id	sid	tid	token	lemma	pos
ma-140	1	1	2023	2023	NUM
ma-140	1	2	ada	ada	PROPN
ma-140	1	3	academica	academica	PROPN
ma-140	1	4	https://adac.eeeur	https://adac.eeeur	PROPN
ma-140	1	5	.	.	PUNCT
ma-140	2	1	j.	j.	PROPN
ma-140	2	2	math	math	PROPN
ma-140	2	3	.	.	PUNCT
ma-140	3	1	anal	anal	ADJ
ma-140	3	2	.	.	PUNCT
ma-140	4	1	3	3	NUM
ma-140	4	2	(	(	PUNCT
ma-140	4	3	2023	2023	NUM
ma-140	4	4	)	)	PUNCT
ma-140	4	5	13doi	13doi	NOUN
ma-140	4	6	:	:	PUNCT
ma-140	4	7	10.28924	10.28924	NUM
ma-140	4	8	/	/	SYM
ma-140	4	9	ada	ada	PROPN
ma-140	4	10	/	/	SYM
ma-140	4	11	ma.3.13	ma.3.13	PROPN
ma-140	4	12	group	group	NOUN
ma-140	4	13	analysis	analysis	NOUN
ma-140	4	14	of	of	ADP
ma-140	4	15	equal	equal	ADJ
ma-140	4	16	-	-	PUNCT
ma-140	4	17	width	width	NOUN
ma-140	4	18	equation	equation	NOUN
ma-140	4	19	joseph	joseph	PROPN
ma-140	4	20	owuor	owuor	PROPN
ma-140	4	21	owino	owino	PROPN
ma-140	4	22	faculty	faculty	NOUN
ma-140	4	23	of	of	ADP
ma-140	4	24	applied	apply	VERB
ma-140	4	25	sciences	science	NOUN
ma-140	4	26	and	and	CCONJ
ma-140	4	27	technology	technology	NOUN
ma-140	4	28	,	,	PUNCT
ma-140	4	29	school	school	NOUN
ma-140	4	30	of	of	ADP
ma-140	4	31	mathematics	mathematic	NOUN
ma-140	4	32	and	and	CCONJ
ma-140	4	33	actuarial	actuarial	ADJ
ma-140	4	34	science	science	NOUN
ma-140	4	35	,	,	PUNCT
ma-140	4	36	department	department	NOUN
ma-140	4	37	of	of	ADP
ma-140	4	38	pure	pure	ADJ
ma-140	4	39	and	and	CCONJ
ma-140	4	40	applied	applied	ADJ
ma-140	4	41	mathematics	mathematic	NOUN
ma-140	4	42	,	,	PUNCT
ma-140	4	43	the	the	DET
ma-140	4	44	technical	technical	ADJ
ma-140	4	45	university	university	PROPN
ma-140	4	46	of	of	ADP
ma-140	4	47	kenya	kenya	PROPN
ma-140	4	48	,	,	PUNCT
ma-140	4	49	kenya	kenya	PROPN
ma-140	4	50	correspondence	correspondence	NOUN
ma-140	4	51	:	:	PUNCT
ma-140	4	52	josephowuorowino@gmail.com	josephowuorowino@gmail.com	X
ma-140	5	1	abstract	abstract	ADJ
ma-140	5	2	.	.	PUNCT
ma-140	6	1	we	we	PRON
ma-140	6	2	study	study	VERB
ma-140	6	3	a	a	DET
ma-140	6	4	third	third	ADJ
ma-140	6	5	-	-	PUNCT
ma-140	6	6	order	order	NOUN
ma-140	6	7	nonlinear	nonlinear	ADJ
ma-140	6	8	equal	equal	ADJ
ma-140	6	9	width	width	ADJ
ma-140	6	10	equation	equation	NOUN
ma-140	6	11	,	,	PUNCT
ma-140	6	12	which	which	PRON
ma-140	6	13	has	have	AUX
ma-140	6	14	been	be	AUX
ma-140	6	15	used	use	VERB
ma-140	6	16	for	for	ADP
ma-140	6	17	simulationof	simulationof	NOUN
ma-140	6	18	a	a	DET
ma-140	6	19	one	one	NUM
ma-140	6	20	-	-	PUNCT
ma-140	6	21	dimensional	dimensional	ADJ
ma-140	6	22	wave	wave	NOUN
ma-140	6	23	propagation	propagation	NOUN
ma-140	6	24	in	in	ADP
ma-140	6	25	a	a	DET
ma-140	6	26	non	non	ADJ
ma-140	6	27	-	-	ADJ
ma-140	6	28	linear	linear	ADJ
ma-140	6	29	medium	medium	NOUN
ma-140	6	30	with	with	ADP
ma-140	6	31	dispersion	dispersion	NOUN
ma-140	6	32	process	process	NOUN
ma-140	6	33	,	,	PUNCT
ma-140	6	34	by	by	ADP
ma-140	6	35	symmetryanalysis	symmetryanalysis	PROPN
ma-140	6	36	.	.	PUNCT
ma-140	7	1	first	first	ADV
ma-140	7	2	,	,	PUNCT
ma-140	7	3	lie	lie	NOUN
ma-140	7	4	point	point	NOUN
ma-140	7	5	symmetries	symmetry	NOUN
ma-140	7	6	are	be	AUX
ma-140	7	7	obtained	obtain	VERB
ma-140	7	8	and	and	CCONJ
ma-140	7	9	used	use	VERB
ma-140	7	10	to	to	PART
ma-140	7	11	reduce	reduce	VERB
ma-140	7	12	reduce	reduce	VERB
ma-140	7	13	the	the	DET
ma-140	7	14	equal	equal	ADJ
ma-140	7	15	width	width	NOUN
ma-140	7	16	equationthereby	equationthereby	ADV
ma-140	7	17	constructing	construct	VERB
ma-140	7	18	exact	exact	ADJ
ma-140	7	19	solutions	solution	NOUN
ma-140	7	20	.	.	PUNCT
ma-140	8	1	traveling	travel	VERB
ma-140	8	2	waves	wave	NOUN
ma-140	8	3	are	be	AUX
ma-140	8	4	constructed	construct	VERB
ma-140	8	5	using	use	VERB
ma-140	8	6	of	of	ADP
ma-140	8	7	a	a	DET
ma-140	8	8	linear	linear	ADJ
ma-140	8	9	combination	combination	NOUN
ma-140	8	10	ofspace	ofspace	NOUN
ma-140	8	11	and	and	CCONJ
ma-140	8	12	time	time	NOUN
ma-140	8	13	translation	translation	NOUN
ma-140	8	14	symmetries	symmetry	NOUN
ma-140	8	15	.	.	PUNCT
ma-140	9	1	we	we	PRON
ma-140	9	2	have	have	AUX
ma-140	9	3	used	use	VERB
ma-140	9	4	the	the	DET
ma-140	9	5	multiplier	multipli	ADJ
ma-140	9	6	technique	technique	NOUN
ma-140	9	7	to	to	ADP
ma-140	9	8	compute	compute	VERB
ma-140	9	9	conservationlaws	conservationlaw	NOUN
ma-140	9	10	.	.	PUNCT
ma-140	10	1	1	1	X
ma-140	10	2	.	.	X
ma-140	10	3	introduction	introduction	NOUN
ma-140	10	4	the	the	DET
ma-140	10	5	equal	equal	ADJ
ma-140	10	6	width	width	ADJ
ma-140	10	7	equation	equation	NOUN
ma-140	10	8	[	[	X
ma-140	10	9	1	1	X
ma-140	10	10	]	]	PUNCT
ma-140	10	11	is	be	AUX
ma-140	10	12	given	give	VERB
ma-140	10	13	by	by	ADP
ma-140	10	14	,	,	PUNCT
ma-140	10	15	∆	∆	PROPN
ma-140	10	16	≡	≡	PROPN
ma-140	10	17	ut	ut	PROPN
ma-140	11	1	+	+	CCONJ
ma-140	11	2	αuux	αuux	PROPN
ma-140	11	3	+	+	CCONJ
ma-140	11	4	βutxx	βutxx	ADJ
ma-140	11	5	=	=	SYM
ma-140	11	6	0	0	NUM
ma-140	11	7	,	,	PUNCT
ma-140	11	8	(	(	PUNCT
ma-140	11	9	1.1	1.1	NUM
ma-140	11	10	)	)	PUNCT
ma-140	12	1	where	where	SCONJ
ma-140	12	2	t	t	NOUN
ma-140	12	3	and	and	CCONJ
ma-140	12	4	x	x	PRON
ma-140	12	5	represents	represent	VERB
ma-140	12	6	time	time	NOUN
ma-140	12	7	and	and	CCONJ
ma-140	12	8	spatial	spatial	ADJ
ma-140	12	9	independent	independent	ADJ
ma-140	12	10	variables	variable	NOUN
ma-140	12	11	;	;	PUNCT
ma-140	12	12	α	α	PROPN
ma-140	12	13	and	and	CCONJ
ma-140	12	14	β	β	X
ma-140	12	15	are	be	AUX
ma-140	12	16	the	the	DET
ma-140	12	17	nonlinearityand	nonlinearityand	PROPN
ma-140	12	18	the	the	DET
ma-140	12	19	dispersion	dispersion	NOUN
ma-140	12	20	parameters	parameter	NOUN
ma-140	12	21	respectively	respectively	ADV
ma-140	12	22	.	.	PUNCT
ma-140	13	1	equation	equation	NOUN
ma-140	13	2	(	(	PUNCT
ma-140	13	3	1.1	1.1	NUM
ma-140	13	4	)	)	PUNCT
ma-140	13	5	was	be	AUX
ma-140	13	6	first	first	ADV
ma-140	13	7	studied	study	VERB
ma-140	13	8	by	by	ADP
ma-140	13	9	morrison	morrison	PROPN
ma-140	13	10	[	[	X
ma-140	13	11	2	2	NUM
ma-140	13	12	]	]	PUNCT
ma-140	13	13	anddescribes	anddescribe	NOUN
ma-140	13	14	nonlinear	nonlinear	ADJ
ma-140	13	15	dispersive	dispersive	ADJ
ma-140	13	16	waves	wave	NOUN
ma-140	13	17	,	,	PUNCT
ma-140	13	18	particularly	particularly	ADV
ma-140	13	19	those	those	PRON
ma-140	13	20	generated	generate	VERB
ma-140	13	21	in	in	ADP
ma-140	13	22	a	a	DET
ma-140	13	23	shallow	shallow	ADJ
ma-140	13	24	water	water	NOUN
ma-140	13	25	channel.several	channel.several	ADJ
ma-140	13	26	techniques	technique	NOUN
ma-140	13	27	have	have	AUX
ma-140	13	28	been	be	AUX
ma-140	13	29	employed	employ	VERB
ma-140	13	30	to	to	PART
ma-140	13	31	compute	compute	VERB
ma-140	13	32	solutions	solution	NOUN
ma-140	13	33	of	of	ADP
ma-140	13	34	equation	equation	NOUN
ma-140	13	35	(	(	PUNCT
ma-140	13	36	1.1	1.1	NUM
ma-140	13	37	)	)	PUNCT
ma-140	13	38	.	.	PUNCT
ma-140	14	1	a	a	DET
ma-140	14	2	case	case	NOUN
ma-140	14	3	in	in	ADP
ma-140	14	4	point	point	NOUN
ma-140	14	5	,	,	PUNCT
ma-140	14	6	is	be	AUX
ma-140	14	7	in	in	ADP
ma-140	14	8	[	[	X
ma-140	14	9	3	3	NUM
ma-140	14	10	]	]	PUNCT
ma-140	14	11	,	,	PUNCT
ma-140	14	12	where	where	SCONJ
ma-140	14	13	a	a	DET
ma-140	14	14	petrov	petrov	PROPN
ma-140	14	15	-	-	PUNCT
ma-140	14	16	galerkin	galerkin	ADJ
ma-140	14	17	approach	approach	NOUN
ma-140	14	18	applied	apply	VERB
ma-140	14	19	quadratic	quadratic	ADJ
ma-140	14	20	b	b	NOUN
ma-140	14	21	-	-	PUNCT
ma-140	14	22	spline	spline	ADJ
ma-140	14	23	finite	finite	PROPN
ma-140	14	24	element	element	NOUN
ma-140	14	25	.	.	PUNCT
ma-140	15	1	in	in	ADP
ma-140	15	2	[	[	X
ma-140	15	3	4	4	NUM
ma-140	15	4	]	]	PUNCT
ma-140	15	5	,	,	PUNCT
ma-140	15	6	theresearchers	theresearcher	NOUN
ma-140	15	7	applied	apply	VERB
ma-140	15	8	least	least	ADJ
ma-140	15	9	-	-	PUNCT
ma-140	15	10	squares	square	NOUN
ma-140	15	11	approach	approach	NOUN
ma-140	15	12	in	in	ADP
ma-140	15	13	the	the	DET
ma-140	15	14	construction	construction	NOUN
ma-140	15	15	of	of	ADP
ma-140	15	16	numerical	numerical	ADJ
ma-140	15	17	solutions	solution	NOUN
ma-140	15	18	.	.	PUNCT
ma-140	16	1	we	we	PRON
ma-140	16	2	presenta	presenta	VERB
ma-140	16	3	group	group	NOUN
ma-140	16	4	analysis	analysis	NOUN
ma-140	16	5	approach	approach	NOUN
ma-140	16	6	in	in	ADP
ma-140	16	7	this	this	DET
ma-140	16	8	paper	paper	NOUN
ma-140	16	9	by	by	ADP
ma-140	16	10	first	first	ADV
ma-140	16	11	giving	give	VERB
ma-140	16	12	the	the	DET
ma-140	16	13	preliminaries	preliminary	NOUN
ma-140	16	14	.	.	PUNCT
ma-140	17	1	2	2	X
ma-140	17	2	.	.	X
ma-140	17	3	preliminaries	preliminary	NOUN
ma-140	17	4	this	this	DET
ma-140	17	5	section	section	NOUN
ma-140	17	6	is	be	AUX
ma-140	17	7	a	a	DET
ma-140	17	8	prelude	prelude	NOUN
ma-140	17	9	to	to	ADP
ma-140	17	10	the	the	DET
ma-140	17	11	sequel	sequel	NOUN
ma-140	17	12	.	.	PUNCT
ma-140	18	1	received	receive	VERB
ma-140	18	2	:	:	PUNCT
ma-140	18	3	3	3	NUM
ma-140	18	4	nov	nov	PROPN
ma-140	18	5	2022	2022	NUM
ma-140	18	6	.	.	PUNCT
ma-140	19	1	key	key	ADJ
ma-140	19	2	words	word	NOUN
ma-140	19	3	and	and	CCONJ
ma-140	19	4	phrases	phrase	NOUN
ma-140	19	5	.	.	PUNCT
ma-140	20	1	equal	equal	ADJ
ma-140	20	2	width	width	ADJ
ma-140	20	3	equation	equation	NOUN
ma-140	20	4	;	;	PUNCT
ma-140	20	5	lie	lie	NOUN
ma-140	20	6	group	group	NOUN
ma-140	20	7	analysis	analysis	NOUN
ma-140	20	8	;	;	PUNCT
ma-140	20	9	group	group	NOUN
ma-140	20	10	-	-	PUNCT
ma-140	20	11	invariant	invariant	ADJ
ma-140	20	12	solutions	solution	NOUN
ma-140	20	13	;	;	PUNCT
ma-140	20	14	stationary	stationary	ADJ
ma-140	20	15	solutions;symmetry	solutions;symmetry	NOUN
ma-140	20	16	reductions	reduction	NOUN
ma-140	20	17	;	;	PUNCT
ma-140	20	18	solitons	soliton	NOUN
ma-140	20	19	;	;	PUNCT
ma-140	20	20	traveling	travel	VERB
ma-140	20	21	waves	wave	NOUN
ma-140	20	22	.	.	PUNCT
ma-140	21	1	1	1	NUM
ma-140	21	2	https://adac.ee	https://adac.ee	PROPN
ma-140	21	3	https://doi.org/10.28924/ada/ma.3.13	https://doi.org/10.28924/ada/ma.3.13	PROPN
ma-140	21	4	https://orcid.org/0000-0002-4178-736x	https://orcid.org/0000-0002-4178-736x	PROPN
ma-140	21	5	eur	eur	PROPN
ma-140	21	6	.	.	PUNCT
ma-140	22	1	j.	j.	PROPN
ma-140	22	2	math	math	PROPN
ma-140	22	3	.	.	PUNCT
ma-140	23	1	anal	anal	PROPN
ma-140	23	2	.	.	PUNCT
ma-140	24	1	10.28924	10.28924	NUM
ma-140	24	2	/	/	SYM
ma-140	24	3	ada	ada	PROPN
ma-140	24	4	/	/	SYM
ma-140	24	5	ma.3.13	ma.3.13	PROPN
ma-140	24	6	2	2	NUM
ma-140	24	7	local	local	ADJ
ma-140	24	8	lie	lie	NOUN
ma-140	24	9	groups	group	NOUN
ma-140	24	10	.	.	PUNCT
ma-140	25	1	[	[	X
ma-140	25	2	5	5	NUM
ma-140	25	3	]	]	PUNCT
ma-140	25	4	we	we	PRON
ma-140	25	5	will	will	AUX
ma-140	25	6	consider	consider	VERB
ma-140	25	7	the	the	DET
ma-140	25	8	transformations	transformation	NOUN
ma-140	25	9	tε	tε	ADP
ma-140	25	10	:	:	PUNCT
ma-140	25	11	x̄	x̄	X
ma-140	25	12	i	i	PRON
ma-140	25	13	=	=	SYM
ma-140	26	1	ϕi(x	ϕi(x	PROPN
ma-140	27	1	i	i	PRON
ma-140	27	2	,	,	PUNCT
ma-140	27	3	uα	uα	PROPN
ma-140	27	4	,	,	PUNCT
ma-140	27	5	ε	ε	PROPN
ma-140	27	6	)	)	PUNCT
ma-140	27	7	,	,	PUNCT
ma-140	27	8	ūα	ūα	PROPN
ma-140	27	9	=	=	SYM
ma-140	27	10	ψα(x	ψα(x	PROPN
ma-140	27	11	i	i	PRON
ma-140	27	12	,	,	PUNCT
ma-140	27	13	uα	uα	PROPN
ma-140	27	14	,	,	PUNCT
ma-140	27	15	ε	ε	PROPN
ma-140	27	16	)	)	PUNCT
ma-140	27	17	,	,	PUNCT
ma-140	27	18	(	(	PUNCT
ma-140	27	19	2.1	2.1	NUM
ma-140	27	20	)	)	PUNCT
ma-140	27	21	in	in	ADP
ma-140	27	22	the	the	DET
ma-140	27	23	euclidean	euclidean	ADJ
ma-140	27	24	space	space	NOUN
ma-140	27	25	rn	rn	PROPN
ma-140	27	26	of	of	ADP
ma-140	27	27	x	x	X
ma-140	27	28	=	=	PUNCT
ma-140	27	29	x	x	SYM
ma-140	27	30	i	i	PRON
ma-140	27	31	independent	independent	ADJ
ma-140	27	32	variables	variable	NOUN
ma-140	27	33	and	and	CCONJ
ma-140	27	34	rm	rm	NOUN
ma-140	27	35	of	of	ADP
ma-140	27	36	u	u	PROPN
ma-140	27	37	=	=	PUNCT
ma-140	27	38	uα	uα	PROPN
ma-140	27	39	dependent	dependent	ADJ
ma-140	27	40	variables.the	variables.the	DET
ma-140	27	41	continuous	continuous	ADJ
ma-140	27	42	parameter	parameter	NOUN
ma-140	27	43	ε	ε	PROPN
ma-140	27	44	ranges	range	VERB
ma-140	27	45	from	from	ADP
ma-140	27	46	a	a	DET
ma-140	27	47	neighbourhood	neighbourhood	NOUN
ma-140	28	1	n	n	NOUN
ma-140	28	2	′	′	NUM
ma-140	29	1	⊂	⊂	PROPN
ma-140	29	2	n	n	PROPN
ma-140	29	3	⊂	⊂	X
ma-140	29	4	r	r	NOUN
ma-140	29	5	of	of	ADP
ma-140	29	6	ε	ε	PROPN
ma-140	29	7	=	=	SYM
ma-140	29	8	0	0	PROPN
ma-140	29	9	for	for	ADP
ma-140	29	10	ϕi	ϕi	PRON
ma-140	29	11	and	and	CCONJ
ma-140	29	12	ψαdifferentiable	ψαdifferentiable	ADJ
ma-140	29	13	and	and	CCONJ
ma-140	29	14	analytic	analytic	ADJ
ma-140	29	15	in	in	ADP
ma-140	29	16	the	the	DET
ma-140	29	17	parameter	parameter	NOUN
ma-140	29	18	ε	ε	PROPN
ma-140	29	19	.	.	PUNCT
ma-140	29	20	definition	definition	NOUN
ma-140	29	21	2.1	2.1	NUM
ma-140	29	22	.	.	PUNCT
ma-140	30	1	let	let	VERB
ma-140	30	2	g	g	PRON
ma-140	30	3	be	be	AUX
ma-140	30	4	a	a	DET
ma-140	30	5	set	set	NOUN
ma-140	30	6	of	of	ADP
ma-140	30	7	transformations	transformation	NOUN
ma-140	30	8	in	in	ADP
ma-140	30	9	(	(	PUNCT
ma-140	30	10	2.1	2.1	NUM
ma-140	30	11	)	)	PUNCT
ma-140	30	12	.	.	PUNCT
ma-140	31	1	then	then	ADV
ma-140	31	2	g	g	PROPN
ma-140	31	3	is	be	AUX
ma-140	31	4	a	a	DET
ma-140	31	5	local	local	ADJ
ma-140	31	6	lie	lie	NOUN
ma-140	31	7	group	group	NOUN
ma-140	31	8	if:(i	if:(i	NOUN
ma-140	31	9	)	)	PUNCT
ma-140	31	10	.	.	PUNCT
ma-140	32	1	given	give	VERB
ma-140	32	2	tε1	tε1	PROPN
ma-140	32	3	,	,	PUNCT
ma-140	32	4	tε2	tε2	NOUN
ma-140	32	5	∈	∈	NOUN
ma-140	32	6	g	g	PROPN
ma-140	32	7	,	,	PUNCT
ma-140	32	8	for	for	ADP
ma-140	32	9	ε1	ε1	PROPN
ma-140	32	10	,	,	PUNCT
ma-140	32	11	ε2	ε2	PROPN
ma-140	32	12	∈	∈	PROPN
ma-140	32	13	n	n	CCONJ
ma-140	32	14	′	′	NUM
ma-140	32	15	⊂	⊂	PROPN
ma-140	32	16	n	n	CCONJ
ma-140	32	17	,	,	PUNCT
ma-140	32	18	then	then	ADV
ma-140	32	19	tε1tε2	tε1tε2	ADV
ma-140	32	20	=	=	PUNCT
ma-140	32	21	tε3	tε3	INTJ
ma-140	32	22	∈	∈	PROPN
ma-140	32	23	g	g	PROPN
ma-140	32	24	,	,	PUNCT
ma-140	32	25	ε3	ε3	PROPN
ma-140	32	26	=	=	SYM
ma-140	32	27	φ(ε1	φ(ε1	PROPN
ma-140	32	28	,	,	PUNCT
ma-140	32	29	ε2	ε2	ADJ
ma-140	32	30	)	)	PUNCT
ma-140	32	31	∈	∈	PROPN
ma-140	32	32	n	n	CCONJ
ma-140	32	33	(	(	PUNCT
ma-140	32	34	closure).(ii	closure).(ii	NOUN
ma-140	32	35	)	)	PUNCT
ma-140	32	36	.	.	PUNCT
ma-140	33	1	there	there	PRON
ma-140	33	2	exists	exist	VERB
ma-140	33	3	a	a	DET
ma-140	33	4	unique	unique	ADJ
ma-140	33	5	t0	t0	PROPN
ma-140	33	6	∈	∈	PROPN
ma-140	33	7	g	g	PROPN
ma-140	34	1	if	if	SCONJ
ma-140	34	2	and	and	CCONJ
ma-140	34	3	only	only	ADV
ma-140	34	4	if	if	SCONJ
ma-140	34	5	ε	ε	PROPN
ma-140	34	6	=	=	SYM
ma-140	34	7	0	0	PROPN
ma-140	34	8	such	such	ADJ
ma-140	34	9	that	that	DET
ma-140	34	10	tεt0	tεt0	NOUN
ma-140	34	11	=	=	PUNCT
ma-140	34	12	t0tε	t0tε	PUNCT
ma-140	35	1	=	=	PUNCT
ma-140	35	2	tε(identity).(iii	tε(identity).(iii	NOUN
ma-140	35	3	)	)	PUNCT
ma-140	35	4	.	.	PUNCT
ma-140	36	1	there	there	PRON
ma-140	36	2	exists	exist	VERB
ma-140	36	3	a	a	DET
ma-140	36	4	unique	unique	ADJ
ma-140	36	5	tε−1	tε−1	PROPN
ma-140	36	6	∈	∈	PROPN
ma-140	36	7	g	g	NOUN
ma-140	36	8	for	for	ADP
ma-140	36	9	every	every	DET
ma-140	36	10	transformation	transformation	NOUN
ma-140	36	11	tε	tε	ADP
ma-140	36	12	∈	∈	PROPN
ma-140	36	13	g	g	PROPN
ma-140	36	14	,	,	PUNCT
ma-140	36	15	where	where	SCONJ
ma-140	36	16	ε	ε	PROPN
ma-140	36	17	∈	∈	PROPN
ma-140	36	18	n	n	ADP
ma-140	36	19	′	′	NUM
ma-140	36	20	⊂	⊂	PROPN
ma-140	36	21	n	n	CCONJ
ma-140	36	22	and	and	CCONJ
ma-140	36	23	ε−1	ε−1	PROPN
ma-140	36	24	∈	∈	PROPN
ma-140	36	25	n	n	PRON
ma-140	36	26	such	such	ADJ
ma-140	36	27	that	that	SCONJ
ma-140	36	28	tεtε−1	tεtε−1	X
ma-140	36	29	=	=	SYM
ma-140	36	30	tε−1tε	tε−1tε	NOUN
ma-140	36	31	=	=	SYM
ma-140	36	32	t0	t0	PROPN
ma-140	36	33	(	(	PUNCT
ma-140	36	34	inverse	inverse	NOUN
ma-140	36	35	)	)	PUNCT
ma-140	36	36	.	.	PUNCT
ma-140	37	1	remark	remark	PROPN
ma-140	37	2	2.2	2.2	NUM
ma-140	37	3	.	.	PUNCT
ma-140	38	1	the	the	DET
ma-140	38	2	condition	condition	NOUN
ma-140	38	3	(	(	PUNCT
ma-140	38	4	i	i	NOUN
ma-140	38	5	)	)	PUNCT
ma-140	38	6	is	be	AUX
ma-140	38	7	sufficient	sufficient	ADJ
ma-140	38	8	for	for	ADP
ma-140	38	9	associativity	associativity	NOUN
ma-140	38	10	of	of	ADP
ma-140	38	11	g.	g.	PROPN
ma-140	38	12	prolongations	prolongation	NOUN
ma-140	38	13	.	.	PUNCT
ma-140	39	1	consider	consider	VERB
ma-140	39	2	the	the	DET
ma-140	39	3	system	system	NOUN
ma-140	39	4	,	,	PUNCT
ma-140	39	5	∆α	∆α	PROPN
ma-140	39	6	(	(	PUNCT
ma-140	39	7	x	x	X
ma-140	39	8	i	i	PRON
ma-140	39	9	,	,	PUNCT
ma-140	39	10	uα	uα	PROPN
ma-140	39	11	,	,	PUNCT
ma-140	39	12	u(1	u(1	PROPN
ma-140	39	13	)	)	PUNCT
ma-140	39	14	,	,	PUNCT
ma-140	39	15	.	.	PUNCT
ma-140	39	16	.	.	PUNCT
ma-140	40	1	.	.	PUNCT
ma-140	41	1	,	,	PUNCT
ma-140	41	2	u(π	u(π	PROPN
ma-140	41	3	)	)	PUNCT
ma-140	41	4	)	)	PUNCT
ma-140	42	1	=	=	PUNCT
ma-140	42	2	∆α	∆α	PROPN
ma-140	42	3	=	=	SYM
ma-140	42	4	0	0	PROPN
ma-140	42	5	,	,	PUNCT
ma-140	42	6	(	(	PUNCT
ma-140	42	7	2.2	2.2	NUM
ma-140	42	8	)	)	PUNCT
ma-140	42	9	where	where	SCONJ
ma-140	42	10	uα	uα	PROPN
ma-140	42	11	are	be	AUX
ma-140	42	12	dependent	dependent	ADJ
ma-140	42	13	variables	variable	NOUN
ma-140	42	14	with	with	ADP
ma-140	42	15	partial	partial	ADJ
ma-140	42	16	derivatives	derivative	NOUN
ma-140	42	17	u(1	u(1	PROPN
ma-140	42	18	)	)	PUNCT
ma-140	42	19	=	=	PRON
ma-140	42	20	{	{	PUNCT
ma-140	42	21	uαi	uαi	ADV
ma-140	42	22	}	}	PUNCT
ma-140	42	23	,	,	PUNCT
ma-140	42	24	u(2	u(2	PROPN
ma-140	42	25	)	)	PUNCT
ma-140	42	26	=	=	PRON
ma-140	42	27	{	{	PUNCT
ma-140	42	28	uαij	uαij	ADV
ma-140	42	29	}	}	PUNCT
ma-140	42	30	,	,	PUNCT
ma-140	42	31	.	.	PUNCT
ma-140	42	32	.	.	PUNCT
ma-140	42	33	.	.	PUNCT
ma-140	43	1	,	,	PUNCT
ma-140	43	2	u(π	u(π	PROPN
ma-140	43	3	)	)	PUNCT
ma-140	44	1	=	=	PRON
ma-140	44	2	{	{	PUNCT
ma-140	44	3	uαi1	uαi1	PROPN
ma-140	44	4	...	...	PUNCT
ma-140	44	5	iπ	iπ	NOUN
ma-140	44	6	}	}	PUNCT
ma-140	44	7	,	,	PUNCT
ma-140	44	8	of	of	ADP
ma-140	44	9	the	the	DET
ma-140	44	10	first	first	ADJ
ma-140	44	11	,	,	PUNCT
ma-140	44	12	second	second	ADJ
ma-140	44	13	,	,	PUNCT
ma-140	44	14	.	.	PUNCT
ma-140	44	15	.	.	PUNCT
ma-140	45	1	.	.	PUNCT
ma-140	46	1	,	,	PUNCT
ma-140	46	2	up	up	ADP
ma-140	46	3	to	to	ADP
ma-140	46	4	the	the	DET
ma-140	46	5	πth	πth	NOUN
ma-140	46	6	-	-	PUNCT
ma-140	46	7	orders	order	NOUN
ma-140	46	8	.	.	PUNCT
ma-140	47	1	we	we	PRON
ma-140	47	2	shall	shall	AUX
ma-140	47	3	denoteby	denoteby	ADV
ma-140	47	4	di	di	VERB
ma-140	47	5	=	=	SYM
ma-140	47	6	∂	∂	NOUN
ma-140	47	7	∂x	∂x	PROPN
ma-140	48	1	i	i	PRON
ma-140	48	2	+	+	PROPN
ma-140	48	3	uαi	uαi	ADJ
ma-140	48	4	∂	∂	NOUN
ma-140	49	1	∂uα	∂uα	NOUN
ma-140	50	1	+	+	CCONJ
ma-140	50	2	uαij	uαij	PROPN
ma-140	50	3	∂	∂	NOUN
ma-140	50	4	∂uαj	∂uαj	NOUN
ma-140	50	5	+	+	CCONJ
ma-140	50	6	.	.	PUNCT
ma-140	50	7	.	.	PUNCT
ma-140	50	8	.	.	PUNCT
ma-140	51	1	,	,	PUNCT
ma-140	51	2	(	(	PUNCT
ma-140	51	3	2.3	2.3	NUM
ma-140	51	4	)	)	PUNCT
ma-140	51	5	the	the	DET
ma-140	51	6	total	total	ADJ
ma-140	51	7	differentiation	differentiation	NOUN
ma-140	51	8	operator	operator	NOUN
ma-140	51	9	with	with	ADP
ma-140	51	10	respect	respect	NOUN
ma-140	51	11	to	to	ADP
ma-140	51	12	the	the	DET
ma-140	51	13	variables	variable	NOUN
ma-140	51	14	x	x	PUNCT
ma-140	52	1	i	i	PRON
ma-140	52	2	and	and	CCONJ
ma-140	52	3	δji	δji	PROPN
ma-140	52	4	,	,	PUNCT
ma-140	52	5	the	the	DET
ma-140	52	6	kronecker	kronecker	NOUN
ma-140	52	7	delta	delta	NOUN
ma-140	52	8	.	.	PUNCT
ma-140	53	1	then	then	ADV
ma-140	53	2	di(x	di(x	NUM
ma-140	53	3	j	j	NOUN
ma-140	53	4	)	)	PUNCT
ma-140	53	5	=	=	SYM
ma-140	53	6	δji	δji	PROPN
ma-140	53	7	,	,	PUNCT
ma-140	53	8	′	′	PROPN
ma-140	53	9	,	,	PUNCT
ma-140	53	10	uαi	uαi	ADJ
ma-140	53	11	=	=	SYM
ma-140	53	12	di(u	di(u	NOUN
ma-140	53	13	α	α	NOUN
ma-140	53	14	)	)	PUNCT
ma-140	53	15	,	,	PUNCT
ma-140	53	16	uαij	uαij	NOUN
ma-140	53	17	=	=	X
ma-140	53	18	dj(di(u	dj(di(u	NOUN
ma-140	53	19	α	α	NOUN
ma-140	53	20	)	)	PUNCT
ma-140	53	21	)	)	PUNCT
ma-140	53	22	,	,	PUNCT
ma-140	53	23	.	.	PUNCT
ma-140	53	24	.	.	PUNCT
ma-140	53	25	.	.	PUNCT
ma-140	54	1	,	,	PUNCT
ma-140	54	2	(	(	PUNCT
ma-140	54	3	2.4	2.4	NUM
ma-140	54	4	)	)	PUNCT
ma-140	54	5	where	where	SCONJ
ma-140	54	6	uαi	uαi	PROPN
ma-140	54	7	defined	define	VERB
ma-140	54	8	in	in	ADP
ma-140	54	9	(	(	PUNCT
ma-140	54	10	2.4	2.4	NUM
ma-140	54	11	)	)	PUNCT
ma-140	54	12	are	be	AUX
ma-140	54	13	differential	differential	ADJ
ma-140	54	14	variables	variable	NOUN
ma-140	54	15	[	[	X
ma-140	54	16	6].(1	6].(1	NUM
ma-140	54	17	)	)	PUNCT
ma-140	54	18	prolonged	prolonged	ADJ
ma-140	54	19	groups	group	NOUN
ma-140	54	20	let	let	VERB
ma-140	54	21	g	g	NOUN
ma-140	54	22	given	give	VERB
ma-140	54	23	by	by	ADP
ma-140	54	24	x̄	x̄	NOUN
ma-140	54	25	i	i	PRON
ma-140	54	26	=	=	SYM
ma-140	54	27	ϕi(x	ϕi(x	PROPN
ma-140	55	1	i	i	PRON
ma-140	55	2	,	,	PUNCT
ma-140	55	3	uα	uα	PROPN
ma-140	55	4	,	,	PUNCT
ma-140	55	5	ε	ε	PROPN
ma-140	55	6	)	)	PUNCT
ma-140	55	7	,	,	PUNCT
ma-140	55	8	ϕi	ϕi	ADP
ma-140	55	9	∣∣∣	∣∣∣	ADJ
ma-140	55	10	ε=0	ε=0	X
ma-140	55	11	=	=	PUNCT
ma-140	55	12	x	x	PUNCT
ma-140	55	13	i	i	NOUN
ma-140	55	14	,	,	PUNCT
ma-140	55	15	ūα	ūα	PROPN
ma-140	55	16	=	=	PUNCT
ma-140	55	17	ψα(x	ψα(x	PROPN
ma-140	55	18	i	i	PRON
ma-140	55	19	,	,	PUNCT
ma-140	55	20	uα	uα	PROPN
ma-140	55	21	,	,	PUNCT
ma-140	55	22	ε	ε	PROPN
ma-140	55	23	)	)	PUNCT
ma-140	55	24	,	,	PUNCT
ma-140	55	25	ψα	ψα	ADP
ma-140	55	26	∣∣∣	∣∣∣	ADJ
ma-140	55	27	ε=0	ε=0	X
ma-140	55	28	=	=	SYM
ma-140	55	29	uα	uα	PROPN
ma-140	55	30	,	,	PUNCT
ma-140	55	31	(	(	PUNCT
ma-140	55	32	2.5	2.5	NUM
ma-140	55	33	)	)	PUNCT
ma-140	55	34	where	where	SCONJ
ma-140	55	35	∣∣∣	∣∣∣	ADJ
ma-140	55	36	ε=0	ε=0	NOUN
ma-140	55	37	means	mean	NOUN
ma-140	55	38	evaluated	evaluate	VERB
ma-140	55	39	on	on	ADP
ma-140	55	40	ε	ε	PROPN
ma-140	55	41	=	=	SYM
ma-140	55	42	0	0	PROPN
ma-140	55	43	.	.	PUNCT
ma-140	55	44	definition	definition	NOUN
ma-140	55	45	2.3	2.3	NUM
ma-140	55	46	.	.	PUNCT
ma-140	56	1	the	the	DET
ma-140	56	2	construction	construction	NOUN
ma-140	56	3	of	of	ADP
ma-140	56	4	g	g	NOUN
ma-140	56	5	in	in	ADP
ma-140	56	6	(	(	PUNCT
ma-140	56	7	2.5	2.5	NUM
ma-140	56	8	)	)	PUNCT
ma-140	56	9	is	be	AUX
ma-140	56	10	equivalent	equivalent	ADJ
ma-140	56	11	to	to	ADP
ma-140	56	12	the	the	DET
ma-140	56	13	computation	computation	NOUN
ma-140	56	14	of	of	ADP
ma-140	56	15	infinitesimaltransformations	infinitesimaltransformation	NOUN
ma-140	56	16	x̄	x̄	PRON
ma-140	57	1	i	i	PRON
ma-140	58	1	≈	≈	PROPN
ma-140	58	2	x	x	PUNCT
ma-140	59	1	i	i	PRON
ma-140	59	2	+	+	CCONJ
ma-140	59	3	ξi(x	ξi(x	NOUN
ma-140	59	4	i	i	PRON
ma-140	59	5	,	,	PUNCT
ma-140	59	6	uα)ε	uα)ε	PROPN
ma-140	59	7	,	,	PUNCT
ma-140	59	8	ϕi	ϕi	ADP
ma-140	59	9	∣∣∣	∣∣∣	ADJ
ma-140	59	10	ε=0	ε=0	X
ma-140	59	11	=	=	PUNCT
ma-140	59	12	x	x	PUNCT
ma-140	59	13	i	i	NOUN
ma-140	59	14	,	,	PUNCT
ma-140	59	15	ūα	ūα	PROPN
ma-140	59	16	≈	≈	PROPN
ma-140	59	17	uα	uα	PROPN
ma-140	59	18	+	+	CCONJ
ma-140	59	19	ηα(x	ηα(x	VERB
ma-140	59	20	i	i	PRON
ma-140	59	21	,	,	PUNCT
ma-140	59	22	uα)ε	uα)ε	ADJ
ma-140	59	23	,	,	PUNCT
ma-140	59	24	ψα	ψα	ADP
ma-140	59	25	∣∣∣	∣∣∣	ADJ
ma-140	59	26	ε=0	ε=0	X
ma-140	59	27	=	=	SYM
ma-140	59	28	uα	uα	PROPN
ma-140	59	29	,	,	PUNCT
ma-140	59	30	(	(	PUNCT
ma-140	59	31	2.6	2.6	NUM
ma-140	59	32	)	)	PUNCT
ma-140	59	33	https://doi.org/10.28924/ada/ma.3.13	https://doi.org/10.28924/ada/ma.3.13	PROPN
ma-140	59	34	eur	eur	NOUN
ma-140	59	35	.	.	PUNCT
ma-140	60	1	j.	j.	PROPN
ma-140	60	2	math	math	PROPN
ma-140	60	3	.	.	PUNCT
ma-140	61	1	anal	anal	PROPN
ma-140	61	2	.	.	PUNCT
ma-140	62	1	10.28924	10.28924	NUM
ma-140	62	2	/	/	SYM
ma-140	62	3	ada	ada	PROPN
ma-140	62	4	/	/	SYM
ma-140	62	5	ma.3.13	ma.3.13	PROPN
ma-140	62	6	3obtained	3obtained	NUM
ma-140	62	7	from	from	ADP
ma-140	62	8	(	(	PUNCT
ma-140	62	9	2.1	2.1	NUM
ma-140	62	10	)	)	PUNCT
ma-140	62	11	by	by	ADP
ma-140	62	12	a	a	DET
ma-140	62	13	taylor	taylor	PROPN
ma-140	62	14	series	series	PROPN
ma-140	62	15	expansion	expansion	NOUN
ma-140	62	16	of	of	ADP
ma-140	62	17	ϕi(x	ϕi(x	NOUN
ma-140	63	1	i	i	PRON
ma-140	63	2	,	,	PUNCT
ma-140	63	3	uα	uα	PROPN
ma-140	63	4	,	,	PUNCT
ma-140	63	5	ε	ε	PROPN
ma-140	63	6	)	)	PUNCT
ma-140	63	7	and	and	CCONJ
ma-140	63	8	ψi(x	ψi(x	NUM
ma-140	64	1	i	i	PRON
ma-140	64	2	,	,	PUNCT
ma-140	64	3	uα	uα	PROPN
ma-140	64	4	,	,	PUNCT
ma-140	64	5	ε	ε	PROPN
ma-140	64	6	)	)	PUNCT
ma-140	64	7	in	in	ADP
ma-140	64	8	ε	ε	PROPN
ma-140	64	9	about	about	ADP
ma-140	64	10	ε	ε	PROPN
ma-140	64	11	=	=	SYM
ma-140	64	12	0	0	PUNCT
ma-140	64	13	and	and	CCONJ
ma-140	64	14	keeping	keep	VERB
ma-140	64	15	only	only	ADV
ma-140	64	16	the	the	DET
ma-140	64	17	terms	term	NOUN
ma-140	64	18	linear	linear	VERB
ma-140	64	19	in	in	ADP
ma-140	64	20	ε	ε	PROPN
ma-140	64	21	,	,	PUNCT
ma-140	64	22	where	where	SCONJ
ma-140	64	23	ξi(x	ξi(x	ADP
ma-140	64	24	i	i	PRON
ma-140	64	25	,	,	PUNCT
ma-140	64	26	uα	uα	NOUN
ma-140	64	27	)	)	PUNCT
ma-140	64	28	=	=	NOUN
ma-140	65	1	∂ϕi(x	∂ϕi(x	NOUN
ma-140	65	2	i	i	PRON
ma-140	65	3	,	,	PUNCT
ma-140	65	4	uα	uα	PROPN
ma-140	65	5	,	,	PUNCT
ma-140	65	6	ε	ε	PROPN
ma-140	65	7	)	)	PUNCT
ma-140	65	8	∂ε	∂ε	PROPN
ma-140	65	9	∣∣∣	∣∣∣	ADJ
ma-140	65	10	ε=0	ε=0	NOUN
ma-140	65	11	,	,	PUNCT
ma-140	65	12	ηα(x	ηα(x	PUNCT
ma-140	65	13	i	i	PRON
ma-140	65	14	,	,	PUNCT
ma-140	65	15	uα	uα	NOUN
ma-140	65	16	)	)	PUNCT
ma-140	65	17	=	=	SYM
ma-140	66	1	∂ψα(x	∂ψα(x	PROPN
ma-140	66	2	i	i	PRON
ma-140	66	3	,	,	PUNCT
ma-140	66	4	uα	uα	PROPN
ma-140	66	5	,	,	PUNCT
ma-140	66	6	ε	ε	PROPN
ma-140	66	7	)	)	PUNCT
ma-140	66	8	∂ε	∂ε	PROPN
ma-140	66	9	∣∣∣	∣∣∣	ADJ
ma-140	66	10	ε=0	ε=0	X
ma-140	66	11	.	.	PUNCT
ma-140	67	1	(	(	PUNCT
ma-140	67	2	2.7	2.7	NUM
ma-140	67	3	)	)	PUNCT
ma-140	67	4	remark	remark	NOUN
ma-140	67	5	2.4	2.4	NUM
ma-140	67	6	.	.	PUNCT
ma-140	68	1	by	by	ADP
ma-140	68	2	using	use	VERB
ma-140	68	3	the	the	DET
ma-140	68	4	symbol	symbol	NOUN
ma-140	68	5	of	of	ADP
ma-140	68	6	infinitesimal	infinitesimal	ADJ
ma-140	68	7	transformations	transformation	NOUN
ma-140	68	8	,	,	PUNCT
ma-140	68	9	x	x	X
ma-140	68	10	,	,	PUNCT
ma-140	68	11	(	(	PUNCT
ma-140	68	12	2.6	2.6	NUM
ma-140	68	13	)	)	PUNCT
ma-140	68	14	becomes	become	VERB
ma-140	68	15	x̄	x̄	NOUN
ma-140	69	1	i	i	PROPN
ma-140	70	1	≈	≈	PROPN
ma-140	70	2	(	(	PUNCT
ma-140	70	3	1	1	NUM
ma-140	70	4	+	+	NOUN
ma-140	70	5	x)x	x)x	X
ma-140	71	1	i	i	PRON
ma-140	71	2	,	,	PUNCT
ma-140	71	3	ūα	ūα	PROPN
ma-140	71	4	≈	≈	PROPN
ma-140	71	5	(	(	PUNCT
ma-140	71	6	1	1	NUM
ma-140	71	7	+	+	NOUN
ma-140	71	8	x)uα	x)uα	PROPN
ma-140	71	9	,	,	PUNCT
ma-140	71	10	(	(	PUNCT
ma-140	71	11	2.8	2.8	NUM
ma-140	71	12	)	)	PUNCT
ma-140	71	13	where	where	SCONJ
ma-140	71	14	x	x	X
ma-140	71	15	=	=	PRON
ma-140	71	16	ξi(x	ξi(x	PRON
ma-140	71	17	i	i	PRON
ma-140	71	18	,	,	PUNCT
ma-140	71	19	uα	uα	PROPN
ma-140	71	20	)	)	PUNCT
ma-140	71	21	∂	∂	NOUN
ma-140	72	1	∂x	∂x	PROPN
ma-140	72	2	i	i	PRON
ma-140	72	3	+	+	CCONJ
ma-140	72	4	ηα(x	ηα(x	VERB
ma-140	72	5	i	i	PRON
ma-140	72	6	,	,	PUNCT
ma-140	72	7	uα	uα	PROPN
ma-140	72	8	)	)	PUNCT
ma-140	72	9	∂	∂	NOUN
ma-140	73	1	∂uα	∂uα	PROPN
ma-140	73	2	,	,	PUNCT
ma-140	73	3	(	(	PUNCT
ma-140	73	4	2.9	2.9	NUM
ma-140	73	5	)	)	PUNCT
ma-140	73	6	is	be	AUX
ma-140	73	7	the	the	DET
ma-140	73	8	generator	generator	NOUN
ma-140	73	9	g	g	PROPN
ma-140	73	10	in	in	ADP
