id	sid	tid	token	lemma	pos
ap-8351	1	1	acta	acta	PROPN
ap-8351	1	2	polytechnica	polytechnica	PROPN
ap-8351	1	3	https://doi.org/10.14311/ap.2023.63.0019	https://doi.org/10.14311/ap.2023.63.0019	PROPN
ap-8351	1	4	acta	acta	PROPN
ap-8351	1	5	polytechnica	polytechnica	PROPN
ap-8351	1	6	63(1):19–22	63(1):19–22	NUM
ap-8351	1	7	,	,	PUNCT
ap-8351	1	8	2023	2023	NUM
ap-8351	1	9	©	©	ADP
ap-8351	1	10	2023	2023	NUM
ap-8351	1	11	the	the	DET
ap-8351	1	12	author(s	author(s	NOUN
ap-8351	1	13	)	)	PUNCT
ap-8351	1	14	.	.	PUNCT
ap-8351	2	1	licensed	license	VERB
ap-8351	2	2	under	under	ADP
ap-8351	2	3	a	a	DET
ap-8351	2	4	cc	cc	NOUN
ap-8351	2	5	-	-	PUNCT
ap-8351	2	6	by	by	ADP
ap-8351	2	7	4.0	4.0	NUM
ap-8351	2	8	licence	licence	NOUN
ap-8351	2	9	published	publish	VERB
ap-8351	2	10	by	by	ADP
ap-8351	2	11	the	the	DET
ap-8351	2	12	czech	czech	PROPN
ap-8351	2	13	technical	technical	PROPN
ap-8351	2	14	university	university	PROPN
ap-8351	2	15	in	in	ADP
ap-8351	2	16	prague	prague	PROPN
ap-8351	2	17	linearisation	linearisation	NOUN
ap-8351	2	18	of	of	ADP
ap-8351	2	19	a	a	DET
ap-8351	2	20	second	second	ADJ
ap-8351	2	21	-	-	PUNCT
ap-8351	2	22	order	order	NOUN
ap-8351	2	23	nonlinear	nonlinear	ADJ
ap-8351	2	24	ordinary	ordinary	ADJ
ap-8351	2	25	differential	differential	ADJ
ap-8351	2	26	equation	equation	NOUN
ap-8351	2	27	adhir	adhir	ADP
ap-8351	2	28	maharaj∗	maharaj∗	PROPN
ap-8351	2	29	,	,	PUNCT
ap-8351	2	30	peter	peter	PROPN
ap-8351	2	31	g.	g.	PROPN
ap-8351	2	32	l.	l.	PROPN
ap-8351	2	33	leach	leach	PROPN
ap-8351	2	34	,	,	PUNCT
ap-8351	2	35	megan	megan	NOUN
ap-8351	2	36	govender	govender	NOUN
ap-8351	2	37	,	,	PUNCT
ap-8351	2	38	david	david	PROPN
ap-8351	2	39	p.	p.	PROPN
ap-8351	2	40	day	day	PROPN
ap-8351	2	41	durban	durban	PROPN
ap-8351	2	42	university	university	PROPN
ap-8351	2	43	of	of	ADP
ap-8351	2	44	technology	technology	NOUN
ap-8351	2	45	,	,	PUNCT
ap-8351	2	46	steve	steve	PROPN
ap-8351	2	47	biko	biko	PROPN
ap-8351	2	48	campus	campus	PROPN
ap-8351	2	49	,	,	PUNCT
ap-8351	2	50	department	department	NOUN
ap-8351	2	51	of	of	ADP
ap-8351	2	52	mathematics	mathematics	PROPN
ap-8351	2	53	,	,	PUNCT
ap-8351	2	54	durban	durban	NOUN
ap-8351	2	55	,	,	PUNCT
ap-8351	2	56	4000	4000	NUM
ap-8351	2	57	,	,	PUNCT
ap-8351	2	58	republic	republic	NOUN
ap-8351	2	59	of	of	ADP
ap-8351	2	60	south	south	PROPN
ap-8351	2	61	africa	africa	PROPN
ap-8351	2	62	∗	∗	PROPN
ap-8351	2	63	corresponding	correspond	VERB
ap-8351	2	64	author	author	NOUN
ap-8351	2	65	:	:	PUNCT
ap-8351	2	66	adhirm@dut.ac.za	adhirm@dut.ac.za	NOUN
ap-8351	2	67	abstract	abstract	NOUN
ap-8351	2	68	.	.	PUNCT
ap-8351	3	1	we	we	PRON
ap-8351	3	2	analyse	analyse	VERB
ap-8351	3	3	nonlinear	nonlinear	ADJ
ap-8351	3	4	second	second	ADJ
ap-8351	3	5	-	-	PUNCT
ap-8351	3	6	order	order	NOUN
ap-8351	3	7	differential	differential	ADJ
ap-8351	3	8	equations	equation	NOUN
ap-8351	3	9	in	in	ADP
ap-8351	3	10	terms	term	NOUN
ap-8351	3	11	of	of	ADP
ap-8351	3	12	algebraic	algebraic	ADJ
ap-8351	3	13	properties	property	NOUN
ap-8351	3	14	by	by	ADP
ap-8351	3	15	reducing	reduce	VERB
ap-8351	3	16	a	a	DET
ap-8351	3	17	nonlinear	nonlinear	ADJ
ap-8351	3	18	partial	partial	ADJ
ap-8351	3	19	differential	differential	NOUN
ap-8351	3	20	equation	equation	NOUN
ap-8351	3	21	to	to	ADP
ap-8351	3	22	a	a	DET
ap-8351	3	23	nonlinear	nonlinear	ADJ
ap-8351	3	24	second	second	ADJ
ap-8351	3	25	-	-	PUNCT
ap-8351	3	26	order	order	NOUN
ap-8351	3	27	ordinary	ordinary	ADJ
ap-8351	3	28	differential	differential	ADJ
ap-8351	3	29	equation	equation	NOUN
ap-8351	3	30	via	via	ADP
ap-8351	3	31	the	the	DET
ap-8351	3	32	point	point	NOUN
ap-8351	3	33	symmetry	symmetry	NOUN
ap-8351	3	34	f(v)∂v	f(v)∂v	NOUN
ap-8351	3	35	.	.	PUNCT
ap-8351	4	1	the	the	DET
ap-8351	4	2	eight	eight	NUM
ap-8351	4	3	lie	lie	NOUN
ap-8351	4	4	point	point	NOUN
ap-8351	4	5	symmetries	symmetry	NOUN
ap-8351	4	6	obtained	obtain	VERB
ap-8351	4	7	for	for	ADP
ap-8351	4	8	the	the	DET
ap-8351	4	9	second	second	ADJ
ap-8351	4	10	-	-	PUNCT
ap-8351	4	11	order	order	NOUN
ap-8351	4	12	ordinary	ordinary	ADJ
ap-8351	4	13	differential	differential	ADJ
ap-8351	4	14	equation	equation	NOUN
ap-8351	4	15	is	be	AUX
ap-8351	4	16	of	of	ADP
ap-8351	4	17	maximal	maximal	ADJ
ap-8351	4	18	number	number	NOUN
ap-8351	4	19	and	and	CCONJ
ap-8351	4	20	a	a	DET
ap-8351	4	21	representation	representation	NOUN
ap-8351	4	22	of	of	ADP
ap-8351	4	23	the	the	DET
ap-8351	4	24	sl(3	sl(3	PROPN
ap-8351	4	25	,	,	PUNCT
ap-8351	4	26	r	r	NOUN
ap-8351	4	27	)	)	PUNCT
ap-8351	4	28	algebra	algebra	NOUN
ap-8351	4	29	.	.	PUNCT
ap-8351	5	1	we	we	PRON
ap-8351	5	2	extend	extend	VERB
ap-8351	5	3	this	this	DET
ap-8351	5	4	analysis	analysis	NOUN
ap-8351	5	5	to	to	ADP
ap-8351	5	6	a	a	DET
ap-8351	5	7	more	more	ADV
ap-8351	5	8	general	general	ADJ
ap-8351	5	9	nonlinear	nonlinear	ADJ
ap-8351	5	10	second	second	ADJ
ap-8351	5	11	-	-	PUNCT
ap-8351	5	12	order	order	NOUN
ap-8351	5	13	differential	differential	ADJ
ap-8351	5	14	equation	equation	NOUN
ap-8351	5	15	and	and	CCONJ
ap-8351	5	16	we	we	PRON
ap-8351	5	17	obtain	obtain	VERB
ap-8351	5	18	similar	similar	ADJ
ap-8351	5	19	interesting	interesting	ADJ
ap-8351	5	20	algebraic	algebraic	ADJ
ap-8351	5	21	properties	property	NOUN
ap-8351	5	22	.	.	PUNCT
ap-8351	6	1	keywords	keyword	NOUN
ap-8351	6	2	:	:	PUNCT
ap-8351	6	3	lie	lie	NOUN
ap-8351	6	4	symmetries	symmetry	NOUN
ap-8351	6	5	,	,	PUNCT
ap-8351	6	6	integrability	integrability	NOUN
ap-8351	6	7	,	,	PUNCT
ap-8351	6	8	linearisation	linearisation	NOUN
ap-8351	6	9	.	.	PUNCT
ap-8351	7	1	1	1	X
ap-8351	7	2	.	.	X
ap-8351	7	3	introduction	introduction	NOUN
ap-8351	7	4	nonlinear	nonlinear	PROPN
ap-8351	7	5	differential	differential	ADJ
ap-8351	7	6	equations	equation	NOUN
ap-8351	7	7	are	be	AUX
ap-8351	7	8	ubiquitous	ubiquitous	ADJ
ap-8351	7	9	in	in	ADP
ap-8351	7	10	mathematically	mathematically	ADV
ap-8351	7	11	orientated	orientate	VERB
ap-8351	7	12	scientific	scientific	ADJ
ap-8351	7	13	fields	field	NOUN
ap-8351	7	14	,	,	PUNCT
ap-8351	7	15	such	such	ADJ
ap-8351	7	16	as	as	ADP
ap-8351	7	17	physics	physics	NOUN
ap-8351	7	18	,	,	PUNCT
ap-8351	7	19	engineering	engineering	NOUN
ap-8351	7	20	,	,	PUNCT
ap-8351	7	21	epidemiology	epidemiology	NOUN
ap-8351	7	22	etc	etc	X
ap-8351	7	23	.	.	X
ap-8351	7	24	therefore	therefore	ADV
ap-8351	7	25	,	,	PUNCT
ap-8351	7	26	the	the	DET
ap-8351	7	27	analysis	analysis	NOUN
ap-8351	7	28	and	and	CCONJ
ap-8351	7	29	closed	closed	ADJ
ap-8351	7	30	-	-	PUNCT
ap-8351	7	31	form	form	NOUN
ap-8351	7	32	solutions	solution	NOUN
ap-8351	7	33	of	of	ADP
ap-8351	7	34	differential	differential	ADJ
ap-8351	7	35	equations	equation	NOUN
ap-8351	7	36	are	be	AUX
ap-8351	7	37	important	important	ADJ
ap-8351	7	38	to	to	PART
ap-8351	7	39	understand	understand	VERB
ap-8351	7	40	natural	natural	ADJ
ap-8351	7	41	phenomena	phenomenon	NOUN
ap-8351	7	42	.	.	PUNCT
ap-8351	8	1	in	in	ADP
ap-8351	8	2	the	the	DET
ap-8351	8	3	search	search	NOUN
ap-8351	8	4	for	for	ADP
ap-8351	8	5	solutions	solution	NOUN
ap-8351	8	6	of	of	ADP
ap-8351	8	7	differential	differential	ADJ
ap-8351	8	8	equations	equation	NOUN
ap-8351	8	9	,	,	PUNCT
ap-8351	8	10	one	one	PRON
ap-8351	8	11	discovers	discover	VERB
ap-8351	8	12	the	the	DET
ap-8351	8	13	beauty	beauty	NOUN
ap-8351	8	14	of	of	ADP
ap-8351	8	15	the	the	DET
ap-8351	8	16	algebraic	algebraic	ADJ
ap-8351	8	17	properties	property	NOUN
ap-8351	8	18	that	that	PRON
ap-8351	8	19	the	the	DET
ap-8351	8	20	equations	equation	NOUN
ap-8351	8	21	possess	possess	VERB
ap-8351	8	22	.	.	PUNCT
ap-8351	9	1	even	even	ADV
ap-8351	9	2	though	though	SCONJ
ap-8351	9	3	closed	close	VERB
ap-8351	9	4	-	-	PUNCT
ap-8351	9	5	form	form	NOUN
ap-8351	9	6	solutions	solution	NOUN
ap-8351	9	7	are	be	AUX
ap-8351	9	8	the	the	DET
ap-8351	9	9	primary	primary	ADJ
ap-8351	9	10	objective	objective	NOUN
ap-8351	9	11	,	,	PUNCT
ap-8351	9	12	one	one	PRON
ap-8351	9	13	can	can	AUX
ap-8351	9	14	not	not	PART
ap-8351	9	15	ignore	ignore	VERB
ap-8351	9	16	the	the	DET
ap-8351	9	17	interesting	interesting	ADJ
ap-8351	9	18	properties	property	NOUN
ap-8351	9	19	of	of	ADP
ap-8351	9	20	the	the	DET
ap-8351	9	21	equations	equation	NOUN
ap-8351	9	22	[	[	X
ap-8351	9	23	1–6	1–6	X
ap-8351	9	24	]	]	X
ap-8351	9	25	.	.	PUNCT
ap-8351	10	1	in	in	ADP
ap-8351	10	2	recent	recent	ADJ
ap-8351	10	3	years	year	NOUN
ap-8351	10	4	,	,	PUNCT
ap-8351	10	5	one	one	NUM
ap-8351	10	6	such	such	ADJ
ap-8351	10	7	area	area	NOUN
ap-8351	10	8	in	in	ADP
ap-8351	10	9	relativistic	relativistic	ADJ
ap-8351	10	10	astrophysics	astrophysic	NOUN
ap-8351	10	11	involves	involve	VERB
ap-8351	10	12	the	the	DET
ap-8351	10	13	embedding	embedding	NOUN
ap-8351	10	14	of	of	ADP
ap-8351	10	15	a	a	DET
ap-8351	10	16	four	four	NUM
ap-8351	10	17	-	-	PUNCT
ap-8351	10	18	dimensional	dimensional	ADJ
ap-8351	10	19	differentiable	differentiable	NOUN
ap-8351	10	20	manifold	manifold	NOUN
ap-8351	10	21	into	into	ADP
ap-8351	10	22	a	a	DET
ap-8351	10	23	higher	high	ADJ
ap-8351	10	24	dimensional	dimensional	ADJ
ap-8351	10	25	euclidean	euclidean	ADJ
ap-8351	10	26	space	space	NOUN
ap-8351	10	27	which	which	PRON
ap-8351	10	28	gives	give	VERB
ap-8351	10	29	rise	rise	NOUN
ap-8351	10	30	to	to	ADP
ap-8351	10	31	the	the	DET
ap-8351	10	32	so	so	ADV
ap-8351	10	33	-	-	PUNCT
ap-8351	10	34	called	call	VERB
ap-8351	10	35	karmarkar	karmarkar	NOUN
ap-8351	10	36	condition	condition	NOUN
ap-8351	10	37	for	for	ADP
ap-8351	10	38	class	class	NOUN
ap-8351	10	39	i	i	PRON
ap-8351	10	40	spacetimes	spacetime	VERB
ap-8351	10	41	[	[	X
ap-8351	10	42	7	7	NUM
ap-8351	10	43	]	]	PUNCT
ap-8351	10	44	.	.	PUNCT
ap-8351	11	1	the	the	DET
ap-8351	11	2	karmarkar	karmarkar	NOUN
ap-8351	11	3	condition	condition	NOUN
ap-8351	11	4	leads	lead	VERB
ap-8351	11	5	to	to	ADP
ap-8351	11	6	a	a	DET
ap-8351	11	7	quadrature	quadrature	NOUN
ap-8351	11	8	,	,	PUNCT
ap-8351	11	9	which	which	PRON
ap-8351	11	10	reduces	reduce	VERB
ap-8351	11	11	the	the	DET
ap-8351	11	12	problem	problem	NOUN
ap-8351	11	13	of	of	ADP
ap-8351	11	14	determinig	determinig	NOUN
ap-8351	11	15	the	the	DET
ap-8351	11	16	gravitational	gravitational	ADJ
ap-8351	11	17	behaviour	behaviour	NOUN
ap-8351	11	18	of	of	ADP
ap-8351	11	19	a	a	DET
ap-8351	11	20	gravitating	gravitate	VERB
ap-8351	11	21	system	system	NOUN
ap-8351	11	22	to	to	ADP
ap-8351	11	23	a	a	DET
ap-8351	11	24	single	single	ADJ
ap-8351	11	25	generating	generating	NOUN
ap-8351	11	26	function	function	NOUN
ap-8351	11	27	.	.	PUNCT
ap-8351	12	1	this	this	PRON
ap-8351	12	2	is	be	AUX
ap-8351	12	3	then	then	ADV
ap-8351	12	4	used	use	VERB
ap-8351	12	5	to	to	PART
ap-8351	12	6	close	close	VERB
ap-8351	12	7	the	the	DET
ap-8351	12	8	system	system	NOUN
ap-8351	12	9	of	of	ADP
ap-8351	12	10	field	field	NOUN
ap-8351	12	11	equations	equation	NOUN
ap-8351	12	12	in	in	ADP
ap-8351	12	13	order	order	NOUN
ap-8351	12	14	to	to	PART
ap-8351	12	15	get	get	VERB
ap-8351	12	16	a	a	DET
ap-8351	12	17	full	full	ADJ
ap-8351	12	18	description	description	NOUN
ap-8351	12	19	of	of	ADP
ap-8351	12	20	the	the	DET
ap-8351	12	21	thermodynamical	thermodynamical	ADJ
ap-8351	12	22	and	and	CCONJ
ap-8351	12	23	gravitational	gravitational	ADJ
ap-8351	12	24	evolution	evolution	NOUN
ap-8351	12	25	of	of	ADP
ap-8351	12	26	the	the	DET
ap-8351	12	27	model	model	NOUN
ap-8351	12	28	.	.	PUNCT
ap-8351	13	1	in	in	ADP
ap-8351	13	2	a	a	DET
ap-8351	13	3	recent	recent	ADJ
ap-8351	13	4	approach	approach	NOUN
ap-8351	13	5	,	,	PUNCT
