id	sid	tid	token	lemma	pos
ma-24	1	1	2021	2021	NUM
ma-24	1	2	ada	ada	PROPN
ma-24	1	3	academica	academica	PROPN
ma-24	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-24	1	5	.	.	PUNCT
ma-24	2	1	j.	j.	PROPN
ma-24	2	2	math	math	PROPN
ma-24	2	3	.	.	PUNCT
ma-24	3	1	anal	anal	ADJ
ma-24	3	2	.	.	PUNCT
ma-24	4	1	1	1	NUM
ma-24	4	2	(	(	PUNCT
ma-24	4	3	2021	2021	NUM
ma-24	4	4	)	)	PUNCT
ma-24	4	5	133	133	NUM
ma-24	4	6	-	-	SYM
ma-24	4	7	150doi	150doi	NUM
ma-24	4	8	:	:	PUNCT
ma-24	4	9	10.28924	10.28924	NUM
ma-24	4	10	/	/	SYM
ma-24	4	11	ada	ada	PROPN
ma-24	4	12	/	/	SYM
ma-24	4	13	ma.1.133	ma.1.133	PROPN
ma-24	4	14	lie	lie	VERB
ma-24	4	15	group	group	NOUN
ma-24	4	16	analysis	analysis	NOUN
ma-24	4	17	of	of	ADP
ma-24	4	18	a	a	DET
ma-24	4	19	nonlinear	nonlinear	ADJ
ma-24	4	20	coupled	couple	VERB
ma-24	4	21	system	system	NOUN
ma-24	4	22	of	of	ADP
ma-24	4	23	korteweg	korteweg	NOUN
ma-24	4	24	-	-	PUNCT
ma-24	4	25	de	de	PROPN
ma-24	4	26	vries	vries	PROPN
ma-24	4	27	equations	equations	PROPN
ma-24	4	28	joseph	joseph	PROPN
ma-24	4	29	owuor	owuor	PROPN
ma-24	4	30	owino∗	owino∗	PROPN
ma-24	4	31	,	,	PUNCT
ma-24	4	32	benard	benard	PROPN
ma-24	4	33	okelo	okelo	PROPN
ma-24	4	34	department	department	PROPN
ma-24	4	35	of	of	ADP
ma-24	4	36	pure	pure	ADJ
ma-24	4	37	and	and	CCONJ
ma-24	4	38	applied	applied	ADJ
ma-24	4	39	mathematics	mathematic	NOUN
ma-24	4	40	,	,	PUNCT
ma-24	4	41	jaramogi	jaramogi	PROPN
ma-24	4	42	oginga	oginga	PROPN
ma-24	4	43	odinga	odinga	PROPN
ma-24	4	44	university	university	PROPN
ma-24	4	45	of	of	ADP
ma-24	4	46	science	science	NOUN
ma-24	4	47	and	and	CCONJ
ma-24	4	48	technology	technology	NOUN
ma-24	4	49	,	,	PUNCT
ma-24	4	50	box	box	NOUN
ma-24	4	51	210	210	NUM
ma-24	4	52	-	-	SYM
ma-24	4	53	40601	40601	NUM
ma-24	4	54	,	,	PUNCT
ma-24	4	55	bondo	bondo	NOUN
ma-24	4	56	,	,	PUNCT
ma-24	4	57	kenya	kenya	PROPN
ma-24	4	58	bnyaare@yahoo.com	bnyaare@yahoo.com	PROPN
ma-24	4	59	,	,	PUNCT
ma-24	4	60	josephowuorowino@gmail.com	josephowuorowino@gmail.com	X
ma-24	5	1	∗correspondence	∗correspondence	NOUN
ma-24	5	2	:	:	PUNCT
ma-24	6	1	josephowuorowino@gmail.com	josephowuorowino@gmail.com	X
ma-24	6	2	abstract	abstract	ADJ
ma-24	6	3	.	.	PUNCT
ma-24	7	1	in	in	ADP
ma-24	7	2	this	this	DET
ma-24	7	3	paper	paper	NOUN
ma-24	7	4	,	,	PUNCT
ma-24	7	5	we	we	PRON
ma-24	7	6	consider	consider	VERB
ma-24	7	7	coupled	couple	VERB
ma-24	7	8	korteweg	korteweg	NOUN
ma-24	7	9	-	-	PUNCT
ma-24	7	10	de	de	PROPN
ma-24	7	11	vries	vries	PROPN
ma-24	7	12	equations	equation	NOUN
ma-24	7	13	that	that	PRON
ma-24	7	14	model	model	VERB
ma-24	7	15	the	the	DET
ma-24	7	16	propagationof	propagationof	NOUN
ma-24	7	17	shallow	shallow	ADJ
ma-24	7	18	water	water	NOUN
ma-24	7	19	waves	wave	NOUN
ma-24	7	20	,	,	PUNCT
ma-24	7	21	ion	ion	NOUN
ma-24	7	22	-	-	PUNCT
ma-24	7	23	acoustic	acoustic	ADJ
ma-24	7	24	waves	wave	NOUN
ma-24	7	25	in	in	ADP
ma-24	7	26	plasmas	plasma	NOUN
ma-24	7	27	,	,	PUNCT
ma-24	7	28	solitons	soliton	NOUN
ma-24	7	29	,	,	PUNCT
ma-24	7	30	and	and	CCONJ
ma-24	7	31	nonlinear	nonlinear	ADJ
ma-24	7	32	perturbations	perturbation	NOUN
ma-24	7	33	alonginternal	alonginternal	ADJ
ma-24	7	34	surfaces	surface	NOUN
ma-24	7	35	between	between	ADP
ma-24	7	36	layers	layer	NOUN
ma-24	7	37	of	of	ADP
ma-24	7	38	different	different	ADJ
ma-24	7	39	densities	density	NOUN
ma-24	7	40	in	in	ADP
ma-24	7	41	stratified	stratified	ADJ
ma-24	7	42	fluids	fluid	NOUN
ma-24	7	43	,	,	PUNCT
ma-24	7	44	for	for	ADP
ma-24	7	45	example	example	NOUN
ma-24	7	46	propagation	propagation	NOUN
ma-24	7	47	ofsolitons	ofsoliton	NOUN
ma-24	7	48	of	of	ADP
ma-24	7	49	long	long	ADJ
ma-24	7	50	internal	internal	ADJ
ma-24	7	51	waves	wave	NOUN
ma-24	7	52	in	in	ADP
ma-24	7	53	oceans	ocean	NOUN
ma-24	7	54	.	.	PUNCT
ma-24	8	1	the	the	DET
ma-24	8	2	method	method	NOUN
ma-24	8	3	of	of	ADP
ma-24	8	4	lie	lie	NOUN
ma-24	8	5	group	group	NOUN
ma-24	8	6	analysis	analysis	NOUN
ma-24	8	7	is	be	AUX
ma-24	8	8	used	use	VERB
ma-24	8	9	to	to	PART
ma-24	8	10	on	on	ADP
ma-24	8	11	the	the	DET
ma-24	8	12	systemto	systemto	NOUN
ma-24	8	13	obtain	obtain	VERB
ma-24	8	14	symmetry	symmetry	NOUN
ma-24	8	15	reductions	reduction	NOUN
ma-24	8	16	.	.	PUNCT
ma-24	9	1	soliton	soliton	NOUN
ma-24	9	2	solutions	solution	NOUN
ma-24	9	3	are	be	AUX
ma-24	9	4	constructed	construct	VERB
ma-24	9	5	by	by	ADP
ma-24	9	6	use	use	NOUN
ma-24	9	7	of	of	ADP
ma-24	9	8	a	a	DET
ma-24	9	9	linear	linear	ADJ
ma-24	9	10	combination	combination	NOUN
ma-24	9	11	oftime	oftime	NOUN
ma-24	9	12	and	and	CCONJ
ma-24	9	13	space	space	NOUN
ma-24	9	14	translation	translation	NOUN
ma-24	9	15	symmetries	symmetry	NOUN
ma-24	9	16	.	.	PUNCT
ma-24	10	1	furthermore	furthermore	ADV
ma-24	10	2	,	,	PUNCT
ma-24	10	3	we	we	PRON
ma-24	10	4	compute	compute	VERB
ma-24	10	5	conservation	conservation	NOUN
ma-24	10	6	laws	law	NOUN
ma-24	10	7	in	in	ADP
ma-24	10	8	two	two	NUM
ma-24	10	9	waysthat	waysthat	PRON
ma-24	10	10	is	be	AUX
ma-24	10	11	by	by	ADP
ma-24	10	12	multiplier	multipli	ADJ
ma-24	10	13	method	method	NOUN
ma-24	10	14	and	and	CCONJ
ma-24	10	15	by	by	ADP
ma-24	10	16	an	an	DET
ma-24	10	17	application	application	NOUN
ma-24	10	18	of	of	ADP
ma-24	10	19	new	new	ADJ
ma-24	10	20	conservation	conservation	NOUN
ma-24	10	21	theorem	theorem	NOUN
ma-24	10	22	developed	develop	VERB
ma-24	10	23	by	by	ADP
ma-24	10	24	nailibragimov	nailibragimov	NOUN
ma-24	10	25	.	.	PUNCT
ma-24	11	1	1	1	X
ma-24	11	2	.	.	X
ma-24	11	3	introduction	introduction	NOUN
ma-24	11	4	the	the	DET
ma-24	11	5	dynamics	dynamic	NOUN
ma-24	11	6	of	of	ADP
ma-24	11	7	shallow	shallow	ADJ
ma-24	11	8	-	-	PUNCT
ma-24	11	9	water	water	NOUN
ma-24	11	10	waves	wave	NOUN
ma-24	11	11	,	,	PUNCT
ma-24	11	12	ion	ion	NOUN
ma-24	11	13	-	-	PUNCT
ma-24	11	14	acoustic	acoustic	ADJ
ma-24	11	15	waves	wave	NOUN
ma-24	11	16	in	in	ADP
ma-24	11	17	plasmas	plasma	NOUN
ma-24	11	18	,	,	PUNCT
ma-24	11	19	and	and	CCONJ
ma-24	11	20	long	long	ADJ
ma-24	11	21	internal	internal	ADJ
ma-24	11	22	waves	wave	NOUN
ma-24	11	23	inoceans	inocean	NOUN
ma-24	11	24	can	can	AUX
ma-24	11	25	be	be	AUX
ma-24	11	26	described	describe	VERB
ma-24	11	27	by	by	ADP
ma-24	11	28	coupled	couple	VERB
ma-24	11	29	kdv	kdv	NOUN
ma-24	11	30	equations	equation	NOUN
ma-24	11	31	.	.	PUNCT
ma-24	12	1	the	the	DET
ma-24	12	2	equations	equation	NOUN
ma-24	12	3	are	be	AUX
ma-24	12	4	derived	derive	VERB
ma-24	12	5	from	from	ADP
ma-24	12	6	the	the	DET
ma-24	12	7	classicalkdv	classicalkdv	NOUN
ma-24	12	8	equation	equation	NOUN
ma-24	12	9	.	.	PUNCT
ma-24	13	1	this	this	DET
ma-24	13	2	section	section	NOUN
ma-24	13	3	extends	extend	VERB
ma-24	13	4	the	the	DET
ma-24	13	5	previous	previous	ADJ
ma-24	13	6	study	study	NOUN
ma-24	13	7	of	of	ADP
ma-24	13	8	kdv	kdv	NOUN
ma-24	13	9	equations	equation	NOUN
ma-24	13	10	to	to	ADP
ma-24	13	11	that	that	PRON
ma-24	13	12	of	of	ADP
ma-24	13	13	a	a	DET
ma-24	13	14	couplednonlinear	couplednonlinear	ADJ
ma-24	13	15	system	system	NOUN
ma-24	13	16	.	.	PUNCT
ma-24	14	1	from	from	ADP
ma-24	14	2	the	the	DET
ma-24	14	3	kortweg	kortweg	PROPN
ma-24	14	4	-	-	PUNCT
ma-24	14	5	de	de	PROPN
ma-24	14	6	vries	vries	PROPN
ma-24	14	7	equation	equation	NOUN
ma-24	14	8	qt	qt	X
ma-24	14	9	+	+	CCONJ
ma-24	14	10	αqqx	αqqx	NOUN
ma-24	14	11	+	+	CCONJ
ma-24	14	12	βqxxx	βqxxx	X
ma-24	14	13	=	=	SYM
ma-24	14	14	0	0	NUM
ma-24	14	15	,	,	PUNCT
ma-24	14	16	(	(	PUNCT
ma-24	14	17	1	1	X
ma-24	14	18	)	)	PUNCT
ma-24	14	19	for	for	ADP
ma-24	14	20	α	α	PROPN
ma-24	14	21	and	and	CCONJ
ma-24	14	22	β	β	NOUN
ma-24	14	23	as	as	ADP
ma-24	14	24	constants	constant	NOUN
ma-24	14	25	,	,	PUNCT
ma-24	14	26	we	we	PRON
ma-24	14	27	let	let	VERB
ma-24	14	28	q(t	q(t	NOUN
ma-24	14	29	,	,	PUNCT
ma-24	14	30	x	x	NOUN
ma-24	14	31	)	)	PUNCT
ma-24	14	32	=	=	SYM
ma-24	14	33	u(t	u(t	NOUN
ma-24	14	34	,	,	PUNCT
ma-24	14	35	x	x	NOUN
ma-24	14	36	)	)	PUNCT
ma-24	14	37	+	+	CCONJ
ma-24	14	38	iv(t	iv(t	NOUN
ma-24	14	39	,	,	PUNCT
ma-24	14	40	x	x	X
ma-24	14	41	)	)	PUNCT
ma-24	14	42	,	,	PUNCT
ma-24	14	43	(	(	PUNCT
ma-24	14	44	2	2	X
ma-24	14	45	)	)	PUNCT
ma-24	14	46	where	where	SCONJ
ma-24	14	47	i2	i2	PROPN
ma-24	14	48	=	=	SYM
ma-24	14	49	−1	−1	NOUN
ma-24	14	50	.	.	PUNCT
ma-24	15	1	then	then	ADV
ma-24	15	2	substituting	substitute	VERB
ma-24	15	3	(	(	PUNCT
ma-24	15	4	2	2	NUM
ma-24	15	5	)	)	PUNCT
ma-24	15	6	into	into	ADP
ma-24	15	7	(	(	PUNCT
ma-24	15	8	1	1	NUM
ma-24	15	9	)	)	PUNCT
ma-24	15	10	and	and	CCONJ
ma-24	15	11	separating	separate	VERB
ma-24	15	12	the	the	DET
ma-24	15	13	real	real	ADJ
ma-24	15	14	and	and	CCONJ
ma-24	15	15	imaginary	imaginary	ADJ
ma-24	15	16	parts	part	NOUN
ma-24	15	17	,	,	PUNCT
ma-24	15	18	weobtain	weobtain	NOUN
ma-24	15	19	∆1	∆1	PROPN
ma-24	15	20	≡	≡	PROPN
ma-24	15	21	ut	ut	PROPN
ma-24	16	1	+	+	CCONJ
ma-24	16	2	αuux	αuux	PROPN
ma-24	16	3	−	−	PROPN
ma-24	16	4	αvvx	αvvx	NOUN
ma-24	16	5	+	+	CCONJ
ma-24	16	6	βuxxx	βuxxx	ADJ
ma-24	17	1	=	=	SYM
ma-24	18	1	0	0	NUM
ma-24	18	2	,	,	PUNCT
ma-24	18	3	∆2	∆2	PROPN
ma-24	18	4	≡	≡	PROPN
ma-24	18	5	vt	vt	PROPN
ma-24	18	6	+	+	CCONJ
ma-24	18	7	αuvx	αuvx	PROPN
ma-24	18	8	+	+	CCONJ
ma-24	18	9	αvux	αvux	NOUN
ma-24	18	10	+	+	CCONJ
ma-24	18	11	βvxxx	βvxxx	NOUN
ma-24	18	12	=	=	SYM
ma-24	18	13	0	0	NUM
ma-24	18	14	,	,	PUNCT
ma-24	18	15	(	(	PUNCT
ma-24	18	16	3	3	X
ma-24	18	17	)	)	PUNCT
ma-24	18	18	received	receive	VERB
ma-24	18	19	:	:	PUNCT
ma-24	18	20	3	3	NUM
ma-24	18	21	sep	sep	NOUN
ma-24	18	22	2021	2021	NUM
ma-24	18	23	.	.	PUNCT
ma-24	19	1	key	key	ADJ
ma-24	19	2	words	word	NOUN
ma-24	19	3	and	and	CCONJ
ma-24	19	4	phrases	phrase	NOUN
ma-24	19	5	.	.	PUNCT
ma-24	20	1	coupled	couple	VERB
ma-24	20	2	kdv	kdv	NOUN
ma-24	20	3	equations	equation	NOUN
ma-24	20	4	;	;	PUNCT
ma-24	21	1	lie	lie	NOUN
ma-24	21	2	group	group	NOUN
ma-24	21	3	analysis	analysis	NOUN
ma-24	21	4	;	;	PUNCT
ma-24	21	5	group	group	NOUN
ma-24	21	6	-	-	PUNCT
ma-24	21	7	invariant	invariant	ADJ
ma-24	21	8	solutions	solution	NOUN
ma-24	21	9	;	;	PUNCT
ma-24	21	10	stationary	stationary	ADJ
ma-24	21	11	solutions;symmetry	solutions;symmetry	NOUN
ma-24	21	12	reductions	reduction	NOUN
ma-24	21	13	;	;	PUNCT
ma-24	21	14	soliton	soliton	NOUN
ma-24	21	15	;	;	PUNCT
ma-24	21	16	multipliers	multiplier	NOUN
ma-24	21	17	;	;	PUNCT
ma-24	21	18	conservation	conservation	NOUN
ma-24	21	19	laws.133	laws.133	PROPN
ma-24	21	20	https://adac.ee	https://adac.ee	PROPN
ma-24	21	21	https://doi.org/10.28924/ada/ma.1.133	https://doi.org/10.28924/ada/ma.1.133	PROPN
ma-24	21	22	eur	eur	PROPN
ma-24	21	23	.	.	PUNCT
ma-24	22	1	j.	j.	PROPN
ma-24	22	2	math	math	PROPN
ma-24	22	3	.	.	PUNCT
ma-24	23	1	anal	anal	ADJ
ma-24	23	2	.	.	PUNCT
ma-24	24	1	1	1	NUM
ma-24	24	2	(	(	PUNCT
ma-24	24	3	2021	2021	NUM
ma-24	24	4	)	)	PUNCT
ma-24	25	1	134which	134which	PROPN
ma-24	25	2	is	be	AUX
ma-24	25	3	a	a	DET
ma-24	25	4	nonlinear	nonlinear	ADJ
ma-24	25	5	system	system	NOUN
ma-24	25	6	of	of	ADP
ma-24	25	7	coupled	couple	VERB
ma-24	25	8	kdv	kdv	NOUN
ma-24	25	9	equations	equation	NOUN
ma-24	25	10	.	.	PUNCT
ma-24	26	1	we	we	PRON
ma-24	26	2	perform	perform	VERB
ma-24	26	3	lie	lie	NOUN
ma-24	26	4	symmetry	symmetry	NOUN
ma-24	26	5	analysis	analysis	NOUN
ma-24	26	6	on	on	ADP
ma-24	26	7	(	(	PUNCT
ma-24	26	8	3),that	3),that	NUM
ma-24	26	9	is	be	AUX
ma-24	26	10	,	,	PUNCT
ma-24	26	11	we	we	PRON
ma-24	26	12	obtain	obtain	VERB
ma-24	26	13	lie	lie	NOUN
ma-24	26	14	point	point	NOUN
ma-24	26	15	symmetries	symmetry	NOUN
ma-24	26	16	,	,	PUNCT
ma-24	26	17	invariant	invariant	ADJ
ma-24	26	18	solutions	solution	NOUN
ma-24	26	19	and	and	CCONJ
ma-24	26	20	conservation	conservation	NOUN
ma-24	26	21	laws	law	NOUN
ma-24	26	22	of	of	ADP
ma-24	26	23	(	(	PUNCT
ma-24	26	24	3).this	3).this	DET
ma-24	26	25	paperuses	paperuse	NOUN
ma-24	26	26	symmetry	symmetry	NOUN
ma-24	26	27	analysis	analysis	NOUN
ma-24	26	28	method	method	NOUN
ma-24	26	29	to	to	PART
ma-24	26	30	construct	construct	VERB
ma-24	26	31	exact	exact	ADJ
ma-24	26	32	solutions	solution	NOUN
ma-24	26	33	and	and	CCONJ
ma-24	26	34	conservation	conservation	NOUN
ma-24	26	35	laws	law	NOUN
ma-24	26	36	for	for	ADP
ma-24	26	37	a	a	DET
ma-24	26	38	nonlinearcoupled	nonlinearcouple	VERB
ma-24	26	39	kdv	kdv	NOUN
ma-24	26	40	system	system	NOUN
ma-24	26	41	(	(	PUNCT
ma-24	26	42	3	3	NUM
ma-24	26	43	)	)	PUNCT
ma-24	26	44	.	.	PUNCT
ma-24	27	1	2	2	X
ma-24	27	2	.	.	X
ma-24	27	3	preliminaries	preliminary	NOUN
ma-24	27	4	in	in	ADP
ma-24	27	5	this	this	DET
ma-24	27	6	section	section	NOUN
ma-24	27	7	,	,	PUNCT
ma-24	27	8	we	we	PRON
ma-24	27	9	outline	outline	VERB
ma-24	27	10	preliminary	preliminary	ADJ
ma-24	27	11	concepts	concept	NOUN
ma-24	27	12	which	which	PRON
ma-24	27	13	are	be	AUX
ma-24	27	14	useful	useful	ADJ
ma-24	27	15	in	in	ADP
ma-24	27	16	the	the	DET
ma-24	27	17	sequel	sequel	NOUN
ma-24	27	18	.	.	PUNCT
ma-24	28	1	in	in	ADP
ma-24	28	2	euclideanspaces	euclideanspace	NOUN
ma-24	28	3	rn	rn	PROPN
ma-24	28	4	of	of	ADP
ma-24	28	5	x	x	X
ma-24	28	6	=	=	PUNCT
ma-24	28	7	x	x	SYM
ma-24	28	8	i	i	PRON
ma-24	28	9	independent	independent	ADJ
ma-24	28	10	variables	variable	NOUN
ma-24	28	11	and	and	CCONJ
ma-24	28	12	rm	rm	NOUN
ma-24	28	13	of	of	ADP
ma-24	28	14	u	u	PROPN
ma-24	28	15	=	=	PUNCT
ma-24	28	16	uα	uα	PROPN
ma-24	28	17	dependent	dependent	ADJ
ma-24	28	18	variables	variable	NOUN
ma-24	28	19	,	,	PUNCT
ma-24	28	20	we	we	PRON
ma-24	28	21	considerthe	considerthe	VERB
ma-24	28	22	transformations	transformation	NOUN
ma-24	28	23	tε	tε	ADP
ma-24	28	24	:	:	PUNCT
ma-24	28	25	x̄	x̄	X
ma-24	29	1	i	i	PRON
ma-24	29	2	=	=	SYM
ma-24	30	1	ϕi(x	ϕi(x	PROPN
ma-24	31	1	i	i	PRON
ma-24	31	2	,	,	PUNCT
ma-24	31	3	uα	uα	PROPN
ma-24	31	4	,	,	PUNCT
ma-24	31	5	ε	ε	PROPN
ma-24	31	6	)	)	PUNCT
ma-24	31	7	,	,	PUNCT
ma-24	31	8	ūα	ūα	PROPN
ma-24	31	9	=	=	SYM
ma-24	31	10	ψα(x	ψα(x	PROPN
ma-24	31	11	i	i	PRON
ma-24	31	12	,	,	PUNCT
ma-24	31	13	uα	uα	PROPN
ma-24	31	14	,	,	PUNCT
ma-24	31	15	ε	ε	PROPN
ma-24	31	16	)	)	PUNCT
ma-24	31	17	,	,	PUNCT
ma-24	31	18	(	(	PUNCT
ma-24	31	19	4	4	X
ma-24	31	20	)	)	PUNCT
ma-24	31	21	involving	involve	VERB
ma-24	31	22	the	the	DET
ma-24	31	23	continuous	continuous	ADJ
ma-24	31	24	parameter	parameter	NOUN
ma-24	31	25	ε	ε	PROPN
ma-24	31	26	which	which	PRON
ma-24	31	27	ranges	range	VERB
ma-24	31	28	from	from	ADP
ma-24	31	29	a	a	DET
ma-24	31	30	neighbourhood	neighbourhood	NOUN
ma-24	31	31	n	n	NOUN
ma-24	31	32	′	′	NUM
ma-24	31	33	⊂	⊂	PROPN
ma-24	32	1	n	n	PROPN
ma-24	32	2	⊂	⊂	X
ma-24	32	3	r	r	NOUN
ma-24	32	4	of	of	ADP
ma-24	32	5	ε	ε	PROPN
ma-24	32	6	=	=	PUNCT
ma-24	33	1	0where	0where	PUNCT
ma-24	33	2	the	the	DET
ma-24	33	3	functions	function	NOUN
ma-24	33	4	ϕi	ϕi	ADP
ma-24	33	5	and	and	CCONJ
ma-24	33	6	ψα	ψα	ADP
ma-24	33	7	differentiable	differentiable	ADJ
ma-24	33	8	and	and	CCONJ
ma-24	33	9	analytic	analytic	ADJ
ma-24	33	10	in	in	ADP
ma-24	33	11	the	the	DET
ma-24	33	12	parameter	parameter	NOUN
ma-24	33	13	ε	ε	PROPN
ma-24	33	14	.	.	PUNCT
ma-24	33	15	definition	definition	NOUN
ma-24	33	16	2.1	2.1	NUM
ma-24	33	17	.	.	PUNCT
ma-24	34	1	the	the	DET
ma-24	34	2	set	set	ADJ
ma-24	34	3	g	g	NOUN
ma-24	34	4	of	of	ADP
ma-24	34	5	transformations	transformation	NOUN
ma-24	34	6	given	give	VERB
ma-24	34	7	by	by	ADP
ma-24	34	8	(	(	PUNCT
ma-24	34	9	4	4	NUM
ma-24	34	10	)	)	PUNCT
ma-24	34	11	is	be	AUX
ma-24	34	12	a	a	DET
ma-24	34	13	local	local	ADJ
ma-24	34	14	lie	lie	NOUN
ma-24	34	15	group	group	NOUN
ma-24	34	16	if	if	SCONJ
ma-24	34	17	it	it	PRON
ma-24	34	18	holds	hold	VERB
ma-24	34	19	true	true	ADJ
ma-24	34	20	that(1	that(1	NOUN
ma-24	34	21	)	)	PUNCT
ma-24	34	22	(	(	PUNCT
ma-24	34	23	i	i	NOUN
ma-24	34	24	)	)	PUNCT
ma-24	34	25	.	.	PUNCT
ma-24	35	1	(	(	PUNCT
ma-24	35	2	closure	closure	NOUN
ma-24	35	3	)	)	PUNCT
ma-24	35	4	given	give	VERB
ma-24	35	5	tε1	tε1	PROPN
ma-24	35	6	,	,	PUNCT
ma-24	35	7	tε2	tε2	NOUN
ma-24	35	8	∈	∈	NOUN
ma-24	35	9	g	g	PROPN
ma-24	35	10	,	,	PUNCT
ma-24	35	11	for	for	ADP
ma-24	35	12	ε1	ε1	PROPN
ma-24	35	13	,	,	PUNCT
ma-24	35	14	ε2	ε2	PROPN
ma-24	35	15	∈	∈	PROPN
ma-24	35	16	n	n	CCONJ
ma-24	35	17	′	′	NUM
ma-24	35	18	⊂	⊂	PROPN
ma-24	35	19	n	n	CCONJ
ma-24	35	20	,	,	PUNCT
ma-24	35	21	then	then	ADV
ma-24	35	22	tε1tε2	tε1tε2	ADV
ma-24	35	23	=	=	PUNCT
ma-24	35	24	tε3	tε3	INTJ
ma-24	35	25	∈	∈	PROPN
ma-24	35	26	g	g	PROPN
ma-24	35	27	,	,	PUNCT
ma-24	35	28	ε3	ε3	PROPN
ma-24	35	29	=	=	SYM
ma-24	35	30	φ(ε1	φ(ε1	PROPN
ma-24	35	31	,	,	PUNCT
ma-24	35	32	ε2	ε2	ADJ
ma-24	35	33	)	)	PUNCT
ma-24	35	34	∈	∈	PROPN
ma-24	35	35	n	n	PRON
ma-24	35	36	.(2	.(2	NUM
ma-24	35	37	)	)	PUNCT
ma-24	35	38	(	(	PUNCT
ma-24	35	39	ii	ii	NOUN
ma-24	35	40	)	)	PUNCT
ma-24	35	41	.	.	PUNCT
ma-24	36	1	(	(	PUNCT
ma-24	36	2	identity	identity	NOUN
ma-24	36	3	)	)	PUNCT
ma-24	36	4	there	there	PRON
ma-24	36	5	exists	exist	VERB
ma-24	36	6	a	a	DET
ma-24	36	7	unique	unique	ADJ
ma-24	36	8	t0	t0	PROPN
ma-24	36	9	∈	∈	PROPN
ma-24	36	10	g	g	PROPN
ma-24	37	1	if	if	SCONJ
ma-24	37	2	and	and	CCONJ
ma-24	37	3	only	only	ADV
ma-24	37	4	if	if	SCONJ
ma-24	37	5	ε	ε	PROPN
ma-24	37	6	=	=	SYM
ma-24	37	7	0	0	PROPN
ma-24	37	8	such	such	ADJ
ma-24	37	9	that	that	DET
ma-24	37	10	tεt0	tεt0	NOUN
ma-24	37	11	=	=	PUNCT
ma-24	37	12	t0tε	t0tε	PUNCT
ma-24	37	13	=	=	SYM
ma-24	37	14	tε.(3	tε.(3	NOUN
ma-24	37	15	)	)	PUNCT
ma-24	37	16	(	(	PUNCT
ma-24	37	17	iii	iii	NOUN
ma-24	37	18	)	)	PUNCT
ma-24	37	19	.	.	PUNCT
ma-24	38	1	(	(	PUNCT
ma-24	38	2	inverse	inverse	NOUN
ma-24	38	3	)	)	PUNCT
ma-24	38	4	there	there	PRON
ma-24	38	5	exists	exist	VERB
ma-24	38	6	a	a	DET
ma-24	38	7	unique	unique	ADJ
ma-24	38	8	tε−1	tε−1	PROPN
ma-24	38	9	∈	∈	PROPN
ma-24	38	10	g	g	NOUN
ma-24	38	11	for	for	ADP
ma-24	38	12	every	every	DET
ma-24	38	13	transformation	transformation	NOUN
ma-24	38	14	tε	tε	ADP
ma-24	38	15	∈	∈	PROPN
ma-24	38	16	g	g	PROPN
ma-24	38	17	,	,	PUNCT
ma-24	38	18	where	where	SCONJ
ma-24	38	19	ε	ε	PROPN
ma-24	38	20	∈	∈	PROPN
ma-24	38	21	n	n	ADP
ma-24	38	22	′	′	NUM
ma-24	38	23	⊂	⊂	PROPN
ma-24	39	1	n	n	CCONJ
ma-24	40	1	and	and	CCONJ
ma-24	40	2	ε−1	ε−1	PROPN
ma-24	40	3	∈	∈	PROPN
ma-24	40	4	n	n	PRON
ma-24	40	5	such	such	ADJ
ma-24	40	6	that	that	SCONJ
ma-24	40	7	tεtε−1	tεtε−1	X
ma-24	40	8	=	=	SYM
ma-24	40	9	tε−1tε	tε−1tε	NUM
ma-24	40	10	=	=	SYM
ma-24	40	11	t0	t0	PROPN
ma-24	40	12	.	.	PUNCT
ma-24	41	1	remark	remark	PROPN
ma-24	41	2	2.2	2.2	NUM
ma-24	41	3	.	.	PUNCT
ma-24	42	1	associativity	associativity	NOUN
ma-24	42	2	of	of	ADP
ma-24	42	3	the	the	DET
ma-24	42	4	group	group	NOUN
ma-24	42	5	g	g	PROPN
ma-24	42	6	in	in	ADP
ma-24	42	7	(	(	PUNCT
ma-24	42	8	4	4	NUM
ma-24	42	9	)	)	PUNCT
ma-24	42	10	follows	follow	VERB
ma-24	42	11	from	from	ADP
ma-24	42	12	(	(	PUNCT
ma-24	42	13	1	1	NUM
ma-24	42	14	)	)	PUNCT
ma-24	42	15	.	.	PUNCT
ma-24	43	1	in	in	ADP
ma-24	43	2	the	the	DET
ma-24	43	3	system	system	NOUN
ma-24	43	4	,	,	PUNCT
ma-24	43	5	∆α	∆α	PROPN
ma-24	43	6	(	(	PUNCT
ma-24	43	7	x	x	X
ma-24	43	8	i	i	PRON
ma-24	43	9	,	,	PUNCT
ma-24	43	10	uα	uα	PROPN
ma-24	43	11	,	,	PUNCT
ma-24	43	12	u(1	u(1	PROPN
ma-24	43	13	)	)	PUNCT
ma-24	43	14	,	,	PUNCT
ma-24	43	15	.	.	PUNCT
ma-24	43	16	.	.	PUNCT
ma-24	43	17	.	.	PUNCT
ma-24	44	1	,	,	PUNCT
ma-24	44	2	u(π	u(π	PROPN
ma-24	44	3	)	)	PUNCT
ma-24	44	4	)	)	PUNCT
ma-24	45	1	=	=	PUNCT
ma-24	45	2	∆α	∆α	PROPN
ma-24	45	3	=	=	SYM
ma-24	45	4	0	0	NUM
ma-24	45	5	,	,	PUNCT
ma-24	45	6	(	(	PUNCT
ma-24	45	7	5)the	5)the	DET
ma-24	45	8	variables	variable	NOUN
ma-24	45	9	uα	uα	PROPN
ma-24	45	10	are	be	AUX
ma-24	45	11	dependent	dependent	ADJ
ma-24	45	12	.	.	PUNCT
ma-24	46	1	the	the	DET
ma-24	46	2	partial	partial	ADJ
ma-24	46	3	derivatives	derivative	NOUN
ma-24	46	4	u(1	u(1	PROPN
ma-24	46	5	)	)	PUNCT
ma-24	46	6	=	=	PRON
ma-24	46	7	{	{	PUNCT
ma-24	46	8	uαi	uαi	ADV
ma-24	46	9	}	}	PUNCT
ma-24	46	10	,	,	PUNCT
ma-24	46	11	u(2	u(2	PROPN
ma-24	46	12	)	)	PUNCT
ma-24	46	13	=	=	PRON
ma-24	46	14	{	{	PUNCT
ma-24	46	15	uαij	uαij	ADV
ma-24	46	16	}	}	PUNCT
ma-24	46	17	,	,	PUNCT
ma-24	46	18	.	.	PUNCT
ma-24	46	19	.	.	PUNCT
ma-24	46	20	.	.	PUNCT
ma-24	47	1	,	,	PUNCT
ma-24	47	2	u(π	u(π	PROPN
ma-24	47	3	)	)	PUNCT
ma-24	48	1	=	=	PRON
ma-24	48	2	{	{	PUNCT
ma-24	48	3	uαi1	uαi1	PROPN
ma-24	48	4	...	...	PUNCT
ma-24	48	5	iπ	iπ	NOUN
ma-24	48	6	}	}	PUNCT
ma-24	48	7	,	,	PUNCT
ma-24	48	8	are	be	AUX
ma-24	48	9	of	of	ADP
ma-24	48	10	the	the	DET
ma-24	48	11	first	first	ADJ
ma-24	48	12	,	,	PUNCT
ma-24	48	13	second	second	ADJ
ma-24	48	14	,	,	PUNCT
ma-24	48	15	.	.	PUNCT
ma-24	48	16	.	.	PUNCT
ma-24	49	1	.	.	PUNCT
ma-24	50	1	,	,	PUNCT
ma-24	50	2	up	up	ADP
ma-24	50	3	to	to	ADP
ma-24	50	4	the	the	DET
ma-24	50	5	πth-orders.denoting	πth-orders.denote	VERB
ma-24	50	6	di	di	X
ma-24	50	7	=	=	SYM
ma-24	50	8	∂	∂	NOUN
ma-24	50	9	∂x	∂x	PROPN
ma-24	50	10	i	i	PRON
ma-24	50	11	+	+	PROPN
ma-24	50	12	uαi	uαi	ADJ
ma-24	50	13	∂	∂	NOUN
ma-24	51	1	∂uα	∂uα	NOUN
ma-24	51	2	+	+	CCONJ
ma-24	51	3	uαij	uαij	PROPN
ma-24	51	4	∂	∂	NOUN
ma-24	51	5	∂uαj	∂uαj	NOUN
ma-24	51	6	+	+	CCONJ
ma-24	51	7	.	.	PUNCT
ma-24	51	8	.	.	PUNCT
ma-24	51	9	.	.	PUNCT
ma-24	52	1	,	,	PUNCT
ma-24	52	2	(	(	PUNCT
ma-24	52	3	6	6	X
ma-24	52	4	)	)	PUNCT
ma-24	52	5	the	the	DET
ma-24	52	6	total	total	ADJ
ma-24	52	7	differentiation	differentiation	NOUN
ma-24	52	8	operator	operator	NOUN
ma-24	52	9	with	with	ADP
ma-24	52	10	respect	respect	NOUN
ma-24	52	11	to	to	ADP
ma-24	52	12	the	the	DET
ma-24	52	13	variables	variable	NOUN
ma-24	52	14	x	x	PUNCT
ma-24	53	1	i	i	PRON
ma-24	53	2	and	and	CCONJ
ma-24	53	3	δji	δji	PROPN
ma-24	53	4	,	,	PUNCT
ma-24	53	5	the	the	DET
ma-24	53	6	kronecker	kronecker	NOUN
ma-24	53	7	delta	delta	NOUN
ma-24	53	8	,	,	PUNCT
ma-24	53	9	wehave	wehave	NOUN
ma-24	53	10	di(x	di(x	NUM
ma-24	53	11	j	j	NOUN
ma-24	53	12	)	)	PUNCT
ma-24	53	13	=	=	SYM
ma-24	53	14	δji	δji	PROPN
ma-24	53	15	,	,	PUNCT
ma-24	53	16	′	′	PROPN
ma-24	53	17	,	,	PUNCT
ma-24	53	18	uαi	uαi	ADJ
ma-24	53	19	=	=	SYM
ma-24	53	20	di(u	di(u	NOUN
ma-24	53	21	α	α	NOUN
ma-24	53	22	)	)	PUNCT
ma-24	53	23	,	,	PUNCT
ma-24	53	24	uαij	uαij	NOUN
ma-24	53	25	=	=	X
ma-24	53	26	dj(di(u	dj(di(u	NOUN
ma-24	53	27	α	α	NOUN
ma-24	53	28	)	)	PUNCT
ma-24	53	29	)	)	PUNCT
ma-24	53	30	,	,	PUNCT
ma-24	53	31	.	.	PUNCT
ma-24	53	32	.	.	PUNCT
ma-24	53	33	.	.	PUNCT
ma-24	54	1	,	,	PUNCT
ma-24	54	2	(	(	PUNCT
ma-24	54	3	7	7	X
ma-24	54	4	)	)	PUNCT
ma-24	54	5	where	where	SCONJ
ma-24	54	6	uαi	uαi	PROPN
ma-24	54	7	defined	define	VERB
ma-24	54	8	in	in	ADP
ma-24	54	9	(	(	PUNCT
ma-24	54	10	7	7	X
ma-24	54	11	)	)	PUNCT
ma-24	54	12	are	be	AUX
ma-24	54	13	differential	differential	ADJ
ma-24	54	14	variables	variable	NOUN
ma-24	55	1	[	[	X
ma-24	55	2	7].consider	7].consider	NUM
ma-24	55	3	the	the	DET
ma-24	55	4	local	local	ADJ
ma-24	55	5	lie	lie	NOUN
ma-24	55	6	group	group	NOUN
ma-24	55	7	g	g	PROPN
ma-24	55	8	given	give	VERB
ma-24	55	9	by	by	ADP
ma-24	55	10	the	the	DET
ma-24	55	11	transformations	transformation	NOUN
ma-24	55	12	x̄	x̄	NOUN
ma-24	56	1	i	i	PRON
ma-24	56	2	=	=	SYM
ma-24	56	3	ϕi(x	ϕi(x	PROPN
ma-24	57	1	i	i	PRON
ma-24	57	2	,	,	PUNCT
ma-24	57	3	uα	uα	PROPN
ma-24	57	4	,	,	PUNCT
ma-24	57	5	ε	ε	PROPN
ma-24	57	6	)	)	PUNCT
ma-24	57	7	,	,	PUNCT
ma-24	57	8	ϕi	ϕi	ADP
ma-24	57	9	∣∣∣	∣∣∣	ADJ
ma-24	57	10	ε=0	ε=0	X
ma-24	57	11	=	=	PUNCT
ma-24	57	12	x	x	PUNCT
ma-24	57	13	i	i	NOUN
ma-24	57	14	,	,	PUNCT
ma-24	57	15	ūα	ūα	PROPN
ma-24	57	16	=	=	PUNCT
ma-24	57	17	ψα(x	ψα(x	PROPN
ma-24	57	18	i	i	PRON
ma-24	57	19	,	,	PUNCT
ma-24	57	20	uα	uα	PROPN
ma-24	57	21	,	,	PUNCT
ma-24	57	22	ε	ε	PROPN
ma-24	57	23	)	)	PUNCT
ma-24	57	24	,	,	PUNCT
ma-24	57	25	ψα	ψα	ADP
ma-24	57	26	∣∣∣	∣∣∣	ADJ
ma-24	57	27	ε=0	ε=0	X
ma-24	57	28	=	=	SYM
ma-24	57	29	uα	uα	PROPN
ma-24	57	30	,	,	PUNCT
ma-24	57	31	(	(	PUNCT
ma-24	57	32	8)	8)	NUM
ma-24	57	33	where	where	SCONJ
ma-24	57	34	the	the	DET
ma-24	57	35	symbol	symbol	NOUN
ma-24	57	36	∣∣∣	∣∣∣	NOUN
ma-24	57	37	ε=0	ε=0	PROPN
ma-24	57	38	means	mean	NOUN
ma-24	57	39	evaluated	evaluate	VERB
ma-24	57	40	on	on	ADP
ma-24	57	41	ε	ε	PROPN
ma-24	57	42	=	=	SYM
ma-24	57	43	0	0	PROPN
ma-24	57	44	.	.	PUNCT
ma-24	57	45	eur	eur	PROPN
ma-24	57	46	.	.	PUNCT
ma-24	58	1	j.	j.	PROPN
ma-24	58	2	math	math	PROPN
ma-24	58	3	.	.	PUNCT
ma-24	59	1	anal	anal	ADJ
ma-24	59	2	.	.	PUNCT
ma-24	60	1	1	1	NUM
ma-24	60	2	(	(	PUNCT
ma-24	60	3	2021	2021	NUM
ma-24	60	4	)	)	PUNCT
ma-24	60	5	135	135	NUM
ma-24	60	6	definition	definition	NOUN