ma-140	73	11	(	(	PUNCT
ma-140	73	12	2.5	2.5	NUM
ma-140	73	13	)	)	PUNCT
ma-140	73	14	.	.	PUNCT
ma-140	74	1	remark	remark	VERB
ma-140	74	2	2.5	2.5	NUM
ma-140	74	3	.	.	PUNCT
ma-140	75	1	the	the	DET
ma-140	75	2	change	change	NOUN
ma-140	75	3	of	of	ADP
ma-140	75	4	variables	variable	NOUN
ma-140	75	5	formula	formula	NOUN
ma-140	75	6	di	di	X
ma-140	75	7	=	=	SYM
ma-140	75	8	di(ϕ	di(ϕ	X
ma-140	75	9	j)d̄j	j)d̄j	PROPN
ma-140	75	10	,	,	PUNCT
ma-140	75	11	(	(	PUNCT
ma-140	75	12	2.10	2.10	NUM
ma-140	75	13	)	)	PUNCT
ma-140	75	14	is	be	AUX
ma-140	75	15	employed	employ	VERB
ma-140	75	16	to	to	PART
ma-140	75	17	construct	construct	VERB
ma-140	75	18	transformed	transform	VERB
ma-140	75	19	derivatives	derivative	NOUN
ma-140	75	20	from	from	ADP
ma-140	75	21	(	(	PUNCT
ma-140	75	22	2.1	2.1	NUM
ma-140	75	23	)	)	PUNCT
ma-140	75	24	.	.	PUNCT
ma-140	76	1	the	the	DET
ma-140	76	2	d̄j	d̄j	PROPN
ma-140	76	3	is	be	AUX
ma-140	76	4	total	total	ADJ
ma-140	76	5	differentiation	differentiation	NOUN
ma-140	76	6	x̄	x̄	NOUN
ma-140	77	1	i	i	PRON
ma-140	77	2	.	.	PUNCT
ma-140	78	1	as	as	ADP
ma-140	78	2	a	a	DET
ma-140	78	3	result	result	NOUN
ma-140	78	4	ūαi	ūαi	PROPN
ma-140	78	5	=	=	PUNCT
ma-140	78	6	d̄i(ū	d̄i(ū	PROPN
ma-140	78	7	α	α	X
ma-140	78	8	)	)	PUNCT
ma-140	78	9	,	,	PUNCT
ma-140	78	10	ūαij	ūαij	ADV
ma-140	78	11	=	=	PUNCT
ma-140	78	12	d̄j(ū	d̄j(ū	PROPN
ma-140	78	13	α	α	NOUN
ma-140	78	14	i	i	NOUN
ma-140	78	15	)	)	PUNCT
ma-140	79	1	=	=	PUNCT
ma-140	80	1	d̄i(ū	d̄i(ū	PROPN
ma-140	80	2	α	α	X
ma-140	80	3	j	j	PROPN
ma-140	80	4	)	)	PUNCT
ma-140	80	5	.	.	PUNCT
ma-140	81	1	(	(	PUNCT
ma-140	81	2	2.11	2.11	NUM
ma-140	81	3	)	)	PUNCT
ma-140	81	4	if	if	SCONJ
ma-140	81	5	we	we	PRON
ma-140	81	6	apply	apply	VERB
ma-140	81	7	the	the	DET
ma-140	81	8	change	change	NOUN
ma-140	81	9	of	of	ADP
ma-140	81	10	variable	variable	ADJ
ma-140	81	11	formula	formula	NOUN
ma-140	81	12	given	give	VERB
ma-140	81	13	in	in	ADP
ma-140	81	14	(	(	PUNCT
ma-140	81	15	2.10	2.10	NUM
ma-140	81	16	)	)	PUNCT
ma-140	81	17	on	on	ADP
ma-140	81	18	g	g	NOUN
ma-140	81	19	given	give	VERB
ma-140	81	20	by	by	ADP
ma-140	81	21	(	(	PUNCT
ma-140	81	22	2.5	2.5	NUM
ma-140	81	23	)	)	PUNCT
ma-140	81	24	,	,	PUNCT
ma-140	81	25	we	we	PRON
ma-140	81	26	get	get	VERB
ma-140	81	27	di(ψ	di(ψ	NOUN
ma-140	81	28	α	α	NOUN
ma-140	81	29	)	)	PUNCT
ma-140	81	30	=	=	SYM
ma-140	81	31	di(ϕ	di(ϕ	X
ma-140	81	32	j	j	NOUN
ma-140	81	33	)	)	PUNCT
ma-140	81	34	,	,	PUNCT
ma-140	81	35	d̄j(ū	d̄j(ū	PROPN
ma-140	81	36	α	α	NOUN
ma-140	81	37	)	)	PUNCT
ma-140	81	38	=	=	SYM
ma-140	81	39	ūαj	ūαj	PROPN
ma-140	81	40	di(ϕ	di(ϕ	X
ma-140	81	41	j	j	NOUN
ma-140	81	42	)	)	PUNCT
ma-140	81	43	.	.	PUNCT
ma-140	82	1	(	(	PUNCT
ma-140	82	2	2.12	2.12	NUM
ma-140	82	3	)	)	PUNCT
ma-140	82	4	if	if	SCONJ
ma-140	82	5	we	we	PRON
ma-140	82	6	expand	expand	VERB
ma-140	82	7	(	(	PUNCT
ma-140	82	8	2.12	2.12	NUM
ma-140	82	9	)	)	PUNCT
ma-140	82	10	,	,	PUNCT
ma-140	82	11	we	we	PRON
ma-140	82	12	obtain	obtain	VERB
ma-140	82	13	(	(	PUNCT
ma-140	82	14	∂ϕj	∂ϕj	PROPN
ma-140	82	15	∂x	∂x	VERB
ma-140	83	1	i	i	PRON
ma-140	83	2	+	+	CCONJ
ma-140	83	3	uβi	uβi	ADP
ma-140	83	4	∂ϕj	∂ϕj	PROPN
ma-140	83	5	∂uβ	∂uβ	PROPN
ma-140	83	6	)	)	PUNCT
ma-140	84	1	ūβj	ūβj	PROPN
ma-140	84	2	=	=	PUNCT
ma-140	85	1	∂ψα	∂ψα	PROPN
ma-140	85	2	∂x	∂x	PROPN
ma-140	85	3	i	i	PRON
ma-140	86	1	+	+	CCONJ
ma-140	87	1	uβi	uβi	PROPN
ma-140	87	2	∂ψα	∂ψα	PROPN
ma-140	87	3	∂uβ	∂uβ	PROPN
ma-140	87	4	.	.	PUNCT
ma-140	88	1	(	(	PUNCT
ma-140	88	2	2.13	2.13	NUM
ma-140	88	3	)	)	PUNCT
ma-140	88	4	the	the	DET
ma-140	88	5	ūαi	ūαi	PROPN
ma-140	88	6	can	can	AUX
ma-140	88	7	be	be	AUX
ma-140	88	8	written	write	VERB
ma-140	88	9	as	as	ADP
ma-140	88	10	functions	function	NOUN
ma-140	88	11	of	of	ADP
ma-140	88	12	x	x	X
ma-140	88	13	i	i	PROPN
ma-140	88	14	,	,	PUNCT
ma-140	88	15	uα	uα	PROPN
ma-140	88	16	,	,	PUNCT
ma-140	88	17	u(1	u(1	PROPN
ma-140	88	18	)	)	PUNCT
ma-140	88	19	,	,	PUNCT
ma-140	88	20	meaning	mean	VERB
ma-140	88	21	that	that	SCONJ
ma-140	88	22	,	,	PUNCT
ma-140	88	23	ūαi	ūαi	PROPN
ma-140	88	24	=	=	SYM
ma-140	88	25	φα(x	φα(x	NUM
ma-140	88	26	i	i	PRON
ma-140	88	27	,	,	PUNCT
ma-140	88	28	uα	uα	PROPN
ma-140	88	29	,	,	PUNCT
ma-140	88	30	u(1	u(1	PROPN
ma-140	88	31	)	)	PUNCT
ma-140	88	32	,	,	PUNCT
ma-140	88	33	ε	ε	PROPN
ma-140	88	34	)	)	PUNCT
ma-140	88	35	,	,	PUNCT
ma-140	88	36	φα	φα	ADP
ma-140	88	37	∣∣∣	∣∣∣	ADJ
ma-140	88	38	ε=0	ε=0	X
ma-140	88	39	=	=	SYM
ma-140	88	40	uαi	uαi	PROPN
ma-140	88	41	.	.	PUNCT
ma-140	89	1	(	(	PUNCT
ma-140	89	2	2.14	2.14	NUM
ma-140	89	3	)	)	PUNCT
ma-140	89	4	definition	definition	NOUN
ma-140	89	5	2.6	2.6	NUM
ma-140	89	6	.	.	PUNCT
ma-140	90	1	the	the	DET
ma-140	90	2	transformations	transformation	NOUN
ma-140	90	3	in	in	ADP
ma-140	90	4	(	(	PUNCT
ma-140	90	5	2.5	2.5	NUM
ma-140	90	6	)	)	PUNCT
ma-140	90	7	and	and	CCONJ
ma-140	90	8	(	(	PUNCT
ma-140	90	9	2.14	2.14	NUM
ma-140	90	10	)	)	PUNCT
ma-140	90	11	give	give	VERB
ma-140	90	12	the	the	DET
ma-140	90	13	first	first	ADJ
ma-140	90	14	prolongation	prolongation	NOUN
ma-140	90	15	group	group	NOUN
ma-140	90	16	g[1	g[1	PROPN
ma-140	90	17	]	]	PUNCT
ma-140	90	18	.	.	PUNCT
ma-140	91	1	definition	definition	NOUN
ma-140	91	2	2.7	2.7	NUM
ma-140	91	3	.	.	PUNCT
ma-140	91	4	infinitesimal	infinitesimal	ADJ
ma-140	91	5	transformation	transformation	NOUN
ma-140	91	6	of	of	ADP
ma-140	91	7	the	the	DET
ma-140	91	8	first	first	ADJ
ma-140	91	9	derivatives	derivative	NOUN
ma-140	91	10	is	be	AUX
ma-140	91	11	ūαi	ūαi	PROPN
ma-140	92	1	≈	≈	PROPN
ma-140	92	2	uαi	uαi	PROPN
ma-140	92	3	+	+	X
ma-140	92	4	ζαi	ζαi	NOUN
ma-140	92	5	ε	ε	PROPN
ma-140	92	6	,	,	PUNCT
ma-140	92	7	where	where	SCONJ
ma-140	92	8	ζαi	ζαi	NOUN
ma-140	92	9	=	=	SYM
ma-140	92	10	ζαi	ζαi	NOUN
ma-140	92	11	(	(	PUNCT
ma-140	92	12	x	x	PROPN
ma-140	92	13	i	i	PRON
ma-140	92	14	,	,	PUNCT
ma-140	92	15	uα	uα	PROPN
ma-140	92	16	,	,	PUNCT
ma-140	92	17	u(1	u(1	PROPN
ma-140	92	18	)	)	PUNCT
ma-140	92	19	,	,	PUNCT
ma-140	92	20	ε	ε	PROPN
ma-140	92	21	)	)	PUNCT
ma-140	92	22	.	.	PUNCT
ma-140	93	1	(	(	PUNCT
ma-140	93	2	2.15	2.15	NUM
ma-140	93	3	)	)	PUNCT
ma-140	93	4	remark	remark	NOUN
ma-140	93	5	2.8	2.8	NUM
ma-140	93	6	.	.	PUNCT
ma-140	94	1	in	in	ADP
ma-140	94	2	terms	term	NOUN
ma-140	94	3	of	of	ADP
ma-140	94	4	infinitesimal	infinitesimal	ADJ
ma-140	94	5	transformations	transformation	NOUN
ma-140	94	6	,	,	PUNCT
ma-140	94	7	g[1	g[1	PROPN
ma-140	94	8	]	]	PUNCT
ma-140	94	9	is	be	AUX
ma-140	94	10	given	give	VERB
ma-140	94	11	by	by	ADP
ma-140	94	12	(	(	PUNCT
ma-140	94	13	2.6	2.6	NUM
ma-140	94	14	)	)	PUNCT
ma-140	94	15	and	and	CCONJ
ma-140	94	16	(	(	PUNCT
ma-140	94	17	2.15	2.15	NUM
ma-140	94	18	)	)	PUNCT
ma-140	94	19	.	.	PUNCT
ma-140	95	1	(	(	PUNCT
ma-140	95	2	2	2	X
ma-140	95	3	)	)	PUNCT
ma-140	95	4	prolonged	prolonged	ADJ
ma-140	95	5	generators	generator	NOUN
ma-140	95	6	https://doi.org/10.28924/ada/ma.3.13	https://doi.org/10.28924/ada/ma.3.13	PROPN
ma-140	95	7	eur	eur	PROPN
ma-140	95	8	.	.	PUNCT
ma-140	96	1	j.	j.	PROPN
ma-140	96	2	math	math	PROPN
ma-140	96	3	.	.	PUNCT
ma-140	97	1	anal	anal	PROPN
ma-140	97	2	.	.	PUNCT
ma-140	98	1	10.28924	10.28924	NUM
ma-140	98	2	/	/	SYM
ma-140	98	3	ada	ada	PROPN
ma-140	98	4	/	/	SYM
ma-140	98	5	ma.3.13	ma.3.13	PROPN
ma-140	98	6	4	4	NUM
ma-140	98	7	definition	definition	NOUN
ma-140	98	8	2.9	2.9	NUM
ma-140	98	9	.	.	PUNCT
ma-140	99	1	by	by	ADP
ma-140	99	2	the	the	DET
ma-140	99	3	relation	relation	NOUN
ma-140	99	4	(	(	PUNCT
ma-140	99	5	2.12	2.12	NUM
ma-140	99	6	)	)	PUNCT
ma-140	99	7	on	on	ADP
ma-140	99	8	g[1	g[1	PROPN
ma-140	99	9	]	]	PUNCT
ma-140	99	10	from	from	ADP
ma-140	99	11	2.6	2.6	NUM
ma-140	99	12	,	,	PUNCT
ma-140	99	13	we	we	PRON
ma-140	99	14	obtain	obtain	VERB
ma-140	99	15	[	[	X
ma-140	99	16	7	7	NUM
ma-140	99	17	]	]	PUNCT
ma-140	99	18	di(x	di(x	NUM
ma-140	99	19	j	j	PROPN
ma-140	99	20	+	+	NUM
ma-140	99	21	ξjε)(uαj	ξjε)(uαj	PROPN
ma-140	99	22	+	+	CCONJ
ma-140	99	23	ζαj	ζαj	PROPN
ma-140	99	24	ε	ε	PROPN
ma-140	99	25	)	)	PUNCT
ma-140	99	26	=	=	NOUN
ma-140	99	27	di(u	di(u	X
ma-140	99	28	α	α	NOUN
ma-140	99	29	+	+	CCONJ
ma-140	99	30	ηαε	ηαε	ADJ
ma-140	99	31	)	)	PUNCT
ma-140	99	32	,	,	PUNCT
ma-140	99	33	which	which	PRON
ma-140	99	34	gives	give	VERB
ma-140	99	35	(	(	PUNCT
ma-140	99	36	2.16	2.16	NUM
ma-140	99	37	)	)	PUNCT
ma-140	100	1	uαi	uαi	PROPN
ma-140	101	1	+	+	X
ma-140	101	2	ζαj	ζαj	X
ma-140	101	3	ε+	ε+	X
ma-140	101	4	uαj	uαj	PROPN
ma-140	101	5	εdiξ	εdiξ	PROPN
ma-140	101	6	j	j	AUX
ma-140	102	1	=	=	PRON
ma-140	102	2	uαi	uαi	PROPN
ma-140	103	1	+	+	NOUN
ma-140	103	2	diη	diη	NOUN
ma-140	103	3	αε	αε	ADP
ma-140	103	4	,	,	PUNCT
ma-140	103	5	(	(	PUNCT
ma-140	103	6	2.17	2.17	NUM
ma-140	103	7	)	)	PUNCT
ma-140	103	8	and	and	CCONJ
ma-140	103	9	thus	thus	ADV
ma-140	103	10	ζαi	ζαi	VERB
ma-140	103	11	=	=	NOUN
ma-140	103	12	di(η	di(η	PART
ma-140	103	13	α)−	α)−	NOUN
ma-140	103	14	uαj	uαj	VERB
ma-140	103	15	di(ξj	di(ξj	NOUN
ma-140	103	16	)	)	PUNCT
ma-140	104	1	,	,	PUNCT
ma-140	104	2	(	(	PUNCT
ma-140	104	3	2.18	2.18	NUM
ma-140	104	4	)	)	PUNCT
ma-140	104	5	is	be	AUX
ma-140	104	6	the	the	DET
ma-140	104	7	first	first	ADJ
ma-140	104	8	prolongation	prolongation	NOUN
ma-140	104	9	formula	formula	NOUN
ma-140	104	10	.	.	PUNCT
ma-140	105	1	remark	remark	PROPN
ma-140	105	2	2.10	2.10	NUM
ma-140	105	3	.	.	PUNCT
ma-140	106	1	analogously	analogously	ADV
ma-140	106	2	,	,	PUNCT
ma-140	106	3	one	one	NUM
ma-140	106	4	constructs	construct	VERB
ma-140	106	5	higher	high	ADJ
ma-140	106	6	order	order	NOUN
ma-140	106	7	prolongations	prolongation	NOUN
ma-140	106	8	[	[	X
ma-140	106	9	7	7	NUM
ma-140	106	10	]	]	PUNCT
ma-140	106	11	,	,	PUNCT
ma-140	106	12	ζαij	ζαij	NOUN
ma-140	106	13	=	=	SYM
ma-140	106	14	dj(ζ	dj(ζ	X
ma-140	106	15	α	α	NOUN
ma-140	106	16	i	i	NOUN
ma-140	106	17	)	)	PUNCT
ma-140	106	18	−	−	PROPN
ma-140	106	19	uαiκdj(ξκ	uαiκdj(ξκ	NOUN
ma-140	106	20	)	)	PUNCT
ma-140	106	21	,	,	PUNCT
ma-140	106	22	.	.	PUNCT
ma-140	106	23	.	.	PUNCT
ma-140	107	1	.	.	PUNCT
ma-140	108	1	,	,	PUNCT
ma-140	108	2	ζαi1,	ζαi1,	PRON
ma-140	108	3	...	...	PUNCT
ma-140	108	4	,iκ	,iκ	SYM
ma-140	109	1	=	=	SYM
ma-140	109	2	diκ(ζαi1,	diκ(ζαi1,	NOUN
ma-140	109	3	...	...	PUNCT
ma-140	109	4	,iκ−1	,iκ−1	NUM
ma-140	109	5	)	)	PUNCT
ma-140	109	6	−	−	PROPN
ma-140	110	1	uαi1,i2,	uαi1,i2,	PROPN
ma-140	110	2	...	...	PUNCT
ma-140	110	3	,iκ−1j	,iκ−1j	PUNCT
ma-140	110	4	diκ(ξj	diκ(ξj	NOUN
ma-140	110	5	)	)	PUNCT
ma-140	110	6	.	.	PUNCT
ma-140	111	1	(	(	PUNCT
ma-140	111	2	2.19	2.19	NUM
ma-140	111	3	)	)	PUNCT
ma-140	111	4	remark	remark	NOUN
ma-140	111	5	2.11	2.11	NUM
ma-140	111	6	.	.	PUNCT
ma-140	112	1	the	the	DET
ma-140	112	2	prolonged	prolonged	ADJ
ma-140	112	3	generators	generator	NOUN
ma-140	112	4	of	of	ADP
ma-140	112	5	the	the	DET
ma-140	112	6	prolongations	prolongation	NOUN
ma-140	112	7	g[1	g[1	PROPN
ma-140	112	8	]	]	PUNCT
ma-140	112	9	,	,	PUNCT
ma-140	112	10	.	.	PUNCT
ma-140	112	11	.	.	PUNCT
ma-140	112	12	.	.	PUNCT
ma-140	113	1	,	,	PUNCT
ma-140	113	2	g[κ	g[κ	X
ma-140	113	3	]	]	X
ma-140	113	4	of	of	ADP
ma-140	113	5	the	the	DET
ma-140	113	6	group	group	NOUN
ma-140	113	7	gare	gare	PROPN
ma-140	113	8	x[1	x[1	PROPN
ma-140	113	9	]	]	X
ma-140	114	1	=	=	PUNCT
ma-140	114	2	x	x	PUNCT
ma-140	115	1	+	+	NUM
ma-140	115	2	ζαi	ζαi	NOUN
ma-140	115	3	∂	∂	X
ma-140	115	4	∂uαi	∂uαi	NUM
ma-140	115	5	,	,	PUNCT
ma-140	115	6	.	.	PUNCT
ma-140	115	7	.	.	PUNCT
ma-140	116	1	.	.	PUNCT
ma-140	117	1	,	,	PUNCT
ma-140	117	2	x[κ	x[κ	PROPN
ma-140	117	3	]	]	X
ma-140	117	4	=	=	SYM
ma-140	117	5	x[κ−1	x[κ−1	PROPN
ma-140	117	6	]	]	X
ma-140	117	7	+	+	CCONJ
ma-140	117	8	ζαi1,	ζαi1,	X
ma-140	117	9	...	...	PUNCT
ma-140	117	10	,iκ	,iκ	NUM
ma-140	117	11	∂	∂	NUM
ma-140	117	12	∂ζαi1,	∂ζαi1,	PROPN
ma-140	117	13	...	...	PUNCT
ma-140	117	14	,iκ	,iκ	PUNCT
ma-140	117	15	,	,	PUNCT
ma-140	117	16	κ	κ	X
ma-140	117	17	≥	≥	NOUN
ma-140	117	18	1	1	NUM
ma-140	117	19	,	,	PUNCT
ma-140	117	20	(	(	PUNCT
ma-140	117	21	2.20	2.20	NUM
ma-140	117	22	)	)	PUNCT
ma-140	117	23	for	for	ADP
ma-140	117	24	the	the	DET
ma-140	117	25	group	group	NOUN
ma-140	117	26	generator	generator	NOUN
ma-140	117	27	x	x	INTJ
ma-140	117	28	in	in	ADP
ma-140	117	29	(	(	PUNCT
ma-140	117	30	2.9	2.9	NUM
ma-140	117	31	)	)	PUNCT
ma-140	117	32	.	.	PUNCT
ma-140	118	1	group	group	NOUN
ma-140	118	2	invariants	invariant	NOUN
ma-140	118	3	.	.	PUNCT
ma-140	119	1	definition	definition	NOUN
ma-140	119	2	2.12	2.12	NUM
ma-140	119	3	.	.	PUNCT
ma-140	120	1	a	a	DET
ma-140	120	2	function	function	NOUN
ma-140	120	3	γ(x	γ(x	VERB
ma-140	120	4	i	i	PRON
ma-140	120	5	,	,	PUNCT
ma-140	120	6	uα	uα	PROPN
ma-140	120	7	)	)	PUNCT
ma-140	120	8	is	be	AUX
ma-140	120	9	said	say	VERB
ma-140	120	10	to	to	PART
ma-140	120	11	be	be	AUX
ma-140	120	12	an	an	DET
ma-140	120	13	invariant	invariant	NOUN
ma-140	120	14	of	of	ADP
ma-140	120	15	g	g	NOUN
ma-140	120	16	of	of	ADP
ma-140	120	17	in	in	ADP
ma-140	120	18	(	(	PUNCT
ma-140	120	19	2.1	2.1	NUM
ma-140	120	20	)	)	PUNCT
ma-140	121	1	if	if	SCONJ
ma-140	121	2	γ(x̄	γ(x̄	NUM
ma-140	121	3	i	i	PRON
ma-140	121	4	,	,	PUNCT
ma-140	121	5	ūα	ūα	PROPN
ma-140	121	6	)	)	PUNCT
ma-140	121	7	=	=	PUNCT
ma-140	121	8	γ(x	γ(x	NOUN
ma-140	121	9	i	i	PRON
ma-140	121	10	,	,	PUNCT
ma-140	121	11	uα	uα	PROPN
ma-140	121	12	)	)	PUNCT
ma-140	121	13	.	.	PUNCT
ma-140	122	1	(	(	PUNCT
ma-140	122	2	2.21	2.21	NUM
ma-140	122	3	)	)	PUNCT
ma-140	122	4	theorem	theorem	VERB
ma-140	122	5	2.13	2.13	NUM
ma-140	122	6	.	.	PUNCT
ma-140	123	1	a	a	DET
ma-140	123	2	function	function	NOUN
ma-140	123	3	γ(x	γ(x	VERB
ma-140	123	4	i	i	PRON
ma-140	123	5	,	,	PUNCT
ma-140	123	6	uα	uα	PROPN
ma-140	123	7	)	)	PUNCT
ma-140	123	8	is	be	AUX
ma-140	123	9	an	an	DET
ma-140	123	10	invariant	invariant	NOUN
ma-140	123	11	of	of	ADP
ma-140	123	12	the	the	DET
ma-140	123	13	group	group	NOUN
ma-140	123	14	g	g	NOUN
ma-140	123	15	given	give	VERB
ma-140	123	16	by	by	ADP
ma-140	123	17	(	(	PUNCT
ma-140	123	18	2.1	2.1	NUM
ma-140	123	19	)	)	PUNCT
ma-140	123	20	if	if	SCONJ
ma-140	123	21	and	and	CCONJ
ma-140	123	22	only	only	ADV
ma-140	123	23	if	if	SCONJ
ma-140	123	24	it	it	PRON
ma-140	123	25	solves	solve	VERB
ma-140	123	26	the	the	DET
ma-140	123	27	following	follow	VERB
ma-140	123	28	first	first	ADJ
ma-140	123	29	-	-	PUNCT
ma-140	123	30	order	order	NOUN
ma-140	123	31	linear	linear	ADJ
ma-140	123	32	pde	pde	NOUN
ma-140	123	33	:	:	PUNCT
ma-140	124	1	[	[	X
ma-140	124	2	8	8	NUM
ma-140	124	3	]	]	SYM
ma-140	124	4	xγ	xγ	NOUN
ma-140	124	5	=	=	SYM
ma-140	124	6	ξi(x	ξi(x	PROPN
ma-140	125	1	i	i	PRON
ma-140	125	2	,	,	PUNCT
ma-140	125	3	uα	uα	PROPN
ma-140	125	4	)	)	PUNCT
ma-140	125	5	∂γ	∂γ	NOUN
ma-140	126	1	∂x	∂x	NOUN
ma-140	126	2	i	i	PRON
ma-140	126	3	+	+	CCONJ
ma-140	126	4	ηα(x	ηα(x	VERB
ma-140	126	5	i	i	PRON
ma-140	126	6	,	,	PUNCT
ma-140	126	7	uα	uα	PROPN
ma-140	126	8	)	)	PUNCT
ma-140	126	9	∂γ	∂γ	PROPN
ma-140	126	10	∂uα	∂uα	NOUN
ma-140	126	11	=	=	SYM
ma-140	126	12	0	0	X
ma-140	126	13	.	.	PUNCT
ma-140	126	14	(	(	PUNCT
ma-140	126	15	2.22	2.22	NUM
ma-140	126	16	)	)	PUNCT
ma-140	126	17	from	from	ADP
ma-140	126	18	theorem	theorem	NOUN
ma-140	126	19	(	(	PUNCT
ma-140	126	20	2.13	2.13	NUM
ma-140	126	21	)	)	PUNCT
ma-140	126	22	,	,	PUNCT
ma-140	126	23	we	we	PRON
ma-140	126	24	have	have	VERB
ma-140	126	25	the	the	DET
ma-140	126	26	following	follow	VERB
ma-140	126	27	result	result	NOUN
ma-140	126	28	.	.	PUNCT
ma-140	127	1	theorem	theorem	VERB
ma-140	127	2	2.14	2.14	NUM
ma-140	127	3	.	.	PUNCT
ma-140	128	1	the	the	DET
ma-140	128	2	lie	lie	NOUN
ma-140	128	3	group	group	NOUN
ma-140	128	4	g	g	PROPN
ma-140	128	5	in	in	ADP
ma-140	128	6	(	(	PUNCT
ma-140	128	7	2.1	2.1	NUM
ma-140	128	8	)	)	PUNCT
ma-140	129	1	[	[	X
ma-140	129	2	9	9	NUM
ma-140	129	3	]	]	PUNCT
ma-140	129	4	has	have	VERB
ma-140	129	5	precisely	precisely	ADV
ma-140	129	6	n−1	n−1	ADJ
ma-140	129	7	functionally	functionally	ADV
ma-140	129	8	independent	independent	ADJ
ma-140	129	9	invariants	invariant	NOUN
ma-140	129	10	and	and	CCONJ
ma-140	129	11	one	one	PRON
ma-140	129	12	can	can	AUX
ma-140	129	13	take	take	VERB
ma-140	129	14	as	as	ADP
ma-140	129	15	the	the	DET
ma-140	129	16	basic	basic	ADJ
ma-140	129	17	invariants	invariant	NOUN
ma-140	129	18	,	,	PUNCT
ma-140	129	19	the	the	DET
ma-140	129	20	left	left	ADJ
ma-140	129	21	-	-	PUNCT
ma-140	129	22	hand	hand	NOUN
ma-140	129	23	sides	side	NOUN
ma-140	129	24	of	of	ADP
ma-140	129	25	the	the	DET
ma-140	129	26	first	first	ADJ
ma-140	129	27	integrals	integral	NOUN
ma-140	130	1	ψ1(x	ψ1(x	VERB
ma-140	130	2	i	i	PRON
ma-140	130	3	,	,	PUNCT
ma-140	130	4	uα	uα	NOUN
ma-140	130	5	)	)	PUNCT
ma-140	130	6	=	=	SYM
ma-140	130	7	c1	c1	PROPN
ma-140	130	8	,	,	PUNCT
ma-140	130	9	.	.	PUNCT
ma-140	130	10	.	.	PUNCT
ma-140	130	11	.	.	PUNCT
ma-140	131	1	,	,	PUNCT
ma-140	131	2	ψn−1(x	ψn−1(x	VERB
ma-140	131	3	i	i	PRON
ma-140	131	4	,	,	PUNCT
ma-140	131	5	uα	uα	PROPN
ma-140	131	6	)	)	PUNCT
ma-140	131	7	=	=	SYM
ma-140	131	8	cn−1	cn−1	PROPN
ma-140	131	9	,	,	PUNCT
ma-140	131	10	(	(	PUNCT
ma-140	131	11	2.23	2.23	NUM
ma-140	131	12	)	)	PUNCT
ma-140	131	13	of	of	ADP
ma-140	131	14	the	the	DET
ma-140	131	15	characteristic	characteristic	ADJ
ma-140	131	16	equations	equation	NOUN
ma-140	131	17	for	for	ADP
ma-140	131	18	(	(	PUNCT
ma-140	131	19	2.22	2.22	NUM
ma-140	131	20	):	):	PUNCT
ma-140	131	21	dx	dx	PROPN
ma-140	132	1	i	i	PRON
ma-140	132	2	ξi(x	ξi(x	VERB
ma-140	132	3	i	i	PRON
ma-140	132	4	,	,	PUNCT
ma-140	132	5	uα	uα	PROPN
ma-140	132	6	)	)	PUNCT
ma-140	132	7	=	=	SYM
ma-140	132	8	duα	duα	NOUN
ma-140	132	9	ηα(x	ηα(x	PUNCT
ma-140	132	10	i	i	PRON
ma-140	132	11	,	,	PUNCT
ma-140	132	12	uα	uα	PROPN
ma-140	132	13	)	)	PUNCT
ma-140	132	14	.	.	PUNCT
ma-140	133	1	(	(	PUNCT
ma-140	133	2	2.24	2.24	NUM
ma-140	133	3	)	)	PUNCT
ma-140	133	4	https://doi.org/10.28924/ada/ma.3.13	https://doi.org/10.28924/ada/ma.3.13	PROPN
ma-140	133	5	eur	eur	NOUN
ma-140	133	6	.	.	PUNCT
ma-140	134	1	j.	j.	PROPN
ma-140	134	2	math	math	PROPN
ma-140	134	3	.	.	PUNCT
ma-140	135	1	anal	anal	PROPN
ma-140	135	2	.	.	PUNCT
ma-140	136	1	10.28924	10.28924	NUM
ma-140	136	2	/	/	SYM
ma-140	136	3	ada	ada	PROPN
ma-140	136	4	/	/	SYM
ma-140	136	5	ma.3.13	ma.3.13	PROPN
ma-140	136	6	5	5	NUM
ma-140	136	7	symmetry	symmetry	NOUN
ma-140	136	8	groups	group	NOUN
ma-140	136	9	.	.	PUNCT
ma-140	137	1	definition	definition	NOUN
ma-140	137	2	2.15	2.15	NUM
ma-140	137	3	.	.	PUNCT
ma-140	138	1	we	we	PRON
ma-140	138	2	define	define	VERB
ma-140	138	3	the	the	DET
ma-140	138	4	vector	vector	NOUN
ma-140	138	5	field	field	NOUN
ma-140	138	6	x	x	SYM
ma-140	138	7	(	(	PUNCT
ma-140	138	8	2.9	2.9	NUM
ma-140	138	9	)	)	PUNCT
ma-140	138	10	as	as	ADP
ma-140	138	11	a	a	DET
ma-140	138	12	lie	lie	NOUN
ma-140	138	13	point	point	NOUN
ma-140	138	14	symmetry	symmetry	NOUN
ma-140	138	15	of	of	ADP
ma-140	138	16	(	(	PUNCT
ma-140	138	17	2.2	2.2	NUM
ma-140	138	18	)	)	PUNCT
ma-140	138	19	if	if	SCONJ
ma-140	138	20	the	the	DET
ma-140	138	21	determiningequations	determiningequation	NOUN
ma-140	138	22	x[π]∆α	x[π]∆α	PROPN
ma-140	138	23	∣∣∣	∣∣∣	NOUN
ma-140	138	24	∆α=0	∆α=0	PROPN
ma-140	138	25	=	=	SYM
ma-140	138	26	0	0	PROPN
ma-140	138	27	,	,	PUNCT
ma-140	138	28	α	α	NOUN
ma-140	138	29	=	=	SYM
ma-140	138	30	1	1	NUM
ma-140	138	31	,	,	PUNCT
ma-140	138	32	.	.	PUNCT
ma-140	138	33	.	.	PUNCT
ma-140	139	1	.	.	PUNCT
ma-140	140	1	,	,	PUNCT
ma-140	140	2	m	m	PROPN
ma-140	140	3	,	,	PUNCT
ma-140	140	4	π	π	PROPN
ma-140	140	5	≥	≥	NUM
ma-140	140	6	1	1	NUM
ma-140	140	7	,	,	PUNCT
ma-140	140	8	(	(	PUNCT
ma-140	140	9	2.25	2.25	NUM
ma-140	140	10	)	)	PUNCT
ma-140	140	11	are	be	AUX
ma-140	140	12	satisfied	satisfied	ADJ
ma-140	140	13	for	for	ADP
ma-140	140	14	the	the	DET
ma-140	140	15	π	π	PROPN
ma-140	140	16	-	-	PUNCT
ma-140	140	17	th	th	VERB
ma-140	140	18	prolongation	prolongation	NOUN
ma-140	140	19	of	of	ADP
ma-140	140	20	x	x	SYM
ma-140	140	21	,	,	PUNCT
ma-140	140	22	namely	namely	ADV
ma-140	140	23	x[π	x[π	PROPN
ma-140	140	24	]	]	PUNCT
ma-140	140	25	.	.	PUNCT
ma-140	141	1	definition	definition	NOUN
ma-140	141	2	2.16	2.16	NUM
ma-140	141	3	.	.	PUNCT
ma-140	142	1	the	the	DET
ma-140	142	2	lie	lie	NOUN
ma-140	142	3	group	group	NOUN
ma-140	142	4	g	g	PROPN
ma-140	142	5	is	be	AUX
ma-140	142	6	a	a	DET
ma-140	142	7	symmetry	symmetry	NOUN
ma-140	142	8	group	group	NOUN
ma-140	142	9	of	of	ADP
ma-140	142	10	(	(	PUNCT
ma-140	142	11	2.2	2.2	NUM
ma-140	142	12	)	)	PUNCT
ma-140	142	13	if	if	SCONJ
ma-140	142	14	(	(	PUNCT
ma-140	142	15	2.2	2.2	NUM
ma-140	142	16	)	)	PUNCT
ma-140	142	17	is	be	AUX
ma-140	142	18	form	form	NOUN
ma-140	142	19	-	-	PUNCT
ma-140	142	20	invariant	invariant	ADJ
ma-140	142	21	,	,	PUNCT
ma-140	142	22	that	that	PRON
ma-140	142	23	is	be	AUX
ma-140	142	24	∆α	∆α	PROPN
ma-140	142	25	(	(	PUNCT
ma-140	142	26	x̄	x̄	NOUN
ma-140	142	27	i	i	PRON
ma-140	142	28	,	,	PUNCT
ma-140	142	29	ūα	ūα	PROPN
ma-140	142	30	,	,	PUNCT
ma-140	142	31	ū(1	ū(1	NUM
ma-140	142	32	)	)	PUNCT
ma-140	142	33	,	,	PUNCT
ma-140	142	34	.	.	PUNCT
ma-140	142	35	.	.	PUNCT
ma-140	143	1	.	.	PUNCT
ma-140	144	1	,	,	PUNCT
ma-140	144	2	ū(π	ū(π	PROPN
ma-140	144	3	)	)	PUNCT
ma-140	144	4	)	)	PUNCT
ma-140	145	1	=	=	PUNCT
ma-140	145	2	0	0	X
ma-140	145	3	.	.	PUNCT
ma-140	146	1	(	(	PUNCT
ma-140	146	2	2.26	2.26	NUM
ma-140	146	3	)	)	PUNCT
ma-140	146	4	theorem	theorem	VERB
ma-140	146	5	2.17	2.17	NUM
ma-140	146	6	.	.	PUNCT
ma-140	147	1	the	the	DET
ma-140	147	2	lie	lie	NOUN
ma-140	147	3	group	group	NOUN
ma-140	147	4	g	g	PROPN
ma-140	147	5	(	(	PUNCT
ma-140	147	6	2.1	2.1	NUM
ma-140	147	7	)	)	PUNCT
ma-140	147	8	can	can	AUX
ma-140	147	9	be	be	AUX
ma-140	147	10	constructed	construct	VERB
ma-140	147	11	from	from	ADP
ma-140	147	12	the	the	DET
ma-140	147	13	infinitesimal	infinitesimal	ADJ
ma-140	147	14	transformations	transformation	NOUN
ma-140	147	15	in	in	ADP
ma-140	147	16	(	(	PUNCT
ma-140	147	17	2.5	2.5	NUM
ma-140	147	18	)	)	PUNCT
ma-140	147	19	by	by	ADP
ma-140	147	20	integrating	integrate	VERB
ma-140	147	21	the	the	DET
ma-140	147	22	lie	lie	NOUN
ma-140	147	23	equations	equation	NOUN
ma-140	147	24	dx̄	dx̄	VERB
ma-140	147	25	i	i	PRON
ma-140	147	26	dε	dε	VERB
ma-140	147	27	=	=	VERB
ma-140	147	28	ξi(x̄	ξi(x̄	VERB
ma-140	147	29	i	i	PRON
ma-140	147	30	,	,	PUNCT
ma-140	147	31	ūα	ūα	PROPN
ma-140	147	32	)	)	PUNCT
ma-140	147	33	,	,	PUNCT
ma-140	147	34	x̄	x̄	NUM
ma-140	147	35	i	i	PRON
ma-140	147	36	∣∣∣	∣∣∣	VERB
ma-140	147	37	ε=0	ε=0	X
ma-140	147	38	=	=	PUNCT
ma-140	147	39	x	x	SYM
ma-140	147	40	i	i	PROPN
ma-140	147	41	,	,	PUNCT
ma-140	147	42	dūα	dūα	NOUN
ma-140	147	43	dε	dε	NOUN
ma-140	147	44	=	=	SYM
ma-140	147	45	ηα(x̄	ηα(x̄	INTJ
ma-140	147	46	i	i	PRON
ma-140	147	47	,	,	PUNCT
ma-140	147	48	ūα	ūα	PROPN
ma-140	147	49	)	)	PUNCT
ma-140	147	50	,	,	PUNCT
ma-140	147	51	ūα	ūα	NOUN
ma-140	147	52	∣∣∣	∣∣∣	NOUN
ma-140	147	53	ε=0	ε=0	PROPN
ma-140	147	54	=	=	SYM
ma-140	147	55	uα	uα	PROPN
ma-140	147	56	.	.	PUNCT
ma-140	148	1	(	(	PUNCT
ma-140	148	2	2.27	2.27	NUM
ma-140	148	3	)	)	PUNCT
ma-140	148	4	lie	lie	NOUN
ma-140	148	5	algebras	algebra	NOUN
ma-140	148	6	.	.	PUNCT
ma-140	149	1	definition	definition	NOUN
ma-140	149	2	2.18	2.18	NUM
ma-140	149	3	.	.	PUNCT
ma-140	150	1	a	a	DET
ma-140	150	2	vector	vector	NOUN
ma-140	150	3	space	space	NOUN
ma-140	150	4	vr	vr	NOUN
ma-140	150	5	of	of	ADP
ma-140	150	6	operators	operator	NOUN
ma-140	150	7	[	[	X
ma-140	150	8	8	8	NUM
ma-140	150	9	]	]	SYM
ma-140	150	10	x	x	X
ma-140	150	11	(	(	PUNCT
ma-140	150	12	2.9	2.9	NUM
ma-140	150	13	)	)	PUNCT
ma-140	150	14	is	be	AUX
ma-140	150	15	a	a	DET
ma-140	150	16	lie	lie	NOUN
ma-140	150	17	algebra	algebra	NOUN
ma-140	150	18	if	if	SCONJ
ma-140	150	19	for	for	ADP
ma-140	150	20	any	any	DET
ma-140	150	21	xi	xi	X
ma-140	150	22	,	,	PUNCT
ma-140	150	23	xj	xj	PROPN
ma-140	150	24	∈	∈	PROPN
ma-140	150	25	vr	vr	NOUN
ma-140	150	26	,	,	PUNCT
ma-140	150	27	[	[	X
ma-140	150	28	xi	xi	X
ma-140	150	29	,	,	PUNCT
ma-140	150	30	xj	xj	PROPN
ma-140	150	31	]	]	PUNCT
ma-140	151	1	=	=	PUNCT
ma-140	151	2	xixj	xixj	PROPN
ma-140	151	3	−xjxi	−xjxi	PROPN
ma-140	151	4	,	,	PUNCT
ma-140	151	5	(	(	PUNCT
ma-140	151	6	2.28	2.28	NUM
ma-140	151	7	)	)	PUNCT
ma-140	151	8	is	be	AUX
ma-140	151	9	in	in	ADP
ma-140	151	10	vr	vr	NOUN
ma-140	151	11	for	for	ADP
ma-140	151	12	all	all	DET
ma-140	151	13	i	i	PRON
ma-140	151	14	,	,	PUNCT
ma-140	151	15	j	j	PROPN
ma-140	151	16	=	=	SYM
ma-140	151	17	1	1	NUM
ma-140	151	18	,	,	PUNCT
ma-140	151	19	.	.	PUNCT
ma-140	151	20	.	.	PUNCT
ma-140	152	1	.	.	PUNCT
ma-140	153	1	,	,	PUNCT
ma-140	153	2	r	r	NOUN
ma-140	153	3	.	.	PUNCT
ma-140	153	4	remark	remark	PROPN
ma-140	153	5	2.19	2.19	NUM
ma-140	153	6	.	.	PUNCT
ma-140	154	1	the	the	DET
ma-140	154	2	commutator	commutator	NOUN
ma-140	154	3	is	be	AUX
ma-140	154	4	bilinear	bilinear	ADJ
ma-140	154	5	,	,	PUNCT
ma-140	154	6	skew	skew	ADJ
ma-140	154	7	symmetric	symmetric	NOUN
ma-140	154	8	and	and	CCONJ
ma-140	154	9	admits	admit	VERB
ma-140	154	10	to	to	ADP
ma-140	154	11	the	the	DET
ma-140	154	12	jacobi	jacobi	PROPN
ma-140	154	13	identity	identity	NOUN
ma-140	154	14	[	[	X
ma-140	154	15	5	5	NUM
ma-140	154	16	]	]	PUNCT
ma-140	154	17	.	.	PUNCT
ma-140	155	1	theorem	theorem	VERB
ma-140	155	2	2.20	2.20	NUM
ma-140	155	3	.	.	PUNCT
ma-140	156	1	the	the	DET
ma-140	156	2	set	set	NOUN
ma-140	156	3	of	of	ADP
ma-140	156	4	solutions	solution	NOUN
ma-140	156	5	of	of	ADP
ma-140	156	6	(	(	PUNCT
ma-140	156	7	2.25	2.25	NUM
ma-140	156	8	)	)	PUNCT
ma-140	156	9	forms	form	VERB
ma-140	156	10	a	a	DET
ma-140	156	11	lie	lie	NOUN
ma-140	156	12	algebra	algebra	NOUN
ma-140	156	13	[	[	X
ma-140	156	14	10	10	NUM
ma-140	156	15	]	]	PUNCT
ma-140	156	16	.	.	PUNCT
ma-140	157	1	exact	exact	ADJ
ma-140	157	2	solutions	solution	NOUN
ma-140	157	3	.	.	PUNCT
ma-140	158	1	the	the	DET
ma-140	158	2	methods	method	NOUN
ma-140	158	3	of	of	ADP
ma-140	158	4	(	(	PUNCT
ma-140	158	5	g’/g)-expansion	g’/g)-expansion	NOUN
ma-140	158	6	method	method	NOUN
ma-140	158	7	[	[	X
ma-140	158	8	7	7	NUM
ma-140	158	9	]	]	PUNCT
ma-140	158	10	,	,	PUNCT
ma-140	158	11	extended	extend	VERB
ma-140	158	12	jacobi	jacobi	PROPN
ma-140	158	13	elliptic	elliptic	ADJ
ma-140	158	14	functionexpansion	functionexpansion	NOUN
ma-140	158	15	[	[	X
ma-140	158	16	9	9	NUM
ma-140	158	17	]	]	PUNCT
ma-140	158	18	and	and	CCONJ
ma-140	158	19	kudryashov	kudryashov	PROPN
ma-140	158	20	[	[	X
ma-140	158	21	11	11	NUM
ma-140	158	22	]	]	PUNCT
ma-140	158	23	are	be	AUX
ma-140	158	24	usually	usually	ADV
ma-140	158	25	applied	apply	VERB
ma-140	158	26	after	after	ADP
ma-140	158	27	symmetry	symmetry	NOUN
ma-140	158	28	reductions	reduction	NOUN
ma-140	158	29	.	.	PUNCT
ma-140	159	1	conservation	conservation	NOUN
ma-140	159	2	laws	law	NOUN
ma-140	159	3	.	.	PUNCT
ma-140	160	1	[	[	X
ma-140	160	2	11	11	NUM
ma-140	160	3	]	]	SYM
ma-140	160	4	fundamental	fundamental	ADJ
ma-140	160	5	operators	operator	NOUN
ma-140	160	6	.	.	PUNCT
ma-140	161	1	definition	definition	NOUN
ma-140	161	2	2.21	2.21	NUM
ma-140	161	3	.	.	PUNCT
ma-140	162	1	the	the	DET
ma-140	162	2	euler	euler	NOUN
ma-140	162	3	-	-	PUNCT
ma-140	162	4	lagrange	lagrange	NOUN
ma-140	162	5	operator	operator	NOUN
ma-140	162	6	δ	δ	PROPN
ma-140	162	7	δuα	δuα	NOUN
ma-140	162	8	is	be	AUX
ma-140	162	9	δ	δ	PROPN
ma-140	162	10	δuα	δuα	NOUN