ap-8351	13	6	nikolaev	nikolaev	NOUN
ap-8351	13	7	and	and	CCONJ
ap-8351	13	8	maharaj	maharaj	NOUN
ap-8351	13	9	[	[	X
ap-8351	13	10	8	8	NUM
ap-8351	13	11	]	]	PUNCT
ap-8351	13	12	investigated	investigate	VERB
ap-8351	13	13	the	the	DET
ap-8351	13	14	embedding	embed	VERB
ap-8351	13	15	properties	property	NOUN
ap-8351	13	16	of	of	ADP
ap-8351	13	17	the	the	DET
ap-8351	13	18	vaidya	vaidya	PROPN
ap-8351	13	19	metric	metric	NOUN
ap-8351	13	20	[	[	X
ap-8351	13	21	9	9	NUM
ap-8351	13	22	]	]	PUNCT
ap-8351	13	23	.	.	PUNCT
ap-8351	14	1	the	the	DET
ap-8351	14	2	vaidya	vaidya	PROPN
ap-8351	14	3	solution	solution	NOUN
ap-8351	14	4	is	be	AUX
ap-8351	14	5	the	the	DET
ap-8351	14	6	unique	unique	ADJ
ap-8351	14	7	solution	solution	NOUN
ap-8351	14	8	of	of	ADP
ap-8351	14	9	the	the	DET
ap-8351	14	10	einstein	einstein	ADJ
ap-8351	14	11	field	field	NOUN
ap-8351	14	12	equations	equation	NOUN
ap-8351	14	13	describing	describe	VERB
ap-8351	14	14	the	the	DET
ap-8351	14	15	exterior	exterior	ADJ
ap-8351	14	16	spacetime	spacetime	NOUN
ap-8351	14	17	filled	fill	VERB
ap-8351	14	18	with	with	ADP
ap-8351	14	19	null	null	ADJ
ap-8351	14	20	radition	radition	NOUN
ap-8351	14	21	of	of	ADP
ap-8351	14	22	a	a	DET
ap-8351	14	23	spherical	spherical	ADJ
ap-8351	14	24	mass	mass	NOUN
ap-8351	14	25	distribution	distribution	NOUN
ap-8351	14	26	undergoing	undergo	VERB
ap-8351	14	27	dissipative	dissipative	ADJ
ap-8351	14	28	gravitational	gravitational	ADJ
ap-8351	14	29	collapse	collapse	NOUN
ap-8351	14	30	.	.	PUNCT
ap-8351	15	1	in	in	ADP
ap-8351	15	2	their	their	PRON
ap-8351	15	3	work	work	NOUN
ap-8351	15	4	,	,	PUNCT
ap-8351	15	5	nikolaev	nikolaev	ADV
ap-8351	15	6	and	and	CCONJ
ap-8351	15	7	maharaj	maharaj	PROPN
ap-8351	15	8	showed	show	VERB
ap-8351	15	9	that	that	SCONJ
ap-8351	15	10	the	the	DET
ap-8351	15	11	vaidya	vaidya	ADJ
ap-8351	15	12	solution	solution	NOUN
ap-8351	15	13	is	be	AUX
ap-8351	15	14	not	not	PART
ap-8351	15	15	class	class	NOUN
ap-8351	15	16	i	i	PRON
ap-8351	15	17	embeddable	embeddable	ADJ
ap-8351	15	18	but	but	CCONJ
ap-8351	15	19	the	the	DET
ap-8351	15	20	generalised	generalise	VERB
ap-8351	15	21	vaidya	vaidya	PROPN
ap-8351	15	22	metric	metric	PROPN
ap-8351	15	23	describing	describe	VERB
ap-8351	15	24	an	an	DET
ap-8351	15	25	anisotropic	anisotropic	NOUN
ap-8351	15	26	and	and	CCONJ
ap-8351	15	27	inhomogeneous	inhomogeneous	ADJ
ap-8351	15	28	atmosphere	atmosphere	NOUN
ap-8351	15	29	comprising	comprising	NOUN
ap-8351	15	30	of	of	ADP
ap-8351	15	31	a	a	DET
ap-8351	15	32	mixture	mixture	NOUN
ap-8351	15	33	of	of	ADP
ap-8351	15	34	strings	string	NOUN
ap-8351	15	35	and	and	CCONJ
ap-8351	15	36	null	null	ADJ
ap-8351	15	37	radiation	radiation	NOUN
ap-8351	15	38	gives	give	VERB
ap-8351	15	39	rise	rise	NOUN
ap-8351	15	40	to	to	ADP
ap-8351	15	41	interesting	interesting	ADJ
ap-8351	15	42	embedding	embed	VERB
ap-8351	15	43	properties	property	NOUN
ap-8351	15	44	.	.	PUNCT
ap-8351	16	1	here	here	ADV
ap-8351	16	2	,	,	PUNCT
ap-8351	16	3	we	we	PRON
ap-8351	16	4	consider	consider	VERB
ap-8351	16	5	the	the	DET
ap-8351	16	6	nonlinear	nonlinear	ADJ
ap-8351	16	7	partial	partial	ADJ
ap-8351	16	8	differential	differential	NOUN
ap-8351	16	9	equation	equation	NOUN
ap-8351	16	10	arising	arise	VERB
ap-8351	16	11	from	from	ADP
ap-8351	16	12	the	the	DET
ap-8351	16	13	generalised	generalise	VERB
ap-8351	16	14	vaidya	vaidya	PROPN
ap-8351	16	15	metric	metric	PROPN
ap-8351	16	16	be	be	NOUN
ap-8351	16	17	of	of	ADP
ap-8351	16	18	class	class	NOUN
ap-8351	16	19	i.	i.	NOUN
ap-8351	16	20	the	the	DET
ap-8351	16	21	governing	govern	VERB
ap-8351	16	22	equation	equation	NOUN
ap-8351	16	23	is	be	AUX
ap-8351	16	24	2r2mm′′	2r2mm′′	NUM
ap-8351	16	25	−	−	PROPN
ap-8351	16	26	r2m′2	r2m′2	PROPN
ap-8351	17	1	−	−	PROPN
ap-8351	18	1	2rmm′	2rmm′	NUM
ap-8351	18	2	+	+	CCONJ
ap-8351	18	3	3m2	3m2	NUM
ap-8351	18	4	=	=	SYM
ap-8351	18	5	0	0	NUM
ap-8351	18	6	,	,	PUNCT
ap-8351	18	7	(	(	PUNCT
ap-8351	18	8	1	1	X
ap-8351	18	9	)	)	PUNCT
ap-8351	18	10	where	where	SCONJ
ap-8351	18	11	the	the	DET
ap-8351	18	12	prime	prime	ADJ
ap-8351	18	13	denotes	denote	NOUN
ap-8351	18	14	differentiation	differentiation	NOUN
ap-8351	18	15	of	of	ADP
ap-8351	18	16	the	the	DET
ap-8351	18	17	dependent	dependent	ADJ
ap-8351	18	18	variable	variable	NOUN
ap-8351	18	19	,	,	PUNCT
ap-8351	18	20	m(v	m(v	PROPN
ap-8351	18	21	,	,	PUNCT
ap-8351	18	22	r	r	NOUN
ap-8351	18	23	)	)	PUNCT
ap-8351	18	24	,	,	PUNCT
ap-8351	18	25	with	with	ADP
ap-8351	18	26	respect	respect	NOUN
ap-8351	18	27	to	to	ADP
ap-8351	18	28	the	the	DET
ap-8351	18	29	independent	independent	ADJ
ap-8351	18	30	variable	variable	NOUN
ap-8351	18	31	,	,	PUNCT
ap-8351	18	32	r.	r.	NOUN
ap-8351	18	33	equation	equation	NOUN
ap-8351	18	34	(	(	PUNCT
ap-8351	18	35	1	1	X
ap-8351	18	36	)	)	PUNCT
ap-8351	18	37	is	be	AUX
ap-8351	18	38	not	not	PART
ap-8351	18	39	v	v	NOUN
ap-8351	18	40	-	-	PUNCT
ap-8351	18	41	dependent	dependent	ADJ
ap-8351	18	42	explicitly	explicitly	ADV
ap-8351	18	43	and	and	CCONJ
ap-8351	18	44	possesses	possess	VERB
ap-8351	18	45	the	the	DET
ap-8351	18	46	point	point	NOUN
ap-8351	18	47	symmetry	symmetry	NOUN
ap-8351	18	48	f(v)∂v	f(v)∂v	PROPN
ap-8351	18	49	where	where	SCONJ
ap-8351	18	50	f(v	f(v	NOUN
ap-8351	18	51	)	)	PUNCT
ap-8351	18	52	is	be	AUX
ap-8351	18	53	an	an	DET
ap-8351	18	54	arbitrary	arbitrary	ADJ
ap-8351	18	55	function	function	NOUN
ap-8351	18	56	of	of	ADP
ap-8351	18	57	v	v	NOUN
ap-8351	18	58	only	only	ADV
ap-8351	18	59	.	.	PUNCT
ap-8351	19	1	using	use	VERB
ap-8351	19	2	this	this	DET
ap-8351	19	3	symmetry	symmetry	NOUN
ap-8351	19	4	,	,	PUNCT
ap-8351	19	5	we	we	PRON
ap-8351	19	6	obtain	obtain	VERB
ap-8351	19	7	the	the	DET
ap-8351	19	8	invariants	invariant	NOUN
ap-8351	19	9	r	r	NOUN
ap-8351	19	10	=	=	PUNCT
ap-8351	19	11	x	x	X
ap-8351	19	12	and	and	CCONJ
ap-8351	19	13	m	m	PROPN
ap-8351	19	14	=	=	ADJ
ap-8351	19	15	y(x	y(x	PROPN
ap-8351	19	16	)	)	PUNCT
ap-8351	19	17	,	,	PUNCT
ap-8351	19	18	which	which	PRON
ap-8351	19	19	reduces	reduce	VERB
ap-8351	19	20	(	(	PUNCT
ap-8351	19	21	1	1	NUM
ap-8351	19	22	)	)	PUNCT
ap-8351	19	23	to	to	ADP
ap-8351	19	24	a	a	DET
ap-8351	19	25	nonlinear	nonlinear	ADJ
ap-8351	19	26	nonautonomous	nonautonomous	ADJ
ap-8351	19	27	second	second	ADJ
ap-8351	19	28	-	-	PUNCT
ap-8351	19	29	order	order	NOUN
ap-8351	19	30	ordinary	ordinary	ADJ
ap-8351	19	31	differential	differential	ADJ
ap-8351	19	32	equation	equation	NOUN
ap-8351	19	33	2x2yy′′	2x2yy′′	NOUN
ap-8351	19	34	−	−	PROPN
ap-8351	19	35	x2y′2	x2y′2	PROPN
ap-8351	20	1	−	−	ADP
ap-8351	20	2	2xyy′	2xyy′	NUM
ap-8351	21	1	+	+	CCONJ
ap-8351	21	2	3y2	3y2	NUM
ap-8351	21	3	=	=	SYM
ap-8351	21	4	0	0	NUM
ap-8351	21	5	,	,	PUNCT
ap-8351	21	6	(	(	PUNCT
ap-8351	21	7	2	2	X
ap-8351	21	8	)	)	PUNCT
ap-8351	21	9	where	where	SCONJ
ap-8351	21	10	y	y	PROPN
ap-8351	21	11	is	be	AUX
ap-8351	21	12	a	a	DET
ap-8351	21	13	function	function	NOUN
ap-8351	21	14	of	of	ADP
ap-8351	21	15	x	x	PUNCT
ap-8351	21	16	only	only	ADV
ap-8351	21	17	.	.	PUNCT
ap-8351	22	1	we	we	PRON
ap-8351	22	2	use	use	VERB
ap-8351	22	3	the	the	DET
ap-8351	22	4	lie	lie	NOUN
ap-8351	22	5	symmetry	symmetry	NOUN
ap-8351	22	6	approach	approach	NOUN
ap-8351	22	7	to	to	PART
ap-8351	22	8	obtain	obtain	VERB
ap-8351	22	9	the	the	DET
ap-8351	22	10	solution	solution	NOUN
ap-8351	22	11	of	of	ADP
ap-8351	22	12	(	(	PUNCT
ap-8351	22	13	2	2	NUM
ap-8351	22	14	)	)	PUNCT
ap-8351	22	15	.	.	PUNCT
ap-8351	23	1	using	use	VERB
ap-8351	23	2	the	the	DET
ap-8351	23	3	solution	solution	NOUN
ap-8351	23	4	of	of	ADP
ap-8351	23	5	(	(	PUNCT
ap-8351	23	6	2	2	NUM
ap-8351	23	7	)	)	PUNCT
ap-8351	23	8	,	,	PUNCT
ap-8351	23	9	we	we	PRON
ap-8351	23	10	obtain	obtain	VERB
ap-8351	23	11	the	the	DET
ap-8351	23	12	solution	solution	NOUN
ap-8351	23	13	of	of	ADP
ap-8351	23	14	(	(	PUNCT
ap-8351	23	15	1	1	NUM
ap-8351	23	16	)	)	PUNCT
ap-8351	23	17	.	.	PUNCT
ap-8351	24	1	2	2	X
ap-8351	24	2	.	.	X
ap-8351	24	3	preliminaries	preliminary	NOUN
ap-8351	24	4	let	let	AUX
ap-8351	24	5	(	(	PUNCT
ap-8351	24	6	x	x	NOUN
ap-8351	24	7	,	,	PUNCT
ap-8351	24	8	y	y	NOUN
ap-8351	24	9	)	)	PUNCT
ap-8351	24	10	denote	denote	VERB
ap-8351	24	11	the	the	DET
ap-8351	24	12	variables	variable	NOUN
ap-8351	24	13	of	of	ADP
ap-8351	24	14	a	a	DET
ap-8351	24	15	two	two	NUM
ap-8351	24	16	-	-	PUNCT
ap-8351	24	17	dimensional	dimensional	ADJ
ap-8351	24	18	space	space	NOUN
ap-8351	24	19	.	.	PUNCT
ap-8351	25	1	suppose	suppose	VERB
ap-8351	25	2	that	that	SCONJ
ap-8351	25	3	x	x	PRON
ap-8351	25	4	is	be	AUX
ap-8351	25	5	the	the	DET
ap-8351	25	6	independent	independent	ADJ
ap-8351	25	7	variable	variable	NOUN
ap-8351	25	8	and	and	CCONJ
ap-8351	25	9	y	y	PROPN
ap-8351	25	10	is	be	AUX
ap-8351	25	11	the	the	DET
ap-8351	25	12	dependent	dependent	ADJ
ap-8351	25	13	variable	variable	NOUN
ap-8351	25	14	.	.	PUNCT
ap-8351	26	1	an	an	DET
ap-8351	26	2	infinitesimal	infinitesimal	ADJ
ap-8351	26	3	transformation	transformation	NOUN
ap-8351	26	4	in	in	ADP
ap-8351	26	5	this	this	DET
ap-8351	26	6	space	space	NOUN
ap-8351	26	7	has	have	VERB
ap-8351	26	8	the	the	DET
ap-8351	26	9	form	form	NOUN
ap-8351	26	10	x̄	x̄	PUNCT
ap-8351	27	1	=	=	PUNCT
ap-8351	28	1	x	x	PUNCT
ap-8351	29	1	+	+	NUM
ap-8351	29	2	ϵξ(x	ϵξ(x	NUM
ap-8351	29	3	,	,	PUNCT
ap-8351	29	4	y	y	PROPN
ap-8351	29	5	)	)	PUNCT
ap-8351	29	6	(	(	PUNCT
ap-8351	29	7	3	3	X
ap-8351	29	8	)	)	PUNCT
ap-8351	29	9	ȳ	ȳ	NOUN
ap-8351	29	10	=	=	SYM
ap-8351	29	11	y	y	PROPN
ap-8351	29	12	+	+	CCONJ
ap-8351	29	13	ϵη(x	ϵη(x	PROPN
ap-8351	29	14	,	,	PUNCT
ap-8351	29	15	y	y	NOUN
ap-8351	29	16	)	)	PUNCT
ap-8351	29	17	(	(	PUNCT
ap-8351	29	18	4	4	X
ap-8351	29	19	)	)	PUNCT
ap-8351	29	20	which	which	PRON
ap-8351	29	21	can	can	AUX
ap-8351	29	22	be	be	AUX
ap-8351	29	23	regarded	regard	VERB
ap-8351	29	24	as	as	ADP
ap-8351	29	25	generated	generate	VERB
ap-8351	29	26	by	by	ADP
ap-8351	29	27	the	the	DET
ap-8351	29	28	differential	differential	ADJ
ap-8351	29	29	operator	operator	NOUN
ap-8351	29	30	γ	γ	X
ap-8351	29	31	=	=	SYM
ap-8351	29	32	ξ(x	ξ(x	PROPN
ap-8351	29	33	,	,	PUNCT
ap-8351	29	34	y	y	NOUN
ap-8351	29	35	)	)	PUNCT
ap-8351	29	36	∂	∂	NOUN
ap-8351	29	37	∂x	∂x	PROPN
ap-8351	29	38	+	+	CCONJ
ap-8351	29	39	η(x	η(x	PROPN
ap-8351	29	40	,	,	PUNCT
ap-8351	29	41	y	y	NOUN
ap-8351	29	42	)	)	PUNCT
ap-8351	29	43	∂	∂	NOUN
ap-8351	29	44	∂y	∂y	NOUN
ap-8351	29	45	.	.	PUNCT
ap-8351	30	1	(	(	PUNCT
ap-8351	30	2	5	5	NUM
ap-8351	30	3	)	)	PUNCT
ap-8351	30	4	since	since	SCONJ
ap-8351	30	5	we	we	PRON
ap-8351	30	6	are	be	AUX
ap-8351	30	7	concerned	concern	VERB
ap-8351	30	8	with	with	ADP
ap-8351	30	9	point	point	NOUN
ap-8351	30	10	symmetries	symmetry	NOUN
ap-8351	30	11	in	in	ADP
ap-8351	30	12	this	this	DET
ap-8351	30	13	paper	paper	NOUN
ap-8351	30	14	,	,	PUNCT
ap-8351	30	15	ξ	ξ	PROPN
ap-8351	30	16	and	and	CCONJ
ap-8351	30	17	η	η	PROPN
ap-8351	30	18	depend	depend	VERB
ap-8351	30	19	upon	upon	SCONJ
ap-8351	30	20	x	x	PUNCT
ap-8351	30	21	and	and	CCONJ
ap-8351	30	22	y	y	PROPN
ap-8351	30	23	only	only	ADV
ap-8351	30	24	.	.	PUNCT
ap-8351	31	1	under	under	ADP
ap-8351	31	2	the	the	DET
ap-8351	31	3	infinitesimal	infinitesimal	ADJ
ap-8351	31	4	transformation	transformation	NOUN
ap-8351	31	5	(	(	PUNCT
ap-8351	31	6	3	3	NUM
ap-8351	31	7	)	)	PUNCT
ap-8351	31	8	and	and	CCONJ
ap-8351	31	9	(	(	PUNCT
ap-8351	31	10	4	4	NUM
ap-8351	31	11	)	)	PUNCT
ap-8351	31	12	,	,	PUNCT
ap-8351	31	13	the	the	DET
ap-8351	31	14	nth	nth	NOUN
ap-8351	31	15	derivative	derivative	ADJ
