id	sid	tid	token	lemma	pos
ap-3411	1	1	acta	acta	PROPN
ap-3411	1	2	polytechnica	polytechnica	PROPN
ap-3411	1	3	doi:10.14311	doi:10.14311	PROPN
ap-3411	1	4	/	/	SYM
ap-3411	1	5	ap.2016.56.0193	ap.2016.56.0193	PROPN
ap-3411	1	6	acta	acta	PROPN
ap-3411	1	7	polytechnica	polytechnica	PROPN
ap-3411	1	8	56(3):193–201	56(3):193–201	PROPN
ap-3411	1	9	,	,	PUNCT
ap-3411	1	10	2016	2016	NUM
ap-3411	1	11	©	©	PROPN
ap-3411	1	12	czech	czech	PROPN
ap-3411	1	13	technical	technical	PROPN
ap-3411	1	14	university	university	PROPN
ap-3411	1	15	in	in	ADP
ap-3411	1	16	prague	prague	PROPN
ap-3411	1	17	,	,	PUNCT
ap-3411	1	18	2016	2016	NUM
ap-3411	1	19	available	available	ADJ
ap-3411	1	20	online	online	ADV
ap-3411	1	21	at	at	ADP
ap-3411	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3411	1	23	on	on	ADP
ap-3411	1	24	partial	partial	ADJ
ap-3411	1	25	differential	differential	NOUN
ap-3411	1	26	and	and	CCONJ
ap-3411	1	27	difference	difference	NOUN
ap-3411	1	28	equations	equation	NOUN
ap-3411	1	29	with	with	ADP
ap-3411	1	30	symmetries	symmetry	NOUN
ap-3411	1	31	depending	depend	VERB
ap-3411	1	32	on	on	ADP
ap-3411	1	33	arbitrary	arbitrary	ADJ
ap-3411	1	34	functions	function	NOUN
ap-3411	1	35	giorgio	giorgio	PROPN
ap-3411	1	36	gubbiotti	gubbiotti	PROPN
ap-3411	1	37	,	,	PUNCT
ap-3411	1	38	decio	decio	NOUN
ap-3411	1	39	levi∗	levi∗	PROPN
ap-3411	1	40	,	,	PUNCT
ap-3411	1	41	christian	christian	ADJ
ap-3411	1	42	scimiterna	scimiterna	NOUN
ap-3411	1	43	dipartimento	dipartimento	ADP
ap-3411	1	44	di	di	X
ap-3411	1	45	matematica	matematica	PROPN
ap-3411	1	46	e	e	PROPN
ap-3411	1	47	fisica	fisica	PROPN
ap-3411	1	48	,	,	PUNCT
ap-3411	1	49	università	università	PROPN
ap-3411	1	50	degli	degli	PROPN
ap-3411	1	51	studi	studi	PROPN
ap-3411	1	52	roma	roma	PROPN
ap-3411	1	53	tre	tre	PROPN
ap-3411	1	54	,	,	PUNCT
ap-3411	1	55	e	e	PROPN
ap-3411	1	56	sezione	sezione	PROPN
ap-3411	1	57	infn	infn	PROPN
ap-3411	1	58	di	di	PROPN
ap-3411	1	59	roma	roma	PROPN
ap-3411	1	60	tre	tre	PROPN
ap-3411	1	61	,	,	PUNCT
ap-3411	1	62	via	via	ADP
ap-3411	1	63	della	della	PROPN
ap-3411	1	64	vasca	vasca	PROPN
ap-3411	1	65	navale	navale	PROPN
ap-3411	1	66	84	84	NUM
ap-3411	1	67	,	,	PUNCT
ap-3411	1	68	00146	00146	NUM
ap-3411	1	69	roma	roma	PROPN
ap-3411	1	70	(	(	PUNCT
ap-3411	1	71	italy	italy	PROPN
ap-3411	1	72	)	)	PUNCT
ap-3411	1	73	∗	∗	VERB
ap-3411	1	74	corresponding	correspond	VERB
ap-3411	1	75	author	author	NOUN