ma-140	162	11	=	=	SYM
ma-140	162	12	∂	∂	NOUN
ma-140	162	13	∂uα	∂uα	NOUN
ma-140	162	14	+	+	CCONJ
ma-140	162	15	∑	∑	PROPN
ma-140	162	16	κ≥1	κ≥1	PROPN
ma-140	162	17	(	(	PUNCT
ma-140	162	18	−1)κdi1	−1)κdi1	ADV
ma-140	162	19	,	,	PUNCT
ma-140	162	20	.	.	PUNCT
ma-140	162	21	.	.	PUNCT
ma-140	163	1	.	.	PUNCT
ma-140	164	1	,	,	PUNCT
ma-140	164	2	diκ	diκ	NOUN
ma-140	164	3	∂	∂	NUM
ma-140	164	4	∂uαi1i2	∂uαi1i2	NOUN
ma-140	164	5	...	...	PUNCT
ma-140	164	6	iκ	iκ	NOUN
ma-140	164	7	,	,	PUNCT
ma-140	164	8	(	(	PUNCT
ma-140	164	9	2.29	2.29	NUM
ma-140	164	10	)	)	PUNCT
ma-140	164	11	and	and	CCONJ
ma-140	164	12	the	the	DET
ma-140	164	13	liebäcklund	liebäcklund	ADJ
ma-140	164	14	operator	operator	NOUN
ma-140	164	15	in	in	ADP
ma-140	164	16	abbreviated	abbreviate	VERB
ma-140	164	17	form	form	NOUN
ma-140	164	18	[	[	X
ma-140	164	19	11	11	NUM
ma-140	164	20	]	]	X
ma-140	164	21	is	be	AUX
ma-140	164	22	x	x	X
ma-140	164	23	=	=	SYM
ma-140	164	24	ξi	ξi	NOUN
ma-140	164	25	∂	∂	NOUN
ma-140	164	26	∂x	∂x	PROPN
ma-140	165	1	i	i	PRON
ma-140	165	2	+	+	NUM
ma-140	165	3	ηα	ηα	PROPN
ma-140	165	4	∂	∂	NOUN
ma-140	165	5	∂uα	∂uα	PROPN
ma-140	165	6	+	+	X
ma-140	165	7	.	.	PUNCT
ma-140	165	8	.	.	PUNCT
ma-140	165	9	.	.	PUNCT
ma-140	165	10	.	.	PUNCT
ma-140	166	1	(	(	PUNCT
ma-140	166	2	2.30	2.30	NUM
ma-140	166	3	)	)	PUNCT
ma-140	166	4	https://doi.org/10.28924/ada/ma.3.13	https://doi.org/10.28924/ada/ma.3.13	PROPN
ma-140	166	5	eur	eur	NOUN
ma-140	166	6	.	.	PUNCT
ma-140	167	1	j.	j.	PROPN
ma-140	167	2	math	math	PROPN
ma-140	167	3	.	.	PUNCT
ma-140	168	1	anal	anal	PROPN
ma-140	168	2	.	.	PUNCT
ma-140	169	1	10.28924	10.28924	NUM
ma-140	169	2	/	/	SYM
ma-140	169	3	ada	ada	PROPN
ma-140	169	4	/	/	SYM
ma-140	169	5	ma.3.13	ma.3.13	PROPN
ma-140	169	6	6	6	NUM
ma-140	169	7	remark	remark	NOUN
ma-140	169	8	2.22	2.22	NUM
ma-140	169	9	.	.	PUNCT
ma-140	170	1	the	the	DET
ma-140	170	2	liebäcklund	liebäcklund	ADJ
ma-140	170	3	operator	operator	NOUN
ma-140	170	4	(	(	PUNCT
ma-140	170	5	2.30	2.30	NUM
ma-140	170	6	)	)	PUNCT
ma-140	170	7	in	in	ADP
ma-140	170	8	its	its	PRON
ma-140	170	9	prolonged	prolonged	ADJ
ma-140	170	10	form	form	NOUN
ma-140	170	11	is	be	AUX
ma-140	170	12	x	x	X
ma-140	170	13	=	=	NOUN
ma-140	170	14	ξi	ξi	NOUN
ma-140	170	15	∂	∂	NOUN
ma-140	170	16	∂x	∂x	PROPN
ma-140	171	1	i	i	PRON
ma-140	171	2	+	+	NUM
ma-140	171	3	ηα	ηα	PROPN
ma-140	171	4	∂	∂	NOUN
ma-140	171	5	∂uα	∂uα	NOUN
ma-140	171	6	+	+	CCONJ
ma-140	171	7	∑	∑	PROPN
ma-140	171	8	κ≥1	κ≥1	PROPN
ma-140	171	9	ζi1	ζi1	NOUN
ma-140	171	10	...	...	PUNCT
ma-140	171	11	iκ	iκ	NOUN
ma-140	171	12	∂	∂	NUM
ma-140	171	13	∂uαi1i2	∂uαi1i2	NOUN
ma-140	171	14	...	...	PUNCT
ma-140	171	15	iκ	iκ	NOUN
ma-140	171	16	,	,	PUNCT
ma-140	171	17	(	(	PUNCT
ma-140	171	18	2.31	2.31	NUM
ma-140	171	19	)	)	PUNCT
ma-140	171	20	for	for	ADP
ma-140	171	21	ζαi	ζαi	NOUN
ma-140	171	22	=	=	SYM
ma-140	171	23	di(w	di(w	X
ma-140	171	24	α	α	X
ma-140	171	25	)	)	PUNCT
ma-140	172	1	+	+	CCONJ
ma-140	172	2	ξjuαij	ξjuαij	ADJ
ma-140	172	3	,	,	PUNCT
ma-140	172	4	.	.	PUNCT
ma-140	172	5	.	.	PUNCT
ma-140	173	1	.	.	PUNCT
ma-140	174	1	,	,	PUNCT
ma-140	174	2	ζαi1	ζαi1	PROPN
ma-140	174	3	...	...	PUNCT
ma-140	174	4	iκ	iκ	NOUN
ma-140	174	5	=	=	NOUN
ma-140	174	6	di1	di1	NOUN
ma-140	174	7	...	...	PUNCT
ma-140	174	8	iκ(wα	iκ(wα	PROPN
ma-140	174	9	)	)	PUNCT
ma-140	175	1	+	+	NUM
ma-140	175	2	ξjuαji1	ξjuαji1	NOUN
ma-140	175	3	...	...	PUNCT
ma-140	175	4	iκ	iκ	INTJ
ma-140	175	5	,	,	PUNCT
ma-140	175	6	j	j	PROPN
ma-140	175	7	=	=	NOUN
ma-140	175	8	1	1	NUM
ma-140	175	9	,	,	PUNCT
ma-140	175	10	.	.	PUNCT
ma-140	175	11	.	.	PUNCT
ma-140	175	12	.	.	PUNCT
ma-140	176	1	,	,	PUNCT
ma-140	176	2	n.	n.	NOUN
ma-140	176	3	(	(	PUNCT
ma-140	176	4	2.32	2.32	NUM
ma-140	176	5	)	)	PUNCT
ma-140	176	6	and	and	CCONJ
ma-140	176	7	the	the	DET
ma-140	176	8	lie	lie	NOUN
ma-140	176	9	characteristic	characteristic	ADJ
ma-140	176	10	function	function	NOUN
ma-140	176	11	wα	wα	NOUN
ma-140	176	12	=	=	NOUN
ma-140	176	13	ηα	ηα	PROPN
ma-140	176	14	−	−	PROPN
ma-140	176	15	ξjuαj	ξjuαj	PROPN
ma-140	176	16	.	.	PUNCT
ma-140	177	1	(	(	PUNCT
ma-140	177	2	2.33	2.33	NUM
ma-140	177	3	)	)	PUNCT
ma-140	177	4	remark	remark	NOUN
ma-140	177	5	2.23	2.23	NUM
ma-140	177	6	.	.	PUNCT
ma-140	178	1	the	the	DET
ma-140	178	2	characteristic	characteristic	ADJ
ma-140	178	3	form	form	NOUN
ma-140	178	4	of	of	ADP
ma-140	178	5	liebäcklund	liebäcklund	ADJ
ma-140	178	6	operator	operator	NOUN
ma-140	178	7	(	(	PUNCT
ma-140	178	8	2.31	2.31	NUM
ma-140	178	9	)	)	PUNCT
ma-140	178	10	is	be	AUX
ma-140	178	11	x	x	NOUN
ma-140	178	12	=	=	PUNCT
ma-140	178	13	ξidi	ξidi	NOUN
ma-140	178	14	+	+	PROPN
ma-140	178	15	wα	wα	NOUN
ma-140	178	16	∂	∂	NOUN
ma-140	178	17	∂uα	∂uα	NOUN
ma-140	178	18	+	+	NOUN
ma-140	178	19	di1	di1	ADJ
ma-140	178	20	...	...	PUNCT
ma-140	178	21	iκ(wα	iκ(wα	PROPN
ma-140	178	22	)	)	PUNCT
ma-140	178	23	∂	∂	NUM
ma-140	179	1	∂uαi1i2	∂uαi1i2	NOUN
ma-140	179	2	...	...	PUNCT
ma-140	179	3	iκ	iκ	NOUN
ma-140	179	4	.	.	PUNCT
ma-140	180	1	(	(	PUNCT
ma-140	180	2	2.34	2.34	NUM
ma-140	180	3	)	)	PUNCT
ma-140	180	4	the	the	DET
ma-140	180	5	method	method	NOUN
ma-140	180	6	of	of	ADP
ma-140	180	7	multipliers	multiplier	NOUN
ma-140	180	8	.	.	PUNCT
ma-140	181	1	definition	definition	NOUN
ma-140	181	2	2.24	2.24	NUM
ma-140	181	3	.	.	PUNCT
ma-140	182	1	a	a	DET
ma-140	182	2	function	function	NOUN
ma-140	182	3	λα	λα	PROPN
ma-140	183	1	(	(	PUNCT
ma-140	183	2	x	x	X
ma-140	183	3	i	i	PRON
ma-140	183	4	,	,	PUNCT
ma-140	183	5	uα	uα	PROPN
ma-140	183	6	,	,	PUNCT
ma-140	183	7	u(1	u(1	PROPN
ma-140	183	8	)	)	PUNCT
ma-140	183	9	,	,	PUNCT
ma-140	183	10	.	.	PUNCT
ma-140	183	11	.	.	PUNCT
ma-140	183	12	.	.	PUNCT
ma-140	183	13	)	)	PUNCT
ma-140	184	1	=	=	SYM
ma-140	184	2	λα	λα	PROPN
ma-140	184	3	,	,	PUNCT
ma-140	184	4	is	be	AUX
ma-140	184	5	a	a	DET
ma-140	184	6	multiplier	multipli	ADJ
ma-140	184	7	of	of	ADP
ma-140	184	8	(	(	PUNCT
ma-140	184	9	2.2	2.2	NUM
ma-140	184	10	)	)	PUNCT
ma-140	184	11	if	if	SCONJ
ma-140	184	12	[	[	X
ma-140	184	13	7	7	X
ma-140	184	14	]	]	X
ma-140	185	1	λα∆α	λα∆α	X
ma-140	185	2	=	=	SYM
ma-140	185	3	dit	dit	PROPN
ma-140	185	4	i	i	NOUN
ma-140	185	5	,	,	PUNCT
ma-140	185	6	(	(	PUNCT
ma-140	185	7	2.35	2.35	NUM
ma-140	185	8	)	)	PUNCT
ma-140	185	9	where	where	SCONJ
ma-140	185	10	dit	dit	NOUN
ma-140	185	11	i	i	PRON
ma-140	185	12	is	be	AUX
ma-140	185	13	a	a	DET
ma-140	185	14	divergence	divergence	NOUN
ma-140	185	15	expression	expression	NOUN
ma-140	185	16	.	.	PUNCT
ma-140	186	1	definition	definition	NOUN
ma-140	186	2	2.25	2.25	NUM
ma-140	186	3	.	.	PUNCT
ma-140	187	1	to	to	PART
ma-140	187	2	find	find	VERB
ma-140	187	3	the	the	DET
ma-140	187	4	multipliers	multiplier	NOUN
ma-140	187	5	λα	λα	PROPN
ma-140	187	6	,	,	PUNCT
ma-140	187	7	one	one	NUM
ma-140	187	8	solves	solve	VERB
ma-140	187	9	the	the	DET
ma-140	187	10	determining	determine	VERB
ma-140	187	11	equations	equation	NOUN
ma-140	187	12	(	(	PUNCT
ma-140	187	13	2.36	2.36	NUM
ma-140	187	14	)	)	PUNCT
ma-140	188	1	[	[	X
ma-140	188	2	10	10	NUM
ma-140	188	3	]	]	PUNCT
ma-140	188	4	,	,	PUNCT
ma-140	188	5	δ	δ	PROPN
ma-140	188	6	δuα	δuα	X
ma-140	188	7	(	(	PUNCT
ma-140	188	8	λα∆α	λα∆α	PROPN
ma-140	188	9	)	)	PUNCT
ma-140	188	10	=	=	SYM
ma-140	188	11	0	0	X
ma-140	188	12	.	.	PUNCT
ma-140	188	13	(	(	PUNCT
ma-140	188	14	2.36	2.36	NUM
ma-140	188	15	)	)	PUNCT
ma-140	188	16	ibragimov	ibragimov	NOUN
ma-140	188	17	’s	’s	PART
ma-140	188	18	conservation	conservation	NOUN
ma-140	188	19	theorem	theorem	NOUN
ma-140	188	20	.	.	PUNCT
ma-140	189	1	the	the	DET
ma-140	189	2	technique	technique	NOUN
ma-140	189	3	[	[	X
ma-140	189	4	5	5	NUM
ma-140	189	5	]	]	PUNCT
ma-140	189	6	enables	enable	VERB
ma-140	189	7	one	one	NUM
ma-140	189	8	to	to	PART
ma-140	189	9	construct	construct	VERB
ma-140	189	10	conserved	conserve	VERB
ma-140	189	11	vectorsassociated	vectorsassociate	VERB
ma-140	189	12	with	with	ADP
ma-140	189	13	each	each	DET
ma-140	189	14	lie	lie	NOUN
ma-140	189	15	point	point	NOUN
ma-140	189	16	symmetry	symmetry	NOUN
ma-140	189	17	of	of	ADP
ma-140	189	18	(	(	PUNCT
ma-140	189	19	2.2	2.2	NUM
ma-140	189	20	)	)	PUNCT
ma-140	189	21	.	.	PUNCT
ma-140	190	1	definition	definition	NOUN
ma-140	190	2	2.26	2.26	NUM
ma-140	190	3	.	.	PUNCT
ma-140	191	1	the	the	DET
ma-140	191	2	adjoint	adjoint	PROPN
ma-140	191	3	equations	equation	NOUN
ma-140	191	4	of	of	ADP
ma-140	191	5	(	(	PUNCT
ma-140	191	6	2.2	2.2	NUM
ma-140	191	7	)	)	PUNCT
ma-140	191	8	are	be	AUX
ma-140	191	9	∆∗α	∆∗α	NOUN
ma-140	191	10	(	(	PUNCT
ma-140	191	11	x	x	X
ma-140	191	12	i	i	PRON
ma-140	191	13	,	,	PUNCT
ma-140	191	14	uα	uα	PROPN
ma-140	191	15	,	,	PUNCT
ma-140	191	16	vα	vα	PROPN
ma-140	191	17	,	,	PUNCT
ma-140	191	18	.	.	PUNCT
ma-140	191	19	.	.	PUNCT
ma-140	192	1	.	.	PUNCT
ma-140	193	1	,	,	PUNCT
ma-140	193	2	u(π	u(π	PROPN
ma-140	193	3	)	)	PUNCT
ma-140	193	4	,	,	PUNCT
ma-140	193	5	v(π	v(π	PROPN
ma-140	193	6	)	)	PUNCT
ma-140	193	7	)	)	PUNCT
ma-140	194	1	≡	≡	PROPN
ma-140	194	2	δ	δ	PROPN
ma-140	194	3	δuα	δuα	X
ma-140	194	4	(	(	PUNCT
ma-140	194	5	vβ∆β	vβ∆β	PROPN
ma-140	194	6	)	)	PUNCT
ma-140	194	7	=	=	SYM
ma-140	194	8	0	0	NUM
ma-140	194	9	,	,	PUNCT
ma-140	194	10	(	(	PUNCT
ma-140	194	11	2.37	2.37	NUM
ma-140	194	12	)	)	PUNCT
ma-140	194	13	for	for	ADP
ma-140	194	14	a	a	DET
ma-140	194	15	new	new	ADJ
ma-140	194	16	dependent	dependent	ADJ
ma-140	194	17	variable	variable	ADJ
ma-140	194	18	vα	vα	PROPN
ma-140	194	19	.	.	PUNCT
ma-140	194	20	definition	definition	NOUN
ma-140	194	21	2.27	2.27	NUM
ma-140	194	22	.	.	PUNCT
ma-140	195	1	the	the	DET
ma-140	195	2	formal	formal	ADJ
ma-140	195	3	lagrangian	lagrangian	ADJ
ma-140	195	4	l	l	NOUN
ma-140	195	5	of	of	ADP
ma-140	195	6	(	(	PUNCT
ma-140	195	7	2.2	2.2	NUM
ma-140	195	8	)	)	PUNCT
ma-140	195	9	and	and	CCONJ
ma-140	195	10	its	its	PRON
ma-140	195	11	adjoint	adjoint	NOUN
ma-140	195	12	equations	equation	NOUN
ma-140	195	13	(	(	PUNCT
ma-140	195	14	2.37	2.37	NUM
ma-140	195	15	)	)	PUNCT
ma-140	195	16	is	be	AUX
ma-140	195	17	[	[	X
ma-140	195	18	8	8	NUM
ma-140	195	19	]	]	X
ma-140	195	20	l	l	NOUN
ma-140	196	1	=	=	SYM
ma-140	196	2	vα∆α(x	vα∆α(x	NOUN
ma-140	197	1	i	i	PRON
ma-140	197	2	,	,	PUNCT
ma-140	197	3	uα	uα	PROPN
ma-140	197	4	,	,	PUNCT
ma-140	197	5	u(1	u(1	PROPN
ma-140	197	6	)	)	PUNCT
ma-140	197	7	,	,	PUNCT
ma-140	197	8	.	.	PUNCT
ma-140	197	9	.	.	PUNCT
ma-140	197	10	.	.	PUNCT
ma-140	198	1	,	,	PUNCT
ma-140	198	2	u(π	u(π	PROPN
ma-140	198	3	)	)	PUNCT
ma-140	198	4	)	)	PUNCT
ma-140	198	5	.	.	PUNCT
ma-140	199	1	(	(	PUNCT
ma-140	199	2	2.38	2.38	NUM
ma-140	199	3	)	)	PUNCT
ma-140	199	4	theorem	theorem	VERB
ma-140	199	5	2.28	2.28	NUM
ma-140	199	6	.	.	PUNCT
ma-140	200	1	every	every	DET
ma-140	200	2	infinitesimal	infinitesimal	ADJ
ma-140	200	3	symmetry	symmetry	NOUN
ma-140	200	4	xof	xof	PROPN
ma-140	200	5	(	(	PUNCT
ma-140	200	6	2.2	2.2	NUM
ma-140	200	7	)	)	PUNCT
ma-140	200	8	leads	lead	VERB
ma-140	200	9	to	to	ADP
ma-140	200	10	conservation	conservation	NOUN
ma-140	200	11	laws	law	NOUN
ma-140	200	12	[	[	X
ma-140	200	13	6	6	NUM
ma-140	200	14	]	]	X
ma-140	200	15	dit	dit	NOUN
ma-140	200	16	i	i	PRON
ma-140	200	17	∣∣∣	∣∣∣	VERB
ma-140	200	18	∆α=0	∆α=0	PROPN
ma-140	200	19	=	=	PUNCT
ma-140	200	20	0	0	NUM
ma-140	200	21	,	,	PUNCT
ma-140	200	22	(	(	PUNCT
ma-140	200	23	2.39	2.39	NUM
ma-140	200	24	)	)	PUNCT
ma-140	200	25	where	where	SCONJ
ma-140	200	26	the	the	DET
ma-140	200	27	conserved	conserved	ADJ
ma-140	200	28	vector	vector	NOUN
ma-140	200	29	t	t	NOUN
ma-140	201	1	i	i	PRON
ma-140	201	2	=	=	PUNCT
ma-140	202	1	ξil+wα	ξil+wα	PROPN
ma-140	202	2	[	[	PUNCT
ma-140	202	3	∂l	∂l	X
ma-140	202	4	∂uαi	∂uαi	X
ma-140	202	5	−dj	−dj	NOUN
ma-140	202	6	(	(	PUNCT
ma-140	202	7	∂l	∂l	VERB
ma-140	202	8	∂uαij	∂uαij	NOUN
ma-140	202	9	)	)	PUNCT
ma-140	203	1	+	+	ADJ
ma-140	203	2	djdk	djdk	NOUN
ma-140	203	3	(	(	PUNCT
ma-140	203	4	∂l	∂l	PROPN
ma-140	203	5	∂uαijk	∂uαijk	X
ma-140	203	6	)	)	PUNCT
ma-140	203	7	−	−	PROPN
ma-140	203	8	.	.	PUNCT
ma-140	203	9	.	.	PUNCT
ma-140	203	10	.	.	PUNCT
ma-140	204	1	]	]	PUNCT
ma-140	205	1	+	+	CCONJ
ma-140	205	2	dj(w	dj(w	PROPN
ma-140	205	3	α	α	X
ma-140	205	4	)	)	PUNCT
ma-140	205	5	[	[	PUNCT
ma-140	205	6	∂l	∂l	PROPN
ma-140	205	7	∂uαij	∂uαij	NOUN
ma-140	205	8	−dk	−dk	NOUN
ma-140	205	9	(	(	PUNCT
ma-140	205	10	∂l	∂l	PROPN
ma-140	205	11	∂uαijk	∂uαijk	X
ma-140	205	12	)	)	PUNCT
ma-140	206	1	+	+	CCONJ
ma-140	206	2	.	.	PUNCT
ma-140	206	3	.	.	PUNCT
ma-140	206	4	.	.	PUNCT
ma-140	207	1	]	]	PUNCT
ma-140	208	1	+	+	PUNCT
ma-140	208	2	djdk(wα	djdk(wα	ADJ
ma-140	208	3	)	)	PUNCT
ma-140	208	4	[	[	PUNCT
ma-140	208	5	∂l	∂l	NOUN
ma-140	208	6	∂uαijk	∂uαijk	ADV
ma-140	208	7	−	−	PROPN
ma-140	208	8	.	.	PUNCT
ma-140	208	9	.	.	PUNCT
ma-140	208	10	.	.	PUNCT
ma-140	208	11	]	]	PUNCT
ma-140	208	12	.	.	PUNCT
ma-140	209	1	(	(	PUNCT
ma-140	209	2	2.40	2.40	NUM
ma-140	209	3	)	)	PUNCT
ma-140	209	4	https://doi.org/10.28924/ada/ma.3.13	https://doi.org/10.28924/ada/ma.3.13	PROPN
ma-140	209	5	eur	eur	NOUN
ma-140	209	6	.	.	PUNCT
ma-140	210	1	j.	j.	PROPN
ma-140	210	2	math	math	PROPN
ma-140	210	3	.	.	PUNCT
ma-140	211	1	anal	anal	PROPN
ma-140	211	2	.	.	PUNCT
ma-140	212	1	10.28924	10.28924	NUM
ma-140	212	2	/	/	SYM
ma-140	212	3	ada	ada	PROPN
ma-140	212	4	/	/	SYM
ma-140	212	5	ma.3.13	ma.3.13	PROPN
ma-140	212	6	73	73	NUM
ma-140	212	7	.	.	PUNCT
ma-140	213	1	main	main	ADJ
ma-140	213	2	results	result	NOUN
ma-140	213	3	3.1	3.1	NUM
ma-140	213	4	.	.	PUNCT
ma-140	213	5	lie	lie	NOUN
ma-140	213	6	point	point	NOUN
ma-140	213	7	symmetries	symmetry	NOUN
ma-140	213	8	of	of	ADP
ma-140	213	9	equal	equal	ADJ
ma-140	213	10	width	width	ADJ
ma-140	213	11	equation(1.1	equation(1.1	NOUN
ma-140	213	12	)	)	PUNCT
ma-140	213	13	.	.	PUNCT
ma-140	214	1	we	we	PRON
ma-140	214	2	start	start	VERB
ma-140	214	3	first	first	ADV
ma-140	214	4	by	by	ADP
ma-140	214	5	computing	compute	VERB
ma-140	214	6	lie	lie	NOUN
ma-140	214	7	pointsymmetries	pointsymmetrie	NOUN
ma-140	214	8	of	of	ADP
ma-140	214	9	the	the	DET
ma-140	214	10	equal	equal	ADJ
ma-140	214	11	width	width	ADJ
ma-140	214	12	equation	equation	NOUN
ma-140	214	13	(	(	PUNCT
ma-140	214	14	1.1	1.1	NUM
ma-140	214	15	)	)	PUNCT
ma-140	214	16	,	,	PUNCT
ma-140	214	17	which	which	PRON
ma-140	214	18	admits	admit	VERB
ma-140	214	19	the	the	DET
ma-140	214	20	one	one	NUM
ma-140	214	21	-	-	PUNCT
ma-140	214	22	parameter	parameter	NOUN
ma-140	214	23	lie	lie	NOUN
ma-140	214	24	group	group	NOUN
ma-140	214	25	of	of	ADP
ma-140	214	26	trans	tran	NOUN
ma-140	214	27	-	-	NOUN
ma-140	214	28	formations	formation	NOUN
ma-140	214	29	with	with	ADP
ma-140	214	30	infinitesimal	infinitesimal	ADJ
ma-140	214	31	generator	generator	NOUN
ma-140	214	32	x	x	NOUN
ma-140	214	33	=	=	SYM
ma-140	214	34	τ(t	τ(t	PROPN
ma-140	214	35	,	,	PUNCT
ma-140	214	36	x	x	NOUN
ma-140	214	37	,	,	PUNCT
ma-140	214	38	u	u	NOUN
ma-140	214	39	)	)	PUNCT
ma-140	214	40	∂	∂	PUNCT
ma-140	214	41	∂t	∂t	PROPN
ma-140	214	42	+	+	CCONJ
ma-140	214	43	ξ(t	ξ(t	PROPN
ma-140	214	44	,	,	PUNCT
ma-140	214	45	x	x	NOUN
ma-140	214	46	,	,	PUNCT
ma-140	214	47	u	u	NOUN
ma-140	214	48	)	)	PUNCT
ma-140	214	49	∂	∂	NUM
ma-140	214	50	∂x	∂x	PROPN
ma-140	214	51	+	+	CCONJ
ma-140	214	52	η(t	η(t	NOUN
ma-140	214	53	,	,	PUNCT
ma-140	214	54	x	x	NOUN
ma-140	214	55	,	,	PUNCT
ma-140	214	56	u	u	NOUN
ma-140	214	57	)	)	PUNCT
ma-140	214	58	∂	∂	NOUN
ma-140	215	1	∂u	∂u	PROPN
ma-140	215	2	(	(	PUNCT
ma-140	215	3	3.1	3.1	NUM
ma-140	215	4	)	)	PUNCT
ma-140	215	5	if	if	SCONJ
ma-140	215	6	and	and	CCONJ
ma-140	215	7	only	only	ADV
ma-140	215	8	if	if	SCONJ
ma-140	215	9	x[3]∆	x[3]∆	PROPN
ma-140	215	10	∣∣∣∣	∣∣∣∣	PROPN
ma-140	215	11	∆=0	∆=0	PROPN
ma-140	215	12	=	=	SYM
ma-140	215	13	0	0	X
ma-140	215	14	.	.	PUNCT
ma-140	215	15	(	(	PUNCT
ma-140	215	16	3.2	3.2	NUM
ma-140	215	17	)	)	PUNCT
ma-140	215	18	where	where	SCONJ
ma-140	215	19	x[3	x[3	PROPN
ma-140	215	20	]	]	X
ma-140	215	21	=	=	PUNCT
ma-140	215	22	x	x	SYM
ma-140	215	23	+	+	NUM
ma-140	215	24	ζ1	ζ1	NOUN
ma-140	215	25	∂	∂	NOUN
ma-140	215	26	∂ut	∂ut	PROPN
ma-140	215	27	+	+	CCONJ
ma-140	215	28	ζ2	ζ2	NOUN
ma-140	215	29	∂	∂	NOUN
ma-140	215	30	∂ux	∂ux	PROPN
ma-140	215	31	+	+	CCONJ
ma-140	215	32	ζ122	ζ122	PROPN
ma-140	215	33	∂	∂	NUM
ma-140	215	34	∂utxx	∂utxx	NUM
ma-140	215	35	,	,	PUNCT
ma-140	215	36	(	(	PUNCT
ma-140	215	37	3.3	3.3	NUM
ma-140	215	38	)	)	PUNCT
ma-140	215	39	is	be	AUX
ma-140	215	40	the	the	DET
ma-140	215	41	third	third	ADJ
ma-140	215	42	prolongation	prolongation	NOUN
ma-140	215	43	of	of	ADP
ma-140	215	44	the	the	DET
ma-140	215	45	lie	lie	NOUN
ma-140	215	46	point	point	NOUN
ma-140	215	47	symmetry	symmetry	NOUN
ma-140	215	48	x	x	PUNCT
ma-140	215	49	as	as	SCONJ
ma-140	215	50	defined	define	VERB
ma-140	215	51	in	in	ADP
ma-140	215	52	(	(	PUNCT
ma-140	215	53	2.20	2.20	NUM
ma-140	215	54	)	)	PUNCT
ma-140	215	55	and	and	CCONJ
ma-140	215	56	ζ1	ζ1	NOUN
ma-140	215	57	=	=	SYM
ma-140	215	58	dt(η)−	dt(η)−	NOUN
ma-140	215	59	utdt(τ)−	utdt(τ)−	PROPN
ma-140	215	60	uxdt(ξ	uxdt(ξ	PROPN
ma-140	215	61	)	)	PUNCT
ma-140	215	62	,	,	PUNCT
ma-140	215	63	(	(	PUNCT
ma-140	215	64	3.4	3.4	NUM
ma-140	215	65	)	)	PUNCT
ma-140	215	66	ζ12	ζ12	NOUN
ma-140	215	67	=	=	SYM
ma-140	215	68	dx(ζ1)−	dx(ζ1)−	PROPN
ma-140	215	69	uttdx(τ)−	uttdx(τ)−	PROPN
ma-140	215	70	utxdx(ξ	utxdx(ξ	PROPN
ma-140	215	71	)	)	PUNCT
ma-140	215	72	,	,	PUNCT
ma-140	215	73	(	(	PUNCT
ma-140	215	74	3.5	3.5	NUM
ma-140	215	75	)	)	PUNCT
ma-140	215	76	ζ2	ζ2	NOUN
ma-140	215	77	=	=	SYM
ma-140	215	78	dx(η)−	dx(η)−	NOUN
ma-140	215	79	utdx(τ)−	utdx(τ)−	ADJ
ma-140	215	80	uxdx(ξ	uxdx(ξ	NOUN
ma-140	215	81	)	)	PUNCT
ma-140	215	82	,	,	PUNCT
ma-140	215	83	(	(	PUNCT
ma-140	215	84	3.6	3.6	NUM
ma-140	215	85	)	)	PUNCT
ma-140	215	86	ζ122	ζ122	PROPN
ma-140	216	1	=	=	PRON
ma-140	216	2	dx(ζ12)−	dx(ζ12)−	VERB
ma-140	216	3	uttxdx(τ)−	uttxdx(τ)−	PROPN
ma-140	216	4	utxxdx(ξ	utxxdx(ξ	PROPN
ma-140	216	5	)	)	PUNCT
ma-140	216	6	,	,	PUNCT
ma-140	216	7	(	(	PUNCT
ma-140	216	8	3.7	3.7	NUM
ma-140	216	9	)	)	PUNCT
ma-140	216	10	as	as	SCONJ
ma-140	216	11	defined	define	VERB
ma-140	216	12	in	in	ADP
ma-140	216	13	(	(	PUNCT
ma-140	216	14	2.19	2.19	NUM
ma-140	216	15	)	)	PUNCT
ma-140	216	16	,	,	PUNCT
ma-140	216	17	and	and	CCONJ
ma-140	216	18	dt	dt	X
ma-140	216	19	=	=	SYM
ma-140	216	20	∂	∂	PROPN
ma-140	217	1	∂t	∂t	PROPN
ma-140	217	2	+	+	CCONJ
ma-140	217	3	ut	ut	PROPN
ma-140	217	4	∂	∂	PROPN
ma-140	217	5	∂u	∂u	PROPN
ma-140	218	1	+	+	CCONJ
ma-140	218	2	utx	utx	PROPN
ma-140	218	3	∂	∂	NUM
ma-140	218	4	∂ux	∂ux	PROPN
ma-140	218	5	+	+	CCONJ
ma-140	218	6	utt	utt	PROPN
ma-140	218	7	∂	∂	NOUN
ma-140	218	8	∂ut	∂ut	PROPN
ma-140	218	9	+	+	CCONJ
ma-140	218	10	·	·	PUNCT
ma-140	218	11	·	·	PUNCT
ma-140	218	12	·	·	PUNCT
ma-140	218	13	,	,	PUNCT
ma-140	218	14	(	(	PUNCT
ma-140	218	15	3.8	3.8	NUM
ma-140	218	16	)	)	PUNCT
ma-140	218	17	dx	dx	PROPN
ma-140	218	18	=	=	SYM
ma-140	218	19	∂	∂	NOUN
ma-140	218	20	∂x	∂x	PROPN
ma-140	219	1	+	+	CCONJ
ma-140	219	2	ux	ux	PROPN
ma-140	219	3	∂	∂	NUM
ma-140	219	4	∂u	∂u	PROPN
ma-140	220	1	+	+	CCONJ
ma-140	220	2	uxx	uxx	PROPN
ma-140	220	3	∂	∂	X
ma-140	220	4	∂ux	∂ux	PROPN
ma-140	220	5	+	+	PROPN
ma-140	220	6	utx	utx	PROPN
ma-140	220	7	∂	∂	NOUN
ma-140	220	8	∂ut	∂ut	PROPN
ma-140	220	9	+	+	PUNCT
ma-140	220	10	.	.	PUNCT
ma-140	220	11	.	.	PUNCT
ma-140	220	12	.	.	PUNCT
ma-140	220	13	.	.	PUNCT
ma-140	221	1	(	(	PUNCT
ma-140	221	2	3.9	3.9	NUM
ma-140	221	3	)	)	PUNCT
ma-140	221	4	applying	apply	VERB
ma-140	221	5	the	the	DET
ma-140	221	6	definitions	definition	NOUN
ma-140	221	7	of	of	ADP
ma-140	221	8	dt	dt	PUNCT
ma-140	221	9	and	and	CCONJ
ma-140	221	10	dx	dx	PROPN
ma-140	221	11	given	give	VERB
ma-140	221	12	in	in	ADP
ma-140	221	13	(	(	PUNCT
ma-140	221	14	3.8	3.8	NUM
ma-140	221	15	)	)	PUNCT
ma-140	221	16	and	and	CCONJ
ma-140	221	17	(	(	PUNCT
ma-140	221	18	3.9	3.9	NUM
ma-140	221	19	)	)	PUNCT
ma-140	221	20	,	,	PUNCT
ma-140	221	21	we	we	PRON
ma-140	221	22	obtain	obtain	VERB
ma-140	221	23	the	the	DET
ma-140	221	24	expanded	expand	VERB
ma-140	221	25	form	form	NOUN
ma-140	221	26	of	of	ADP
ma-140	221	27	the	the	DET
ma-140	221	28	ζs	ζs	NOUN
ma-140	221	29	as	as	ADP
ma-140	221	30	ζ1	ζ1	NOUN
ma-140	221	31	=	=	NOUN
ma-140	221	32	ηt	ηt	ADP
ma-140	221	33	+	+	ADJ
ma-140	221	34	ut(ηu	ut(ηu	PROPN
ma-140	221	35	−	−	PROPN
ma-140	221	36	τt	τt	NOUN
ma-140	221	37	)	)	PUNCT
ma-140	222	1	+	+	CCONJ
ma-140	222	2	ux(−ξt	ux(−ξt	X
ma-140	222	3	)	)	PUNCT
ma-140	223	1	+	+	CCONJ
ma-140	223	2	utux(−ξu	utux(−ξu	X
ma-140	223	3	)	)	PUNCT
ma-140	224	1	+	+	CCONJ
ma-140	224	2	u2	u2	PROPN
ma-140	224	3	t	t	PROPN
ma-140	224	4	(	(	PUNCT
ma-140	224	5	−τu	−τu	NOUN
ma-140	224	6	)	)	PUNCT
ma-140	224	7	,	,	PUNCT
ma-140	224	8	ζ12	ζ12	X
ma-140	224	9	=	=	SYM
ma-140	224	10	ηtx	ηtx	PROPN
ma-140	225	1	+	+	CCONJ
ma-140	225	2	ux(ηtu	ux(ηtu	PROPN
ma-140	225	3	−	−	PROPN
ma-140	225	4	ξtx	ξtx	PROPN
ma-140	225	5	)	)	PUNCT
ma-140	226	1	+	+	CCONJ
ma-140	226	2	utx(ηu	utx(ηu	PROPN
ma-140	226	3	−	−	PROPN
ma-140	227	1	τt	τt	NOUN
ma-140	227	2	−	−	PROPN
ma-140	228	1	ξx	ξx	NOUN
ma-140	228	2	)	)	PUNCT
ma-140	229	1	+	+	CCONJ
ma-140	229	2	ut(ηxu	ut(ηxu	ADJ
ma-140	229	3	−	−	NOUN
ma-140	229	4	τtx	τtx	ADJ
ma-140	229	5	)	)	PUNCT
ma-140	229	6	+	+	CCONJ
ma-140	229	7	utux(ηuu	utux(ηuu	NOUN
ma-140	229	8	−	−	PROPN
ma-140	229	9	ξxu	ξxu	NOUN
ma-140	229	10	−	−	NOUN
ma-140	229	11	τtu	τtu	ADV
ma-140	229	12	)	)	PUNCT
ma-140	230	1	+	+	CCONJ
ma-140	230	2	ututx(−2τu	ututx(−2τu	X
ma-140	230	3	)	)	PUNCT
ma-140	231	1	+	+	CCONJ
ma-140	231	2	u2	u2	PROPN
ma-140	231	3	t	t	PROPN
ma-140	231	4	(	(	PUNCT
ma-140	231	5	−τxu	−τxu	NOUN
ma-140	231	6	)	)	PUNCT
ma-140	231	7	+	+	CCONJ
ma-140	231	8	u2	u2	PROPN
ma-140	231	9	t	t	PROPN
ma-140	231	10	ux(−τuu	ux(−τuu	PROPN
ma-140	231	11	)	)	PUNCT
ma-140	231	12	+	+	CCONJ
ma-140	231	13	uxx(−ξt	uxx(−ξt	ADJ
ma-140	231	14	)	)	PUNCT
ma-140	231	15	+	+	CCONJ
ma-140	231	16	u2	u2	NOUN
ma-140	231	17	x	x	SYM
ma-140	231	18	(	(	PUNCT
ma-140	231	19	−ξtu	−ξtu	NOUN
ma-140	231	20	)	)	PUNCT
ma-140	231	21	+	+	CCONJ
ma-140	231	22	uxutx(−2ξu	uxutx(−2ξu	NOUN
ma-140	231	23	)	)	PUNCT
ma-140	232	1	+	+	CCONJ
ma-140	232	2	utu	utu	PROPN
ma-140	232	3	2	2	NUM
ma-140	232	4	x	x	SYM
ma-140	232	5	(	(	PUNCT
ma-140	232	6	−ξuu	−ξuu	ADJ
ma-140	232	7	)	)	PUNCT
ma-140	232	8	+	+	CCONJ
ma-140	232	9	utuxx(−ξu	utuxx(−ξu	X
ma-140	232	10	)	)	PUNCT
ma-140	232	11	+	+	CCONJ
ma-140	232	12	utt(−τx	utt(−τx	ADJ
ma-140	232	13	)	)	PUNCT
ma-140	232	14	+	+	NUM
ma-140	232	15	uxutt(−τu	uxutt(−τu	ADJ
ma-140	232	16	)	)	PUNCT
ma-140	232	17	ζ2	ζ2	NOUN
ma-140	232	18	=	=	SYM
ma-140	232	19	ηx	ηx	NOUN
ma-140	233	1	+	+	CCONJ
ma-140	233	2	ux(ηu	ux(ηu	PROPN
ma-140	233	3	−	−	NUM
ma-140	233	4	ξx	ξx	NOUN
ma-140	233	5	)	)	PUNCT
ma-140	234	1	+	+	CCONJ
ma-140	234	2	ut(−τx	ut(−τx	X
ma-140	234	3	)	)	PUNCT
ma-140	235	1	+	+	CCONJ
ma-140	235	2	utux(−τu	utux(−τu	NUM
ma-140	235	3	)	)	PUNCT
ma-140	235	4	+	+	CCONJ
ma-140	235	5	u2	u2	NOUN
ma-140	235	6	x	x	SYM
ma-140	235	7	(	(	PUNCT
ma-140	235	8	−ξu	−ξu	ADV
ma-140	235	9	)	)	PUNCT
ma-140	235	10	,	,	PUNCT
ma-140	235	11	https://doi.org/10.28924/ada/ma.3.13	https://doi.org/10.28924/ada/ma.3.13	PROPN
ma-140	235	12	eur	eur	PROPN
ma-140	235	13	.	.	PUNCT
ma-140	236	1	j.	j.	PROPN
ma-140	236	2	math	math	PROPN
ma-140	236	3	.	.	PUNCT
ma-140	237	1	anal	anal	PROPN
ma-140	237	2	.	.	PUNCT
ma-140	238	1	10.28924	10.28924	NUM
ma-140	238	2	/	/	SYM
ma-140	238	3	ada	ada	PROPN
ma-140	238	4	/	/	SYM
ma-140	238	5	ma.3.13	ma.3.13	PROPN
ma-140	238	6	8	8	NUM
ma-140	238	7	ζ122	ζ122	NOUN
ma-140	238	8	=	=	NOUN
ma-140	238	9	ηtxx	ηtxx	VERB
ma-140	238	10	+	+	CCONJ
ma-140	238	11	ux(2ηtxu	ux(2ηtxu	ADJ
ma-140	238	12	−	−	NOUN
ma-140	238	13	ξtxx	ξtxx	NOUN
ma-140	238	14	)	)	PUNCT
ma-140	239	1	+	+	NUM
ma-140	239	2	uxx(ηtu	uxx(ηtu	NOUN
ma-140	239	3	−	−	PROPN
ma-140	239	4	2ξtx	2ξtx	NUM
ma-140	239	5	)	)	PUNCT
ma-140	239	6	+	+	CCONJ
ma-140	239	7	u2	u2	NOUN
ma-140	239	8	x	x	SYM
ma-140	239	9	(	(	PUNCT
ma-140	239	10	ηtuu	ηtuu	VERB
ma-140	239	11	−	−	PROPN
ma-140	239	12	2ξtxu	2ξtxu	NUM
ma-140	239	13	)	)	PUNCT
ma-140	240	1	+	+	CCONJ
ma-140	240	2	utxx(ηu	utxx(ηu	PROPN
ma-140	240	3	−	−	PROPN
ma-140	240	4	τt	τt	NOUN
ma-140	240	5	−	−	PROPN
ma-140	240	6	2ξx	2ξx	ADJ
ma-140	240	7	)	)	PUNCT
ma-140	241	1	+	+	CCONJ
ma-140	241	2	utux(2ηxuu	utux(2ηxuu	ADJ
ma-140	241	3	−	−	PROPN
ma-140	241	4	ξxxu	ξxxu	NOUN
ma-140	241	5	−	−	PROPN
ma-140	241	6	2τtxu	2τtxu	NUM
ma-140	241	7	)	)	PUNCT
ma-140	242	1	+	+	CCONJ
ma-140	242	2	uxutx(2ηuu	uxutx(2ηuu	ADV
ma-140	242	3	−	−	PROPN
ma-140	243	1	4ξxu	4ξxu	PRON
ma-140	243	2	−	−	NOUN
ma-140	243	3	τtu	τtu	NUM
ma-140	243	4	)	)	PUNCT
ma-140	244	1	+	+	CCONJ
ma-140	244	2	utx(2ηxu	utx(2ηxu	VERB
ma-140	244	3	−	−	PROPN
ma-140	244	4	2τtx	2τtx	NUM
ma-140	244	5	−	−	PROPN
ma-140	244	6	ξxx	ξxx	NUM
ma-140	244	7	)	)	PUNCT
ma-140	244	8	+	+	CCONJ
ma-140	244	9	ut(ηxxu	ut(ηxxu	PROPN
ma-140	244	10	−	−	PROPN
ma-140	244	11	τtxx	τtxx	VERB
ma-140	244	12	)	)	PUNCT
ma-140	245	1	+	+	CCONJ
ma-140	245	2	utuxx(ηuu	utuxx(ηuu	ADJ
ma-140	245	3	−	−	NOUN
ma-140	245	4	2ξxu	2ξxu	NOUN
ma-140	245	5	−	−	NOUN
ma-140	245	6	τtu	τtu	ADV
ma-140	245	7	)	)	PUNCT
ma-140	246	1	+	+	CCONJ
ma-140	246	2	utu	utu	PROPN
ma-140	246	3	2	2	NUM
ma-140	246	4	x	x	X
ma-140	246	5	(	(	PUNCT
ma-140	246	6	ηuuu	ηuuu	NOUN
ma-140	246	7	−	−	PROPN
ma-140	246	8	2ξxuu	2ξxuu	NUM
ma-140	246	9	−	−	PROPN
ma-140	246	10	τtuu	τtuu	NOUN
ma-140	246	11	)	)	PUNCT
ma-140	247	1	+	+	CCONJ
ma-140	247	2	u2	u2	PROPN
ma-140	247	3	tx(−2τu	tx(−2τu	PROPN
ma-140	247	4	)	)	PUNCT
ma-140	247	5	ututxx(−2τu	ututxx(−2τu	ADJ
ma-140	247	6	)	)	PUNCT
ma-140	248	1	+	+	CCONJ
ma-140	248	2	ututx(−4τxu	ututx(−4τxu	NOUN
ma-140	248	3	)	)	PUNCT
ma-140	248	4	+	+	NUM
ma-140	248	5	u2	u2	PROPN
ma-140	248	6	t	t	PROPN
ma-140	248	7	(	(	PUNCT
ma-140	248	8	−τxxu	−τxxu	NUM
ma-140	248	9	)	)	PUNCT
ma-140	248	10	+	+	CCONJ
ma-140	248	11	uxu	uxu	PROPN
ma-140	248	12	2	2	NUM
ma-140	248	13	t	t	NOUN
ma-140	248	14	(	(	PUNCT
ma-140	248	15	−2τxuu	−2τxuu	NUM
ma-140	248	16	)	)	PUNCT
ma-140	248	17	+	+	CCONJ
ma-140	248	18	utuxutx(−4τuu	utuxutx(−4τuu	NOUN
ma-140	248	19	)	)	PUNCT
ma-140	248	20	,	,	PUNCT
ma-140	248	21	+	+	CCONJ
ma-140	248	22	u2	u2	PROPN
ma-140	248	23	xu	xu	PROPN
ma-140	248	24	2	2	NUM
ma-140	248	25	t	t	PROPN
ma-140	248	26	(	(	PUNCT
ma-140	248	27	−τuuu	−τuuu	NOUN
ma-140	248	28	)	)	PUNCT
ma-140	248	29	+	+	CCONJ
ma-140	248	30	uxxx(−ξt	uxxx(−ξt	ADJ
ma-140	248	31	)	)	PUNCT
ma-140	249	1	+	+	CCONJ
ma-140	249	2	u2	u2	PROPN
ma-140	249	3	t	t	PROPN
ma-140	249	4	uxx(−τuu	uxx(−τuu	PROPN
ma-140	249	5	)	)	PUNCT
ma-140	249	6	+	+	CCONJ
ma-140	249	7	uxuxx(−4ξtu	uxuxx(−4ξtu	VERB
ma-140	249	8	)	)	PUNCT
ma-140	249	9	+	+	NUM
ma-140	249	10	u3	u3	X
ma-140	249	11	x	x	SYM
ma-140	249	12	(	(	PUNCT
ma-140	249	13	−ξtuu	−ξtuu	NOUN
ma-140	249	14	)	)	PUNCT
ma-140	249	15	+	+	CCONJ
ma-140	249	16	uxxutx(−3ξu	uxxutx(−3ξu	NOUN
ma-140	249	17	)	)	PUNCT
ma-140	249	18	uxutxx(−2ξu	uxutxx(−2ξu	PROPN
ma-140	249	19	)	)	PUNCT
ma-140	250	1	+	+	CCONJ
ma-140	250	2	u2	u2	PROPN
ma-140	250	3	xutx(−3ξuu	xutx(−3ξuu	PROPN
ma-140	250	4	)	)	PUNCT
ma-140	250	5	+	+	CCONJ
ma-140	250	6	uxutuxx(−3ξuu	uxutuxx(−3ξuu	NOUN
ma-140	250	7	)	)	PUNCT
ma-140	250	8	+	+	CCONJ
ma-140	250	9	utu	utu	PROPN
ma-140	250	10	3	3	NUM
ma-140	250	11	x	x	SYM
ma-140	250	12	(	(	PUNCT