ap-8351	31	16	transform	transform	NOUN
ap-8351	31	17	is	be	AUX
ap-8351	31	18	given	give	VERB
ap-8351	31	19	by	by	ADP
ap-8351	31	20	ζn	ζn	PRON
ap-8351	31	21	=	=	SYM
ap-8351	31	22	η(n	η(n	NOUN
ap-8351	31	23	)	)	PUNCT
ap-8351	31	24	−	−	PROPN
ap-8351	32	1	n∑	n∑	INTJ
ap-8351	32	2	j=1	j=1	NOUN
ap-8351	32	3	(	(	PUNCT
ap-8351	32	4	n	n	CCONJ
ap-8351	32	5	j	j	PROPN
ap-8351	32	6	)	)	PUNCT
ap-8351	32	7	y(n+1−j)ξ(j	y(n+1−j)ξ(j	PROPN
ap-8351	32	8	)	)	PUNCT
ap-8351	32	9	(	(	PUNCT
ap-8351	32	10	6	6	NUM
ap-8351	32	11	)	)	PUNCT
ap-8351	32	12	and	and	CCONJ
ap-8351	32	13	γn	γn	X
ap-8351	32	14	=	=	VERB
ap-8351	32	15	ζn	ζn	DET
ap-8351	32	16	∂	∂	NUM
ap-8351	32	17	∂y(n	∂y(n	NOUN
ap-8351	32	18	)	)	PUNCT
ap-8351	32	19	,	,	PUNCT
ap-8351	32	20	(	(	PUNCT
ap-8351	32	21	7	7	X
ap-8351	32	22	)	)	PUNCT
ap-8351	32	23	19	19	NUM
ap-8351	32	24	https://doi.org/10.14311/ap.2023.63.0019	https://doi.org/10.14311/ap.2023.63.0019	NOUN
ap-8351	32	25	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
ap-8351	32	26	https://www.cvut.cz/en	https://www.cvut.cz/en	NOUN
ap-8351	32	27	a.	a.	NOUN
ap-8351	32	28	maharaj	maharaj	PROPN
ap-8351	32	29	,	,	PUNCT
ap-8351	32	30	p.	p.	NOUN
ap-8351	32	31	g.	g.	PROPN
ap-8351	32	32	l.	l.	PROPN
ap-8351	32	33	leach	leach	PROPN
ap-8351	32	34	,	,	PUNCT
ap-8351	32	35	m.	m.	NOUN
ap-8351	32	36	govender	govender	NOUN
ap-8351	32	37	,	,	PUNCT
ap-8351	32	38	d.	d.	PROPN
ap-8351	32	39	p.	p.	PROPN
ap-8351	32	40	day	day	PROPN
ap-8351	33	1	acta	acta	PROPN
ap-8351	33	2	polytechnica	polytechnica	PROPN
ap-8351	33	3	where	where	SCONJ
ap-8351	33	4	the	the	DET
ap-8351	33	5	notation	notation	NOUN
ap-8351	33	6	η(n	η(n	NOUN
ap-8351	33	7	)	)	PUNCT
ap-8351	33	8	,	,	PUNCT
ap-8351	33	9	ξ(j	ξ(j	NUM
ap-8351	33	10	)	)	PUNCT
ap-8351	33	11	and	and	CCONJ
ap-8351	33	12	y(n	y(n	PROPN
ap-8351	33	13	)	)	PUNCT
ap-8351	33	14	denote	denote	VERB
ap-8351	33	15	the	the	DET
ap-8351	33	16	nth	nth	NOUN
ap-8351	33	17	,	,	PUNCT
ap-8351	33	18	jth	jth	PROPN
ap-8351	33	19	and	and	CCONJ
ap-8351	33	20	nth	nth	PROPN
ap-8351	33	21	derivative	derivative	NOUN
ap-8351	33	22	of	of	ADP
ap-8351	33	23	the	the	DET
ap-8351	33	24	dependent	dependent	ADJ
ap-8351	33	25	variable	variable	NOUN
ap-8351	33	26	with	with	ADP
ap-8351	33	27	respect	respect	NOUN
ap-8351	33	28	to	to	ADP
ap-8351	33	29	x.	x.	NOUN
ap-8351	33	30	in	in	ADP
ap-8351	33	31	the	the	DET
ap-8351	33	32	case	case	NOUN
ap-8351	33	33	of	of	ADP
ap-8351	33	34	a	a	DET
ap-8351	33	35	function	function	NOUN
ap-8351	33	36	,	,	PUNCT
ap-8351	33	37	f(x	f(x	PROPN
ap-8351	33	38	,	,	PUNCT
ap-8351	33	39	y	y	PROPN
ap-8351	33	40	,	,	PUNCT
ap-8351	33	41	y′	y′	NUM
ap-8351	33	42	,	,	PUNCT
ap-8351	33	43	...	...	PUNCT
ap-8351	33	44	,	,	PUNCT
ap-8351	33	45	y(n	y(n	PROPN
ap-8351	33	46	)	)	PUNCT
ap-8351	33	47	)	)	PUNCT
ap-8351	33	48	,	,	PUNCT
ap-8351	33	49	the	the	DET
ap-8351	33	50	infinitesimal	infinitesimal	ADJ
ap-8351	33	51	transformation	transformation	NOUN
ap-8351	33	52	is	be	AUX
ap-8351	33	53	generated	generate	VERB
ap-8351	33	54	by	by	ADP
ap-8351	33	55	γ	γ	PROPN
ap-8351	33	56	+	+	SYM
ap-8351	33	57	γ1	γ1	NOUN
ap-8351	33	58	+	+	CCONJ
ap-8351	33	59	γ2	γ2	PROPN
ap-8351	33	60	+	+	CCONJ
ap-8351	33	61	...	...	PUNCT
ap-8351	34	1	+	+	CCONJ
ap-8351	34	2	γn	γn	NOUN
ap-8351	34	3	which	which	PRON
ap-8351	34	4	we	we	PRON
ap-8351	34	5	write	write	VERB
ap-8351	34	6	as	as	ADP
ap-8351	34	7	γ[n	γ[n	NOUN
ap-8351	34	8	]	]	PUNCT
ap-8351	34	9	,	,	PUNCT
ap-8351	34	10	where	where	SCONJ
ap-8351	34	11	[	[	X
ap-8351	34	12	10	10	NUM
ap-8351	34	13	]	]	PUNCT
ap-8351	34	14	γ[n	γ[n	NUM
ap-8351	34	15	]	]	X
ap-8351	34	16	=	=	X
ap-8351	34	17	γ	γ	X
ap-8351	34	18	+	+	PROPN
ap-8351	34	19	n∑	n∑	ADJ
ap-8351	34	20	i=1	i=1	X
ap-8351	34	21	[	[	PUNCT
ap-8351	34	22	η(i	η(i	NOUN
ap-8351	34	23	)	)	PUNCT
ap-8351	34	24	−	−	PROPN
ap-8351	34	25	i∑	i∑	NOUN
ap-8351	34	26	j=1	j=1	NOUN
ap-8351	34	27	(	(	PUNCT
ap-8351	34	28	i	i	PRON
ap-8351	34	29	j	j	PROPN
ap-8351	34	30	)	)	PUNCT
ap-8351	34	31	y(i+1−j)ξ(j	y(i+1−j)ξ(j	PROPN
ap-8351	34	32	)	)	PUNCT
ap-8351	34	33	]	]	PUNCT
ap-8351	34	34	∂	∂	NUM
ap-8351	34	35	∂y(i	∂y(i	PROPN
ap-8351	34	36	)	)	PUNCT
ap-8351	34	37	,	,	PUNCT
ap-8351	34	38	(	(	PUNCT
ap-8351	34	39	8)	8)	NUM
ap-8351	34	40	is	be	AUX
ap-8351	34	41	called	call	VERB
ap-8351	34	42	the	the	DET
ap-8351	34	43	nth	nth	NOUN
ap-8351	34	44	extension	extension	NOUN
ap-8351	34	45	of	of	ADP
ap-8351	34	46	γ	γ	PROPN
ap-8351	34	47	.	.	PROPN
ap-8351	34	48	in	in	ADP
ap-8351	34	49	the	the	DET
ap-8351	34	50	case	case	NOUN
ap-8351	34	51	of	of	ADP
ap-8351	34	52	an	an	DET
ap-8351	34	53	equation	equation	NOUN
ap-8351	34	54	e(x	e(x	NUM
ap-8351	34	55	,	,	PUNCT
ap-8351	34	56	y	y	PROPN
ap-8351	34	57	,	,	PUNCT
ap-8351	34	58	y′	y′	NUM
ap-8351	34	59	,	,	PUNCT
ap-8351	34	60	...	...	PUNCT
ap-8351	34	61	,	,	PUNCT
ap-8351	34	62	y(n	y(n	PROPN
ap-8351	34	63	)	)	PUNCT
ap-8351	34	64	)	)	PUNCT
ap-8351	35	1	=	=	SYM
ap-8351	35	2	0	0	PUNCT
ap-8351	35	3	(	(	PUNCT
ap-8351	35	4	9	9	NUM
ap-8351	35	5	)	)	PUNCT
ap-8351	35	6	the	the	DET
ap-8351	35	7	equation	equation	NOUN
ap-8351	35	8	is	be	AUX
ap-8351	35	9	a	a	DET
ap-8351	35	10	constraint	constraint	NOUN
ap-8351	35	11	and	and	CCONJ
ap-8351	35	12	the	the	DET
ap-8351	35	13	condition	condition	NOUN
ap-8351	35	14	[	[	X
ap-8351	35	15	11	11	NUM
ap-8351	35	16	,	,	PUNCT
ap-8351	35	17	12	12	NUM
ap-8351	35	18	]	]	X
ap-8351	35	19	γ	γ	X
ap-8351	35	20	a	a	DET
ap-8351	35	21	symmetry	symmetry	NOUN
ap-8351	35	22	of	of	ADP
ap-8351	35	23	the	the	DET
ap-8351	35	24	equation	equation	NOUN
ap-8351	35	25	γ[n]e|e=0	γ[n]e|e=0	PROPN
ap-8351	35	26	=	=	SYM
ap-8351	35	27	0	0	NUM
ap-8351	35	28	,	,	PUNCT
ap-8351	35	29	(	(	PUNCT
ap-8351	35	30	10	10	NUM
ap-8351	35	31	)	)	PUNCT
ap-8351	35	32	i.e.	i.e.	X
ap-8351	35	33	the	the	DET
ap-8351	35	34	action	action	NOUN
ap-8351	35	35	of	of	ADP
ap-8351	35	36	th	th	NUM
ap-8351	35	37	nth	nth	NOUN
ap-8351	35	38	extension	extension	NOUN
ap-8351	35	39	of	of	ADP
ap-8351	35	40	γ	γ	NOUN
ap-8351	35	41	on	on	ADP
ap-8351	35	42	the	the	DET
ap-8351	35	43	function	function	NOUN
ap-8351	35	44	e	e	NOUN
ap-8351	35	45	is	be	AUX
ap-8351	35	46	zero	zero	NUM
ap-8351	35	47	when	when	SCONJ
ap-8351	35	48	the	the	DET
ap-8351	35	49	equation	equation	NOUN
ap-8351	35	50	(	(	PUNCT
ap-8351	35	51	9	9	NUM
ap-8351	35	52	)	)	PUNCT
ap-8351	35	53	is	be	AUX
ap-8351	35	54	taken	take	VERB
ap-8351	35	55	into	into	ADP
ap-8351	35	56	account	account	NOUN
ap-8351	35	57	.	.	PUNCT
ap-8351	36	1	we	we	PRON
ap-8351	36	2	note	note	VERB
ap-8351	36	3	that	that	SCONJ
ap-8351	36	4	e	e	NOUN
ap-8351	36	5	=	=	SYM
ap-8351	36	6	0	0	PROPN
ap-8351	36	7	may	may	AUX
ap-8351	36	8	be	be	AUX
ap-8351	36	9	a	a	DET
ap-8351	36	10	scalar	scalar	ADJ
ap-8351	36	11	equation	equation	NOUN
ap-8351	36	12	or	or	CCONJ
ap-8351	36	13	a	a	DET
ap-8351	36	14	system	system	NOUN
ap-8351	36	15	of	of	ADP
ap-8351	36	16	equations1	equations1	NOUN
ap-8351	36	17	.	.	PUNCT
ap-8351	37	1	3	3	X
ap-8351	37	2	.	.	X
ap-8351	37	3	symmetry	symmetry	NOUN
ap-8351	37	4	analysis	analysis	NOUN
ap-8351	37	5	the	the	DET
ap-8351	37	6	lie	lie	NOUN
ap-8351	37	7	point	point	NOUN
ap-8351	37	8	symmetries2	symmetries2	PROPN
ap-8351	37	9	of	of	ADP
ap-8351	37	10	(	(	PUNCT
ap-8351	37	11	2	2	X
ap-8351	37	12	)	)	PUNCT
ap-8351	37	13	are	be	AUX
ap-8351	37	14	γ1	γ1	NOUN
ap-8351	37	15	=	=	SYM
ap-8351	37	16	x	x	SYM
ap-8351	37	17	∂	∂	NUM
ap-8351	37	18	∂x	∂x	PROPN
ap-8351	37	19	γ2	γ2	NOUN
ap-8351	37	20	=	=	SYM
ap-8351	37	21	y	y	PROPN
ap-8351	37	22	∂	∂	NOUN
ap-8351	37	23	∂y	∂y	PROPN
ap-8351	37	24	γ3	γ3	NOUN
ap-8351	37	25	=	=	PUNCT
ap-8351	38	1	x3/2√	x3/2√	PROPN
ap-8351	38	2	y	y	PROPN
ap-8351	38	3	∂	∂	NOUN
ap-8351	38	4	∂y	∂y	PROPN
ap-8351	38	5	γ4	γ4	PROPN
ap-8351	38	6	=	=	NOUN
ap-8351	38	7	√	√	NUM
ap-8351	38	8	xy	xy	NOUN
ap-8351	38	9	∂	∂	NOUN
ap-8351	38	10	∂y	∂y	NOUN
ap-8351	38	11	γ5	γ5	NOUN
ap-8351	38	12	=	=	SYM
ap-8351	38	13	2x	2x	X
ap-8351	38	14	∂	∂	NUM
ap-8351	38	15	∂x	∂x	NOUN
ap-8351	39	1	+	+	CCONJ
ap-8351	39	2	3y	3y	NUM
ap-8351	39	3	∂	∂	X
ap-8351	39	4	∂y	∂y	NUM
ap-8351	39	5	γ6	γ6	NOUN
ap-8351	39	6	=	=	SYM
ap-8351	39	7	x2	x2	PROPN
ap-8351	39	8	∂	∂	NUM
ap-8351	39	9	∂x	∂x	PROPN
ap-8351	39	10	+	+	CCONJ
ap-8351	39	11	3xy	3xy	NOUN
ap-8351	39	12	∂	∂	NOUN
ap-8351	39	13	∂y	∂y	NUM
ap-8351	39	14	γ7	γ7	PROPN
ap-8351	39	15	=	=	PROPN
ap-8351	39	16	√	√	PROPN
ap-8351	39	17	y	y	PROPN
ap-8351	39	18	x	x	SYM
ap-8351	39	19	∂	∂	NUM
ap-8351	39	20	∂x	∂x	PROPN
ap-8351	39	21	+	+	CCONJ
ap-8351	39	22	(	(	PUNCT
ap-8351	39	23	y	y	NOUN
ap-8351	39	24	x	x	PROPN
ap-8351	39	25	)	)	PUNCT
ap-8351	39	26	3/2	3/2	NUM
ap-8351	39	27	∂y	∂y	PROPN
ap-8351	39	28	γ8	γ8	NOUN
ap-8351	39	29	=	=	NOUN
ap-8351	39	30	√	√	PROPN
ap-8351	39	31	xy	xy	NOUN
ap-8351	39	32	∂	∂	NOUN
ap-8351	39	33	∂x	∂x	PROPN
ap-8351	40	1	+	+	CCONJ
ap-8351	40	2	3y3/2	3y3/2	NUM
ap-8351	40	3	√	√	NUM
ap-8351	40	4	x	x	SYM
ap-8351	40	5	∂	∂	NUM
ap-8351	40	6	∂y	∂y	NOUN
ap-8351	40	7	which	which	PRON
ap-8351	40	8	is	be	AUX
ap-8351	40	9	a	a	DET
ap-8351	40	10	maximal	maximal	ADJ
ap-8351	40	11	number	number	NOUN
ap-8351	40	12	for	for	ADP
ap-8351	40	13	a	a	DET
ap-8351	40	14	second	second	ADJ
ap-8351	40	15	-	-	PUNCT
ap-8351	40	16	order	order	NOUN
ap-8351	40	17	ordinary	ordinary	ADJ
ap-8351	40	18	differential	differential	ADJ
ap-8351	40	19	equation	equation	NOUN
ap-8351	40	20	and	and	CCONJ
ap-8351	40	21	must	must	AUX
ap-8351	40	22	be	be	AUX
ap-8351	40	23	a	a	DET
ap-8351	40	24	representation	representation	NOUN
ap-8351	40	25	of	of	ADP
ap-8351	40	26	the	the	DET
ap-8351	40	27	sl(3	sl(3	PROPN
ap-8351	40	28	,	,	PUNCT
ap-8351	40	29	r	r	NOUN
ap-8351	40	30	)	)	PUNCT
ap-8351	40	31	algebra	algebra	NOUN
ap-8351	40	32	in	in	ADP
ap-8351	40	33	the	the	DET
ap-8351	40	34	mubarakzyanov	mubarakzyanov	NOUN
ap-8351	40	35	classification	classification	NOUN
ap-8351	40	36	scheme	scheme	NOUN
ap-8351	41	1	[	[	X
ap-8351	41	2	21–24	21–24	NUM
ap-8351	41	3	]	]	X
ap-8351	41	4	.	.	PUNCT
ap-8351	42	1	equation	equation	NOUN
ap-8351	42	2	(	(	PUNCT
ap-8351	42	3	2	2	X
ap-8351	42	4	)	)	PUNCT
ap-8351	42	5	is	be	AUX
ap-8351	42	6	linearisable	linearisable	ADJ
ap-8351	42	7	to	to	PART
ap-8351	42	8	d2y	d2y	VERB
ap-8351	42	9	dx2	dx2	PROPN
ap-8351	42	10	=	=	SYM
ap-8351	42	11	0	0	PROPN
ap-8351	42	12	,	,	PUNCT
ap-8351	42	13	(	(	PUNCT
ap-8351	42	14	11	11	NUM
ap-8351	42	15	)	)	PUNCT
ap-8351	42	16	1an	1an	ADJ
ap-8351	42	17	interested	interested	ADJ
ap-8351	42	18	reader	reader	NOUN
ap-8351	42	19	is	be	AUX
ap-8351	42	20	referred	refer	VERB
ap-8351	42	21	to	to	ADP
ap-8351	42	22	[	[	X
ap-8351	42	23	13–16	13–16	NUM
ap-8351	42	24	]	]	X
ap-8351	42	25	.	.	PUNCT
ap-8351	43	1	2the	2the	PROPN
ap-8351	43	2	mathematica	mathematica	PROPN
ap-8351	43	3	add	add	VERB
ap-8351	43	4	-	-	PUNCT
ap-8351	43	5	on	on	ADP
ap-8351	43	6	package	package	NOUN
ap-8351	43	7	sym	sym	NOUN
ap-8351	43	8	[	[	X
ap-8351	43	9	17–20	17–20	NUM
ap-8351	43	10	]	]	PUNCT
ap-8351	43	11	was	be	AUX
ap-8351	43	12	used	use	VERB
ap-8351	43	13	to	to	PART
ap-8351	43	14	obtain	obtain	VERB
ap-8351	43	15	the	the	DET
ap-8351	43	16	symmetries	symmetry	NOUN
ap-8351	43	17	.	.	PUNCT
ap-8351	44	1	by	by	ADP
ap-8351	44	2	means	mean	NOUN
ap-8351	44	3	of	of	ADP
ap-8351	44	4	a	a	DET
ap-8351	44	5	point	point	NOUN
ap-8351	44	6	transformation	transformation	NOUN
ap-8351	44	7	.	.	PUNCT
ap-8351	45	1	the	the	DET
ap-8351	45	2	solution	solution	NOUN
ap-8351	45	3	of	of	ADP
ap-8351	45	4	(	(	PUNCT
ap-8351	45	5	11	11	NUM
ap-8351	45	6	)	)	PUNCT
ap-8351	45	7	is	be	AUX
