejpam-6325	206	17	the	the	DET
ejpam-6325	206	18	damping	damp	VERB
ejpam-6325	206	19	dominates	dominate	VERB
ejpam-6325	206	20	and	and	CCONJ
ejpam-6325	206	21	prevents	prevent	VERB
ejpam-6325	206	22	any	any	DET
ejpam-6325	206	23	explosive	explosive	ADJ
ejpam-6325	206	24	behavior	behavior	NOUN
ejpam-6325	206	25	.	.	PUNCT
ejpam-6325	207	1	such	such	ADJ
ejpam-6325	207	2	behavior	behavior	NOUN
ejpam-6325	207	3	is	be	AUX
ejpam-6325	207	4	desirable	desirable	ADJ
ejpam-6325	207	5	in	in	ADP
ejpam-6325	207	6	engineering	engineering	NOUN
ejpam-6325	207	7	applications	application	NOUN
ejpam-6325	207	8	where	where	SCONJ
ejpam-6325	207	9	stability	stability	NOUN
ejpam-6325	207	10	under	under	ADP
ejpam-6325	207	11	oscillations	oscillation	NOUN
ejpam-6325	207	12	is	be	AUX
ejpam-6325	207	13	critical	critical	ADJ
ejpam-6325	207	14	,	,	PUNCT
ejpam-6325	207	15	such	such	ADJ
ejpam-6325	207	16	as	as	ADP
ejpam-6325	207	17	suspension	suspension	NOUN
ejpam-6325	207	18	bridges	bridge	NOUN
ejpam-6325	207	19	,	,	PUNCT
ejpam-6325	207	20	skyscraper	skyscraper	NOUN
ejpam-6325	207	21	design	design	NOUN
ejpam-6325	207	22	,	,	PUNCT
ejpam-6325	207	23	and	and	CCONJ
ejpam-6325	207	24	vibration	vibration	NOUN
ejpam-6325	207	25	control	control	NOUN
ejpam-6325	207	26	in	in	ADP
ejpam-6325	207	27	aerospace	aerospace	NOUN
ejpam-6325	207	28	structures	structure	NOUN
ejpam-6325	207	29	.	.	PUNCT
ejpam-6325	208	1	the	the	DET
ejpam-6325	208	2	advantage	advantage	NOUN
ejpam-6325	208	3	of	of	ADP
ejpam-6325	208	4	this	this	DET
ejpam-6325	208	5	explicit	explicit	ADJ
ejpam-6325	208	6	solution	solution	NOUN
ejpam-6325	208	7	structure	structure	NOUN
ejpam-6325	208	8	is	be	AUX
ejpam-6325	208	9	profound	profound	ADJ
ejpam-6325	208	10	.	.	PUNCT
ejpam-6325	209	1	it	it	PRON
ejpam-6325	209	2	provides	provide	VERB
ejpam-6325	209	3	a	a	DET
ejpam-6325	209	4	direct	direct	ADJ
ejpam-6325	209	5	and	and	CCONJ
ejpam-6325	209	6	exact	exact	ADJ
ejpam-6325	209	7	way	way	NOUN
ejpam-6325	209	8	to	to	PART
ejpam-6325	209	9	understand	understand	VERB
ejpam-6325	209	10	how	how	SCONJ
ejpam-6325	209	11	damping	damp	VERB
ejpam-6325	209	12	parameters	parameter	NOUN
ejpam-6325	209	13	α	α	X
ejpam-6325	209	14	,	,	PUNCT
ejpam-6325	209	15	β	β	X
ejpam-6325	209	16	and	and	CCONJ
ejpam-6325	209	17	the	the	DET
ejpam-6325	209	18	wave	wave	NOUN
ejpam-6325	209	19	propagation	propagation	NOUN
ejpam-6325	209	20	speed	speed	NOUN
ejpam-6325	209	21	c	c	PRON
ejpam-6325	209	22	interact	interact	VERB
ejpam-6325	209	23	to	to	PART
ejpam-6325	209	24	govern	govern	VERB
ejpam-6325	209	25	the	the	DET
ejpam-6325	209	26	overall	overall	ADJ
ejpam-6325	209	27	behavior	behavior	NOUN
ejpam-6325	209	28	of	of	ADP
ejpam-6325	209	29	the	the	DET
ejpam-6325	209	30	system	system	NOUN
ejpam-6325	209	31	.	.	PUNCT
ejpam-6325	210	1	analytical	analytical	ADJ
ejpam-6325	210	2	solutions	solution	NOUN
ejpam-6325	210	3	like	like	ADP
ejpam-6325	210	4	these	these	PRON
ejpam-6325	210	5	are	be	AUX
ejpam-6325	210	6	extremely	extremely	ADV
ejpam-6325	210	7	valuable	valuable	ADJ
ejpam-6325	210	8	because	because	SCONJ
ejpam-6325	210	9	they	they	PRON
ejpam-6325	210	10	offer	offer	VERB
ejpam-6325	210	11	insight	insight	NOUN
ejpam-6325	210	12	into	into	ADP
ejpam-6325	210	13	the	the	DET
ejpam-6325	210	14	qualitative	qualitative	ADJ
ejpam-6325	210	15	behavior	behavior	NOUN
ejpam-6325	210	16	of	of	ADP
ejpam-6325	210	17	the	the	DET
ejpam-6325	210	18	system	system	NOUN
ejpam-6325	210	19	without	without	ADP
ejpam-6325	210	20	requiring	require	VERB
ejpam-6325	210	21	extensive	extensive	ADJ
ejpam-6325	210	22	numerical	numerical	ADJ
ejpam-6325	210	23	simulations	simulation	NOUN
ejpam-6325	210	24	.	.	PUNCT
ejpam-6325	211	1	they	they	PRON
ejpam-6325	211	2	allow	allow	VERB
ejpam-6325	211	3	for	for	ADP
ejpam-6325	211	4	a	a	DET
ejpam-6325	211	5	clear	clear	ADJ
ejpam-6325	211	6	understanding	understanding	NOUN
ejpam-6325	211	7	of	of	ADP
ejpam-6325	211	8	stability	stability	NOUN
ejpam-6325	211	9	conditions	condition	NOUN
ejpam-6325	211	10	,	,	PUNCT
ejpam-6325	211	11	energy	energy	NOUN
ejpam-6325	211	12	dissipation	dissipation	NOUN
ejpam-6325	211	13	,	,	PUNCT
ejpam-6325	211	14	and	and	CCONJ
ejpam-6325	211	15	the	the	DET
ejpam-6325	211	16	critical	critical	ADJ
ejpam-6325	211	17	thresholds	threshold	NOUN
ejpam-6325	211	18	for	for	ADP
ejpam-6325	211	19	transition	transition	NOUN
ejpam-6325	211	20	from	from	ADP
ejpam-6325	211	21	m.	m.	PROPN
ejpam-6325	211	22	noman	noman	PROPN
ejpam-6325	211	23	et	et	PROPN
ejpam-6325	211	24	al	al	PROPN
ejpam-6325	211	25	.	.	PUNCT
ejpam-6325	211	26	/	/	SYM
ejpam-6325	211	27	eur	eur	PROPN
ejpam-6325	211	28	.	.	PUNCT
ejpam-6325	212	1	j.	j.	PROPN
ejpam-6325	212	2	pure	pure	PROPN
ejpam-6325	212	3	appl	appl	PROPN
ejpam-6325	212	4	.	.	PROPN
ejpam-6325	212	5	math	math	PROPN
ejpam-6325	212	6	,	,	PUNCT
ejpam-6325	212	7	18	18	NUM
ejpam-6325	212	8	(	(	PUNCT
ejpam-6325	212	9	3	3	NUM
ejpam-6325	212	10	)	)	PUNCT
ejpam-6325	212	11	(	(	PUNCT
ejpam-6325	212	12	2025	2025	NUM
ejpam-6325	212	13	)	)	PUNCT
ejpam-6325	212	14	,	,	PUNCT
ejpam-6325	212	15	6235	6235	NUM
ejpam-6325	212	16	13	13	NUM
ejpam-6325	212	17	of	of	ADP
ejpam-6325	212	18	16	16	NUM
ejpam-6325	212	19	stability	stability	NOUN
ejpam-6325	212	20	to	to	ADP
ejpam-6325	212	21	instability	instability	NOUN
ejpam-6325	212	22	.	.	PUNCT
ejpam-6325	213	1	furthermore	furthermore	ADV
ejpam-6325	213	2	,	,	PUNCT
ejpam-6325	213	3	in	in	ADP
ejpam-6325	213	4	practical	practical	ADJ
ejpam-6325	213	5	applications	application	NOUN
ejpam-6325	213	6	,	,	PUNCT
ejpam-6325	213	7	having	have	VERB
ejpam-6325	213	8	an	an	DET
ejpam-6325	213	9	explicit	explicit	ADJ
ejpam-6325	213	10	solution	solution	NOUN
ejpam-6325	213	11	enables	enable	VERB
ejpam-6325	213	12	engineers	engineer	NOUN
ejpam-6325	213	13	and	and	CCONJ
ejpam-6325	213	14	scientists	scientist	NOUN
ejpam-6325	213	15	to	to	PART
ejpam-6325	213	16	design	design	VERB
ejpam-6325	213	17	systems	system	NOUN
ejpam-6325	213	18	with	with	ADP
ejpam-6325	213	19	desired	desire	VERB
ejpam-6325	213	20	dynamic	dynamic	ADJ
ejpam-6325	213	21	properties	property	NOUN
ejpam-6325	213	22	.	.	PUNCT
ejpam-6325	214	1	by	by	ADP
ejpam-6325	214	2	adjusting	adjust	VERB
ejpam-6325	214	3	the	the	DET
ejpam-6325	214	4	parameters	parameter	NOUN
ejpam-6325	214	5	based	base	VERB
ejpam-6325	214	6	on	on	ADP
ejpam-6325	214	7	the	the	DET
ejpam-6325	214	8	explicit	explicit	ADJ
ejpam-6325	214	9	formula	formula	NOUN
ejpam-6325	214	10	,	,	PUNCT
ejpam-6325	214	11	one	one	PRON
ejpam-6325	214	12	can	can	AUX
ejpam-6325	214	13	tailor	tailor	VERB
ejpam-6325	214	14	the	the	DET
ejpam-6325	214	15	system	system	NOUN
ejpam-6325	214	16	’s	’s	PART
ejpam-6325	214	17	response	response	NOUN
ejpam-6325	214	18	to	to	PART
ejpam-6325	214	19	prevent	prevent	VERB
ejpam-6325	214	20	dangerous	dangerous	ADJ
ejpam-6325	214	21	instabilities	instability	NOUN
ejpam-6325	214	22	or	or	CCONJ
ejpam-6325	214	23	to	to	ADP
ejpam-6325	214	24	harness	harness	NOUN
ejpam-6325	214	25	controlled	control	VERB
ejpam-6325	214	26	amplification	amplification	NOUN
ejpam-6325	214	27	where	where	SCONJ
ejpam-6325	214	28	needed	need	VERB
ejpam-6325	214	29	(	(	PUNCT
ejpam-6325	214	30	such	such	ADJ
ejpam-6325	214	31	as	as	ADP
ejpam-6325	214	32	signal	signal	ADJ
ejpam-6325	214	33	boosting	boosting	NOUN
ejpam-6325	214	34	)	)	PUNCT
ejpam-6325	214	35	.	.	PUNCT
ejpam-6325	215	1	the	the	DET
ejpam-6325	215	2	importance	importance	NOUN
ejpam-6325	215	3	of	of	ADP
ejpam-6325	215	4	such	such	ADJ
ejpam-6325	215	5	solutions	solution	NOUN
ejpam-6325	215	6	extends	extend	VERB
ejpam-6325	215	7	to	to	ADP
ejpam-6325	215	8	various	various	ADJ
ejpam-6325	215	9	fields	field	NOUN