ap-3411	1	76	:	:	PUNCT
ap-3411	1	77	decio.levi@roma3.infn.it	decio.levi@roma3.infn.it	PROPN
ap-3411	1	78	abstract	abstract	NOUN
ap-3411	1	79	.	.	PUNCT
ap-3411	2	1	in	in	ADP
ap-3411	2	2	this	this	DET
ap-3411	2	3	note	note	NOUN
ap-3411	2	4	we	we	PRON
ap-3411	2	5	present	present	VERB
ap-3411	2	6	some	some	DET
ap-3411	2	7	ideas	idea	NOUN
ap-3411	2	8	on	on	ADP
ap-3411	2	9	when	when	SCONJ
ap-3411	2	10	lie	lie	NOUN
ap-3411	2	11	symmetries	symmetry	NOUN
ap-3411	2	12	,	,	PUNCT
ap-3411	2	13	both	both	PRON
ap-3411	2	14	point	point	VERB
ap-3411	2	15	and	and	CCONJ
ap-3411	2	16	generalized	generalize	VERB
ap-3411	2	17	,	,	PUNCT
ap-3411	2	18	can	can	AUX
ap-3411	2	19	depend	depend	VERB
ap-3411	2	20	on	on	ADP
ap-3411	2	21	arbitrary	arbitrary	ADJ
ap-3411	2	22	functions	function	NOUN
ap-3411	2	23	.	.	PUNCT
ap-3411	3	1	we	we	PRON
ap-3411	3	2	show	show	VERB
ap-3411	3	3	a	a	DET
ap-3411	3	4	few	few	ADJ
ap-3411	3	5	examples	example	NOUN
ap-3411	3	6	,	,	PUNCT
ap-3411	3	7	both	both	CCONJ
ap-3411	3	8	in	in	ADP
ap-3411	3	9	partial	partial	ADJ
ap-3411	3	10	differential	differential	NOUN
ap-3411	3	11	and	and	CCONJ
ap-3411	3	12	partial	partial	ADJ
ap-3411	3	13	difference	difference	NOUN
ap-3411	3	14	equations	equation	NOUN
ap-3411	3	15	where	where	SCONJ
ap-3411	3	16	this	this	PRON
ap-3411	3	17	happens	happen	VERB
ap-3411	3	18	.	.	PUNCT
ap-3411	4	1	moreover	moreover	ADV
ap-3411	4	2	we	we	PRON
ap-3411	4	3	show	show	VERB
ap-3411	4	4	that	that	SCONJ
ap-3411	4	5	the	the	DET
ap-3411	4	6	infinitesimal	infinitesimal	ADJ
ap-3411	4	7	generators	generator	NOUN
ap-3411	4	8	of	of	ADP
ap-3411	4	9	generalized	generalized	ADJ
ap-3411	4	10	symmetries	symmetry	NOUN
ap-3411	4	11	depending	depend	VERB
ap-3411	4	12	on	on	ADP
ap-3411	4	13	arbitrary	arbitrary	ADJ
ap-3411	4	14	functions	function	NOUN
ap-3411	4	15	,	,	PUNCT
ap-3411	4	16	both	both	PRON
ap-3411	4	17	for	for	ADP
ap-3411	4	18	continuous	continuous	ADJ
ap-3411	4	19	and	and	CCONJ
ap-3411	4	20	discrete	discrete	ADJ
ap-3411	4	21	equations	equation	NOUN
ap-3411	4	22	,	,	PUNCT
ap-3411	4	23	effectively	effectively	ADV
ap-3411	4	24	play	play	VERB
ap-3411	4	25	the	the	DET
ap-3411	4	26	role	role	NOUN
ap-3411	4	27	of	of	ADP
ap-3411	4	28	master	master	NOUN
ap-3411	4	29	symmetries	symmetry	NOUN
ap-3411	4	30	.	.	PUNCT
ap-3411	5	1	keywords	keyword	NOUN
ap-3411	5	2	:	:	PUNCT
ap-3411	5	3	partial	partial	ADJ