ma-24	60	7	2.3	2.3	NUM
ma-24	60	8	.	.	PUNCT
ma-24	61	1	the	the	DET
ma-24	61	2	construction	construction	NOUN
ma-24	61	3	of	of	ADP
ma-24	61	4	the	the	DET
ma-24	61	5	group	group	NOUN
ma-24	61	6	g	g	NOUN
ma-24	61	7	given	give	VERB
ma-24	61	8	by	by	ADP
ma-24	61	9	(	(	PUNCT
ma-24	61	10	8)	8)	NUM
ma-24	61	11	is	be	AUX
ma-24	61	12	an	an	DET
ma-24	61	13	equivalence	equivalence	NOUN
ma-24	61	14	of	of	ADP
ma-24	61	15	the	the	DET
ma-24	61	16	computationof	computationof	ADJ
ma-24	61	17	infinitesimal	infinitesimal	ADJ
ma-24	61	18	transformations	transformation	NOUN
ma-24	61	19	x̄	x̄	NOUN
ma-24	62	1	i	i	PRON
ma-24	63	1	≈	≈	PROPN
ma-24	63	2	x	x	PUNCT
ma-24	64	1	i	i	PRON
ma-24	64	2	+	+	CCONJ
ma-24	64	3	ξi(x	ξi(x	NOUN
ma-24	64	4	i	i	PRON
ma-24	64	5	,	,	PUNCT
ma-24	64	6	uα)ε	uα)ε	PROPN
ma-24	64	7	,	,	PUNCT
ma-24	64	8	ϕi	ϕi	ADP
ma-24	64	9	∣∣∣	∣∣∣	ADJ
ma-24	64	10	ε=0	ε=0	X
ma-24	64	11	=	=	PUNCT
ma-24	64	12	x	x	PUNCT
ma-24	64	13	i	i	NOUN
ma-24	64	14	,	,	PUNCT
ma-24	64	15	ūα	ūα	PROPN
ma-24	64	16	≈	≈	PROPN
ma-24	64	17	uα	uα	PROPN
ma-24	64	18	+	+	CCONJ
ma-24	64	19	ηα(x	ηα(x	VERB
ma-24	64	20	i	i	PRON
ma-24	64	21	,	,	PUNCT
ma-24	64	22	uα)ε	uα)ε	ADJ
ma-24	64	23	,	,	PUNCT
ma-24	64	24	ψα	ψα	ADP
ma-24	64	25	∣∣∣	∣∣∣	ADJ
ma-24	64	26	ε=0	ε=0	X
ma-24	64	27	=	=	SYM
ma-24	64	28	uα	uα	PROPN
ma-24	64	29	,	,	PUNCT
ma-24	64	30	(	(	PUNCT
ma-24	64	31	9	9	X
ma-24	64	32	)	)	PUNCT
ma-24	64	33	obtained	obtain	VERB
ma-24	64	34	from	from	ADP
ma-24	64	35	(	(	PUNCT
ma-24	64	36	4	4	NUM
ma-24	64	37	)	)	PUNCT
ma-24	64	38	by	by	ADP
ma-24	64	39	a	a	DET
ma-24	64	40	taylor	taylor	PROPN
ma-24	64	41	series	series	PROPN
ma-24	64	42	expansion	expansion	NOUN
ma-24	64	43	of	of	ADP
ma-24	64	44	ϕi(x	ϕi(x	NOUN
ma-24	64	45	i	i	PRON
ma-24	64	46	,	,	PUNCT
ma-24	64	47	uα	uα	PROPN
ma-24	64	48	,	,	PUNCT
ma-24	64	49	ε	ε	PROPN
ma-24	64	50	)	)	PUNCT
ma-24	64	51	and	and	CCONJ
ma-24	64	52	ψi(x	ψi(x	NUM
ma-24	65	1	i	i	PRON
ma-24	65	2	,	,	PUNCT
ma-24	65	3	uα	uα	PROPN
ma-24	65	4	,	,	PUNCT
ma-24	65	5	ε	ε	PROPN
ma-24	65	6	)	)	PUNCT
ma-24	65	7	in	in	ADP
ma-24	65	8	ε	ε	PROPN
ma-24	65	9	about	about	ADP
ma-24	65	10	ε	ε	PROPN
ma-24	65	11	=	=	SYM
ma-24	65	12	0and	0and	PROPN
ma-24	65	13	keeping	keep	VERB
ma-24	65	14	only	only	ADV
ma-24	65	15	the	the	DET
ma-24	65	16	terms	term	NOUN
ma-24	65	17	linear	linear	VERB
ma-24	65	18	in	in	ADP
ma-24	65	19	ε	ε	PROPN
ma-24	65	20	,	,	PUNCT
ma-24	65	21	where	where	SCONJ
ma-24	65	22	ξi(x	ξi(x	ADP
ma-24	65	23	i	i	PRON
ma-24	65	24	,	,	PUNCT
ma-24	65	25	uα	uα	NOUN
ma-24	65	26	)	)	PUNCT
ma-24	65	27	=	=	NOUN
ma-24	66	1	∂ϕi(x	∂ϕi(x	NOUN
ma-24	66	2	i	i	PRON
ma-24	66	3	,	,	PUNCT
ma-24	66	4	uα	uα	PROPN
ma-24	66	5	,	,	PUNCT
ma-24	66	6	ε	ε	PROPN
ma-24	66	7	)	)	PUNCT
ma-24	66	8	∂ε	∂ε	PROPN
ma-24	66	9	∣∣∣	∣∣∣	ADJ
ma-24	66	10	ε=0	ε=0	NOUN
ma-24	66	11	,	,	PUNCT
ma-24	66	12	ηα(x	ηα(x	PUNCT
ma-24	66	13	i	i	PRON
ma-24	66	14	,	,	PUNCT
ma-24	66	15	uα	uα	NOUN
ma-24	66	16	)	)	PUNCT
ma-24	66	17	=	=	SYM
ma-24	67	1	∂ψα(x	∂ψα(x	PROPN
ma-24	67	2	i	i	PRON
ma-24	67	3	,	,	PUNCT
ma-24	67	4	uα	uα	PROPN
ma-24	67	5	,	,	PUNCT
ma-24	67	6	ε	ε	PROPN
ma-24	67	7	)	)	PUNCT
ma-24	67	8	∂ε	∂ε	PROPN
ma-24	67	9	∣∣∣	∣∣∣	ADJ
ma-24	67	10	ε=0	ε=0	X
ma-24	67	11	.	.	PUNCT
ma-24	68	1	(	(	PUNCT
ma-24	68	2	10	10	NUM
ma-24	68	3	)	)	PUNCT
ma-24	68	4	remark	remark	NOUN
ma-24	68	5	2.4	2.4	NUM
ma-24	68	6	.	.	PUNCT
ma-24	69	1	the	the	DET
ma-24	69	2	symbol	symbol	NOUN
ma-24	69	3	of	of	ADP
ma-24	69	4	infinitesimal	infinitesimal	ADJ
ma-24	69	5	transformations	transformation	NOUN
ma-24	69	6	,	,	PUNCT
ma-24	69	7	x	x	X
ma-24	69	8	,	,	PUNCT
ma-24	69	9	is	be	AUX
ma-24	69	10	used	use	VERB
ma-24	69	11	to	to	PART
ma-24	69	12	write	write	VERB
ma-24	69	13	(	(	PUNCT
ma-24	69	14	9	9	NUM
ma-24	69	15	)	)	PUNCT
ma-24	69	16	as	as	ADP
ma-24	69	17	x̄	x̄	NOUN
ma-24	70	1	i	i	PROPN
ma-24	71	1	≈	≈	PROPN
ma-24	71	2	(	(	PUNCT
ma-24	71	3	1	1	NUM
ma-24	71	4	+	+	NOUN
ma-24	71	5	x)x	x)x	X
ma-24	72	1	i	i	PRON
ma-24	72	2	,	,	PUNCT
ma-24	72	3	ūα	ūα	PROPN
ma-24	72	4	≈	≈	PROPN
ma-24	72	5	(	(	PUNCT
ma-24	72	6	1	1	NUM
ma-24	72	7	+	+	NOUN
ma-24	72	8	x)uα	x)uα	PROPN
ma-24	72	9	,	,	PUNCT
ma-24	72	10	(	(	PUNCT
ma-24	72	11	11	11	NUM
ma-24	72	12	)	)	PUNCT
ma-24	72	13	where	where	SCONJ
ma-24	72	14	x	x	X
ma-24	72	15	=	=	PRON
ma-24	72	16	ξi(x	ξi(x	PRON
ma-24	72	17	i	i	PRON
ma-24	72	18	,	,	PUNCT
ma-24	72	19	uα	uα	PROPN
ma-24	72	20	)	)	PUNCT
ma-24	72	21	∂	∂	NOUN
ma-24	73	1	∂x	∂x	PROPN
ma-24	73	2	i	i	PRON
ma-24	73	3	+	+	CCONJ
ma-24	73	4	ηα(x	ηα(x	VERB
ma-24	73	5	i	i	PRON
ma-24	73	6	,	,	PUNCT
ma-24	73	7	uα	uα	PROPN
ma-24	73	8	)	)	PUNCT
ma-24	73	9	∂	∂	NOUN
ma-24	74	1	∂uα	∂uα	NOUN
ma-24	74	2	,	,	PUNCT
ma-24	74	3	(	(	PUNCT
ma-24	74	4	12	12	NUM
ma-24	74	5	)	)	PUNCT
ma-24	74	6	is	be	AUX
ma-24	74	7	the	the	DET
ma-24	74	8	generator	generator	NOUN
ma-24	74	9	of	of	ADP
ma-24	74	10	the	the	DET
ma-24	74	11	group	group	NOUN
ma-24	74	12	g	g	NOUN
ma-24	74	13	given	give	VERB
ma-24	74	14	by	by	ADP
ma-24	74	15	(	(	PUNCT
ma-24	74	16	8)	8)	NUM
ma-24	74	17	.	.	PUNCT
ma-24	74	18	remark	remark	NOUN
ma-24	74	19	2.5	2.5	NUM
ma-24	74	20	.	.	PUNCT
ma-24	75	1	to	to	PART
ma-24	75	2	obtain	obtain	VERB
ma-24	75	3	transformed	transform	VERB
ma-24	75	4	derivatives	derivative	NOUN
ma-24	75	5	from	from	ADP
ma-24	75	6	(	(	PUNCT
ma-24	75	7	4	4	NUM
ma-24	75	8	)	)	PUNCT
ma-24	75	9	,	,	PUNCT
ma-24	75	10	we	we	PRON
ma-24	75	11	use	use	VERB
ma-24	75	12	a	a	DET
ma-24	75	13	change	change	NOUN
ma-24	75	14	of	of	ADP
ma-24	75	15	variable	variable	ADJ
ma-24	75	16	formulae	formulae	NOUN
ma-24	75	17	di	di	X
ma-24	75	18	=	=	PUNCT
ma-24	75	19	di(ϕ	di(ϕ	X
ma-24	75	20	j)d̄j	j)d̄j	PROPN
ma-24	75	21	,	,	PUNCT
ma-24	75	22	(	(	PUNCT
ma-24	75	23	13	13	NUM
ma-24	75	24	)	)	PUNCT
ma-24	75	25	where	where	SCONJ
ma-24	75	26	d̄j	d̄j	PROPN
ma-24	75	27	is	be	AUX
ma-24	75	28	the	the	DET
ma-24	75	29	total	total	ADJ
ma-24	75	30	differentiation	differentiation	NOUN
ma-24	75	31	in	in	ADP
ma-24	75	32	the	the	DET
ma-24	75	33	variables	variable	NOUN
ma-24	75	34	x̄	x̄	PUNCT
ma-24	76	1	i	i	PRON
ma-24	76	2	.	.	PUNCT
ma-24	77	1	this	this	PRON
ma-24	77	2	means	mean	VERB
ma-24	77	3	that	that	SCONJ
ma-24	77	4	ūαi	ūαi	PROPN
ma-24	77	5	=	=	PUNCT
ma-24	77	6	d̄i(ū	d̄i(ū	PROPN
ma-24	77	7	α	α	X
ma-24	77	8	)	)	PUNCT
ma-24	77	9	,	,	PUNCT
ma-24	77	10	ūαij	ūαij	ADV
ma-24	77	11	=	=	PUNCT
ma-24	77	12	d̄j(ū	d̄j(ū	PROPN
ma-24	77	13	α	α	NOUN
ma-24	77	14	i	i	NOUN
ma-24	77	15	)	)	PUNCT
ma-24	78	1	=	=	PUNCT
ma-24	79	1	d̄i(ū	d̄i(ū	PROPN
ma-24	79	2	α	α	X
ma-24	79	3	j	j	PROPN
ma-24	79	4	)	)	PUNCT
ma-24	79	5	.	.	PUNCT
ma-24	80	1	(	(	PUNCT
ma-24	80	2	14	14	NUM
ma-24	80	3	)	)	PUNCT
ma-24	80	4	if	if	SCONJ
ma-24	80	5	we	we	PRON
ma-24	80	6	apply	apply	VERB
ma-24	80	7	the	the	DET
ma-24	80	8	change	change	NOUN
ma-24	80	9	of	of	ADP
ma-24	80	10	variable	variable	ADJ
ma-24	80	11	formula	formula	NOUN
ma-24	80	12	given	give	VERB
ma-24	80	13	in	in	ADP
ma-24	80	14	(	(	PUNCT
ma-24	80	15	13	13	NUM
ma-24	80	16	)	)	PUNCT
ma-24	80	17	on	on	ADP
ma-24	80	18	g	g	NOUN
ma-24	80	19	given	give	VERB
ma-24	80	20	by	by	ADP
ma-24	80	21	(	(	PUNCT
ma-24	80	22	8)	8)	NUM
ma-24	80	23	,	,	PUNCT
ma-24	80	24	we	we	PRON
ma-24	80	25	get	get	VERB
ma-24	80	26	di(ψ	di(ψ	NOUN
ma-24	80	27	α	α	NOUN
ma-24	80	28	)	)	PUNCT
ma-24	80	29	=	=	SYM
ma-24	80	30	di(ϕ	di(ϕ	X
ma-24	80	31	j	j	NOUN
ma-24	80	32	)	)	PUNCT
ma-24	80	33	,	,	PUNCT
ma-24	80	34	d̄j(ū	d̄j(ū	PROPN
ma-24	80	35	α	α	NOUN
ma-24	80	36	)	)	PUNCT
ma-24	80	37	=	=	SYM
ma-24	80	38	ūαj	ūαj	PROPN
ma-24	80	39	di(ϕ	di(ϕ	X
ma-24	80	40	j	j	NOUN
ma-24	80	41	)	)	PUNCT
ma-24	80	42	.	.	PUNCT
ma-24	81	1	(	(	PUNCT
ma-24	81	2	15	15	NUM
ma-24	81	3	)	)	PUNCT
ma-24	81	4	expansion	expansion	NOUN
ma-24	81	5	of	of	ADP
ma-24	81	6	(	(	PUNCT
ma-24	81	7	15	15	NUM
ma-24	81	8	)	)	PUNCT
ma-24	81	9	yields	yield	NOUN
ma-24	81	10	(	(	PUNCT
ma-24	81	11	∂ϕj	∂ϕj	PROPN
ma-24	81	12	∂x	∂x	VERB
ma-24	81	13	i	i	PRON
ma-24	82	1	+	+	CCONJ
ma-24	82	2	uβi	uβi	ADP
ma-24	82	3	∂ϕj	∂ϕj	PROPN
ma-24	82	4	∂uβ	∂uβ	PROPN
ma-24	82	5	)	)	PUNCT
ma-24	83	1	ūβj	ūβj	PROPN
ma-24	83	2	=	=	PUNCT
ma-24	84	1	∂ψα	∂ψα	PROPN
ma-24	84	2	∂x	∂x	PROPN
ma-24	84	3	i	i	PRON
ma-24	85	1	+	+	CCONJ
ma-24	86	1	uβi	uβi	PROPN
ma-24	86	2	∂ψα	∂ψα	PROPN
ma-24	86	3	∂uβ	∂uβ	PROPN
ma-24	86	4	.	.	PUNCT
ma-24	87	1	(	(	PUNCT
ma-24	87	2	16	16	NUM
ma-24	87	3	)	)	PUNCT
ma-24	87	4	the	the	DET
ma-24	87	5	variables	variable	NOUN
ma-24	87	6	ūαi	ūαi	PROPN
ma-24	87	7	can	can	AUX
ma-24	87	8	be	be	AUX
ma-24	87	9	written	write	VERB
ma-24	87	10	as	as	ADP
ma-24	87	11	functions	function	NOUN
ma-24	87	12	of	of	ADP
ma-24	87	13	x	x	X
ma-24	87	14	i	i	PROPN
ma-24	87	15	,	,	PUNCT
ma-24	87	16	uα	uα	PROPN
ma-24	87	17	,	,	PUNCT
ma-24	87	18	u(1	u(1	PROPN
ma-24	87	19	)	)	PUNCT
ma-24	87	20	,	,	PUNCT
ma-24	87	21	that	that	PRON
ma-24	87	22	is	be	AUX
ma-24	87	23	ūαi	ūαi	PROPN
ma-24	87	24	=	=	SYM
ma-24	87	25	φα(x	φα(x	NUM
ma-24	87	26	i	i	PRON
ma-24	87	27	,	,	PUNCT
ma-24	87	28	uα	uα	PROPN
ma-24	87	29	,	,	PUNCT
ma-24	87	30	u(1	u(1	PROPN
ma-24	87	31	)	)	PUNCT
ma-24	87	32	,	,	PUNCT
ma-24	87	33	ε	ε	PROPN
ma-24	87	34	)	)	PUNCT
ma-24	87	35	,	,	PUNCT
ma-24	87	36	φα	φα	ADP
ma-24	87	37	∣∣∣	∣∣∣	ADJ
ma-24	87	38	ε=0	ε=0	X
ma-24	87	39	=	=	SYM
ma-24	87	40	uαi	uαi	PROPN
ma-24	87	41	.	.	PUNCT
ma-24	88	1	(	(	PUNCT
ma-24	88	2	17	17	NUM
ma-24	88	3	)	)	PUNCT
ma-24	88	4	definition	definition	NOUN
ma-24	88	5	2.6	2.6	NUM
ma-24	88	6	.	.	PUNCT
ma-24	89	1	the	the	DET
ma-24	89	2	transformations	transformation	NOUN
ma-24	89	3	in	in	ADP
ma-24	89	4	the	the	DET
ma-24	89	5	space	space	NOUN
ma-24	89	6	of	of	ADP
ma-24	89	7	the	the	DET
ma-24	89	8	variables	variable	NOUN
ma-24	89	9	x	x	PUNCT
ma-24	89	10	i	i	PRON
ma-24	89	11	,	,	PUNCT
ma-24	89	12	uα	uα	PROPN
ma-24	89	13	,	,	PUNCT
ma-24	89	14	u(1	u(1	PROPN
ma-24	89	15	)	)	PUNCT
ma-24	89	16	given	give	VERB
ma-24	89	17	in	in	ADP
ma-24	89	18	(	(	PUNCT
ma-24	89	19	8)	8)	NUM
ma-24	89	20	and	and	CCONJ
ma-24	89	21	(	(	PUNCT
ma-24	89	22	17)form	17)form	NUM
ma-24	89	23	the	the	DET
ma-24	89	24	first	first	ADJ
ma-24	89	25	prolongation	prolongation	NOUN
ma-24	89	26	group	group	NOUN
ma-24	89	27	g[1	g[1	PROPN
ma-24	89	28	]	]	PUNCT
ma-24	89	29	.	.	PUNCT
ma-24	90	1	definition	definition	NOUN
ma-24	90	2	2.7	2.7	NUM
ma-24	90	3	.	.	PUNCT
ma-24	90	4	infinitesimal	infinitesimal	ADJ
ma-24	90	5	transformation	transformation	NOUN
ma-24	90	6	of	of	ADP
ma-24	90	7	the	the	DET
ma-24	90	8	first	first	ADJ
ma-24	90	9	derivatives	derivative	NOUN
ma-24	90	10	is	be	AUX
ma-24	90	11	ūαi	ūαi	PROPN
ma-24	91	1	≈	≈	PROPN
ma-24	91	2	uαi	uαi	PROPN
ma-24	91	3	+	+	X
ma-24	91	4	ζαi	ζαi	NOUN
ma-24	91	5	ε	ε	PROPN
ma-24	91	6	,	,	PUNCT
ma-24	91	7	where	where	SCONJ
ma-24	91	8	ζαi	ζαi	NOUN
ma-24	91	9	=	=	SYM
ma-24	91	10	ζαi	ζαi	NOUN
ma-24	91	11	(	(	PUNCT
ma-24	91	12	x	x	PROPN
ma-24	91	13	i	i	PRON
ma-24	91	14	,	,	PUNCT
ma-24	91	15	uα	uα	PROPN
ma-24	91	16	,	,	PUNCT
ma-24	91	17	u(1	u(1	PROPN
ma-24	91	18	)	)	PUNCT
ma-24	91	19	,	,	PUNCT
ma-24	91	20	ε	ε	PROPN
ma-24	91	21	)	)	PUNCT
ma-24	91	22	.	.	PUNCT
ma-24	92	1	(	(	PUNCT
ma-24	92	2	18	18	NUM
ma-24	92	3	)	)	PUNCT
ma-24	92	4	remark	remark	NOUN
ma-24	92	5	2.8	2.8	NUM
ma-24	92	6	.	.	PUNCT
ma-24	93	1	in	in	ADP
ma-24	93	2	terms	term	NOUN
ma-24	93	3	of	of	ADP
ma-24	93	4	infinitesimal	infinitesimal	ADJ
ma-24	93	5	transformations	transformation	NOUN
ma-24	93	6	,	,	PUNCT
ma-24	93	7	the	the	DET
ma-24	93	8	first	first	ADJ
ma-24	93	9	prolongation	prolongation	NOUN
ma-24	93	10	group	group	NOUN
ma-24	93	11	g[1	g[1	PROPN
ma-24	93	12	]	]	PUNCT
ma-24	93	13	is	be	AUX
ma-24	93	14	given	give	VERB
ma-24	93	15	by(9	by(9	NOUN
ma-24	93	16	)	)	PUNCT
ma-24	93	17	and	and	CCONJ
ma-24	93	18	(	(	PUNCT
ma-24	93	19	18	18	NUM
ma-24	93	20	)	)	PUNCT
ma-24	93	21	.	.	PUNCT
ma-24	94	1	eur	eur	PROPN
ma-24	94	2	.	.	PUNCT
ma-24	95	1	j.	j.	PROPN
ma-24	95	2	math	math	PROPN
ma-24	95	3	.	.	PUNCT
ma-24	96	1	anal	anal	ADJ
ma-24	96	2	.	.	PUNCT
ma-24	97	1	1	1	NUM
ma-24	97	2	(	(	PUNCT
ma-24	97	3	2021	2021	NUM
ma-24	97	4	)	)	PUNCT
ma-24	97	5	136	136	NUM
ma-24	97	6	definition	definition	NOUN
ma-24	97	7	2.9	2.9	NUM
ma-24	97	8	.	.	PUNCT
ma-24	98	1	by	by	ADP
ma-24	98	2	using	use	VERB
ma-24	98	3	the	the	DET
ma-24	98	4	relation	relation	NOUN
ma-24	98	5	given	give	VERB
ma-24	98	6	in	in	ADP
ma-24	98	7	(	(	PUNCT
ma-24	98	8	15	15	NUM
ma-24	98	9	)	)	PUNCT
ma-24	98	10	on	on	ADP
ma-24	98	11	the	the	DET
ma-24	98	12	first	first	ADJ
ma-24	98	13	prolongation	prolongation	NOUN
ma-24	98	14	group	group	NOUN
ma-24	98	15	g[1	g[1	PROPN
ma-24	98	16	]	]	PUNCT
ma-24	98	17	given	give	VERB
ma-24	98	18	bydefinition	bydefinition	NOUN
ma-24	98	19	2.6	2.6	NUM
ma-24	98	20	,	,	PUNCT
ma-24	98	21	we	we	PRON
ma-24	98	22	obtain	obtain	VERB
ma-24	98	23	[	[	PUNCT
ma-24	98	24	5	5	NUM
ma-24	98	25	]	]	PUNCT
ma-24	98	26	di(x	di(x	NUM
ma-24	98	27	j	j	PROPN
ma-24	98	28	+	+	NUM
ma-24	98	29	ξjε)(uαj	ξjε)(uαj	PROPN
ma-24	98	30	+	+	CCONJ
ma-24	98	31	ζαj	ζαj	PROPN
ma-24	98	32	ε	ε	PROPN
ma-24	98	33	)	)	PUNCT
ma-24	98	34	=	=	NOUN
ma-24	98	35	di(u	di(u	X
ma-24	98	36	α	α	NOUN
ma-24	98	37	+	+	CCONJ
ma-24	98	38	ηαε	ηαε	ADJ
ma-24	98	39	)	)	PUNCT
ma-24	98	40	,	,	PUNCT
ma-24	98	41	which	which	PRON
ma-24	98	42	gives	give	VERB
ma-24	98	43	uαi	uαi	ADP
ma-24	98	44	+	+	X
ma-24	98	45	ζαj	ζαj	X
ma-24	98	46	ε+	ε+	X
ma-24	98	47	uαj	uαj	PROPN
ma-24	98	48	εdiξ	εdiξ	PROPN
ma-24	98	49	j	j	PROPN
ma-24	99	1	=	=	PRON
ma-24	99	2	uαi	uαi	PROPN
ma-24	99	3	+	+	ADJ
ma-24	99	4	diη	diη	NOUN
ma-24	99	5	αε,(19	αε,(19	NUM
ma-24	99	6	)	)	PUNCT
ma-24	99	7	and	and	CCONJ
ma-24	99	8	thus	thus	ADV
ma-24	99	9	ζαi	ζαi	VERB
ma-24	99	10	=	=	NOUN
ma-24	99	11	di(η	di(η	PART
ma-24	99	12	α)−	α)−	NOUN
ma-24	99	13	uαj	uαj	VERB
ma-24	99	14	di(ξj	di(ξj	NOUN
ma-24	99	15	)	)	PUNCT
ma-24	99	16	,	,	PUNCT
ma-24	99	17	(	(	PUNCT
ma-24	99	18	20	20	NUM
ma-24	99	19	)	)	PUNCT
ma-24	99	20	is	be	AUX
ma-24	99	21	the	the	DET
ma-24	99	22	first	first	ADJ
ma-24	99	23	prolongation	prolongation	NOUN
ma-24	99	24	formula	formula	NOUN
ma-24	99	25	.	.	PUNCT
ma-24	100	1	remark	remark	PROPN
ma-24	100	2	2.10	2.10	NUM
ma-24	100	3	.	.	PUNCT
ma-24	101	1	similarly	similarly	ADV
ma-24	101	2	,	,	PUNCT
ma-24	101	3	we	we	PRON
ma-24	101	4	get	get	VERB
ma-24	101	5	higher	high	ADJ
ma-24	101	6	order	order	NOUN
ma-24	101	7	prolongations	prolongation	NOUN
ma-24	101	8	[	[	X
ma-24	101	9	8	8	NUM
ma-24	101	10	]	]	PUNCT
ma-24	101	11	,	,	PUNCT
ma-24	101	12	ζαij	ζαij	NOUN
ma-24	101	13	=	=	SYM
ma-24	101	14	dj(ζ	dj(ζ	X
ma-24	101	15	α	α	NOUN
ma-24	101	16	i	i	NOUN
ma-24	101	17	)	)	PUNCT
ma-24	101	18	−	−	PROPN
ma-24	101	19	uαiκdj(ξκ	uαiκdj(ξκ	NOUN
ma-24	101	20	)	)	PUNCT
ma-24	101	21	,	,	PUNCT
ma-24	101	22	.	.	PUNCT
ma-24	101	23	.	.	PUNCT
ma-24	102	1	.	.	PUNCT
ma-24	103	1	,	,	PUNCT
ma-24	103	2	ζαi1,	ζαi1,	PRON
ma-24	103	3	...	...	PUNCT
ma-24	103	4	,iκ	,iκ	SYM
ma-24	104	1	=	=	SYM
ma-24	104	2	diκ(ζαi1,	diκ(ζαi1,	NOUN
ma-24	104	3	...	...	PUNCT
ma-24	104	4	,iκ−1	,iκ−1	NUM
ma-24	104	5	)	)	PUNCT
ma-24	104	6	−	−	PROPN
ma-24	105	1	uαi1,i2,	uαi1,i2,	PROPN
ma-24	105	2	...	...	PUNCT
ma-24	105	3	,iκ−1j	,iκ−1j	PUNCT
ma-24	105	4	diκ(ξj	diκ(ξj	NOUN
ma-24	105	5	)	)	PUNCT
ma-24	105	6	.	.	PUNCT
ma-24	106	1	(	(	PUNCT
ma-24	106	2	21	21	NUM
ma-24	106	3	)	)	PUNCT
ma-24	106	4	remark	remark	NOUN
ma-24	106	5	2.11	2.11	NUM
ma-24	106	6	.	.	PUNCT
ma-24	107	1	the	the	DET
ma-24	107	2	prolonged	prolonged	ADJ
ma-24	107	3	generators	generator	NOUN
ma-24	107	4	of	of	ADP
ma-24	107	5	the	the	DET
ma-24	107	6	prolongations	prolongation	NOUN
ma-24	107	7	g[1	g[1	PROPN
ma-24	107	8	]	]	PUNCT
ma-24	107	9	,	,	PUNCT
ma-24	107	10	.	.	PUNCT
ma-24	107	11	.	.	PUNCT
ma-24	107	12	.	.	PUNCT
ma-24	108	1	,	,	PUNCT
ma-24	108	2	g[κ	g[κ	X
ma-24	108	3	]	]	X
ma-24	108	4	of	of	ADP
ma-24	108	5	the	the	DET
ma-24	108	6	group	group	NOUN
ma-24	108	7	g	g	PROPN
ma-24	108	8	are	be	AUX
ma-24	108	9	x[1	x[1	PROPN
ma-24	108	10	]	]	X
ma-24	109	1	=	=	PUNCT
ma-24	109	2	x	x	PUNCT
ma-24	110	1	+	+	NUM
ma-24	110	2	ζαi	ζαi	NOUN
ma-24	110	3	∂	∂	X
ma-24	110	4	∂uαi	∂uαi	NUM
ma-24	110	5	,	,	PUNCT
ma-24	110	6	.	.	PUNCT
ma-24	110	7	.	.	PUNCT
ma-24	111	1	.	.	PUNCT
ma-24	112	1	,	,	PUNCT
ma-24	112	2	x[κ	x[κ	PROPN
ma-24	112	3	]	]	X
ma-24	112	4	=	=	SYM
ma-24	112	5	x[κ−1	x[κ−1	PROPN
ma-24	112	6	]	]	X
ma-24	112	7	+	+	CCONJ
ma-24	112	8	ζαi1,	ζαi1,	X
ma-24	112	9	...	...	PUNCT
ma-24	112	10	,iκ	,iκ	NUM
ma-24	112	11	∂	∂	NUM
ma-24	112	12	∂ζαi1,	∂ζαi1,	PROPN
ma-24	112	13	...	...	PUNCT
ma-24	112	14	,iκ	,iκ	PUNCT
ma-24	112	15	,	,	PUNCT
ma-24	112	16	κ	κ	X
ma-24	112	17	≥	≥	NOUN
ma-24	112	18	1	1	NUM
ma-24	112	19	,	,	PUNCT
ma-24	112	20	(	(	PUNCT
ma-24	112	21	22	22	NUM
ma-24	112	22	)	)	PUNCT
ma-24	112	23	where	where	SCONJ
ma-24	112	24	x	x	PRON
ma-24	112	25	is	be	AUX
ma-24	112	26	the	the	DET
ma-24	112	27	group	group	NOUN
ma-24	112	28	generator	generator	NOUN
ma-24	112	29	given	give	VERB
ma-24	112	30	by	by	ADP
ma-24	112	31	(	(	PUNCT
ma-24	112	32	12	12	NUM
ma-24	112	33	)	)	PUNCT
ma-24	112	34	.	.	PUNCT
ma-24	113	1	definition	definition	NOUN
ma-24	113	2	2.12	2.12	NUM
ma-24	113	3	.	.	PUNCT
ma-24	114	1	a	a	DET
ma-24	114	2	function	function	NOUN
ma-24	114	3	γ(x	γ(x	VERB
ma-24	114	4	i	i	PRON
ma-24	114	5	,	,	PUNCT
ma-24	114	6	uα	uα	PROPN
ma-24	114	7	)	)	PUNCT
ma-24	114	8	is	be	AUX
ma-24	114	9	called	call	VERB
ma-24	114	10	an	an	DET
ma-24	114	11	invariant	invariant	NOUN
ma-24	114	12	of	of	ADP
ma-24	114	13	the	the	DET
ma-24	114	14	group	group	NOUN
ma-24	114	15	g	g	NOUN
ma-24	114	16	of	of	ADP
ma-24	114	17	transformations	transformation	NOUN
ma-24	114	18	givenby	givenby	NOUN
ma-24	114	19	(	(	PUNCT
ma-24	114	20	4	4	NUM
ma-24	114	21	)	)	PUNCT
ma-24	114	22	if	if	SCONJ
ma-24	114	23	γ(x̄	γ(x̄	NUM
ma-24	114	24	i	i	PRON
ma-24	114	25	,	,	PUNCT
ma-24	114	26	ūα	ūα	PROPN
ma-24	114	27	)	)	PUNCT
ma-24	114	28	=	=	PUNCT
ma-24	115	1	γ(x	γ(x	NOUN
ma-24	115	2	i	i	PRON
ma-24	115	3	,	,	PUNCT
ma-24	115	4	uα	uα	PROPN
ma-24	115	5	)	)	PUNCT
ma-24	115	6	.	.	PUNCT
ma-24	116	1	(	(	PUNCT
ma-24	116	2	23	23	NUM
ma-24	116	3	)	)	PUNCT
ma-24	116	4	theorem	theorem	VERB
ma-24	116	5	2.13	2.13	NUM
ma-24	116	6	.	.	PUNCT
ma-24	117	1	a	a	DET
ma-24	117	2	function	function	NOUN
ma-24	117	3	γ(x	γ(x	VERB
ma-24	117	4	i	i	PRON
ma-24	117	5	,	,	PUNCT
ma-24	117	6	uα	uα	PROPN
ma-24	117	7	)	)	PUNCT
ma-24	117	8	is	be	AUX
ma-24	117	9	an	an	DET
ma-24	117	10	invariant	invariant	NOUN
ma-24	117	11	of	of	ADP
ma-24	117	12	the	the	DET
ma-24	117	13	group	group	NOUN
ma-24	117	14	g	g	NOUN
ma-24	117	15	given	give	VERB
ma-24	117	16	by	by	ADP
ma-24	117	17	(	(	PUNCT
ma-24	117	18	4	4	NUM
ma-24	117	19	)	)	PUNCT
ma-24	117	20	if	if	SCONJ
ma-24	118	1	and	and	CCONJ
ma-24	118	2	only	only	ADV
ma-24	118	3	if	if	SCONJ
ma-24	118	4	it	it	PRON
ma-24	118	5	solves	solve	VERB
ma-24	118	6	the	the	DET
ma-24	118	7	following	follow	VERB
ma-24	118	8	first	first	ADJ
ma-24	118	9	-	-	PUNCT
ma-24	118	10	order	order	NOUN
ma-24	118	11	linear	linear	ADJ
ma-24	118	12	pde	pde	NOUN
ma-24	118	13	:	:	PUNCT
ma-24	119	1	[	[	X
ma-24	119	2	5	5	NUM
ma-24	119	3	]	]	SYM
ma-24	119	4	xγ	xγ	PROPN
ma-24	119	5	=	=	SYM
ma-24	119	6	ξi(x	ξi(x	PROPN
ma-24	120	1	i	i	PRON
ma-24	120	2	,	,	PUNCT
ma-24	120	3	uα	uα	PROPN
ma-24	120	4	)	)	PUNCT
ma-24	120	5	∂γ	∂γ	NOUN
ma-24	121	1	∂x	∂x	NOUN
ma-24	121	2	i	i	PRON
ma-24	121	3	+	+	CCONJ
ma-24	121	4	ηα(x	ηα(x	VERB
ma-24	121	5	i	i	PRON
ma-24	121	6	,	,	PUNCT
ma-24	121	7	uα	uα	PROPN
ma-24	121	8	)	)	PUNCT
ma-24	121	9	∂γ	∂γ	PROPN
ma-24	121	10	∂uα	∂uα	NOUN
ma-24	121	11	=	=	SYM
ma-24	121	12	0	0	X
ma-24	121	13	.	.	PUNCT
ma-24	122	1	(	(	PUNCT
ma-24	122	2	24	24	NUM
ma-24	122	3	)	)	PUNCT
ma-24	122	4	from	from	ADP
ma-24	122	5	theorem	theorem	NOUN
ma-24	122	6	(	(	PUNCT
ma-24	122	7	2.13	2.13	NUM
ma-24	122	8	)	)	PUNCT
ma-24	122	9	,	,	PUNCT
ma-24	122	10	we	we	PRON
ma-24	122	11	have	have	VERB
ma-24	122	12	the	the	DET
ma-24	122	13	following	follow	VERB
ma-24	122	14	result	result	NOUN
ma-24	122	15	.	.	PUNCT
ma-24	123	1	theorem	theorem	VERB
ma-24	123	2	2.14	2.14	NUM
ma-24	123	3	.	.	PUNCT
ma-24	124	1	the	the	DET
ma-24	124	2	local	local	ADJ
ma-24	124	3	lie	lie	NOUN
ma-24	124	4	group	group	NOUN
ma-24	124	5	g	g	NOUN
ma-24	124	6	of	of	ADP
ma-24	124	7	transformations	transformation	NOUN
ma-24	124	8	in	in	ADP
ma-24	124	9	rn	rn	NOUN
ma-24	124	10	given	give	VERB
ma-24	124	11	by	by	ADP
ma-24	124	12	(	(	PUNCT
ma-24	124	13	4	4	NUM
ma-24	124	14	)	)	PUNCT
ma-24	124	15	[	[	X
ma-24	124	16	7	7	X
ma-24	124	17	]	]	PUNCT
ma-24	124	18	has	have	VERB
ma-24	124	19	precisely	precisely	ADV
ma-24	124	20	n−	n−	NOUN
ma-24	124	21	1	1	NUM
ma-24	124	22	functionally	functionally	ADV
ma-24	124	23	independent	independent	ADJ
ma-24	124	24	invariants	invariant	NOUN
ma-24	124	25	.	.	PUNCT
ma-24	125	1	one	one	PRON
ma-24	125	2	can	can	AUX
ma-24	125	3	take	take	VERB
ma-24	125	4	,	,	PUNCT
ma-24	125	5	as	as	ADP
ma-24	125	6	the	the	DET
ma-24	125	7	basic	basic	ADJ
ma-24	125	8	invariants	invariant	NOUN
ma-24	125	9	,	,	PUNCT
ma-24	125	10	the	the	DET
ma-24	125	11	left	left	ADJ
ma-24	125	12	-	-	PUNCT
ma-24	125	13	hand	hand	NOUN
ma-24	125	14	sides	side	NOUN
ma-24	125	15	of	of	ADP
ma-24	125	16	the	the	DET
ma-24	125	17	first	first	ADJ
ma-24	125	18	integrals	integral	NOUN
ma-24	125	19	ψ1(x	ψ1(x	VERB
ma-24	125	20	i	i	PRON
ma-24	125	21	,	,	PUNCT
ma-24	125	22	uα	uα	NOUN
ma-24	125	23	)	)	PUNCT
ma-24	125	24	=	=	SYM
ma-24	125	25	c1	c1	PROPN
ma-24	125	26	,	,	PUNCT
ma-24	125	27	.	.	PUNCT
ma-24	125	28	.	.	PUNCT
ma-24	126	1	.	.	PUNCT
ma-24	127	1	,	,	PUNCT
ma-24	127	2	ψn−1(x	ψn−1(x	VERB
ma-24	127	3	i	i	PRON
ma-24	127	4	,	,	PUNCT
ma-24	127	5	uα	uα	PROPN
ma-24	127	6	)	)	PUNCT
ma-24	127	7	=	=	SYM
ma-24	127	8	cn−1	cn−1	PROPN
ma-24	127	9	,	,	PUNCT
ma-24	127	10	(	(	PUNCT
ma-24	127	11	25	25	NUM
ma-24	127	12	)	)	PUNCT
ma-24	127	13	of	of	ADP
ma-24	127	14	the	the	DET
ma-24	127	15	characteristic	characteristic	ADJ
ma-24	127	16	equations	equation	NOUN
ma-24	127	17	for	for	ADP
ma-24	127	18	(	(	PUNCT
ma-24	127	19	24	24	NUM
ma-24	127	20	):	):	PUNCT
ma-24	127	21	dx	dx	PROPN
ma-24	128	1	i	i	PRON
ma-24	128	2	ξi(x	ξi(x	VERB
ma-24	128	3	i	i	PRON
ma-24	128	4	,	,	PUNCT
ma-24	128	5	uα	uα	PROPN
ma-24	128	6	)	)	PUNCT
ma-24	128	7	=	=	SYM
ma-24	128	8	duα	duα	NOUN
ma-24	128	9	ηα(x	ηα(x	PUNCT
ma-24	128	10	i	i	PRON
ma-24	128	11	,	,	PUNCT
ma-24	128	12	uα	uα	PROPN
ma-24	128	13	)	)	PUNCT
ma-24	128	14	.	.	PUNCT
ma-24	129	1	(	(	PUNCT
ma-24	129	2	26	26	NUM
ma-24	129	3	)	)	PUNCT
ma-24	129	4	eur	eur	PROPN
ma-24	129	5	.	.	PUNCT
ma-24	130	1	j.	j.	PROPN
ma-24	130	2	math	math	PROPN
ma-24	130	3	.	.	PUNCT
ma-24	131	1	anal	anal	ADJ
ma-24	131	2	.	.	PUNCT
ma-24	132	1	1	1	NUM
ma-24	132	2	(	(	PUNCT
ma-24	132	3	2021	2021	NUM
ma-24	132	4	)	)	PUNCT
ma-24	132	5	137	137	NUM
ma-24	132	6	definition	definition	NOUN
ma-24	132	7	2.15	2.15	NUM
ma-24	132	8	.	.	PUNCT
ma-24	133	1	the	the	DET
ma-24	133	2	vector	vector	NOUN
ma-24	133	3	field	field	NOUN
ma-24	133	4	x	x	SYM
ma-24	133	5	(	(	PUNCT
ma-24	133	6	12	12	NUM
ma-24	133	7	)	)	PUNCT
ma-24	133	8	is	be	AUX
ma-24	133	9	a	a	DET
ma-24	133	10	lie	lie	NOUN
ma-24	133	11	point	point	NOUN
ma-24	133	12	symmetry	symmetry	NOUN
ma-24	133	13	of	of	ADP
ma-24	133	14	the	the	DET
ma-24	133	15	pde	pde	NOUN
ma-24	133	16	system	system	NOUN
ma-24	133	17	(	(	PUNCT
ma-24	133	18	5	5	X
ma-24	133	19	)	)	PUNCT
ma-24	133	20	if	if	SCONJ
ma-24	133	21	thedetermining	thedetermining	NOUN
ma-24	133	22	equations	equation	NOUN
ma-24	133	23	x[π]∆α	x[π]∆α	PROPN
ma-24	133	24	∣∣∣	∣∣∣	NOUN
ma-24	133	25	∆α=0	∆α=0	PROPN
ma-24	133	26	=	=	SYM
ma-24	133	27	0	0	PROPN
ma-24	133	28	,	,	PUNCT
ma-24	133	29	α	α	NOUN
ma-24	133	30	=	=	SYM
ma-24	133	31	1	1	NUM
ma-24	133	32	,	,	PUNCT
ma-24	133	33	.	.	PUNCT
ma-24	133	34	.	.	PUNCT
ma-24	133	35	.	.	PUNCT
ma-24	134	1	,	,	PUNCT
ma-24	134	2	m	m	PROPN
ma-24	134	3	,	,	PUNCT
ma-24	134	4	π	π	PROPN
ma-24	134	5	≥	≥	NUM
ma-24	134	6	1	1	NUM
ma-24	134	7	,	,	PUNCT
ma-24	134	8	(	(	PUNCT
ma-24	134	9	27	27	NUM
ma-24	134	10	)	)	PUNCT
ma-24	134	11	are	be	AUX
ma-24	134	12	satisfied	satisfied	ADJ
ma-24	134	13	,	,	PUNCT
ma-24	134	14	where	where	SCONJ
ma-24	134	15	∣∣∣	∣∣∣	ADJ
ma-24	134	16	∆α=0	∆α=0	PROPN
ma-24	134	17	means	mean	VERB
ma-24	134	18	evaluated	evaluate	VERB
ma-24	134	19	on	on	ADP
ma-24	134	20	∆α	∆α	PROPN
ma-24	134	21	=	=	SYM
ma-24	134	22	0	0	NUM
ma-24	134	23	and	and	CCONJ