ejpam-6325	215	10	,	,	PUNCT
ejpam-6325	215	11	including	include	VERB
ejpam-6325	215	12	mechanical	mechanical	ADJ
ejpam-6325	215	13	and	and	CCONJ
ejpam-6325	215	14	civil	civil	ADJ
ejpam-6325	215	15	engineering	engineering	NOUN
ejpam-6325	215	16	,	,	PUNCT
ejpam-6325	215	17	physics	physics	NOUN
ejpam-6325	215	18	,	,	PUNCT
ejpam-6325	215	19	materials	material	NOUN
ejpam-6325	215	20	science	science	NOUN
ejpam-6325	215	21	,	,	PUNCT
ejpam-6325	215	22	and	and	CCONJ
ejpam-6325	215	23	control	control	NOUN
ejpam-6325	215	24	theory	theory	NOUN
ejpam-6325	215	25	.	.	PUNCT
ejpam-6325	216	1	in	in	ADP
ejpam-6325	216	2	conclusion	conclusion	NOUN
ejpam-6325	216	3	,	,	PUNCT
ejpam-6325	216	4	the	the	DET
ejpam-6325	216	5	diverse	diverse	ADJ
ejpam-6325	216	6	behaviors	behavior	NOUN
ejpam-6325	216	7	captured	capture	VERB
ejpam-6325	216	8	by	by	ADP
ejpam-6325	216	9	these	these	DET
ejpam-6325	216	10	graphs	graph	NOUN
ejpam-6325	216	11	ranging	range	VERB
ejpam-6325	216	12	from	from	ADP
ejpam-6325	216	13	explosive	explosive	ADJ
ejpam-6325	216	14	growth	growth	NOUN
ejpam-6325	216	15	to	to	ADP
ejpam-6325	216	16	smooth	smooth	ADJ
ejpam-6325	216	17	decay	decay	NOUN
ejpam-6325	216	18	highlight	highlight	VERB
ejpam-6325	216	19	the	the	DET
ejpam-6325	216	20	richness	richness	NOUN
ejpam-6325	216	21	of	of	ADP
ejpam-6325	216	22	the	the	DET
ejpam-6325	216	23	dynamics	dynamic	NOUN
ejpam-6325	216	24	described	describe	VERB
ejpam-6325	216	25	by	by	ADP
ejpam-6325	216	26	the	the	DET
ejpam-6325	216	27	damped	damped	NOUN
ejpam-6325	216	28	wave	wave	NOUN
ejpam-6325	216	29	equation	equation	NOUN
ejpam-6325	216	30	.	.	PUNCT
ejpam-6325	217	1	the	the	DET
ejpam-6325	217	2	explicit	explicit	ADJ
ejpam-6325	217	3	solutions	solution	NOUN
ejpam-6325	217	4	serve	serve	VERB
ejpam-6325	217	5	as	as	ADP
ejpam-6325	217	6	powerful	powerful	ADJ
ejpam-6325	217	7	tools	tool	NOUN
ejpam-6325	217	8	both	both	PRON
ejpam-6325	217	9	for	for	ADP
ejpam-6325	217	10	theoretical	theoretical	ADJ
ejpam-6325	217	11	analysis	analysis	NOUN
ejpam-6325	217	12	and	and	CCONJ
ejpam-6325	217	13	for	for	ADP
ejpam-6325	217	14	practical	practical	ADJ
ejpam-6325	217	15	design	design	NOUN
ejpam-6325	217	16	and	and	CCONJ
ejpam-6325	217	17	optimization	optimization	NOUN
ejpam-6325	217	18	in	in	ADP
ejpam-6325	217	19	complex	complex	ADJ
ejpam-6325	217	20	systems	system	NOUN
ejpam-6325	217	21	.	.	PUNCT
ejpam-6325	218	1	5	5	X
ejpam-6325	218	2	.	.	X
ejpam-6325	218	3	stability	stability	NOUN
ejpam-6325	218	4	analysis	analysis	NOUN
ejpam-6325	218	5	of	of	ADP
ejpam-6325	218	6	the	the	DET
ejpam-6325	218	7	exact	exact	ADJ
ejpam-6325	218	8	solution	solution	NOUN
ejpam-6325	218	9	to	to	PART
ejpam-6325	218	10	assess	assess	VERB
ejpam-6325	218	11	the	the	DET
ejpam-6325	218	12	stability	stability	NOUN
ejpam-6325	218	13	of	of	ADP
ejpam-6325	218	14	the	the	DET
ejpam-6325	218	15	exact	exact	ADJ
ejpam-6325	218	16	traveling	travel	VERB
ejpam-6325	218	17	wave	wave	NOUN
ejpam-6325	218	18	solution	solution	NOUN
ejpam-6325	218	19	f(ξ	f(ξ	NOUN
ejpam-6325	218	20	)	)	PUNCT
ejpam-6325	218	21	=	=	SYM
ejpam-6325	218	22	exp	exp	NOUN
ejpam-6325	218	23	(	(	PUNCT
ejpam-6325	218	24	αβ(ξ	αβ(ξ	NUM
ejpam-6325	218	25	−k	−k	NOUN
ejpam-6325	218	26	)	)	PUNCT
ejpam-6325	218	27	b(1−	b(1−	PROPN
ejpam-6325	218	28	c2	c2	PROPN
ejpam-6325	218	29	)	)	PUNCT
ejpam-6325	218	30	)	)	PUNCT
ejpam-6325	218	31	,	,	PUNCT
ejpam-6325	218	32	we	we	PRON
ejpam-6325	218	33	consider	consider	VERB
ejpam-6325	218	34	a	a	DET
ejpam-6325	218	35	small	small	ADJ
ejpam-6325	218	36	perturbation	perturbation	NOUN
ejpam-6325	218	37	of	of	ADP
ejpam-6325	218	38	the	the	DET
ejpam-6325	218	39	form	form	NOUN
ejpam-6325	218	40	,	,	PUNCT
ejpam-6325	218	41	u(ξ	u(ξ	NOUN
ejpam-6325	218	42	,	,	PUNCT
ejpam-6325	218	43	t	t	PROPN
ejpam-6325	218	44	)	)	PUNCT
ejpam-6325	218	45	=	=	SYM
ejpam-6325	219	1	f(ξ	f(ξ	NOUN
ejpam-6325	219	2	)	)	PUNCT
ejpam-6325	220	1	+	+	CCONJ
ejpam-6325	220	2	ϵϕ(ξ	ϵϕ(ξ	NUM
ejpam-6325	220	3	,	,	PUNCT
ejpam-6325	220	4	t	t	PROPN
ejpam-6325	220	5	)	)	PUNCT
ejpam-6325	220	6	,	,	PUNCT
ejpam-6325	220	7	where	where	SCONJ
ejpam-6325	220	8	0	0	X
ejpam-6325	220	9	<	<	X
ejpam-6325	220	10	ϵ≪	ϵ≪	PROPN
ejpam-6325	220	11	1	1	NUM
ejpam-6325	220	12	and	and	CCONJ
ejpam-6325	220	13	ϕ(ξ	ϕ(ξ	PROPN
ejpam-6325	220	14	,	,	PUNCT
ejpam-6325	220	15	t	t	PROPN
ejpam-6325	220	16	)	)	PUNCT
ejpam-6325	220	17	denotes	denote	VERB
ejpam-6325	220	18	the	the	DET
ejpam-6325	220	19	perturbation	perturbation	NOUN
ejpam-6325	220	20	function	function	NOUN
ejpam-6325	220	21	.	.	PUNCT
ejpam-6325	221	1	substituting	substitute	VERB
ejpam-6325	221	2	this	this	DET
ejpam-6325	221	3	perturbed	perturb	VERB
ejpam-6325	221	4	solution	solution	NOUN
ejpam-6325	221	5	into	into	ADP
ejpam-6325	221	6	the	the	DET
ejpam-6325	221	7	original	original	ADJ
ejpam-6325	221	8	equation	equation	NOUN
ejpam-6325	221	9	and	and	CCONJ
ejpam-6325	221	10	linearizing	linearize	VERB
ejpam-6325	221	11	by	by	ADP
ejpam-6325	221	12	neglecting	neglect	VERB
ejpam-6325	221	13	terms	term	NOUN
ejpam-6325	221	14	of	of	ADP
ejpam-6325	221	15	order	order	NOUN
ejpam-6325	221	16	ϵ2	ϵ2	ADJ
ejpam-6325	221	17	and	and	CCONJ
ejpam-6325	221	18	higher	high	ADJ
ejpam-6325	221	19	,	,	PUNCT
ejpam-6325	221	20	we	we	PRON
ejpam-6325	221	21	obtain	obtain	VERB
ejpam-6325	221	22	the	the	DET
ejpam-6325	221	23	linearized	linearize	VERB
ejpam-6325	221	24	equation	equation	NOUN
ejpam-6325	221	25	governing	govern	VERB
ejpam-6325	221	26	the	the	DET
ejpam-6325	221	27	perturbation	perturbation	NOUN
ejpam-6325	221	28	dynamics	dynamic	NOUN
ejpam-6325	221	29	:	:	PUNCT
ejpam-6325	222	1	ϕtt	ϕtt	INTJ
ejpam-6325	222	2	+	+	CCONJ
ejpam-6325	222	3	(	(	PUNCT
ejpam-6325	222	4	α+	α+	PRON
ejpam-6325	222	5	β)ϕt	β)ϕt	NOUN
ejpam-6325	222	6	+	+	NUM
ejpam-6325	222	7	αβϕ	αβϕ	NOUN
ejpam-6325	222	8	=	=	SYM
ejpam-6325	222	9	c2ϕxx	c2ϕxx	PROPN
ejpam-6325	222	10	.	.	PUNCT
ejpam-6325	223	1	assuming	assume	VERB
ejpam-6325	223	2	a	a	DET
ejpam-6325	223	3	solution	solution	NOUN
ejpam-6325	223	4	of	of	ADP
ejpam-6325	223	5	the	the	DET
ejpam-6325	223	6	form	form	NOUN
ejpam-6325	223	7	ϕ(ξ	ϕ(ξ	PROPN
ejpam-6325	223	8	,	,	PUNCT
ejpam-6325	223	9	t	t	PROPN
ejpam-6325	223	10	)	)	PUNCT
ejpam-6325	223	11	=	=	SYM
ejpam-6325	223	12	eλtψ(ξ	eλtψ(ξ	PROPN
ejpam-6325	223	13	)	)	PUNCT
ejpam-6325	223	14	,	,	PUNCT
ejpam-6325	223	15	where	where	SCONJ
ejpam-6325	223	16	λ	λ	PROPN
ejpam-6325	223	17	is	be	AUX
ejpam-6325	223	18	the	the	DET
ejpam-6325	223	19	growth	growth	NOUN
ejpam-6325	223	20	rate	rate	NOUN
ejpam-6325	223	21	parameter	parameter	NOUN
ejpam-6325	223	22	,	,	PUNCT
ejpam-6325	223	23	leads	lead	VERB
ejpam-6325	223	24	to	to	ADP
ejpam-6325	223	25	the	the	DET
ejpam-6325	223	26	characteristic	characteristic	ADJ
ejpam-6325	223	27	equation	equation	NOUN
ejpam-6325	223	28	λ2	λ2	NOUN
ejpam-6325	223	29	+	+	CCONJ
ejpam-6325	223	30	(	(	PUNCT
ejpam-6325	223	31	α+	α+	ADP
ejpam-6325	223	32	β)λ+	β)λ+	NUM
ejpam-6325	223	33	αβ	αβ	NOUN
ejpam-6325	223	34	=	=	NOUN
ejpam-6325	223	35	0	0	PROPN
ejpam-6325	223	36	.	.	PUNCT
ejpam-6325	224	1	the	the	DET
ejpam-6325	224	2	roots	root	NOUN
ejpam-6325	224	3	of	of	ADP
ejpam-6325	224	4	this	this	DET
ejpam-6325	224	5	quadratic	quadratic	ADJ
ejpam-6325	224	6	equation	equation	NOUN
ejpam-6325	224	7	are	be	AUX
ejpam-6325	224	8	λ	λ	X
ejpam-6325	224	9	=	=	SYM
ejpam-6325	225	1	−(α+	−(α+	NUM
ejpam-6325	225	2	β)±	β)±	X
ejpam-6325	225	3	√	√	NUM
ejpam-6325	225	4	(	(	PUNCT
ejpam-6325	225	5	α+	α+	X
ejpam-6325	225	6	β)2	β)2	ADV
ejpam-6325	225	7	−	−	NOUN
ejpam-6325	225	8	4αβ	4αβ	ADJ
ejpam-6325	225	9	2	2	NUM
ejpam-6325	225	10	.	.	PUNCT
ejpam-6325	226	1	for	for	ADP
ejpam-6325	226	2	positive	positive	ADJ
