id	sid	tid	token	lemma	pos
ejpam-6248	1	1	european	european	PROPN
ejpam-6248	1	2	journal	journal	PROPN
ejpam-6248	1	3	of	of	ADP
ejpam-6248	1	4	pure	pure	ADJ
ejpam-6248	1	5	and	and	CCONJ
ejpam-6248	1	6	applied	applied	ADJ
ejpam-6248	1	7	mathematics	mathematic	NOUN
ejpam-6248	1	8	2025	2025	NUM
ejpam-6248	1	9	,	,	PUNCT
ejpam-6248	1	10	vol	vol	NOUN
ejpam-6248	1	11	.	.	PROPN
ejpam-6248	1	12	18	18	NUM
ejpam-6248	1	13	,	,	PUNCT
ejpam-6248	1	14	issue	issue	NOUN
ejpam-6248	1	15	3	3	NUM
ejpam-6248	1	16	,	,	PUNCT
ejpam-6248	1	17	article	article	NOUN
ejpam-6248	1	18	number	number	NOUN
ejpam-6248	1	19	6248	6248	NUM
ejpam-6248	1	20	issn	issn	PROPN
ejpam-6248	1	21	1307	1307	NUM
ejpam-6248	1	22	-	-	SYM
ejpam-6248	1	23	5543	5543	NUM
ejpam-6248	1	24	–	–	PUNCT
ejpam-6248	1	25	ejpam.com	ejpam.com	X
ejpam-6248	1	26	published	publish	VERB
ejpam-6248	1	27	by	by	ADP
ejpam-6248	1	28	new	new	PROPN
ejpam-6248	1	29	york	york	PROPN
ejpam-6248	1	30	business	business	PROPN
ejpam-6248	1	31	global	global	ADJ
ejpam-6248	1	32	self	self	NOUN
ejpam-6248	1	33	-	-	PUNCT
ejpam-6248	1	34	similar	similar	ADJ
ejpam-6248	1	35	solutions	solution	NOUN
ejpam-6248	1	36	to	to	ADP
ejpam-6248	1	37	the	the	DET
ejpam-6248	1	38	lin	lin	PROPN
ejpam-6248	1	39	–	–	PUNCT
ejpam-6248	1	40	reissner	reissner	NOUN
ejpam-6248	1	41	–	–	PUNCT
ejpam-6248	1	42	tsien	tsien	NOUN
ejpam-6248	1	43	equation	equation	NOUN
ejpam-6248	1	44	via	via	ADP
ejpam-6248	1	45	the	the	DET
ejpam-6248	1	46	power	power	NOUN
ejpam-6248	1	47	index	index	NOUN
ejpam-6248	1	48	method	method	PROPN
ejpam-6248	1	49	zeshan	zeshan	PROPN
ejpam-6248	1	50	haider1,∗	haider1,∗	PROPN
ejpam-6248	1	51	,	,	PUNCT
ejpam-6248	1	52	khalil	khalil	PROPN
ejpam-6248	1	53	ahmad1	ahmad1	PROPN
ejpam-6248	1	54	,	,	PUNCT
ejpam-6248	1	55	muhammad	muhammad	PROPN
ejpam-6248	1	56	shoaib	shoaib	PROPN
ejpam-6248	1	57	arif2	arif2	PROPN
ejpam-6248	1	58	,	,	PUNCT
ejpam-6248	1	59	ateeq	ateeq	ADV
ejpam-6248	1	60	ur	ur	PROPN
ejpam-6248	1	61	rehman2	rehman2	PROPN
ejpam-6248	1	62	,	,	PUNCT
ejpam-6248	1	63	muhammad	muhammad	PROPN
ejpam-6248	1	64	noman	noman	PROPN
ejpam-6248	1	65	qureshi1	qureshi1	PROPN
ejpam-6248	1	66	1	1	NUM
ejpam-6248	1	67	department	department	NOUN
ejpam-6248	1	68	of	of	ADP
ejpam-6248	1	69	mathematics	mathematic	NOUN
ejpam-6248	1	70	,	,	PUNCT
ejpam-6248	1	71	faculty	faculty	NOUN
ejpam-6248	1	72	of	of	ADP
ejpam-6248	1	73	basic	basic	ADJ
ejpam-6248	1	74	and	and	CCONJ
ejpam-6248	1	75	applied	applied	ADJ
ejpam-6248	1	76	sciences	science	NOUN
ejpam-6248	1	77	,	,	PUNCT
ejpam-6248	1	78	air	air	NOUN
ejpam-6248	1	79	university	university	PROPN
ejpam-6248	1	80	,	,	PUNCT
ejpam-6248	1	81	paf	paf	PROPN
ejpam-6248	1	82	complex	complex	PROPN
ejpam-6248	1	83	e-9	e-9	PROPN
ejpam-6248	1	84	,	,	PUNCT
ejpam-6248	1	85	islamabad	islamabad	NOUN
ejpam-6248	1	86	44000	44000	NUM
ejpam-6248	1	87	,	,	PUNCT
ejpam-6248	1	88	pakistan	pakistan	PROPN
ejpam-6248	1	89	2	2	NUM
ejpam-6248	1	90	department	department	NOUN
ejpam-6248	1	91	of	of	ADP
ejpam-6248	1	92	mathematics	mathematic	NOUN
ejpam-6248	1	93	and	and	CCONJ
ejpam-6248	1	94	sciences	science	NOUN
ejpam-6248	1	95	,	,	PUNCT
ejpam-6248	1	96	college	college	NOUN
ejpam-6248	1	97	of	of	ADP
ejpam-6248	1	98	humanities	humanity	NOUN
ejpam-6248	1	99	and	and	CCONJ
ejpam-6248	1	100	sciences	science	NOUN
ejpam-6248	1	101	,	,	PUNCT
ejpam-6248	1	102	prince	prince	PROPN
ejpam-6248	1	103	sultan	sultan	PROPN
ejpam-6248	1	104	university	university	PROPN
ejpam-6248	1	105	,	,	PUNCT
ejpam-6248	1	106	riyadh	riyadh	PROPN
ejpam-6248	1	107	11586	11586	NUM
ejpam-6248	1	108	,	,	PUNCT
ejpam-6248	1	109	saudi	saudi	PROPN
ejpam-6248	1	110	arabia	arabia	PROPN
ejpam-6248	1	111	abstract	abstract	NOUN
ejpam-6248	1	112	.	.	PUNCT
ejpam-6248	2	1	in	in	ADP
ejpam-6248	2	2	this	this	DET
ejpam-6248	2	3	paper	paper	NOUN
ejpam-6248	2	4	,	,	PUNCT
ejpam-6248	2	5	the	the	DET
ejpam-6248	2	6	(	(	PUNCT
ejpam-6248	2	7	2	2	NUM
ejpam-6248	2	8	+	+	NUM
ejpam-6248	2	9	1)-dimensional	1)-dimensional	NUM
ejpam-6248	2	10	lin	lin	PROPN
ejpam-6248	2	11	–	–	PUNCT
ejpam-6248	2	12	reissner	reissner	NOUN
ejpam-6248	2	13	–	–	PUNCT
ejpam-6248	2	14	tsien	tsien	NOUN
ejpam-6248	2	15	(	(	PUNCT
ejpam-6248	2	16	lrt	lrt	PROPN
ejpam-6248	2	17	)	)	PUNCT
ejpam-6248	2	18	equation	equation	NOUN
ejpam-6248	2	19	is	be	AUX
ejpam-6248	2	20	investigated	investigate	VERB
ejpam-6248	2	21	using	use	VERB
ejpam-6248	2	22	the	the	DET
ejpam-6248	2	23	power	power	NOUN
ejpam-6248	2	24	index	index	NOUN
ejpam-6248	2	25	method	method	NOUN
ejpam-6248	2	26	(	(	PUNCT
ejpam-6248	2	27	pim	pim	PROPN
ejpam-6248	2	28	)	)	PUNCT
ejpam-6248	2	29	.	.	PUNCT
ejpam-6248	3	1	a	a	DET
ejpam-6248	3	2	self	self	NOUN
ejpam-6248	3	3	-	-	PUNCT
ejpam-6248	3	4	similar	similar	ADJ
ejpam-6248	3	5	transformation	transformation	NOUN
ejpam-6248	3	6	is	be	AUX
ejpam-6248	3	7	applied	apply	VERB
ejpam-6248	3	8	to	to	PART
ejpam-6248	3	9	reduce	reduce	VERB
ejpam-6248	3	10	the	the	DET
ejpam-6248	3	11	given	give	VERB
ejpam-6248	3	12	partial	partial	ADJ
ejpam-6248	3	13	differential	differential	NOUN
ejpam-6248	3	14	equation	equation	NOUN
ejpam-6248	3	15	(	(	PUNCT
ejpam-6248	3	16	pde	pde	NOUN
ejpam-6248	3	17	)	)	PUNCT
ejpam-6248	3	18	into	into	ADP
ejpam-6248	3	19	an	an	DET
ejpam-6248	3	20	ordinary	ordinary	ADJ
ejpam-6248	3	21	differential	differential	ADJ
ejpam-6248	3	22	equation	equation	NOUN
ejpam-6248	3	23	(	(	PUNCT
ejpam-6248	3	24	ode	ode	PROPN
ejpam-6248	3	25	)	)	PUNCT
ejpam-6248	3	26	through	through	ADP
ejpam-6248	3	27	a	a	DET
ejpam-6248	3	28	change	change	NOUN
ejpam-6248	3	29	of	of	ADP
ejpam-6248	3	30	variables	variable	NOUN
ejpam-6248	3	31	based	base	VERB
ejpam-6248	3	32	on	on	ADP
ejpam-6248	3	33	scaling	scale	VERB
ejpam-6248	3	34	symmetry	symmetry	NOUN
ejpam-6248	3	35	.	.	PUNCT
ejpam-6248	4	1	the	the	DET
ejpam-6248	4	2	analytic	analytic	ADJ
ejpam-6248	4	3	solution	solution	NOUN
ejpam-6248	4	4	of	of	ADP
ejpam-6248	4	5	the	the	DET
ejpam-6248	4	6	resulting	result	VERB
ejpam-6248	4	7	ode	ode	NOUN
ejpam-6248	4	8	is	be	AUX
ejpam-6248	4	9	obtained	obtain	VERB
ejpam-6248	4	10	using	use	VERB
ejpam-6248	4	11	the	the	DET
ejpam-6248	4	12	symbolic	symbolic	ADJ
ejpam-6248	4	13	computation	computation	NOUN
ejpam-6248	4	14	software	software	NOUN
ejpam-6248	4	15	maple	maple	NOUN
ejpam-6248	4	16	18	18	NUM
ejpam-6248	4	17	and	and	CCONJ
ejpam-6248	4	18	basic	basic	ADJ
ejpam-6248	4	19	techniques	technique	NOUN
ejpam-6248	4	20	.	.	PUNCT
ejpam-6248	5	1	the	the	DET
ejpam-6248	5	2	self	self	NOUN
ejpam-6248	5	3	-	-	PUNCT
ejpam-6248	5	4	similar	similar	ADJ
ejpam-6248	5	5	solutions	solution	NOUN
ejpam-6248	5	6	of	of	ADP
ejpam-6248	5	7	the	the	DET
ejpam-6248	5	8	lrt	lrt	PROPN
ejpam-6248	5	9	equation	equation	NOUN
ejpam-6248	5	10	are	be	AUX
ejpam-6248	5	11	then	then	ADV
ejpam-6248	5	12	derived	derive	VERB
ejpam-6248	5	13	by	by	ADP
ejpam-6248	5	14	combining	combine	VERB
ejpam-6248	5	15	the	the	DET
ejpam-6248	5	16	ode	ode	ADJ
ejpam-6248	5	17	solution	solution	NOUN
ejpam-6248	5	18	with	with	ADP
ejpam-6248	5	19	the	the	DET
ejpam-6248	5	20	self	self	NOUN
ejpam-6248	5	21	-	-	PUNCT
ejpam-6248	5	22	similar	similar	ADJ
ejpam-6248	5	23	transformation	transformation	NOUN
ejpam-6248	5	24	.	.	PUNCT
ejpam-6248	6	1	the	the	DET
ejpam-6248	6	2	proposed	propose	VERB
ejpam-6248	6	3	method	method	NOUN
ejpam-6248	6	4	is	be	AUX
ejpam-6248	6	5	effectively	effectively	ADV
ejpam-6248	6	6	applied	apply	VERB
ejpam-6248	6	7	to	to	PART
ejpam-6248	6	8	generate	generate	VERB
ejpam-6248	6	9	new	new	ADJ
ejpam-6248	6	10	self	self	NOUN
ejpam-6248	6	11	-	-	PUNCT
ejpam-6248	6	12	similar	similar	ADJ
ejpam-6248	6	13	solutions	solution	NOUN
ejpam-6248	6	14	of	of	ADP
ejpam-6248	6	15	the	the	DET
ejpam-6248	6	16	lrt	lrt	PROPN
ejpam-6248	6	17	equation	equation	NOUN
ejpam-6248	6	18	.	.	PUNCT
ejpam-6248	7	1	finally	finally	ADV
ejpam-6248	7	2	,	,	PUNCT
ejpam-6248	7	3	graphical	graphical	ADJ
ejpam-6248	7	4	representations	representation	NOUN
ejpam-6248	7	5	of	of	ADP
ejpam-6248	7	6	all	all	DET
ejpam-6248	7	7	the	the	DET
ejpam-6248	7	8	obtained	obtain	VERB
ejpam-6248	7	9	solutions	solution	NOUN
ejpam-6248	7	10	are	be	AUX
ejpam-6248	7	11	presented	present	VERB
ejpam-6248	7	12	as	as	ADP
ejpam-6248	7	13	3d	3d	NUM
ejpam-6248	7	14	plots	plot	NOUN
ejpam-6248	7	15	generated	generate	VERB
ejpam-6248	7	16	using	use	VERB
ejpam-6248	7	17	maple	maple	PROPN
ejpam-6248	7	18	18	18	NUM
ejpam-6248	7	19	.	.	PUNCT
ejpam-6248	8	1	2020	2020	NUM
ejpam-6248	8	2	mathematics	mathematic	NOUN
ejpam-6248	8	3	subject	subject	NOUN
ejpam-6248	8	4	classifications	classification	NOUN
ejpam-6248	8	5	:	:	PUNCT
ejpam-6248	8	6	35qxx	35qxx	NOUN
ejpam-6248	8	7	,	,	PUNCT
ejpam-6248	8	8	26a33	26a33	NUM
ejpam-6248	8	9	key	key	ADJ
ejpam-6248	8	10	words	word	NOUN
ejpam-6248	8	11	and	and	CCONJ
ejpam-6248	8	12	phrases	phrase	NOUN
ejpam-6248	8	13	:	:	PUNCT
ejpam-6248	8	14	lin	lin	PROPN
ejpam-6248	8	15	–	–	PUNCT
ejpam-6248	8	16	reissner	reissner	NOUN
ejpam-6248	8	17	–	–	PUNCT
ejpam-6248	8	18	tsien	tsien	NOUN
ejpam-6248	8	19	equation	equation	NOUN
ejpam-6248	8	20	,	,	PUNCT
ejpam-6248	8	21	power	power	NOUN
ejpam-6248	8	22	index	index	NOUN
ejpam-6248	8	23	method	method	NOUN
ejpam-6248	8	24	,	,	PUNCT
ejpam-6248	8	25	self	self	NOUN
ejpam-6248	8	26	-	-	PUNCT
ejpam-6248	8	27	similar	similar	ADJ
ejpam-6248	8	28	transformation	transformation	NOUN
ejpam-6248	8	29	,	,	PUNCT
ejpam-6248	8	30	self	self	NOUN
ejpam-6248	8	31	-	-	PUNCT
ejpam-6248	8	32	similar	similar	ADJ
ejpam-6248	8	33	solutions	solution	NOUN
ejpam-6248	8	34	,	,	PUNCT
ejpam-6248	8	35	nonlinear	nonlinear	ADJ
ejpam-6248	8	36	partial	partial	ADJ
ejpam-6248	8	37	differential	differential	ADJ
ejpam-6248	8	38	equations	equation	NOUN
ejpam-6248	8	39	1	1	NUM
ejpam-6248	8	40	.	.	X
ejpam-6248	8	41	introduction	introduction	NOUN
ejpam-6248	8	42	many	many	ADJ
ejpam-6248	8	43	real	real	ADJ
ejpam-6248	8	44	-	-	PUNCT
ejpam-6248	8	45	world	world	NOUN
ejpam-6248	8	46	physical	physical	ADJ
ejpam-6248	8	47	phenomena	phenomenon	NOUN
ejpam-6248	8	48	are	be	AUX
ejpam-6248	8	49	described	describe	VERB
ejpam-6248	8	50	by	by	ADP
ejpam-6248	8	51	nonlinear	nonlinear	ADJ
ejpam-6248	8	52	partial	partial	ADJ
ejpam-6248	8	53	differential	differential	NOUN
ejpam-6248	8	54	equations	equation	NOUN
ejpam-6248	8	55	(	(	PUNCT
ejpam-6248	8	56	nlpdes	nlpde	NOUN
ejpam-6248	8	57	)	)	PUNCT
ejpam-6248	8	58	.	.	PUNCT
ejpam-6248	9	1	consequently	consequently	ADV
ejpam-6248	9	2	,	,	PUNCT
ejpam-6248	9	3	studying	study	VERB
ejpam-6248	9	4	these	these	DET
ejpam-6248	9	5	equations	equation	NOUN
ejpam-6248	9	6	to	to	PART
ejpam-6248	9	7	assess	assess	VERB
ejpam-6248	9	8	their	their	PRON
ejpam-6248	9	9	integrability	integrability	NOUN
ejpam-6248	9	10	and	and	CCONJ
ejpam-6248	9	11	determine	determine	VERB
ejpam-6248	9	12	exact	exact	ADJ
ejpam-6248	9	13	solutions	solution	NOUN
ejpam-6248	9	14	is	be	AUX
ejpam-6248	9	15	essential	essential	ADJ
ejpam-6248	9	16	.	.	PUNCT
ejpam-6248	10	1	while	while	SCONJ
ejpam-6248	10	2	this	this	DET
ejpam-6248	10	3	task	task	NOUN
ejpam-6248	10	4	is	be	AUX
ejpam-6248	10	5	challenging	challenging	ADJ
ejpam-6248	10	6	,	,	PUNCT
ejpam-6248	10	7	several	several	ADJ
ejpam-6248	10	8	analytical	analytical	ADJ
ejpam-6248	10	9	techniques	technique	NOUN
ejpam-6248	10	10	have	have	AUX
ejpam-6248	10	11	been	be	AUX
ejpam-6248	10	12	developed	develop	VERB
ejpam-6248	10	13	by	by	ADP
ejpam-6248	10	14	researchers	researcher	NOUN
ejpam-6248	10	15	to	to	PART
ejpam-6248	10	16	obtain	obtain	VERB
ejpam-6248	10	17	exact	exact	ADJ
ejpam-6248	10	18	solutions	solution	NOUN
ejpam-6248	10	19	.	.	PUNCT
ejpam-6248	11	1	among	among	ADP
ejpam-6248	11	2	these	these	PRON
ejpam-6248	11	3	are	be	AUX
ejpam-6248	11	4	the	the	DET
ejpam-6248	11	5	exp	exp	NOUN
ejpam-6248	11	6	-	-	PUNCT
ejpam-6248	11	7	function	function	NOUN
ejpam-6248	11	8	method	method	NOUN
ejpam-6248	11	9	[	[	X
ejpam-6248	11	10	1	1	NUM
ejpam-6248	11	11	]	]	PUNCT
ejpam-6248	11	12	,	,	PUNCT
ejpam-6248	11	13	modified	modify	VERB
ejpam-6248	11	14	exp	exp	NOUN
ejpam-6248	11	15	-	-	PUNCT
ejpam-6248	11	16	function	function	NOUN
ejpam-6248	11	17	method	method	NOUN
ejpam-6248	11	18	[	[	X
ejpam-6248	11	19	2	2	NUM
ejpam-6248	11	20	]	]	PUNCT
ejpam-6248	11	21	,	,	PUNCT
ejpam-6248	11	22	[	[	X
ejpam-6248	11	23	3	3	NUM
ejpam-6248	11	24	]	]	PUNCT
ejpam-6248	11	25	,	,	PUNCT
ejpam-6248	11	26	[	[	X
ejpam-6248	11	27	4	4	NUM
ejpam-6248	11	28	]	]	PUNCT
ejpam-6248	11	29	,	,	PUNCT
ejpam-6248	11	30	simple	simple	ADJ
ejpam-6248	11	31	equations	equation	NOUN
ejpam-6248	11	32	method	method	NOUN
ejpam-6248	11	33	(	(	PUNCT
ejpam-6248	11	34	sesm	sesm	PROPN
ejpam-6248	11	35	)	)	PUNCT
ejpam-6248	12	1	[	[	X
ejpam-6248	12	2	5	5	NUM
ejpam-6248	12	3	]	]	PUNCT
ejpam-6248	12	4	,	,	PUNCT
ejpam-6248	12	5	[	[	X
ejpam-6248	12	6	6	6	NUM
ejpam-6248	12	7	]	]	PUNCT
ejpam-6248	12	8	,	,	PUNCT
ejpam-6248	12	9	[	[	X
ejpam-6248	12	10	7	7	NUM
ejpam-6248	12	11	]	]	PUNCT
ejpam-6248	12	12	,	,	PUNCT
ejpam-6248	12	13	[	[	X
ejpam-6248	12	14	8	8	NUM
ejpam-6248	12	15	]	]	PUNCT
ejpam-6248	12	16	,	,	PUNCT
ejpam-6248	12	17	sine	sine	ADJ
ejpam-6248	12	18	-	-	PUNCT
ejpam-6248	12	19	cosine	cosine	NOUN
ejpam-6248	12	20	method	method	NOUN
ejpam-6248	12	21	[	[	X
ejpam-6248	12	22	9	9	NUM
ejpam-6248	12	23	]	]	PUNCT
ejpam-6248	12	24	,	,	PUNCT
ejpam-6248	12	25	[	[	X
ejpam-6248	12	26	10	10	NUM
ejpam-6248	12	27	]	]	PUNCT
ejpam-6248	12	28	,	,	PUNCT
ejpam-6248	12	29	first	first	ADJ
ejpam-6248	12	30	integral	integral	ADJ
ejpam-6248	12	31	method	method	NOUN
ejpam-6248	12	32	[	[	X
ejpam-6248	12	33	11	11	NUM
ejpam-6248	12	34	]	]	PUNCT
ejpam-6248	12	35	,	,	PUNCT
ejpam-6248	12	36	[	[	X
ejpam-6248	12	37	12	12	NUM
ejpam-6248	12	38	]	]	PUNCT
ejpam-6248	12	39	,	,	PUNCT
ejpam-6248	12	40	sardar	sardar	PROPN
ejpam-6248	12	41	sub	sub	ADJ
ejpam-6248	12	42	-	-	ADJ
ejpam-6248	12	43	equation	equation	ADJ
ejpam-6248	12	44	method	method	NOUN
ejpam-6248	12	45	[	[	X
ejpam-6248	12	46	13	13	NUM
ejpam-6248	12	47	]	]	PUNCT
ejpam-6248	12	48	,	,	PUNCT
ejpam-6248	12	49	modified	modify	VERB
ejpam-6248	12	50	sardar	sardar	PROPN
ejpam-6248	12	51	sub	sub	NOUN
ejpam-6248	12	52	-	-	ADJ
ejpam-6248	12	53	equation	equation	ADJ
ejpam-6248	12	54	method	method	NOUN
ejpam-6248	12	55	[	[	X
ejpam-6248	12	56	14	14	NUM
ejpam-6248	12	57	]	]	PUNCT
ejpam-6248	12	58	,	,	PUNCT
ejpam-6248	12	59	∗corresponding	∗corresponde	VERB
ejpam-6248	12	60	author	author	NOUN
ejpam-6248	12	61	.	.	PUNCT
ejpam-6248	13	1	doi	doi	PROPN
ejpam-6248	13	2	:	:	PUNCT
ejpam-6248	13	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6248	https://doi.org/10.29020/nybg.ejpam.v18i3.6248	PROPN
ejpam-6248	13	4	email	email	NOUN
ejpam-6248	13	5	addresses	address	NOUN
ejpam-6248	13	6	:	:	PUNCT
ejpam-6248	13	7	211904@students.au.edu.pk	211904@students.au.edu.pk	NUM
ejpam-6248	13	8	(	(	PUNCT
ejpam-6248	13	9	z.	z.	PROPN
ejpam-6248	13	10	haider	haider	PROPN
ejpam-6248	13	11	)	)	PUNCT
ejpam-6248	13	12	,	,	PUNCT
ejpam-6248	14	1	khalilmalik@au.edu.pk	khalilmalik@au.edu.pk	PROPN
ejpam-6248	14	2	(	(	PUNCT
ejpam-6248	14	3	k.	k.	PROPN
ejpam-6248	14	4	ahmad	ahmad	PROPN
ejpam-6248	14	5	)	)	PUNCT
ejpam-6248	14	6	,	,	PUNCT
ejpam-6248	14	7	marif@psu.edu.sa	marif@psu.edu.sa	NOUN
ejpam-6248	14	8	(	(	PUNCT
ejpam-6248	14	9	m.	m.	PROPN
ejpam-6248	14	10	s.	s.	PROPN
ejpam-6248	14	11	arif	arif	PROPN
ejpam-6248	14	12	)	)	PUNCT
ejpam-6248	14	13	,	,	PUNCT
ejpam-6248	14	14	airshad@psu.edu.sa	airshad@psu.edu.sa	NOUN
ejpam-6248	14	15	(	(	PUNCT
ejpam-6248	14	16	a.	a.	NOUN
ejpam-6248	14	17	u.	u.	PROPN
ejpam-6248	14	18	rehman	rehman	PROPN
ejpam-6248	14	19	)	)	PUNCT
ejpam-6248	14	20	,	,	PUNCT
ejpam-6248	14	21	211900@students.au.edu.pk	211900@students.au.edu.pk	NUM
ejpam-6248	14	22	(	(	PUNCT
ejpam-6248	14	23	m.	m.	PROPN
ejpam-6248	14	24	n.	n.	PROPN
ejpam-6248	14	25	qureshi	qureshi	PROPN
ejpam-6248	14	26	)	)	PUNCT
ejpam-6248	14	27	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6248	14	28	1	1	NUM
ejpam-6248	14	29	copyright	copyright	NOUN
ejpam-6248	14	30	:	:	PUNCT
ejpam-6248	14	31	©	©	PROPN
ejpam-6248	14	32	2025	2025	NUM
ejpam-6248	14	33	the	the	DET
ejpam-6248	14	34	author(s	author(s	NOUN
ejpam-6248	14	35	)	)	PUNCT
ejpam-6248	14	36	.	.	PUNCT
ejpam-6248	15	1	(	(	PUNCT
ejpam-6248	15	2	cc	cc	NOUN
ejpam-6248	15	3	by	by	ADP
ejpam-6248	15	4	-	-	PUNCT
ejpam-6248	15	5	nc	nc	PROPN
ejpam-6248	15	6	4.0	4.0	NUM
ejpam-6248	15	7	)	)	PUNCT
ejpam-6248	15	8	z.	z.	PROPN
ejpam-6248	15	9	haider	haider	PROPN
ejpam-6248	15	10	et	et	PROPN
ejpam-6248	15	11	al	al	PROPN
ejpam-6248	15	12	.	.	PUNCT
ejpam-6248	15	13	/	/	SYM
ejpam-6248	15	14	eur	eur	PROPN
ejpam-6248	15	15	.	.	PUNCT
ejpam-6248	16	1	j.	j.	PROPN
ejpam-6248	16	2	pure	pure	PROPN
ejpam-6248	16	3	appl	appl	PROPN
ejpam-6248	16	4	.	.	PROPN
ejpam-6248	16	5	math	math	PROPN
ejpam-6248	16	6	,	,	PUNCT
ejpam-6248	16	7	18	18	NUM
ejpam-6248	16	8	(	(	PUNCT
ejpam-6248	16	9	3	3	NUM
ejpam-6248	16	10	)	)	PUNCT
ejpam-6248	16	11	(	(	PUNCT
ejpam-6248	16	12	2025	2025	NUM
ejpam-6248	16	13	)	)	PUNCT
ejpam-6248	16	14	,	,	PUNCT
ejpam-6248	16	15	6248	6248	NUM
ejpam-6248	16	16	2	2	NUM
ejpam-6248	16	17	of	of	ADP
ejpam-6248	16	18	20	20	NUM
ejpam-6248	17	1	[	[	SYM
ejpam-6248	17	2	15	15	NUM
ejpam-6248	17	3	]	]	PUNCT
ejpam-6248	17	4	,	,	PUNCT
ejpam-6248	17	5	modified	modify	VERB
ejpam-6248	17	6	extended	extend	VERB
ejpam-6248	17	7	direct	direct	ADJ
ejpam-6248	17	8	algebraic	algebraic	ADJ
ejpam-6248	17	9	method	method	NOUN
ejpam-6248	18	1	[	[	X
ejpam-6248	18	2	16	16	NUM
ejpam-6248	18	3	]	]	PUNCT
ejpam-6248	18	4	,	,	PUNCT
ejpam-6248	18	5	[	[	X
ejpam-6248	18	6	17	17	NUM
ejpam-6248	18	7	]	]	PUNCT
ejpam-6248	18	8	,	,	PUNCT
ejpam-6248	18	9	(	(	PUNCT
ejpam-6248	18	10	g	g	NOUN
ejpam-6248	18	11	′	′	NUM
ejpam-6248	18	12	g	g	NOUN
ejpam-6248	18	13	)	)	PUNCT
ejpam-6248	18	14	-expansion	-expansion	PROPN
ejpam-6248	18	15	method	method	NOUN
ejpam-6248	18	16	[	[	X
ejpam-6248	18	17	18	18	NUM
ejpam-6248	18	18	]	]	PUNCT
ejpam-6248	18	19	,	,	PUNCT
ejpam-6248	18	20	lie	lie	NOUN
ejpam-6248	18	21	symmetry	symmetry	NOUN
ejpam-6248	18	22	method	method	NOUN
ejpam-6248	18	23	[	[	X
ejpam-6248	18	24	19	19	NUM
ejpam-6248	18	25	]	]	PUNCT
ejpam-6248	18	26	,	,	PUNCT
ejpam-6248	18	27	the	the	DET
ejpam-6248	18	28	hirota	hirota	PROPN
ejpam-6248	18	29	bilinear	bilinear	PROPN
ejpam-6248	18	30	method	method	NOUN
ejpam-6248	18	31	[	[	X
ejpam-6248	18	32	20	20	NUM
ejpam-6248	18	33	]	]	PUNCT
ejpam-6248	18	34	,	,	PUNCT
ejpam-6248	18	35	and	and	CCONJ
ejpam-6248	18	36	the	the	DET
ejpam-6248	18	37	power	power	NOUN
ejpam-6248	18	38	index	index	NOUN
ejpam-6248	18	39	method	method	NOUN
ejpam-6248	18	40	[	[	X
ejpam-6248	18	41	21	21	NUM
ejpam-6248	18	42	]	]	PUNCT
ejpam-6248	18	43	,	,	PUNCT
ejpam-6248	18	44	[	[	X
ejpam-6248	18	45	22	22	NUM
ejpam-6248	18	46	]	]	PUNCT
ejpam-6248	18	47	.	.	PUNCT
ejpam-6248	19	1	in	in	ADP
ejpam-6248	19	2	this	this	DET
ejpam-6248	19	3	paper	paper	NOUN
ejpam-6248	19	4	,	,	PUNCT
ejpam-6248	19	5	we	we	PRON
ejpam-6248	19	6	examine	examine	VERB
ejpam-6248	19	7	the	the	DET
ejpam-6248	19	8	(	(	PUNCT
ejpam-6248	19	9	2	2	NUM
ejpam-6248	19	10	+	+	NUM
ejpam-6248	19	11	1)-dimensional	1)-dimensional	NUM
ejpam-6248	19	12	lin	lin	PROPN
ejpam-6248	19	13	–	–	PUNCT
ejpam-6248	19	14	reissner	reissner	NOUN
ejpam-6248	19	15	–	–	PUNCT
ejpam-6248	19	16	tsien	tsien	NOUN
ejpam-6248	19	17	(	(	PUNCT
ejpam-6248	19	18	lrt	lrt	PROPN
ejpam-6248	19	19	)	)	PUNCT
ejpam-6248	19	20	equation	equation	NOUN
ejpam-6248	19	21	:	:	PUNCT
ejpam-6248	19	22	2uxt	2uxt	NUM
ejpam-6248	19	23	+	+	CCONJ
ejpam-6248	19	24	uxuxx	uxuxx	ADJ
ejpam-6248	19	25	−	−	PROPN
ejpam-6248	19	26	uyy	uyy	PROPN
ejpam-6248	19	27	=	=	PROPN
ejpam-6248	19	28	0	0	PROPN
ejpam-6248	19	29	.	.	PUNCT
ejpam-6248	20	1	(	(	PUNCT
ejpam-6248	20	2	1	1	X
ejpam-6248	20	3	)	)	PUNCT
ejpam-6248	20	4	which	which	PRON
ejpam-6248	20	5	represents	represent	VERB
ejpam-6248	20	6	a	a	DET
ejpam-6248	20	7	significant	significant	ADJ
ejpam-6248	20	8	class	class	NOUN
ejpam-6248	20	9	of	of	ADP
ejpam-6248	20	10	nonlinear	nonlinear	ADJ
ejpam-6248	20	11	partial	partial	ADJ
ejpam-6248	20	12	differential	differential	NOUN
ejpam-6248	20	13	equations	equation	NOUN
ejpam-6248	20	14	(	(	PUNCT
ejpam-6248	20	15	npdes	npde	NOUN
ejpam-6248	20	16	)	)	PUNCT
ejpam-6248	20	17	that	that	PRON
ejpam-6248	20	18	plays	play	VERB
ejpam-6248	20	19	a	a	DET
ejpam-6248	20	20	crucial	crucial	ADJ
ejpam-6248	20	21	role	role	NOUN
ejpam-6248	20	22	in	in	ADP
ejpam-6248	20	23	high	high	ADJ
ejpam-6248	20	24	-	-	PUNCT
ejpam-6248	20	25	speed	speed	NOUN
ejpam-6248	20	26	aerodynamic	aerodynamic	ADJ
ejpam-6248	20	27	applications	application	NOUN
ejpam-6248	20	28	,	,	PUNCT
ejpam-6248	20	29	particularly	particularly	ADV
ejpam-6248	20	30	in	in	ADP
ejpam-6248	20	31	the	the	DET
ejpam-6248	20	32	analysis	analysis	NOUN
ejpam-6248	20	33	of	of	ADP
ejpam-6248	20	34	transonic	transonic	ADJ
ejpam-6248	20	35	flow	flow	NOUN
ejpam-6248	20	36	phenomena	phenomenon	NOUN
ejpam-6248	20	37	around	around	ADP
ejpam-6248	20	38	airfoil	airfoil	NOUN
ejpam-6248	20	39	surfaces	surface	NOUN
ejpam-6248	20	40	.	.	PUNCT
ejpam-6248	21	1	the	the	DET
ejpam-6248	21	2	lin	lin	PROPN
ejpam-6248	21	3	–	–	PUNCT
ejpam-6248	21	4	reissner	reissner	NOUN
ejpam-6248	21	5	–	–	PUNCT
ejpam-6248	21	6	tsien	tsien	NOUN
ejpam-6248	21	7	(	(	PUNCT
ejpam-6248	21	8	lrt	lrt	PROPN
ejpam-6248	21	9	)	)	PUNCT
ejpam-6248	21	10	equation	equation	NOUN
ejpam-6248	21	11	mathematically	mathematically	ADV
ejpam-6248	21	12	characterizes	characterize	VERB
ejpam-6248	21	13	the	the	DET
ejpam-6248	21	14	complex	complex	ADJ
ejpam-6248	21	15	transitional	transitional	ADJ
ejpam-6248	21	16	flow	flow	NOUN
ejpam-6248	21	17	regime	regime	NOUN
ejpam-6248	21	18	around	around	ADP
ejpam-6248	21	19	aerodynamic	aerodynamic	ADJ
ejpam-6248	21	20	surfaces	surface	NOUN
ejpam-6248	21	21	,	,	PUNCT
ejpam-6248	21	22	where	where	SCONJ
ejpam-6248	21	23	the	the	DET
ejpam-6248	21	24	term	term	NOUN
ejpam-6248	21	25	uxt	uxt	NOUN
ejpam-6248	21	26	represents	represent	VERB
ejpam-6248	21	27	unsteady	unsteady	ADJ
ejpam-6248	21	28	flow	flow	NOUN
ejpam-6248	21	29	effects	effect	NOUN
ejpam-6248	21	30	,	,	PUNCT
ejpam-6248	21	31	uxuxx	uxuxx	PROPN
ejpam-6248	21	32	captures	capture	VERB
ejpam-6248	21	33	nonlinear	nonlinear	ADJ
ejpam-6248	21	34	wave	wave	NOUN
ejpam-6248	21	35	steepening	steepening	NOUN
ejpam-6248	21	36	,	,	PUNCT
ejpam-6248	21	37	and	and	CCONJ
ejpam-6248	21	38	uyy	uyy	PROPN
ejpam-6248	21	39	accounts	account	VERB
ejpam-6248	21	40	for	for	ADP
ejpam-6248	21	41	spanwise	spanwise	ADJ
ejpam-6248	21	42	pressure	pressure	NOUN
ejpam-6248	21	43	gradients	gradient	NOUN
ejpam-6248	21	44	.	.	PUNCT
ejpam-6248	22	1	physically	physically	ADV
ejpam-6248	22	2	,	,	PUNCT
ejpam-6248	22	3	u	u	NOUN
ejpam-6248	22	4	is	be	AUX
ejpam-6248	22	5	the	the	DET
ejpam-6248	22	6	potential	potential	NOUN
ejpam-6248	22	7	of	of	ADP
ejpam-6248	22	8	the	the	DET
ejpam-6248	22	9	velocity	velocity	NOUN
ejpam-6248	22	10	field	field	NOUN
ejpam-6248	22	11	,	,	PUNCT
ejpam-6248	22	12	x	x	PUNCT
ejpam-6248	22	13	and	and	CCONJ
ejpam-6248	22	14	y	y	PROPN
ejpam-6248	22	15	are	be	AUX
ejpam-6248	22	16	the	the	DET
ejpam-6248	22	17	spatial	spatial	ADJ
ejpam-6248	22	18	coordinates	coordinate	NOUN
ejpam-6248	22	19	,	,	PUNCT
ejpam-6248	22	20	and	and	CCONJ
ejpam-6248	22	21	t	t	PROPN
ejpam-6248	22	22	represents	represent	VERB
ejpam-6248	22	23	the	the	DET
ejpam-6248	22	24	temporal	temporal	ADJ
ejpam-6248	22	25	coordinate	coordinate	NOUN
ejpam-6248	22	26	in	in	ADP
ejpam-6248	22	27	equation	equation	NOUN
ejpam-6248	22	28	(	(	PUNCT
ejpam-6248	22	29	1	1	NUM
ejpam-6248	22	30	)	)	PUNCT
ejpam-6248	22	31	.	.	PUNCT
ejpam-6248	23	1	several	several	ADJ
ejpam-6248	23	2	researchers	researcher	NOUN
ejpam-6248	23	3	have	have	AUX
ejpam-6248	23	4	successfully	successfully	ADV
ejpam-6248	23	5	derived	derive	VERB
ejpam-6248	23	6	self	self	NOUN
ejpam-6248	23	7	-	-	PUNCT
ejpam-6248	23	8	similar	similar	ADJ
ejpam-6248	23	9	and	and	CCONJ
ejpam-6248	23	10	exact	exact	ADJ
ejpam-6248	23	11	analytic	analytic	ADJ
ejpam-6248	23	12	solutions	solution	NOUN
ejpam-6248	23	13	for	for	ADP
ejpam-6248	23	14	the	the	DET
ejpam-6248	23	15	lin	lin	PROPN
ejpam-6248	23	16	–	–	PUNCT
ejpam-6248	23	17	reissner	reissner	NOUN
ejpam-6248	23	18	–	–	PUNCT
ejpam-6248	23	19	tsien	tsien	NOUN
ejpam-6248	23	20	(	(	PUNCT
ejpam-6248	23	21	lrt	lrt	PROPN
ejpam-6248	23	22	)	)	PUNCT
ejpam-6248	23	23	equation	equation	NOUN
ejpam-6248	23	24	.	.	PUNCT
ejpam-6248	24	1	haussermann	haussermann	PROPN
ejpam-6248	24	2	,	,	PUNCT
ejpam-6248	24	3	vajravelu	vajravelu	NOUN
ejpam-6248	24	4	,	,	PUNCT
ejpam-6248	24	5	and	and	CCONJ
ejpam-6248	24	6	van	van	PROPN
ejpam-6248	24	7	gorder	gorder	NOUN
ejpam-6248	25	1	[	[	X
ejpam-6248	25	2	23	23	NUM
ejpam-6248	25	3	]	]	PUNCT
ejpam-6248	25	4	derived	derived	ADJ
ejpam-6248	25	5	and	and	CCONJ
ejpam-6248	25	6	analyzed	analyze	VERB
ejpam-6248	25	7	self	self	NOUN
ejpam-6248	25	8	-	-	PUNCT
ejpam-6248	25	9	similar	similar	ADJ
ejpam-6248	25	10	solutions	solution	NOUN
ejpam-6248	25	11	for	for	ADP
ejpam-6248	25	12	the	the	DET
ejpam-6248	25	13	lrt	lrt	PROPN
ejpam-6248	25	14	equation	equation	NOUN
ejpam-6248	25	15	,	,	PUNCT
ejpam-6248	25	16	a	a	DET
ejpam-6248	25	17	nonlinear	nonlinear	ADJ
ejpam-6248	25	18	partial	partial	ADJ
ejpam-6248	25	19	differential	differential	NOUN
ejpam-6248	25	20	equation	equation	NOUN
ejpam-6248	25	21	governing	govern	VERB
ejpam-6248	25	22	high	high	ADJ
ejpam-6248	25	23	-	-	PUNCT
ejpam-6248	25	24	speed	speed	NOUN
ejpam-6248	25	25	fluid	fluid	NOUN
ejpam-6248	25	26	flows	flow	NOUN
ejpam-6248	25	27	.	.	PUNCT
ejpam-6248	26	1	the	the	DET
ejpam-6248	26	2	authors	author	NOUN
ejpam-6248	26	3	employed	employ	VERB
ejpam-6248	26	4	symmetry	symmetry	NOUN
ejpam-6248	26	5	reduction	reduction	NOUN
ejpam-6248	26	6	techniques	technique	NOUN
ejpam-6248	26	7	to	to	PART
ejpam-6248	26	8	transform	transform	VERB
ejpam-6248	26	9	the	the	DET
ejpam-6248	26	10	partial	partial	ADJ
ejpam-6248	26	11	differential	differential	NOUN
ejpam-6248	26	12	equation	equation	NOUN
ejpam-6248	26	13	(	(	PUNCT
ejpam-6248	26	14	pde	pde	NOUN
ejpam-6248	26	15	)	)	PUNCT
ejpam-6248	26	16	into	into	ADP
ejpam-6248	26	17	an	an	DET
ejpam-6248	26	18	ordinary	ordinary	ADJ
ejpam-6248	26	19	differential	differential	ADJ
ejpam-6248	26	20	equation	equation	NOUN
ejpam-6248	26	21	(	(	PUNCT
ejpam-6248	26	22	ode	ode	PROPN
ejpam-6248	26	23	)	)	PUNCT
ejpam-6248	26	24	,	,	PUNCT
ejpam-6248	26	25	obtaining	obtain	VERB
ejpam-6248	26	26	exact	exact	ADJ
ejpam-6248	26	27	solutions	solution	NOUN
ejpam-6248	26	28	that	that	PRON
ejpam-6248	26	29	describe	describe	VERB
ejpam-6248	26	30	the	the	DET
ejpam-6248	26	31	system	system	NOUN
ejpam-6248	26	32	’s	’s	PART
ejpam-6248	26	33	behavior	behavior	NOUN
ejpam-6248	26	34	under	under	ADP
ejpam-6248	26	35	scaling	scale	VERB
ejpam-6248	26	36	invariance	invariance	NOUN
ejpam-6248	26	37	.	.	PUNCT
ejpam-6248	27	1	filimonov	filimonov	PROPN
ejpam-6248	28	1	[	[	X
ejpam-6248	28	2	24	24	NUM
ejpam-6248	28	3	]	]	PUNCT
ejpam-6248	28	4	employed	employ	VERB
ejpam-6248	28	5	a	a	DET
ejpam-6248	28	6	novel	novel	ADJ
ejpam-6248	28	7	special	special	ADJ
ejpam-6248	28	8	series	series	NOUN
ejpam-6248	28	9	method	method	NOUN
ejpam-6248	28	10	to	to	PART
ejpam-6248	28	11	construct	construct	VERB
ejpam-6248	28	12	analytic	analytic	ADJ
ejpam-6248	28	13	solutions	solution	NOUN
ejpam-6248	28	14	for	for	ADP
ejpam-6248	28	15	the	the	DET
ejpam-6248	28	16	lrt	lrt	PROPN
ejpam-6248	28	17	equation	equation	NOUN
ejpam-6248	28	18	.	.	PUNCT
ejpam-6248	29	1	this	this	DET
ejpam-6248	29	2	approach	approach	NOUN
ejpam-6248	29	3	systematically	systematically	ADV
ejpam-6248	29	4	generates	generate	VERB
ejpam-6248	29	5	exact	exact	ADJ
ejpam-6248	29	6	solutions	solution	NOUN
ejpam-6248	29	7	and	and	CCONJ
ejpam-6248	29	8	offers	offer	VERB
ejpam-6248	29	9	new	new	ADJ
ejpam-6248	29	10	representations	representation	NOUN
ejpam-6248	29	11	that	that	PRON
ejpam-6248	29	12	capture	capture	VERB
ejpam-6248	29	13	the	the	DET
ejpam-6248	29	14	equation	equation	NOUN
ejpam-6248	29	15	’s	’s	PART
ejpam-6248	29	16	complex	complex	ADJ
ejpam-6248	29	17	dynamics	dynamic	NOUN
ejpam-6248	29	18	.	.	PUNCT
ejpam-6248	30	1	theaker	theaker	NOUN
ejpam-6248	30	2	and	and	CCONJ
ejpam-6248	30	3	van	van	PROPN
ejpam-6248	30	4	gorder	gorder	NOUN
ejpam-6248	31	1	[	[	X
ejpam-6248	31	2	25	25	NUM
ejpam-6248	31	3	]	]	PUNCT
ejpam-6248	31	4	analyzed	analyze	VERB
ejpam-6248	31	5	both	both	CCONJ
ejpam-6248	31	6	forced	force	VERB
ejpam-6248	31	7	and	and	CCONJ
ejpam-6248	31	8	unforced	unforced	ADJ
ejpam-6248	31	9	forms	form	NOUN
ejpam-6248	31	10	of	of	ADP
ejpam-6248	31	11	the	the	DET
ejpam-6248	31	12	lrt	lrt	PROPN
ejpam-6248	31	13	equation	equation	NOUN
ejpam-6248	31	14	,	,	PUNCT
ejpam-6248	31	15	which	which	PRON
ejpam-6248	31	16	govern	govern	VERB
ejpam-6248	31	17	transonic	transonic	ADJ
ejpam-6248	31	18	gas	gas	NOUN
ejpam-6248	31	19	flows	flow	NOUN
ejpam-6248	31	20	at	at	ADP
ejpam-6248	31	21	various	various	ADJ
ejpam-6248	31	22	length	length	NOUN
ejpam-6248	31	23	scales	scale	NOUN
ejpam-6248	31	24	,	,	PUNCT
ejpam-6248	31	25	deriving	derive	VERB
ejpam-6248	31	26	exact	exact	ADJ
ejpam-6248	31	27	and	and	CCONJ
ejpam-6248	31	28	asymptotic	asymptotic	ADJ
ejpam-6248	31	29	solutions	solution	NOUN
ejpam-6248	31	30	to	to	PART
ejpam-6248	31	31	characterize	characterize	VERB
ejpam-6248	31	32	the	the	DET
ejpam-6248	31	33	flow	flow	NOUN
ejpam-6248	31	34	dynamics	dynamic	NOUN
ejpam-6248	31	35	.	.	PUNCT
ejpam-6248	32	1	while	while	SCONJ
ejpam-6248	32	2	the	the	DET
ejpam-6248	32	3	lin	lin	PROPN
ejpam-6248	32	4	–	–	PUNCT
ejpam-6248	32	5	reissner	reissner	NOUN
ejpam-6248	32	6	–	–	PUNCT
ejpam-6248	32	7	tsien	tsien	NOUN
ejpam-6248	32	8	(	(	PUNCT
ejpam-6248	32	9	lrt	lrt	PROPN
ejpam-6248	32	10	)	)	PUNCT
ejpam-6248	32	11	equation	equation	NOUN
ejpam-6248	32	12	has	have	AUX
ejpam-6248	32	13	been	be	AUX
ejpam-6248	32	14	extensively	extensively	ADV
ejpam-6248	32	15	studied	study	VERB
ejpam-6248	32	16	through	through	ADP
ejpam-6248	32	17	traditional	traditional	ADJ
ejpam-6248	32	18	analytical	analytical	ADJ
ejpam-6248	32	19	and	and	CCONJ
ejpam-6248	32	20	numerical	numerical	ADJ
ejpam-6248	32	21	approaches	approach	NOUN
ejpam-6248	32	22	,	,	PUNCT
ejpam-6248	32	23	several	several	ADJ
ejpam-6248	32	24	critical	critical	ADJ
ejpam-6248	32	25	gaps	gap	NOUN
ejpam-6248	32	26	remain	remain	VERB
ejpam-6248	32	27	in	in	ADP
ejpam-6248	32	28	the	the	DET
ejpam-6248	32	29	literature	literature	NOUN
ejpam-6248	32	30	regarding	regard	VERB
ejpam-6248	32	31	its	its	PRON