ma-24	134	24	x[π	x[π	PROPN
ma-24	134	25	]	]	X
ma-24	134	26	is	be	AUX
ma-24	134	27	the	the	DET
ma-24	134	28	π	π	PROPN
ma-24	134	29	-	-	PUNCT
ma-24	134	30	th	th	VERB
ma-24	134	31	prolongation	prolongation	NOUN
ma-24	134	32	of	of	ADP
ma-24	134	33	x	x	X
ma-24	134	34	.	.	PUNCT
ma-24	135	1	definition	definition	NOUN
ma-24	135	2	2.16	2.16	NUM
ma-24	135	3	.	.	PUNCT
ma-24	136	1	the	the	DET
ma-24	136	2	lie	lie	NOUN
ma-24	136	3	group	group	NOUN
ma-24	136	4	g	g	PROPN
ma-24	136	5	is	be	AUX
ma-24	136	6	a	a	DET
ma-24	136	7	symmetry	symmetry	NOUN
ma-24	136	8	group	group	NOUN
ma-24	136	9	of	of	ADP
ma-24	136	10	the	the	DET
ma-24	136	11	pde	pde	NOUN
ma-24	136	12	system	system	NOUN
ma-24	136	13	given	give	VERB
ma-24	136	14	in	in	ADP
ma-24	136	15	(	(	PUNCT
ma-24	136	16	5	5	NUM
ma-24	136	17	)	)	PUNCT
ma-24	136	18	if	if	SCONJ
ma-24	136	19	the	the	DET
ma-24	136	20	pdesystem	pdesystem	NOUN
ma-24	136	21	(	(	PUNCT
ma-24	136	22	5	5	NUM
ma-24	136	23	)	)	PUNCT
ma-24	136	24	is	be	AUX
ma-24	136	25	form	form	NOUN
ma-24	136	26	-	-	PUNCT
ma-24	136	27	invariant	invariant	ADJ
ma-24	136	28	,	,	PUNCT
ma-24	136	29	that	that	PRON
ma-24	136	30	is	be	AUX
ma-24	136	31	∆α	∆α	PROPN
ma-24	137	1	(	(	PUNCT
ma-24	137	2	x̄	x̄	NOUN
ma-24	137	3	i	i	PRON
ma-24	137	4	,	,	PUNCT
ma-24	137	5	ūα	ūα	PROPN
ma-24	137	6	,	,	PUNCT
ma-24	137	7	ū(1	ū(1	NUM
ma-24	137	8	)	)	PUNCT
ma-24	137	9	,	,	PUNCT
ma-24	137	10	.	.	PUNCT
ma-24	137	11	.	.	PUNCT
ma-24	137	12	.	.	PUNCT
ma-24	138	1	,	,	PUNCT
ma-24	138	2	ū(π	ū(π	PROPN
ma-24	138	3	)	)	PUNCT
ma-24	138	4	)	)	PUNCT
ma-24	139	1	=	=	PUNCT
ma-24	139	2	0	0	X
ma-24	139	3	.	.	PUNCT
ma-24	140	1	(	(	PUNCT
ma-24	140	2	28	28	NUM
ma-24	140	3	)	)	PUNCT
ma-24	140	4	theorem	theorem	VERB
ma-24	140	5	2.17	2.17	NUM
ma-24	140	6	.	.	PUNCT
ma-24	141	1	given	give	VERB
ma-24	141	2	the	the	DET
ma-24	141	3	infinitesimal	infinitesimal	ADJ
ma-24	141	4	transformations	transformation	NOUN
ma-24	141	5	in	in	ADP
ma-24	141	6	(	(	PUNCT
ma-24	141	7	8)	8)	NUM
ma-24	141	8	,	,	PUNCT
ma-24	141	9	the	the	DET
ma-24	141	10	lie	lie	NOUN
ma-24	141	11	group	group	NOUN
ma-24	141	12	g	g	PROPN
ma-24	141	13	in	in	ADP
ma-24	141	14	(	(	PUNCT
ma-24	141	15	4	4	NUM
ma-24	141	16	)	)	PUNCT
ma-24	141	17	is	be	AUX
ma-24	141	18	found	find	VERB
ma-24	141	19	by	by	ADP
ma-24	141	20	integrating	integrate	VERB
ma-24	141	21	the	the	DET
ma-24	141	22	lie	lie	NOUN
ma-24	141	23	equations	equation	NOUN
ma-24	141	24	dx̄	dx̄	VERB
ma-24	141	25	i	i	PRON
ma-24	141	26	dε	dε	VERB
ma-24	141	27	=	=	VERB
ma-24	141	28	ξi(x̄	ξi(x̄	VERB
ma-24	141	29	i	i	PRON
ma-24	141	30	,	,	PUNCT
ma-24	141	31	ūα	ūα	PROPN
ma-24	141	32	)	)	PUNCT
ma-24	141	33	,	,	PUNCT
ma-24	141	34	x̄	x̄	NUM
ma-24	141	35	i	i	PRON
ma-24	141	36	∣∣∣	∣∣∣	VERB
ma-24	141	37	ε=0	ε=0	X
ma-24	141	38	=	=	PUNCT
ma-24	141	39	x	x	SYM
ma-24	141	40	i	i	PROPN
ma-24	141	41	,	,	PUNCT
ma-24	141	42	dūα	dūα	NOUN
ma-24	141	43	dε	dε	NOUN
ma-24	141	44	=	=	SYM
ma-24	141	45	ηα(x̄	ηα(x̄	INTJ
ma-24	141	46	i	i	PRON
ma-24	141	47	,	,	PUNCT
ma-24	141	48	ūα	ūα	PROPN
ma-24	141	49	)	)	PUNCT
ma-24	141	50	,	,	PUNCT
ma-24	141	51	ūα	ūα	NOUN
ma-24	141	52	∣∣∣	∣∣∣	NOUN
ma-24	141	53	ε=0	ε=0	PROPN
ma-24	141	54	=	=	SYM
ma-24	141	55	uα	uα	PROPN
ma-24	141	56	.	.	PUNCT
ma-24	142	1	(	(	PUNCT
ma-24	142	2	29	29	NUM
ma-24	142	3	)	)	PUNCT
ma-24	142	4	definition	definition	NOUN
ma-24	142	5	2.18	2.18	NUM
ma-24	142	6	.	.	PUNCT
ma-24	143	1	a	a	DET
ma-24	143	2	vector	vector	NOUN
ma-24	143	3	space	space	NOUN
ma-24	143	4	vr	vr	NOUN
ma-24	143	5	of	of	ADP
ma-24	143	6	operators	operator	NOUN
ma-24	143	7	[	[	X
ma-24	143	8	5	5	X
ma-24	143	9	]	]	SYM
ma-24	143	10	x	x	X
ma-24	143	11	(	(	PUNCT
ma-24	143	12	12	12	NUM
ma-24	143	13	)	)	PUNCT
ma-24	143	14	is	be	AUX
ma-24	143	15	a	a	DET
ma-24	143	16	lie	lie	NOUN
ma-24	143	17	algebra	algebra	NOUN
ma-24	143	18	if	if	SCONJ
ma-24	143	19	for	for	ADP
ma-24	143	20	any	any	DET
ma-24	143	21	two	two	NUM
ma-24	143	22	operators	operator	NOUN
ma-24	143	23	,	,	PUNCT
ma-24	143	24	xi	xi	PROPN
ma-24	143	25	,	,	PUNCT
ma-24	143	26	xj	xj	PROPN
ma-24	143	27	∈	∈	PROPN
ma-24	143	28	vr	vr	PROPN
ma-24	143	29	,	,	PUNCT
ma-24	143	30	their	their	PRON
ma-24	143	31	commutator	commutator	NOUN
ma-24	144	1	[	[	X
ma-24	144	2	xi	xi	X
ma-24	144	3	,	,	PUNCT
ma-24	144	4	xj	xj	PROPN
ma-24	144	5	]	]	PUNCT
ma-24	144	6	=	=	PUNCT
ma-24	144	7	xixj	xixj	PROPN
ma-24	144	8	−xjxi	−xjxi	PROPN
ma-24	144	9	,	,	PUNCT
ma-24	144	10	(	(	PUNCT
ma-24	144	11	30	30	NUM
ma-24	144	12	)	)	PUNCT
ma-24	144	13	is	be	AUX
ma-24	144	14	in	in	ADP
ma-24	144	15	vr	vr	NOUN
ma-24	144	16	for	for	ADP
ma-24	144	17	all	all	DET
ma-24	144	18	i	i	PRON
ma-24	144	19	,	,	PUNCT
ma-24	144	20	j	j	PROPN
ma-24	144	21	=	=	SYM
ma-24	144	22	1	1	NUM
ma-24	144	23	,	,	PUNCT
ma-24	144	24	.	.	PUNCT
ma-24	144	25	.	.	PUNCT
ma-24	145	1	.	.	PUNCT
ma-24	146	1	,	,	PUNCT
ma-24	146	2	r	r	NOUN
ma-24	146	3	.	.	PUNCT
ma-24	146	4	remark	remark	PROPN
ma-24	146	5	2.19	2.19	NUM
ma-24	146	6	.	.	PUNCT
ma-24	147	1	the	the	DET
ma-24	147	2	commutator	commutator	NOUN
ma-24	147	3	satisfies	satisfy	VERB
ma-24	147	4	the	the	DET
ma-24	147	5	properties	property	NOUN
ma-24	147	6	of	of	ADP
ma-24	147	7	bilinearity	bilinearity	NOUN
ma-24	147	8	,	,	PUNCT
ma-24	147	9	skew	skew	ADJ
ma-24	147	10	symmetry	symmetry	NOUN
ma-24	147	11	and	and	CCONJ
ma-24	147	12	the	the	DET
ma-24	147	13	jacobiidentity	jacobiidentity	NOUN
ma-24	148	1	[	[	X
ma-24	148	2	5	5	NUM
ma-24	148	3	]	]	PUNCT
ma-24	148	4	.	.	PUNCT
ma-24	149	1	theorem	theorem	VERB
ma-24	149	2	2.20	2.20	NUM
ma-24	149	3	.	.	PUNCT
ma-24	150	1	the	the	DET
ma-24	150	2	set	set	NOUN
ma-24	150	3	of	of	ADP
ma-24	150	4	solutions	solution	NOUN
ma-24	150	5	of	of	ADP
ma-24	150	6	the	the	DET
ma-24	150	7	determining	determine	VERB
ma-24	150	8	equation	equation	NOUN
ma-24	150	9	given	give	VERB
ma-24	150	10	by	by	ADP
ma-24	150	11	(	(	PUNCT
ma-24	150	12	27	27	NUM
ma-24	150	13	)	)	PUNCT
ma-24	150	14	forms	form	VERB
ma-24	150	15	a	a	DET
ma-24	150	16	lie	lie	NOUN
ma-24	150	17	algebra	algebra	NOUN
ma-24	150	18	[	[	X
ma-24	150	19	5	5	NUM
ma-24	150	20	]	]	PUNCT
ma-24	150	21	.	.	PUNCT
ma-24	151	1	the	the	DET
ma-24	151	2	methods	method	NOUN
ma-24	151	3	of	of	ADP
ma-24	151	4	(	(	PUNCT
ma-24	151	5	g’/g)-expansion	g’/g)-expansion	NOUN
ma-24	151	6	method	method	NOUN
ma-24	151	7	[	[	X
ma-24	151	8	20	20	NUM
ma-24	151	9	]	]	PUNCT
ma-24	151	10	,	,	PUNCT
ma-24	151	11	extended	extend	VERB
ma-24	151	12	jacobi	jacobi	PROPN
ma-24	151	13	elliptic	elliptic	ADJ
ma-24	151	14	function	function	NOUN
ma-24	151	15	expansion	expansion	NOUN
ma-24	152	1	[	[	X
ma-24	152	2	21]and	21]and	NUM
ma-24	152	3	kudryashov	kudryashov	ADJ
ma-24	152	4	[	[	X
ma-24	152	5	22	22	NUM
ma-24	152	6	]	]	PUNCT
ma-24	152	7	are	be	AUX
ma-24	152	8	usually	usually	ADV
ma-24	152	9	applied	apply	VERB
ma-24	152	10	after	after	ADP
ma-24	152	11	symmetry	symmetry	NOUN
ma-24	152	12	reductions	reduction	NOUN
ma-24	152	13	.	.	PUNCT
ma-24	153	1	let	let	VERB
ma-24	153	2	a	a	DET
ma-24	153	3	system	system	NOUN
ma-24	153	4	of	of	ADP
ma-24	153	5	πth	πth	NOUN
ma-24	153	6	-	-	PUNCT
ma-24	153	7	orderpdes	orderpde	NOUN
ma-24	153	8	be	be	AUX
ma-24	153	9	given	give	VERB
ma-24	153	10	by	by	ADP
ma-24	153	11	(	(	PUNCT
ma-24	153	12	5	5	NUM
ma-24	153	13	)	)	PUNCT
ma-24	153	14	.	.	PUNCT
ma-24	154	1	definition	definition	NOUN
ma-24	154	2	2.21	2.21	NUM
ma-24	154	3	.	.	PUNCT
ma-24	155	1	the	the	DET
ma-24	155	2	euler	euler	NOUN
ma-24	155	3	-	-	PUNCT
ma-24	155	4	lagrange	lagrange	NOUN
ma-24	155	5	operator	operator	NOUN
ma-24	155	6	δ	δ	PROPN
ma-24	155	7	/	/	SYM
ma-24	155	8	δuα	δuα	PROPN
ma-24	155	9	is	be	AUX
ma-24	155	10	δ	δ	PROPN
ma-24	155	11	δuα	δuα	NOUN
ma-24	155	12	=	=	SYM
ma-24	155	13	∂	∂	NOUN
ma-24	155	14	∂uα	∂uα	NOUN
ma-24	155	15	+	+	CCONJ
ma-24	155	16	∑	∑	PROPN
ma-24	155	17	κ≥1	κ≥1	PROPN
ma-24	155	18	(	(	PUNCT
ma-24	155	19	−1)κdi1	−1)κdi1	ADV
ma-24	155	20	,	,	PUNCT
ma-24	155	21	.	.	PUNCT
ma-24	155	22	.	.	PUNCT
ma-24	156	1	.	.	PUNCT
ma-24	157	1	,	,	PUNCT
ma-24	157	2	diκ	diκ	NOUN
ma-24	157	3	∂	∂	NUM
ma-24	157	4	∂uαi1i2	∂uαi1i2	NOUN
ma-24	157	5	...	...	PUNCT
ma-24	157	6	iκ	iκ	NOUN
ma-24	157	7	,	,	PUNCT
ma-24	157	8	(	(	PUNCT
ma-24	157	9	31	31	NUM
ma-24	157	10	)	)	PUNCT
ma-24	157	11	and	and	CCONJ
ma-24	157	12	the	the	DET
ma-24	157	13	liebäcklund	liebäcklund	ADJ
ma-24	157	14	operator	operator	NOUN
ma-24	157	15	in	in	ADP
ma-24	157	16	abbreviated	abbreviate	VERB
ma-24	157	17	form	form	NOUN
ma-24	158	1	[	[	X
ma-24	158	2	5	5	NUM
ma-24	158	3	]	]	PUNCT
ma-24	158	4	is	be	AUX
ma-24	158	5	x	x	X
ma-24	158	6	=	=	SYM
ma-24	158	7	ξi	ξi	NOUN
ma-24	158	8	∂	∂	NOUN
ma-24	158	9	∂x	∂x	PROPN
ma-24	159	1	i	i	PRON
ma-24	159	2	+	+	NUM
ma-24	159	3	ηα	ηα	PROPN
ma-24	159	4	∂	∂	NOUN
ma-24	159	5	∂uα	∂uα	PROPN
ma-24	159	6	+	+	X
ma-24	159	7	.	.	PUNCT
ma-24	159	8	.	.	PUNCT
ma-24	159	9	.	.	PUNCT
ma-24	159	10	.	.	PUNCT
ma-24	160	1	(	(	PUNCT
ma-24	160	2	32	32	NUM
ma-24	160	3	)	)	PUNCT
ma-24	160	4	remark	remark	NOUN
ma-24	160	5	2.22	2.22	NUM
ma-24	160	6	.	.	PUNCT
ma-24	161	1	the	the	DET
ma-24	161	2	liebäcklund	liebäcklund	ADJ
ma-24	161	3	operator	operator	NOUN
ma-24	161	4	(	(	PUNCT
ma-24	161	5	32	32	NUM
ma-24	161	6	)	)	PUNCT
ma-24	161	7	in	in	ADP
ma-24	161	8	its	its	PRON
ma-24	161	9	prolonged	prolonged	ADJ
ma-24	161	10	form	form	NOUN
ma-24	161	11	is	be	AUX
ma-24	161	12	x	x	X
ma-24	161	13	=	=	NOUN
ma-24	161	14	ξi	ξi	NOUN
ma-24	161	15	∂	∂	NOUN
ma-24	161	16	∂x	∂x	PROPN
ma-24	162	1	i	i	PRON
ma-24	162	2	+	+	NUM
ma-24	162	3	ηα	ηα	PROPN
ma-24	162	4	∂	∂	NOUN
ma-24	162	5	∂uα	∂uα	NOUN
ma-24	162	6	+	+	CCONJ
ma-24	162	7	∑	∑	PROPN
ma-24	162	8	κ≥1	κ≥1	PROPN
ma-24	162	9	ζi1	ζi1	NOUN
ma-24	162	10	...	...	PUNCT
ma-24	162	11	iκ	iκ	NOUN
ma-24	162	12	∂	∂	NUM
ma-24	162	13	∂uαi1i2	∂uαi1i2	NOUN
ma-24	162	14	...	...	PUNCT
ma-24	162	15	iκ	iκ	NOUN
ma-24	162	16	,	,	PUNCT
ma-24	162	17	(	(	PUNCT
ma-24	162	18	33	33	NUM
ma-24	162	19	)	)	PUNCT
ma-24	162	20	eur	eur	PROPN
ma-24	162	21	.	.	PUNCT
ma-24	163	1	j.	j.	PROPN
ma-24	163	2	math	math	PROPN
ma-24	163	3	.	.	PUNCT
ma-24	164	1	anal	anal	ADJ
ma-24	164	2	.	.	PUNCT
ma-24	165	1	1	1	NUM
ma-24	165	2	(	(	PUNCT
ma-24	165	3	2021	2021	NUM
ma-24	165	4	)	)	PUNCT
ma-24	166	1	138where	138where	NUM
ma-24	166	2	ζαi	ζαi	NOUN
ma-24	166	3	=	=	SYM
ma-24	166	4	di(w	di(w	X
ma-24	166	5	α	α	X
ma-24	166	6	)	)	PUNCT
ma-24	166	7	+	+	CCONJ
ma-24	166	8	ξjuαij	ξjuαij	ADJ
ma-24	166	9	,	,	PUNCT
ma-24	166	10	.	.	PUNCT
ma-24	166	11	.	.	PUNCT
ma-24	166	12	.	.	PUNCT
ma-24	167	1	,	,	PUNCT
ma-24	167	2	ζαi1	ζαi1	PROPN
ma-24	167	3	...	...	PUNCT
ma-24	167	4	iκ	iκ	NOUN
ma-24	167	5	=	=	NOUN
ma-24	167	6	di1	di1	NOUN
ma-24	167	7	...	...	PUNCT
ma-24	167	8	iκ(wα	iκ(wα	PROPN
ma-24	167	9	)	)	PUNCT
ma-24	168	1	+	+	NUM
ma-24	168	2	ξjuαji1	ξjuαji1	NOUN
ma-24	168	3	...	...	PUNCT
ma-24	168	4	iκ	iκ	INTJ
ma-24	168	5	,	,	PUNCT
ma-24	168	6	j	j	PROPN
ma-24	168	7	=	=	NOUN
ma-24	168	8	1	1	NUM
ma-24	168	9	,	,	PUNCT
ma-24	168	10	.	.	PUNCT
ma-24	168	11	.	.	PUNCT
ma-24	168	12	.	.	PUNCT
ma-24	169	1	,	,	PUNCT
ma-24	169	2	n.	n.	PROPN
ma-24	169	3	(	(	PUNCT
ma-24	169	4	34	34	NUM
ma-24	169	5	)	)	PUNCT
ma-24	169	6	and	and	CCONJ
ma-24	169	7	the	the	DET
ma-24	169	8	lie	lie	NOUN
ma-24	169	9	characteristic	characteristic	ADJ
ma-24	169	10	function	function	NOUN
ma-24	169	11	is	be	AUX
ma-24	169	12	wα	wα	NOUN
ma-24	169	13	=	=	SYM
ma-24	169	14	ηα	ηα	PROPN
ma-24	169	15	−	−	PROPN
ma-24	169	16	ξjuαj	ξjuαj	PROPN
ma-24	169	17	.	.	PUNCT
ma-24	170	1	(	(	PUNCT
ma-24	170	2	35	35	NUM
ma-24	170	3	)	)	PUNCT
ma-24	170	4	remark	remark	NOUN
ma-24	170	5	2.23	2.23	NUM
ma-24	170	6	.	.	PUNCT
ma-24	171	1	the	the	DET
ma-24	171	2	characteristic	characteristic	ADJ
ma-24	171	3	form	form	NOUN
ma-24	171	4	of	of	ADP
ma-24	171	5	liebäcklund	liebäcklund	ADJ
ma-24	171	6	operator	operator	NOUN
ma-24	171	7	(	(	PUNCT
ma-24	171	8	33	33	NUM
ma-24	171	9	)	)	PUNCT
ma-24	171	10	is	be	AUX
ma-24	171	11	x	x	NOUN
ma-24	171	12	=	=	PUNCT
ma-24	171	13	ξidi	ξidi	NOUN
ma-24	171	14	+	+	PROPN
ma-24	171	15	wα	wα	NOUN
ma-24	171	16	∂	∂	NOUN
ma-24	171	17	∂uα	∂uα	NOUN
ma-24	171	18	+	+	NOUN
ma-24	171	19	di1	di1	ADJ
ma-24	171	20	...	...	PUNCT
ma-24	171	21	iκ(wα	iκ(wα	PROPN
ma-24	171	22	)	)	PUNCT
ma-24	171	23	∂	∂	NUM
ma-24	171	24	∂uαi1i2	∂uαi1i2	NOUN
ma-24	171	25	...	...	PUNCT
ma-24	171	26	iκ	iκ	NOUN
ma-24	171	27	.	.	PUNCT
ma-24	172	1	(	(	PUNCT
ma-24	172	2	36	36	NUM
ma-24	172	3	)	)	PUNCT
ma-24	172	4	remark	remark	NOUN
ma-24	172	5	2.24	2.24	NUM
ma-24	172	6	.	.	PUNCT
ma-24	173	1	noether	noether	PROPN
ma-24	173	2	’s	’s	PART
ma-24	173	3	theorem	theorem	NOUN
ma-24	173	4	is	be	AUX
ma-24	173	5	applicable	applicable	ADJ
ma-24	173	6	to	to	ADP
ma-24	173	7	systems	system	NOUN
ma-24	173	8	from	from	ADP
ma-24	173	9	variational	variational	ADJ
ma-24	173	10	problems	problem	NOUN
ma-24	173	11	definition	definition	NOUN
ma-24	173	12	2.25	2.25	NUM
ma-24	173	13	.	.	PUNCT
ma-24	174	1	a	a	DET
ma-24	174	2	function	function	NOUN
ma-24	174	3	λα	λα	PROPN
ma-24	175	1	(	(	PUNCT
ma-24	175	2	x	x	X
ma-24	175	3	i	i	PRON
ma-24	175	4	,	,	PUNCT
ma-24	175	5	uα	uα	PROPN
ma-24	175	6	,	,	PUNCT
ma-24	175	7	u(1	u(1	PROPN
ma-24	175	8	)	)	PUNCT
ma-24	175	9	,	,	PUNCT
ma-24	175	10	.	.	PUNCT
ma-24	175	11	.	.	PUNCT
ma-24	175	12	.	.	PUNCT
ma-24	175	13	)	)	PUNCT
ma-24	176	1	=	=	SYM
ma-24	176	2	λα	λα	PROPN
ma-24	176	3	,	,	PUNCT
ma-24	176	4	is	be	AUX
ma-24	176	5	a	a	DET
ma-24	176	6	multiplier	multipli	ADJ
ma-24	176	7	of	of	ADP
ma-24	176	8	the	the	DET
ma-24	176	9	pde	pde	NOUN
ma-24	176	10	system	system	NOUN
ma-24	176	11	given	give	VERB
ma-24	176	12	by(5	by(5	PROPN
ma-24	176	13	)	)	PUNCT
ma-24	176	14	if	if	SCONJ
ma-24	176	15	it	it	PRON
ma-24	176	16	satisfies	satisfy	VERB
ma-24	176	17	the	the	DET
ma-24	176	18	condition	condition	NOUN
ma-24	176	19	that	that	SCONJ
ma-24	176	20	[	[	X
ma-24	176	21	16	16	NUM
ma-24	176	22	]	]	X
ma-24	176	23	λα∆α	λα∆α	X
ma-24	177	1	=	=	SYM
ma-24	177	2	dit	dit	PROPN
ma-24	177	3	i	i	NOUN
ma-24	177	4	,	,	PUNCT
ma-24	177	5	(	(	PUNCT
ma-24	177	6	37	37	NUM
ma-24	177	7	)	)	PUNCT
ma-24	177	8	where	where	SCONJ
ma-24	177	9	dit	dit	NOUN
ma-24	177	10	i	i	PRON
ma-24	177	11	is	be	AUX
ma-24	177	12	a	a	DET
ma-24	177	13	divergence	divergence	NOUN
ma-24	177	14	expression	expression	NOUN
ma-24	177	15	.	.	PUNCT
ma-24	178	1	definition	definition	NOUN
ma-24	178	2	2.26	2.26	NUM
ma-24	178	3	.	.	PUNCT
ma-24	179	1	to	to	PART
ma-24	179	2	find	find	VERB
ma-24	179	3	the	the	DET
ma-24	179	4	multipliers	multiplier	NOUN
ma-24	179	5	λα	λα	PROPN
ma-24	179	6	,	,	PUNCT
ma-24	179	7	one	one	NUM
ma-24	179	8	solves	solve	VERB
ma-24	179	9	the	the	DET
ma-24	179	10	determining	determine	VERB
ma-24	179	11	equations	equation	NOUN
ma-24	179	12	(	(	PUNCT
ma-24	179	13	38	38	NUM
ma-24	179	14	)	)	PUNCT
ma-24	180	1	[	[	X
ma-24	180	2	3	3	NUM
ma-24	180	3	]	]	PUNCT
ma-24	180	4	,	,	PUNCT
ma-24	180	5	δ	δ	PROPN
ma-24	180	6	δuα	δuα	X
ma-24	180	7	(	(	PUNCT
ma-24	180	8	λα∆α	λα∆α	PROPN
ma-24	180	9	)	)	PUNCT
ma-24	180	10	=	=	SYM
ma-24	180	11	0	0	X
ma-24	180	12	.	.	PUNCT
ma-24	181	1	(	(	PUNCT
ma-24	181	2	38	38	NUM
ma-24	181	3	)	)	PUNCT
ma-24	181	4	the	the	DET
ma-24	181	5	technique	technique	NOUN
ma-24	181	6	[	[	X
ma-24	181	7	9	9	NUM
ma-24	181	8	]	]	PUNCT
ma-24	181	9	enables	enable	VERB
ma-24	181	10	one	one	NUM
ma-24	181	11	to	to	PART
ma-24	181	12	construct	construct	VERB
ma-24	181	13	conserved	conserved	ADJ
ma-24	181	14	vectors	vector	NOUN
ma-24	181	15	associated	associate	VERB
ma-24	181	16	with	with	ADP
ma-24	181	17	each	each	DET
ma-24	181	18	lie	lie	NOUN
ma-24	181	19	pointsymmetry	pointsymmetry	NOUN
ma-24	181	20	of	of	ADP
ma-24	181	21	the	the	DET
ma-24	181	22	pde	pde	NOUN
ma-24	181	23	system	system	NOUN
ma-24	181	24	given	give	VERB
ma-24	181	25	by	by	ADP
ma-24	181	26	(	(	PUNCT
ma-24	181	27	5	5	NUM
ma-24	181	28	)	)	PUNCT
ma-24	181	29	.	.	PUNCT
ma-24	182	1	definition	definition	NOUN
ma-24	182	2	2.27	2.27	NUM
ma-24	182	3	.	.	PUNCT
ma-24	183	1	the	the	DET
ma-24	183	2	adjoint	adjoint	PROPN
ma-24	183	3	equations	equation	NOUN
ma-24	183	4	of	of	ADP
ma-24	183	5	the	the	DET
ma-24	183	6	system	system	NOUN
ma-24	183	7	given	give	VERB
ma-24	183	8	by	by	ADP
ma-24	183	9	(	(	PUNCT
ma-24	183	10	5	5	NUM
ma-24	183	11	)	)	PUNCT
ma-24	183	12	are	be	AUX
ma-24	183	13	∆∗α	∆∗α	NOUN
ma-24	183	14	(	(	PUNCT
ma-24	183	15	x	x	X
ma-24	183	16	i	i	PRON
ma-24	183	17	,	,	PUNCT
ma-24	183	18	uα	uα	PROPN
ma-24	183	19	,	,	PUNCT
ma-24	183	20	vα	vα	PROPN
ma-24	183	21	,	,	PUNCT
ma-24	183	22	.	.	PUNCT
ma-24	183	23	.	.	PUNCT
ma-24	184	1	.	.	PUNCT
ma-24	185	1	,	,	PUNCT
ma-24	185	2	u(π	u(π	PROPN
ma-24	185	3	)	)	PUNCT
ma-24	185	4	,	,	PUNCT
ma-24	185	5	v(π	v(π	PROPN
ma-24	185	6	)	)	PUNCT
ma-24	185	7	)	)	PUNCT
ma-24	186	1	≡	≡	PROPN
ma-24	186	2	δ	δ	PROPN
ma-24	186	3	δuα	δuα	X
ma-24	186	4	(	(	PUNCT
ma-24	186	5	vβ∆β	vβ∆β	PROPN
ma-24	186	6	)	)	PUNCT
ma-24	186	7	=	=	SYM
ma-24	186	8	0	0	NUM
ma-24	186	9	,	,	PUNCT
ma-24	186	10	(	(	PUNCT
ma-24	186	11	39	39	NUM
ma-24	186	12	)	)	PUNCT
ma-24	186	13	where	where	SCONJ
ma-24	186	14	vα	vα	PROPN
ma-24	186	15	is	be	AUX
ma-24	186	16	the	the	DET
ma-24	186	17	new	new	ADJ
ma-24	186	18	dependent	dependent	ADJ
ma-24	186	19	variable	variable	NOUN
ma-24	186	20	.	.	PUNCT
ma-24	187	1	definition	definition	NOUN
ma-24	187	2	2.28	2.28	NUM
ma-24	187	3	.	.	PUNCT
ma-24	188	1	formal	formal	ADJ
ma-24	188	2	lagrangian	lagrangian	ADJ
ma-24	188	3	l	l	NOUN
ma-24	188	4	of	of	ADP
ma-24	188	5	the	the	DET
ma-24	188	6	system	system	NOUN
ma-24	188	7	(	(	PUNCT
ma-24	188	8	5	5	NUM
ma-24	188	9	)	)	PUNCT
ma-24	188	10	and	and	CCONJ
ma-24	188	11	its	its	PRON
ma-24	188	12	adjoint	adjoint	NOUN
ma-24	188	13	equations	equation	NOUN
ma-24	188	14	(	(	PUNCT
ma-24	188	15	39	39	NUM
ma-24	188	16	)	)	PUNCT
ma-24	188	17	is	be	AUX
ma-24	188	18	[	[	X
ma-24	188	19	9	9	NUM
ma-24	188	20	]	]	X
ma-24	188	21	l	l	NOUN
ma-24	189	1	=	=	SYM
ma-24	189	2	vα∆α(x	vα∆α(x	NOUN
ma-24	190	1	i	i	PRON
ma-24	190	2	,	,	PUNCT
ma-24	190	3	uα	uα	PROPN
ma-24	190	4	,	,	PUNCT
ma-24	190	5	u(1	u(1	PROPN
ma-24	190	6	)	)	PUNCT
ma-24	190	7	,	,	PUNCT
ma-24	190	8	.	.	PUNCT
ma-24	190	9	.	.	PUNCT
ma-24	190	10	.	.	PUNCT
ma-24	191	1	,	,	PUNCT
ma-24	191	2	u(π	u(π	PROPN
ma-24	191	3	)	)	PUNCT
ma-24	191	4	)	)	PUNCT
ma-24	191	5	.	.	PUNCT
ma-24	192	1	(	(	PUNCT
ma-24	192	2	40	40	NUM
ma-24	192	3	)	)	PUNCT
ma-24	192	4	theorem	theorem	VERB
ma-24	192	5	2.29	2.29	NUM
ma-24	192	6	.	.	PUNCT
ma-24	193	1	every	every	DET
ma-24	193	2	infinitesimal	infinitesimal	ADJ
ma-24	193	3	symmetry	symmetry	NOUN
ma-24	193	4	xof	xof	PROPN
ma-24	193	5	the	the	DET
ma-24	193	6	system	system	NOUN
ma-24	193	7	given	give	VERB
ma-24	193	8	by	by	ADP
ma-24	193	9	(	(	PUNCT
ma-24	193	10	5	5	NUM
ma-24	193	11	)	)	PUNCT
ma-24	193	12	leads	lead	VERB
ma-24	193	13	to	to	ADP
ma-24	193	14	conservation	conservation	NOUN
ma-24	193	15	laws	law	NOUN
ma-24	193	16	[	[	X
ma-24	193	17	9	9	NUM
ma-24	193	18	]	]	SYM
ma-24	193	19	dit	dit	NOUN
ma-24	193	20	i	i	PRON
ma-24	193	21	∣∣∣	∣∣∣	VERB
ma-24	193	22	∆α=0	∆α=0	PROPN
ma-24	193	23	=	=	PUNCT
ma-24	193	24	0	0	NUM
ma-24	193	25	,	,	PUNCT
ma-24	193	26	(	(	PUNCT
ma-24	193	27	41	41	NUM
ma-24	193	28	)	)	PUNCT
ma-24	193	29	where	where	SCONJ
ma-24	193	30	the	the	DET
ma-24	193	31	conserved	conserve	VERB
ma-24	193	32	vector	vector	NOUN
ma-24	193	33	t	t	NOUN
ma-24	194	1	i	i	PRON
ma-24	194	2	=	=	PUNCT
ma-24	195	1	ξil+wα	ξil+wα	PROPN
ma-24	195	2	[	[	PUNCT
ma-24	195	3	∂l	∂l	X
ma-24	195	4	∂uαi	∂uαi	X
ma-24	195	5	−dj	−dj	NOUN
ma-24	195	6	(	(	PUNCT
ma-24	195	7	∂l	∂l	VERB
ma-24	195	8	∂uαij	∂uαij	NOUN
ma-24	195	9	)	)	PUNCT
ma-24	196	1	+	+	ADJ
ma-24	196	2	djdk	djdk	NOUN
ma-24	196	3	(	(	PUNCT
ma-24	196	4	∂l	∂l	PROPN
ma-24	196	5	∂uαijk	∂uαijk	X
ma-24	196	6	)	)	PUNCT
ma-24	196	7	−	−	PROPN
ma-24	196	8	.	.	PUNCT
ma-24	196	9	.	.	PUNCT
ma-24	196	10	.	.	PUNCT
ma-24	197	1	]	]	PUNCT
ma-24	198	1	+	+	CCONJ
ma-24	198	2	dj(w	dj(w	PROPN
ma-24	198	3	α	α	X
ma-24	198	4	)	)	PUNCT
ma-24	198	5	[	[	PUNCT
ma-24	198	6	∂l	∂l	PROPN
ma-24	198	7	∂uαij	∂uαij	NOUN
ma-24	198	8	−dk	−dk	NOUN
ma-24	198	9	(	(	PUNCT
ma-24	198	10	∂l	∂l	PROPN
ma-24	198	11	∂uαijk	∂uαijk	X
ma-24	198	12	)	)	PUNCT
ma-24	199	1	+	+	CCONJ
ma-24	199	2	.	.	PUNCT
ma-24	199	3	.	.	PUNCT
ma-24	199	4	.	.	PUNCT
ma-24	200	1	]	]	PUNCT
ma-24	201	1	+	+	PUNCT
ma-24	201	2	djdk(wα	djdk(wα	ADJ
ma-24	201	3	)	)	PUNCT
ma-24	201	4	[	[	PUNCT
ma-24	201	5	∂l	∂l	NOUN
ma-24	201	6	∂uαijk	∂uαijk	ADV
ma-24	201	7	−	−	PROPN
ma-24	201	8	.	.	PUNCT
ma-24	201	9	.	.	PUNCT
ma-24	201	10	.	.	PUNCT
ma-24	201	11	]	]	PUNCT
ma-24	201	12	.	.	PUNCT
ma-24	202	1	(	(	PUNCT
ma-24	202	2	42	42	NUM
ma-24	202	3	)	)	PUNCT
ma-24	202	4	eur	eur	PROPN
ma-24	202	5	.	.	PUNCT
ma-24	203	1	j.	j.	PROPN
ma-24	203	2	math	math	PROPN
ma-24	203	3	.	.	PUNCT
ma-24	204	1	anal	anal	ADJ
ma-24	204	2	.	.	PUNCT
ma-24	205	1	1	1	NUM
ma-24	205	2	(	(	PUNCT
ma-24	205	3	2021	2021	NUM
ma-24	205	4	)	)	PUNCT
ma-24	205	5	1393	1393	NUM
ma-24	205	6	.	.	PUNCT
ma-24	206	1	main	main	ADJ
ma-24	206	2	results	result	NOUN
ma-24	206	3	we	we	PRON
ma-24	206	4	now	now	ADV
ma-24	206	5	present	present	VERB
ma-24	206	6	our	our	PRON
ma-24	206	7	results	result	NOUN
ma-24	206	8	in	in	ADP
ma-24	206	9	this	this	DET
ma-24	206	10	section	section	NOUN
ma-24	206	11	.	.	PUNCT
ma-24	207	1	an	an	DET
ma-24	207	2	illustrative	illustrative	ADJ
ma-24	207	3	example	example	NOUN
ma-24	207	4	with	with	ADP
ma-24	207	5	a	a	DET
ma-24	207	6	simple	simple	ADJ
ma-24	207	7	kdv	kdv	NOUN
ma-24	207	8	equationcan	equationcan	AUX
ma-24	207	9	be	be	AUX
ma-24	207	10	found	find	VERB
ma-24	207	11	in	in	ADP
ma-24	207	12	[	[	X
ma-24	207	13	6	6	NUM
ma-24	207	14	]	]	PUNCT
ma-24	207	15	.	.	PUNCT
ma-24	208	1	the	the	DET
ma-24	208	2	infinitesimal	infinitesimal	ADJ
ma-24	208	3	transformations	transformation	NOUN
ma-24	208	4	of	of	ADP
ma-24	208	5	the	the	DET
ma-24	208	6	lie	lie	NOUN
ma-24	208	7	group	group	NOUN
ma-24	208	8	with	with	ADP
ma-24	208	9	parameter	parameter	PROPN
ma-24	208	10	ε	ε	PROPN
ma-24	208	11	are	be	AUX
ma-24	208	12	t̄	t̄	PROPN
ma-24	208	13	=	=	SYM
ma-24	208	14	t	t	PROPN
ma-24	209	1	+	+	CCONJ
ma-24	209	2	ξt(t	ξt(t	PROPN
ma-24	209	3	,	,	PUNCT
ma-24	209	4	x	x	X
ma-24	209	5	,	,	PUNCT
ma-24	209	6	u	u	NOUN
ma-24	209	7	,	,	PUNCT
ma-24	209	8	v)ε	v)ε	NOUN
ma-24	209	9	,	,	PUNCT
ma-24	209	10	x̄	x̄	PUNCT
ma-24	210	1	=	=	PUNCT
ma-24	210	2	x	x	PUNCT
ma-24	211	1	+	+	X
ma-24	211	2	ξx(t	ξx(t	NOUN
ma-24	211	3	,	,	PUNCT
ma-24	211	4	x	x	X
ma-24	211	5	,	,	PUNCT
ma-24	211	6	u	u	NOUN
ma-24	211	7	,	,	PUNCT
ma-24	211	8	v)ε	v)ε	NOUN
ma-24	211	9	,	,	PUNCT
ma-24	211	10	ū	ū	NOUN
ma-24	211	11	=	=	SYM
ma-24	211	12	u	u	NOUN
ma-24	211	13	+	+	X
ma-24	211	14	ηu(t	ηu(t	NOUN
ma-24	211	15	,	,	PUNCT
ma-24	211	16	x	x	NOUN
ma-24	211	17	,	,	PUNCT
ma-24	211	18	u	u	NOUN
ma-24	211	19	,	,	PUNCT
ma-24	211	20	v)ε	v)ε	NOUN
ma-24	211	21	,	,	PUNCT
ma-24	211	22	v̄	v̄	NOUN
ma-24	211	23	=	=	SYM
ma-24	211	24	v	v	PROPN
ma-24	211	25	+	+	CCONJ
ma-24	211	26	ηv	ηv	PROPN
ma-24	211	27	(	(	PUNCT
ma-24	211	28	t	t	PROPN
ma-24	211	29	,	,	PUNCT
ma-24	211	30	x	x	NOUN
ma-24	211	31	,	,	PUNCT
ma-24	211	32	u	u	NOUN
ma-24	211	33	,	,	PUNCT
ma-24	211	34	v)ε.(43	v)ε.(43	NUM
ma-24	211	35	)	)	PUNCT
ma-24	211	36	the	the	DET
ma-24	211	37	vector	vector	NOUN
ma-24	211	38	field	field	NOUN
ma-24	211	39	x	x	PUNCT
ma-24	212	1	=	=	PUNCT
ma-24	212	2	ξt(t	ξt(t	NOUN
ma-24	212	3	,	,	PUNCT
ma-24	212	4	x	x	X
ma-24	212	5	,	,	PUNCT
ma-24	212	6	u	u	NOUN
ma-24	212	7	,	,	PUNCT
ma-24	212	8	v	v	NOUN
ma-24	212	9	)	)	PUNCT
ma-24	212	10	∂	∂	NOUN
ma-24	212	11	∂t	∂t	PROPN
ma-24	212	12	+	+	CCONJ
ma-24	212	13	ξx(t	ξx(t	NOUN
ma-24	212	14	,	,	PUNCT
ma-24	212	15	x	x	X
ma-24	212	16	,	,	PUNCT
ma-24	212	17	u	u	NOUN
ma-24	212	18	,	,	PUNCT
ma-24	212	19	v	v	NOUN
ma-24	212	20	)	)	PUNCT
ma-24	212	21	∂	∂	NOUN
ma-24	213	1	∂x	∂x	PROPN
ma-24	213	2	+	+	CCONJ
ma-24	213	3	ηu(t	ηu(t	NOUN
ma-24	213	4	,	,	PUNCT
ma-24	213	5	x	x	NOUN
ma-24	213	6	,	,	PUNCT
ma-24	213	7	u	u	NOUN
ma-24	213	8	,	,	PUNCT
ma-24	213	9	v	v	NOUN
ma-24	213	10	)	)	PUNCT
ma-24	213	11	∂	∂	NOUN
ma-24	213	12	∂u	∂u	NOUN
ma-24	214	1	+	+	CCONJ
ma-24	214	2	ηv	ηv	PROPN
ma-24	214	3	(	(	PUNCT
ma-24	214	4	t	t	PROPN
ma-24	214	5	,	,	PUNCT
ma-24	214	6	x	x	X
ma-24	214	7	,	,	PUNCT
ma-24	214	8	u	u	NOUN
ma-24	214	9	,	,	PUNCT
ma-24	214	10	v	v	NOUN
ma-24	214	11	)	)	PUNCT