ejpam-6325	226	3	damping	damp	VERB
ejpam-6325	226	4	coefficients	coefficient	NOUN
ejpam-6325	226	5	α	α	INTJ
ejpam-6325	226	6	>	>	X
ejpam-6325	226	7	0	0	PUNCT
ejpam-6325	226	8	and	and	CCONJ
ejpam-6325	226	9	β	β	X
ejpam-6325	226	10	>	>	X
ejpam-6325	226	11	0	0	PROPN
ejpam-6325	226	12	,	,	PUNCT
ejpam-6325	226	13	both	both	DET
ejpam-6325	226	14	roots	root	NOUN
ejpam-6325	226	15	have	have	VERB
ejpam-6325	226	16	negative	negative	ADJ
ejpam-6325	226	17	real	real	ADJ
ejpam-6325	226	18	parts	part	NOUN
ejpam-6325	226	19	.	.	PUNCT
ejpam-6325	227	1	this	this	PRON
ejpam-6325	227	2	implies	imply	VERB
ejpam-6325	227	3	that	that	SCONJ
ejpam-6325	227	4	any	any	DET
ejpam-6325	227	5	small	small	ADJ
ejpam-6325	227	6	perturbation	perturbation	NOUN
ejpam-6325	227	7	will	will	AUX
ejpam-6325	227	8	decay	decay	VERB
ejpam-6325	227	9	exponentially	exponentially	ADV
ejpam-6325	227	10	over	over	ADP
ejpam-6325	227	11	time	time	NOUN
ejpam-6325	227	12	,	,	PUNCT
ejpam-6325	227	13	confirming	confirm	VERB
ejpam-6325	227	14	the	the	DET
ejpam-6325	227	15	linear	linear	ADJ
ejpam-6325	227	16	stability	stability	NOUN
ejpam-6325	227	17	of	of	ADP
ejpam-6325	227	18	the	the	DET
ejpam-6325	227	19	exact	exact	ADJ
ejpam-6325	227	20	traveling	travel	VERB
ejpam-6325	227	21	wave	wave	NOUN
ejpam-6325	227	22	solution	solution	NOUN
ejpam-6325	227	23	.	.	PUNCT
ejpam-6325	228	1	hence	hence	ADV
ejpam-6325	228	2	,	,	PUNCT
ejpam-6325	228	3	the	the	DET
ejpam-6325	228	4	solution	solution	NOUN
ejpam-6325	228	5	obtained	obtain	VERB
ejpam-6325	228	6	through	through	ADP
ejpam-6325	228	7	the	the	DET
ejpam-6325	228	8	generalized	generalized	ADJ
ejpam-6325	228	9	first	first	ADJ
ejpam-6325	228	10	integral	integral	ADJ
ejpam-6325	228	11	method	method	NOUN
ejpam-6325	228	12	is	be	AUX
ejpam-6325	228	13	stable	stable	ADJ
ejpam-6325	228	14	and	and	CCONJ
ejpam-6325	228	15	physically	physically	ADV
ejpam-6325	228	16	relevant	relevant	ADJ
ejpam-6325	228	17	for	for	ADP
ejpam-6325	228	18	modeling	model	VERB
ejpam-6325	228	19	wave	wave	NOUN
ejpam-6325	228	20	propagation	propagation	NOUN
ejpam-6325	228	21	under	under	ADP
ejpam-6325	228	22	the	the	DET
ejpam-6325	228	23	influence	influence	NOUN
ejpam-6325	228	24	of	of	ADP
ejpam-6325	228	25	damping	damp	VERB
ejpam-6325	228	26	and	and	CCONJ
ejpam-6325	228	27	harmonic	harmonic	ADJ
ejpam-6325	228	28	potential	potential	NOUN
ejpam-6325	228	29	.	.	PUNCT
ejpam-6325	229	1	m.	m.	PROPN
ejpam-6325	229	2	noman	noman	PROPN
ejpam-6325	229	3	et	et	PROPN
ejpam-6325	229	4	al	al	PROPN
ejpam-6325	229	5	.	.	PUNCT
ejpam-6325	229	6	/	/	SYM
ejpam-6325	229	7	eur	eur	PROPN
ejpam-6325	229	8	.	.	PUNCT
ejpam-6325	230	1	j.	j.	PROPN
ejpam-6325	230	2	pure	pure	PROPN
ejpam-6325	230	3	appl	appl	PROPN
ejpam-6325	230	4	.	.	PROPN
ejpam-6325	230	5	math	math	PROPN
ejpam-6325	230	6	,	,	PUNCT
ejpam-6325	230	7	18	18	NUM
ejpam-6325	230	8	(	(	PUNCT
ejpam-6325	230	9	3	3	NUM
ejpam-6325	230	10	)	)	PUNCT
ejpam-6325	230	11	(	(	PUNCT
ejpam-6325	230	12	2025	2025	NUM
ejpam-6325	230	13	)	)	PUNCT
ejpam-6325	230	14	,	,	PUNCT
ejpam-6325	230	15	6235	6235	NUM
ejpam-6325	230	16	14	14	NUM
ejpam-6325	230	17	of	of	ADP
ejpam-6325	230	18	16	16	NUM
ejpam-6325	230	19	6	6	NUM
ejpam-6325	230	20	.	.	PUNCT
ejpam-6325	231	1	conclusions	conclusion	NOUN
ejpam-6325	231	2	this	this	DET
ejpam-6325	231	3	paper	paper	NOUN
ejpam-6325	231	4	introduces	introduce	VERB
ejpam-6325	231	5	a	a	DET
ejpam-6325	231	6	novel	novel	ADJ
ejpam-6325	231	7	approach	approach	NOUN
ejpam-6325	231	8	to	to	ADP
ejpam-6325	231	9	solving	solve	VERB
ejpam-6325	231	10	partial	partial	ADJ
ejpam-6325	231	11	differential	differential	ADJ
ejpam-6325	231	12	equations	equation	NOUN
ejpam-6325	231	13	exactly	exactly	ADV
ejpam-6325	231	14	,	,	PUNCT
ejpam-6325	231	15	by	by	ADP
ejpam-6325	231	16	replacing	replace	VERB
ejpam-6325	231	17	conventional	conventional	ADJ
ejpam-6325	231	18	polynomials	polynomial	NOUN
ejpam-6325	231	19	with	with	ADP
ejpam-6325	231	20	laurent	laurent	NOUN
ejpam-6325	231	21	polynomials	polynomial	NOUN
ejpam-6325	231	22	within	within	ADP
ejpam-6325	231	23	the	the	DET
ejpam-6325	231	24	first	first	ADJ
ejpam-6325	231	25	integral	integral	ADJ
ejpam-6325	231	26	method	method	NOUN
ejpam-6325	231	27	.	.	PUNCT
ejpam-6325	232	1	this	this	DET
ejpam-6325	232	2	innovation	innovation	NOUN
ejpam-6325	232	3	is	be	AUX
ejpam-6325	232	4	grounded	ground	VERB
ejpam-6325	232	5	in	in	ADP
ejpam-6325	232	6	the	the	DET
ejpam-6325	232	7	division	division	NOUN
ejpam-6325	232	8	theorem	theorem	VERB
ejpam-6325	232	9	for	for	ADP
ejpam-6325	232	10	laurent	laurent	NOUN
ejpam-6325	232	11	polynomials	polynomial	NOUN
ejpam-6325	232	12	in	in	ADP
ejpam-6325	232	13	two	two	NUM
ejpam-6325	232	14	complex	complex	ADJ
ejpam-6325	232	15	variables	variable	NOUN
ejpam-6325	232	16	,	,	PUNCT
ejpam-6325	232	17	which	which	PRON
ejpam-6325	232	18	provides	provide	VERB
ejpam-6325	232	19	a	a	DET
ejpam-6325	232	20	more	more	ADV
ejpam-6325	232	21	flexible	flexible	ADJ
ejpam-6325	232	22	and	and	CCONJ
ejpam-6325	232	23	powerful	powerful	ADJ
ejpam-6325	232	24	algebraic	algebraic	ADJ
ejpam-6325	232	25	framework	framework	NOUN
ejpam-6325	232	26	for	for	ADP
ejpam-6325	232	27	deriving	derive	VERB
ejpam-6325	232	28	first	first	ADJ
ejpam-6325	232	29	integrals	integral	NOUN
ejpam-6325	232	30	.	.	PUNCT
ejpam-6325	233	1	to	to	PART
ejpam-6325	233	2	validate	validate	VERB
ejpam-6325	233	3	the	the	DET
ejpam-6325	233	4	proposed	propose	VERB
ejpam-6325	233	5	technique	technique	NOUN
ejpam-6325	233	6	,	,	PUNCT
ejpam-6325	233	7	we	we	PRON
ejpam-6325	233	8	revisit	revisit	VERB
ejpam-6325	233	9	and	and	CCONJ
ejpam-6325	233	10	apply	apply	VERB
ejpam-6325	233	11	the	the	DET
ejpam-6325	233	12	euclidean	euclidean	ADJ
ejpam-6325	233	13	algorithm	algorithm	NOUN
ejpam-6325	233	14	for	for	ADP
ejpam-6325	233	15	laurent	laurent	NOUN
ejpam-6325	233	16	polynomials	polynomial	NOUN
ejpam-6325	233	17	,	,	PUNCT
ejpam-6325	233	18	demonstrating	demonstrate	VERB
ejpam-6325	233	19	its	its	PRON
ejpam-6325	233	20	effectiveness	effectiveness	NOUN
ejpam-6325	233	21	in	in	ADP
ejpam-6325	233	22	simplifying	simplify	VERB
ejpam-6325	233	23	the	the	DET
ejpam-6325	233	24	solution	solution	NOUN
ejpam-6325	233	25	process	process	NOUN
ejpam-6325	233	26	for	for	ADP
ejpam-6325	233	27	nonlinear	nonlinear	ADJ
ejpam-6325	233	28	differential	differential	ADJ
ejpam-6325	233	29	equations	equation	NOUN
ejpam-6325	233	30	.	.	PUNCT
ejpam-6325	234	1	the	the	DET
ejpam-6325	234	2	core	core	NOUN
ejpam-6325	234	3	contribution	contribution	NOUN
ejpam-6325	234	4	of	of	ADP
ejpam-6325	234	5	this	this	DET
ejpam-6325	234	6	work	work	NOUN
ejpam-6325	234	7	is	be	AUX
ejpam-6325	234	8	the	the	DET
ejpam-6325	234	9	development	development	NOUN
ejpam-6325	234	10	of	of	ADP
ejpam-6325	234	11	the	the	DET
ejpam-6325	234	12	generalized	generalized	ADJ
ejpam-6325	234	13	first	first	ADJ
ejpam-6325	234	14	integral	integral	ADJ
ejpam-6325	234	15	method	method	NOUN
ejpam-6325	234	16	,	,	PUNCT
ejpam-6325	234	17	a	a	DET
ejpam-6325	234	18	new	new	ADJ
ejpam-6325	234	19	tool	tool	NOUN
ejpam-6325	234	20	for	for	ADP
ejpam-6325	234	21	obtaining	obtain	VERB
ejpam-6325	234	22	exact	exact	ADJ
ejpam-6325	234	23	solutions	solution	NOUN
ejpam-6325	234	24	to	to	ADP
ejpam-6325	234	25	complex	complex	ADJ
ejpam-6325	234	26	dynamical	dynamical	ADJ
ejpam-6325	234	27	systems	system	NOUN
ejpam-6325	234	28	,	,	PUNCT
ejpam-6325	234	29	particularly	particularly	ADV
ejpam-6325	234	30	those	those	PRON
ejpam-6325	234	31	involving	involve	VERB
ejpam-6325	234	32	damping	damp	VERB
ejpam-6325	234	33	effects	effect	NOUN
ejpam-6325	234	34	and	and	CCONJ
ejpam-6325	234	35	external	external	ADJ
ejpam-6325	234	36	potentials	potential	NOUN