ap-3411	5	4	differential	differential	NOUN
ap-3411	5	5	equation	equation	NOUN
ap-3411	5	6	;	;	PUNCT
ap-3411	5	7	partial	partial	ADJ
ap-3411	5	8	difference	difference	NOUN
ap-3411	5	9	equation	equation	NOUN
ap-3411	5	10	;	;	PUNCT
ap-3411	5	11	lie	lie	NOUN
ap-3411	5	12	symmetries	symmetry	NOUN
ap-3411	5	13	.	.	PUNCT
ap-3411	6	1	1	1	X
ap-3411	6	2	.	.	X
ap-3411	6	3	introduction	introduction	NOUN
ap-3411	6	4	in	in	ADP
ap-3411	6	5	a	a	DET
ap-3411	6	6	seminal	seminal	ADJ
ap-3411	6	7	work	work	NOUN
ap-3411	6	8	of	of	ADP
ap-3411	6	9	two	two	NUM
ap-3411	6	10	century	century	NOUN
ap-3411	6	11	ago	ago	ADV
ap-3411	6	12	medolaghi	medolaghi	PROPN
ap-3411	7	1	[	[	X
ap-3411	7	2	27	27	NUM
ap-3411	7	3	]	]	PUNCT
ap-3411	7	4	,	,	PUNCT
ap-3411	7	5	following	follow	VERB
ap-3411	7	6	sophus	sophus	PROPN
ap-3411	7	7	lie	lie	VERB
ap-3411	7	8	results	result	NOUN
ap-3411	7	9	on	on	ADP
ap-3411	7	10	ordinary	ordinary	ADJ
ap-3411	7	11	differential	differential	ADJ
ap-3411	7	12	equations	equation	NOUN
ap-3411	7	13	[	[	X
ap-3411	7	14	24	24	NUM
ap-3411	7	15	,	,	PUNCT
ap-3411	7	16	25	25	NUM
ap-3411	7	17	]	]	PUNCT
ap-3411	7	18	,	,	PUNCT
ap-3411	7	19	proposed	propose	VERB
ap-3411	7	20	the	the	DET
ap-3411	7	21	following	follow	VERB
ap-3411	7	22	work	work	NOUN
ap-3411	7	23	program	program	NOUN
ap-3411	7	24	for	for	ADP
ap-3411	7	25	partial	partial	ADJ
ap-3411	7	26	differential	differential	ADJ
ap-3411	7	27	equations	equation	NOUN
ap-3411	7	28	(	(	PUNCT
ap-3411	7	29	pde	pde	NOUN
ap-3411	7	30	’s	’s	ADV
ap-3411	7	31	):	):	PUNCT
ap-3411	7	32	(	(	PUNCT
ap-3411	7	33	1	1	NUM
ap-3411	7	34	.	.	PUNCT
ap-3411	7	35	)	)	PUNCT
ap-3411	7	36	determine	determine	VERB
ap-3411	7	37	all	all	DET
ap-3411	7	38	different	different	ADJ
ap-3411	7	39	kinds	kind	NOUN
ap-3411	7	40	of	of	ADP
ap-3411	7	41	infinite	infinite	ADJ
ap-3411	7	42	groups	group	NOUN
ap-3411	7	43	of	of	ADP
ap-3411	7	44	point	point	NOUN
ap-3411	7	45	transformations	transformation	NOUN
ap-3411	7	46	in	in	ADP
ap-3411	7	47	3	3	NUM
ap-3411	7	48	variables	variable	NOUN
ap-3411	7	49	.	.	PUNCT
ap-3411	8	1	(	(	PUNCT
ap-3411	8	2	2	2	NUM
ap-3411	8	3	.	.	PUNCT
ap-3411	8	4	)	)	PUNCT
ap-3411	8	5	for	for	ADP
ap-3411	8	6	each	each	PRON
ap-3411	8	7	of	of	ADP
ap-3411	8	8	the	the	DET
ap-3411	8	9	obtained	obtain	VERB
ap-3411	8	10	groups	group	NOUN
ap-3411	8	11	determine	determine	VERB
ap-3411	8	12	the	the	DET
ap-3411	8	13	invariant	invariant	ADJ