ma-24	214	12	∂	∂	NOUN
ma-24	214	13	∂v	∂v	PROPN
ma-24	214	14	,	,	PUNCT
ma-24	214	15	(	(	PUNCT
ma-24	214	16	44	44	NUM
ma-24	214	17	)	)	PUNCT
ma-24	214	18	is	be	AUX
ma-24	214	19	a	a	DET
ma-24	214	20	lie	lie	NOUN
ma-24	214	21	point	point	NOUN
ma-24	214	22	symmetry	symmetry	NOUN
ma-24	214	23	of	of	ADP
ma-24	214	24	(	(	PUNCT
ma-24	214	25	3	3	X
ma-24	214	26	)	)	PUNCT
ma-24	214	27	if	if	SCONJ
ma-24	214	28	x[3]∆1	x[3]∆1	PROPN
ma-24	214	29	∣∣∣	∣∣∣	PROPN
ma-24	214	30	∆1=0	∆1=0	PROPN
ma-24	214	31	,	,	PUNCT
ma-24	214	32	∆2=0	∆2=0	PROPN
ma-24	214	33	=	=	SYM
ma-24	214	34	0	0	NUM
ma-24	214	35	,	,	PUNCT
ma-24	214	36	x[3]∆2	x[3]∆2	X
ma-24	214	37	∣∣∣	∣∣∣	ADP
ma-24	214	38	∆1=0	∆1=0	PROPN
ma-24	214	39	,	,	PUNCT
ma-24	214	40	∆2=0	∆2=0	PROPN
ma-24	214	41	=	=	SYM
ma-24	214	42	0	0	PROPN
ma-24	214	43	.	.	PUNCT
ma-24	215	1	(	(	PUNCT
ma-24	215	2	45	45	NUM
ma-24	215	3	)	)	PUNCT
ma-24	215	4	expanding	expand	VERB
ma-24	215	5	(	(	PUNCT
ma-24	215	6	45	45	NUM
ma-24	215	7	)	)	PUNCT
ma-24	215	8	and	and	CCONJ
ma-24	215	9	and	and	CCONJ
ma-24	215	10	splitting	splitting	NOUN
ma-24	215	11	on	on	ADP
ma-24	215	12	derivatives	derivative	NOUN
ma-24	215	13	of	of	ADP
ma-24	215	14	v	v	NOUN
ma-24	215	15	and	and	CCONJ
ma-24	215	16	u	u	NOUN
ma-24	215	17	,	,	PUNCT
ma-24	215	18	we	we	PRON
ma-24	215	19	have	have	VERB
ma-24	215	20	an	an	DET
ma-24	215	21	overdetermined	overdetermine	VERB
ma-24	215	22	system	system	NOUN
ma-24	215	23	often	often	ADV
ma-24	215	24	pdes	pde	VERB
ma-24	215	25	,	,	PUNCT
ma-24	215	26	namely	namely	ADV
ma-24	215	27	,	,	PUNCT
ma-24	215	28	ξtu	ξtu	PROPN
ma-24	215	29	=	=	SYM
ma-24	215	30	0	0	NUM
ma-24	215	31	,	,	PUNCT
ma-24	215	32	ξtv	ξtv	NOUN
ma-24	215	33	=	=	SYM
ma-24	215	34	0	0	NUM
ma-24	215	35	,	,	PUNCT
ma-24	215	36	ξtx	ξtx	NOUN
ma-24	215	37	=	=	SYM
ma-24	215	38	0	0	NUM
ma-24	215	39	,	,	PUNCT
ma-24	215	40	ξxu	ξxu	NOUN
ma-24	215	41	=	=	SYM
ma-24	215	42	0	0	NUM
ma-24	215	43	,	,	PUNCT
ma-24	215	44	ξxv	ξxv	VERB
ma-24	215	45	=	=	SYM
ma-24	215	46	0	0	PROPN
ma-24	215	47	,	,	PUNCT
ma-24	215	48	ξttt	ξttt	NOUN
ma-24	215	49	=	=	SYM
ma-24	215	50	0	0	NUM
ma-24	215	51	,	,	PUNCT
ma-24	215	52	ξxtt	ξxtt	NOUN
ma-24	215	53	=	=	SYM
ma-24	215	54	0	0	NUM
ma-24	215	55	,	,	PUNCT
ma-24	215	56	3ξxx	3ξxx	NUM
ma-24	215	57	−	−	NOUN
ma-24	215	58	ξtt	ξtt	NOUN
ma-24	215	59	=	=	X
ma-24	215	60	0	0	PROPN
ma-24	215	61	,	,	PUNCT
ma-24	215	62	3ηv	3ηv	ADJ
ma-24	215	63	+	+	CCONJ
ma-24	216	1	2ξttv	2ξttv	NUM
ma-24	216	2	=	=	SYM
ma-24	216	3	0	0	NUM
ma-24	216	4	,	,	PUNCT
ma-24	216	5	3αηu	3αηu	ADJ
ma-24	216	6	+	+	CCONJ
ma-24	216	7	2αξttu	2αξttu	NUM
ma-24	216	8	−	−	NOUN
ma-24	216	9	3ξxt	3ξxt	NUM
ma-24	216	10	=	=	SYM
ma-24	216	11	0	0	NUM
ma-24	216	12	.	.	PUNCT
ma-24	217	1	(	(	PUNCT
ma-24	217	2	46	46	X
ma-24	217	3	)	)	PUNCT
ma-24	217	4	solving	solve	VERB
ma-24	217	5	the	the	DET
ma-24	217	6	system	system	NOUN
ma-24	217	7	(	(	PUNCT
ma-24	217	8	46	46	NUM
ma-24	217	9	)	)	PUNCT
ma-24	217	10	yields	yield	VERB
ma-24	217	11	ξt	ξt	X
ma-24	217	12	=	=	SYM
ma-24	217	13	a1	a1	NOUN
ma-24	217	14	+	+	CCONJ
ma-24	217	15	3a2	3a2	NUM
ma-24	217	16	t	t	NOUN
ma-24	217	17	,	,	PUNCT
ma-24	217	18	ξx	ξx	NOUN
ma-24	217	19	=	=	PUNCT
ma-24	218	1	a2x	a2x	PROPN
ma-24	218	2	+	+	SYM
ma-24	218	3	αa3	αa3	PROPN
ma-24	218	4	t	t	NOUN
ma-24	218	5	+	+	SYM
ma-24	218	6	a4	a4	PROPN
ma-24	218	7	,	,	PUNCT
ma-24	218	8	η	η	X
ma-24	218	9	u	u	NOUN
ma-24	218	10	=	=	PROPN
ma-24	218	11	−2a2u	−2a2u	PROPN
ma-24	218	12	+	+	NUM
ma-24	218	13	a3	a3	NOUN
ma-24	218	14	,	,	PUNCT
ma-24	218	15	η	η	PROPN
ma-24	218	16	v	v	X
ma-24	218	17	=	=	SYM
ma-24	218	18	−2a2v	−2a2v	PROPN
ma-24	218	19	,	,	PUNCT
ma-24	218	20	(	(	PUNCT
ma-24	218	21	47	47	NUM
ma-24	218	22	)	)	PUNCT
ma-24	218	23	for	for	ADP
ma-24	218	24	arbitrary	arbitrary	ADJ
ma-24	218	25	constants	constant	NOUN
ma-24	218	26	a1	a1	NOUN
ma-24	218	27	,	,	PUNCT
ma-24	218	28	a2	a2	PROPN
ma-24	218	29	,	,	PUNCT
ma-24	218	30	a3	a3	NOUN
ma-24	218	31	,	,	PUNCT
ma-24	218	32	a4	a4	NOUN
ma-24	218	33	.	.	PUNCT
ma-24	219	1	hence	hence	ADV
ma-24	219	2	from	from	ADP
ma-24	219	3	(	(	PUNCT
ma-24	219	4	47	47	NUM
ma-24	219	5	)	)	PUNCT
ma-24	219	6	,	,	PUNCT
ma-24	219	7	the	the	DET
ma-24	219	8	infinitesimal	infinitesimal	ADJ
ma-24	219	9	symmetries	symmetry	NOUN
ma-24	219	10	of	of	ADP
ma-24	219	11	the	the	DET
ma-24	219	12	coupledkdv	coupledkdv	NOUN
ma-24	219	13	equations	equation	NOUN
ma-24	219	14	(	(	PUNCT
ma-24	219	15	3	3	X
ma-24	219	16	)	)	PUNCT
ma-24	219	17	is	be	AUX
ma-24	219	18	a	a	DET
ma-24	219	19	lie	lie	NOUN
ma-24	219	20	algebra	algebra	NOUN
ma-24	219	21	generated	generate	VERB
ma-24	219	22	by	by	ADP
ma-24	219	23	the	the	DET
ma-24	219	24	vector	vector	NOUN
ma-24	219	25	fields	field	VERB
ma-24	219	26	x1	x1	PROPN
ma-24	220	1	=	=	SYM
ma-24	220	2	∂	∂	NUM
ma-24	220	3	∂t	∂t	PROPN
ma-24	220	4	,	,	PUNCT
ma-24	220	5	x2	x2	PROPN
ma-24	220	6	=	=	SYM
ma-24	220	7	∂	∂	NUM
ma-24	220	8	∂x	∂x	PROPN
ma-24	220	9	,	,	PUNCT
ma-24	220	10	x3	x3	PROPN
ma-24	220	11	=	=	SYM
ma-24	221	1	αt	αt	PROPN
ma-24	221	2	∂	∂	NOUN
ma-24	221	3	∂x	∂x	PROPN
ma-24	221	4	+	+	CCONJ
ma-24	221	5	∂	∂	NUM
ma-24	221	6	∂u	∂u	PROPN
ma-24	221	7	,	,	PUNCT
ma-24	221	8	x4	x4	PROPN
ma-24	221	9	=	=	PROPN
ma-24	221	10	3	3	NUM
ma-24	221	11	t	t	NOUN
ma-24	221	12	∂	∂	NOUN
ma-24	221	13	∂t	∂t	PROPN
ma-24	222	1	+	+	CCONJ
ma-24	222	2	x	x	SYM
ma-24	222	3	∂	∂	NUM
ma-24	222	4	∂x	∂x	PROPN
ma-24	222	5	−	−	PROPN
ma-24	222	6	2u	2u	PROPN
ma-24	222	7	∂	∂	NOUN
ma-24	222	8	∂u	∂u	PROPN
ma-24	222	9	−	−	PROPN
ma-24	222	10	2v	2v	PROPN
ma-24	222	11	∂	∂	PROPN
ma-24	223	1	∂v	∂v	PROPN
ma-24	223	2	.	.	PUNCT
ma-24	224	1	(	(	PUNCT
ma-24	224	2	48	48	NUM
ma-24	224	3	)	)	PUNCT
ma-24	224	4	the	the	DET
ma-24	224	5	set	set	NOUN
ma-24	224	6	of	of	ADP
ma-24	224	7	all	all	DET
ma-24	224	8	infinitesimal	infinitesimal	ADJ
ma-24	224	9	symmetries	symmetry	NOUN
ma-24	224	10	of	of	ADP
ma-24	224	11	coupled	couple	VERB
ma-24	224	12	kdv	kdv	NOUN
ma-24	224	13	equations	equation	NOUN
ma-24	224	14	forms	form	VERB
ma-24	224	15	a	a	DET
ma-24	224	16	lie	lie	NOUN
ma-24	224	17	algebra	algebra	NOUN
ma-24	224	18	and	and	CCONJ
ma-24	224	19	yield	yield	VERB
ma-24	224	20	thefollowing	thefollowing	NOUN
ma-24	224	21	commutation	commutation	NOUN
ma-24	224	22	relations	relation	NOUN
ma-24	224	23	in	in	ADP
ma-24	224	24	table	table	NOUN
ma-24	224	25	1	1	NUM
ma-24	224	26	.	.	PUNCT
ma-24	225	1	[	[	X
ma-24	225	2	xi	xi	X
ma-24	225	3	,	,	PUNCT
ma-24	225	4	xj	xj	PROPN
ma-24	225	5	]	]	PUNCT
ma-24	226	1	x1	x1	PROPN
ma-24	227	1	x2	x2	NOUN
ma-24	227	2	x3	x3	PROPN
ma-24	227	3	x4	x4	PROPN
ma-24	228	1	x1	x1	PROPN
ma-24	228	2	0	0	NUM
ma-24	228	3	0	0	NUM
ma-24	228	4	αx2	αx2	NOUN
ma-24	228	5	3x1	3x1	NUM
ma-24	228	6	x2	x2	NOUN
ma-24	228	7	0	0	NUM
ma-24	228	8	0	0	NUM
ma-24	228	9	0	0	NUM
ma-24	229	1	x2	x2	NOUN
ma-24	229	2	x3	x3	PROPN
ma-24	229	3	-αx2	-αx2	PUNCT
ma-24	229	4	0	0	NUM
ma-24	229	5	0	0	NUM
ma-24	230	1	-2x3	-2x3	NUM
ma-24	230	2	x4	x4	PROPN
ma-24	230	3	-3x1	-3x1	PROPN
ma-24	230	4	-x2	-x2	PROPN
ma-24	230	5	2x3	2x3	NUM
ma-24	230	6	0table	0table	NUM
ma-24	230	7	1	1	NUM
ma-24	230	8	:	:	PUNCT
ma-24	230	9	a	a	DET
ma-24	230	10	commutator	commutator	NOUN
ma-24	230	11	table	table	NOUN
ma-24	230	12	for	for	ADP
ma-24	230	13	the	the	DET
ma-24	230	14	lie	lie	NOUN
ma-24	230	15	algebra	algebra	NOUN
ma-24	230	16	generated	generate	VERB
ma-24	230	17	by	by	ADP
ma-24	230	18	the	the	DET
ma-24	230	19	symmetries	symmetry	NOUN
ma-24	230	20	of	of	ADP
ma-24	230	21	coupled	couple	VERB
ma-24	230	22	kdvequation	kdvequation	NOUN
ma-24	230	23	.	.	PUNCT
ma-24	231	1	eur	eur	PROPN
ma-24	231	2	.	.	PUNCT
ma-24	232	1	j.	j.	PROPN
ma-24	232	2	math	math	PROPN
ma-24	232	3	.	.	PUNCT
ma-24	233	1	anal	anal	ADJ
ma-24	233	2	.	.	PUNCT
ma-24	234	1	1	1	NUM
ma-24	234	2	(	(	PUNCT
ma-24	234	3	2021	2021	NUM
ma-24	234	4	)	)	PUNCT
ma-24	235	1	140the	140the	DET
ma-24	235	2	following	follow	VERB
ma-24	235	3	lie	lie	NOUN
ma-24	235	4	groups	group	NOUN
ma-24	235	5	,	,	PUNCT
ma-24	235	6	for	for	ADP
ma-24	235	7	i	i	PROPN
ma-24	235	8	=	=	SYM
ma-24	235	9	1	1	NUM
ma-24	235	10	,	,	PUNCT
ma-24	235	11	2	2	NUM
ma-24	235	12	,	,	PUNCT
ma-24	235	13	3	3	NUM
ma-24	235	14	,	,	PUNCT
ma-24	235	15	4	4	NUM
ma-24	235	16	,	,	PUNCT
ma-24	235	17	are	be	AUX
ma-24	235	18	obtained	obtain	VERB
ma-24	235	19	tε1	tε1	PROPN
ma-24	235	20	:	:	PUNCT
ma-24	236	1	t̄	t̄	PROPN
ma-24	236	2	=	=	PUNCT
ma-24	236	3	t	t	PROPN
ma-24	236	4	+	+	CCONJ
ma-24	236	5	ε1	ε1	PROPN
ma-24	236	6	,	,	PUNCT
ma-24	236	7	x̄	x̄	PUNCT
ma-24	236	8	=	=	SYM
ma-24	237	1	x	x	X
ma-24	237	2	,	,	PUNCT
ma-24	237	3	ū	ū	NOUN
ma-24	237	4	=	=	SYM
ma-24	237	5	u	u	NOUN
ma-24	237	6	,	,	PUNCT
ma-24	237	7	v̄	v̄	NOUN
ma-24	237	8	=	=	SYM
ma-24	237	9	v	v	NOUN
ma-24	237	10	,	,	PUNCT
ma-24	237	11	(	(	PUNCT
ma-24	237	12	49	49	NUM
ma-24	237	13	)	)	PUNCT
ma-24	237	14	tε2	tε2	NOUN
ma-24	237	15	:	:	PUNCT
ma-24	237	16	t̄	t̄	PROPN
ma-24	237	17	=	=	SYM
ma-24	237	18	t	t	PROPN
ma-24	237	19	,	,	PUNCT
ma-24	237	20	x̄	x̄	PUNCT
ma-24	237	21	=	=	PUNCT
ma-24	238	1	x	x	PUNCT
ma-24	239	1	+	+	CCONJ
ma-24	239	2	ε2	ε2	ADJ
ma-24	239	3	,	,	PUNCT
ma-24	239	4	ū	ū	NOUN
ma-24	239	5	=	=	SYM
ma-24	239	6	u	u	NOUN
ma-24	239	7	,	,	PUNCT
ma-24	239	8	v̄	v̄	NOUN
ma-24	239	9	=	=	SYM
ma-24	239	10	v	v	NOUN
ma-24	239	11	,	,	PUNCT
ma-24	239	12	(	(	PUNCT
ma-24	239	13	50	50	NUM
ma-24	239	14	)	)	PUNCT
ma-24	239	15	tε3	tε3	NOUN
ma-24	239	16	:	:	PUNCT
ma-24	239	17	t̄	t̄	PROPN
ma-24	239	18	=	=	SYM
ma-24	239	19	t	t	PROPN
ma-24	239	20	,	,	PUNCT
ma-24	239	21	x̄	x̄	PUNCT
ma-24	239	22	=	=	PUNCT
ma-24	239	23	x	x	PUNCT
ma-24	239	24	+	+	X
ma-24	239	25	αε3	αε3	PROPN
ma-24	239	26	t	t	NOUN
ma-24	239	27	,	,	PUNCT
ma-24	239	28	ū	ū	NOUN
ma-24	239	29	=	=	SYM
ma-24	239	30	u	u	PROPN
ma-24	239	31	+	+	X
ma-24	239	32	ε3	ε3	ADJ
ma-24	239	33	,	,	PUNCT
ma-24	239	34	v̄	v̄	NOUN
ma-24	239	35	=	=	SYM
ma-24	239	36	v	v	NOUN
ma-24	239	37	,	,	PUNCT
ma-24	239	38	(	(	PUNCT
ma-24	239	39	51	51	NUM
ma-24	239	40	)	)	PUNCT
ma-24	239	41	tε4	tε4	PROPN
ma-24	239	42	:	:	PUNCT
ma-24	240	1	t̄	t̄	PROPN
ma-24	240	2	=	=	SYM
ma-24	240	3	te3ε4	te3ε4	PROPN
ma-24	240	4	,	,	PUNCT
ma-24	240	5	x̄	x̄	NOUN
ma-24	240	6	=	=	SYM
ma-24	240	7	xeε4	xeε4	PROPN
ma-24	240	8	,	,	PUNCT
ma-24	240	9	ū	ū	NOUN
ma-24	240	10	=	=	SYM
ma-24	240	11	ue−2ε4	ue−2ε4	PROPN
ma-24	240	12	,	,	PUNCT
ma-24	240	13	v̄	v̄	NOUN
ma-24	240	14	=	=	NOUN
ma-24	241	1	ve−2ε4	ve−2ε4	PROPN
ma-24	241	2	.	.	PUNCT
ma-24	242	1	(	(	PUNCT
ma-24	242	2	52	52	NUM
ma-24	242	3	)	)	PUNCT
ma-24	242	4	the	the	DET
ma-24	242	5	symmetries	symmetry	NOUN
ma-24	242	6	obtained	obtain	VERB
ma-24	242	7	yield	yield	VERB
ma-24	242	8	the	the	DET
ma-24	242	9	following	follow	VERB
ma-24	242	10	symmetry	symmetry	NOUN
ma-24	242	11	reductions	reduction	NOUN
ma-24	242	12	.	.	PUNCT
ma-24	243	1	x1	x1	PRON
ma-24	243	2	=	=	SYM
ma-24	243	3	∂	∂	NUM
ma-24	243	4	∂t	∂t	PROPN
ma-24	243	5	.	.	PUNCT
ma-24	244	1	(	(	PUNCT
ma-24	244	2	53	53	X
ma-24	244	3	)	)	PUNCT
ma-24	244	4	solving	solve	VERB
ma-24	244	5	the	the	DET
ma-24	244	6	characteristic	characteristic	ADJ
ma-24	244	7	equations	equation	NOUN
ma-24	244	8	dt	dt	X
ma-24	244	9	1	1	NUM
ma-24	244	10	=	=	SYM
ma-24	244	11	dx	dx	PROPN
ma-24	244	12	c	c	NOUN
ma-24	244	13	=	=	SYM
ma-24	244	14	du	du	PROPN
ma-24	244	15	0	0	NUM
ma-24	245	1	=	=	SYM
ma-24	245	2	dv	dv	PROPN
ma-24	245	3	0	0	NUM
ma-24	245	4	,	,	PUNCT
ma-24	245	5	(	(	PUNCT
ma-24	245	6	54	54	NUM
ma-24	245	7	)	)	PUNCT
ma-24	245	8	associated	associate	VERB
ma-24	245	9	to	to	ADP
ma-24	245	10	the	the	DET
ma-24	245	11	operator	operator	NOUN
ma-24	245	12	x1	x1	PROPN
ma-24	245	13	gives	give	VERB
ma-24	245	14	the	the	DET
ma-24	245	15	invariants	invariant	NOUN
ma-24	245	16	j1	j1	NOUN
ma-24	245	17	=	=	SYM
ma-24	245	18	x	x	PROPN
ma-24	245	19	,	,	PUNCT
ma-24	245	20	j2	j2	PROPN
ma-24	245	21	=	=	SYM
ma-24	245	22	u	u	PROPN
ma-24	245	23	,	,	PUNCT
ma-24	245	24	j3	j3	PROPN
ma-24	245	25	=	=	PUNCT
ma-24	245	26	v	v	PROPN
ma-24	245	27	.	.	PUNCT
ma-24	246	1	(	(	PUNCT
ma-24	246	2	55	55	NUM
ma-24	246	3	)	)	PUNCT
ma-24	246	4	hence	hence	ADV
ma-24	246	5	,	,	PUNCT
ma-24	246	6	we	we	PRON
ma-24	246	7	have	have	VERB
ma-24	246	8	u	u	NOUN
ma-24	246	9	=	=	NOUN
ma-24	246	10	ϕ(x	ϕ(x	PROPN
ma-24	246	11	)	)	PUNCT
ma-24	246	12	,	,	PUNCT
ma-24	246	13	v	v	X
ma-24	246	14	=	=	SYM
ma-24	246	15	ψ(x	ψ(x	NOUN
ma-24	246	16	)	)	PUNCT
ma-24	246	17	,	,	PUNCT
ma-24	246	18	(	(	PUNCT
ma-24	246	19	56	56	NUM
ma-24	246	20	)	)	PUNCT
ma-24	246	21	for	for	ADP
ma-24	246	22	arbitrary	arbitrary	ADJ
ma-24	246	23	functions	function	NOUN
ma-24	246	24	ϕ	ϕ	NOUN
ma-24	246	25	and	and	CCONJ
ma-24	246	26	ψ	ψ	NOUN
ma-24	246	27	.	.	PUNCT
ma-24	247	1	substituting	substitute	VERB
ma-24	247	2	the	the	DET
ma-24	247	3	expressions	expression	NOUN
ma-24	247	4	for	for	ADP
ma-24	247	5	u	u	NOUN
ma-24	247	6	and	and	CCONJ
ma-24	247	7	v	v	NOUN
ma-24	247	8	given	give	VERB
ma-24	247	9	by	by	ADP
ma-24	247	10	(	(	PUNCT
ma-24	247	11	56	56	NUM
ma-24	247	12	)	)	PUNCT
ma-24	247	13	into	into	ADP
ma-24	247	14	thesystem	thesystem	NOUN
ma-24	247	15	(	(	PUNCT
ma-24	247	16	3	3	NUM
ma-24	247	17	)	)	PUNCT
ma-24	247	18	,	,	PUNCT
ma-24	247	19	we	we	PRON
ma-24	247	20	get	get	VERB
ma-24	247	21	a	a	DET
ma-24	247	22	system	system	NOUN
ma-24	247	23	of	of	ADP
ma-24	247	24	third	third	ADJ
ma-24	247	25	order	order	NOUN
ma-24	247	26	ordinary	ordinary	ADJ
ma-24	247	27	des	de	NOUN
ma-24	247	28	namely	namely	ADV
ma-24	247	29	,	,	PUNCT
ma-24	247	30	α	α	PROPN
ma-24	247	31	[	[	PUNCT
ma-24	247	32	ϕ(x)ϕ′(x)−	ϕ(x)ϕ′(x)−	NOUN
ma-24	247	33	ψ(x)ψ′(x	ψ(x)ψ′(x	PROPN
ma-24	247	34	)	)	PUNCT
ma-24	247	35	]	]	PUNCT
ma-24	248	1	+	+	PUNCT
ma-24	248	2	βϕ′′′(x	βϕ′′′(x	NOUN
ma-24	248	3	)	)	PUNCT
ma-24	248	4	=	=	SYM
ma-24	248	5	0	0	NUM
ma-24	248	6	,	,	PUNCT
ma-24	248	7	α	α	PROPN
ma-24	248	8	(	(	PUNCT
ma-24	248	9	ϕ(x)ψ(x))′	ϕ(x)ψ(x))′	NOUN
ma-24	248	10	+	+	NUM
ma-24	248	11	βψ′′′(x	βψ′′′(x	NOUN
ma-24	248	12	)	)	PUNCT
ma-24	248	13	=	=	SYM
ma-24	248	14	0	0	X
ma-24	248	15	.	.	PUNCT
ma-24	249	1	(	(	PUNCT
ma-24	249	2	57	57	NUM
ma-24	249	3	)	)	PUNCT
ma-24	249	4	integration	integration	NOUN
ma-24	249	5	of	of	ADP
ma-24	249	6	the	the	DET
ma-24	249	7	system	system	NOUN
ma-24	249	8	(	(	PUNCT
ma-24	249	9	57	57	NUM
ma-24	249	10	)	)	PUNCT
ma-24	249	11	yields	yield	NOUN
ma-24	249	12	;	;	PUNCT
ma-24	249	13	α	α	X
ma-24	249	14	2	2	NUM
ma-24	249	15	[	[	PUNCT
ma-24	249	16	ϕ(x)2	ϕ(x)2	NOUN
ma-24	249	17	−	−	PUNCT
ma-24	249	18	ψ(x)2	ψ(x)2	PRON
ma-24	249	19	]	]	PUNCT
ma-24	249	20	+	+	CCONJ
ma-24	249	21	βϕ′′(x	βϕ′′(x	NOUN
ma-24	249	22	)	)	PUNCT
ma-24	249	23	=	=	SYM
ma-24	249	24	c1	c1	PROPN
ma-24	249	25	,	,	PUNCT
ma-24	249	26	(	(	PUNCT
ma-24	249	27	58	58	X
ma-24	249	28	)	)	PUNCT
ma-24	249	29	α	α	NOUN
ma-24	250	1	[	[	X
ma-24	250	2	ϕ(x)ψ(x	ϕ(x)ψ(x	NUM
ma-24	250	3	)	)	PUNCT
ma-24	250	4	]	]	PUNCT
ma-24	251	1	+	+	CCONJ
ma-24	251	2	βψ′′(x	βψ′′(x	X
ma-24	251	3	)	)	PUNCT
ma-24	251	4	=	=	SYM
ma-24	251	5	c2	c2	PROPN
ma-24	251	6	,	,	PUNCT
ma-24	251	7	(	(	PUNCT
ma-24	251	8	59	59	NUM
ma-24	251	9	)	)	PUNCT
ma-24	251	10	for	for	ADP
ma-24	251	11	arbitrary	arbitrary	ADJ
ma-24	251	12	constants	constant	NOUN
ma-24	251	13	c1	c1	PROPN
ma-24	251	14	and	and	CCONJ
ma-24	251	15	c2	c2	PROPN
ma-24	251	16	.	.	PUNCT
ma-24	252	1	if	if	SCONJ
ma-24	252	2	we	we	PRON
ma-24	252	3	take	take	VERB
ma-24	252	4	c1	c1	NOUN
ma-24	252	5	=	=	PROPN
ma-24	252	6	c2	c2	PROPN
ma-24	252	7	=	=	SYM
ma-24	252	8	0	0	PROPN
ma-24	252	9	,	,	PUNCT
ma-24	252	10	(	(	PUNCT
ma-24	252	11	60	60	NUM
ma-24	252	12	)	)	PUNCT
ma-24	252	13	the	the	DET
ma-24	252	14	system	system	NOUN
ma-24	252	15	(	(	PUNCT
ma-24	252	16	58)-(59	58)-(59	NUM
ma-24	252	17	)	)	PUNCT
ma-24	252	18	becomes	become	VERB
ma-24	252	19	α	α	PROPN
ma-24	252	20	2	2	NUM
ma-24	252	21	[	[	PUNCT
ma-24	252	22	ϕ(x)2	ϕ(x)2	NOUN
ma-24	252	23	−	−	PUNCT
ma-24	252	24	ψ(x)2	ψ(x)2	PRON
ma-24	252	25	]	]	PUNCT
ma-24	253	1	+	+	CCONJ
ma-24	253	2	βϕ′′(x	βϕ′′(x	NOUN
ma-24	253	3	)	)	PUNCT
ma-24	253	4	=	=	SYM
ma-24	253	5	0	0	NUM
ma-24	253	6	,	,	PUNCT
ma-24	253	7	(	(	PUNCT
ma-24	253	8	61	61	NUM
ma-24	253	9	)	)	PUNCT
ma-24	253	10	α	α	NOUN
ma-24	254	1	[	[	X
ma-24	254	2	ϕ(x)ψ(x	ϕ(x)ψ(x	NUM
ma-24	254	3	)	)	PUNCT
ma-24	254	4	]	]	PUNCT
ma-24	255	1	+	+	CCONJ
ma-24	255	2	βψ′′(x	βψ′′(x	X
ma-24	255	3	)	)	PUNCT
ma-24	255	4	=	=	SYM
ma-24	255	5	0	0	X
ma-24	255	6	.	.	PUNCT
ma-24	255	7	(	(	PUNCT
ma-24	255	8	62	62	NUM
ma-24	255	9	)	)	PUNCT
ma-24	255	10	eur	eur	PROPN
ma-24	255	11	.	.	PUNCT
ma-24	256	1	j.	j.	PROPN
ma-24	256	2	math	math	PROPN
ma-24	256	3	.	.	PUNCT
ma-24	257	1	anal	anal	ADJ
ma-24	257	2	.	.	PUNCT
ma-24	258	1	1	1	NUM
ma-24	258	2	(	(	PUNCT
ma-24	258	3	2021	2021	NUM
ma-24	258	4	)	)	PUNCT
ma-24	258	5	141to	141to	NOUN
ma-24	258	6	find	find	VERB
ma-24	258	7	more	more	ADJ
ma-24	258	8	solutions	solution	NOUN
ma-24	258	9	of	of	ADP
ma-24	258	10	the	the	DET
ma-24	258	11	system	system	NOUN
ma-24	258	12	(	(	PUNCT
ma-24	258	13	61)-(62	61)-(62	NUM
ma-24	258	14	)	)	PUNCT
ma-24	258	15	,	,	PUNCT
ma-24	258	16	we	we	PRON
ma-24	258	17	determine	determine	VERB
ma-24	258	18	its	its	PRON
ma-24	258	19	lie	lie	NOUN
ma-24	258	20	point	point	NOUN
ma-24	258	21	symmetries	symmetry	NOUN
ma-24	258	22	.	.	PUNCT
ma-24	259	1	using	use	VERB
ma-24	259	2	thelie	thelie	NOUN
ma-24	259	3	’s	’s	PART
ma-24	259	4	algorithm	algorithm	NOUN
ma-24	259	5	for	for	ADP
ma-24	259	6	computing	computing	NOUN
ma-24	259	7	point	point	NOUN
ma-24	259	8	symmetries	symmetry	NOUN
ma-24	259	9	,	,	PUNCT
ma-24	259	10	we	we	PRON
ma-24	259	11	see	see	VERB
ma-24	259	12	that	that	SCONJ
ma-24	259	13	the	the	DET
ma-24	259	14	lie	lie	NOUN
ma-24	259	15	point	point	NOUN
ma-24	259	16	symmetries	symmetry	NOUN
ma-24	259	17	of	of	ADP
ma-24	259	18	(	(	PUNCT
ma-24	259	19	61)-(62)are	61)-(62)are	NUM
ma-24	259	20	x∗1	x∗1	VERB
ma-24	259	21	=	=	SYM
ma-24	260	1	∂	∂	NUM
ma-24	260	2	∂x	∂x	PROPN
ma-24	260	3	,	,	PUNCT
ma-24	260	4	x∗2	x∗2	PROPN
ma-24	260	5	=	=	SYM
ma-24	260	6	x	x	SYM
ma-24	260	7	∂	∂	NUM
ma-24	260	8	∂x	∂x	PROPN
ma-24	260	9	−	−	NUM
ma-24	260	10	2ϕ	2ϕ	NUM
ma-24	260	11	∂	∂	NOUN
ma-24	260	12	∂ϕ	∂ϕ	PROPN
ma-24	260	13	−	−	PROPN
ma-24	260	14	2ψ	2ψ	NOUN
ma-24	260	15	∂	∂	NUM
ma-24	260	16	∂ψ	∂ψ	PROPN
ma-24	260	17	.	.	PUNCT
ma-24	261	1	(	(	PUNCT
ma-24	261	2	63	63	NUM
ma-24	261	3	)	)	PUNCT
ma-24	261	4	proceeding	proceeding	NOUN
ma-24	261	5	as	as	ADP
ma-24	261	6	above	above	ADV
ma-24	261	7	,	,	PUNCT
ma-24	261	8	we	we	PRON
ma-24	261	9	see	see	VERB
ma-24	261	10	that	that	SCONJ
ma-24	261	11	the	the	DET
ma-24	261	12	symmetry	symmetry	NOUN
ma-24	261	13	x∗1	x∗1	VERB
ma-24	261	14	yields	yield	VERB
ma-24	261	15	the	the	DET
ma-24	261	16	trivial	trivial	ADJ
ma-24	261	17	solution	solution	NOUN
ma-24	261	18	u	u	NOUN
ma-24	261	19	=	=	PROPN
ma-24	261	20	0	0	NUM
ma-24	261	21	,	,	PUNCT
ma-24	261	22	v	v	NOUN
ma-24	261	23	=	=	SYM
ma-24	261	24	0	0	NUM
ma-24	261	25	.	.	PUNCT
ma-24	262	1	(	(	PUNCT
ma-24	262	2	64	64	NUM
ma-24	262	3	)	)	PUNCT
ma-24	262	4	the	the	DET
ma-24	262	5	second	second	ADJ
ma-24	262	6	symmetry	symmetry	NOUN
ma-24	262	7	x∗2	x∗2	PROPN
ma-24	262	8	has	have	VERB
ma-24	262	9	the	the	DET
ma-24	262	10	characteristic	characteristic	ADJ
ma-24	262	11	equations	equation	NOUN
ma-24	262	12	dx	dx	VERB
ma-24	262	13	x	x	PUNCT
ma-24	262	14	=	=	PRON
ma-24	262	15	dϕ	dϕ	PROPN
ma-24	262	16	−2ϕ	−2ϕ	NOUN
ma-24	262	17	=	=	SYM
ma-24	262	18	dψ	dψ	PROPN
ma-24	262	19	−2ψ	−2ψ	PROPN
ma-24	262	20	,	,	PUNCT
ma-24	262	21	(	(	PUNCT
ma-24	262	22	65	65	NUM
ma-24	262	23	)	)	PUNCT
ma-24	262	24	which	which	PRON
ma-24	262	25	provides	provide	VERB
ma-24	262	26	the	the	DET
ma-24	262	27	invariants	invariant	NOUN
ma-24	262	28	j1	j1	PROPN
ma-24	262	29	=	=	PUNCT
ma-24	262	30	x2ϕ	x2ϕ	PROPN
ma-24	262	31	,	,	PUNCT
ma-24	262	32	j2	j2	PROPN
ma-24	262	33	=	=	SYM
ma-24	262	34	x2ψ	x2ψ	PROPN
ma-24	262	35	.	.	PUNCT
ma-24	263	1	(	(	PUNCT
ma-24	263	2	66	66	NUM
ma-24	263	3	)	)	PUNCT
ma-24	263	4	letting	let	VERB
ma-24	263	5	ϕ	ϕ	X
ma-24	264	1	=	=	PUNCT
ma-24	264	2	λ	λ	X
ma-24	264	3	x2	x2	PROPN
ma-24	264	4	,	,	PUNCT
ma-24	264	5	ψ	ψ	X
ma-24	264	6	=	=	X
ma-24	264	7	µ	µ	X
ma-24	264	8	x2	x2	NOUN
ma-24	264	9	,	,	PUNCT
ma-24	264	10	(	(	PUNCT
ma-24	264	11	67	67	NUM
ma-24	264	12	)	)	PUNCT
ma-24	264	13	substituting	substitute	VERB
ma-24	264	14	the	the	DET
ma-24	264	15	values	value	NOUN
ma-24	264	16	of	of	ADP
ma-24	264	17	ϕ	ϕ	NOUN
ma-24	264	18	and	and	CCONJ
ma-24	264	19	ψ	ψ	X
ma-24	264	20	into	into	ADP
ma-24	264	21	(	(	PUNCT
ma-24	264	22	61)-(62	61)-(62	NUM
ma-24	264	23	)	)	PUNCT
ma-24	264	24	and	and	CCONJ
ma-24	264	25	solving	solve	VERB
ma-24	264	26	the	the	DET
ma-24	264	27	resulting	result	VERB
ma-24	264	28	equations	equation	NOUN
ma-24	264	29	yield	yield	NOUN
ma-24	264	30	:	:	PUNCT
ma-24	264	31	case	case	NOUN
ma-24	264	32	one	one	NUM
ma-24	264	33	.	.	PUNCT
ma-24	265	1	taking	take	VERB
ma-24	265	2	µ	µ	NOUN
ma-24	265	3	=	=	SYM
ma-24	265	4	0	0	NUM
ma-24	265	5	(	(	PUNCT
ma-24	265	6	68	68	NUM
ma-24	265	7	)	)	PUNCT
ma-24	265	8	gives	give	VERB
ma-24	265	9	λ	λ	X
ma-24	265	10	=	=	SYM
ma-24	265	11	0	0	NUM
ma-24	265	12	(	(	PUNCT
ma-24	265	13	69	69	NUM
ma-24	265	14	)	)	PUNCT
ma-24	265	15	or	or	CCONJ
ma-24	265	16	λ	λ	X
ma-24	265	17	=	=	SYM
ma-24	265	18	−	−	PROPN
ma-24	265	19	12β	12β	NUM
ma-24	265	20	α	α	NOUN
ma-24	265	21	.	.	PUNCT
ma-24	266	1	(	(	PUNCT
ma-24	266	2	70	70	NUM
ma-24	266	3	)	)	PUNCT
ma-24	266	4	when	when	SCONJ
ma-24	266	5	λ	λ	X
ma-24	266	6	=	=	SYM
ma-24	266	7	0	0	NUM
ma-24	266	8	,	,	PUNCT
ma-24	266	9	and	and	CCONJ
ma-24	266	10	µ	µ	X
ma-24	266	11	=	=	SYM
ma-24	266	12	0	0	NUM
ma-24	266	13	,	,	PUNCT
ma-24	266	14	(	(	PUNCT
ma-24	266	15	71	71	NUM
ma-24	266	16	)	)	PUNCT
ma-24	266	17	we	we	PRON
ma-24	266	18	also	also	ADV
ma-24	266	19	get	get	VERB
ma-24	266	20	the	the	DET
ma-24	266	21	trivial	trivial	ADJ
ma-24	266	22	solution	solution	NOUN
ma-24	266	23	(	(	PUNCT
ma-24	266	24	64	64	NUM
ma-24	266	25	)	)	PUNCT
ma-24	266	26	.	.	PUNCT
ma-24	267	1	one	one	PRON
ma-24	267	2	can	can	AUX
ma-24	267	3	easily	easily	ADV
ma-24	267	4	see	see	VERB
ma-24	267	5	that	that	SCONJ
ma-24	267	6	if	if	SCONJ
ma-24	267	7	λ	λ	PROPN
ma-24	267	8	=	=	SYM
ma-24	267	9	−	−	PROPN
ma-24	267	10	12β	12β	X
ma-24	267	11	α	α	NOUN
ma-24	267	12	,	,	PUNCT
ma-24	267	13	and	and	CCONJ
ma-24	267	14	µ	µ	X
ma-24	267	15	=	=	SYM
ma-24	267	16	0	0	NUM
ma-24	267	17	,	,	PUNCT
ma-24	267	18	(	(	PUNCT
ma-24	267	19	72	72	NUM
ma-24	267	20	)	)	PUNCT
ma-24	267	21	then	then	ADV
ma-24	267	22	ϕ	ϕ	X
ma-24	267	23	=	=	SYM
ma-24	267	24	−	−	PROPN
ma-24	267	25	12β	12β	NOUN
ma-24	267	26	αx2	αx2	NOUN
ma-24	267	27	,	,	PUNCT
ma-24	267	28	ψ	ψ	X
ma-24	267	29	=	=	SYM
ma-24	267	30	0	0	NUM
ma-24	267	31	,	,	PUNCT
ma-24	267	32	(	(	PUNCT
ma-24	267	33	73	73	NUM
ma-24	267	34	)	)	PUNCT
ma-24	267	35	which	which	PRON
ma-24	267	36	is	be	AUX
ma-24	267	37	a	a	DET
ma-24	267	38	solution	solution	NOUN
ma-24	267	39	of	of	ADP
ma-24	267	40	the	the	DET
ma-24	267	41	system	system	NOUN
ma-24	267	42	(	(	PUNCT
ma-24	267	43	61)-(62	61)-(62	NUM
ma-24	267	44	)	)	PUNCT
ma-24	267	45	.	.	PUNCT
ma-24	268	1	hence	hence	ADV
ma-24	268	2	u1(t	u1(t	ADP
ma-24	268	3	,	,	PUNCT
ma-24	268	4	x	x	X
ma-24	268	5	)	)	PUNCT
ma-24	268	6	=	=	SYM
ma-24	268	7	−	−	PROPN
ma-24	268	8	12β	12β	NUM
ma-24	268	9	αx2	αx2	NOUN
ma-24	268	10	,	,	PUNCT
ma-24	268	11	v1(t	v1(t	ADV
ma-24	268	12	,	,	PUNCT
ma-24	268	13	x	x	X
ma-24	268	14	)	)	PUNCT
ma-24	268	15	=	=	SYM
ma-24	268	16	0	0	NUM
ma-24	268	17	,	,	PUNCT
ma-24	268	18	(	(	PUNCT
ma-24	268	19	74	74	X
ma-24	268	20	)	)	PUNCT
ma-24	268	21	eur	eur	PROPN
ma-24	268	22	.	.	PUNCT
ma-24	269	1	j.	j.	PROPN
ma-24	269	2	math	math	PROPN
ma-24	269	3	.	.	PUNCT
ma-24	270	1	anal	anal	ADJ
ma-24	270	2	.	.	PUNCT
ma-24	271	1	1	1	NUM
ma-24	271	2	(	(	PUNCT
ma-24	271	3	2021	2021	NUM
ma-24	271	4	)	)	PUNCT
ma-24	271	5	142is	142is	VERB
ma-24	271	6	a	a	DET
ma-24	271	7	solution	solution	NOUN
ma-24	271	8	of	of	ADP
ma-24	271	9	the	the	DET
ma-24	271	10	coupled	couple	VERB
ma-24	271	11	kdv	kdv	NOUN
ma-24	271	12	system	system	NOUN
ma-24	271	13	(	(	PUNCT
ma-24	271	14	3	3	NUM
ma-24	271	15	)	)	PUNCT
ma-24	271	16	.	.	PUNCT
ma-24	272	1	case	case	NOUN
ma-24	272	2	two	two	NUM
ma-24	272	3	.	.	PUNCT
ma-24	273	1	taking	take	VERB
ma-24	273	2	λ	λ	X
ma-24	273	3	=	=	PUNCT
ma-24	273	4	−	−	PROPN
ma-24	273	5	6β	6β	NOUN
ma-24	273	6	α	α	NOUN
ma-24	273	7	(	(	PUNCT