ejpam-6325	234	37	.	.	PUNCT
ejpam-6325	235	1	this	this	DET
ejpam-6325	235	2	method	method	NOUN
ejpam-6325	235	3	not	not	PART
ejpam-6325	235	4	only	only	ADV
ejpam-6325	235	5	facilitates	facilitate	VERB
ejpam-6325	235	6	the	the	DET
ejpam-6325	235	7	derivation	derivation	NOUN
ejpam-6325	235	8	of	of	ADP
ejpam-6325	235	9	precise	precise	ADJ
ejpam-6325	235	10	analytical	analytical	ADJ
ejpam-6325	235	11	solutions	solution	NOUN
ejpam-6325	235	12	but	but	CCONJ
ejpam-6325	235	13	also	also	ADV
ejpam-6325	235	14	highlights	highlight	VERB
ejpam-6325	235	15	the	the	DET
ejpam-6325	235	16	critical	critical	ADJ
ejpam-6325	235	17	role	role	NOUN
ejpam-6325	235	18	of	of	ADP
ejpam-6325	235	19	algebraic	algebraic	ADJ
ejpam-6325	235	20	methods	method	NOUN
ejpam-6325	235	21	,	,	PUNCT
ejpam-6325	235	22	particularly	particularly	ADV
ejpam-6325	235	23	the	the	DET
ejpam-6325	235	24	properties	property	NOUN
ejpam-6325	235	25	of	of	ADP
ejpam-6325	235	26	laurent	laurent	NOUN
ejpam-6325	235	27	polynomials	polynomial	NOUN
ejpam-6325	235	28	,	,	PUNCT
ejpam-6325	235	29	in	in	ADP
ejpam-6325	235	30	advancing	advance	VERB
ejpam-6325	235	31	the	the	DET
ejpam-6325	235	32	theory	theory	NOUN
ejpam-6325	235	33	of	of	ADP
ejpam-6325	235	34	nonlinear	nonlinear	ADJ
ejpam-6325	235	35	evolution	evolution	NOUN
ejpam-6325	235	36	equations	equation	NOUN
ejpam-6325	235	37	.	.	PUNCT
ejpam-6325	236	1	by	by	ADP
ejpam-6325	236	2	transforming	transform	VERB
ejpam-6325	236	3	complex	complex	ADJ
ejpam-6325	236	4	systems	system	NOUN
ejpam-6325	236	5	into	into	ADP
ejpam-6325	236	6	integrable	integrable	ADJ
ejpam-6325	236	7	first	first	ADJ
ejpam-6325	236	8	-	-	PUNCT
ejpam-6325	236	9	order	order	NOUN
ejpam-6325	236	10	ordinary	ordinary	ADJ
ejpam-6325	236	11	differential	differential	ADJ
ejpam-6325	236	12	equations	equation	NOUN
ejpam-6325	236	13	,	,	PUNCT
ejpam-6325	236	14	we	we	PRON
ejpam-6325	236	15	were	be	AUX
ejpam-6325	236	16	able	able	ADJ
ejpam-6325	236	17	to	to	PART
ejpam-6325	236	18	uncover	uncover	VERB
ejpam-6325	236	19	exact	exact	ADJ
ejpam-6325	236	20	solutions	solution	NOUN
ejpam-6325	236	21	that	that	PRON
ejpam-6325	236	22	provide	provide	VERB
ejpam-6325	236	23	valuable	valuable	ADJ
ejpam-6325	236	24	insights	insight	NOUN
ejpam-6325	236	25	into	into	ADP
ejpam-6325	236	26	the	the	DET
ejpam-6325	236	27	dynamic	dynamic	ADJ
ejpam-6325	236	28	behavior	behavior	NOUN
ejpam-6325	236	29	of	of	ADP
ejpam-6325	236	30	such	such	ADJ
ejpam-6325	236	31	systems	system	NOUN
ejpam-6325	236	32	.	.	PUNCT
ejpam-6325	237	1	the	the	DET
ejpam-6325	237	2	importance	importance	NOUN
ejpam-6325	237	3	of	of	ADP
ejpam-6325	237	4	this	this	DET
ejpam-6325	237	5	approach	approach	NOUN
ejpam-6325	237	6	extends	extend	VERB
ejpam-6325	237	7	beyond	beyond	ADP
ejpam-6325	237	8	the	the	DET
ejpam-6325	237	9	specific	specific	ADJ
ejpam-6325	237	10	case	case	NOUN
ejpam-6325	237	11	studied	study	VERB
ejpam-6325	237	12	here	here	ADV
ejpam-6325	237	13	.	.	PUNCT
ejpam-6325	238	1	the	the	DET
ejpam-6325	238	2	generalized	generalized	ADJ
ejpam-6325	238	3	first	first	ADJ
ejpam-6325	238	4	integral	integral	ADJ
ejpam-6325	238	5	method	method	NOUN
ejpam-6325	238	6	represents	represent	VERB
ejpam-6325	238	7	a	a	DET
ejpam-6325	238	8	significant	significant	ADJ
ejpam-6325	238	9	advancement	advancement	NOUN
ejpam-6325	238	10	in	in	ADP
ejpam-6325	238	11	the	the	DET
ejpam-6325	238	12	analytical	analytical	ADJ
ejpam-6325	238	13	study	study	NOUN
ejpam-6325	238	14	of	of	ADP
ejpam-6325	238	15	nonlinear	nonlinear	ADJ
ejpam-6325	238	16	systems	system	NOUN
ejpam-6325	238	17	,	,	PUNCT
ejpam-6325	238	18	offering	offer	VERB
ejpam-6325	238	19	a	a	DET
ejpam-6325	238	20	systematic	systematic	ADJ
ejpam-6325	238	21	and	and	CCONJ
ejpam-6325	238	22	efficient	efficient	ADJ
ejpam-6325	238	23	tool	tool	NOUN
ejpam-6325	238	24	for	for	ADP
ejpam-6325	238	25	obtaining	obtain	VERB
ejpam-6325	238	26	exact	exact	ADJ
ejpam-6325	238	27	solutions	solution	NOUN
ejpam-6325	238	28	to	to	ADP
ejpam-6325	238	29	a	a	DET
ejpam-6325	238	30	wide	wide	ADJ
ejpam-6325	238	31	range	range	NOUN
ejpam-6325	238	32	of	of	ADP
ejpam-6325	238	33	partial	partial	ADJ
ejpam-6325	238	34	differential	differential	ADJ
ejpam-6325	238	35	equations	equation	NOUN
ejpam-6325	238	36	that	that	PRON
ejpam-6325	238	37	involve	involve	VERB
ejpam-6325	238	38	damping	damp	VERB
ejpam-6325	238	39	or	or	CCONJ
ejpam-6325	238	40	dissipation	dissipation	NOUN
ejpam-6325	238	41	.	.	PUNCT
ejpam-6325	239	1	the	the	DET
ejpam-6325	239	2	technique	technique	NOUN
ejpam-6325	239	3	is	be	AUX
ejpam-6325	239	4	applicable	applicable	ADJ
ejpam-6325	239	5	to	to	ADP
ejpam-6325	239	6	various	various	ADJ
ejpam-6325	239	7	fields	field	NOUN
ejpam-6325	239	8	of	of	ADP
ejpam-6325	239	9	applied	applied	ADJ
ejpam-6325	239	10	mathematics	mathematic	NOUN
ejpam-6325	239	11	,	,	PUNCT
ejpam-6325	239	12	such	such	ADJ
ejpam-6325	239	13	as	as	ADP
ejpam-6325	239	14	fluid	fluid	ADJ
ejpam-6325	239	15	dynamics	dynamic	NOUN
ejpam-6325	239	16	,	,	PUNCT
ejpam-6325	239	17	signal	signal	ADJ
ejpam-6325	239	18	processing	processing	NOUN
ejpam-6325	239	19	,	,	PUNCT
ejpam-6325	239	20	and	and	CCONJ
ejpam-6325	239	21	heat	heat	NOUN
ejpam-6325	239	22	diffusion	diffusion	NOUN
ejpam-6325	239	23	,	,	PUNCT
ejpam-6325	239	24	where	where	SCONJ
ejpam-6325	239	25	the	the	DET
ejpam-6325	239	26	need	need	NOUN
ejpam-6325	239	27	for	for	ADP
ejpam-6325	239	28	exact	exact	ADJ
ejpam-6325	239	29	solutions	solution	NOUN
ejpam-6325	239	30	to	to	ADP
ejpam-6325	239	31	nonlinear	nonlinear	ADJ
ejpam-6325	239	32	models	model	NOUN
ejpam-6325	239	33	is	be	AUX
ejpam-6325	239	34	critical	critical	ADJ
ejpam-6325	239	35	.	.	PUNCT
ejpam-6325	240	1	in	in	ADP
ejpam-6325	240	2	conclusion	conclusion	NOUN
ejpam-6325	240	3	,	,	PUNCT
ejpam-6325	240	4	this	this	DET
ejpam-6325	240	5	paper	paper	NOUN
ejpam-6325	240	6	not	not	PART
ejpam-6325	240	7	only	only	ADV
ejpam-6325	240	8	introduces	introduce	VERB
ejpam-6325	240	9	an	an	DET
ejpam-6325	240	10	effective	effective	ADJ
ejpam-6325	240	11	new	new	ADJ
ejpam-6325	240	12	method	method	NOUN
ejpam-6325	240	13	for	for	ADP
ejpam-6325	240	14	solving	solve	VERB
ejpam-6325	240	15	nonlinear	nonlinear	ADJ
ejpam-6325	240	16	partial	partial	ADJ
ejpam-6325	240	17	differential	differential	NOUN
ejpam-6325	240	18	equations	equation	NOUN
ejpam-6325	240	19	but	but	CCONJ
ejpam-6325	240	20	also	also	ADV
ejpam-6325	240	21	contributes	contribute	VERB
ejpam-6325	240	22	to	to	ADP
ejpam-6325	240	23	the	the	DET
ejpam-6325	240	24	broader	broad	ADJ
ejpam-6325	240	25	analytical	analytical	ADJ
ejpam-6325	240	26	framework	framework	NOUN
ejpam-6325	240	27	available	available	ADJ
ejpam-6325	240	28	for	for	ADP
ejpam-6325	240	29	the	the	DET
ejpam-6325	240	30	study	study	NOUN
ejpam-6325	240	31	of	of	ADP
ejpam-6325	240	32	complex	complex	ADJ
ejpam-6325	240	33	dynamical	dynamical	ADJ
ejpam-6325	240	34	systems	system	NOUN
ejpam-6325	240	35	.	.	PUNCT
ejpam-6325	241	1	future	future	ADJ
ejpam-6325	241	2	research	research	NOUN
ejpam-6325	241	3	could	could	AUX
ejpam-6325	241	4	explore	explore	VERB
ejpam-6325	241	5	the	the	DET
ejpam-6325	241	6	application	application	NOUN
ejpam-6325	241	7	of	of	ADP
ejpam-6325	241	8	the	the	DET
ejpam-6325	241	9	generalized	generalized	ADJ
ejpam-6325	241	10	first	first	ADJ
ejpam-6325	241	11	integral	integral	ADJ
ejpam-6325	241	12	method	method	NOUN
ejpam-6325	241	13	to	to	ADP
ejpam-6325	241	14	other	other	ADJ
ejpam-6325	241	15	types	type	NOUN
ejpam-6325	241	16	of	of	ADP
ejpam-6325	241	17	nonlinear	nonlinear	ADJ
ejpam-6325	241	18	differential	differential	ADJ
ejpam-6325	241	19	equations	equation	NOUN
ejpam-6325	241	20	and	and	CCONJ