ejpam-6248	32	32	self	self	NOUN
ejpam-6248	32	33	-	-	PUNCT
ejpam-6248	32	34	similar	similar	ADJ
ejpam-6248	32	35	solutions	solution	NOUN
ejpam-6248	32	36	and	and	CCONJ
ejpam-6248	32	37	their	their	PRON
ejpam-6248	32	38	systematic	systematic	ADJ
ejpam-6248	32	39	derivation	derivation	NOUN
ejpam-6248	32	40	via	via	ADP
ejpam-6248	32	41	the	the	DET
ejpam-6248	32	42	power	power	NOUN
ejpam-6248	32	43	index	index	NOUN
ejpam-6248	32	44	method	method	NOUN
ejpam-6248	32	45	(	(	PUNCT
ejpam-6248	32	46	pim	pim	PROPN
ejpam-6248	32	47	)	)	PUNCT
ejpam-6248	32	48	.	.	PUNCT
ejpam-6248	33	1	this	this	DET
ejpam-6248	33	2	study	study	NOUN
ejpam-6248	33	3	introduces	introduce	VERB
ejpam-6248	33	4	self	self	NOUN
ejpam-6248	33	5	-	-	PUNCT
ejpam-6248	33	6	similar	similar	ADJ
ejpam-6248	33	7	solutions	solution	NOUN
ejpam-6248	33	8	to	to	ADP
ejpam-6248	33	9	the	the	DET
ejpam-6248	33	10	lrt	lrt	PROPN
ejpam-6248	33	11	equation	equation	NOUN
ejpam-6248	33	12	through	through	ADP
ejpam-6248	33	13	the	the	DET
ejpam-6248	33	14	power	power	NOUN
ejpam-6248	33	15	index	index	NOUN
ejpam-6248	33	16	method	method	NOUN
ejpam-6248	33	17	–	–	PUNCT
ejpam-6248	33	18	an	an	DET
ejpam-6248	33	19	innovative	innovative	ADJ
ejpam-6248	33	20	approach	approach	NOUN
ejpam-6248	33	21	that	that	PRON
ejpam-6248	33	22	has	have	AUX
ejpam-6248	33	23	been	be	AUX
ejpam-6248	33	24	scarcely	scarcely	ADV
ejpam-6248	33	25	explored	explore	VERB
ejpam-6248	33	26	for	for	ADP
ejpam-6248	33	27	this	this	DET
ejpam-6248	33	28	class	class	NOUN
ejpam-6248	33	29	of	of	ADP
ejpam-6248	33	30	nonlinear	nonlinear	ADJ
ejpam-6248	33	31	partial	partial	ADJ
ejpam-6248	33	32	differential	differential	NOUN
ejpam-6248	33	33	equations	equation	NOUN
ejpam-6248	33	34	(	(	PUNCT
ejpam-6248	33	35	nlpdes	nlpde	NOUN
ejpam-6248	33	36	)	)	PUNCT
ejpam-6248	33	37	.	.	PUNCT
ejpam-6248	34	1	by	by	ADP
ejpam-6248	34	2	leveraging	leverage	VERB
ejpam-6248	34	3	the	the	DET
ejpam-6248	34	4	inherent	inherent	ADJ
ejpam-6248	34	5	scaling	scale	VERB
ejpam-6248	34	6	symmetries	symmetry	NOUN
ejpam-6248	34	7	of	of	ADP
ejpam-6248	34	8	the	the	DET
ejpam-6248	34	9	lrt	lrt	PROPN
ejpam-6248	34	10	equation	equation	NOUN
ejpam-6248	34	11	,	,	PUNCT
ejpam-6248	34	12	we	we	PRON
ejpam-6248	34	13	demonstrate	demonstrate	VERB
ejpam-6248	34	14	how	how	SCONJ
ejpam-6248	34	15	self	self	NOUN
ejpam-6248	34	16	-	-	PUNCT
ejpam-6248	34	17	similarity	similarity	NOUN
ejpam-6248	34	18	systematically	systematically	ADV
ejpam-6248	34	19	decouples	decouple	VERB
ejpam-6248	34	20	the	the	DET
ejpam-6248	34	21	variables	variable	NOUN
ejpam-6248	34	22	and	and	CCONJ
ejpam-6248	34	23	reduces	reduce	VERB
ejpam-6248	34	24	the	the	DET
ejpam-6248	34	25	governing	govern	VERB
ejpam-6248	34	26	partial	partial	ADJ
ejpam-6248	34	27	differential	differential	NOUN
ejpam-6248	34	28	equation	equation	NOUN
ejpam-6248	34	29	(	(	PUNCT
ejpam-6248	34	30	pde	pde	NOUN
ejpam-6248	34	31	)	)	PUNCT
ejpam-6248	34	32	into	into	ADP
ejpam-6248	34	33	a	a	DET
ejpam-6248	34	34	more	more	ADV
ejpam-6248	34	35	tractable	tractable	ADJ
ejpam-6248	34	36	ordinary	ordinary	ADJ
ejpam-6248	34	37	differential	differential	ADJ
ejpam-6248	34	38	equation	equation	NOUN
ejpam-6248	34	39	(	(	PUNCT
ejpam-6248	34	40	ode	ode	PROPN
ejpam-6248	34	41	)	)	PUNCT
ejpam-6248	34	42	.	.	PUNCT
ejpam-6248	35	1	this	this	DET
ejpam-6248	35	2	transformation	transformation	NOUN
ejpam-6248	35	3	not	not	PART
ejpam-6248	35	4	only	only	ADV
ejpam-6248	35	5	simplifies	simplify	VERB
ejpam-6248	35	6	the	the	DET
ejpam-6248	35	7	analytic	analytic	ADJ
ejpam-6248	35	8	treatment	treatment	NOUN
ejpam-6248	35	9	but	but	CCONJ
ejpam-6248	35	10	also	also	ADV
ejpam-6248	35	11	reveals	reveal	VERB
ejpam-6248	35	12	critical	critical	ADJ
ejpam-6248	35	13	insights	insight	NOUN
ejpam-6248	35	14	into	into	ADP
ejpam-6248	35	15	the	the	DET
ejpam-6248	35	16	equation	equation	NOUN
ejpam-6248	35	17	’s	’s	PART
ejpam-6248	35	18	long	long	ADJ
ejpam-6248	35	19	-	-	PUNCT
ejpam-6248	35	20	time	time	NOUN
ejpam-6248	35	21	behavior	behavior	NOUN
ejpam-6248	35	22	and	and	CCONJ
ejpam-6248	35	23	singularity	singularity	NOUN
ejpam-6248	35	24	formation	formation	NOUN
ejpam-6248	35	25	,	,	PUNCT
ejpam-6248	35	26	which	which	PRON
ejpam-6248	35	27	often	often	ADV
ejpam-6248	35	28	remain	remain	VERB
ejpam-6248	35	29	obscured	obscured	ADJ
ejpam-6248	35	30	in	in	ADP
ejpam-6248	35	31	traditional	traditional	ADJ
ejpam-6248	35	32	symmetrybased	symmetrybase	VERB
ejpam-6248	35	33	or	or	CCONJ
ejpam-6248	35	34	numerical	numerical	ADJ
ejpam-6248	35	35	approaches	approach	NOUN
ejpam-6248	35	36	.	.	PUNCT
ejpam-6248	36	1	the	the	DET
ejpam-6248	36	2	power	power	NOUN
ejpam-6248	36	3	index	index	NOUN
ejpam-6248	36	4	method	method	NOUN
ejpam-6248	36	5	further	far	ADV
ejpam-6248	36	6	distinguishes	distinguish	VERB
ejpam-6248	36	7	itself	itself	PRON
ejpam-6248	36	8	by	by	ADP
ejpam-6248	36	9	rigorously	rigorously	ADV
ejpam-6248	36	10	determining	determine	VERB
ejpam-6248	36	11	scaling	scale	VERB
ejpam-6248	36	12	exponents	exponent	NOUN
ejpam-6248	36	13	,	,	PUNCT
ejpam-6248	36	14	bypassing	bypass	VERB
ejpam-6248	36	15	ad	ad	X
ejpam-6248	36	16	hoc	hoc	X
ejpam-6248	36	17	assumptions	assumption	NOUN
ejpam-6248	36	18	,	,	PUNCT
ejpam-6248	36	19	and	and	CCONJ
ejpam-6248	36	20	offering	offer	VERB
ejpam-6248	36	21	a	a	DET
ejpam-6248	36	22	unified	unified	ADJ
ejpam-6248	36	23	framework	framework	NOUN
ejpam-6248	36	24	to	to	PART
ejpam-6248	36	25	address	address	VERB
ejpam-6248	36	26	multi	multi	ADJ
ejpam-6248	36	27	-	-	ADJ
ejpam-6248	36	28	parameter	parameter	ADJ
ejpam-6248	36	29	nonlinearities	nonlinearitie	NOUN
ejpam-6248	36	30	.	.	PUNCT
ejpam-6248	37	1	our	our	PRON
ejpam-6248	37	2	work	work	NOUN
ejpam-6248	37	3	thus	thus	ADV
ejpam-6248	37	4	bridges	bridge	VERB
ejpam-6248	37	5	a	a	DET
ejpam-6248	37	6	significant	significant	ADJ
ejpam-6248	37	7	gap	gap	NOUN
ejpam-6248	37	8	in	in	ADP
ejpam-6248	37	9	the	the	DET
ejpam-6248	37	10	literature	literature	NOUN
ejpam-6248	37	11	,	,	PUNCT
ejpam-6248	37	12	providing	provide	VERB
ejpam-6248	37	13	a	a	DET
ejpam-6248	37	14	robust	robust	ADJ
ejpam-6248	37	15	analytical	analytical	ADJ
ejpam-6248	37	16	tool	tool	NOUN
ejpam-6248	37	17	to	to	PART
ejpam-6248	37	18	explore	explore	VERB
ejpam-6248	37	19	scale	scale	NOUN
ejpam-6248	37	20	-	-	PUNCT
ejpam-6248	37	21	invariant	invariant	ADJ
ejpam-6248	37	22	phenomena	phenomenon	NOUN
ejpam-6248	37	23	in	in	ADP
ejpam-6248	37	24	high	high	ADJ
ejpam-6248	37	25	-	-	PUNCT
ejpam-6248	37	26	speed	speed	NOUN
ejpam-6248	37	27	aerodynamics	aerodynamic	NOUN
ejpam-6248	37	28	and	and	CCONJ
ejpam-6248	37	29	beyond	beyond	ADP
ejpam-6248	37	30	.	.	PUNCT
ejpam-6248	38	1	while	while	SCONJ
ejpam-6248	38	2	numerous	numerous	ADJ
ejpam-6248	38	3	analytical	analytical	ADJ
ejpam-6248	38	4	and	and	CCONJ
ejpam-6248	38	5	numerical	numerical	ADJ
ejpam-6248	38	6	techniques	technique	NOUN
ejpam-6248	38	7	[	[	X
ejpam-6248	38	8	26	26	NUM
ejpam-6248	38	9	]	]	PUNCT
ejpam-6248	38	10	,	,	PUNCT
ejpam-6248	38	11	[	[	X
ejpam-6248	38	12	27	27	NUM
ejpam-6248	38	13	]	]	PUNCT
ejpam-6248	38	14	have	have	AUX
ejpam-6248	38	15	been	be	AUX
ejpam-6248	38	16	developed	develop	VERB
ejpam-6248	38	17	to	to	ADP
ejpam-6248	38	18	z.	z.	PROPN
ejpam-6248	38	19	haider	haider	PROPN
ejpam-6248	38	20	et	et	PROPN
ejpam-6248	38	21	al	al	PROPN
ejpam-6248	38	22	.	.	PUNCT
ejpam-6248	38	23	/	/	SYM
ejpam-6248	38	24	eur	eur	PROPN
ejpam-6248	38	25	.	.	PUNCT
ejpam-6248	39	1	j.	j.	PROPN
ejpam-6248	39	2	pure	pure	PROPN
ejpam-6248	39	3	appl	appl	PROPN
ejpam-6248	39	4	.	.	PROPN
ejpam-6248	39	5	math	math	PROPN
ejpam-6248	39	6	,	,	PUNCT
ejpam-6248	39	7	18	18	NUM
ejpam-6248	39	8	(	(	PUNCT
ejpam-6248	39	9	3	3	NUM
ejpam-6248	39	10	)	)	PUNCT
ejpam-6248	39	11	(	(	PUNCT
ejpam-6248	39	12	2025	2025	NUM
ejpam-6248	39	13	)	)	PUNCT
ejpam-6248	39	14	,	,	PUNCT
ejpam-6248	39	15	6248	6248	NUM
ejpam-6248	39	16	3	3	NUM
ejpam-6248	39	17	of	of	ADP
ejpam-6248	39	18	20	20	NUM
ejpam-6248	39	19	solve	solve	NOUN
ejpam-6248	39	20	nonlinear	nonlinear	ADJ
ejpam-6248	39	21	partial	partial	ADJ
ejpam-6248	39	22	differential	differential	NOUN
ejpam-6248	39	23	equations	equation	NOUN
ejpam-6248	39	24	,	,	PUNCT
ejpam-6248	39	25	the	the	DET
ejpam-6248	39	26	power	power	NOUN
ejpam-6248	39	27	index	index	NOUN
ejpam-6248	39	28	method	method	NOUN
ejpam-6248	39	29	(	(	PUNCT
ejpam-6248	39	30	pim	pim	PROPN
ejpam-6248	39	31	)	)	PUNCT
ejpam-6248	39	32	offers	offer	VERB
ejpam-6248	39	33	a	a	DET
ejpam-6248	39	34	distinctive	distinctive	ADJ
ejpam-6248	39	35	and	and	CCONJ
ejpam-6248	39	36	systematic	systematic	ADJ
ejpam-6248	39	37	approach	approach	NOUN
ejpam-6248	39	38	grounded	ground	VERB
ejpam-6248	39	39	in	in	ADP
ejpam-6248	39	40	the	the	DET
ejpam-6248	39	41	theory	theory	NOUN
ejpam-6248	39	42	of	of	ADP
ejpam-6248	39	43	scaling	scale	VERB
ejpam-6248	39	44	symmetries	symmetry	NOUN
ejpam-6248	39	45	.	.	PUNCT
ejpam-6248	40	1	unlike	unlike	ADP
ejpam-6248	40	2	many	many	ADJ
ejpam-6248	40	3	recognized	recognize	VERB
ejpam-6248	40	4	methods	method	NOUN
ejpam-6248	40	5	that	that	PRON
ejpam-6248	40	6	often	often	ADV
ejpam-6248	40	7	rely	rely	VERB
ejpam-6248	40	8	on	on	ADP
ejpam-6248	40	9	predefined	predefine	VERB
ejpam-6248	40	10	ansätze	ansätze	ADJ
ejpam-6248	40	11	,	,	PUNCT
ejpam-6248	40	12	functional	functional	ADJ
ejpam-6248	40	13	assumptions	assumption	NOUN
ejpam-6248	40	14	,	,	PUNCT
ejpam-6248	40	15	or	or	CCONJ
ejpam-6248	40	16	trial	trial	NOUN
ejpam-6248	40	17	solution	solution	NOUN
ejpam-6248	40	18	forms	form	NOUN
ejpam-6248	40	19	,	,	PUNCT
ejpam-6248	40	20	pim	pim	PROPN
ejpam-6248	40	21	derives	derive	VERB
ejpam-6248	40	22	self	self	NOUN
ejpam-6248	40	23	-	-	PUNCT
ejpam-6248	40	24	similar	similar	ADJ
ejpam-6248	40	25	transformations	transformation	NOUN
ejpam-6248	40	26	directly	directly	ADV
ejpam-6248	40	27	from	from	ADP
ejpam-6248	40	28	the	the	DET
ejpam-6248	40	29	intrinsic	intrinsic	ADJ
ejpam-6248	40	30	scaling	scale	VERB
ejpam-6248	40	31	properties	property	NOUN
ejpam-6248	40	32	of	of	ADP
ejpam-6248	40	33	the	the	DET
ejpam-6248	40	34	governing	govern	VERB
ejpam-6248	40	35	equation	equation	NOUN
ejpam-6248	40	36	.	.	PUNCT
ejpam-6248	41	1	this	this	PRON
ejpam-6248	41	2	avoids	avoid	VERB
ejpam-6248	41	3	arbitrary	arbitrary	ADJ
ejpam-6248	41	4	guesswork	guesswork	NOUN
ejpam-6248	41	5	and	and	CCONJ
ejpam-6248	41	6	ensures	ensure	VERB
ejpam-6248	41	7	that	that	SCONJ
ejpam-6248	41	8	the	the	DET
ejpam-6248	41	9	resulting	result	VERB
ejpam-6248	41	10	similarity	similarity	NOUN
ejpam-6248	41	11	variables	variable	NOUN
ejpam-6248	41	12	are	be	AUX
ejpam-6248	41	13	mathematically	mathematically	ADV
ejpam-6248	41	14	consistent	consistent	ADJ
ejpam-6248	41	15	with	with	ADP
ejpam-6248	41	16	the	the	DET
ejpam-6248	41	17	equation	equation	NOUN
ejpam-6248	41	18	’s	’s	PART
ejpam-6248	41	19	structure	structure	NOUN
ejpam-6248	41	20	.	.	PUNCT
ejpam-6248	42	1	furthermore	furthermore	ADV
ejpam-6248	42	2	,	,	PUNCT
ejpam-6248	42	3	pim	pim	PROPN
ejpam-6248	42	4	rigorously	rigorously	ADV
ejpam-6248	42	5	determines	determine	VERB
ejpam-6248	42	6	the	the	DET
ejpam-6248	42	7	scaling	scale	VERB
ejpam-6248	42	8	exponents	exponent	NOUN
ejpam-6248	42	9	by	by	ADP
ejpam-6248	42	10	balancing	balance	VERB
ejpam-6248	42	11	the	the	DET
ejpam-6248	42	12	dominant	dominant	ADJ
ejpam-6248	42	13	terms	term	NOUN
ejpam-6248	42	14	in	in	ADP
ejpam-6248	42	15	the	the	DET
ejpam-6248	42	16	original	original	ADJ
ejpam-6248	42	17	equation	equation	NOUN
ejpam-6248	42	18	,	,	PUNCT
ejpam-6248	42	19	providing	provide	VERB
ejpam-6248	42	20	a	a	DET
ejpam-6248	42	21	clear	clear	ADJ
ejpam-6248	42	22	theoretical	theoretical	ADJ
ejpam-6248	42	23	foundation	foundation	NOUN
ejpam-6248	42	24	rooted	root	VERB
ejpam-6248	42	25	in	in	ADP
ejpam-6248	42	26	dimensional	dimensional	ADJ
ejpam-6248	42	27	analysis	analysis	NOUN
ejpam-6248	42	28	and	and	CCONJ
ejpam-6248	42	29	self	self	NOUN
ejpam-6248	42	30	-	-	PUNCT
ejpam-6248	42	31	similarity	similarity	NOUN
ejpam-6248	42	32	theory	theory	NOUN
ejpam-6248	42	33	.	.	PUNCT
ejpam-6248	43	1	this	this	DET
ejpam-6248	43	2	process	process	NOUN
ejpam-6248	43	3	transforms	transform	VERB
ejpam-6248	43	4	the	the	DET
ejpam-6248	43	5	original	original	ADJ
ejpam-6248	43	6	pde	pde	NOUN
ejpam-6248	43	7	into	into	ADP
ejpam-6248	43	8	an	an	DET
ejpam-6248	43	9	ordinary	ordinary	ADJ
ejpam-6248	43	10	differential	differential	ADJ
ejpam-6248	43	11	equation	equation	NOUN
ejpam-6248	43	12	(	(	PUNCT
ejpam-6248	43	13	ode	ode	PROPN
ejpam-6248	43	14	)	)	PUNCT
ejpam-6248	43	15	without	without	ADP
ejpam-6248	43	16	requiring	require	VERB
ejpam-6248	43	17	symmetry	symmetry	NOUN
ejpam-6248	43	18	generators	generator	NOUN
ejpam-6248	43	19	or	or	CCONJ
ejpam-6248	43	20	complicated	complicate	VERB
ejpam-6248	43	21	algebraic	algebraic	ADJ
ejpam-6248	43	22	frameworks	framework	NOUN
ejpam-6248	43	23	.	.	PUNCT
ejpam-6248	44	1	as	as	ADP
ejpam-6248	44	2	such	such	ADJ
ejpam-6248	44	3	,	,	PUNCT
ejpam-6248	44	4	pim	pim	INTJ
ejpam-6248	44	5	not	not	PART
ejpam-6248	44	6	only	only	ADV
ejpam-6248	44	7	broadens	broaden	VERB
ejpam-6248	44	8	the	the	DET
ejpam-6248	44	9	class	class	NOUN
ejpam-6248	44	10	of	of	ADP
ejpam-6248	44	11	solvable	solvable	ADJ
ejpam-6248	44	12	equations	equation	NOUN
ejpam-6248	44	13	but	but	CCONJ
ejpam-6248	44	14	also	also	ADV
ejpam-6248	44	15	enhances	enhance	VERB
ejpam-6248	44	16	transparency	transparency	NOUN
ejpam-6248	44	17	and	and	CCONJ
ejpam-6248	44	18	reproducibility	reproducibility	NOUN
ejpam-6248	44	19	in	in	ADP
ejpam-6248	44	20	the	the	DET
ejpam-6248	44	21	solution	solution	NOUN
ejpam-6248	44	22	process	process	NOUN
ejpam-6248	44	23	,	,	PUNCT
ejpam-6248	44	24	making	make	VERB
ejpam-6248	44	25	it	it	PRON
ejpam-6248	44	26	a	a	DET
ejpam-6248	44	27	powerful	powerful	ADJ
ejpam-6248	44	28	alternative	alternative	NOUN
ejpam-6248	44	29	for	for	ADP
ejpam-6248	44	30	deriving	derive	VERB
ejpam-6248	44	31	exact	exact	ADJ
ejpam-6248	44	32	,	,	PUNCT
ejpam-6248	44	33	self	self	NOUN
ejpam-6248	44	34	-	-	PUNCT
ejpam-6248	44	35	similar	similar	ADJ
ejpam-6248	44	36	solutions	solution	NOUN
ejpam-6248	44	37	to	to	ADP
ejpam-6248	44	38	nonlinear	nonlinear	ADJ
ejpam-6248	44	39	pdes	pde	NOUN
ejpam-6248	44	40	.	.	PUNCT
ejpam-6248	45	1	the	the	DET
ejpam-6248	45	2	role	role	NOUN
ejpam-6248	45	3	of	of	ADP
ejpam-6248	45	4	similarity	similarity	NOUN
ejpam-6248	45	5	transformations	transformation	NOUN
ejpam-6248	45	6	in	in	ADP
ejpam-6248	45	7	deriving	derive	VERB
ejpam-6248	45	8	self	self	NOUN
ejpam-6248	45	9	-	-	PUNCT
ejpam-6248	45	10	similar	similar	ADJ
ejpam-6248	45	11	solutions	solution	NOUN
ejpam-6248	45	12	to	to	ADP
ejpam-6248	45	13	the	the	DET
ejpam-6248	45	14	lin	lin	PROPN
ejpam-6248	45	15	–	–	PUNCT
ejpam-6248	45	16	reissner	reissner	NOUN
ejpam-6248	45	17	–	–	PUNCT
ejpam-6248	45	18	tsien	tsien	NOUN
ejpam-6248	45	19	(	(	PUNCT
ejpam-6248	45	20	lrt	lrt	PROPN
ejpam-6248	45	21	)	)	PUNCT
ejpam-6248	45	22	equation	equation	NOUN
ejpam-6248	45	23	is	be	AUX
ejpam-6248	45	24	pivotal	pivotal	ADJ
ejpam-6248	45	25	,	,	PUNCT
ejpam-6248	45	26	as	as	SCONJ
ejpam-6248	45	27	these	these	DET
ejpam-6248	45	28	transformations	transformation	NOUN
ejpam-6248	45	29	facilitate	facilitate	VERB
ejpam-6248	45	30	the	the	DET
ejpam-6248	45	31	reduction	reduction	NOUN
ejpam-6248	45	32	of	of	ADP
ejpam-6248	45	33	complex	complex	ADJ
ejpam-6248	45	34	partial	partial	ADJ
ejpam-6248	45	35	differential	differential	ADJ
ejpam-6248	45	36	equations	equation	NOUN
ejpam-6248	45	37	into	into	ADP
ejpam-6248	45	38	more	more	ADV
ejpam-6248	45	39	manageable	manageable	ADJ
ejpam-6248	45	40	ordinary	ordinary	ADJ
ejpam-6248	45	41	differential	differential	ADJ
ejpam-6248	45	42	equations	equation	NOUN
ejpam-6248	45	43	.	.	PUNCT
ejpam-6248	46	1	this	this	DET
ejpam-6248	46	2	process	process	NOUN
ejpam-6248	46	3	allows	allow	VERB
ejpam-6248	46	4	for	for	ADP
ejpam-6248	46	5	the	the	DET
ejpam-6248	46	6	identification	identification	NOUN
ejpam-6248	46	7	of	of	ADP
ejpam-6248	46	8	exact	exact	ADJ
ejpam-6248	46	9	solutions	solution	NOUN
ejpam-6248	46	10	and	and	CCONJ
ejpam-6248	46	11	enhances	enhance	VERB
ejpam-6248	46	12	understanding	understanding	NOUN
ejpam-6248	46	13	of	of	ADP
ejpam-6248	46	14	transonic	transonic	ADJ
ejpam-6248	46	15	flows	flow	NOUN
ejpam-6248	46	16	.	.	PUNCT
ejpam-6248	47	1	while	while	SCONJ
ejpam-6248	47	2	similarity	similarity	NOUN
ejpam-6248	47	3	transformations	transformation	NOUN
ejpam-6248	47	4	are	be	AUX
ejpam-6248	47	5	powerful	powerful	ADJ
ejpam-6248	47	6	tools	tool	NOUN
ejpam-6248	47	7	for	for	ADP
ejpam-6248	47	8	deriving	derive	VERB
ejpam-6248	47	9	selfsimilar	selfsimilar	ADJ
ejpam-6248	47	10	solutions	solution	NOUN
ejpam-6248	47	11	,	,	PUNCT
ejpam-6248	47	12	they	they	PRON
ejpam-6248	47	13	may	may	AUX
ejpam-6248	47	14	not	not	PART
ejpam-6248	47	15	capture	capture	VERB
ejpam-6248	47	16	the	the	DET
ejpam-6248	47	17	full	full	ADJ
ejpam-6248	47	18	dynamics	dynamic	NOUN
ejpam-6248	47	19	of	of	ADP
ejpam-6248	47	20	the	the	DET
ejpam-6248	47	21	system	system	NOUN
ejpam-6248	47	22	,	,	PUNCT
ejpam-6248	47	23	particularly	particularly	ADV
ejpam-6248	47	24	in	in	ADP
ejpam-6248	47	25	cases	case	NOUN
ejpam-6248	47	26	of	of	ADP
ejpam-6248	47	27	rapid	rapid	ADJ
ejpam-6248	47	28	wave	wave	NOUN
ejpam-6248	47	29	propagation	propagation	NOUN
ejpam-6248	47	30	or	or	CCONJ
ejpam-6248	47	31	complex	complex	ADJ
ejpam-6248	47	32	boundary	boundary	ADJ
ejpam-6248	47	33	conditions	condition	NOUN
ejpam-6248	47	34	which	which	PRON
ejpam-6248	47	35	could	could	AUX
ejpam-6248	47	36	necessitate	necessitate	VERB
ejpam-6248	47	37	the	the	DET
ejpam-6248	47	38	alternative	alternative	ADJ
ejpam-6248	47	39	analytical	analytical	ADJ
ejpam-6248	47	40	or	or	CCONJ
ejpam-6248	47	41	numerical	numerical	ADJ
ejpam-6248	47	42	approaches	approach	NOUN
ejpam-6248	47	43	.	.	PUNCT
ejpam-6248	48	1	the	the	DET
ejpam-6248	48	2	paper	paper	NOUN
ejpam-6248	48	3	is	be	AUX
ejpam-6248	48	4	structured	structure	VERB
ejpam-6248	48	5	as	as	SCONJ
ejpam-6248	48	6	follows	follow	VERB
ejpam-6248	48	7	:	:	PUNCT
ejpam-6248	48	8	in	in	ADP
ejpam-6248	48	9	section	section	NOUN
ejpam-6248	48	10	2	2	NUM
ejpam-6248	48	11	,	,	PUNCT
ejpam-6248	48	12	we	we	PRON
ejpam-6248	48	13	briefly	briefly	ADV
ejpam-6248	48	14	describe	describe	VERB
ejpam-6248	48	15	the	the	DET
ejpam-6248	48	16	power	power	NOUN
ejpam-6248	48	17	index	index	NOUN
ejpam-6248	48	18	method	method	NOUN
ejpam-6248	48	19	(	(	PUNCT
ejpam-6248	48	20	pim	pim	PROPN
ejpam-6248	48	21	)	)	PUNCT
ejpam-6248	48	22	.	.	PUNCT
ejpam-6248	49	1	in	in	ADP
ejpam-6248	49	2	section	section	NOUN
ejpam-6248	49	3	3	3	NUM
ejpam-6248	49	4	,	,	PUNCT
ejpam-6248	49	5	we	we	PRON
ejpam-6248	49	6	apply	apply	VERB
ejpam-6248	49	7	this	this	DET
ejpam-6248	49	8	method	method	NOUN
ejpam-6248	49	9	to	to	ADP
ejpam-6248	49	10	the	the	DET
ejpam-6248	49	11	lin	lin	PROPN
ejpam-6248	49	12	–	–	PUNCT
ejpam-6248	49	13	reissner	reissner	NOUN
ejpam-6248	49	14	–	–	PUNCT
ejpam-6248	49	15	tsien	tsien	NOUN
ejpam-6248	49	16	(	(	PUNCT
ejpam-6248	49	17	lrt	lrt	PROPN
ejpam-6248	49	18	)	)	PUNCT
ejpam-6248	49	19	equation	equation	NOUN
ejpam-6248	49	20	using	use	VERB
ejpam-6248	49	21	a	a	DET
ejpam-6248	49	22	self	self	NOUN
ejpam-6248	49	23	-	-	PUNCT
ejpam-6248	49	24	similar	similar	ADJ
ejpam-6248	49	25	function	function	NOUN
ejpam-6248	49	26	transformation	transformation	NOUN
ejpam-6248	49	27	and	and	CCONJ
ejpam-6248	49	28	derive	derive	VERB
ejpam-6248	49	29	its	its	PRON
ejpam-6248	49	30	self	self	NOUN
ejpam-6248	49	31	-	-	PUNCT
ejpam-6248	49	32	similar	similar	ADJ
ejpam-6248	49	33	solution	solution	NOUN
ejpam-6248	49	34	.	.	PUNCT
ejpam-6248	50	1	the	the	DET
ejpam-6248	50	2	results	result	NOUN
ejpam-6248	50	3	and	and	CCONJ
ejpam-6248	50	4	discussion	discussion	NOUN
ejpam-6248	50	5	are	be	AUX
ejpam-6248	50	6	presented	present	VERB
ejpam-6248	50	7	in	in	ADP
ejpam-6248	50	8	section	section	NOUN
ejpam-6248	50	9	4	4	NUM
ejpam-6248	50	10	,	,	PUNCT
ejpam-6248	50	11	followed	follow	VERB
ejpam-6248	50	12	by	by	ADP
ejpam-6248	50	13	the	the	DET
ejpam-6248	50	14	conclusions	conclusion	NOUN
ejpam-6248	50	15	in	in	ADP
ejpam-6248	50	16	section	section	NOUN
ejpam-6248	50	17	5	5	NUM
ejpam-6248	50	18	.	.	PUNCT
ejpam-6248	51	1	finally	finally	ADV
ejpam-6248	51	2	,	,	PUNCT
ejpam-6248	51	3	future	future	ADJ
ejpam-6248	51	4	recommendations	recommendation	NOUN
ejpam-6248	51	5	are	be	AUX
ejpam-6248	51	6	provided	provide	VERB
ejpam-6248	51	7	in	in	ADP
ejpam-6248	51	8	section	section	NOUN
ejpam-6248	51	9	6	6	NUM
ejpam-6248	51	10	.	.	NOUN
ejpam-6248	51	11	2	2	NUM
ejpam-6248	51	12	.	.	X
ejpam-6248	51	13	power	power	NOUN
ejpam-6248	51	14	index	index	NOUN
ejpam-6248	51	15	method	method	NOUN
ejpam-6248	51	16	step:-1	step:-1	NOUN
ejpam-6248	51	17	consider	consider	VERB
ejpam-6248	51	18	the	the	DET
ejpam-6248	51	19	nonlinear	nonlinear	ADJ
ejpam-6248	51	20	partial	partial	ADJ
ejpam-6248	51	21	differential	differential	NOUN
ejpam-6248	51	22	equation	equation	NOUN
ejpam-6248	51	23	(	(	PUNCT
ejpam-6248	51	24	1	1	NUM
ejpam-6248	51	25	)	)	PUNCT
ejpam-6248	51	26	,	,	PUNCT
ejpam-6248	51	27	for	for	ADP
ejpam-6248	51	28	which	which	PRON
ejpam-6248	51	29	we	we	PRON
ejpam-6248	51	30	seek	seek	VERB
ejpam-6248	51	31	an	an	DET
ejpam-6248	51	32	exact	exact	ADJ
ejpam-6248	51	33	solution	solution	NOUN
ejpam-6248	51	34	.	.	PUNCT
ejpam-6248	52	1	to	to	PART
ejpam-6248	52	2	facilitate	facilitate	VERB
ejpam-6248	52	3	this	this	PRON
ejpam-6248	52	4	,	,	PUNCT
ejpam-6248	52	5	we	we	PRON
ejpam-6248	52	6	introduce	introduce	VERB
ejpam-6248	52	7	the	the	DET
ejpam-6248	52	8	wave	wave	NOUN
ejpam-6248	52	9	variable	variable	NOUN
ejpam-6248	52	10	ξ	ξ	PROPN
ejpam-6248	52	11	,	,	PUNCT
ejpam-6248	52	12	defined	define	VERB
ejpam-6248	52	13	as	as	ADP
ejpam-6248	52	14	a	a	DET
ejpam-6248	52	15	combination	combination	NOUN
ejpam-6248	52	16	of	of	ADP
ejpam-6248	52	17	the	the	DET
ejpam-6248	52	18	independent	independent	ADJ
ejpam-6248	52	19	variables	variable	NOUN
ejpam-6248	52	20	x	x	NOUN
ejpam-6248	52	21	,	,	PUNCT
ejpam-6248	52	22	y	y	PROPN
ejpam-6248	52	23	,	,	PUNCT
ejpam-6248	52	24	and	and	CCONJ
ejpam-6248	52	25	t	t	PROPN
ejpam-6248	52	26	,	,	PUNCT
ejpam-6248	52	27	each	each	PRON
ejpam-6248	52	28	raised	raise	VERB
ejpam-6248	52	29	to	to	ADP
ejpam-6248	52	30	a	a	DET
ejpam-6248	52	31	specific	specific	ADJ
ejpam-6248	52	32	power	power	NOUN
ejpam-6248	52	33	-	-	PUNCT
ejpam-6248	52	34	law	law	NOUN
ejpam-6248	52	35	exponent	exponent	NOUN
ejpam-6248	52	36	:	:	PUNCT
ejpam-6248	52	37	ξ	ξ	X
ejpam-6248	52	38	=	=	PUNCT
ejpam-6248	52	39	xmyrtp	xmyrtp	PROPN
ejpam-6248	52	40	.	.	PUNCT
ejpam-6248	53	1	(	(	PUNCT
ejpam-6248	53	2	2	2	X
ejpam-6248	53	3	)	)	PUNCT
ejpam-6248	53	4	here	here	ADV
ejpam-6248	53	5	,	,	PUNCT
ejpam-6248	53	6	m	m	PRON
ejpam-6248	53	7	,	,	PUNCT
ejpam-6248	53	8	r	r	NOUN
ejpam-6248	53	9	,	,	PUNCT
ejpam-6248	53	10	and	and	CCONJ
ejpam-6248	53	11	p	p	NOUN
ejpam-6248	53	12	are	be	AUX
ejpam-6248	53	13	constants	constant	NOUN
ejpam-6248	53	14	to	to	PART
ejpam-6248	53	15	be	be	AUX
ejpam-6248	53	16	determined	determine	VERB
ejpam-6248	53	17	.	.	PUNCT
ejpam-6248	54	1	in	in	ADP
ejpam-6248	54	2	a	a	DET
ejpam-6248	54	3	similar	similar	ADJ
ejpam-6248	54	4	manner	manner	NOUN
ejpam-6248	54	5	,	,	PUNCT
ejpam-6248	54	6	we	we	PRON
ejpam-6248	54	7	assume	assume	VERB
ejpam-6248	54	8	a	a	DET
ejpam-6248	54	9	self	self	NOUN
ejpam-6248	54	10	-	-	PUNCT
ejpam-6248	54	11	similar	similar	ADJ
ejpam-6248	54	12	transformation	transformation	NOUN
ejpam-6248	54	13	for	for	ADP
ejpam-6248	54	14	the	the	DET
ejpam-6248	54	15	dependent	dependent	ADJ
ejpam-6248	54	16	variable	variable	ADJ
ejpam-6248	54	17	u(x	u(x	NOUN
ejpam-6248	54	18	,	,	PUNCT
ejpam-6248	54	19	y	y	PROPN
ejpam-6248	54	20	,	,	PUNCT
ejpam-6248	54	21	t	t	PROPN
ejpam-6248	54	22	)	)	PUNCT
ejpam-6248	54	23	expressed	express	VERB
ejpam-6248	54	24	in	in	ADP
ejpam-6248	54	25	terms	term	NOUN
ejpam-6248	54	26	of	of	ADP
ejpam-6248	54	27	the	the	DET
ejpam-6248	54	28	similarity	similarity	NOUN
ejpam-6248	54	29	variable	variable	NOUN
ejpam-6248	54	30	ξ	ξ	PROPN
ejpam-6248	54	31	:	:	PUNCT
ejpam-6248	54	32	u	u	PROPN
ejpam-6248	54	33	=	=	PROPN
ejpam-6248	54	34	xnystqf(ξ	xnystqf(ξ	PROPN
ejpam-6248	54	35	)	)	PUNCT
ejpam-6248	54	36	.	.	PUNCT
ejpam-6248	55	1	(	(	PUNCT
ejpam-6248	55	2	3	3	X
ejpam-6248	55	3	)	)	PUNCT
ejpam-6248	55	4	in	in	ADP
ejpam-6248	55	5	this	this	DET
ejpam-6248	55	6	expression	expression	NOUN
ejpam-6248	55	7	,	,	PUNCT
ejpam-6248	55	8	n	n	CCONJ
ejpam-6248	55	9	,	,	PUNCT
ejpam-6248	55	10	s	s	X
ejpam-6248	55	11	,	,	PUNCT
ejpam-6248	55	12	and	and	CCONJ
ejpam-6248	55	13	q	q	NOUN
ejpam-6248	55	14	are	be	AUX
ejpam-6248	55	15	additional	additional	ADJ
ejpam-6248	55	16	exponents	exponent	NOUN
ejpam-6248	55	17	to	to	PART
ejpam-6248	55	18	be	be	AUX
ejpam-6248	55	19	determined	determine	VERB
ejpam-6248	55	20	,	,	PUNCT
ejpam-6248	55	21	and	and	CCONJ
ejpam-6248	55	22	f(ξ	f(ξ	NOUN
ejpam-6248	55	23	)	)	PUNCT
ejpam-6248	55	24	represents	represent	VERB
ejpam-6248	55	25	the	the	DET
ejpam-6248	55	26	unknown	unknown	ADJ
ejpam-6248	55	27	function	function	NOUN
ejpam-6248	55	28	to	to	PART
ejpam-6248	55	29	be	be	AUX
ejpam-6248	55	30	solved	solve	VERB
ejpam-6248	55	31	.	.	PUNCT
ejpam-6248	56	1	step:-2	step:-2	PROPN
ejpam-6248	56	2	z.	z.	PROPN
ejpam-6248	56	3	haider	haider	PROPN
ejpam-6248	56	4	et	et	PROPN
ejpam-6248	56	5	al	al	PROPN
ejpam-6248	56	6	.	.	PUNCT
ejpam-6248	56	7	/	/	SYM
ejpam-6248	56	8	eur	eur	PROPN
ejpam-6248	56	9	.	.	PUNCT
ejpam-6248	57	1	j.	j.	PROPN
ejpam-6248	57	2	pure	pure	PROPN
ejpam-6248	57	3	appl	appl	PROPN
ejpam-6248	57	4	.	.	PROPN
ejpam-6248	57	5	math	math	PROPN
ejpam-6248	57	6	,	,	PUNCT
ejpam-6248	57	7	18	18	NUM
ejpam-6248	57	8	(	(	PUNCT
ejpam-6248	57	9	3	3	NUM
ejpam-6248	57	10	)	)	PUNCT
ejpam-6248	57	11	(	(	PUNCT
ejpam-6248	57	12	2025	2025	NUM
ejpam-6248	57	13	)	)	PUNCT
ejpam-6248	57	14	,	,	PUNCT
ejpam-6248	57	15	6248	6248	NUM
ejpam-6248	57	16	4	4	NUM
ejpam-6248	57	17	of	of	ADP
ejpam-6248	57	18	20	20	NUM
ejpam-6248	57	19	we	we	PRON
ejpam-6248	57	20	now	now	ADV
ejpam-6248	57	21	differentiate	differentiate	VERB
ejpam-6248	57	22	equations	equation	NOUN
ejpam-6248	57	23	(	(	PUNCT
ejpam-6248	57	24	2	2	NUM
ejpam-6248	57	25	)	)	PUNCT
ejpam-6248	57	26	and	and	CCONJ
ejpam-6248	57	27	(	(	PUNCT
ejpam-6248	57	28	3	3	X
ejpam-6248	57	29	)	)	PUNCT
ejpam-6248	57	30	with	with	ADP
ejpam-6248	57	31	respect	respect	NOUN
ejpam-6248	57	32	to	to	ADP
ejpam-6248	57	33	the	the	DET
ejpam-6248	57	34	original	original	ADJ
ejpam-6248	57	35	pde	pde	NOUN
ejpam-6248	57	36	(	(	PUNCT
ejpam-6248	57	37	1	1	NUM
ejpam-6248	57	38	)	)	PUNCT
ejpam-6248	57	39	in	in	ADP
ejpam-6248	57	40	order	order	NOUN
ejpam-6248	57	41	to	to	PART
ejpam-6248	57	42	determine	determine	VERB
ejpam-6248	57	43	the	the	DET
ejpam-6248	57	44	relationships	relationship	NOUN
ejpam-6248	57	45	among	among	ADP
ejpam-6248	57	46	the	the	DET
ejpam-6248	57	47	exponents	exponent	NOUN
ejpam-6248	57	48	of	of	ADP
ejpam-6248	57	49	x	x	PROPN
ejpam-6248	57	50	,	,	PUNCT
ejpam-6248	57	51	y	y	PROPN
ejpam-6248	57	52	,	,	PUNCT
ejpam-6248	57	53	and	and	CCONJ
ejpam-6248	57	54	t	t	PROPN
ejpam-6248	57	55	in	in	ADP
ejpam-6248	57	56	each	each	DET
ejpam-6248	57	57	term	term	NOUN
ejpam-6248	57	58	.	.	PUNCT
ejpam-6248	58	1	substituting	substitute	VERB
ejpam-6248	58	2	these	these	PRON
ejpam-6248	58	3	into	into	ADP
ejpam-6248	58	4	equation	equation	NOUN
ejpam-6248	58	5	(	(	PUNCT
ejpam-6248	58	6	1	1	NUM
ejpam-6248	58	7	)	)	PUNCT
ejpam-6248	58	8	,	,	PUNCT
ejpam-6248	58	9	the	the	DET
ejpam-6248	58	10	nonlinear	nonlinear	ADJ
ejpam-6248	58	11	partial	partial	ADJ
ejpam-6248	58	12	differential	differential	NOUN
ejpam-6248	58	13	equation	equation	NOUN
ejpam-6248	58	14	is	be	AUX
ejpam-6248	58	15	transformed	transform	VERB
ejpam-6248	58	16	into	into	ADP
ejpam-6248	58	17	a	a	DET
ejpam-6248	58	18	mixed	mixed	ADJ
ejpam-6248	58	19	algebraic	algebraic	ADJ
ejpam-6248	58	20	form	form	NOUN
ejpam-6248	58	21	as	as	SCONJ
ejpam-6248	58	22	follows	follow	VERB
ejpam-6248	58	23	:	:	PUNCT
ejpam-6248	58	24	f	f	PROPN
ejpam-6248	58	25	(	(	PUNCT
ejpam-6248	58	26	t	t	PROPN
ejpam-6248	58	27	,	,	PUNCT
ejpam-6248	58	28	x	x	NOUN
ejpam-6248	58	29	,	,	PUNCT
ejpam-6248	58	30	y	y	NOUN
ejpam-6248	58	31	)	)	PUNCT
ejpam-6248	58	32	=	=	SYM
ejpam-6248	58	33	tatxaxyayϕ(ξ	tatxaxyayϕ(ξ	PROPN
ejpam-6248	58	34	,	,	PUNCT
ejpam-6248	58	35	g′(ξ	g′(ξ	PROPN
ejpam-6248	58	36	)	)	PUNCT
ejpam-6248	58	37	,	,	PUNCT
ejpam-6248	58	38	g′′(ξ	g′′(ξ	NOUN
ejpam-6248	58	39	)	)	PUNCT
ejpam-6248	58	40	,	,	PUNCT
ejpam-6248	58	41	...	...	PUNCT
ejpam-6248	58	42	)	)	PUNCT
ejpam-6248	58	43	.	.	PUNCT
ejpam-6248	59	1	(	(	PUNCT
ejpam-6248	59	2	4	4	X
ejpam-6248	59	3	)	)	PUNCT
ejpam-6248	59	4	the	the	DET
ejpam-6248	59	5	resulting	result	VERB
ejpam-6248	59	6	relationships	relationship	NOUN
ejpam-6248	59	7	among	among	ADP
ejpam-6248	59	8	the	the	DET
ejpam-6248	59	9	exponents	exponent	NOUN
ejpam-6248	59	10	can	can	AUX
ejpam-6248	59	11	be	be	AUX
ejpam-6248	59	12	represented	represent	VERB
ejpam-6248	59	13	by	by	ADP
ejpam-6248	59	14	the	the	DET
ejpam-6248	59	15	following	follow	VERB
ejpam-6248	59	16	functions	function	NOUN
ejpam-6248	59	17	:	:	PUNCT
ejpam-6248	59	18	at	at	ADP
ejpam-6248	59	19	=	=	PUNCT
ejpam-6248	59	20	a1p+	a1p+	NOUN
ejpam-6248	59	21	a2q	a2q	NOUN
ejpam-6248	59	22	+	+	NUM
ejpam-6248	59	23	a3	a3	NOUN
ejpam-6248	59	24	.	.	PUNCT
ejpam-6248	60	1	(	(	PUNCT
ejpam-6248	60	2	5	5	X
ejpam-6248	60	3	)	)	PUNCT
ejpam-6248	60	4	ax	ax	NOUN
ejpam-6248	60	5	=	=	NOUN
ejpam-6248	60	6	b1m+	b1m+	NOUN
ejpam-6248	60	7	b2n+	b2n+	PROPN
ejpam-6248	60	8	b3	b3	PROPN
ejpam-6248	60	9	.	.	PUNCT
ejpam-6248	61	1	(	(	PUNCT
ejpam-6248	61	2	6	6	NUM
ejpam-6248	61	3	)	)	PUNCT
ejpam-6248	61	4	ay	ay	NOUN
ejpam-6248	62	1	=	=	PUNCT
ejpam-6248	62	2	c1r	c1r	PROPN
ejpam-6248	63	1	+	+	CCONJ
ejpam-6248	63	2	c2s+	c2s+	PROPN
ejpam-6248	63	3	c3	c3	PROPN
ejpam-6248	63	4	.	.	PUNCT
ejpam-6248	64	1	(	(	PUNCT
ejpam-6248	64	2	7	7	NUM
ejpam-6248	64	3	)	)	PUNCT
ejpam-6248	64	4	by	by	ADP
ejpam-6248	64	5	analyzing	analyze	VERB
ejpam-6248	64	6	the	the	DET
ejpam-6248	64	7	coefficients	coefficient	NOUN
ejpam-6248	64	8	of	of	ADP
ejpam-6248	64	9	at	at	ADP
ejpam-6248	64	10	,	,	PUNCT
ejpam-6248	64	11	ax	ax	NOUN
ejpam-6248	64	12	,	,	PUNCT
ejpam-6248	64	13	and	and	CCONJ
ejpam-6248	64	14	ay	ay	INTJ
ejpam-6248	64	15	,	,	PUNCT
ejpam-6248	64	16	we	we	PRON
ejpam-6248	64	17	ensure	ensure	VERB
ejpam-6248	64	18	that	that	SCONJ
ejpam-6248	64	19	the	the	DET