ap-3411	8	14	second	second	ADJ
ap-3411	8	15	order	order	NOUN
ap-3411	8	16	equations	equation	NOUN
ap-3411	8	17	.	.	PUNCT
ap-3411	9	1	in	in	ADP
ap-3411	9	2	the	the	DET
ap-3411	9	3	framework	framework	NOUN
ap-3411	9	4	of	of	ADP
ap-3411	9	5	this	this	DET
ap-3411	9	6	research	research	NOUN
ap-3411	9	7	medolaghi	medolaghi	PROPN
ap-3411	9	8	got	get	VERB
ap-3411	9	9	,	,	PUNCT
ap-3411	9	10	among	among	ADP
ap-3411	9	11	other	other	ADJ
ap-3411	9	12	equations	equation	NOUN
ap-3411	9	13	,	,	PUNCT
ap-3411	9	14	the	the	DET
ap-3411	9	15	liouville	liouville	NOUN
ap-3411	9	16	equation	equation	NOUN
ap-3411	9	17	uxt(x	uxt(x	PROPN
ap-3411	9	18	,	,	PUNCT
ap-3411	9	19	t	t	PROPN
ap-3411	9	20	)	)	PUNCT
ap-3411	9	21	=	=	SYM
ap-3411	10	1	eu(x	eu(x	ADV
ap-3411	10	2	,	,	PUNCT
ap-3411	10	3	t	t	PROPN
ap-3411	10	4	)	)	PUNCT
ap-3411	10	5	.	.	PUNCT
ap-3411	11	1	(	(	PUNCT
ap-3411	11	2	1.1	1.1	NUM
ap-3411	11	3	)	)	PUNCT
ap-3411	11	4	the	the	DET
ap-3411	11	5	symmetry	symmetry	NOUN
ap-3411	11	6	algebra	algebra	NOUN
ap-3411	11	7	of	of	ADP
ap-3411	11	8	the	the	DET
ap-3411	11	9	liouville	liouville	NOUN
ap-3411	11	10	equation	equation	NOUN
ap-3411	11	11	(	(	PUNCT
ap-3411	11	12	1.1	1.1	NUM
ap-3411	11	13	)	)	PUNCT
ap-3411	11	14	is	be	AUX
ap-3411	11	15	given	give	VERB
ap-3411	11	16	by	by	ADP
ap-3411	11	17	the	the	DET
ap-3411	11	18	vector	vector	NOUN
ap-3411	11	19	fields	field	NOUN
ap-3411	11	20	x(f(x	x(f(x	PROPN
ap-3411	11	21	)	)	PUNCT
ap-3411	11	22	)	)	PUNCT
ap-3411	12	1	=	=	PRON
ap-3411	12	2	f(x)∂x	f(x)∂x	NOUN
ap-3411	12	3	−	−	NOUN
ap-3411	12	4	fx(x)∂u	fx(x)∂u	NOUN
ap-3411	12	5	,	,	PUNCT
ap-3411	12	6	y	y	PROPN
ap-3411	12	7	(	(	PUNCT
ap-3411	12	8	g(t	g(t	PROPN
ap-3411	12	9	)	)	PUNCT
ap-3411	12	10	)	)	PUNCT
ap-3411	13	1	=	=	PUNCT
ap-3411	13	2	g(t)∂t	g(t)∂t	VERB
ap-3411	14	1	−	−	PROPN
ap-3411	14	2	gt(t)∂u	gt(t)∂u	INTJ
ap-3411	14	3	,	,	PUNCT
ap-3411	14	4	(	(	PUNCT
ap-3411	14	5	1.2	1.2	NUM
ap-3411	14	6	)	)	PUNCT
ap-3411	14	7	where	where	SCONJ
ap-3411	14	8	f(x	f(x	PROPN
ap-3411	14	9	)	)	PUNCT
ap-3411	14	10	and	and	CCONJ
ap-3411	14	11	g(t	g(t	PROPN
ap-3411	14	12	)	)	PUNCT
ap-3411	14	13	are	be	AUX
ap-3411	14	14	arbitrary	arbitrary	ADJ
ap-3411	14	15	smooth	smooth	ADJ
ap-3411	14	16	functions	function	NOUN
ap-3411	14	17	of	of	ADP
ap-3411	14	18	their	their	PRON
ap-3411	14	19	argument	argument	NOUN
ap-3411	14	20	and	and	CCONJ
ap-3411	14	21	by	by	ADP
ap-3411	14	22	fx(x	fx(x	ADV
ap-3411	14	23	)	)	PUNCT