ejpam-6325	241	21	more	more	ADV
ejpam-6325	241	22	complicated	complicated	ADJ
ejpam-6325	241	23	systems	system	NOUN
ejpam-6325	241	24	involving	involve	VERB
ejpam-6325	241	25	variable	variable	ADJ
ejpam-6325	241	26	coefficients	coefficient	NOUN
ejpam-6325	241	27	or	or	CCONJ
ejpam-6325	241	28	coupled	couple	VERB
ejpam-6325	241	29	components	component	NOUN
ejpam-6325	241	30	.	.	PUNCT
ejpam-6325	242	1	furthermore	furthermore	ADV
ejpam-6325	242	2	,	,	PUNCT
ejpam-6325	242	3	extending	extend	VERB
ejpam-6325	242	4	this	this	DET
ejpam-6325	242	5	method	method	NOUN
ejpam-6325	242	6	to	to	ADP
ejpam-6325	242	7	higher	higher	ADV
ejpam-6325	242	8	-	-	PUNCT
ejpam-6325	242	9	dimensional	dimensional	ADJ
ejpam-6325	242	10	problems	problem	NOUN
ejpam-6325	242	11	and	and	CCONJ
ejpam-6325	242	12	systems	system	NOUN
ejpam-6325	242	13	with	with	ADP
ejpam-6325	242	14	spatially	spatially	ADV
ejpam-6325	242	15	or	or	CCONJ
ejpam-6325	242	16	temporally	temporally	ADV
ejpam-6325	242	17	varying	vary	VERB
ejpam-6325	242	18	damping	damp	VERB
ejpam-6325	242	19	and	and	CCONJ
ejpam-6325	242	20	potential	potential	ADJ
ejpam-6325	242	21	terms	term	NOUN
ejpam-6325	242	22	could	could	AUX
ejpam-6325	242	23	significantly	significantly	ADV
ejpam-6325	242	24	broaden	broaden	VERB
ejpam-6325	242	25	its	its	PRON
ejpam-6325	242	26	applicability	applicability	NOUN
ejpam-6325	242	27	.	.	PUNCT
ejpam-6325	243	1	another	another	DET
ejpam-6325	243	2	valuable	valuable	ADJ
ejpam-6325	243	3	direction	direction	NOUN
ejpam-6325	243	4	would	would	AUX
ejpam-6325	243	5	be	be	AUX
ejpam-6325	243	6	integrating	integrate	VERB
ejpam-6325	243	7	this	this	DET
ejpam-6325	243	8	technique	technique	NOUN
ejpam-6325	243	9	with	with	ADP
ejpam-6325	243	10	numerical	numerical	ADJ
ejpam-6325	243	11	or	or	CCONJ
ejpam-6325	243	12	perturbation	perturbation	NOUN
ejpam-6325	243	13	-	-	PUNCT
ejpam-6325	243	14	based	base	VERB
ejpam-6325	243	15	approaches	approach	NOUN
ejpam-6325	243	16	to	to	PART
ejpam-6325	243	17	develop	develop	VERB
ejpam-6325	243	18	hybrid	hybrid	ADJ
ejpam-6325	243	19	analytical	analytical	ADJ
ejpam-6325	243	20	-	-	PUNCT
ejpam-6325	243	21	numerical	numerical	ADJ
ejpam-6325	243	22	frameworks	framework	NOUN
ejpam-6325	243	23	for	for	ADP
ejpam-6325	243	24	problems	problem	NOUN
ejpam-6325	243	25	where	where	SCONJ
ejpam-6325	243	26	exact	exact	ADJ
ejpam-6325	243	27	solutions	solution	NOUN
ejpam-6325	243	28	are	be	AUX
ejpam-6325	243	29	difficult	difficult	ADJ
ejpam-6325	243	30	to	to	PART
ejpam-6325	243	31	obtain	obtain	VERB
ejpam-6325	243	32	.	.	PUNCT
ejpam-6325	244	1	these	these	DET
ejpam-6325	244	2	prospective	prospective	ADJ
ejpam-6325	244	3	extensions	extension	NOUN
ejpam-6325	244	4	would	would	AUX
ejpam-6325	244	5	enhance	enhance	VERB
ejpam-6325	244	6	the	the	DET
ejpam-6325	244	7	versatility	versatility	NOUN
ejpam-6325	244	8	of	of	ADP
ejpam-6325	244	9	the	the	DET
ejpam-6325	244	10	method	method	NOUN
ejpam-6325	244	11	and	and	CCONJ
ejpam-6325	244	12	promote	promote	VERB
ejpam-6325	244	13	its	its	PRON
ejpam-6325	244	14	adoption	adoption	NOUN
ejpam-6325	244	15	in	in	ADP
ejpam-6325	244	16	various	various	ADJ
ejpam-6325	244	17	scientific	scientific	ADJ
ejpam-6325	244	18	and	and	CCONJ
ejpam-6325	244	19	engineering	engineering	NOUN
ejpam-6325	244	20	disciplines	discipline	NOUN
ejpam-6325	244	21	.	.	PUNCT
ejpam-6325	245	1	acknowledgements	acknowledgement	NOUN
ejpam-6325	245	2	the	the	DET
ejpam-6325	245	3	authors	author	NOUN
ejpam-6325	245	4	muhammad	muhammad	PROPN
ejpam-6325	245	5	noman	noman	PROPN
ejpam-6325	245	6	qureshi	qureshi	PROPN
ejpam-6325	245	7	,	,	PUNCT
ejpam-6325	245	8	dr	dr	PROPN
ejpam-6325	245	9	.	.	PROPN
ejpam-6325	245	10	atif	atif	PROPN
ejpam-6325	245	11	hassan	hassan	PROPN
ejpam-6325	245	12	soori	soori	PROPN
ejpam-6325	245	13	,	,	PUNCT
ejpam-6325	245	14	zeshan	zeshan	PROPN
ejpam-6325	245	15	haider	haider	PROPN
ejpam-6325	245	16	,	,	PUNCT
ejpam-6325	245	17	dr	dr	PROPN
ejpam-6325	245	18	.	.	PROPN
ejpam-6325	245	19	waqar	waqar	PROPN
ejpam-6325	245	20	azeem	azeem	PROPN
ejpam-6325	245	21	khan	khan	PROPN
ejpam-6325	245	22	and	and	CCONJ
ejpam-6325	245	23	zohaib	zohaib	PROPN
ejpam-6325	245	24	arshad	arshad	PROPN
ejpam-6325	245	25	would	would	AUX
ejpam-6325	245	26	like	like	VERB
ejpam-6325	245	27	to	to	PART
ejpam-6325	245	28	thankful	thankful	VERB
ejpam-6325	245	29	the	the	DET
ejpam-6325	245	30	air	air	NOUN
ejpam-6325	245	31	marshal	marshal	NOUN
ejpam-6325	245	32	abdul	abdul	PROPN
ejpam-6325	245	33	moeed	moeed	PROPN
ejpam-6325	245	34	khan	khan	PROPN
ejpam-6325	245	35	,	,	PUNCT
ejpam-6325	245	36	hi(m	hi(m	NOUN
ejpam-6325	245	37	)	)	PUNCT
ejpam-6325	245	38	,	,	PUNCT
ejpam-6325	245	39	vice	vice	NOUN
ejpam-6325	245	40	chancellor	chancellor	NOUN
ejpam-6325	245	41	,	,	PUNCT
ejpam-6325	245	42	air	air	NOUN
ejpam-6325	245	43	university	university	PROPN
ejpam-6325	245	44	,	,	PUNCT
ejpam-6325	245	45	islamabad	islamabad	PROPN
ejpam-6325	245	46	,	,	PUNCT
ejpam-6325	245	47	pakistan	pakistan	PROPN
ejpam-6325	245	48	.	.	PUNCT
ejpam-6325	246	1	competing	compete	VERB
ejpam-6325	246	2	interests	interest	NOUN
ejpam-6325	246	3	the	the	DET
ejpam-6325	246	4	authors	author	NOUN
ejpam-6325	246	5	declare	declare	VERB
ejpam-6325	246	6	that	that	SCONJ
ejpam-6325	246	7	they	they	PRON
ejpam-6325	246	8	have	have	VERB
ejpam-6325	246	9	no	no	DET
ejpam-6325	246	10	competing	compete	VERB
ejpam-6325	246	11	interests	interest	NOUN
ejpam-6325	246	12	.	.	PUNCT
ejpam-6325	247	1	data	datum	NOUN
ejpam-6325	247	2	availability	availability	NOUN
ejpam-6325	247	3	statement	statement	NOUN
ejpam-6325	247	4	please	please	INTJ
ejpam-6325	247	5	contact	contact	VERB
ejpam-6325	247	6	the	the	DET
ejpam-6325	247	7	authors	author	NOUN
ejpam-6325	247	8	for	for	ADP
ejpam-6325	247	9	data	data	NOUN
ejpam-6325	247	10	requests	request	NOUN
ejpam-6325	247	11	.	.	PUNCT
ejpam-6325	248	1	m.	m.	PROPN
ejpam-6325	248	2	noman	noman	PROPN
ejpam-6325	248	3	et	et	PROPN
ejpam-6325	248	4	al	al	PROPN
ejpam-6325	248	5	.	.	PUNCT
ejpam-6325	248	6	/	/	SYM
ejpam-6325	248	7	eur	eur	PROPN
ejpam-6325	248	8	.	.	PUNCT
ejpam-6325	249	1	j.	j.	PROPN
ejpam-6325	249	2	pure	pure	PROPN
ejpam-6325	249	3	appl	appl	PROPN
ejpam-6325	249	4	.	.	PROPN
ejpam-6325	249	5	math	math	PROPN
ejpam-6325	249	6	,	,	PUNCT
ejpam-6325	249	7	18	18	NUM
ejpam-6325	249	8	(	(	PUNCT
ejpam-6325	249	9	3	3	NUM
ejpam-6325	249	10	)	)	PUNCT
ejpam-6325	249	11	(	(	PUNCT
ejpam-6325	249	12	2025	2025	NUM
ejpam-6325	249	13	)	)	PUNCT
ejpam-6325	249	14	,	,	PUNCT
ejpam-6325	249	15	6235	6235	NUM
ejpam-6325	249	16	15	15	NUM
ejpam-6325	249	17	of	of	ADP
ejpam-6325	249	18	16	16	NUM
ejpam-6325	249	19	references	reference	NOUN
ejpam-6325	249	20	[	[	X
ejpam-6325	249	21	1	1	NUM
ejpam-6325	249	22	]	]	PUNCT
ejpam-6325	249	23	viorel	viorel	PROPN
ejpam-6325	249	24	barbu	barbu	PROPN
ejpam-6325	249	25	,	,	PUNCT
ejpam-6325	249	26	irena	irena	PROPN
ejpam-6325	249	27	lasiecka	lasiecka	PROPN
ejpam-6325	249	28	,	,	PUNCT
ejpam-6325	249	29	and	and	CCONJ
ejpam-6325	249	30	mohammad	mohammad	PROPN
ejpam-6325	249	31	rammaha	rammaha	PROPN
ejpam-6325	249	32	.	.	PUNCT
ejpam-6325	250	1	on	on	ADP
ejpam-6325	250	2	nonlinear	nonlinear	ADJ
ejpam-6325	250	3	wave	wave	NOUN
ejpam-6325	250	4	equations	equation	NOUN
ejpam-6325	250	5	with	with	ADP
ejpam-6325	250	6	degenerate	degenerate	ADJ
ejpam-6325	250	7	damping	damp	VERB
ejpam-6325	250	8	and	and	CCONJ
ejpam-6325	250	9	source	source	NOUN
ejpam-6325	250	10	terms	term	NOUN
ejpam-6325	250	11	.	.	PUNCT
ejpam-6325	251	1	transactions	transaction	NOUN
ejpam-6325	251	2	of	of	ADP
ejpam-6325	251	3	the	the	DET
ejpam-6325	251	4	american	american	PROPN
ejpam-6325	251	5	mathematical	mathematical	PROPN