ap-8351	45	8	y	y	NOUN
ap-8351	45	9	=	=	NOUN
ap-8351	45	10	ax	ax	NOUN
ap-8351	45	11	+	+	CCONJ
ap-8351	45	12	b	b	NOUN
ap-8351	45	13	,	,	PUNCT
ap-8351	45	14	(	(	PUNCT
ap-8351	45	15	12	12	NUM
ap-8351	45	16	)	)	PUNCT
ap-8351	45	17	while	while	SCONJ
ap-8351	45	18	the	the	DET
ap-8351	45	19	solution	solution	NOUN
ap-8351	45	20	of	of	ADP
ap-8351	45	21	(	(	PUNCT
ap-8351	45	22	2	2	NUM
ap-8351	45	23	)	)	PUNCT
ap-8351	45	24	is	be	AUX
ap-8351	45	25	not	not	PART
ap-8351	45	26	exactly	exactly	ADV
ap-8351	45	27	obvious	obvious	ADJ
ap-8351	45	28	.	.	PUNCT
ap-8351	46	1	however	however	ADV
ap-8351	46	2	,	,	PUNCT
ap-8351	46	3	one	one	PRON
ap-8351	46	4	can	can	AUX
ap-8351	46	5	transform	transform	VERB
ap-8351	46	6	(	(	PUNCT
ap-8351	46	7	2	2	NUM
ap-8351	46	8	)	)	PUNCT
ap-8351	46	9	to	to	ADP
ap-8351	46	10	(	(	PUNCT
ap-8351	46	11	11	11	NUM
ap-8351	46	12	)	)	PUNCT
ap-8351	46	13	.	.	PUNCT
ap-8351	47	1	we	we	PRON
ap-8351	47	2	seek	seek	VERB
ap-8351	47	3	the	the	DET
ap-8351	47	4	transformation	transformation	NOUN
ap-8351	47	5	from	from	ADP
ap-8351	47	6	(	(	PUNCT
ap-8351	47	7	2	2	NUM
ap-8351	47	8	)	)	PUNCT
ap-8351	47	9	to	to	ADP
ap-8351	47	10	(	(	PUNCT
ap-8351	47	11	11	11	NUM
ap-8351	47	12	)	)	PUNCT
ap-8351	47	13	which	which	PRON
ap-8351	47	14	casts	cast	VERB
ap-8351	47	15	γ4	γ4	NOUN
ap-8351	47	16	=	=	SYM
ap-8351	47	17	√	√	PROPN
ap-8351	47	18	xy∂y	xy∂y	NOUN
ap-8351	47	19	into	into	ADP
ap-8351	47	20	canonical	canonical	ADJ
ap-8351	47	21	form	form	NOUN
ap-8351	47	22	.	.	PUNCT
ap-8351	48	1	γ4	γ4	NOUN
ap-8351	48	2	assumes	assume	VERB
ap-8351	48	3	canonical	canonical	ADJ
ap-8351	48	4	form	form	NOUN
ap-8351	48	5	provided	provide	VERB
ap-8351	48	6	ξ(x	ξ(x	NOUN
ap-8351	48	7	,	,	PUNCT
ap-8351	48	8	y)∂x	y)∂x	PROPN
ap-8351	48	9	∂x	∂x	PROPN
ap-8351	48	10	+	+	CCONJ
ap-8351	48	11	η(x	η(x	PROPN
ap-8351	48	12	,	,	PUNCT
ap-8351	48	13	y)∂x	y)∂x	PROPN
ap-8351	48	14	∂y	∂y	SYM
ap-8351	48	15	=	=	SYM
ap-8351	48	16	0	0	PROPN
ap-8351	48	17	(	(	PUNCT
ap-8351	48	18	13	13	NUM
ap-8351	48	19	)	)	PUNCT
ap-8351	48	20	ξ(x	ξ(x	NOUN
ap-8351	48	21	,	,	PUNCT
ap-8351	48	22	y)∂y	y)∂y	PROPN
ap-8351	48	23	∂x	∂x	PROPN
ap-8351	48	24	+	+	CCONJ
ap-8351	48	25	η(x	η(x	PROPN
ap-8351	48	26	,	,	PUNCT
ap-8351	48	27	y)∂y	y)∂y	PROPN
ap-8351	48	28	∂y	∂y	X
ap-8351	48	29	=	=	SYM
ap-8351	48	30	1	1	NUM
ap-8351	48	31	,	,	PUNCT
ap-8351	48	32	(	(	PUNCT
ap-8351	48	33	14	14	NUM
ap-8351	48	34	)	)	PUNCT
ap-8351	48	35	where	where	SCONJ
ap-8351	48	36	ξ	ξ	X
ap-8351	48	37	=	=	SYM
ap-8351	48	38	0	0	NUM
ap-8351	48	39	and	and	CCONJ
ap-8351	48	40	η	η	PROPN
ap-8351	48	41	=	=	PROPN
ap-8351	49	1	√	√	PROPN
ap-8351	49	2	xy	xy	VERB
ap-8351	50	1	because	because	SCONJ
ap-8351	50	2	(	(	PUNCT
ap-8351	50	3	2	2	X
ap-8351	50	4	)	)	PUNCT
ap-8351	50	5	possesses	possess	VERB
ap-8351	50	6	a	a	DET
ap-8351	50	7	symmetry	symmetry	NOUN
ap-8351	50	8	of	of	ADP
ap-8351	50	9	the	the	DET
ap-8351	50	10	general	general	ADJ
ap-8351	50	11	form	form	NOUN
ap-8351	50	12	γ	γ	X
ap-8351	50	13	=	=	SYM
ap-8351	50	14	ξ∂x	ξ∂x	VERB
ap-8351	50	15	+	+	CCONJ
ap-8351	50	16	η∂y	η∂y	PROPN
ap-8351	50	17	.	.	PUNCT
ap-8351	51	1	when	when	SCONJ
ap-8351	51	2	we	we	PRON
ap-8351	51	3	apply	apply	VERB
ap-8351	51	4	the	the	DET
ap-8351	51	5	method	method	NOUN
ap-8351	51	6	of	of	ADP
ap-8351	51	7	characteristics	characteristic	NOUN
ap-8351	51	8	for	for	ADP
ap-8351	51	9	first	first	ADJ
ap-8351	51	10	-	-	PUNCT
ap-8351	51	11	order	order	NOUN
ap-8351	51	12	partial	partial	ADJ
ap-8351	51	13	differential	differential	NOUN
ap-8351	51	14	equations	equation	NOUN
ap-8351	51	15	to	to	ADP
ap-8351	51	16	(	(	PUNCT
ap-8351	51	17	13	13	NUM
ap-8351	51	18	)	)	PUNCT
ap-8351	51	19	and	and	CCONJ
ap-8351	51	20	(	(	PUNCT
ap-8351	51	21	14	14	NUM
ap-8351	51	22	)	)	PUNCT
ap-8351	51	23	,	,	PUNCT
ap-8351	51	24	we	we	PRON
ap-8351	51	25	obtain	obtain	VERB
ap-8351	51	26	dx	dx	PROPN
ap-8351	51	27	0	0	PUNCT
ap-8351	52	1	=	=	PUNCT
ap-8351	52	2	dy	dy	NOUN
ap-8351	52	3	√	√	PROPN
ap-8351	52	4	xy	xy	PROPN
ap-8351	53	1	=	=	PUNCT
ap-8351	53	2	dx	dx	PROPN
ap-8351	53	3	0	0	NUM
ap-8351	53	4	(	(	PUNCT
ap-8351	53	5	15	15	NUM
ap-8351	53	6	)	)	PUNCT
ap-8351	53	7	dx	dx	PROPN
ap-8351	53	8	0	0	NUM
ap-8351	54	1	=	=	PUNCT
ap-8351	54	2	dy	dy	NOUN
ap-8351	54	3	√	√	NOUN
ap-8351	54	4	xy	xy	NOUN
ap-8351	55	1	=	=	PUNCT
ap-8351	55	2	dy	dy	NOUN
ap-8351	55	3	1	1	NUM
ap-8351	55	4	(	(	PUNCT
ap-8351	55	5	16	16	NUM
ap-8351	55	6	)	)	PUNCT
ap-8351	55	7	for	for	ADP
ap-8351	55	8	which	which	PRON
ap-8351	55	9	the	the	DET
ap-8351	55	10	solutions	solution	NOUN
ap-8351	55	11	are	be	AUX
ap-8351	55	12	x	x	X
ap-8351	55	13	=	=	SYM
ap-8351	55	14	x	x	X
ap-8351	55	15	,	,	PUNCT
ap-8351	55	16	y	y	PROPN
ap-8351	55	17	2	2	NUM
ap-8351	55	18	=	=	SYM
ap-8351	55	19	4y	4y	PROPN
ap-8351	55	20	x	x	X
ap-8351	55	21	.	.	PUNCT
ap-8351	56	1	(	(	PUNCT
ap-8351	56	2	17	17	NUM
ap-8351	56	3	)	)	PUNCT
ap-8351	56	4	under	under	ADP
ap-8351	56	5	the	the	DET
ap-8351	56	6	transformation	transformation	NOUN
ap-8351	56	7	(	(	PUNCT
ap-8351	56	8	17	17	NUM
ap-8351	56	9	)	)	PUNCT
ap-8351	56	10	,	,	PUNCT
ap-8351	56	11	equation	equation	NOUN
ap-8351	56	12	(	(	PUNCT
ap-8351	56	13	2	2	X
ap-8351	56	14	)	)	PUNCT
ap-8351	56	15	takes	take	VERB
ap-8351	56	16	the	the	DET
ap-8351	56	17	form	form	NOUN
ap-8351	56	18	in	in	ADP
ap-8351	56	19	(	(	PUNCT
ap-8351	56	20	11	11	NUM
ap-8351	56	21	)	)	PUNCT
ap-8351	56	22	.	.	PUNCT
ap-8351	57	1	hence	hence	ADV
ap-8351	57	2	we	we	PRON
ap-8351	57	3	may	may	AUX
ap-8351	57	4	apply	apply	VERB
ap-8351	57	5	(	(	PUNCT
ap-8351	57	6	17	17	NUM
ap-8351	57	7	)	)	PUNCT
ap-8351	57	8	to	to	ADP
ap-8351	57	9	(	(	PUNCT
ap-8351	57	10	12	12	NUM
ap-8351	57	11	)	)	PUNCT
ap-8351	57	12	to	to	PART
ap-8351	57	13	obtain	obtain	VERB
ap-8351	57	14	the	the	DET
ap-8351	57	15	solution	solution	NOUN
ap-8351	57	16	to	to	ADP
ap-8351	57	17	(	(	PUNCT
ap-8351	57	18	2	2	NUM
ap-8351	57	19	)	)	PUNCT
ap-8351	57	20	,	,	PUNCT
ap-8351	57	21	which	which	PRON
ap-8351	57	22	is	be	AUX
ap-8351	57	23	y(x	y(x	NOUN
ap-8351	57	24	)	)	PUNCT
ap-8351	57	25	=	=	PUNCT
ap-8351	57	26	1	1	NUM
ap-8351	57	27	4x(ax	4x(ax	NUM
ap-8351	57	28	+	+	CCONJ
ap-8351	57	29	b)2	b)2	ADJ
ap-8351	57	30	,	,	PUNCT
ap-8351	57	31	(	(	PUNCT
ap-8351	57	32	18	18	NUM
ap-8351	57	33	)	)	PUNCT
ap-8351	57	34	where	where	SCONJ
ap-8351	57	35	a	a	PRON
ap-8351	57	36	and	and	CCONJ
ap-8351	57	37	b	b	NOUN
ap-8351	57	38	are	be	AUX
ap-8351	57	39	two	two	NUM
ap-8351	57	40	constants	constant	NOUN
ap-8351	57	41	of	of	ADP
ap-8351	57	42	integration	integration	NOUN
ap-8351	57	43	.	.	PUNCT
ap-8351	58	1	by	by	ADP
ap-8351	58	2	using	use	VERB
ap-8351	58	3	the	the	DET
ap-8351	58	4	invariants	invariant	NOUN
ap-8351	58	5	r	r	NOUN
ap-8351	58	6	=	=	PUNCT
ap-8351	58	7	x	x	X
ap-8351	58	8	and	and	CCONJ
ap-8351	58	9	m	m	PROPN
ap-8351	58	10	=	=	ADJ
ap-8351	58	11	y(x	y(x	PROPN
ap-8351	58	12	)	)	PUNCT
ap-8351	58	13	,	,	PUNCT
ap-8351	58	14	the	the	DET
ap-8351	58	15	solution	solution	NOUN
ap-8351	58	16	of	of	ADP
ap-8351	58	17	(	(	PUNCT
ap-8351	58	18	1	1	X
ap-8351	58	19	)	)	PUNCT
ap-8351	58	20	follows	follow	VERB
ap-8351	58	21	from	from	ADP
ap-8351	58	22	(	(	PUNCT
ap-8351	58	23	18	18	NUM
ap-8351	58	24	)	)	PUNCT
ap-8351	58	25	and	and	CCONJ
ap-8351	58	26	is	be	AUX
ap-8351	58	27	m(v	m(v	NOUN
ap-8351	58	28	,	,	PUNCT
ap-8351	58	29	r	r	NOUN
ap-8351	58	30	)	)	PUNCT
ap-8351	58	31	=	=	SYM
ap-8351	59	1	1	1	NUM
ap-8351	59	2	4r(a(v)r	4r(a(v)r	NUM
ap-8351	59	3	+	+	CCONJ
ap-8351	59	4	b(v))2	b(v))2	PROPN
ap-8351	59	5	,	,	PUNCT
ap-8351	59	6	(	(	PUNCT
ap-8351	59	7	19	19	NUM
ap-8351	59	8	)	)	PUNCT
ap-8351	59	9	where	where	SCONJ
ap-8351	59	10	a(v	a(v	NOUN
ap-8351	59	11	)	)	PUNCT
ap-8351	59	12	and	and	CCONJ
ap-8351	59	13	b(v	b(v	NOUN
ap-8351	59	14	)	)	PUNCT
ap-8351	59	15	are	be	AUX
ap-8351	59	16	functions	function	NOUN
ap-8351	59	17	of	of	ADP
ap-8351	59	18	integration	integration	NOUN
ap-8351	59	19	.	.	PUNCT
ap-8351	60	1	4	4	X
ap-8351	60	2	.	.	X
ap-8351	60	3	the	the	DET
ap-8351	60	4	general	general	ADJ
ap-8351	60	5	case	case	NOUN
ap-8351	60	6	we	we	PRON
ap-8351	60	7	consider	consider	VERB
ap-8351	60	8	a	a	DET
ap-8351	60	9	general	general	ADJ
ap-8351	60	10	case	case	NOUN
ap-8351	60	11	by	by	ADP
ap-8351	60	12	setting	set	VERB
ap-8351	60	13	y(x	y(x	NOUN
ap-8351	60	14	)	)	PUNCT
ap-8351	60	15	=	=	SYM
ap-8351	60	16	un	un	PROPN
ap-8351	60	17	,	,	PUNCT
ap-8351	60	18	where	where	SCONJ
ap-8351	60	19	u	u	NOUN
ap-8351	60	20	is	be	AUX
ap-8351	60	21	a	a	DET
ap-8351	60	22	function	function	NOUN
ap-8351	60	23	of	of	ADP
ap-8351	60	24	x	x	PUNCT
ap-8351	60	25	in	in	ADP
ap-8351	60	26	equation	equation	NOUN
ap-8351	60	27	(	(	PUNCT
ap-8351	60	28	2	2	NUM
ap-8351	60	29	)	)	PUNCT
ap-8351	60	30	,	,	PUNCT
ap-8351	60	31	we	we	PRON
ap-8351	60	32	obtain	obtain	VERB
ap-8351	60	33	a	a	DET
ap-8351	60	34	more	more	ADV
ap-8351	60	35	general	general	ADJ
ap-8351	60	36	second	second	ADJ
ap-8351	60	37	-	-	PUNCT
ap-8351	60	38	order	order	NOUN
ap-8351	60	39	equation	equation	NOUN
ap-8351	60	40	2nx2uu′′	2nx2uu′′	NUM
ap-8351	61	1	+	+	CCONJ
ap-8351	62	1	n(n	n(n	PROPN
ap-8351	62	2	−	−	PROPN
ap-8351	62	3	2)x2u′2	2)x2u′2	NUM
ap-8351	62	4	−	−	PROPN
ap-8351	62	5	2nxuu′	2nxuu′	PROPN
ap-8351	63	1	+	+	CCONJ
ap-8351	63	2	3u2	3u2	NUM
ap-8351	63	3	=	=	SYM
ap-8351	63	4	0	0	X
ap-8351	63	5	.	.	PUNCT
ap-8351	64	1	(	(	PUNCT
ap-8351	64	2	20	20	NUM
ap-8351	64	3	)	)	PUNCT
ap-8351	64	4	20	20	NUM
ap-8351	64	5	vol	vol	NOUN
ap-8351	64	6	.	.	PUNCT
ap-8351	65	1	63	63	NUM
ap-8351	65	2	no	no	NOUN
ap-8351	65	3	.	.	PUNCT
ap-8351	66	1	1/2023	1/2023	NUM
ap-8351	66	2	linearisation	linearisation	NOUN
ap-8351	66	3	of	of	ADP
ap-8351	66	4	a	a	DET
ap-8351	66	5	second	second	ADJ
ap-8351	66	6	-	-	PUNCT
ap-8351	66	7	order	order	NOUN
ap-8351	66	8	nonlinear	nonlinear	ADJ
ap-8351	66	9	ordinary	ordinary	ADJ
ap-8351	66	10	differential	differential	ADJ
ap-8351	66	11	equation	equation	NOUN
ap-8351	66	12	the	the	DET
ap-8351	66	13	lie	lie	NOUN
ap-8351	66	14	point	point	NOUN
ap-8351	66	15	symmetries	symmetry	NOUN
ap-8351	66	16	of	of	ADP
ap-8351	66	17	(	(	PUNCT
ap-8351	66	18	20	20	NUM
ap-8351	66	19	)	)	PUNCT
ap-8351	66	20	are	be	AUX
ap-8351	66	21	λ1	λ1	ADJ
ap-8351	66	22	=	=	SYM
ap-8351	66	23	x	x	SYM
ap-8351	66	24	∂	∂	NUM
ap-8351	66	25	∂x	∂x	PROPN
ap-8351	66	26	λ2	λ2	NOUN
ap-8351	66	27	=	=	SYM
ap-8351	66	28	∂	∂	NOUN
ap-8351	67	1	∂x	∂x	PROPN
ap-8351	68	1	+	+	CCONJ
ap-8351	68	2	u	u	NOUN
ap-8351	68	3	nx	nx	PROPN
ap-8351	68	4	∂	∂	NOUN
ap-8351	68	5	∂u	∂u	PROPN
ap-8351	69	1	λ3	λ3	PROPN
ap-8351	69	2	=	=	SYM
ap-8351	69	3	1	1	NUM
ap-8351	69	4	n	n	PROPN
ap-8351	69	5	x3/2u1−n/2	x3/2u1−n/2	PROPN
ap-8351	69	6	∂	∂	PUNCT
ap-8351	70	1	∂u	∂u	NUM
ap-8351	70	2	λ4	λ4	NOUN
ap-8351	70	3	=	=	NOUN
ap-8351	70	4	1	1	NUM
ap-8351	70	5	n	n	NUM
ap-8351	70	6	√	√	PROPN
ap-8351	70	7	xu1−n/2	xu1−n/2	PROPN
ap-8351	70	8	∂	∂	NOUN
ap-8351	70	9	∂u	∂u	PROPN
ap-8351	70	10	λ5	λ5	NOUN
ap-8351	70	11	=	=	PUNCT
ap-8351	70	12	2x	2x	NUM
ap-8351	70	13	∂	∂	NUM
ap-8351	70	14	∂x	∂x	NOUN
ap-8351	70	15	+	+	CCONJ
ap-8351	70	16	3	3	NUM
ap-8351	70	17	n	n	CCONJ
ap-8351	70	18	u	u	NOUN
ap-8351	70	19	∂	∂	NOUN
ap-8351	70	20	∂u	∂u	PROPN
ap-8351	70	21	λ6	λ6	NOUN
ap-8351	70	22	=	=	SYM
ap-8351	70	23	x2	x2	PROPN
ap-8351	70	24	∂	∂	NOUN
ap-8351	71	1	∂x	∂x	NOUN
ap-8351	72	1	+	+	CCONJ
ap-8351	72	2	3	3	NUM
ap-8351	72	3	n	n	NOUN
ap-8351	72	4	xu	xu	PROPN
ap-8351	72	5	∂	∂	NOUN
ap-8351	73	1	∂u	∂u	PROPN
ap-8351	73	2	λ7	λ7	PROPN
ap-8351	73	3	=	=	PUNCT
ap-8351	74	1	√	√	PROPN
ap-8351	74	2	un	un	PROPN
ap-8351	74	3	x	x	PROPN