ejpam-6248	64	20	partial	partial	ADJ
ejpam-6248	64	21	differential	differential	NOUN
ejpam-6248	64	22	equation	equation	NOUN
ejpam-6248	64	23	(	(	PUNCT
ejpam-6248	64	24	pde	pde	NOUN
ejpam-6248	64	25	)	)	PUNCT
ejpam-6248	64	26	given	give	VERB
ejpam-6248	64	27	in	in	ADP
ejpam-6248	64	28	equation	equation	NOUN
ejpam-6248	64	29	(	(	PUNCT
ejpam-6248	64	30	1	1	X
ejpam-6248	64	31	)	)	PUNCT
ejpam-6248	64	32	can	can	AUX
ejpam-6248	64	33	be	be	AUX
ejpam-6248	64	34	reduced	reduce	VERB
ejpam-6248	64	35	to	to	ADP
ejpam-6248	64	36	an	an	DET
ejpam-6248	64	37	ordinary	ordinary	ADJ
ejpam-6248	64	38	differential	differential	ADJ
ejpam-6248	64	39	equation	equation	NOUN
ejpam-6248	64	40	(	(	PUNCT
ejpam-6248	64	41	ode	ode	PROPN
ejpam-6248	64	42	)	)	PUNCT
ejpam-6248	64	43	.	.	PUNCT
ejpam-6248	65	1	the	the	DET
ejpam-6248	65	2	optimal	optimal	ADJ
ejpam-6248	65	3	exponents	exponent	NOUN
ejpam-6248	65	4	for	for	ADP
ejpam-6248	65	5	x	x	PROPN
ejpam-6248	65	6	,	,	PUNCT
ejpam-6248	65	7	y	y	PROPN
ejpam-6248	65	8	,	,	PUNCT
ejpam-6248	65	9	and	and	CCONJ
ejpam-6248	65	10	t	t	PROPN
ejpam-6248	65	11	are	be	AUX
ejpam-6248	65	12	selected	select	VERB
ejpam-6248	65	13	such	such	ADJ
ejpam-6248	65	14	that	that	SCONJ
ejpam-6248	65	15	only	only	ADV
ejpam-6248	65	16	three	three	NUM
ejpam-6248	65	17	indices	index	NOUN
ejpam-6248	65	18	are	be	AUX
ejpam-6248	65	19	allowed	allow	VERB
ejpam-6248	65	20	to	to	PART
ejpam-6248	65	21	vary	vary	VERB
ejpam-6248	65	22	simultaneously	simultaneously	ADV
ejpam-6248	65	23	,	,	PUNCT
ejpam-6248	65	24	while	while	SCONJ
ejpam-6248	65	25	the	the	DET
ejpam-6248	65	26	remaining	remain	VERB
ejpam-6248	65	27	exponents	exponent	NOUN
ejpam-6248	65	28	are	be	AUX
ejpam-6248	65	29	treated	treat	VERB
ejpam-6248	65	30	as	as	ADP
ejpam-6248	65	31	fixed	fix	VERB
ejpam-6248	65	32	constants	constant	NOUN
ejpam-6248	65	33	.	.	PUNCT
ejpam-6248	66	1	we	we	PRON
ejpam-6248	66	2	repeat	repeat	VERB
ejpam-6248	66	3	this	this	DET
ejpam-6248	66	4	process	process	NOUN
ejpam-6248	66	5	with	with	ADP
ejpam-6248	66	6	different	different	ADJ
ejpam-6248	66	7	indices	index	NOUN
ejpam-6248	66	8	of	of	ADP
ejpam-6248	66	9	x	x	PROPN
ejpam-6248	66	10	,	,	PUNCT
ejpam-6248	66	11	y	y	PROPN
ejpam-6248	66	12	,	,	PUNCT
ejpam-6248	66	13	and	and	CCONJ
ejpam-6248	66	14	t	t	X
ejpam-6248	66	15	to	to	PART
ejpam-6248	66	16	find	find	VERB
ejpam-6248	66	17	all	all	DET
ejpam-6248	66	18	welldefined	welldefine	VERB
ejpam-6248	66	19	transformations	transformation	NOUN
ejpam-6248	66	20	.	.	PUNCT
ejpam-6248	67	1	step:-3	step:-3	NOUN
ejpam-6248	67	2	upon	upon	SCONJ
ejpam-6248	67	3	substituting	substitute	VERB
ejpam-6248	67	4	the	the	DET
ejpam-6248	67	5	power	power	NOUN
ejpam-6248	67	6	-	-	PUNCT
ejpam-6248	67	7	law	law	NOUN
ejpam-6248	67	8	exponents	exponent	NOUN
ejpam-6248	67	9	into	into	ADP
ejpam-6248	67	10	the	the	DET
ejpam-6248	67	11	transformation	transformation	NOUN
ejpam-6248	67	12	,	,	PUNCT
ejpam-6248	67	13	the	the	DET
ejpam-6248	67	14	partial	partial	ADJ
ejpam-6248	67	15	differential	differential	NOUN
ejpam-6248	67	16	equation	equation	NOUN
ejpam-6248	67	17	(	(	PUNCT
ejpam-6248	67	18	pde	pde	NOUN
ejpam-6248	67	19	)	)	PUNCT
ejpam-6248	67	20	given	give	VERB
ejpam-6248	67	21	in	in	ADP
ejpam-6248	67	22	equation	equation	NOUN
ejpam-6248	67	23	(	(	PUNCT
ejpam-6248	67	24	1	1	X
ejpam-6248	67	25	)	)	PUNCT
ejpam-6248	67	26	is	be	AUX
ejpam-6248	67	27	reduced	reduce	VERB
ejpam-6248	67	28	to	to	ADP
ejpam-6248	67	29	an	an	DET
ejpam-6248	67	30	ordinary	ordinary	ADJ
ejpam-6248	67	31	differential	differential	ADJ
ejpam-6248	67	32	equation	equation	NOUN
ejpam-6248	67	33	(	(	PUNCT
ejpam-6248	67	34	ode	ode	PROPN
ejpam-6248	67	35	)	)	PUNCT
ejpam-6248	67	36	in	in	ADP
ejpam-6248	67	37	terms	term	NOUN
ejpam-6248	67	38	of	of	ADP
ejpam-6248	67	39	the	the	DET
ejpam-6248	67	40	function	function	NOUN
ejpam-6248	67	41	f(ξ	f(ξ	NOUN
ejpam-6248	67	42	)	)	PUNCT
ejpam-6248	67	43	.	.	PUNCT
ejpam-6248	68	1	g(ξ	g(ξ	PROPN
ejpam-6248	68	2	,	,	PUNCT
ejpam-6248	68	3	f(ξ	f(ξ	PROPN
ejpam-6248	68	4	)	)	PUNCT
ejpam-6248	68	5	,	,	PUNCT
ejpam-6248	68	6	f	f	PROPN
ejpam-6248	68	7	′(ξ	′(ξ	PROPN
ejpam-6248	68	8	)	)	PUNCT
ejpam-6248	68	9	,	,	PUNCT
ejpam-6248	68	10	f	f	PROPN
ejpam-6248	68	11	′′(ξ	′′(ξ	PROPN
ejpam-6248	68	12	)	)	PUNCT
ejpam-6248	68	13	,	,	PUNCT
ejpam-6248	68	14	f	f	PROPN
ejpam-6248	68	15	′′′(ξ	′′′(ξ	PROPN
ejpam-6248	68	16	)	)	PUNCT
ejpam-6248	68	17	,	,	PUNCT
ejpam-6248	68	18	...	...	PUNCT
ejpam-6248	68	19	)	)	PUNCT
ejpam-6248	69	1	=	=	SYM
ejpam-6248	69	2	0	0	X
ejpam-6248	69	3	.	.	PUNCT
ejpam-6248	70	1	(	(	PUNCT
ejpam-6248	70	2	8)	8)	NUM
ejpam-6248	70	3	step:-4	step:-4	VERB
ejpam-6248	70	4	the	the	DET
ejpam-6248	70	5	solution	solution	NOUN
ejpam-6248	70	6	of	of	ADP
ejpam-6248	70	7	the	the	DET
ejpam-6248	70	8	ordinary	ordinary	ADJ
ejpam-6248	70	9	differential	differential	ADJ
ejpam-6248	70	10	equation	equation	NOUN
ejpam-6248	70	11	(	(	PUNCT
ejpam-6248	70	12	ode	ode	PROPN
ejpam-6248	70	13	)	)	PUNCT
ejpam-6248	70	14	given	give	VERB
ejpam-6248	70	15	in	in	ADP
ejpam-6248	70	16	eqaution	eqaution	NOUN
ejpam-6248	70	17	(	(	PUNCT
ejpam-6248	70	18	8)	8)	NUM
ejpam-6248	70	19	is	be	AUX
ejpam-6248	70	20	obtained	obtain	VERB
ejpam-6248	70	21	figure	figure	NOUN
ejpam-6248	70	22	1	1	NUM
ejpam-6248	70	23	:	:	PUNCT
ejpam-6248	70	24	flow	flow	VERB
ejpam-6248	70	25	chart	chart	NOUN
ejpam-6248	70	26	of	of	ADP
ejpam-6248	70	27	power	power	NOUN
ejpam-6248	70	28	index	index	NOUN
ejpam-6248	70	29	method	method	NOUN
ejpam-6248	70	30	by	by	ADP
ejpam-6248	70	31	using	use	VERB
ejpam-6248	70	32	computerized	computerized	ADJ
ejpam-6248	70	33	symbolic	symbolic	ADJ
ejpam-6248	70	34	package	package	NOUN
ejpam-6248	70	35	like	like	ADP
ejpam-6248	70	36	maple	maple	NOUN
ejpam-6248	70	37	18	18	NUM
ejpam-6248	70	38	and	and	CCONJ
ejpam-6248	70	39	basic	basic	ADJ
ejpam-6248	70	40	techniques	technique	NOUN
ejpam-6248	70	41	.	.	PUNCT
ejpam-6248	71	1	subsequently	subsequently	ADV
ejpam-6248	71	2	,	,	PUNCT
ejpam-6248	71	3	the	the	DET
ejpam-6248	71	4	exact	exact	ADJ
ejpam-6248	71	5	solution	solution	NOUN
ejpam-6248	71	6	of	of	ADP
ejpam-6248	71	7	equation	equation	NOUN
ejpam-6248	71	8	(	(	PUNCT
ejpam-6248	71	9	1	1	X
ejpam-6248	71	10	)	)	PUNCT
ejpam-6248	71	11	is	be	AUX
ejpam-6248	71	12	derived	derive	VERB
ejpam-6248	71	13	by	by	ADP
ejpam-6248	71	14	substituting	substitute	VERB
ejpam-6248	71	15	the	the	DET
ejpam-6248	71	16	obtained	obtain	VERB
ejpam-6248	71	17	function	function	NOUN
ejpam-6248	71	18	f(ξ	f(ξ	NOUN
ejpam-6248	71	19	)	)	PUNCT
ejpam-6248	71	20	into	into	ADP
ejpam-6248	71	21	the	the	DET
ejpam-6248	71	22	transformation	transformation	NOUN
ejpam-6248	71	23	defined	define	VERB
ejpam-6248	71	24	in	in	ADP
ejpam-6248	71	25	equation	equation	NOUN
ejpam-6248	71	26	(	(	PUNCT
ejpam-6248	71	27	3	3	NUM
ejpam-6248	71	28	)	)	PUNCT
ejpam-6248	71	29	.	.	PUNCT
ejpam-6248	72	1	z.	z.	PROPN
ejpam-6248	72	2	haider	haider	PROPN
ejpam-6248	72	3	et	et	PROPN
ejpam-6248	72	4	al	al	PROPN
ejpam-6248	72	5	.	.	PUNCT
ejpam-6248	72	6	/	/	SYM
ejpam-6248	72	7	eur	eur	PROPN
ejpam-6248	72	8	.	.	PUNCT
ejpam-6248	73	1	j.	j.	PROPN
ejpam-6248	73	2	pure	pure	PROPN
ejpam-6248	73	3	appl	appl	PROPN
ejpam-6248	73	4	.	.	PROPN
ejpam-6248	73	5	math	math	PROPN
ejpam-6248	73	6	,	,	PUNCT
ejpam-6248	73	7	18	18	NUM
ejpam-6248	73	8	(	(	PUNCT
ejpam-6248	73	9	3	3	NUM
ejpam-6248	73	10	)	)	PUNCT
ejpam-6248	73	11	(	(	PUNCT
ejpam-6248	73	12	2025	2025	NUM
ejpam-6248	73	13	)	)	PUNCT
ejpam-6248	73	14	,	,	PUNCT
ejpam-6248	73	15	6248	6248	NUM
ejpam-6248	73	16	5	5	NUM
ejpam-6248	73	17	of	of	ADP
ejpam-6248	73	18	20	20	NUM
ejpam-6248	73	19	3	3	NUM
ejpam-6248	73	20	.	.	PUNCT
ejpam-6248	74	1	new	new	ADJ
ejpam-6248	74	2	self	self	NOUN
ejpam-6248	74	3	-	-	PUNCT
ejpam-6248	74	4	similar	similar	ADJ
ejpam-6248	74	5	solutions	solution	NOUN
ejpam-6248	74	6	of	of	ADP
ejpam-6248	74	7	lin	lin	PROPN
ejpam-6248	74	8	–	–	PUNCT
ejpam-6248	74	9	reissner	reissner	NOUN
ejpam-6248	74	10	–	–	PUNCT
ejpam-6248	74	11	tsien	tsien	NOUN
ejpam-6248	74	12	equation	equation	NOUN
ejpam-6248	74	13	case:-1	case:-1	ADP
ejpam-6248	74	14	we	we	PRON
ejpam-6248	74	15	consider	consider	VERB
ejpam-6248	74	16	the	the	DET
ejpam-6248	74	17	self	self	NOUN
ejpam-6248	74	18	-	-	PUNCT
ejpam-6248	74	19	similar	similar	ADJ
ejpam-6248	74	20	function	function	NOUN
ejpam-6248	74	21	transformation	transformation	NOUN
ejpam-6248	74	22	given	give	VERB
ejpam-6248	74	23	by	by	ADP
ejpam-6248	74	24	:	:	PUNCT
ejpam-6248	74	25	ξ	ξ	X
ejpam-6248	74	26	=	=	SYM
ejpam-6248	74	27	x	x	SYM
ejpam-6248	74	28	tm	tm	NOUN
ejpam-6248	74	29	.	.	PUNCT
ejpam-6248	75	1	(	(	PUNCT
ejpam-6248	75	2	9	9	X
ejpam-6248	75	3	)	)	PUNCT
ejpam-6248	75	4	u	u	NOUN
ejpam-6248	75	5	=	=	SYM
ejpam-6248	75	6	tnf(ξ	tnf(ξ	NUM
ejpam-6248	75	7	)	)	PUNCT
ejpam-6248	75	8	.	.	PUNCT
ejpam-6248	76	1	(	(	PUNCT
ejpam-6248	76	2	10	10	NUM
ejpam-6248	76	3	)	)	PUNCT
ejpam-6248	76	4	where	where	SCONJ
ejpam-6248	76	5	m	m	VERB
ejpam-6248	76	6	and	and	CCONJ
ejpam-6248	76	7	n	n	PROPN
ejpam-6248	76	8	are	be	AUX
ejpam-6248	76	9	constants	constant	NOUN
ejpam-6248	76	10	to	to	PART
ejpam-6248	76	11	be	be	AUX
ejpam-6248	76	12	determined	determine	VERB
ejpam-6248	76	13	.	.	PUNCT
ejpam-6248	77	1	differentiating	differentiate	VERB
ejpam-6248	77	2	equations	equation	NOUN
ejpam-6248	77	3	(	(	PUNCT
ejpam-6248	77	4	9	9	NUM
ejpam-6248	77	5	)	)	PUNCT
ejpam-6248	77	6	and	and	CCONJ
ejpam-6248	77	7	(	(	PUNCT
ejpam-6248	77	8	10	10	NUM
ejpam-6248	77	9	)	)	PUNCT
ejpam-6248	77	10	with	with	ADP
ejpam-6248	77	11	respect	respect	NOUN
ejpam-6248	77	12	to	to	ADP
ejpam-6248	77	13	equation	equation	NOUN
ejpam-6248	77	14	(	(	PUNCT
ejpam-6248	77	15	1	1	X
ejpam-6248	77	16	)	)	PUNCT
ejpam-6248	77	17	yields	yield	VERB
ejpam-6248	77	18	the	the	DET
ejpam-6248	77	19	following	follow	VERB
ejpam-6248	77	20	partial	partial	ADJ
ejpam-6248	77	21	derivatives	derivative	NOUN
ejpam-6248	77	22	:	:	PUNCT
ejpam-6248	77	23	uxt	uxt	NOUN
ejpam-6248	77	24	=	=	SYM
ejpam-6248	77	25	tn−m−1(nf	tn−m−1(nf	NUM
ejpam-6248	77	26	′	′	NUM
ejpam-6248	77	27	(	(	PUNCT
ejpam-6248	77	28	ξ)−mξf	ξ)−mξf	ADP
ejpam-6248	77	29	′′	′′	PROPN
ejpam-6248	77	30	(	(	PUNCT
ejpam-6248	77	31	ξ)−mf	ξ)−mf	PROPN
ejpam-6248	77	32	′	′	NUM
ejpam-6248	77	33	(	(	PUNCT
ejpam-6248	77	34	ξ	ξ	NOUN
ejpam-6248	77	35	)	)	PUNCT
ejpam-6248	77	36	)	)	PUNCT
ejpam-6248	77	37	.	.	PUNCT
ejpam-6248	78	1	(	(	PUNCT
ejpam-6248	78	2	11	11	NUM
ejpam-6248	78	3	)	)	PUNCT
ejpam-6248	78	4	ux	ux	NOUN
ejpam-6248	79	1	=	=	PUNCT
ejpam-6248	79	2	tn−mf	tn−mf	NOUN
ejpam-6248	79	3	′	′	NUM
ejpam-6248	79	4	(	(	PUNCT
ejpam-6248	79	5	ξ	ξ	NOUN
ejpam-6248	79	6	)	)	PUNCT
ejpam-6248	79	7	.	.	PUNCT
ejpam-6248	80	1	(	(	PUNCT
ejpam-6248	80	2	12	12	NUM
ejpam-6248	80	3	)	)	PUNCT
ejpam-6248	80	4	uxx	uxx	NOUN
ejpam-6248	80	5	=	=	PUNCT
ejpam-6248	81	1	tn−2mf	tn−2mf	PRON
ejpam-6248	81	2	′′	′′	PROPN
ejpam-6248	81	3	(	(	PUNCT
ejpam-6248	81	4	ξ	ξ	NOUN
ejpam-6248	81	5	)	)	PUNCT
ejpam-6248	81	6	.	.	PUNCT
ejpam-6248	82	1	(	(	PUNCT
ejpam-6248	82	2	13	13	NUM
ejpam-6248	82	3	)	)	PUNCT
ejpam-6248	82	4	uyy	uyy	PROPN
ejpam-6248	82	5	=	=	SYM
ejpam-6248	82	6	0	0	PROPN
ejpam-6248	82	7	.	.	PUNCT
ejpam-6248	83	1	(	(	PUNCT
ejpam-6248	83	2	14	14	NUM
ejpam-6248	83	3	)	)	PUNCT
ejpam-6248	83	4	substituting	substitute	VERB
ejpam-6248	83	5	equations	equation	NOUN
ejpam-6248	83	6	(	(	PUNCT
ejpam-6248	83	7	11	11	NUM
ejpam-6248	83	8	)	)	PUNCT
ejpam-6248	83	9	,	,	PUNCT
ejpam-6248	83	10	(	(	PUNCT
ejpam-6248	83	11	12	12	NUM
ejpam-6248	83	12	)	)	PUNCT
ejpam-6248	83	13	,	,	PUNCT
ejpam-6248	83	14	(	(	PUNCT
ejpam-6248	83	15	13	13	NUM
ejpam-6248	83	16	)	)	PUNCT
ejpam-6248	83	17	,	,	PUNCT
ejpam-6248	83	18	and	and	CCONJ
ejpam-6248	83	19	(	(	PUNCT
ejpam-6248	83	20	14	14	NUM
ejpam-6248	83	21	)	)	PUNCT
ejpam-6248	83	22	into	into	ADP
ejpam-6248	83	23	equation	equation	NOUN
ejpam-6248	83	24	(	(	PUNCT
ejpam-6248	83	25	1	1	X
ejpam-6248	83	26	)	)	PUNCT
ejpam-6248	83	27	yields	yield	NOUN
ejpam-6248	83	28	:	:	PUNCT
ejpam-6248	83	29	2(n−m)tn−m−1f	2(n−m)tn−m−1f	NUM
ejpam-6248	83	30	′	′	NUM
ejpam-6248	83	31	(	(	PUNCT
ejpam-6248	83	32	ξ)−	ξ)−	PROPN
ejpam-6248	83	33	2mxtn−2m−1f	2mxtn−2m−1f	NUM
ejpam-6248	83	34	′′	′′	PROPN
ejpam-6248	83	35	(	(	PUNCT
ejpam-6248	83	36	ξ	ξ	PROPN
ejpam-6248	83	37	)	)	PUNCT
ejpam-6248	83	38	+	+	CCONJ
ejpam-6248	83	39	t2n−3mf	t2n−3mf	ADJ
ejpam-6248	83	40	′	′	NUM
ejpam-6248	83	41	(	(	PUNCT
ejpam-6248	83	42	ξ)f	ξ)f	NOUN
ejpam-6248	83	43	′′	′′	PROPN
ejpam-6248	83	44	(	(	PUNCT
ejpam-6248	83	45	ξ	ξ	PROPN
ejpam-6248	83	46	)	)	PUNCT
ejpam-6248	83	47	=	=	SYM
ejpam-6248	84	1	0	0	X
ejpam-6248	84	2	.	.	PUNCT
ejpam-6248	85	1	(	(	PUNCT
ejpam-6248	85	2	15	15	NUM
ejpam-6248	85	3	)	)	PUNCT
ejpam-6248	85	4	since	since	SCONJ
ejpam-6248	85	5	ξ	ξ	X
ejpam-6248	85	6	=	=	SYM
ejpam-6248	85	7	x	x	SYM
ejpam-6248	85	8	tm	tm	NOUN
ejpam-6248	85	9	,	,	PUNCT
ejpam-6248	85	10	equation	equation	NOUN
ejpam-6248	85	11	(	(	PUNCT
ejpam-6248	85	12	15	15	NUM
ejpam-6248	85	13	)	)	PUNCT
ejpam-6248	85	14	simplifies	simplifie	NOUN
ejpam-6248	85	15	to	to	ADP
ejpam-6248	85	16	:	:	PUNCT
ejpam-6248	85	17	2(n−m)tn−m−1f	2(n−m)tn−m−1f	NUM
ejpam-6248	85	18	′	′	NUM
ejpam-6248	85	19	(	(	PUNCT
ejpam-6248	85	20	ξ)−	ξ)−	PROPN
ejpam-6248	85	21	2mtn−m−1ξf	2mtn−m−1ξf	NUM
ejpam-6248	86	1	′′	′′	PROPN
ejpam-6248	86	2	(	(	PUNCT
ejpam-6248	86	3	ξ	ξ	PROPN
ejpam-6248	86	4	)	)	PUNCT
ejpam-6248	86	5	+	+	CCONJ
ejpam-6248	86	6	t2n−3mf	t2n−3mf	ADJ
ejpam-6248	86	7	′	′	NUM
ejpam-6248	86	8	(	(	PUNCT
ejpam-6248	86	9	ξ)f	ξ)f	NOUN
ejpam-6248	86	10	′′	′′	PROPN
ejpam-6248	86	11	(	(	PUNCT
ejpam-6248	86	12	ξ	ξ	PROPN
ejpam-6248	86	13	)	)	PUNCT
ejpam-6248	86	14	=	=	SYM
ejpam-6248	86	15	0	0	X
ejpam-6248	86	16	.	.	PUNCT
ejpam-6248	87	1	(	(	PUNCT
ejpam-6248	87	2	16	16	NUM
ejpam-6248	87	3	)	)	PUNCT
ejpam-6248	87	4	dividing	divide	VERB
ejpam-6248	87	5	both	both	DET
ejpam-6248	87	6	sides	side	NOUN
ejpam-6248	87	7	of	of	ADP
ejpam-6248	87	8	equation	equation	NOUN
ejpam-6248	87	9	(	(	PUNCT
ejpam-6248	87	10	16	16	NUM
ejpam-6248	87	11	)	)	PUNCT
ejpam-6248	87	12	by	by	ADP
ejpam-6248	87	13	tn−m−1	tn−m−1	PROPN
ejpam-6248	87	14	,	,	PUNCT
ejpam-6248	87	15	we	we	PRON
ejpam-6248	87	16	obtain	obtain	VERB
ejpam-6248	87	17	:	:	PUNCT
ejpam-6248	87	18	2(n−m)f	2(n−m)f	NUM
ejpam-6248	87	19	′	′	NUM
ejpam-6248	87	20	(	(	PUNCT
ejpam-6248	87	21	ξ)−	ξ)−	PROPN
ejpam-6248	87	22	2mξf	2mξf	PROPN
ejpam-6248	88	1	′′	′′	PROPN
ejpam-6248	88	2	(	(	PUNCT
ejpam-6248	88	3	ξ	ξ	PROPN
ejpam-6248	88	4	)	)	PUNCT
ejpam-6248	88	5	+	+	NUM
ejpam-6248	88	6	tn−2m+1f	tn−2m+1f	ADJ
ejpam-6248	88	7	′	′	NUM
ejpam-6248	88	8	(	(	PUNCT
ejpam-6248	88	9	ξ)f	ξ)f	NOUN
ejpam-6248	88	10	′′	′′	PROPN
ejpam-6248	88	11	(	(	PUNCT
ejpam-6248	88	12	ξ	ξ	PROPN
ejpam-6248	88	13	)	)	PUNCT
ejpam-6248	88	14	=	=	SYM
ejpam-6248	88	15	0	0	X
ejpam-6248	88	16	.	.	PUNCT
ejpam-6248	88	17	(	(	PUNCT
ejpam-6248	88	18	17	17	NUM
ejpam-6248	88	19	)	)	PUNCT
ejpam-6248	88	20	the	the	DET
ejpam-6248	88	21	last	last	ADJ
ejpam-6248	88	22	term	term	NOUN
ejpam-6248	88	23	in	in	ADP
ejpam-6248	88	24	equation	equation	NOUN
ejpam-6248	88	25	(	(	PUNCT
ejpam-6248	88	26	17	17	NUM
ejpam-6248	88	27	)	)	PUNCT
ejpam-6248	88	28	involves	involve	VERB
ejpam-6248	88	29	the	the	DET
ejpam-6248	88	30	factor	factor	NOUN
ejpam-6248	88	31	tn−2m+1	tn−2m+1	NOUN
ejpam-6248	88	32	,	,	PUNCT
ejpam-6248	88	33	which	which	PRON
ejpam-6248	88	34	must	must	AUX
ejpam-6248	88	35	reduce	reduce	VERB
ejpam-6248	88	36	to	to	ADP
ejpam-6248	88	37	unity	unity	NOUN
ejpam-6248	88	38	(	(	PUNCT
ejpam-6248	88	39	i.e.	i.e.	X
ejpam-6248	88	40	,	,	PUNCT
ejpam-6248	88	41	t0	t0	PROPN
ejpam-6248	88	42	)	)	PUNCT
ejpam-6248	88	43	to	to	PART
ejpam-6248	88	44	preserve	preserve	VERB
ejpam-6248	88	45	dimensional	dimensional	ADJ
ejpam-6248	88	46	consistency	consistency	NOUN
ejpam-6248	88	47	.	.	PUNCT
ejpam-6248	89	1	this	this	DET
ejpam-6248	89	2	requirement	requirement	NOUN
ejpam-6248	89	3	yields	yield	VERB
ejpam-6248	89	4	the	the	DET
ejpam-6248	89	5	scaling	scaling	NOUN
ejpam-6248	89	6	relation	relation	NOUN
ejpam-6248	89	7	n	n	NOUN
ejpam-6248	89	8	=	=	SYM
ejpam-6248	89	9	2	2	NUM
ejpam-6248	89	10	m	m	NOUN
ejpam-6248	89	11	−	−	NOUN
ejpam-6248	89	12	1	1	NUM
ejpam-6248	89	13	.	.	PUNCT
ejpam-6248	89	14	for	for	ADP
ejpam-6248	89	15	selected	select	VERB
ejpam-6248	89	16	values	value	NOUN
ejpam-6248	89	17	of	of	ADP
ejpam-6248	89	18	m	m	PROPN
ejpam-6248	89	19	and	and	CCONJ
ejpam-6248	89	20	n	n	CCONJ
ejpam-6248	89	21	,	,	PUNCT
ejpam-6248	89	22	we	we	PRON
ejpam-6248	89	23	are	be	AUX
ejpam-6248	89	24	able	able	ADJ
ejpam-6248	89	25	to	to	PART
ejpam-6248	89	26	find	find	VERB
ejpam-6248	89	27	the	the	DET
ejpam-6248	89	28	solutions	solution	NOUN
ejpam-6248	89	29	of	of	ADP
ejpam-6248	89	30	ode	ode	PROPN
ejpam-6248	89	31	(	(	PUNCT
ejpam-6248	89	32	17	17	NUM
ejpam-6248	89	33	)	)	PUNCT
ejpam-6248	89	34	.	.	PUNCT
ejpam-6248	90	1	however	however	ADV
ejpam-6248	90	2	,	,	PUNCT
ejpam-6248	90	3	for	for	ADP
ejpam-6248	90	4	arbitrary	arbitrary	ADJ
ejpam-6248	90	5	values	value	NOUN
ejpam-6248	90	6	of	of	ADP
ejpam-6248	90	7	these	these	DET
ejpam-6248	90	8	parameters	parameter	NOUN
ejpam-6248	90	9	,	,	PUNCT
ejpam-6248	90	10	the	the	DET
ejpam-6248	90	11	general	general	ADJ
ejpam-6248	90	12	solution	solution	NOUN
ejpam-6248	90	13	of	of	ADP
ejpam-6248	90	14	the	the	DET
ejpam-6248	90	15	ode	ode	PROPN
ejpam-6248	90	16	(	(	PUNCT
ejpam-6248	90	17	17	17	NUM
ejpam-6248	90	18	)	)	PUNCT
ejpam-6248	90	19	can	can	AUX
ejpam-6248	90	20	not	not	PART
ejpam-6248	90	21	be	be	AUX
ejpam-6248	90	22	obtained	obtain	VERB
ejpam-6248	90	23	.	.	PUNCT
ejpam-6248	91	1	n	n	NOUN
ejpam-6248	92	1	=	=	SYM
ejpam-6248	92	2	2m−	2m−	NUM
ejpam-6248	92	3	1	1	NUM
ejpam-6248	92	4	m	m	NOUN
ejpam-6248	92	5	−1	−1	NOUN
ejpam-6248	92	6	1	1	NUM
ejpam-6248	92	7	n	n	NUM
ejpam-6248	92	8	−3	−3	NOUN
ejpam-6248	92	9	1	1	NUM
ejpam-6248	92	10	table	table	NOUN
ejpam-6248	92	11	1	1	NUM
ejpam-6248	92	12	.	.	PUNCT
ejpam-6248	92	13	specific	specific	ADJ
ejpam-6248	92	14	values	value	NOUN
ejpam-6248	92	15	of	of	ADP
ejpam-6248	92	16	m	m	PROPN
ejpam-6248	92	17	and	and	CCONJ
ejpam-6248	92	18	n	n	PROPN
ejpam-6248	92	19	for	for	ADP
ejpam-6248	92	20	obtainig	obtainig	NOUN
ejpam-6248	92	21	exact	exact	ADJ
ejpam-6248	92	22	solutions	solution	NOUN
ejpam-6248	92	23	family	family	NOUN
ejpam-6248	92	24	solutions	solution	NOUN
ejpam-6248	92	25	z.	z.	PROPN
ejpam-6248	92	26	haider	haider	PROPN
ejpam-6248	92	27	et	et	PROPN
ejpam-6248	92	28	al	al	PROPN
ejpam-6248	92	29	.	.	PUNCT
ejpam-6248	92	30	/	/	SYM
ejpam-6248	92	31	eur	eur	PROPN
ejpam-6248	92	32	.	.	PUNCT
ejpam-6248	93	1	j.	j.	PROPN
ejpam-6248	93	2	pure	pure	PROPN
ejpam-6248	93	3	appl	appl	PROPN
ejpam-6248	93	4	.	.	PROPN
ejpam-6248	93	5	math	math	PROPN
ejpam-6248	93	6	,	,	PUNCT
ejpam-6248	93	7	18	18	NUM
ejpam-6248	93	8	(	(	PUNCT
ejpam-6248	93	9	3	3	NUM
ejpam-6248	93	10	)	)	PUNCT
ejpam-6248	93	11	(	(	PUNCT
ejpam-6248	93	12	2025	2025	NUM
ejpam-6248	93	13	)	)	PUNCT
ejpam-6248	93	14	,	,	PUNCT
ejpam-6248	93	15	6248	6248	NUM
ejpam-6248	93	16	6	6	NUM
ejpam-6248	93	17	of	of	ADP
ejpam-6248	93	18	20	20	NUM
ejpam-6248	93	19	figure	figure	NOUN
ejpam-6248	93	20	2	2	NUM
ejpam-6248	93	21	:	:	PUNCT
ejpam-6248	93	22	3d	3d	NUM
ejpam-6248	93	23	plot	plot	NOUN
ejpam-6248	93	24	of	of	ADP
ejpam-6248	93	25	(	(	PUNCT
ejpam-6248	93	26	24	24	NUM
ejpam-6248	93	27	)	)	PUNCT
ejpam-6248	93	28	for	for	ADP
ejpam-6248	93	29	c	c	NOUN
ejpam-6248	93	30	=	=	SYM
ejpam-6248	93	31	1	1	NUM
ejpam-6248	93	32	.	.	PUNCT
ejpam-6248	93	33	(	(	PUNCT
ejpam-6248	93	34	i	i	NOUN
ejpam-6248	93	35	)	)	PUNCT
ejpam-6248	93	36	for	for	ADP
ejpam-6248	93	37	the	the	DET
ejpam-6248	93	38	parameter	parameter	NOUN
ejpam-6248	93	39	values	value	VERB
ejpam-6248	93	40	m	m	VERB
ejpam-6248	93	41	=	=	SYM
ejpam-6248	93	42	1	1	NUM
ejpam-6248	93	43	and	and	CCONJ
ejpam-6248	93	44	n	n	CCONJ
ejpam-6248	93	45	=	=	SYM
ejpam-6248	93	46	1	1	NUM
ejpam-6248	93	47	,	,	PUNCT
ejpam-6248	93	48	the	the	DET
ejpam-6248	93	49	similarity	similarity	NOUN
ejpam-6248	93	50	function	function	NOUN
ejpam-6248	93	51	transformation	transformation	NOUN
ejpam-6248	93	52	given	give	VERB
ejpam-6248	93	53	in	in	ADP
ejpam-6248	93	54	equations	equation	NOUN
ejpam-6248	93	55	(	(	PUNCT
ejpam-6248	93	56	9	9	NUM
ejpam-6248	93	57	)	)	PUNCT
ejpam-6248	93	58	and	and	CCONJ
ejpam-6248	93	59	(	(	PUNCT
ejpam-6248	93	60	10	10	NUM
ejpam-6248	93	61	)	)	PUNCT
ejpam-6248	93	62	reduce	reduce	VERB
ejpam-6248	93	63	to	to	ADP
ejpam-6248	93	64	the	the	DET
ejpam-6248	93	65	form	form	NOUN
ejpam-6248	93	66	:	:	PUNCT
ejpam-6248	93	67	ξ	ξ	X
ejpam-6248	93	68	=	=	PUNCT
ejpam-6248	93	69	x	x	SYM
ejpam-6248	93	70	t	t	NOUN
ejpam-6248	93	71	.	.	PUNCT
ejpam-6248	94	1	(	(	PUNCT
ejpam-6248	94	2	18	18	NUM
ejpam-6248	94	3	)	)	PUNCT
ejpam-6248	94	4	u	u	NOUN
ejpam-6248	94	5	=	=	NOUN
ejpam-6248	94	6	tf(ξ	tf(ξ	NUM
ejpam-6248	94	7	)	)	PUNCT
ejpam-6248	94	8	.	.	PUNCT
ejpam-6248	95	1	(	(	PUNCT
ejpam-6248	95	2	19	19	NUM
ejpam-6248	95	3	)	)	PUNCT
ejpam-6248	95	4	substituting	substitute	VERB
ejpam-6248	95	5	the	the	DET
ejpam-6248	95	6	parameter	parameter	NOUN
ejpam-6248	95	7	values	value	NOUN
ejpam-6248	95	8	m	m	VERB
ejpam-6248	95	9	=	=	SYM
ejpam-6248	95	10	1	1	NUM
ejpam-6248	95	11	and	and	CCONJ
ejpam-6248	95	12	n	n	CCONJ
ejpam-6248	95	13	=	=	SYM
ejpam-6248	95	14	1	1	NUM
ejpam-6248	95	15	in	in	ADP
ejpam-6248	95	16	equation	equation	NOUN
ejpam-6248	95	17	(	(	PUNCT
ejpam-6248	95	18	17	17	NUM
ejpam-6248	95	19	)	)	PUNCT
ejpam-6248	95	20	,	,	PUNCT
ejpam-6248	95	21	we	we	PRON
ejpam-6248	95	22	obtain	obtain	VERB
ejpam-6248	95	23	the	the	DET
ejpam-6248	95	24	following	follow	VERB
ejpam-6248	95	25	ordinary	ordinary	ADJ
ejpam-6248	95	26	differential	differential	ADJ
ejpam-6248	95	27	equation	equation	NOUN
ejpam-6248	95	28	(	(	PUNCT
ejpam-6248	95	29	ode	ode	ADJ
ejpam-6248	95	30	):	):	PUNCT
ejpam-6248	95	31	−2ξf	−2ξf	ADJ
ejpam-6248	95	32	′′(ξ	′′(ξ	NOUN
ejpam-6248	95	33	)	)	PUNCT
ejpam-6248	96	1	+	+	CCONJ
ejpam-6248	96	2	f	f	PROPN
ejpam-6248	96	3	′(ξ)f	′(ξ)f	PROPN
ejpam-6248	96	4	′′(ξ	′′(ξ	PROPN
ejpam-6248	96	5	)	)	PUNCT
ejpam-6248	97	1	=	=	NOUN
ejpam-6248	98	1	0	0	X
ejpam-6248	98	2	.	.	PUNCT
ejpam-6248	99	1	(	(	PUNCT
ejpam-6248	99	2	20	20	NUM
ejpam-6248	99	3	)	)	PUNCT
ejpam-6248	99	4	we	we	PRON
ejpam-6248	99	5	rewrite	rewrite	VERB
ejpam-6248	99	6	equation	equation	NOUN
ejpam-6248	99	7	(	(	PUNCT
ejpam-6248	99	8	20	20	NUM
ejpam-6248	99	9	)	)	PUNCT
ejpam-6248	99	10	in	in	ADP
ejpam-6248	99	11	factored	factored	ADJ
ejpam-6248	99	12	form	form	NOUN
ejpam-6248	99	13	:	:	PUNCT
ejpam-6248	99	14	f	f	PROPN
ejpam-6248	99	15	′′(ξ)(f	′′(ξ)(f	NOUN
ejpam-6248	99	16	′(ξ)−	′(ξ)−	PROPN
ejpam-6248	99	17	2ξ	2ξ	NUM
ejpam-6248	99	18	)	)	PUNCT
ejpam-6248	100	1	=	=	SYM
ejpam-6248	100	2	0	0	X
ejpam-6248	100	3	.	.	PUNCT
ejpam-6248	101	1	(	(	PUNCT
ejpam-6248	101	2	21	21	NUM
ejpam-6248	101	3	)	)	PUNCT
ejpam-6248	101	4	this	this	DET
ejpam-6248	101	5	factored	factor	VERB
ejpam-6248	101	6	form	form	NOUN
ejpam-6248	101	7	suggests	suggest	VERB
ejpam-6248	101	8	two	two	NUM
ejpam-6248	101	9	possibilities	possibility	NOUN
ejpam-6248	101	10	,	,	PUNCT
ejpam-6248	101	11	since	since	SCONJ
ejpam-6248	101	12	the	the	DET
ejpam-6248	101	13	product	product	NOUN
ejpam-6248	101	14	of	of	ADP
ejpam-6248	101	15	two	two	NUM
ejpam-6248	101	16	terms	term	NOUN
ejpam-6248	101	17	is	be	AUX
ejpam-6248	101	18	zero	zero	NUM
ejpam-6248	101	19	:	:	PUNCT
ejpam-6248	101	20	z.	z.	PROPN
ejpam-6248	101	21	haider	haider	PROPN
ejpam-6248	101	22	et	et	PROPN
ejpam-6248	101	23	al	al	PROPN
ejpam-6248	101	24	.	.	PUNCT
ejpam-6248	101	25	/	/	SYM
ejpam-6248	101	26	eur	eur	PROPN
ejpam-6248	101	27	.	.	PUNCT
ejpam-6248	102	1	j.	j.	PROPN
ejpam-6248	102	2	pure	pure	PROPN
ejpam-6248	102	3	appl	appl	PROPN
ejpam-6248	102	4	.	.	PROPN
ejpam-6248	102	5	math	math	PROPN
ejpam-6248	102	6	,	,	PUNCT
ejpam-6248	102	7	18	18	NUM
ejpam-6248	102	8	(	(	PUNCT
ejpam-6248	102	9	3	3	NUM
ejpam-6248	102	10	)	)	PUNCT
ejpam-6248	102	11	(	(	PUNCT
ejpam-6248	102	12	2025	2025	NUM
ejpam-6248	102	13	)	)	PUNCT
ejpam-6248	102	14	,	,	PUNCT
ejpam-6248	102	15	6248	6248	NUM
ejpam-6248	102	16	7	7	NUM
ejpam-6248	102	17	of	of	ADP
ejpam-6248	102	18	20	20	NUM
ejpam-6248	102	19	i.	i.	NOUN
ejpam-6248	102	20	f	f	PROPN
ejpam-6248	102	21	′′(ξ	′′(ξ	PROPN
ejpam-6248	102	22	)	)	PUNCT
ejpam-6248	102	23	=	=	SYM
ejpam-6248	102	24	0	0	PUNCT
ejpam-6248	103	1	(	(	PUNCT
ejpam-6248	103	2	trivial	trivial	ADJ
ejpam-6248	103	3	case	case	NOUN
ejpam-6248	103	4	)	)	PUNCT
ejpam-6248	103	5	ii	ii	PROPN
ejpam-6248	103	6	.	.	PUNCT
ejpam-6248	104	1	f	f	PROPN
ejpam-6248	105	1	′(ξ)−	′(ξ)−	PROPN
ejpam-6248	105	2	2ξ	2ξ	NUM
ejpam-6248	105	3	=	=	SYM
ejpam-6248	105	4	0	0	PUNCT
ejpam-6248	105	5	(	(	PUNCT
ejpam-6248	105	6	non	non	ADJ
ejpam-6248	105	7	-	-	ADJ
ejpam-6248	105	8	trivial	trivial	ADJ
ejpam-6248	105	9	case	case	NOUN
ejpam-6248	105	10	)	)	PUNCT
ejpam-6248	105	11	we	we	PRON
ejpam-6248	105	12	focus	focus	VERB
ejpam-6248	105	13	on	on	ADP
ejpam-6248	105	14	the	the	DET
ejpam-6248	105	15	non	non	ADJ
ejpam-6248	105	16	-	-	ADJ
ejpam-6248	105	17	trivial	trivial	ADJ
ejpam-6248	105	18	case	case	NOUN
ejpam-6248	105	19	:	:	PUNCT
ejpam-6248	105	20	f	f	PROPN
ejpam-6248	105	21	′(ξ)−	′(ξ)−	PROPN
ejpam-6248	105	22	2ξ	2ξ	NUM
ejpam-6248	105	23	=	=	SYM
ejpam-6248	106	1	0	0	NUM
ejpam-6248	106	2	.	.	PUNCT
ejpam-6248	107	1	f	f	PROPN
ejpam-6248	107	2	′(ξ	′(ξ	PROPN
ejpam-6248	107	3	)	)	PUNCT
ejpam-6248	107	4	=	=	PUNCT
ejpam-6248	108	1	2ξ	2ξ	X
ejpam-6248	108	2	.	.	PUNCT
ejpam-6248	109	1	(	(	PUNCT
ejpam-6248	109	2	22	22	NUM
ejpam-6248	109	3	)	)	PUNCT
ejpam-6248	109	4	integrate	integrate	VERB
ejpam-6248	109	5	both	both	DET
ejpam-6248	109	6	sides	side	NOUN
ejpam-6248	109	7	of	of	ADP
ejpam-6248	109	8	equation	equation	NOUN
ejpam-6248	109	9	(	(	PUNCT
ejpam-6248	109	10	22	22	NUM
ejpam-6248	109	11	)	)	PUNCT
ejpam-6248	109	12	w.r.t	w.r.t	VERB
ejpam-6248	109	13	ξ	ξ	PROPN
ejpam-6248	109	14	,	,	PUNCT
ejpam-6248	109	15	we	we	PRON
ejpam-6248	109	16	obtain	obtain	VERB
ejpam-6248	109	17	:	:	PUNCT
ejpam-6248	109	18	f(ξ	f(ξ	X
ejpam-6248	109	19	)	)	PUNCT
ejpam-6248	109	20	=	=	SYM
ejpam-6248	109	21	ξ2	ξ2	NOUN
ejpam-6248	109	22	+	+	CCONJ
ejpam-6248	109	23	c.	c.	NOUN
ejpam-6248	109	24	(	(	PUNCT
ejpam-6248	109	25	23	23	NUM
ejpam-6248	109	26	)	)	PUNCT
ejpam-6248	109	27	where	where	SCONJ
ejpam-6248	109	28	c	c	NOUN
ejpam-6248	109	29	is	be	AUX
ejpam-6248	109	30	an	an	DET
ejpam-6248	109	31	arbitrary	arbitrary	ADJ
ejpam-6248	109	32	constant	constant	NOUN
ejpam-6248	109	33	of	of	ADP
ejpam-6248	109	34	integration	integration	NOUN
ejpam-6248	109	35	.	.	PUNCT
ejpam-6248	110	1	applying	apply	VERB
ejpam-6248	110	2	the	the	DET
ejpam-6248	110	3	similarity	similarity	NOUN
ejpam-6248	110	4	transformations	transformation	NOUN
ejpam-6248	110	5	(	(	PUNCT
ejpam-6248	110	6	18	18	NUM
ejpam-6248	110	7	)	)	PUNCT
ejpam-6248	110	8	and	and	CCONJ
ejpam-6248	110	9	(	(	PUNCT
ejpam-6248	110	10	19	19	NUM
ejpam-6248	110	11	)	)	PUNCT
ejpam-6248	110	12	,	,	PUNCT
ejpam-6248	110	13	together	together	ADV
ejpam-6248	110	14	with	with	ADP
ejpam-6248	110	15	the	the	DET
ejpam-6248	110	16	analytic	analytic	ADJ
ejpam-6248	110	17	solution	solution	NOUN
ejpam-6248	110	18	of	of	ADP
ejpam-6248	110	19	ode	ode	PROPN
ejpam-6248	110	20	in	in	ADP
ejpam-6248	110	21	equation	equation	NOUN
ejpam-6248	110	22	(	(	PUNCT
ejpam-6248	110	23	23	23	NUM
ejpam-6248	110	24	)	)	PUNCT
ejpam-6248	110	25	,	,	PUNCT
ejpam-6248	110	26	we	we	PRON
ejpam-6248	110	27	derive	derive	VERB
ejpam-6248	110	28	the	the	DET
ejpam-6248	110	29	exact	exact	ADJ
ejpam-6248	110	30	solution	solution	NOUN
ejpam-6248	110	31	to	to	ADP
ejpam-6248	110	32	the	the	DET
ejpam-6248	110	33	original	original	ADJ
ejpam-6248	110	34	pde	pde	NOUN
ejpam-6248	110	35	(	(	PUNCT
ejpam-6248	110	36	1	1	NUM
ejpam-6248	110	37	):	):	PUNCT
ejpam-6248	110	38	u(x	u(x	PROPN
ejpam-6248	110	39	,	,	PUNCT
ejpam-6248	110	40	t	t	NOUN
ejpam-6248	110	41	)	)	PUNCT
ejpam-6248	110	42	=	=	SYM
ejpam-6248	111	1	x2	x2	PROPN
ejpam-6248	112	1	+	+	CCONJ
ejpam-6248	112	2	ct2	ct2	PROPN
ejpam-6248	112	3	t	t	PROPN
ejpam-6248	112	4	.	.	PUNCT
ejpam-6248	113	1	(	(	PUNCT
ejpam-6248	113	2	24	24	NUM
ejpam-6248	113	3	)	)	PUNCT
ejpam-6248	113	4	(	(	PUNCT
ejpam-6248	113	5	ii	ii	NOUN
ejpam-6248	113	6	)	)	PUNCT
ejpam-6248	113	7	for	for	ADP
ejpam-6248	113	8	the	the	DET
ejpam-6248	113	9	parameter	parameter	NOUN
ejpam-6248	113	10	values	value	NOUN
ejpam-6248	113	11	m	m	VERB
ejpam-6248	113	12	=	=	SYM
ejpam-6248	113	13	−1	−1	NOUN
ejpam-6248	113	14	and	and	CCONJ
ejpam-6248	113	15	n	n	NOUN
ejpam-6248	113	16	=	=	SYM
ejpam-6248	113	17	−3	−3	PROPN
ejpam-6248	113	18	,	,	PUNCT
ejpam-6248	113	19	the	the	DET
ejpam-6248	113	20	similarity	similarity	NOUN
ejpam-6248	113	21	transformations	transformation	NOUN
ejpam-6248	113	22	given	give	VERB
ejpam-6248	113	23	in	in	ADP
ejpam-6248	113	24	equations	equation	NOUN
ejpam-6248	113	25	(	(	PUNCT
ejpam-6248	113	26	9	9	NUM
ejpam-6248	113	27	)	)	PUNCT
ejpam-6248	113	28	and	and	CCONJ
ejpam-6248	113	29	(	(	PUNCT
ejpam-6248	113	30	10	10	NUM
ejpam-6248	113	31	)	)	PUNCT
ejpam-6248	113	32	reduce	reduce	VERB
ejpam-6248	113	33	to	to	ADP
ejpam-6248	113	34	:	:	PUNCT
ejpam-6248	113	35	ξ	ξ	PROPN
ejpam-6248	113	36	=	=	SYM
ejpam-6248	113	37	xt	xt	PROPN
ejpam-6248	113	38	.	.	PUNCT
ejpam-6248	114	1	(	(	PUNCT
ejpam-6248	114	2	25	25	NUM
ejpam-6248	114	3	)	)	PUNCT
ejpam-6248	114	4	u	u	NOUN
ejpam-6248	114	5	=	=	SYM
ejpam-6248	114	6	f(ξ	f(ξ	PROPN
ejpam-6248	114	7	)	)	PUNCT
ejpam-6248	114	8	t3	t3	NOUN
ejpam-6248	114	9	.	.	PUNCT
ejpam-6248	115	1	(	(	PUNCT
ejpam-6248	115	2	26	26	NUM
ejpam-6248	115	3	)	)	PUNCT
ejpam-6248	115	4	substituting	substitute	VERB
ejpam-6248	115	5	the	the	DET
ejpam-6248	115	6	parameter	parameter	NOUN
ejpam-6248	115	7	values	value	NOUN
ejpam-6248	115	8	m	m	VERB
ejpam-6248	115	9	=	=	SYM
ejpam-6248	115	10	−1	−1	NOUN
ejpam-6248	115	11	and	and	CCONJ
ejpam-6248	115	12	n	n	NOUN
ejpam-6248	115	13	=	=	SYM
ejpam-6248	115	14	−3	−3	PROPN
ejpam-6248	115	15	into	into	ADP
ejpam-6248	115	16	equation	equation	NOUN
ejpam-6248	115	17	(	(	PUNCT
ejpam-6248	115	18	17	17	NUM
ejpam-6248	115	19	)	)	PUNCT
ejpam-6248	115	20	,	,	PUNCT
ejpam-6248	115	21	we	we	PRON
ejpam-6248	115	22	obtain	obtain	VERB
ejpam-6248	115	23	the	the	DET
ejpam-6248	115	24	following	follow	VERB
ejpam-6248	115	25	ordinary	ordinary	ADJ
ejpam-6248	115	26	differential	differential	ADJ
ejpam-6248	115	27	equation	equation	NOUN
ejpam-6248	115	28	(	(	PUNCT
ejpam-6248	115	29	ode	ode	ADJ
ejpam-6248	115	30	):	):	PUNCT
ejpam-6248	115	31	2ξf	2ξf	ADJ
ejpam-6248	115	32	′′(ξ	′′(ξ	NOUN