ejpam-6325	251	6	society	society	NOUN
ejpam-6325	251	7	,	,	PUNCT
ejpam-6325	251	8	357(7):2571–2611	357(7):2571–2611	PROPN
ejpam-6325	251	9	,	,	PUNCT
ejpam-6325	251	10	2005	2005	NUM
ejpam-6325	251	11	.	.	PUNCT
ejpam-6325	252	1	[	[	X
ejpam-6325	252	2	2	2	X
ejpam-6325	252	3	]	]	PUNCT
ejpam-6325	252	4	pedro	pedro	PROPN
ejpam-6325	252	5	freitas	freitas	PROPN
ejpam-6325	252	6	,	,	PUNCT
ejpam-6325	252	7	nicolas	nicolas	PROPN
ejpam-6325	252	8	hefti	hefti	PROPN
ejpam-6325	252	9	,	,	PUNCT
ejpam-6325	252	10	and	and	CCONJ
ejpam-6325	252	11	petr	petr	PROPN
ejpam-6325	252	12	siegl	siegl	PROPN
ejpam-6325	252	13	.	.	PUNCT
ejpam-6325	253	1	the	the	DET
ejpam-6325	253	2	damped	damp	VERB
ejpam-6325	253	3	wave	wave	NOUN
ejpam-6325	253	4	equation	equation	NOUN
ejpam-6325	253	5	with	with	ADP
ejpam-6325	253	6	singular	singular	ADJ
ejpam-6325	253	7	damping	damping	NOUN
ejpam-6325	253	8	.	.	PUNCT
ejpam-6325	254	1	proceedings	proceeding	NOUN
ejpam-6325	254	2	of	of	ADP
ejpam-6325	254	3	the	the	DET
ejpam-6325	254	4	american	american	PROPN
ejpam-6325	254	5	mathematical	mathematical	PROPN
ejpam-6325	254	6	society	society	NOUN
ejpam-6325	254	7	,	,	PUNCT
ejpam-6325	254	8	148(10):4273–4284	148(10):4273–4284	NUM
ejpam-6325	254	9	,	,	PUNCT
ejpam-6325	254	10	2020	2020	NUM
ejpam-6325	254	11	.	.	PUNCT
ejpam-6325	255	1	[	[	X
ejpam-6325	255	2	3	3	X
ejpam-6325	255	3	]	]	X
ejpam-6325	255	4	yuri	yuri	PROPN
ejpam-6325	255	5	luchko	luchko	PROPN
ejpam-6325	255	6	.	.	PUNCT
ejpam-6325	256	1	fractional	fractional	ADJ
ejpam-6325	256	2	wave	wave	NOUN
ejpam-6325	256	3	equation	equation	NOUN
ejpam-6325	256	4	and	and	CCONJ
ejpam-6325	256	5	damped	damped	ADJ
ejpam-6325	256	6	waves	wave	NOUN
ejpam-6325	256	7	.	.	PUNCT
ejpam-6325	257	1	journal	journal	PROPN
ejpam-6325	257	2	of	of	ADP
ejpam-6325	257	3	mathematical	mathematical	ADJ
ejpam-6325	257	4	physics	physics	NOUN
ejpam-6325	257	5	,	,	PUNCT
ejpam-6325	257	6	54(3	54(3	NUM
ejpam-6325	257	7	)	)	PUNCT
ejpam-6325	257	8	,	,	PUNCT
ejpam-6325	257	9	2013	2013	NUM
ejpam-6325	257	10	.	.	PUNCT
ejpam-6325	258	1	[	[	X
ejpam-6325	258	2	4	4	X
ejpam-6325	258	3	]	]	X
ejpam-6325	258	4	serge	serge	PROPN
ejpam-6325	258	5	nicaise	nicaise	PROPN
ejpam-6325	258	6	.	.	PUNCT
ejpam-6325	259	1	stabilization	stabilization	NOUN
ejpam-6325	259	2	and	and	CCONJ
ejpam-6325	259	3	asymptotic	asymptotic	ADJ
ejpam-6325	259	4	behavior	behavior	NOUN
ejpam-6325	259	5	of	of	ADP
ejpam-6325	259	6	a	a	DET
ejpam-6325	259	7	generalized	generalized	ADJ
ejpam-6325	259	8	telegraph	telegraph	NOUN
ejpam-6325	259	9	equation	equation	NOUN
ejpam-6325	259	10	.	.	PUNCT
ejpam-6325	260	1	zeitschrift	zeitschrift	PROPN
ejpam-6325	260	2	für	für	PROPN
ejpam-6325	260	3	angewandte	angewandte	PROPN
ejpam-6325	260	4	mathematik	mathematik	PROPN
ejpam-6325	260	5	und	und	PROPN
ejpam-6325	260	6	physik	physik	PROPN
ejpam-6325	260	7	,	,	PUNCT
ejpam-6325	260	8	66(6):3221–3247	66(6):3221–3247	PROPN
ejpam-6325	260	9	,	,	PUNCT
ejpam-6325	260	10	2015	2015	NUM
ejpam-6325	260	11	.	.	PUNCT
ejpam-6325	261	1	[	[	X
ejpam-6325	261	2	5	5	NUM
ejpam-6325	261	3	]	]	X
ejpam-6325	261	4	fang	fang	X
ejpam-6325	261	5	li	li	PROPN
ejpam-6325	261	6	and	and	CCONJ
ejpam-6325	261	7	xiangyu	xiangyu	PROPN
ejpam-6325	261	8	zhu	zhu	PROPN
ejpam-6325	261	9	.	.	PUNCT
ejpam-6325	261	10	convergence	convergence	NOUN
ejpam-6325	261	11	rate	rate	NOUN
ejpam-6325	261	12	of	of	ADP
ejpam-6325	261	13	solutions	solution	NOUN
ejpam-6325	261	14	to	to	ADP
ejpam-6325	261	15	the	the	DET
ejpam-6325	261	16	generalized	generalized	ADJ
ejpam-6325	261	17	telegraph	telegraph	NOUN
ejpam-6325	261	18	equation	equation	NOUN
ejpam-6325	261	19	with	with	ADP
ejpam-6325	261	20	an	an	DET
ejpam-6325	261	21	inhomogeneous	inhomogeneous	ADJ
ejpam-6325	261	22	force	force	NOUN
ejpam-6325	261	23	.	.	PUNCT
ejpam-6325	262	1	journal	journal	PROPN
ejpam-6325	262	2	of	of	ADP
ejpam-6325	262	3	mathematical	mathematical	ADJ
ejpam-6325	262	4	analysis	analysis	NOUN
ejpam-6325	262	5	and	and	CCONJ
ejpam-6325	262	6	applications	application	NOUN
ejpam-6325	262	7	,	,	PUNCT
ejpam-6325	262	8	517(1):126564	517(1):126564	NUM
ejpam-6325	262	9	,	,	PUNCT
ejpam-6325	262	10	2023	2023	NUM
ejpam-6325	262	11	.	.	PUNCT
ejpam-6325	263	1	[	[	X
ejpam-6325	263	2	6	6	NUM
ejpam-6325	263	3	]	]	X
ejpam-6325	263	4	paul	paul	PROPN
ejpam-6325	263	5	massatt	massatt	PROPN
ejpam-6325	263	6	.	.	PUNCT
ejpam-6325	264	1	limiting	limit	VERB
ejpam-6325	264	2	behavior	behavior	NOUN
ejpam-6325	264	3	for	for	ADP
ejpam-6325	264	4	strongly	strongly	ADV
ejpam-6325	264	5	damped	damp	VERB
ejpam-6325	264	6	nonlinear	nonlinear	ADJ
ejpam-6325	264	7	wave	wave	NOUN
ejpam-6325	264	8	equations	equation	NOUN
ejpam-6325	264	9	.	.	PUNCT
ejpam-6325	265	1	journal	journal	PROPN
ejpam-6325	265	2	of	of	ADP
ejpam-6325	265	3	differential	differential	ADJ
ejpam-6325	265	4	equations	equation	NOUN
ejpam-6325	265	5	,	,	PUNCT
ejpam-6325	265	6	48(3):334–349	48(3):334–349	PROPN
ejpam-6325	265	7	,	,	PUNCT
ejpam-6325	265	8	1983	1983	NUM
ejpam-6325	265	9	.	.	PUNCT
ejpam-6325	266	1	[	[	X
ejpam-6325	266	2	7	7	X
ejpam-6325	266	3	]	]	X
ejpam-6325	266	4	vittorino	vittorino	NOUN
ejpam-6325	266	5	pata	pata	PROPN
ejpam-6325	266	6	and	and	CCONJ
ejpam-6325	266	7	marco	marco	PROPN
ejpam-6325	266	8	squassina	squassina	PROPN
ejpam-6325	266	9	.	.	PUNCT
ejpam-6325	267	1	on	on	ADP
ejpam-6325	267	2	the	the	DET
ejpam-6325	267	3	strongly	strongly	ADV
ejpam-6325	267	4	damped	damp	VERB
ejpam-6325	267	5	wave	wave	NOUN
ejpam-6325	267	6	equation	equation	NOUN
ejpam-6325	267	7	.	.	PUNCT
ejpam-6325	268	1	communications	communication	NOUN
ejpam-6325	268	2	in	in	ADP
ejpam-6325	268	3	mathematical	mathematical	ADJ
ejpam-6325	268	4	physics	physics	NOUN
ejpam-6325	268	5	,	,	PUNCT
ejpam-6325	268	6	253(3):511–533	253(3):511–533	NUM
ejpam-6325	268	7	,	,	PUNCT
ejpam-6325	268	8	2005	2005	NUM
ejpam-6325	268	9	.	.	PUNCT
ejpam-6325	269	1	[	[	X
ejpam-6325	269	2	8	8	NUM
ejpam-6325	269	3	]	]	PUNCT
ejpam-6325	269	4	fabrizio	fabrizio	NOUN
ejpam-6325	269	5	colombo	colombo	NOUN
ejpam-6325	269	6	.	.	PUNCT
ejpam-6325	270	1	an	an	DET
ejpam-6325	270	2	inverse	inverse	ADJ
ejpam-6325	270	3	problem	problem	NOUN
ejpam-6325	270	4	for	for	ADP
ejpam-6325	270	5	the	the	DET
ejpam-6325	270	6	strongly	strongly	ADV
ejpam-6325	270	7	damped	damp	VERB
ejpam-6325	270	8	wave	wave	NOUN
ejpam-6325	270	9	equation	equation	NOUN
ejpam-6325	270	10	with	with	ADP
ejpam-6325	270	11	memory	memory	NOUN
ejpam-6325	270	12	.	.	PUNCT
ejpam-6325	271	1	nonlinearity	nonlinearity	NOUN
ejpam-6325	271	2	,	,	PUNCT
ejpam-6325	271	3	20(3):659	20(3):659	NOUN
ejpam-6325	271	4	,	,	PUNCT
ejpam-6325	271	5	2007	2007	NUM
ejpam-6325	271	6	.	.	PUNCT
ejpam-6325	272	1	[	[	X
ejpam-6325	272	2	9	9	NUM
ejpam-6325	272	3	]	]	X
ejpam-6325	272	4	nguyen	nguyen	PROPN
ejpam-6325	272	5	vu	vu	PROPN
ejpam-6325	272	6	dzung	dzung	PROPN
ejpam-6325	272	7	,	,	PUNCT
ejpam-6325	272	8	nguyen	nguyen	NOUN
ejpam-6325	272	9	huu	huu	PROPN
ejpam-6325	272	10	nhan	nhan	PROPN
ejpam-6325	272	11	,	,	PUNCT
ejpam-6325	272	12	nguyen	nguyen	PROPN
ejpam-6325	272	13	thanh	thanh	PROPN
ejpam-6325	272	14	long	long	ADV
ejpam-6325	272	15	,	,	PUNCT
ejpam-6325	272	16	et	et	PROPN
ejpam-6325	272	17	al	al	PROPN
ejpam-6325	272	18	.	.	PROPN
ejpam-6325	272	19	existence	existence	PROPN
ejpam-6325	272	20	,	,	PUNCT
ejpam-6325	272	21	uniqueness	uniqueness	NOUN
ejpam-6325	272	22	,	,	PUNCT
ejpam-6325	272	23	and	and	CCONJ
ejpam-6325	272	24	convergence	convergence	NOUN
ejpam-6325	272	25	of	of	ADP
ejpam-6325	272	26	solutions	solution	NOUN
ejpam-6325	272	27	of	of	ADP
ejpam-6325	272	28	strongly	strongly	ADV
ejpam-6325	272	29	damped	damp	VERB
ejpam-6325	272	30	wave	wave	NOUN