ma-140	250	13	−ξuuu	−ξuuu	NOUN
ma-140	250	14	)	)	PUNCT
ma-140	250	15	+	+	CCONJ
ma-140	250	16	utuxxx(−ξu	utuxxx(−ξu	ADV
ma-140	250	17	)	)	PUNCT
ma-140	250	18	+	+	CCONJ
ma-140	250	19	uttx(−2τx	uttx(−2τx	X
ma-140	250	20	)	)	PUNCT
ma-140	250	21	+	+	CCONJ
ma-140	250	22	utt(−τxx	utt(−τxx	NUM
ma-140	250	23	)	)	PUNCT
ma-140	250	24	+	+	CCONJ
ma-140	250	25	uxutt(−2τxu	uxutt(−2τxu	NOUN
ma-140	250	26	)	)	PUNCT
ma-140	250	27	+	+	CCONJ
ma-140	250	28	u2	u2	PROPN
ma-140	250	29	xutt(−τuu	xutt(−τuu	PROPN
ma-140	250	30	)	)	PUNCT
ma-140	251	1	+	+	PUNCT
ma-140	251	2	uxxutt(−τu	uxxutt(−τu	X
ma-140	251	3	)	)	PUNCT
ma-140	252	1	+	+	CCONJ
ma-140	252	2	uxuttx(−2τu	uxuttx(−2τu	ADJ
ma-140	252	3	−	−	PROPN
ma-140	252	4	ξu	ξu	NOUN
ma-140	252	5	)	)	PUNCT
ma-140	252	6	(	(	PUNCT
ma-140	252	7	3.10	3.10	NUM
ma-140	252	8	)	)	PUNCT
ma-140	252	9	now	now	ADV
ma-140	252	10	from	from	ADP
ma-140	252	11	equation	equation	NOUN
ma-140	252	12	(	(	PUNCT
ma-140	252	13	3.2	3.2	NUM
ma-140	252	14	)	)	PUNCT
ma-140	252	15	,	,	PUNCT
ma-140	252	16	we	we	PRON
ma-140	252	17	have	have	VERB
ma-140	252	18	ζ1	ζ1	NOUN
ma-140	252	19	+	+	CCONJ
ma-140	252	20	αηux	αηux	NOUN
ma-140	253	1	+	+	NUM
ma-140	253	2	αζ2u	αζ2u	NOUN
ma-140	253	3	+	+	CCONJ
ma-140	253	4	βζ122	βζ122	PUNCT
ma-140	253	5	∣∣	∣∣	NUM
ma-140	253	6	utxx=−	utxx=−	VERB
ma-140	253	7	ut	ut	PROPN
ma-140	253	8	β	β	PROPN
ma-140	253	9	−α	−α	PROPN
ma-140	253	10	β	β	X
ma-140	253	11	uux	uux	PROPN
ma-140	253	12	=	=	SYM
ma-140	253	13	0	0	PROPN
ma-140	253	14	,	,	PUNCT
ma-140	253	15	(	(	PUNCT
ma-140	253	16	3.11	3.11	NUM
ma-140	253	17	)	)	PUNCT
ma-140	253	18	if	if	SCONJ
ma-140	253	19	we	we	PRON
ma-140	253	20	substitute	substitute	VERB
ma-140	253	21	for	for	ADP
ma-140	253	22	ζ1	ζ1	NOUN
ma-140	253	23	,	,	PUNCT
ma-140	253	24	ζ2	ζ2	NOUN
ma-140	253	25	and	and	CCONJ
ma-140	253	26	ζ122	ζ122	PROPN
ma-140	253	27	in	in	ADP
ma-140	253	28	the	the	DET
ma-140	253	29	determining	determine	VERB
ma-140	253	30	equation	equation	NOUN
ma-140	253	31	(	(	PUNCT
ma-140	253	32	3.11	3.11	NUM
ma-140	253	33	)	)	PUNCT
ma-140	253	34	,	,	PUNCT
ma-140	253	35	we	we	PRON
ma-140	253	36	obtain	obtain	VERB
ma-140	253	37	the	the	DET
ma-140	253	38	following	following	NOUN
ma-140	253	39	;	;	PUNCT
ma-140	253	40	ηt	ηt	ADP
ma-140	253	41	+	+	CCONJ
ma-140	253	42	ut(ηu	ut(ηu	PROPN
ma-140	253	43	−	−	PROPN
ma-140	253	44	τt	τt	NOUN
ma-140	253	45	)	)	PUNCT
ma-140	254	1	+	+	CCONJ
ma-140	254	2	ux(−ξt	ux(−ξt	X
ma-140	254	3	)	)	PUNCT
ma-140	255	1	+	+	CCONJ
ma-140	255	2	utux(−ξu	utux(−ξu	X
ma-140	255	3	)	)	PUNCT
ma-140	256	1	+	+	CCONJ
ma-140	256	2	u2	u2	PROPN
ma-140	256	3	t	t	PROPN
ma-140	256	4	(	(	PUNCT
ma-140	256	5	−τu	−τu	NOUN
ma-140	256	6	)	)	PUNCT
ma-140	256	7	+	+	CCONJ
ma-140	256	8	αηux	αηux	NOUN
ma-140	256	9	+	+	NUM
ma-140	256	10	αu{ηx	αu{ηx	NOUN
ma-140	257	1	+	+	CCONJ
ma-140	257	2	ux(ηu	ux(ηu	PROPN
ma-140	257	3	−	−	NUM
ma-140	257	4	ξx	ξx	NOUN
ma-140	257	5	)	)	PUNCT
ma-140	257	6	+	+	CCONJ
ma-140	257	7	ut(−τx	ut(−τx	X
ma-140	257	8	)	)	PUNCT
ma-140	258	1	+	+	CCONJ
ma-140	258	2	utux(−τu	utux(−τu	NUM
ma-140	258	3	)	)	PUNCT
ma-140	258	4	+	+	CCONJ
ma-140	258	5	u2	u2	NOUN
ma-140	258	6	x	x	SYM
ma-140	258	7	(	(	PUNCT
ma-140	258	8	−ξu	−ξu	ADV
ma-140	258	9	)	)	PUNCT
ma-140	258	10	}	}	PUNCT
ma-140	259	1	+	+	CCONJ
ma-140	259	2	β	β	X
ma-140	259	3	{	{	PUNCT
ma-140	259	4	ηtxx	ηtxx	NOUN
ma-140	259	5	+	+	CCONJ
ma-140	259	6	ux(2ηtxu	ux(2ηtxu	ADP
ma-140	259	7	−	−	NOUN
ma-140	259	8	ξtxx	ξtxx	NOUN
ma-140	259	9	)	)	PUNCT
ma-140	259	10	+	+	NUM
ma-140	259	11	uxx(ηtu	uxx(ηtu	NOUN
ma-140	259	12	−	−	PROPN
ma-140	259	13	2ξtx	2ξtx	NUM
ma-140	259	14	)	)	PUNCT
ma-140	260	1	+	+	CCONJ
ma-140	260	2	u2	u2	NOUN
ma-140	260	3	x	x	SYM
ma-140	260	4	(	(	PUNCT
ma-140	260	5	ηtuu	ηtuu	VERB
ma-140	260	6	−	−	PROPN
ma-140	260	7	2ξtxu	2ξtxu	NUM
ma-140	260	8	)	)	PUNCT
ma-140	261	1	+	+	CCONJ
ma-140	261	2	utxx(ηu	utxx(ηu	PROPN
ma-140	261	3	−	−	PROPN
ma-140	261	4	τt	τt	NOUN
ma-140	261	5	−	−	PROPN
ma-140	261	6	2ξx	2ξx	ADJ
ma-140	261	7	)	)	PUNCT
ma-140	262	1	+	+	CCONJ
ma-140	262	2	utux(2ηxuu	utux(2ηxuu	ADJ
ma-140	262	3	−	−	PROPN
ma-140	262	4	ξxxu	ξxxu	NOUN
ma-140	262	5	−	−	PROPN
ma-140	262	6	2τtxu	2τtxu	NUM
ma-140	262	7	)	)	PUNCT
ma-140	263	1	+	+	CCONJ
ma-140	263	2	uxutx(2ηuu	uxutx(2ηuu	ADV
ma-140	263	3	−	−	PROPN
ma-140	264	1	4ξxu	4ξxu	PRON
ma-140	264	2	−	−	NOUN
ma-140	264	3	τtu	τtu	NUM
ma-140	264	4	)	)	PUNCT
ma-140	265	1	+	+	CCONJ
ma-140	265	2	utx(2ηxu	utx(2ηxu	VERB
ma-140	265	3	−	−	PROPN
ma-140	265	4	2τtx	2τtx	NUM
ma-140	265	5	−	−	PROPN
ma-140	265	6	ξxx	ξxx	NUM
ma-140	265	7	)	)	PUNCT
ma-140	265	8	+	+	CCONJ
ma-140	265	9	ut(ηxxu	ut(ηxxu	PROPN
ma-140	265	10	−	−	PROPN
ma-140	265	11	τtxx	τtxx	VERB
ma-140	265	12	)	)	PUNCT
ma-140	266	1	+	+	CCONJ
ma-140	266	2	utuxx(ηuu	utuxx(ηuu	ADJ
ma-140	266	3	−	−	NOUN
ma-140	266	4	2ξxu	2ξxu	NOUN
ma-140	266	5	−	−	NOUN
ma-140	266	6	τtu	τtu	ADV
ma-140	266	7	)	)	PUNCT
ma-140	267	1	+	+	CCONJ
ma-140	267	2	utu	utu	PROPN
ma-140	267	3	2	2	NUM
ma-140	267	4	x	x	X
ma-140	267	5	(	(	PUNCT
ma-140	267	6	ηuuu	ηuuu	NOUN
ma-140	267	7	−	−	PROPN
ma-140	267	8	2ξxuu	2ξxuu	NUM
ma-140	267	9	−	−	PROPN
ma-140	267	10	τtuu	τtuu	NOUN
ma-140	267	11	)	)	PUNCT
ma-140	268	1	+	+	CCONJ
ma-140	268	2	u2	u2	PROPN
ma-140	268	3	tx(−2τu	tx(−2τu	PROPN
ma-140	268	4	)	)	PUNCT
ma-140	268	5	ututxx(−2τu	ututxx(−2τu	ADJ
ma-140	268	6	)	)	PUNCT
ma-140	269	1	+	+	CCONJ
ma-140	269	2	ututx(−4τxu	ututx(−4τxu	NOUN
ma-140	269	3	)	)	PUNCT
ma-140	269	4	+	+	NUM
ma-140	269	5	u2	u2	PROPN
ma-140	269	6	t	t	PROPN
ma-140	269	7	(	(	PUNCT
ma-140	269	8	−τxxu	−τxxu	NUM
ma-140	269	9	)	)	PUNCT
ma-140	269	10	+	+	CCONJ
ma-140	269	11	uxu	uxu	PROPN
ma-140	269	12	2	2	NUM
ma-140	269	13	t	t	NOUN
ma-140	269	14	(	(	PUNCT
ma-140	269	15	−2τxuu	−2τxuu	NUM
ma-140	269	16	)	)	PUNCT
ma-140	269	17	+	+	CCONJ
ma-140	269	18	utuxutx(−4τuu	utuxutx(−4τuu	NOUN
ma-140	269	19	)	)	PUNCT
ma-140	269	20	,	,	PUNCT
ma-140	269	21	+	+	CCONJ
ma-140	269	22	u2	u2	PROPN
ma-140	269	23	xu	xu	PROPN
ma-140	269	24	2	2	NUM
ma-140	269	25	t	t	PROPN
ma-140	269	26	(	(	PUNCT
ma-140	269	27	−τuuu	−τuuu	NOUN
ma-140	269	28	)	)	PUNCT
ma-140	269	29	+	+	CCONJ
ma-140	269	30	uxxx(−ξt	uxxx(−ξt	ADJ
ma-140	269	31	)	)	PUNCT
ma-140	270	1	+	+	CCONJ
ma-140	270	2	u2	u2	PROPN
ma-140	270	3	t	t	PROPN
ma-140	270	4	uxx(−τuu	uxx(−τuu	PROPN
ma-140	270	5	)	)	PUNCT
ma-140	270	6	+	+	CCONJ
ma-140	270	7	uxuxx(−4ξtu	uxuxx(−4ξtu	VERB
ma-140	270	8	)	)	PUNCT
ma-140	270	9	+	+	NUM
ma-140	270	10	u3	u3	X
ma-140	270	11	x	x	SYM
ma-140	270	12	(	(	PUNCT
ma-140	270	13	−ξtuu	−ξtuu	NOUN
ma-140	270	14	)	)	PUNCT
ma-140	270	15	+	+	CCONJ
ma-140	270	16	uxxutx(−3ξu	uxxutx(−3ξu	NOUN
ma-140	270	17	)	)	PUNCT
ma-140	270	18	uxutxx(−2ξu	uxutxx(−2ξu	PROPN
ma-140	270	19	)	)	PUNCT
ma-140	271	1	+	+	CCONJ
ma-140	271	2	u2	u2	PROPN
ma-140	271	3	xutx(−3ξuu	xutx(−3ξuu	PROPN
ma-140	271	4	)	)	PUNCT
ma-140	271	5	+	+	CCONJ
ma-140	271	6	uxutuxx(−3ξuu	uxutuxx(−3ξuu	NOUN
ma-140	271	7	)	)	PUNCT
ma-140	271	8	+	+	CCONJ
ma-140	271	9	utu	utu	PROPN
ma-140	271	10	3	3	NUM
ma-140	271	11	x	x	SYM
ma-140	271	12	(	(	PUNCT
ma-140	271	13	−ξuuu	−ξuuu	NOUN
ma-140	271	14	)	)	PUNCT
ma-140	271	15	+	+	CCONJ
ma-140	271	16	utuxxx(−ξu	utuxxx(−ξu	ADV
ma-140	271	17	)	)	PUNCT
ma-140	271	18	+	+	CCONJ
ma-140	271	19	uttx(−2τx	uttx(−2τx	X
ma-140	271	20	)	)	PUNCT
ma-140	271	21	+	+	CCONJ
ma-140	271	22	utt(−τxx	utt(−τxx	NUM
ma-140	271	23	)	)	PUNCT
ma-140	271	24	+	+	CCONJ
ma-140	271	25	uxutt(−2τxu	uxutt(−2τxu	NOUN
ma-140	271	26	)	)	PUNCT
ma-140	271	27	+	+	CCONJ
ma-140	271	28	u2	u2	PROPN
ma-140	271	29	xutt(−τuu	xutt(−τuu	PROPN
ma-140	271	30	)	)	PUNCT
ma-140	272	1	+	+	PUNCT
ma-140	272	2	uxxutt(−τu	uxxutt(−τu	X
ma-140	272	3	)	)	PUNCT
ma-140	273	1	+	+	CCONJ
ma-140	273	2	uxuttx(−2τu	uxuttx(−2τu	ADJ
ma-140	273	3	−	−	PROPN
ma-140	273	4	ξu	ξu	NOUN
ma-140	273	5	)	)	PUNCT
ma-140	273	6	}	}	PUNCT
ma-140	273	7	∣∣∣∣∣	∣∣∣∣∣	SYM
ma-140	273	8	u	u	NOUN
ma-140	273	9	txx=−	txx=−	PROPN
ma-140	273	10	ut	ut	PROPN
ma-140	273	11	β	β	PROPN
ma-140	273	12	−α	−α	PROPN
ma-140	273	13	β	β	X
ma-140	273	14	uux	uux	PROPN
ma-140	273	15	=	=	SYM
ma-140	273	16	0	0	PUNCT
ma-140	273	17	(	(	PUNCT
ma-140	273	18	3.12	3.12	NUM
ma-140	273	19	)	)	PUNCT
ma-140	273	20	now	now	ADV
ma-140	273	21	replacing	replace	VERB
ma-140	273	22	utxx	utxx	NOUN
ma-140	273	23	by	by	ADP
ma-140	273	24	−utβ	−utβ	NOUN
ma-140	273	25	−	−	PROPN
ma-140	274	1	α	α	X
ma-140	274	2	β	β	PROPN
ma-140	274	3	uux	uux	PROPN
ma-140	274	4	in	in	ADP
ma-140	274	5	equation	equation	NOUN
ma-140	274	6	(	(	PUNCT
ma-140	274	7	3.12	3.12	NUM
ma-140	274	8	)	)	PUNCT
ma-140	274	9	,	,	PUNCT
ma-140	274	10	we	we	PRON
ma-140	274	11	have	have	VERB
ma-140	274	12	https://doi.org/10.28924/ada/ma.3.13	https://doi.org/10.28924/ada/ma.3.13	PROPN
ma-140	274	13	eur	eur	NOUN
ma-140	274	14	.	.	PUNCT
ma-140	275	1	j.	j.	PROPN
ma-140	275	2	math	math	PROPN
ma-140	275	3	.	.	PUNCT
ma-140	276	1	anal	anal	PROPN
ma-140	276	2	.	.	PUNCT
ma-140	277	1	10.28924	10.28924	NUM
ma-140	277	2	/	/	SYM
ma-140	277	3	ada	ada	PROPN
ma-140	277	4	/	/	SYM
ma-140	277	5	ma.3.13	ma.3.13	PROPN
ma-140	277	6	9	9	NUM
ma-140	277	7	ηt	ηt	ADP
ma-140	277	8	+	+	CCONJ
ma-140	277	9	ut(ηu	ut(ηu	PROPN
ma-140	277	10	−	−	PROPN
ma-140	277	11	τt	τt	NOUN
ma-140	277	12	)	)	PUNCT
ma-140	278	1	+	+	CCONJ
ma-140	278	2	ux(−ξt	ux(−ξt	X
ma-140	278	3	)	)	PUNCT
ma-140	279	1	+	+	CCONJ
ma-140	279	2	utux(−ξu	utux(−ξu	X
ma-140	279	3	)	)	PUNCT
ma-140	280	1	+	+	CCONJ
ma-140	280	2	u2	u2	PROPN
ma-140	280	3	t	t	PROPN
ma-140	280	4	(	(	PUNCT
ma-140	280	5	−τu	−τu	NOUN
ma-140	280	6	)	)	PUNCT
ma-140	280	7	+	+	CCONJ
ma-140	280	8	αηux	αηux	NOUN
ma-140	280	9	+	+	NUM
ma-140	280	10	αu{ηx	αu{ηx	NOUN
ma-140	281	1	+	+	CCONJ
ma-140	281	2	ux(ηu	ux(ηu	PROPN
ma-140	281	3	−	−	NUM
ma-140	281	4	ξx	ξx	NOUN
ma-140	281	5	)	)	PUNCT
ma-140	281	6	+	+	CCONJ
ma-140	281	7	ut(−τx	ut(−τx	X
ma-140	281	8	)	)	PUNCT
ma-140	282	1	+	+	CCONJ
ma-140	282	2	utux(−τu	utux(−τu	NUM
ma-140	282	3	)	)	PUNCT
ma-140	282	4	+	+	CCONJ
ma-140	282	5	u2	u2	NOUN
ma-140	282	6	x	x	SYM
ma-140	282	7	(	(	PUNCT
ma-140	282	8	−ξu	−ξu	ADV
ma-140	282	9	)	)	PUNCT
ma-140	282	10	}	}	PUNCT
ma-140	283	1	+	+	CCONJ
ma-140	283	2	β	β	X
ma-140	283	3	{	{	PUNCT
ma-140	283	4	ηtxx	ηtxx	NOUN
ma-140	283	5	+	+	CCONJ
ma-140	283	6	ux(2ηtxu	ux(2ηtxu	ADP
ma-140	283	7	−	−	NOUN
ma-140	283	8	ξtxx	ξtxx	NOUN
ma-140	283	9	)	)	PUNCT
ma-140	283	10	+	+	NUM
ma-140	283	11	uxx(ηtu	uxx(ηtu	NOUN
ma-140	283	12	−	−	PROPN
ma-140	283	13	2ξtx	2ξtx	NUM
ma-140	283	14	)	)	PUNCT
ma-140	284	1	+	+	CCONJ
ma-140	284	2	u2	u2	NOUN
ma-140	284	3	x	x	SYM
ma-140	284	4	(	(	PUNCT
ma-140	284	5	ηtuu	ηtuu	PROPN
ma-140	284	6	−	−	PROPN
ma-140	284	7	2ξtxu)+	2ξtxu)+	NUM
ma-140	284	8	[	[	PUNCT
ma-140	284	9	−	−	PROPN
ma-140	284	10	ut	ut	PROPN
ma-140	284	11	β	β	X
ma-140	284	12	−	−	PROPN
ma-140	284	13	α	α	X
ma-140	284	14	β	β	X
ma-140	284	15	uux	uux	PROPN
ma-140	284	16	]	]	PUNCT
ma-140	284	17	(	(	PUNCT
ma-140	284	18	ηu	ηu	X
ma-140	284	19	−	−	NOUN
ma-140	284	20	τt	τt	NOUN
ma-140	284	21	−	−	NOUN
ma-140	284	22	2ξx	2ξx	ADJ
ma-140	284	23	)	)	PUNCT
ma-140	285	1	+	+	CCONJ
ma-140	285	2	utux(2ηxuu	utux(2ηxuu	ADJ
ma-140	285	3	−	−	PROPN
ma-140	285	4	ξxxu	ξxxu	NOUN
ma-140	285	5	−	−	PROPN
ma-140	285	6	2τtxu	2τtxu	NUM
ma-140	285	7	)	)	PUNCT
ma-140	286	1	+	+	CCONJ
ma-140	286	2	uxutx(2ηuu	uxutx(2ηuu	ADV
ma-140	286	3	−	−	PROPN
ma-140	287	1	4ξxu	4ξxu	PRON
ma-140	287	2	−	−	NOUN
ma-140	287	3	τtu	τtu	NUM
ma-140	287	4	)	)	PUNCT
ma-140	288	1	+	+	CCONJ
ma-140	288	2	utx(2ηxu	utx(2ηxu	VERB
ma-140	288	3	−	−	PROPN
ma-140	288	4	2τtx	2τtx	NUM
ma-140	288	5	−	−	PROPN
ma-140	288	6	ξxx	ξxx	NUM
ma-140	288	7	)	)	PUNCT
ma-140	288	8	+	+	CCONJ
ma-140	288	9	ut(ηxxu	ut(ηxxu	PROPN
ma-140	288	10	−	−	PROPN
ma-140	288	11	τtxx	τtxx	VERB
ma-140	288	12	)	)	PUNCT
ma-140	289	1	+	+	CCONJ
ma-140	289	2	utuxx(ηuu	utuxx(ηuu	ADJ
ma-140	289	3	−	−	NOUN
ma-140	289	4	2ξxu	2ξxu	NOUN
ma-140	289	5	−	−	NOUN
ma-140	289	6	τtu	τtu	ADV
ma-140	289	7	)	)	PUNCT
ma-140	290	1	+	+	CCONJ
ma-140	290	2	utu	utu	PROPN
ma-140	290	3	2	2	NUM
ma-140	290	4	x	x	X
ma-140	290	5	(	(	PUNCT
ma-140	290	6	ηuuu	ηuuu	NOUN
ma-140	290	7	−	−	PROPN
ma-140	290	8	2ξxuu	2ξxuu	NUM
ma-140	290	9	−	−	PROPN
ma-140	290	10	τtuu	τtuu	NOUN
ma-140	290	11	)	)	PUNCT
ma-140	291	1	+	+	CCONJ
ma-140	291	2	u2	u2	PROPN
ma-140	291	3	tx(−2τu	tx(−2τu	PROPN
ma-140	291	4	)	)	PUNCT
ma-140	292	1	+	+	CCONJ
ma-140	292	2	ut	ut	PROPN
ma-140	292	3	[	[	PUNCT
ma-140	292	4	−	−	PROPN
ma-140	292	5	ut	ut	PROPN
ma-140	292	6	β	β	X
ma-140	292	7	−	−	PROPN
ma-140	292	8	α	α	X
ma-140	292	9	β	β	X
ma-140	292	10	uux	uux	PROPN
ma-140	292	11	]	]	PUNCT
ma-140	292	12	(	(	PUNCT
ma-140	292	13	−2τu	−2τu	NOUN
ma-140	292	14	)	)	PUNCT
ma-140	292	15	+	+	CCONJ
ma-140	292	16	ututx(−4τxu	ututx(−4τxu	NOUN
ma-140	292	17	)	)	PUNCT
ma-140	292	18	+	+	NUM
ma-140	292	19	u2	u2	PROPN
ma-140	292	20	t	t	PROPN
ma-140	292	21	(	(	PUNCT
ma-140	292	22	−τxxu	−τxxu	NUM
ma-140	292	23	)	)	PUNCT
ma-140	292	24	+	+	CCONJ
ma-140	292	25	uxu	uxu	PROPN
ma-140	292	26	2	2	NUM
ma-140	292	27	t	t	NOUN
ma-140	292	28	(	(	PUNCT
ma-140	292	29	−2τxuu	−2τxuu	NUM
ma-140	292	30	)	)	PUNCT
ma-140	292	31	+	+	CCONJ
ma-140	292	32	utuxutx(−4τuu	utuxutx(−4τuu	NOUN
ma-140	292	33	)	)	PUNCT
ma-140	292	34	,	,	PUNCT
ma-140	292	35	+	+	CCONJ
ma-140	292	36	u2	u2	PROPN
ma-140	292	37	xu	xu	PROPN
ma-140	292	38	2	2	NUM
ma-140	292	39	t	t	PROPN
ma-140	292	40	(	(	PUNCT
ma-140	292	41	−τuuu	−τuuu	NOUN
ma-140	292	42	)	)	PUNCT
ma-140	292	43	+	+	CCONJ
ma-140	292	44	uxxx(−ξt	uxxx(−ξt	ADJ
ma-140	292	45	)	)	PUNCT
ma-140	292	46	+	+	CCONJ
ma-140	292	47	u2	u2	PROPN
ma-140	292	48	t	t	PROPN
ma-140	292	49	uxx(−τuu	uxx(−τuu	PROPN
ma-140	292	50	)	)	PUNCT
ma-140	292	51	+	+	CCONJ
ma-140	292	52	uxuxx(−4ξtu	uxuxx(−4ξtu	VERB
ma-140	292	53	)	)	PUNCT
ma-140	292	54	+	+	NUM
ma-140	292	55	u3	u3	X
ma-140	292	56	x	x	SYM
ma-140	292	57	(	(	PUNCT
ma-140	292	58	−ξtuu	−ξtuu	NOUN
ma-140	292	59	)	)	PUNCT
ma-140	292	60	+	+	CCONJ
ma-140	292	61	uxxutx(−3ξu	uxxutx(−3ξu	NUM
ma-140	292	62	)	)	PUNCT
ma-140	292	63	ux	ux	NOUN
ma-140	292	64	[	[	PUNCT
ma-140	292	65	−	−	PROPN
ma-140	292	66	ut	ut	PROPN
ma-140	292	67	β	β	X
ma-140	292	68	−	−	PROPN
ma-140	292	69	α	α	X
ma-140	292	70	β	β	X
ma-140	292	71	uux	uux	PROPN
ma-140	292	72	]	]	PUNCT
ma-140	292	73	(	(	PUNCT
ma-140	292	74	−2ξu	−2ξu	PROPN
ma-140	292	75	)	)	PUNCT
ma-140	292	76	+	+	CCONJ
ma-140	292	77	u2	u2	PROPN
ma-140	292	78	xutx(−3ξuu	xutx(−3ξuu	PROPN
ma-140	292	79	)	)	PUNCT
ma-140	292	80	+	+	CCONJ
ma-140	292	81	uxutuxx(−3ξuu	uxutuxx(−3ξuu	NOUN
ma-140	292	82	)	)	PUNCT
ma-140	292	83	+	+	CCONJ
ma-140	292	84	utu	utu	PROPN
ma-140	292	85	3	3	NUM
ma-140	292	86	x	x	SYM
ma-140	292	87	(	(	PUNCT
ma-140	292	88	−ξuuu	−ξuuu	NOUN
ma-140	292	89	)	)	PUNCT
ma-140	292	90	+	+	CCONJ
ma-140	292	91	utuxxx(−ξu	utuxxx(−ξu	ADV
ma-140	292	92	)	)	PUNCT
ma-140	292	93	+	+	CCONJ
ma-140	292	94	uttx(−2τx	uttx(−2τx	X
ma-140	292	95	)	)	PUNCT
ma-140	292	96	+	+	CCONJ
ma-140	292	97	utt(−τxx	utt(−τxx	NUM
ma-140	292	98	)	)	PUNCT
ma-140	292	99	+	+	CCONJ
ma-140	292	100	uxutt(−2τxu	uxutt(−2τxu	NOUN
ma-140	292	101	)	)	PUNCT
ma-140	292	102	+	+	CCONJ
ma-140	292	103	u2	u2	PROPN
ma-140	292	104	xutt(−τuu	xutt(−τuu	PROPN
ma-140	292	105	)	)	PUNCT
ma-140	293	1	+	+	PUNCT
ma-140	293	2	uxxutt(−τu	uxxutt(−τu	X
ma-140	293	3	)	)	PUNCT
ma-140	294	1	+	+	CCONJ
ma-140	294	2	uxuttx(−2τu	uxuttx(−2τu	ADJ
ma-140	294	3	−	−	PROPN
ma-140	294	4	ξu	ξu	NOUN
ma-140	294	5	)	)	PUNCT
ma-140	294	6	}	}	PUNCT
ma-140	295	1	=	=	SYM
ma-140	295	2	0	0	PUNCT
ma-140	295	3	(	(	PUNCT
ma-140	295	4	3.13	3.13	NUM
ma-140	295	5	)	)	PUNCT
ma-140	295	6	which	which	PRON
ma-140	295	7	can	can	AUX
ma-140	295	8	be	be	AUX
ma-140	295	9	written	write	VERB
ma-140	295	10	as	as	ADP
ma-140	295	11	ηt	ηt	ADP
ma-140	295	12	+	+	CCONJ
ma-140	295	13	αuηx	αuηx	NOUN
ma-140	295	14	+	+	CCONJ
ma-140	295	15	βηtxx	βηtxx	X
ma-140	296	1	+	+	CCONJ
ma-140	296	2	ut(βηxxu	ut(βηxxu	PROPN
ma-140	296	3	−	−	NOUN
ma-140	296	4	βτtxx	βτtxx	NOUN
ma-140	296	5	+	+	CCONJ
ma-140	296	6	2ξx	2ξx	ADJ
ma-140	296	7	−	−	NOUN
ma-140	296	8	αuτx	αuτx	NOUN
ma-140	296	9	)	)	PUNCT
ma-140	297	1	+	+	CCONJ
ma-140	297	2	ux	ux	PROPN
ma-140	297	3	(	(	PUNCT
ma-140	297	4	2βηtxu	2βηtxu	NUM
ma-140	297	5	−	−	PROPN
ma-140	297	6	βξtxx	βξtxx	VERB
ma-140	297	7	−	−	PROPN
ma-140	297	8	ξt	ξt	SYM
ma-140	297	9	+	+	NUM
ma-140	297	10	αuξx	αuξx	NOUN
ma-140	297	11	+	+	CCONJ
ma-140	297	12	αuτt	αuτt	NOUN
ma-140	297	13	+	+	CCONJ
ma-140	297	14	αη	αη	X
ma-140	297	15	)	)	PUNCT
ma-140	298	1	+	+	CCONJ
ma-140	298	2	utux(2ξu	utux(2ξu	PROPN
ma-140	298	3	+	+	CCONJ
ma-140	298	4	2βηxuu	2βηxuu	NUM
ma-140	298	5	−	−	NOUN
ma-140	298	6	βξxxu	βξxxu	ADJ
ma-140	298	7	−	−	PROPN
ma-140	298	8	2βτtxu	2βτtxu	NUM
ma-140	298	9	+	+	CCONJ
ma-140	298	10	αuτu	αuτu	ADJ
ma-140	298	11	)	)	PUNCT
ma-140	299	1	+	+	CCONJ
ma-140	299	2	u2	u2	PROPN
ma-140	299	3	t	t	PROPN
ma-140	299	4	(	(	PUNCT
ma-140	299	5	τu	τu	ADP
ma-140	299	6	−	−	PROPN
ma-140	299	7	βτxxu)+	βτxxu)+	PUNCT
ma-140	299	8	u2	u2	PROPN
ma-140	299	9	x	x	X
ma-140	299	10	(	(	PUNCT
ma-140	299	11	2αuξu	2αuξu	NUM
ma-140	299	12	+	+	CCONJ
ma-140	299	13	βηtuu	βηtuu	ADJ
ma-140	299	14	−	−	NOUN
ma-140	299	15	2βξtxu	2βξtxu	NUM
ma-140	299	16	)	)	PUNCT
ma-140	300	1	+	+	CCONJ
ma-140	300	2	β	β	X
ma-140	300	3	{	{	PUNCT
ma-140	300	4	uxx(ηtu	uxx(ηtu	NOUN
ma-140	300	5	−	−	PROPN
ma-140	300	6	2ξtx	2ξtx	NUM
ma-140	300	7	)	)	PUNCT
ma-140	300	8	+	+	CCONJ
ma-140	301	1	uxutx(2ηuu	uxutx(2ηuu	ADV
ma-140	301	2	−	−	PROPN
ma-140	302	1	4ξxu	4ξxu	PRON
ma-140	302	2	−	−	NOUN
ma-140	302	3	τtu	τtu	NUM
ma-140	302	4	)	)	PUNCT
ma-140	303	1	+	+	CCONJ
ma-140	303	2	utx(2ηxu	utx(2ηxu	VERB
ma-140	303	3	−	−	PROPN
ma-140	303	4	2τtx	2τtx	NUM
ma-140	303	5	−	−	PROPN
ma-140	303	6	ξxx	ξxx	NUM
ma-140	303	7	)	)	PUNCT
ma-140	303	8	+	+	CCONJ
ma-140	303	9	utuxx(ηuu	utuxx(ηuu	ADJ
ma-140	303	10	−	−	NOUN
ma-140	303	11	2ξxu	2ξxu	NOUN
ma-140	303	12	−	−	NOUN
ma-140	303	13	τtu	τtu	ADV
ma-140	303	14	)	)	PUNCT
ma-140	304	1	+	+	CCONJ
ma-140	304	2	utu	utu	PROPN
ma-140	304	3	2	2	NUM
ma-140	304	4	x	x	X
ma-140	304	5	(	(	PUNCT
ma-140	304	6	ηuuu	ηuuu	NOUN
ma-140	304	7	−	−	PROPN
ma-140	304	8	2ξxuu	2ξxuu	NUM
ma-140	304	9	−	−	PROPN
ma-140	304	10	τtuu	τtuu	NOUN
ma-140	304	11	)	)	PUNCT
ma-140	305	1	+	+	CCONJ
ma-140	305	2	u2	u2	PROPN
ma-140	305	3	tx(−2τu	tx(−2τu	PROPN
ma-140	305	4	)	)	PUNCT
ma-140	305	5	+	+	CCONJ
ma-140	305	6	ututx(−4τxu	ututx(−4τxu	NOUN
ma-140	305	7	)	)	PUNCT
ma-140	305	8	+	+	CCONJ
ma-140	305	9	uxu	uxu	PROPN
ma-140	305	10	2	2	NUM
ma-140	305	11	t	t	NOUN
ma-140	305	12	(	(	PUNCT
ma-140	305	13	−2τxuu	−2τxuu	NUM
ma-140	305	14	)	)	PUNCT
ma-140	305	15	+	+	CCONJ
ma-140	305	16	utuxutx(−4τuu	utuxutx(−4τuu	NOUN
ma-140	305	17	)	)	PUNCT
ma-140	305	18	,	,	PUNCT
ma-140	305	19	+	+	CCONJ
ma-140	305	20	u2	u2	PROPN
ma-140	305	21	xu	xu	PROPN
ma-140	305	22	2	2	NUM
ma-140	305	23	t	t	PROPN
ma-140	305	24	(	(	PUNCT
ma-140	305	25	−τuuu	−τuuu	NOUN
ma-140	305	26	)	)	PUNCT
ma-140	305	27	+	+	CCONJ
ma-140	305	28	uxxx(−ξt	uxxx(−ξt	ADJ
ma-140	305	29	)	)	PUNCT
ma-140	305	30	+	+	CCONJ
ma-140	305	31	u2	u2	PROPN
ma-140	305	32	t	t	PROPN
ma-140	305	33	uxx(−τuu	uxx(−τuu	PROPN
ma-140	305	34	)	)	PUNCT
ma-140	306	1	+	+	CCONJ
ma-140	306	2	uxuxx(−3ξtu	uxuxx(−3ξtu	NOUN
ma-140	306	3	)	)	PUNCT
ma-140	306	4	+	+	NUM
ma-140	306	5	u3	u3	X
ma-140	306	6	x	x	SYM
ma-140	306	7	(	(	PUNCT
ma-140	306	8	−ξtuu	−ξtuu	NOUN
ma-140	306	9	)	)	PUNCT
ma-140	306	10	+	+	CCONJ
ma-140	306	11	uxxutx(−3ξu	uxxutx(−3ξu	NUM
ma-140	306	12	)	)	PUNCT
ma-140	307	1	+	+	CCONJ
ma-140	307	2	u2	u2	PROPN
ma-140	307	3	xutx(−3ξuu	xutx(−3ξuu	PROPN
ma-140	307	4	)	)	PUNCT
ma-140	307	5	+	+	CCONJ
ma-140	307	6	uxutuxx(−3ξuu	uxutuxx(−3ξuu	NOUN
ma-140	307	7	)	)	PUNCT
ma-140	307	8	+	+	CCONJ
ma-140	307	9	utu	utu	PROPN
ma-140	307	10	3	3	NUM
ma-140	307	11	x	x	SYM
ma-140	307	12	(	(	PUNCT
ma-140	307	13	−ξuuu	−ξuuu	NOUN
ma-140	307	14	)	)	PUNCT
ma-140	307	15	+	+	CCONJ
ma-140	307	16	utuxxx(−ξu	utuxxx(−ξu	ADV
ma-140	307	17	)	)	PUNCT
ma-140	307	18	+	+	CCONJ
ma-140	307	19	uttx(−2τx	uttx(−2τx	X
ma-140	307	20	)	)	PUNCT
ma-140	307	21	+	+	CCONJ
ma-140	307	22	utt(−τxx	utt(−τxx	NUM
ma-140	307	23	)	)	PUNCT
ma-140	307	24	+	+	CCONJ
ma-140	307	25	uxutt(−2τxu	uxutt(−2τxu	NOUN
ma-140	307	26	)	)	PUNCT
ma-140	307	27	+	+	CCONJ
ma-140	307	28	u2	u2	PROPN
ma-140	307	29	xutt(−τuu	xutt(−τuu	PROPN
ma-140	307	30	)	)	PUNCT
ma-140	308	1	+	+	PUNCT
ma-140	308	2	uxxutt(−τu	uxxutt(−τu	X
ma-140	308	3	)	)	PUNCT
ma-140	309	1	+	+	CCONJ
ma-140	309	2	uxuttx(−2τu	uxuttx(−2τu	X
ma-140	309	3	)	)	PUNCT
ma-140	309	4	}	}	PUNCT
ma-140	310	1	=	=	SYM
ma-140	310	2	0	0	NUM
ma-140	310	3	(	(	PUNCT
ma-140	310	4	3.14	3.14	NUM
ma-140	310	5	)	)	PUNCT
ma-140	310	6	https://doi.org/10.28924/ada/ma.3.13	https://doi.org/10.28924/ada/ma.3.13	PROPN
ma-140	310	7	eur	eur	NOUN
ma-140	310	8	.	.	PUNCT
ma-140	311	1	j.	j.	PROPN
ma-140	311	2	math	math	PROPN
ma-140	311	3	.	.	PUNCT
ma-140	312	1	anal	anal	PROPN
ma-140	312	2	.	.	PUNCT
ma-140	313	1	10.28924	10.28924	NUM
ma-140	313	2	/	/	SYM
ma-140	313	3	ada	ada	PROPN
ma-140	313	4	/	/	SYM
ma-140	313	5	ma.3.13	ma.3.13	PROPN
ma-140	313	6	10since	10since	NUM
ma-140	314	1	the	the	DET
ma-140	314	2	functions	function	NOUN
ma-140	314	3	τ	τ	PROPN
ma-140	314	4	,	,	PUNCT
ma-140	314	5	ξ	ξ	PROPN
ma-140	314	6	and	and	CCONJ
ma-140	314	7	η	η	PROPN
ma-140	314	8	depend	depend	VERB
ma-140	314	9	only	only	ADV
ma-140	314	10	on	on	ADP
ma-140	314	11	t	t	PROPN
ma-140	314	12	,	,	PUNCT
ma-140	314	13	x	x	X
ma-140	314	14	and	and	CCONJ
ma-140	314	15	u	u	PROPN
ma-140	314	16	and	and	CCONJ
ma-140	314	17	are	be	AUX
ma-140	314	18	independent	independent	ADJ
ma-140	314	19	of	of	ADP
ma-140	314	20	the	the	DET
ma-140	314	21	derivativesof	derivativesof	NOUN
ma-140	314	22	u	u	NOUN
ma-140	314	23	,	,	PUNCT
ma-140	314	24	we	we	PRON
ma-140	314	25	can	can	AUX
ma-140	314	26	then	then	ADV
ma-140	314	27	split	split	VERB
ma-140	314	28	the	the	DET
ma-140	314	29	above	above	ADJ
ma-140	314	30	equation	equation	NOUN
ma-140	314	31	on	on	ADP
ma-140	314	32	the	the	DET
ma-140	314	33	derivatives	derivative	NOUN
ma-140	314	34	of	of	ADP
ma-140	314	35	u	u	NOUN
ma-140	314	36	and	and	CCONJ
ma-140	314	37	obtain	obtain	VERB
ma-140	314	38	τx	τx	ADP
ma-140	314	39	=	=	SYM
ma-140	314	40	τu	τu	ADP
ma-140	314	41	=	=	ADJ
ma-140	315	1	ξu	ξu	PROPN
ma-140	315	2	=	=	SYM
ma-140	315	3	ξt	ξt	PROPN
ma-140	315	4	=	=	SYM
ma-140	315	5	ξx	ξx	PROPN
ma-140	315	6	=	=	PUNCT
ma-140	315	7	ηuu	ηuu	NOUN
ma-140	315	8	=	=	NOUN
ma-140	315	9	ηtu	ηtu	ADP
ma-140	315	10	=	=	PROPN
ma-140	315	11	0	0	PROPN
ma-140	315	12	,	,	PUNCT
ma-140	315	13	(	(	PUNCT
ma-140	315	14	3.15	3.15	NUM
ma-140	315	15	)	)	PUNCT
ma-140	315	16	η	η	PROPN
ma-140	315	17	+	+	CCONJ
ma-140	315	18	uτt	uτt	ADJ
ma-140	315	19	=	=	NOUN
ma-140	315	20	0	0	NUM
ma-140	315	21	,	,	PUNCT
ma-140	315	22	(	(	PUNCT
ma-140	315	23	3.16	3.16	NUM
ma-140	315	24	)	)	PUNCT
ma-140	315	25	ηt	ηt	ADP
ma-140	315	26	+	+	ADJ
ma-140	315	27	αuηx	αuηx	NOUN
ma-140	315	28	+	+	CCONJ
ma-140	315	29	βηtxx	βηtxx	X
ma-140	315	30	=	=	X
ma-140	315	31	0	0	NUM
ma-140	315	32	(	(	PUNCT
ma-140	315	33	3.17	3.17	NUM
ma-140	315	34	)	)	PUNCT
ma-140	315	35	from	from	ADP
ma-140	315	36	equation	equation	NOUN
ma-140	315	37	(	(	PUNCT
ma-140	315	38	3.15	3.15	NUM
ma-140	315	39	)	)	PUNCT
ma-140	315	40	,	,	PUNCT
ma-140	315	41	we	we	PRON
ma-140	315	42	find	find	VERB
ma-140	315	43	that	that	SCONJ
ma-140	315	44	τ	τ	PROPN
ma-140	315	45	=	=	SYM
ma-140	315	46	τ(t	τ(t	PROPN
ma-140	315	47	)	)	PUNCT
ma-140	315	48	,	,	PUNCT
ma-140	315	49	(	(	PUNCT
ma-140	315	50	3.18	3.18	NUM
ma-140	315	51	)	)	PUNCT
ma-140	315	52	ξ	ξ	PROPN
ma-140	315	53	=	=	SYM
ma-140	315	54	c1	c1	PROPN
ma-140	315	55	,	,	PUNCT
ma-140	315	56	(	(	PUNCT
ma-140	315	57	3.19	3.19	NUM
ma-140	315	58	)	)	PUNCT
ma-140	315	59	η	η	NOUN
ma-140	315	60	=	=	PROPN
ma-140	315	61	a(x)u	a(x)u	PROPN
ma-140	315	62	+	+	CCONJ
ma-140	315	63	b(t	b(t	PROPN
ma-140	315	64	,	,	PUNCT
ma-140	315	65	x	x	NOUN
ma-140	315	66	)	)	PUNCT
ma-140	315	67	.	.	PUNCT
ma-140	316	1	(	(	PUNCT
ma-140	316	2	3.20	3.20	NUM
ma-140	316	3	)	)	PUNCT
ma-140	316	4	now	now	ADV
ma-140	316	5	substituting	substitute	VERB
ma-140	316	6	η	η	PROPN
ma-140	316	7	into	into	ADP
ma-140	316	8	equation	equation	NOUN
ma-140	316	9	(	(	PUNCT
ma-140	316	10	3.17	3.17	NUM
ma-140	316	11	)	)	PUNCT
ma-140	316	12	yields	yield	NOUN
ma-140	316	13	bt(t	bt(t	NOUN
ma-140	316	14	,	,	PUNCT
ma-140	316	15	x	x	X
ma-140	316	16	)	)	PUNCT
ma-140	316	17	+	+	NUM
ma-140	316	18	αu	αu	ADJ
ma-140	316	19	[	[	PUNCT
ma-140	316	20	a(x)xu	a(x)xu	X
ma-140	316	21	+	+	CCONJ
ma-140	316	22	bx(t	bx(t	PROPN
ma-140	316	23	,	,	PUNCT
ma-140	316	24	x	x	NOUN
ma-140	316	25	)	)	PUNCT
ma-140	316	26	]	]	PUNCT
ma-140	317	1	+	+	CCONJ
ma-140	317	2	βbtxx(t	βbtxx(t	NUM
ma-140	317	3	,	,	PUNCT
ma-140	317	4	x	x	NOUN
ma-140	317	5	)	)	PUNCT
ma-140	317	6	=	=	SYM
ma-140	317	7	0	0	X
ma-140	317	8	.	.	PUNCT
ma-140	318	1	(	(	PUNCT
ma-140	318	2	3.21	3.21	NUM
ma-140	318	3	)	)	PUNCT
ma-140	318	4	separation	separation	NOUN
ma-140	318	5	of	of	ADP
ma-140	318	6	(	(	PUNCT
ma-140	318	7	3.21	3.21	NUM
ma-140	318	8	)	)	PUNCT
ma-140	318	9	on	on	ADP
ma-140	318	10	powers	power	NOUN
ma-140	318	11	of	of	ADP
ma-140	318	12	u	u	PRON
ma-140	318	13	gives	give	VERB
ma-140	318	14	the	the	DET
ma-140	318	15	following	follow	VERB
ma-140	318	16	equations	equation	NOUN
ma-140	318	17	u2	u2	NOUN
ma-140	318	18	:	:	PUNCT
ma-140	318	19	a(x)x	a(x)x	PROPN
ma-140	318	20	=	=	SYM
ma-140	318	21	0	0	NUM
ma-140	318	22	,	,	PUNCT
ma-140	318	23	(	(	PUNCT
ma-140	318	24	3.22	3.22	NUM
ma-140	318	25	)	)	PUNCT
ma-140	318	26	u	u	NOUN
ma-140	318	27	:	:	PUNCT
ma-140	318	28	bx(t	bx(t	PROPN
ma-140	318	29	,	,	PUNCT
ma-140	318	30	x	x	NOUN
ma-140	318	31	)	)	PUNCT
ma-140	318	32	=	=	SYM
ma-140	318	33	0	0	NUM
ma-140	318	34	,	,	PUNCT
ma-140	318	35	(	(	PUNCT
ma-140	318	36	3.23	3.23	NUM
ma-140	318	37	)	)	PUNCT
ma-140	318	38	u0	u0	ADJ
ma-140	318	39	:	:	PUNCT
ma-140	318	40	bt(t	bt(t	NOUN
ma-140	318	41	,	,	PUNCT
ma-140	318	42	x	x	X
ma-140	318	43	)	)	PUNCT
ma-140	318	44	+	+	CCONJ
ma-140	318	45	βbtxx(t	βbtxx(t	NUM
ma-140	318	46	,	,	PUNCT
ma-140	318	47	x	x	NOUN
ma-140	318	48	)	)	PUNCT
ma-140	318	49	=	=	SYM
ma-140	318	50	0	0	X
ma-140	318	51	.	.	PUNCT
ma-140	319	1	(	(	PUNCT
ma-140	319	2	3.24	3.24	NUM
ma-140	319	3	)	)	PUNCT
ma-140	319	4	integration	integration	NOUN
ma-140	319	5	of	of	ADP
ma-140	319	6	equations	equation	NOUN
ma-140	319	7	(	(	PUNCT
ma-140	319	8	3.22	3.22	NUM
ma-140	319	9	)	)	PUNCT
ma-140	319	10	and	and	CCONJ
ma-140	319	11	(	(	PUNCT
ma-140	319	12	3.23	3.23	NUM
ma-140	319	13	)	)	PUNCT
ma-140	319	14	with	with	ADP
ma-140	319	15	respect	respect	NOUN
ma-140	319	16	to	to	ADP
ma-140	319	17	x	x	X
ma-140	319	18	gives	give	VERB
ma-140	319	19	that	that	PRON
ma-140	319	20	a(x	a(x	NOUN
ma-140	319	21	)	)	PUNCT
ma-140	319	22	=	=	SYM
ma-140	319	23	c2	c2	PROPN
ma-140	319	24	(	(	PUNCT
ma-140	319	25	3.25	3.25	NUM
ma-140	319	26	)	)	PUNCT
ma-140	319	27	b(t	b(t	PROPN
ma-140	319	28	,	,	PUNCT
ma-140	319	29	x	x	NOUN
ma-140	319	30	)	)	PUNCT
ma-140	319	31	=	=	SYM
ma-140	319	32	b(t	b(t	PROPN
ma-140	319	33	)	)	PUNCT
ma-140	319	34	.	.	PUNCT
ma-140	320	1	(	(	PUNCT
ma-140	320	2	3.26	3.26	NUM
ma-140	320	3	)	)	PUNCT