ejpam-6248	115	33	)	)	PUNCT
ejpam-6248	116	1	+	+	CCONJ
ejpam-6248	116	2	f	f	PROPN
ejpam-6248	116	3	′(ξ)f	′(ξ)f	PROPN
ejpam-6248	116	4	′′(ξ)−	′′(ξ)−	PROPN
ejpam-6248	116	5	4f	4f	NUM
ejpam-6248	116	6	′(ξ	′(ξ	NOUN
ejpam-6248	116	7	)	)	PUNCT
ejpam-6248	116	8	=	=	SYM
ejpam-6248	117	1	0	0	X
ejpam-6248	117	2	.	.	PUNCT
ejpam-6248	118	1	(	(	PUNCT
ejpam-6248	118	2	27	27	NUM
ejpam-6248	118	3	)	)	PUNCT
ejpam-6248	118	4	to	to	PART
ejpam-6248	118	5	simplify	simplify	VERB
ejpam-6248	118	6	,	,	PUNCT
ejpam-6248	118	7	we	we	PRON
ejpam-6248	118	8	let	let	VERB
ejpam-6248	118	9	u	u	PRON
ejpam-6248	118	10	=	=	NOUN
ejpam-6248	118	11	f	f	PROPN
ejpam-6248	118	12	′(ξ	′(ξ	PROPN
ejpam-6248	118	13	)	)	PUNCT
ejpam-6248	118	14	and	and	CCONJ
ejpam-6248	118	15	u′	u′	PROPN
ejpam-6248	118	16	=	=	SYM
ejpam-6248	118	17	f	f	PROPN
ejpam-6248	118	18	′′(ξ	′′(ξ	NUM
ejpam-6248	118	19	)	)	PUNCT
ejpam-6248	118	20	.	.	PUNCT
ejpam-6248	119	1	then	then	ADV
ejpam-6248	119	2	equation	equation	NOUN
ejpam-6248	119	3	(	(	PUNCT
ejpam-6248	119	4	27	27	NUM
ejpam-6248	119	5	)	)	PUNCT
ejpam-6248	119	6	becomes	become	VERB
ejpam-6248	119	7	:	:	PUNCT
ejpam-6248	119	8	2ξu′	2ξu′	PROPN
ejpam-6248	119	9	+	+	CCONJ
ejpam-6248	119	10	uu′	uu′	PROPN
ejpam-6248	120	1	−	−	PROPN
ejpam-6248	120	2	4u	4u	NOUN
ejpam-6248	120	3	=	=	NOUN
ejpam-6248	120	4	0	0	X
ejpam-6248	120	5	.	.	PUNCT
ejpam-6248	121	1	(	(	PUNCT
ejpam-6248	121	2	28	28	NUM
ejpam-6248	121	3	)	)	PUNCT
ejpam-6248	121	4	rewriting	rewrite	VERB
ejpam-6248	121	5	equation	equation	NOUN
ejpam-6248	121	6	(	(	PUNCT
ejpam-6248	121	7	28	28	NUM
ejpam-6248	121	8	)	)	PUNCT
ejpam-6248	121	9	in	in	ADP
ejpam-6248	121	10	a	a	DET
ejpam-6248	121	11	solvable	solvable	ADJ
ejpam-6248	121	12	form	form	NOUN
ejpam-6248	121	13	,	,	PUNCT
ejpam-6248	121	14	we	we	PRON
ejpam-6248	121	15	obtain	obtain	VERB
ejpam-6248	121	16	:	:	PUNCT
ejpam-6248	121	17	u′	u′	PROPN
ejpam-6248	121	18	=	=	SYM
ejpam-6248	121	19	4u	4u	NOUN
ejpam-6248	121	20	u+	u+	NUM
ejpam-6248	121	21	2ξ	2ξ	NUM
ejpam-6248	121	22	.	.	PUNCT
ejpam-6248	122	1	(	(	PUNCT
ejpam-6248	122	2	29	29	NUM
ejpam-6248	122	3	)	)	PUNCT
ejpam-6248	122	4	assuming	assume	VERB
ejpam-6248	122	5	u	u	NOUN
ejpam-6248	122	6	=	=	NOUN
ejpam-6248	122	7	vξ	vξ	PROPN
ejpam-6248	122	8	,	,	PUNCT
ejpam-6248	122	9	so	so	SCONJ
ejpam-6248	122	10	that	that	SCONJ
ejpam-6248	122	11	u′	u′	PRON
ejpam-6248	122	12	=	=	SYM
ejpam-6248	122	13	v	v	PROPN
ejpam-6248	122	14	+	+	CCONJ
ejpam-6248	122	15	v′ξ	v′ξ	NOUN
ejpam-6248	122	16	,	,	PUNCT
ejpam-6248	122	17	and	and	CCONJ
ejpam-6248	122	18	substituting	substitute	VERB
ejpam-6248	122	19	into	into	ADP
ejpam-6248	122	20	equation	equation	NOUN
ejpam-6248	122	21	(	(	PUNCT
ejpam-6248	122	22	29	29	NUM
ejpam-6248	122	23	)	)	PUNCT
ejpam-6248	122	24	,	,	PUNCT
ejpam-6248	122	25	we	we	PRON
ejpam-6248	122	26	obtain	obtain	VERB
ejpam-6248	122	27	:	:	PUNCT
ejpam-6248	122	28	(	(	PUNCT
ejpam-6248	122	29	1	1	NUM
ejpam-6248	122	30	v	v	NOUN
ejpam-6248	122	31	+	+	CCONJ
ejpam-6248	122	32	2	2	NUM
ejpam-6248	122	33	2−	2−	NUM
ejpam-6248	122	34	v	v	NOUN
ejpam-6248	122	35	)	)	PUNCT
ejpam-6248	122	36	dv	dv	PROPN
ejpam-6248	122	37	=	=	PROPN
ejpam-6248	122	38	1	1	NUM
ejpam-6248	122	39	ξ	ξ	PROPN
ejpam-6248	122	40	dξ	dξ	PROPN
ejpam-6248	122	41	.	.	PUNCT
ejpam-6248	123	1	(	(	PUNCT
ejpam-6248	123	2	30	30	X
ejpam-6248	123	3	)	)	PUNCT
ejpam-6248	123	4	integrating	integrate	VERB
ejpam-6248	123	5	both	both	DET
ejpam-6248	123	6	sides	side	NOUN
ejpam-6248	123	7	of	of	ADP
ejpam-6248	123	8	equation	equation	NOUN
ejpam-6248	123	9	(	(	PUNCT
ejpam-6248	123	10	30	30	NUM
ejpam-6248	123	11	)	)	PUNCT
ejpam-6248	123	12	yields	yield	NOUN
ejpam-6248	123	13	:	:	PUNCT
ejpam-6248	123	14	ln	ln	NOUN
ejpam-6248	123	15	v	v	NOUN
ejpam-6248	123	16	−	−	PROPN
ejpam-6248	123	17	2	2	NUM
ejpam-6248	123	18	ln(2−	ln(2−	NOUN
ejpam-6248	123	19	v	v	NOUN
ejpam-6248	123	20	)	)	PUNCT
ejpam-6248	123	21	=	=	PUNCT
ejpam-6248	123	22	ln	ln	PROPN
ejpam-6248	123	23	ξ	ξ	PROPN
ejpam-6248	123	24	+	+	PUNCT
ejpam-6248	123	25	lnc1	lnc1	NOUN
ejpam-6248	123	26	.	.	PUNCT
ejpam-6248	124	1	(	(	PUNCT
ejpam-6248	124	2	31	31	NUM
ejpam-6248	124	3	)	)	PUNCT
ejpam-6248	124	4	z.	z.	PROPN
ejpam-6248	124	5	haider	haider	PROPN
ejpam-6248	124	6	et	et	PROPN
ejpam-6248	124	7	al	al	PROPN
ejpam-6248	124	8	.	.	PUNCT
ejpam-6248	124	9	/	/	SYM
ejpam-6248	124	10	eur	eur	PROPN
ejpam-6248	124	11	.	.	PUNCT
ejpam-6248	125	1	j.	j.	PROPN
ejpam-6248	125	2	pure	pure	PROPN
ejpam-6248	125	3	appl	appl	PROPN
ejpam-6248	125	4	.	.	PROPN
ejpam-6248	125	5	math	math	PROPN
ejpam-6248	125	6	,	,	PUNCT
ejpam-6248	125	7	18	18	NUM
ejpam-6248	125	8	(	(	PUNCT
ejpam-6248	125	9	3	3	NUM
ejpam-6248	125	10	)	)	PUNCT
ejpam-6248	125	11	(	(	PUNCT
ejpam-6248	125	12	2025	2025	NUM
ejpam-6248	125	13	)	)	PUNCT
ejpam-6248	125	14	,	,	PUNCT
ejpam-6248	125	15	6248	6248	NUM
ejpam-6248	125	16	8	8	NUM
ejpam-6248	125	17	of	of	ADP
ejpam-6248	125	18	20	20	NUM
ejpam-6248	125	19	figure	figure	NOUN
ejpam-6248	125	20	3	3	NUM
ejpam-6248	125	21	:	:	PUNCT
ejpam-6248	125	22	3d	3d	NUM
ejpam-6248	125	23	plot	plot	NOUN
ejpam-6248	125	24	of	of	ADP
ejpam-6248	125	25	(	(	PUNCT
ejpam-6248	125	26	36	36	NUM
ejpam-6248	125	27	)	)	PUNCT
ejpam-6248	125	28	for	for	ADP
ejpam-6248	125	29	c1	c1	NOUN
ejpam-6248	125	30	=	=	PUNCT
ejpam-6248	125	31	1	1	NUM
ejpam-6248	125	32	and	and	CCONJ
ejpam-6248	125	33	c2	c2	PROPN
ejpam-6248	125	34	=	=	SYM
ejpam-6248	125	35	1	1	X
ejpam-6248	125	36	.	.	PUNCT
ejpam-6248	126	1	simplifying	simplify	VERB
ejpam-6248	126	2	equation	equation	NOUN
ejpam-6248	126	3	(	(	PUNCT
ejpam-6248	126	4	31	31	NUM
ejpam-6248	126	5	)	)	PUNCT
ejpam-6248	126	6	,	,	PUNCT
ejpam-6248	126	7	we	we	PRON
ejpam-6248	126	8	obtain	obtain	VERB
ejpam-6248	126	9	:	:	PUNCT
ejpam-6248	126	10	vξ	vξ	PROPN
ejpam-6248	126	11	=	=	PUNCT
ejpam-6248	126	12	(	(	PUNCT
ejpam-6248	126	13	4c1ξ	4c1ξ	NOUN
ejpam-6248	127	1	+	+	CCONJ
ejpam-6248	127	2	1	1	X
ejpam-6248	127	3	)	)	PUNCT
ejpam-6248	127	4	+	+	CCONJ
ejpam-6248	127	5	√	√	ADJ
ejpam-6248	127	6	8c1ξ	8c1ξ	NOUN
ejpam-6248	128	1	+	+	CCONJ
ejpam-6248	128	2	1	1	NUM
ejpam-6248	128	3	2c1	2c1	NUM
ejpam-6248	128	4	.	.	PUNCT
ejpam-6248	129	1	(	(	PUNCT
ejpam-6248	129	2	32	32	NUM
ejpam-6248	129	3	)	)	PUNCT
ejpam-6248	129	4	since	since	SCONJ
ejpam-6248	129	5	vξ	vξ	NOUN
ejpam-6248	129	6	=	=	PUNCT
ejpam-6248	129	7	u	u	PROPN
ejpam-6248	129	8	and	and	CCONJ
ejpam-6248	129	9	u	u	NOUN
ejpam-6248	129	10	=	=	PROPN
ejpam-6248	129	11	f	f	PROPN
ejpam-6248	129	12	′(ξ	′(ξ	PROPN
ejpam-6248	129	13	)	)	PUNCT
ejpam-6248	129	14	,	,	PUNCT
ejpam-6248	129	15	equation	equation	NOUN
ejpam-6248	129	16	(	(	PUNCT
ejpam-6248	129	17	32	32	NUM
ejpam-6248	129	18	)	)	PUNCT
ejpam-6248	129	19	becomes	become	VERB
ejpam-6248	129	20	:	:	PUNCT
ejpam-6248	129	21	f	f	PROPN
ejpam-6248	129	22	′(ξ	′(ξ	NOUN
ejpam-6248	129	23	)	)	PUNCT
ejpam-6248	129	24	=	=	SYM
ejpam-6248	130	1	(	(	PUNCT
ejpam-6248	130	2	4c1ξ	4c1ξ	NOUN
ejpam-6248	130	3	+	+	CCONJ
ejpam-6248	130	4	1	1	X
ejpam-6248	130	5	)	)	PUNCT
ejpam-6248	131	1	+	+	CCONJ
ejpam-6248	131	2	√	√	ADJ
ejpam-6248	131	3	8c1ξ	8c1ξ	NOUN
ejpam-6248	132	1	+	+	CCONJ
ejpam-6248	132	2	1	1	NUM
ejpam-6248	132	3	2c1	2c1	NUM
ejpam-6248	132	4	.	.	PUNCT
ejpam-6248	133	1	(	(	PUNCT
ejpam-6248	133	2	33	33	NUM
ejpam-6248	133	3	)	)	PUNCT
ejpam-6248	133	4	after	after	ADP
ejpam-6248	133	5	simplification	simplification	NOUN
ejpam-6248	133	6	,	,	PUNCT
ejpam-6248	133	7	equation	equation	NOUN
ejpam-6248	133	8	(	(	PUNCT
ejpam-6248	133	9	33	33	NUM
ejpam-6248	133	10	)	)	PUNCT
ejpam-6248	133	11	becomes	become	VERB
ejpam-6248	133	12	:	:	PUNCT
ejpam-6248	133	13	f	f	PROPN
ejpam-6248	133	14	′(ξ	′(ξ	NOUN
ejpam-6248	133	15	)	)	PUNCT
ejpam-6248	133	16	=	=	PUNCT
ejpam-6248	134	1	2ξ	2ξ	NOUN
ejpam-6248	134	2	+	+	CCONJ
ejpam-6248	134	3	1	1	NUM
ejpam-6248	134	4	2c1	2c1	NUM
ejpam-6248	135	1	+	+	CCONJ
ejpam-6248	135	2	√	√	ADJ
ejpam-6248	135	3	8c1ξ	8c1ξ	NOUN
ejpam-6248	136	1	+	+	CCONJ
ejpam-6248	136	2	1	1	NUM
ejpam-6248	136	3	2c1	2c1	NUM
ejpam-6248	136	4	.	.	PUNCT
ejpam-6248	137	1	(	(	PUNCT
ejpam-6248	137	2	34	34	NUM
ejpam-6248	137	3	)	)	PUNCT
ejpam-6248	137	4	integrating	integrate	VERB
ejpam-6248	137	5	both	both	DET
ejpam-6248	137	6	sides	side	NOUN
ejpam-6248	137	7	of	of	ADP
ejpam-6248	137	8	equation	equation	NOUN
ejpam-6248	137	9	(	(	PUNCT
ejpam-6248	137	10	34	34	NUM
ejpam-6248	137	11	)	)	PUNCT
ejpam-6248	137	12	gives	give	VERB
ejpam-6248	137	13	the	the	DET
ejpam-6248	137	14	analytic	analytic	ADJ
ejpam-6248	137	15	solution	solution	NOUN
ejpam-6248	137	16	to	to	ADP
ejpam-6248	137	17	the	the	DET
ejpam-6248	137	18	ode	ode	PROPN
ejpam-6248	137	19	(	(	PUNCT
ejpam-6248	137	20	27	27	NUM
ejpam-6248	137	21	):	):	PUNCT
ejpam-6248	137	22	f(ξ	f(ξ	NOUN
ejpam-6248	137	23	)	)	PUNCT
ejpam-6248	138	1	=	=	SYM
ejpam-6248	138	2	ξ2	ξ2	NOUN
ejpam-6248	138	3	+	+	CCONJ
ejpam-6248	139	1	ξ	ξ	X
ejpam-6248	139	2	2c1	2c1	NUM
ejpam-6248	140	1	+	+	CCONJ
ejpam-6248	140	2	(	(	PUNCT
ejpam-6248	140	3	8c1ξ	8c1ξ	NOUN
ejpam-6248	140	4	+	+	CCONJ
ejpam-6248	140	5	1	1	X
ejpam-6248	140	6	)	)	PUNCT
ejpam-6248	140	7	3	3	NUM
ejpam-6248	140	8	2	2	NUM
ejpam-6248	140	9	24c2	24c2	NUM
ejpam-6248	140	10	1	1	NUM
ejpam-6248	140	11	+	+	NUM
ejpam-6248	140	12	c2	c2	PROPN
ejpam-6248	140	13	.	.	PUNCT
ejpam-6248	141	1	(	(	PUNCT
ejpam-6248	141	2	35	35	NUM
ejpam-6248	141	3	)	)	PUNCT
ejpam-6248	141	4	z.	z.	PROPN
ejpam-6248	141	5	haider	haider	PROPN
ejpam-6248	141	6	et	et	PROPN
ejpam-6248	141	7	al	al	PROPN
ejpam-6248	141	8	.	.	PUNCT
ejpam-6248	141	9	/	/	SYM
ejpam-6248	141	10	eur	eur	PROPN
ejpam-6248	141	11	.	.	PUNCT
ejpam-6248	142	1	j.	j.	PROPN
ejpam-6248	142	2	pure	pure	PROPN
ejpam-6248	142	3	appl	appl	PROPN
ejpam-6248	142	4	.	.	PROPN
ejpam-6248	142	5	math	math	PROPN
ejpam-6248	142	6	,	,	PUNCT
ejpam-6248	142	7	18	18	NUM
ejpam-6248	142	8	(	(	PUNCT
ejpam-6248	142	9	3	3	NUM
ejpam-6248	142	10	)	)	PUNCT
ejpam-6248	142	11	(	(	PUNCT
ejpam-6248	142	12	2025	2025	NUM
ejpam-6248	142	13	)	)	PUNCT
ejpam-6248	142	14	,	,	PUNCT
ejpam-6248	142	15	6248	6248	NUM
ejpam-6248	142	16	9	9	NUM
ejpam-6248	142	17	of	of	ADP
ejpam-6248	142	18	20	20	NUM
ejpam-6248	142	19	using	use	VERB
ejpam-6248	142	20	the	the	DET
ejpam-6248	142	21	similarity	similarity	NOUN
ejpam-6248	142	22	transformations	transformation	NOUN
ejpam-6248	142	23	(	(	PUNCT
ejpam-6248	142	24	25	25	NUM
ejpam-6248	142	25	)	)	PUNCT
ejpam-6248	142	26	and	and	CCONJ
ejpam-6248	142	27	(	(	PUNCT
ejpam-6248	142	28	26	26	NUM
ejpam-6248	142	29	)	)	PUNCT
ejpam-6248	142	30	,	,	PUNCT
ejpam-6248	142	31	along	along	ADP
ejpam-6248	142	32	with	with	ADP
ejpam-6248	142	33	the	the	DET
ejpam-6248	142	34	analytic	analytic	ADJ
ejpam-6248	142	35	solution	solution	NOUN
ejpam-6248	142	36	of	of	ADP
ejpam-6248	142	37	the	the	DET
ejpam-6248	142	38	ode	ode	NOUN
ejpam-6248	142	39	in	in	ADP
ejpam-6248	142	40	equation	equation	NOUN
ejpam-6248	142	41	(	(	PUNCT
ejpam-6248	142	42	35	35	NUM
ejpam-6248	142	43	)	)	PUNCT
ejpam-6248	142	44	,	,	PUNCT
ejpam-6248	142	45	we	we	PRON
ejpam-6248	142	46	obtain	obtain	VERB
ejpam-6248	142	47	the	the	DET
ejpam-6248	142	48	exact	exact	ADJ
ejpam-6248	142	49	solution	solution	NOUN
ejpam-6248	142	50	to	to	ADP
ejpam-6248	142	51	the	the	DET
ejpam-6248	142	52	original	original	ADJ
ejpam-6248	142	53	pde	pde	NOUN
ejpam-6248	142	54	(	(	PUNCT
ejpam-6248	142	55	1	1	NUM
ejpam-6248	142	56	):	):	PUNCT
ejpam-6248	142	57	u(x	u(x	PROPN
ejpam-6248	142	58	,	,	PUNCT
ejpam-6248	142	59	t	t	PROPN
ejpam-6248	142	60	)	)	PUNCT
ejpam-6248	142	61	=	=	SYM
ejpam-6248	143	1	x2t2	x2t2	PROPN
ejpam-6248	144	1	+	+	NUM
ejpam-6248	144	2	xt	xt	ADP
ejpam-6248	144	3	2c1	2c1	NUM
ejpam-6248	145	1	−	−	PROPN
ejpam-6248	146	1	(	(	PUNCT
ejpam-6248	146	2	8c1xt+1	8c1xt+1	NOUN
ejpam-6248	146	3	)	)	PUNCT
ejpam-6248	146	4	3	3	NUM
ejpam-6248	146	5	2	2	NUM
ejpam-6248	146	6	24c2	24c2	NUM
ejpam-6248	146	7	1	1	NUM
ejpam-6248	147	1	+	+	CCONJ
ejpam-6248	147	2	c2	c2	PROPN
ejpam-6248	147	3	t3	t3	PROPN
ejpam-6248	147	4	.	.	PUNCT
ejpam-6248	148	1	(	(	PUNCT
ejpam-6248	148	2	36	36	NUM
ejpam-6248	148	3	)	)	PUNCT
ejpam-6248	148	4	case:-2	case:-2	NOUN
ejpam-6248	148	5	we	we	PRON
ejpam-6248	148	6	introduce	introduce	VERB
ejpam-6248	148	7	the	the	DET
ejpam-6248	148	8	following	follow	VERB
ejpam-6248	148	9	similarity	similarity	NOUN
ejpam-6248	148	10	function	function	NOUN
ejpam-6248	148	11	transformation	transformation	NOUN
ejpam-6248	148	12	:	:	PUNCT
ejpam-6248	148	13	ξ	ξ	X
ejpam-6248	148	14	=	=	SYM
ejpam-6248	148	15	y	y	PROPN
ejpam-6248	148	16	xm	xm	PROPN
ejpam-6248	148	17	.	.	PUNCT
ejpam-6248	149	1	(	(	PUNCT
ejpam-6248	149	2	37	37	NUM
ejpam-6248	149	3	)	)	PUNCT
ejpam-6248	149	4	u	u	NOUN
ejpam-6248	149	5	=	=	PROPN
ejpam-6248	149	6	xnf(ξ	xnf(ξ	PROPN
ejpam-6248	149	7	)	)	PUNCT
ejpam-6248	149	8	.	.	PUNCT
ejpam-6248	150	1	(	(	PUNCT
ejpam-6248	150	2	38	38	NUM
ejpam-6248	150	3	)	)	PUNCT
ejpam-6248	150	4	differentiating	differentiate	VERB
ejpam-6248	150	5	equations	equation	NOUN
ejpam-6248	150	6	(	(	PUNCT
ejpam-6248	150	7	37	37	NUM
ejpam-6248	150	8	)	)	PUNCT
ejpam-6248	150	9	and	and	CCONJ
ejpam-6248	150	10	(	(	PUNCT
ejpam-6248	150	11	38	38	NUM
ejpam-6248	150	12	)	)	PUNCT
ejpam-6248	150	13	with	with	ADP
ejpam-6248	150	14	respect	respect	NOUN
ejpam-6248	150	15	to	to	ADP
ejpam-6248	150	16	equation	equation	NOUN
ejpam-6248	150	17	(	(	PUNCT
ejpam-6248	150	18	1	1	NUM
ejpam-6248	150	19	)	)	PUNCT
ejpam-6248	150	20	,	,	PUNCT
ejpam-6248	150	21	we	we	PRON
ejpam-6248	150	22	obtain	obtain	VERB
ejpam-6248	150	23	:	:	PUNCT
ejpam-6248	150	24	ux	ux	PROPN
ejpam-6248	150	25	=	=	SYM
ejpam-6248	150	26	nxn−1f(ξ)−myxn−m−1f	nxn−1f(ξ)−myxn−m−1f	NUM
ejpam-6248	150	27	′(ξ	′(ξ	NOUN
ejpam-6248	150	28	)	)	PUNCT
ejpam-6248	150	29	.	.	PUNCT
ejpam-6248	151	1	(	(	PUNCT
ejpam-6248	151	2	39	39	NUM
ejpam-6248	151	3	)	)	PUNCT
ejpam-6248	151	4	uyy	uyy	PROPN
ejpam-6248	151	5	=	=	PUNCT
ejpam-6248	152	1	xn−2mf	xn−2mf	NUM
ejpam-6248	152	2	′′(ξ	′′(ξ	PROPN
ejpam-6248	152	3	)	)	PUNCT
ejpam-6248	152	4	.	.	PUNCT
ejpam-6248	153	1	(	(	PUNCT
ejpam-6248	153	2	40	40	NUM
ejpam-6248	153	3	)	)	PUNCT
ejpam-6248	153	4	uxx	uxx	NOUN
ejpam-6248	154	1	=	=	PUNCT
ejpam-6248	155	1	xn−2(n2	xn−2(n2	PROPN
ejpam-6248	155	2	−	−	NUM
ejpam-6248	155	3	n)f(ξ)−	n)f(ξ)−	NUM
ejpam-6248	155	4	(	(	PUNCT
ejpam-6248	155	5	2mnξ	2mnξ	PROPN
ejpam-6248	155	6	+	+	ADJ
ejpam-6248	155	7	m2ξ	m2ξ	PROPN
ejpam-6248	155	8	+	+	ADJ
ejpam-6248	155	9	mξ)f	mξ)f	PROPN
ejpam-6248	155	10	′(ξ	′(ξ	NOUN
ejpam-6248	155	11	)	)	PUNCT
ejpam-6248	156	1	+	+	ADJ
ejpam-6248	156	2	m2y2x−2f	m2y2x−2f	NOUN
ejpam-6248	156	3	′′(ξ	′′(ξ	NOUN
ejpam-6248	156	4	)	)	PUNCT
ejpam-6248	156	5	.	.	PUNCT
ejpam-6248	157	1	(	(	PUNCT
ejpam-6248	157	2	41	41	NUM
ejpam-6248	157	3	)	)	PUNCT
ejpam-6248	157	4	uxt	uxt	NOUN
ejpam-6248	157	5	=	=	SYM
ejpam-6248	157	6	0	0	NUM
ejpam-6248	157	7	.	.	PUNCT
ejpam-6248	158	1	(	(	PUNCT
ejpam-6248	158	2	42	42	X
ejpam-6248	158	3	)	)	PUNCT
ejpam-6248	158	4	using	use	VERB
ejpam-6248	158	5	equations	equation	NOUN
ejpam-6248	158	6	(	(	PUNCT
ejpam-6248	158	7	39	39	NUM
ejpam-6248	158	8	)	)	PUNCT
ejpam-6248	158	9	,	,	PUNCT
ejpam-6248	158	10	(	(	PUNCT
ejpam-6248	158	11	40	40	NUM
ejpam-6248	158	12	)	)	PUNCT
ejpam-6248	158	13	,	,	PUNCT
ejpam-6248	158	14	(	(	PUNCT
ejpam-6248	158	15	41	41	NUM
ejpam-6248	158	16	)	)	PUNCT
ejpam-6248	158	17	and	and	CCONJ
ejpam-6248	158	18	(	(	PUNCT
ejpam-6248	158	19	42	42	NUM
ejpam-6248	158	20	)	)	PUNCT
ejpam-6248	158	21	in	in	ADP
ejpam-6248	158	22	equation	equation	NOUN
ejpam-6248	158	23	(	(	PUNCT
ejpam-6248	158	24	1	1	NUM
ejpam-6248	158	25	)	)	PUNCT
ejpam-6248	158	26	,	,	PUNCT
ejpam-6248	158	27	we	we	PRON
ejpam-6248	158	28	obtain	obtain	VERB
ejpam-6248	158	29	the	the	DET
ejpam-6248	158	30	following	follow	VERB
ejpam-6248	158	31	ordinary	ordinary	ADJ
ejpam-6248	158	32	differential	differential	ADJ
ejpam-6248	158	33	equation	equation	NOUN
ejpam-6248	158	34	(	(	PUNCT
ejpam-6248	158	35	ode	ode	PROPN
ejpam-6248	158	36	):	):	PUNCT
ejpam-6248	158	37	(	(	PUNCT
ejpam-6248	158	38	m3	m3	PROPN
ejpam-6248	158	39	−	−	PROPN
ejpam-6248	158	40	n2)f2(ξ	n2)f2(ξ	NOUN
ejpam-6248	158	41	)	)	PUNCT
ejpam-6248	158	42	+	+	CCONJ
ejpam-6248	158	43	(	(	PUNCT
ejpam-6248	158	44	2mn−	2mn−	NUM
ejpam-6248	158	45	3mn2	3mn2	NUM
ejpam-6248	158	46	+	+	CCONJ
ejpam-6248	158	47	nm2)ξf(ξ)f	nm2)ξf(ξ)f	ADJ
ejpam-6248	158	48	′(ξ	′(ξ	NOUN
ejpam-6248	158	49	)	)	PUNCT
ejpam-6248	159	1	+	+	CCONJ
ejpam-6248	159	2	n2m2ξ2f(ξ)f	n2m2ξ2f(ξ)f	ADJ
ejpam-6248	159	3	′′(ξ	′′(ξ	NOUN
ejpam-6248	159	4	)	)	PUNCT
ejpam-6248	160	1	+	+	CCONJ
ejpam-6248	160	2	(	(	PUNCT
ejpam-6248	160	3	2m2n−m2	2m2n−m2	NUM
ejpam-6248	160	4	−m3)ξ2f	−m3)ξ2f	NOUN
ejpam-6248	160	5	′2(ξ)−m3ξ3f	′2(ξ)−m3ξ3f	ADJ
ejpam-6248	160	6	′(ξ)f	′(ξ)f	PROPN
ejpam-6248	160	7	′′(ξ)−	′′(ξ)−	PROPN
ejpam-6248	160	8	x−2m−n+3f	x−2m−n+3f	PROPN
ejpam-6248	160	9	′′(ξ	′′(ξ	NUM
ejpam-6248	160	10	)	)	PUNCT
ejpam-6248	160	11	=	=	NOUN
ejpam-6248	160	12	0	0	X
ejpam-6248	160	13	.	.	PUNCT
ejpam-6248	161	1	(	(	PUNCT
ejpam-6248	161	2	43	43	NUM
ejpam-6248	161	3	)	)	PUNCT
ejpam-6248	161	4	the	the	DET
ejpam-6248	161	5	last	last	ADJ
ejpam-6248	161	6	term	term	NOUN
ejpam-6248	161	7	in	in	ADP
ejpam-6248	161	8	equation	equation	NOUN
ejpam-6248	161	9	(	(	PUNCT
ejpam-6248	161	10	43	43	NUM
ejpam-6248	161	11	)	)	PUNCT
ejpam-6248	161	12	contains	contain	VERB
ejpam-6248	161	13	the	the	DET
ejpam-6248	161	14	factor	factor	NOUN
ejpam-6248	161	15	x−2m−n+3	x−2m−n+3	PROPN
ejpam-6248	161	16	,	,	PUNCT
ejpam-6248	161	17	which	which	PRON
ejpam-6248	161	18	must	must	AUX
ejpam-6248	161	19	equal	equal	VERB
ejpam-6248	161	20	unity	unity	NOUN
ejpam-6248	161	21	(	(	PUNCT
ejpam-6248	161	22	i.e.	i.e.	X
ejpam-6248	161	23	,	,	PUNCT
ejpam-6248	161	24	x0	x0	PROPN
ejpam-6248	161	25	)	)	PUNCT
ejpam-6248	161	26	to	to	PART
ejpam-6248	161	27	ensure	ensure	VERB
ejpam-6248	161	28	dimensional	dimensional	ADJ
ejpam-6248	161	29	consistency	consistency	NOUN
ejpam-6248	161	30	.	.	PUNCT
ejpam-6248	162	1	this	this	PRON
ejpam-6248	162	2	leads	lead	VERB
ejpam-6248	162	3	to	to	ADP
ejpam-6248	162	4	the	the	DET
ejpam-6248	162	5	condition	condition	NOUN
ejpam-6248	162	6	n	n	NOUN
ejpam-6248	162	7	=	=	SYM
ejpam-6248	162	8	−2	−2	NOUN
ejpam-6248	162	9	m	m	VERB
ejpam-6248	162	10	+	+	NOUN
ejpam-6248	162	11	3	3	X
ejpam-6248	162	12	.	.	X
ejpam-6248	162	13	for	for	ADP
ejpam-6248	162	14	a	a	DET
ejpam-6248	162	15	few	few	ADJ
ejpam-6248	162	16	values	value	NOUN
ejpam-6248	162	17	of	of	ADP
ejpam-6248	162	18	m	m	PROPN
ejpam-6248	162	19	and	and	CCONJ
ejpam-6248	162	20	n	n	CCONJ
ejpam-6248	162	21	,	,	PUNCT
ejpam-6248	162	22	we	we	PRON
ejpam-6248	162	23	are	be	AUX
ejpam-6248	162	24	able	able	ADJ
ejpam-6248	162	25	to	to	PART
ejpam-6248	162	26	find	find	VERB
ejpam-6248	162	27	the	the	DET
ejpam-6248	162	28	solution	solution	NOUN
ejpam-6248	162	29	of	of	ADP
ejpam-6248	162	30	ode	ode	PROPN
ejpam-6248	162	31	(	(	PUNCT
ejpam-6248	162	32	43	43	NUM
ejpam-6248	162	33	)	)	PUNCT
ejpam-6248	162	34	.	.	PUNCT
ejpam-6248	163	1	however	however	ADV
ejpam-6248	163	2	,	,	PUNCT
ejpam-6248	163	3	for	for	ADP
ejpam-6248	163	4	all	all	DET
ejpam-6248	163	5	values	value	NOUN
ejpam-6248	163	6	of	of	ADP
ejpam-6248	163	7	these	these	DET
ejpam-6248	163	8	parameters	parameter	NOUN
ejpam-6248	163	9	,	,	PUNCT
ejpam-6248	163	10	the	the	DET
ejpam-6248	163	11	general	general	ADJ
ejpam-6248	163	12	solution	solution	NOUN
ejpam-6248	163	13	of	of	ADP
ejpam-6248	163	14	the	the	PRON
ejpam-6248	163	15	ode	ode	PROPN
ejpam-6248	163	16	(	(	PUNCT
ejpam-6248	163	17	43	43	NUM
ejpam-6248	163	18	)	)	PUNCT
ejpam-6248	163	19	can	can	AUX
ejpam-6248	163	20	not	not	PART
ejpam-6248	163	21	be	be	AUX
ejpam-6248	163	22	obtained	obtain	VERB
ejpam-6248	163	23	.	.	PUNCT
ejpam-6248	164	1	n	n	NOUN
ejpam-6248	164	2	=	=	SYM
ejpam-6248	164	3	−2m+	−2m+	NOUN
ejpam-6248	164	4	3	3	NUM
ejpam-6248	164	5	m	m	NOUN
ejpam-6248	164	6	1	1	NUM
ejpam-6248	164	7	0	0	NUM
ejpam-6248	164	8	n	n	CCONJ
ejpam-6248	164	9	1	1	NUM
ejpam-6248	164	10	3	3	NUM
ejpam-6248	164	11	table	table	NOUN
ejpam-6248	164	12	2	2	NUM
ejpam-6248	164	13	.	.	PUNCT
ejpam-6248	164	14	specific	specific	ADJ
ejpam-6248	164	15	values	value	NOUN
ejpam-6248	164	16	of	of	ADP
ejpam-6248	164	17	m	m	PROPN
ejpam-6248	164	18	and	and	CCONJ
ejpam-6248	164	19	n	n	PROPN
ejpam-6248	164	20	for	for	ADP
ejpam-6248	164	21	obtainig	obtainig	NOUN
ejpam-6248	164	22	exact	exact	ADJ
ejpam-6248	164	23	solutions	solution	NOUN
ejpam-6248	164	24	family	family	NOUN
ejpam-6248	164	25	solutions	solution	NOUN
ejpam-6248	164	26	(	(	PUNCT
ejpam-6248	164	27	i	i	NOUN
ejpam-6248	164	28	)	)	PUNCT
ejpam-6248	164	29	for	for	ADP
ejpam-6248	164	30	the	the	DET
ejpam-6248	164	31	parameter	parameter	NOUN
ejpam-6248	164	32	values	value	VERB
ejpam-6248	164	33	m	m	VERB
ejpam-6248	164	34	=	=	SYM
ejpam-6248	164	35	1	1	NUM
ejpam-6248	164	36	and	and	CCONJ
ejpam-6248	164	37	n	n	CCONJ
ejpam-6248	164	38	=	=	SYM
ejpam-6248	164	39	1	1	NUM
ejpam-6248	164	40	,	,	PUNCT
ejpam-6248	164	41	the	the	DET
ejpam-6248	164	42	similarity	similarity	NOUN
ejpam-6248	164	43	transformations	transformation	NOUN
ejpam-6248	164	44	(	(	PUNCT
ejpam-6248	164	45	37	37	NUM
ejpam-6248	164	46	)	)	PUNCT
ejpam-6248	164	47	and	and	CCONJ
ejpam-6248	164	48	(	(	PUNCT
ejpam-6248	164	49	38	38	NUM
ejpam-6248	164	50	)	)	PUNCT
ejpam-6248	164	51	reduce	reduce	VERB
ejpam-6248	164	52	to	to	ADP
ejpam-6248	164	53	:	:	PUNCT
ejpam-6248	164	54	ξ	ξ	PROPN
ejpam-6248	164	55	=	=	SYM
ejpam-6248	164	56	y	y	PROPN
ejpam-6248	164	57	x	x	PROPN
ejpam-6248	164	58	.	.	PUNCT
ejpam-6248	165	1	(	(	PUNCT
ejpam-6248	165	2	44	44	NUM
ejpam-6248	165	3	)	)	PUNCT
ejpam-6248	165	4	u	u	NOUN
ejpam-6248	165	5	=	=	NOUN
ejpam-6248	165	6	xf(ξ	xf(ξ	PROPN
ejpam-6248	165	7	)	)	PUNCT
ejpam-6248	165	8	.	.	PUNCT
ejpam-6248	166	1	(	(	PUNCT
ejpam-6248	166	2	45	45	NUM
ejpam-6248	166	3	)	)	PUNCT
ejpam-6248	166	4	z.	z.	PROPN
ejpam-6248	166	5	haider	haider	PROPN
ejpam-6248	166	6	et	et	PROPN
ejpam-6248	166	7	al	al	PROPN
ejpam-6248	166	8	.	.	PUNCT
ejpam-6248	166	9	/	/	SYM
ejpam-6248	166	10	eur	eur	PROPN
ejpam-6248	166	11	.	.	PUNCT
ejpam-6248	167	1	j.	j.	PROPN
ejpam-6248	167	2	pure	pure	PROPN
ejpam-6248	167	3	appl	appl	PROPN
ejpam-6248	167	4	.	.	PROPN
ejpam-6248	167	5	math	math	PROPN
ejpam-6248	167	6	,	,	PUNCT
ejpam-6248	167	7	18	18	NUM
ejpam-6248	167	8	(	(	PUNCT
ejpam-6248	167	9	3	3	NUM
ejpam-6248	167	10	)	)	PUNCT
ejpam-6248	167	11	(	(	PUNCT
ejpam-6248	167	12	2025	2025	NUM
ejpam-6248	167	13	)	)	PUNCT
ejpam-6248	167	14	,	,	PUNCT
ejpam-6248	167	15	6248	6248	NUM
ejpam-6248	167	16	10	10	NUM
ejpam-6248	167	17	of	of	ADP
ejpam-6248	167	18	20	20	NUM
ejpam-6248	167	19	figure	figure	NOUN
ejpam-6248	167	20	4	4	NUM
ejpam-6248	167	21	:	:	PUNCT
ejpam-6248	167	22	3d	3d	NUM
ejpam-6248	167	23	plot	plot	NOUN
ejpam-6248	167	24	of	of	ADP
ejpam-6248	167	25	(	(	PUNCT
ejpam-6248	167	26	48	48	NUM
ejpam-6248	167	27	)	)	PUNCT
ejpam-6248	167	28	for	for	ADP
ejpam-6248	167	29	c1	c1	NOUN
ejpam-6248	167	30	=	=	PUNCT
ejpam-6248	167	31	−2	−2	NOUN
ejpam-6248	167	32	.	.	PUNCT
ejpam-6248	168	1	substituting	substitute	VERB
ejpam-6248	168	2	these	these	DET
ejpam-6248	168	3	values	value	NOUN
ejpam-6248	168	4	of	of	ADP
ejpam-6248	168	5	m	m	NOUN
ejpam-6248	168	6	and	and	CCONJ
ejpam-6248	168	7	n	n	ADV
ejpam-6248	168	8	into	into	ADP
ejpam-6248	168	9	equation	equation	NOUN
ejpam-6248	168	10	(	(	PUNCT
ejpam-6248	168	11	43	43	NUM
ejpam-6248	168	12	)	)	PUNCT
ejpam-6248	168	13	,	,	PUNCT
ejpam-6248	168	14	we	we	PRON
ejpam-6248	168	15	obtain	obtain	VERB
ejpam-6248	168	16	the	the	DET
ejpam-6248	168	17	following	following	ADJ
ejpam-6248	168	18	ode	ode	ADJ
ejpam-6248	168	19	:	:	PUNCT
ejpam-6248	168	20	ξ2f(ξ)f	ξ2f(ξ)f	ADJ
ejpam-6248	168	21	′′(ξ)−	′′(ξ)−	NOUN
ejpam-6248	168	22	ξ3f	ξ3f	PROPN
ejpam-6248	168	23	′(ξ)f	′(ξ)f	PROPN
ejpam-6248	168	24	′′(ξ)−	′′(ξ)−	PROPN
ejpam-6248	168	25	f	f	PROPN
ejpam-6248	168	26	′′(ξ	′′(ξ	PROPN
ejpam-6248	168	27	)	)	PUNCT
ejpam-6248	168	28	=	=	NOUN
ejpam-6248	169	1	0	0	X
ejpam-6248	169	2	.	.	PUNCT
ejpam-6248	170	1	(	(	PUNCT
ejpam-6248	170	2	46	46	NUM
ejpam-6248	170	3	)	)	PUNCT
ejpam-6248	170	4	the	the	DET
ejpam-6248	170	5	analytic	analytic	ADJ
ejpam-6248	170	6	solution	solution	NOUN
ejpam-6248	170	7	to	to	PART
ejpam-6248	170	8	ode	ode	VERB
ejpam-6248	170	9	(	(	PUNCT
ejpam-6248	170	10	46	46	NUM
ejpam-6248	170	11	)	)	PUNCT
ejpam-6248	170	12	is	be	AUX
ejpam-6248	170	13	:	:	PUNCT
ejpam-6248	170	14	f(ξ	f(ξ	X
ejpam-6248	170	15	)	)	PUNCT
ejpam-6248	170	16	=	=	SYM
ejpam-6248	170	17	1	1	NUM
ejpam-6248	170	18	3ξ2	3ξ2	NUM
ejpam-6248	170	19	+	+	CCONJ
ejpam-6248	170	20	c1ξ	c1ξ	NOUN
ejpam-6248	170	21	.	.	PUNCT
ejpam-6248	171	1	(	(	PUNCT
ejpam-6248	171	2	47	47	NUM
ejpam-6248	171	3	)	)	PUNCT
ejpam-6248	171	4	using	use	VERB
ejpam-6248	171	5	the	the	DET
ejpam-6248	171	6	similarity	similarity	NOUN
ejpam-6248	171	7	function	function	NOUN
ejpam-6248	171	8	transformations	transformation	NOUN
ejpam-6248	171	9	(	(	PUNCT
ejpam-6248	171	10	44	44	NUM
ejpam-6248	171	11	)	)	PUNCT
ejpam-6248	171	12	,	,	PUNCT
ejpam-6248	171	13	(	(	PUNCT
ejpam-6248	171	14	45	45	NUM
ejpam-6248	171	15	)	)	PUNCT
ejpam-6248	171	16	and	and	CCONJ
ejpam-6248	171	17	the	the	DET
ejpam-6248	171	18	analytic	analytic	ADJ
ejpam-6248	171	19	solution	solution	NOUN
ejpam-6248	171	20	of	of	ADP
ejpam-6248	171	21	ode	ode	PROPN
ejpam-6248	171	22	(	(	PUNCT
ejpam-6248	171	23	47	47	NUM
ejpam-6248	171	24	)	)	PUNCT
ejpam-6248	171	25	,	,	PUNCT
ejpam-6248	171	26	we	we	PRON
ejpam-6248	171	27	derive	derive	VERB
ejpam-6248	171	28	the	the	DET
ejpam-6248	171	29	exact	exact	ADJ
ejpam-6248	171	30	solution	solution	NOUN
ejpam-6248	171	31	to	to	ADP
ejpam-6248	171	32	pde	pde	PROPN
ejpam-6248	171	33	(	(	PUNCT
ejpam-6248	171	34	1	1	NUM
ejpam-6248	171	35	):	):	PUNCT
ejpam-6248	171	36	u(x	u(x	PROPN
ejpam-6248	171	37	,	,	PUNCT
ejpam-6248	171	38	y	y	NOUN
ejpam-6248	171	39	)	)	PUNCT
ejpam-6248	171	40	=	=	SYM
ejpam-6248	172	1	x3	x3	ADJ
ejpam-6248	172	2	+	+	CCONJ
ejpam-6248	172	3	3c1y	3c1y	NOUN
ejpam-6248	172	4	3	3	NUM
ejpam-6248	172	5	3y2	3y2	NUM
ejpam-6248	172	6	.	.	PUNCT
ejpam-6248	173	1	(	(	PUNCT
ejpam-6248	173	2	48	48	NUM
ejpam-6248	173	3	)	)	PUNCT
ejpam-6248	173	4	(	(	PUNCT
ejpam-6248	173	5	ii	ii	NOUN
ejpam-6248	173	6	)	)	PUNCT
ejpam-6248	173	7	for	for	ADP
ejpam-6248	173	8	m	m	PROPN
ejpam-6248	173	9	=	=	SYM
ejpam-6248	173	10	0	0	NUM
ejpam-6248	173	11	and	and	CCONJ
ejpam-6248	173	12	n	n	CCONJ
ejpam-6248	173	13	=	=	SYM
ejpam-6248	173	14	3	3	NUM
ejpam-6248	173	15	,	,	PUNCT
ejpam-6248	173	16	the	the	DET
ejpam-6248	173	17	similarity	similarity	NOUN
ejpam-6248	173	18	transformations	transformation	NOUN
ejpam-6248	173	19	(	(	PUNCT
ejpam-6248	173	20	37	37	NUM
ejpam-6248	173	21	)	)	PUNCT
ejpam-6248	173	22	and	and	CCONJ
ejpam-6248	173	23	(	(	PUNCT
ejpam-6248	173	24	38	38	NUM
ejpam-6248	173	25	)	)	PUNCT
ejpam-6248	173	26	reduce	reduce	VERB
ejpam-6248	173	27	to	to	ADP
ejpam-6248	173	28	:	:	PUNCT
ejpam-6248	173	29	ξ	ξ	X
ejpam-6248	173	30	=	=	SYM
ejpam-6248	173	31	y.	y.	NOUN
ejpam-6248	173	32	(	(	PUNCT
ejpam-6248	173	33	49	49	NUM
ejpam-6248	173	34	)	)	PUNCT
ejpam-6248	173	35	u	u	NOUN
ejpam-6248	173	36	=	=	PROPN
ejpam-6248	173	37	x3f(ξ	x3f(ξ	PROPN
ejpam-6248	173	38	)	)	PUNCT
ejpam-6248	173	39	.	.	PUNCT
ejpam-6248	174	1	(	(	PUNCT
ejpam-6248	174	2	50	50	NUM
ejpam-6248	174	3	)	)	PUNCT
ejpam-6248	174	4	z.	z.	PROPN
ejpam-6248	174	5	haider	haider	PROPN
ejpam-6248	174	6	et	et	PROPN
ejpam-6248	174	7	al	al	PROPN
ejpam-6248	174	8	.	.	PUNCT
ejpam-6248	174	9	/	/	SYM
ejpam-6248	174	10	eur	eur	PROPN
ejpam-6248	174	11	.	.	PUNCT
ejpam-6248	175	1	j.	j.	PROPN
ejpam-6248	175	2	pure	pure	PROPN
ejpam-6248	175	3	appl	appl	PROPN
ejpam-6248	175	4	.	.	PROPN
ejpam-6248	175	5	math	math	PROPN
ejpam-6248	175	6	,	,	PUNCT
ejpam-6248	175	7	18	18	NUM
ejpam-6248	175	8	(	(	PUNCT
ejpam-6248	175	9	3	3	NUM
ejpam-6248	175	10	)	)	PUNCT
ejpam-6248	175	11	(	(	PUNCT
ejpam-6248	175	12	2025	2025	NUM
ejpam-6248	175	13	)	)	PUNCT
ejpam-6248	175	14	,	,	PUNCT
ejpam-6248	175	15	6248	6248	NUM
ejpam-6248	175	16	11	11	NUM
ejpam-6248	175	17	of	of	ADP
ejpam-6248	175	18	20	20	NUM
ejpam-6248	175	19	figure	figure	NOUN
ejpam-6248	175	20	5	5	NUM
ejpam-6248	175	21	:	:	PUNCT
ejpam-6248	175	22	3d	3d	NUM
ejpam-6248	175	23	plot	plot	NOUN
ejpam-6248	175	24	of	of	ADP
ejpam-6248	175	25	(	(	PUNCT
ejpam-6248	175	26	53	53	NUM
ejpam-6248	175	27	)	)	PUNCT
ejpam-6248	175	28	for	for	ADP
ejpam-6248	175	29	c1	c1	PROPN
ejpam-6248	175	30	=	=	SYM
ejpam-6248	175	31	−1	−1	NOUN
ejpam-6248	175	32	and	and	CCONJ
ejpam-6248	175	33	c2	c2	PROPN
ejpam-6248	175	34	=	=	SYM
ejpam-6248	175	35	1	1	X
ejpam-6248	175	36	.	.	X
ejpam-6248	175	37	substituting	substitute	VERB
ejpam-6248	175	38	these	these	DET
ejpam-6248	175	39	parameter	parameter	NOUN
ejpam-6248	175	40	values	value	NOUN
ejpam-6248	175	41	into	into	ADP
ejpam-6248	175	42	equation	equation	NOUN
ejpam-6248	175	43	(	(	PUNCT
ejpam-6248	175	44	43	43	NUM
ejpam-6248	175	45	)	)	PUNCT
ejpam-6248	175	46	,	,	PUNCT
ejpam-6248	175	47	we	we	PRON
ejpam-6248	175	48	obtain	obtain	VERB
ejpam-6248	175	49	the	the	DET
ejpam-6248	175	50	following	following	ADJ
ejpam-6248	175	51	ode	ode	PROPN
ejpam-6248	175	52	:	:	PUNCT
ejpam-6248	175	53	18f2(ξ)−	18f2(ξ)−	NUM
ejpam-6248	175	54	f	f	X
ejpam-6248	175	55	′′(ξ	′′(ξ	PROPN
ejpam-6248	175	56	)	)	PUNCT
ejpam-6248	175	57	=	=	NOUN
ejpam-6248	176	1	0	0	X
ejpam-6248	176	2	.	.	PUNCT
ejpam-6248	177	1	(	(	PUNCT
ejpam-6248	177	2	51	51	NUM
ejpam-6248	177	3	)	)	PUNCT
ejpam-6248	177	4	the	the	DET
ejpam-6248	177	5	analytic	analytic	ADJ
ejpam-6248	177	6	solution	solution	NOUN
ejpam-6248	177	7	to	to	PART
ejpam-6248	177	8	ode	ode	VERB
ejpam-6248	177	9	(	(	PUNCT
ejpam-6248	177	10	51	51	NUM
ejpam-6248	177	11	)	)	PUNCT
ejpam-6248	177	12	is	be	AUX
ejpam-6248	177	13	expressed	express	VERB
ejpam-6248	177	14	in	in	ADP
ejpam-6248	177	15	terms	term	NOUN
ejpam-6248	177	16	of	of	ADP
ejpam-6248	177	17	the	the	DET
ejpam-6248	177	18	weierstrass	weierstrass	NOUN
ejpam-6248	177	19	elliptic	elliptic	ADJ
ejpam-6248	177	20	function	function	NOUN
ejpam-6248	177	21	:	:	PUNCT
ejpam-6248	178	1	f(ξ	f(ξ	X
ejpam-6248	178	2	)	)	PUNCT
ejpam-6248	178	3	=	=	SYM
ejpam-6248	178	4	1	1	NUM
ejpam-6248	178	5	3	3	NUM
ejpam-6248	178	6	℘(ξ	℘(ξ	PROPN
ejpam-6248	178	7	+	+	PROPN
ejpam-6248	178	8	c1	c1	PROPN
ejpam-6248	178	9	;	;	PUNCT
ejpam-6248	178	10	g2	g2	PROPN
ejpam-6248	178	11	,	,	PUNCT
ejpam-6248	178	12	g3	g3	PROPN
ejpam-6248	178	13	)	)	PUNCT
ejpam-6248	178	14	.	.	PUNCT
ejpam-6248	179	1	(	(	PUNCT
ejpam-6248	179	2	52	52	NUM
ejpam-6248	179	3	)	)	PUNCT
ejpam-6248	179	4	the	the	DET
ejpam-6248	179	5	weierstrass	weierstrass	NOUN
ejpam-6248	179	6	elliptic	elliptic	ADJ
ejpam-6248	179	7	function	function	NOUN