ap-8351	74	4	∂	∂	NUM
ap-8351	74	5	∂x	∂x	PROPN
ap-8351	74	6	+	+	CCONJ
ap-8351	74	7	u1+n/2	u1+n/2	PROPN
ap-8351	74	8	nx3/2	nx3/2	PROPN
ap-8351	74	9	∂	∂	NOUN
ap-8351	74	10	∂u	∂u	PROPN
ap-8351	74	11	λ8	λ8	NOUN
ap-8351	74	12	=	=	SYM
ap-8351	74	13	√	√	PROPN
ap-8351	74	14	xun	xun	PROPN
ap-8351	74	15	∂	∂	PROPN
ap-8351	74	16	∂x	∂x	PROPN
ap-8351	75	1	+	+	CCONJ
ap-8351	76	1	3	3	NUM
ap-8351	76	2	n	n	CCONJ
ap-8351	76	3	√	√	ADV
ap-8351	76	4	un+2	un+2	NUM
ap-8351	76	5	x	x	SYM
ap-8351	76	6	∂	∂	NUM
ap-8351	76	7	∂u	∂u	PROPN
ap-8351	76	8	.	.	PUNCT
ap-8351	77	1	as	as	ADP
ap-8351	77	2	(	(	PUNCT
ap-8351	77	3	20	20	NUM
ap-8351	77	4	)	)	PUNCT
ap-8351	77	5	is	be	AUX
ap-8351	77	6	a	a	DET
ap-8351	77	7	second	second	ADJ
ap-8351	77	8	-	-	PUNCT
ap-8351	77	9	order	order	NOUN
ap-8351	77	10	ordinary	ordinary	ADJ
ap-8351	77	11	differential	differential	ADJ
ap-8351	77	12	equation	equation	NOUN
ap-8351	77	13	and	and	CCONJ
ap-8351	77	14	possesses	possess	VERB
ap-8351	77	15	eight	eight	NUM
ap-8351	77	16	lie	lie	NOUN
ap-8351	77	17	point	point	NOUN
ap-8351	77	18	symmetries	symmetry	NOUN
ap-8351	77	19	,	,	PUNCT
ap-8351	77	20	it	it	PRON
ap-8351	77	21	is	be	AUX
ap-8351	77	22	related	relate	VERB
ap-8351	77	23	to	to	ADP
ap-8351	77	24	the	the	DET
ap-8351	77	25	generic	generic	ADJ
ap-8351	77	26	second	second	ADJ
ap-8351	77	27	-	-	PUNCT
ap-8351	77	28	order	order	NOUN
ap-8351	77	29	equation	equation	NOUN
ap-8351	77	30	[	[	X
ap-8351	77	31	25	25	NUM
ap-8351	77	32	]	]	PUNCT
ap-8351	77	33	d2y	d2y	ADJ
ap-8351	77	34	dx2	dx2	PROPN
ap-8351	77	35	=	=	NOUN
ap-8351	77	36	0	0	PROPN
ap-8351	77	37	.	.	PUNCT
ap-8351	78	1	(	(	PUNCT
ap-8351	78	2	21	21	NUM
ap-8351	78	3	)	)	PUNCT
ap-8351	78	4	when	when	SCONJ
ap-8351	78	5	we	we	PRON
ap-8351	78	6	apply	apply	VERB
ap-8351	78	7	the	the	DET
ap-8351	78	8	method	method	NOUN
ap-8351	78	9	of	of	ADP
ap-8351	78	10	characteristics	characteristic	NOUN
ap-8351	78	11	for	for	ADP
ap-8351	78	12	firstorder	firstorder	NOUN
ap-8351	78	13	partial	partial	ADJ
ap-8351	78	14	differential	differential	NOUN
ap-8351	78	15	equations	equation	NOUN
ap-8351	78	16	to	to	ADP
ap-8351	78	17	(	(	PUNCT
ap-8351	78	18	13	13	NUM
ap-8351	78	19	)	)	PUNCT
ap-8351	78	20	and	and	CCONJ
ap-8351	78	21	(	(	PUNCT
ap-8351	78	22	14	14	NUM
ap-8351	78	23	)	)	PUNCT
ap-8351	78	24	,	,	PUNCT
ap-8351	78	25	and	and	CCONJ
ap-8351	78	26	using	use	VERB
ap-8351	78	27	symmetry	symmetry	NOUN
ap-8351	78	28	λ4	λ4	PROPN
ap-8351	78	29	,	,	PUNCT
ap-8351	78	30	we	we	PRON
ap-8351	78	31	obtain	obtain	VERB
ap-8351	78	32	dx	dx	PROPN
ap-8351	78	33	0	0	PUNCT
ap-8351	79	1	=	=	SYM
ap-8351	79	2	du	du	PROPN
ap-8351	79	3	1	1	NUM
ap-8351	79	4	n	n	CCONJ
ap-8351	79	5	√	√	ADV
ap-8351	79	6	xu1−n/2	xu1−n/2	X
ap-8351	79	7	=	=	SYM
ap-8351	79	8	dx	dx	PROPN
ap-8351	79	9	0	0	NUM
ap-8351	80	1	(	(	PUNCT
ap-8351	80	2	22	22	NUM
ap-8351	80	3	)	)	PUNCT
ap-8351	80	4	dx	dx	PROPN
ap-8351	80	5	0	0	NUM
ap-8351	81	1	=	=	SYM
ap-8351	81	2	du	du	PROPN
ap-8351	81	3	1	1	NUM
ap-8351	81	4	n	n	CCONJ
ap-8351	81	5	√	√	ADV
ap-8351	81	6	xu1−n/2	xu1−n/2	X
ap-8351	81	7	=	=	PUNCT
ap-8351	81	8	dy	dy	NOUN
ap-8351	81	9	1	1	NUM
ap-8351	81	10	(	(	PUNCT
ap-8351	81	11	23	23	NUM
ap-8351	81	12	)	)	PUNCT
ap-8351	81	13	for	for	ADP
ap-8351	81	14	which	which	PRON
ap-8351	81	15	the	the	DET
ap-8351	81	16	solutions	solution	NOUN
ap-8351	81	17	are	be	AUX
ap-8351	81	18	x	x	X
ap-8351	81	19	=	=	SYM
ap-8351	81	20	x	x	X
ap-8351	81	21	,	,	PUNCT
ap-8351	81	22	y	y	PROPN
ap-8351	81	23	2	2	NUM
ap-8351	81	24	=	=	SYM
ap-8351	81	25	4un	4un	NOUN
ap-8351	81	26	x	x	X
ap-8351	81	27	.	.	PUNCT
ap-8351	82	1	(	(	PUNCT
ap-8351	82	2	24	24	NUM
ap-8351	82	3	)	)	PUNCT
ap-8351	82	4	from	from	ADP
ap-8351	82	5	the	the	DET
ap-8351	82	6	solution	solution	NOUN
ap-8351	82	7	of	of	ADP
ap-8351	82	8	(	(	PUNCT
ap-8351	82	9	21	21	NUM
ap-8351	82	10	)	)	PUNCT
ap-8351	82	11	,	,	PUNCT
ap-8351	82	12	by	by	ADP
ap-8351	82	13	means	mean	NOUN
ap-8351	82	14	of	of	ADP
ap-8351	82	15	the	the	DET
ap-8351	82	16	transformation	transformation	NOUN
ap-8351	82	17	(	(	PUNCT
ap-8351	82	18	24	24	NUM
ap-8351	82	19	)	)	PUNCT
ap-8351	82	20	,	,	PUNCT
ap-8351	82	21	we	we	PRON
ap-8351	82	22	obtain	obtain	VERB
ap-8351	82	23	the	the	DET
ap-8351	82	24	solution	solution	NOUN
ap-8351	82	25	of	of	ADP
ap-8351	82	26	(	(	PUNCT
ap-8351	82	27	20	20	NUM
ap-8351	82	28	)	)	PUNCT
ap-8351	82	29	as	as	ADP
ap-8351	82	30	u(x	u(x	NOUN
ap-8351	82	31	)	)	PUNCT
ap-8351	82	32	=	=	SYM
ap-8351	83	1	(	(	PUNCT
ap-8351	83	2	x	x	SYM
ap-8351	83	3	4	4	X
ap-8351	83	4	)	)	SYM
ap-8351	83	5	1	1	NUM
ap-8351	83	6	n	n	CCONJ
ap-8351	83	7	(	(	PUNCT
ap-8351	83	8	c1x	c1x	PROPN
ap-8351	83	9	+	+	CCONJ
ap-8351	83	10	c2	c2	PROPN
ap-8351	83	11	)	)	PUNCT
ap-8351	83	12	2	2	NUM
ap-8351	83	13	n	n	NOUN
ap-8351	83	14	,	,	PUNCT
ap-8351	83	15	(	(	PUNCT
ap-8351	83	16	25	25	NUM
ap-8351	83	17	)	)	PUNCT
ap-8351	83	18	where	where	SCONJ
ap-8351	83	19	c1	c1	PROPN
ap-8351	83	20	and	and	CCONJ
ap-8351	83	21	c2	c2	PROPN
ap-8351	83	22	are	be	AUX
ap-8351	83	23	constants	constant	NOUN
ap-8351	83	24	of	of	ADP
ap-8351	83	25	integration	integration	NOUN
ap-8351	83	26	.	.	PUNCT
ap-8351	84	1	5	5	X
ap-8351	84	2	.	.	X
ap-8351	84	3	conclusion	conclusion	NOUN
ap-8351	84	4	most	most	ADJ
ap-8351	84	5	studies	study	NOUN
ap-8351	84	6	of	of	ADP
ap-8351	84	7	the	the	DET
ap-8351	84	8	algebraic	algebraic	ADJ
ap-8351	84	9	properties	property	NOUN
ap-8351	84	10	of	of	ADP
ap-8351	84	11	ordinary	ordinary	ADJ
ap-8351	84	12	differential	differential	ADJ
ap-8351	84	13	equations	equation	NOUN
ap-8351	84	14	are	be	AUX
ap-8351	84	15	focused	focus	VERB
ap-8351	84	16	on	on	ADP
ap-8351	84	17	the	the	DET
ap-8351	84	18	first	first	ADJ
ap-8351	84	19	,	,	PUNCT
ap-8351	84	20	second	second	ADJ
ap-8351	84	21	and	and	CCONJ
ap-8351	84	22	third	third	ADJ
ap-8351	84	23	order	order	NOUN
ap-8351	84	24	equations	equation	NOUN
ap-8351	84	25	,	,	PUNCT
ap-8351	84	26	which	which	PRON
ap-8351	84	27	is	be	AUX
ap-8351	84	28	most	most	ADV
ap-8351	84	29	natural	natural	ADJ
ap-8351	84	30	since	since	SCONJ
ap-8351	84	31	these	these	PRON
ap-8351	84	32	are	be	AUX
ap-8351	84	33	the	the	DET
ap-8351	84	34	equations	equation	NOUN
ap-8351	84	35	which	which	PRON
ap-8351	84	36	arise	arise	VERB
ap-8351	84	37	in	in	ADP
ap-8351	84	38	the	the	DET
ap-8351	84	39	modelling	modelling	NOUN
ap-8351	84	40	of	of	ADP
ap-8351	84	41	natural	natural	ADJ
ap-8351	84	42	phenomena	phenomenon	NOUN
ap-8351	84	43	.	.	PUNCT
ap-8351	85	1	in	in	ADP
ap-8351	85	2	this	this	DET
ap-8351	85	3	paper	paper	NOUN
ap-8351	85	4	,	,	PUNCT
ap-8351	85	5	we	we	PRON
ap-8351	85	6	performed	perform	VERB
ap-8351	85	7	the	the	DET
ap-8351	85	8	symmetry	symmetry	NOUN
ap-8351	85	9	analysis	analysis	NOUN
ap-8351	85	10	of	of	ADP
ap-8351	85	11	equation	equation	NOUN
ap-8351	85	12	(	(	PUNCT
ap-8351	85	13	2	2	NUM
ap-8351	85	14	)	)	PUNCT
ap-8351	85	15	and	and	CCONJ
ap-8351	85	16	showed	show	VERB
ap-8351	85	17	that	that	SCONJ
ap-8351	85	18	the	the	DET
ap-8351	85	19	equation	equation	NOUN
ap-8351	85	20	possesses	possess	VERB
ap-8351	85	21	the	the	DET
ap-8351	85	22	sl(3	sl(3	PROPN
ap-8351	85	23	,	,	PUNCT
ap-8351	85	24	r	r	NOUN
ap-8351	85	25	)	)	PUNCT
ap-8351	85	26	algebra	algebra	NOUN
ap-8351	85	27	.	.	PUNCT
ap-8351	86	1	in	in	ADP
ap-8351	86	2	turn	turn	NOUN
ap-8351	86	3	,	,	PUNCT
ap-8351	86	4	we	we	PRON
ap-8351	86	5	reported	report	VERB
ap-8351	86	6	the	the	DET
ap-8351	86	7	solution	solution	NOUN
ap-8351	86	8	of	of	ADP
ap-8351	86	9	(	(	PUNCT
ap-8351	86	10	2	2	NUM
ap-8351	86	11	)	)	PUNCT
ap-8351	86	12	and	and	CCONJ
ap-8351	86	13	thus	thus	ADV
ap-8351	86	14	obtained	obtain	VERB
ap-8351	86	15	the	the	DET
ap-8351	86	16	solution	solution	NOUN
ap-8351	86	17	of	of	ADP
ap-8351	86	18	(	(	PUNCT
ap-8351	86	19	1	1	NUM
ap-8351	86	20	)	)	PUNCT
ap-8351	86	21	.	.	PUNCT
ap-8351	87	1	a	a	DET
ap-8351	87	2	natural	natural	ADJ
ap-8351	87	3	generalisation	generalisation	NOUN
ap-8351	87	4	of	of	ADP
ap-8351	87	5	(	(	PUNCT
ap-8351	87	6	2	2	NUM
ap-8351	87	7	)	)	PUNCT
ap-8351	87	8	followed	follow	VERB
ap-8351	87	9	.	.	PUNCT
ap-8351	88	1	by	by	ADP
ap-8351	88	2	setting	set	VERB
ap-8351	88	3	m(v	m(v	NOUN
ap-8351	88	4	,	,	PUNCT
ap-8351	88	5	r	r	NOUN
ap-8351	88	6	)	)	PUNCT
ap-8351	88	7	=	=	SYM
ap-8351	88	8	zn	zn	PROPN
ap-8351	88	9	,	,	PUNCT
ap-8351	88	10	where	where	SCONJ
ap-8351	88	11	z	z	NOUN
ap-8351	88	12	is	be	AUX
ap-8351	88	13	a	a	DET
ap-8351	88	14	function	function	NOUN
ap-8351	88	15	of	of	ADP
ap-8351	88	16	v	v	NOUN
ap-8351	88	17	and	and	CCONJ
ap-8351	88	18	r	r	NOUN
ap-8351	88	19	in	in	ADP
ap-8351	88	20	equation	equation	NOUN
ap-8351	88	21	(	(	PUNCT
ap-8351	88	22	1	1	NUM
ap-8351	88	23	)	)	PUNCT
ap-8351	88	24	,	,	PUNCT
ap-8351	88	25	we	we	PRON
ap-8351	88	26	obtain	obtain	VERB
ap-8351	88	27	a	a	DET
ap-8351	88	28	more	more	ADV
ap-8351	88	29	general	general	ADJ
ap-8351	88	30	partial	partial	ADJ
ap-8351	88	31	differential	differential	NOUN
ap-8351	88	32	differential	differential	NOUN
ap-8351	88	33	2nr2zz′′	2nr2zz′′	NUM
ap-8351	88	34	+	+	CCONJ
ap-8351	88	35	n(n	n(n	PROPN
ap-8351	88	36	−	−	PROPN
ap-8351	88	37	2)r2z′2	2)r2z′2	NUM
ap-8351	89	1	−	−	PROPN
ap-8351	89	2	2nrzz′	2nrzz′	NUM
ap-8351	89	3	+	+	CCONJ
ap-8351	89	4	3z2	3z2	NUM
ap-8351	89	5	=	=	SYM
ap-8351	89	6	0	0	NUM
ap-8351	89	7	,	,	PUNCT
ap-8351	89	8	(	(	PUNCT
ap-8351	89	9	26	26	NUM
ap-8351	89	10	)	)	PUNCT
ap-8351	89	11	where	where	SCONJ
ap-8351	89	12	the	the	DET
ap-8351	89	13	prime	prime	ADJ
ap-8351	89	14	denotes	denote	NOUN
ap-8351	89	15	differentiation	differentiation	NOUN
ap-8351	89	16	of	of	ADP
ap-8351	89	17	the	the	DET
ap-8351	89	18	dependent	dependent	ADJ
ap-8351	89	19	variable	variable	NOUN
ap-8351	89	20	,	,	PUNCT
ap-8351	89	21	z(v	z(v	PROPN
ap-8351	89	22	,	,	PUNCT
ap-8351	89	23	r	r	NOUN
ap-8351	89	24	)	)	PUNCT
ap-8351	89	25	,	,	PUNCT
ap-8351	89	26	with	with	ADP
ap-8351	89	27	respect	respect	NOUN
ap-8351	89	28	to	to	ADP
ap-8351	89	29	the	the	DET
ap-8351	89	30	independent	independent	ADJ
ap-8351	89	31	variable	variable	NOUN
ap-8351	89	32	,	,	PUNCT
ap-8351	89	33	r.	r.	PROPN
ap-8351	89	34	we	we	PRON
ap-8351	89	35	note	note	VERB
ap-8351	89	36	that	that	SCONJ
ap-8351	89	37	,	,	PUNCT
ap-8351	89	38	as	as	ADP
ap-8351	89	39	in	in	ADP
ap-8351	89	40	equation	equation	NOUN
ap-8351	89	41	(	(	PUNCT
ap-8351	89	42	1	1	NUM
ap-8351	89	43	)	)	PUNCT
ap-8351	89	44	,	,	PUNCT
ap-8351	89	45	(	(	PUNCT
ap-8351	89	46	26	26	NUM
ap-8351	89	47	)	)	PUNCT
ap-8351	89	48	is	be	AUX
ap-8351	89	49	not	not	PART
ap-8351	89	50	explicitly	explicitly	ADV
ap-8351	89	51	dependent	dependent	ADJ
ap-8351	89	52	on	on	ADP
ap-8351	89	53	v	v	NOUN
ap-8351	89	54	,	,	PUNCT
ap-8351	89	55	and	and	CCONJ
ap-8351	89	56	therefore	therefore	ADV
ap-8351	89	57	possesses	possess	VERB
ap-8351	89	58	the	the	DET
ap-8351	89	59	point	point	NOUN
ap-8351	89	60	symmetry	symmetry	NOUN
ap-8351	89	61	g(v)∂v	g(v)∂v	ADJ
ap-8351	89	62	,	,	PUNCT
ap-8351	89	63	where	where	SCONJ
ap-8351	89	64	g(v	g(v	NOUN
ap-8351	89	65	)	)	PUNCT
ap-8351	89	66	is	be	AUX
ap-8351	89	67	an	an	DET
ap-8351	89	68	arbitrary	arbitrary	ADJ
ap-8351	89	69	function	function	NOUN
ap-8351	89	70	of	of	ADP
ap-8351	89	71	v	v	NOUN
ap-8351	89	72	only	only	ADV
ap-8351	89	73	.	.	PUNCT
ap-8351	90	1	we	we	PRON
ap-8351	90	2	use	use	VERB
ap-8351	90	3	this	this	DET
ap-8351	90	4	symmetry	symmetry	NOUN
ap-8351	90	5	to	to	PART
ap-8351	90	6	obtain	obtain	VERB
ap-8351	90	7	the	the	DET
ap-8351	90	8	invariants	invariant	NOUN
ap-8351	90	9	r	r	NOUN