ap-3411	14	24	and	and	CCONJ
ap-3411	14	25	gt(t	gt(t	NOUN
ap-3411	14	26	)	)	PUNCT
ap-3411	15	1	we	we	PRON
ap-3411	15	2	mean	mean	VERB
ap-3411	15	3	their	their	PRON
ap-3411	15	4	first	first	ADJ
ap-3411	15	5	derivatives	derivative	NOUN
ap-3411	15	6	.	.	PUNCT
ap-3411	16	1	the	the	DET
ap-3411	16	2	commutation	commutation	NOUN
ap-3411	16	3	relations	relation	NOUN
ap-3411	16	4	of	of	ADP
ap-3411	16	5	the	the	DET
ap-3411	16	6	vector	vector	NOUN
ap-3411	16	7	fields	field	NOUN
ap-3411	16	8	(	(	PUNCT
ap-3411	16	9	1.2	1.2	NUM
ap-3411	16	10	)	)	PUNCT
ap-3411	16	11	are	be	AUX
ap-3411	16	12	[	[	PUNCT
ap-3411	16	13	x(f	x(f	PROPN
ap-3411	16	14	)	)	PUNCT
ap-3411	16	15	,	,	PUNCT
ap-3411	16	16	x(f̃	x(f̃	PROPN
ap-3411	16	17	)	)	PUNCT
ap-3411	16	18	]	]	PUNCT
ap-3411	17	1	=	=	PUNCT
ap-3411	17	2	x(ff̃x	x(ff̃x	NUM
ap-3411	18	1	−	−	PROPN
ap-3411	18	2	f̃fx	f̃fx	NUM
ap-3411	18	3	)	)	PUNCT
ap-3411	18	4	,	,	PUNCT
ap-3411	18	5	[	[	PUNCT
ap-3411	18	6	y	y	NOUN
ap-3411	18	7	(	(	PUNCT
ap-3411	18	8	g	g	PROPN
ap-3411	18	9	)	)	PUNCT
ap-3411	18	10	,	,	PUNCT
ap-3411	18	11	y	y	PROPN
ap-3411	18	12	(	(	PUNCT
ap-3411	18	13	g̃	g̃	PROPN
ap-3411	18	14	)	)	PUNCT
ap-3411	18	15	]	]	PUNCT
ap-3411	19	1	=	=	PUNCT
ap-3411	19	2	y	y	PROPN
ap-3411	19	3	(	(	PUNCT
ap-3411	19	4	gg̃t	gg̃t	NOUN
ap-3411	19	5	−	−	PROPN
ap-3411	19	6	g̃gt	g̃gt	PROPN
ap-3411	19	7	)	)	PUNCT
ap-3411	19	8	,	,	PUNCT
ap-3411	19	9	[	[	PUNCT
ap-3411	19	10	x(f	x(f	PROPN
ap-3411	19	11	)	)	PUNCT
ap-3411	19	12	,	,	PUNCT
ap-3411	19	13	y	y	PROPN
ap-3411	19	14	(	(	PUNCT
ap-3411	19	15	g	g	NOUN
ap-3411	19	16	)	)	PUNCT
ap-3411	19	17	]	]	PUNCT
ap-3411	20	1	=	=	PUNCT
ap-3411	20	2	0	0	X
ap-3411	20	3	.	.	PUNCT
ap-3411	21	1	(	(	PUNCT
ap-3411	21	2	1.3	1.3	NUM
ap-3411	21	3	)	)	PUNCT
ap-3411	21	4	the	the	DET
ap-3411	21	5	algebra	algebra	NOUN
ap-3411	21	6	(	(	PUNCT
ap-3411	21	7	1.2	1.2	NUM
ap-3411	21	8	)	)	PUNCT
ap-3411	21	9	,	,	PUNCT
ap-3411	21	10	(	(	PUNCT
ap-3411	21	11	1.3	1.3	NUM
ap-3411	21	12	)	)	PUNCT
ap-3411	21	13	is	be	AUX
ap-3411	21	14	isomorphic	isomorphic	ADJ
ap-3411	21	15	to	to	ADP
ap-3411	21	16	the	the	DET
ap-3411	21	17	direct	direct	ADJ
ap-3411	21	18	sum	sum	NOUN
ap-3411	21	19	of	of	ADP
ap-3411	21	20	two	two	NUM
ap-3411	21	21	virasoro	virasoro	NOUN
ap-3411	21	22	algebras	algebra	NOUN
ap-3411	21	23	.	.	PUNCT
ap-3411	22	1	we	we	PRON
ap-3411	22	2	can	can	AUX
ap-3411	22	3	find	find	VERB
ap-3411	22	4	also	also	ADV