ma-140	320	4	now	now	ADV
ma-140	320	5	use	use	VERB
ma-140	320	6	equation	equation	NOUN
ma-140	320	7	(	(	PUNCT
ma-140	320	8	3.26	3.26	NUM
ma-140	320	9	)	)	PUNCT
ma-140	320	10	in	in	ADP
ma-140	320	11	equation	equation	NOUN
ma-140	320	12	(	(	PUNCT
ma-140	320	13	3.24	3.24	NUM
ma-140	320	14	)	)	PUNCT
ma-140	320	15	to	to	PART
ma-140	320	16	obtain	obtain	VERB
ma-140	320	17	btxx(t	btxx(t	PROPN
ma-140	320	18	,	,	PUNCT
ma-140	320	19	x	x	NOUN
ma-140	320	20	)	)	PUNCT
ma-140	320	21	=	=	SYM
ma-140	320	22	0	0	NUM
ma-140	320	23	and	and	CCONJ
ma-140	320	24	as	as	ADP
ma-140	320	25	a	a	DET
ma-140	320	26	result	result	NOUN
ma-140	320	27	bt(t	bt(t	NOUN
ma-140	320	28	,	,	PUNCT
ma-140	320	29	x	x	X
ma-140	320	30	)	)	PUNCT
ma-140	320	31	=	=	SYM
ma-140	320	32	0	0	X
ma-140	320	33	.	.	PUNCT
ma-140	321	1	(	(	PUNCT
ma-140	321	2	3.27	3.27	NUM
ma-140	321	3	)	)	PUNCT
ma-140	321	4	integrating	integrate	VERB
ma-140	321	5	equation	equation	NOUN
ma-140	321	6	(	(	PUNCT
ma-140	321	7	3.27	3.27	NUM
ma-140	321	8	)	)	PUNCT
ma-140	321	9	with	with	ADP
ma-140	321	10	respect	respect	NOUN
ma-140	321	11	to	to	ADP
ma-140	321	12	t	t	PROPN
ma-140	321	13	gives	give	VERB
ma-140	321	14	b(t	b(t	PROPN
ma-140	321	15	,	,	PUNCT
ma-140	321	16	x	x	X
ma-140	321	17	)	)	PUNCT
ma-140	321	18	=	=	SYM
ma-140	321	19	c3	c3	PROPN
ma-140	321	20	.	.	PUNCT
ma-140	322	1	(	(	PUNCT
ma-140	322	2	3.28	3.28	NUM
ma-140	322	3	)	)	PUNCT
ma-140	322	4	if	if	SCONJ
ma-140	322	5	we	we	PRON
ma-140	322	6	substitute	substitute	VERB
ma-140	322	7	η	η	PROPN
ma-140	322	8	=	=	PROPN
ma-140	322	9	c2u	c2u	X
ma-140	322	10	+	+	CCONJ
ma-140	322	11	c3	c3	NOUN
ma-140	322	12	into	into	ADP
ma-140	322	13	equation	equation	NOUN
ma-140	322	14	(	(	PUNCT
ma-140	322	15	3.16	3.16	NUM
ma-140	322	16	)	)	PUNCT
ma-140	322	17	,	,	PUNCT
ma-140	322	18	we	we	PRON
ma-140	322	19	have	have	VERB
ma-140	322	20	c2u	c2u	X
ma-140	322	21	+	+	CCONJ
ma-140	322	22	c3	c3	X
ma-140	323	1	+	+	X
ma-140	323	2	τtu	τtu	CCONJ
ma-140	323	3	=	=	SYM
ma-140	323	4	0	0	X
ma-140	323	5	.	.	PUNCT
ma-140	324	1	(	(	PUNCT
ma-140	324	2	3.29	3.29	NUM
ma-140	324	3	)	)	PUNCT
ma-140	324	4	from	from	ADP
ma-140	324	5	equation	equation	NOUN
ma-140	324	6	(	(	PUNCT
ma-140	324	7	3.29	3.29	NUM
ma-140	324	8	)	)	PUNCT
ma-140	324	9	,	,	PUNCT
ma-140	324	10	if	if	SCONJ
ma-140	324	11	we	we	PRON
ma-140	324	12	obtain	obtain	VERB
ma-140	324	13	τ(t	τ(t	NOUN
ma-140	324	14	)	)	PUNCT
ma-140	325	1	=	=	SYM
ma-140	325	2	−c2	−c2	PROPN
ma-140	325	3	t	t	PROPN
ma-140	325	4	−	−	PROPN
ma-140	326	1	c3	c3	PROPN
ma-140	326	2	t	t	PROPN
ma-140	326	3	u	u	PROPN
ma-140	326	4	+	+	X
ma-140	326	5	c4	c4	NOUN
ma-140	326	6	.	.	PUNCT
ma-140	327	1	(	(	PUNCT
ma-140	327	2	3.30	3.30	NUM
ma-140	327	3	)	)	PUNCT
ma-140	327	4	https://doi.org/10.28924/ada/ma.3.13	https://doi.org/10.28924/ada/ma.3.13	PROPN
ma-140	327	5	eur	eur	NOUN
ma-140	327	6	.	.	PUNCT
ma-140	328	1	j.	j.	PROPN
ma-140	328	2	math	math	PROPN
ma-140	328	3	.	.	PUNCT
ma-140	329	1	anal	anal	PROPN
ma-140	329	2	.	.	PUNCT
ma-140	330	1	10.28924	10.28924	NUM
ma-140	330	2	/	/	SYM
ma-140	330	3	ada	ada	PROPN
ma-140	330	4	/	/	SYM
ma-140	330	5	ma.3.13	ma.3.13	PROPN
ma-140	330	6	11and	11and	NOUN
ma-140	330	7	finally	finally	ADV
ma-140	330	8	;	;	PUNCT
ma-140	331	1	τ	τ	PROPN
ma-140	331	2	=	=	NOUN
ma-140	331	3	−	−	PROPN
ma-140	331	4	c2	c2	PROPN
ma-140	331	5	t	t	PROPN
ma-140	331	6	−	−	PROPN
ma-140	332	1	c3	c3	PROPN
ma-140	332	2	t	t	PROPN
ma-140	332	3	u	u	PROPN
ma-140	332	4	+	+	CCONJ
ma-140	332	5	c4	c4	NOUN
ma-140	332	6	,	,	PUNCT
ma-140	332	7	(	(	PUNCT
ma-140	332	8	3.31	3.31	NUM
ma-140	332	9	)	)	PUNCT
ma-140	332	10	ξ	ξ	PROPN
ma-140	333	1	=	=	PROPN
ma-140	333	2	c1	c1	PROPN
ma-140	333	3	(	(	PUNCT
ma-140	333	4	3.32	3.32	NUM
ma-140	333	5	)	)	PUNCT
ma-140	333	6	η	η	X
ma-140	333	7	=	=	PRON
ma-140	333	8	c2u	c2u	X
ma-140	333	9	+	+	X
ma-140	333	10	c3	c3	PROPN
ma-140	333	11	.	.	PUNCT
ma-140	334	1	(	(	PUNCT
ma-140	334	2	3.33	3.33	NUM
ma-140	334	3	)	)	PUNCT
ma-140	334	4	we	we	PRON
ma-140	334	5	have	have	AUX
ma-140	334	6	obtained	obtain	VERB
ma-140	334	7	a	a	DET
ma-140	334	8	four	four	NUM
ma-140	334	9	-	-	PUNCT
ma-140	334	10	dimensional	dimensional	ADJ
ma-140	334	11	lie	lie	NOUN
ma-140	334	12	algebra	algebra	NOUN
ma-140	334	13	of	of	ADP
ma-140	334	14	symmetries	symmetry	NOUN
ma-140	334	15	spanned	span	VERB
ma-140	334	16	by	by	ADP
ma-140	334	17	x1	x1	PROPN
ma-140	334	18	=	=	SYM
ma-140	334	19	∂	∂	NUM
ma-140	334	20	∂x	∂x	PROPN
ma-140	334	21	,	,	PUNCT
ma-140	334	22	(	(	PUNCT
ma-140	334	23	3.34	3.34	NUM
ma-140	334	24	)	)	PUNCT
ma-140	334	25	x2	x2	NOUN
ma-140	335	1	=	=	PUNCT
ma-140	335	2	u	u	NOUN
ma-140	335	3	∂	∂	NOUN
ma-140	335	4	∂u	∂u	PROPN
ma-140	335	5	−	−	PROPN
ma-140	335	6	t	t	PROPN
ma-140	335	7	∂	∂	NOUN
ma-140	335	8	∂t	∂t	PROPN
ma-140	335	9	,	,	PUNCT
ma-140	335	10	(	(	PUNCT
ma-140	335	11	3.35	3.35	NUM
ma-140	335	12	)	)	PUNCT
ma-140	335	13	x3	x3	NOUN
ma-140	335	14	=	=	SYM
ma-140	335	15	∂	∂	NUM
ma-140	335	16	∂u	∂u	PROPN
ma-140	335	17	−	−	PROPN
ma-140	335	18	t	t	PROPN
ma-140	335	19	u	u	PROPN
ma-140	335	20	∂	∂	NOUN
ma-140	335	21	∂t	∂t	PROPN
ma-140	335	22	,	,	PUNCT
ma-140	335	23	(	(	PUNCT
ma-140	335	24	3.36	3.36	NUM
ma-140	335	25	)	)	PUNCT
ma-140	335	26	x4	x4	PROPN
ma-140	335	27	=	=	SYM
ma-140	335	28	∂	∂	NUM
ma-140	335	29	∂t	∂t	PROPN
ma-140	335	30	.	.	PUNCT
ma-140	336	1	(	(	PUNCT
ma-140	336	2	3.37	3.37	NUM
ma-140	336	3	)	)	PUNCT
ma-140	336	4	3.2	3.2	NUM
ma-140	336	5	.	.	PUNCT
ma-140	337	1	commutator	commutator	NOUN
ma-140	337	2	table	table	NOUN
ma-140	337	3	for	for	ADP
ma-140	337	4	symmetries	symmetry	NOUN
ma-140	337	5	.	.	PUNCT
ma-140	338	1	we	we	PRON
ma-140	338	2	evaluate	evaluate	VERB
ma-140	338	3	the	the	DET
ma-140	338	4	commutation	commutation	NOUN
ma-140	338	5	relations	relation	NOUN
ma-140	338	6	for	for	ADP
ma-140	338	7	the	the	DET
ma-140	338	8	symmetrygenerators	symmetrygenerator	NOUN
ma-140	338	9	.	.	PUNCT
ma-140	339	1	by	by	ADP
ma-140	339	2	definition	definition	NOUN
ma-140	339	3	of	of	ADP
ma-140	339	4	lie	lie	NOUN
ma-140	339	5	bracket	bracket	NOUN
ma-140	339	6	[	[	X
ma-140	339	7	9	9	NUM
ma-140	339	8	]	]	PUNCT
ma-140	339	9	,	,	PUNCT
ma-140	339	10	for	for	ADP
ma-140	339	11	example	example	NOUN
ma-140	339	12	,	,	PUNCT
ma-140	339	13	we	we	PRON
ma-140	339	14	have	have	VERB
ma-140	339	15	that	that	PRON
ma-140	340	1	[	[	X
ma-140	340	2	x1	x1	PROPN
ma-140	340	3	,	,	PUNCT
ma-140	340	4	x4	x4	PROPN
ma-140	340	5	]	]	PUNCT
ma-140	340	6	=	=	PUNCT
ma-140	340	7	x1x4	x1x4	PUNCT
ma-140	340	8	−x4x1	−x4x1	NOUN
ma-140	340	9	=	=	PUNCT
ma-140	340	10	(	(	PUNCT
ma-140	340	11	∂	∂	NUM
ma-140	340	12	∂x	∂x	PROPN
ma-140	340	13	∂	∂	NUM
ma-140	340	14	∂t	∂t	PROPN
ma-140	340	15	)	)	PUNCT
ma-140	340	16	−	−	PROPN
ma-140	340	17	(	(	PUNCT
ma-140	340	18	∂	∂	NUM
ma-140	340	19	∂t	∂t	PROPN
ma-140	340	20	∂	∂	NOUN
ma-140	340	21	∂x	∂x	PROPN
ma-140	340	22	)	)	PUNCT
ma-140	341	1	=	=	PUNCT
ma-140	341	2	0	0	X
ma-140	341	3	.	.	PUNCT
ma-140	342	1	(	(	PUNCT
ma-140	342	2	3.38	3.38	NUM
ma-140	342	3	)	)	PUNCT
ma-140	342	4	remark	remark	NOUN
ma-140	342	5	3.1	3.1	NUM
ma-140	342	6	.	.	PUNCT
ma-140	343	1	the	the	DET
ma-140	343	2	remaining	remain	VERB
ma-140	343	3	commutation	commutation	NOUN
ma-140	343	4	relations	relation	NOUN
ma-140	343	5	are	be	AUX
ma-140	343	6	obtained	obtain	VERB
ma-140	343	7	analogously	analogously	ADV
ma-140	343	8	.	.	PUNCT
ma-140	344	1	we	we	PRON
ma-140	344	2	present	present	VERB
ma-140	344	3	all	all	DET
ma-140	344	4	commutation	commutation	NOUN
ma-140	344	5	relations	relation	NOUN
ma-140	344	6	in	in	ADP
ma-140	344	7	table	table	NOUN
ma-140	344	8	(	(	PUNCT
ma-140	344	9	1	1	NUM
ma-140	344	10	)	)	PUNCT
ma-140	344	11	below	below	ADV
ma-140	344	12	.	.	PUNCT
ma-140	345	1	[	[	X
ma-140	345	2	xi	xi	X
ma-140	345	3	,	,	PUNCT
ma-140	345	4	xj	xj	PROPN
ma-140	345	5	]	]	PUNCT
ma-140	346	1	x1	x1	PROPN
ma-140	347	1	x2	x2	NOUN
ma-140	347	2	x3	x3	PROPN
ma-140	347	3	x4	x4	PROPN
ma-140	348	1	x1	x1	PROPN
ma-140	348	2	0	0	NUM
ma-140	348	3	0	0	NUM
ma-140	348	4	0	0	NUM
ma-140	348	5	0	0	NUM
ma-140	349	1	x2	x2	NOUN
ma-140	349	2	0	0	NUM
ma-140	349	3	0	0	NUM
ma-140	349	4	-x3	-x3	NOUN
ma-140	350	1	x4	x4	ADJ
ma-140	350	2	x3	x3	NOUN
ma-140	350	3	0	0	PUNCT
ma-140	351	1	−x3	−x3	NOUN
ma-140	351	2	0	0	NUM
ma-140	351	3	1	1	NUM
ma-140	351	4	ux4	ux4	NOUN
ma-140	351	5	x4	x4	PROPN
ma-140	351	6	0	0	PUNCT
ma-140	351	7	-x4	-x4	NOUN
ma-140	351	8	1	1	NUM
ma-140	351	9	ux4	ux4	NOUN
ma-140	351	10	0	0	NUM
ma-140	351	11	table	table	NOUN
ma-140	351	12	1	1	NUM
ma-140	351	13	.	.	PUNCT
ma-140	352	1	a	a	DET
ma-140	352	2	commutator	commutator	NOUN
ma-140	352	3	table	table	NOUN
ma-140	352	4	for	for	ADP
ma-140	352	5	lie	lie	NOUN
ma-140	352	6	algebra	algebra	NOUN
ma-140	352	7	of	of	ADP
ma-140	352	8	equal	equal	ADJ
ma-140	352	9	width	width	ADJ
ma-140	352	10	equation	equation	NOUN
ma-140	352	11	.	.	PUNCT
ma-140	353	1	3.3	3.3	NUM
ma-140	353	2	.	.	PUNCT
ma-140	354	1	group	group	NOUN
ma-140	354	2	transformations	transformation	NOUN
ma-140	354	3	.	.	PUNCT
ma-140	355	1	the	the	DET
ma-140	355	2	corresponding	correspond	VERB
ma-140	355	3	one	one	NUM
ma-140	355	4	-	-	PUNCT
ma-140	355	5	parameter	parameter	NOUN
ma-140	355	6	group	group	NOUN
ma-140	355	7	of	of	ADP
ma-140	355	8	transformations	transformation	NOUN
ma-140	355	9	can	can	AUX
ma-140	355	10	bedetermined	bedetermine	VERB
ma-140	355	11	by	by	ADP
ma-140	355	12	solving	solve	VERB
ma-140	355	13	the	the	DET
ma-140	355	14	lie	lie	NOUN
ma-140	355	15	equations	equation	NOUN
ma-140	355	16	[	[	X
ma-140	355	17	6	6	NUM
ma-140	355	18	]	]	PUNCT
ma-140	355	19	.	.	PUNCT
ma-140	356	1	let	let	VERB
ma-140	356	2	tεi	tεi	NOUN
ma-140	356	3	be	be	AUX
ma-140	356	4	the	the	DET
ma-140	356	5	group	group	NOUN
ma-140	356	6	of	of	ADP
ma-140	356	7	transformations	transformation	NOUN
ma-140	356	8	for	for	ADP
ma-140	356	9	each	each	PRON
ma-140	356	10	xi	xi	X
ma-140	356	11	,	,	PUNCT
ma-140	356	12	i	i	PRON
ma-140	356	13	=	=	NOUN
ma-140	356	14	1	1	NUM
ma-140	356	15	,	,	PUNCT
ma-140	356	16	2	2	NUM
ma-140	356	17	,	,	PUNCT
ma-140	356	18	3	3	NUM
ma-140	356	19	,	,	PUNCT
ma-140	356	20	4	4	NUM
ma-140	356	21	.	.	PUNCT
ma-140	357	1	we	we	PRON
ma-140	357	2	display	display	VERB
ma-140	357	3	how	how	SCONJ
ma-140	357	4	to	to	PART
ma-140	357	5	obtain	obtain	VERB
ma-140	357	6	tεi	tεi	NOUN
ma-140	357	7	from	from	ADP
ma-140	357	8	xi	xi	NUM
ma-140	357	9	by	by	ADP
ma-140	357	10	finding	find	VERB
ma-140	357	11	one	one	NUM
ma-140	357	12	-	-	PUNCT
ma-140	357	13	parameter	parameter	NOUN
ma-140	357	14	group	group	NOUN
ma-140	357	15	for	for	ADP
ma-140	357	16	theinfinitesimal	theinfinitesimal	ADJ
ma-140	357	17	generator	generator	NOUN
ma-140	357	18	x1	x1	PROPN
ma-140	357	19	,	,	PUNCT
ma-140	357	20	namely	namely	ADV
ma-140	357	21	,	,	PUNCT
ma-140	357	22	x1	x1	PROPN
ma-140	357	23	=	=	SYM
ma-140	357	24	∂	∂	NUM
ma-140	357	25	∂x	∂x	PROPN
ma-140	357	26	.	.	PUNCT
ma-140	358	1	(	(	PUNCT
ma-140	358	2	3.39	3.39	NUM
ma-140	358	3	)	)	PUNCT
ma-140	358	4	https://doi.org/10.28924/ada/ma.3.13	https://doi.org/10.28924/ada/ma.3.13	PROPN
ma-140	358	5	eur	eur	NOUN
ma-140	358	6	.	.	PUNCT
ma-140	359	1	j.	j.	PROPN
ma-140	359	2	math	math	PROPN
ma-140	359	3	.	.	PUNCT
ma-140	360	1	anal	anal	PROPN
ma-140	360	2	.	.	PUNCT
ma-140	361	1	10.28924	10.28924	NUM
ma-140	361	2	/	/	SYM
ma-140	361	3	ada	ada	PROPN
ma-140	361	4	/	/	SYM
ma-140	361	5	ma.3.13	ma.3.13	PROPN
ma-140	361	6	12	12	NUM
ma-140	361	7	in	in	ADP
ma-140	361	8	particular	particular	ADJ
ma-140	361	9	,	,	PUNCT
ma-140	361	10	we	we	PRON
ma-140	361	11	have	have	VERB
ma-140	361	12	the	the	DET
ma-140	361	13	lie	lie	NOUN
ma-140	361	14	equations	equation	NOUN
ma-140	361	15	dt̄	dt̄	X
ma-140	361	16	dε	dε	VERB
ma-140	361	17	=	=	NOUN
ma-140	361	18	0	0	NUM
ma-140	361	19	,	,	PUNCT
ma-140	361	20	t̄	t̄	NOUN
ma-140	361	21	∣∣∣	∣∣∣	NOUN
ma-140	361	22	ε=0	ε=0	PROPN
ma-140	361	23	=	=	SYM
ma-140	361	24	t	t	PROPN
ma-140	361	25	,	,	PUNCT
ma-140	361	26	dx̄	dx̄	NOUN
ma-140	361	27	dε	dε	VERB
ma-140	361	28	=	=	NOUN
ma-140	361	29	1	1	NUM
ma-140	361	30	,	,	PUNCT
ma-140	361	31	x̄	x̄	NOUN
ma-140	361	32	∣∣∣	∣∣∣	ADJ
ma-140	361	33	ε=0	ε=0	PROPN
ma-140	361	34	=	=	SYM
ma-140	361	35	x	x	NOUN
ma-140	361	36	,	,	PUNCT
ma-140	361	37	dū	dū	NOUN
ma-140	361	38	dε	dε	ADP
ma-140	361	39	=	=	NOUN
ma-140	361	40	0	0	NUM
ma-140	361	41	,	,	PUNCT
ma-140	361	42	ū	ū	NOUN
ma-140	361	43	∣∣∣	∣∣∣	NOUN
ma-140	361	44	ε=0	ε=0	PROPN
ma-140	361	45	=	=	PUNCT
ma-140	361	46	u.	u.	PROPN
ma-140	361	47	(	(	PUNCT
ma-140	361	48	3.40	3.40	NUM
ma-140	361	49	)	)	PUNCT
ma-140	361	50	solving	solve	VERB
ma-140	361	51	the	the	DET
ma-140	361	52	system	system	NOUN
ma-140	361	53	(	(	PUNCT
ma-140	361	54	3.40	3.40	NUM
ma-140	361	55	)	)	PUNCT
ma-140	361	56	one	one	NUM
ma-140	361	57	obtains	obtain	VERB
ma-140	361	58	,	,	PUNCT
ma-140	361	59	t̄	t̄	PROPN
ma-140	361	60	=	=	SYM
ma-140	361	61	t	t	PROPN
ma-140	361	62	,	,	PUNCT
ma-140	361	63	x̄	x̄	PUNCT
ma-140	362	1	=	=	PUNCT
ma-140	362	2	x	x	PUNCT
ma-140	362	3	+	+	NUM
ma-140	362	4	ε	ε	PROPN
ma-140	362	5	,	,	PUNCT
ma-140	362	6	ū	ū	NOUN
ma-140	362	7	=	=	SYM
ma-140	362	8	u	u	NOUN
ma-140	362	9	,	,	PUNCT
ma-140	362	10	(	(	PUNCT
ma-140	362	11	3.41	3.41	NUM
ma-140	362	12	)	)	PUNCT
ma-140	362	13	and	and	CCONJ
ma-140	362	14	hence	hence	ADV
ma-140	362	15	the	the	DET
ma-140	362	16	one	one	NUM
ma-140	362	17	-	-	PUNCT
ma-140	362	18	parameter	parameter	NOUN
ma-140	362	19	group	group	NOUN
ma-140	362	20	tε4	tε4	PROPN
ma-140	362	21	corresponding	correspond	VERB
ma-140	362	22	to	to	ADP
ma-140	362	23	the	the	DET
ma-140	362	24	operator	operator	NOUN
ma-140	362	25	x1	x1	PROPN
ma-140	362	26	is	be	AUX
ma-140	362	27	tε1	tε1	NOUN
ma-140	362	28	:	:	PUNCT
ma-140	362	29	(	(	PUNCT
ma-140	362	30	t̄	t̄	NOUN
ma-140	362	31	,	,	PUNCT
ma-140	362	32	x̄	x̄	NOUN
ma-140	362	33	,	,	PUNCT
ma-140	362	34	ū	ū	NOUN
ma-140	362	35	)	)	PUNCT
ma-140	362	36	=	=	SYM
ma-140	362	37	(	(	PUNCT
ma-140	362	38	t	t	PROPN
ma-140	362	39	,	,	PUNCT
ma-140	362	40	x	x	PROPN
ma-140	362	41	+	+	SYM
ma-140	362	42	ε1	ε1	PROPN
ma-140	362	43	,	,	PUNCT
ma-140	362	44	u	u	NOUN
ma-140	362	45	)	)	PUNCT
ma-140	362	46	.	.	PUNCT
ma-140	363	1	(	(	PUNCT
ma-140	363	2	3.42	3.42	NUM
ma-140	363	3	)	)	PUNCT
ma-140	363	4	all	all	DET
ma-140	363	5	the	the	DET
ma-140	363	6	five	five	NUM
ma-140	363	7	one	one	NUM
ma-140	363	8	-	-	PUNCT
ma-140	363	9	parameter	parameter	NOUN
ma-140	363	10	groups	group	NOUN
ma-140	363	11	are	be	AUX
ma-140	363	12	presented	present	VERB
ma-140	363	13	below	below	ADP
ma-140	363	14	:	:	PUNCT
ma-140	363	15	tε1	tε1	INTJ
ma-140	363	16	:	:	PUNCT
ma-140	363	17	(	(	PUNCT
ma-140	363	18	t̄	t̄	NOUN
ma-140	363	19	,	,	PUNCT
ma-140	363	20	x̄	x̄	NOUN
ma-140	363	21	,	,	PUNCT
ma-140	363	22	ū	ū	NOUN
ma-140	363	23	)	)	PUNCT
ma-140	363	24	=	=	SYM
ma-140	363	25	(	(	PUNCT
ma-140	363	26	t	t	PROPN
ma-140	363	27	,	,	PUNCT
ma-140	363	28	x	x	PROPN
ma-140	363	29	+	+	SYM
ma-140	363	30	ε1	ε1	PROPN
ma-140	363	31	,	,	PUNCT
ma-140	363	32	u	u	NOUN
ma-140	363	33	)	)	PUNCT
ma-140	363	34	tε2	tε2	NOUN
ma-140	363	35	:	:	PUNCT
ma-140	363	36	(	(	PUNCT
ma-140	363	37	t̄	t̄	NOUN
ma-140	363	38	,	,	PUNCT
ma-140	363	39	x̄	x̄	NOUN
ma-140	363	40	,	,	PUNCT
ma-140	363	41	ū	ū	NOUN
ma-140	363	42	)	)	PUNCT
ma-140	363	43	=	=	PUNCT
ma-140	364	1	(	(	PUNCT
ma-140	364	2	te−ε2	te−ε2	X
ma-140	364	3	,	,	PUNCT
ma-140	364	4	x	x	NOUN
ma-140	364	5	,	,	PUNCT
ma-140	364	6	ueε2	ueε2	PROPN
ma-140	364	7	)	)	PUNCT
ma-140	364	8	tε3	tε3	INTJ
ma-140	364	9	:	:	PUNCT
ma-140	364	10	(	(	PUNCT
ma-140	364	11	t̄	t̄	NOUN
ma-140	364	12	,	,	PUNCT
ma-140	364	13	x̄	x̄	NOUN
ma-140	364	14	,	,	PUNCT
ma-140	364	15	ū	ū	NOUN
ma-140	364	16	)	)	PUNCT
ma-140	364	17	=	=	PUNCT
ma-140	364	18	(	(	PUNCT
ma-140	364	19	te−	te−	NUM
ma-140	364	20	ε3	ε3	PROPN
ma-140	364	21	u	u	NOUN
ma-140	364	22	,	,	PUNCT
ma-140	364	23	x	x	PROPN
ma-140	364	24	,	,	PUNCT
ma-140	364	25	u	u	PROPN
ma-140	364	26	+	+	X
ma-140	364	27	ε3	ε3	PROPN
ma-140	364	28	)	)	PUNCT
ma-140	364	29	tε4	tε4	NOUN
ma-140	364	30	:	:	PUNCT
ma-140	364	31	(	(	PUNCT
ma-140	364	32	t̄	t̄	NOUN
ma-140	364	33	,	,	PUNCT
ma-140	364	34	x̄	x̄	NOUN
ma-140	364	35	,	,	PUNCT
ma-140	364	36	ū	ū	NOUN
ma-140	364	37	)	)	PUNCT
ma-140	364	38	=	=	PUNCT
ma-140	364	39	(	(	PUNCT
ma-140	364	40	t	t	PROPN
ma-140	364	41	+	+	CCONJ
ma-140	364	42	ε4	ε4	PROPN
ma-140	364	43	,	,	PUNCT
ma-140	364	44	x	x	NOUN
ma-140	364	45	,	,	PUNCT
ma-140	364	46	u	u	NOUN
ma-140	364	47	)	)	PUNCT
ma-140	364	48	.	.	PUNCT
ma-140	365	1	(	(	PUNCT
ma-140	365	2	3.43	3.43	NUM
ma-140	365	3	)	)	PUNCT
ma-140	365	4	3.4	3.4	NUM
ma-140	365	5	.	.	PUNCT
ma-140	366	1	symmetry	symmetry	NOUN
ma-140	366	2	transformations	transformation	NOUN
ma-140	366	3	.	.	PUNCT
ma-140	367	1	we	we	PRON
ma-140	367	2	now	now	ADV
ma-140	367	3	show	show	VERB
ma-140	367	4	how	how	SCONJ
ma-140	367	5	the	the	DET
ma-140	367	6	symmetries	symmetry	NOUN
ma-140	367	7	we	we	PRON
ma-140	367	8	have	have	AUX
ma-140	367	9	obtained	obtain	VERB
ma-140	367	10	can	can	AUX
ma-140	367	11	be	be	AUX
ma-140	367	12	usedto	usedto	PROPN
ma-140	367	13	transform	transform	VERB
ma-140	367	14	special	special	ADJ
ma-140	367	15	exact	exact	ADJ
ma-140	367	16	solutions	solution	NOUN
ma-140	367	17	of	of	ADP
ma-140	367	18	the	the	DET
ma-140	367	19	equal	equal	ADJ
ma-140	367	20	width	width	ADJ
ma-140	367	21	equation	equation	NOUN
ma-140	367	22	into	into	ADP
ma-140	367	23	new	new	ADJ
ma-140	367	24	solutions	solution	NOUN
ma-140	367	25	.	.	PUNCT
ma-140	368	1	the	the	DET
ma-140	368	2	lie	lie	NOUN
ma-140	368	3	groupanalysis	groupanalysis	NOUN
ma-140	368	4	vouches	vouch	VERB
ma-140	368	5	for	for	ADP
ma-140	368	6	fundamental	fundamental	ADJ
ma-140	368	7	ways	way	NOUN
ma-140	368	8	of	of	ADP
ma-140	368	9	e	e	NOUN
ma-140	368	10	constructing	construct	VERB
ma-140	368	11	exact	exact	ADJ
ma-140	368	12	solutions	solution	NOUN
ma-140	368	13	of	of	ADP
ma-140	368	14	pdes	pde	NOUN
ma-140	368	15	,	,	PUNCT
ma-140	368	16	that	that	ADV
ma-140	368	17	is	is	ADV
ma-140	368	18	,	,	PUNCT
ma-140	368	19	grouptransformations	grouptransformation	NOUN
ma-140	368	20	of	of	ADP
ma-140	368	21	known	know	VERB
ma-140	368	22	solutions	solution	NOUN
ma-140	368	23	and	and	CCONJ
ma-140	368	24	construction	construction	NOUN
ma-140	368	25	of	of	ADP
ma-140	368	26	group	group	NOUN
ma-140	368	27	-	-	PUNCT
ma-140	368	28	invariant	invariant	ADJ
ma-140	368	29	solutions	solution	NOUN
ma-140	368	30	.	.	PUNCT
ma-140	369	1	we	we	PRON
ma-140	369	2	will	will	AUX
ma-140	369	3	illustratethese	illustratethese	VERB
ma-140	369	4	methods	method	NOUN
ma-140	369	5	with	with	ADP
ma-140	369	6	examples	example	NOUN
ma-140	369	7	.	.	PUNCT
ma-140	370	1	if	if	SCONJ
ma-140	370	2	ū	ū	PRON
ma-140	370	3	=	=	SYM
ma-140	370	4	g(t̄	g(t̄	X
ma-140	370	5	,	,	PUNCT
ma-140	370	6	x̄	x̄	PROPN
ma-140	370	7	)	)	PUNCT
ma-140	370	8	is	be	AUX
ma-140	370	9	a	a	DET
ma-140	370	10	solution	solution	NOUN
ma-140	370	11	of	of	ADP
ma-140	370	12	equation	equation	NOUN
ma-140	370	13	(	(	PUNCT
ma-140	370	14	1.1	1.1	NUM
ma-140	370	15	)	)	PUNCT
ma-140	370	16	φ(t	φ(t	PROPN
ma-140	370	17	,	,	PUNCT
ma-140	370	18	x	x	X
ma-140	370	19	,	,	PUNCT
ma-140	370	20	u	u	NOUN
ma-140	370	21	,	,	PUNCT
ma-140	370	22	ε	ε	PROPN
ma-140	370	23	)	)	PUNCT
ma-140	370	24	=	=	SYM
ma-140	370	25	g(f1(t	g(f1(t	PROPN
ma-140	370	26	,	,	PUNCT
ma-140	370	27	x	x	X
ma-140	370	28	,	,	PUNCT
ma-140	370	29	u	u	NOUN
ma-140	370	30	,	,	PUNCT
ma-140	370	31	ε	ε	PROPN
ma-140	370	32	)	)	PUNCT
ma-140	370	33	,	,	PUNCT
ma-140	370	34	f2(t	f2(t	PROPN
ma-140	370	35	,	,	PUNCT
ma-140	370	36	x	x	NOUN
ma-140	370	37	,	,	PUNCT
ma-140	370	38	u	u	NOUN
ma-140	370	39	,	,	PUNCT
ma-140	370	40	ε	ε	PROPN
ma-140	370	41	)	)	PUNCT
ma-140	370	42	)	)	PUNCT
ma-140	370	43	,	,	PUNCT
ma-140	370	44	(	(	PUNCT
ma-140	370	45	3.44	3.44	NUM
ma-140	370	46	)	)	PUNCT
ma-140	370	47	is	be	AUX
ma-140	370	48	also	also	ADV
ma-140	370	49	a	a	DET
ma-140	370	50	solution	solution	NOUN
ma-140	370	51	.	.	PUNCT
ma-140	371	1	the	the	DET
ma-140	371	2	one	one	NUM
ma-140	371	3	parameter	parameter	NOUN
ma-140	371	4	groups	group	NOUN
ma-140	371	5	dictate	dictate	VERB
ma-140	371	6	to	to	ADP
ma-140	371	7	the	the	DET
ma-140	371	8	following	follow	VERB
ma-140	371	9	generated	generate	VERB
ma-140	371	10	solutions	solution	NOUN
ma-140	371	11	:	:	PUNCT
ma-140	371	12	tε1	tε1	INTJ
ma-140	371	13	:	:	PUNCT
ma-140	371	14	u	u	PROPN
ma-140	371	15	=	=	PROPN
ma-140	371	16	g(t	g(t	PROPN
ma-140	371	17	,	,	PUNCT
ma-140	371	18	x	x	PROPN
ma-140	371	19	+	+	SYM
ma-140	371	20	ε1	ε1	PROPN
ma-140	371	21	)	)	PUNCT
ma-140	371	22	tε2	tε2	NOUN
ma-140	371	23	:	:	PUNCT
ma-140	371	24	u	u	NOUN
ma-140	371	25	=	=	NOUN
ma-140	371	26	g(te−ε2	g(te−ε2	NOUN
ma-140	371	27	,	,	PUNCT
ma-140	371	28	x)e−ε2	x)e−ε2	PROPN
ma-140	371	29	,	,	PUNCT
ma-140	371	30	tε3	tε3	PROPN
ma-140	371	31	:	:	PUNCT
ma-140	371	32	u	u	X
ma-140	371	33	=	=	PROPN
ma-140	371	34	g(te−	g(te−	PROPN
ma-140	371	35	ε3	ε3	PROPN
ma-140	371	36	u	u	PROPN
ma-140	371	37	,	,	PUNCT
ma-140	371	38	x)−	x)−	PROPN
ma-140	371	39	ε3	ε3	PROPN
ma-140	371	40	,	,	PUNCT
ma-140	371	41	tε4	tε4	X
ma-140	371	42	:	:	PUNCT
ma-140	371	43	u	u	PROPN
ma-140	371	44	=	=	PROPN
ma-140	371	45	g(t	g(t	PROPN
ma-140	371	46	+	+	CCONJ
ma-140	371	47	ε4	ε4	PROPN
ma-140	371	48	,	,	PUNCT
ma-140	371	49	x	x	NOUN
ma-140	371	50	)	)	PUNCT
ma-140	371	51	.	.	PUNCT
ma-140	372	1	(	(	PUNCT
ma-140	372	2	3.45	3.45	NUM
ma-140	372	3	)	)	PUNCT
ma-140	372	4	3.5	3.5	NUM
ma-140	372	5	.	.	PUNCT
ma-140	373	1	construction	construction	NOUN
ma-140	373	2	of	of	ADP
ma-140	373	3	group	group	NOUN
ma-140	373	4	-	-	PUNCT
ma-140	373	5	invariant	invariant	ADJ
ma-140	373	6	solutions	solution	NOUN
ma-140	373	7	.	.	PUNCT
ma-140	374	1	now	now	ADV
ma-140	374	2	we	we	PRON
ma-140	374	3	compute	compute	VERB
ma-140	374	4	the	the	DET
ma-140	374	5	group	group	NOUN
ma-140	374	6	invariant	invariant	ADJ
ma-140	374	7	solutions	solution	NOUN
ma-140	374	8	ofburger	ofburger	NOUN
ma-140	374	9	’s	’s	PART
ma-140	374	10	equation.(i	equation.(i	NUM
ma-140	374	11	)	)	PUNCT
ma-140	375	1	x1	x1	NOUN
ma-140	376	1	=	=	SYM
ma-140	376	2	∂	∂	NUM
ma-140	376	3	∂xthe	∂xthe	DET
ma-140	376	4	associated	associated	ADJ
ma-140	376	5	lagrangian	lagrangian	ADJ
ma-140	376	6	equations	equation	NOUN
ma-140	376	7	https://doi.org/10.28924/ada/ma.3.13	https://doi.org/10.28924/ada/ma.3.13	PUNCT
ma-140	376	8	eur	eur	PROPN
ma-140	376	9	.	.	PUNCT
ma-140	377	1	j.	j.	PROPN
ma-140	377	2	math	math	PROPN
ma-140	377	3	.	.	PUNCT
ma-140	378	1	anal	anal	PROPN
ma-140	378	2	.	.	PUNCT
ma-140	379	1	10.28924	10.28924	NUM
ma-140	379	2	/	/	SYM
ma-140	379	3	ada	ada	PROPN
ma-140	379	4	/	/	SYM
ma-140	379	5	ma.3.13	ma.3.13	PROPN
ma-140	379	6	13	13	NUM
ma-140	379	7	dt	dt	NOUN
ma-140	379	8	0	0	NUM
ma-140	380	1	=	=	SYM
ma-140	380	2	dx	dx	PROPN
ma-140	380	3	1	1	NUM
ma-140	380	4	=	=	SYM
ma-140	380	5	du	du	X
ma-140	380	6	0	0	NUM
ma-140	380	7	,	,	PUNCT
ma-140	380	8	(	(	PUNCT
ma-140	380	9	3.46	3.46	NUM
ma-140	380	10	)	)	PUNCT
ma-140	380	11	yield	yield	VERB
ma-140	380	12	two	two	NUM
ma-140	380	13	invariants	invariant	NOUN
ma-140	380	14	,	,	PUNCT
ma-140	380	15	j1	j1	PROPN
ma-140	380	16	=	=	PUNCT
ma-140	380	17	t	t	PROPN
ma-140	380	18	and	and	CCONJ
ma-140	380	19	j2	j2	PROPN
ma-140	380	20	=	=	PUNCT
ma-140	380	21	u.	u.	PROPN
ma-140	380	22	thus	thus	ADV
ma-140	380	23	using	use	VERB
ma-140	380	24	j2	j2	PROPN
ma-140	380	25	=	=	PUNCT
ma-140	380	26	φ(j1	φ(j1	X
ma-140	380	27	)	)	PUNCT
ma-140	380	28	,	,	PUNCT
ma-140	380	29	we	we	PRON
ma-140	380	30	have	have	VERB
ma-140	380	31	u(t	u(t	NOUN
ma-140	380	32	,	,	PUNCT
ma-140	380	33	x	x	NOUN
ma-140	380	34	)	)	PUNCT
ma-140	380	35	=	=	SYM
ma-140	380	36	φ(t	φ(t	PROPN
ma-140	380	37	)	)	PUNCT
ma-140	380	38	.	.	PUNCT
ma-140	381	1	(	(	PUNCT
ma-140	381	2	3.47	3.47	NUM
ma-140	381	3	)	)	PUNCT
ma-140	381	4	the	the	DET
ma-140	381	5	derivatives	derivative	NOUN
ma-140	381	6	are	be	AUX
ma-140	381	7	given	give	VERB
ma-140	381	8	by	by	ADP
ma-140	381	9	:	:	PUNCT
ma-140	381	10	ut	ut	PROPN
ma-140	381	11	=	=	NOUN
ma-140	381	12	φ′(t	φ′(t	PROPN
ma-140	381	13	)	)	PUNCT
ma-140	381	14	,	,	PUNCT
ma-140	381	15	ux	ux	PROPN
ma-140	382	1	=	=	SYM
ma-140	382	2	0	0	PROPN
ma-140	382	3	,	,	PUNCT
ma-140	382	4	utxx	utxx	NOUN
ma-140	382	5	=	=	NOUN
ma-140	382	6	0	0	NUM
ma-140	382	7	.	.	PUNCT
ma-140	383	1	if	if	SCONJ
ma-140	383	2	we	we	PRON
ma-140	383	3	substitute	substitute	VERB
ma-140	383	4	these	these	DET
ma-140	383	5	derivatives	derivative	NOUN
ma-140	383	6	into	into	ADP
ma-140	383	7	equation	equation	NOUN
ma-140	383	8	(	(	PUNCT
ma-140	383	9	1.1	1.1	NUM
ma-140	383	10	)	)	PUNCT
ma-140	383	11	,	,	PUNCT
ma-140	383	12	we	we	PRON
ma-140	383	13	obtain	obtain	VERB
ma-140	383	14	the	the	DET
ma-140	383	15	first	first	ADJ
ma-140	383	16	order	order	NOUN
ma-140	383	17	ordinarydifferential	ordinarydifferential	ADJ
ma-140	383	18	equation	equation	NOUN
ma-140	383	19	φ′(t	φ′(t	NOUN
ma-140	383	20	)	)	PUNCT
ma-140	383	21	=	=	SYM
ma-140	383	22	0	0	NUM
ma-140	383	23	,	,	PUNCT
ma-140	383	24	whose	whose	DET
ma-140	383	25	space	space	NOUN
ma-140	383	26	invariant	invariant	ADJ
ma-140	383	27	solution	solution	NOUN
ma-140	383	28	is	be	AUX
ma-140	383	29	φ(t	φ(t	NOUN
ma-140	383	30	)	)	PUNCT
ma-140	383	31	=	=	SYM
ma-140	383	32	c1	c1	PROPN
ma-140	383	33	,	,	PUNCT
ma-140	383	34	(	(	PUNCT
ma-140	383	35	3.48	3.48	NUM
ma-140	383	36	)	)	PUNCT
ma-140	383	37	and	and	CCONJ
ma-140	383	38	the	the	DET
ma-140	383	39	group	group	NOUN
ma-140	383	40	-	-	PUNCT
ma-140	383	41	invariant	invariant	ADJ
ma-140	383	42	solution	solution	NOUN
ma-140	383	43	associated	associate	VERB
ma-140	383	44	to	to	ADP
ma-140	383	45	the	the	DET
ma-140	383	46	x1	x1	PROPN
ma-140	383	47	is	be	AUX
ma-140	383	48	u(t	u(t	NOUN
ma-140	383	49	,	,	PUNCT
ma-140	383	50	x	x	NOUN
ma-140	383	51	)	)	PUNCT
ma-140	383	52	=	=	SYM
ma-140	383	53	c1	c1	PROPN
ma-140	383	54	.	.	PUNCT
ma-140	384	1	(	(	PUNCT
ma-140	384	2	ii	ii	NOUN
ma-140	384	3	)	)	PUNCT
ma-140	384	4	x2	x2	NOUN
ma-140	385	1	=	=	PUNCT
ma-140	385	2	u	u	PROPN
ma-140	385	3	∂	∂	NOUN
ma-140	385	4	∂u	∂u	PROPN
ma-140	385	5	−	−	PROPN
ma-140	385	6	t	t	NOUN
ma-140	385	7	∂	∂	NOUN
ma-140	385	8	∂t	∂t	PROPN
ma-140	386	1	the	the	DET
ma-140	386	2	lagrangian	lagrangian	ADJ
ma-140	386	3	equations	equation	NOUN
ma-140	386	4	associated	associate	VERB
ma-140	386	5	to	to	ADP
ma-140	386	6	this	this	DET
ma-140	386	7	symmetry	symmetry	NOUN
ma-140	386	8	are	be	AUX
ma-140	386	9	dt	dt	NOUN
ma-140	386	10	−t	−t	PROPN
ma-140	386	11	=	=	PUNCT
ma-140	386	12	dx	dx	PROPN
ma-140	386	13	0	0	NUM
ma-140	387	1	=	=	SYM
ma-140	387	2	du	du	PROPN
ma-140	387	3	u	u	PROPN
ma-140	387	4	.	.	PUNCT
ma-140	388	1	(	(	PUNCT
ma-140	388	2	3.49	3.49	NUM
ma-140	388	3	)	)	PUNCT
ma-140	388	4	this	this	PRON
ma-140	388	5	gives	give	VERB
ma-140	388	6	the	the	DET
ma-140	388	7	constants	constant	NOUN
ma-140	388	8	j1	j1	NOUN
ma-140	388	9	=	=	PUNCT
ma-140	388	10	x	x	PROPN
ma-140	388	11	and	and	CCONJ
ma-140	388	12	j2	j2	PROPN
ma-140	388	13	=	=	SYM
ma-140	388	14	tu	tu	PROPN
ma-140	388	15	,	,	PUNCT
ma-140	388	16	giving	give	VERB
ma-140	388	17	the	the	DET
ma-140	388	18	solution	solution	NOUN
ma-140	388	19	u	u	NOUN
ma-140	388	20	=	=	PROPN
ma-140	388	21	f	f	X