ma-24	273	8	75	75	NUM
ma-24	273	9	)	)	PUNCT
ma-24	273	10	gives	give	VERB
ma-24	273	11	µ	µ	NOUN
ma-24	273	12	=	=	SYM
ma-24	273	13	±	±	NUM
ma-24	273	14	6βi	6βi	PROPN
ma-24	273	15	α	α	PROPN
ma-24	273	16	,	,	PUNCT
ma-24	273	17	(	(	PUNCT
ma-24	273	18	76	76	NUM
ma-24	273	19	)	)	PUNCT
ma-24	273	20	with	with	ADP
ma-24	273	21	i2	i2	PROPN
ma-24	273	22	=	=	SYM
ma-24	273	23	−1	−1	NOUN
ma-24	273	24	.	.	PUNCT
ma-24	274	1	consequently	consequently	ADV
ma-24	274	2	,	,	PUNCT
ma-24	274	3	u2(t	u2(t	PROPN
ma-24	274	4	,	,	PUNCT
ma-24	274	5	x	x	NOUN
ma-24	274	6	)	)	PUNCT
ma-24	274	7	=	=	SYM
ma-24	274	8	−	−	PROPN
ma-24	274	9	6β	6β	NOUN
ma-24	274	10	αx2	αx2	NOUN
ma-24	274	11	,	,	PUNCT
ma-24	274	12	v2(t	v2(t	PROPN
ma-24	274	13	,	,	PUNCT
ma-24	274	14	x	x	NOUN
ma-24	274	15	)	)	PUNCT
ma-24	274	16	=	=	SYM
ma-24	275	1	6iβ	6iβ	NOUN
ma-24	275	2	αx2	αx2	NOUN
ma-24	275	3	,	,	PUNCT
ma-24	275	4	(	(	PUNCT
ma-24	275	5	77	77	NUM
ma-24	275	6	)	)	PUNCT
ma-24	275	7	and	and	CCONJ
ma-24	275	8	u3(t	u3(t	PROPN
ma-24	275	9	,	,	PUNCT
ma-24	275	10	x	x	X
ma-24	275	11	)	)	PUNCT
ma-24	275	12	=	=	SYM
ma-24	276	1	−	−	PROPN
ma-24	276	2	6β	6β	NOUN
ma-24	276	3	αx2	αx2	NOUN
ma-24	276	4	,	,	PUNCT
ma-24	276	5	v3(t	v3(t	NOUN
ma-24	276	6	,	,	PUNCT
ma-24	276	7	x	x	X
ma-24	276	8	)	)	PUNCT
ma-24	276	9	=	=	SYM
ma-24	277	1	−	−	PROPN
ma-24	277	2	6iβ	6iβ	ADJ
ma-24	277	3	αx2	αx2	NOUN
ma-24	277	4	,	,	PUNCT
ma-24	277	5	(	(	PUNCT
ma-24	277	6	78	78	NUM
ma-24	277	7	)	)	PUNCT
ma-24	277	8	are	be	AUX
ma-24	277	9	solutions	solution	NOUN
ma-24	277	10	of	of	ADP
ma-24	277	11	the	the	DET
ma-24	277	12	coupled	couple	VERB
ma-24	277	13	kdv	kdv	NOUN
ma-24	277	14	system	system	NOUN
ma-24	277	15	.	.	PUNCT
ma-24	278	1	hence	hence	ADV
ma-24	278	2	lie	lie	VERB
ma-24	278	3	group	group	NOUN
ma-24	278	4	analysis	analysis	NOUN
ma-24	278	5	has	have	AUX
ma-24	278	6	given	give	VERB
ma-24	278	7	us	we	PRON
ma-24	278	8	three	three	NUM
ma-24	278	9	steady	steady	ADJ
ma-24	278	10	-	-	PUNCT
ma-24	278	11	statesolutions	statesolution	NOUN
ma-24	278	12	for	for	ADP
ma-24	278	13	the	the	DET
ma-24	278	14	coupled	couple	VERB
ma-24	278	15	kdv	kdv	NOUN
ma-24	278	16	system	system	NOUN
ma-24	278	17	under	under	ADP
ma-24	278	18	the	the	DET
ma-24	278	19	time	time	NOUN
ma-24	278	20	translation	translation	NOUN
ma-24	278	21	symmetry	symmetry	NOUN
ma-24	279	1	x1	x1	PROPN
ma-24	279	2	=	=	SYM
ma-24	279	3	∂	∂	NUM
ma-24	279	4	∂t	∂t	PROPN
ma-24	279	5	.	.	PUNCT
ma-24	280	1	x2	x2	PROPN
ma-24	280	2	=	=	SYM
ma-24	281	1	∂	∂	NUM
ma-24	281	2	∂x	∂x	PROPN
ma-24	281	3	.	.	PUNCT
ma-24	282	1	(	(	PUNCT
ma-24	282	2	79	79	X
ma-24	282	3	)	)	PUNCT
ma-24	282	4	solving	solve	VERB
ma-24	282	5	the	the	DET
ma-24	282	6	characteristic	characteristic	ADJ
ma-24	282	7	equations	equation	NOUN
ma-24	282	8	dt	dt	X
ma-24	282	9	0	0	NUM
ma-24	283	1	=	=	SYM
ma-24	283	2	dx	dx	PROPN
ma-24	283	3	1	1	NUM
ma-24	283	4	=	=	SYM
ma-24	283	5	du	du	X
ma-24	283	6	0	0	NUM
ma-24	284	1	=	=	SYM
ma-24	284	2	dv	dv	PROPN
ma-24	284	3	0	0	NUM
ma-24	284	4	,	,	PUNCT
ma-24	284	5	(	(	PUNCT
ma-24	284	6	80	80	NUM
ma-24	284	7	)	)	PUNCT
ma-24	284	8	associated	associate	VERB
ma-24	284	9	to	to	ADP
ma-24	284	10	x2	x2	PROPN
ma-24	284	11	gives	give	VERB
ma-24	284	12	the	the	DET
ma-24	284	13	invariants	invariant	NOUN
ma-24	284	14	j1	j1	PROPN
ma-24	284	15	=	=	SYM
ma-24	284	16	t	t	PROPN
ma-24	284	17	,	,	PUNCT
ma-24	284	18	,	,	PUNCT
ma-24	284	19	j2	j2	PROPN
ma-24	284	20	=	=	SYM
ma-24	284	21	u	u	PROPN
ma-24	284	22	j3	j3	PROPN
ma-24	284	23	=	=	SYM
ma-24	284	24	v	v	PROPN
ma-24	284	25	.	.	PUNCT
ma-24	285	1	(	(	PUNCT
ma-24	285	2	81	81	NUM
ma-24	285	3	)	)	PUNCT
ma-24	285	4	therefore	therefore	ADV
ma-24	285	5	,	,	PUNCT
ma-24	285	6	the	the	DET
ma-24	285	7	group	group	NOUN
ma-24	285	8	-	-	PUNCT
ma-24	285	9	invariant	invariant	ADJ
ma-24	285	10	solution	solution	NOUN
ma-24	285	11	is	be	AUX
ma-24	285	12	u	u	NOUN
ma-24	285	13	=	=	PROPN
ma-24	285	14	φ(t	φ(t	PROPN
ma-24	285	15	)	)	PUNCT
ma-24	285	16	,	,	PUNCT
ma-24	285	17	v	v	X
ma-24	285	18	=	=	SYM
ma-24	285	19	h(t	h(t	NUM
ma-24	285	20	)	)	PUNCT
ma-24	285	21	,	,	PUNCT
ma-24	285	22	(	(	PUNCT
ma-24	285	23	82	82	NUM
ma-24	285	24	)	)	PUNCT
ma-24	285	25	for	for	ADP
ma-24	285	26	arbitrary	arbitrary	ADJ
ma-24	285	27	functions	function	NOUN
ma-24	285	28	h	h	NOUN
ma-24	285	29	and	and	CCONJ
ma-24	285	30	φ	φ	PROPN
ma-24	285	31	.	.	PROPN
ma-24	285	32	substitution	substitution	NOUN
ma-24	285	33	of	of	ADP
ma-24	285	34	the	the	DET
ma-24	285	35	solutions	solution	NOUN
ma-24	285	36	from	from	ADP
ma-24	285	37	(	(	PUNCT
ma-24	285	38	82	82	NUM
ma-24	285	39	)	)	PUNCT
ma-24	285	40	into	into	ADP
ma-24	285	41	(	(	PUNCT
ma-24	285	42	3	3	NUM
ma-24	285	43	)	)	PUNCT
ma-24	285	44	,	,	PUNCT
ma-24	285	45	we	we	PRON
ma-24	285	46	get	get	VERB
ma-24	285	47	a	a	DET
ma-24	285	48	system	system	NOUN
ma-24	285	49	offirst	offirst	ADV
ma-24	285	50	order	order	NOUN
ma-24	285	51	ordinary	ordinary	ADJ
ma-24	285	52	des	des	PROPN
ma-24	285	53	,	,	PUNCT
ma-24	285	54	namely	namely	ADV
ma-24	285	55	,	,	PUNCT
ma-24	285	56	φ′(t	φ′(t	PROPN
ma-24	285	57	)	)	PUNCT
ma-24	285	58	=	=	SYM
ma-24	285	59	0	0	NUM
ma-24	285	60	,	,	PUNCT
ma-24	285	61	h′(t	h′(t	VERB
ma-24	285	62	)	)	PUNCT
ma-24	285	63	=	=	SYM
ma-24	285	64	0	0	NUM
ma-24	285	65	,	,	PUNCT
ma-24	285	66	(	(	PUNCT
ma-24	285	67	83	83	NUM
ma-24	285	68	)	)	PUNCT
ma-24	285	69	which	which	PRON
ma-24	285	70	is	be	AUX
ma-24	285	71	integrated	integrate	VERB
ma-24	285	72	once	once	ADV
ma-24	285	73	with	with	ADP
ma-24	285	74	respect	respect	NOUN
ma-24	285	75	to	to	ADP
ma-24	285	76	t	t	PROPN
ma-24	285	77	to	to	PART
ma-24	285	78	yield	yield	VERB
ma-24	285	79	,	,	PUNCT
ma-24	285	80	φ(t	φ(t	PROPN
ma-24	285	81	)	)	PUNCT
ma-24	285	82	=	=	SYM
ma-24	285	83	c1	c1	NOUN
ma-24	285	84	,	,	PUNCT
ma-24	285	85	h(t	h(t	PROPN
ma-24	285	86	)	)	PUNCT
ma-24	285	87	=	=	SYM
ma-24	285	88	c2	c2	PROPN
ma-24	285	89	,	,	PUNCT
ma-24	285	90	(	(	PUNCT
ma-24	285	91	84	84	NUM
ma-24	285	92	)	)	PUNCT
ma-24	285	93	for	for	ADP
ma-24	285	94	arbitrary	arbitrary	ADJ
ma-24	285	95	constants	constant	NOUN
ma-24	285	96	c1	c1	PROPN
ma-24	285	97	and	and	CCONJ
ma-24	285	98	c2	c2	PROPN
ma-24	285	99	.	.	PUNCT
ma-24	286	1	consequently	consequently	ADV
ma-24	286	2	,	,	PUNCT
ma-24	286	3	the	the	DET
ma-24	286	4	space	space	NOUN
ma-24	286	5	translation	translation	NOUN
ma-24	286	6	group	group	NOUN
ma-24	286	7	-	-	PUNCT
ma-24	286	8	invariant	invariant	ADJ
ma-24	286	9	solution	solution	NOUN
ma-24	286	10	ofthe	ofthe	NOUN
ma-24	286	11	system	system	NOUN
ma-24	286	12	(	(	PUNCT
ma-24	286	13	3	3	X
ma-24	286	14	)	)	PUNCT
ma-24	286	15	is	be	AUX
ma-24	286	16	u(t	u(t	NOUN
ma-24	286	17	,	,	PUNCT
ma-24	286	18	x	x	NOUN
ma-24	286	19	)	)	PUNCT
ma-24	286	20	=	=	SYM
ma-24	286	21	c1	c1	PROPN
ma-24	286	22	,	,	PUNCT
ma-24	286	23	v(t	v(t	PROPN
ma-24	286	24	,	,	PUNCT
ma-24	286	25	x	x	NOUN
ma-24	286	26	)	)	PUNCT
ma-24	286	27	=	=	SYM
ma-24	286	28	c2	c2	PROPN
ma-24	286	29	.	.	PUNCT
ma-24	287	1	(	(	PUNCT
ma-24	287	2	85	85	NUM
ma-24	287	3	)	)	PUNCT
ma-24	287	4	x3	x3	NOUN
ma-24	287	5	=	=	SYM
ma-24	287	6	αt	αt	PROPN
ma-24	287	7	∂	∂	NOUN
ma-24	287	8	∂x	∂x	PROPN
ma-24	287	9	+	+	CCONJ
ma-24	287	10	∂	∂	NUM
ma-24	287	11	∂u	∂u	PROPN
ma-24	287	12	.	.	PUNCT
ma-24	288	1	(	(	PUNCT
ma-24	288	2	86	86	NUM
ma-24	288	3	)	)	PUNCT
ma-24	288	4	eur	eur	PROPN
ma-24	288	5	.	.	PUNCT
ma-24	289	1	j.	j.	PROPN
ma-24	289	2	math	math	PROPN
ma-24	289	3	.	.	PUNCT
ma-24	290	1	anal	anal	ADJ
ma-24	290	2	.	.	PUNCT
ma-24	291	1	1	1	NUM
ma-24	291	2	(	(	PUNCT
ma-24	291	3	2021	2021	NUM
ma-24	291	4	)	)	PUNCT
ma-24	292	1	143solving	143solve	VERB
ma-24	292	2	the	the	DET
ma-24	292	3	characteristic	characteristic	ADJ
ma-24	292	4	equations	equation	NOUN
ma-24	292	5	dt	dt	X
ma-24	292	6	0	0	NUM
ma-24	293	1	=	=	NUM
ma-24	293	2	dx	dx	PROPN
ma-24	293	3	αt	αt	PROPN
ma-24	293	4	=	=	SYM
ma-24	293	5	du	du	PROPN
ma-24	293	6	1	1	NUM
ma-24	293	7	=	=	SYM
ma-24	293	8	dv	dv	PROPN
ma-24	293	9	0	0	NUM
ma-24	293	10	,	,	PUNCT
ma-24	293	11	(	(	PUNCT
ma-24	293	12	87	87	NUM
ma-24	293	13	)	)	PUNCT
ma-24	293	14	associated	associate	VERB
ma-24	293	15	to	to	ADP
ma-24	293	16	galilean	galilean	PROPN
ma-24	293	17	boost	boost	NOUN
ma-24	293	18	gives	give	VERB
ma-24	293	19	the	the	DET
ma-24	293	20	invariants	invariant	NOUN
ma-24	293	21	j1	j1	PROPN
ma-24	293	22	=	=	SYM
ma-24	293	23	t	t	PROPN
ma-24	293	24	,	,	PUNCT
ma-24	293	25	j2	j2	PROPN
ma-24	293	26	=	=	SYM
ma-24	293	27	v	v	PROPN
ma-24	293	28	,	,	PUNCT
ma-24	293	29	j3	j3	PROPN
ma-24	293	30	=	=	PROPN
ma-24	293	31	−u	−u	PROPN
ma-24	294	1	+	+	CCONJ
ma-24	294	2	x	x	SYM
ma-24	294	3	αt	αt	PROPN
ma-24	294	4	,	,	PUNCT
ma-24	294	5	t	t	PROPN
ma-24	294	6	6=	6=	PROPN
ma-24	294	7	0	0	NUM
ma-24	294	8	.	.	PUNCT
ma-24	295	1	(	(	PUNCT
ma-24	295	2	88	88	NUM
ma-24	295	3	)	)	PUNCT
ma-24	295	4	thus	thus	ADV
ma-24	295	5	the	the	DET
ma-24	295	6	invariant	invariant	ADJ
ma-24	295	7	solution	solution	NOUN
ma-24	295	8	of	of	ADP
ma-24	295	9	(	(	PUNCT
ma-24	295	10	3	3	NUM
ma-24	295	11	)	)	PUNCT
ma-24	295	12	is	be	AUX
ma-24	295	13	u	u	NOUN
ma-24	295	14	=	=	NOUN
ma-24	295	15	x	x	SYM
ma-24	295	16	αt	αt	NOUN
ma-24	295	17	−	−	PROPN
ma-24	295	18	g(t	g(t	PROPN
ma-24	295	19	)	)	PUNCT
ma-24	295	20	,	,	PUNCT
ma-24	295	21	v	v	X
ma-24	295	22	=	=	SYM
ma-24	295	23	f	f	PROPN
ma-24	295	24	(	(	PUNCT
ma-24	295	25	t	t	PROPN
ma-24	295	26	)	)	PUNCT
ma-24	295	27	,	,	PUNCT
ma-24	295	28	t	t	PROPN
ma-24	295	29	6=	6=	PROPN
ma-24	295	30	0	0	NUM
ma-24	295	31	,	,	PUNCT
ma-24	295	32	(	(	PUNCT
ma-24	295	33	89	89	NUM
ma-24	295	34	)	)	PUNCT
ma-24	295	35	for	for	ADP
ma-24	295	36	arbitrary	arbitrary	ADJ
ma-24	295	37	functions	function	NOUN
ma-24	295	38	f	f	PROPN
ma-24	295	39	and	and	CCONJ
ma-24	295	40	g.	g.	PROPN
ma-24	295	41	substitution	substitution	NOUN
ma-24	295	42	of	of	ADP
ma-24	295	43	the	the	DET
ma-24	295	44	values	value	NOUN
ma-24	295	45	of	of	ADP
ma-24	295	46	u	u	NOUN
ma-24	295	47	and	and	CCONJ
ma-24	295	48	v	v	NOUN
ma-24	295	49	from	from	ADP
ma-24	295	50	(	(	PUNCT
ma-24	295	51	89	89	NUM
ma-24	295	52	)	)	PUNCT
ma-24	295	53	into	into	ADP
ma-24	295	54	the	the	DET
ma-24	295	55	system	system	NOUN
ma-24	295	56	(	(	PUNCT
ma-24	295	57	3),we	3),we	NUM
ma-24	295	58	get	get	VERB
ma-24	295	59	a	a	DET
ma-24	295	60	nonlinear	nonlinear	ADJ
ma-24	295	61	system	system	NOUN
ma-24	295	62	of	of	ADP
ma-24	295	63	coupled	couple	VERB
ma-24	295	64	first	first	ADJ
ma-24	295	65	order	order	NOUN
ma-24	295	66	ordinary	ordinary	ADJ
ma-24	295	67	des	des	PROPN
ma-24	295	68	,	,	PUNCT
ma-24	295	69	namely	namely	ADV
ma-24	295	70	,	,	PUNCT
ma-24	295	71	tg′(t	tg′(t	NOUN
ma-24	295	72	)	)	PUNCT
ma-24	296	1	+	+	SYM
ma-24	296	2	g(t	g(t	PROPN
ma-24	296	3	)	)	PUNCT
ma-24	296	4	=	=	SYM
ma-24	297	1	0	0	NUM
ma-24	297	2	,	,	PUNCT
ma-24	297	3	tf	tf	NOUN
ma-24	297	4	′(t	′(t	PROPN
ma-24	297	5	)	)	PUNCT
ma-24	298	1	+	+	NUM
ma-24	298	2	f	f	X
ma-24	298	3	(	(	PUNCT
ma-24	298	4	t	t	PROPN
ma-24	298	5	)	)	PUNCT
ma-24	298	6	=	=	SYM
ma-24	298	7	0	0	NUM
ma-24	298	8	,	,	PUNCT
ma-24	298	9	(	(	PUNCT
ma-24	298	10	90	90	NUM
ma-24	298	11	)	)	PUNCT
ma-24	298	12	whose	whose	DET
ma-24	298	13	solutions	solution	NOUN
ma-24	298	14	are	be	AUX
ma-24	298	15	g(t	g(t	PROPN
ma-24	298	16	)	)	PUNCT
ma-24	298	17	=	=	SYM
ma-24	298	18	c1	c1	PROPN
ma-24	298	19	t	t	PROPN
ma-24	298	20	f	f	PROPN
ma-24	298	21	(	(	PUNCT
ma-24	298	22	t	t	PROPN
ma-24	298	23	)	)	PUNCT
ma-24	298	24	=	=	SYM
ma-24	299	1	c2	c2	PROPN
ma-24	299	2	t	t	PROPN
ma-24	299	3	,	,	PUNCT
ma-24	299	4	(	(	PUNCT
ma-24	299	5	91	91	NUM
ma-24	299	6	)	)	PUNCT
ma-24	299	7	for	for	ADP
ma-24	299	8	arbitrary	arbitrary	ADJ
ma-24	299	9	constants	constant	NOUN
ma-24	299	10	c1	c1	PROPN
ma-24	299	11	and	and	CCONJ
ma-24	299	12	c2	c2	PROPN
ma-24	299	13	.	.	PUNCT
ma-24	300	1	hence	hence	ADV
ma-24	300	2	the	the	DET
ma-24	300	3	galilean	galilean	PROPN
ma-24	300	4	boost	boost	PROPN
ma-24	300	5	group	group	NOUN
ma-24	300	6	-	-	PUNCT
ma-24	300	7	invariant	invariant	ADJ
ma-24	300	8	solution	solution	NOUN
ma-24	300	9	of	of	ADP
ma-24	300	10	the	the	DET
ma-24	300	11	system(3	system(3	NOUN
ma-24	300	12	)	)	PUNCT
ma-24	300	13	is	be	AUX
ma-24	300	14	u(t	u(t	NOUN
ma-24	300	15	,	,	PUNCT
ma-24	300	16	x	x	NOUN
ma-24	300	17	)	)	PUNCT
ma-24	300	18	=	=	SYM
ma-24	301	1	x	x	PUNCT
ma-24	301	2	+	+	CCONJ
ma-24	301	3	a	a	DET
ma-24	301	4	αt	αt	NOUN
ma-24	301	5	,	,	PUNCT
ma-24	301	6	v(t	v(t	PROPN
ma-24	301	7	,	,	PUNCT
ma-24	301	8	x	x	NOUN
ma-24	301	9	)	)	PUNCT
ma-24	301	10	=	=	SYM
ma-24	301	11	c2	c2	PROPN
ma-24	301	12	t	t	PROPN
ma-24	301	13	(	(	PUNCT
ma-24	301	14	92	92	NUM
ma-24	301	15	)	)	PUNCT
ma-24	301	16	where	where	SCONJ
ma-24	301	17	a	a	DET
ma-24	301	18	=	=	X
ma-24	301	19	−αc1	−αc1	PROPN
ma-24	301	20	and	and	CCONJ
ma-24	301	21	t	t	PROPN
ma-24	301	22	6=	6=	NUM
ma-24	301	23	0	0	NUM
ma-24	301	24	.	.	PUNCT
ma-24	302	1	the	the	DET
ma-24	302	2	scaling	scale	VERB
ma-24	302	3	x4	x4	PROPN
ma-24	302	4	=	=	PUNCT
ma-24	302	5	3	3	NUM
ma-24	302	6	t	t	NOUN
ma-24	302	7	∂	∂	NOUN
ma-24	302	8	∂t	∂t	PROPN
ma-24	303	1	+	+	CCONJ
ma-24	303	2	x	x	SYM
ma-24	303	3	∂	∂	NUM
ma-24	303	4	∂x	∂x	PROPN
ma-24	303	5	−	−	PROPN
ma-24	303	6	2u	2u	PROPN
ma-24	303	7	∂	∂	NOUN
ma-24	303	8	∂u	∂u	PROPN
ma-24	303	9	−	−	PROPN
ma-24	303	10	2v	2v	PROPN
ma-24	303	11	∂	∂	PROPN
ma-24	304	1	∂v	∂v	PROPN
ma-24	304	2	(	(	PUNCT
ma-24	304	3	93	93	NUM
ma-24	304	4	)	)	PUNCT
ma-24	304	5	.	.	PUNCT
ma-24	305	1	by	by	ADP
ma-24	305	2	solving	solve	VERB
ma-24	305	3	of	of	ADP
ma-24	305	4	the	the	DET
ma-24	305	5	characteristic	characteristic	ADJ
ma-24	305	6	equations	equation	NOUN
ma-24	305	7	dt	dt	X
ma-24	305	8	3	3	NUM
ma-24	305	9	t	t	NOUN
ma-24	305	10	=	=	SYM
ma-24	305	11	dx	dx	PROPN
ma-24	305	12	x	x	PUNCT
ma-24	306	1	=	=	PUNCT
ma-24	306	2	−	−	PROPN
ma-24	306	3	du	du	PROPN
ma-24	306	4	2u	2u	NOUN
ma-24	306	5	=	=	SYM
ma-24	306	6	−	−	PROPN
ma-24	306	7	dv	dv	PROPN
ma-24	306	8	2v	2v	PROPN
ma-24	306	9	,	,	PUNCT
ma-24	306	10	(	(	PUNCT
ma-24	306	11	94	94	NUM
ma-24	306	12	)	)	PUNCT
ma-24	306	13	associated	associate	VERB
ma-24	306	14	to	to	ADP
ma-24	306	15	this	this	DET
ma-24	306	16	symmetry	symmetry	NOUN
ma-24	306	17	,	,	PUNCT
ma-24	306	18	we	we	PRON
ma-24	306	19	obtain	obtain	VERB
ma-24	306	20	the	the	DET
ma-24	306	21	invariants	invariant	NOUN
ma-24	306	22	j1	j1	NOUN
ma-24	306	23	=	=	PUNCT
ma-24	306	24	x3	x3	PROPN
ma-24	306	25	t	t	PROPN
ma-24	306	26	,	,	PUNCT
ma-24	306	27	j2	j2	PROPN
ma-24	306	28	=	=	SYM
ma-24	306	29	ux2	ux2	PROPN
ma-24	306	30	,	,	PUNCT
ma-24	306	31	j3	j3	PROPN
ma-24	306	32	=	=	SYM
ma-24	306	33	vx2	vx2	PROPN
ma-24	306	34	.	.	PUNCT
ma-24	307	1	(	(	PUNCT
ma-24	307	2	95	95	NUM
ma-24	307	3	)	)	PUNCT
ma-24	307	4	generally	generally	ADV
ma-24	307	5	,	,	PUNCT
ma-24	307	6	the	the	DET
ma-24	307	7	group	group	NOUN
ma-24	307	8	-	-	PUNCT
ma-24	307	9	invariant	invariant	ADJ
ma-24	307	10	solution	solution	NOUN
ma-24	307	11	pair	pair	NOUN
ma-24	307	12	is	be	AUX
ma-24	307	13	u(t	u(t	NOUN
ma-24	307	14	,	,	PUNCT
ma-24	307	15	x	x	NOUN
ma-24	307	16	)	)	PUNCT
ma-24	307	17	=	=	SYM
ma-24	307	18	f	f	PROPN
ma-24	307	19	(	(	PUNCT
ma-24	307	20	λ	λ	NOUN
ma-24	307	21	)	)	PUNCT
ma-24	307	22	x2	x2	PROPN
ma-24	307	23	,	,	PUNCT
ma-24	307	24	v(t	v(t	PROPN
ma-24	307	25	,	,	PUNCT
ma-24	307	26	x	x	NOUN
ma-24	307	27	)	)	PUNCT
ma-24	307	28	=	=	SYM
ma-24	307	29	g(λ	g(λ	PROPN
ma-24	307	30	)	)	PUNCT
ma-24	307	31	x2	x2	NOUN
ma-24	307	32	,	,	PUNCT
ma-24	307	33	where	where	SCONJ
ma-24	307	34	λ	λ	X
ma-24	307	35	=	=	SYM
ma-24	307	36	x3	x3	PROPN
ma-24	307	37	t	t	PROPN
ma-24	307	38	,	,	PUNCT
ma-24	307	39	(	(	PUNCT
ma-24	307	40	96	96	NUM
ma-24	307	41	)	)	PUNCT
ma-24	307	42	and	and	CCONJ
ma-24	307	43	the	the	DET
ma-24	307	44	functions	function	NOUN
ma-24	307	45	f	f	PROPN
ma-24	307	46	and	and	CCONJ
ma-24	307	47	g	g	PROPN
ma-24	307	48	satisfy	satisfy	VERB
ma-24	307	49	the	the	DET
ma-24	307	50	system	system	NOUN
ma-24	307	51	of	of	ADP
ma-24	307	52	third	third	ADJ
ma-24	307	53	order	order	NOUN
ma-24	307	54	nonlinear	nonlinear	NOUN
ma-24	307	55	coupled	couple	VERB
ma-24	307	56	ordinary	ordinary	ADJ
ma-24	307	57	des	des	X
ma-24	307	58	2α(g2	2α(g2	NUM
ma-24	307	59	−	−	PROPN
ma-24	307	60	f	f	PROPN
ma-24	307	61	2)−	2)−	PROPN
ma-24	307	62	λ2f	λ2f	PROPN
ma-24	307	63	′	′	NUM
ma-24	308	1	+	+	CCONJ
ma-24	309	1	3αλ(f	3αλ(f	NUM
ma-24	309	2	f	f	NOUN
ma-24	309	3	′	′	NUM
ma-24	309	4	−	−	PROPN
ma-24	309	5	gg′	gg′	PROPN
ma-24	309	6	)	)	PUNCT
ma-24	310	1	+	+	SYM
ma-24	310	2	β(−24f	β(−24f	SYM
ma-24	311	1	+	+	NUM
ma-24	311	2	24λf	24λf	NOUN
ma-24	311	3	′	′	NOUN
ma-24	312	1	+	+	CCONJ
ma-24	312	2	27λ3f	27λ3f	PROPN
ma-24	312	3	′′′	′′′	NOUN
ma-24	312	4	)	)	PUNCT
ma-24	313	1	=	=	SYM
ma-24	313	2	0	0	NUM
ma-24	313	3	,	,	PUNCT
ma-24	313	4	(	(	PUNCT
ma-24	313	5	97	97	NUM
ma-24	313	6	)	)	PUNCT
ma-24	313	7	−4αf	−4αf	NOUN
ma-24	313	8	g	g	NOUN
ma-24	313	9	−	−	NOUN
ma-24	313	10	λ2g′	λ2g′	NOUN
ma-24	313	11	+	+	CCONJ
ma-24	313	12	3αλ(f	3αλ(f	NUM
ma-24	313	13	g)′	g)′	NOUN
ma-24	313	14	+	+	CCONJ
ma-24	314	1	β(−24	β(−24	PROPN
ma-24	314	2	g	g	NOUN
ma-24	314	3	+	+	NOUN
ma-24	314	4	24λg′	24λg′	NUM
ma-24	314	5	+	+	CCONJ
ma-24	314	6	27λ3g′′′	27λ3g′′′	NUM
ma-24	314	7	)	)	PUNCT
ma-24	314	8	=	=	NOUN
ma-24	314	9	0	0	NUM
ma-24	314	10	.	.	PUNCT
ma-24	315	1	(	(	PUNCT
ma-24	315	2	98	98	NUM
ma-24	315	3	)	)	PUNCT
ma-24	315	4	x	x	X
ma-24	316	1	=	=	PUNCT
ma-24	316	2	x1	x1	PROPN
ma-24	316	3	+	+	NUM
ma-24	316	4	cx2	cx2	X
ma-24	316	5	.	.	PUNCT
ma-24	317	1	(	(	PUNCT
ma-24	317	2	99	99	NUM
ma-24	317	3	)	)	PUNCT
ma-24	317	4	eur	eur	PROPN
ma-24	317	5	.	.	PUNCT
ma-24	318	1	j.	j.	PROPN
ma-24	318	2	math	math	PROPN
ma-24	318	3	.	.	PUNCT
ma-24	319	1	anal	anal	ADJ
ma-24	319	2	.	.	PUNCT
ma-24	320	1	1	1	NUM
ma-24	320	2	(	(	PUNCT
ma-24	320	3	2021	2021	NUM
ma-24	320	4	)	)	PUNCT
ma-24	320	5	144we	144we	PROPN
ma-24	320	6	consider	consider	VERB
ma-24	320	7	a	a	DET
ma-24	320	8	symmetry	symmetry	NOUN
ma-24	320	9	x	x	SYM
ma-24	320	10	,	,	PUNCT
ma-24	320	11	which	which	PRON
ma-24	320	12	is	be	AUX
ma-24	320	13	a	a	DET
ma-24	320	14	linear	linear	ADJ
ma-24	320	15	combination	combination	NOUN
ma-24	320	16	of	of	ADP
ma-24	320	17	the	the	DET
ma-24	320	18	time	time	NOUN
ma-24	320	19	and	and	CCONJ
ma-24	320	20	space	space	NOUN
ma-24	320	21	translationssymmetries	translationssymmetrie	NOUN
ma-24	320	22	,	,	PUNCT
ma-24	320	23	that	that	ADV
ma-24	320	24	is	be	AUX
ma-24	320	25	,	,	PUNCT
ma-24	320	26	x	x	SYM
ma-24	320	27	=	=	SYM
ma-24	320	28	∂	∂	NUM
ma-24	321	1	∂t	∂t	PROPN
ma-24	321	2	+	+	CCONJ
ma-24	321	3	c	c	PROPN
ma-24	321	4	∂	∂	NOUN
ma-24	321	5	∂x	∂x	PROPN
ma-24	321	6	,	,	PUNCT
ma-24	321	7	(	(	PUNCT
ma-24	321	8	100	100	NUM
ma-24	321	9	)	)	PUNCT
ma-24	321	10	for	for	ADP
ma-24	321	11	a	a	DET
ma-24	321	12	constant	constant	ADJ
ma-24	321	13	c	c	NOUN
ma-24	321	14	.	.	PUNCT
ma-24	322	1	the	the	DET
ma-24	322	2	invariants	invariant	NOUN
ma-24	322	3	associated	associate	VERB
ma-24	322	4	to	to	ADP
ma-24	322	5	this	this	DET
ma-24	322	6	symmetry	symmetry	NOUN
ma-24	322	7	x	x	PUNCT
ma-24	322	8	are	be	AUX
ma-24	322	9	j1	j1	NOUN
ma-24	322	10	=	=	PUNCT
ma-24	322	11	x	x	PUNCT
ma-24	322	12	−	−	PROPN
ma-24	322	13	ct	ct	PROPN
ma-24	322	14	,	,	PUNCT
ma-24	322	15	j2	j2	PROPN
ma-24	322	16	=	=	SYM
ma-24	322	17	u	u	PROPN
ma-24	322	18	,	,	PUNCT
ma-24	322	19	j3	j3	PROPN
ma-24	322	20	=	=	PUNCT
ma-24	322	21	v	v	PROPN
ma-24	322	22	.	.	PUNCT
ma-24	323	1	(	(	PUNCT
ma-24	323	2	101	101	NUM
ma-24	323	3	)	)	PUNCT
ma-24	323	4	hence	hence	ADV
ma-24	323	5	,	,	PUNCT
ma-24	323	6	the	the	DET
ma-24	323	7	invariant	invariant	ADJ
ma-24	323	8	solution	solution	NOUN
ma-24	323	9	for	for	ADP
ma-24	323	10	the	the	DET
ma-24	323	11	symmetry	symmetry	NOUN
ma-24	323	12	x	x	PUNCT
ma-24	323	13	is	be	AUX
ma-24	323	14	u	u	NOUN
ma-24	323	15	=	=	PROPN
ma-24	323	16	f	f	X
ma-24	323	17	(	(	PUNCT
ma-24	323	18	x	x	PROPN
ma-24	323	19	−	−	PROPN
ma-24	323	20	ct	ct	PROPN
ma-24	323	21	)	)	PUNCT
ma-24	323	22	,	,	PUNCT
ma-24	323	23	v	v	X
ma-24	323	24	=	=	SYM
ma-24	323	25	g(x	g(x	PROPN
ma-24	323	26	−	−	PROPN
ma-24	323	27	ct	ct	PROPN
ma-24	323	28	)	)	PUNCT
ma-24	323	29	,	,	PUNCT
ma-24	323	30	(	(	PUNCT
ma-24	323	31	102	102	NUM
ma-24	323	32	)	)	PUNCT
ma-24	323	33	for	for	ADP
ma-24	323	34	arbitrary	arbitrary	ADJ
ma-24	323	35	functions	function	NOUN
ma-24	323	36	f	f	PROPN
ma-24	323	37	and	and	CCONJ
ma-24	323	38	g.	g.	PROPN
ma-24	323	39	substitution	substitution	NOUN
ma-24	323	40	of	of	ADP
ma-24	323	41	u	u	NOUN
ma-24	323	42	and	and	CCONJ
ma-24	323	43	v	v	NOUN
ma-24	323	44	from	from	ADP
ma-24	323	45	(	(	PUNCT
ma-24	323	46	102	102	NUM
ma-24	323	47	)	)	PUNCT
ma-24	323	48	into	into	ADP
ma-24	323	49	the	the	DET
ma-24	323	50	system	system	NOUN
ma-24	323	51	(	(	PUNCT
ma-24	323	52	3	3	X
ma-24	323	53	)	)	PUNCT
ma-24	323	54	yields	yield	VERB
ma-24	323	55	asystem	asystem	NOUN
ma-24	323	56	of	of	ADP
ma-24	323	57	nonlinear	nonlinear	ADJ
ma-24	323	58	third	third	ADJ
ma-24	323	59	order	order	NOUN
ma-24	323	60	ordinary	ordinary	ADJ
ma-24	323	61	des	des	PROPN
ma-24	323	62	,	,	PUNCT
ma-24	323	63	namely	namely	ADV
ma-24	323	64	−cf	−cf	VERB
ma-24	323	65	′(ξ	′(ξ	NOUN
ma-24	323	66	)	)	PUNCT
ma-24	324	1	+	+	CCONJ
ma-24	324	2	α	α	PROPN
ma-24	324	3	{	{	PUNCT
ma-24	324	4	f	f	PROPN
ma-24	324	5	(	(	PUNCT
ma-24	324	6	ξ)f	ξ)f	PROPN
ma-24	324	7	′(ξ)−	′(ξ)−	PROPN
ma-24	324	8	g(ξ)g′(ξ	g(ξ)g′(ξ	PROPN
ma-24	324	9	)	)	PUNCT
ma-24	324	10	}	}	PUNCT
ma-24	325	1	+	+	CCONJ
ma-24	325	2	βf	βf	X
ma-24	325	3	′′′(ξ	′′′(ξ	NOUN
ma-24	325	4	)	)	PUNCT
ma-24	325	5	=	=	SYM
ma-24	325	6	0	0	NUM
ma-24	325	7	,	,	PUNCT
ma-24	325	8	−cg′(ξ	−cg′(ξ	PROPN
ma-24	325	9	)	)	PUNCT
ma-24	326	1	+	+	NUM
ma-24	326	2	α(f	α(f	X
ma-24	326	3	(	(	PUNCT
ma-24	326	4	ξ)g(ξ))′	ξ)g(ξ))′	PROPN
ma-24	326	5	+	+	NUM
ma-24	326	6	βg′′′(ξ	βg′′′(ξ	NOUN
ma-24	326	7	)	)	PUNCT
ma-24	326	8	=	=	PUNCT
ma-24	326	9	0,(103)which	0,(103)which	PRON
ma-24	326	10	on	on	ADP
ma-24	326	11	integrating	integrate	VERB
ma-24	326	12	once	once	ADV
ma-24	326	13	with	with	ADP
ma-24	326	14	respect	respect	NOUN
ma-24	326	15	to	to	ADP
ma-24	326	16	ξ	ξ	PROPN
ma-24	326	17	yields	yield	NOUN
ma-24	326	18	−cf	−cf	NOUN
ma-24	326	19	+	+	NOUN
ma-24	326	20	1	1	NUM
ma-24	326	21	2	2	NUM
ma-24	326	22	α(f	α(f	ADP
ma-24	326	23	2	2	NUM
ma-24	326	24	−	−	PROPN
ma-24	326	25	g2	g2	PROPN
ma-24	326	26	)	)	PUNCT
ma-24	327	1	+	+	CCONJ
ma-24	327	2	βf	βf	X
ma-24	328	1	′′	′′	PROPN
ma-24	328	2	+	+	CCONJ
ma-24	328	3	c1	c1	PROPN
ma-24	328	4	=	=	PUNCT
ma-24	328	5	0	0	PROPN
ma-24	328	6	,	,	PUNCT
ma-24	328	7	−cg	−cg	X
ma-24	328	8	+	+	CCONJ
ma-24	328	9	αf	αf	VERB
ma-24	328	10	g	g	NOUN
ma-24	328	11	+	+	NOUN
ma-24	328	12	βg′′	βg′′	PUNCT
ma-24	329	1	+	+	CCONJ
ma-24	329	2	c2	c2	PROPN
ma-24	329	3	=	=	SYM
ma-24	329	4	0	0	PROPN
ma-24	329	5	,	,	PUNCT
ma-24	329	6	(	(	PUNCT
ma-24	329	7	104	104	NUM
ma-24	329	8	)	)	PUNCT
ma-24	329	9	for	for	ADP
ma-24	329	10	arbitrary	arbitrary	ADJ
ma-24	329	11	constants	constant	NOUN
ma-24	329	12	c1	c1	PROPN
ma-24	329	13	and	and	CCONJ
ma-24	329	14	c2	c2	PROPN
ma-24	329	15	.	.	PUNCT
ma-24	330	1	remark	remark	PROPN
ma-24	330	2	3.1	3.1	NUM
ma-24	330	3	.	.	PUNCT
ma-24	331	1	if	if	SCONJ
ma-24	331	2	we	we	PRON
ma-24	331	3	take	take	VERB
ma-24	331	4	the	the	DET
ma-24	331	5	constants	constant	NOUN
ma-24	331	6	c1	c1	NOUN
ma-24	331	7	=	=	PROPN
ma-24	331	8	c2	c2	PROPN
ma-24	331	9	=	=	SYM
ma-24	331	10	0	0	PROPN
ma-24	331	11	,	,	PUNCT
ma-24	331	12	then	then	ADV
ma-24	331	13	when	when	SCONJ
ma-24	331	14	the	the	DET
ma-24	331	15	wave	wave	NOUN
ma-24	331	16	velocity	velocity	NOUN
ma-24	331	17	c	c	NOUN
ma-24	331	18	=	=	SYM
ma-24	331	19	0	0	NUM
ma-24	331	20	,	,	PUNCT
ma-24	331	21	we	we	PRON
ma-24	331	22	canrecover	canrecover	VERB
ma-24	331	23	the	the	DET
ma-24	331	24	stationary	stationary	ADJ
ma-24	331	25	solutions	solution	NOUN
ma-24	331	26	given	give	VERB
ma-24	331	27	in	in	ADP
ma-24	331	28	(	(	PUNCT
ma-24	331	29	3	3	NUM
ma-24	331	30	)	)	PUNCT
ma-24	331	31	.	.	PUNCT
ma-24	332	1	remark	remark	PROPN
ma-24	332	2	3.2	3.2	NUM
ma-24	332	3	.	.	PUNCT
ma-24	333	1	traveling	travel	VERB
ma-24	333	2	wave	wave	NOUN
ma-24	333	3	solutions	solution	NOUN
ma-24	333	4	of	of	ADP
ma-24	333	5	the	the	DET
ma-24	333	6	system	system	NOUN
ma-24	333	7	(	(	PUNCT
ma-24	333	8	3	3	X
ma-24	333	9	)	)	PUNCT
ma-24	333	10	must	must	AUX