ap-8351	90	10	=	=	PUNCT
ap-8351	90	11	x	x	X
ap-8351	90	12	and	and	CCONJ
ap-8351	90	13	z	z	NOUN
ap-8351	90	14	=	=	SYM
ap-8351	90	15	u(x	u(x	PROPN
ap-8351	90	16	)	)	PUNCT
ap-8351	90	17	which	which	PRON
ap-8351	90	18	reduce	reduce	VERB
ap-8351	90	19	(	(	PUNCT
ap-8351	90	20	26	26	NUM
ap-8351	90	21	)	)	PUNCT
ap-8351	90	22	to	to	ADP
ap-8351	90	23	the	the	DET
ap-8351	90	24	second	second	ADJ
ap-8351	90	25	-	-	PUNCT
ap-8351	90	26	order	order	NOUN
ap-8351	90	27	nonlinear	nonlinear	ADJ
ap-8351	90	28	equation	equation	NOUN
ap-8351	90	29	(	(	PUNCT
ap-8351	90	30	20	20	NUM
ap-8351	90	31	)	)	PUNCT
ap-8351	90	32	with	with	ADP
ap-8351	90	33	the	the	DET
ap-8351	90	34	solution	solution	NOUN
ap-8351	90	35	given	give	VERB
ap-8351	90	36	by	by	ADP
ap-8351	90	37	(	(	PUNCT
ap-8351	90	38	25	25	NUM
ap-8351	90	39	)	)	PUNCT
ap-8351	90	40	.	.	PUNCT
ap-8351	91	1	using	use	VERB
ap-8351	91	2	(	(	PUNCT
ap-8351	91	3	25	25	NUM
ap-8351	91	4	)	)	PUNCT
ap-8351	91	5	and	and	CCONJ
ap-8351	91	6	the	the	DET
ap-8351	91	7	invariants	invariant	NOUN
ap-8351	91	8	mentioned	mention	VERB
ap-8351	91	9	above	above	ADV
ap-8351	91	10	,	,	PUNCT
ap-8351	91	11	we	we	PRON
ap-8351	91	12	obtain	obtain	VERB
ap-8351	91	13	the	the	DET
ap-8351	91	14	solution	solution	NOUN
ap-8351	91	15	for	for	ADP
ap-8351	91	16	equation	equation	NOUN
ap-8351	91	17	(	(	PUNCT
ap-8351	91	18	26	26	NUM
ap-8351	91	19	)	)	PUNCT
ap-8351	91	20	to	to	PART
ap-8351	91	21	be	be	AUX
ap-8351	91	22	z(v	z(v	PROPN
ap-8351	91	23	,	,	PUNCT
ap-8351	91	24	r	r	NOUN
ap-8351	91	25	)	)	PUNCT
ap-8351	91	26	=	=	SYM
ap-8351	92	1	(	(	PUNCT
ap-8351	92	2	r	r	NOUN
ap-8351	92	3	4	4	NUM
ap-8351	92	4	)	)	SYM
ap-8351	92	5	1	1	NUM
ap-8351	92	6	n	n	CCONJ
ap-8351	92	7	(	(	PUNCT
ap-8351	92	8	c1(v)r	c1(v)r	VERB
ap-8351	92	9	+	+	CCONJ
ap-8351	92	10	c2(v	c2(v	NOUN
ap-8351	92	11	)	)	PUNCT
ap-8351	92	12	)	)	PUNCT
ap-8351	92	13	2	2	NUM
ap-8351	92	14	n	n	NOUN
ap-8351	92	15	,	,	PUNCT
ap-8351	92	16	(	(	PUNCT
ap-8351	92	17	27	27	NUM
ap-8351	92	18	)	)	PUNCT
ap-8351	92	19	where	where	SCONJ
ap-8351	92	20	c1(v	c1(v	NOUN
ap-8351	92	21	)	)	PUNCT
ap-8351	92	22	and	and	CCONJ
ap-8351	92	23	c2(v	c2(v	PRON
ap-8351	92	24	)	)	PUNCT
ap-8351	92	25	are	be	AUX
ap-8351	92	26	functions	function	NOUN
ap-8351	92	27	of	of	ADP
ap-8351	92	28	integration	integration	NOUN
ap-8351	92	29	.	.	PUNCT
ap-8351	93	1	this	this	DET
ap-8351	93	2	paper	paper	NOUN
ap-8351	93	3	demonstrates	demonstrate	VERB
ap-8351	93	4	that	that	SCONJ
ap-8351	93	5	the	the	DET
ap-8351	93	6	equations	equation	NOUN
ap-8351	93	7	(	(	PUNCT
ap-8351	93	8	1	1	NUM
ap-8351	93	9	)	)	PUNCT
ap-8351	93	10	,	,	PUNCT
ap-8351	93	11	hence	hence	ADV
ap-8351	93	12	(	(	PUNCT
ap-8351	93	13	26	26	NUM
ap-8351	93	14	)	)	PUNCT
ap-8351	93	15	,	,	PUNCT
ap-8351	93	16	which	which	PRON
ap-8351	93	17	,	,	PUNCT
ap-8351	93	18	at	at	ADP
ap-8351	93	19	first	first	ADJ
ap-8351	93	20	glance	glance	NOUN
ap-8351	93	21	,	,	PUNCT
ap-8351	93	22	looks	look	VERB
ap-8351	93	23	complicated	complicated	ADJ
ap-8351	93	24	,	,	PUNCT
ap-8351	93	25	has	have	VERB
ap-8351	93	26	some	some	DET
ap-8351	93	27	very	very	ADV
ap-8351	93	28	interesting	interesting	ADJ
ap-8351	93	29	properties	property	NOUN
ap-8351	93	30	from	from	ADP
ap-8351	93	31	the	the	DET
ap-8351	93	32	viewpoint	viewpoint	NOUN
ap-8351	93	33	of	of	ADP
ap-8351	93	34	symmetry	symmetry	NOUN
ap-8351	93	35	analysis	analysis	NOUN
ap-8351	93	36	.	.	PUNCT
ap-8351	94	1	using	use	VERB
ap-8351	94	2	the	the	DET
ap-8351	94	3	symmetry	symmetry	NOUN
ap-8351	94	4	approach	approach	NOUN
ap-8351	94	5	we	we	PRON
ap-8351	94	6	were	be	AUX
ap-8351	94	7	able	able	ADJ
ap-8351	94	8	to	to	PART
ap-8351	94	9	show	show	VERB
ap-8351	94	10	that	that	SCONJ
ap-8351	94	11	these	these	DET
ap-8351	94	12	equations	equation	NOUN
ap-8351	94	13	are	be	AUX
ap-8351	94	14	integrable	integrable	ADJ
ap-8351	94	15	and	and	CCONJ
ap-8351	94	16	have	have	VERB
ap-8351	94	17	closed	close	VERB
ap-8351	94	18	-	-	PUNCT
ap-8351	94	19	form	form	NOUN
ap-8351	94	20	solutions	solution	NOUN
ap-8351	94	21	.	.	PUNCT
ap-8351	95	1	acknowledgements	acknowledgement	NOUN
ap-8351	95	2	mg	mg	PROPN
ap-8351	95	3	expresses	express	VERB
ap-8351	95	4	grateful	grateful	ADJ
ap-8351	95	5	thanks	thank	NOUN
ap-8351	95	6	to	to	ADP
ap-8351	95	7	the	the	DET
ap-8351	95	8	national	national	PROPN
ap-8351	95	9	research	research	PROPN
ap-8351	95	10	foundation	foundation	PROPN
ap-8351	95	11	of	of	ADP
ap-8351	95	12	south	south	PROPN
ap-8351	95	13	africa	africa	PROPN
ap-8351	95	14	and	and	CCONJ
ap-8351	95	15	the	the	DET
ap-8351	95	16	durban	durban	PROPN
ap-8351	95	17	university	university	PROPN
ap-8351	95	18	of	of	ADP
ap-8351	95	19	technology	technology	NOUN
ap-8351	95	20	for	for	ADP
ap-8351	95	21	their	their	PRON
ap-8351	95	22	continuing	continue	VERB
ap-8351	95	23	support	support	NOUN
ap-8351	95	24	.	.	PUNCT
ap-8351	96	1	am	am	VERB
ap-8351	96	2	acknowledges	acknowledge	VERB
ap-8351	96	3	support	support	NOUN
ap-8351	96	4	of	of	ADP
ap-8351	96	5	the	the	DET
ap-8351	96	6	durban	durban	PROPN
ap-8351	96	7	university	university	PROPN
ap-8351	96	8	of	of	ADP
ap-8351	96	9	technology	technology	PROPN
ap-8351	96	10	.	.	PUNCT
ap-8351	97	1	pgll	pgll	PROPN
ap-8351	97	2	appreciates	appreciate	VERB
ap-8351	97	3	the	the	DET
ap-8351	97	4	support	support	NOUN
ap-8351	97	5	of	of	ADP
ap-8351	97	6	the	the	DET
ap-8351	97	7	national	national	PROPN
ap-8351	97	8	research	research	PROPN
ap-8351	97	9	foundation	foundation	PROPN
ap-8351	97	10	of	of	ADP
ap-8351	97	11	south	south	PROPN
ap-8351	97	12	africa	africa	PROPN
ap-8351	97	13	,	,	PUNCT
ap-8351	97	14	the	the	DET
ap-8351	97	15	university	university	NOUN
ap-8351	97	16	of	of	ADP
ap-8351	97	17	kwazulunatal	kwazulunatal	NOUN
ap-8351	97	18	and	and	CCONJ
ap-8351	97	19	the	the	DET
ap-8351	97	20	durban	durban	PROPN
ap-8351	97	21	university	university	PROPN
ap-8351	97	22	of	of	ADP
ap-8351	97	23	technology	technology	NOUN
ap-8351	97	24	.	.	PUNCT
ap-8351	98	1	dpd	dpd	PROPN
ap-8351	98	2	acknowledges	acknowledge	VERB
ap-8351	98	3	the	the	DET
ap-8351	98	4	support	support	NOUN
ap-8351	98	5	provided	provide	VERB
ap-8351	98	6	by	by	ADP
ap-8351	98	7	durban	durban	PROPN
ap-8351	98	8	university	university	PROPN
ap-8351	98	9	of	of	ADP
ap-8351	98	10	technology	technology	NOUN
ap-8351	98	11	.	.	PUNCT
ap-8351	99	1	references	reference	NOUN
ap-8351	99	2	[	[	X
ap-8351	99	3	1	1	NUM
ap-8351	99	4	]	]	PUNCT
ap-8351	99	5	b.	b.	PROPN
ap-8351	99	6	abraham	abraham	PROPN
ap-8351	99	7	-	-	PUNCT
ap-8351	99	8	shrauner	shrauner	NOUN
ap-8351	99	9	,	,	PUNCT
ap-8351	99	10	p.	p.	NOUN
ap-8351	99	11	g.	g.	PROPN
ap-8351	99	12	l.	l.	PROPN
ap-8351	99	13	leach	leach	PROPN
ap-8351	99	14	,	,	PUNCT
ap-8351	99	15	k.	k.	PROPN
ap-8351	99	16	s.	s.	PROPN
ap-8351	99	17	govinder	govinder	PROPN
ap-8351	99	18	,	,	PUNCT
ap-8351	99	19	g.	g.	PROPN
ap-8351	99	20	ratcliff	ratcliff	PROPN
ap-8351	99	21	.	.	PUNCT
ap-8351	100	1	hidden	hidden	ADJ
ap-8351	100	2	and	and	CCONJ
ap-8351	100	3	contact	contact	NOUN
ap-8351	100	4	symmetries	symmetry	NOUN
ap-8351	100	5	of	of	ADP
ap-8351	100	6	ordinary	ordinary	ADJ
ap-8351	100	7	differential	differential	ADJ
ap-8351	100	8	equations	equation	NOUN
ap-8351	100	9	.	.	PUNCT
ap-8351	101	1	journal	journal	PROPN
ap-8351	101	2	of	of	ADP
ap-8351	101	3	physics	physics	PROPN
ap-8351	101	4	a	a	PRON
ap-8351	101	5	:	:	PUNCT
ap-8351	101	6	mathematical	mathematical	ADJ
ap-8351	101	7	and	and	CCONJ
ap-8351	101	8	general	general	ADJ
ap-8351	101	9	28(23):6707	28(23):6707	NUM
ap-8351	101	10	,	,	PUNCT
ap-8351	101	11	1995	1995	NUM
ap-8351	101	12	.	.	PUNCT
ap-8351	102	1	https://doi.org/10.1088/0305-4470/28/23/020	https://doi.org/10.1088/0305-4470/28/23/020	VERB
ap-8351	102	2	[	[	X
ap-8351	102	3	2	2	NUM
ap-8351	102	4	]	]	PUNCT
ap-8351	102	5	k.	k.	PROPN
ap-8351	102	6	andriopoulos	andriopoulos	PROPN
ap-8351	102	7	,	,	PUNCT
ap-8351	102	8	p.	p.	NOUN
ap-8351	102	9	g.	g.	PROPN
ap-8351	102	10	l.	l.	PROPN
ap-8351	102	11	leach	leach	PROPN
ap-8351	102	12	,	,	PUNCT
ap-8351	102	13	a.	a.	NOUN
ap-8351	102	14	maharaj	maharaj	PROPN
ap-8351	102	15	.	.	PUNCT
ap-8351	103	1	on	on	ADP
ap-8351	103	2	differential	differential	ADJ
ap-8351	103	3	sequences	sequence	NOUN
ap-8351	103	4	.	.	PUNCT
ap-8351	104	1	applied	apply	VERB
ap-8351	104	2	mathematics	mathematics	PROPN
ap-8351	104	3	&	&	CCONJ
ap-8351	104	4	information	information	PROPN
ap-8351	104	5	sciences	sciences	PROPN
ap-8351	104	6	5(3):525–546	5(3):525–546	NUM
ap-8351	104	7	,	,	PUNCT
ap-8351	104	8	2011	2011	NUM
ap-8351	104	9	.	.	PUNCT
ap-8351	105	1	[	[	X
ap-8351	105	2	3	3	X
ap-8351	105	3	]	]	X
ap-8351	105	4	c.	c.	PROPN
ap-8351	105	5	géronimi	géronimi	PROPN
ap-8351	105	6	,	,	PUNCT
ap-8351	105	7	m.	m.	PROPN
ap-8351	105	8	r.	r.	PROPN
ap-8351	105	9	feix	feix	PROPN
ap-8351	105	10	,	,	PUNCT
ap-8351	105	11	p.	p.	NOUN
ap-8351	105	12	g.	g.	PROPN
ap-8351	105	13	l.	l.	PROPN
ap-8351	105	14	leach	leach	NOUN
ap-8351	105	15	.	.	PUNCT
ap-8351	106	1	third	third	ADJ
ap-8351	106	2	order	order	NOUN
ap-8351	106	3	differential	differential	NOUN
ap-8351	106	4	equation	equation	NOUN
ap-8351	106	5	possessing	possess	VERB
ap-8351	106	6	three	three	NUM
ap-8351	106	7	symmetries	symmetry	NOUN
ap-8351	106	8	the	the	DET
ap-8351	106	9	two	two	NUM
ap-8351	106	10	homogeneous	homogeneous	ADJ
ap-8351	106	11	ones	one	NOUN
ap-8351	106	12	plus	plus	CCONJ
ap-8351	106	13	the	the	DET
ap-8351	106	14	time	time	NOUN
ap-8351	106	15	translation	translation	NOUN
ap-8351	106	16	.	.	PUNCT
ap-8351	107	1	tech	tech	PROPN
ap-8351	107	2	.	.	PUNCT
ap-8351	108	1	rep	rep	PROPN
ap-8351	108	2	.	.	PROPN
ap-8351	108	3	,	,	PUNCT
ap-8351	108	4	scan-9905040	scan-9905040	ADJ
ap-8351	108	5	,	,	PUNCT
ap-8351	108	6	1999	1999	NUM
ap-8351	108	7	.	.	PUNCT
ap-8351	109	1	[	[	X
ap-8351	109	2	4	4	NUM
ap-8351	109	3	]	]	PUNCT
ap-8351	109	4	a.	a.	NOUN
ap-8351	109	5	k.	k.	PROPN
ap-8351	109	6	halder	halder	PROPN
ap-8351	109	7	,	,	PUNCT
ap-8351	109	8	a.	a.	NOUN
ap-8351	109	9	paliathanasis	paliathanasis	NOUN
ap-8351	109	10	,	,	PUNCT
ap-8351	109	11	p.	p.	NOUN
ap-8351	109	12	g.	g.	PROPN
ap-8351	109	13	l.	l.	PROPN
ap-8351	109	14	leach	leach	NOUN
ap-8351	109	15	.	.	PUNCT
ap-8351	110	1	singularity	singularity	NOUN
ap-8351	110	2	analysis	analysis	NOUN
ap-8351	110	3	of	of	ADP
ap-8351	110	4	a	a	DET
ap-8351	110	5	variant	variant	NOUN
ap-8351	110	6	of	of	ADP
ap-8351	110	7	the	the	DET
ap-8351	110	8	painlevé	painlevé	NOUN
ap-8351	110	9	–	–	PUNCT
ap-8351	110	10	ince	ince	NOUN
ap-8351	110	11	equation	equation	NOUN
ap-8351	110	12	.	.	PUNCT
ap-8351	111	1	applied	apply	VERB
ap-8351	111	2	mathematics	mathematics	NOUN
ap-8351	111	3	letters	letter	NOUN
ap-8351	111	4	98:70–73	98:70–73	NUM
ap-8351	111	5	,	,	PUNCT
ap-8351	111	6	2019	2019	NUM
ap-8351	111	7	.	.	PUNCT
ap-8351	112	1	https://doi.org/10.1016/j.aml.2019.05.042	https://doi.org/10.1016/j.aml.2019.05.042	AUX
ap-8351	113	1	[	[	X
ap-8351	113	2	5	5	NUM
ap-8351	113	3	]	]	PUNCT
ap-8351	113	4	a.	a.	NOUN
ap-8351	113	5	maharaj	maharaj	PROPN
ap-8351	113	6	,	,	PUNCT
ap-8351	113	7	p.	p.	NOUN
ap-8351	113	8	g.	g.	PROPN
ap-8351	113	9	l.	l.	PROPN
ap-8351	113	10	leach	leach	NOUN
ap-8351	113	11	.	.	PUNCT
ap-8351	114	1	properties	property	NOUN
ap-8351	114	2	of	of	ADP
ap-8351	114	3	the	the	DET
ap-8351	114	4	dominant	dominant	ADJ
ap-8351	114	5	behaviour	behaviour	NOUN
ap-8351	114	6	of	of	ADP
ap-8351	114	7	quadratic	quadratic	ADJ
ap-8351	114	8	systems	system	NOUN
ap-8351	114	9	.	.	PUNCT