ma-140	388	22	(	(	PUNCT
ma-140	388	23	x	x	PROPN
ma-140	388	24	)	)	PUNCT
ma-140	388	25	t	t	PROPN
ma-140	388	26	.	.	PUNCT
ma-140	389	1	(	(	PUNCT
ma-140	389	2	3.50	3.50	NUM
ma-140	389	3	)	)	PUNCT
ma-140	389	4	we	we	PRON
ma-140	389	5	obtain	obtain	VERB
ma-140	389	6	the	the	DET
ma-140	389	7	derivatives	derivative	NOUN
ma-140	389	8	as	as	SCONJ
ma-140	389	9	follows	follow	VERB
ma-140	389	10	:	:	PUNCT
ma-140	389	11	ut	ut	PROPN
ma-140	389	12	=	=	PROPN
ma-140	389	13	−	−	PROPN
ma-140	389	14	f	f	PROPN
ma-140	389	15	(	(	PUNCT
ma-140	389	16	x	x	NOUN
ma-140	389	17	)	)	PUNCT
ma-140	389	18	t2	t2	NOUN
ma-140	389	19	,	,	PUNCT
ma-140	389	20	(	(	PUNCT
ma-140	389	21	3.51	3.51	NUM
ma-140	389	22	)	)	PUNCT
ma-140	389	23	ux	ux	NOUN
ma-140	390	1	=	=	SYM
ma-140	390	2	f	f	PROPN
ma-140	390	3	′(x	′(x	PROPN
ma-140	390	4	)	)	PUNCT
ma-140	390	5	t	t	NOUN
ma-140	390	6	(	(	PUNCT
ma-140	390	7	3.52	3.52	NUM
ma-140	390	8	)	)	PUNCT
ma-140	390	9	utxx	utxx	NOUN
ma-140	390	10	=	=	NOUN
ma-140	390	11	−	−	PROPN
ma-140	390	12	f	f	PROPN
ma-140	390	13	′′(x	′′(x	PROPN
ma-140	390	14	)	)	PUNCT
ma-140	390	15	t2	t2	NOUN
ma-140	390	16	(	(	PUNCT
ma-140	390	17	3.53	3.53	NUM
ma-140	390	18	)	)	PUNCT
ma-140	390	19	if	if	SCONJ
ma-140	390	20	we	we	PRON
ma-140	390	21	substitute	substitute	VERB
ma-140	390	22	the	the	DET
ma-140	390	23	above	above	ADJ
ma-140	390	24	derivatives	derivative	NOUN
ma-140	390	25	in	in	ADP
ma-140	390	26	equation	equation	NOUN
ma-140	390	27	(	(	PUNCT
ma-140	390	28	1.1	1.1	NUM
ma-140	390	29	)	)	PUNCT
ma-140	390	30	,	,	PUNCT
ma-140	390	31	we	we	PRON
ma-140	390	32	obtain	obtain	VERB
ma-140	390	33	the	the	DET
ma-140	390	34	second	second	ADJ
ma-140	390	35	order	order	NOUN
ma-140	390	36	ordinarydifferential	ordinarydifferential	ADJ
ma-140	390	37	equation	equation	NOUN
ma-140	390	38	f	f	X
ma-140	390	39	(	(	PUNCT
ma-140	390	40	x)−	x)−	PROPN
ma-140	390	41	αf	αf	PROPN
ma-140	390	42	(	(	PUNCT
ma-140	390	43	x)f	x)f	X
ma-140	390	44	′(x	′(x	NOUN
ma-140	390	45	)	)	PUNCT
ma-140	391	1	+	+	CCONJ
ma-140	391	2	βf	βf	PRON
ma-140	391	3	′′(x	′′(x	NOUN
ma-140	391	4	)	)	PUNCT
ma-140	391	5	=	=	SYM
ma-140	392	1	0	0	X
ma-140	392	2	.	.	PUNCT
ma-140	393	1	(	(	PUNCT
ma-140	393	2	3.54	3.54	NUM
ma-140	393	3	)	)	PUNCT
ma-140	393	4	https://doi.org/10.28924/ada/ma.3.13	https://doi.org/10.28924/ada/ma.3.13	PROPN
ma-140	393	5	eur	eur	NOUN
ma-140	393	6	.	.	PUNCT
ma-140	394	1	j.	j.	PROPN
ma-140	394	2	math	math	PROPN
ma-140	394	3	.	.	PUNCT
ma-140	395	1	anal	anal	PROPN
ma-140	395	2	.	.	PUNCT
ma-140	396	1	10.28924	10.28924	NUM
ma-140	396	2	/	/	SYM
ma-140	396	3	ada	ada	PROPN
ma-140	396	4	/	/	SYM
ma-140	396	5	ma.3.13	ma.3.13	PROPN
ma-140	396	6	14hence	14hence	NUM
ma-140	397	1	the	the	DET
ma-140	397	2	group	group	NOUN
ma-140	397	3	invariant	invariant	ADJ
ma-140	397	4	solution	solution	NOUN
ma-140	397	5	to	to	ADP
ma-140	397	6	equation	equation	NOUN
ma-140	397	7	to	to	ADP
ma-140	397	8	(	(	PUNCT
ma-140	397	9	1.1	1.1	NUM
ma-140	397	10	)	)	PUNCT
ma-140	397	11	will	will	AUX
ma-140	397	12	be	be	AUX
ma-140	397	13	given	give	VERB
ma-140	397	14	by	by	ADP
ma-140	397	15	u(t	u(t	NOUN
ma-140	397	16	,	,	PUNCT
ma-140	397	17	x	x	NOUN
ma-140	397	18	)	)	PUNCT
ma-140	397	19	=	=	SYM
ma-140	397	20	f	f	X
ma-140	397	21	(	(	PUNCT
ma-140	397	22	x	x	X
ma-140	397	23	)	)	PUNCT
ma-140	397	24	t	t	NOUN
ma-140	397	25	,	,	PUNCT
ma-140	397	26	(	(	PUNCT
ma-140	397	27	3.55	3.55	NUM
ma-140	397	28	)	)	PUNCT
ma-140	397	29	where	where	SCONJ
ma-140	397	30	f	f	PROPN
ma-140	397	31	satisfies	satisfy	VERB
ma-140	397	32	equation	equation	NOUN
ma-140	397	33	(	(	PUNCT
ma-140	397	34	3.54).(iii	3.54).(iii	NUM
ma-140	397	35	)	)	PUNCT
ma-140	397	36	x3	x3	NOUN
ma-140	397	37	=	=	SYM
ma-140	397	38	∂	∂	NUM
ma-140	398	1	∂u	∂u	PROPN
ma-140	398	2	−	−	PROPN
ma-140	398	3	t	t	PROPN
ma-140	398	4	u	u	PROPN
ma-140	398	5	∂	∂	NUM
ma-140	398	6	∂tthe	∂tthe	DET
ma-140	398	7	lagrangian	lagrangian	ADJ
ma-140	398	8	system	system	NOUN
ma-140	398	9	associated	associate	VERB
ma-140	398	10	with	with	ADP
ma-140	398	11	the	the	DET
ma-140	398	12	operator	operator	NOUN
ma-140	398	13	x3	x3	NOUN
ma-140	398	14	is	be	AUX
ma-140	398	15	dt	dt	VERB
ma-140	398	16	−	−	PROPN
ma-140	398	17	tu	tu	PROPN
ma-140	398	18	=	=	PUNCT
ma-140	398	19	dx	dx	PROPN
ma-140	398	20	0	0	NUM
ma-140	399	1	=	=	SYM
ma-140	399	2	du	du	PROPN
ma-140	399	3	1	1	NUM
ma-140	399	4	,	,	PUNCT
ma-140	399	5	(	(	PUNCT
ma-140	399	6	3.56	3.56	NUM
ma-140	399	7	)	)	PUNCT
ma-140	399	8	whose	whose	DET
ma-140	399	9	invariants	invariant	NOUN
ma-140	399	10	are	be	AUX
ma-140	399	11	j1	j1	NOUN
ma-140	399	12	=	=	PUNCT
ma-140	399	13	x	x	PROPN
ma-140	399	14	and	and	CCONJ
ma-140	399	15	j2	j2	PROPN
ma-140	399	16	=	=	SYM
ma-140	399	17	tu	tu	PROPN
ma-140	399	18	.	.	PUNCT
ma-140	400	1	so	so	ADV
ma-140	400	2	,	,	PUNCT
ma-140	400	3	u	u	NOUN
ma-140	400	4	=	=	PROPN
ma-140	400	5	g(x	g(x	NOUN
ma-140	400	6	)	)	PUNCT
ma-140	400	7	t	t	PROPN
ma-140	400	8	is	be	AUX
ma-140	400	9	the	the	DET
ma-140	400	10	group	group	NOUN
ma-140	400	11	-	-	PUNCT
ma-140	400	12	invariant	invariant	ADJ
ma-140	400	13	solution.(iv	solution.(iv	NOUN
ma-140	400	14	)	)	PUNCT
ma-140	401	1	x4	x4	PROPN
ma-140	402	1	=	=	SYM
ma-140	403	1	∂	∂	NUM
ma-140	404	1	∂tcharacteristic	∂tcharacteristic	ADJ
ma-140	404	2	equations	equation	NOUN
ma-140	404	3	associated	associate	VERB
ma-140	404	4	to	to	ADP
ma-140	404	5	the	the	DET
ma-140	404	6	operator	operator	NOUN
ma-140	404	7	x4	x4	NOUN
ma-140	404	8	are	be	AUX
ma-140	404	9	dt	dt	X
ma-140	404	10	1	1	NUM
ma-140	404	11	=	=	SYM
ma-140	404	12	dx	dx	PROPN
ma-140	404	13	0	0	PUNCT
ma-140	405	1	=	=	SYM
ma-140	405	2	du	du	X
ma-140	405	3	0	0	NUM
ma-140	405	4	,	,	PUNCT
ma-140	405	5	(	(	PUNCT
ma-140	405	6	3.57	3.57	NUM
ma-140	405	7	)	)	PUNCT
ma-140	405	8	yieldsj1	yieldsj1	X
ma-140	406	1	=	=	PUNCT
ma-140	406	2	x	x	PUNCT
ma-140	406	3	and	and	CCONJ
ma-140	406	4	j2	j2	PROPN
ma-140	406	5	=	=	SYM
ma-140	406	6	u.	u.	PROPN
ma-140	406	7	as	as	ADP
ma-140	406	8	a	a	DET
ma-140	406	9	result	result	NOUN
ma-140	406	10	,	,	PUNCT
ma-140	406	11	the	the	DET
ma-140	406	12	group	group	NOUN
ma-140	406	13	-	-	PUNCT
ma-140	406	14	invariant	invariant	ADJ
ma-140	406	15	solution	solution	NOUN
ma-140	406	16	of	of	ADP
ma-140	406	17	(	(	PUNCT
ma-140	406	18	1.1	1.1	NUM
ma-140	406	19	)	)	PUNCT
ma-140	406	20	for	for	ADP
ma-140	406	21	this	this	DET
ma-140	406	22	case	case	NOUN
ma-140	406	23	is	be	AUX
ma-140	406	24	j2	j2	PROPN
ma-140	406	25	=	=	PUNCT
ma-140	406	26	φ(j1	φ(j1	X
ma-140	406	27	)	)	PUNCT
ma-140	406	28	,	,	PUNCT
ma-140	406	29	for	for	ADP
ma-140	406	30	some	some	DET
ma-140	406	31	φ	φ	NOUN
ma-140	406	32	an	an	DET
ma-140	406	33	arbitrary	arbitrary	ADJ
ma-140	406	34	function	function	NOUN
ma-140	406	35	.	.	PUNCT
ma-140	407	1	that	that	PRON
ma-140	407	2	is	be	AUX
ma-140	407	3	,	,	PUNCT
ma-140	407	4	u(t	u(t	NOUN
ma-140	407	5	,	,	PUNCT
ma-140	407	6	x	x	NOUN
ma-140	407	7	)	)	PUNCT
ma-140	407	8	=	=	SYM
ma-140	407	9	φ(x	φ(x	NOUN
ma-140	407	10	)	)	PUNCT
ma-140	407	11	.	.	PUNCT
ma-140	408	1	(	(	PUNCT
ma-140	408	2	3.58	3.58	NUM
ma-140	408	3	)	)	PUNCT
ma-140	408	4	the	the	DET
ma-140	408	5	derivatives	derivative	NOUN
ma-140	408	6	of	of	ADP
ma-140	408	7	given	give	VERB
ma-140	408	8	function	function	NOUN
ma-140	408	9	are	be	AUX
ma-140	408	10	ut	ut	PROPN
ma-140	408	11	=	=	SYM
ma-140	408	12	0	0	PROPN
ma-140	408	13	,	,	PUNCT
ma-140	408	14	(	(	PUNCT
ma-140	408	15	3.59	3.59	NUM
ma-140	408	16	)	)	PUNCT
ma-140	408	17	ux	ux	NOUN
ma-140	408	18	=	=	PUNCT
ma-140	408	19	φ′(x	φ′(x	PROPN
ma-140	408	20	)	)	PUNCT
ma-140	408	21	,	,	PUNCT
ma-140	408	22	(	(	PUNCT
ma-140	408	23	3.60	3.60	NUM
ma-140	408	24	)	)	PUNCT
ma-140	408	25	utxx	utxx	NOUN
ma-140	408	26	=	=	NOUN
ma-140	408	27	0	0	X
ma-140	408	28	.	.	PUNCT
ma-140	409	1	(	(	PUNCT
ma-140	409	2	3.61	3.61	NUM
ma-140	409	3	)	)	PUNCT
ma-140	409	4	substitution	substitution	NOUN
ma-140	409	5	of	of	ADP
ma-140	409	6	the	the	DET
ma-140	409	7	value	value	NOUN
ma-140	409	8	of	of	ADP
ma-140	409	9	φ(x	φ(x	NOUN
ma-140	409	10	)	)	PUNCT
ma-140	409	11	into	into	ADP
ma-140	409	12	equation	equation	NOUN
ma-140	409	13	(	(	PUNCT
ma-140	409	14	1.1	1.1	NUM
ma-140	409	15	)	)	PUNCT
ma-140	409	16	yields	yield	VERB
ma-140	409	17	a	a	DET
ma-140	409	18	first	first	ADJ
ma-140	409	19	order	order	NOUN
ma-140	409	20	nonlinear	nonlinear	ADJ
ma-140	409	21	ordinarydifferential	ordinarydifferential	ADJ
ma-140	409	22	equation	equation	NOUN
ma-140	409	23	φ(x)φ′(x	φ(x)φ′(x	PROPN
ma-140	409	24	)	)	PUNCT
ma-140	409	25	=	=	SYM
ma-140	410	1	0	0	X
ma-140	410	2	.	.	PUNCT
ma-140	411	1	(	(	PUNCT
ma-140	411	2	3.62	3.62	NUM
ma-140	411	3	)	)	PUNCT
ma-140	411	4	from	from	ADP
ma-140	411	5	equation	equation	NOUN
ma-140	411	6	(	(	PUNCT
ma-140	411	7	3.62	3.62	NUM
ma-140	411	8	)	)	PUNCT
ma-140	411	9	,	,	PUNCT
ma-140	411	10	either	either	CCONJ
ma-140	411	11	φ(x	φ(x	NOUN
ma-140	411	12	)	)	PUNCT
ma-140	411	13	=	=	SYM
ma-140	411	14	0	0	NUM
ma-140	411	15	or	or	CCONJ
ma-140	411	16	φ′(x	φ′(x	NOUN
ma-140	411	17	)	)	PUNCT
ma-140	412	1	=	=	SYM
ma-140	412	2	0	0	X
ma-140	412	3	.	.	PUNCT
ma-140	413	1	the	the	DET
ma-140	413	2	case	case	NOUN
ma-140	413	3	φ(x	φ(x	NOUN
ma-140	413	4	)	)	PUNCT
ma-140	413	5	=	=	PUNCT
ma-140	413	6	0	0	PUNCT
ma-140	414	1	=	=	VERB
ma-140	414	2	⇒	⇒	NOUN
ma-140	414	3	φ′(x	φ′(x	NOUN
ma-140	414	4	)	)	PUNCT
ma-140	414	5	=	=	SYM
ma-140	415	1	0,and	0,and	NUM
ma-140	415	2	the	the	DET
ma-140	415	3	equation	equation	NOUN
ma-140	415	4	is	be	AUX
ma-140	415	5	satisfied	satisfied	ADJ
ma-140	415	6	.	.	PUNCT
ma-140	416	1	the	the	DET
ma-140	416	2	case	case	NOUN
ma-140	416	3	φ(x	φ(x	NOUN
ma-140	416	4	)	)	PUNCT
ma-140	416	5	6=	6=	ADP
ma-140	416	6	0	0	NUM
ma-140	416	7	implies	imply	VERB
ma-140	416	8	that	that	SCONJ
ma-140	416	9	φ′(x	φ′(x	VERB
ma-140	416	10	)	)	PUNCT
ma-140	416	11	=	=	SYM
ma-140	416	12	0	0	NUM
ma-140	416	13	and	and	CCONJ
ma-140	416	14	by	by	ADP
ma-140	416	15	integration	integration	NOUN
ma-140	416	16	,	,	PUNCT
ma-140	416	17	φ(x	φ(x	PROPN
ma-140	416	18	)	)	PUNCT
ma-140	416	19	=	=	SYM
ma-140	416	20	c1	c1	NOUN
ma-140	416	21	,	,	PUNCT
ma-140	416	22	hence	hence	ADV
ma-140	416	23	the	the	DET
ma-140	416	24	group	group	NOUN
ma-140	416	25	invariant	invariant	ADJ
ma-140	416	26	solution	solution	NOUN
ma-140	416	27	is	be	AUX
ma-140	416	28	given	give	VERB
ma-140	416	29	by	by	ADP
ma-140	416	30	u(t	u(t	NOUN
ma-140	416	31	,	,	PUNCT
ma-140	416	32	x	x	X
ma-140	416	33	)	)	PUNCT
ma-140	416	34	=	=	SYM
ma-140	416	35	c2	c2	PROPN
ma-140	416	36	.	.	PUNCT
ma-140	417	1	(	(	PUNCT
ma-140	417	2	3.63	3.63	NUM
ma-140	417	3	)	)	PUNCT
ma-140	417	4	3.6	3.6	NUM
ma-140	417	5	.	.	PUNCT
ma-140	418	1	soliton	soliton	NOUN
ma-140	418	2	.	.	PUNCT
ma-140	419	1	we	we	PRON
ma-140	419	2	obtain	obtain	VERB
ma-140	419	3	a	a	DET
ma-140	419	4	traveling	travel	VERB
ma-140	419	5	wave	wave	NOUN
ma-140	419	6	solution	solution	NOUN
ma-140	419	7	of	of	ADP
ma-140	419	8	the	the	DET
ma-140	419	9	equal	equal	ADJ
ma-140	419	10	width	width	ADJ
ma-140	419	11	equation(1.1	equation(1.1	NOUN
ma-140	419	12	)	)	PUNCT
ma-140	419	13	by	by	ADP
ma-140	419	14	consideringa	consideringa	NOUN
ma-140	419	15	linear	linear	ADJ
ma-140	419	16	combination	combination	NOUN
ma-140	419	17	of	of	ADP
ma-140	419	18	the	the	DET
ma-140	419	19	symmetries	symmetry	NOUN
ma-140	419	20	x1	x1	PROPN
ma-140	419	21	and	and	CCONJ
ma-140	419	22	x4	x4	PROPN
ma-140	419	23	,	,	PUNCT
ma-140	419	24	namely	namely	ADV
ma-140	419	25	,	,	PUNCT
ma-140	419	26	[	[	X
ma-140	419	27	7	7	NUM
ma-140	419	28	]	]	PUNCT
ma-140	419	29	x	x	X
ma-140	419	30	=	=	SYM
ma-140	419	31	cx1	cx1	X
ma-140	419	32	+	+	NOUN
ma-140	419	33	x4	x4	PROPN
ma-140	419	34	=	=	SYM
ma-140	419	35	c	c	PROPN
ma-140	419	36	∂	∂	NOUN
ma-140	419	37	∂x	∂x	PROPN
ma-140	419	38	+	+	CCONJ
ma-140	419	39	∂	∂	NUM
ma-140	419	40	∂t	∂t	PROPN
ma-140	419	41	,	,	PUNCT
ma-140	419	42	for	for	ADP
ma-140	419	43	some	some	DET
ma-140	419	44	constant	constant	ADJ
ma-140	419	45	c	c	NOUN
ma-140	419	46	.	.	PUNCT
ma-140	420	1	(	(	PUNCT
ma-140	420	2	3.64	3.64	NUM
ma-140	420	3	)	)	PUNCT
ma-140	420	4	the	the	DET
ma-140	420	5	characteristic	characteristic	ADJ
ma-140	420	6	equations	equation	NOUN
ma-140	420	7	are	be	AUX
ma-140	420	8	dt	dt	ADP
ma-140	420	9	1	1	NUM
ma-140	420	10	=	=	SYM
ma-140	420	11	dx	dx	PROPN
ma-140	420	12	c	c	NOUN
ma-140	420	13	=	=	SYM
ma-140	420	14	du	du	X
ma-140	420	15	0	0	NUM
ma-140	420	16	(	(	PUNCT
ma-140	420	17	3.65	3.65	NUM
ma-140	420	18	)	)	PUNCT
ma-140	420	19	https://doi.org/10.28924/ada/ma.3.13	https://doi.org/10.28924/ada/ma.3.13	PROPN
ma-140	420	20	eur	eur	NOUN
ma-140	420	21	.	.	PUNCT
ma-140	421	1	j.	j.	PROPN
ma-140	421	2	math	math	PROPN
ma-140	421	3	.	.	PUNCT
ma-140	422	1	anal	anal	PROPN
ma-140	422	2	.	.	PUNCT
ma-140	423	1	10.28924	10.28924	NUM
ma-140	423	2	/	/	SYM
ma-140	423	3	ada	ada	PROPN
ma-140	423	4	/	/	SYM
ma-140	423	5	ma.3.13	ma.3.13	PROPN
ma-140	423	6	15we	15we	NOUN
ma-140	423	7	get	get	VERB
ma-140	423	8	two	two	NUM
ma-140	423	9	invariants	invariant	NOUN
ma-140	423	10	,	,	PUNCT
ma-140	423	11	j1	j1	NOUN
ma-140	423	12	=	=	PUNCT
ma-140	424	1	x	x	PUNCT
ma-140	424	2	−	−	PROPN
ma-140	424	3	ct	ct	PROPN
ma-140	424	4	and	and	CCONJ
ma-140	424	5	j2	j2	PROPN
ma-140	424	6	=	=	SYM
ma-140	424	7	u.	u.	PROPN
ma-140	425	1	so	so	SCONJ
ma-140	425	2	the	the	DET
ma-140	425	3	group	group	NOUN
ma-140	425	4	-	-	PUNCT
ma-140	425	5	invariant	invariant	ADJ
ma-140	425	6	solution	solution	NOUN
ma-140	425	7	is	be	AUX
ma-140	425	8	u(t	u(t	NOUN
ma-140	425	9	,	,	PUNCT
ma-140	425	10	x	x	NOUN
ma-140	425	11	)	)	PUNCT
ma-140	425	12	=	=	SYM
ma-140	425	13	q(x	q(x	NOUN
ma-140	425	14	−	−	PROPN
ma-140	425	15	ct	ct	PROPN
ma-140	425	16	)	)	PUNCT
ma-140	425	17	,	,	PUNCT
ma-140	425	18	(	(	PUNCT
ma-140	425	19	3.66	3.66	NUM
ma-140	425	20	)	)	PUNCT
ma-140	425	21	for	for	ADP
ma-140	425	22	some	some	DET
ma-140	425	23	arbitrary	arbitrary	ADJ
ma-140	425	24	function	function	NOUN
ma-140	425	25	ϕ	ϕ	NOUN
ma-140	425	26	and	and	CCONJ
ma-140	425	27	c	c	X
ma-140	425	28	the	the	DET
ma-140	425	29	velocity	velocity	NOUN
ma-140	425	30	of	of	ADP
ma-140	425	31	the	the	DET
ma-140	425	32	wave.substitution	wave.substitution	NOUN
ma-140	425	33	of	of	ADP
ma-140	425	34	u	u	NOUN
ma-140	425	35	into	into	ADP
ma-140	425	36	(	(	PUNCT
ma-140	425	37	1.1	1.1	NUM
ma-140	425	38	)	)	PUNCT
ma-140	425	39	yields	yield	VERB
ma-140	425	40	a	a	DET
ma-140	425	41	second	second	ADJ
ma-140	425	42	order	order	NOUN
ma-140	425	43	ordinary	ordinary	ADJ
ma-140	425	44	differential	differential	ADJ
ma-140	425	45	equation	equation	NOUN
ma-140	425	46	cq′	cq′	PROPN
ma-140	425	47	−	−	PROPN
ma-140	425	48	αqq′	αqq′	VERB
ma-140	425	49	+	+	CCONJ
ma-140	425	50	βcq′′′	βcq′′′	X
ma-140	425	51	=	=	SYM
ma-140	425	52	0	0	NUM
ma-140	425	53	,	,	PUNCT
ma-140	425	54	(	(	PUNCT
ma-140	425	55	3.67	3.67	NUM
ma-140	425	56	)	)	PUNCT
ma-140	425	57	which	which	PRON
ma-140	425	58	can	can	AUX
ma-140	425	59	be	be	AUX
ma-140	425	60	integrated	integrate	VERB
ma-140	425	61	with	with	ADP
ma-140	425	62	respect	respect	NOUN
ma-140	425	63	to	to	ADP
ma-140	425	64	q	q	PUNCT
ma-140	425	65	to	to	PART
ma-140	425	66	give	give	VERB
ma-140	425	67	cq−	cq−	NUM
ma-140	425	68	α	α	DET
ma-140	425	69	q2	q2	NOUN
ma-140	425	70	2	2	NUM
ma-140	426	1	+	+	CCONJ
ma-140	426	2	βcq′	βcq′	NOUN
ma-140	426	3	=	=	SYM
ma-140	426	4	0	0	NUM
ma-140	426	5	,	,	PUNCT
ma-140	426	6	(	(	PUNCT
ma-140	426	7	3.68	3.68	NUM
ma-140	426	8	)	)	PUNCT
ma-140	426	9	where	where	SCONJ
ma-140	426	10	we	we	PRON
ma-140	426	11	have	have	AUX
ma-140	426	12	used	use	VERB
ma-140	426	13	0	0	PUNCT
ma-140	426	14	as	as	ADP
ma-140	426	15	a	a	DET
ma-140	426	16	constant	constant	NOUN
ma-140	426	17	of	of	ADP
ma-140	426	18	integration	integration	NOUN
ma-140	426	19	.	.	PUNCT
ma-140	427	1	equation	equation	NOUN
ma-140	427	2	(	(	PUNCT
ma-140	427	3	3.68	3.68	NUM
ma-140	427	4	)	)	PUNCT
ma-140	427	5	can	can	AUX
ma-140	427	6	be	be	AUX
ma-140	427	7	rearranged	rearrange	VERB
ma-140	427	8	and	and	CCONJ
ma-140	427	9	variablesseparated	variablesseparate	VERB
ma-140	427	10	to	to	PART
ma-140	427	11	have	have	VERB
ma-140	427	12	dξ	dξ	PROPN
ma-140	427	13	2βc	2βc	NOUN
ma-140	427	14	=	=	SYM
ma-140	428	1	dq	dq	NOUN
ma-140	428	2	αq2	αq2	NOUN
ma-140	428	3	−	−	PROPN
ma-140	428	4	2cq	2cq	NOUN
ma-140	428	5	,	,	PUNCT
ma-140	428	6	ξ	ξ	X
ma-140	428	7	=	=	PUNCT
ma-140	428	8	x	x	X
ma-140	428	9	−	−	PROPN
ma-140	429	1	ct	ct	PRON
ma-140	429	2	.	.	PUNCT
ma-140	430	1	(	(	PUNCT
ma-140	430	2	3.69	3.69	NUM
ma-140	430	3	)	)	PUNCT
ma-140	430	4	the	the	DET
ma-140	430	5	right	right	ADJ
ma-140	430	6	hand	hand	NOUN
ma-140	430	7	side	side	NOUN
ma-140	430	8	can	can	AUX
ma-140	430	9	be	be	AUX
ma-140	430	10	resolved	resolve	VERB
ma-140	430	11	into	into	ADP
ma-140	430	12	partial	partial	ADJ
ma-140	430	13	fractions	fraction	NOUN
ma-140	430	14	to	to	PART
ma-140	430	15	obtain	obtain	VERB
ma-140	430	16	ξ	ξ	PRON
ma-140	430	17	2βc	2βc	NOUN
ma-140	430	18	=	=	SYM
ma-140	430	19	1	1	NUM
ma-140	430	20	2c	2c	NUM
ma-140	430	21	∫	∫	NOUN
ma-140	430	22	[	[	PUNCT
ma-140	430	23	α	α	PROPN
ma-140	430	24	αq−	αq−	PROPN
ma-140	430	25	2c	2c	NOUN
ma-140	430	26	−	−	NOUN
ma-140	430	27	1	1	NUM
ma-140	430	28	q	q	NOUN
ma-140	430	29	]	]	PUNCT
ma-140	430	30	dq	dq	NOUN
ma-140	430	31	=	=	SYM
ma-140	430	32	1	1	NUM
ma-140	430	33	2c	2c	NUM
ma-140	430	34	ln	ln	NOUN
ma-140	430	35	∣∣∣∣∣αq−	∣∣∣∣∣αq−	PROPN
ma-140	430	36	2c	2c	PROPN
ma-140	430	37	q	q	PROPN
ma-140	430	38	∣∣∣∣∣+	∣∣∣∣∣+	PROPN
ma-140	430	39	ln	ln	ADJ
ma-140	430	40	|c3|	|c3|	NOUN
ma-140	430	41	,	,	PUNCT
ma-140	430	42	(	(	PUNCT
ma-140	430	43	3.70	3.70	NUM
ma-140	430	44	)	)	PUNCT
ma-140	430	45	where	where	SCONJ
ma-140	430	46	c3	c3	PROPN
ma-140	430	47	is	be	AUX
ma-140	430	48	a	a	DET
ma-140	430	49	constant	constant	ADJ
ma-140	430	50	of	of	ADP
ma-140	430	51	integration	integration	NOUN
ma-140	430	52	.	.	PUNCT
ma-140	431	1	after	after	ADP
ma-140	431	2	rewriting	rewrite	VERB
ma-140	431	3	,	,	PUNCT
ma-140	431	4	we	we	PRON
ma-140	431	5	have	have	VERB
ma-140	431	6	q(x	q(x	NOUN
ma-140	431	7	−	−	PROPN
ma-140	431	8	ct	ct	PROPN
ma-140	431	9	)	)	PUNCT
ma-140	431	10	=	=	SYM
ma-140	432	1	2cc3	2cc3	NUM
ma-140	432	2	αc3	αc3	NOUN
ma-140	432	3	−	−	PROPN
ma-140	432	4	e	e	PROPN
ma-140	432	5	x−ct	x−ct	PROPN
ma-140	432	6	β	β	X
ma-140	432	7	.	.	PUNCT
ma-140	433	1	(	(	PUNCT
ma-140	433	2	3.71	3.71	NUM
ma-140	433	3	)	)	PUNCT
ma-140	433	4	finally	finally	ADV
ma-140	433	5	,	,	PUNCT
ma-140	433	6	the	the	DET
ma-140	433	7	soliton	soliton	NOUN
ma-140	433	8	solutions	solution	NOUN
ma-140	433	9	are	be	AUX
ma-140	433	10	given	give	VERB
ma-140	433	11	by	by	ADP
ma-140	433	12	u(t	u(t	NOUN
ma-140	433	13	,	,	PUNCT
ma-140	433	14	x	x	NOUN
ma-140	433	15	)	)	PUNCT
ma-140	433	16	=	=	SYM
ma-140	433	17	2cc3	2cc3	NUM
ma-140	433	18	αc3	αc3	NOUN
ma-140	433	19	−	−	PROPN
ma-140	433	20	e	e	PROPN
ma-140	433	21	x−ct	x−ct	PROPN
ma-140	433	22	β	β	X
ma-140	433	23	.	.	PUNCT
ma-140	434	1	(	(	PUNCT
ma-140	434	2	3.72	3.72	NUM
ma-140	434	3	)	)	PUNCT
ma-140	434	4	4	4	NUM
ma-140	434	5	.	.	PUNCT
ma-140	434	6	conservation	conservation	NOUN
ma-140	434	7	laws	law	NOUN
ma-140	434	8	of	of	ADP
ma-140	434	9	equation	equation	NOUN
ma-140	434	10	(	(	PUNCT
ma-140	434	11	1.1	1.1	NUM
ma-140	434	12	)	)	PUNCT
ma-140	434	13	we	we	PRON
ma-140	434	14	will	will	AUX
ma-140	434	15	employ	employ	VERB
ma-140	434	16	multipliers	multiplier	NOUN
ma-140	434	17	in	in	ADP
ma-140	434	18	the	the	DET
ma-140	434	19	construction	construction	NOUN
ma-140	434	20	of	of	ADP
ma-140	434	21	conservation	conservation	NOUN
ma-140	434	22	laws	law	NOUN
ma-140	434	23	.	.	PUNCT
ma-140	435	1	4.1	4.1	NUM
ma-140	435	2	.	.	PUNCT
ma-140	436	1	the	the	DET
ma-140	436	2	multipliers	multiplier	NOUN
ma-140	436	3	.	.	PUNCT
ma-140	437	1	we	we	PRON
ma-140	437	2	make	make	VERB
ma-140	437	3	use	use	NOUN
ma-140	437	4	of	of	ADP
ma-140	437	5	the	the	DET
ma-140	437	6	euler	euler	NOUN
ma-140	437	7	-	-	PUNCT
ma-140	437	8	lagrange	lagrange	NOUN
ma-140	437	9	operator	operator	NOUN
ma-140	437	10	defined	define	VERB
ma-140	437	11	as	as	SCONJ
ma-140	437	12	defined	define	VERB
ma-140	437	13	in	in	ADP
ma-140	437	14	[	[	X
ma-140	437	15	6	6	NUM
ma-140	437	16	]	]	PUNCT
ma-140	437	17	to	to	PART
ma-140	437	18	lookfor	lookfor	VERB
ma-140	437	19	a	a	DET
ma-140	437	20	zeroth	zeroth	ADJ
ma-140	437	21	order	order	NOUN
ma-140	437	22	multiplier	multipli	ADJ
ma-140	437	23	λ	λ	NOUN
ma-140	437	24	=	=	SYM
ma-140	437	25	λ(t	λ(t	PROPN
ma-140	437	26	,	,	PUNCT
ma-140	437	27	x	x	X
ma-140	437	28	,	,	PUNCT
ma-140	437	29	u	u	NOUN
ma-140	437	30	)	)	PUNCT
ma-140	437	31	.	.	PUNCT
ma-140	438	1	the	the	DET
ma-140	438	2	resulting	result	VERB
ma-140	438	3	determining	determine	VERB
ma-140	438	4	equation	equation	NOUN
ma-140	438	5	for	for	ADP
ma-140	438	6	computing	compute	VERB
ma-140	438	7	λ	λ	PROPN
ma-140	438	8	is	be	AUX
ma-140	438	9	δ	δ	NOUN
ma-140	438	10	δu	δu	ADP
ma-140	438	11	[	[	X
ma-140	438	12	λ{ut	λ{ut	X
ma-140	438	13	+	+	CCONJ
ma-140	438	14	αuux	αuux	NOUN
ma-140	438	15	+	+	CCONJ
ma-140	438	16	βutxx	βutxx	X
ma-140	438	17	}	}	PUNCT
ma-140	438	18	]	]	PUNCT
ma-140	439	1	=	=	PUNCT
ma-140	439	2	0	0	X
ma-140	439	3	.	.	PUNCT
ma-140	440	1	(	(	PUNCT
ma-140	440	2	4.1	4.1	NUM
ma-140	440	3	)	)	PUNCT
ma-140	440	4	where	where	SCONJ
ma-140	440	5	δ	δ	PROPN
ma-140	440	6	δu	δu	ADP
ma-140	440	7	=	=	SYM
ma-140	440	8	∂	∂	NUM
ma-140	440	9	∂u	∂u	PROPN
ma-140	440	10	−dt	−dt	PROPN
ma-140	440	11	∂	∂	NUM
ma-140	440	12	∂ut	∂ut	PROPN
ma-140	440	13	−dx	−dx	PROPN
ma-140	440	14	∂	∂	NUM
ma-140	440	15	∂ux	∂ux	PROPN
ma-140	440	16	−dtd2	−dtd2	PROPN
ma-140	440	17	x	x	SYM
ma-140	440	18	∂	∂	NUM
ma-140	440	19	∂utxx	∂utxx	NUM
ma-140	440	20	+	+	PUNCT
ma-140	440	21	.	.	PUNCT
ma-140	440	22	.	.	PUNCT
ma-140	441	1	.	.	PUNCT
ma-140	442	1	(	(	PUNCT
ma-140	442	2	4.2	4.2	NUM
ma-140	442	3	)	)	PUNCT
ma-140	442	4	expansion	expansion	NOUN
ma-140	442	5	of	of	ADP
ma-140	442	6	equation	equation	NOUN
ma-140	442	7	(	(	PUNCT
ma-140	442	8	4.1	4.1	NUM
ma-140	442	9	)	)	PUNCT
ma-140	442	10	yields	yield	NOUN
ma-140	442	11	λu(ut	λu(ut	PROPN
ma-140	443	1	+	+	CCONJ
ma-140	443	2	αuux	αuux	NOUN
ma-140	443	3	+	+	CCONJ
ma-140	443	4	βutxx	βutxx	X
ma-140	443	5	)	)	PUNCT
ma-140	444	1	+	+	CCONJ
ma-140	444	2	αuxλ−dt(λ)−	αuxλ−dt(λ)−	VERB
ma-140	444	3	αdx(uλ)−	αdx(uλ)−	VERB
ma-140	444	4	βdtd2	βdtd2	NOUN
ma-140	444	5	x	x	SYM
ma-140	444	6	(	(	PUNCT
ma-140	444	7	λ	λ	NOUN
ma-140	444	8	)	)	PUNCT
ma-140	444	9	=	=	SYM
ma-140	444	10	0	0	X
ma-140	444	11	.	.	PUNCT
ma-140	445	1	(	(	PUNCT
ma-140	445	2	4.3	4.3	NUM
ma-140	445	3	)	)	PUNCT
ma-140	445	4	invoking	invoke	VERB
ma-140	445	5	the	the	DET
ma-140	445	6	total	total	ADJ
ma-140	445	7	derivatives	derivative	NOUN
ma-140	445	8	https://doi.org/10.28924/ada/ma.3.13	https://doi.org/10.28924/ada/ma.3.13	PROPN
ma-140	445	9	eur	eur	NOUN
ma-140	445	10	.	.	PUNCT
ma-140	446	1	j.	j.	PROPN
ma-140	446	2	math	math	PROPN
ma-140	446	3	.	.	PUNCT
ma-140	447	1	anal	anal	PROPN
ma-140	447	2	.	.	PUNCT
ma-140	448	1	10.28924	10.28924	NUM
ma-140	448	2	/	/	SYM
ma-140	448	3	ada	ada	PROPN
ma-140	448	4	/	/	SYM
ma-140	448	5	ma.3.13	ma.3.13	PROPN
ma-140	448	6	16	16	NUM
ma-140	448	7	dt	dt	NOUN
ma-140	448	8	=	=	SYM
ma-140	448	9	∂	∂	PROPN
ma-140	449	1	∂t	∂t	PROPN
ma-140	449	2	+	+	CCONJ
ma-140	449	3	ut	ut	PROPN
ma-140	449	4	∂	∂	PROPN
ma-140	449	5	∂u	∂u	PROPN
ma-140	450	1	+	+	CCONJ
ma-140	450	2	utx	utx	PROPN
ma-140	450	3	∂	∂	NUM
ma-140	450	4	∂ux	∂ux	PROPN
ma-140	450	5	+	+	CCONJ
ma-140	450	6	utt	utt	PROPN
ma-140	450	7	∂	∂	NOUN
ma-140	450	8	∂ut	∂ut	PROPN
ma-140	450	9	+	+	CCONJ
ma-140	450	10	·	·	PUNCT
ma-140	450	11	·	·	PUNCT
ma-140	450	12	·	·	PUNCT
ma-140	450	13	,	,	PUNCT
ma-140	450	14	(	(	PUNCT
ma-140	450	15	4.4	4.4	NUM
ma-140	450	16	)	)	PUNCT
ma-140	450	17	dx	dx	PROPN
ma-140	450	18	=	=	SYM
ma-140	450	19	∂	∂	NOUN
ma-140	450	20	∂x	∂x	PROPN
ma-140	451	1	+	+	CCONJ
ma-140	451	2	ux	ux	PROPN
ma-140	451	3	∂	∂	NUM
ma-140	451	4	∂u	∂u	PROPN
ma-140	452	1	+	+	CCONJ
ma-140	452	2	uxx	uxx	PROPN
ma-140	452	3	∂	∂	X
ma-140	452	4	∂ux	∂ux	PROPN
ma-140	452	5	+	+	PROPN
ma-140	452	6	utx	utx	PROPN
ma-140	452	7	∂	∂	NOUN
ma-140	452	8	∂ut	∂ut	PROPN
ma-140	452	9	+	+	PUNCT
ma-140	452	10	.	.	PUNCT
ma-140	452	11	.	.	PUNCT
ma-140	452	12	.	.	PUNCT
ma-140	452	13	.	.	PUNCT
ma-140	453	1	(	(	PUNCT
ma-140	453	2	4.5	4.5	NUM
ma-140	453	3	)	)	PUNCT
ma-140	453	4	on	on	ADP
ma-140	453	5	equation	equation	NOUN
ma-140	453	6	(	(	PUNCT
ma-140	453	7	4.3	4.3	NUM
ma-140	453	8	)	)	PUNCT
ma-140	453	9	produces	produce	VERB
ma-140	453	10	λt	λt	ADP
ma-140	453	11	+	+	CCONJ
ma-140	453	12	αuλx	αuλx	NOUN
ma-140	453	13	+	+	CCONJ
ma-140	453	14	βλtxx	βλtxx	NOUN
ma-140	453	15	+	+	CCONJ
ma-140	453	16	2β(λtxu)ux	2β(λtxu)ux	ADJ
ma-140	453	17	+	+	CCONJ
ma-140	453	18	β(λtu)uxx	β(λtu)uxx	ADJ
ma-140	453	19	+	+	CCONJ
ma-140	453	20	β(λtuu)u2	β(λtuu)u2	NOUN
ma-140	453	21	x	x	PUNCT
ma-140	453	22	+	+	NUM
ma-140	453	23	2β(λxu)utx	2β(λxu)utx	NUM
ma-140	454	1	+	+	CCONJ
ma-140	454	2	2β(λuu)uxutx	2β(λuu)uxutx	NOUN
ma-140	454	3	+	+	CCONJ
ma-140	454	4	β(λxxu)ut	β(λxxu)ut	PUNCT
ma-140	454	5	+	+	NUM
ma-140	454	6	2β(λxuu)uxux	2β(λxuu)uxux	NUM
ma-140	454	7	+	+	NUM
ma-140	454	8	β(λuu)utuxx	β(λuu)utuxx	NOUN
ma-140	454	9	+	+	CCONJ
ma-140	454	10	β(λuuu)utu	β(λuuu)utu	NOUN
ma-140	454	11	2	2	NUM
ma-140	454	12	x	x	SYM
ma-140	454	13	=	=	SYM
ma-140	454	14	0	0	NUM
ma-140	454	15	(	(	PUNCT
ma-140	454	16	4.6	4.6	NUM
ma-140	454	17	)	)	PUNCT
ma-140	454	18	splitting	splitting	NOUN
ma-140	454	19	equation	equation	NOUN
ma-140	454	20	(	(	PUNCT
ma-140	454	21	4.6	4.6	NUM
ma-140	454	22	)	)	PUNCT
ma-140	454	23	on	on	ADP
ma-140	454	24	derivatives	derivative	NOUN
ma-140	454	25	of	of	ADP
ma-140	454	26	u	u	NOUN
ma-140	454	27	produces	produce	VERB
ma-140	454	28	an	an	DET
ma-140	454	29	overdetermined	overdetermined	ADJ
ma-140	454	30	system	system	NOUN
ma-140	454	31	of	of	ADP
ma-140	454	32	four	four	NUM
ma-140	454	33	partialdifferentialequations	partialdifferentialequation	NOUN
ma-140	454	34	,	,	PUNCT
ma-140	454	35	namely	namely	ADV
ma-140	454	36	,	,	PUNCT
ma-140	454	37	λuu	λuu	PROPN
ma-140	454	38	=	=	PROPN
ma-140	454	39	0	0	NUM
ma-140	454	40	,	,	PUNCT
ma-140	454	41	(	(	PUNCT
ma-140	454	42	4.7	4.7	NUM
ma-140	454	43	)	)	PUNCT
ma-140	454	44	λxu	λxu	NOUN
ma-140	454	45	=	=	NOUN
ma-140	454	46	0	0	NUM
ma-140	454	47	,	,	PUNCT
ma-140	454	48	(	(	PUNCT
ma-140	454	49	4.8	4.8	NUM
ma-140	454	50	)	)	PUNCT
ma-140	454	51	λtu	λtu	NOUN
ma-140	454	52	=	=	SYM
ma-140	454	53	0	0	PROPN
ma-140	454	54	(	(	PUNCT
ma-140	454	55	4.9	4.9	NUM
ma-140	454	56	)	)	PUNCT
ma-140	454	57	λt	λt	ADP
ma-140	454	58	+	+	X
ma-140	454	59	αuλx	αuλx	NOUN
ma-140	454	60	+	+	CCONJ
ma-140	454	61	βλtxx	βλtxx	NOUN
ma-140	454	62	=	=	X
ma-140	454	63	0	0	X
ma-140	454	64	(	(	PUNCT
ma-140	454	65	4.10	4.10	NUM
ma-140	454	66	)	)	PUNCT
ma-140	454	67	by	by	ADP
ma-140	454	68	equation	equation	NOUN
ma-140	454	69	(	(	PUNCT
ma-140	454	70	4.7	4.7	NUM
ma-140	454	71	)	)	PUNCT
ma-140	454	72	,	,	PUNCT
ma-140	454	73	we	we	PRON
ma-140	454	74	have	have	VERB
ma-140	454	75	λ	λ	NOUN
ma-140	454	76	=	=	SYM
ma-140	454	77	a(t	a(t	PROPN
ma-140	454	78	,	,	PUNCT
ma-140	454	79	x)u	x)u	PUNCT