ma-24	333	11	satisfy	satisfy	VERB
ma-24	333	12	the	the	DET
ma-24	333	13	system	system	NOUN
ma-24	333	14	(	(	PUNCT
ma-24	333	15	104	104	NUM
ma-24	333	16	)	)	PUNCT
ma-24	333	17	.	.	PUNCT
ma-24	334	1	computation	computation	NOUN
ma-24	334	2	of	of	ADP
ma-24	334	3	conservation	conservation	NOUN
ma-24	334	4	laws	law	NOUN
ma-24	334	5	for	for	ADP
ma-24	334	6	the	the	DET
ma-24	334	7	coupled	couple	VERB
ma-24	334	8	kdv	kdv	NOUN
ma-24	334	9	equations	equation	NOUN
ma-24	334	10	(	(	PUNCT
ma-24	334	11	3	3	X
ma-24	334	12	)	)	PUNCT
ma-24	334	13	is	be	AUX
ma-24	334	14	done	do	VERB
ma-24	334	15	using	use	VERB
ma-24	334	16	two	two	NUM
ma-24	334	17	meth	meth	NOUN
ma-24	334	18	-	-	PUNCT
ma-24	334	19	ods	od	NOUN
ma-24	334	20	;	;	PUNCT
ma-24	334	21	the	the	DET
ma-24	334	22	method	method	NOUN
ma-24	334	23	of	of	ADP
ma-24	334	24	multipliers	multiplier	NOUN
ma-24	334	25	and	and	CCONJ
ma-24	334	26	a	a	DET
ma-24	334	27	theorem	theorem	NOUN
ma-24	334	28	due	due	ADP
ma-24	334	29	to	to	ADP
ma-24	334	30	ibragimov	ibragimov	ADJ
ma-24	334	31	.	.	PUNCT
ma-24	335	1	we	we	PRON
ma-24	335	2	seek	seek	VERB
ma-24	335	3	local	local	ADJ
ma-24	335	4	conservation	conservation	NOUN
ma-24	335	5	lawmultipliers	lawmultiplier	NOUN
ma-24	335	6	for	for	ADP
ma-24	335	7	the	the	DET
ma-24	335	8	system	system	NOUN
ma-24	335	9	(	(	PUNCT
ma-24	335	10	3	3	NUM
ma-24	335	11	)	)	PUNCT
ma-24	335	12	,	,	PUNCT
ma-24	335	13	whose	whose	DET
ma-24	335	14	determining	determine	VERB
ma-24	335	15	equations	equation	NOUN
ma-24	335	16	are	be	AUX
ma-24	335	17	δ	δ	NOUN
ma-24	335	18	δu	δu	ADP
ma-24	335	19	[	[	PUNCT
ma-24	335	20	λ1∆1	λ1∆1	NOUN
ma-24	335	21	+	+	CCONJ
ma-24	335	22	λ2∆2	λ2∆2	X
ma-24	335	23	]	]	X
ma-24	335	24	=	=	SYM
ma-24	335	25	0	0	NUM
ma-24	335	26	,	,	PUNCT
ma-24	335	27	δ	δ	PROPN
ma-24	335	28	δv	δv	ADV
ma-24	335	29	[	[	PUNCT
ma-24	335	30	λ1∆1	λ1∆1	X
ma-24	335	31	+	+	CCONJ
ma-24	335	32	λ2∆2	λ2∆2	X
ma-24	335	33	]	]	X
ma-24	335	34	=	=	SYM
ma-24	335	35	0	0	NUM
ma-24	335	36	,	,	PUNCT
ma-24	335	37	(	(	PUNCT
ma-24	335	38	105	105	NUM
ma-24	335	39	)	)	PUNCT
ma-24	335	40	where	where	SCONJ
ma-24	335	41	δ	δ	PROPN
ma-24	335	42	δu	δu	ADP
ma-24	335	43	=	=	SYM
ma-24	335	44	∂	∂	NUM
ma-24	335	45	∂u	∂u	PROPN
ma-24	335	46	−dt	−dt	PROPN
ma-24	335	47	∂	∂	NUM
ma-24	335	48	∂ut	∂ut	PROPN
ma-24	335	49	−dx	−dx	PROPN
ma-24	335	50	∂	∂	NUM
ma-24	335	51	∂ux	∂ux	PROPN
ma-24	335	52	+	+	PROPN
ma-24	335	53	d2	d2	PROPN
ma-24	335	54	x	x	SYM
ma-24	335	55	∂	∂	NUM
ma-24	335	56	∂uxx	∂uxx	NUM
ma-24	335	57	−d3	−d3	NOUN
ma-24	335	58	x	x	SYM
ma-24	335	59	∂	∂	NUM
ma-24	335	60	∂uxxx	∂uxxx	PROPN
ma-24	335	61	+	+	PROPN
ma-24	335	62	.	.	PUNCT
ma-24	335	63	.	.	PUNCT
ma-24	335	64	.	.	PUNCT
ma-24	336	1	,	,	PUNCT
ma-24	336	2	(	(	PUNCT
ma-24	336	3	106	106	NUM
ma-24	336	4	)	)	PUNCT
ma-24	336	5	δ	δ	PROPN
ma-24	336	6	δv	δv	ADV
ma-24	336	7	=	=	SYM
ma-24	336	8	∂	∂	NUM
ma-24	336	9	∂v	∂v	PROPN
ma-24	336	10	−dt	−dt	X
ma-24	336	11	∂	∂	NUM
ma-24	336	12	∂vt	∂vt	PROPN
ma-24	336	13	−dx	−dx	PROPN
ma-24	336	14	∂	∂	NUM
ma-24	336	15	∂vx	∂vx	PROPN
ma-24	336	16	+	+	PROPN
ma-24	336	17	d2	d2	PROPN
ma-24	336	18	x	x	SYM
ma-24	336	19	∂	∂	NUM
ma-24	336	20	∂vxx	∂vxx	NUM
ma-24	336	21	−d3	−d3	NOUN
ma-24	336	22	x	x	SYM
ma-24	336	23	∂	∂	NOUN
ma-24	336	24	∂vxxx	∂vxxx	X
ma-24	336	25	+	+	X
ma-24	336	26	·	·	PUNCT
ma-24	336	27	·	·	PUNCT
ma-24	336	28	·	·	PUNCT
ma-24	336	29	,	,	PUNCT
ma-24	336	30	(	(	PUNCT
ma-24	336	31	107	107	NUM
ma-24	336	32	)	)	PUNCT
ma-24	336	33	are	be	AUX
ma-24	336	34	the	the	DET
ma-24	336	35	euler	euler	NOUN
ma-24	336	36	-	-	PUNCT
ma-24	336	37	lagrange	lagrange	NOUN
ma-24	336	38	operators	operator	NOUN
ma-24	336	39	and	and	CCONJ
ma-24	336	40	dt	dt	NOUN
ma-24	336	41	=	=	SYM
ma-24	336	42	∂	∂	PROPN
ma-24	337	1	∂t	∂t	PROPN
ma-24	337	2	+	+	CCONJ
ma-24	337	3	ut	ut	PROPN
ma-24	337	4	∂	∂	PROPN
ma-24	337	5	∂u	∂u	PROPN
ma-24	338	1	+	+	PROPN
ma-24	338	2	vt	vt	PROPN
ma-24	338	3	∂	∂	NOUN
ma-24	339	1	∂v	∂v	PROPN
ma-24	339	2	+	+	CCONJ
ma-24	339	3	utx	utx	PROPN
ma-24	339	4	∂	∂	NUM
ma-24	339	5	∂ux	∂ux	PROPN
ma-24	339	6	+	+	PROPN
ma-24	339	7	vtx	vtx	PROPN
ma-24	339	8	∂	∂	PROPN
ma-24	339	9	∂vx	∂vx	PROPN
ma-24	339	10	+	+	CCONJ
ma-24	339	11	utt	utt	PROPN
ma-24	339	12	∂	∂	NOUN
ma-24	339	13	∂ut	∂ut	PROPN
ma-24	339	14	+	+	CCONJ
ma-24	339	15	vtt	vtt	PROPN
ma-24	339	16	∂	∂	NUM
ma-24	339	17	∂vt	∂vt	PROPN
ma-24	339	18	+	+	X
ma-24	339	19	·	·	PUNCT
ma-24	339	20	·	·	PUNCT
ma-24	339	21	·	·	PUNCT
ma-24	339	22	,	,	PUNCT
ma-24	339	23	(	(	PUNCT
ma-24	339	24	108	108	NUM
ma-24	339	25	)	)	PUNCT
ma-24	339	26	dx	dx	PROPN
ma-24	339	27	=	=	SYM
ma-24	339	28	∂	∂	NOUN
ma-24	340	1	∂x	∂x	PROPN
ma-24	340	2	+	+	CCONJ
ma-24	340	3	ux	ux	PROPN
ma-24	340	4	∂	∂	NUM
ma-24	340	5	∂u	∂u	PROPN
ma-24	341	1	+	+	CCONJ
ma-24	341	2	vx	vx	PROPN
ma-24	341	3	∂	∂	NOUN
ma-24	341	4	∂v	∂v	PROPN
ma-24	341	5	+	+	PROPN
ma-24	341	6	uxx	uxx	PROPN
ma-24	341	7	∂	∂	X
ma-24	341	8	∂ux	∂ux	PROPN
ma-24	341	9	+	+	CCONJ
ma-24	341	10	vxx	vxx	PROPN
ma-24	341	11	∂	∂	X
ma-24	341	12	∂vx	∂vx	PROPN
ma-24	341	13	+	+	PROPN
ma-24	341	14	utx	utx	PROPN
ma-24	341	15	∂	∂	NOUN
ma-24	341	16	∂ut	∂ut	PROPN
ma-24	341	17	+	+	PROPN
ma-24	341	18	vtx	vtx	PROPN
ma-24	341	19	∂	∂	NOUN
ma-24	341	20	∂vt	∂vt	PROPN
ma-24	341	21	+	+	X
ma-24	341	22	·	·	PUNCT
ma-24	341	23	·	·	PUNCT
ma-24	341	24	·	·	PUNCT
ma-24	341	25	,	,	PUNCT
ma-24	341	26	(	(	PUNCT
ma-24	341	27	109	109	NUM
ma-24	341	28	)	)	PUNCT
ma-24	341	29	eur	eur	PROPN
ma-24	341	30	.	.	PUNCT
ma-24	342	1	j.	j.	PROPN
ma-24	342	2	math	math	PROPN
ma-24	342	3	.	.	PUNCT
ma-24	343	1	anal	anal	ADJ
ma-24	343	2	.	.	PUNCT
ma-24	344	1	1	1	NUM
ma-24	344	2	(	(	PUNCT
ma-24	344	3	2021	2021	NUM
ma-24	344	4	)	)	PUNCT
ma-24	344	5	145are	145are	NUM
ma-24	344	6	total	total	ADJ
ma-24	344	7	derivatives	derivative	NOUN
ma-24	344	8	operators	operator	NOUN
ma-24	344	9	.	.	PUNCT
ma-24	345	1	we	we	PRON
ma-24	345	2	look	look	VERB
ma-24	345	3	for	for	ADP
ma-24	345	4	second	second	ADJ
ma-24	345	5	order	order	NOUN
ma-24	345	6	multipliers	multiplier	NOUN
ma-24	345	7	,	,	PUNCT
ma-24	345	8	that	that	ADV
ma-24	345	9	is	is	ADV
ma-24	345	10	,	,	PUNCT
ma-24	345	11	λn	λn	PROPN
ma-24	345	12	=	=	PUNCT
ma-24	345	13	λn(t	λn(t	NUM
ma-24	345	14	,	,	PUNCT
ma-24	345	15	x	x	X
ma-24	345	16	,	,	PUNCT
ma-24	345	17	u	u	NOUN
ma-24	345	18	,	,	PUNCT
ma-24	345	19	ux	ux	PROPN
ma-24	345	20	,	,	PUNCT
ma-24	345	21	uxx	uxx	PROPN
ma-24	345	22	,	,	PUNCT
ma-24	345	23	v	v	INTJ
ma-24	345	24	,	,	PUNCT
ma-24	345	25	vx	vx	PROPN
ma-24	345	26	,	,	PUNCT
ma-24	345	27	vxx	vxx	PROPN
ma-24	345	28	)	)	PUNCT
ma-24	345	29	,	,	PUNCT
ma-24	345	30	n	n	NOUN
ma-24	345	31	=	=	SYM
ma-24	345	32	1	1	NUM
ma-24	345	33	,	,	PUNCT
ma-24	345	34	2	2	NUM
ma-24	345	35	.	.	PUNCT
ma-24	346	1	(	(	PUNCT
ma-24	346	2	110	110	NUM
ma-24	346	3	)	)	PUNCT
ma-24	346	4	the	the	DET
ma-24	346	5	determining	determine	VERB
ma-24	346	6	equations	equation	NOUN
ma-24	346	7	(	(	PUNCT
ma-24	346	8	105	105	NUM
ma-24	346	9	)	)	PUNCT
ma-24	346	10	become	become	VERB
ma-24	346	11	δ	δ	X
ma-24	346	12	δu	δu	ADP
ma-24	346	13	[	[	PUNCT
ma-24	346	14	λ1{ut	λ1{ut	X
ma-24	346	15	+	+	CCONJ
ma-24	346	16	αuux	αuux	PROPN
ma-24	346	17	−	−	PROPN
ma-24	346	18	αvvx	αvvx	NOUN
ma-24	346	19	+	+	CCONJ
ma-24	346	20	βuxxx}+	βuxxx}+	NOUN
ma-24	346	21	λ2{vt	λ2{vt	NOUN
ma-24	346	22	+	+	CCONJ
ma-24	346	23	αuvx	αuvx	PROPN
ma-24	346	24	+	+	CCONJ
ma-24	346	25	αvux	αvux	NOUN
ma-24	346	26	+	+	NOUN
ma-24	346	27	βvxxx	βvxxx	ADJ
ma-24	346	28	}	}	PUNCT
ma-24	346	29	]	]	PUNCT
ma-24	347	1	=	=	PUNCT
ma-24	347	2	0	0	NUM
ma-24	347	3	,	,	PUNCT
ma-24	347	4	(	(	PUNCT
ma-24	347	5	111	111	NUM
ma-24	347	6	)	)	PUNCT
ma-24	347	7	δ	δ	NOUN
ma-24	347	8	δv	δv	ADV
ma-24	347	9	[	[	PUNCT
ma-24	347	10	λ1{ut	λ1{ut	X
ma-24	347	11	+	+	CCONJ
ma-24	347	12	αuux	αuux	PROPN
ma-24	347	13	−	−	PROPN
ma-24	347	14	αvvx	αvvx	NOUN
ma-24	347	15	+	+	CCONJ
ma-24	347	16	βuxxx}+	βuxxx}+	NOUN
ma-24	347	17	λ2{vt	λ2{vt	NOUN
ma-24	347	18	+	+	CCONJ
ma-24	347	19	αuvx	αuvx	PROPN
ma-24	347	20	+	+	CCONJ
ma-24	347	21	αvux	αvux	NOUN
ma-24	347	22	+	+	NOUN
ma-24	347	23	βvxxx	βvxxx	ADJ
ma-24	347	24	}	}	PUNCT
ma-24	347	25	]	]	PUNCT
ma-24	348	1	=	=	PUNCT
ma-24	348	2	0	0	X
ma-24	348	3	.	.	PUNCT
ma-24	349	1	(	(	PUNCT
ma-24	349	2	112	112	NUM
ma-24	349	3	)	)	PUNCT
ma-24	349	4	expanding	expand	VERB
ma-24	349	5	(	(	PUNCT
ma-24	349	6	111)-(112	111)-(112	NUM
ma-24	349	7	)	)	PUNCT
ma-24	349	8	and	and	CCONJ
ma-24	349	9	splitting	splitting	NOUN
ma-24	349	10	on	on	ADP
ma-24	349	11	derivatives	derivative	NOUN
ma-24	349	12	of	of	ADP
ma-24	349	13	u	u	NOUN
ma-24	349	14	and	and	CCONJ
ma-24	349	15	v	v	NOUN
ma-24	349	16	yields	yield	NOUN
ma-24	349	17	an	an	DET
ma-24	349	18	overdetermined	overdetermined	ADJ
ma-24	349	19	system	system	NOUN
ma-24	349	20	of22	of22	PROPN
ma-24	349	21	pdes	pde	NOUN
ma-24	349	22	,	,	PUNCT
ma-24	349	23	namely	namely	ADV
ma-24	349	24	λ1	λ1	ADJ
ma-24	349	25	xx	xx	NUM
ma-24	350	1	=	=	SYM
ma-24	350	2	0	0	NUM
ma-24	350	3	,	,	PUNCT
ma-24	350	4	λ2	λ2	NOUN
ma-24	350	5	xx	xx	NUM
ma-24	351	1	=	=	SYM
ma-24	351	2	0	0	NUM
ma-24	352	1	λ1	λ1	ADJ
ma-24	352	2	vx	vx	PROPN
ma-24	352	3	=	=	SYM
ma-24	352	4	0	0	PROPN
ma-24	352	5	,	,	PUNCT
ma-24	352	6	λ2	λ2	PROPN
ma-24	352	7	vx	vx	PROPN
ma-24	352	8	=	=	SYM
ma-24	352	9	0	0	PROPN
ma-24	352	10	,	,	PUNCT
ma-24	352	11	λ1	λ1	ADJ
ma-24	352	12	xvxx	xvxx	NOUN
ma-24	352	13	=	=	X
ma-24	352	14	0	0	NUM
ma-24	352	15	,	,	PUNCT
ma-24	352	16	λ2	λ2	NOUN
ma-24	352	17	xvxx	xvxx	NOUN
ma-24	352	18	=	=	X
ma-24	353	1	0	0	NUM
ma-24	353	2	,	,	PUNCT
ma-24	353	3	βλ1	βλ1	PUNCT
ma-24	354	1	vv	vv	CCONJ
ma-24	354	2	−	−	PROPN
ma-24	354	3	αλ2	αλ2	VERB
ma-24	354	4	vxx	vxx	PROPN
ma-24	354	5	=	=	SYM
ma-24	354	6	0	0	PROPN
ma-24	354	7	,	,	PUNCT
ma-24	354	8	βλ2	βλ2	VERB
ma-24	354	9	vv	vv	PUNCT
ma-24	355	1	+	+	CCONJ
ma-24	355	2	αλ1	αλ1	SCONJ
ma-24	355	3	vvxx	vvxx	NOUN
ma-24	355	4	=	=	SYM
ma-24	355	5	0	0	NUM
ma-24	355	6	,	,	PUNCT
ma-24	355	7	λ1	λ1	ADJ
ma-24	355	8	vvxx	vvxx	NOUN
ma-24	355	9	=	=	SYM
ma-24	355	10	0	0	NUM
ma-24	355	11	,	,	PUNCT
ma-24	355	12	λ2	λ2	NOUN
ma-24	355	13	vvxx	vvxx	NOUN
ma-24	355	14	=	=	SYM
ma-24	355	15	0	0	NUM
ma-24	355	16	,	,	PUNCT
ma-24	355	17	λ1	λ1	ADJ
ma-24	355	18	vxxvxx	vxxvxx	NOUN
ma-24	355	19	=	=	SYM
ma-24	355	20	0	0	NUM
ma-24	355	21	,	,	PUNCT
ma-24	355	22	λ2	λ2	NOUN
ma-24	355	23	vxxvxx	vxxvxx	NOUN
ma-24	355	24	=	=	SYM
ma-24	355	25	0	0	NUM
ma-24	355	26	,	,	PUNCT
ma-24	355	27	λ1	λ1	ADJ
ma-24	355	28	u	u	NOUN
ma-24	355	29	+	+	CCONJ
ma-24	355	30	λ2	λ2	NOUN
ma-24	355	31	v	v	NOUN
ma-24	355	32	=	=	SYM
ma-24	355	33	0	0	NUM
ma-24	355	34	,	,	PUNCT
ma-24	355	35	λ1	λ1	PROPN
ma-24	355	36	t	t	PROPN
ma-24	355	37	+	+	CCONJ
ma-24	356	1	α	α	PROPN
ma-24	356	2	(	(	PUNCT
ma-24	356	3	λ2	λ2	NOUN
ma-24	356	4	xv	xv	PROPN
ma-24	357	1	+	+	X
ma-24	357	2	λ1	λ1	PROPN
ma-24	357	3	xu	xu	INTJ
ma-24	357	4	)	)	PUNCT
ma-24	358	1	=	=	SYM
ma-24	358	2	0	0	NUM
ma-24	358	3	,	,	PUNCT
ma-24	358	4	λ2	λ2	NOUN
ma-24	358	5	t	t	NOUN
ma-24	358	6	+	+	CCONJ
ma-24	358	7	α	α	PROPN
ma-24	358	8	(	(	PUNCT
ma-24	358	9	λ2	λ2	PROPN
ma-24	358	10	xu	xu	PROPN
ma-24	358	11	−	−	PROPN
ma-24	359	1	λ1	λ1	PROPN
ma-24	359	2	xv	xv	X
ma-24	359	3	)	)	PUNCT
ma-24	360	1	=	=	SYM
ma-24	360	2	0	0	NUM
ma-24	360	3	,	,	PUNCT
ma-24	360	4	λ2	λ2	NOUN
ma-24	360	5	u	u	NOUN
ma-24	360	6	−	−	PROPN
ma-24	360	7	λ1	λ1	PROPN
ma-24	360	8	v	v	NOUN
ma-24	360	9	=	=	SYM
ma-24	360	10	0	0	NUM
ma-24	360	11	,	,	PUNCT
ma-24	360	12	λ1	λ1	PROPN
ma-24	360	13	ux	ux	NOUN
ma-24	360	14	=	=	SYM
ma-24	360	15	0	0	PROPN
ma-24	360	16	,	,	PUNCT
ma-24	360	17	λ2	λ2	NOUN
ma-24	360	18	ux	ux	NOUN
ma-24	360	19	=	=	SYM
ma-24	360	20	0	0	PROPN
ma-24	360	21	,	,	PUNCT
ma-24	360	22	λ1	λ1	PROPN
ma-24	360	23	uxx	uxx	NOUN
ma-24	360	24	+	+	CCONJ
ma-24	361	1	λ2	λ2	NOUN
ma-24	361	2	vxx	vxx	NOUN
ma-24	361	3	=	=	SYM
ma-24	361	4	0	0	NUM
ma-24	361	5	,	,	PUNCT
ma-24	361	6	λ2	λ2	PROPN
ma-24	361	7	uxx	uxx	NOUN
ma-24	361	8	−	−	PROPN
ma-24	362	1	λ1	λ1	PROPN
ma-24	362	2	vxx	vxx	PROPN
ma-24	362	3	=	=	SYM
ma-24	362	4	0	0	NUM
ma-24	362	5	,	,	PUNCT
ma-24	362	6	λ2	λ2	NOUN
ma-24	362	7	vx	vx	PROPN
ma-24	362	8	=	=	SYM
ma-24	362	9	0	0	PROPN
ma-24	363	1	λ1	λ1	ADJ
ma-24	363	2	vx	vx	PROPN
ma-24	363	3	=	=	SYM
ma-24	363	4	0.(113)calculations	0.(113)calculation	NOUN
ma-24	363	5	reveal	reveal	VERB
ma-24	363	6	the	the	DET
ma-24	363	7	solution	solution	NOUN
ma-24	363	8	of	of	ADP
ma-24	363	9	the	the	DET
ma-24	363	10	system	system	NOUN
ma-24	363	11	(	(	PUNCT
ma-24	363	12	113	113	NUM
ma-24	363	13	)	)	PUNCT
ma-24	363	14	as	as	ADP
ma-24	363	15	λ1	λ1	PROPN
ma-24	363	16	=	=	SYM
ma-24	363	17	α	α	NOUN
ma-24	363	18	2β	2β	NOUN
ma-24	363	19	(	(	PUNCT
ma-24	363	20	c3{u2	c3{u2	PROPN
ma-24	363	21	−	−	NOUN
ma-24	363	22	v2}+	v2}+	NOUN
ma-24	363	23	2c4uv	2c4uv	NUM
ma-24	363	24	)	)	PUNCT
ma-24	364	1	+	+	CCONJ
ma-24	364	2	(	(	PUNCT
ma-24	364	3	c2	c2	PROPN
ma-24	364	4	t	t	PROPN
ma-24	364	5	+	+	CCONJ
ma-24	364	6	c5)u	c5)u	NOUN
ma-24	364	7	+	+	CCONJ
ma-24	364	8	(	(	PUNCT
ma-24	364	9	c1	c1	PROPN
ma-24	364	10	t	t	PROPN
ma-24	364	11	+	+	CCONJ
ma-24	364	12	c6)v	c6)v	VERB
ma-24	364	13	+	+	CCONJ
ma-24	364	14	c3uxx	c3uxx	ADJ
ma-24	364	15	+	+	CCONJ
ma-24	364	16	c4vxx	c4vxx	PROPN
ma-24	364	17	+	+	NUM
ma-24	364	18	c7	c7	PROPN
ma-24	364	19	−	−	PROPN
ma-24	364	20	1	1	NUM
ma-24	364	21	α	α	PROPN
ma-24	364	22	c2x	c2x	NOUN
ma-24	364	23	,	,	PUNCT
ma-24	364	24	λ2	λ2	NOUN
ma-24	364	25	=	=	SYM
ma-24	364	26	α	α	NUM
ma-24	364	27	2β	2β	NOUN
ma-24	364	28	(	(	PUNCT
ma-24	364	29	c4{u2	c4{u2	PROPN
ma-24	364	30	−	−	PROPN
ma-24	364	31	v2	v2	PROPN
ma-24	364	32	}	}	PUNCT
ma-24	364	33	−	−	PROPN
ma-24	364	34	2c3uv+	2c3uv+	NUM
ma-24	364	35	)	)	PUNCT
ma-24	365	1	+	+	CCONJ
ma-24	365	2	(	(	PUNCT
ma-24	365	3	c1	c1	PROPN
ma-24	365	4	t	t	PROPN
ma-24	365	5	+	+	CCONJ
ma-24	365	6	c6)u	c6)u	PROPN
ma-24	365	7	−	−	PROPN
ma-24	365	8	(	(	PUNCT
ma-24	365	9	c2	c2	PROPN
ma-24	365	10	t	t	PROPN
ma-24	365	11	+	+	CCONJ
ma-24	365	12	c5)v	c5)v	NOUN
ma-24	365	13	+	+	CCONJ
ma-24	365	14	c4uxx	c4uxx	NUM
ma-24	365	15	−	−	NOUN
ma-24	366	1	c3vxx	c3vxx	PROPN
ma-24	366	2	+	+	CCONJ
ma-24	366	3	c8	c8	PROPN
ma-24	366	4	−	−	PROPN
ma-24	366	5	1	1	NUM
ma-24	366	6	α	α	NOUN
ma-24	366	7	c1x,(114)for	c1x,(114)for	ADP
ma-24	366	8	arbitrary	arbitrary	ADJ
ma-24	366	9	constants	constant	NOUN
ma-24	366	10	c1	c1	PROPN
ma-24	366	11	,	,	PUNCT
ma-24	366	12	.	.	PUNCT
ma-24	366	13	.	.	PUNCT
ma-24	366	14	.	.	PUNCT
ma-24	367	1	,	,	PUNCT
ma-24	368	1	c8	c8	PROPN
ma-24	368	2	.	.	PUNCT
ma-24	369	1	remark	remark	PROPN
ma-24	369	2	3.3	3.3	NUM
ma-24	369	3	.	.	PUNCT
ma-24	370	1	essentially	essentially	ADV
ma-24	370	2	,	,	PUNCT
ma-24	370	3	the	the	DET
ma-24	370	4	nonlinear	nonlinear	ADJ
ma-24	370	5	coupled	couple	VERB
ma-24	370	6	system	system	NOUN
ma-24	370	7	of	of	ADP
ma-24	370	8	kdv	kdv	NOUN
ma-24	370	9	equations	equation	NOUN
ma-24	370	10	(	(	PUNCT
ma-24	370	11	3	3	X
ma-24	370	12	)	)	PUNCT
ma-24	370	13	has	have	VERB
ma-24	370	14	eight	eight	NUM
ma-24	370	15	sets	set	NOUN
ma-24	370	16	of	of	ADP
ma-24	370	17	localconservation	localconservation	NOUN
ma-24	370	18	law	law	NOUN
ma-24	370	19	multipliers	multiplier	NOUN
ma-24	370	20	.	.	PUNCT
ma-24	371	1	solving	solve	VERB
ma-24	371	2	(	(	PUNCT
ma-24	371	3	105	105	NUM
ma-24	371	4	)	)	PUNCT
ma-24	371	5	„	„	PUNCT
ma-24	371	6	we	we	PRON
ma-24	371	7	obtain	obtain	VERB
ma-24	371	8	conserved	conserved	ADJ
ma-24	371	9	vectors	vector	NOUN
ma-24	371	10	corresponding	correspond	VERB
ma-24	371	11	to	to	ADP
ma-24	371	12	each	each	DET
ma-24	371	13	set	set	NOUN
ma-24	371	14	of	of	ADP
ma-24	371	15	multipliers	multiplier	NOUN
ma-24	371	16	as	as	ADP
ma-24	371	17	shownbelow.(i	shownbelow.(i	NOUN
ma-24	371	18	)	)	PUNCT
ma-24	371	19	the	the	DET
ma-24	371	20	multiplier	multipli	ADJ
ma-24	371	21	(	(	PUNCT
ma-24	371	22	λ1	λ1	PROPN
ma-24	371	23	1,λ2	1,λ2	NUM
ma-24	371	24	1	1	NUM
ma-24	371	25	)	)	PUNCT
ma-24	371	26	=	=	SYM
ma-24	371	27	(	(	PUNCT
ma-24	371	28	tv	tv	NOUN
ma-24	371	29	,	,	PUNCT
ma-24	371	30	tu	tu	PROPN
ma-24	371	31	−	−	PROPN
ma-24	371	32	x	x	SYM
ma-24	371	33	α	α	PROPN
ma-24	371	34	)	)	PUNCT
ma-24	371	35	,	,	PUNCT
ma-24	371	36	(	(	PUNCT
ma-24	371	37	115	115	NUM
ma-24	371	38	)	)	PUNCT
ma-24	371	39	has	have	VERB
ma-24	371	40	the	the	DET
ma-24	371	41	conserved	conserve	VERB
ma-24	371	42	vectors	vector	NOUN
ma-24	371	43	t	t	PROPN
ma-24	371	44	t1	t1	PROPN
ma-24	371	45	=	=	PROPN
ma-24	372	1	tuv	tuv	PROPN
ma-24	373	1	−	−	PROPN
ma-24	373	2	xv	xv	PROPN
ma-24	374	1	α	α	PROPN
ma-24	374	2	,	,	PUNCT
ma-24	374	3	t	t	PROPN
ma-24	374	4	x1	x1	PROPN
ma-24	375	1	=	=	PUNCT
ma-24	375	2	β	β	X
ma-24	375	3	[	[	PUNCT
ma-24	375	4	t{vuxx	t{vuxx	X
ma-24	375	5	+	+	CCONJ
ma-24	375	6	uvxx	uvxx	NOUN
ma-24	375	7	−	−	NOUN
ma-24	375	8	vxux}+	vxux}+	NOUN
ma-24	375	9	1	1	NUM
ma-24	375	10	α	α	NOUN
ma-24	375	11	{	{	PUNCT
ma-24	375	12	vx	vx	PROPN
ma-24	375	13	−	−	PROPN
ma-24	375	14	xvxx	xvxx	NOUN
ma-24	375	15	}	}	PUNCT
ma-24	375	16	]	]	PUNCT
ma-24	376	1	+	+	CCONJ
ma-24	376	2	α	α	PROPN
ma-24	376	3	[	[	PUNCT
ma-24	376	4	t	t	X
ma-24	376	5	(	(	PUNCT
ma-24	376	6	u2v	u2v	PROPN
ma-24	376	7	−	−	PROPN
ma-24	376	8	v3	v3	PROPN
ma-24	376	9	3	3	NUM
ma-24	376	10	)	)	PUNCT
ma-24	376	11	]	]	PUNCT
ma-24	377	1	(	(	PUNCT
ma-24	377	2	116	116	NUM
ma-24	377	3	)	)	PUNCT
ma-24	377	4	−xuv	−xuv	NOUN
ma-24	377	5	.	.	PUNCT
ma-24	378	1	(	(	PUNCT
ma-24	378	2	117	117	NUM
ma-24	378	3	)	)	PUNCT
ma-24	378	4	(	(	PUNCT
ma-24	378	5	ii	ii	NOUN
ma-24	378	6	)	)	PUNCT
ma-24	378	7	the	the	DET
ma-24	378	8	multiplier	multipli	ADJ
ma-24	378	9	(	(	PUNCT
ma-24	378	10	λ1	λ1	ADJ
ma-24	378	11	2,λ2	2,λ2	NUM
ma-24	378	12	2	2	NUM
ma-24	378	13	)	)	PUNCT
ma-24	378	14	=	=	PUNCT
ma-24	379	1	(	(	PUNCT
ma-24	379	2	tu	tu	PROPN
ma-24	379	3	−	−	PROPN
ma-24	379	4	x	x	SYM
ma-24	379	5	α	α	PROPN
ma-24	379	6	,	,	PUNCT
ma-24	379	7	−tv	−tv	NOUN
ma-24	379	8	)	)	PUNCT
ma-24	379	9	,	,	PUNCT
ma-24	379	10	(	(	PUNCT
ma-24	379	11	118	118	NUM
ma-24	379	12	)	)	PUNCT
ma-24	379	13	eur	eur	PROPN
ma-24	379	14	.	.	PUNCT
ma-24	380	1	j.	j.	PROPN
ma-24	380	2	math	math	PROPN
ma-24	380	3	.	.	PUNCT
ma-24	381	1	anal	anal	ADJ
ma-24	381	2	.	.	PUNCT
ma-24	382	1	1	1	NUM
ma-24	382	2	(	(	PUNCT
ma-24	382	3	2021	2021	NUM
ma-24	382	4	)	)	PUNCT
ma-24	383	1	146has	146has	NUM
ma-24	383	2	the	the	DET
ma-24	383	3	conserved	conserve	VERB
ma-24	383	4	vectors	vector	NOUN
ma-24	383	5	t	t	NOUN
ma-24	383	6	t2	t2	PROPN
ma-24	383	7	=	=	SYM
ma-24	383	8	t	t	PROPN
ma-24	383	9	2	2	NUM
ma-24	383	10	{	{	PUNCT
ma-24	383	11	u2	u2	PROPN
ma-24	383	12	−	−	PROPN
ma-24	383	13	v2	v2	PROPN
ma-24	383	14	}	}	PUNCT
ma-24	383	15	−	−	PROPN
ma-24	384	1	xu	xu	PROPN
ma-24	384	2	α	α	PROPN
ma-24	384	3	,	,	PUNCT
ma-24	384	4	t	t	PROPN
ma-24	384	5	x2	x2	PROPN
ma-24	385	1	=	=	PUNCT
ma-24	385	2	β	β	X
ma-24	385	3	[	[	PUNCT
ma-24	385	4	t	t	X
ma-24	385	5	(	(	PUNCT
ma-24	385	6	uuxx	uuxx	ADJ
ma-24	385	7	−	−	PROPN
ma-24	385	8	vvxx	vvxx	NOUN
ma-24	385	9	+	+	CCONJ
ma-24	385	10	1	1	NUM
ma-24	385	11	2	2	NUM
ma-24	385	12	{	{	PUNCT
ma-24	385	13	v2	v2	NOUN
ma-24	385	14	x	x	PUNCT
ma-24	385	15	−	−	PROPN
ma-24	385	16	u2	u2	PROPN
ma-24	385	17	x	x	PROPN
ma-24	385	18	}	}	PUNCT
ma-24	385	19	)	)	PUNCT
ma-24	386	1	+	+	CCONJ
ma-24	386	2	1	1	NUM
ma-24	386	3	α	α	NOUN
ma-24	386	4	{	{	PUNCT
ma-24	386	5	ux	ux	ADV
ma-24	386	6	−	−	PROPN
ma-24	386	7	xuxx	xuxx	PROPN
ma-24	386	8	}	}	PUNCT
ma-24	386	9	]	]	PUNCT
ma-24	387	1	+	+	CCONJ
ma-24	387	2	αt	αt	NOUN
ma-24	387	3	[	[	PUNCT
ma-24	387	4	u3	u3	NOUN
ma-24	387	5	3	3	NUM
ma-24	387	6	−	−	PROPN
ma-24	387	7	uv2	uv2	ADV
ma-24	387	8	]	]	X
ma-24	388	1	+	+	CCONJ
ma-24	388	2	x	x	SYM
ma-24	388	3	2	2	NUM
ma-24	388	4	{	{	PUNCT
ma-24	388	5	v2	v2	NOUN
ma-24	388	6	−	−	PROPN
ma-24	388	7	u2	u2	PROPN
ma-24	388	8	}	}	PUNCT
ma-24	388	9	.	.	PUNCT
ma-24	389	1	(	(	PUNCT
ma-24	389	2	119	119	NUM
ma-24	389	3	)	)	PUNCT
ma-24	389	4	(	(	PUNCT
ma-24	389	5	iii	iii	X
ma-24	389	6	)	)	PUNCT
ma-24	389	7	the	the	PRON
ma-24	389	8	multiplier	multipli	ADJ
ma-24	389	9	(	(	PUNCT
ma-24	389	10	λ1	λ1	PROPN
ma-24	389	11	3,λ2	3,λ2	NUM
ma-24	389	12	3	3	NUM
ma-24	389	13	)	)	PUNCT
ma-24	389	14	=	=	SYM
ma-24	389	15	(	(	PUNCT
ma-24	389	16	α	α	PRON
ma-24	389	17	2β	2β	NOUN
ma-24	389	18	{	{	PUNCT
ma-24	389	19	u2	u2	PROPN
ma-24	389	20	−	−	PROPN
ma-24	389	21	v2}+	v2}+	PROPN
ma-24	389	22	uxx	uxx	NOUN
ma-24	389	23	,	,	PUNCT
ma-24	389	24	−	−	PROPN
ma-24	389	25	{	{	PUNCT
ma-24	389	26	αuv	αuv	ADJ
ma-24	389	27	β	β	X
ma-24	389	28	+	+	CCONJ
ma-24	389	29	vxx	vxx	PROPN
ma-24	389	30	}	}	PUNCT
ma-24	389	31	)	)	PUNCT
ma-24	389	32	,	,	PUNCT
ma-24	389	33	(	(	PUNCT
ma-24	389	34	120	120	NUM
ma-24	389	35	)	)	PUNCT
ma-24	389	36	has	have	VERB
ma-24	389	37	the	the	DET
ma-24	389	38	conserved	conserve	VERB
ma-24	389	39	vectors	vector	NOUN
ma-24	389	40	t	t	PROPN
ma-24	389	41	t3	t3	NOUN
ma-24	389	42	=	=	PUNCT
ma-24	390	1	α	α	NUM
ma-24	390	2	2β	2β	NOUN
ma-24	390	3	(	(	PUNCT
ma-24	390	4	u3	u3	NOUN
ma-24	390	5	3	3	NUM
ma-24	390	6	−	−	PROPN
ma-24	390	7	uv2	uv2	PROPN
ma-24	390	8	)	)	PUNCT
ma-24	390	9	,	,	PUNCT
ma-24	390	10	t	t	NOUN
ma-24	390	11	x3	x3	NOUN
ma-24	390	12	=	=	SYM
ma-24	391	1	α	α	X
ma-24	391	2	2	2	NUM
ma-24	391	3	[	[	PUNCT
ma-24	391	4	(	(	PUNCT
ma-24	391	5	u2	u2	PROPN
ma-24	391	6	−	−	PROPN
ma-24	391	7	v2)uxx	v2)uxx	NOUN
ma-24	391	8	−	−	PROPN
ma-24	391	9	v2vxx	v2vxx	NOUN
ma-24	391	10	]	]	PUNCT
ma-24	392	1	−	−	PROPN
ma-24	392	2	αuvvxx+	αuvvxx+	X
ma-24	392	3	(	(	PUNCT
ma-24	392	4	121	121	NUM
ma-24	392	5	)	)	PUNCT
ma-24	392	6	β	β	NOUN
ma-24	392	7	2	2	NUM
ma-24	392	8	[	[	PUNCT
ma-24	392	9	u2	u2	PROPN
ma-24	392	10	xx	xx	PROPN
ma-24	392	11	−	−	PROPN
ma-24	392	12	v2	v2	PROPN
ma-24	392	13	xx	xx	X
ma-24	392	14	]	]	PUNCT
ma-24	393	1	+	+	CCONJ
ma-24	393	2	utux	utux	PROPN
ma-24	393	3	−	−	PROPN
ma-24	393	4	vtvx	vtvx	NOUN
ma-24	393	5	+	+	CCONJ
ma-24	393	6	α2	α2	ADJ
ma-24	393	7	4β	4β	NOUN
ma-24	393	8	[	[	PUNCT
ma-24	393	9	1	1	NUM
ma-24	393	10	2	2	NUM
ma-24	393	11	{	{	PUNCT
ma-24	393	12	u4	u4	PROPN
ma-24	393	13	+	+	PROPN
ma-24	393	14	v4	v4	PROPN
ma-24	393	15	}	}	PUNCT
ma-24	393	16	−	−	PROPN
ma-24	393	17	3u2v2	3u2v2	NUM
ma-24	393	18	]	]	PUNCT
ma-24	393	19	.	.	PUNCT
ma-24	394	1	(	(	PUNCT
ma-24	394	2	122	122	NUM
ma-24	394	3	)	)	PUNCT
ma-24	394	4	(	(	PUNCT
ma-24	394	5	iv	iv	X
ma-24	394	6	)	)	PUNCT
ma-24	394	7	the	the	PRON
ma-24	394	8	multiplier	multipli	ADJ
ma-24	394	9	(	(	PUNCT
ma-24	394	10	λ1	λ1	VERB
ma-24	394	11	4,λ2	4,λ2	NUM
ma-24	394	12	4	4	NUM
ma-24	394	13	)	)	PUNCT
ma-24	394	14	=	=	SYM
ma-24	394	15	(	(	PUNCT
ma-24	394	16	{	{	PUNCT
ma-24	394	17	αuv	αuv	ADJ
ma-24	394	18	β	β	X
ma-24	394	19	+	+	CCONJ
ma-24	394	20	vxx	vxx	PROPN
ma-24	394	21	}	}	PUNCT
ma-24	394	22	,	,	PUNCT
ma-24	394	23	α[u2	α[u2	DET
ma-24	394	24	−	−	PROPN
ma-24	394	25	v2	v2	NOUN
ma-24	394	26	]	]	X
ma-24	394	27	2β	2β	PROPN
ma-24	394	28	+	+	CCONJ
ma-24	394	29	uxx	uxx	X
ma-24	394	30	)	)	PUNCT
ma-24	394	31	,	,	PUNCT
ma-24	394	32	(	(	PUNCT
ma-24	394	33	123	123	NUM
ma-24	394	34	)	)	PUNCT
ma-24	394	35	has	have	VERB
ma-24	394	36	the	the	DET
ma-24	394	37	conserved	conserve	VERB
ma-24	394	38	vectors	vector	NOUN
ma-24	394	39	t	t	PROPN
ma-24	394	40	t4	t4	PROPN
ma-24	394	41	=	=	PROPN
ma-24	395	1	α	α	PROPN
ma-24	395	2	2β	2β	NOUN
ma-24	395	3	(	(	PUNCT
ma-24	395	4	u2v	u2v	ADP
ma-24	395	5	−	−	PROPN
ma-24	395	6	v3	v3	PROPN
ma-24	395	7	3	3	NUM
ma-24	395	8	)	)	PUNCT
ma-24	395	9	,	,	PUNCT
ma-24	395	10	(	(	PUNCT
ma-24	395	11	124	124	NUM
ma-24	395	12	)	)	PUNCT
ma-24	395	13	t	t	NOUN
ma-24	395	14	x4	x4	NOUN
ma-24	395	15	=	=	SYM
ma-24	396	1	α2	α2	PROPN
ma-24	396	2	2β	2β	NOUN
ma-24	396	3	[	[	PUNCT
ma-24	396	4	(	(	PUNCT
ma-24	396	5	u3v	u3v	NOUN
ma-24	396	6	−	−	NOUN
ma-24	396	7	uv3	uv3	NOUN
ma-24	396	8	)	)	PUNCT
ma-24	396	9	]	]	PUNCT
ma-24	397	1	+	+	CCONJ
ma-24	397	2	vtux	vtux	NOUN
ma-24	397	3	+	+	CCONJ
ma-24	397	4	utvx	utvx	ADJ
ma-24	397	5	+	+	X
ma-24	397	6	α	α	NOUN
ma-24	397	7	2	2	NUM
ma-24	397	8	(	(	PUNCT
ma-24	397	9	u2	u2	PROPN
ma-24	397	10	−	−	PROPN
ma-24	397	11	v2)vxx	v2)vxx	NOUN
ma-24	397	12	+	+	CCONJ
ma-24	397	13	{	{	PUNCT
ma-24	397	14	αuv	αuv	ADJ
ma-24	397	15	+	+	X
ma-24	397	16	βvxx}uxx	βvxx}uxx	X
ma-24	397	17	.	.	PUNCT
ma-24	398	1	(	(	PUNCT
ma-24	398	2	125	125	NUM
ma-24	398	3	)	)	PUNCT
ma-24	398	4	(	(	PUNCT
ma-24	398	5	v	v	NOUN
ma-24	398	6	)	)	PUNCT
ma-24	398	7	the	the	DET
ma-24	398	8	multiplier	multipli	ADJ
ma-24	398	9	(	(	PUNCT