ap-8351	115	1	journal	journal	PROPN
ap-8351	115	2	of	of	ADP
ap-8351	115	3	nonlinear	nonlinear	PROPN
ap-8351	115	4	mathematical	mathematical	ADJ
ap-8351	115	5	physics	physics	PROPN
ap-8351	115	6	13(1):129–144	13(1):129–144	PROPN
ap-8351	115	7	,	,	PUNCT
ap-8351	115	8	2006	2006	NUM
ap-8351	115	9	.	.	PUNCT
ap-8351	116	1	https://doi.org/10.2991/jnmp.2006.13.1.11	https://doi.org/10.2991/jnmp.2006.13.1.11	PROPN
ap-8351	116	2	21	21	NUM
ap-8351	116	3	https://doi.org/10.1088/0305-4470/28/23/020	https://doi.org/10.1088/0305-4470/28/23/020	NOUN
ap-8351	116	4	https://doi.org/10.1016/j.aml.2019.05.042	https://doi.org/10.1016/j.aml.2019.05.042	NOUN
ap-8351	116	5	https://doi.org/10.2991/jnmp.2006.13.1.11	https://doi.org/10.2991/jnmp.2006.13.1.11	ADJ
ap-8351	116	6	a.	a.	NOUN
ap-8351	116	7	maharaj	maharaj	NOUN
ap-8351	116	8	,	,	PUNCT
ap-8351	116	9	p.	p.	NOUN
ap-8351	116	10	g.	g.	PROPN
ap-8351	116	11	l.	l.	PROPN
ap-8351	116	12	leach	leach	PROPN
ap-8351	116	13	,	,	PUNCT
ap-8351	116	14	m.	m.	NOUN
ap-8351	116	15	govender	govender	NOUN
ap-8351	116	16	,	,	PUNCT
ap-8351	116	17	d.	d.	PROPN
ap-8351	116	18	p.	p.	PROPN
ap-8351	116	19	day	day	PROPN
ap-8351	117	1	acta	acta	PROPN
ap-8351	117	2	polytechnica	polytechnica	PROPN
ap-8351	118	1	[	[	X
ap-8351	118	2	6	6	NUM
ap-8351	118	3	]	]	PUNCT
ap-8351	118	4	a.	a.	NOUN
ap-8351	118	5	maharaj	maharaj	PROPN
ap-8351	118	6	,	,	PUNCT
ap-8351	118	7	k.	k.	PROPN
ap-8351	118	8	andriopoulos	andriopoulos	PROPN
ap-8351	118	9	,	,	PUNCT
ap-8351	118	10	p.	p.	NOUN
ap-8351	118	11	g.	g.	PROPN
ap-8351	118	12	l.	l.	PROPN
ap-8351	118	13	leach	leach	NOUN
ap-8351	118	14	.	.	PUNCT
ap-8351	119	1	properties	property	NOUN
ap-8351	119	2	of	of	ADP
ap-8351	119	3	a	a	DET
ap-8351	119	4	differential	differential	ADJ
ap-8351	119	5	sequence	sequence	NOUN
ap-8351	119	6	based	base	VERB
ap-8351	119	7	upon	upon	SCONJ
ap-8351	119	8	the	the	DET
ap-8351	119	9	kummer	kummer	NOUN
ap-8351	119	10	-	-	PUNCT
ap-8351	119	11	schwarz	schwarz	PROPN
ap-8351	119	12	equation	equation	NOUN
ap-8351	119	13	.	.	PUNCT
ap-8351	120	1	acta	acta	PROPN
ap-8351	120	2	polytechnica	polytechnica	PROPN
ap-8351	120	3	60(5):428–434	60(5):428–434	PROPN
ap-8351	120	4	,	,	PUNCT
ap-8351	120	5	2020	2020	NUM
ap-8351	120	6	.	.	PUNCT
ap-8351	121	1	https://doi.org/10.14311/ap.2020.60.0428	https://doi.org/10.14311/ap.2020.60.0428	X
ap-8351	122	1	[	[	X
ap-8351	122	2	7	7	NUM
ap-8351	122	3	]	]	PUNCT
ap-8351	122	4	k.	k.	PROPN
ap-8351	122	5	karmarkar	karmarkar	PROPN
ap-8351	122	6	.	.	PUNCT
ap-8351	123	1	gravitational	gravitational	ADJ
ap-8351	123	2	metrics	metric	NOUN
ap-8351	123	3	of	of	ADP
ap-8351	123	4	spherical	spherical	ADJ
ap-8351	123	5	symmetry	symmetry	NOUN
ap-8351	123	6	and	and	CCONJ
ap-8351	123	7	class	class	NOUN
ap-8351	123	8	one	one	NUM
ap-8351	123	9	.	.	PUNCT
ap-8351	124	1	proceedings	proceeding	NOUN
ap-8351	124	2	of	of	ADP
ap-8351	124	3	the	the	DET
ap-8351	124	4	indian	indian	PROPN
ap-8351	124	5	academy	academy	PROPN
ap-8351	124	6	of	of	ADP
ap-8351	124	7	sciences	sciences	PROPN
ap-8351	124	8	–	–	PUNCT
ap-8351	124	9	section	section	NOUN
ap-8351	124	10	a	a	DET
ap-8351	124	11	27:56	27:56	NUM
ap-8351	124	12	,	,	PUNCT
ap-8351	124	13	1948	1948	NUM
ap-8351	124	14	.	.	PUNCT
ap-8351	125	1	https://doi.org/10.1007/bf03173443	https://doi.org/10.1007/bf03173443	NOUN
ap-8351	126	1	[	[	X
ap-8351	126	2	8	8	NUM
ap-8351	126	3	]	]	X
ap-8351	126	4	a.	a.	NOUN
ap-8351	126	5	v.	v.	PROPN
ap-8351	126	6	nikolaev	nikolaev	ADV
ap-8351	126	7	,	,	PUNCT
ap-8351	126	8	s.	s.	PROPN
ap-8351	126	9	d.	d.	PROPN
ap-8351	126	10	maharaj	maharaj	PROPN
ap-8351	126	11	.	.	PUNCT
ap-8351	127	1	embedding	embed	VERB
ap-8351	127	2	with	with	ADP
ap-8351	127	3	vaidya	vaidya	PROPN
ap-8351	127	4	geometry	geometry	PROPN
ap-8351	127	5	.	.	PUNCT
ap-8351	128	1	the	the	DET
ap-8351	128	2	european	european	PROPN
ap-8351	128	3	physical	physical	PROPN
ap-8351	128	4	journal	journal	PROPN
ap-8351	128	5	c	c	PROPN
ap-8351	128	6	80(7):1–9	80(7):1–9	NUM
ap-8351	128	7	,	,	PUNCT
ap-8351	128	8	2020	2020	NUM
ap-8351	128	9	.	.	PUNCT
ap-8351	129	1	https://doi.org/10.1140/epjc/s10052-020-8231-0	https://doi.org/10.1140/epjc/s10052-020-8231-0	PROPN
ap-8351	129	2	[	[	X
ap-8351	129	3	9	9	NUM
ap-8351	129	4	]	]	PUNCT
ap-8351	129	5	p.	p.	PROPN
ap-8351	129	6	chunilal	chunilal	PROPN
ap-8351	129	7	vaidya	vaidya	PROPN
ap-8351	129	8	.	.	PUNCT
ap-8351	130	1	the	the	DET
ap-8351	130	2	external	external	ADJ
ap-8351	130	3	field	field	NOUN
ap-8351	130	4	of	of	ADP
ap-8351	130	5	a	a	DET
ap-8351	130	6	radiating	radiating	NOUN
ap-8351	130	7	star	star	NOUN
ap-8351	130	8	in	in	ADP
ap-8351	130	9	general	general	ADJ
ap-8351	130	10	relativity	relativity	NOUN
ap-8351	130	11	.	.	PUNCT
ap-8351	131	1	current	current	ADJ
ap-8351	131	2	science	science	NOUN
ap-8351	131	3	12:183	12:183	NUM
ap-8351	131	4	,	,	PUNCT
ap-8351	131	5	1943	1943	NUM
ap-8351	131	6	.	.	PUNCT
ap-8351	132	1	[	[	X
ap-8351	132	2	10	10	NUM
ap-8351	132	3	]	]	X
ap-8351	132	4	f.	f.	PROPN
ap-8351	132	5	m.	m.	PROPN
ap-8351	132	6	mahomed	mahome	VERB
ap-8351	132	7	,	,	PUNCT
ap-8351	132	8	p.	p.	NOUN
ap-8351	132	9	g.	g.	PROPN
ap-8351	132	10	l.	l.	PROPN
ap-8351	132	11	leach	leach	NOUN
ap-8351	132	12	.	.	PUNCT
ap-8351	133	1	symmetry	symmetry	NOUN
ap-8351	133	2	lie	lie	NOUN
ap-8351	133	3	algebras	algebra	NOUN
ap-8351	133	4	of	of	ADP
ap-8351	133	5	nth	nth	NOUN
ap-8351	133	6	order	order	NOUN
ap-8351	133	7	ordinary	ordinary	ADJ
ap-8351	133	8	differential	differential	ADJ
ap-8351	133	9	equations	equation	NOUN
ap-8351	133	10	.	.	PUNCT
ap-8351	134	1	journal	journal	PROPN
ap-8351	134	2	of	of	ADP
ap-8351	134	3	mathematical	mathematical	ADJ
ap-8351	134	4	analysis	analysis	NOUN
ap-8351	134	5	and	and	CCONJ
ap-8351	134	6	applications	application	NOUN
ap-8351	134	7	151(1):80–107	151(1):80–107	NUM
ap-8351	134	8	,	,	PUNCT
ap-8351	134	9	1990	1990	NUM
ap-8351	134	10	.	.	PUNCT
ap-8351	135	1	https://doi.org/10.1016/0022-247x(90)90244-a	https://doi.org/10.1016/0022-247x(90)90244-a	PUNCT
ap-8351	135	2	[	[	X
ap-8351	135	3	11	11	NUM
ap-8351	135	4	]	]	PUNCT
ap-8351	135	5	h.	h.	PROPN
ap-8351	135	6	stephani	stephani	PROPN
ap-8351	135	7	.	.	PUNCT
ap-8351	135	8	differential	differential	PROPN
ap-8351	135	9	equations	equation	NOUN
ap-8351	135	10	:	:	PUNCT
ap-8351	135	11	their	their	PRON
ap-8351	135	12	solution	solution	NOUN
ap-8351	135	13	using	use	VERB
ap-8351	135	14	symmetries	symmetry	NOUN
ap-8351	135	15	.	.	PUNCT
ap-8351	136	1	cambridge	cambridge	PROPN
ap-8351	136	2	university	university	PROPN
ap-8351	136	3	press	press	NOUN
ap-8351	136	4	,	,	PUNCT
ap-8351	136	5	1989	1989	NUM
ap-8351	136	6	.	.	PUNCT
ap-8351	137	1	[	[	X
ap-8351	137	2	12	12	NUM
ap-8351	137	3	]	]	X
ap-8351	137	4	g.	g.	PROPN
ap-8351	137	5	w.	w.	PROPN
ap-8351	137	6	bluman	bluman	PROPN
ap-8351	137	7	,	,	PUNCT
ap-8351	137	8	s.	s.	PROPN
ap-8351	137	9	kumei	kumei	PROPN
ap-8351	137	10	.	.	PUNCT
ap-8351	138	1	symmetries	symmetry	NOUN
ap-8351	138	2	and	and	CCONJ
ap-8351	138	3	differential	differential	ADJ
ap-8351	138	4	equations	equation	NOUN
ap-8351	138	5	,	,	PUNCT
ap-8351	138	6	vol	vol	NOUN
ap-8351	138	7	.	.	PROPN
ap-8351	138	8	81	81	NUM
ap-8351	138	9	.	.	PUNCT
ap-8351	139	1	springer	springer	NOUN
ap-8351	139	2	science	science	PROPN
ap-8351	139	3	&	&	CCONJ
ap-8351	139	4	business	business	NOUN
ap-8351	139	5	media	medium	NOUN
ap-8351	139	6	,	,	PUNCT
ap-8351	139	7	2013	2013	NUM
ap-8351	139	8	.	.	PUNCT
ap-8351	140	1	[	[	X
ap-8351	140	2	13	13	NUM
ap-8351	140	3	]	]	PUNCT
ap-8351	140	4	a.	a.	NOUN
ap-8351	140	5	maharaj	maharaj	PROPN
ap-8351	140	6	,	,	PUNCT
ap-8351	140	7	p.	p.	NOUN
ap-8351	140	8	g.	g.	PROPN
ap-8351	140	9	l.	l.	PROPN
ap-8351	140	10	leach	leach	NOUN
ap-8351	140	11	.	.	PUNCT
ap-8351	141	1	the	the	DET
ap-8351	141	2	method	method	NOUN
ap-8351	141	3	of	of	ADP
ap-8351	141	4	reduction	reduction	NOUN
ap-8351	141	5	of	of	ADP
ap-8351	141	6	order	order	NOUN
ap-8351	141	7	and	and	CCONJ
ap-8351	141	8	linearization	linearization	NOUN
ap-8351	141	9	of	of	ADP
ap-8351	141	10	the	the	DET
ap-8351	141	11	two	two	NUM
ap-8351	141	12	-	-	PUNCT
ap-8351	141	13	dimensional	dimensional	ADJ
ap-8351	141	14	ermakov	ermakov	NOUN
ap-8351	141	15	system	system	NOUN
ap-8351	141	16	.	.	PUNCT
ap-8351	142	1	mathematical	mathematical	ADJ
ap-8351	142	2	methods	method	NOUN
ap-8351	142	3	in	in	ADP
ap-8351	142	4	the	the	DET
ap-8351	142	5	applied	apply	VERB
ap-8351	142	6	sciences	science	NOUN
ap-8351	142	7	30(16):2125–2145	30(16):2125–2145	NUM
ap-8351	142	8	,	,	PUNCT
ap-8351	142	9	2007	2007	NUM
ap-8351	142	10	.	.	PUNCT
ap-8351	143	1	https://doi.org/10.1002/mma.919	https://doi.org/10.1002/mma.919	PROPN
ap-8351	144	1	[	[	X
ap-8351	144	2	14	14	NUM
ap-8351	144	3	]	]	PUNCT
ap-8351	144	4	a.	a.	NOUN
ap-8351	144	5	maharaj	maharaj	PROPN
ap-8351	144	6	,	,	PUNCT
ap-8351	144	7	p.	p.	NOUN
ap-8351	144	8	g.	g.	PROPN
ap-8351	144	9	l.	l.	PROPN
ap-8351	144	10	leach	leach	NOUN
ap-8351	144	11	.	.	PUNCT
ap-8351	145	1	application	application	NOUN
ap-8351	145	2	of	of	ADP
ap-8351	145	3	symmetry	symmetry	NOUN
ap-8351	145	4	and	and	CCONJ
ap-8351	145	5	singularity	singularity	NOUN
ap-8351	145	6	analyses	analysis	NOUN
ap-8351	145	7	to	to	ADP
ap-8351	145	8	mathematical	mathematical	ADJ
ap-8351	145	9	models	model	NOUN
ap-8351	145	10	of	of	ADP
ap-8351	145	11	biological	biological	ADJ
ap-8351	145	12	systems	system	NOUN
ap-8351	145	13	.	.	PUNCT
ap-8351	146	1	mathematics	mathematic	NOUN
ap-8351	146	2	and	and	CCONJ
ap-8351	146	3	computers	computer	NOUN
ap-8351	146	4	in	in	ADP
ap-8351	146	5	simulation	simulation	NOUN
ap-8351	146	6	96:104–123	96:104–123	PROPN
ap-8351	146	7	,	,	PUNCT
ap-8351	146	8	2014	2014	NUM
ap-8351	146	9	.	.	PUNCT
ap-8351	147	1	https://doi.org/10.1016/j.matcom.2013.06.005	https://doi.org/10.1016/j.matcom.2013.06.005	VERB
ap-8351	147	2	[	[	X
ap-8351	147	3	15	15	NUM
ap-8351	147	4	]	]	X
ap-8351	147	5	p.	p.	NOUN
ap-8351	147	6	g.	g.	PROPN
ap-8351	147	7	l.	l.	PROPN
ap-8351	147	8	leach	leach	PROPN
ap-8351	147	9	.	.	PUNCT
ap-8351	148	1	symmetry	symmetry	NOUN
ap-8351	148	2	and	and	CCONJ
ap-8351	148	3	singularity	singularity	NOUN
ap-8351	148	4	properties	property	NOUN
ap-8351	148	5	of	of	ADP
ap-8351	148	6	a	a	DET
ap-8351	148	7	system	system	NOUN
ap-8351	148	8	of	of	ADP
ap-8351	148	9	ordinary	ordinary	ADJ
ap-8351	148	10	differential	differential	ADJ
ap-8351	148	11	equations	equation	NOUN
ap-8351	148	12	arising	arise	VERB
ap-8351	148	13	in	in	ADP
ap-8351	148	14	the	the	DET
ap-8351	148	15	analysis	analysis	NOUN
ap-8351	148	16	of	of	ADP
ap-8351	148	17	the	the	DET
ap-8351	148	18	nonlinear	nonlinear	ADJ
ap-8351	148	19	telegraph	telegraph	NOUN
ap-8351	148	20	equations	equation	NOUN
ap-8351	148	21	.	.	PUNCT
ap-8351	149	1	journal	journal	PROPN
ap-8351	149	2	of	of	ADP
ap-8351	149	3	mathematical	mathematical	ADJ
ap-8351	149	4	analysis	analysis	NOUN
ap-8351	149	5	and	and	CCONJ
ap-8351	149	6	applications	application	NOUN
ap-8351	149	7	336(2):987–994	336(2):987–994	NUM
ap-8351	149	8	,	,	PUNCT
ap-8351	149	9	2007	2007	NUM
ap-8351	149	10	.	.	PUNCT
ap-8351	150	1	https://doi.org/10.1016/j.jmaa.2007.03.045	https://doi.org/10.1016/j.jmaa.2007.03.045	PROPN
ap-8351	150	2	[	[	X
ap-8351	150	3	16	16	NUM
ap-8351	150	4	]	]	PUNCT
ap-8351	150	5	p.	p.	NOUN
ap-8351	150	6	g.	g.	PROPN
ap-8351	150	7	l.	l.	PROPN
ap-8351	150	8	leach	leach	PROPN
ap-8351	150	9	,	,	PUNCT
ap-8351	150	10	j.	j.	PROPN
ap-8351	150	11	miritzis	miritzis	PROPN