ma-140	454	80	+	+	CCONJ
ma-140	454	81	b(t	b(t	PROPN
ma-140	454	82	,	,	PUNCT
ma-140	454	83	x	x	NOUN
ma-140	454	84	)	)	PUNCT
ma-140	454	85	,	,	PUNCT
ma-140	454	86	(	(	PUNCT
ma-140	454	87	4.11	4.11	NUM
ma-140	454	88	)	)	PUNCT
ma-140	454	89	which	which	PRON
ma-140	454	90	if	if	SCONJ
ma-140	454	91	used	use	VERB
ma-140	454	92	in	in	ADP
ma-140	454	93	equations	equation	NOUN
ma-140	454	94	(	(	PUNCT
ma-140	454	95	4.8	4.8	NUM
ma-140	454	96	-	-	SYM
ma-140	454	97	4.9	4.9	NUM
ma-140	454	98	)	)	PUNCT
ma-140	454	99	,	,	PUNCT
ma-140	454	100	implies	imply	VERB
ma-140	454	101	that	that	SCONJ
ma-140	454	102	λ	λ	PROPN
ma-140	454	103	=	=	SYM
ma-140	454	104	c1u	c1u	PROPN
ma-140	454	105	+	+	CCONJ
ma-140	454	106	b(t	b(t	PROPN
ma-140	454	107	,	,	PUNCT
ma-140	454	108	x	x	NOUN
ma-140	454	109	)	)	PUNCT
ma-140	454	110	.	.	PUNCT
ma-140	455	1	(	(	PUNCT
ma-140	455	2	4.12	4.12	NUM
ma-140	455	3	)	)	PUNCT
ma-140	455	4	if	if	SCONJ
ma-140	455	5	we	we	PRON
ma-140	455	6	substitute	substitute	VERB
ma-140	455	7	(	(	PUNCT
ma-140	455	8	4.12	4.12	NUM
ma-140	455	9	)	)	PUNCT
ma-140	455	10	into	into	ADP
ma-140	455	11	equation	equation	NOUN
ma-140	455	12	(	(	PUNCT
ma-140	455	13	4.10	4.10	NUM
ma-140	455	14	)	)	PUNCT
ma-140	455	15	,	,	PUNCT
ma-140	455	16	we	we	PRON
ma-140	455	17	obtain	obtain	VERB
ma-140	455	18	bt(t	bt(t	NOUN
ma-140	455	19	,	,	PUNCT
ma-140	455	20	x	x	X
ma-140	455	21	)	)	PUNCT
ma-140	456	1	+	+	CCONJ
ma-140	456	2	αubx(t	αubx(t	PROPN
ma-140	456	3	,	,	PUNCT
ma-140	456	4	x	x	PRON
ma-140	456	5	)	)	PUNCT
ma-140	456	6	+	+	CCONJ
ma-140	456	7	βbtxx(t	βbtxx(t	NUM
ma-140	456	8	,	,	PUNCT
ma-140	456	9	x	x	NOUN
ma-140	456	10	)	)	PUNCT
ma-140	456	11	=	=	SYM
ma-140	456	12	0	0	X
ma-140	456	13	.	.	PUNCT
ma-140	457	1	(	(	PUNCT
ma-140	457	2	4.13	4.13	NUM
ma-140	457	3	)	)	PUNCT
ma-140	457	4	separation	separation	NOUN
ma-140	457	5	of	of	ADP
ma-140	457	6	equation	equation	NOUN
ma-140	457	7	(	(	PUNCT
ma-140	457	8	4.13	4.13	NUM
ma-140	457	9	)	)	PUNCT
ma-140	457	10	into	into	ADP
ma-140	457	11	powers	power	NOUN
ma-140	457	12	of	of	ADP
ma-140	457	13	u	u	PRON
ma-140	457	14	gives	give	VERB
ma-140	457	15	us	we	PRON
ma-140	457	16	u	u	NOUN
ma-140	457	17	:	:	PUNCT
ma-140	457	18	bx(t	bx(t	PROPN
ma-140	457	19	,	,	PUNCT
ma-140	457	20	x	x	NOUN
ma-140	457	21	)	)	PUNCT
ma-140	457	22	=	=	SYM
ma-140	457	23	0	0	NUM
ma-140	457	24	,	,	PUNCT
ma-140	457	25	(	(	PUNCT
ma-140	457	26	4.14	4.14	NUM
ma-140	457	27	)	)	PUNCT
ma-140	457	28	u0	u0	ADJ
ma-140	457	29	:	:	PUNCT
ma-140	457	30	bt(t	bt(t	NOUN
ma-140	457	31	,	,	PUNCT
ma-140	457	32	x	x	X
ma-140	457	33	)	)	PUNCT
ma-140	457	34	+	+	CCONJ
ma-140	457	35	βbtxx(t	βbtxx(t	NUM
ma-140	457	36	,	,	PUNCT
ma-140	457	37	x	x	NOUN
ma-140	457	38	)	)	PUNCT
ma-140	457	39	=	=	SYM
ma-140	457	40	0	0	X
ma-140	457	41	.	.	PUNCT
ma-140	458	1	(	(	PUNCT
ma-140	458	2	4.15	4.15	NUM
ma-140	458	3	)	)	PUNCT
ma-140	458	4	equation	equation	NOUN
ma-140	458	5	(	(	PUNCT
ma-140	458	6	4.14	4.14	NUM
ma-140	458	7	)	)	PUNCT
ma-140	458	8	insists	insist	VERB
ma-140	459	1	that	that	SCONJ
ma-140	459	2	btxx(t	btxx(t	PROPN
ma-140	459	3	,	,	PUNCT
ma-140	459	4	x	x	NOUN
ma-140	459	5	)	)	PUNCT
ma-140	459	6	=	=	SYM
ma-140	459	7	0	0	PUNCT
ma-140	459	8	=	=	NOUN
ma-140	459	9	⇒	⇒	NOUN
ma-140	459	10	bt(t	bt(t	NUM
ma-140	459	11	,	,	PUNCT
ma-140	459	12	x	x	X
ma-140	459	13	)	)	PUNCT
ma-140	459	14	=	=	SYM
ma-140	459	15	0	0	NUM
ma-140	459	16	=	=	SYM
ma-140	459	17	bx(t	bx(t	PROPN
ma-140	459	18	,	,	PUNCT
ma-140	459	19	x	x	NOUN
ma-140	459	20	)	)	PUNCT
ma-140	459	21	,	,	PUNCT
ma-140	459	22	(	(	PUNCT
ma-140	459	23	4.16	4.16	NUM
ma-140	459	24	)	)	PUNCT
ma-140	459	25	and	and	CCONJ
ma-140	459	26	thus	thus	ADV
ma-140	459	27	b(t	b(t	VERB
ma-140	459	28	,	,	PUNCT
ma-140	459	29	x	x	X
ma-140	459	30	)	)	PUNCT
ma-140	459	31	=	=	SYM
ma-140	459	32	c2	c2	PROPN
ma-140	459	33	.	.	PUNCT
ma-140	460	1	(	(	PUNCT
ma-140	460	2	4.17	4.17	NUM
ma-140	460	3	)	)	PUNCT
ma-140	460	4	as	as	ADP
ma-140	460	5	a	a	DET
ma-140	460	6	result	result	NOUN
ma-140	460	7	λ(t	λ(t	PRON
ma-140	460	8	,	,	PUNCT
ma-140	460	9	x	x	X
ma-140	460	10	,	,	PUNCT
ma-140	460	11	u	u	NOUN
ma-140	460	12	)	)	PUNCT
ma-140	460	13	=	=	SYM
ma-140	460	14	c1u	c1u	PROPN
ma-140	460	15	+	+	CCONJ
ma-140	460	16	c2	c2	PROPN
ma-140	460	17	.	.	PUNCT
ma-140	461	1	(	(	PUNCT
ma-140	461	2	4.18	4.18	NUM
ma-140	461	3	)	)	PUNCT
ma-140	461	4	https://doi.org/10.28924/ada/ma.3.13	https://doi.org/10.28924/ada/ma.3.13	NOUN
ma-140	461	5	eur	eur	NOUN
ma-140	461	6	.	.	PUNCT
ma-140	462	1	j.	j.	PROPN
ma-140	462	2	math	math	PROPN
ma-140	462	3	.	.	PUNCT
ma-140	463	1	anal	anal	PROPN
ma-140	463	2	.	.	PUNCT
ma-140	464	1	10.28924	10.28924	NUM
ma-140	464	2	/	/	SYM
ma-140	464	3	ada	ada	PROPN
ma-140	464	4	/	/	SYM
ma-140	464	5	ma.3.13	ma.3.13	PROPN
ma-140	464	6	17essentially	17essentially	VERB
ma-140	464	7	,	,	PUNCT
ma-140	464	8	we	we	PRON
ma-140	464	9	extract	extract	VERB
ma-140	464	10	the	the	DET
ma-140	464	11	two	two	NUM
ma-140	464	12	multiplies	multiplie	NOUN
ma-140	464	13	λ1	λ1	ADJ
ma-140	464	14	=	=	SYM
ma-140	464	15	1	1	NUM
ma-140	464	16	(	(	PUNCT
ma-140	464	17	4.19	4.19	NUM
ma-140	464	18	)	)	PUNCT
ma-140	464	19	λ2	λ2	NOUN
ma-140	465	1	=	=	NOUN
ma-140	465	2	u.	u.	PROPN
ma-140	465	3	(	(	PUNCT
ma-140	465	4	4.20	4.20	NUM
ma-140	465	5	)	)	PUNCT
ma-140	465	6	remark	remark	NOUN
ma-140	465	7	4.1	4.1	NUM
ma-140	465	8	.	.	PUNCT
ma-140	466	1	recall	recall	VERB
ma-140	466	2	that	that	SCONJ
ma-140	466	3	a	a	DET
ma-140	466	4	multiplier	multipli	ADJ
ma-140	466	5	λ	λ	NOUN
ma-140	466	6	for	for	ADP
ma-140	466	7	equation(1.1	equation(1.1	NOUN
ma-140	466	8	)	)	PUNCT
ma-140	466	9	has	have	VERB
ma-140	466	10	the	the	DET
ma-140	466	11	property	property	NOUN
ma-140	467	1	that	that	PRON
ma-140	467	2	for	for	ADP
ma-140	467	3	the	the	DET
ma-140	467	4	density	density	NOUN
ma-140	467	5	t	t	PROPN
ma-140	467	6	t	t	PROPN
ma-140	467	7	=	=	SYM
ma-140	467	8	t	t	PROPN
ma-140	467	9	t(t	t(t	NOUN
ma-140	467	10	,	,	PUNCT
ma-140	467	11	x	x	NOUN
ma-140	467	12	,	,	PUNCT
ma-140	467	13	u	u	NOUN
ma-140	467	14	,	,	PUNCT
ma-140	467	15	ux	ux	ADJ
ma-140	467	16	)	)	PUNCT
ma-140	467	17	and	and	CCONJ
ma-140	467	18	flux	flux	PROPN
ma-140	467	19	t	t	NOUN
ma-140	467	20	x	x	X
ma-140	467	21	=	=	SYM
ma-140	467	22	t	t	PROPN
ma-140	467	23	x(t	x(t	PROPN
ma-140	467	24	,	,	PUNCT
ma-140	467	25	x	x	X
ma-140	467	26	,	,	PUNCT
ma-140	467	27	u	u	NOUN
ma-140	467	28	,	,	PUNCT
ma-140	467	29	ux	ux	PROPN
ma-140	467	30	,	,	PUNCT
ma-140	467	31	utx	utx	PROPN
ma-140	467	32	)	)	PUNCT
ma-140	467	33	,	,	PUNCT
ma-140	467	34	λ	λ	PROPN
ma-140	467	35	(	(	PUNCT
ma-140	467	36	ut	ut	PROPN
ma-140	467	37	+	+	CCONJ
ma-140	467	38	αuux	αuux	PROPN
ma-140	467	39	+	+	CCONJ
ma-140	467	40	βutxx	βutxx	X
ma-140	467	41	)	)	PUNCT
ma-140	467	42	=	=	PUNCT
ma-140	467	43	dtt	dtt	PROPN
ma-140	467	44	t	t	PROPN
ma-140	467	45	+	+	NOUN
ma-140	467	46	dxt	dxt	PROPN
ma-140	467	47	x	x	X
ma-140	467	48	.	.	PUNCT
ma-140	468	1	(	(	PUNCT
ma-140	468	2	4.21	4.21	NUM
ma-140	468	3	)	)	PUNCT
ma-140	468	4	we	we	PRON
ma-140	468	5	derive	derive	VERB
ma-140	468	6	a	a	DET
ma-140	468	7	conservation	conservation	NOUN
ma-140	468	8	law	law	NOUN
ma-140	468	9	corresponding	correspond	VERB
ma-140	468	10	to	to	ADP
ma-140	468	11	each	each	PRON
ma-140	468	12	of	of	ADP
ma-140	468	13	the	the	DET
ma-140	468	14	multipliers.(i	multipliers.(i	NOUN
ma-140	468	15	)	)	PUNCT
ma-140	468	16	.	.	PUNCT
ma-140	469	1	conservation	conservation	NOUN
ma-140	469	2	law	law	NOUN
ma-140	469	3	for	for	ADP
ma-140	469	4	the	the	DET
ma-140	469	5	multiplier	multipli	ADJ
ma-140	469	6	λ1	λ1	NOUN
ma-140	469	7	=	=	SYM
ma-140	469	8	1expansion	1expansion	NUM
ma-140	469	9	of	of	ADP
ma-140	469	10	equation	equation	NOUN
ma-140	469	11	(	(	PUNCT
ma-140	469	12	4.21	4.21	NUM
ma-140	469	13	)	)	PUNCT
ma-140	469	14	gives	give	VERB
ma-140	469	15	1{ut	1{ut	NUM
ma-140	469	16	+	+	CCONJ
ma-140	469	17	αuux	αuux	NOUN
ma-140	469	18	+	+	CCONJ
ma-140	469	19	βutxx	βutxx	X
ma-140	469	20	}	}	PUNCT
ma-140	469	21	=	=	SYM
ma-140	469	22	t	t	PROPN
ma-140	469	23	tt	tt	PROPN
ma-140	469	24	+	+	CCONJ
ma-140	469	25	utt	utt	PROPN
ma-140	469	26	t	t	NOUN
ma-140	469	27	u	u	NOUN
ma-140	469	28	+	+	CCONJ
ma-140	469	29	utxt	utxt	ADJ
ma-140	469	30	t	t	X
ma-140	469	31	ux	ux	PROPN
ma-140	470	1	+	+	CCONJ
ma-140	470	2	t	t	PROPN
ma-140	470	3	xx	xx	X
ma-140	471	1	+	+	CCONJ
ma-140	471	2	uxt	uxt	ADJ
ma-140	471	3	x	x	PUNCT
ma-140	471	4	u	u	NOUN
ma-140	471	5	+	+	X
ma-140	471	6	uxxt	uxxt	ADJ
ma-140	471	7	x	x	SYM
ma-140	471	8	ux	ux	PROPN
ma-140	471	9	+	+	CCONJ
ma-140	471	10	utxxt	utxxt	NOUN
ma-140	471	11	x	x	X
ma-140	471	12	utx	utx	NOUN
ma-140	471	13	.	.	PUNCT
ma-140	472	1	(	(	PUNCT
ma-140	472	2	4.22	4.22	NUM
ma-140	472	3	)	)	PUNCT
ma-140	472	4	splitting	splitting	NOUN
ma-140	472	5	equation	equation	NOUN
ma-140	472	6	(	(	PUNCT
ma-140	472	7	4.22	4.22	NUM
ma-140	472	8	)	)	PUNCT
ma-140	472	9	on	on	ADP
ma-140	472	10	the	the	DET
ma-140	472	11	third	third	ADJ
ma-140	472	12	derivative	derivative	NOUN
ma-140	472	13	of	of	ADP
ma-140	472	14	u	u	PROPN
ma-140	472	15	yields	yield	VERB
ma-140	472	16	utxx	utxx	NOUN
ma-140	472	17	:	:	PUNCT
ma-140	472	18	t	t	NOUN
ma-140	472	19	xutx	xutx	NOUN
ma-140	472	20	=	=	PUNCT
ma-140	472	21	β	β	X
ma-140	472	22	,	,	PUNCT
ma-140	472	23	(	(	PUNCT
ma-140	472	24	4.23)rest	4.23)rest	NUM
ma-140	472	25	:	:	PUNCT
ma-140	472	26	ut	ut	PROPN
ma-140	473	1	+	+	CCONJ
ma-140	473	2	αuux	αuux	NOUN
ma-140	473	3	=	=	SYM
ma-140	473	4	t	t	X
ma-140	473	5	tt	tt	PROPN
ma-140	473	6	+	+	CCONJ
ma-140	473	7	utt	utt	PROPN
ma-140	473	8	t	t	NOUN
ma-140	473	9	u	u	NOUN
ma-140	473	10	+	+	CCONJ
ma-140	473	11	utxt	utxt	ADJ
ma-140	473	12	t	t	X
ma-140	473	13	ux	ux	PROPN
ma-140	474	1	+	+	CCONJ
ma-140	474	2	t	t	PROPN
ma-140	474	3	xx	xx	X
ma-140	475	1	+	+	CCONJ
ma-140	475	2	uxt	uxt	ADJ
ma-140	475	3	x	x	PUNCT
ma-140	475	4	u	u	NOUN
ma-140	475	5	+	+	X
ma-140	475	6	uxxt	uxxt	ADJ
ma-140	475	7	x	x	SYM
ma-140	475	8	ux	ux	INTJ
ma-140	475	9	.	.	PUNCT
ma-140	476	1	(	(	PUNCT
ma-140	476	2	4.24	4.24	NUM
ma-140	476	3	)	)	PUNCT
ma-140	476	4	the	the	DET
ma-140	476	5	integration	integration	NOUN
ma-140	476	6	of	of	ADP
ma-140	476	7	equation	equation	NOUN
ma-140	476	8	(	(	PUNCT
ma-140	476	9	4.23	4.23	NUM
ma-140	476	10	)	)	PUNCT
ma-140	476	11	with	with	ADP
ma-140	476	12	respect	respect	NOUN
ma-140	476	13	to	to	ADP
ma-140	476	14	utx	utx	PROPN
ma-140	476	15	gives	give	VERB
ma-140	476	16	t	t	NOUN
ma-140	476	17	x	x	SYM
ma-140	476	18	=	=	PUNCT
ma-140	476	19	βutx	βutx	PROPN
ma-140	476	20	+	+	CCONJ
ma-140	476	21	a(t	a(t	PROPN
ma-140	476	22	,	,	PUNCT
ma-140	476	23	x	x	NOUN
ma-140	476	24	,	,	PUNCT
ma-140	476	25	u	u	NOUN
ma-140	476	26	,	,	PUNCT
ma-140	476	27	ux	ux	PROPN
ma-140	476	28	)	)	PUNCT
ma-140	476	29	.	.	PUNCT
ma-140	477	1	(	(	PUNCT
ma-140	477	2	4.25	4.25	NUM
ma-140	477	3	)	)	PUNCT
ma-140	477	4	substituting	substitute	VERB
ma-140	477	5	the	the	DET
ma-140	477	6	expression	expression	NOUN
ma-140	477	7	of	of	ADP
ma-140	477	8	t	t	PROPN
ma-140	477	9	x	x	PUNCT
ma-140	477	10	from	from	ADP
ma-140	477	11	(	(	PUNCT
ma-140	477	12	4.25	4.25	NUM
ma-140	477	13	)	)	PUNCT
ma-140	477	14	into	into	ADP
ma-140	477	15	equation	equation	NOUN
ma-140	477	16	(	(	PUNCT
ma-140	477	17	4.22	4.22	NUM
ma-140	477	18	)	)	PUNCT
ma-140	477	19	we	we	PRON
ma-140	477	20	get	get	VERB
ma-140	477	21	{	{	PUNCT
ma-140	477	22	ut	ut	PROPN
ma-140	477	23	+	+	CCONJ
ma-140	477	24	αuux	αuux	ADJ
ma-140	477	25	}	}	PUNCT
ma-140	477	26	=	=	NOUN
ma-140	477	27	t	t	X
ma-140	477	28	tt	tt	PROPN
ma-140	477	29	+	+	CCONJ
ma-140	477	30	utt	utt	PROPN
ma-140	477	31	t	t	NOUN
ma-140	477	32	u	u	NOUN
ma-140	477	33	+	+	CCONJ
ma-140	477	34	utxt	utxt	ADJ
ma-140	477	35	t	t	X
ma-140	477	36	ux	ux	NOUN
ma-140	478	1	+	+	CCONJ
ma-140	478	2	ax	ax	NOUN
ma-140	478	3	+	+	CCONJ
ma-140	478	4	uxau	uxau	ADJ
ma-140	478	5	+	+	CCONJ
ma-140	478	6	uxxaux	uxxaux	ADJ
ma-140	478	7	(	(	PUNCT
ma-140	478	8	4.26	4.26	NUM
ma-140	478	9	)	)	PUNCT
ma-140	478	10	which	which	PRON
ma-140	478	11	splits	split	VERB
ma-140	478	12	on	on	ADP
ma-140	478	13	second	second	ADJ
ma-140	478	14	derivatives	derivative	NOUN
ma-140	478	15	of	of	ADP
ma-140	478	16	u	u	NOUN
ma-140	478	17	,	,	PUNCT
ma-140	478	18	to	to	PART
ma-140	478	19	give	give	VERB
ma-140	478	20	uxx	uxx	PROPN
ma-140	478	21	:	:	PUNCT
ma-140	478	22	aux	aux	PROPN
ma-140	478	23	=	=	SYM
ma-140	478	24	0	0	PROPN
ma-140	478	25	,	,	PUNCT
ma-140	478	26	(	(	PUNCT
ma-140	478	27	4.27	4.27	NUM
ma-140	478	28	)	)	PUNCT
ma-140	478	29	utx	utx	NOUN
ma-140	478	30	:	:	PUNCT
ma-140	478	31	t	t	NOUN
ma-140	478	32	tux	tux	NOUN
ma-140	478	33	=	=	SYM
ma-140	478	34	0	0	NUM
ma-140	478	35	,	,	PUNCT
ma-140	478	36	(	(	PUNCT
ma-140	478	37	4.28)rest	4.28)rest	NUM
ma-140	478	38	:	:	PUNCT
ma-140	478	39	{	{	PUNCT
ma-140	478	40	ut	ut	PROPN
ma-140	478	41	+	+	CCONJ
ma-140	478	42	αuux	αuux	ADJ
ma-140	478	43	}	}	PUNCT
ma-140	478	44	=	=	SYM
ma-140	478	45	t	t	PROPN
ma-140	478	46	tt	tt	PROPN
ma-140	478	47	+	+	CCONJ
ma-140	478	48	utt	utt	PROPN
ma-140	478	49	t	t	NOUN
ma-140	478	50	u	u	NOUN
ma-140	478	51	+	+	CCONJ
ma-140	478	52	ax	ax	NOUN
ma-140	478	53	+	+	CCONJ
ma-140	478	54	uxau	uxau	ADJ
ma-140	478	55	.	.	PUNCT
ma-140	479	1	(	(	PUNCT
ma-140	479	2	4.29	4.29	X
ma-140	479	3	)	)	PUNCT
ma-140	479	4	integrating	integrate	VERB
ma-140	479	5	equations	equation	NOUN
ma-140	479	6	(	(	PUNCT
ma-140	479	7	4.27	4.27	NUM
ma-140	479	8	)	)	PUNCT
ma-140	479	9	and	and	CCONJ
ma-140	479	10	(	(	PUNCT
ma-140	479	11	4.28	4.28	NUM
ma-140	479	12	)	)	PUNCT
ma-140	479	13	with	with	ADP
ma-140	479	14	respect	respect	NOUN
ma-140	479	15	to	to	ADP
ma-140	479	16	ux	ux	NOUN
ma-140	479	17	manifests	manifest	NOUN
ma-140	479	18	that	that	PRON
ma-140	479	19	t	t	PROPN
ma-140	479	20	t	t	PROPN
ma-140	479	21	=	=	SYM
ma-140	479	22	t	t	PROPN
ma-140	479	23	t(t	t(t	NOUN
ma-140	479	24	,	,	PUNCT
ma-140	479	25	x	x	NOUN
ma-140	479	26	,	,	PUNCT
ma-140	479	27	u	u	NOUN
ma-140	479	28	)	)	PUNCT
ma-140	479	29	and	and	CCONJ
ma-140	479	30	a	a	DET
ma-140	479	31	=	=	X
ma-140	479	32	a(t	a(t	NOUN
ma-140	479	33	,	,	PUNCT
ma-140	479	34	x	x	NOUN
ma-140	479	35	,	,	PUNCT
ma-140	479	36	u	u	NOUN
ma-140	479	37	)	)	PUNCT
ma-140	479	38	.	.	PUNCT
ma-140	480	1	using	use	VERB
ma-140	480	2	values	value	NOUN
ma-140	480	3	of	of	ADP
ma-140	480	4	a	a	PRON
ma-140	480	5	and	and	CCONJ
ma-140	480	6	t	t	NOUN
ma-140	480	7	t	t	NOUN
ma-140	480	8	in	in	ADP
ma-140	480	9	equation	equation	NOUN
ma-140	480	10	(	(	PUNCT
ma-140	480	11	4.29	4.29	NUM
ma-140	480	12	)	)	PUNCT
ma-140	480	13	,	,	PUNCT
ma-140	480	14	we	we	PRON
ma-140	480	15	have	have	VERB
ma-140	480	16	{	{	PUNCT
ma-140	480	17	ut	ut	PROPN
ma-140	480	18	+	+	CCONJ
ma-140	480	19	αuux	αuux	ADJ
ma-140	480	20	}	}	PUNCT
ma-140	480	21	=	=	SYM
ma-140	480	22	t	t	PROPN
ma-140	480	23	tt	tt	PROPN
ma-140	480	24	+	+	CCONJ
ma-140	480	25	utt	utt	PROPN
ma-140	480	26	t	t	NOUN
ma-140	480	27	u	u	NOUN
ma-140	480	28	+	+	CCONJ
ma-140	480	29	ax	ax	NOUN
ma-140	480	30	+	+	CCONJ
ma-140	480	31	uxau	uxau	ADJ
ma-140	480	32	,	,	PUNCT
ma-140	480	33	(	(	PUNCT
ma-140	480	34	4.30	4.30	NUM
ma-140	480	35	)	)	PUNCT
ma-140	480	36	which	which	PRON
ma-140	480	37	separates	separate	VERB
ma-140	480	38	on	on	ADP
ma-140	480	39	first	first	ADJ
ma-140	480	40	derivatives	derivative	NOUN
ma-140	480	41	to	to	PART
ma-140	480	42	give	give	VERB
ma-140	480	43	us	we	PRON
ma-140	480	44	ut	ut	PROPN
ma-140	480	45	:	:	PUNCT
ma-140	480	46	t	t	PROPN
ma-140	480	47	tu	tu	PROPN
ma-140	481	1	=	=	SYM
ma-140	482	1	1	1	PROPN
ma-140	482	2	,	,	PUNCT
ma-140	482	3	(	(	PUNCT
ma-140	482	4	4.31	4.31	NUM
ma-140	482	5	)	)	PUNCT
ma-140	482	6	ux	ux	NOUN
ma-140	482	7	:	:	PUNCT
ma-140	482	8	au	au	PROPN
ma-140	482	9	=	=	SYM
ma-140	482	10	αu	αu	PROPN
ma-140	482	11	,	,	PUNCT
ma-140	482	12	(	(	PUNCT
ma-140	482	13	4.32)rest	4.32)rest	NUM
ma-140	482	14	:	:	PUNCT
ma-140	483	1	t	t	PROPN
ma-140	483	2	tt	tt	PROPN
ma-140	484	1	+	+	CCONJ
ma-140	484	2	ax	ax	NOUN
ma-140	484	3	=	=	NOUN
ma-140	484	4	0	0	PROPN
ma-140	484	5	.	.	PUNCT
ma-140	485	1	(	(	PUNCT
ma-140	485	2	4.33	4.33	NUM
ma-140	485	3	)	)	PUNCT
ma-140	485	4	https://doi.org/10.28924/ada/ma.3.13	https://doi.org/10.28924/ada/ma.3.13	PROPN
ma-140	485	5	eur	eur	NOUN
ma-140	485	6	.	.	PUNCT
ma-140	486	1	j.	j.	PROPN
ma-140	486	2	math	math	PROPN
ma-140	486	3	.	.	PUNCT
ma-140	487	1	anal	anal	PROPN
ma-140	487	2	.	.	PUNCT
ma-140	488	1	10.28924	10.28924	NUM
ma-140	488	2	/	/	SYM
ma-140	488	3	ada	ada	PROPN
ma-140	488	4	/	/	SYM
ma-140	488	5	ma.3.13	ma.3.13	PROPN
ma-140	488	6	18equations	18equations	X
ma-140	489	1	(	(	PUNCT
ma-140	489	2	4.31	4.31	NUM
ma-140	489	3	-	-	SYM
ma-140	489	4	4.32	4.32	NUM
ma-140	489	5	)	)	PUNCT
ma-140	489	6	,	,	PUNCT
ma-140	489	7	can	can	AUX
ma-140	489	8	be	be	AUX
ma-140	489	9	integrated	integrate	VERB
ma-140	489	10	with	with	ADP
ma-140	489	11	respect	respect	NOUN
ma-140	489	12	u	u	NOUN
ma-140	489	13	to	to	PART
ma-140	489	14	obtain	obtain	VERB
ma-140	489	15	t	t	PROPN
ma-140	489	16	tu	tu	PROPN
ma-140	489	17	=	=	SYM
ma-140	489	18	u	u	PROPN
ma-140	489	19	+	+	PROPN
ma-140	489	20	b(t	b(t	PROPN
ma-140	489	21	,	,	PUNCT
ma-140	489	22	x	x	NOUN
ma-140	489	23	)	)	PUNCT
ma-140	489	24	,	,	PUNCT
ma-140	489	25	(	(	PUNCT
ma-140	489	26	4.34	4.34	NUM
ma-140	489	27	)	)	PUNCT
ma-140	489	28	a	a	PRON
ma-140	489	29	=	=	PUNCT
ma-140	489	30	α	α	NOUN
ma-140	489	31	u2	u2	PROPN
ma-140	489	32	2	2	NUM
ma-140	489	33	+	+	CCONJ
ma-140	489	34	c(t	c(t	PROPN
ma-140	489	35	,	,	PUNCT
ma-140	489	36	x	x	NOUN
ma-140	489	37	)	)	PUNCT
ma-140	489	38	,	,	PUNCT
ma-140	489	39	(	(	PUNCT
ma-140	489	40	4.35	4.35	NUM
ma-140	489	41	)	)	PUNCT
ma-140	489	42	if	if	SCONJ
ma-140	489	43	we	we	PRON
ma-140	489	44	use	use	VERB
ma-140	489	45	the	the	DET
ma-140	489	46	obtained	obtain	VERB
ma-140	489	47	values	value	NOUN
ma-140	489	48	in	in	ADP
ma-140	489	49	(	(	PUNCT
ma-140	489	50	4.33	4.33	NUM
ma-140	489	51	)	)	PUNCT
ma-140	489	52	,	,	PUNCT
ma-140	489	53	we	we	PRON
ma-140	489	54	have	have	AUX
ma-140	489	55	bt(t	bt(t	NOUN
ma-140	489	56	,	,	PUNCT
ma-140	489	57	x	x	X
ma-140	489	58	)	)	PUNCT
ma-140	490	1	+	+	CCONJ
ma-140	490	2	cx(t	cx(t	NOUN
ma-140	490	3	,	,	PUNCT
ma-140	490	4	x	x	X
ma-140	490	5	)	)	PUNCT
ma-140	490	6	=	=	SYM
ma-140	490	7	0	0	X
ma-140	490	8	.	.	PUNCT
ma-140	491	1	(	(	PUNCT
ma-140	491	2	4.36	4.36	NUM
ma-140	491	3	)	)	PUNCT
ma-140	491	4	since	since	SCONJ
ma-140	491	5	b(t	b(t	PROPN
ma-140	491	6	,	,	PUNCT
ma-140	491	7	x	x	NOUN
ma-140	491	8	)	)	PUNCT
ma-140	491	9	and	and	CCONJ
ma-140	491	10	c(t	c(t	PROPN
ma-140	491	11	,	,	PUNCT
ma-140	491	12	x	x	NOUN
ma-140	491	13	)	)	PUNCT
ma-140	491	14	contribute	contribute	VERB
ma-140	491	15	to	to	ADP
ma-140	491	16	the	the	DET
ma-140	491	17	trivial	trivial	ADJ
ma-140	491	18	part	part	NOUN
ma-140	491	19	of	of	ADP
ma-140	491	20	the	the	DET
ma-140	491	21	conservation	conservation	NOUN
ma-140	491	22	law	law	NOUN
ma-140	491	23	,	,	PUNCT
ma-140	491	24	we	we	PRON
ma-140	491	25	take	take	VERB
ma-140	491	26	b(t	b(t	PROPN
ma-140	491	27	,	,	PUNCT
ma-140	491	28	x	x	NOUN
ma-140	491	29	)	)	PUNCT
ma-140	491	30	=	=	SYM
ma-140	491	31	c(t	c(t	PROPN
ma-140	491	32	,	,	PUNCT
ma-140	491	33	x	x	NOUN
ma-140	491	34	)	)	PUNCT
ma-140	491	35	=	=	SYM
ma-140	491	36	0	0	PUNCT
ma-140	491	37	and	and	CCONJ
ma-140	491	38	obtain	obtain	VERB
ma-140	491	39	the	the	DET
ma-140	491	40	conserved	conserve	VERB
ma-140	491	41	quantities	quantity	NOUN
ma-140	491	42	t	t	X
ma-140	491	43	t	t	PROPN
ma-140	491	44	=	=	SYM
ma-140	491	45	u	u	PROPN
ma-140	491	46	,	,	PUNCT
ma-140	491	47	(	(	PUNCT
ma-140	491	48	4.37	4.37	NUM
ma-140	491	49	)	)	PUNCT
ma-140	491	50	t	t	NOUN
ma-140	491	51	x	x	X
ma-140	492	1	=	=	NOUN
ma-140	492	2	α	α	NOUN
ma-140	492	3	u2	u2	NOUN
ma-140	492	4	2	2	NUM
ma-140	492	5	+	+	CCONJ
ma-140	492	6	βutx	βutx	PROPN
ma-140	492	7	(	(	PUNCT
ma-140	492	8	4.38	4.38	NUM
ma-140	492	9	)	)	PUNCT
ma-140	492	10	from	from	ADP
ma-140	492	11	which	which	PRON
ma-140	492	12	the	the	DET
ma-140	492	13	conservation	conservation	NOUN
ma-140	492	14	law	law	NOUN
ma-140	492	15	corresponding	correspond	VERB
ma-140	492	16	to	to	ADP
ma-140	492	17	the	the	DET
ma-140	492	18	multiplier	multipli	ADJ
ma-140	492	19	λ1	λ1	NOUN
ma-140	492	20	=	=	SYM
ma-140	492	21	1	1	NUM
ma-140	492	22	is	be	AUX
ma-140	492	23	given	give	VERB
ma-140	492	24	by	by	ADP
ma-140	492	25	dt(u	dt(u	NOUN
ma-140	492	26	)	)	PUNCT
ma-140	493	1	+	+	X
ma-140	493	2	dx	dx	PROPN
ma-140	493	3	(	(	PUNCT
ma-140	493	4	α	α	NOUN
ma-140	493	5	u2	u2	PROPN
ma-140	493	6	2	2	NUM
ma-140	493	7	+	+	CCONJ
ma-140	493	8	βutx	βutx	ADJ
ma-140	493	9	)	)	PUNCT
ma-140	493	10	=	=	PUNCT
ma-140	494	1	0	0	X
ma-140	494	2	.	.	PUNCT
ma-140	495	1	(	(	PUNCT
ma-140	495	2	4.39	4.39	NUM
ma-140	495	3	)	)	PUNCT
ma-140	495	4	(	(	PUNCT
ma-140	495	5	ii	ii	NOUN
ma-140	495	6	)	)	PUNCT
ma-140	495	7	.	.	PUNCT
ma-140	496	1	conservation	conservation	NOUN
ma-140	496	2	law	law	NOUN
ma-140	496	3	for	for	ADP
ma-140	496	4	the	the	DET
ma-140	496	5	multiplier	multipli	ADJ
ma-140	496	6	λ2	λ2	NOUN
ma-140	496	7	=	=	SYM
ma-140	496	8	u	u	NOUN
ma-140	496	9	u{ut	u{ut	PROPN
ma-140	496	10	+	+	CCONJ
ma-140	496	11	αuux	αuux	NOUN
ma-140	496	12	+	+	CCONJ
ma-140	496	13	βutxx	βutxx	X
ma-140	496	14	}	}	PUNCT
ma-140	496	15	=	=	SYM
ma-140	496	16	t	t	PROPN
ma-140	496	17	tt	tt	PROPN
ma-140	496	18	+	+	CCONJ
ma-140	496	19	utt	utt	PROPN
ma-140	496	20	t	t	NOUN
ma-140	496	21	u	u	NOUN
ma-140	496	22	+	+	CCONJ
ma-140	496	23	utxt	utxt	ADJ
ma-140	496	24	t	t	X
ma-140	496	25	ux	ux	PROPN
ma-140	497	1	+	+	CCONJ
ma-140	497	2	t	t	PROPN
ma-140	497	3	xx	xx	X
ma-140	498	1	+	+	CCONJ
ma-140	498	2	uxt	uxt	ADJ
ma-140	498	3	x	x	PUNCT
ma-140	498	4	u	u	NOUN
ma-140	498	5	+	+	X
ma-140	498	6	uxxt	uxxt	ADJ
ma-140	498	7	x	x	SYM
ma-140	498	8	ux	ux	PROPN
ma-140	498	9	+	+	CCONJ
ma-140	498	10	utxxt	utxxt	NOUN
ma-140	498	11	x	x	X
ma-140	498	12	utx	utx	NOUN
ma-140	498	13	.	.	PUNCT
ma-140	499	1	(	(	PUNCT
ma-140	499	2	4.40	4.40	NUM
ma-140	499	3	)	)	PUNCT
ma-140	499	4	splitting	splitting	NOUN
ma-140	499	5	equation	equation	NOUN
ma-140	499	6	(	(	PUNCT
ma-140	499	7	4.40	4.40	NUM
ma-140	499	8	)	)	PUNCT
ma-140	499	9	on	on	ADP
ma-140	499	10	the	the	DET
ma-140	499	11	third	third	ADJ
ma-140	499	12	derivative	derivative	NOUN
ma-140	499	13	of	of	ADP
ma-140	499	14	u	u	PROPN
ma-140	499	15	yields	yield	VERB
ma-140	499	16	utxx	utxx	NOUN
ma-140	499	17	:	:	PUNCT
ma-140	499	18	t	t	PROPN
ma-140	499	19	xutx	xutx	PROPN
ma-140	499	20	=	=	SYM
ma-140	499	21	βu	βu	PROPN
ma-140	499	22	,	,	PUNCT
ma-140	499	23	(	(	PUNCT
ma-140	499	24	4.41)rest	4.41)rest	NUM
ma-140	499	25	:	:	PUNCT
ma-140	499	26	ut	ut	PROPN
ma-140	500	1	+	+	NUM
ma-140	500	2	αuux	αuux	NOUN
ma-140	500	3	=	=	SYM
ma-140	500	4	t	t	X
ma-140	500	5	tt	tt	PROPN
ma-140	500	6	+	+	CCONJ
ma-140	500	7	utt	utt	PROPN
ma-140	500	8	t	t	NOUN
ma-140	500	9	u	u	NOUN
ma-140	500	10	+	+	CCONJ
ma-140	500	11	utxt	utxt	ADJ
ma-140	500	12	t	t	X
ma-140	500	13	ux	ux	PROPN
ma-140	501	1	+	+	CCONJ
ma-140	501	2	t	t	PROPN
ma-140	501	3	xx	xx	X
ma-140	502	1	+	+	CCONJ
ma-140	502	2	uxt	uxt	ADJ
ma-140	502	3	x	x	PUNCT
ma-140	502	4	u	u	NOUN
ma-140	502	5	+	+	X
ma-140	502	6	uxxt	uxxt	ADJ
ma-140	502	7	x	x	SYM
ma-140	502	8	ux	ux	INTJ
ma-140	502	9	.	.	PUNCT
ma-140	503	1	(	(	PUNCT
ma-140	503	2	4.42	4.42	NUM
ma-140	503	3	)	)	PUNCT
ma-140	503	4	the	the	DET
ma-140	503	5	integration	integration	NOUN
ma-140	503	6	of	of	ADP
ma-140	503	7	equation	equation	NOUN
ma-140	503	8	(	(	PUNCT
ma-140	503	9	4.41	4.41	NUM
ma-140	503	10	)	)	PUNCT
ma-140	503	11	with	with	ADP
ma-140	503	12	respect	respect	NOUN
ma-140	503	13	to	to	ADP
ma-140	503	14	utx	utx	PROPN
ma-140	503	15	gives	give	VERB
ma-140	503	16	t	t	NOUN
ma-140	503	17	x	x	PUNCT
ma-140	503	18	=	=	PUNCT
ma-140	503	19	βuutx	βuutx	NOUN
ma-140	503	20	+	+	CCONJ
ma-140	503	21	a(t	a(t	PROPN
ma-140	503	22	,	,	PUNCT
ma-140	503	23	x	x	NOUN
ma-140	503	24	,	,	PUNCT
ma-140	503	25	u	u	NOUN
ma-140	503	26	,	,	PUNCT
ma-140	503	27	ux	ux	PROPN
ma-140	503	28	)	)	PUNCT
ma-140	503	29	.	.	PUNCT
ma-140	504	1	(	(	PUNCT
ma-140	504	2	4.43	4.43	NUM
ma-140	504	3	)	)	PUNCT
ma-140	504	4	substituting	substitute	VERB
ma-140	504	5	the	the	DET
ma-140	504	6	expression	expression	NOUN
ma-140	504	7	of	of	ADP
ma-140	504	8	t	t	PROPN
ma-140	504	9	x	x	PUNCT
ma-140	504	10	from	from	ADP
ma-140	504	11	(	(	PUNCT
ma-140	504	12	4.43	4.43	NUM
ma-140	504	13	)	)	PUNCT
ma-140	504	14	into	into	ADP
ma-140	504	15	equation	equation	NOUN
ma-140	504	16	(	(	PUNCT
ma-140	504	17	4.40	4.40	NUM
ma-140	504	18	)	)	PUNCT
ma-140	504	19	we	we	PRON
ma-140	504	20	get	get	VERB
ma-140	504	21	u{ut	u{ut	PROPN
ma-140	504	22	+	+	CCONJ
ma-140	504	23	αuux	αuux	ADJ
ma-140	504	24	}	}	PUNCT
ma-140	504	25	=	=	NOUN
ma-140	504	26	t	t	X
ma-140	504	27	tt	tt	PROPN
ma-140	504	28	+	+	CCONJ
ma-140	504	29	utt	utt	PROPN
ma-140	504	30	t	t	NOUN
ma-140	504	31	u	u	NOUN
ma-140	504	32	+	+	CCONJ
ma-140	504	33	utxt	utxt	ADJ
ma-140	504	34	t	t	X
ma-140	504	35	ux	ux	NOUN
ma-140	505	1	+	+	CCONJ
ma-140	505	2	ax	ax	NOUN
ma-140	505	3	+	+	CCONJ
ma-140	505	4	uxau	uxau	ADJ
ma-140	505	5	+	+	CCONJ
ma-140	505	6	uxβutx	uxβutx	NOUN
ma-140	505	7	+	+	CCONJ
ma-140	505	8	uxxaux	uxxaux	ADJ
ma-140	505	9	.	.	PUNCT
ma-140	506	1	(	(	PUNCT
ma-140	506	2	4.44	4.44	NUM
ma-140	506	3	)	)	PUNCT
ma-140	506	4	which	which	PRON
ma-140	506	5	splits	split	VERB
ma-140	506	6	on	on	ADP
ma-140	506	7	second	second	ADJ
ma-140	506	8	derivatives	derivative	NOUN
ma-140	506	9	of	of	ADP
ma-140	506	10	u	u	NOUN
ma-140	506	11	,	,	PUNCT
ma-140	506	12	to	to	PART
ma-140	506	13	give	give	VERB
ma-140	506	14	uxx	uxx	PROPN
ma-140	506	15	:	:	PUNCT
ma-140	506	16	aux	aux	PROPN
ma-140	506	17	=	=	SYM
ma-140	506	18	0	0	PROPN
ma-140	506	19	,	,	PUNCT
ma-140	506	20	(	(	PUNCT
ma-140	506	21	4.45	4.45	X
ma-140	506	22	)	)	PUNCT
ma-140	506	23	utx	utx	NOUN
ma-140	506	24	:	:	PUNCT
ma-140	506	25	t	t	NOUN
ma-140	506	26	tux	tux	NOUN
ma-140	506	27	=	=	SYM
ma-140	506	28	−βux	−βux	NOUN
ma-140	506	29	,	,	PUNCT
ma-140	506	30	(	(	PUNCT
ma-140	506	31	4.46)rest	4.46)rest	NUM
ma-140	506	32	:	:	PUNCT
ma-140	507	1	u{ut	u{ut	NOUN
ma-140	507	2	+	+	CCONJ
ma-140	507	3	αuux	αuux	ADJ
ma-140	507	4	}	}	PUNCT
ma-140	507	5	=	=	SYM
ma-140	507	6	t	t	PROPN
ma-140	507	7	tt	tt	PROPN
ma-140	507	8	+	+	CCONJ
ma-140	507	9	utt	utt	PROPN
ma-140	507	10	t	t	NOUN
ma-140	507	11	u	u	NOUN
ma-140	507	12	+	+	CCONJ
ma-140	507	13	ax	ax	NOUN
ma-140	507	14	+	+	CCONJ
ma-140	507	15	uxau	uxau	ADJ
ma-140	507	16	.	.	PUNCT
ma-140	508	1	(	(	PUNCT
ma-140	508	2	4.47	4.47	X
ma-140	508	3	)	)	PUNCT
ma-140	508	4	https://doi.org/10.28924/ada/ma.3.13	https://doi.org/10.28924/ada/ma.3.13	PROPN
ma-140	508	5	eur	eur	NOUN
ma-140	508	6	.	.	PUNCT
ma-140	509	1	j.	j.	PROPN
ma-140	509	2	math	math	PROPN
ma-140	509	3	.	.	PUNCT
ma-140	510	1	anal	anal	PROPN
ma-140	510	2	.	.	PUNCT
ma-140	511	1	10.28924	10.28924	NUM
ma-140	511	2	/	/	SYM
ma-140	511	3	ada	ada	PROPN
ma-140	511	4	/	/	SYM
ma-140	511	5	ma.3.13	ma.3.13	PROPN
ma-140	511	6	19integrating	19integrating	NUM
ma-140	511	7	equations	equation	NOUN
ma-140	511	8	(	(	PUNCT
ma-140	511	9	4.45	4.45	NUM
ma-140	511	10	)	)	PUNCT
ma-140	511	11	and	and	CCONJ
ma-140	511	12	(	(	PUNCT
ma-140	511	13	4.46	4.46	NUM
ma-140	511	14	)	)	PUNCT