ejpam-6325	272	31	equations	equation	NOUN
ejpam-6325	272	32	with	with	ADP
ejpam-6325	272	33	arithmeticmean	arithmeticmean	ADJ
ejpam-6325	272	34	terms	term	NOUN
ejpam-6325	272	35	.	.	PUNCT
ejpam-6325	273	1	results	result	NOUN
ejpam-6325	273	2	in	in	ADP
ejpam-6325	273	3	nonlinear	nonlinear	ADJ
ejpam-6325	273	4	analysis	analysis	NOUN
ejpam-6325	273	5	,	,	PUNCT
ejpam-6325	273	6	5(2):191–212	5(2):191–212	NUM
ejpam-6325	273	7	,	,	PUNCT
ejpam-6325	273	8	2022	2022	NUM
ejpam-6325	273	9	.	.	PUNCT
ejpam-6325	274	1	[	[	X
ejpam-6325	274	2	10	10	NUM
ejpam-6325	274	3	]	]	X
ejpam-6325	274	4	bruno	bruno	PROPN
ejpam-6325	274	5	de	de	PROPN
ejpam-6325	274	6	andrade	andrade	PROPN
ejpam-6325	274	7	and	and	CCONJ
ejpam-6325	274	8	carlos	carlos	PROPN
ejpam-6325	274	9	lizama	lizama	PROPN
ejpam-6325	274	10	.	.	PUNCT
ejpam-6325	275	1	existence	existence	NOUN
ejpam-6325	275	2	of	of	ADP
ejpam-6325	275	3	asymptotically	asymptotically	ADV
ejpam-6325	275	4	almost	almost	ADV
ejpam-6325	275	5	periodic	periodic	ADJ
ejpam-6325	275	6	solutions	solution	NOUN
ejpam-6325	275	7	for	for	ADP
ejpam-6325	275	8	damped	damped	ADJ
ejpam-6325	275	9	wave	wave	NOUN
ejpam-6325	275	10	equations	equation	NOUN
ejpam-6325	275	11	.	.	PUNCT
ejpam-6325	276	1	journal	journal	PROPN
ejpam-6325	276	2	of	of	ADP
ejpam-6325	276	3	mathematical	mathematical	ADJ
ejpam-6325	276	4	analysis	analysis	NOUN
ejpam-6325	276	5	and	and	CCONJ
ejpam-6325	276	6	applications	application	NOUN
ejpam-6325	276	7	,	,	PUNCT
ejpam-6325	276	8	382(2):761–771	382(2):761–771	NUM
ejpam-6325	276	9	,	,	PUNCT
ejpam-6325	276	10	2011	2011	NUM
ejpam-6325	276	11	.	.	PUNCT
ejpam-6325	277	1	[	[	X
ejpam-6325	277	2	11	11	NUM
ejpam-6325	277	3	]	]	X
ejpam-6325	277	4	ronald	ronald	PROPN
ejpam-6325	277	5	e.	e.	PROPN
ejpam-6325	277	6	mickens	mickens	PROPN
ejpam-6325	277	7	and	and	CCONJ
ejpam-6325	277	8	p.	p.	PROPN
ejpam-6325	277	9	m.	m.	PROPN
ejpam-6325	277	10	jordan	jordan	PROPN
ejpam-6325	277	11	.	.	PUNCT
ejpam-6325	278	1	a	a	DET
ejpam-6325	278	2	positivity	positivity	NOUN
ejpam-6325	278	3	-	-	PUNCT
ejpam-6325	278	4	preserving	preserve	VERB
ejpam-6325	278	5	nonstandard	nonstandard	ADJ
ejpam-6325	278	6	finite	finite	ADJ
ejpam-6325	278	7	difference	difference	NOUN
ejpam-6325	278	8	scheme	scheme	NOUN
ejpam-6325	278	9	for	for	ADP
ejpam-6325	278	10	the	the	DET
ejpam-6325	278	11	damped	damped	NOUN
ejpam-6325	278	12	wave	wave	NOUN
ejpam-6325	278	13	equation	equation	NOUN
ejpam-6325	278	14	.	.	PUNCT
ejpam-6325	279	1	numerical	numerical	ADJ
ejpam-6325	279	2	methods	method	NOUN
ejpam-6325	279	3	for	for	ADP
ejpam-6325	279	4	partial	partial	ADJ
ejpam-6325	279	5	differential	differential	NOUN
ejpam-6325	279	6	equations	equation	NOUN
ejpam-6325	279	7	,	,	PUNCT
ejpam-6325	279	8	20(5):639–649	20(5):639–649	NOUN
ejpam-6325	279	9	,	,	PUNCT
ejpam-6325	279	10	2004	2004	NUM
ejpam-6325	279	11	.	.	PUNCT
ejpam-6325	280	1	[	[	X
ejpam-6325	280	2	12	12	NUM
ejpam-6325	280	3	]	]	PUNCT
ejpam-6325	280	4	muhammad	muhammad	PROPN
ejpam-6325	280	5	minarul	minarul	PROPN
ejpam-6325	280	6	islam	islam	PROPN
ejpam-6325	280	7	and	and	CCONJ
ejpam-6325	280	8	mohammad	mohammad	PROPN
ejpam-6325	280	9	sanjeed	sanjeed	PROPN
ejpam-6325	280	10	hasan	hasan	PROPN
ejpam-6325	280	11	.	.	PUNCT
ejpam-6325	281	1	a	a	DET
ejpam-6325	281	2	study	study	NOUN
ejpam-6325	281	3	on	on	ADP
ejpam-6325	281	4	exact	exact	ADJ
ejpam-6325	281	5	solution	solution	NOUN
ejpam-6325	281	6	of	of	ADP
ejpam-6325	281	7	the	the	DET
ejpam-6325	281	8	telegraph	telegraph	NOUN
ejpam-6325	281	9	equation	equation	NOUN
ejpam-6325	281	10	by	by	ADP
ejpam-6325	281	11	(	(	PUNCT
ejpam-6325	281	12	g’/g)-expansion	g’/g)-expansion	NOUN
ejpam-6325	281	13	method	method	NOUN
ejpam-6325	281	14	.	.	PUNCT
ejpam-6325	282	1	african	african	ADJ
ejpam-6325	282	2	journal	journal	PROPN
ejpam-6325	282	3	of	of	ADP
ejpam-6325	282	4	mathematics	mathematics	PROPN
ejpam-6325	282	5	and	and	CCONJ
ejpam-6325	282	6	computer	computer	NOUN
ejpam-6325	282	7	science	science	NOUN
ejpam-6325	282	8	research	research	NOUN
ejpam-6325	282	9	,	,	PUNCT
ejpam-6325	282	10	11(7):103–108	11(7):103–108	NUM
ejpam-6325	282	11	,	,	PUNCT
ejpam-6325	282	12	2018	2018	NUM
ejpam-6325	282	13	.	.	PUNCT
ejpam-6325	283	1	[	[	X
ejpam-6325	283	2	13	13	NUM
ejpam-6325	283	3	]	]	X
ejpam-6325	283	4	mustafa	mustafa	PROPN
ejpam-6325	283	5	inc	inc	PROPN
ejpam-6325	283	6	,	,	PUNCT
ejpam-6325	283	7	ali	ali	PROPN
ejpam-6325	283	8	akgül	akgül	PROPN
ejpam-6325	283	9	,	,	PUNCT
ejpam-6325	283	10	and	and	CCONJ
ejpam-6325	283	11	adem	adem	PROPN
ejpam-6325	283	12	kiliçman	kiliçman	PROPN
ejpam-6325	283	13	.	.	PUNCT
ejpam-6325	283	14	explicit	explicit	ADJ
ejpam-6325	283	15	solution	solution	NOUN
ejpam-6325	283	16	of	of	ADP
ejpam-6325	283	17	telegraph	telegraph	NOUN
ejpam-6325	283	18	equation	equation	NOUN
ejpam-6325	283	19	based	base	VERB
ejpam-6325	283	20	on	on	ADP
ejpam-6325	283	21	reproducing	reproduce	VERB
ejpam-6325	283	22	kernel	kernel	PROPN
ejpam-6325	283	23	method	method	NOUN
ejpam-6325	283	24	.	.	PUNCT
ejpam-6325	283	25	journal	journal	NOUN
ejpam-6325	283	26	of	of	ADP
ejpam-6325	283	27	function	function	NOUN
ejpam-6325	283	28	spaces	space	NOUN
ejpam-6325	283	29	,	,	PUNCT
ejpam-6325	283	30	2012(1):984682	2012(1):984682	ADV
ejpam-6325	283	31	,	,	PUNCT
ejpam-6325	283	32	2012	2012	NUM
ejpam-6325	283	33	.	.	PUNCT
ejpam-6325	284	1	[	[	X
ejpam-6325	284	2	14	14	NUM
ejpam-6325	284	3	]	]	PUNCT
ejpam-6325	284	4	mehrdad	mehrdad	NOUN
ejpam-6325	284	5	lakestani	lakestani	PROPN
ejpam-6325	284	6	and	and	CCONJ
ejpam-6325	284	7	behzad	behzad	PROPN
ejpam-6325	284	8	nemati	nemati	PROPN
ejpam-6325	284	9	saray	saray	PROPN
ejpam-6325	284	10	.	.	PUNCT
ejpam-6325	285	1	numerical	numerical	ADJ
ejpam-6325	285	2	solution	solution	NOUN
ejpam-6325	285	3	of	of	ADP
ejpam-6325	285	4	telegraph	telegraph	NOUN
ejpam-6325	285	5	equation	equation	NOUN
ejpam-6325	285	6	using	use	VERB
ejpam-6325	285	7	interpolating	interpolate	VERB
ejpam-6325	285	8	scaling	scale	VERB
ejpam-6325	285	9	functions	function	NOUN
ejpam-6325	285	10	.	.	PUNCT
ejpam-6325	286	1	computers	computer	NOUN
ejpam-6325	286	2	mathematics	mathematic	NOUN
ejpam-6325	286	3	with	with	ADP
ejpam-6325	286	4	applications	application	NOUN
ejpam-6325	286	5	,	,	PUNCT
ejpam-6325	286	6	60(7):1964–1972	60(7):1964–1972	NUM
ejpam-6325	286	7	,	,	PUNCT
ejpam-6325	286	8	2010	2010	NUM
ejpam-6325	286	9	.	.	PUNCT
ejpam-6325	287	1	[	[	X
ejpam-6325	287	2	15	15	NUM
ejpam-6325	287	3	]	]	X
ejpam-6325	287	4	f.	f.	PROPN
ejpam-6325	287	5	ureña	ureña	PROPN
ejpam-6325	287	6	,	,	PUNCT
ejpam-6325	287	7	l.	l.	PROPN
ejpam-6325	287	8	gavete	gavete	PROPN
ejpam-6325	287	9	,	,	PUNCT
ejpam-6325	287	10	j.	j.	PROPN
ejpam-6325	287	11	j.	j.	PROPN
ejpam-6325	287	12	benito	benito	PROPN
ejpam-6325	287	13	,	,	PUNCT
ejpam-6325	287	14	a.	a.	NOUN
ejpam-6325	287	15	garćıa	garćıa	NOUN
ejpam-6325	287	16	,	,	PUNCT
ejpam-6325	287	17	and	and	CCONJ
ejpam-6325	287	18	a.	a.	NOUN
ejpam-6325	287	19	m.	m.	NOUN
ejpam-6325	287	20	vargas	vargas	PROPN
ejpam-6325	287	21	.	.	PUNCT
ejpam-6325	288	1	solving	solve	VERB
ejpam-6325	288	2	the	the	DET
ejpam-6325	288	3	telegraph	telegraph	NOUN
ejpam-6325	288	4	equation	equation	NOUN
ejpam-6325	288	5	in	in	ADP
ejpam-6325	288	6	2	2	NUM
ejpam-6325	288	7	-	-	PUNCT
ejpam-6325	288	8	d	d	NOUN
ejpam-6325	288	9	and	and	CCONJ
ejpam-6325	288	10	3	3	NUM
ejpam-6325	288	11	-	-	SYM
ejpam-6325	288	12	d	d	NOUN
ejpam-6325	288	13	using	use	VERB
ejpam-6325	288	14	generalized	generalized	ADJ
ejpam-6325	288	15	finite	finite	ADJ
ejpam-6325	288	16	difference	difference	NOUN
ejpam-6325	288	17	method	method	NOUN
ejpam-6325	288	18	(	(	PUNCT
ejpam-6325	288	19	gfdm	gfdm	NOUN
ejpam-6325	288	20	)	)	PUNCT