ma-24	398	10	λ1	λ1	ADJ
ma-24	398	11	5,λ2	5,λ2	NUM
ma-24	398	12	5	5	NUM
ma-24	398	13	)	)	PUNCT
ma-24	398	14	=	=	SYM
ma-24	398	15	(	(	PUNCT
ma-24	398	16	u,−v	u,−v	PROPN
ma-24	398	17	)	)	PUNCT
ma-24	398	18	,	,	PUNCT
ma-24	398	19	(	(	PUNCT
ma-24	398	20	126	126	NUM
ma-24	398	21	)	)	PUNCT
ma-24	398	22	has	have	VERB
ma-24	398	23	the	the	DET
ma-24	398	24	conserved	conserve	VERB
ma-24	398	25	vectors	vector	NOUN
ma-24	398	26	t	t	PROPN
ma-24	398	27	t5	t5	PROPN
ma-24	398	28	=	=	SYM
ma-24	398	29	1	1	NUM
ma-24	398	30	2	2	NUM
ma-24	398	31	{	{	PUNCT
ma-24	398	32	u2	u2	PROPN
ma-24	398	33	−	−	PROPN
ma-24	398	34	v2	v2	PROPN
ma-24	398	35	}	}	PUNCT
ma-24	398	36	,	,	PUNCT
ma-24	398	37	t	t	PROPN
ma-24	398	38	x5	x5	PROPN
ma-24	399	1	=	=	SYM
ma-24	399	2	β	β	X
ma-24	399	3	(	(	PUNCT
ma-24	399	4	uuxx	uuxx	ADJ
ma-24	399	5	−	−	PROPN
ma-24	399	6	vvxx	vvxx	NOUN
ma-24	399	7	+	+	CCONJ
ma-24	399	8	v2	v2	X
ma-24	399	9	x	x	PUNCT
ma-24	399	10	−	−	PROPN
ma-24	399	11	u2	u2	NOUN
ma-24	399	12	x	x	SYM
ma-24	399	13	2	2	NUM
ma-24	399	14	)	)	PUNCT
ma-24	399	15	+	+	CCONJ
ma-24	399	16	α	α	PROPN
ma-24	399	17	(	(	PUNCT
ma-24	399	18	u3	u3	NOUN
ma-24	399	19	3	3	NUM
ma-24	399	20	−	−	PROPN
ma-24	399	21	uv2	uv2	PROPN
ma-24	399	22	)	)	PUNCT
ma-24	399	23	.	.	PUNCT
ma-24	400	1	(	(	PUNCT
ma-24	400	2	127	127	NUM
ma-24	400	3	)	)	PUNCT
ma-24	400	4	(	(	PUNCT
ma-24	400	5	vi	vi	X
ma-24	400	6	)	)	PUNCT
ma-24	400	7	the	the	DET
ma-24	400	8	multiplier	multipli	ADJ
ma-24	400	9	(	(	PUNCT
ma-24	400	10	λ1	λ1	ADJ
ma-24	400	11	6,λ2	6,λ2	NUM
ma-24	400	12	6	6	NUM
ma-24	400	13	)	)	PUNCT
ma-24	400	14	=	=	SYM
ma-24	400	15	(	(	PUNCT
ma-24	400	16	v	v	NOUN
ma-24	400	17	,	,	PUNCT
ma-24	400	18	u	u	NOUN
ma-24	400	19	)	)	PUNCT
ma-24	400	20	,	,	PUNCT
ma-24	400	21	(	(	PUNCT
ma-24	400	22	128	128	NUM
ma-24	400	23	)	)	PUNCT
ma-24	400	24	has	have	VERB
ma-24	400	25	the	the	DET
ma-24	400	26	conserved	conserve	VERB
ma-24	400	27	vectors	vector	NOUN
ma-24	400	28	t	t	PROPN
ma-24	400	29	t6	t6	PROPN
ma-24	400	30	=	=	PUNCT
ma-24	401	1	uv	uv	PROPN
ma-24	401	2	,	,	PUNCT
ma-24	401	3	t	t	NOUN
ma-24	401	4	x6	x6	PROPN
ma-24	401	5	=	=	SYM
ma-24	401	6	β	β	X
ma-24	401	7	(	(	PUNCT
ma-24	401	8	vuxx	vuxx	NOUN
ma-24	401	9	+	+	CCONJ
ma-24	401	10	uvxx	uvxx	VERB
ma-24	401	11	−	−	NOUN
ma-24	401	12	uxvx	uxvx	NOUN
ma-24	401	13	)	)	PUNCT
ma-24	402	1	+	+	CCONJ
ma-24	402	2	α	α	PROPN
ma-24	402	3	(	(	PUNCT
ma-24	402	4	u2v	u2v	PROPN
ma-24	402	5	−	−	PROPN
ma-24	402	6	v3	v3	PROPN
ma-24	402	7	3	3	NUM
ma-24	402	8	)	)	PUNCT
ma-24	402	9	.	.	PUNCT
ma-24	403	1	(	(	PUNCT
ma-24	403	2	129	129	NUM
ma-24	403	3	)	)	PUNCT
ma-24	403	4	(	(	PUNCT
ma-24	403	5	vii	vii	PROPN
ma-24	403	6	)	)	PUNCT
ma-24	403	7	the	the	PRON
ma-24	403	8	multiplier	multipli	ADJ
ma-24	403	9	(	(	PUNCT
ma-24	403	10	λ1	λ1	ADJ
ma-24	403	11	7,λ2	7,λ2	NUM
ma-24	403	12	7	7	NUM
ma-24	403	13	)	)	PUNCT
ma-24	403	14	=	=	SYM
ma-24	403	15	(	(	PUNCT
ma-24	403	16	1	1	NUM
ma-24	403	17	,	,	PUNCT
ma-24	403	18	0	0	NUM
ma-24	403	19	)	)	PUNCT
ma-24	403	20	,	,	PUNCT
ma-24	403	21	(	(	PUNCT
ma-24	403	22	130	130	NUM
ma-24	403	23	)	)	PUNCT
ma-24	403	24	has	have	VERB
ma-24	403	25	the	the	DET
ma-24	403	26	conserved	conserve	VERB
ma-24	403	27	vectors	vector	NOUN
ma-24	403	28	t	t	PROPN
ma-24	403	29	t7	t7	PROPN
ma-24	403	30	=	=	SYM
ma-24	403	31	u	u	PROPN
ma-24	403	32	,	,	PUNCT
ma-24	403	33	t	t	NOUN
ma-24	403	34	x7	x7	NOUN
ma-24	403	35	=	=	SYM
ma-24	403	36	α	α	PRON
ma-24	403	37	2	2	NUM
ma-24	403	38	{	{	PUNCT
ma-24	403	39	u2	u2	PROPN
ma-24	403	40	−	−	PROPN
ma-24	403	41	v2}+	v2}+	PROPN
ma-24	403	42	βuxx	βuxx	NOUN
ma-24	403	43	.	.	PUNCT
ma-24	404	1	(	(	PUNCT
ma-24	404	2	131	131	X
ma-24	404	3	)	)	PUNCT
ma-24	404	4	eur	eur	PROPN
ma-24	404	5	.	.	PUNCT
ma-24	405	1	j.	j.	PROPN
ma-24	405	2	math	math	PROPN
ma-24	405	3	.	.	PUNCT
ma-24	406	1	anal	anal	ADJ
ma-24	406	2	.	.	PUNCT
ma-24	407	1	1	1	NUM
ma-24	407	2	(	(	PUNCT
ma-24	407	3	2021	2021	NUM
ma-24	407	4	)	)	PUNCT
ma-24	407	5	147(viii	147(viii	NUM
ma-24	407	6	)	)	PUNCT
ma-24	407	7	the	the	DET
ma-24	407	8	multiplier	multipli	ADJ
ma-24	407	9	has	have	AUX
ma-24	407	10	(	(	PUNCT
ma-24	407	11	λ1	λ1	PROPN
ma-24	407	12	8,λ2	8,λ2	NUM
ma-24	407	13	8	8	NUM
ma-24	407	14	)	)	PUNCT
ma-24	407	15	=	=	SYM
ma-24	407	16	(	(	PUNCT
ma-24	407	17	0	0	NUM
ma-24	407	18	,	,	PUNCT
ma-24	407	19	1	1	NUM
ma-24	407	20	)	)	PUNCT
ma-24	407	21	,	,	PUNCT
ma-24	407	22	(	(	PUNCT
ma-24	407	23	132	132	X
ma-24	407	24	)	)	PUNCT
ma-24	407	25	the	the	DET
ma-24	407	26	conserved	conserve	VERB
ma-24	407	27	vectors	vector	NOUN
ma-24	407	28	t	t	X
ma-24	407	29	t8	t8	PROPN
ma-24	407	30	=	=	SYM
ma-24	407	31	v	v	PROPN
ma-24	407	32	,	,	PUNCT
ma-24	407	33	t	t	PROPN
ma-24	407	34	x8	x8	PROPN
ma-24	407	35	=	=	SYM
ma-24	407	36	αuv	αuv	ADJ
ma-24	407	37	+	+	X
ma-24	407	38	βvxx	βvxx	NOUN
ma-24	407	39	.	.	PUNCT
ma-24	408	1	(	(	PUNCT
ma-24	408	2	133	133	NUM
ma-24	408	3	)	)	PUNCT
ma-24	408	4	remark	remark	NOUN
ma-24	408	5	3.4	3.4	NUM
ma-24	408	6	.	.	PUNCT
ma-24	409	1	it	it	PRON
ma-24	409	2	can	can	AUX
ma-24	409	3	be	be	AUX
ma-24	409	4	verified	verify	VERB
ma-24	409	5	that	that	SCONJ
ma-24	409	6	dtt	dtt	NOUN
ma-24	409	7	t	t	PROPN
ma-24	409	8	i	i	PRON
ma-24	410	1	+	+	NOUN
ma-24	410	2	dxt	dxt	X
ma-24	410	3	x	x	VERB
ma-24	410	4	i	i	PRON
ma-24	410	5	∣∣∣	∣∣∣	VERB
ma-24	410	6	∆1=0	∆1=0	PROPN
ma-24	410	7	,	,	PUNCT
ma-24	410	8	∆2=0	∆2=0	PROPN
ma-24	410	9	=	=	SYM
ma-24	410	10	0	0	NUM
ma-24	410	11	,	,	PUNCT
ma-24	410	12	(	(	PUNCT
ma-24	410	13	134	134	NUM
ma-24	410	14	)	)	PUNCT
ma-24	410	15	for	for	ADP
ma-24	410	16	i	i	PROPN
ma-24	410	17	=	=	NOUN
ma-24	411	1	1	1	NUM
ma-24	411	2	,	,	PUNCT
ma-24	411	3	.	.	PUNCT
ma-24	411	4	.	.	PUNCT
ma-24	412	1	.	.	PUNCT
ma-24	413	1	,	,	PUNCT
ma-24	413	2	8	8	X
ma-24	413	3	.	.	PUNCT
ma-24	413	4	remark	remark	NOUN
ma-24	413	5	3.5	3.5	NUM
ma-24	413	6	.	.	PUNCT
ma-24	414	1	the	the	DET
ma-24	414	2	expressions	expression	NOUN
ma-24	414	3	in	in	ADP
ma-24	414	4	(	(	PUNCT
ma-24	414	5	134	134	NUM
ma-24	414	6	)	)	PUNCT
ma-24	414	7	are	be	AUX
ma-24	414	8	eight	eight	NUM
ma-24	414	9	conservation	conservation	NOUN
ma-24	414	10	laws	law	NOUN
ma-24	414	11	for	for	ADP
ma-24	414	12	the	the	DET
ma-24	414	13	coupled	couple	VERB
ma-24	414	14	kdv	kdv	NOUN
ma-24	414	15	system	system	NOUN
ma-24	414	16	(	(	PUNCT
ma-24	414	17	3	3	NUM
ma-24	414	18	)	)	PUNCT
ma-24	414	19	.	.	PUNCT
ma-24	415	1	remark	remark	PROPN
ma-24	415	2	3.6	3.6	NUM
ma-24	415	3	.	.	PUNCT
ma-24	416	1	the	the	DET
ma-24	416	2	presence	presence	NOUN
ma-24	416	3	of	of	ADP
ma-24	416	4	multipliers	multiplier	NOUN
ma-24	416	5	(	(	PUNCT
ma-24	416	6	λ1	λ1	PROPN
ma-24	416	7	7,λ2	7,λ2	PROPN
ma-24	416	8	7	7	NUM
ma-24	416	9	)	)	PUNCT
ma-24	416	10	=	=	SYM
ma-24	416	11	(	(	PUNCT
ma-24	416	12	1	1	NUM
ma-24	416	13	,	,	PUNCT
ma-24	416	14	0	0	NUM
ma-24	416	15	)	)	PUNCT
ma-24	416	16	,	,	PUNCT
ma-24	416	17	(	(	PUNCT
ma-24	416	18	λ1	λ1	PROPN
ma-24	416	19	8,λ2	8,λ2	NUM
ma-24	416	20	8	8	NUM
ma-24	416	21	)	)	PUNCT
ma-24	416	22	=	=	SYM
ma-24	416	23	(	(	PUNCT
ma-24	416	24	0	0	NUM
ma-24	416	25	,	,	PUNCT
ma-24	416	26	1	1	NUM
ma-24	416	27	)	)	PUNCT
ma-24	416	28	(	(	PUNCT
ma-24	416	29	135	135	NUM
ma-24	416	30	)	)	PUNCT
ma-24	416	31	manifest	manifest	NOUN
ma-24	416	32	that	that	SCONJ
ma-24	416	33	the	the	DET
ma-24	416	34	coupled	couple	VERB
ma-24	416	35	kdv	kdv	NOUN
ma-24	416	36	equations	equation	NOUN
ma-24	416	37	are	be	AUX
ma-24	416	38	themselves	themselves	PRON
ma-24	416	39	conservation	conservation	NOUN
ma-24	416	40	laws	law	NOUN
ma-24	416	41	.	.	PUNCT
ma-24	417	1	at	at	ADP
ma-24	417	2	this	this	DET
ma-24	417	3	point	point	NOUN
ma-24	417	4	,	,	PUNCT
ma-24	417	5	we	we	PRON
ma-24	417	6	derive	derive	VERB
ma-24	417	7	conserved	conserved	ADJ
ma-24	417	8	vectors	vector	NOUN
ma-24	417	9	for	for	ADP
ma-24	417	10	coupled	couple	VERB
ma-24	417	11	kdv	kdv	NOUN
ma-24	417	12	equations	equation	NOUN
ma-24	417	13	(	(	PUNCT
ma-24	417	14	3	3	NUM
ma-24	417	15	)	)	PUNCT
ma-24	417	16	by	by	ADP
ma-24	417	17	a	a	DET
ma-24	417	18	new	new	ADJ
ma-24	417	19	theorem	theorem	ADJ
ma-24	417	20	due	due	ADJ
ma-24	417	21	toibragimov	toibragimov	NOUN
ma-24	417	22	.	.	PUNCT
ma-24	418	1	the	the	DET
ma-24	418	2	adjoint	adjoint	PROPN
ma-24	418	3	equations	equation	NOUN
ma-24	418	4	for	for	ADP
ma-24	418	5	the	the	DET
ma-24	418	6	nonlinear	nonlinear	ADJ
ma-24	418	7	system	system	NOUN
ma-24	418	8	coupled	couple	VERB
ma-24	418	9	kdv	kdv	NOUN
ma-24	418	10	equations	equation	NOUN
ma-24	418	11	(	(	PUNCT
ma-24	418	12	3	3	X
ma-24	418	13	)	)	PUNCT
ma-24	418	14	are	be	AUX
ma-24	418	15	∆∗1	∆∗1	ADP
ma-24	418	16	≡	≡	PROPN
ma-24	418	17	ft	ft	PROPN
ma-24	419	1	+	+	CCONJ
ma-24	419	2	α	α	NUM
ma-24	419	3	ufx	ufx	NOUN
ma-24	420	1	+	+	CCONJ
ma-24	420	2	αvgx	αvgx	NOUN
ma-24	420	3	+	+	CCONJ
ma-24	420	4	βfxxx	βfxxx	NOUN
ma-24	420	5	=	=	SYM
ma-24	420	6	0	0	NUM
ma-24	420	7	,	,	PUNCT
ma-24	420	8	∆∗2gt	∆∗2gt	PROPN
ma-24	420	9	−	−	NOUN
ma-24	420	10	αvfx	αvfx	NOUN
ma-24	420	11	+	+	CCONJ
ma-24	420	12	αugx	αugx	NOUN
ma-24	420	13	+	+	CCONJ
ma-24	420	14	βgxxx	βgxxx	NOUN
ma-24	420	15	=	=	NOUN
ma-24	420	16	0	0	NUM
ma-24	420	17	.	.	PUNCT
ma-24	421	1	(	(	PUNCT
ma-24	421	2	136	136	NUM
ma-24	421	3	)	)	PUNCT
ma-24	421	4	the	the	DET
ma-24	421	5	formal	formal	ADJ
ma-24	421	6	lagrangian	lagrangian	ADJ
ma-24	421	7	l	l	NOUN
ma-24	421	8	for	for	ADP
ma-24	421	9	the	the	DET
ma-24	421	10	nonlinear	nonlinear	ADJ
ma-24	421	11	coupled	couple	VERB
ma-24	421	12	system	system	NOUN
ma-24	421	13	of	of	ADP
ma-24	421	14	the	the	DET
ma-24	421	15	kdv	kdv	NOUN
ma-24	421	16	equations	equation	NOUN
ma-24	421	17	(	(	PUNCT
ma-24	421	18	3	3	NUM
ma-24	421	19	)	)	PUNCT
ma-24	421	20	and	and	CCONJ
ma-24	421	21	its	its	PRON
ma-24	421	22	adjointequations	adjointequation	NOUN
ma-24	421	23	(	(	PUNCT
ma-24	421	24	136	136	NUM
ma-24	421	25	)	)	PUNCT
ma-24	421	26	is	be	AUX
ma-24	421	27	given	give	VERB
ma-24	421	28	by	by	ADP
ma-24	421	29	l	l	NOUN
ma-24	421	30	=	=	SYM
ma-24	421	31	f	f	PROPN
ma-24	421	32	{	{	PUNCT
ma-24	421	33	ut	ut	PROPN
ma-24	421	34	+	+	NUM
ma-24	421	35	αuux	αuux	PROPN
ma-24	421	36	−	−	PROPN
ma-24	421	37	αvvx	αvvx	NOUN
ma-24	421	38	+	+	CCONJ
ma-24	421	39	βuxxx}+	βuxxx}+	NOUN
ma-24	421	40	g{vt	g{vt	PROPN
ma-24	421	41	+	+	CCONJ
ma-24	421	42	αuvx	αuvx	NOUN
ma-24	421	43	+	+	CCONJ
ma-24	421	44	αvux	αvux	NOUN
ma-24	421	45	+	+	CCONJ
ma-24	421	46	βvxxx	βvxxx	ADV
ma-24	421	47	}	}	PUNCT
ma-24	421	48	,	,	PUNCT
ma-24	421	49	(	(	PUNCT
ma-24	421	50	137	137	NUM
ma-24	421	51	)	)	PUNCT
ma-24	421	52	where	where	SCONJ
ma-24	421	53	f	f	PROPN
ma-24	421	54	and	and	CCONJ
ma-24	421	55	g	g	PROPN
ma-24	421	56	are	be	AUX
ma-24	421	57	new	new	ADJ
ma-24	421	58	variables	variable	NOUN
ma-24	421	59	.	.	PUNCT
ma-24	422	1	we	we	PRON
ma-24	422	2	shall	shall	AUX
ma-24	422	3	use	use	VERB
ma-24	422	4	the	the	DET
ma-24	422	5	lie	lie	NOUN
ma-24	422	6	point	point	NOUN
ma-24	422	7	symmetries	symmetry	NOUN
ma-24	422	8	of	of	ADP
ma-24	422	9	the	the	DET
ma-24	422	10	system	system	NOUN
ma-24	422	11	(	(	PUNCT
ma-24	422	12	3	3	NUM
ma-24	422	13	)	)	PUNCT
ma-24	422	14	,	,	PUNCT
ma-24	423	1	namely	namely	ADV
ma-24	423	2	x1	x1	PRON
ma-24	423	3	=	=	SYM
ma-24	423	4	∂t	∂t	PROPN
ma-24	423	5	,	,	PUNCT
ma-24	423	6	x2	x2	PROPN
ma-24	423	7	=	=	SYM
ma-24	423	8	∂x	∂x	PROPN
ma-24	423	9	,	,	PUNCT
ma-24	424	1	x3	x3	ADJ
ma-24	424	2	=	=	SYM
ma-24	424	3	αt∂x	αt∂x	PROPN
ma-24	424	4	+	+	CCONJ
ma-24	424	5	∂u	∂u	PROPN
ma-24	424	6	,	,	PUNCT
ma-24	424	7	x4	x4	PROPN
ma-24	424	8	=	=	SYM
ma-24	425	1	3t∂t	3t∂t	PROPN
ma-24	426	1	+	+	NUM
ma-24	426	2	x∂x	x∂x	NUM
ma-24	427	1	−	−	PROPN
ma-24	428	1	2u∂u	2u∂u	NUM
ma-24	429	1	−	−	PROPN
ma-24	429	2	2v∂v	2v∂v	NUM
ma-24	429	3	,	,	PUNCT
ma-24	429	4	(	(	PUNCT
ma-24	429	5	138	138	NUM
ma-24	429	6	)	)	PUNCT
ma-24	429	7	to	to	PART
ma-24	429	8	derive	derive	VERB
ma-24	429	9	conserved	conserved	ADJ
ma-24	429	10	vectors	vector	NOUN
ma-24	429	11	corresponding	correspond	VERB
ma-24	429	12	to	to	ADP
ma-24	429	13	each	each	DET
ma-24	429	14	symmetry	symmetry	NOUN
ma-24	429	15	below.case	below.case	INTJ
ma-24	429	16	(	(	PUNCT
ma-24	429	17	i	i	NOUN
ma-24	429	18	)	)	PUNCT
ma-24	429	19	the	the	DET
ma-24	429	20	symmetry	symmetry	NOUN
ma-24	430	1	x1	x1	PROPN
ma-24	430	2	=	=	SYM
ma-24	430	3	∂	∂	PROPN
ma-24	430	4	∂t	∂t	PROPN
ma-24	430	5	,	,	PUNCT
ma-24	430	6	yields	yield	NOUN
ma-24	430	7	lie	lie	VERB
ma-24	430	8	characteristic	characteristic	ADJ
ma-24	430	9	functions	function	NOUN
ma-24	430	10	given	give	VERB
ma-24	430	11	by	by	ADP
ma-24	430	12	w	w	PROPN
ma-24	430	13	1	1	NUM
ma-24	430	14	1	1	NUM
ma-24	430	15	=	=	SYM
ma-24	431	1	−ut	−ut	NOUN
ma-24	431	2	,	,	PUNCT
ma-24	431	3	w	w	PROPN
ma-24	431	4	2	2	NUM
ma-24	431	5	1	1	NUM
ma-24	431	6	=	=	SYM
ma-24	431	7	−vt	−vt	PROPN
ma-24	431	8	.	.	PUNCT
ma-24	432	1	(	(	PUNCT
ma-24	432	2	139	139	NUM
ma-24	432	3	)	)	PUNCT
ma-24	432	4	hence	hence	ADV
ma-24	432	5	by	by	ADP
ma-24	432	6	ibragimov	ibragimov	NOUN
ma-24	432	7	’s	’s	PART
ma-24	432	8	theorem	theorem	NOUN
ma-24	432	9	[	[	X
ma-24	432	10	9	9	NUM
ma-24	432	11	]	]	PUNCT
ma-24	432	12	,	,	PUNCT
ma-24	432	13	the	the	DET
ma-24	432	14	associated	associate	VERB
ma-24	432	15	conserved	conserve	VERB
ma-24	432	16	vector	vector	NOUN
ma-24	432	17	is	be	AUX
ma-24	432	18	given	give	VERB
ma-24	432	19	by	by	ADP
ma-24	432	20	t	t	PROPN
ma-24	432	21	t1	t1	NOUN
ma-24	433	1	=	=	NOUN
ma-24	433	2	α	α	X
ma-24	434	1	[	[	X
ma-24	434	2	f	f	X
ma-24	434	3	{	{	PUNCT
ma-24	434	4	uux	uux	PROPN
ma-24	434	5	−	−	PROPN
ma-24	434	6	vvx}+	vvx}+	PROPN
ma-24	434	7	g{vux	g{vux	PROPN
ma-24	434	8	+	+	CCONJ
ma-24	434	9	uvx	uvx	NOUN
ma-24	434	10	}	}	PUNCT
ma-24	434	11	]	]	PUNCT
ma-24	435	1	+	+	CCONJ
ma-24	435	2	β{f	β{f	X
ma-24	435	3	uxxx	uxxx	PROPN
ma-24	435	4	+	+	CCONJ
ma-24	435	5	gvxxx	gvxxx	PROPN
ma-24	435	6	}	}	PUNCT
ma-24	435	7	,	,	PUNCT
ma-24	435	8	t	t	PROPN
ma-24	435	9	x1	x1	PROPN
ma-24	436	1	=	=	NOUN
ma-24	436	2	α	α	X
ma-24	437	1	[	[	X
ma-24	437	2	f	f	X
ma-24	437	3	{	{	PUNCT
ma-24	437	4	−uut	−uut	NOUN
ma-24	437	5	+	+	CCONJ
ma-24	437	6	vvt	vvt	NOUN
ma-24	437	7	}	}	PUNCT
ma-24	437	8	−	−	PROPN
ma-24	438	1	g{vut	g{vut	PROPN
ma-24	438	2	+	+	NUM
ma-24	438	3	uvt	uvt	NOUN
ma-24	438	4	}	}	PUNCT
ma-24	438	5	]	]	PUNCT
ma-24	439	1	+	+	CCONJ
ma-24	439	2	β{fxutx	β{fxutx	NOUN
ma-24	439	3	+	+	CCONJ
ma-24	439	4	gxvtx	gxvtx	VERB
ma-24	439	5	−	−	PROPN
ma-24	439	6	ut	ut	PROPN
ma-24	439	7	fxx	fxx	PROPN
ma-24	439	8	−	−	PROPN
ma-24	439	9	vtgxx	vtgxx	PROPN
ma-24	439	10	−	−	PROPN
ma-24	439	11	f	f	PROPN
ma-24	439	12	utxx	utxx	NOUN
ma-24	439	13	−	−	PROPN
ma-24	439	14	gvtxx	gvtxx	PROPN
ma-24	439	15	}	}	PUNCT
ma-24	439	16	.	.	PUNCT
ma-24	440	1	(	(	PUNCT
ma-24	440	2	140	140	NUM
ma-24	440	3	)	)	PUNCT
ma-24	440	4	eur	eur	NOUN
ma-24	440	5	.	.	PUNCT
ma-24	441	1	j.	j.	PROPN
ma-24	441	2	math	math	PROPN
ma-24	441	3	.	.	PUNCT
ma-24	442	1	anal	anal	ADJ
ma-24	442	2	.	.	PUNCT
ma-24	443	1	1	1	NUM
ma-24	443	2	(	(	PUNCT
ma-24	443	3	2021	2021	NUM
ma-24	443	4	)	)	PUNCT
ma-24	444	1	148case	148case	PROPN
ma-24	444	2	(	(	PUNCT
ma-24	444	3	ii	ii	PROPN
ma-24	444	4	)	)	PUNCT
ma-24	444	5	the	the	DET
ma-24	444	6	symmetry	symmetry	NOUN
ma-24	444	7	x2	x2	PROPN
ma-24	444	8	=	=	SYM
ma-24	444	9	∂	∂	NUM
ma-24	444	10	∂x	∂x	PROPN
ma-24	444	11	,	,	PUNCT
ma-24	444	12	yields	yield	NOUN
ma-24	444	13	lie	lie	VERB
ma-24	444	14	characteristic	characteristic	ADJ
ma-24	444	15	functions	function	NOUN
ma-24	444	16	w	w	ADP
ma-24	444	17	1	1	NUM
ma-24	444	18	2	2	NUM
ma-24	444	19	=	=	SYM
ma-24	444	20	−ux	−ux	NOUN
ma-24	444	21	,	,	PUNCT
ma-24	444	22	w	w	PROPN
ma-24	444	23	2	2	NUM
ma-24	444	24	2	2	NUM
ma-24	444	25	=	=	SYM
ma-24	444	26	−vx	−vx	NUM
ma-24	444	27	.	.	PUNCT
ma-24	445	1	(	(	PUNCT
ma-24	445	2	141	141	NUM
ma-24	445	3	)	)	PUNCT
ma-24	445	4	therefore	therefore	ADV
ma-24	445	5	by	by	ADP
ma-24	445	6	ibragimov	ibragimov	NOUN
ma-24	445	7	’s	’s	PART
ma-24	445	8	theorem	theorem	NOUN
ma-24	445	9	[	[	X
ma-24	445	10	9	9	NUM
ma-24	445	11	]	]	PUNCT
ma-24	445	12	,	,	PUNCT
ma-24	445	13	the	the	DET
ma-24	445	14	associated	associate	VERB
ma-24	445	15	conserved	conserve	VERB
ma-24	445	16	vector	vector	NOUN
ma-24	445	17	is	be	AUX
ma-24	445	18	t	t	NOUN
ma-24	445	19	t2	t2	NOUN
ma-24	445	20	=	=	PUNCT
ma-24	445	21	−ux	−ux	PROPN
ma-24	445	22	f	f	PROPN
ma-24	445	23	−	−	PROPN
ma-24	445	24	vxg	vxg	PROPN
ma-24	445	25	,	,	PUNCT
ma-24	445	26	t	t	PROPN
ma-24	445	27	x2	x2	PROPN
ma-24	446	1	=	=	SYM
ma-24	446	2	f	f	AUX
ma-24	446	3	ut	ut	PROPN
ma-24	446	4	+	+	CCONJ
ma-24	446	5	gvt	gvt	NOUN
ma-24	446	6	+	+	NUM
ma-24	446	7	β{−ux	β{−ux	X
ma-24	446	8	fxx	fxx	PROPN
ma-24	446	9	−	−	PROPN
ma-24	446	10	vxgxx	vxgxx	VERB
ma-24	446	11	+	+	CCONJ
ma-24	446	12	fxuxx	fxuxx	X
ma-24	446	13	+	+	CCONJ
ma-24	446	14	gxvxx	gxvxx	NOUN
ma-24	446	15	}	}	PUNCT
ma-24	446	16	.	.	PUNCT
ma-24	447	1	(	(	PUNCT
ma-24	447	2	142	142	NUM
ma-24	447	3	)	)	PUNCT
ma-24	447	4	case	case	NOUN
ma-24	447	5	(	(	PUNCT
ma-24	447	6	iii	iii	X
ma-24	447	7	)	)	PUNCT
ma-24	447	8	the	the	DET
ma-24	447	9	symmetry	symmetry	NOUN
ma-24	447	10	x3	x3	NOUN
ma-24	447	11	=	=	SYM
ma-24	448	1	αt	αt	PROPN
ma-24	448	2	∂	∂	NOUN
ma-24	448	3	∂x	∂x	PROPN
ma-24	448	4	+	+	CCONJ
ma-24	448	5	∂	∂	NUM
ma-24	448	6	∂u	∂u	PROPN
ma-24	448	7	(	(	PUNCT
ma-24	448	8	143	143	NUM
ma-24	448	9	)	)	PUNCT
ma-24	448	10	yields	yield	NOUN
ma-24	448	11	lie	lie	VERB
ma-24	448	12	characteristic	characteristic	ADJ
ma-24	448	13	functions	function	NOUN
ma-24	448	14	given	give	VERB
ma-24	448	15	by	by	ADP
ma-24	448	16	w	w	PROPN
ma-24	448	17	1	1	NUM
ma-24	448	18	3	3	NUM
ma-24	448	19	=	=	SYM
ma-24	448	20	1−	1−	NUM
ma-24	448	21	αtux	αtux	NOUN
ma-24	448	22	,	,	PUNCT
ma-24	448	23	w	w	PROPN
ma-24	448	24	2	2	NUM
ma-24	448	25	3	3	NUM
ma-24	448	26	=	=	SYM
ma-24	448	27	−αtvx	−αtvx	NOUN
ma-24	448	28	.	.	PUNCT
ma-24	449	1	(	(	PUNCT
ma-24	449	2	144	144	NUM
ma-24	449	3	)	)	PUNCT
ma-24	449	4	hence	hence	ADV
ma-24	449	5	by	by	ADP
ma-24	449	6	ibragimov	ibragimov	NOUN
ma-24	449	7	’s	’s	PART
ma-24	449	8	theorem	theorem	NOUN
ma-24	449	9	[	[	X
ma-24	449	10	9	9	NUM
ma-24	449	11	]	]	PUNCT
ma-24	449	12	,	,	PUNCT
ma-24	449	13	the	the	DET
ma-24	449	14	associated	associate	VERB
ma-24	449	15	conserved	conserve	VERB
ma-24	449	16	vector	vector	NOUN
ma-24	449	17	is	be	AUX
ma-24	449	18	given	give	VERB
ma-24	449	19	by	by	ADP
ma-24	449	20	t	t	PROPN
ma-24	449	21	t3	t3	PROPN
ma-24	450	1	=	=	PUNCT
ma-24	450	2	f	f	PROPN
ma-24	451	1	−	−	PROPN
ma-24	451	2	αt{ux	αt{ux	NUM
ma-24	451	3	f	f	PROPN
ma-24	451	4	+	+	CCONJ
ma-24	451	5	vxg	vxg	NOUN
ma-24	451	6	}	}	PUNCT
ma-24	451	7	,	,	PUNCT
ma-24	451	8	t	t	NOUN
ma-24	451	9	x3	x3	PROPN
ma-24	451	10	=	=	SYM
ma-24	451	11	α	α	PROPN
ma-24	451	12	[	[	PUNCT
ma-24	451	13	f	f	NOUN
ma-24	451	14	u	u	NOUN
ma-24	451	15	+	+	X
ma-24	451	16	gv	gv	ADP
ma-24	451	17	+	+	PUNCT
ma-24	451	18	t{ut	t{ut	NOUN
ma-24	451	19	f	f	NOUN
ma-24	452	1	+	+	CCONJ
ma-24	452	2	vtg}+	vtg}+	PROPN
ma-24	452	3	βt	βt	PROPN
ma-24	452	4	{	{	PUNCT
ma-24	452	5	fxx	fxx	PROPN
ma-24	452	6	αt	αt	PROPN
ma-24	452	7	−	−	PROPN
ma-24	452	8	ux	ux	PROPN
ma-24	452	9	fxx	fxx	PROPN
ma-24	452	10	−	−	PROPN
ma-24	452	11	vxgxx	vxgxx	VERB
ma-24	452	12	+	+	CCONJ
ma-24	452	13	fxuxx	fxuxx	X
ma-24	452	14	+	+	CCONJ
ma-24	452	15	gxvxx	gxvxx	NOUN
ma-24	452	16	}	}	PUNCT
ma-24	452	17	]	]	PUNCT
ma-24	452	18	.	.	PUNCT
ma-24	453	1	(	(	PUNCT
ma-24	453	2	145	145	NUM
ma-24	453	3	)	)	PUNCT
ma-24	453	4	case	case	NOUN
ma-24	453	5	(	(	PUNCT
ma-24	453	6	iv	iv	X
ma-24	453	7	)	)	PUNCT
ma-24	453	8	the	the	DET
ma-24	453	9	symmetry	symmetry	NOUN
ma-24	453	10	x4	x4	PROPN
ma-24	453	11	=	=	PUNCT
ma-24	453	12	3	3	NUM
ma-24	453	13	t	t	NOUN
ma-24	453	14	∂	∂	NOUN
ma-24	453	15	∂t	∂t	PROPN
ma-24	454	1	+	+	CCONJ
ma-24	454	2	x	x	SYM
ma-24	454	3	∂	∂	NUM
ma-24	454	4	∂x	∂x	PROPN
ma-24	454	5	−	−	PROPN
ma-24	454	6	2u	2u	PROPN
ma-24	454	7	∂	∂	NOUN
ma-24	454	8	∂u	∂u	PROPN
ma-24	454	9	−	−	PROPN
ma-24	454	10	2v	2v	PROPN
ma-24	454	11	∂	∂	PROPN
ma-24	455	1	∂v	∂v	PROPN
ma-24	455	2	(	(	PUNCT
ma-24	455	3	146	146	NUM
ma-24	455	4	)	)	PUNCT
ma-24	455	5	yields	yield	VERB
ma-24	455	6	the	the	DET
ma-24	455	7	lie	lie	NOUN
ma-24	455	8	characteristic	characteristic	ADJ
ma-24	455	9	functions	function	NOUN
ma-24	455	10	w	w	ADP
ma-24	455	11	1	1	NUM
ma-24	455	12	4	4	NUM
ma-24	455	13	=	=	NOUN
ma-24	455	14	−2u	−2u	PROPN
ma-24	455	15	−	−	PROPN
ma-24	456	1	3tut	3tut	INTJ
ma-24	456	2	−	−	X
ma-24	456	3	xux	xux	X
ma-24	456	4	,	,	PUNCT
ma-24	456	5	w	w	PROPN
ma-24	456	6	2	2	NUM
ma-24	456	7	4	4	NUM
ma-24	456	8	=	=	SYM
ma-24	456	9	−2v	−2v	PROPN
ma-24	456	10	−	−	NOUN
ma-24	457	1	3tvt	3tvt	NUM
ma-24	457	2	−	−	PROPN
ma-24	457	3	xvx	xvx	PROPN
ma-24	457	4	.	.	PUNCT
ma-24	458	1	(	(	PUNCT
ma-24	458	2	147	147	NUM
ma-24	458	3	)	)	PUNCT
ma-24	458	4	consequently	consequently	ADV
ma-24	458	5	by	by	ADP
ma-24	458	6	ibragimov	ibragimov	NOUN
ma-24	458	7	’s	’s	PART
ma-24	458	8	theorem	theorem	NOUN
ma-24	458	9	[	[	X
ma-24	458	10	9	9	NUM
ma-24	458	11	]	]	PUNCT
ma-24	458	12	,	,	PUNCT
ma-24	458	13	the	the	DET
ma-24	458	14	corresponding	corresponding	ADJ
ma-24	458	15	conserved	conserved	ADJ
ma-24	458	16	vector	vector	NOUN
ma-24	458	17	is	be	AUX
ma-24	458	18	given	give	VERB
ma-24	458	19	by	by	ADP
ma-24	458	20	t	t	PROPN
ma-24	458	21	t4	t4	PROPN
ma-24	458	22	=	=	PROPN
ma-24	458	23	α	α	PROPN
ma-24	459	1	[	[	X
ma-24	459	2	3t{f	3t{f	NUM
ma-24	459	3	uux	uux	PROPN
ma-24	459	4	−	−	PROPN
ma-24	459	5	f	f	PROPN
ma-24	459	6	vvx	vvx	NOUN
ma-24	459	7	+	+	CCONJ
ma-24	459	8	guvx	guvx	NOUN
ma-24	459	9	+	+	CCONJ
ma-24	459	10	gvux	gvux	ADJ
ma-24	459	11	}	}	PUNCT
ma-24	459	12	]	]	PUNCT
ma-24	460	1	+	+	CCONJ
ma-24	460	2	β	β	X
ma-24	460	3	[	[	X
ma-24	460	4	3t{f	3t{f	NUM
ma-24	460	5	uxxx	uxxx	PROPN
ma-24	460	6	+	+	CCONJ
ma-24	460	7	gvxxx	gvxxx	NOUN
ma-24	460	8	}	}	PUNCT
ma-24	460	9	]	]	PUNCT
ma-24	460	10	−	−	PROPN
ma-24	460	11	2{f	2{f	NUM
ma-24	460	12	u	u	NOUN
ma-24	460	13	+	+	X
ma-24	460	14	gv	gv	ADP
ma-24	460	15	}	}	PUNCT
ma-24	460	16	−	−	PROPN
ma-24	460	17	x{f	x{f	PROPN
ma-24	460	18	ux	ux	PROPN
ma-24	460	19	+	+	CCONJ
ma-24	460	20	gvx	gvx	PROPN
ma-24	460	21	}	}	PUNCT
ma-24	460	22	,	,	PUNCT
ma-24	460	23	t	t	PROPN
ma-24	460	24	x4	x4	PROPN
ma-24	460	25	=	=	PUNCT
ma-24	461	1	x{f	x{f	PROPN
ma-24	461	2	ut	ut	PROPN
ma-24	462	1	+	+	CCONJ
ma-24	462	2	gvt}+	gvt}+	PROPN
ma-24	462	3	β	β	NOUN
ma-24	462	4	[	[	PUNCT
ma-24	462	5	3	3	NUM
ma-24	462	6	(	(	PUNCT
ma-24	462	7	fxux	fxux	NOUN
ma-24	462	8	+	+	CCONJ
ma-24	462	9	gxvx	gxvx	NOUN
ma-24	462	10	+	+	CCONJ
ma-24	462	11	t{fxutx	t{fxutx	PROPN
ma-24	462	12	+	+	CCONJ
ma-24	462	13	gxvtx	gxvtx	VERB
ma-24	462	14	}	}	PUNCT
ma-24	462	15	)	)	PUNCT
ma-24	462	16	]	]	PUNCT
ma-24	463	1	−	−	PROPN
ma-24	463	2	α	α	X
ma-24	463	3	[	[	PUNCT
ma-24	463	4	2	2	NUM
ma-24	463	5	(	(	PUNCT
ma-24	463	6	f	f	X
ma-24	463	7	{	{	PUNCT
ma-24	463	8	u2	u2	PROPN
ma-24	463	9	−	−	PROPN
ma-24	463	10	v2}+	v2}+	PROPN
ma-24	463	11	2guv	2guv	NUM
ma-24	463	12	)	)	PUNCT
ma-24	464	1	+	+	CCONJ
ma-24	464	2	3	3	NUM
ma-24	464	3	t	t	NOUN
ma-24	464	4	(	(	PUNCT
ma-24	464	5	f	f	X
ma-24	464	6	{	{	PUNCT
ma-24	464	7	uut	uut	PROPN
ma-24	464	8	−	−	PROPN
ma-24	464	9	vvt}+	vvt}+	PROPN
ma-24	464	10	g{vut	g{vut	PROPN
ma-24	464	11	+	+	NUM
ma-24	464	12	uvt	uvt	NOUN
ma-24	464	13	}	}	PUNCT
ma-24	464	14	)	)	PUNCT
ma-24	464	15	]	]	PUNCT
ma-24	465	1	−	−	PUNCT
ma-24	465	2	β	β	X
ma-24	465	3	[	[	X
ma-24	465	4	x{ux	x{ux	PROPN
ma-24	465	5	fxx	fxx	PROPN
ma-24	465	6	+	+	CCONJ
ma-24	465	7	vxgxx	vxgxx	VERB
ma-24	465	8	−	−	PROPN
ma-24	465	9	fxuxx	fxuxx	PROPN
ma-24	465	10	−	−	PROPN
ma-24	466	1	gxvxx}+	gxvxx}+	PROPN
ma-24	466	2	2{ufxx	2{ufxx	NOUN
ma-24	466	3	+	+	CCONJ
ma-24	466	4	vgxx	vgxx	NOUN
ma-24	466	5	}	}	PUNCT
ma-24	466	6	]	]	PUNCT
ma-24	467	1	−	−	PUNCT
ma-24	467	2	β	β	X
ma-24	467	3	[	[	X
ma-24	467	4	3t{fxxut	3t{fxxut	NUM
ma-24	467	5	+	+	CCONJ
ma-24	467	6	gxxvt	gxxvt	VERB
ma-24	467	7	+	+	CCONJ
ma-24	467	8	f	f	X
ma-24	467	9	utxx	utxx	NOUN
ma-24	467	10	+	+	CCONJ
ma-24	467	11	gvtxx}+	gvtxx}+	NOUN
ma-24	467	12	4{f	4{f	NUM
ma-24	467	13	uxx	uxx	NOUN
ma-24	467	14	+	+	CCONJ
ma-24	467	15	gvxx	gvxx	ADJ
ma-24	467	16	}	}	PUNCT
ma-24	467	17	]	]	PUNCT
ma-24	467	18	.	.	PUNCT
ma-24	468	1	(	(	PUNCT
ma-24	468	2	148	148	NUM
ma-24	468	3	)	)	PUNCT
ma-24	468	4	remark	remark	NOUN
ma-24	468	5	3.7	3.7	NUM
ma-24	468	6	.	.	PUNCT
ma-24	469	1	the	the	DET