ap-8351	150	12	.	.	PUNCT
ap-8351	151	1	analytic	analytic	ADJ
ap-8351	151	2	behaviour	behaviour	NOUN
ap-8351	151	3	of	of	ADP
ap-8351	151	4	competition	competition	NOUN
ap-8351	151	5	among	among	ADP
ap-8351	151	6	three	three	NUM
ap-8351	151	7	species	specie	NOUN
ap-8351	151	8	.	.	PUNCT
ap-8351	152	1	journal	journal	PROPN
ap-8351	152	2	of	of	ADP
ap-8351	152	3	nonlinear	nonlinear	PROPN
ap-8351	152	4	mathematical	mathematical	ADJ
ap-8351	152	5	physics	physics	NOUN
ap-8351	152	6	13(4):535–548	13(4):535–548	NUM
ap-8351	152	7	,	,	PUNCT
ap-8351	152	8	2006	2006	NUM
ap-8351	152	9	.	.	PUNCT
ap-8351	153	1	https://doi.org/10.2991/jnmp.2006.13.4.8	https://doi.org/10.2991/jnmp.2006.13.4.8	PUNCT
ap-8351	154	1	[	[	X
ap-8351	154	2	17	17	NUM
ap-8351	154	3	]	]	PUNCT
ap-8351	154	4	k.	k.	PROPN
ap-8351	154	5	andriopoulos	andriopoulos	PROPN
ap-8351	154	6	,	,	PUNCT
ap-8351	154	7	s.	s.	PROPN
ap-8351	154	8	dimas	dimas	PROPN
ap-8351	154	9	,	,	PUNCT
ap-8351	154	10	p.	p.	NOUN
ap-8351	154	11	g.	g.	PROPN
ap-8351	154	12	l.	l.	PROPN
ap-8351	154	13	leach	leach	PROPN
ap-8351	154	14	,	,	PUNCT
ap-8351	154	15	d.	d.	PROPN
ap-8351	154	16	tsoubelis	tsoubelis	PROPN
ap-8351	154	17	.	.	PUNCT
ap-8351	155	1	on	on	ADP
ap-8351	155	2	the	the	DET
ap-8351	155	3	systematic	systematic	ADJ
ap-8351	155	4	approach	approach	NOUN
ap-8351	155	5	to	to	ADP
ap-8351	155	6	the	the	DET
ap-8351	155	7	classification	classification	NOUN
ap-8351	155	8	of	of	ADP
ap-8351	155	9	differential	differential	ADJ
ap-8351	155	10	equations	equation	NOUN
ap-8351	155	11	by	by	ADP
ap-8351	155	12	group	group	NOUN
ap-8351	155	13	theoretical	theoretical	ADJ
ap-8351	155	14	methods	method	NOUN
ap-8351	155	15	.	.	PUNCT
ap-8351	156	1	journal	journal	NOUN
ap-8351	156	2	of	of	ADP
ap-8351	156	3	computational	computational	ADJ
ap-8351	156	4	and	and	CCONJ
ap-8351	156	5	applied	apply	VERB
ap-8351	156	6	mathematics	mathematics	PROPN
ap-8351	156	7	230(1):224–232	230(1):224–232	NUM
ap-8351	156	8	,	,	PUNCT
ap-8351	156	9	2009	2009	NUM
ap-8351	156	10	.	.	PUNCT
ap-8351	157	1	https://doi.org/10.1016/j.cam.2008.11.002	https://doi.org/10.1016/j.cam.2008.11.002	PUNCT
ap-8351	158	1	[	[	X
ap-8351	158	2	18	18	NUM
ap-8351	158	3	]	]	X
ap-8351	158	4	s.	s.	PROPN
ap-8351	158	5	dimas	dimas	PROPN
ap-8351	158	6	,	,	PUNCT
ap-8351	158	7	d.	d.	PROPN
ap-8351	158	8	tsoubelis	tsoubelis	PROPN
ap-8351	158	9	.	.	PUNCT
ap-8351	159	1	sym	sym	NOUN
ap-8351	159	2	:	:	PUNCT
ap-8351	159	3	a	a	DET
ap-8351	159	4	new	new	ADJ
ap-8351	159	5	symmetryfinding	symmetryfinde	VERB
ap-8351	159	6	package	package	NOUN
ap-8351	159	7	for	for	ADP
ap-8351	159	8	mathematica	mathematica	PROPN
ap-8351	159	9	.	.	PUNCT
ap-8351	160	1	in	in	ADP
ap-8351	160	2	proceedings	proceeding	NOUN
ap-8351	160	3	of	of	ADP
ap-8351	160	4	the	the	DET
ap-8351	160	5	10th	10th	ADJ
ap-8351	160	6	international	international	ADJ
ap-8351	160	7	conference	conference	NOUN
ap-8351	160	8	in	in	ADP
ap-8351	160	9	modern	modern	ADJ
ap-8351	160	10	group	group	NOUN
ap-8351	160	11	analysis	analysis	NOUN
ap-8351	160	12	,	,	PUNCT
ap-8351	160	13	pp	pp	X
ap-8351	160	14	.	.	PUNCT
ap-8351	161	1	64–70	64–70	NUM
ap-8351	161	2	.	.	PUNCT
ap-8351	162	1	university	university	PROPN
ap-8351	162	2	of	of	ADP
ap-8351	162	3	cyprus	cyprus	PROPN
ap-8351	162	4	press	press	PROPN
ap-8351	162	5	,	,	PUNCT
ap-8351	162	6	2004	2004	NUM
ap-8351	162	7	.	.	PUNCT
ap-8351	163	1	[	[	X
ap-8351	163	2	19	19	NUM
ap-8351	163	3	]	]	X
ap-8351	163	4	s.	s.	PROPN
ap-8351	163	5	dimas	dimas	PROPN
ap-8351	163	6	,	,	PUNCT
ap-8351	163	7	d.	d.	PROPN
ap-8351	163	8	tsoubelis	tsoubelis	PROPN
ap-8351	163	9	.	.	PUNCT
ap-8351	164	1	a	a	DET
ap-8351	164	2	new	new	ADJ
ap-8351	164	3	mathematica	mathematica	PROPN
ap-8351	164	4	-	-	PUNCT
ap-8351	164	5	based	base	VERB
ap-8351	164	6	program	program	NOUN
ap-8351	164	7	for	for	ADP
ap-8351	164	8	solving	solve	VERB
ap-8351	164	9	overdetermined	overdetermine	VERB
ap-8351	164	10	systems	system	NOUN
ap-8351	164	11	of	of	ADP
ap-8351	164	12	pdes	pde	NOUN
ap-8351	164	13	.	.	PUNCT
ap-8351	165	1	in	in	ADP
ap-8351	165	2	8th	8th	PROPN
ap-8351	165	3	international	international	PROPN
ap-8351	165	4	mathematica	mathematica	PROPN
ap-8351	165	5	symposium	symposium	PROPN
ap-8351	165	6	,	,	PUNCT
ap-8351	165	7	pp	pp	ADJ
ap-8351	165	8	.	.	PUNCT
ap-8351	166	1	1–5	1–5	X
ap-8351	166	2	.	.	PUNCT
ap-8351	166	3	avignon	avignon	PROPN
ap-8351	166	4	,	,	PUNCT
ap-8351	166	5	2006	2006	NUM
ap-8351	166	6	.	.	PUNCT
ap-8351	167	1	[	[	X
ap-8351	167	2	20	20	NUM
ap-8351	167	3	]	]	PUNCT
ap-8351	167	4	s.	s.	PROPN
ap-8351	167	5	dimas	dimas	PROPN
ap-8351	167	6	.	.	PUNCT
ap-8351	168	1	partial	partial	ADJ
ap-8351	168	2	differential	differential	NOUN
ap-8351	168	3	equations	equation	NOUN
ap-8351	168	4	,	,	PUNCT
ap-8351	168	5	algebraic	algebraic	PROPN
ap-8351	168	6	computing	computing	NOUN
ap-8351	168	7	and	and	CCONJ
ap-8351	168	8	nonlinear	nonlinear	ADJ
ap-8351	168	9	systems	system	NOUN
ap-8351	168	10	.	.	PUNCT
ap-8351	169	1	ph.d	ph.d	PROPN
ap-8351	169	2	.	.	PUNCT
ap-8351	170	1	thesis	thesis	NOUN
ap-8351	170	2	,	,	PUNCT
ap-8351	170	3	university	university	PROPN
ap-8351	170	4	of	of	ADP
ap-8351	170	5	patras	patras	PROPN
ap-8351	170	6	,	,	PUNCT
ap-8351	170	7	greece	greece	PROPN
ap-8351	170	8	,	,	PUNCT
ap-8351	170	9	2008	2008	NUM
ap-8351	170	10	.	.	PUNCT
ap-8351	171	1	[	[	X
ap-8351	171	2	21	21	NUM
ap-8351	171	3	]	]	X
ap-8351	171	4	v.	v.	PROPN
ap-8351	171	5	v.	v.	ADP
ap-8351	171	6	morozov	morozov	NOUN
ap-8351	171	7	.	.	PUNCT
ap-8351	172	1	classification	classification	NOUN
ap-8351	172	2	of	of	ADP
ap-8351	172	3	nilpotent	nilpotent	ADJ
ap-8351	172	4	lie	lie	NOUN
ap-8351	172	5	algebras	algebra	NOUN
ap-8351	172	6	of	of	ADP
ap-8351	172	7	sixth	sixth	ADJ
ap-8351	172	8	order	order	NOUN
ap-8351	172	9	.	.	PUNCT
ap-8351	173	1	izvestiya	izvestiya	PROPN
ap-8351	173	2	vysshikh	vysshikh	PROPN
ap-8351	173	3	uchebnykh	uchebnykh	ADJ
ap-8351	173	4	zavedenii	zavedenii	NOUN
ap-8351	173	5	matematika	matematika	PROPN
ap-8351	173	6	4:161–171	4:161–171	PROPN
ap-8351	173	7	,	,	PUNCT
ap-8351	173	8	1958	1958	NUM
ap-8351	173	9	.	.	PUNCT
ap-8351	174	1	[	[	X
ap-8351	174	2	22	22	NUM
ap-8351	174	3	]	]	X
ap-8351	174	4	g.	g.	PROPN
ap-8351	174	5	m.	m.	PROPN
ap-8351	174	6	mubarakzyanov	mubarakzyanov	PROPN
ap-8351	174	7	.	.	PUNCT
ap-8351	175	1	on	on	ADP
ap-8351	175	2	solvable	solvable	ADJ
ap-8351	175	3	lie	lie	NOUN
ap-8351	175	4	algebras	algebras	PROPN
ap-8351	175	5	.	.	PUNCT
ap-8351	176	1	izvestiya	izvestiya	PROPN
ap-8351	176	2	vysshikh	vysshikh	PROPN
ap-8351	176	3	uchebnykh	uchebnykh	ADJ
ap-8351	176	4	zavedenii	zavedenii	NOUN
ap-8351	176	5	matematika	matematika	X
ap-8351	176	6	(	(	PUNCT
ap-8351	176	7	1):114–123	1):114–123	NUM
ap-8351	176	8	,	,	PUNCT
ap-8351	176	9	1963	1963	NUM
ap-8351	176	10	.	.	PUNCT
ap-8351	177	1	[	[	X
ap-8351	177	2	23	23	NUM
ap-8351	177	3	]	]	X
ap-8351	177	4	g.	g.	PROPN
ap-8351	177	5	m.	m.	PROPN
ap-8351	177	6	mubarakzyanov	mubarakzyanov	PROPN
ap-8351	177	7	.	.	PUNCT
ap-8351	178	1	classification	classification	NOUN
ap-8351	178	2	of	of	ADP
ap-8351	178	3	real	real	ADJ
ap-8351	178	4	structures	structure	NOUN
ap-8351	178	5	of	of	ADP
ap-8351	178	6	lie	lie	NOUN
ap-8351	178	7	algebras	algebra	NOUN
ap-8351	178	8	of	of	ADP
ap-8351	178	9	fifth	fifth	ADJ
ap-8351	178	10	order	order	NOUN
ap-8351	178	11	.	.	PUNCT
ap-8351	179	1	izvestiya	izvestiya	PROPN
ap-8351	179	2	vysshikh	vysshikh	PROPN
ap-8351	179	3	uchebnykh	uchebnykh	ADJ
ap-8351	179	4	zavedenii	zavedenii	NOUN
ap-8351	179	5	matematika	matematika	X
ap-8351	179	6	(	(	PUNCT
ap-8351	179	7	3):99–106	3):99–106	NUM
ap-8351	179	8	,	,	PUNCT
ap-8351	179	9	1963	1963	NUM
ap-8351	179	10	.	.	PUNCT
ap-8351	180	1	[	[	X
ap-8351	180	2	24	24	NUM
ap-8351	180	3	]	]	X
ap-8351	180	4	g.	g.	PROPN
ap-8351	180	5	m.	m.	PROPN
ap-8351	180	6	mubarakzyanov	mubarakzyanov	PROPN
ap-8351	180	7	.	.	PUNCT
ap-8351	181	1	classification	classification	NOUN
ap-8351	181	2	of	of	ADP
ap-8351	181	3	solvable	solvable	ADJ
ap-8351	181	4	lie	lie	NOUN
ap-8351	181	5	algebras	algebra	NOUN
ap-8351	181	6	of	of	ADP
ap-8351	181	7	sixth	sixth	ADJ
ap-8351	181	8	order	order	NOUN
ap-8351	181	9	with	with	ADP
ap-8351	181	10	a	a	DET
ap-8351	181	11	non	non	ADJ
ap-8351	181	12	-	-	ADJ
ap-8351	181	13	nilpotent	nilpotent	ADJ
ap-8351	181	14	basis	basis	NOUN
ap-8351	181	15	element	element	NOUN
ap-8351	181	16	.	.	PUNCT
ap-8351	182	1	izvestiya	izvestiya	PROPN
ap-8351	182	2	vysshikh	vysshikh	PROPN
ap-8351	182	3	uchebnykh	uchebnykh	ADJ
ap-8351	182	4	zavedenii	zavedenii	NOUN
ap-8351	182	5	matematika	matematika	X
ap-8351	182	6	(	(	PUNCT
ap-8351	182	7	4):104–116	4):104–116	NUM
ap-8351	182	8	,	,	PUNCT
ap-8351	182	9	1963	1963	NUM
ap-8351	182	10	.	.	PUNCT
ap-8351	183	1	[	[	X
ap-8351	183	2	25	25	NUM
ap-8351	183	3	]	]	X
ap-8351	183	4	f.	f.	PROPN
ap-8351	183	5	m.	m.	PROPN
ap-8351	183	6	mahomed	mahome	VERB
ap-8351	183	7	,	,	PUNCT
ap-8351	183	8	p.	p.	NOUN
ap-8351	183	9	g.	g.	PROPN
ap-8351	183	10	l.	l.	PROPN
ap-8351	183	11	leach	leach	NOUN
ap-8351	183	12	.	.	PUNCT
ap-8351	184	1	the	the	DET
ap-8351	184	2	linear	linear	ADJ
ap-8351	184	3	symmetries	symmetry	NOUN
ap-8351	184	4	of	of	ADP
ap-8351	184	5	a	a	DET
ap-8351	184	6	nonlinear	nonlinear	ADJ
ap-8351	184	7	differential	differential	ADJ
ap-8351	184	8	equation	equation	NOUN
ap-8351	184	9	.	.	PUNCT
ap-8351	185	1	quaestiones	quaestione	NOUN
ap-8351	185	2	mathematicae	mathematicae	PROPN
ap-8351	185	3	8(3):241–274	8(3):241–274	NUM
ap-8351	185	4	,	,	PUNCT
ap-8351	185	5	1985	1985	NUM
ap-8351	185	6	.	.	PUNCT
ap-8351	186	1	https://doi.org/10.1080/16073606.1985.9631915	https://doi.org/10.1080/16073606.1985.9631915	PROPN
ap-8351	186	2	22	22	NUM
ap-8351	186	3	https://doi.org/10.14311/ap.2020.60.0428	https://doi.org/10.14311/ap.2020.60.0428	NOUN
ap-8351	186	4	https://doi.org/10.1007/bf03173443	https://doi.org/10.1007/bf03173443	NOUN
ap-8351	186	5	https://doi.org/10.1140/epjc/s10052-020-8231-0	https://doi.org/10.1140/epjc/s10052-020-8231-0	PROPN
ap-8351	186	6	https://doi.org/10.1016/0022-247x(90)90244-a	https://doi.org/10.1016/0022-247x(90)90244-a	PROPN
ap-8351	186	7	https://doi.org/10.1002/mma.919	https://doi.org/10.1002/mma.919	PROPN
ap-8351	186	8	https://doi.org/10.1016/j.matcom.2013.06.005	https://doi.org/10.1016/j.matcom.2013.06.005	VERB
ap-8351	186	9	https://doi.org/10.1016/j.jmaa.2007.03.045	https://doi.org/10.1016/j.jmaa.2007.03.045	NUM
ap-8351	186	10	https://doi.org/10.2991/jnmp.2006.13.4.8	https://doi.org/10.2991/jnmp.2006.13.4.8	PROPN
ap-8351	186	11	https://doi.org/10.1016/j.cam.2008.11.002	https://doi.org/10.1016/j.cam.2008.11.002	PROPN
ap-8351	186	12	https://doi.org/10.1080/16073606.1985.9631915	https://doi.org/10.1080/16073606.1985.9631915	PROPN
ap-8351	186	13	acta	acta	PROPN
ap-8351	186	14	polytechnica	polytechnica	PROPN
ap-8351	186	15	63(1):19–22	63(1):19–22	NUM
ap-8351	186	16	,	,	PUNCT
ap-8351	186	17	2023	2023	NUM
ap-8351	186	18	1	1	NUM
ap-8351	186	19	introduction	introduction	NOUN
ap-8351	186	20	2	2	NUM
ap-8351	186	21	preliminaries	preliminary	NOUN
ap-8351	186	22	3	3	NUM
ap-8351	186	23	symmetry	symmetry	NOUN
ap-8351	186	24	analysis	analysis	NOUN
ap-8351	186	25	4	4	NUM
ap-8351	186	26	the	the	DET
ap-8351	186	27	general	general	ADJ
ap-8351	186	28	case	case	NOUN
ap-8351	186	29	5	5	NUM
ap-8351	186	30	conclusion	conclusion	NOUN
ap-8351	186	31	acknowledgements	acknowledgement	NOUN
ap-8351	186	32	references	reference	NOUN