ejpam-6248	179	8	is	be	AUX
ejpam-6248	179	9	defined	define	VERB
ejpam-6248	179	10	as	as	ADP
ejpam-6248	179	11	:	:	PUNCT
ejpam-6248	179	12	℘(ξ	℘(ξ	PROPN
ejpam-6248	179	13	;	;	PUNCT
ejpam-6248	179	14	g2	g2	PROPN
ejpam-6248	179	15	,	,	PUNCT
ejpam-6248	179	16	g3	g3	PROPN
ejpam-6248	179	17	)	)	PUNCT
ejpam-6248	179	18	=	=	SYM
ejpam-6248	179	19	1	1	NUM
ejpam-6248	179	20	ξ2	ξ2	NOUN
ejpam-6248	179	21	+	+	CCONJ
ejpam-6248	179	22	∑	∑	ADV
ejpam-6248	179	23	ω∈λ\{0	ω∈λ\{0	ADJ
ejpam-6248	179	24	}	}	PUNCT
ejpam-6248	179	25	(	(	PUNCT
ejpam-6248	179	26	1	1	NUM
ejpam-6248	179	27	(	(	PUNCT
ejpam-6248	179	28	ξ	ξ	PROPN
ejpam-6248	179	29	−	−	PROPN
ejpam-6248	179	30	ω)2	ω)2	NOUN
ejpam-6248	179	31	−	−	PROPN
ejpam-6248	179	32	1	1	NUM
ejpam-6248	179	33	ω2	ω2	ADJ
ejpam-6248	179	34	)	)	PUNCT
ejpam-6248	179	35	.	.	PUNCT
ejpam-6248	180	1	the	the	DET
ejpam-6248	180	2	corresponding	corresponding	ADJ
ejpam-6248	180	3	exact	exact	ADJ
ejpam-6248	180	4	solution	solution	NOUN
ejpam-6248	180	5	of	of	ADP
ejpam-6248	180	6	pde	pde	NOUN
ejpam-6248	180	7	(	(	PUNCT
ejpam-6248	180	8	1	1	NUM
ejpam-6248	180	9	)	)	PUNCT
ejpam-6248	180	10	is	be	AUX
ejpam-6248	180	11	:	:	PUNCT
ejpam-6248	180	12	u(x	u(x	PROPN
ejpam-6248	180	13	,	,	PUNCT
ejpam-6248	180	14	y	y	NOUN
ejpam-6248	180	15	)	)	PUNCT
ejpam-6248	180	16	=	=	SYM
ejpam-6248	181	1	x3	x3	VERB
ejpam-6248	181	2	3	3	NUM
ejpam-6248	181	3	℘(y	℘(y	PROPN
ejpam-6248	181	4	+	+	PROPN
ejpam-6248	181	5	c1	c1	PROPN
ejpam-6248	181	6	;	;	PUNCT
ejpam-6248	181	7	0	0	NUM
ejpam-6248	181	8	,	,	PUNCT
ejpam-6248	181	9	c2	c2	PROPN
ejpam-6248	181	10	)	)	PUNCT
ejpam-6248	181	11	.	.	PUNCT
ejpam-6248	182	1	(	(	PUNCT
ejpam-6248	182	2	53	53	NUM
ejpam-6248	182	3	)	)	PUNCT
ejpam-6248	182	4	in	in	ADP
ejpam-6248	182	5	equation	equation	NOUN
ejpam-6248	182	6	(	(	PUNCT
ejpam-6248	182	7	53	53	NUM
ejpam-6248	182	8	)	)	PUNCT
ejpam-6248	182	9	,	,	PUNCT
ejpam-6248	182	10	℘	℘	PROPN
ejpam-6248	182	11	denotes	denote	VERB
ejpam-6248	182	12	the	the	DET
ejpam-6248	182	13	weierstrass	weierstrass	PROPN
ejpam-6248	182	14	elliptic	elliptic	ADJ
ejpam-6248	182	15	function	function	NOUN
ejpam-6248	182	16	,	,	PUNCT
ejpam-6248	182	17	which	which	PRON
ejpam-6248	182	18	plays	play	VERB
ejpam-6248	182	19	a	a	DET
ejpam-6248	182	20	fundamental	fundamental	ADJ
ejpam-6248	182	21	role	role	NOUN
ejpam-6248	182	22	in	in	ADP
ejpam-6248	182	23	solving	solve	VERB
ejpam-6248	182	24	certain	certain	ADJ
ejpam-6248	182	25	nonlinear	nonlinear	ADJ
ejpam-6248	182	26	differential	differential	ADJ
ejpam-6248	182	27	equations	equation	NOUN
ejpam-6248	182	28	.	.	PUNCT
ejpam-6248	183	1	here	here	ADV
ejpam-6248	183	2	,	,	PUNCT
ejpam-6248	183	3	g2	g2	PROPN
ejpam-6248	183	4	=	=	PUNCT
ejpam-6248	183	5	0	0	NUM
ejpam-6248	183	6	and	and	CCONJ
ejpam-6248	183	7	g3	g3	PROPN
ejpam-6248	183	8	=	=	PROPN
ejpam-6248	183	9	c2	c2	PROPN
ejpam-6248	183	10	.	.	PUNCT
ejpam-6248	184	1	z.	z.	PROPN
ejpam-6248	184	2	haider	haider	PROPN
ejpam-6248	184	3	et	et	PROPN
ejpam-6248	184	4	al	al	PROPN
ejpam-6248	184	5	.	.	PUNCT
ejpam-6248	184	6	/	/	SYM
ejpam-6248	184	7	eur	eur	PROPN
ejpam-6248	184	8	.	.	PUNCT
ejpam-6248	185	1	j.	j.	PROPN
ejpam-6248	185	2	pure	pure	PROPN
ejpam-6248	185	3	appl	appl	PROPN
ejpam-6248	185	4	.	.	PROPN
ejpam-6248	185	5	math	math	PROPN
ejpam-6248	185	6	,	,	PUNCT
ejpam-6248	185	7	18	18	NUM
ejpam-6248	185	8	(	(	PUNCT
ejpam-6248	185	9	3	3	NUM
ejpam-6248	185	10	)	)	PUNCT
ejpam-6248	185	11	(	(	PUNCT
ejpam-6248	185	12	2025	2025	NUM
ejpam-6248	185	13	)	)	PUNCT
ejpam-6248	185	14	,	,	PUNCT
ejpam-6248	185	15	6248	6248	NUM
ejpam-6248	185	16	12	12	NUM
ejpam-6248	185	17	of	of	ADP
ejpam-6248	185	18	20	20	NUM
ejpam-6248	185	19	remark	remark	NOUN
ejpam-6248	185	20	:	:	PUNCT
ejpam-6248	185	21	the	the	DET
ejpam-6248	185	22	weierstrass	weierstrass	NOUN
ejpam-6248	185	23	elliptic	elliptic	ADJ
ejpam-6248	185	24	function	function	NOUN
ejpam-6248	185	25	℘(z	℘(z	PROPN
ejpam-6248	185	26	;	;	PUNCT
ejpam-6248	185	27	g2	g2	PROPN
ejpam-6248	185	28	,	,	PUNCT
ejpam-6248	185	29	g3	g3	PROPN
ejpam-6248	185	30	)	)	PUNCT
ejpam-6248	185	31	is	be	AUX
ejpam-6248	185	32	a	a	DET
ejpam-6248	185	33	doubly	doubly	ADV
ejpam-6248	185	34	periodic	periodic	ADJ
ejpam-6248	185	35	meromorphic	meromorphic	ADJ
ejpam-6248	185	36	function	function	NOUN
ejpam-6248	185	37	with	with	ADP
ejpam-6248	185	38	branch	branch	NOUN
ejpam-6248	185	39	points	point	NOUN
ejpam-6248	185	40	occuring	occur	VERB
ejpam-6248	185	41	where	where	SCONJ
ejpam-6248	185	42	the	the	DET
ejpam-6248	185	43	discriminant	discriminant	NOUN
ejpam-6248	185	44	∆	∆	X
ejpam-6248	185	45	=	=	PUNCT
ejpam-6248	185	46	g32	g32	NOUN
ejpam-6248	185	47	−	−	PROPN
ejpam-6248	185	48	27g23	27g23	NUM
ejpam-6248	185	49	vanishes	vanish	VERB
ejpam-6248	185	50	.	.	PUNCT
ejpam-6248	186	1	its	its	PRON
ejpam-6248	186	2	branch	branch	NOUN
ejpam-6248	186	3	structure	structure	NOUN
ejpam-6248	186	4	and	and	CCONJ
ejpam-6248	186	5	complex	complex	ADJ
ejpam-6248	186	6	periodicity	periodicity	NOUN
ejpam-6248	186	7	must	must	AUX
ejpam-6248	186	8	be	be	AUX
ejpam-6248	186	9	carefully	carefully	ADV
ejpam-6248	186	10	analyzed	analyze	VERB
ejpam-6248	186	11	,	,	PUNCT
ejpam-6248	186	12	as	as	SCONJ
ejpam-6248	186	13	they	they	PRON
ejpam-6248	186	14	affect	affect	VERB
ejpam-6248	186	15	the	the	DET
ejpam-6248	186	16	solution	solution	NOUN
ejpam-6248	186	17	’s	’s	PART
ejpam-6248	186	18	analyticity	analyticity	NOUN
ejpam-6248	186	19	and	and	CCONJ
ejpam-6248	186	20	physical	physical	ADJ
ejpam-6248	186	21	interpretation	interpretation	NOUN
ejpam-6248	186	22	—	—	PUNCT
ejpam-6248	186	23	particularly	particularly	ADV
ejpam-6248	186	24	in	in	ADP
ejpam-6248	186	25	modeling	model	VERB
ejpam-6248	186	26	nonlinear	nonlinear	ADJ
ejpam-6248	186	27	wave	wave	NOUN
ejpam-6248	186	28	structures	structure	NOUN
ejpam-6248	186	29	and	and	CCONJ
ejpam-6248	186	30	oscillatory	oscillatory	ADJ
ejpam-6248	186	31	flow	flow	NOUN
ejpam-6248	186	32	fields	field	NOUN
ejpam-6248	186	33	.	.	PUNCT
ejpam-6248	187	1	in	in	ADP
ejpam-6248	187	2	aerodynamics	aerodynamic	NOUN
ejpam-6248	187	3	,	,	PUNCT
ejpam-6248	187	4	weierstrass	weierstrass	NOUN
ejpam-6248	187	5	functions	function	NOUN
ejpam-6248	187	6	are	be	AUX
ejpam-6248	187	7	valuable	valuable	ADJ
ejpam-6248	187	8	for	for	ADP
ejpam-6248	187	9	describing	describe	VERB
ejpam-6248	187	10	periodic	periodic	ADJ
ejpam-6248	187	11	or	or	CCONJ
ejpam-6248	187	12	solitary	solitary	ADJ
ejpam-6248	187	13	wave	wave	NOUN
ejpam-6248	187	14	patterns	pattern	NOUN
ejpam-6248	187	15	in	in	ADP
ejpam-6248	187	16	nonlinear	nonlinear	ADJ
ejpam-6248	187	17	potential	potential	ADJ
ejpam-6248	187	18	flows	flow	NOUN
ejpam-6248	187	19	and	and	CCONJ
ejpam-6248	187	20	boundary	boundary	ADJ
ejpam-6248	187	21	layer	layer	NOUN
ejpam-6248	187	22	separation	separation	NOUN
ejpam-6248	187	23	phenomena	phenomena	PROPN
ejpam-6248	187	24	.	.	PUNCT
ejpam-6248	188	1	case:-3	case:-3	NOUN
ejpam-6248	188	2	we	we	PRON
ejpam-6248	188	3	choose	choose	VERB
ejpam-6248	188	4	the	the	DET
ejpam-6248	188	5	similarity	similarity	NOUN
ejpam-6248	188	6	function	function	NOUN
ejpam-6248	188	7	transformation	transformation	NOUN
ejpam-6248	188	8	as	as	ADP
ejpam-6248	188	9	ξ	ξ	X
ejpam-6248	188	10	=	=	SYM
ejpam-6248	188	11	xeat	xeat	PROPN
ejpam-6248	188	12	.	.	PUNCT
ejpam-6248	189	1	(	(	PUNCT
ejpam-6248	189	2	54	54	NUM
ejpam-6248	189	3	)	)	PUNCT
ejpam-6248	189	4	u	u	NOUN
ejpam-6248	189	5	=	=	PUNCT
ejpam-6248	189	6	e−btf(ξ	e−btf(ξ	PROPN
ejpam-6248	189	7	)	)	PUNCT
ejpam-6248	189	8	.	.	PUNCT
ejpam-6248	190	1	(	(	PUNCT
ejpam-6248	190	2	55	55	X
ejpam-6248	190	3	)	)	PUNCT
ejpam-6248	190	4	differentiating	differentiate	VERB
ejpam-6248	190	5	equations	equation	NOUN
ejpam-6248	190	6	(	(	PUNCT
ejpam-6248	190	7	54	54	NUM
ejpam-6248	190	8	)	)	PUNCT
ejpam-6248	190	9	and	and	CCONJ
ejpam-6248	190	10	(	(	PUNCT
ejpam-6248	190	11	55	55	NUM
ejpam-6248	190	12	)	)	PUNCT
ejpam-6248	190	13	according	accord	VERB
ejpam-6248	190	14	to	to	ADP
ejpam-6248	190	15	equation	equation	NOUN
ejpam-6248	190	16	(	(	PUNCT
ejpam-6248	190	17	1	1	NUM
ejpam-6248	190	18	)	)	PUNCT
ejpam-6248	190	19	,	,	PUNCT
ejpam-6248	190	20	we	we	PRON
ejpam-6248	190	21	get	get	VERB
ejpam-6248	190	22	ux	ux	PROPN
ejpam-6248	190	23	=	=	SYM
ejpam-6248	190	24	et(a−b)f	et(a−b)f	PROPN
ejpam-6248	190	25	′(ξ	′(ξ	PROPN
ejpam-6248	190	26	)	)	PUNCT
ejpam-6248	190	27	.	.	PUNCT
ejpam-6248	191	1	(	(	PUNCT
ejpam-6248	191	2	56	56	NUM
ejpam-6248	191	3	)	)	PUNCT
ejpam-6248	191	4	uxx	uxx	NOUN
ejpam-6248	192	1	=	=	PUNCT
ejpam-6248	193	1	et(2a−b)f	et(2a−b)f	NUM
ejpam-6248	193	2	′′(ξ	′′(ξ	PROPN
ejpam-6248	193	3	)	)	PUNCT
ejpam-6248	193	4	.	.	PUNCT
ejpam-6248	194	1	(	(	PUNCT
ejpam-6248	194	2	57	57	NUM
ejpam-6248	194	3	)	)	PUNCT
ejpam-6248	194	4	uxt	uxt	NOUN
ejpam-6248	194	5	=	=	SYM
ejpam-6248	194	6	−bf	−bf	VERB
ejpam-6248	194	7	′(ξ	′(ξ	NOUN
ejpam-6248	194	8	)	)	PUNCT
ejpam-6248	195	1	+	+	CCONJ
ejpam-6248	195	2	aξf	aξf	ADJ
ejpam-6248	195	3	′′(ξ	′′(ξ	NUM
ejpam-6248	195	4	)	)	PUNCT
ejpam-6248	196	1	+	+	CCONJ
ejpam-6248	196	2	af	af	X
ejpam-6248	196	3	′(ξ	′(ξ	NOUN
ejpam-6248	196	4	)	)	PUNCT
ejpam-6248	196	5	.	.	PUNCT
ejpam-6248	197	1	(	(	PUNCT
ejpam-6248	197	2	58	58	X
ejpam-6248	197	3	)	)	PUNCT
ejpam-6248	197	4	uyy	uyy	PROPN
ejpam-6248	197	5	=	=	SYM
ejpam-6248	197	6	0	0	PROPN
ejpam-6248	197	7	.	.	PUNCT
ejpam-6248	198	1	(	(	PUNCT
ejpam-6248	198	2	59	59	NUM
ejpam-6248	198	3	)	)	PUNCT
ejpam-6248	198	4	substituting	substitute	VERB
ejpam-6248	198	5	equations	equation	NOUN
ejpam-6248	198	6	(	(	PUNCT
ejpam-6248	198	7	56	56	NUM
ejpam-6248	198	8	)	)	PUNCT
ejpam-6248	198	9	,	,	PUNCT
ejpam-6248	198	10	(	(	PUNCT
ejpam-6248	198	11	57	57	NUM
ejpam-6248	198	12	)	)	PUNCT
ejpam-6248	198	13	,	,	PUNCT
ejpam-6248	198	14	(	(	PUNCT
ejpam-6248	198	15	58	58	NUM
ejpam-6248	198	16	)	)	PUNCT
ejpam-6248	198	17	and	and	CCONJ
ejpam-6248	198	18	(	(	PUNCT
ejpam-6248	198	19	59	59	NUM
ejpam-6248	198	20	)	)	PUNCT
ejpam-6248	198	21	into	into	ADP
ejpam-6248	198	22	equation	equation	NOUN
ejpam-6248	198	23	(	(	PUNCT
ejpam-6248	198	24	1	1	NUM
ejpam-6248	198	25	)	)	PUNCT
ejpam-6248	198	26	,	,	PUNCT
ejpam-6248	198	27	we	we	PRON
ejpam-6248	198	28	obtain	obtain	VERB
ejpam-6248	198	29	an	an	DET
ejpam-6248	198	30	ordinary	ordinary	ADJ
ejpam-6248	198	31	differential	differential	ADJ
ejpam-6248	198	32	equation	equation	NOUN
ejpam-6248	198	33	(	(	PUNCT
ejpam-6248	198	34	ode	ode	PROPN
ejpam-6248	198	35	)	)	PUNCT
ejpam-6248	198	36	of	of	ADP
ejpam-6248	198	37	the	the	DET
ejpam-6248	198	38	following	follow	VERB
ejpam-6248	198	39	form	form	NOUN
ejpam-6248	198	40	:	:	PUNCT
ejpam-6248	198	41	−2bf	−2bf	NUM
ejpam-6248	198	42	′(ξ	′(ξ	NOUN
ejpam-6248	198	43	)	)	PUNCT
ejpam-6248	198	44	+	+	CCONJ
ejpam-6248	198	45	2axeatf	2axeatf	NUM
ejpam-6248	198	46	′′(ξ	′′(ξ	NOUN
ejpam-6248	198	47	)	)	PUNCT
ejpam-6248	199	1	+	+	NUM
ejpam-6248	199	2	2af	2af	ADJ
ejpam-6248	199	3	′(ξ	′(ξ	NOUN
ejpam-6248	199	4	)	)	PUNCT
ejpam-6248	200	1	+	+	CCONJ
ejpam-6248	200	2	et(2a−b)f	et(2a−b)f	PROPN
ejpam-6248	200	3	′(ξ)f	′(ξ)f	PROPN
ejpam-6248	200	4	′′(ξ	′′(ξ	PROPN
ejpam-6248	200	5	)	)	PUNCT
ejpam-6248	201	1	=	=	NOUN
ejpam-6248	201	2	0	0	X
ejpam-6248	201	3	.	.	PUNCT
ejpam-6248	202	1	(	(	PUNCT
ejpam-6248	202	2	60	60	NUM
ejpam-6248	202	3	)	)	PUNCT
ejpam-6248	202	4	since	since	SCONJ
ejpam-6248	202	5	ξ	ξ	X
ejpam-6248	202	6	=	=	SYM
ejpam-6248	202	7	xeat	xeat	PROPN
ejpam-6248	202	8	,	,	PUNCT
ejpam-6248	202	9	equation	equation	NOUN
ejpam-6248	202	10	(	(	PUNCT
ejpam-6248	202	11	60	60	NUM
ejpam-6248	202	12	)	)	PUNCT
ejpam-6248	202	13	becomes	become	VERB
ejpam-6248	202	14	:	:	PUNCT
ejpam-6248	202	15	−2bf	−2bf	ADJ
ejpam-6248	202	16	′(ξ	′(ξ	PROPN
ejpam-6248	202	17	)	)	PUNCT
ejpam-6248	203	1	+	+	CCONJ
ejpam-6248	204	1	2aξf	2aξf	NUM
ejpam-6248	204	2	′′(ξ	′′(ξ	NOUN
ejpam-6248	204	3	)	)	PUNCT
ejpam-6248	205	1	+	+	NUM
ejpam-6248	205	2	2af	2af	ADJ
ejpam-6248	205	3	′(ξ	′(ξ	NOUN
ejpam-6248	205	4	)	)	PUNCT
ejpam-6248	206	1	+	+	CCONJ
ejpam-6248	206	2	et(2a−b)f	et(2a−b)f	PROPN
ejpam-6248	206	3	′(ξ)f	′(ξ)f	PROPN
ejpam-6248	206	4	′′(ξ	′′(ξ	PROPN
ejpam-6248	206	5	)	)	PUNCT
ejpam-6248	207	1	=	=	NOUN
ejpam-6248	207	2	0	0	X
ejpam-6248	207	3	.	.	PUNCT
ejpam-6248	208	1	(	(	PUNCT
ejpam-6248	208	2	61	61	NUM
ejpam-6248	208	3	)	)	PUNCT
ejpam-6248	208	4	the	the	DET
ejpam-6248	208	5	last	last	ADJ
ejpam-6248	208	6	term	term	NOUN
ejpam-6248	208	7	in	in	ADP
ejpam-6248	208	8	equation	equation	NOUN
ejpam-6248	208	9	(	(	PUNCT
ejpam-6248	208	10	61	61	NUM
ejpam-6248	208	11	)	)	PUNCT
ejpam-6248	208	12	contains	contain	VERB
ejpam-6248	208	13	the	the	DET
ejpam-6248	208	14	factor	factor	NOUN
ejpam-6248	208	15	et(2a−b	et(2a−b	NOUN
ejpam-6248	208	16	)	)	PUNCT
ejpam-6248	208	17	,	,	PUNCT
ejpam-6248	208	18	which	which	PRON
ejpam-6248	208	19	must	must	AUX
ejpam-6248	208	20	equal	equal	VERB
ejpam-6248	208	21	unity	unity	NOUN
ejpam-6248	208	22	(	(	PUNCT
ejpam-6248	208	23	i.e.	i.e.	X
ejpam-6248	208	24	,	,	PUNCT
ejpam-6248	208	25	e0	e0	PROPN
ejpam-6248	208	26	)	)	PUNCT
ejpam-6248	208	27	.	.	PUNCT
ejpam-6248	209	1	this	this	DET
ejpam-6248	209	2	requirement	requirement	NOUN
ejpam-6248	209	3	yields	yield	VERB
ejpam-6248	209	4	the	the	DET
ejpam-6248	209	5	relation	relation	NOUN
ejpam-6248	209	6	b	b	NOUN
ejpam-6248	209	7	=	=	SYM
ejpam-6248	209	8	2a	2a	NUM
ejpam-6248	209	9	.	.	PUNCT
ejpam-6248	210	1	although	although	SCONJ
ejpam-6248	210	2	it	it	PRON
ejpam-6248	210	3	is	be	AUX
ejpam-6248	210	4	possible	possible	ADJ
ejpam-6248	210	5	to	to	PART
ejpam-6248	210	6	find	find	VERB
ejpam-6248	210	7	solutions	solution	NOUN
ejpam-6248	210	8	to	to	ADP
ejpam-6248	210	9	the	the	DET
ejpam-6248	210	10	ode	ode	PROPN
ejpam-6248	210	11	(	(	PUNCT
ejpam-6248	210	12	61	61	NUM
ejpam-6248	210	13	)	)	PUNCT
ejpam-6248	210	14	for	for	ADP
ejpam-6248	210	15	general	general	ADJ
ejpam-6248	210	16	values	value	NOUN
ejpam-6248	210	17	of	of	ADP
ejpam-6248	210	18	a	a	PRON
ejpam-6248	210	19	and	and	CCONJ
ejpam-6248	210	20	b	b	NOUN
ejpam-6248	210	21	,	,	PUNCT
ejpam-6248	210	22	we	we	PRON
ejpam-6248	210	23	consider	consider	VERB
ejpam-6248	210	24	specific	specific	ADJ
ejpam-6248	210	25	values	value	NOUN
ejpam-6248	210	26	of	of	ADP
ejpam-6248	210	27	these	these	DET
ejpam-6248	210	28	parameters	parameter	NOUN
ejpam-6248	210	29	to	to	PART
ejpam-6248	210	30	obtain	obtain	VERB
ejpam-6248	210	31	exact	exact	ADJ
ejpam-6248	210	32	solutions	solution	NOUN
ejpam-6248	210	33	.	.	PUNCT
ejpam-6248	211	1	b	b	X
ejpam-6248	211	2	=	=	SYM
ejpam-6248	211	3	2a	2a	NUM
ejpam-6248	211	4	a	a	DET
ejpam-6248	211	5	1	1	NUM
ejpam-6248	211	6	2	2	NUM
ejpam-6248	211	7	−1	−1	NOUN
ejpam-6248	211	8	b	b	SYM
ejpam-6248	211	9	1	1	NUM
ejpam-6248	211	10	−2	−2	NOUN
ejpam-6248	211	11	table	table	NOUN
ejpam-6248	211	12	3	3	NUM
ejpam-6248	211	13	.	.	PUNCT
ejpam-6248	211	14	specific	specific	ADJ
ejpam-6248	211	15	values	value	NOUN
ejpam-6248	211	16	of	of	ADP
ejpam-6248	211	17	a	a	PRON
ejpam-6248	211	18	and	and	CCONJ
ejpam-6248	211	19	b	b	NOUN
ejpam-6248	211	20	for	for	ADP
ejpam-6248	211	21	obtainig	obtainig	NOUN
ejpam-6248	211	22	exact	exact	ADJ
ejpam-6248	211	23	solution	solution	NOUN
ejpam-6248	211	24	family	family	NOUN
ejpam-6248	211	25	solutions	solution	NOUN
ejpam-6248	211	26	z.	z.	PROPN
ejpam-6248	211	27	haider	haider	PROPN
ejpam-6248	211	28	et	et	PROPN
ejpam-6248	211	29	al	al	PROPN
ejpam-6248	211	30	.	.	PUNCT
ejpam-6248	211	31	/	/	SYM
ejpam-6248	211	32	eur	eur	PROPN
ejpam-6248	211	33	.	.	PUNCT
ejpam-6248	212	1	j.	j.	PROPN
ejpam-6248	212	2	pure	pure	PROPN
ejpam-6248	212	3	appl	appl	PROPN
ejpam-6248	212	4	.	.	PROPN
ejpam-6248	212	5	math	math	PROPN
ejpam-6248	212	6	,	,	PUNCT
ejpam-6248	212	7	18	18	NUM
ejpam-6248	212	8	(	(	PUNCT
ejpam-6248	212	9	3	3	NUM
ejpam-6248	212	10	)	)	PUNCT
ejpam-6248	212	11	(	(	PUNCT
ejpam-6248	212	12	2025	2025	NUM
ejpam-6248	212	13	)	)	PUNCT
ejpam-6248	212	14	,	,	PUNCT
ejpam-6248	212	15	6248	6248	NUM
ejpam-6248	212	16	13	13	NUM
ejpam-6248	212	17	of	of	ADP
ejpam-6248	212	18	20	20	NUM
ejpam-6248	212	19	figure	figure	NOUN
ejpam-6248	212	20	6	6	NUM
ejpam-6248	212	21	:	:	PUNCT
ejpam-6248	212	22	3d	3d	NUM
ejpam-6248	212	23	plot	plot	NOUN
ejpam-6248	212	24	of	of	ADP
ejpam-6248	212	25	(	(	PUNCT
ejpam-6248	212	26	66	66	NUM
ejpam-6248	212	27	)	)	PUNCT
ejpam-6248	212	28	for	for	ADP
ejpam-6248	212	29	c1	c1	NOUN
ejpam-6248	212	30	=	=	PUNCT
ejpam-6248	212	31	1	1	NUM
ejpam-6248	212	32	and	and	CCONJ
ejpam-6248	212	33	c2	c2	PROPN
ejpam-6248	212	34	=	=	SYM
ejpam-6248	213	1	3	3	X
ejpam-6248	213	2	.	.	PUNCT
ejpam-6248	213	3	(	(	PUNCT
ejpam-6248	213	4	i	i	NOUN
ejpam-6248	213	5	)	)	PUNCT
ejpam-6248	213	6	for	for	ADP
ejpam-6248	213	7	the	the	DET
ejpam-6248	213	8	parameter	parameter	NOUN
ejpam-6248	213	9	values	value	VERB
ejpam-6248	213	10	a	a	DET
ejpam-6248	213	11	=	=	SYM
ejpam-6248	213	12	1	1	NUM
ejpam-6248	213	13	2	2	NUM
ejpam-6248	213	14	and	and	CCONJ
ejpam-6248	213	15	b	b	NOUN
ejpam-6248	213	16	=	=	SYM
ejpam-6248	213	17	1	1	NUM
ejpam-6248	213	18	,	,	PUNCT
ejpam-6248	213	19	the	the	DET
ejpam-6248	213	20	similarity	similarity	NOUN
ejpam-6248	213	21	transformation	transformation	NOUN
ejpam-6248	213	22	given	give	VERB
ejpam-6248	213	23	in	in	ADP
ejpam-6248	213	24	equations	equation	NOUN
ejpam-6248	213	25	(	(	PUNCT
ejpam-6248	213	26	54	54	NUM
ejpam-6248	213	27	)	)	PUNCT
ejpam-6248	213	28	and	and	CCONJ
ejpam-6248	213	29	(	(	PUNCT
ejpam-6248	213	30	55	55	NUM
ejpam-6248	213	31	)	)	PUNCT
ejpam-6248	213	32	become	become	VERB
ejpam-6248	213	33	:	:	PUNCT
ejpam-6248	213	34	ξ	ξ	X
ejpam-6248	213	35	=	=	SYM
ejpam-6248	213	36	xe	xe	PROPN
ejpam-6248	213	37	t	t	PROPN
ejpam-6248	213	38	2	2	NUM
ejpam-6248	213	39	.	.	PUNCT
ejpam-6248	214	1	(	(	PUNCT
ejpam-6248	214	2	62	62	NUM
ejpam-6248	214	3	)	)	PUNCT
ejpam-6248	214	4	u	u	NOUN
ejpam-6248	214	5	=	=	NOUN
ejpam-6248	214	6	e−tf(ξ	e−tf(ξ	NOUN
ejpam-6248	214	7	)	)	PUNCT
ejpam-6248	214	8	.	.	PUNCT
ejpam-6248	215	1	(	(	PUNCT
ejpam-6248	215	2	63	63	NUM
ejpam-6248	215	3	)	)	PUNCT
ejpam-6248	215	4	using	use	VERB
ejpam-6248	215	5	these	these	DET
ejpam-6248	215	6	parameter	parameter	NOUN
ejpam-6248	215	7	values	value	NOUN
ejpam-6248	215	8	in	in	ADP
ejpam-6248	215	9	equation	equation	NOUN
ejpam-6248	215	10	(	(	PUNCT
ejpam-6248	215	11	61	61	NUM
ejpam-6248	215	12	)	)	PUNCT
ejpam-6248	215	13	,	,	PUNCT
ejpam-6248	215	14	we	we	PRON
ejpam-6248	215	15	obtain	obtain	VERB
ejpam-6248	215	16	the	the	DET
ejpam-6248	215	17	the	the	DET
ejpam-6248	215	18	following	following	ADJ
ejpam-6248	215	19	ordinary	ordinary	ADJ
ejpam-6248	215	20	differential	differential	ADJ
ejpam-6248	215	21	equation	equation	NOUN
ejpam-6248	215	22	(	(	PUNCT
ejpam-6248	215	23	ode	ode	ADJ
ejpam-6248	215	24	):	):	PUNCT
ejpam-6248	215	25	−f	−f	ADJ
ejpam-6248	215	26	′(ξ	′(ξ	NOUN
ejpam-6248	215	27	)	)	PUNCT
ejpam-6248	216	1	+	+	CCONJ
ejpam-6248	216	2	ξf	ξf	PROPN
ejpam-6248	216	3	′′(ξ	′′(ξ	NUM
ejpam-6248	216	4	)	)	PUNCT
ejpam-6248	216	5	)	)	PUNCT
ejpam-6248	217	1	+	+	CCONJ
ejpam-6248	217	2	f	f	PROPN
ejpam-6248	217	3	′(ξ)f	′(ξ)f	PROPN
ejpam-6248	217	4	′′(ξ	′′(ξ	PROPN
ejpam-6248	217	5	)	)	PUNCT
ejpam-6248	217	6	=	=	NOUN
ejpam-6248	218	1	0	0	X
ejpam-6248	218	2	.	.	PUNCT
ejpam-6248	219	1	(	(	PUNCT
ejpam-6248	219	2	64	64	NUM
ejpam-6248	219	3	)	)	PUNCT
ejpam-6248	219	4	the	the	DET
ejpam-6248	219	5	analytic	analytic	ADJ
ejpam-6248	219	6	solution	solution	NOUN
ejpam-6248	219	7	to	to	PART
ejpam-6248	219	8	ode	ode	VERB
ejpam-6248	219	9	(	(	PUNCT
ejpam-6248	219	10	64	64	NUM
ejpam-6248	219	11	)	)	PUNCT
ejpam-6248	219	12	is	be	AUX
ejpam-6248	219	13	:	:	PUNCT
ejpam-6248	219	14	f(ξ	f(ξ	X
ejpam-6248	219	15	)	)	PUNCT
ejpam-6248	219	16	=	=	SYM
ejpam-6248	219	17	(	(	PUNCT
ejpam-6248	219	18	2lambertw(c1ξ	2lambertw(c1ξ	NOUN
ejpam-6248	219	19	)	)	PUNCT
ejpam-6248	220	1	+	+	CCONJ
ejpam-6248	221	1	1)ξ2	1)ξ2	NUM
ejpam-6248	221	2	4lambertw(c1ξ)2	4lambertw(c1ξ)2	NUM
ejpam-6248	221	3	+	+	PROPN
ejpam-6248	221	4	c2	c2	PROPN
ejpam-6248	221	5	.	.	PUNCT
ejpam-6248	222	1	(	(	PUNCT
ejpam-6248	222	2	65	65	NUM
ejpam-6248	222	3	)	)	PUNCT
ejpam-6248	222	4	z.	z.	PROPN
ejpam-6248	222	5	haider	haider	PROPN
ejpam-6248	222	6	et	et	PROPN
ejpam-6248	222	7	al	al	PROPN
ejpam-6248	222	8	.	.	PUNCT
ejpam-6248	222	9	/	/	SYM
ejpam-6248	222	10	eur	eur	PROPN
ejpam-6248	222	11	.	.	PUNCT
ejpam-6248	223	1	j.	j.	PROPN
ejpam-6248	223	2	pure	pure	PROPN
ejpam-6248	223	3	appl	appl	PROPN
ejpam-6248	223	4	.	.	PROPN
ejpam-6248	223	5	math	math	PROPN
ejpam-6248	223	6	,	,	PUNCT
ejpam-6248	223	7	18	18	NUM
ejpam-6248	223	8	(	(	PUNCT
ejpam-6248	223	9	3	3	NUM
ejpam-6248	223	10	)	)	PUNCT
ejpam-6248	223	11	(	(	PUNCT
ejpam-6248	223	12	2025	2025	NUM
ejpam-6248	223	13	)	)	PUNCT
ejpam-6248	223	14	,	,	PUNCT
ejpam-6248	223	15	6248	6248	NUM
ejpam-6248	223	16	14	14	NUM
ejpam-6248	223	17	of	of	ADP
ejpam-6248	223	18	20	20	NUM
ejpam-6248	223	19	using	use	VERB
ejpam-6248	223	20	the	the	DET
ejpam-6248	223	21	similarity	similarity	NOUN
ejpam-6248	223	22	function	function	NOUN
ejpam-6248	223	23	transformations	transformation	NOUN
ejpam-6248	223	24	(	(	PUNCT
ejpam-6248	223	25	62	62	NUM
ejpam-6248	223	26	)	)	PUNCT
ejpam-6248	223	27	and	and	CCONJ
ejpam-6248	223	28	(	(	PUNCT
ejpam-6248	223	29	63	63	NUM
ejpam-6248	223	30	)	)	PUNCT
ejpam-6248	223	31	,	,	PUNCT
ejpam-6248	223	32	together	together	ADV
ejpam-6248	223	33	with	with	ADP
ejpam-6248	223	34	the	the	DET
ejpam-6248	223	35	analytic	analytic	ADJ
ejpam-6248	223	36	solution	solution	NOUN
ejpam-6248	223	37	of	of	ADP
ejpam-6248	223	38	the	the	DET
ejpam-6248	223	39	ode	ode	PROPN
ejpam-6248	223	40	(	(	PUNCT
ejpam-6248	223	41	65	65	NUM
ejpam-6248	223	42	)	)	PUNCT
ejpam-6248	224	1	,	,	PUNCT
ejpam-6248	224	2	we	we	PRON
ejpam-6248	224	3	obtain	obtain	VERB
ejpam-6248	224	4	the	the	DET
ejpam-6248	224	5	exact	exact	ADJ
ejpam-6248	224	6	solution	solution	NOUN
ejpam-6248	224	7	of	of	ADP
ejpam-6248	224	8	the	the	DET
ejpam-6248	224	9	pde	pde	NOUN
ejpam-6248	224	10	(	(	PUNCT
ejpam-6248	224	11	1	1	NUM
ejpam-6248	224	12	):	):	PUNCT
ejpam-6248	224	13	u(x	u(x	PROPN
ejpam-6248	224	14	,	,	PUNCT
ejpam-6248	224	15	t	t	NOUN
ejpam-6248	224	16	)	)	PUNCT
ejpam-6248	224	17	=	=	SYM
ejpam-6248	224	18	e−t(2lambertw(c1xe	e−t(2lambertw(c1xe	PROPN
ejpam-6248	224	19	t	t	NOUN
ejpam-6248	224	20	2	2	NUM
ejpam-6248	224	21	)	)	PUNCT
ejpam-6248	225	1	+	+	CCONJ
ejpam-6248	226	1	1)x2et	1)x2et	NUM
ejpam-6248	226	2	4lambertw(c1xe	4lambertw(c1xe	NUM
ejpam-6248	226	3	t	t	NOUN
ejpam-6248	226	4	2	2	NUM
ejpam-6248	226	5	)	)	SYM
ejpam-6248	226	6	2	2	NUM
ejpam-6248	226	7	+	+	NUM
ejpam-6248	226	8	c2	c2	PROPN
ejpam-6248	226	9	.	.	PUNCT
ejpam-6248	227	1	(	(	PUNCT
ejpam-6248	227	2	66	66	NUM
ejpam-6248	227	3	)	)	PUNCT
ejpam-6248	227	4	(	(	PUNCT
ejpam-6248	227	5	ii	ii	NOUN
ejpam-6248	227	6	)	)	PUNCT
ejpam-6248	227	7	for	for	ADP
ejpam-6248	227	8	the	the	DET
ejpam-6248	227	9	parameter	parameter	NOUN
ejpam-6248	227	10	values	value	VERB
ejpam-6248	227	11	a	a	DET
ejpam-6248	227	12	=	=	PUNCT
ejpam-6248	227	13	−1	−1	NOUN
ejpam-6248	227	14	and	and	CCONJ
ejpam-6248	227	15	b	b	NOUN
ejpam-6248	227	16	=	=	SYM
ejpam-6248	227	17	−2	−2	PROPN
ejpam-6248	227	18	,	,	PUNCT
ejpam-6248	227	19	the	the	DET
ejpam-6248	227	20	similarity	similarity	NOUN
ejpam-6248	227	21	function	function	NOUN
ejpam-6248	227	22	transformations	transformation	NOUN
ejpam-6248	227	23	(	(	PUNCT
ejpam-6248	227	24	54	54	NUM
ejpam-6248	227	25	)	)	PUNCT
ejpam-6248	227	26	and	and	CCONJ
ejpam-6248	227	27	(	(	PUNCT
ejpam-6248	227	28	55	55	NUM
ejpam-6248	227	29	)	)	PUNCT
ejpam-6248	227	30	become	become	VERB
ejpam-6248	227	31	:	:	PUNCT
ejpam-6248	227	32	ξ	ξ	X
ejpam-6248	227	33	=	=	SYM
ejpam-6248	227	34	xe−t	xe−t	PROPN
ejpam-6248	227	35	.	.	PUNCT
ejpam-6248	228	1	(	(	PUNCT
ejpam-6248	228	2	67	67	NUM
ejpam-6248	228	3	)	)	PUNCT
ejpam-6248	228	4	u	u	NOUN
ejpam-6248	228	5	=	=	NOUN
ejpam-6248	228	6	e−2tf(ξ	e−2tf(ξ	PROPN
ejpam-6248	228	7	)	)	PUNCT
ejpam-6248	228	8	.	.	PUNCT
ejpam-6248	229	1	(	(	PUNCT
ejpam-6248	229	2	68	68	NUM
ejpam-6248	229	3	)	)	PUNCT
ejpam-6248	229	4	using	use	VERB
ejpam-6248	229	5	these	these	DET
ejpam-6248	229	6	parameter	parameter	NOUN
ejpam-6248	229	7	values	value	NOUN
ejpam-6248	229	8	in	in	ADP
ejpam-6248	229	9	equation	equation	NOUN
ejpam-6248	229	10	(	(	PUNCT
ejpam-6248	229	11	61	61	NUM
ejpam-6248	229	12	)	)	PUNCT
ejpam-6248	229	13	,	,	PUNCT
ejpam-6248	229	14	we	we	PRON
ejpam-6248	229	15	obtain	obtain	VERB
ejpam-6248	229	16	the	the	DET
ejpam-6248	229	17	following	follow	VERB
ejpam-6248	229	18	ordinary	ordinary	ADJ
ejpam-6248	229	19	differential	differential	ADJ
ejpam-6248	229	20	equation	equation	NOUN
ejpam-6248	229	21	(	(	PUNCT
ejpam-6248	229	22	ode	ode	ADJ
ejpam-6248	229	23	):	):	PUNCT
ejpam-6248	229	24	figure	figure	NOUN
ejpam-6248	229	25	7	7	NUM
ejpam-6248	229	26	:	:	PUNCT
ejpam-6248	229	27	3d	3d	NUM
ejpam-6248	229	28	plot	plot	NOUN
ejpam-6248	229	29	of	of	ADP
ejpam-6248	229	30	(	(	PUNCT
ejpam-6248	229	31	71	71	NUM
ejpam-6248	229	32	)	)	PUNCT
ejpam-6248	229	33	for	for	ADP
ejpam-6248	229	34	c1	c1	PROPN
ejpam-6248	229	35	=	=	SYM
ejpam-6248	229	36	−1	−1	NOUN
ejpam-6248	229	37	and	and	CCONJ
ejpam-6248	229	38	c2	c2	PROPN
ejpam-6248	229	39	=	=	PUNCT
ejpam-6248	230	1	−3	−3	PROPN
ejpam-6248	230	2	.	.	PUNCT
ejpam-6248	231	1	2f	2f	NUM
ejpam-6248	231	2	′(ξ)−	′(ξ)−	NUM
ejpam-6248	231	3	2ξf	2ξf	ADJ
ejpam-6248	231	4	′′(ξ	′′(ξ	NOUN
ejpam-6248	231	5	)	)	PUNCT
ejpam-6248	231	6	)	)	PUNCT
ejpam-6248	232	1	+	+	CCONJ
ejpam-6248	232	2	f	f	PROPN
ejpam-6248	232	3	′(ξ)f	′(ξ)f	PROPN
ejpam-6248	232	4	′′(ξ	′′(ξ	PROPN
ejpam-6248	232	5	)	)	PUNCT
ejpam-6248	232	6	=	=	NOUN
ejpam-6248	233	1	0	0	X
ejpam-6248	233	2	.	.	PUNCT
ejpam-6248	234	1	(	(	PUNCT
ejpam-6248	234	2	69	69	NUM
ejpam-6248	234	3	)	)	PUNCT
ejpam-6248	234	4	z.	z.	PROPN
ejpam-6248	234	5	haider	haider	PROPN
ejpam-6248	234	6	et	et	PROPN
ejpam-6248	234	7	al	al	PROPN
ejpam-6248	234	8	.	.	PUNCT
ejpam-6248	234	9	/	/	SYM
ejpam-6248	234	10	eur	eur	PROPN
ejpam-6248	234	11	.	.	PUNCT
ejpam-6248	235	1	j.	j.	PROPN
ejpam-6248	235	2	pure	pure	PROPN
ejpam-6248	235	3	appl	appl	PROPN
ejpam-6248	235	4	.	.	PROPN
ejpam-6248	235	5	math	math	PROPN
ejpam-6248	235	6	,	,	PUNCT
ejpam-6248	235	7	18	18	NUM
ejpam-6248	235	8	(	(	PUNCT
ejpam-6248	235	9	3	3	NUM
ejpam-6248	235	10	)	)	PUNCT
ejpam-6248	235	11	(	(	PUNCT
ejpam-6248	235	12	2025	2025	NUM
ejpam-6248	235	13	)	)	PUNCT
ejpam-6248	235	14	,	,	PUNCT
ejpam-6248	235	15	6248	6248	NUM
ejpam-6248	235	16	15	15	NUM
ejpam-6248	235	17	of	of	ADP
ejpam-6248	235	18	20	20	NUM
ejpam-6248	235	19	the	the	DET
ejpam-6248	235	20	exact	exact	ADJ
ejpam-6248	235	21	solution	solution	NOUN
ejpam-6248	235	22	to	to	PART
ejpam-6248	235	23	ode	ode	VERB
ejpam-6248	235	24	(	(	PUNCT
ejpam-6248	235	25	69	69	NUM
ejpam-6248	235	26	)	)	PUNCT
ejpam-6248	235	27	is	be	AUX
ejpam-6248	235	28	:	:	PUNCT
ejpam-6248	235	29	f(ξ	f(ξ	X
ejpam-6248	235	30	)	)	PUNCT
ejpam-6248	235	31	=	=	SYM
ejpam-6248	235	32	(	(	PUNCT
ejpam-6248	235	33	2lambertw(−2c1ξ	2lambertw(−2c1ξ	NUM
ejpam-6248	235	34	)	)	PUNCT
ejpam-6248	236	1	+	+	CCONJ
ejpam-6248	237	1	1)ξ2	1)ξ2	NUM
ejpam-6248	237	2	2lambertw(−2c1ξ)2	2lambertw(−2c1ξ)2	NUM
ejpam-6248	237	3	+	+	CCONJ
ejpam-6248	237	4	c2	c2	PROPN
ejpam-6248	237	5	.	.	PUNCT
ejpam-6248	238	1	(	(	PUNCT
ejpam-6248	238	2	70	70	X
ejpam-6248	238	3	)	)	PUNCT
ejpam-6248	238	4	using	use	VERB
ejpam-6248	238	5	the	the	DET
ejpam-6248	238	6	similarity	similarity	NOUN
ejpam-6248	238	7	function	function	NOUN
ejpam-6248	238	8	transformations	transformation	NOUN
ejpam-6248	238	9	(	(	PUNCT
ejpam-6248	238	10	67	67	NUM
ejpam-6248	238	11	)	)	PUNCT
ejpam-6248	238	12	and	and	CCONJ
ejpam-6248	238	13	(	(	PUNCT
ejpam-6248	238	14	68	68	NUM
ejpam-6248	238	15	)	)	PUNCT
ejpam-6248	238	16	,	,	PUNCT
ejpam-6248	238	17	together	together	ADV
ejpam-6248	238	18	with	with	ADP
ejpam-6248	238	19	the	the	DET
ejpam-6248	238	20	analytic	analytic	ADJ
ejpam-6248	238	21	solution	solution	NOUN
ejpam-6248	238	22	of	of	ADP
ejpam-6248	238	23	the	the	DET
ejpam-6248	238	24	ode	ode	PROPN
ejpam-6248	238	25	(	(	PUNCT
ejpam-6248	238	26	70	70	NUM
ejpam-6248	238	27	)	)	PUNCT
ejpam-6248	238	28	,	,	PUNCT
ejpam-6248	238	29	we	we	PRON
ejpam-6248	238	30	obtain	obtain	VERB
ejpam-6248	238	31	the	the	DET
ejpam-6248	238	32	exact	exact	ADJ
ejpam-6248	238	33	solution	solution	NOUN
ejpam-6248	238	34	of	of	ADP
ejpam-6248	238	35	the	the	DET
ejpam-6248	238	36	pde	pde	NOUN
ejpam-6248	238	37	(	(	PUNCT
ejpam-6248	238	38	1	1	NUM
ejpam-6248	238	39	):	):	PUNCT
ejpam-6248	238	40	u(x	u(x	PROPN
ejpam-6248	238	41	,	,	PUNCT
ejpam-6248	238	42	t	t	NOUN
ejpam-6248	238	43	)	)	PUNCT
ejpam-6248	238	44	=	=	SYM
ejpam-6248	239	1	(	(	PUNCT
ejpam-6248	239	2	2lambertw(−2c1xe	2lambertw(−2c1xe	PROPN
ejpam-6248	239	3	−t	−t	NOUN
ejpam-6248	239	4	)	)	PUNCT
ejpam-6248	240	1	+	+	PUNCT
ejpam-6248	241	1	1)x2	1)x2	NUM
ejpam-6248	241	2	2lambertw(−2c1xe−t)2	2lambertw(−2c1xe−t)2	PROPN
ejpam-6248	242	1	+	+	CCONJ
ejpam-6248	242	2	c2e	c2e	PROPN
ejpam-6248	242	3	2	2	NUM
ejpam-6248	242	4	t.	t.	NOUN
ejpam-6248	242	5	(	(	PUNCT
ejpam-6248	242	6	71	71	NUM
ejpam-6248	242	7	)	)	PUNCT
ejpam-6248	242	8	remark	remark	NOUN
ejpam-6248	242	9	:	:	PUNCT
ejpam-6248	242	10	the	the	DET
ejpam-6248	242	11	lambertw	lambertw	NOUN
ejpam-6248	242	12	function	function	NOUN
ejpam-6248	242	13	,	,	PUNCT
ejpam-6248	242	14	defined	define	VERB
ejpam-6248	242	15	as	as	ADP
ejpam-6248	242	16	the	the	DET
ejpam-6248	242	17	inverse	inverse	NOUN
ejpam-6248	242	18	of	of	ADP
ejpam-6248	242	19	wew	wew	PROPN
ejpam-6248	242	20	=	=	SYM
ejpam-6248	242	21	z	z	NOUN
ejpam-6248	242	22	,	,	PUNCT
ejpam-6248	242	23	is	be	AUX
ejpam-6248	242	24	multivalued	multivalue	VERB
ejpam-6248	242	25	with	with	ADP
ejpam-6248	242	26	two	two	NUM
ejpam-6248	242	27	real	real	ADJ
ejpam-6248	242	28	branches	branch	NOUN
ejpam-6248	242	29	:	:	PUNCT
ejpam-6248	242	30	the	the	DET
ejpam-6248	242	31	principal	principal	ADJ
ejpam-6248	242	32	branch	branch	NOUN
ejpam-6248	242	33	w0	w0	PROPN
ejpam-6248	242	34	,	,	PUNCT
ejpam-6248	242	35	defined	define	VERB
ejpam-6248	242	36	for	for	ADP
ejpam-6248	242	37	z	z	PROPN
ejpam-6248	242	38	≥	≥	NOUN
ejpam-6248	242	39	−1	−1	NOUN
ejpam-6248	242	40	e	e	NOUN
ejpam-6248	242	41	,	,	PUNCT
ejpam-6248	242	42	and	and	CCONJ
ejpam-6248	242	43	the	the	DET
ejpam-6248	242	44	lower	low	ADJ
ejpam-6248	242	45	branch	branch	NOUN
ejpam-6248	242	46	w−1	w−1	PROPN
ejpam-6248	242	47	defined	define	VERB
ejpam-6248	242	48	for	for	ADP
ejpam-6248	242	49	1	1	NUM
ejpam-6248	242	50	e	e	NOUN
ejpam-6248	242	51	≤	≤	X
ejpam-6248	242	52	z	z	NOUN
ejpam-6248	242	53	≤	≤	NOUN
ejpam-6248	242	54	0	0	NUM
ejpam-6248	242	55	.	.	PUNCT
ejpam-6248	243	1	the	the	DET