ma-24	469	2	appearance	appearance	NOUN
ma-24	469	3	of	of	ADP
ma-24	469	4	arbitrary	arbitrary	ADJ
ma-24	469	5	functions	function	NOUN
ma-24	469	6	f	f	X
ma-24	469	7	(	(	PUNCT
ma-24	469	8	t	t	PROPN
ma-24	469	9	,	,	PUNCT
ma-24	469	10	x	x	NOUN
ma-24	469	11	)	)	PUNCT
ma-24	469	12	and	and	CCONJ
ma-24	469	13	g(t	g(t	PROPN
ma-24	469	14	,	,	PUNCT
ma-24	469	15	x	x	NOUN
ma-24	469	16	)	)	PUNCT
ma-24	469	17	in	in	ADP
ma-24	469	18	the	the	DET
ma-24	469	19	conserved	conserve	VERB
ma-24	469	20	vectorsproves	vectorsprove	VERB
ma-24	469	21	the	the	DET
ma-24	469	22	existence	existence	NOUN
ma-24	469	23	of	of	ADP
ma-24	469	24	infinite	infinite	ADJ
ma-24	469	25	conservation	conservation	NOUN
ma-24	469	26	laws	law	NOUN
ma-24	469	27	for	for	ADP
ma-24	469	28	coupled	couple	VERB
ma-24	469	29	kdv	kdv	NOUN
ma-24	469	30	system	system	NOUN
ma-24	469	31	obtained	obtain	VERB
ma-24	469	32	by	by	ADP
ma-24	469	33	ibagimov’smethod	ibagimov’smethod	NOUN
ma-24	469	34	.	.	PROPN
ma-24	469	35	eur	eur	PROPN
ma-24	469	36	.	.	PUNCT
ma-24	470	1	j.	j.	PROPN
ma-24	470	2	math	math	PROPN
ma-24	470	3	.	.	PUNCT
ma-24	471	1	anal	anal	ADJ
ma-24	471	2	.	.	PUNCT
ma-24	472	1	1	1	NUM
ma-24	472	2	(	(	PUNCT
ma-24	472	3	2021	2021	NUM
ma-24	472	4	)	)	PUNCT
ma-24	472	5	1494	1494	NUM
ma-24	472	6	.	.	PUNCT
ma-24	473	1	conclusion	conclusion	NOUN
ma-24	473	2	in	in	ADP
ma-24	473	3	this	this	DET
ma-24	473	4	paper	paper	NOUN
ma-24	473	5	,	,	PUNCT
ma-24	473	6	lie	lie	NOUN
ma-24	473	7	group	group	NOUN
ma-24	473	8	analysis	analysis	NOUN
ma-24	473	9	was	be	AUX
ma-24	473	10	employed	employ	VERB
ma-24	473	11	in	in	ADP
ma-24	473	12	studying	study	VERB
ma-24	473	13	a	a	DET
ma-24	473	14	nonlinear	nonlinear	NOUN
ma-24	473	15	coupled	couple	VERB
ma-24	473	16	kdv	kdv	NOUN
ma-24	473	17	system.a	system.a	PROPN
ma-24	473	18	four	four	NUM
ma-24	473	19	-	-	PUNCT
ma-24	473	20	dimensional	dimensional	ADJ
ma-24	473	21	lie	lie	NOUN
ma-24	473	22	algebra	algebra	NOUN
ma-24	473	23	of	of	ADP
ma-24	473	24	symmetries	symmetry	NOUN
ma-24	473	25	was	be	AUX
ma-24	473	26	found	find	VERB
ma-24	473	27	for	for	ADP
ma-24	473	28	the	the	DET
ma-24	473	29	nonlinear	nonlinear	ADJ
ma-24	473	30	coupled	couple	VERB
ma-24	473	31	system	system	NOUN
ma-24	473	32	kdvequations	kdvequation	NOUN
ma-24	473	33	.	.	PUNCT
ma-24	474	1	this	this	PRON
ma-24	474	2	was	be	AUX
ma-24	474	3	spanned	span	VERB
ma-24	474	4	by	by	ADP
ma-24	474	5	space	space	NOUN
ma-24	474	6	and	and	CCONJ
ma-24	474	7	time	time	NOUN
ma-24	474	8	translations	translation	NOUN
ma-24	474	9	,	,	PUNCT
ma-24	474	10	galilean	galilean	PROPN
ma-24	474	11	boost	boost	NOUN
ma-24	474	12	and	and	CCONJ
ma-24	474	13	scaling	scale	VERB
ma-24	474	14	symmetrieswhere	symmetrieswhere	ADV
ma-24	474	15	the	the	DET
ma-24	474	16	scaling	scaling	NOUN
ma-24	474	17	symmetry	symmetry	NOUN
ma-24	474	18	acts	act	VERB
ma-24	474	19	on	on	ADP
ma-24	474	20	four	four	NUM
ma-24	474	21	variables	variable	NOUN
ma-24	474	22	.	.	PUNCT
ma-24	475	1	associated	associate	VERB
ma-24	475	2	to	to	ADP
ma-24	475	3	each	each	DET
ma-24	475	4	symmetry	symmetry	NOUN
ma-24	475	5	,	,	PUNCT
ma-24	475	6	we	we	PRON
ma-24	475	7	obtainedsymmetry	obtainedsymmetry	VERB
ma-24	475	8	reductions	reduction	NOUN
ma-24	475	9	that	that	PRON
ma-24	475	10	gave	give	VERB
ma-24	475	11	six	six	NUM
ma-24	475	12	nontrivial	nontrivial	ADJ
ma-24	475	13	solutions	solution	NOUN
ma-24	475	14	for	for	ADP
ma-24	475	15	the	the	DET
ma-24	475	16	coupled	couple	VERB
ma-24	475	17	system	system	NOUN
ma-24	475	18	.	.	PUNCT
ma-24	476	1	all	all	DET
ma-24	476	2	the	the	DET
ma-24	476	3	group	group	NOUN
ma-24	476	4	-	-	PUNCT
ma-24	476	5	invariant	invariant	ADJ
ma-24	476	6	solutions	solution	NOUN
ma-24	476	7	describe	describe	VERB
ma-24	476	8	the	the	DET
ma-24	476	9	various	various	ADJ
ma-24	476	10	states	state	NOUN
ma-24	476	11	of	of	ADP
ma-24	476	12	the	the	DET
ma-24	476	13	system	system	NOUN
ma-24	476	14	.	.	PUNCT
ma-24	477	1	the	the	DET
ma-24	477	2	obtained	obtain	VERB
ma-24	477	3	solutions	solution	NOUN
ma-24	477	4	can	can	AUX
ma-24	477	5	be	be	AUX
ma-24	477	6	usedas	usedas	ADJ
ma-24	477	7	a	a	DET
ma-24	477	8	benchmark	benchmark	NOUN
ma-24	477	9	against	against	ADP
ma-24	477	10	numerical	numerical	ADJ
ma-24	477	11	simulations	simulation	NOUN
ma-24	477	12	.	.	PUNCT
ma-24	478	1	lastly	lastly	ADV
ma-24	478	2	,	,	PUNCT
ma-24	478	3	we	we	PRON
ma-24	478	4	constructed	construct	VERB
ma-24	478	5	infinite	infinite	ADJ
ma-24	478	6	conservation	conservation	NOUN
ma-24	478	7	laws	law	NOUN
ma-24	478	8	ofa	ofa	PROPN
ma-24	478	9	nonlinear	nonlinear	PROPN
ma-24	478	10	coupled	couple	VERB
ma-24	478	11	kdv	kdv	NOUN
ma-24	478	12	system	system	NOUN
ma-24	478	13	by	by	ADP
ma-24	478	14	using	use	VERB
ma-24	478	15	multipliers	multiplier	NOUN
ma-24	478	16	and	and	CCONJ
ma-24	478	17	a	a	DET
ma-24	478	18	theorem	theorem	NOUN
ma-24	478	19	proposed	propose	VERB
ma-24	478	20	by	by	ADP
ma-24	478	21	nail	nail	NOUN
ma-24	478	22	ibragimov	ibragimov	NOUN
ma-24	478	23	.	.	PUNCT
ma-24	479	1	acknowledgement	acknowledgement	NOUN
ma-24	479	2	the	the	DET
ma-24	479	3	first	first	ADJ
ma-24	479	4	author	author	NOUN
ma-24	479	5	acknowledges	acknowledge	VERB
ma-24	479	6	the	the	DET
ma-24	479	7	financial	financial	ADJ
ma-24	479	8	support	support	NOUN
ma-24	479	9	of	of	ADP
ma-24	479	10	aims	aim	NOUN
ma-24	479	11	-	-	PUNCT
ma-24	479	12	south	south	NOUN
ma-24	479	13	africa	africa	PROPN
ma-24	479	14	and	and	CCONJ
ma-24	479	15	mastercard	mastercard	PROPN
ma-24	479	16	foun	foun	PROPN
ma-24	479	17	-	-	PUNCT
ma-24	479	18	dation	dation	NOUN
ma-24	479	19	.	.	PUNCT
ma-24	480	1	the	the	DET
ma-24	480	2	authors	author	NOUN
ma-24	480	3	are	be	AUX
ma-24	480	4	also	also	ADV
ma-24	480	5	grateful	grateful	ADJ
ma-24	480	6	to	to	ADP
ma-24	480	7	the	the	DET
ma-24	480	8	referees	referee	NOUN
ma-24	480	9	for	for	ADP
ma-24	480	10	their	their	PRON
ma-24	480	11	careful	careful	ADJ
ma-24	480	12	reading	reading	NOUN
ma-24	480	13	of	of	ADP
ma-24	480	14	the	the	DET
ma-24	480	15	manuscript	manuscript	NOUN
ma-24	480	16	andvaluable	andvaluable	ADJ
ma-24	480	17	comments	comment	NOUN
ma-24	480	18	.	.	PUNCT
ma-24	481	1	references	reference	NOUN
ma-24	481	2	[	[	X
ma-24	481	3	1	1	X
ma-24	481	4	]	]	PUNCT
ma-24	481	5	d.	d.	PROPN
ma-24	481	6	j.	j.	PROPN
ma-24	481	7	arigo	arigo	PROPN
ma-24	481	8	,	,	PUNCT
ma-24	481	9	symmetry	symmetry	NOUN
ma-24	481	10	analysis	analysis	NOUN
ma-24	481	11	of	of	ADP
ma-24	481	12	differential	differential	ADJ
ma-24	481	13	equations	equation	NOUN
ma-24	481	14	:	:	PUNCT
ma-24	481	15	an	an	DET
ma-24	481	16	introduction	introduction	NOUN
ma-24	481	17	,	,	PUNCT
ma-24	481	18	john	john	PROPN
ma-24	481	19	wiley	wiley	PROPN
ma-24	481	20	&	&	CCONJ
ma-24	481	21	sons	son	NOUN
ma-24	481	22	,	,	PUNCT
ma-24	481	23	2015.[2	2015.[2	NUM
ma-24	481	24	]	]	X
ma-24	481	25	g.	g.	PROPN
ma-24	481	26	bluman	bluman	PROPN
ma-24	481	27	,	,	PUNCT
ma-24	481	28	s.	s.	PROPN
ma-24	481	29	anco	anco	PROPN
ma-24	481	30	,	,	PUNCT
ma-24	481	31	symmetry	symmetry	NOUN
ma-24	481	32	and	and	CCONJ
ma-24	481	33	integration	integration	NOUN
ma-24	481	34	methods	method	NOUN
ma-24	481	35	for	for	ADP
ma-24	481	36	differential	differential	ADJ
ma-24	481	37	equations	equation	NOUN
ma-24	481	38	,	,	PUNCT
ma-24	481	39	springer	springer	NOUN
ma-24	481	40	science	science	PROPN
ma-24	481	41	&	&	CCONJ
ma-24	481	42	businessmedia	businessmedia	PROPN
ma-24	481	43	,	,	PUNCT
ma-24	481	44	2008.[3	2008.[3	NUM
ma-24	481	45	]	]	X
ma-24	481	46	g.	g.	PROPN
ma-24	481	47	w.	w.	PROPN
ma-24	481	48	bluman	bluman	PROPN
ma-24	481	49	,	,	PUNCT
ma-24	481	50	s.	s.	PROPN
ma-24	481	51	kumei	kumei	PROPN
ma-24	481	52	,	,	PUNCT
ma-24	481	53	symmetries	symmetry	NOUN
ma-24	481	54	and	and	CCONJ
ma-24	481	55	differential	differential	ADJ
ma-24	481	56	equations	equation	NOUN
ma-24	481	57	,	,	PUNCT
ma-24	481	58	springer	springer	NOUN
ma-24	481	59	science	science	PROPN
ma-24	481	60	&	&	CCONJ
ma-24	481	61	business	business	NOUN
ma-24	481	62	media	medium	NOUN
ma-24	481	63	,	,	PUNCT
ma-24	481	64	1989.[4	1989.[4	NUM
ma-24	481	65	]	]	X
ma-24	481	66	bluman	bluman	NOUN
ma-24	481	67	,	,	PUNCT
ma-24	481	68	g.	g.	PROPN
ma-24	481	69	w.	w.	PROPN
ma-24	481	70	,	,	PUNCT
ma-24	481	71	cheviakov	cheviakov	PROPN
ma-24	481	72	,	,	PUNCT
ma-24	481	73	a.	a.	PROPN
ma-24	481	74	f.	f.	PROPN
ma-24	481	75	,	,	PUNCT
ma-24	481	76	and	and	CCONJ
ma-24	481	77	anco	anco	PROPN
ma-24	481	78	,	,	PUNCT
ma-24	481	79	s.	s.	PROPN
ma-24	481	80	c	c	PROPN
ma-24	481	81	,	,	PUNCT
ma-24	481	82	applications	application	NOUN
ma-24	481	83	of	of	ADP
ma-24	481	84	symmetry	symmetry	NOUN
ma-24	481	85	methods	method	NOUN
ma-24	481	86	to	to	ADP
ma-24	481	87	partial	partial	ADJ
ma-24	481	88	differential	differential	NOUN
ma-24	481	89	equations	equation	NOUN
ma-24	481	90	,	,	PUNCT
ma-24	481	91	springer	springer	NOUN
ma-24	481	92	,	,	PUNCT
ma-24	481	93	2010.[5	2010.[5	NUM
ma-24	481	94	]	]	X
ma-24	481	95	n.	n.	PROPN
ma-24	481	96	h.	h.	PROPN
ma-24	481	97	ibragimov	ibragimov	PROPN
ma-24	481	98	,	,	PUNCT
ma-24	481	99	elementary	elementary	ADJ
ma-24	481	100	lie	lie	NOUN
ma-24	481	101	group	group	NOUN
ma-24	481	102	analysis	analysis	NOUN
ma-24	481	103	and	and	CCONJ
ma-24	481	104	ordinary	ordinary	ADJ
ma-24	481	105	differential	differential	ADJ
ma-24	481	106	equations	equation	NOUN
ma-24	481	107	,	,	PUNCT
ma-24	481	108	wiley	wiley	NOUN
ma-24	481	109	,	,	PUNCT
ma-24	481	110	1999.[6	1999.[6	NUM
ma-24	481	111	]	]	PUNCT
ma-24	481	112	j.	j.	PROPN
ma-24	481	113	owuor	owuor	PROPN
ma-24	481	114	,	,	PUNCT
ma-24	481	115	m.	m.	NOUN
ma-24	481	116	khalique	khalique	PROPN
ma-24	481	117	,	,	PUNCT
ma-24	481	118	lie	lie	NOUN
ma-24	481	119	group	group	NOUN
ma-24	481	120	analysis	analysis	NOUN
ma-24	481	121	of	of	ADP
ma-24	481	122	nonlinear	nonlinear	ADJ
ma-24	481	123	partial	partial	ADJ
ma-24	481	124	differential	differential	NOUN
ma-24	481	125	equations	equation	NOUN
ma-24	481	126	,	,	PUNCT
ma-24	481	127	lambert	lambert	PROPN
ma-24	481	128	academic	academic	PROPN
ma-24	481	129	publishers,2021[7	publishers,2021[7	PROPN
ma-24	481	130	]	]	PUNCT
ma-24	481	131	n.	n.	PROPN
ma-24	481	132	h.	h.	PROPN
ma-24	481	133	ibragimov	ibragimov	PROPN
ma-24	481	134	,	,	PUNCT
ma-24	481	135	crc	crc	NOUN
ma-24	481	136	handbook	handbook	NOUN
ma-24	481	137	of	of	ADP
ma-24	481	138	lie	lie	NOUN
ma-24	481	139	group	group	NOUN
ma-24	481	140	analysis	analysis	NOUN
ma-24	481	141	of	of	ADP
ma-24	481	142	differential	differential	ADJ
ma-24	481	143	equations	equation	NOUN
ma-24	481	144	,	,	PUNCT
ma-24	481	145	crc	crc	NOUN
ma-24	481	146	-	-	PUNCT
ma-24	481	147	press	press	NOUN
ma-24	481	148	,	,	PUNCT
ma-24	481	149	1994.[8	1994.[8	NUM
ma-24	481	150	]	]	X
ma-24	481	151	n.	n.	PROPN
ma-24	481	152	h.	h.	PROPN
ma-24	481	153	ibragimov	ibragimov	PROPN
ma-24	481	154	,	,	PUNCT
ma-24	481	155	selected	select	VERB
ma-24	481	156	works	work	NOUN
ma-24	481	157	,	,	PUNCT
ma-24	481	158	alga	alga	ADJ
ma-24	481	159	publications	publication	NOUN
ma-24	481	160	,	,	PUNCT
ma-24	481	161	blekinge	blekinge	PROPN
ma-24	481	162	institute	institute	PROPN
ma-24	481	163	of	of	ADP
ma-24	481	164	technology	technology	PROPN
ma-24	481	165	,	,	PUNCT
ma-24	481	166	selected	select	VERB
ma-24	481	167	works	work	NOUN
ma-24	481	168	,	,	PUNCT
ma-24	481	169	2009.[9	2009.[9	NUM
ma-24	481	170	]	]	X
ma-24	481	171	n.	n.	PROPN
ma-24	481	172	h.	h.	PROPN
ma-24	481	173	ibragimov	ibragimov	PROPN
ma-24	481	174	,	,	PUNCT
ma-24	481	175	a	a	DET
ma-24	481	176	new	new	ADJ
ma-24	481	177	conservation	conservation	NOUN
ma-24	481	178	theorem	theorem	NOUN
ma-24	481	179	,	,	PUNCT
ma-24	481	180	j.	j.	PROPN
ma-24	481	181	math	math	PROPN
ma-24	481	182	.	.	PUNCT
ma-24	482	1	anal	anal	PROPN
ma-24	482	2	.	.	PUNCT
ma-24	482	3	appl	appl	PROPN
ma-24	482	4	.	.	PUNCT
ma-24	483	1	333(2007	333(2007	NUM
ma-24	483	2	)	)	PUNCT
ma-24	483	3	,	,	PUNCT
ma-24	483	4	311	311	NUM
ma-24	483	5	-	-	SYM
ma-24	483	6	328	328	NUM
ma-24	483	7	.	.	PUNCT
ma-24	484	1	https://doi.org/10	https://doi.org/10	PROPN
ma-24	484	2	.	.	PUNCT
ma-24	485	1	1016	1016	NUM
ma-24	485	2	/	/	SYM
ma-24	485	3	j.jmaa.2006.10.078.[10	j.jmaa.2006.10.078.[10	CCONJ
ma-24	485	4	]	]	PUNCT
ma-24	485	5	n.	n.	PROPN
ma-24	485	6	h.	h.	PROPN
ma-24	485	7	ibragimov	ibragimov	PROPN
ma-24	485	8	,	,	PUNCT
ma-24	485	9	a	a	DET
ma-24	485	10	practical	practical	ADJ
ma-24	485	11	course	course	NOUN
ma-24	485	12	in	in	ADP
ma-24	485	13	differential	differential	ADJ
ma-24	485	14	equations	equation	NOUN
ma-24	485	15	and	and	CCONJ
ma-24	485	16	mathematical	mathematical	ADJ
ma-24	485	17	modelling	modelling	NOUN
ma-24	485	18	:	:	PUNCT
ma-24	485	19	classical	classical	ADJ
ma-24	485	20	and	and	CCONJ
ma-24	485	21	newmethods	newmethod	NOUN
ma-24	485	22	.	.	PUNCT
ma-24	486	1	nonlinear	nonlinear	ADJ
ma-24	486	2	mathematical	mathematical	ADJ
ma-24	486	3	models	model	NOUN
ma-24	486	4	.	.	PUNCT
ma-24	487	1	symmetry	symmetry	NOUN
ma-24	487	2	and	and	CCONJ
ma-24	487	3	invariance	invariance	NOUN
ma-24	487	4	principles	principle	NOUN
ma-24	487	5	,	,	PUNCT
ma-24	487	6	world	world	NOUN
ma-24	487	7	scientific	scientific	ADJ
ma-24	487	8	publishing	publishing	NOUN
ma-24	487	9	com	com	NOUN
ma-24	487	10	-	-	PUNCT
ma-24	487	11	pany	pany	NOUN
ma-24	487	12	,	,	PUNCT
ma-24	487	13	2009.[11	2009.[11	NUM
ma-24	487	14	]	]	X
ma-24	487	15	c.	c.	PROPN
ma-24	487	16	m.	m.	PROPN
ma-24	487	17	khalique	khalique	PROPN
ma-24	487	18	,	,	PUNCT
ma-24	487	19	s.	s.	PROPN
ma-24	487	20	a.	a.	PROPN
ma-24	487	21	abdallah	abdallah	PROPN
ma-24	487	22	,	,	PUNCT
ma-24	487	23	coupled	couple	VERB
ma-24	487	24	burgers	burger	NOUN
ma-24	487	25	equations	equation	NOUN
ma-24	487	26	governing	govern	VERB
ma-24	487	27	polydispersive	polydispersive	ADJ
ma-24	487	28	sedimentation	sedimentation	NOUN
ma-24	487	29	;	;	PUNCT
ma-24	487	30	a	a	DET
ma-24	487	31	lie	lie	NOUN
ma-24	487	32	symmetryapproach	symmetryapproach	NOUN
ma-24	487	33	.	.	PUNCT
ma-24	488	1	results	result	VERB
ma-24	488	2	phys	phy	NOUN
ma-24	488	3	.	.	PUNCT
ma-24	489	1	16(2020	16(2020	NUM
ma-24	489	2	)	)	PUNCT
ma-24	489	3	,	,	PUNCT
ma-24	489	4	76	76	NUM
ma-24	489	5	-	-	SYM
ma-24	489	6	90	90	NUM
ma-24	489	7	.	.	PUNCT
ma-24	490	1	https://doi.org/10.1016/j.rinp.2020.102967.[12	https://doi.org/10.1016/j.rinp.2020.102967.[12	PROPN
ma-24	490	2	]	]	X
ma-24	490	3	r.	r.	PROPN
ma-24	490	4	j.	j.	PROPN
ma-24	490	5	leveque	leveque	PROPN
ma-24	490	6	,	,	PUNCT
ma-24	490	7	numerical	numerical	ADJ
ma-24	490	8	methods	method	NOUN
ma-24	490	9	for	for	ADP
ma-24	490	10	conservation	conservation	NOUN
ma-24	490	11	laws	law	NOUN
ma-24	490	12	,	,	PUNCT
ma-24	490	13	springer	springer	NOUN
ma-24	490	14	verlag	verlag	PROPN
ma-24	490	15	,	,	PUNCT
ma-24	490	16	new	new	PROPN
ma-24	490	17	york	york	PROPN
ma-24	490	18	,	,	PUNCT
ma-24	491	1	1992.[13	1992.[13	PROPN
ma-24	491	2	]	]	X
ma-24	491	3	s	s	AUX
ma-24	491	4	lie	lie	NOUN
ma-24	491	5	,	,	PUNCT
ma-24	491	6	vorlesungen	vorlesungen	PROPN
ma-24	491	7	aber	aber	PROPN
ma-24	491	8	differentialgleichungen	differentialgleichungen	PROPN
ma-24	491	9	mit	mit	PROPN
ma-24	491	10	bekannten	bekannten	X
ma-24	491	11	infinitesimalen	infinitesimalen	ADJ
ma-24	491	12	transformationen	transformationen	NOUN
ma-24	491	13	.	.	PUNCT
ma-24	492	1	bg	bg	PROPN
ma-24	492	2	teubner	teubner	NOUN
ma-24	492	3	,	,	PUNCT
ma-24	492	4	1891.[14	1891.[14	NUM
ma-24	492	5	]	]	X
ma-24	492	6	i.	i.	PROPN
ma-24	492	7	mhlanga	mhlanga	PROPN
ma-24	492	8	,	,	PUNCT
ma-24	492	9	c.	c.	PROPN
ma-24	492	10	khalique	khalique	PROPN
ma-24	492	11	,	,	PUNCT
ma-24	492	12	travelling	travel	VERB
ma-24	492	13	wave	wave	NOUN
ma-24	492	14	solutions	solution	NOUN
ma-24	492	15	and	and	CCONJ
ma-24	492	16	conservation	conservation	NOUN
ma-24	492	17	laws	law	NOUN
ma-24	492	18	of	of	ADP
ma-24	492	19	the	the	DET
ma-24	492	20	korteweg	korteweg	NOUN
ma-24	492	21	-	-	PUNCT
ma-24	492	22	de	de	NOUN
ma-24	492	23	vriesburgers	vriesburger	NOUN
ma-24	492	24	equationwith	equationwith	ADP
ma-24	492	25	power	power	NOUN
ma-24	492	26	law	law	NOUN
ma-24	492	27	nonlinearity	nonlinearity	NOUN
ma-24	492	28	.	.	PUNCT
ma-24	493	1	malays	malays	PROPN
ma-24	493	2	.	.	PUNCT
ma-24	494	1	j.	j.	PROPN
ma-24	494	2	math	math	PROPN
ma-24	494	3	.	.	PUNCT
ma-24	495	1	sci	sci	PROPN
ma-24	495	2	.	.	PROPN
ma-24	496	1	11(2017	11(2017	NUM
ma-24	496	2	)	)	PUNCT
ma-24	496	3	,	,	PUNCT
ma-24	496	4	1	1	NUM
ma-24	496	5	-	-	SYM
ma-24	496	6	8.[15	8.[15	NUM
ma-24	496	7	]	]	PUNCT
ma-24	496	8	e.	e.	PROPN
ma-24	496	9	noether	noether	PROPN
ma-24	496	10	,	,	PUNCT
ma-24	496	11	invariant	invariant	ADJ
ma-24	496	12	variations	variation	NOUN
ma-24	496	13	problem	problem	NOUN
ma-24	496	14	,	,	PUNCT
ma-24	496	15	nachr	nachr	PROPN
ma-24	496	16	.	.	PUNCT
ma-24	497	1	konig	konig	PROPN
ma-24	497	2	.	.	PUNCT
ma-24	498	1	gissel	gissel	PROPN
ma-24	498	2	.	.	PUNCT
ma-24	499	1	wissen	wissen	PROPN
ma-24	499	2	,	,	PUNCT
ma-24	499	3	gottingen	gottingen	NOUN
ma-24	499	4	.	.	PUNCT
ma-24	499	5	math	math	NOUN
ma-24	499	6	.	.	PUNCT
ma-24	500	1	phys	phy	NOUN
ma-24	500	2	.	.	PUNCT
ma-24	501	1	kl	kl	PROPN
ma-24	501	2	,	,	PUNCT
ma-24	501	3	6(1918	6(1918	NUM
ma-24	501	4	)	)	PUNCT
ma-24	501	5	,	,	PUNCT
ma-24	501	6	235	235	NUM
ma-24	501	7	-	-	SYM
ma-24	501	8	257.[16	257.[16	NUM
ma-24	501	9	]	]	PUNCT
ma-24	501	10	p.	p.	NOUN
ma-24	501	11	j.	j.	PROPN
ma-24	501	12	olver	olver	PROPN
ma-24	501	13	,	,	PUNCT
ma-24	501	14	applications	application	NOUN
ma-24	501	15	of	of	ADP
ma-24	501	16	lie	lie	NOUN
ma-24	501	17	groups	group	NOUN
ma-24	501	18	to	to	PART
ma-24	501	19	differential	differential	VERB
ma-24	501	20	equations	equation	NOUN
ma-24	501	21	,	,	PUNCT
ma-24	501	22	springer	springer	NOUN
ma-24	501	23	science	science	PROPN
ma-24	501	24	&	&	CCONJ
ma-24	501	25	business	business	NOUN
ma-24	501	26	media	medium	NOUN
ma-24	501	27	,	,	PUNCT
ma-24	501	28	1993	1993	NUM
ma-24	501	29	.	.	PUNCT
ma-24	502	1	https://doi.org/10.1016/j.jmaa.2006.10.078	https://doi.org/10.1016/j.jmaa.2006.10.078	PROPN
ma-24	502	2	https://doi.org/10.1016/j.jmaa.2006.10.078	https://doi.org/10.1016/j.jmaa.2006.10.078	PROPN
ma-24	502	3	https://doi.org/10.1016/j.rinp.2020.102967	https://doi.org/10.1016/j.rinp.2020.102967	PROPN
ma-24	502	4	eur	eur	PROPN
ma-24	502	5	.	.	PUNCT
ma-24	503	1	j.	j.	PROPN
ma-24	503	2	math	math	PROPN
ma-24	503	3	.	.	PUNCT
ma-24	504	1	anal	anal	ADJ
ma-24	504	2	.	.	PUNCT
ma-24	505	1	1	1	NUM
ma-24	505	2	(	(	PUNCT
ma-24	505	3	2021	2021	NUM
ma-24	505	4	)	)	PUNCT
ma-24	506	1	150	150	NUM
ma-24	507	1	[	[	SYM
ma-24	507	2	17	17	NUM
ma-24	507	3	]	]	X
ma-24	507	4	l.	l.	PROPN
ma-24	507	5	ovsyannikov	ovsyannikov	PROPN
ma-24	507	6	,	,	PUNCT
ma-24	507	7	lectures	lecture	VERB
ma-24	507	8	on	on	ADP
ma-24	507	9	the	the	DET
ma-24	507	10	theory	theory	NOUN
ma-24	507	11	of	of	ADP
ma-24	507	12	group	group	NOUN
ma-24	507	13	properties	property	NOUN
ma-24	507	14	of	of	ADP
ma-24	507	15	differential	differential	ADJ
ma-24	507	16	equations	equation	NOUN
ma-24	507	17	,	,	PUNCT
ma-24	507	18	world	world	NOUN
ma-24	507	19	scientific	scientific	ADJ
ma-24	507	20	publishingcompany	publishingcompany	NOUN
ma-24	507	21	,	,	PUNCT
ma-24	507	22	2013.[18	2013.[18	NUM
ma-24	507	23	]	]	PUNCT
ma-24	507	24	h.	h.	NOUN
ma-24	507	25	pie	pie	PROPN
ma-24	507	26	,	,	PUNCT
ma-24	507	27	symmetry	symmetry	NOUN
ma-24	507	28	methods	method	NOUN
ma-24	507	29	for	for	ADP
ma-24	507	30	differential	differential	ADJ
ma-24	507	31	equations	equation	NOUN
ma-24	507	32	:	:	PUNCT
ma-24	507	33	a	a	DET
ma-24	507	34	beginners	beginner	NOUN
ma-24	507	35	guide	guide	VERB
ma-24	507	36	,	,	PUNCT
ma-24	507	37	cambridge	cambridge	PROPN
ma-24	507	38	university	university	PROPN
ma-24	507	39	pres	pres	PROPN
ma-24	507	40	,	,	PUNCT
ma-24	507	41	cambridge,2013.[19	cambridge,2013.[19	PROPN
ma-24	507	42	]	]	PUNCT
ma-24	507	43	a.	a.	NOUN
ma-24	507	44	m.	m.	NOUN
ma-24	507	45	wazwaz	wazwaz	PROPN
ma-24	507	46	,	,	PUNCT
ma-24	507	47	partial	partial	ADJ
ma-24	507	48	differential	differential	ADJ
ma-24	507	49	equations	equation	NOUN
ma-24	507	50	and	and	CCONJ
ma-24	507	51	solitary	solitary	ADJ
ma-24	507	52	waves	wave	NOUN
ma-24	507	53	theory	theory	NOUN
ma-24	507	54	,	,	PUNCT
ma-24	507	55	springer	springer	NOUN
ma-24	507	56	science	science	PROPN
ma-24	507	57	&	&	CCONJ
ma-24	507	58	business	business	NOUN
ma-24	507	59	media	medium	NOUN
ma-24	507	60	,	,	PUNCT
ma-24	507	61	2010.[20	2010.[20	NUM
ma-24	507	62	]	]	X
ma-24	507	63	n.	n.	PROPN
ma-24	507	64	hasibun	hasibun	PROPN
ma-24	507	65	,	,	PUNCT
ma-24	507	66	l.	l.	PROPN
ma-24	507	67	abdullah	abdullah	PROPN
ma-24	507	68	,	,	PUNCT
ma-24	507	69	f.	f.	PROPN
ma-24	507	70	aini	aini	PROPN
ma-24	507	71	,	,	PUNCT
ma-24	507	72	the	the	DET
ma-24	507	73	improved	improved	ADJ
ma-24	507	74	gg	gg	NOUN
ma-24	507	75	-	-	PUNCT
ma-24	507	76	expansion	expansion	NOUN
ma-24	507	77	method	method	NOUN
ma-24	507	78	to	to	ADP
ma-24	507	79	the	the	DET
ma-24	507	80	(	(	PUNCT
ma-24	507	81	3	3	NUM
ma-24	507	82	dimensional	dimensional	ADJ
ma-24	507	83	kadomstev	kadomstev	NOUN
ma-24	507	84	-	-	PUNCT
ma-24	507	85	petviashviliequation	petviashviliequation	NOUN
ma-24	507	86	,	,	PUNCT
ma-24	507	87	amer	amer	PROPN
ma-24	507	88	.	.	PUNCT
ma-24	508	1	j.	j.	PROPN
ma-24	508	2	appl	appl	PROPN
ma-24	508	3	.	.	PROPN
ma-24	508	4	math	math	PROPN
ma-24	508	5	.	.	PUNCT
ma-24	509	1	stat	stat	PROPN
ma-24	509	2	.	.	PUNCT
ma-24	510	1	1(2013	1(2013	NUM
ma-24	510	2	)	)	PUNCT
ma-24	510	3	,	,	PUNCT
ma-24	511	1	64	64	NUM
ma-24	511	2	-	-	SYM
ma-24	511	3	70.[21	70.[21	PROPN
ma-24	511	4	]	]	X
ma-24	511	5	b.	b.	PROPN
ma-24	511	6	hong	hong	PROPN
ma-24	511	7	,	,	PUNCT
ma-24	511	8	d.	d.	PROPN
ma-24	511	9	lu	lu	PROPN
ma-24	511	10	,	,	PUNCT
ma-24	511	11	f.	f.	PROPN
ma-24	511	12	sun	sun	PROPN
ma-24	511	13	,	,	PUNCT
ma-24	511	14	the	the	DET
ma-24	511	15	extended	extended	ADJ
ma-24	511	16	jacobi	jacobi	PROPN
ma-24	511	17	elliptic	elliptic	ADJ
ma-24	511	18	functions	function	NOUN
ma-24	511	19	expansion	expansion	NOUN
ma-24	511	20	method	method	NOUN
ma-24	511	21	and	and	CCONJ
ma-24	511	22	new	new	ADJ
ma-24	511	23	exact	exact	ADJ
ma-24	511	24	solutions	solution	NOUN
ma-24	511	25	for	for	ADP
ma-24	511	26	thezakharov	thezakharov	NOUN
ma-24	511	27	equations	equation	NOUN
ma-24	511	28	,	,	PUNCT
ma-24	511	29	world	world	PROPN
ma-24	511	30	j.	j.	PROPN
ma-24	511	31	model	model	PROPN
ma-24	511	32	.	.	PUNCT
ma-24	512	1	simul	simul	PROPN
ma-24	512	2	.	.	PUNCT
ma-24	513	1	5(2009	5(2009	NUM
ma-24	513	2	)	)	PUNCT
ma-24	513	3	,	,	PUNCT
ma-24	513	4	78	78	NUM
ma-24	513	5	-	-	SYM
ma-24	513	6	109.[22	109.[22	PROPN
ma-24	513	7	]	]	X
ma-24	513	8	s.m	s.m	PROPN
ma-24	513	9	.	.	PROPN
ma-24	513	10	ege	ege	PROPN
ma-24	513	11	,	,	PUNCT
ma-24	513	12	e.	e.	PROPN
ma-24	513	13	misirli	misirli	PROPN
ma-24	513	14	,	,	PUNCT
ma-24	513	15	the	the	DET
ma-24	513	16	modified	modified	ADJ
ma-24	513	17	kudryashov	kudryashov	PROPN
ma-24	513	18	method	method	NOUN
ma-24	513	19	for	for	ADP
ma-24	513	20	solving	solve	VERB
ma-24	513	21	some	some	DET
ma-24	513	22	fractional	fractional	ADJ
ma-24	513	23	-	-	PUNCT
ma-24	513	24	order	order	NOUN
ma-24	513	25	nonlinear	nonlinear	ADJ
ma-24	513	26	equations	equation	NOUN
ma-24	513	27	,	,	PUNCT
ma-24	513	28	adv.difference	adv.difference	ADP
ma-24	513	29	equ	equ	PROPN
ma-24	513	30	.	.	PROPN
ma-24	513	31	2014	2014	NUM
ma-24	513	32	(	(	PUNCT
ma-24	513	33	2014	2014	NUM
ma-24	513	34	)	)	PUNCT
ma-24	513	35	,	,	PUNCT
ma-24	513	36	135	135	NUM
ma-24	513	37	.	.	PUNCT
ma-24	513	38	https://doi.org/10.1186/1687-1847-2014-135	https://doi.org/10.1186/1687-1847-2014-135	NOUN
ma-24	513	39	.	.	PUNCT
ma-24	514	1	https://doi.org/10.1186/1687-1847-2014-135	https://doi.org/10.1186/1687-1847-2014-135	PROPN
ma-24	514	2	1	1	NUM
ma-24	514	3	.	.	X
ma-24	514	4	introduction	introduction	NOUN
ma-24	514	5	2	2	NUM
ma-24	514	6	.	.	PUNCT
ma-24	514	7	preliminaries	preliminary	NOUN
ma-24	514	8	3	3	NUM
ma-24	514	9	.	.	X
ma-24	514	10	main	main	ADJ
ma-24	514	11	results	result	NOUN
ma-24	514	12	4	4	NUM
ma-24	514	13	.	.	PUNCT
ma-24	515	1	conclusion	conclusion	NOUN
ma-24	515	2	acknowledgement	acknowledgement	NOUN
ma-24	515	3	references	reference	NOUN