ma-140	511	15	with	with	ADP
ma-140	511	16	respect	respect	NOUN
ma-140	511	17	to	to	ADP
ma-140	511	18	ux	ux	NOUN
ma-140	511	19	manifests	manifest	NOUN
ma-140	511	20	that	that	PRON
ma-140	511	21	t	t	NOUN
ma-140	511	22	t	t	NOUN
ma-140	511	23	=	=	PUNCT
ma-140	511	24	−βu	−βu	NUM
ma-140	511	25	2	2	NUM
ma-140	511	26	x	x	SYM
ma-140	511	27	2	2	NUM
ma-140	511	28	+	+	NUM
ma-140	511	29	b(t	b(t	PROPN
ma-140	511	30	,	,	PUNCT
ma-140	511	31	x	x	X
ma-140	511	32	,	,	PUNCT
ma-140	511	33	u	u	NOUN
ma-140	511	34	)	)	PUNCT
ma-140	511	35	and	and	CCONJ
ma-140	511	36	a	a	DET
ma-140	511	37	=	=	X
ma-140	511	38	a(t	a(t	NOUN
ma-140	511	39	,	,	PUNCT
ma-140	511	40	x	x	NOUN
ma-140	511	41	,	,	PUNCT
ma-140	511	42	u	u	NOUN
ma-140	511	43	)	)	PUNCT
ma-140	511	44	.	.	PUNCT
ma-140	512	1	using	use	VERB
ma-140	512	2	values	value	NOUN
ma-140	512	3	of	of	ADP
ma-140	512	4	a	a	PRON
ma-140	512	5	and	and	CCONJ
ma-140	512	6	t	t	PROPN
ma-140	512	7	t	t	PROPN
ma-140	512	8	in	in	ADP
ma-140	512	9	equation(4.47	equation(4.47	NOUN
ma-140	512	10	)	)	PUNCT
ma-140	512	11	,	,	PUNCT
ma-140	512	12	we	we	PRON
ma-140	512	13	have	have	VERB
ma-140	512	14	u{ut	u{ut	NOUN
ma-140	512	15	+	+	CCONJ
ma-140	512	16	αuux	αuux	ADJ
ma-140	512	17	}	}	PUNCT
ma-140	512	18	=	=	SYM
ma-140	512	19	t	t	PROPN
ma-140	512	20	tt	tt	PROPN
ma-140	512	21	+	+	CCONJ
ma-140	512	22	utt	utt	PROPN
ma-140	512	23	t	t	NOUN
ma-140	512	24	u	u	NOUN
ma-140	512	25	+	+	CCONJ
ma-140	512	26	ax	ax	NOUN
ma-140	512	27	+	+	CCONJ
ma-140	512	28	uxau	uxau	ADJ
ma-140	512	29	,	,	PUNCT
ma-140	512	30	(	(	PUNCT
ma-140	512	31	4.48	4.48	NUM
ma-140	512	32	)	)	PUNCT
ma-140	512	33	which	which	PRON
ma-140	512	34	separates	separate	VERB
ma-140	512	35	on	on	ADP
ma-140	512	36	first	first	ADJ
ma-140	512	37	derivatives	derivative	NOUN
ma-140	512	38	to	to	PART
ma-140	512	39	give	give	VERB
ma-140	512	40	us	we	PRON
ma-140	512	41	ut	ut	PROPN
ma-140	512	42	:	:	PUNCT
ma-140	512	43	b(t	b(t	VERB
ma-140	512	44	,	,	PUNCT
ma-140	512	45	x	x	X
ma-140	512	46	,	,	PUNCT
ma-140	512	47	u)u	u)u	ADJ
ma-140	512	48	=	=	SYM
ma-140	512	49	u	u	NOUN
ma-140	512	50	,	,	PUNCT
ma-140	512	51	(	(	PUNCT
ma-140	512	52	4.49	4.49	NUM
ma-140	512	53	)	)	PUNCT
ma-140	512	54	ux	ux	NOUN
ma-140	512	55	:	:	PUNCT
ma-140	512	56	au	au	PROPN
ma-140	512	57	=	=	SYM
ma-140	512	58	αu2	αu2	PROPN
ma-140	512	59	,	,	PUNCT
ma-140	512	60	(	(	PUNCT
ma-140	512	61	4.50)rest	4.50)rest	NUM
ma-140	512	62	:	:	PUNCT
ma-140	512	63	bt	bt	X
ma-140	512	64	+	+	CCONJ
ma-140	512	65	ax	ax	NOUN
ma-140	512	66	=	=	NOUN
ma-140	512	67	0	0	PROPN
ma-140	512	68	.	.	PUNCT
ma-140	513	1	(	(	PUNCT
ma-140	513	2	4.51	4.51	NUM
ma-140	513	3	)	)	PUNCT
ma-140	513	4	equations	equation	NOUN
ma-140	513	5	(	(	PUNCT
ma-140	513	6	4.49	4.49	NUM
ma-140	513	7	-	-	SYM
ma-140	513	8	4.50	4.50	NUM
ma-140	513	9	)	)	PUNCT
ma-140	513	10	,	,	PUNCT
ma-140	513	11	can	can	AUX
ma-140	513	12	be	be	AUX
ma-140	513	13	integrated	integrate	VERB
ma-140	513	14	with	with	ADP
ma-140	513	15	respect	respect	NOUN
ma-140	513	16	u	u	NOUN
ma-140	513	17	to	to	PART
ma-140	513	18	obtain	obtain	VERB
ma-140	513	19	b	b	NOUN
ma-140	513	20	=	=	SYM
ma-140	513	21	u2	u2	PROPN
ma-140	513	22	2	2	NUM
ma-140	513	23	+	+	CCONJ
ma-140	513	24	c(t	c(t	PROPN
ma-140	513	25	,	,	PUNCT
ma-140	513	26	x	x	NOUN
ma-140	513	27	)	)	PUNCT
ma-140	513	28	,	,	PUNCT
ma-140	513	29	(	(	PUNCT
ma-140	513	30	4.52	4.52	NUM
ma-140	513	31	)	)	PUNCT
ma-140	513	32	a	a	DET
ma-140	513	33	=	=	SYM
ma-140	513	34	α	α	NOUN
ma-140	513	35	u3	u3	NOUN
ma-140	513	36	3	3	NUM
ma-140	513	37	+	+	SYM
ma-140	513	38	d(t	d(t	PROPN
ma-140	513	39	,	,	PUNCT
ma-140	513	40	x	x	NOUN
ma-140	513	41	)	)	PUNCT
ma-140	513	42	,	,	PUNCT
ma-140	513	43	(	(	PUNCT
ma-140	513	44	4.53	4.53	NUM
ma-140	513	45	)	)	PUNCT
ma-140	513	46	if	if	SCONJ
ma-140	513	47	we	we	PRON
ma-140	513	48	use	use	VERB
ma-140	513	49	the	the	DET
ma-140	513	50	obtained	obtain	VERB
ma-140	513	51	values	value	NOUN
ma-140	513	52	in	in	ADP
ma-140	513	53	(	(	PUNCT
ma-140	513	54	4.51	4.51	NUM
ma-140	513	55	)	)	PUNCT
ma-140	513	56	,	,	PUNCT
ma-140	513	57	we	we	PRON
ma-140	513	58	have	have	VERB
ma-140	513	59	ct(t	ct(t	NOUN
ma-140	513	60	,	,	PUNCT
ma-140	513	61	x	x	X
ma-140	513	62	)	)	PUNCT
ma-140	514	1	+	+	ADJ
ma-140	514	2	dx(t	dx(t	NOUN
ma-140	514	3	,	,	PUNCT
ma-140	514	4	x	x	NOUN
ma-140	514	5	)	)	PUNCT
ma-140	514	6	=	=	SYM
ma-140	514	7	0	0	X
ma-140	514	8	.	.	PUNCT
ma-140	515	1	(	(	PUNCT
ma-140	515	2	4.54	4.54	NUM
ma-140	515	3	)	)	PUNCT
ma-140	515	4	since	since	SCONJ
ma-140	515	5	c(t	c(t	PROPN
ma-140	515	6	,	,	PUNCT
ma-140	515	7	x	x	NOUN
ma-140	515	8	)	)	PUNCT
ma-140	515	9	and	and	CCONJ
ma-140	515	10	d(t	d(t	PROPN
ma-140	515	11	,	,	PUNCT
ma-140	515	12	x	x	X
ma-140	515	13	)	)	PUNCT
ma-140	515	14	contribute	contribute	VERB
ma-140	515	15	to	to	ADP
ma-140	515	16	the	the	DET
ma-140	515	17	trivial	trivial	ADJ
ma-140	515	18	part	part	NOUN
ma-140	515	19	of	of	ADP
ma-140	515	20	the	the	DET
ma-140	515	21	conservation	conservation	NOUN
ma-140	515	22	law	law	NOUN
ma-140	515	23	,	,	PUNCT
ma-140	515	24	we	we	PRON
ma-140	515	25	take	take	VERB
ma-140	515	26	c(t	c(t	PROPN
ma-140	515	27	,	,	PUNCT
ma-140	515	28	x	x	NOUN
ma-140	515	29	)	)	PUNCT
ma-140	515	30	=	=	SYM
ma-140	516	1	d(t	d(t	PROPN
ma-140	516	2	,	,	PUNCT
ma-140	516	3	x	x	NOUN
ma-140	516	4	)	)	PUNCT
ma-140	516	5	=	=	SYM
ma-140	516	6	0	0	PUNCT
ma-140	516	7	and	and	CCONJ
ma-140	516	8	obtain	obtain	VERB
ma-140	516	9	the	the	DET
ma-140	516	10	conserved	conserve	VERB
ma-140	516	11	quantities	quantity	NOUN
ma-140	516	12	t	t	X
ma-140	516	13	t	t	NOUN
ma-140	516	14	=	=	NOUN
ma-140	516	15	−	−	PROPN
ma-140	516	16	β	β	X
ma-140	516	17	u2	u2	NOUN
ma-140	516	18	x	x	SYM
ma-140	516	19	2	2	NUM
ma-140	516	20	+	+	CCONJ
ma-140	516	21	u2	u2	PROPN
ma-140	516	22	2	2	NUM
ma-140	516	23	,	,	PUNCT
ma-140	516	24	(	(	PUNCT
ma-140	516	25	4.55	4.55	NUM
ma-140	516	26	)	)	PUNCT
ma-140	516	27	t	t	NOUN
ma-140	516	28	x	x	X
ma-140	517	1	=	=	NOUN
ma-140	517	2	βuutx	βuutx	NOUN
ma-140	517	3	+	+	CCONJ
ma-140	517	4	α	α	NOUN
ma-140	517	5	u3	u3	NOUN
ma-140	517	6	3	3	NUM
ma-140	517	7	(	(	PUNCT
ma-140	517	8	4.56	4.56	NUM
ma-140	517	9	)	)	PUNCT
ma-140	517	10	from	from	ADP
ma-140	517	11	which	which	PRON
ma-140	517	12	the	the	DET
ma-140	517	13	conservation	conservation	NOUN
ma-140	517	14	law	law	NOUN
ma-140	517	15	corresponding	correspond	VERB
ma-140	517	16	to	to	ADP
ma-140	517	17	the	the	DET
ma-140	517	18	multiplier	multipli	ADJ
ma-140	517	19	λ2	λ2	NOUN
ma-140	517	20	=	=	SYM
ma-140	517	21	u	u	NOUN
ma-140	517	22	is	be	AUX
ma-140	517	23	given	give	VERB
ma-140	517	24	by	by	ADP
ma-140	517	25	dt	dt	PROPN
ma-140	518	1	(	(	PUNCT
ma-140	518	2	−	−	PROPN
ma-140	518	3	β	β	X
ma-140	518	4	u2	u2	NOUN
ma-140	518	5	x	x	SYM
ma-140	518	6	2	2	NUM
ma-140	518	7	+	+	CCONJ
ma-140	518	8	u2	u2	PROPN
ma-140	518	9	2	2	NUM
ma-140	518	10	)	)	PUNCT
ma-140	519	1	+	+	NUM
ma-140	519	2	dx	dx	PROPN
ma-140	519	3	(	(	PUNCT
ma-140	519	4	βuutx	βuutx	NOUN
ma-140	519	5	+	+	CCONJ
ma-140	519	6	α	α	NOUN
ma-140	519	7	u3	u3	NOUN
ma-140	519	8	3	3	NUM
ma-140	519	9	)	)	PUNCT
ma-140	519	10	=	=	SYM
ma-140	520	1	0	0	X
ma-140	520	2	.	.	PUNCT
ma-140	521	1	(	(	PUNCT
ma-140	521	2	4.57	4.57	NUM
ma-140	521	3	)	)	PUNCT
ma-140	521	4	remark	remark	NOUN
ma-140	521	5	4.2	4.2	NUM
ma-140	521	6	.	.	PUNCT
ma-140	522	1	it	it	PRON
ma-140	522	2	can	can	AUX
ma-140	522	3	be	be	AUX
ma-140	522	4	shown	show	VERB
ma-140	522	5	that	that	SCONJ
ma-140	522	6	the	the	DET
ma-140	522	7	two	two	NUM
ma-140	522	8	sets	set	NOUN
ma-140	522	9	of	of	ADP
ma-140	522	10	conserved	conserve	VERB
ma-140	522	11	quantities	quantity	NOUN
ma-140	522	12	are	be	AUX
ma-140	522	13	conservation	conservation	NOUN
ma-140	522	14	laws	law	NOUN
ma-140	522	15	.	.	PUNCT
ma-140	523	1	giventhat	giventhat	NOUN
ma-140	523	2	λ1	λ1	PROPN
ma-140	523	3	=	=	SYM
ma-140	523	4	1	1	NUM
ma-140	523	5	,	,	PUNCT
ma-140	523	6	the	the	DET
ma-140	523	7	verification	verification	NOUN
ma-140	523	8	reaffirms	reaffirm	VERB
ma-140	523	9	that	that	SCONJ
ma-140	523	10	the	the	DET
ma-140	523	11	equal	equal	ADJ
ma-140	523	12	width	width	ADJ
ma-140	523	13	equation	equation	NOUN
ma-140	523	14	is	be	AUX
ma-140	523	15	itself	itself	PRON
ma-140	523	16	a	a	DET
ma-140	523	17	conversation	conversation	ADJ
ma-140	523	18	law	law	NOUN
ma-140	523	19	.	.	PUNCT
ma-140	524	1	5	5	X
ma-140	524	2	.	.	X
ma-140	524	3	conclusion	conclusion	NOUN
ma-140	524	4	in	in	ADP
ma-140	524	5	this	this	DET
ma-140	524	6	manuscript	manuscript	NOUN
ma-140	524	7	,	,	PUNCT
ma-140	524	8	an	an	DET
ma-140	524	9	infinite	infinite	ADJ
ma-140	524	10	dimensional	dimensional	ADJ
ma-140	524	11	lie	lie	NOUN
ma-140	524	12	algebra	algebra	NOUN
ma-140	524	13	of	of	ADP
ma-140	524	14	lie	lie	NOUN
ma-140	524	15	point	point	NOUN
ma-140	524	16	symmetries	symmetry	NOUN
ma-140	524	17	has	have	AUX
ma-140	524	18	been	be	AUX
ma-140	524	19	appliedto	appliedto	ADJ
ma-140	524	20	study	study	NOUN
ma-140	524	21	a	a	DET
ma-140	524	22	third	third	ADJ
ma-140	524	23	-	-	PUNCT
ma-140	524	24	order	order	NOUN
ma-140	524	25	equal	equal	ADJ
ma-140	524	26	width	width	ADJ
ma-140	524	27	equation	equation	NOUN
ma-140	524	28	.	.	PUNCT
ma-140	525	1	a	a	DET
ma-140	525	2	commutator	commutator	NOUN
ma-140	525	3	table	table	NOUN
ma-140	525	4	has	have	AUX
ma-140	525	5	been	be	AUX
ma-140	525	6	constructed	construct	VERB
ma-140	525	7	for	for	ADP
ma-140	525	8	theobtained	theobtaine	VERB
ma-140	525	9	lie	lie	NOUN
ma-140	525	10	algebra	algebra	NOUN
ma-140	525	11	.	.	PUNCT
ma-140	526	1	we	we	PRON
ma-140	526	2	have	have	AUX
ma-140	526	3	also	also	ADV
ma-140	526	4	used	use	VERB
ma-140	526	5	symmetry	symmetry	NOUN
ma-140	526	6	reductions	reduction	NOUN
ma-140	526	7	to	to	PART
ma-140	526	8	compute	compute	VERB
ma-140	526	9	exact	exact	ADJ
ma-140	526	10	group	group	NOUN
ma-140	526	11	-	-	PUNCT
ma-140	526	12	invariantsolutions	invariantsolution	NOUN
ma-140	526	13	,	,	PUNCT
ma-140	526	14	including	include	VERB
ma-140	526	15	a	a	DET
ma-140	526	16	soliton	soliton	NOUN
ma-140	526	17	.	.	PUNCT
ma-140	527	1	conservation	conservation	NOUN
ma-140	527	2	laws	law	NOUN
ma-140	527	3	have	have	AUX
ma-140	527	4	also	also	ADV
ma-140	527	5	been	be	AUX
ma-140	527	6	derived	derive	VERB
ma-140	527	7	for	for	ADP
ma-140	527	8	the	the	DET
ma-140	527	9	model	model	NOUN
ma-140	527	10	with	with	ADP
ma-140	527	11	the	the	DET
ma-140	527	12	useof	useof	ADJ
ma-140	527	13	zeroth	zeroth	ADJ
ma-140	527	14	order	order	NOUN
ma-140	527	15	multipliers	multiplier	NOUN
ma-140	527	16	.	.	PUNCT
ma-140	528	1	https://doi.org/10.28924/ada/ma.3.13	https://doi.org/10.28924/ada/ma.3.13	PROPN
ma-140	528	2	eur	eur	PROPN
ma-140	528	3	.	.	PUNCT
ma-140	529	1	j.	j.	PROPN
ma-140	529	2	math	math	PROPN
ma-140	529	3	.	.	PUNCT
ma-140	530	1	anal	anal	PROPN
ma-140	530	2	.	.	PUNCT
ma-140	531	1	10.28924	10.28924	NUM
ma-140	531	2	/	/	SYM
ma-140	531	3	ada	ada	PROPN
ma-140	531	4	/	/	SYM
ma-140	531	5	ma.3.13	ma.3.13	PROPN
ma-140	531	6	20acknowledgement	20acknowledgement	NUM
ma-140	532	1	the	the	DET
ma-140	532	2	author	author	NOUN
ma-140	532	3	thanks	thanks	NUM
ma-140	532	4	referees	referee	NOUN
ma-140	532	5	and	and	CCONJ
ma-140	532	6	the	the	DET
ma-140	532	7	editor	editor	NOUN
ma-140	532	8	for	for	ADP
ma-140	532	9	their	their	PRON
ma-140	532	10	careful	careful	ADJ
ma-140	532	11	reading	reading	NOUN
ma-140	532	12	and	and	CCONJ
ma-140	532	13	comments	comment	NOUN
ma-140	532	14	.	.	PUNCT
ma-140	533	1	author	author	NOUN
ma-140	533	2	’s	’s	PART
ma-140	533	3	contribution	contribution	NOUN
ma-140	533	4	the	the	DET
ma-140	533	5	author	author	NOUN
ma-140	533	6	wrote	write	VERB
ma-140	533	7	the	the	DET
ma-140	533	8	article	article	NOUN
ma-140	533	9	as	as	ADP
ma-140	533	10	a	a	DET
ma-140	533	11	scholarly	scholarly	ADJ
ma-140	533	12	duty	duty	NOUN
ma-140	533	13	and	and	CCONJ
ma-140	533	14	passion	passion	NOUN
ma-140	533	15	to	to	PART
ma-140	533	16	disseminate	disseminate	VERB
ma-140	533	17	mathematical	mathematical	ADJ
ma-140	533	18	re	re	NOUN
ma-140	533	19	-	-	NOUN
ma-140	533	20	search	search	NOUN
ma-140	533	21	and	and	CCONJ
ma-140	533	22	hereby	hereby	ADV
ma-140	533	23	declares	declare	VERB
ma-140	533	24	that	that	SCONJ
ma-140	533	25	there	there	PRON
ma-140	533	26	is	be	VERB
ma-140	533	27	no	no	DET
ma-140	533	28	conflict	conflict	NOUN
ma-140	533	29	of	of	ADP
ma-140	533	30	interest	interest	NOUN
ma-140	533	31	.	.	PUNCT
ma-140	534	1	references	reference	NOUN
ma-140	534	2	[	[	X
ma-140	534	3	1	1	NUM
ma-140	534	4	]	]	X
ma-140	534	5	j.r	j.r	PROPN
ma-140	534	6	.	.	PROPN
ma-140	534	7	cannon	cannon	PROPN
ma-140	534	8	,	,	PUNCT
ma-140	534	9	the	the	DET
ma-140	534	10	one	one	NUM
ma-140	534	11	-	-	PUNCT
ma-140	534	12	dimensional	dimensional	ADJ
ma-140	534	13	heat	heat	NOUN
ma-140	534	14	equation	equation	NOUN
ma-140	534	15	,	,	PUNCT
ma-140	534	16	cambridge	cambridge	PROPN
ma-140	534	17	university	university	PROPN
ma-140	534	18	press	press	PROPN
ma-140	534	19	,	,	PUNCT
ma-140	534	20	cambridge	cambridge	PROPN
ma-140	534	21	,	,	PUNCT
ma-140	534	22	1984.[2	1984.[2	NUM
ma-140	534	23	]	]	X
ma-140	534	24	p.j	p.j	PROPN
ma-140	534	25	.	.	PROPN
ma-140	534	26	morrison	morrison	PROPN
ma-140	534	27	,	,	PUNCT
ma-140	534	28	j.d	j.d	PROPN
ma-140	534	29	.	.	PROPN
ma-140	534	30	meiss	meiss	PROPN
ma-140	534	31	,	,	PUNCT
ma-140	534	32	j.r	j.r	PROPN
ma-140	534	33	.	.	PROPN
ma-140	534	34	cary	cary	PROPN
ma-140	534	35	,	,	PUNCT
ma-140	534	36	scattering	scatter	VERB
ma-140	534	37	of	of	ADP
ma-140	534	38	regularized	regularize	VERB
ma-140	534	39	-	-	PUNCT
ma-140	534	40	long	long	ADJ
ma-140	534	41	-	-	PUNCT
ma-140	534	42	wave	wave	NOUN
ma-140	534	43	solitary	solitary	ADJ
ma-140	534	44	waves	wave	NOUN
ma-140	534	45	,	,	PUNCT
ma-140	534	46	physica	physica	NOUN
ma-140	534	47	d	d	NOUN
ma-140	534	48	:	:	PUNCT
ma-140	534	49	nonlinearphenomena	nonlinearphenomena	PROPN
ma-140	534	50	.	.	PUNCT
ma-140	535	1	11	11	NUM
ma-140	535	2	(	(	PUNCT
ma-140	535	3	1984	1984	NUM
ma-140	535	4	)	)	PUNCT
ma-140	536	1	324–336	324–336	NUM
ma-140	536	2	.	.	PUNCT
ma-140	537	1	https://doi.org/10.1016/0167-2789(84)90014-9.[3	https://doi.org/10.1016/0167-2789(84)90014-9.[3	NOUN
ma-140	537	2	]	]	PUNCT
ma-140	537	3	l.r.t	l.r.t	PROPN
ma-140	537	4	.	.	PUNCT
ma-140	537	5	gardner	gardner	PROPN
ma-140	537	6	,	,	PUNCT
ma-140	537	7	g.a	g.a	PROPN
ma-140	537	8	.	.	PROPN
ma-140	537	9	gardner	gardner	PROPN
ma-140	537	10	,	,	PUNCT
ma-140	537	11	f.a	f.a	PROPN
ma-140	537	12	.	.	PROPN
ma-140	537	13	ayoub	ayoub	PROPN
ma-140	537	14	,	,	PUNCT
ma-140	537	15	n.k	n.k	PROPN
ma-140	537	16	.	.	PROPN
ma-140	537	17	amein	amein	PROPN
ma-140	537	18	,	,	PUNCT
ma-140	537	19	simulations	simulation	NOUN
ma-140	537	20	of	of	ADP
ma-140	537	21	the	the	DET
ma-140	537	22	ew	ew	INTJ
ma-140	537	23	undular	undular	ADJ
ma-140	537	24	bore	bore	NOUN
ma-140	537	25	,	,	PUNCT
ma-140	537	26	commun	commun	PROPN
ma-140	537	27	.	.	PUNCT
ma-140	538	1	numer	numer	PROPN
ma-140	538	2	.	.	PUNCT
ma-140	539	1	meth.engng	meth.engng	PROPN
ma-140	539	2	.	.	NOUN
ma-140	539	3	13	13	NUM
ma-140	539	4	(	(	PUNCT
ma-140	539	5	1997	1997	NUM
ma-140	539	6	)	)	PUNCT
ma-140	540	1	583–592	583–592	NUM
ma-140	540	2	.	.	PUNCT
ma-140	541	1	https://doi.org/10.1002/(sici)1099-0887(199707)13:7<583::aid-cnm90>3	https://doi.org/10.1002/(sici)1099-0887(199707)13:7<583::aid-cnm90>3	NOUN
ma-140	541	2	.	.	PUNCT
ma-140	542	1	0.co;2	0.co;2	NUM
ma-140	542	2	-	-	PUNCT
ma-140	542	3	e.[4	e.[4	NOUN
ma-140	542	4	]	]	PUNCT
ma-140	542	5	l.r.t	l.r.t	PROPN
ma-140	542	6	.	.	PUNCT
ma-140	542	7	gardner	gardner	PROPN
ma-140	542	8	,	,	PUNCT
ma-140	542	9	g.a	g.a	PROPN
ma-140	542	10	.	.	PROPN
ma-140	542	11	gardner	gardner	NOUN
ma-140	542	12	,	,	PUNCT
ma-140	542	13	solitary	solitary	ADJ
ma-140	542	14	waves	wave	NOUN
ma-140	542	15	of	of	ADP
ma-140	542	16	the	the	DET
ma-140	542	17	equal	equal	ADJ
ma-140	542	18	width	width	ADJ
ma-140	542	19	wave	wave	NOUN
ma-140	542	20	equation	equation	NOUN
ma-140	542	21	,	,	PUNCT
ma-140	542	22	j.	j.	PROPN
ma-140	542	23	comput	comput	PROPN
ma-140	542	24	.	.	PUNCT
ma-140	543	1	phys	phy	NOUN
ma-140	543	2	.	.	PUNCT
ma-140	544	1	101	101	NUM
ma-140	544	2	(	(	PUNCT
ma-140	544	3	1992	1992	NUM
ma-140	544	4	)	)	PUNCT
ma-140	544	5	218–223	218–223	NUM
ma-140	544	6	.	.	PUNCT
ma-140	545	1	https://doi.org/10.1016/0021-9991(92)90054-3.[5	https://doi.org/10.1016/0021-9991(92)90054-3.[5	PROPN
ma-140	545	2	]	]	X
ma-140	545	3	j.o	j.o	PROPN
ma-140	545	4	.	.	PROPN
ma-140	545	5	owino	owino	PROPN
ma-140	545	6	,	,	PUNCT
ma-140	545	7	group	group	NOUN
ma-140	545	8	analysis	analysis	NOUN
ma-140	545	9	on	on	ADP
ma-140	545	10	one	one	NUM
ma-140	545	11	-	-	PUNCT
ma-140	545	12	dimensional	dimensional	ADJ
ma-140	545	13	heat	heat	NOUN
ma-140	545	14	equation	equation	NOUN
ma-140	545	15	,	,	PUNCT
ma-140	545	16	int	int	NOUN
ma-140	545	17	.	.	PUNCT
ma-140	546	1	j.	j.	PROPN
ma-140	546	2	adv	adv	PROPN
ma-140	546	3	.	.	PUNCT
ma-140	547	1	multidisc	multidisc	PROPN
ma-140	547	2	.	.	PUNCT
ma-140	548	1	res	re	NOUN
ma-140	548	2	.	.	PUNCT
ma-140	548	3	stud	stud	PROPN
ma-140	548	4	.	.	PUNCT
ma-140	549	1	2	2	NUM
ma-140	549	2	(	(	PUNCT
ma-140	549	3	2022	2022	NUM
ma-140	549	4	)	)	PUNCT
ma-140	549	5	525	525	NUM
ma-140	549	6	-	-	SYM
ma-140	549	7	540.[6	540.[6	NUM
ma-140	549	8	]	]	PUNCT
ma-140	549	9	j.	j.	PROPN
ma-140	549	10	owuor	owuor	PROPN
ma-140	549	11	,	,	PUNCT
ma-140	549	12	exact	exact	ADJ
ma-140	549	13	symmetry	symmetry	NOUN
ma-140	549	14	reduction	reduction	NOUN
ma-140	549	15	solutions	solution	NOUN
ma-140	549	16	of	of	ADP
ma-140	549	17	a	a	DET
ma-140	549	18	nonlinear	nonlinear	ADJ
ma-140	549	19	coupled	couple	VERB
ma-140	549	20	system	system	NOUN
ma-140	549	21	of	of	ADP
ma-140	549	22	korteweg	korteweg	NOUN
ma-140	549	23	-	-	PUNCT
ma-140	549	24	de	de	NOUN
ma-140	549	25	vries	vries	PROPN
ma-140	549	26	equations	equation	NOUN
ma-140	549	27	,	,	PUNCT
ma-140	549	28	int.j	int.j	PROPN
ma-140	549	29	.	.	PUNCT
ma-140	550	1	adv	adv	PROPN
ma-140	550	2	.	.	PUNCT
ma-140	551	1	multidisc	multidisc	PROPN
ma-140	551	2	.	.	PUNCT
ma-140	552	1	res	re	NOUN
ma-140	552	2	.	.	PUNCT
ma-140	552	3	stud	stud	PROPN
ma-140	552	4	.	.	PUNCT
ma-140	553	1	2	2	NUM
ma-140	553	2	(	(	PUNCT
ma-140	553	3	2022	2022	NUM
ma-140	553	4	)	)	PUNCT
ma-140	553	5	76	76	NUM
ma-140	553	6	-	-	SYM
ma-140	553	7	87.[7	87.[7	NUM
ma-140	553	8	]	]	PUNCT
ma-140	553	9	j.	j.	PROPN
ma-140	553	10	owuor	owuor	PROPN
ma-140	553	11	owino	owino	PROPN
ma-140	553	12	,	,	PUNCT
ma-140	553	13	b.	b.	PROPN
ma-140	553	14	okelo	okelo	PROPN
ma-140	553	15	,	,	PUNCT
ma-140	553	16	lie	lie	NOUN
ma-140	553	17	group	group	NOUN
ma-140	553	18	analysis	analysis	NOUN
ma-140	553	19	of	of	ADP
ma-140	553	20	a	a	DET
ma-140	553	21	nonlinear	nonlinear	ADJ
ma-140	553	22	coupled	couple	VERB
ma-140	553	23	system	system	NOUN
ma-140	553	24	of	of	ADP
ma-140	553	25	korteweg	korteweg	NOUN
ma-140	553	26	-	-	PUNCT
ma-140	553	27	de	de	NOUN
ma-140	553	28	vries	vries	PROPN
ma-140	553	29	equations	equation	NOUN
ma-140	553	30	,	,	PUNCT
ma-140	553	31	eur.j	eur.j	PROPN
ma-140	553	32	.	.	PROPN
ma-140	553	33	math	math	NOUN
ma-140	553	34	.	.	PUNCT
ma-140	554	1	anal	anal	ADJ
ma-140	554	2	.	.	PUNCT
ma-140	555	1	1	1	NUM
ma-140	555	2	(	(	PUNCT
ma-140	555	3	2021	2021	NUM
ma-140	555	4	)	)	PUNCT
ma-140	555	5	133–150	133–150	NUM
ma-140	555	6	.	.	PUNCT
ma-140	556	1	https://doi.org/10.28924/ada/ma.1.133.[8	https://doi.org/10.28924/ada/ma.1.133.[8	PROPN
ma-140	556	2	]	]	X
ma-140	556	3	j.o	j.o	PROPN
ma-140	556	4	.	.	PROPN
ma-140	556	5	owino	owino	PROPN
ma-140	556	6	,	,	PUNCT
ma-140	556	7	a	a	DET
ma-140	556	8	group	group	NOUN
ma-140	556	9	approach	approach	NOUN
ma-140	556	10	to	to	ADP
ma-140	556	11	exact	exact	ADJ
ma-140	556	12	solutions	solution	NOUN
ma-140	556	13	and	and	CCONJ
ma-140	556	14	conservation	conservation	NOUN
ma-140	556	15	laws	law	NOUN
ma-140	556	16	of	of	ADP
ma-140	556	17	burger	burger	NOUN
ma-140	556	18	’s	’s	PART
ma-140	556	19	equation	equation	NOUN
ma-140	556	20	,	,	PUNCT
ma-140	556	21	int	int	NOUN
ma-140	556	22	.	.	PUNCT
ma-140	557	1	j.	j.	PROPN
ma-140	557	2	math	math	PROPN
ma-140	557	3	.	.	PUNCT
ma-140	558	1	comp.res	comp.re	NOUN
ma-140	558	2	.	.	PROPN
ma-140	559	1	10	10	NUM
ma-140	559	2	(	(	PUNCT
ma-140	559	3	2022	2022	NUM
ma-140	559	4	)	)	PUNCT
ma-140	559	5	2894	2894	NUM
ma-140	559	6	-	-	SYM
ma-140	559	7	2909	2909	NUM
ma-140	559	8	.	.	PUNCT
ma-140	560	1	https://doi.org/10.47191/ijmcr/v10i9.03.[9	https://doi.org/10.47191/ijmcr/v10i9.03.[9	NOUN
ma-140	560	2	]	]	PUNCT
ma-140	560	3	j.	j.	PROPN
ma-140	560	4	owuor	owuor	PROPN
ma-140	560	5	,	,	PUNCT
ma-140	560	6	conserved	conserve	VERB
ma-140	560	7	quantities	quantity	NOUN
ma-140	560	8	of	of	ADP
ma-140	560	9	a	a	DET
ma-140	560	10	nonlinear	nonlinear	ADJ
ma-140	560	11	coupled	couple	VERB
ma-140	560	12	system	system	NOUN
ma-140	560	13	of	of	ADP
ma-140	560	14	korteweg	korteweg	NOUN
ma-140	560	15	-	-	PUNCT
ma-140	560	16	de	de	NOUN
ma-140	560	17	vries	vries	PROPN
ma-140	560	18	equations	equation	NOUN
ma-140	560	19	,	,	PUNCT
ma-140	560	20	int	int	NOUN
ma-140	560	21	.	.	PUNCT
ma-140	561	1	j.	j.	PROPN
ma-140	561	2	math	math	PROPN
ma-140	561	3	.	.	PUNCT
ma-140	562	1	comp.res	comp.re	NOUN
ma-140	562	2	.	.	PROPN
ma-140	563	1	10	10	NUM
ma-140	563	2	(	(	PUNCT
ma-140	563	3	2022	2022	NUM
ma-140	563	4	)	)	PUNCT
ma-140	563	5	2673	2673	NUM
ma-140	563	6	-	-	SYM
ma-140	563	7	2681	2681	NUM
ma-140	563	8	.	.	PUNCT
ma-140	564	1	https://doi.org/10.47191/ijmcr/v10i5.02.[10	https://doi.org/10.47191/ijmcr/v10i5.02.[10	ADV
ma-140	564	2	]	]	PUNCT
ma-140	564	3	j.	j.	PROPN
ma-140	564	4	o.	o.	PROPN
ma-140	564	5	owino	owino	PROPN
ma-140	564	6	,	,	PUNCT
ma-140	564	7	an	an	DET
ma-140	564	8	application	application	NOUN
ma-140	564	9	of	of	ADP
ma-140	564	10	lie	lie	NOUN
ma-140	564	11	point	point	NOUN
ma-140	564	12	symmetries	symmetry	NOUN
ma-140	564	13	in	in	ADP
ma-140	564	14	the	the	DET
ma-140	564	15	study	study	NOUN
ma-140	564	16	of	of	ADP
ma-140	564	17	potential	potential	ADJ
ma-140	564	18	burger	burger	NOUN
ma-140	564	19	’s	’s	PART
ma-140	564	20	equation	equation	NOUN
ma-140	564	21	,	,	PUNCT
ma-140	564	22	int	int	NOUN
ma-140	564	23	.	.	PUNCT
ma-140	565	1	j.	j.	PROPN
ma-140	565	2	adv	adv	PROPN
ma-140	565	3	.	.	PUNCT
ma-140	566	1	multidisc.res	multidisc.re	NOUN
ma-140	566	2	.	.	PUNCT
ma-140	567	1	stud	stud	NOUN
ma-140	567	2	.	.	PUNCT
ma-140	568	1	2	2	NUM
ma-140	568	2	(	(	PUNCT
ma-140	568	3	2022	2022	NUM
ma-140	568	4	)	)	PUNCT
ma-140	568	5	191	191	NUM
ma-140	568	6	-	-	SYM
ma-140	568	7	207.[11	207.[11	NUM
ma-140	568	8	]	]	PUNCT
ma-140	568	9	j.	j.	PROPN
ma-140	568	10	o.	o.	PROPN
ma-140	568	11	owino	owino	PROPN
ma-140	568	12	,	,	PUNCT
ma-140	568	13	group	group	NOUN
ma-140	568	14	invariant	invariant	ADJ
ma-140	568	15	solutions	solution	NOUN
ma-140	568	16	and	and	CCONJ
ma-140	568	17	conserved	conserve	VERB
ma-140	568	18	vectors	vector	NOUN
ma-140	568	19	for	for	ADP
ma-140	568	20	a	a	DET
ma-140	568	21	special	special	ADJ
ma-140	568	22	kdv	kdv	NOUN
ma-140	568	23	type	type	NOUN
ma-140	568	24	equation	equation	NOUN
ma-140	568	25	,	,	PUNCT
ma-140	568	26	int	int	NOUN
ma-140	568	27	.	.	PUNCT
ma-140	569	1	j.	j.	PROPN
ma-140	569	2	adv	adv	PROPN
ma-140	569	3	.	.	PUNCT
ma-140	570	1	multidisc.res	multidisc.re	NOUN
ma-140	570	2	.	.	PUNCT
ma-140	571	1	stud	stud	NOUN
ma-140	571	2	.	.	PUNCT
ma-140	572	1	2	2	NUM
ma-140	572	2	(	(	PUNCT
ma-140	572	3	2022	2022	NUM
ma-140	572	4	)	)	PUNCT
ma-140	572	5	,	,	PUNCT
ma-140	572	6	9	9	NUM
ma-140	572	7	-	-	SYM
ma-140	572	8	26	26	NUM
ma-140	572	9	.	.	PUNCT
ma-140	573	1	https://doi.org/10.28924/ada/ma.3.13	https://doi.org/10.28924/ada/ma.3.13	NUM
ma-140	573	2	https://doi.org/10.1016/0167-2789(84)90014-9	https://doi.org/10.1016/0167-2789(84)90014-9	PROPN
ma-140	573	3	https://doi.org/10.1002/(sici)1099-0887(199707)13:7<583::aid-cnm90>3.0.co;2-e	https://doi.org/10.1002/(sici)1099-0887(199707)13:7<583::aid-cnm90>3.0.co;2-e	PROPN
ma-140	573	4	https://doi.org/10.1002/(sici)1099-0887(199707)13:7<583::aid-cnm90>3.0.co;2-e	https://doi.org/10.1002/(sici)1099-0887(199707)13:7<583::aid-cnm90>3.0.co;2-e	PROPN
ma-140	573	5	https://doi.org/10.1016/0021-9991(92)90054-3	https://doi.org/10.1016/0021-9991(92)90054-3	PROPN
ma-140	574	1	https://doi.org/10.28924/ada/ma.1.133	https://doi.org/10.28924/ada/ma.1.133	INTJ
ma-140	575	1	https://doi.org/10.47191/ijmcr/v10i9.03	https://doi.org/10.47191/ijmcr/v10i9.03	NOUN
ma-140	575	2	https://doi.org/10.47191/ijmcr/v10i5.02	https://doi.org/10.47191/ijmcr/v10i5.02	NOUN
ma-140	575	3	1	1	NUM
ma-140	575	4	.	.	PUNCT
ma-140	576	1	introduction	introduction	NOUN
ma-140	576	2	2	2	NUM
ma-140	576	3	.	.	PUNCT
ma-140	576	4	preliminaries	preliminary	NOUN
ma-140	576	5	local	local	ADJ
ma-140	576	6	lie	lie	NOUN
ma-140	576	7	groups	group	NOUN
ma-140	576	8	prolongations	prolongation	NOUN
ma-140	576	9	lie	lie	VERB
ma-140	576	10	algebras	algebras	PROPN
ma-140	576	11	conservation	conservation	NOUN
ma-140	576	12	laws	law	NOUN
ma-140	576	13	the	the	DET
ma-140	576	14	method	method	NOUN
ma-140	576	15	of	of	ADP
ma-140	576	16	multipliers	multiplier	NOUN
ma-140	576	17	ibragimov	ibragimov	NOUN
ma-140	576	18	's	's	PART
ma-140	576	19	conservation	conservation	NOUN
ma-140	576	20	theorem	theorem	VERB
ma-140	576	21	3	3	NUM
ma-140	576	22	.	.	NOUN
ma-140	576	23	main	main	ADJ
ma-140	576	24	results	result	NOUN
ma-140	576	25	3.1	3.1	NUM
ma-140	576	26	.	.	PUNCT
ma-140	577	1	lie	lie	NOUN
ma-140	577	2	point	point	NOUN
ma-140	577	3	symmetries	symmetry	NOUN
ma-140	577	4	of	of	ADP
ma-140	577	5	equal	equal	ADJ
ma-140	577	6	width	width	ADJ
ma-140	577	7	equation(1.1	equation(1.1	NOUN
ma-140	577	8	)	)	PUNCT
ma-140	577	9	3.2	3.2	NUM
ma-140	577	10	.	.	PUNCT
ma-140	578	1	commutator	commutator	NOUN
ma-140	578	2	table	table	NOUN
ma-140	578	3	for	for	ADP
ma-140	578	4	symmetries	symmetry	NOUN
ma-140	578	5	3.3	3.3	NUM
ma-140	578	6	.	.	PUNCT
ma-140	579	1	group	group	NOUN
ma-140	579	2	transformations	transformation	VERB
ma-140	579	3	3.4	3.4	NUM
ma-140	579	4	.	.	PUNCT
ma-140	580	1	symmetry	symmetry	NOUN
ma-140	580	2	transformations	transformation	NOUN
ma-140	580	3	3.5	3.5	NUM
ma-140	580	4	.	.	PUNCT
ma-140	581	1	construction	construction	NOUN
ma-140	581	2	of	of	ADP
ma-140	581	3	group	group	NOUN
ma-140	581	4	-	-	PUNCT
ma-140	581	5	invariant	invariant	ADJ
ma-140	581	6	solutions	solution	NOUN
ma-140	581	7	3.6	3.6	NUM
ma-140	581	8	.	.	PUNCT
ma-140	582	1	soliton	soliton	NOUN
ma-140	582	2	4	4	NUM
ma-140	582	3	.	.	PUNCT
ma-140	582	4	conservation	conservation	NOUN
ma-140	582	5	laws	law	NOUN
ma-140	582	6	of	of	ADP
ma-140	582	7	equation	equation	NOUN
ma-140	582	8	(	(	PUNCT
ma-140	582	9	1.1	1.1	NUM
ma-140	582	10	)	)	PUNCT
ma-140	582	11	4.1	4.1	NUM
ma-140	582	12	.	.	PUNCT
ma-140	583	1	the	the	DET
ma-140	583	2	multipliers	multiplier	NOUN
ma-140	583	3	5	5	NUM
ma-140	583	4	.	.	PUNCT
ma-140	583	5	conclusion	conclusion	NOUN
ma-140	583	6	acknowledgement	acknowledgement	NOUN
ma-140	583	7	author	author	NOUN
ma-140	583	8	's	's	PART
ma-140	583	9	contribution	contribution	NOUN
ma-140	583	10	references	reference	NOUN