ejpam-6248	243	2	branch	branch	NOUN
ejpam-6248	243	3	point	point	NOUN
ejpam-6248	243	4	at	at	ADP
ejpam-6248	243	5	z	z	NOUN
ejpam-6248	243	6	=	=	SYM
ejpam-6248	243	7	−1	−1	NOUN
ejpam-6248	243	8	e	e	NOUN
ejpam-6248	243	9	and	and	CCONJ
ejpam-6248	243	10	corresponding	corresponding	ADJ
ejpam-6248	243	11	branch	branch	NOUN
ejpam-6248	243	12	cuts	cut	NOUN
ejpam-6248	243	13	play	play	VERB
ejpam-6248	243	14	a	a	DET
ejpam-6248	243	15	critical	critical	ADJ
ejpam-6248	243	16	role	role	NOUN
ejpam-6248	243	17	in	in	ADP
ejpam-6248	243	18	ensuring	ensure	VERB
ejpam-6248	243	19	the	the	DET
ejpam-6248	243	20	physical	physical	ADJ
ejpam-6248	243	21	validity	validity	NOUN
ejpam-6248	243	22	and	and	CCONJ
ejpam-6248	243	23	continuity	continuity	NOUN
ejpam-6248	243	24	of	of	ADP
ejpam-6248	243	25	solutions	solution	NOUN
ejpam-6248	243	26	in	in	ADP
ejpam-6248	243	27	aerodynamic	aerodynamic	ADJ
ejpam-6248	243	28	models	model	NOUN
ejpam-6248	243	29	,	,	PUNCT
ejpam-6248	243	30	especially	especially	ADV
ejpam-6248	243	31	when	when	SCONJ
ejpam-6248	243	32	dealing	deal	VERB
ejpam-6248	243	33	with	with	ADP
ejpam-6248	243	34	exponential	exponential	ADJ
ejpam-6248	243	35	growth	growth	NOUN
ejpam-6248	243	36	or	or	CCONJ
ejpam-6248	243	37	decay	decay	NOUN
ejpam-6248	243	38	in	in	ADP
ejpam-6248	243	39	boundary	boundary	ADJ
ejpam-6248	243	40	layers	layer	NOUN
ejpam-6248	243	41	or	or	CCONJ
ejpam-6248	243	42	transonic	transonic	ADJ
ejpam-6248	243	43	flows	flow	NOUN
ejpam-6248	243	44	.	.	PUNCT
ejpam-6248	244	1	in	in	ADP
ejpam-6248	244	2	aerodynamics	aerodynamic	NOUN
ejpam-6248	244	3	,	,	PUNCT
ejpam-6248	244	4	lambertw	lambertw	NOUN
ejpam-6248	244	5	function	function	NOUN
ejpam-6248	244	6	appears	appear	VERB
ejpam-6248	244	7	in	in	ADP
ejpam-6248	244	8	exact	exact	ADJ
ejpam-6248	244	9	solutions	solution	NOUN
ejpam-6248	244	10	of	of	ADP
ejpam-6248	244	11	nonlinear	nonlinear	ADJ
ejpam-6248	244	12	equations	equation	NOUN
ejpam-6248	244	13	involving	involve	VERB
ejpam-6248	244	14	compressible	compressible	ADJ
ejpam-6248	244	15	flow	flow	NOUN
ejpam-6248	244	16	and	and	CCONJ
ejpam-6248	244	17	similarity	similarity	NOUN
ejpam-6248	244	18	reductions	reduction	NOUN
ejpam-6248	244	19	.	.	PUNCT
ejpam-6248	245	1	case:-4	case:-4	PUNCT
ejpam-6248	245	2	we	we	PRON
ejpam-6248	245	3	introduce	introduce	VERB
ejpam-6248	245	4	the	the	DET
ejpam-6248	245	5	elementary	elementary	ADJ
ejpam-6248	245	6	exponential	exponential	ADJ
ejpam-6248	245	7	function	function	NOUN
ejpam-6248	245	8	transformation	transformation	NOUN
ejpam-6248	245	9	,	,	PUNCT
ejpam-6248	245	10	defined	define	VERB
ejpam-6248	245	11	as	as	ADP
ejpam-6248	245	12	:	:	PUNCT
ejpam-6248	245	13	ξ	ξ	X
ejpam-6248	245	14	=	=	PUNCT
ejpam-6248	245	15	emx+ny	emx+ny	PROPN
ejpam-6248	245	16	.	.	PUNCT
ejpam-6248	246	1	(	(	PUNCT
ejpam-6248	246	2	72	72	X
ejpam-6248	246	3	)	)	PUNCT
ejpam-6248	246	4	u	u	NOUN
ejpam-6248	246	5	=	=	NOUN
ejpam-6248	246	6	f(ξ	f(ξ	NOUN
ejpam-6248	246	7	)	)	PUNCT
ejpam-6248	246	8	.	.	PUNCT
ejpam-6248	247	1	(	(	PUNCT
ejpam-6248	247	2	73	73	NUM
ejpam-6248	247	3	)	)	PUNCT
ejpam-6248	247	4	differentiating	differentiate	VERB
ejpam-6248	247	5	equations	equation	NOUN
ejpam-6248	247	6	(	(	PUNCT
ejpam-6248	247	7	72	72	NUM
ejpam-6248	247	8	)	)	PUNCT
ejpam-6248	247	9	and	and	CCONJ
ejpam-6248	247	10	(	(	PUNCT
ejpam-6248	247	11	73	73	NUM
ejpam-6248	247	12	)	)	PUNCT
ejpam-6248	247	13	according	accord	VERB
ejpam-6248	247	14	to	to	ADP
ejpam-6248	247	15	equation	equation	NOUN
ejpam-6248	247	16	(	(	PUNCT
ejpam-6248	247	17	1	1	NUM
ejpam-6248	247	18	)	)	PUNCT
ejpam-6248	247	19	,	,	PUNCT
ejpam-6248	247	20	we	we	PRON
ejpam-6248	247	21	obtain	obtain	VERB
ejpam-6248	247	22	:	:	PUNCT
ejpam-6248	247	23	ux	ux	ADJ
ejpam-6248	247	24	=	=	SYM
ejpam-6248	247	25	mξf	mξf	PROPN
ejpam-6248	247	26	′(ξ	′(ξ	NOUN
ejpam-6248	247	27	)	)	PUNCT
ejpam-6248	247	28	.	.	PUNCT
ejpam-6248	248	1	(	(	PUNCT
ejpam-6248	248	2	74	74	NUM
ejpam-6248	248	3	)	)	PUNCT
ejpam-6248	248	4	uxx	uxx	NOUN
ejpam-6248	249	1	=	=	SYM
ejpam-6248	249	2	m2ξ(ξf	m2ξ(ξf	ADJ
ejpam-6248	249	3	′′(ξ	′′(ξ	NUM
ejpam-6248	249	4	)	)	PUNCT
ejpam-6248	250	1	+	+	NUM
ejpam-6248	250	2	f	f	PROPN
ejpam-6248	250	3	′(ξ	′(ξ	NOUN
ejpam-6248	250	4	)	)	PUNCT
ejpam-6248	250	5	)	)	PUNCT
ejpam-6248	250	6	.	.	PUNCT
ejpam-6248	251	1	(	(	PUNCT
ejpam-6248	251	2	75	75	NUM
ejpam-6248	251	3	)	)	PUNCT
ejpam-6248	251	4	uyy	uyy	PROPN
ejpam-6248	251	5	=	=	SYM
ejpam-6248	251	6	n2ξ(ξf	n2ξ(ξf	PROPN
ejpam-6248	251	7	′′(ξ	′′(ξ	PROPN
ejpam-6248	251	8	)	)	PUNCT
ejpam-6248	252	1	+	+	NUM
ejpam-6248	252	2	f	f	PROPN
ejpam-6248	252	3	′(ξ	′(ξ	NOUN
ejpam-6248	252	4	)	)	PUNCT
ejpam-6248	252	5	)	)	PUNCT
ejpam-6248	252	6	.	.	PUNCT
ejpam-6248	253	1	(	(	PUNCT
ejpam-6248	253	2	76	76	NUM
ejpam-6248	253	3	)	)	PUNCT
ejpam-6248	253	4	uxt	uxt	NOUN
ejpam-6248	253	5	=	=	SYM
ejpam-6248	253	6	0	0	NUM
ejpam-6248	253	7	.	.	PUNCT
ejpam-6248	254	1	(	(	PUNCT
ejpam-6248	254	2	77	77	X
ejpam-6248	254	3	)	)	PUNCT
ejpam-6248	254	4	substiuting	substiuting	NOUN
ejpam-6248	254	5	equations	equation	NOUN
ejpam-6248	254	6	(	(	PUNCT
ejpam-6248	254	7	74	74	NUM
ejpam-6248	254	8	)	)	PUNCT
ejpam-6248	254	9	,	,	PUNCT
ejpam-6248	254	10	(	(	PUNCT
ejpam-6248	254	11	75	75	NUM
ejpam-6248	254	12	)	)	PUNCT
ejpam-6248	254	13	,	,	PUNCT
ejpam-6248	254	14	(	(	PUNCT
ejpam-6248	254	15	76	76	NUM
ejpam-6248	254	16	)	)	PUNCT
ejpam-6248	254	17	,	,	PUNCT
ejpam-6248	254	18	and	and	CCONJ
ejpam-6248	254	19	(	(	PUNCT
ejpam-6248	254	20	77	77	NUM
ejpam-6248	254	21	)	)	PUNCT
ejpam-6248	254	22	in	in	ADP
ejpam-6248	254	23	equation	equation	NOUN
ejpam-6248	254	24	(	(	PUNCT
ejpam-6248	254	25	1	1	NUM
ejpam-6248	254	26	)	)	PUNCT
ejpam-6248	254	27	,	,	PUNCT
ejpam-6248	254	28	we	we	PRON
ejpam-6248	254	29	obtain	obtain	VERB
ejpam-6248	254	30	the	the	DET
ejpam-6248	254	31	following	following	ADJ
ejpam-6248	254	32	ode	ode	PROPN
ejpam-6248	254	33	:	:	PUNCT
ejpam-6248	254	34	m3ξ2f	m3ξ2f	PUNCT
ejpam-6248	254	35	′(ξ)f	′(ξ)f	PROPN
ejpam-6248	254	36	′′(ξ	′′(ξ	PROPN
ejpam-6248	254	37	)	)	PUNCT
ejpam-6248	255	1	+	+	ADJ
ejpam-6248	255	2	m3ξf	m3ξf	X
ejpam-6248	255	3	′2(ξ)−	′2(ξ)−	NOUN
ejpam-6248	255	4	n2ξf	n2ξf	PUNCT
ejpam-6248	255	5	′′(ξ)−	′′(ξ)−	PROPN
ejpam-6248	255	6	n2f	n2f	NOUN
ejpam-6248	255	7	′(ξ	′(ξ	NOUN
ejpam-6248	255	8	)	)	PUNCT
ejpam-6248	255	9	=	=	SYM
ejpam-6248	256	1	0	0	X
ejpam-6248	256	2	.	.	PUNCT
ejpam-6248	257	1	(	(	PUNCT
ejpam-6248	257	2	78	78	NUM
ejpam-6248	257	3	)	)	PUNCT
ejpam-6248	257	4	the	the	DET
ejpam-6248	257	5	analytic	analytic	ADJ
ejpam-6248	257	6	solution	solution	NOUN
ejpam-6248	257	7	to	to	PART
ejpam-6248	257	8	ode	ode	VERB
ejpam-6248	257	9	(	(	PUNCT
ejpam-6248	257	10	78	78	NUM
ejpam-6248	257	11	)	)	PUNCT
ejpam-6248	257	12	is	be	AUX
ejpam-6248	257	13	:	:	PUNCT
ejpam-6248	257	14	f(ξ	f(ξ	X
ejpam-6248	257	15	)	)	PUNCT
ejpam-6248	257	16	=	=	SYM
ejpam-6248	257	17	n2	n2	NOUN
ejpam-6248	257	18	ln(ξ	ln(ξ	X
ejpam-6248	257	19	)	)	PUNCT
ejpam-6248	257	20	+	+	NUM
ejpam-6248	257	21	ln(ξ	ln(ξ	NOUN
ejpam-6248	257	22	)	)	PUNCT
ejpam-6248	257	23	√	√	PUNCT
ejpam-6248	258	1	−2c1m3	−2c1m3	VERB
ejpam-6248	258	2	+	+	CCONJ
ejpam-6248	258	3	n4	n4	PROPN
ejpam-6248	258	4	m3	m3	PROPN
ejpam-6248	258	5	+	+	CCONJ
ejpam-6248	258	6	c2	c2	PROPN
ejpam-6248	258	7	.	.	PUNCT
ejpam-6248	259	1	(	(	PUNCT
ejpam-6248	259	2	79	79	NUM
ejpam-6248	259	3	)	)	PUNCT
ejpam-6248	259	4	using	use	VERB
ejpam-6248	259	5	the	the	DET
ejpam-6248	259	6	similarity	similarity	NOUN
ejpam-6248	259	7	function	function	NOUN
ejpam-6248	259	8	transformations	transformation	NOUN
ejpam-6248	259	9	(	(	PUNCT
ejpam-6248	259	10	72	72	NUM
ejpam-6248	259	11	)	)	PUNCT
ejpam-6248	259	12	and	and	CCONJ
ejpam-6248	259	13	(	(	PUNCT
ejpam-6248	259	14	73	73	NUM
ejpam-6248	259	15	)	)	PUNCT
ejpam-6248	259	16	,	,	PUNCT
ejpam-6248	259	17	together	together	ADV
ejpam-6248	259	18	with	with	ADP
ejpam-6248	259	19	the	the	DET
ejpam-6248	259	20	analytic	analytic	ADJ
ejpam-6248	259	21	solution	solution	NOUN
ejpam-6248	259	22	of	of	ADP
ejpam-6248	259	23	ode	ode	PROPN
ejpam-6248	259	24	(	(	PUNCT
ejpam-6248	259	25	79	79	NUM
ejpam-6248	259	26	)	)	PUNCT
ejpam-6248	259	27	,	,	PUNCT
ejpam-6248	259	28	we	we	PRON
ejpam-6248	259	29	obtain	obtain	VERB
ejpam-6248	259	30	the	the	DET
ejpam-6248	259	31	exact	exact	ADJ
ejpam-6248	259	32	solution	solution	NOUN
ejpam-6248	259	33	to	to	ADP
ejpam-6248	259	34	the	the	DET
ejpam-6248	259	35	pde	pde	NOUN
ejpam-6248	259	36	(	(	PUNCT
ejpam-6248	259	37	1	1	NUM
ejpam-6248	259	38	):	):	PUNCT
ejpam-6248	259	39	u(x	u(x	PROPN
ejpam-6248	259	40	,	,	PUNCT
ejpam-6248	259	41	y	y	NOUN
ejpam-6248	259	42	)	)	PUNCT
ejpam-6248	259	43	=	=	SYM
ejpam-6248	259	44	n2(mx+	n2(mx+	NOUN
ejpam-6248	259	45	ny	ny	NOUN
ejpam-6248	259	46	)	)	PUNCT
ejpam-6248	260	1	+	+	CCONJ
ejpam-6248	260	2	(	(	PUNCT
ejpam-6248	260	3	mx+	mx+	PROPN
ejpam-6248	260	4	ny	ny	PROPN
ejpam-6248	260	5	)	)	PUNCT
ejpam-6248	260	6	√	√	PUNCT
ejpam-6248	261	1	−2c1m3	−2c1m3	VERB
ejpam-6248	261	2	+	+	CCONJ
ejpam-6248	261	3	n4	n4	PROPN
ejpam-6248	261	4	m3	m3	PROPN
ejpam-6248	261	5	+	+	CCONJ
ejpam-6248	261	6	c2	c2	PROPN
ejpam-6248	261	7	.	.	PUNCT
ejpam-6248	262	1	(	(	PUNCT
ejpam-6248	262	2	80	80	NUM
ejpam-6248	262	3	)	)	PUNCT
ejpam-6248	262	4	z.	z.	PROPN
ejpam-6248	262	5	haider	haider	PROPN
ejpam-6248	262	6	et	et	PROPN
ejpam-6248	262	7	al	al	PROPN
ejpam-6248	262	8	.	.	PUNCT
ejpam-6248	262	9	/	/	SYM
ejpam-6248	262	10	eur	eur	PROPN
ejpam-6248	262	11	.	.	PUNCT
ejpam-6248	263	1	j.	j.	PROPN
ejpam-6248	263	2	pure	pure	PROPN
ejpam-6248	263	3	appl	appl	PROPN
ejpam-6248	263	4	.	.	PROPN
ejpam-6248	263	5	math	math	PROPN
ejpam-6248	263	6	,	,	PUNCT
ejpam-6248	263	7	18	18	NUM
ejpam-6248	263	8	(	(	PUNCT
ejpam-6248	263	9	3	3	NUM
ejpam-6248	263	10	)	)	PUNCT
ejpam-6248	263	11	(	(	PUNCT
ejpam-6248	263	12	2025	2025	NUM
ejpam-6248	263	13	)	)	PUNCT
ejpam-6248	263	14	,	,	PUNCT
ejpam-6248	263	15	6248	6248	NUM
ejpam-6248	263	16	16	16	NUM
ejpam-6248	263	17	of	of	ADP
ejpam-6248	263	18	20	20	NUM
ejpam-6248	263	19	figure	figure	NOUN
ejpam-6248	263	20	8	8	NUM
ejpam-6248	263	21	:	:	PUNCT
ejpam-6248	263	22	3d	3d	NUM
ejpam-6248	263	23	complex	complex	ADJ
ejpam-6248	263	24	plot	plot	NOUN
ejpam-6248	263	25	of	of	ADP
ejpam-6248	263	26	(	(	PUNCT
ejpam-6248	263	27	80	80	NUM
ejpam-6248	263	28	)	)	PUNCT
ejpam-6248	263	29	for	for	ADP
ejpam-6248	263	30	m	m	PROPN
ejpam-6248	263	31	=	=	SYM
ejpam-6248	263	32	−2	−2	NOUN
ejpam-6248	263	33	,	,	PUNCT
ejpam-6248	263	34	n	n	NOUN
ejpam-6248	263	35	=	=	SYM
ejpam-6248	263	36	3	3	NUM
ejpam-6248	263	37	,	,	PUNCT
ejpam-6248	263	38	c1	c1	NOUN
ejpam-6248	263	39	=	=	PROPN
ejpam-6248	263	40	−8	−8	PROPN
ejpam-6248	263	41	and	and	CCONJ
ejpam-6248	263	42	c2	c2	PROPN
ejpam-6248	263	43	=	=	SYM
ejpam-6248	263	44	1	1	X
ejpam-6248	263	45	.	.	X
ejpam-6248	263	46	convergence	convergence	NOUN
ejpam-6248	263	47	of	of	ADP
ejpam-6248	263	48	self	self	NOUN
ejpam-6248	263	49	-	-	PUNCT
ejpam-6248	263	50	similar	similar	ADJ
ejpam-6248	263	51	solutions	solution	NOUN
ejpam-6248	263	52	the	the	DET
ejpam-6248	263	53	self	self	NOUN
ejpam-6248	263	54	-	-	PUNCT
ejpam-6248	263	55	similar	similar	ADJ
ejpam-6248	263	56	solutions	solution	NOUN
ejpam-6248	263	57	derived	derive	VERB
ejpam-6248	263	58	in	in	ADP
ejpam-6248	263	59	this	this	DET
ejpam-6248	263	60	study	study	NOUN
ejpam-6248	263	61	are	be	AUX
ejpam-6248	263	62	constructed	construct	VERB
ejpam-6248	263	63	through	through	ADP
ejpam-6248	263	64	exact	exact	ADJ
ejpam-6248	263	65	analytical	analytical	ADJ
ejpam-6248	263	66	transformations	transformation	NOUN
ejpam-6248	263	67	that	that	PRON
ejpam-6248	263	68	reduce	reduce	VERB
ejpam-6248	263	69	the	the	DET
ejpam-6248	263	70	original	original	ADJ
ejpam-6248	263	71	partial	partial	ADJ
ejpam-6248	263	72	differential	differential	NOUN
ejpam-6248	263	73	equations	equation	NOUN
ejpam-6248	263	74	to	to	ADP
ejpam-6248	263	75	simpler	simple	ADJ
ejpam-6248	263	76	forms	form	NOUN
ejpam-6248	263	77	.	.	PUNCT
ejpam-6248	264	1	the	the	DET
ejpam-6248	264	2	convergence	convergence	NOUN
ejpam-6248	264	3	of	of	ADP
ejpam-6248	264	4	these	these	DET
ejpam-6248	264	5	solutions	solution	NOUN
ejpam-6248	264	6	is	be	AUX
ejpam-6248	264	7	ensured	ensure	VERB
ejpam-6248	264	8	by	by	ADP
ejpam-6248	264	9	identifying	identify	VERB
ejpam-6248	264	10	and	and	CCONJ
ejpam-6248	264	11	excluding	exclude	VERB
ejpam-6248	264	12	singular	singular	ADJ
ejpam-6248	264	13	points	point	NOUN
ejpam-6248	264	14	from	from	ADP
ejpam-6248	264	15	the	the	DET
ejpam-6248	264	16	solution	solution	NOUN
ejpam-6248	264	17	domain	domain	NOUN
ejpam-6248	264	18	,	,	PUNCT
ejpam-6248	264	19	such	such	ADJ
ejpam-6248	264	20	as	as	ADP
ejpam-6248	264	21	values	value	NOUN
ejpam-6248	264	22	that	that	PRON
ejpam-6248	264	23	lead	lead	VERB
ejpam-6248	264	24	to	to	ADP
ejpam-6248	264	25	division	division	NOUN
ejpam-6248	264	26	by	by	ADP
ejpam-6248	264	27	zero	zero	NUM
ejpam-6248	264	28	or	or	CCONJ
ejpam-6248	264	29	non	non	ADJ
ejpam-6248	264	30	-	-	ADJ
ejpam-6248	264	31	real	real	ADJ
ejpam-6248	264	32	expressions	expression	NOUN
ejpam-6248	264	33	(	(	PUNCT
ejpam-6248	264	34	e.g.	e.g.	ADV
ejpam-6248	264	35	,	,	PUNCT
ejpam-6248	264	36	due	due	ADP
ejpam-6248	264	37	to	to	ADP
ejpam-6248	264	38	square	square	ADJ
ejpam-6248	264	39	roots	root	NOUN
ejpam-6248	264	40	or	or	CCONJ
ejpam-6248	264	41	special	special	ADJ
ejpam-6248	264	42	functions	function	NOUN
ejpam-6248	264	43	)	)	PUNCT
ejpam-6248	264	44	.	.	PUNCT
ejpam-6248	265	1	under	under	ADP
ejpam-6248	265	2	appropriate	appropriate	ADJ
ejpam-6248	265	3	conditions	condition	NOUN
ejpam-6248	265	4	on	on	ADP
ejpam-6248	265	5	the	the	DET
ejpam-6248	265	6	parameters	parameter	NOUN
ejpam-6248	265	7	and	and	CCONJ
ejpam-6248	265	8	variables	variable	NOUN
ejpam-6248	265	9	,	,	PUNCT
ejpam-6248	265	10	the	the	DET
ejpam-6248	265	11	solutions	solution	NOUN
ejpam-6248	265	12	remain	remain	VERB
ejpam-6248	265	13	real	real	ADV
ejpam-6248	265	14	-	-	PUNCT
ejpam-6248	265	15	valued	value	VERB
ejpam-6248	265	16	,	,	PUNCT
ejpam-6248	265	17	continuous	continuous	ADJ
ejpam-6248	265	18	,	,	PUNCT
ejpam-6248	265	19	and	and	CCONJ
ejpam-6248	265	20	physically	physically	ADV
ejpam-6248	265	21	meaningful	meaningful	ADJ
ejpam-6248	265	22	,	,	PUNCT
ejpam-6248	265	23	confirming	confirm	VERB
ejpam-6248	265	24	their	their	PRON
ejpam-6248	265	25	validity	validity	NOUN
ejpam-6248	265	26	and	and	CCONJ
ejpam-6248	265	27	convergence	convergence	NOUN
ejpam-6248	265	28	within	within	ADP
ejpam-6248	265	29	the	the	DET
ejpam-6248	265	30	defined	define	VERB
ejpam-6248	265	31	domains	domain	NOUN
ejpam-6248	265	32	.	.	PUNCT
ejpam-6248	266	1	4	4	X
ejpam-6248	266	2	.	.	NOUN
ejpam-6248	266	3	results	result	NOUN
ejpam-6248	266	4	and	and	CCONJ
ejpam-6248	266	5	discussion	discussion	NOUN
ejpam-6248	266	6	this	this	DET
ejpam-6248	266	7	work	work	NOUN
ejpam-6248	266	8	introduces	introduce	VERB
ejpam-6248	266	9	a	a	DET
ejpam-6248	266	10	novel	novel	ADJ
ejpam-6248	266	11	analytical	analytical	ADJ
ejpam-6248	266	12	framework	framework	NOUN
ejpam-6248	266	13	for	for	ADP
ejpam-6248	266	14	obtaining	obtain	VERB
ejpam-6248	266	15	self	self	NOUN
ejpam-6248	266	16	-	-	PUNCT
ejpam-6248	266	17	similar	similar	ADJ
ejpam-6248	266	18	solutions	solution	NOUN
ejpam-6248	266	19	of	of	ADP
ejpam-6248	266	20	the	the	DET
ejpam-6248	266	21	lin	lin	PROPN
ejpam-6248	266	22	–	–	PUNCT
ejpam-6248	266	23	reissner	reissner	NOUN
ejpam-6248	266	24	–	–	PUNCT
ejpam-6248	266	25	tsien	tsien	NOUN
ejpam-6248	266	26	(	(	PUNCT
ejpam-6248	266	27	lrt	lrt	PROPN
ejpam-6248	266	28	)	)	PUNCT
ejpam-6248	266	29	equation	equation	NOUN
ejpam-6248	266	30	,	,	PUNCT
ejpam-6248	266	31	offering	offer	VERB
ejpam-6248	266	32	new	new	ADJ
ejpam-6248	266	33	insights	insight	NOUN
ejpam-6248	266	34	into	into	ADP
ejpam-6248	266	35	nonlinear	nonlinear	ADJ
ejpam-6248	266	36	dynamical	dynamical	ADJ
ejpam-6248	266	37	systems	system	NOUN
ejpam-6248	266	38	.	.	PUNCT
ejpam-6248	267	1	the	the	DET
ejpam-6248	267	2	power	power	NOUN
ejpam-6248	267	3	index	index	NOUN
ejpam-6248	267	4	method	method	NOUN
ejpam-6248	267	5	(	(	PUNCT
ejpam-6248	267	6	pim	pim	PROPN
ejpam-6248	267	7	)	)	PUNCT
ejpam-6248	267	8	yields	yield	VERB
ejpam-6248	267	9	self	self	NOUN
ejpam-6248	267	10	-	-	PUNCT
ejpam-6248	267	11	similar	similar	ADJ
ejpam-6248	267	12	solutions	solution	NOUN
ejpam-6248	267	13	with	with	ADP
ejpam-6248	267	14	distinct	distinct	ADJ
ejpam-6248	267	15	structures	structure	NOUN
ejpam-6248	267	16	,	,	PUNCT
ejpam-6248	267	17	including	include	VERB
ejpam-6248	267	18	traveling	travel	VERB
ejpam-6248	267	19	waves	wave	NOUN
ejpam-6248	267	20	,	,	PUNCT
ejpam-6248	267	21	blow	blow	NOUN
ejpam-6248	267	22	-	-	PUNCT
ejpam-6248	267	23	up	up	ADP
ejpam-6248	267	24	singularities	singularity	NOUN
ejpam-6248	267	25	,	,	PUNCT
ejpam-6248	267	26	boundary	boundary	ADJ
ejpam-6248	267	27	layers	layer	NOUN
ejpam-6248	267	28	,	,	PUNCT
ejpam-6248	267	29	dissipative	dissipative	NOUN
ejpam-6248	267	30	z.	z.	PROPN
ejpam-6248	267	31	haider	haider	PROPN
ejpam-6248	267	32	et	et	PROPN
ejpam-6248	267	33	al	al	PROPN
ejpam-6248	267	34	.	.	PUNCT
ejpam-6248	267	35	/	/	SYM
ejpam-6248	267	36	eur	eur	PROPN
ejpam-6248	267	37	.	.	PUNCT
ejpam-6248	268	1	j.	j.	PROPN
ejpam-6248	268	2	pure	pure	PROPN
ejpam-6248	268	3	appl	appl	PROPN
ejpam-6248	268	4	.	.	PROPN
ejpam-6248	268	5	math	math	PROPN
ejpam-6248	268	6	,	,	PUNCT
ejpam-6248	268	7	18	18	NUM
ejpam-6248	268	8	(	(	PUNCT
ejpam-6248	268	9	3	3	NUM
ejpam-6248	268	10	)	)	PUNCT
ejpam-6248	268	11	(	(	PUNCT
ejpam-6248	268	12	2025	2025	NUM
ejpam-6248	268	13	)	)	PUNCT
ejpam-6248	268	14	,	,	PUNCT
ejpam-6248	268	15	6248	6248	NUM
ejpam-6248	268	16	17	17	NUM
ejpam-6248	268	17	of	of	ADP
ejpam-6248	268	18	20	20	NUM
ejpam-6248	268	19	solitons	soliton	NOUN
ejpam-6248	268	20	,	,	PUNCT
ejpam-6248	268	21	and	and	CCONJ
ejpam-6248	268	22	localized	localized	ADJ
ejpam-6248	268	23	pulses	pulse	NOUN
ejpam-6248	268	24	–	–	PUNCT
ejpam-6248	268	25	each	each	PRON
ejpam-6248	268	26	emerging	emerge	VERB
ejpam-6248	268	27	from	from	ADP
ejpam-6248	268	28	the	the	DET
ejpam-6248	268	29	scaling	scale	VERB
ejpam-6248	268	30	symmetries	symmetry	NOUN
ejpam-6248	268	31	and	and	CCONJ
ejpam-6248	268	32	nonlinear	nonlinear	ADJ
ejpam-6248	268	33	nature	nature	NOUN
ejpam-6248	268	34	of	of	ADP
ejpam-6248	268	35	the	the	DET
ejpam-6248	268	36	governing	govern	VERB
ejpam-6248	268	37	partial	partial	ADJ
ejpam-6248	268	38	differential	differential	NOUN
ejpam-6248	268	39	equation	equation	NOUN
ejpam-6248	268	40	.	.	PUNCT
ejpam-6248	269	1	fig	fig	NOUN
ejpam-6248	269	2	.	.	PUNCT
ejpam-6248	270	1	2	2	NUM
ejpam-6248	270	2	depicts	depict	VERB
ejpam-6248	270	3	a	a	DET
ejpam-6248	270	4	spatial	spatial	ADJ
ejpam-6248	270	5	blow	blow	NOUN
ejpam-6248	270	6	-	-	PUNCT
ejpam-6248	270	7	up	up	ADP
ejpam-6248	270	8	solution	solution	NOUN
ejpam-6248	270	9	exhibiting	exhibit	VERB
ejpam-6248	270	10	time	time	NOUN
ejpam-6248	270	11	-	-	PUNCT
ejpam-6248	270	12	decaying	decay	VERB
ejpam-6248	270	13	behavior	behavior	NOUN
ejpam-6248	270	14	,	,	PUNCT
ejpam-6248	270	15	the	the	DET
ejpam-6248	270	16	solution	solution	NOUN
ejpam-6248	270	17	u(x	u(x	NOUN
ejpam-6248	270	18	,	,	PUNCT
ejpam-6248	270	19	t	t	NOUN
ejpam-6248	270	20	)	)	PUNCT
ejpam-6248	270	21	becomes	become	VERB
ejpam-6248	270	22	unbounded	unbounded	ADJ
ejpam-6248	270	23	as	as	ADP
ejpam-6248	270	24	|x|	|x|	PROPN
ejpam-6248	270	25	→	→	SYM
ejpam-6248	270	26	∞	∞	PROPN
ejpam-6248	270	27	,	,	PUNCT
ejpam-6248	270	28	indicating	indicate	VERB
ejpam-6248	270	29	spatial	spatial	ADJ
ejpam-6248	270	30	blow	blow	NOUN
ejpam-6248	270	31	-	-	PUNCT
ejpam-6248	270	32	up	up	NOUN
ejpam-6248	270	33	,	,	PUNCT
ejpam-6248	270	34	while	while	SCONJ
ejpam-6248	270	35	simultaneously	simultaneously	ADV
ejpam-6248	270	36	decaying	decay	VERB
ejpam-6248	270	37	in	in	ADP
ejpam-6248	270	38	time	time	NOUN
ejpam-6248	270	39	as	as	ADP
ejpam-6248	270	40	t	t	NOUN
ejpam-6248	270	41	increases	increase	NOUN
ejpam-6248	270	42	.	.	PUNCT
ejpam-6248	271	1	this	this	DET
ejpam-6248	271	2	dual	dual	ADJ
ejpam-6248	271	3	behavior	behavior	NOUN
ejpam-6248	271	4	is	be	AUX
ejpam-6248	271	5	typical	typical	ADJ
ejpam-6248	271	6	of	of	ADP
ejpam-6248	271	7	certain	certain	ADJ
ejpam-6248	271	8	nonlinear	nonlinear	ADJ
ejpam-6248	271	9	pdes	pde	NOUN
ejpam-6248	271	10	where	where	SCONJ
ejpam-6248	271	11	localized	localized	ADJ
ejpam-6248	271	12	structures	structure	NOUN
ejpam-6248	271	13	dissipate	dissipate	VERB
ejpam-6248	271	14	over	over	ADP
ejpam-6248	271	15	time	time	NOUN
ejpam-6248	271	16	but	but	CCONJ
ejpam-6248	271	17	exhibit	exhibit	NOUN
ejpam-6248	271	18	singularities	singularity	NOUN
ejpam-6248	271	19	or	or	CCONJ
ejpam-6248	271	20	steep	steep	ADJ
ejpam-6248	271	21	spatial	spatial	ADJ
ejpam-6248	271	22	gradients	gradient	NOUN
ejpam-6248	271	23	.	.	PUNCT
ejpam-6248	272	1	fig	fig	NOUN
ejpam-6248	272	2	.	.	PUNCT
ejpam-6248	273	1	3	3	NUM
ejpam-6248	273	2	represents	represent	VERB
ejpam-6248	273	3	a	a	DET
ejpam-6248	273	4	shock	shock	NOUN
ejpam-6248	273	5	wave	wave	NOUN
ejpam-6248	273	6	or	or	CCONJ
ejpam-6248	273	7	boundary	boundary	ADJ
ejpam-6248	273	8	layer	layer	NOUN
ejpam-6248	273	9	solution	solution	NOUN
ejpam-6248	273	10	,	,	PUNCT
ejpam-6248	273	11	characterized	characterize	VERB
ejpam-6248	273	12	by	by	ADP
ejpam-6248	273	13	steep	steep	ADJ
ejpam-6248	273	14	spatial	spatial	ADJ
ejpam-6248	273	15	gradients	gradient	NOUN
ejpam-6248	273	16	indicative	indicative	ADJ
ejpam-6248	273	17	of	of	ADP
ejpam-6248	273	18	singular	singular	ADJ
ejpam-6248	273	19	perturbation	perturbation	NOUN
ejpam-6248	273	20	effects	effect	NOUN
ejpam-6248	273	21	.	.	PUNCT
ejpam-6248	274	1	such	such	ADJ
ejpam-6248	274	2	solutions	solution	NOUN
ejpam-6248	274	3	correspond	correspond	VERB
ejpam-6248	274	4	to	to	ADP
ejpam-6248	274	5	abrupt	abrupt	ADJ
ejpam-6248	274	6	transitions	transition	NOUN
ejpam-6248	274	7	in	in	ADP
ejpam-6248	274	8	fluid	fluid	ADJ
ejpam-6248	274	9	properties	property	NOUN
ejpam-6248	274	10	like	like	ADP
ejpam-6248	274	11	velocity	velocity	NOUN
ejpam-6248	274	12	,	,	PUNCT
ejpam-6248	274	13	pressure	pressure	NOUN
ejpam-6248	274	14	,	,	PUNCT
ejpam-6248	274	15	and	and	CCONJ
ejpam-6248	274	16	density	density	NOUN
ejpam-6248	274	17	–	–	PUNCT
ejpam-6248	274	18	phenomena	phenomenon	NOUN
ejpam-6248	274	19	commonly	commonly	ADV
ejpam-6248	274	20	observed	observe	VERB
ejpam-6248	274	21	in	in	ADP
ejpam-6248	274	22	supersonic	supersonic	ADJ
ejpam-6248	274	23	or	or	CCONJ
ejpam-6248	274	24	transonic	transonic	ADJ
ejpam-6248	274	25	flows	flow	NOUN
ejpam-6248	274	26	.	.	PUNCT
ejpam-6248	275	1	fig	fig	NOUN
ejpam-6248	275	2	.	.	PUNCT
ejpam-6248	276	1	4	4	NUM
ejpam-6248	276	2	illustrates	illustrate	VERB
ejpam-6248	276	3	a	a	DET
ejpam-6248	276	4	finite	finite	ADJ
ejpam-6248	276	5	-	-	PUNCT
ejpam-6248	276	6	time	time	NOUN
ejpam-6248	276	7	blow	blow	NOUN
ejpam-6248	276	8	-	-	PUNCT
ejpam-6248	276	9	up	up	ADP
ejpam-6248	276	10	solution	solution	NOUN
ejpam-6248	276	11	,	,	PUNCT
ejpam-6248	276	12	showing	show	VERB
ejpam-6248	276	13	an	an	DET
ejpam-6248	276	14	explosive	explosive	ADJ
ejpam-6248	276	15	growth	growth	NOUN
ejpam-6248	276	16	in	in	ADP
ejpam-6248	276	17	amplitude	amplitude	NOUN
ejpam-6248	276	18	.	.	PUNCT
ejpam-6248	277	1	blow	blow	VERB
ejpam-6248	277	2	-	-	PUNCT
ejpam-6248	277	3	up	up	ADP
ejpam-6248	277	4	phenomena	phenomenon	NOUN
ejpam-6248	277	5	,	,	PUNCT
ejpam-6248	277	6	where	where	SCONJ
ejpam-6248	277	7	solutions	solution	NOUN
ejpam-6248	277	8	become	become	VERB
ejpam-6248	277	9	unbounded	unbounded	ADJ
ejpam-6248	277	10	in	in	ADP
ejpam-6248	277	11	finite	finite	ADJ
ejpam-6248	277	12	time	time	NOUN
ejpam-6248	277	13	or	or	CCONJ
ejpam-6248	277	14	space	space	NOUN
ejpam-6248	277	15	,	,	PUNCT
ejpam-6248	277	16	are	be	AUX
ejpam-6248	277	17	significant	significant	ADJ
ejpam-6248	277	18	in	in	ADP
ejpam-6248	277	19	modeling	model	VERB
ejpam-6248	277	20	wave	wave	NOUN
ejpam-6248	277	21	breaking	breaking	NOUN
ejpam-6248	277	22	,	,	PUNCT
ejpam-6248	277	23	turbulence	turbulence	NOUN
ejpam-6248	277	24	onset	onset	NOUN
ejpam-6248	277	25	,	,	PUNCT
ejpam-6248	277	26	and	and	CCONJ
ejpam-6248	277	27	flow	flow	NOUN
ejpam-6248	277	28	singularities	singularity	NOUN
ejpam-6248	277	29	near	near	ADP
ejpam-6248	277	30	critical	critical	ADJ
ejpam-6248	277	31	points	point	NOUN
ejpam-6248	277	32	in	in	ADP
ejpam-6248	277	33	compressible	compressible	ADJ
ejpam-6248	277	34	flow	flow	NOUN
ejpam-6248	277	35	systems	system	NOUN
ejpam-6248	277	36	.	.	PUNCT
ejpam-6248	278	1	fig	fig	NOUN
ejpam-6248	278	2	.	.	PUNCT
ejpam-6248	279	1	5	5	NUM
ejpam-6248	279	2	presents	present	VERB
ejpam-6248	279	3	a	a	DET
ejpam-6248	279	4	damped	damped	NOUN
ejpam-6248	279	5	oscillatory	oscillatory	ADJ
ejpam-6248	279	6	solution	solution	NOUN
ejpam-6248	279	7	,	,	PUNCT
ejpam-6248	279	8	characterized	characterize	VERB
ejpam-6248	279	9	by	by	ADP
ejpam-6248	279	10	its	its	PRON
ejpam-6248	279	11	decaying	decay	VERB
ejpam-6248	279	12	amplitude	amplitude	NOUN
ejpam-6248	279	13	and	and	CCONJ
ejpam-6248	279	14	wave	wave	NOUN
ejpam-6248	279	15	-	-	PUNCT
ejpam-6248	279	16	like	like	ADJ
ejpam-6248	279	17	temporal	temporal	ADJ
ejpam-6248	279	18	behavior	behavior	NOUN
ejpam-6248	279	19	.	.	PUNCT
ejpam-6248	280	1	fig	fig	NOUN
ejpam-6248	280	2	.	.	PUNCT
ejpam-6248	281	1	6	6	NUM
ejpam-6248	281	2	displays	display	VERB
ejpam-6248	281	3	a	a	DET
ejpam-6248	281	4	localized	localized	ADJ
ejpam-6248	281	5	stationary	stationary	ADJ
ejpam-6248	281	6	soliton	soliton	NOUN
ejpam-6248	281	7	solution	solution	NOUN
ejpam-6248	281	8	,	,	PUNCT
ejpam-6248	281	9	which	which	PRON
ejpam-6248	281	10	maintains	maintain	VERB
ejpam-6248	281	11	a	a	DET
ejpam-6248	281	12	stable	stable	ADJ
ejpam-6248	281	13	,	,	PUNCT
ejpam-6248	281	14	peaked	peak	VERB
ejpam-6248	281	15	profile	profile	NOUN
ejpam-6248	281	16	without	without	ADP
ejpam-6248	281	17	dispersing	disperse	VERB
ejpam-6248	281	18	over	over	ADP
ejpam-6248	281	19	time	time	NOUN
ejpam-6248	281	20	.	.	PUNCT
ejpam-6248	282	1	soliton	soliton	NOUN
ejpam-6248	282	2	solutions	solution	NOUN
ejpam-6248	282	3	are	be	AUX
ejpam-6248	282	4	smooth	smooth	ADJ
ejpam-6248	282	5	,	,	PUNCT
ejpam-6248	282	6	localized	localized	ADJ
ejpam-6248	282	7	waveforms	waveform	NOUN
ejpam-6248	282	8	that	that	PRON
ejpam-6248	282	9	retain	retain	VERB
ejpam-6248	282	10	their	their	PRON
ejpam-6248	282	11	shape	shape	NOUN
ejpam-6248	282	12	due	due	ADP
ejpam-6248	282	13	to	to	ADP
ejpam-6248	282	14	a	a	DET
ejpam-6248	282	15	balance	balance	NOUN
ejpam-6248	282	16	between	between	ADP
ejpam-6248	282	17	nonlinearity	nonlinearity	NOUN
ejpam-6248	282	18	and	and	CCONJ
ejpam-6248	282	19	dispersion	dispersion	NOUN
ejpam-6248	282	20	.	.	PUNCT
ejpam-6248	283	1	they	they	PRON
ejpam-6248	283	2	are	be	AUX
ejpam-6248	283	3	particularly	particularly	ADV
ejpam-6248	283	4	important	important	ADJ
ejpam-6248	283	5	in	in	ADP
ejpam-6248	283	6	modeling	model	VERB
ejpam-6248	283	7	non	non	ADJ
ejpam-6248	283	8	-	-	ADJ
ejpam-6248	283	9	dispersive	dispersive	ADJ
ejpam-6248	283	10	wave	wave	NOUN
ejpam-6248	283	11	interactions	interaction	NOUN
ejpam-6248	283	12	in	in	ADP
ejpam-6248	283	13	nonlinear	nonlinear	ADJ
ejpam-6248	283	14	media	medium	NOUN
ejpam-6248	283	15	,	,	PUNCT
ejpam-6248	283	16	including	include	VERB
ejpam-6248	283	17	boundary	boundary	ADJ
ejpam-6248	283	18	layer	layer	NOUN
ejpam-6248	283	19	effects	effect	NOUN
ejpam-6248	283	20	and	and	CCONJ
ejpam-6248	283	21	internal	internal	ADJ
ejpam-6248	283	22	fluid	fluid	ADJ
ejpam-6248	283	23	waves	wave	NOUN
ejpam-6248	283	24	.	.	PUNCT
ejpam-6248	284	1	these	these	DET
ejpam-6248	284	2	mathematical	mathematical	ADJ
ejpam-6248	284	3	structures	structure	NOUN
ejpam-6248	284	4	provide	provide	VERB
ejpam-6248	284	5	insight	insight	NOUN
ejpam-6248	284	6	into	into	ADP
ejpam-6248	284	7	the	the	DET
ejpam-6248	284	8	qualitative	qualitative	ADJ
ejpam-6248	284	9	behavior	behavior	NOUN
ejpam-6248	284	10	of	of	ADP
ejpam-6248	284	11	solutions	solution	NOUN
ejpam-6248	284	12	and	and	CCONJ
ejpam-6248	284	13	help	help	VERB
ejpam-6248	284	14	interpret	interpret	VERB
ejpam-6248	284	15	complex	complex	ADJ
ejpam-6248	284	16	nonlinear	nonlinear	ADJ
ejpam-6248	284	17	flow	flow	NOUN
ejpam-6248	284	18	features	feature	VERB
ejpam-6248	284	19	relevant	relevant	ADJ
ejpam-6248	284	20	to	to	ADP
ejpam-6248	284	21	engineering	engineering	NOUN
ejpam-6248	284	22	and	and	CCONJ
ejpam-6248	284	23	physical	physical	ADJ
ejpam-6248	284	24	applications	application	NOUN
ejpam-6248	284	25	such	such	ADJ
ejpam-6248	284	26	as	as	ADP
ejpam-6248	284	27	aerodynamic	aerodynamic	ADJ
ejpam-6248	284	28	systems	system	NOUN
ejpam-6248	284	29	,	,	PUNCT
ejpam-6248	284	30	gas	gas	NOUN
ejpam-6248	284	31	dynamic	dynamic	ADJ
ejpam-6248	284	32	processes	process	NOUN
ejpam-6248	284	33	,	,	PUNCT
ejpam-6248	284	34	and	and	CCONJ
ejpam-6248	284	35	transonic	transonic	ADJ
ejpam-6248	284	36	regimes	regime	NOUN
ejpam-6248	284	37	.	.	PUNCT
ejpam-6248	284	38	fig	fig	NOUN
ejpam-6248	284	39	.	.	PUNCT
ejpam-6248	285	1	7	7	NUM
ejpam-6248	285	2	illustrates	illustrate	VERB
ejpam-6248	285	3	a	a	DET
ejpam-6248	285	4	self	self	NOUN
ejpam-6248	285	5	-	-	PUNCT
ejpam-6248	285	6	similar	similar	ADJ
ejpam-6248	285	7	solution	solution	NOUN
ejpam-6248	285	8	of	of	ADP
ejpam-6248	285	9	the	the	DET
ejpam-6248	285	10	second	second	ADJ
ejpam-6248	285	11	kind	kind	NOUN
ejpam-6248	285	12	,	,	PUNCT
ejpam-6248	285	13	characterized	characterize	VERB
ejpam-6248	285	14	by	by	ADP
ejpam-6248	285	15	a	a	DET
ejpam-6248	285	16	dynamically	dynamically	ADV
ejpam-6248	285	17	evolving	evolve	VERB
ejpam-6248	285	18	profile	profile	NOUN
ejpam-6248	285	19	that	that	PRON
ejpam-6248	285	20	preserves	preserve	VERB
ejpam-6248	285	21	its	its	PRON
ejpam-6248	285	22	shape	shape	NOUN
ejpam-6248	285	23	under	under	ADP
ejpam-6248	285	24	scaling	scale	VERB
ejpam-6248	285	25	transformations	transformation	NOUN
ejpam-6248	285	26	while	while	SCONJ
ejpam-6248	285	27	exhibiting	exhibit	VERB
ejpam-6248	285	28	power	power	NOUN
ejpam-6248	285	29	-	-	PUNCT
ejpam-6248	285	30	law	law	NOUN
ejpam-6248	285	31	temporal	temporal	ADJ
ejpam-6248	285	32	decay	decay	NOUN
ejpam-6248	285	33	.	.	PUNCT
ejpam-6248	286	1	fig	fig	NOUN
ejpam-6248	286	2	.	.	PUNCT
ejpam-6248	287	1	8	8	NUM
ejpam-6248	287	2	shows	show	VERB
ejpam-6248	287	3	a	a	DET
ejpam-6248	287	4	nonlinear	nonlinear	ADJ
ejpam-6248	287	5	standing	standing	ADJ
ejpam-6248	287	6	wave	wave	NOUN
ejpam-6248	287	7	solution	solution	NOUN
ejpam-6248	287	8	with	with	ADP
ejpam-6248	287	9	a	a	DET
ejpam-6248	287	10	periodic	periodic	ADJ