ejpam-6325	288	21	.	.	PUNCT
ejpam-6325	289	1	engineering	engineer	VERB
ejpam-6325	289	2	analysis	analysis	NOUN
ejpam-6325	289	3	with	with	ADP
ejpam-6325	289	4	boundary	boundary	ADJ
ejpam-6325	289	5	elements	element	NOUN
ejpam-6325	289	6	,	,	PUNCT
ejpam-6325	289	7	112:13–24	112:13–24	NUM
ejpam-6325	289	8	,	,	PUNCT
ejpam-6325	289	9	2020	2020	NUM
ejpam-6325	289	10	.	.	PUNCT
ejpam-6325	290	1	[	[	X
ejpam-6325	290	2	16	16	NUM
ejpam-6325	290	3	]	]	PUNCT
ejpam-6325	290	4	derya	derya	NOUN
ejpam-6325	290	5	arslan	arslan	PROPN
ejpam-6325	290	6	.	.	PUNCT
ejpam-6325	291	1	the	the	DET
ejpam-6325	291	2	numerical	numerical	ADJ
ejpam-6325	291	3	study	study	NOUN
ejpam-6325	291	4	of	of	ADP
ejpam-6325	291	5	a	a	DET
ejpam-6325	291	6	hybrid	hybrid	ADJ
ejpam-6325	291	7	method	method	NOUN
ejpam-6325	291	8	for	for	ADP
ejpam-6325	291	9	solving	solve	VERB
ejpam-6325	291	10	telegraph	telegraph	NOUN
ejpam-6325	291	11	equation	equation	NOUN
ejpam-6325	291	12	.	.	PUNCT
ejpam-6325	292	1	m.	m.	PROPN
ejpam-6325	292	2	noman	noman	PROPN
ejpam-6325	292	3	et	et	PROPN
ejpam-6325	292	4	al	al	PROPN
ejpam-6325	292	5	.	.	PUNCT
ejpam-6325	292	6	/	/	SYM
ejpam-6325	292	7	eur	eur	PROPN
ejpam-6325	292	8	.	.	PUNCT
ejpam-6325	293	1	j.	j.	PROPN
ejpam-6325	293	2	pure	pure	PROPN
ejpam-6325	293	3	appl	appl	PROPN
ejpam-6325	293	4	.	.	PROPN
ejpam-6325	293	5	math	math	PROPN
ejpam-6325	293	6	,	,	PUNCT
ejpam-6325	293	7	18	18	NUM
ejpam-6325	293	8	(	(	PUNCT
ejpam-6325	293	9	3	3	NUM
ejpam-6325	293	10	)	)	PUNCT
ejpam-6325	293	11	(	(	PUNCT
ejpam-6325	293	12	2025	2025	NUM
ejpam-6325	293	13	)	)	PUNCT
ejpam-6325	293	14	,	,	PUNCT
ejpam-6325	293	15	6235	6235	NUM
ejpam-6325	293	16	16	16	NUM
ejpam-6325	293	17	of	of	ADP
ejpam-6325	293	18	16	16	NUM
ejpam-6325	293	19	applied	apply	VERB
ejpam-6325	293	20	mathematics	mathematic	NOUN
ejpam-6325	293	21	and	and	CCONJ
ejpam-6325	293	22	nonlinear	nonlinear	ADJ
ejpam-6325	293	23	sciences	science	NOUN
ejpam-6325	293	24	,	,	PUNCT
ejpam-6325	293	25	5(1):293–302	5(1):293–302	NUM
ejpam-6325	293	26	,	,	PUNCT
ejpam-6325	293	27	2020	2020	NUM
ejpam-6325	293	28	.	.	PUNCT
ejpam-6325	294	1	[	[	X
ejpam-6325	294	2	17	17	NUM
ejpam-6325	294	3	]	]	X
ejpam-6325	294	4	elaf	elaf	PROPN
ejpam-6325	294	5	sabah	sabah	PROPN
ejpam-6325	294	6	abbas	abbas	PROPN
ejpam-6325	294	7	,	,	PUNCT
ejpam-6325	294	8	emad	emad	PROPN
ejpam-6325	294	9	a.	a.	PROPN
ejpam-6325	294	10	kuffi	kuffi	PROPN
ejpam-6325	294	11	,	,	PUNCT
ejpam-6325	294	12	and	and	CCONJ
ejpam-6325	294	13	lina	lina	PROPN
ejpam-6325	294	14	baker	baker	PROPN
ejpam-6325	294	15	abdlrasol	abdlrasol	PROPN
ejpam-6325	294	16	.	.	PUNCT
ejpam-6325	295	1	general	general	ADJ
ejpam-6325	295	2	solution	solution	NOUN
ejpam-6325	295	3	of	of	ADP
ejpam-6325	295	4	telegraph	telegraph	NOUN
ejpam-6325	295	5	equation	equation	NOUN
ejpam-6325	295	6	using	use	VERB
ejpam-6325	295	7	aboodh	aboodh	ADJ
ejpam-6325	295	8	transform	transform	NOUN
ejpam-6325	295	9	.	.	PUNCT
ejpam-6325	296	1	mathematical	mathematical	ADJ
ejpam-6325	296	2	statistician	statistician	NOUN
ejpam-6325	296	3	and	and	CCONJ
ejpam-6325	296	4	engineering	engineering	NOUN
ejpam-6325	296	5	applications	application	NOUN
ejpam-6325	296	6	,	,	PUNCT
ejpam-6325	296	7	71(2):267–271	71(2):267–271	NOUN
ejpam-6325	296	8	,	,	PUNCT
ejpam-6325	296	9	2022	2022	NUM
ejpam-6325	296	10	.	.	PUNCT
ejpam-6325	297	1	[	[	X
ejpam-6325	297	2	18	18	NUM
ejpam-6325	297	3	]	]	X
ejpam-6325	297	4	ali	ali	PROPN
ejpam-6325	297	5	moazzzam	moazzzam	PROPN
ejpam-6325	297	6	,	,	PUNCT
ejpam-6325	297	7	ayza	ayza	ADJ
ejpam-6325	297	8	anjum	anjum	PROPN
ejpam-6325	297	9	,	,	PUNCT
ejpam-6325	297	10	nimra	nimra	NOUN
ejpam-6325	297	11	saleem	saleem	NOUN
ejpam-6325	297	12	,	,	PUNCT
ejpam-6325	297	13	and	and	CCONJ
ejpam-6325	297	14	emad	emad	PROPN
ejpam-6325	297	15	a.	a.	PROPN
ejpam-6325	297	16	kuffi	kuffi	PROPN
ejpam-6325	297	17	.	.	PUNCT
ejpam-6325	297	18	study	study	NOUN
ejpam-6325	297	19	of	of	ADP
ejpam-6325	297	20	telegraph	telegraph	NOUN
ejpam-6325	297	21	equation	equation	NOUN
ejpam-6325	297	22	via	via	ADP
ejpam-6325	297	23	he	he	PRON
ejpam-6325	297	24	-	-	PUNCT
ejpam-6325	297	25	fractional	fractional	ADJ
ejpam-6325	297	26	laplace	laplace	NOUN
ejpam-6325	297	27	homotopy	homotopy	NOUN
ejpam-6325	297	28	perturbation	perturbation	NOUN
ejpam-6325	297	29	technique	technique	NOUN
ejpam-6325	297	30	.	.	PUNCT
ejpam-6325	298	1	ibn	ibn	PROPN
ejpam-6325	298	2	al	al	PROPN
ejpam-6325	298	3	-	-	PUNCT
ejpam-6325	298	4	haitham	haitham	PROPN
ejpam-6325	298	5	journal	journal	PROPN
ejpam-6325	298	6	for	for	ADP
ejpam-6325	298	7	pure	pure	ADJ
ejpam-6325	298	8	and	and	CCONJ
ejpam-6325	298	9	applied	applied	ADJ
ejpam-6325	298	10	sciences	science	NOUN
ejpam-6325	298	11	,	,	PUNCT
ejpam-6325	298	12	36(3):349–364	36(3):349–364	NUM
ejpam-6325	298	13	,	,	PUNCT
ejpam-6325	298	14	2023	2023	NUM
ejpam-6325	298	15	.	.	PUNCT
ejpam-6325	299	1	[	[	X
ejpam-6325	299	2	19	19	NUM
ejpam-6325	299	3	]	]	X
ejpam-6325	299	4	t.	t.	PROPN
ejpam-6325	299	5	pietrzak	pietrzak	PROPN
ejpam-6325	299	6	,	,	PUNCT
ejpam-6325	299	7	a.	a.	NOUN
ejpam-6325	299	8	horzela	horzela	PROPN
ejpam-6325	299	9	,	,	PUNCT
ejpam-6325	299	10	and	and	CCONJ
ejpam-6325	299	11	k.	k.	PROPN
ejpam-6325	300	1	górska	górska	PROPN
ejpam-6325	300	2	.	.	PUNCT
ejpam-6325	301	1	the	the	DET
ejpam-6325	301	2	generalized	generalized	ADJ
ejpam-6325	301	3	telegraph	telegraph	NOUN
ejpam-6325	301	4	equation	equation	NOUN
ejpam-6325	301	5	with	with	ADP
ejpam-6325	301	6	moving	move	VERB
ejpam-6325	301	7	harmonic	harmonic	ADJ
ejpam-6325	301	8	source	source	NOUN
ejpam-6325	301	9	:	:	PUNCT
ejpam-6325	301	10	solvability	solvability	NOUN
ejpam-6325	301	11	using	use	VERB
ejpam-6325	301	12	the	the	DET
ejpam-6325	301	13	integral	integral	ADJ
ejpam-6325	301	14	decomposition	decomposition	NOUN
ejpam-6325	301	15	technique	technique	NOUN
ejpam-6325	301	16	and	and	CCONJ
ejpam-6325	301	17	wave	wave	NOUN
ejpam-6325	301	18	aspects	aspect	NOUN
ejpam-6325	301	19	.	.	PUNCT
ejpam-6325	302	1	international	international	ADJ
ejpam-6325	302	2	journal	journal	PROPN
ejpam-6325	302	3	of	of	ADP
ejpam-6325	302	4	heat	heat	NOUN
ejpam-6325	302	5	and	and	CCONJ
ejpam-6325	302	6	mass	mass	NOUN
ejpam-6325	302	7	transfer	transfer	NOUN
ejpam-6325	302	8	,	,	PUNCT
ejpam-6325	302	9	225:125373	225:125373	NUM
ejpam-6325	302	10	,	,	PUNCT
ejpam-6325	302	11	2024	2024	NUM
ejpam-6325	302	12	.	.	PUNCT
ejpam-6325	303	1	[	[	X
ejpam-6325	303	2	20	20	NUM
ejpam-6325	303	3	]	]	SYM
ejpam-6325	303	4	jianzhong	jianzhong	PROPN
ejpam-6325	303	5	wang	wang	PROPN
ejpam-6325	303	6	.	.	PUNCT
ejpam-6325	304	1	euclidean	euclidean	ADJ
ejpam-6325	304	2	algorithm	algorithm	NOUN
ejpam-6325	304	3	for	for	ADP
ejpam-6325	304	4	laurent	laurent	NOUN
ejpam-6325	304	5	polynomial	polynomial	ADJ
ejpam-6325	304	6	matrix	matrix	NOUN
ejpam-6325	304	7	extension	extension	NOUN
ejpam-6325	304	8	:	:	PUNCT
ejpam-6325	304	9	a	a	DET
ejpam-6325	304	10	note	note	NOUN
ejpam-6325	304	11	on	on	ADP
ejpam-6325	304	12	dual	dual	ADJ
ejpam-6325	304	13	-	-	PUNCT
ejpam-6325	304	14	chain	chain	NOUN
ejpam-6325	304	15	approach	approach	NOUN
ejpam-6325	304	16	to	to	ADP
ejpam-6325	304	17	construction	construction	NOUN
ejpam-6325	304	18	of	of	ADP
ejpam-6325	304	19	wavelet	wavelet	NOUN
ejpam-6325	304	20	filters	filter	NOUN
ejpam-6325	304	21	.	.	PUNCT
ejpam-6325	305	1	applied	apply	VERB
ejpam-6325	305	2	and	and	CCONJ
ejpam-6325	305	3	computational	computational	ADJ
ejpam-6325	305	4	harmonic	harmonic	ADJ
ejpam-6325	305	5	analysis	analysis	NOUN
ejpam-6325	305	6	,	,	PUNCT
ejpam-6325	305	7	38(2):331–345	38(2):331–345	NUM
ejpam-6325	305	8	,	,	PUNCT
ejpam-6325	305	9	2015	2015	NUM
ejpam-6325	305	10	.	.	PUNCT