ejpam-6248	287	11	spatial	spatial	ADJ
ejpam-6248	287	12	structure	structure	NOUN
ejpam-6248	287	13	and	and	CCONJ
ejpam-6248	287	14	amplitude	amplitude	NOUN
ejpam-6248	287	15	modulated	modulate	VERB
ejpam-6248	287	16	by	by	ADP
ejpam-6248	287	17	the	the	DET
ejpam-6248	287	18	interplay	interplay	NOUN
ejpam-6248	287	19	between	between	ADP
ejpam-6248	287	20	nonlinearity	nonlinearity	NOUN
ejpam-6248	287	21	and	and	CCONJ
ejpam-6248	287	22	dispersion	dispersion	NOUN
ejpam-6248	287	23	.	.	PUNCT
ejpam-6248	288	1	this	this	DET
ejpam-6248	288	2	paper	paper	NOUN
ejpam-6248	288	3	serves	serve	VERB
ejpam-6248	288	4	as	as	ADP
ejpam-6248	288	5	a	a	DET
ejpam-6248	288	6	valuable	valuable	ADJ
ejpam-6248	288	7	resource	resource	NOUN
ejpam-6248	288	8	for	for	ADP
ejpam-6248	288	9	scientists	scientist	NOUN
ejpam-6248	288	10	and	and	CCONJ
ejpam-6248	288	11	researchers	researcher	NOUN
ejpam-6248	288	12	by	by	ADP
ejpam-6248	288	13	offering	offer	VERB
ejpam-6248	288	14	thorough	thorough	ADJ
ejpam-6248	288	15	analysis	analysis	NOUN
ejpam-6248	288	16	and	and	CCONJ
ejpam-6248	288	17	clear	clear	ADJ
ejpam-6248	288	18	graphical	graphical	ADJ
ejpam-6248	288	19	representations	representation	NOUN
ejpam-6248	288	20	that	that	PRON
ejpam-6248	288	21	enhance	enhance	VERB
ejpam-6248	288	22	the	the	DET
ejpam-6248	288	23	understanding	understanding	NOUN
ejpam-6248	288	24	of	of	ADP
ejpam-6248	288	25	the	the	DET
ejpam-6248	288	26	lrt	lrt	PROPN
ejpam-6248	288	27	equation	equation	NOUN
ejpam-6248	288	28	’s	’s	PART
ejpam-6248	288	29	dynamic	dynamic	ADJ
ejpam-6248	288	30	behavior	behavior	NOUN
ejpam-6248	288	31	and	and	CCONJ
ejpam-6248	288	32	associated	associate	VERB
ejpam-6248	288	33	physical	physical	ADJ
ejpam-6248	288	34	phenomena	phenomenon	NOUN
ejpam-6248	288	35	.	.	PUNCT
ejpam-6248	289	1	furthermore	furthermore	ADV
ejpam-6248	289	2	,	,	PUNCT
ejpam-6248	289	3	it	it	PRON
ejpam-6248	289	4	opens	open	VERB
ejpam-6248	289	5	new	new	ADJ
ejpam-6248	289	6	research	research	NOUN
ejpam-6248	289	7	directions	direction	NOUN
ejpam-6248	289	8	across	across	ADP
ejpam-6248	289	9	multiple	multiple	ADJ
ejpam-6248	289	10	scientific	scientific	ADJ
ejpam-6248	289	11	disciplines	discipline	NOUN
ejpam-6248	289	12	by	by	ADP
ejpam-6248	289	13	demonstrating	demonstrate	VERB
ejpam-6248	289	14	the	the	DET
ejpam-6248	289	15	effectiveness	effectiveness	NOUN
ejpam-6248	289	16	of	of	ADP
ejpam-6248	289	17	the	the	DET
ejpam-6248	289	18	power	power	NOUN
ejpam-6248	289	19	index	index	NOUN
ejpam-6248	289	20	method	method	NOUN
ejpam-6248	289	21	in	in	ADP
ejpam-6248	289	22	solving	solve	VERB
ejpam-6248	289	23	nonlinear	nonlinear	ADJ
ejpam-6248	289	24	partial	partial	ADJ
ejpam-6248	289	25	differential	differential	NOUN
ejpam-6248	289	26	equations	equation	NOUN
ejpam-6248	289	27	.	.	PUNCT
ejpam-6248	290	1	5	5	X
ejpam-6248	290	2	.	.	X
ejpam-6248	290	3	conclusions	conclusion	NOUN
ejpam-6248	290	4	this	this	DET
ejpam-6248	290	5	research	research	NOUN
ejpam-6248	290	6	paper	paper	NOUN
ejpam-6248	290	7	aims	aim	VERB
ejpam-6248	290	8	to	to	PART
ejpam-6248	290	9	derive	derive	VERB
ejpam-6248	290	10	self	self	NOUN
ejpam-6248	290	11	-	-	PUNCT
ejpam-6248	290	12	similar	similar	ADJ
ejpam-6248	290	13	solutions	solution	NOUN
ejpam-6248	290	14	involving	involve	VERB
ejpam-6248	290	15	rational	rational	ADJ
ejpam-6248	290	16	,	,	PUNCT
ejpam-6248	290	17	exponential	exponential	ADJ
ejpam-6248	290	18	,	,	PUNCT
ejpam-6248	290	19	and	and	CCONJ
ejpam-6248	290	20	special	special	ADJ
ejpam-6248	290	21	functions	function	NOUN
ejpam-6248	290	22	,	,	PUNCT
ejpam-6248	290	23	obtained	obtain	VERB
ejpam-6248	290	24	from	from	ADP
ejpam-6248	290	25	the	the	DET
ejpam-6248	290	26	lin	lin	PROPN
ejpam-6248	290	27	–	–	PUNCT
ejpam-6248	290	28	reissner	reissner	NOUN
ejpam-6248	290	29	–	–	PUNCT
ejpam-6248	290	30	tsien	tsien	NOUN
ejpam-6248	290	31	(	(	PUNCT
ejpam-6248	290	32	lrt	lrt	PROPN
ejpam-6248	290	33	)	)	PUNCT
ejpam-6248	290	34	equation	equation	NOUN
ejpam-6248	290	35	through	through	ADP
ejpam-6248	290	36	the	the	DET
ejpam-6248	290	37	application	application	NOUN
ejpam-6248	290	38	of	of	ADP
ejpam-6248	290	39	the	the	DET
ejpam-6248	290	40	power	power	NOUN
ejpam-6248	290	41	index	index	NOUN
ejpam-6248	290	42	method	method	NOUN
ejpam-6248	290	43	(	(	PUNCT
ejpam-6248	290	44	pim	pim	PROPN
ejpam-6248	290	45	)	)	PUNCT
ejpam-6248	290	46	.	.	PUNCT
ejpam-6248	291	1	the	the	DET
ejpam-6248	291	2	solutions	solution	NOUN
ejpam-6248	291	3	are	be	AUX
ejpam-6248	291	4	presented	present	VERB
ejpam-6248	291	5	in	in	ADP
ejpam-6248	291	6	explicit	explicit	ADJ
ejpam-6248	291	7	form	form	NOUN
ejpam-6248	291	8	and	and	CCONJ
ejpam-6248	291	9	depend	depend	VERB
ejpam-6248	291	10	on	on	ADP
ejpam-6248	291	11	the	the	DET
ejpam-6248	291	12	independent	independent	ADJ
ejpam-6248	291	13	variables	variable	NOUN
ejpam-6248	291	14	.	.	PUNCT
ejpam-6248	292	1	through	through	ADP
ejpam-6248	292	2	self	self	NOUN
ejpam-6248	292	3	-	-	PUNCT
ejpam-6248	292	4	similar	similar	ADJ
ejpam-6248	292	5	transformations	transformation	NOUN
ejpam-6248	292	6	of	of	ADP
ejpam-6248	292	7	the	the	DET
ejpam-6248	292	8	nonlinear	nonlinear	ADJ
ejpam-6248	292	9	lrt	lrt	PROPN
ejpam-6248	292	10	equation	equation	NOUN
ejpam-6248	292	11	,	,	PUNCT
ejpam-6248	292	12	we	we	PRON
ejpam-6248	292	13	derive	derive	VERB
ejpam-6248	292	14	nonlinear	nonlinear	ADJ
ejpam-6248	292	15	ordinary	ordinary	ADJ
ejpam-6248	292	16	differential	differential	ADJ
ejpam-6248	292	17	equations	equation	NOUN
ejpam-6248	292	18	(	(	PUNCT
ejpam-6248	292	19	odes	ode	NOUN
ejpam-6248	292	20	)	)	PUNCT
ejpam-6248	292	21	with	with	ADP
ejpam-6248	292	22	parameter	parameter	NOUN
ejpam-6248	292	23	-	-	PUNCT
ejpam-6248	292	24	dependent	dependent	ADJ
ejpam-6248	292	25	coefficients	coefficient	NOUN
ejpam-6248	292	26	.	.	PUNCT
ejpam-6248	293	1	using	use	VERB
ejpam-6248	293	2	the	the	DET
ejpam-6248	293	3	symbolic	symbolic	ADJ
ejpam-6248	293	4	computation	computation	NOUN
ejpam-6248	293	5	software	software	NOUN
ejpam-6248	293	6	maple	maple	NOUN
ejpam-6248	293	7	18	18	NUM
ejpam-6248	293	8	,	,	PUNCT
ejpam-6248	293	9	we	we	PRON
ejpam-6248	293	10	obtain	obtain	VERB
ejpam-6248	293	11	analytic	analytic	ADJ
ejpam-6248	293	12	solutions	solution	NOUN
ejpam-6248	293	13	to	to	ADP
ejpam-6248	293	14	the	the	DET
ejpam-6248	293	15	resulting	result	VERB
ejpam-6248	293	16	nonlinear	nonlinear	ADJ
ejpam-6248	293	17	odes	ode	NOUN
ejpam-6248	293	18	.	.	PUNCT
ejpam-6248	294	1	the	the	DET
ejpam-6248	294	2	self	self	NOUN
ejpam-6248	294	3	-	-	PUNCT
ejpam-6248	294	4	similar	similar	ADJ
ejpam-6248	294	5	solutions	solution	NOUN
ejpam-6248	294	6	of	of	ADP
ejpam-6248	294	7	the	the	DET
ejpam-6248	294	8	lin	lin	PROPN
ejpam-6248	294	9	–	–	PUNCT
ejpam-6248	294	10	reissner	reissner	NOUN
ejpam-6248	294	11	–	–	PUNCT
ejpam-6248	294	12	tsien	tsien	NOUN
ejpam-6248	294	13	equation	equation	NOUN
ejpam-6248	294	14	are	be	AUX
ejpam-6248	294	15	obtained	obtain	VERB
ejpam-6248	294	16	using	use	VERB
ejpam-6248	294	17	these	these	DET
ejpam-6248	294	18	transformations	transformation	NOUN
ejpam-6248	294	19	and	and	CCONJ
ejpam-6248	294	20	the	the	DET
ejpam-6248	294	21	analytic	analytic	ADJ
ejpam-6248	294	22	z.	z.	PROPN
ejpam-6248	294	23	haider	haider	PROPN
ejpam-6248	294	24	et	et	PROPN
ejpam-6248	294	25	al	al	PROPN
ejpam-6248	294	26	.	.	PUNCT
ejpam-6248	294	27	/	/	SYM
ejpam-6248	294	28	eur	eur	PROPN
ejpam-6248	294	29	.	.	PUNCT
ejpam-6248	295	1	j.	j.	PROPN
ejpam-6248	295	2	pure	pure	PROPN
ejpam-6248	295	3	appl	appl	PROPN
ejpam-6248	295	4	.	.	PROPN
ejpam-6248	295	5	math	math	PROPN
ejpam-6248	295	6	,	,	PUNCT
ejpam-6248	295	7	18	18	NUM
ejpam-6248	295	8	(	(	PUNCT
ejpam-6248	295	9	3	3	NUM
ejpam-6248	295	10	)	)	PUNCT
ejpam-6248	295	11	(	(	PUNCT
ejpam-6248	295	12	2025	2025	NUM
ejpam-6248	295	13	)	)	PUNCT
ejpam-6248	295	14	,	,	PUNCT
ejpam-6248	295	15	6248	6248	NUM
ejpam-6248	295	16	18	18	NUM
ejpam-6248	295	17	of	of	ADP
ejpam-6248	295	18	20	20	NUM
ejpam-6248	295	19	solutions	solution	NOUN
ejpam-6248	295	20	of	of	ADP
ejpam-6248	295	21	the	the	DET
ejpam-6248	295	22	corresponding	corresponding	ADJ
ejpam-6248	295	23	odes	ode	NOUN
ejpam-6248	295	24	.	.	PUNCT
ejpam-6248	296	1	all	all	PRON
ejpam-6248	296	2	obtained	obtain	VERB
ejpam-6248	296	3	solutions	solution	NOUN
ejpam-6248	296	4	are	be	AUX
ejpam-6248	296	5	novel	novel	ADJ
ejpam-6248	296	6	,	,	PUNCT
ejpam-6248	296	7	with	with	SCONJ
ejpam-6248	296	8	some	some	PRON
ejpam-6248	296	9	expressed	express	VERB
ejpam-6248	296	10	in	in	ADP
ejpam-6248	296	11	terms	term	NOUN
ejpam-6248	296	12	of	of	ADP
ejpam-6248	296	13	special	special	ADJ
ejpam-6248	296	14	functions	function	NOUN
ejpam-6248	296	15	(	(	PUNCT
ejpam-6248	296	16	(	(	PUNCT
ejpam-6248	296	17	refer	refer	VERB
ejpam-6248	296	18	to	to	ADP
ejpam-6248	296	19	(	(	PUNCT
ejpam-6248	296	20	(	(	PUNCT
ejpam-6248	296	21	53	53	NUM
ejpam-6248	296	22	)	)	PUNCT
ejpam-6248	296	23	,	,	PUNCT
ejpam-6248	296	24	(	(	PUNCT
ejpam-6248	296	25	66	66	NUM
ejpam-6248	296	26	)	)	PUNCT
ejpam-6248	296	27	and	and	CCONJ
ejpam-6248	296	28	(	(	PUNCT
ejpam-6248	296	29	71	71	NUM
ejpam-6248	296	30	)	)	PUNCT
ejpam-6248	296	31	)	)	PUNCT
ejpam-6248	296	32	.	.	PUNCT
ejpam-6248	297	1	the	the	DET
ejpam-6248	297	2	exact	exact	ADJ
ejpam-6248	297	3	solutions	solution	NOUN
ejpam-6248	297	4	of	of	ADP
ejpam-6248	297	5	the	the	DET
ejpam-6248	297	6	lrt	lrt	PROPN
ejpam-6248	297	7	equation	equation	NOUN
ejpam-6248	297	8	presented	present	VERB
ejpam-6248	297	9	in	in	ADP
ejpam-6248	297	10	this	this	DET
ejpam-6248	297	11	study	study	NOUN
ejpam-6248	297	12	provide	provide	VERB
ejpam-6248	297	13	valuable	valuable	ADJ
ejpam-6248	297	14	insights	insight	NOUN
ejpam-6248	297	15	into	into	ADP
ejpam-6248	297	16	various	various	ADJ
ejpam-6248	297	17	physical	physical	ADJ
ejpam-6248	297	18	phenomena	phenomenon	NOUN
ejpam-6248	297	19	.	.	PUNCT
ejpam-6248	298	1	additionally	additionally	ADV
ejpam-6248	298	2	,	,	PUNCT
ejpam-6248	298	3	the	the	DET
ejpam-6248	298	4	projective	projective	ADJ
ejpam-6248	298	5	power	power	NOUN
ejpam-6248	298	6	index	index	NOUN
ejpam-6248	298	7	method	method	NOUN
ejpam-6248	298	8	has	have	AUX
ejpam-6248	298	9	been	be	AUX
ejpam-6248	298	10	effectively	effectively	ADV
ejpam-6248	298	11	utilized	utilize	VERB
ejpam-6248	298	12	to	to	PART
ejpam-6248	298	13	obtain	obtain	VERB
ejpam-6248	298	14	these	these	DET
ejpam-6248	298	15	exact	exact	ADJ
ejpam-6248	298	16	solutions	solution	NOUN
ejpam-6248	298	17	.	.	PUNCT
ejpam-6248	299	1	6	6	X
ejpam-6248	299	2	.	.	X
ejpam-6248	299	3	future	future	ADJ
ejpam-6248	299	4	recommendations	recommendation	NOUN
ejpam-6248	299	5	the	the	DET
ejpam-6248	299	6	study	study	NOUN
ejpam-6248	299	7	of	of	ADP
ejpam-6248	299	8	self	self	NOUN
ejpam-6248	299	9	-	-	PUNCT
ejpam-6248	299	10	similar	similar	ADJ
ejpam-6248	299	11	solutions	solution	NOUN
ejpam-6248	299	12	to	to	ADP
ejpam-6248	299	13	the	the	DET
ejpam-6248	299	14	lin	lin	PROPN
ejpam-6248	299	15	–	–	PUNCT
ejpam-6248	299	16	reissner	reissner	NOUN
ejpam-6248	299	17	–	–	PUNCT
ejpam-6248	299	18	tsien	tsien	NOUN
ejpam-6248	299	19	(	(	PUNCT
ejpam-6248	299	20	lrt	lrt	PROPN
ejpam-6248	299	21	)	)	PUNCT
ejpam-6248	299	22	equation	equation	NOUN
ejpam-6248	299	23	using	use	VERB
ejpam-6248	299	24	the	the	DET
ejpam-6248	299	25	power	power	NOUN
ejpam-6248	299	26	index	index	NOUN
ejpam-6248	299	27	method	method	NOUN
ejpam-6248	299	28	(	(	PUNCT
ejpam-6248	299	29	pim	pim	NOUN
ejpam-6248	299	30	)	)	PUNCT
ejpam-6248	299	31	offers	offer	VERB
ejpam-6248	299	32	multiple	multiple	ADJ
ejpam-6248	299	33	avenues	avenue	NOUN
ejpam-6248	299	34	for	for	ADP
ejpam-6248	299	35	further	further	ADJ
ejpam-6248	299	36	investigation	investigation	NOUN
ejpam-6248	299	37	.	.	PUNCT
ejpam-6248	300	1	first	first	ADV
ejpam-6248	300	2	,	,	PUNCT
ejpam-6248	300	3	extending	extend	VERB
ejpam-6248	300	4	the	the	DET
ejpam-6248	300	5	method	method	NOUN
ejpam-6248	300	6	to	to	ADP
ejpam-6248	300	7	higher	higher	ADV
ejpam-6248	300	8	-	-	PUNCT
ejpam-6248	300	9	dimensional	dimensional	ADJ
ejpam-6248	300	10	or	or	CCONJ
ejpam-6248	300	11	more	more	ADV
ejpam-6248	300	12	complex	complex	ADJ
ejpam-6248	300	13	flow	flow	NOUN
ejpam-6248	300	14	configurations	configuration	NOUN
ejpam-6248	300	15	could	could	AUX
ejpam-6248	300	16	enhance	enhance	VERB
ejpam-6248	300	17	its	its	PRON
ejpam-6248	300	18	applicability	applicability	NOUN
ejpam-6248	300	19	in	in	ADP
ejpam-6248	300	20	aerodynamics	aerodynamic	NOUN
ejpam-6248	300	21	and	and	CCONJ
ejpam-6248	300	22	fluid	fluid	ADJ
ejpam-6248	300	23	dynamics	dynamic	NOUN
ejpam-6248	300	24	.	.	PUNCT
ejpam-6248	301	1	investigating	investigate	VERB
ejpam-6248	301	2	the	the	DET
ejpam-6248	301	3	stability	stability	NOUN
ejpam-6248	301	4	and	and	CCONJ
ejpam-6248	301	5	physical	physical	ADJ
ejpam-6248	301	6	realizability	realizability	NOUN
ejpam-6248	301	7	of	of	ADP
ejpam-6248	301	8	obtained	obtain	VERB
ejpam-6248	301	9	solutions	solution	NOUN
ejpam-6248	301	10	through	through	ADP
ejpam-6248	301	11	numerical	numerical	ADJ
ejpam-6248	301	12	simulations	simulation	NOUN
ejpam-6248	301	13	or	or	CCONJ
ejpam-6248	301	14	experiments	experiment	NOUN
ejpam-6248	301	15	would	would	AUX
ejpam-6248	301	16	provide	provide	VERB
ejpam-6248	301	17	deeper	deep	ADJ
ejpam-6248	301	18	insights	insight	NOUN
ejpam-6248	301	19	into	into	ADP
ejpam-6248	301	20	their	their	PRON
ejpam-6248	301	21	practical	practical	ADJ
ejpam-6248	301	22	relevance	relevance	NOUN
ejpam-6248	301	23	.	.	PUNCT
ejpam-6248	302	1	additionally	additionally	ADV
ejpam-6248	302	2	,	,	PUNCT
ejpam-6248	302	3	incorporating	incorporate	VERB
ejpam-6248	302	4	variable	variable	ADJ
ejpam-6248	302	5	power	power	NOUN
ejpam-6248	302	6	indices	index	NOUN
ejpam-6248	302	7	or	or	CCONJ
ejpam-6248	302	8	nonlinear	nonlinear	ADJ
ejpam-6248	302	9	transformations	transformation	NOUN
ejpam-6248	302	10	might	might	AUX
ejpam-6248	302	11	uncover	uncover	VERB
ejpam-6248	302	12	new	new	ADJ
ejpam-6248	302	13	classes	class	NOUN
ejpam-6248	302	14	of	of	ADP
ejpam-6248	302	15	self	self	NOUN
ejpam-6248	302	16	-	-	PUNCT
ejpam-6248	302	17	similar	similar	ADJ
ejpam-6248	302	18	solutions	solution	NOUN
ejpam-6248	302	19	.	.	PUNCT
ejpam-6248	303	1	exploring	explore	VERB
ejpam-6248	303	2	connections	connection	NOUN
ejpam-6248	303	3	with	with	ADP
ejpam-6248	303	4	other	other	ADJ
ejpam-6248	303	5	asymptotic	asymptotic	ADJ
ejpam-6248	303	6	methods	method	NOUN
ejpam-6248	303	7	,	,	PUNCT
ejpam-6248	303	8	such	such	ADJ
ejpam-6248	303	9	as	as	ADP
ejpam-6248	303	10	lie	lie	NOUN
ejpam-6248	303	11	symmetry	symmetry	NOUN
ejpam-6248	303	12	analysis	analysis	NOUN
ejpam-6248	303	13	or	or	CCONJ
ejpam-6248	303	14	perturbation	perturbation	NOUN
ejpam-6248	303	15	techniques	technique	NOUN
ejpam-6248	303	16	,	,	PUNCT
ejpam-6248	303	17	could	could	AUX
ejpam-6248	303	18	further	far	ADV
ejpam-6248	303	19	unify	unify	VERB
ejpam-6248	303	20	the	the	DET
ejpam-6248	303	21	theoretical	theoretical	ADJ
ejpam-6248	303	22	framework	framework	NOUN
ejpam-6248	303	23	.	.	PUNCT
ejpam-6248	304	1	finally	finally	ADV
ejpam-6248	304	2	,	,	PUNCT
ejpam-6248	304	3	applying	apply	VERB
ejpam-6248	304	4	these	these	DET
ejpam-6248	304	5	solutions	solution	NOUN
ejpam-6248	304	6	to	to	ADP
ejpam-6248	304	7	real	real	ADJ
ejpam-6248	304	8	-	-	PUNCT
ejpam-6248	304	9	world	world	NOUN
ejpam-6248	304	10	problems	problem	NOUN
ejpam-6248	304	11	,	,	PUNCT
ejpam-6248	304	12	such	such	ADJ
ejpam-6248	304	13	as	as	ADP
ejpam-6248	304	14	hypersonic	hypersonic	ADJ
ejpam-6248	304	15	flows	flow	NOUN
ejpam-6248	304	16	or	or	CCONJ
ejpam-6248	304	17	boundary	boundary	ADJ
ejpam-6248	304	18	layer	layer	NOUN
ejpam-6248	304	19	phenomena	phenomenon	NOUN
ejpam-6248	304	20	,	,	PUNCT
ejpam-6248	304	21	would	would	AUX
ejpam-6248	304	22	validate	validate	VERB
ejpam-6248	304	23	their	their	PRON
ejpam-6248	304	24	utility	utility	NOUN
ejpam-6248	304	25	and	and	CCONJ
ejpam-6248	304	26	potentially	potentially	ADV
ejpam-6248	304	27	lead	lead	VERB
ejpam-6248	304	28	to	to	ADP
ejpam-6248	304	29	novel	novel	ADJ
ejpam-6248	304	30	engineering	engineering	NOUN
ejpam-6248	304	31	applications	application	NOUN
ejpam-6248	304	32	.	.	PUNCT
ejpam-6248	305	1	acknowledgements	acknowledgement	NOUN
ejpam-6248	305	2	the	the	DET
ejpam-6248	305	3	authors	author	NOUN
ejpam-6248	305	4	wish	wish	VERB
ejpam-6248	305	5	to	to	PART
ejpam-6248	305	6	express	express	VERB
ejpam-6248	305	7	their	their	PRON
ejpam-6248	305	8	gratitude	gratitude	NOUN
ejpam-6248	305	9	to	to	ADP
ejpam-6248	305	10	prince	prince	PROPN
ejpam-6248	305	11	sultan	sultan	PROPN
ejpam-6248	305	12	university	university	PROPN
ejpam-6248	305	13	for	for	ADP
ejpam-6248	305	14	facilitating	facilitate	VERB
ejpam-6248	305	15	the	the	DET
ejpam-6248	305	16	publication	publication	NOUN
ejpam-6248	305	17	of	of	ADP
ejpam-6248	305	18	this	this	DET
ejpam-6248	305	19	article	article	NOUN
ejpam-6248	305	20	through	through	ADP
ejpam-6248	305	21	the	the	DET
ejpam-6248	305	22	theoretical	theoretical	ADJ
ejpam-6248	305	23	and	and	CCONJ
ejpam-6248	305	24	applied	apply	VERB
ejpam-6248	305	25	sciences	science	NOUN
ejpam-6248	305	26	lab	lab	NOUN
ejpam-6248	305	27	.	.	PUNCT
ejpam-6248	306	1	funding	funding	NOUN
ejpam-6248	306	2	statement	statement	NOUN
ejpam-6248	306	3	the	the	DET
ejpam-6248	306	4	authors	author	NOUN
ejpam-6248	306	5	would	would	AUX
ejpam-6248	306	6	like	like	VERB
ejpam-6248	306	7	to	to	PART
ejpam-6248	306	8	acknowledge	acknowledge	VERB
ejpam-6248	306	9	the	the	DET
ejpam-6248	306	10	support	support	NOUN
ejpam-6248	306	11	of	of	ADP
ejpam-6248	306	12	prince	prince	PROPN
ejpam-6248	306	13	sultan	sultan	PROPN
ejpam-6248	306	14	university	university	PROPN
ejpam-6248	306	15	for	for	ADP
ejpam-6248	306	16	paying	pay	VERB
ejpam-6248	306	17	the	the	DET
ejpam-6248	306	18	article	article	NOUN
ejpam-6248	306	19	processing	processing	NOUN
ejpam-6248	306	20	charges	charge	NOUN
ejpam-6248	306	21	(	(	PUNCT
ejpam-6248	306	22	apc	apc	PROPN
ejpam-6248	306	23	)	)	PUNCT
ejpam-6248	306	24	of	of	ADP
ejpam-6248	306	25	this	this	DET
ejpam-6248	306	26	publication	publication	NOUN
ejpam-6248	306	27	.	.	PUNCT
ejpam-6248	307	1	competing	compete	VERB
ejpam-6248	307	2	interests	interest	NOUN
ejpam-6248	307	3	the	the	DET
ejpam-6248	307	4	authors	author	NOUN
ejpam-6248	307	5	declare	declare	VERB
ejpam-6248	307	6	that	that	SCONJ
ejpam-6248	307	7	they	they	PRON
ejpam-6248	307	8	have	have	VERB
ejpam-6248	307	9	no	no	DET
ejpam-6248	307	10	competing	compete	VERB
ejpam-6248	307	11	interests	interest	NOUN
ejpam-6248	307	12	.	.	PUNCT
ejpam-6248	308	1	data	datum	NOUN
ejpam-6248	308	2	availability	availability	NOUN
ejpam-6248	308	3	statement	statement	NOUN
ejpam-6248	308	4	the	the	DET
ejpam-6248	308	5	computations	computation	NOUN
ejpam-6248	308	6	and	and	CCONJ
ejpam-6248	308	7	results	result	NOUN
ejpam-6248	308	8	presented	present	VERB
ejpam-6248	308	9	in	in	ADP
ejpam-6248	308	10	this	this	DET
ejpam-6248	308	11	study	study	NOUN
ejpam-6248	308	12	are	be	AUX
ejpam-6248	308	13	based	base	VERB
ejpam-6248	308	14	entirely	entirely	ADV
ejpam-6248	308	15	on	on	ADP
ejpam-6248	308	16	symbolic	symbolic	ADJ
ejpam-6248	308	17	analysis	analysis	NOUN
ejpam-6248	308	18	performed	perform	VERB
ejpam-6248	308	19	using	use	VERB
ejpam-6248	308	20	maple	maple	PROPN
ejpam-6248	308	21	18	18	NUM
ejpam-6248	308	22	software	software	NOUN
ejpam-6248	308	23	.	.	PUNCT
ejpam-6248	309	1	while	while	SCONJ
ejpam-6248	309	2	no	no	DET
ejpam-6248	309	3	empirical	empirical	ADJ
ejpam-6248	309	4	datasets	dataset	NOUN
ejpam-6248	309	5	were	be	AUX
ejpam-6248	309	6	generated	generate	VERB
ejpam-6248	309	7	or	or	CCONJ
ejpam-6248	309	8	analyzed	analyze	VERB
ejpam-6248	309	9	,	,	PUNCT
ejpam-6248	309	10	the	the	DET
ejpam-6248	309	11	corresponding	correspond	VERB
ejpam-6248	309	12	maple	maple	NOUN
ejpam-6248	309	13	18	18	NUM
ejpam-6248	309	14	worksheets	worksheet	NOUN
ejpam-6248	309	15	that	that	PRON
ejpam-6248	309	16	contain	contain	VERB
ejpam-6248	309	17	all	all	DET
ejpam-6248	309	18	derivations	derivation	NOUN
ejpam-6248	309	19	and	and	CCONJ
ejpam-6248	309	20	solution	solution	NOUN
ejpam-6248	309	21	steps	step	NOUN
ejpam-6248	309	22	are	be	AUX
ejpam-6248	309	23	available	available	ADJ
ejpam-6248	309	24	from	from	ADP
ejpam-6248	309	25	the	the	DET
ejpam-6248	309	26	authors	author	NOUN
ejpam-6248	309	27	upon	upon	SCONJ
ejpam-6248	309	28	reasonable	reasonable	ADJ
ejpam-6248	309	29	request	request	NOUN
ejpam-6248	309	30	to	to	PART
ejpam-6248	309	31	ensure	ensure	VERB
ejpam-6248	309	32	full	full	ADJ
ejpam-6248	309	33	transparency	transparency	NOUN
ejpam-6248	309	34	and	and	CCONJ
ejpam-6248	309	35	reproducibility	reproducibility	NOUN
ejpam-6248	309	36	of	of	ADP
ejpam-6248	309	37	the	the	DET
ejpam-6248	309	38	work	work	NOUN
ejpam-6248	309	39	.	.	PUNCT
ejpam-6248	310	1	z.	z.	PROPN
ejpam-6248	310	2	haider	haider	PROPN
ejpam-6248	310	3	et	et	PROPN
ejpam-6248	310	4	al	al	PROPN
ejpam-6248	310	5	.	.	PUNCT
ejpam-6248	310	6	/	/	SYM
ejpam-6248	310	7	eur	eur	PROPN
ejpam-6248	310	8	.	.	PUNCT
ejpam-6248	311	1	j.	j.	PROPN
ejpam-6248	311	2	pure	pure	PROPN
ejpam-6248	311	3	appl	appl	PROPN
ejpam-6248	311	4	.	.	PROPN
ejpam-6248	311	5	math	math	PROPN
ejpam-6248	311	6	,	,	PUNCT
ejpam-6248	311	7	18	18	NUM
ejpam-6248	311	8	(	(	PUNCT
ejpam-6248	311	9	3	3	NUM
ejpam-6248	311	10	)	)	PUNCT
ejpam-6248	311	11	(	(	PUNCT
ejpam-6248	311	12	2025	2025	NUM
ejpam-6248	311	13	)	)	PUNCT
ejpam-6248	311	14	,	,	PUNCT
ejpam-6248	311	15	6248	6248	NUM
ejpam-6248	311	16	19	19	NUM
ejpam-6248	311	17	of	of	ADP
ejpam-6248	311	18	20	20	NUM
ejpam-6248	311	19	references	reference	NOUN
ejpam-6248	311	20	[	[	X
ejpam-6248	311	21	1	1	NUM
ejpam-6248	311	22	]	]	PUNCT
ejpam-6248	311	23	sajid	sajid	PROPN
ejpam-6248	311	24	,	,	PUNCT
ejpam-6248	311	25	n.	n.	NOUN
ejpam-6248	311	26	;	;	PUNCT
ejpam-6248	311	27	perveen	perveen	PROPN
ejpam-6248	311	28	,	,	PUNCT
ejpam-6248	311	29	z.	z.	PROPN
ejpam-6248	311	30	;	;	PUNCT
ejpam-6248	311	31	sadaf	sadaf	NOUN
ejpam-6248	311	32	,	,	PUNCT
ejpam-6248	311	33	m.	m.	NOUN
ejpam-6248	311	34	;	;	PUNCT
ejpam-6248	311	35	akram	akram	PROPN
ejpam-6248	311	36	,	,	PUNCT
ejpam-6248	311	37	g.	g.	PROPN
ejpam-6248	311	38	;	;	PUNCT
ejpam-6248	311	39	abbas	abbas	PROPN
ejpam-6248	311	40	,	,	PUNCT
ejpam-6248	311	41	m.	m.	NOUN
ejpam-6248	311	42	;	;	PUNCT
ejpam-6248	311	43	abdeljawad	abdeljawad	NOUN
ejpam-6248	311	44	,	,	PUNCT
ejpam-6248	311	45	t.	t.	PROPN
ejpam-6248	311	46	;	;	PUNCT
ejpam-6248	311	47	alqudah	alqudah	PROPN
ejpam-6248	311	48	,	,	PUNCT
ejpam-6248	311	49	m.a	m.a	PROPN
ejpam-6248	311	50	.	.	PROPN
ejpam-6248	311	51	implementation	implementation	NOUN
ejpam-6248	311	52	of	of	ADP
ejpam-6248	311	53	the	the	DET
ejpam-6248	311	54	exp	exp	NOUN
ejpam-6248	311	55	-	-	PUNCT
ejpam-6248	311	56	function	function	NOUN
ejpam-6248	311	57	approach	approach	NOUN
ejpam-6248	311	58	for	for	ADP
ejpam-6248	311	59	the	the	DET
ejpam-6248	311	60	solution	solution	NOUN
ejpam-6248	311	61	of	of	ADP
ejpam-6248	311	62	kdv	kdv	NOUN
ejpam-6248	311	63	equation	equation	NOUN
ejpam-6248	311	64	with	with	ADP
ejpam-6248	311	65	dual	dual	ADJ
ejpam-6248	311	66	power	power	NOUN
ejpam-6248	311	67	law	law	NOUN
ejpam-6248	311	68	nonlinearity	nonlinearity	NOUN
ejpam-6248	311	69	.	.	PUNCT
ejpam-6248	312	1	comput	comput	NOUN
ejpam-6248	312	2	.	.	PUNCT
ejpam-6248	313	1	appl	appl	PROPN
ejpam-6248	313	2	.	.	PROPN
ejpam-6248	313	3	math	math	PROPN
ejpam-6248	313	4	.	.	PUNCT
ejpam-6248	314	1	2022	2022	NUM
ejpam-6248	314	2	,	,	PUNCT
ejpam-6248	314	3	41	41	NUM
ejpam-6248	314	4	,	,	PUNCT
ejpam-6248	314	5	338	338	NUM
ejpam-6248	314	6	.	.	PUNCT
ejpam-6248	315	1	[	[	X
ejpam-6248	315	2	2	2	NUM
ejpam-6248	315	3	]	]	SYM
ejpam-6248	315	4	attaullah	attaullah	ADJ
ejpam-6248	315	5	;	;	PUNCT
ejpam-6248	315	6	shakeel	shakeel	PROPN
ejpam-6248	315	7	,	,	PUNCT
ejpam-6248	315	8	m.	m.	NOUN
ejpam-6248	315	9	;	;	PUNCT
ejpam-6248	315	10	shah	shah	PROPN
ejpam-6248	315	11	,	,	PUNCT
ejpam-6248	315	12	n.a	n.a	PROPN
ejpam-6248	315	13	.	.	PROPN
ejpam-6248	315	14	;	;	PUNCT
ejpam-6248	315	15	chung	chung	PROPN
ejpam-6248	315	16	,	,	PUNCT
ejpam-6248	315	17	j.d	j.d	PROPN
ejpam-6248	315	18	.	.	PROPN
ejpam-6248	315	19	modified	modify	VERB
ejpam-6248	315	20	exp	exp	NOUN
ejpam-6248	315	21	-	-	PUNCT
ejpam-6248	315	22	function	function	NOUN
ejpam-6248	315	23	method	method	NOUN
ejpam-6248	315	24	to	to	PART
ejpam-6248	315	25	find	find	VERB
ejpam-6248	315	26	exact	exact	ADJ
ejpam-6248	315	27	solutions	solution	NOUN
ejpam-6248	315	28	of	of	ADP
ejpam-6248	315	29	ionic	ionic	ADJ
ejpam-6248	315	30	currents	current	NOUN
ejpam-6248	315	31	along	along	ADP
ejpam-6248	315	32	microtubules	microtubule	NOUN
ejpam-6248	315	33	.	.	PUNCT
ejpam-6248	316	1	mathematics	mathematic	NOUN
ejpam-6248	316	2	2022	2022	NUM
ejpam-6248	316	3	,	,	PUNCT
ejpam-6248	316	4	10	10	NUM
ejpam-6248	316	5	,	,	PUNCT
ejpam-6248	316	6	851	851	NUM
ejpam-6248	316	7	.	.	PUNCT
ejpam-6248	317	1	[	[	X
ejpam-6248	317	2	3	3	NUM
ejpam-6248	317	3	]	]	X
ejpam-6248	317	4	shakeel	shakeel	PROPN
ejpam-6248	317	5	,	,	PUNCT
ejpam-6248	317	6	m.	m.	NOUN
ejpam-6248	317	7	;	;	PUNCT
ejpam-6248	317	8	shah	shah	PROPN
ejpam-6248	317	9	,	,	PUNCT
ejpam-6248	317	10	n.a	n.a	PROPN
ejpam-6248	317	11	.	.	PROPN
ejpam-6248	317	12	;	;	PUNCT
ejpam-6248	317	13	chung	chung	PROPN
ejpam-6248	317	14	,	,	PUNCT
ejpam-6248	317	15	j.d	j.d	PROPN
ejpam-6248	317	16	.	.	PROPN
ejpam-6248	317	17	application	application	NOUN
ejpam-6248	317	18	of	of	ADP
ejpam-6248	317	19	modified	modify	VERB
ejpam-6248	317	20	exp	exp	NOUN
ejpam-6248	317	21	-	-	PUNCT
ejpam-6248	317	22	function	function	NOUN
ejpam-6248	317	23	method	method	NOUN
ejpam-6248	317	24	for	for	ADP
ejpam-6248	317	25	strain	strain	NOUN
ejpam-6248	317	26	wave	wave	NOUN
ejpam-6248	317	27	equation	equation	NOUN
ejpam-6248	317	28	for	for	ADP
ejpam-6248	317	29	finding	find	VERB
ejpam-6248	317	30	analytical	analytical	ADJ
ejpam-6248	317	31	solutions	solution	NOUN
ejpam-6248	317	32	.	.	PUNCT
ejpam-6248	318	1	ain	ain	PROPN
ejpam-6248	318	2	shams	shams	PROPN
ejpam-6248	318	3	eng	eng	PROPN
ejpam-6248	318	4	.	.	PUNCT
ejpam-6248	318	5	j.	j.	PROPN
ejpam-6248	318	6	2023	2023	NUM
ejpam-6248	318	7	,	,	PUNCT
ejpam-6248	318	8	14	14	NUM
ejpam-6248	318	9	,	,	PUNCT
ejpam-6248	318	10	101883	101883	NUM
ejpam-6248	318	11	.	.	PUNCT
ejpam-6248	319	1	[	[	X
ejpam-6248	319	2	4	4	NUM
ejpam-6248	319	3	]	]	SYM
ejpam-6248	319	4	shakeel	shakeel	PROPN
ejpam-6248	319	5	,	,	PUNCT
ejpam-6248	319	6	m.	m.	NOUN
ejpam-6248	319	7	;	;	PUNCT
ejpam-6248	319	8	attaullah	attaullah	ADJ
ejpam-6248	319	9	;	;	PUNCT
ejpam-6248	319	10	shah	shah	NOUN
ejpam-6248	319	11	,	,	PUNCT
ejpam-6248	319	12	n.a	n.a	PROPN
ejpam-6248	319	13	.	.	PROPN
ejpam-6248	319	14	;	;	PUNCT
ejpam-6248	319	15	chung	chung	PROPN
ejpam-6248	319	16	,	,	PUNCT
ejpam-6248	319	17	j.d	j.d	PROPN
ejpam-6248	319	18	.	.	PROPN
ejpam-6248	319	19	modified	modify	VERB
ejpam-6248	319	20	exp	exp	NOUN
ejpam-6248	319	21	-	-	PUNCT
ejpam-6248	319	22	function	function	NOUN
ejpam-6248	319	23	method	method	NOUN
ejpam-6248	319	24	to	to	PART
ejpam-6248	319	25	find	find	VERB
ejpam-6248	319	26	exact	exact	ADJ
ejpam-6248	319	27	solutions	solution	NOUN
ejpam-6248	319	28	of	of	ADP
ejpam-6248	319	29	microtubules	microtubule	NOUN
ejpam-6248	319	30	nonlinear	nonlinear	ADJ
ejpam-6248	319	31	dynamics	dynamic	NOUN
ejpam-6248	319	32	models	model	NOUN
ejpam-6248	319	33	.	.	PUNCT
ejpam-6248	320	1	symmetry	symmetry	NOUN
ejpam-6248	320	2	2023	2023	NUM
ejpam-6248	320	3	,	,	PUNCT
ejpam-6248	320	4	15	15	NUM
ejpam-6248	320	5	,	,	PUNCT
ejpam-6248	320	6	360	360	NUM
ejpam-6248	320	7	.	.	PUNCT
ejpam-6248	321	1	[	[	X
ejpam-6248	321	2	5	5	NUM
ejpam-6248	321	3	]	]	PUNCT
ejpam-6248	321	4	vitanov	vitanov	NOUN
ejpam-6248	321	5	,	,	PUNCT
ejpam-6248	321	6	n.k	n.k	PROPN
ejpam-6248	321	7	.	.	PROPN
ejpam-6248	321	8	;	;	PUNCT
ejpam-6248	321	9	dimitrova	dimitrova	PROPN
ejpam-6248	321	10	,	,	PUNCT
ejpam-6248	321	11	z.i	z.i	PROPN
ejpam-6248	321	12	.	.	PROPN
ejpam-6248	321	13	simple	simple	ADJ
ejpam-6248	321	14	equations	equation	NOUN
ejpam-6248	321	15	method	method	NOUN
ejpam-6248	321	16	and	and	CCONJ
ejpam-6248	321	17	non	non	ADJ
ejpam-6248	321	18	-	-	ADJ
ejpam-6248	321	19	linear	linear	ADJ
ejpam-6248	321	20	differential	differential	ADJ
ejpam-6248	321	21	equations	equation	NOUN
ejpam-6248	321	22	with	with	ADP
ejpam-6248	321	23	non	non	ADJ
ejpam-6248	321	24	-	-	ADJ
ejpam-6248	321	25	polynomial	polynomial	ADJ
ejpam-6248	321	26	non	non	ADJ
ejpam-6248	321	27	-	-	NOUN
ejpam-6248	321	28	linearity	linearity	NOUN
ejpam-6248	321	29	.	.	PUNCT
ejpam-6248	322	1	entropy	entropy	PROPN
ejpam-6248	322	2	2021	2021	NUM
ejpam-6248	322	3	,	,	PUNCT
ejpam-6248	322	4	23	23	NUM
ejpam-6248	322	5	,	,	PUNCT
ejpam-6248	322	6	1624	1624	NUM
ejpam-6248	322	7	.	.	PUNCT
ejpam-6248	323	1	[	[	X
ejpam-6248	323	2	6	6	NUM
ejpam-6248	323	3	]	]	PUNCT
ejpam-6248	323	4	vitanov	vitanov	NOUN
ejpam-6248	323	5	,	,	PUNCT
ejpam-6248	323	6	n.k	n.k	PROPN
ejpam-6248	323	7	.	.	PROPN
ejpam-6248	323	8	;	;	PUNCT
ejpam-6248	323	9	dimitrova	dimitrova	PROPN
ejpam-6248	323	10	,	,	PUNCT
ejpam-6248	323	11	z.i	z.i	PROPN
ejpam-6248	323	12	.	.	PROPN
ejpam-6248	323	13	;	;	PUNCT
ejpam-6248	323	14	vitanov	vitanov	PROPN
ejpam-6248	323	15	,	,	PUNCT
ejpam-6248	323	16	k.n	k.n	PROPN
ejpam-6248	323	17	.	.	PROPN
ejpam-6248	323	18	on	on	ADP
ejpam-6248	323	19	the	the	DET
ejpam-6248	323	20	use	use	NOUN
ejpam-6248	323	21	of	of	ADP
ejpam-6248	323	22	composite	composite	ADJ
ejpam-6248	323	23	functions	function	NOUN
ejpam-6248	323	24	in	in	ADP
ejpam-6248	323	25	the	the	DET
ejpam-6248	323	26	simple	simple	ADJ
ejpam-6248	323	27	equations	equation	NOUN
ejpam-6248	323	28	method	method	VERB
ejpam-6248	323	29	to	to	PART
ejpam-6248	323	30	obtain	obtain	VERB
ejpam-6248	323	31	exact	exact	ADJ
ejpam-6248	323	32	solutions	solution	NOUN
ejpam-6248	323	33	of	of	ADP
ejpam-6248	323	34	nonlinear	nonlinear	ADJ
ejpam-6248	323	35	differential	differential	ADJ
ejpam-6248	323	36	equations	equation	NOUN
ejpam-6248	323	37	.	.	PUNCT
ejpam-6248	324	1	computation	computation	NOUN
ejpam-6248	324	2	2021	2021	NUM
ejpam-6248	324	3	,	,	PUNCT
ejpam-6248	324	4	9	9	NUM
ejpam-6248	324	5	,	,	PUNCT
ejpam-6248	324	6	104	104	NUM
ejpam-6248	324	7	.	.	PUNCT
ejpam-6248	325	1	[	[	X
ejpam-6248	325	2	7	7	X
ejpam-6248	325	3	]	]	PUNCT
ejpam-6248	325	4	vitanov	vitanov	NOUN
ejpam-6248	325	5	,	,	PUNCT
ejpam-6248	325	6	n.k	n.k	PROPN
ejpam-6248	325	7	.	.	NOUN
ejpam-6248	325	8	simple	simple	ADJ
ejpam-6248	325	9	equations	equation	NOUN
ejpam-6248	325	10	method	method	NOUN
ejpam-6248	325	11	(	(	PUNCT
ejpam-6248	325	12	sesm	sesm	PROPN
ejpam-6248	325	13	):	):	PUNCT
ejpam-6248	325	14	an	an	DET
ejpam-6248	325	15	effective	effective	ADJ
ejpam-6248	325	16	algorithm	algorithm	NOUN
ejpam-6248	325	17	for	for	ADP
ejpam-6248	325	18	obtaining	obtain	VERB
ejpam-6248	325	19	exact	exact	ADJ
ejpam-6248	325	20	solutions	solution	NOUN
ejpam-6248	325	21	of	of	ADP
ejpam-6248	325	22	nonlinear	nonlinear	ADJ
ejpam-6248	325	23	differential	differential	ADJ
ejpam-6248	325	24	equations	equation	NOUN
ejpam-6248	325	25	.	.	PUNCT
ejpam-6248	326	1	entropy	entropy	PROPN
ejpam-6248	326	2	2022	2022	NUM
ejpam-6248	326	3	,	,	PUNCT
ejpam-6248	326	4	24	24	NUM
ejpam-6248	326	5	,	,	PUNCT
ejpam-6248	326	6	1653	1653	NUM
ejpam-6248	326	7	.	.	PUNCT
ejpam-6248	327	1	[	[	X
ejpam-6248	327	2	8	8	NUM
ejpam-6248	327	3	]	]	SYM
ejpam-6248	327	4	tajadodi	tajadodi	NOUN
ejpam-6248	327	5	,	,	PUNCT
ejpam-6248	327	6	h.	h.	PROPN
ejpam-6248	327	7	;	;	PUNCT
ejpam-6248	327	8	khan	khan	PROPN
ejpam-6248	327	9	,	,	PUNCT
ejpam-6248	327	10	z.a	z.a	PROPN
ejpam-6248	327	11	.	.	PROPN
ejpam-6248	327	12	;	;	PUNCT
ejpam-6248	327	13	gómez	gómez	NOUN
ejpam-6248	327	14	-	-	PUNCT
ejpam-6248	327	15	aguilar	aguilar	ADJ
ejpam-6248	327	16	,	,	PUNCT
ejpam-6248	327	17	j.f	j.f	PROPN
ejpam-6248	327	18	.	.	PROPN
ejpam-6248	327	19	;	;	PUNCT
ejpam-6248	327	20	khan	khan	PROPN
ejpam-6248	327	21	,	,	PUNCT
ejpam-6248	327	22	a.	a.	PROPN
ejpam-6248	327	23	;	;	PUNCT
ejpam-6248	327	24	khan	khan	PROPN
ejpam-6248	327	25	,	,	PUNCT
ejpam-6248	327	26	h.	h.	PROPN
ejpam-6248	327	27	exact	exact	ADJ
ejpam-6248	327	28	solutions	solution	NOUN
ejpam-6248	327	29	of	of	ADP
ejpam-6248	327	30	conformable	conformable	ADJ
ejpam-6248	327	31	fractional	fractional	ADJ
ejpam-6248	327	32	differential	differential	ADJ
ejpam-6248	327	33	equations	equation	NOUN
ejpam-6248	327	34	.	.	PUNCT
ejpam-6248	328	1	results	result	VERB
ejpam-6248	328	2	phys	phy	NOUN
ejpam-6248	328	3	.	.	PUNCT
ejpam-6248	329	1	2021	2021	NUM
ejpam-6248	329	2	,	,	PUNCT
ejpam-6248	329	3	22	22	NUM
ejpam-6248	329	4	,	,	PUNCT
ejpam-6248	329	5	103916	103916	NUM
ejpam-6248	329	6	.	.	PUNCT
ejpam-6248	330	1	[	[	X
ejpam-6248	330	2	9	9	NUM
ejpam-6248	330	3	]	]	SYM
ejpam-6248	330	4	ala	ala	PROPN
ejpam-6248	330	5	,	,	PUNCT
ejpam-6248	330	6	v.	v.	PROPN
ejpam-6248	330	7	;	;	PUNCT
ejpam-6248	330	8	shaikhova	shaikhova	X
ejpam-6248	330	9	,	,	PUNCT
ejpam-6248	330	10	g.	g.	PROPN
ejpam-6248	330	11	analytical	analytical	ADJ
ejpam-6248	330	12	solutions	solution	NOUN
ejpam-6248	330	13	of	of	ADP
ejpam-6248	330	14	nonlinear	nonlinear	ADJ
ejpam-6248	330	15	beta	beta	NOUN
ejpam-6248	330	16	fractional	fractional	ADJ
ejpam-6248	330	17	schrödinger	schrödinger	NOUN
ejpam-6248	330	18	equation	equation	NOUN
ejpam-6248	330	19	via	via	ADP
ejpam-6248	330	20	sine	sine	ADJ
ejpam-6248	330	21	-	-	PUNCT
ejpam-6248	330	22	cosine	cosine	NOUN
ejpam-6248	330	23	method	method	NOUN
ejpam-6248	330	24	.	.	PUNCT
ejpam-6248	331	1	lobachevskii	lobachevskii	PROPN
ejpam-6248	331	2	j.	j.	PROPN
ejpam-6248	331	3	math	math	PROPN
ejpam-6248	331	4	.	.	PUNCT
ejpam-6248	332	1	2022	2022	NUM
ejpam-6248	332	2	,	,	PUNCT
ejpam-6248	332	3	43	43	NUM
ejpam-6248	332	4	,	,	PUNCT
ejpam-6248	332	5	3033–3038	3033–3038	NUM
ejpam-6248	332	6	.	.	PUNCT
ejpam-6248	333	1	[	[	X
ejpam-6248	333	2	10	10	NUM
ejpam-6248	333	3	]	]	X
ejpam-6248	333	4	behera	behera	PROPN
ejpam-6248	333	5	,	,	PUNCT
ejpam-6248	333	6	s.	s.	PROPN
ejpam-6248	333	7	multiple	multiple	ADJ
ejpam-6248	333	8	soliton	soliton	NOUN
ejpam-6248	333	9	solutions	solution	NOUN
ejpam-6248	333	10	of	of	ADP
ejpam-6248	333	11	some	some	DET
ejpam-6248	333	12	conformable	conformable	ADJ
ejpam-6248	333	13	fractional	fractional	ADJ
ejpam-6248	333	14	nonlinear	nonlinear	ADJ
ejpam-6248	333	15	models	model	NOUN
ejpam-6248	333	16	using	use	VERB
ejpam-6248	333	17	sine	sine	NOUN
ejpam-6248	333	18	–	–	PUNCT
ejpam-6248	333	19	cosine	cosine	NOUN
ejpam-6248	333	20	method	method	NOUN
ejpam-6248	333	21	.	.	PUNCT
ejpam-6248	333	22	opt	opt	PROPN
ejpam-6248	333	23	.	.	PUNCT
ejpam-6248	334	1	quantum	quantum	PROPN
ejpam-6248	334	2	electron	electron	NOUN
ejpam-6248	334	3	.	.	PUNCT
ejpam-6248	335	1	2024	2024	NUM
ejpam-6248	335	2	,	,	PUNCT
ejpam-6248	335	3	56	56	NUM
ejpam-6248	335	4	,	,	PUNCT
ejpam-6248	335	5	1235	1235	NUM
ejpam-6248	335	6	.	.	PUNCT
ejpam-6248	336	1	[	[	X
ejpam-6248	336	2	11	11	NUM
ejpam-6248	336	3	]	]	SYM
ejpam-6248	336	4	behera	behera	PROPN
ejpam-6248	336	5	,	,	PUNCT
ejpam-6248	336	6	s.	s.	PROPN
ejpam-6248	336	7	analysis	analysis	NOUN
ejpam-6248	336	8	of	of	ADP
ejpam-6248	336	9	traveling	travel	VERB
ejpam-6248	336	10	wave	wave	NOUN
ejpam-6248	336	11	solutions	solution	NOUN
ejpam-6248	336	12	of	of	ADP
ejpam-6248	336	13	two	two	NUM
ejpam-6248	336	14	space	space	NOUN
ejpam-6248	336	15	-	-	PUNCT
ejpam-6248	336	16	time	time	NOUN
ejpam-6248	336	17	nonlinear	nonlinear	ADJ
ejpam-6248	336	18	fractional	fractional	ADJ
ejpam-6248	336	19	differential	differential	ADJ
ejpam-6248	336	20	equations	equation	NOUN
ejpam-6248	336	21	by	by	ADP
ejpam-6248	336	22	the	the	DET
ejpam-6248	336	23	first	first	ADJ
ejpam-6248	336	24	-	-	PUNCT
ejpam-6248	336	25	integral	integral	ADJ
ejpam-6248	336	26	method	method	NOUN
ejpam-6248	336	27	.	.	PUNCT
ejpam-6248	337	1	mod	mod	PROPN
ejpam-6248	337	2	.	.	PUNCT
ejpam-6248	338	1	phys	phys	PROPN
ejpam-6248	338	2	.	.	PUNCT
ejpam-6248	339	1	lett	lett	PROPN
ejpam-6248	339	2	.	.	PUNCT
ejpam-6248	340	1	b	b	PROPN
ejpam-6248	340	2	2024	2024	NUM
ejpam-6248	340	3	,	,	PUNCT
ejpam-6248	340	4	38	38	NUM
ejpam-6248	340	5	,	,	PUNCT
ejpam-6248	340	6	2350247	2350247	NUM
ejpam-6248	340	7	.	.	PUNCT
ejpam-6248	341	1	[	[	X
ejpam-6248	341	2	12	12	NUM
ejpam-6248	341	3	]	]	X
ejpam-6248	341	4	ghosh	ghosh	PROPN
ejpam-6248	341	5	,	,	PUNCT
ejpam-6248	341	6	a.	a.	PROPN
ejpam-6248	341	7	;	;	PUNCT
ejpam-6248	341	8	maitra	maitra	PROPN
ejpam-6248	341	9	,	,	PUNCT
ejpam-6248	341	10	s.	s.	PROPN
ejpam-6248	341	11	the	the	DET
ejpam-6248	341	12	first	first	ADJ
ejpam-6248	341	13	integral	integral	ADJ
ejpam-6248	341	14	method	method	NOUN
ejpam-6248	341	15	and	and	CCONJ
ejpam-6248	341	16	some	some	DET
ejpam-6248	341	17	nonlinear	nonlinear	ADJ
ejpam-6248	341	18	models	model	NOUN
ejpam-6248	341	19	.	.	PUNCT
ejpam-6248	342	1	comput	comput	NOUN
ejpam-6248	342	2	.	.	PUNCT
ejpam-6248	343	1	appl	appl	PROPN
ejpam-6248	343	2	.	.	PROPN
ejpam-6248	343	3	math	math	PROPN
ejpam-6248	343	4	.	.	PUNCT
ejpam-6248	344	1	2021	2021	NUM
ejpam-6248	344	2	,	,	PUNCT
ejpam-6248	344	3	40	40	NUM
ejpam-6248	344	4	,	,	PUNCT
ejpam-6248	344	5	79	79	NUM
ejpam-6248	344	6	.	.	PUNCT
ejpam-6248	345	1	[	[	X
ejpam-6248	345	2	13	13	NUM
ejpam-6248	345	3	]	]	SYM
ejpam-6248	345	4	yasin	yasin	NOUN
ejpam-6248	345	5	,	,	PUNCT
ejpam-6248	345	6	s.	s.	PROPN
ejpam-6248	345	7	;	;	PUNCT
ejpam-6248	345	8	khan	khan	PROPN
ejpam-6248	345	9	,	,	PUNCT
ejpam-6248	345	10	a.	a.	PROPN
ejpam-6248	345	11	;	;	PUNCT
ejpam-6248	345	12	ahmad	ahmad	PROPN
ejpam-6248	345	13	,	,	PUNCT
ejpam-6248	345	14	s.	s.	PROPN
ejpam-6248	345	15	;	;	PUNCT
ejpam-6248	345	16	osman	osman	PROPN
ejpam-6248	345	17	,	,	PUNCT
ejpam-6248	345	18	m.s	m.s	PROPN
ejpam-6248	345	19	.	.	PROPN
ejpam-6248	346	1	new	new	ADJ
ejpam-6248	346	2	exact	exact	ADJ
ejpam-6248	346	3	solutions	solution	NOUN
ejpam-6248	346	4	of	of	ADP
ejpam-6248	346	5	(	(	PUNCT
ejpam-6248	346	6	3	3	NUM
ejpam-6248	346	7	+	+	NOUN
ejpam-6248	346	8	1)dimensional	1)dimensional	NUM
ejpam-6248	346	9	modified	modify	VERB
ejpam-6248	346	10	kdv	kdv	NOUN
ejpam-6248	346	11	-	-	PUNCT
ejpam-6248	346	12	zakharov	zakharov	ADJ
ejpam-6248	346	13	-	-	PUNCT
ejpam-6248	346	14	kuznetsov	kuznetsov	NOUN
ejpam-6248	346	15	equation	equation	NOUN
ejpam-6248	346	16	by	by	ADP
ejpam-6248	346	17	sardar	sardar	NOUN
ejpam-6248	346	18	-	-	PUNCT
ejpam-6248	346	19	subequation	subequation	NOUN
ejpam-6248	346	20	method	method	NOUN
ejpam-6248	346	21	.	.	PUNCT
ejpam-6248	347	1	opt	opt	PROPN
ejpam-6248	347	2	.	.	PUNCT
ejpam-6248	348	1	quantum	quantum	PROPN
ejpam-6248	348	2	electron	electron	NOUN
ejpam-6248	348	3	.	.	PUNCT
ejpam-6248	349	1	2024	2024	NUM
ejpam-6248	349	2	,	,	PUNCT
ejpam-6248	349	3	56	56	NUM
ejpam-6248	349	4	,	,	PUNCT
ejpam-6248	349	5	90	90	NUM
ejpam-6248	349	6	.	.	PUNCT
ejpam-6248	350	1	[	[	X
ejpam-6248	350	2	14	14	NUM
ejpam-6248	350	3	]	]	X
ejpam-6248	350	4	ahmad	ahmad	PROPN
ejpam-6248	350	5	,	,	PUNCT
ejpam-6248	350	6	j.	j.	PROPN
ejpam-6248	350	7	;	;	PUNCT
ejpam-6248	350	8	hameed	hameed	PROPN
ejpam-6248	350	9	,	,	PUNCT
ejpam-6248	350	10	m.	m.	NOUN
ejpam-6248	350	11	;	;	PUNCT
ejpam-6248	350	12	mustafa	mustafa	PROPN
ejpam-6248	350	13	,	,	PUNCT
ejpam-6248	350	14	z.	z.	PROPN
ejpam-6248	350	15	;	;	PUNCT
ejpam-6248	350	16	rehman	rehman	PROPN
ejpam-6248	350	17	,	,	PUNCT
ejpam-6248	350	18	s.u	s.u	PROPN
ejpam-6248	350	19	.	.	PROPN
ejpam-6248	350	20	soliton	soliton	NOUN
ejpam-6248	350	21	patterns	pattern	NOUN
ejpam-6248	350	22	in	in	ADP
ejpam-6248	350	23	the	the	DET
ejpam-6248	350	24	truncated	truncated	ADJ
ejpam-6248	350	25	m	m	ADJ
ejpam-6248	350	26	-	-	PUNCT
ejpam-6248	350	27	fractional	fractional	ADJ
ejpam-6248	350	28	resonant	resonant	ADJ
ejpam-6248	350	29	nonlinear	nonlinear	ADJ
ejpam-6248	350	30	schrödinger	schrödinger	NOUN
ejpam-6248	350	31	equation	equation	NOUN
ejpam-6248	350	32	via	via	ADP
ejpam-6248	350	33	modified	modify	VERB
ejpam-6248	350	34	sardar	sardar	PROPN
ejpam-6248	350	35	subequation	subequation	NOUN
ejpam-6248	350	36	method	method	NOUN
ejpam-6248	350	37	.	.	PUNCT
ejpam-6248	351	1	j.	j.	PROPN
ejpam-6248	351	2	opt	opt	PROPN
ejpam-6248	351	3	.	.	PUNCT
ejpam-6248	351	4	2024	2024	NUM
ejpam-6248	351	5	,	,	PUNCT
ejpam-6248	351	6	1–22	1–22	NOUN
ejpam-6248	351	7	.	.	PUNCT
ejpam-6248	352	1	[	[	X
ejpam-6248	352	2	15	15	NUM
ejpam-6248	352	3	]	]	X
ejpam-6248	352	4	kamel	kamel	PROPN
ejpam-6248	352	5	,	,	PUNCT
ejpam-6248	352	6	n.m	n.m	PROPN
ejpam-6248	352	7	.	.	PROPN
ejpam-6248	352	8	;	;	PUNCT
ejpam-6248	352	9	ahmed	ahmed	PROPN
ejpam-6248	352	10	,	,	PUNCT
ejpam-6248	352	11	h.m	h.m	PROPN
ejpam-6248	352	12	.	.	PROPN
ejpam-6248	352	13	;	;	PUNCT
ejpam-6248	352	14	rabie	rabie	PROPN
ejpam-6248	352	15	,	,	PUNCT
ejpam-6248	352	16	w.b	w.b	PROPN
ejpam-6248	352	17	.	.	PROPN
ejpam-6248	352	18	retrieval	retrieval	NOUN
ejpam-6248	352	19	of	of	ADP
ejpam-6248	352	20	soliton	soliton	NOUN
ejpam-6248	352	21	solutions	solution	NOUN
ejpam-6248	352	22	for	for	ADP
ejpam-6248	352	23	4th	4th	ADJ
ejpam-6248	352	24	-	-	PUNCT
ejpam-6248	352	25	order	order	NOUN
ejpam-6248	352	26	(	(	PUNCT
ejpam-6248	352	27	2	2	NUM
ejpam-6248	352	28	+	+	NOUN
ejpam-6248	352	29	1)-dimensional	1)-dimensional	ADJ
ejpam-6248	352	30	schrödinger	schrödinger	NOUN
ejpam-6248	352	31	equation	equation	NOUN
ejpam-6248	352	32	with	with	ADP
ejpam-6248	352	33	higher	high	ADJ
ejpam-6248	352	34	-	-	PUNCT
ejpam-6248	352	35	order	order	NOUN
ejpam-6248	352	36	odd	odd	ADJ
ejpam-6248	352	37	and	and	CCONJ
ejpam-6248	352	38	even	even	ADV
ejpam-6248	352	39	terms	term	NOUN
ejpam-6248	352	40	by	by	ADP
ejpam-6248	352	41	modified	modified	ADJ
ejpam-6248	352	42	sardar	sardar	PROPN
ejpam-6248	352	43	sub	sub	ADJ
ejpam-6248	352	44	-	-	ADJ
ejpam-6248	352	45	equation	equation	NOUN
ejpam-6248	352	46	method	method	NOUN
ejpam-6248	352	47	.	.	PUNCT
ejpam-6248	353	1	ain	ain	PROPN
ejpam-6248	353	2	shams	shams	PROPN
ejpam-6248	353	3	eng	eng	PROPN
ejpam-6248	353	4	.	.	PUNCT
ejpam-6248	353	5	j.	j.	PROPN
ejpam-6248	353	6	2024	2024	NUM
ejpam-6248	353	7	,	,	PUNCT
ejpam-6248	353	8	15	15	NUM
ejpam-6248	353	9	,	,	PUNCT
ejpam-6248	353	10	102808	102808	NUM
ejpam-6248	353	11	.	.	PUNCT
ejpam-6248	354	1	[	[	X
ejpam-6248	354	2	16	16	NUM
ejpam-6248	354	3	]	]	X
ejpam-6248	354	4	ghayad	ghayad	NOUN
ejpam-6248	354	5	,	,	PUNCT
ejpam-6248	354	6	m.s	m.s	PROPN
ejpam-6248	354	7	.	.	PROPN
ejpam-6248	354	8	;	;	PUNCT
ejpam-6248	354	9	badra	badra	PROPN
ejpam-6248	354	10	,	,	PUNCT
ejpam-6248	354	11	n.m	n.m	PROPN
ejpam-6248	354	12	.	.	PROPN
ejpam-6248	354	13	;	;	PUNCT
ejpam-6248	354	14	ahmed	ahmed	PROPN
ejpam-6248	354	15	,	,	PUNCT
ejpam-6248	354	16	h.m	h.m	PROPN
ejpam-6248	354	17	.	.	PROPN
ejpam-6248	354	18	;	;	PUNCT
ejpam-6248	354	19	rabie	rabie	PROPN
ejpam-6248	354	20	,	,	PUNCT
ejpam-6248	354	21	w.b	w.b	PROPN
ejpam-6248	354	22	.	.	PROPN
ejpam-6248	354	23	derivation	derivation	NOUN
ejpam-6248	354	24	of	of	ADP
ejpam-6248	354	25	optical	optical	ADJ
ejpam-6248	354	26	solitons	soliton	NOUN
ejpam-6248	354	27	and	and	CCONJ
ejpam-6248	354	28	other	other	ADJ
ejpam-6248	354	29	solutions	solution	NOUN
ejpam-6248	354	30	for	for	ADP
ejpam-6248	354	31	nonlinear	nonlinear	ADJ
ejpam-6248	354	32	schrödinger	schrödinger	NOUN
ejpam-6248	354	33	equation	equation	NOUN
ejpam-6248	354	34	using	use	VERB
ejpam-6248	354	35	modified	modify	VERB
ejpam-6248	354	36	extended	extend	VERB
ejpam-6248	354	37	direct	direct	ADJ
ejpam-6248	354	38	algebraic	algebraic	ADJ
ejpam-6248	354	39	method	method	NOUN
ejpam-6248	354	40	.	.	PUNCT
ejpam-6248	355	1	alexandria	alexandria	PROPN
ejpam-6248	355	2	eng	eng	PROPN
ejpam-6248	355	3	.	.	PUNCT
ejpam-6248	356	1	j.	j.	PROPN
ejpam-6248	356	2	2023	2023	NUM
ejpam-6248	356	3	,	,	PUNCT
ejpam-6248	356	4	64	64	NUM
ejpam-6248	356	5	,	,	PUNCT
ejpam-6248	356	6	801–811	801–811	NUM
ejpam-6248	356	7	.	.	PUNCT
ejpam-6248	357	1	[	[	X
ejpam-6248	357	2	17	17	NUM
ejpam-6248	357	3	]	]	X
ejpam-6248	357	4	bilal	bilal	PROPN
ejpam-6248	357	5	,	,	PUNCT
ejpam-6248	357	6	m.	m.	NOUN
ejpam-6248	357	7	;	;	PUNCT
ejpam-6248	357	8	iqbal	iqbal	PROPN
ejpam-6248	357	9	,	,	PUNCT
ejpam-6248	357	10	j.	j.	PROPN
ejpam-6248	357	11	;	;	PUNCT
ejpam-6248	357	12	shah	shah	PROPN
ejpam-6248	357	13	,	,	PUNCT
ejpam-6248	357	14	k.	k.	PROPN
ejpam-6248	357	15	;	;	PUNCT
ejpam-6248	357	16	abdalla	abdalla	PROPN
ejpam-6248	357	17	,	,	PUNCT
ejpam-6248	357	18	b.	b.	PROPN
ejpam-6248	357	19	;	;	PUNCT
ejpam-6248	357	20	abdeljawad	abdeljawad	NOUN
ejpam-6248	357	21	,	,	PUNCT
ejpam-6248	357	22	t.	t.	PROPN
ejpam-6248	357	23	;	;	PUNCT
ejpam-6248	357	24	ullah	ullah	PROPN
ejpam-6248	357	25	,	,	PUNCT
ejpam-6248	357	26	i.	i.	PROPN
ejpam-6248	357	27	analytical	analytical	ADJ
ejpam-6248	357	28	soluz	soluz	NOUN
ejpam-6248	357	29	.	.	PUNCT
ejpam-6248	358	1	haider	haider	NOUN
ejpam-6248	358	2	et	et	PROPN
ejpam-6248	358	3	al	al	PROPN
ejpam-6248	358	4	.	.	PUNCT
ejpam-6248	358	5	/	/	SYM
ejpam-6248	358	6	eur	eur	PROPN
ejpam-6248	358	7	.	.	PUNCT
ejpam-6248	359	1	j.	j.	PROPN
ejpam-6248	359	2	pure	pure	PROPN
ejpam-6248	359	3	appl	appl	PROPN
ejpam-6248	359	4	.	.	PROPN
ejpam-6248	359	5	math	math	PROPN
ejpam-6248	359	6	,	,	PUNCT
ejpam-6248	359	7	18	18	NUM
ejpam-6248	359	8	(	(	PUNCT
ejpam-6248	359	9	3	3	NUM
ejpam-6248	359	10	)	)	PUNCT
ejpam-6248	359	11	(	(	PUNCT
ejpam-6248	359	12	2025	2025	NUM
ejpam-6248	359	13	)	)	PUNCT
ejpam-6248	359	14	,	,	PUNCT
ejpam-6248	359	15	6248	6248	NUM
ejpam-6248	359	16	20	20	NUM
ejpam-6248	359	17	of	of	ADP
ejpam-6248	359	18	20	20	NUM
ejpam-6248	359	19	tions	tion	NOUN
ejpam-6248	359	20	of	of	ADP
ejpam-6248	359	21	the	the	DET
ejpam-6248	359	22	space	space	NOUN
ejpam-6248	359	23	–	–	PUNCT
ejpam-6248	359	24	time	time	NOUN
ejpam-6248	359	25	fractional	fractional	ADJ
ejpam-6248	359	26	kundu	kundu	NOUN
ejpam-6248	359	27	–	–	PUNCT
ejpam-6248	359	28	eckhaus	eckhaus	NOUN
ejpam-6248	359	29	equation	equation	NOUN
ejpam-6248	359	30	by	by	ADP
ejpam-6248	359	31	using	use	VERB
ejpam-6248	359	32	modified	modify	VERB
ejpam-6248	359	33	extended	extend	VERB
ejpam-6248	359	34	direct	direct	ADJ
ejpam-6248	359	35	algebraic	algebraic	ADJ
ejpam-6248	359	36	method	method	NOUN
ejpam-6248	359	37	.	.	PUNCT
ejpam-6248	360	1	partial	partial	ADJ
ejpam-6248	360	2	differ	differ	VERB
ejpam-6248	360	3	.	.	PUNCT
ejpam-6248	361	1	equ	equ	PROPN
ejpam-6248	361	2	.	.	PUNCT
ejpam-6248	361	3	appl	appl	PROPN
ejpam-6248	361	4	.	.	PROPN
ejpam-6248	361	5	math	math	PROPN
ejpam-6248	361	6	.	.	PUNCT
ejpam-6248	362	1	2024	2024	NUM
ejpam-6248	362	2	,	,	PUNCT
ejpam-6248	362	3	11	11	NUM
ejpam-6248	362	4	,	,	PUNCT
ejpam-6248	362	5	100832	100832	NUM
ejpam-6248	362	6	.	.	PUNCT
ejpam-6248	363	1	[	[	X
ejpam-6248	363	2	18	18	NUM
ejpam-6248	363	3	]	]	PUNCT
ejpam-6248	363	4	mohanty	mohanty	PROPN
ejpam-6248	363	5	,	,	PUNCT
ejpam-6248	363	6	s.k	s.k	PROPN
ejpam-6248	363	7	.	.	PROPN
ejpam-6248	363	8	;	;	PUNCT
ejpam-6248	363	9	kumar	kumar	PROPN
ejpam-6248	363	10	,	,	PUNCT
ejpam-6248	363	11	s.	s.	PROPN
ejpam-6248	363	12	;	;	PUNCT
ejpam-6248	363	13	dev	dev	PROPN
ejpam-6248	363	14	,	,	PUNCT
ejpam-6248	363	15	a.n	a.n	PROPN
ejpam-6248	363	16	.	.	PROPN
ejpam-6248	363	17	;	;	PUNCT
ejpam-6248	363	18	deka	deka	NOUN
ejpam-6248	363	19	,	,	PUNCT
ejpam-6248	363	20	m.k	m.k	PROPN
ejpam-6248	363	21	.	.	PUNCT
ejpam-6248	363	22	;	;	PUNCT
ejpam-6248	363	23	churikov	churikov	PROPN
ejpam-6248	363	24	,	,	PUNCT
ejpam-6248	363	25	d.v	d.v	PROPN
ejpam-6248	363	26	.	.	PROPN
ejpam-6248	363	27	;	;	PUNCT
ejpam-6248	363	28	kravchenko	kravchenko	PROPN
ejpam-6248	363	29	,	,	PUNCT
ejpam-6248	363	30	o.v	o.v	PROPN
ejpam-6248	363	31	.	.	PROPN
ejpam-6248	363	32	an	an	DET
ejpam-6248	363	33	efficient	efficient	ADJ
ejpam-6248	363	34	technique	technique	NOUN
ejpam-6248	363	35	of	of	ADP
ejpam-6248	363	36	(	(	PUNCT
ejpam-6248	363	37	g	g	PROPN
ejpam-6248	363	38	′	′	NUM
ejpam-6248	363	39	g	g	NOUN
ejpam-6248	363	40	)	)	PUNCT
ejpam-6248	363	41	–	–	PUNCT
ejpam-6248	363	42	expansion	expansion	NOUN
ejpam-6248	363	43	method	method	NOUN
ejpam-6248	363	44	for	for	ADP
ejpam-6248	363	45	modified	modified	ADJ
ejpam-6248	363	46	kdv	kdv	NOUN
ejpam-6248	363	47	and	and	CCONJ
ejpam-6248	363	48	burgers	burger	NOUN
ejpam-6248	363	49	equations	equation	NOUN
ejpam-6248	363	50	with	with	ADP
ejpam-6248	363	51	variable	variable	ADJ
ejpam-6248	363	52	coefficients	coefficient	NOUN
ejpam-6248	363	53	.	.	PUNCT
ejpam-6248	363	54	results	result	VERB
ejpam-6248	363	55	phys	phy	NOUN
ejpam-6248	363	56	.	.	PUNCT
ejpam-6248	364	1	2022	2022	NUM
ejpam-6248	364	2	,	,	PUNCT
ejpam-6248	364	3	37	37	NUM
ejpam-6248	364	4	,	,	PUNCT
ejpam-6248	364	5	105504	105504	NUM
ejpam-6248	364	6	.	.	PUNCT
ejpam-6248	365	1	[	[	X
ejpam-6248	365	2	19	19	NUM
ejpam-6248	365	3	]	]	PUNCT
ejpam-6248	365	4	jhangeer	jhangeer	NOUN
ejpam-6248	365	5	,	,	PUNCT
ejpam-6248	365	6	a.	a.	NOUN
ejpam-6248	365	7	;	;	PUNCT
ejpam-6248	365	8	ansari	ansari	PROPN
ejpam-6248	365	9	,	,	PUNCT
ejpam-6248	365	10	a.r	a.r	PROPN
ejpam-6248	365	11	.	.	PROPN
ejpam-6248	365	12	;	;	PUNCT
ejpam-6248	365	13	imran	imran	PROPN
ejpam-6248	365	14	,	,	PUNCT
ejpam-6248	365	15	m.	m.	NOUN
ejpam-6248	365	16	;	;	PUNCT
ejpam-6248	365	17	riaz	riaz	PROPN
ejpam-6248	365	18	,	,	PUNCT
ejpam-6248	365	19	m.b	m.b	PROPN
ejpam-6248	365	20	.	.	PROPN
ejpam-6248	365	21	lie	lie	PROPN
ejpam-6248	365	22	symmetry	symmetry	NOUN
ejpam-6248	365	23	analysis	analysis	NOUN
ejpam-6248	365	24	,	,	PUNCT
ejpam-6248	365	25	and	and	CCONJ
ejpam-6248	365	26	traveling	travel	VERB
ejpam-6248	365	27	wave	wave	NOUN
ejpam-6248	365	28	patterns	pattern	NOUN
ejpam-6248	365	29	arising	arise	VERB
ejpam-6248	365	30	the	the	DET
ejpam-6248	365	31	model	model	NOUN
ejpam-6248	365	32	of	of	ADP
ejpam-6248	365	33	transmission	transmission	NOUN
ejpam-6248	365	34	lines	line	NOUN
ejpam-6248	365	35	.	.	PUNCT
ejpam-6248	366	1	aims	aim	VERB
ejpam-6248	366	2	math	math	NOUN
ejpam-6248	366	3	.	.	PUNCT
ejpam-6248	367	1	2024	2024	NUM
ejpam-6248	367	2	,	,	PUNCT
ejpam-6248	367	3	9	9	NUM
ejpam-6248	367	4	,	,	PUNCT
ejpam-6248	367	5	18013–18033	18013–18033	NUM
ejpam-6248	367	6	.	.	PUNCT
ejpam-6248	368	1	[	[	X
ejpam-6248	368	2	20	20	NUM
ejpam-6248	368	3	]	]	SYM
ejpam-6248	368	4	yang	yang	PROPN
ejpam-6248	368	5	,	,	PUNCT
ejpam-6248	368	6	l.	l.	PROPN
ejpam-6248	368	7	;	;	PUNCT
ejpam-6248	368	8	gao	gao	PROPN
ejpam-6248	368	9	,	,	PUNCT
ejpam-6248	368	10	b.	b.	PROPN
ejpam-6248	368	11	multiple	multiple	ADJ
ejpam-6248	368	12	solitons	soliton	NOUN
ejpam-6248	368	13	solutions	solution	NOUN
ejpam-6248	368	14	,	,	PUNCT
ejpam-6248	368	15	lump	lump	NOUN
ejpam-6248	368	16	solutions	solution	NOUN
ejpam-6248	368	17	and	and	CCONJ
ejpam-6248	368	18	rogue	rogue	NOUN
ejpam-6248	368	19	wave	wave	NOUN
ejpam-6248	368	20	solutions	solution	NOUN
ejpam-6248	368	21	of	of	ADP
ejpam-6248	368	22	the	the	DET
ejpam-6248	368	23	complex	complex	ADJ
ejpam-6248	368	24	cubic	cubic	ADJ
ejpam-6248	368	25	ginzburg	ginzburg	NOUN
ejpam-6248	368	26	–	–	PUNCT
ejpam-6248	368	27	landau	landau	VERB
ejpam-6248	368	28	equation	equation	NOUN
ejpam-6248	368	29	with	with	ADP
ejpam-6248	368	30	the	the	DET
ejpam-6248	368	31	hirota	hirota	PROPN
ejpam-6248	368	32	bilinear	bilinear	PROPN
ejpam-6248	368	33	method	method	NOUN
ejpam-6248	368	34	.	.	PUNCT
ejpam-6248	369	1	indian	indian	ADJ
ejpam-6248	369	2	j.	j.	PROPN
ejpam-6248	369	3	phys	phys	PROPN
ejpam-6248	369	4	.	.	PUNCT
ejpam-6248	370	1	2025	2025	NUM
ejpam-6248	370	2	,	,	PUNCT
ejpam-6248	370	3	99	99	NUM
ejpam-6248	370	4	,	,	PUNCT
ejpam-6248	370	5	221–228	221–228	NUM
ejpam-6248	370	6	.	.	PUNCT
ejpam-6248	371	1	[	[	X
ejpam-6248	371	2	21	21	NUM
ejpam-6248	371	3	]	]	X
ejpam-6248	371	4	haider	haider	PROPN
ejpam-6248	371	5	,	,	PUNCT
ejpam-6248	371	6	z.	z.	PROPN
ejpam-6248	371	7	;	;	PUNCT
ejpam-6248	371	8	ahmad	ahmad	PROPN
ejpam-6248	371	9	,	,	PUNCT
ejpam-6248	371	10	k.	k.	PROPN
ejpam-6248	371	11	novel	novel	PROPN
ejpam-6248	371	12	exact	exact	ADJ
ejpam-6248	371	13	solutions	solution	NOUN
ejpam-6248	371	14	for	for	ADP
ejpam-6248	371	15	a	a	DET
ejpam-6248	371	16	biological	biological	ADJ
ejpam-6248	371	17	population	population	NOUN
ejpam-6248	371	18	model	model	NOUN
ejpam-6248	371	19	using	use	VERB
ejpam-6248	371	20	the	the	DET
ejpam-6248	371	21	power	power	NOUN
ejpam-6248	371	22	index	index	NOUN
ejpam-6248	371	23	method	method	NOUN
ejpam-6248	371	24	.	.	PUNCT
ejpam-6248	372	1	eur	eur	PROPN
ejpam-6248	372	2	.	.	PUNCT
ejpam-6248	373	1	j.	j.	PROPN
ejpam-6248	373	2	pure	pure	PROPN
ejpam-6248	373	3	appl	appl	PROPN
ejpam-6248	373	4	.	.	PUNCT
ejpam-6248	373	5	math	math	PROPN
ejpam-6248	373	6	.	.	PUNCT
ejpam-6248	374	1	2025	2025	NUM
ejpam-6248	374	2	,	,	PUNCT
ejpam-6248	374	3	18	18	NUM
ejpam-6248	374	4	,	,	PUNCT
ejpam-6248	374	5	5936–5936	5936–5936	NUM
ejpam-6248	374	6	.	.	PUNCT
ejpam-6248	375	1	[	[	X
ejpam-6248	375	2	22	22	NUM
ejpam-6248	375	3	]	]	X
ejpam-6248	375	4	ahmad	ahmad	PROPN
ejpam-6248	375	5	,	,	PUNCT
ejpam-6248	375	6	k.	k.	PROPN
ejpam-6248	375	7	;	;	PUNCT
ejpam-6248	375	8	bibi	bibi	PROPN
ejpam-6248	375	9	,	,	PUNCT
ejpam-6248	375	10	k.	k.	PROPN
ejpam-6248	375	11	new	new	ADJ
ejpam-6248	375	12	function	function	NOUN
ejpam-6248	375	13	solutions	solution	NOUN
ejpam-6248	375	14	of	of	ADP
ejpam-6248	375	15	ablowitz	ablowitz	NOUN
ejpam-6248	375	16	-	-	PUNCT
ejpam-6248	375	17	kaup	kaup	PROPN
ejpam-6248	375	18	-	-	PUNCT
ejpam-6248	375	19	newell	newell	PROPN
ejpam-6248	375	20	-	-	PUNCT
ejpam-6248	375	21	segur	segur	NOUN
ejpam-6248	375	22	water	water	NOUN
ejpam-6248	375	23	wave	wave	NOUN
ejpam-6248	375	24	equation	equation	NOUN
ejpam-6248	375	25	via	via	ADP
ejpam-6248	375	26	power	power	NOUN
ejpam-6248	375	27	index	index	NOUN
ejpam-6248	375	28	method	method	NOUN
ejpam-6248	375	29	.	.	PUNCT
ejpam-6248	376	1	j.	j.	PROPN
ejpam-6248	376	2	funct	funct	PROPN
ejpam-6248	376	3	.	.	PUNCT
ejpam-6248	377	1	spaces	space	VERB
ejpam-6248	377	2	2022	2022	NUM
ejpam-6248	377	3	,	,	PUNCT
ejpam-6248	377	4	2022	2022	NUM
ejpam-6248	377	5	,	,	PUNCT
ejpam-6248	377	6	9405644	9405644	NUM
ejpam-6248	377	7	.	.	PUNCT
ejpam-6248	378	1	[	[	X
ejpam-6248	378	2	23	23	NUM
ejpam-6248	378	3	]	]	X
ejpam-6248	378	4	haussermann	haussermann	NOUN
ejpam-6248	378	5	,	,	PUNCT
ejpam-6248	378	6	j.	j.	PROPN
ejpam-6248	378	7	;	;	PUNCT
ejpam-6248	378	8	vajravelu	vajravelu	PROPN
ejpam-6248	378	9	,	,	PUNCT
ejpam-6248	378	10	k.	k.	PROPN
ejpam-6248	378	11	;	;	PUNCT
ejpam-6248	378	12	van	van	PROPN
ejpam-6248	378	13	gorder	gorder	NOUN
ejpam-6248	378	14	,	,	PUNCT
ejpam-6248	378	15	r.a	r.a	PROPN
ejpam-6248	378	16	.	.	PROPN
ejpam-6248	378	17	self	self	NOUN
ejpam-6248	378	18	-	-	PUNCT
ejpam-6248	378	19	similar	similar	ADJ
ejpam-6248	378	20	solutions	solution	NOUN
ejpam-6248	378	21	to	to	ADP
ejpam-6248	378	22	lin	lin	PROPN
ejpam-6248	378	23	–	–	PUNCT
ejpam-6248	378	24	reissner	reissner	NOUN
ejpam-6248	378	25	–	–	PUNCT
ejpam-6248	378	26	tsien	tsien	NOUN
ejpam-6248	378	27	equation	equation	NOUN
ejpam-6248	378	28	.	.	PUNCT
ejpam-6248	379	1	appl	appl	PROPN
ejpam-6248	379	2	.	.	PROPN
ejpam-6248	379	3	math	math	PROPN
ejpam-6248	379	4	.	.	PUNCT
ejpam-6248	380	1	mech	mech	PROPN
ejpam-6248	380	2	.	.	PUNCT
ejpam-6248	381	1	2011	2011	NUM
ejpam-6248	381	2	,	,	PUNCT
ejpam-6248	381	3	32	32	NUM
ejpam-6248	381	4	,	,	PUNCT
ejpam-6248	381	5	1447–1456	1447–1456	NUM
ejpam-6248	381	6	.	.	PUNCT
ejpam-6248	382	1	[	[	X
ejpam-6248	382	2	24	24	NUM
ejpam-6248	382	3	]	]	X
ejpam-6248	382	4	filimonov	filimonov	PROPN
ejpam-6248	382	5	,	,	PUNCT
ejpam-6248	382	6	m.y	m.y	PROPN
ejpam-6248	382	7	.	.	PROPN
ejpam-6248	382	8	application	application	NOUN
ejpam-6248	382	9	of	of	ADP
ejpam-6248	382	10	the	the	DET
ejpam-6248	382	11	method	method	NOUN
ejpam-6248	382	12	of	of	ADP
ejpam-6248	382	13	special	special	ADJ
ejpam-6248	382	14	series	series	NOUN
ejpam-6248	382	15	to	to	ADP
ejpam-6248	382	16	the	the	DET
ejpam-6248	382	17	representation	representation	NOUN
ejpam-6248	382	18	of	of	ADP
ejpam-6248	382	19	solutions	solution	NOUN
ejpam-6248	382	20	of	of	ADP
ejpam-6248	382	21	the	the	DET
ejpam-6248	382	22	lin	lin	PROPN
ejpam-6248	382	23	–	–	PUNCT
ejpam-6248	382	24	reissner	reissner	NOUN
ejpam-6248	382	25	–	–	PUNCT
ejpam-6248	382	26	tsien	tsien	NOUN
ejpam-6248	382	27	equation	equation	NOUN
ejpam-6248	382	28	.	.	PUNCT
ejpam-6248	383	1	proc	proc	PROPN
ejpam-6248	383	2	.	.	PUNCT
ejpam-6248	384	1	steklov	steklov	PROPN
ejpam-6248	384	2	inst	inst	PROPN
ejpam-6248	384	3	.	.	PUNCT
ejpam-6248	385	1	math	math	NOUN
ejpam-6248	385	2	.	.	PUNCT
ejpam-6248	386	1	2008	2008	NUM
ejpam-6248	386	2	,	,	PUNCT
ejpam-6248	386	3	261	261	NUM
ejpam-6248	386	4	,	,	PUNCT
ejpam-6248	386	5	s55	s55	PROPN
ejpam-6248	386	6	–	–	PUNCT
ejpam-6248	386	7	s76	s76	NOUN
ejpam-6248	386	8	.	.	PUNCT
ejpam-6248	387	1	[	[	X
ejpam-6248	387	2	25	25	NUM
ejpam-6248	387	3	]	]	PUNCT
ejpam-6248	387	4	theaker	theaker	NOUN
ejpam-6248	387	5	,	,	PUNCT
ejpam-6248	387	6	k.a	k.a	PROPN
ejpam-6248	387	7	.	.	PROPN
ejpam-6248	387	8	;	;	PUNCT
ejpam-6248	387	9	van	van	PROPN
ejpam-6248	387	10	gorder	gorder	NOUN
ejpam-6248	387	11	,	,	PUNCT
ejpam-6248	387	12	r.a	r.a	PROPN
ejpam-6248	387	13	.	.	PROPN
ejpam-6248	387	14	solutions	solution	NOUN
ejpam-6248	387	15	to	to	AUX
ejpam-6248	387	16	forced	force	VERB
ejpam-6248	387	17	and	and	CCONJ
ejpam-6248	387	18	unforced	unforced	ADJ
ejpam-6248	387	19	lin	lin	PROPN
ejpam-6248	387	20	–	–	PUNCT
ejpam-6248	387	21	reissner	reissner	NOUN
ejpam-6248	387	22	–	–	PUNCT
ejpam-6248	387	23	tsien	tsien	NOUN
ejpam-6248	387	24	equations	equation	NOUN
ejpam-6248	387	25	for	for	ADP
ejpam-6248	387	26	transonic	transonic	ADJ
ejpam-6248	387	27	gas	gas	NOUN
ejpam-6248	387	28	flows	flow	VERB
ejpam-6248	387	29	on	on	ADP
ejpam-6248	387	30	various	various	ADJ
ejpam-6248	387	31	length	length	NOUN
ejpam-6248	387	32	scales	scale	NOUN
ejpam-6248	387	33	.	.	PUNCT
ejpam-6248	388	1	commun	commun	PROPN
ejpam-6248	388	2	.	.	PUNCT
ejpam-6248	389	1	theor	theor	PROPN
ejpam-6248	389	2	.	.	PUNCT
ejpam-6248	390	1	phys	phy	NOUN
ejpam-6248	390	2	.	.	PUNCT
ejpam-6248	391	1	2017	2017	NUM
ejpam-6248	391	2	,	,	PUNCT
ejpam-6248	391	3	67	67	NUM
ejpam-6248	391	4	,	,	PUNCT
ejpam-6248	391	5	309	309	NUM
ejpam-6248	391	6	.	.	PUNCT
ejpam-6248	392	1	[	[	X
ejpam-6248	392	2	26	26	NUM
ejpam-6248	392	3	]	]	X
ejpam-6248	392	4	ahmad	ahmad	PROPN
ejpam-6248	392	5	,	,	PUNCT
ejpam-6248	392	6	i.	i.	PROPN
ejpam-6248	392	7	;	;	PUNCT
ejpam-6248	392	8	amin	amin	PROPN
ejpam-6248	392	9	,	,	PUNCT
ejpam-6248	392	10	r.	r.	PROPN
ejpam-6248	392	11	;	;	PUNCT
ejpam-6248	392	12	abdeljawad	abdeljawad	NOUN
ejpam-6248	392	13	,	,	PUNCT
ejpam-6248	392	14	t.	t.	PROPN
ejpam-6248	392	15	;	;	PUNCT
ejpam-6248	392	16	shah	shah	PROPN
ejpam-6248	392	17	,	,	PUNCT
ejpam-6248	392	18	k.	k.	PROPN
ejpam-6248	393	1	a	a	DET
ejpam-6248	393	2	numerical	numerical	ADJ
ejpam-6248	393	3	method	method	NOUN
ejpam-6248	393	4	for	for	ADP
ejpam-6248	393	5	fractional	fractional	ADJ
ejpam-6248	393	6	pantograph	pantograph	NOUN
ejpam-6248	393	7	delay	delay	NOUN
ejpam-6248	393	8	integro	integro	ADJ
ejpam-6248	393	9	-	-	PUNCT
ejpam-6248	393	10	differential	differential	NOUN
ejpam-6248	393	11	equations	equation	NOUN
ejpam-6248	393	12	on	on	ADP
ejpam-6248	393	13	haar	haar	PROPN
ejpam-6248	393	14	wavelet	wavelet	PROPN
ejpam-6248	393	15	.	.	PUNCT
ejpam-6248	394	1	int	int	NOUN
ejpam-6248	394	2	.	.	PUNCT
ejpam-6248	395	1	j.	j.	PROPN
ejpam-6248	395	2	appl	appl	PROPN
ejpam-6248	395	3	.	.	PUNCT
ejpam-6248	396	1	comput	comput	PROPN
ejpam-6248	396	2	.	.	PUNCT
ejpam-6248	397	1	math	math	NOUN
ejpam-6248	397	2	.	.	PUNCT
ejpam-6248	398	1	2021	2021	NUM
ejpam-6248	398	2	,	,	PUNCT
ejpam-6248	398	3	7	7	NUM
ejpam-6248	398	4	,	,	PUNCT
ejpam-6248	398	5	1–13	1–13	NOUN
ejpam-6248	398	6	.	.	PUNCT
ejpam-6248	399	1	[	[	X
ejpam-6248	399	2	27	27	NUM
ejpam-6248	399	3	]	]	X
ejpam-6248	399	4	rehman	rehman	PROPN
ejpam-6248	399	5	,	,	PUNCT
ejpam-6248	399	6	m.u	m.u	PROPN
ejpam-6248	399	7	.	.	PROPN
ejpam-6248	399	8	;	;	PUNCT
ejpam-6248	399	9	baleanu	baleanu	PROPN
ejpam-6248	399	10	,	,	PUNCT
ejpam-6248	399	11	d.	d.	PROPN
ejpam-6248	399	12	;	;	PUNCT
ejpam-6248	399	13	alzabut	alzabut	PROPN
ejpam-6248	399	14	,	,	PUNCT
ejpam-6248	399	15	j.	j.	PROPN
ejpam-6248	399	16	;	;	PUNCT
ejpam-6248	399	17	ismail	ismail	PROPN
ejpam-6248	399	18	,	,	PUNCT
ejpam-6248	399	19	m.	m.	NOUN
ejpam-6248	399	20	;	;	PUNCT
ejpam-6248	399	21	saeed	saeed	PROPN
ejpam-6248	399	22	,	,	PUNCT
ejpam-6248	399	23	u.	u.	PROPN
ejpam-6248	399	24	green	green	PROPN
ejpam-6248	399	25	–	–	PUNCT
ejpam-6248	399	26	haar	haar	PROPN
ejpam-6248	399	27	wavelets	wavelet	NOUN
ejpam-6248	399	28	method	method	NOUN
ejpam-6248	399	29	for	for	ADP
ejpam-6248	399	30	generalized	generalized	ADJ
ejpam-6248	399	31	fractional	fractional	ADJ
ejpam-6248	399	32	differential	differential	NOUN
ejpam-6248	399	33	equations	equation	NOUN
ejpam-6248	399	34	.	.	PUNCT
ejpam-6248	400	1	adv	adv	PROPN
ejpam-6248	400	2	.	.	PUNCT
ejpam-6248	400	3	difference	difference	PROPN
ejpam-6248	400	4	equ	equ	PROPN
ejpam-6248	400	5	.	.	PROPN
ejpam-6248	400	6	2020	2020	NUM
ejpam-6248	400	7	,	,	PUNCT
ejpam-6248	400	8	2020	2020	NUM
ejpam-6248	400	9	,	,	PUNCT
ejpam-6248	400	10	1–25	1–25	PROPN
ejpam-6248	400	11	.	.	PUNCT