ap-3411	22	5	s	s	PART
ap-3411	22	6	-	-	PUNCT
ap-3411	22	7	integrable	integrable	ADJ
ap-3411	22	8	equations	equation	NOUN
ap-3411	23	1	[	[	X
ap-3411	23	2	5	5	NUM
ap-3411	23	3	]	]	PUNCT
ap-3411	23	4	,	,	PUNCT
ap-3411	23	5	i.e.	i.e.	X
ap-3411	23	6	,	,	PUNCT
ap-3411	23	7	equations	equation	NOUN
ap-3411	23	8	integrable	integrable	ADJ
ap-3411	23	9	by	by	ADP
ap-3411	23	10	the	the	DET
ap-3411	23	11	spectral	spectral	ADJ
ap-3411	23	12	transform	transform	NOUN
ap-3411	23	13	,	,	PUNCT
ap-3411	23	14	which	which	PRON
ap-3411	23	15	have	have	VERB
ap-3411	23	16	an	an	DET
ap-3411	23	17	infinite	infinite	ADJ
ap-3411	23	18	dimensional	dimensional	ADJ
ap-3411	23	19	group	group	NOUN
ap-3411	23	20	of	of	ADP
ap-3411	23	21	point	point	NOUN
ap-3411	23	22	symmetries	symmetry	NOUN
ap-3411	23	23	.	.	PUNCT
ap-3411	24	1	classical	classical	ADJ
ap-3411	24	2	examples	example	NOUN
ap-3411	24	3	are	be	AUX
ap-3411	24	4	the	the	DET
ap-3411	24	5	(	(	PUNCT
ap-3411	24	6	2	2	NUM
ap-3411	24	7	+	+	NUM
ap-3411	24	8	1)-dimensional	1)-dimensional	ADJ
ap-3411	24	9	kadomtsevpetviashvili	kadomtsevpetviashvili	NOUN
ap-3411	24	10	equation	equation	NOUN
ap-3411	24	11	[	[	X
ap-3411	24	12	7	7	NUM
ap-3411	24	13	,	,	PUNCT
ap-3411	24	14	8	8	NUM
ap-3411	24	15	,	,	PUNCT
ap-3411	24	16	29	29	NUM
ap-3411	24	17	]	]	PUNCT
ap-3411	24	18	,	,	PUNCT
ap-3411	24	19	the	the	DET
ap-3411	24	20	(	(	PUNCT
ap-3411	24	21	2	2	NUM
ap-3411	24	22	+	+	NUM
ap-3411	24	23	1)-dimensional	1)-dimensional	ADJ
ap-3411	24	24	davey	davey	NOUN
ap-3411	24	25	-	-	PUNCT
ap-3411	24	26	stewartson	stewartson	NOUN
ap-3411	24	27	equation	equation	NOUN
ap-3411	24	28	[	[	X
ap-3411	24	29	6	6	NUM
ap-3411	24	30	]	]	PUNCT
ap-3411	24	31	,	,	PUNCT
ap-3411	24	32	the	the	DET
ap-3411	24	33	(	(	PUNCT
ap-3411	24	34	2	2	NUM
ap-3411	24	35	+	+	NUM
ap-3411	24	36	1)-dimensional	1)-dimensional	NUM
ap-3411	24	37	toda	toda	NOUN
ap-3411	25	1	[	[	X
ap-3411	25	2	22	22	NUM
ap-3411	25	3	]	]	PUNCT
ap-3411	25	4	,	,	PUNCT
ap-3411	25	5	the	the	DET
ap-3411	25	6	three	three	NUM
ap-3411	25	7	wave	wave	NOUN
ap-3411	25	8	interaction	interaction	NOUN
ap-3411	25	9	in	in	ADP
ap-3411	25	10	three	three	NUM
ap-3411	25	11	dimensions	dimension	NOUN
ap-3411	25	12	[	[	X
ap-3411	25	13	26	26	NUM
ap-3411	25	14	]	]	PUNCT
ap-3411	25	15	.	.	PUNCT
ap-3411	26	1	in	in	ADP
ap-3411	26	2	the	the	DET
ap-3411	26	3	example	example	NOUN
ap-3411	26	4	5.7	5.7	NUM
ap-3411	26	5	of	of	ADP
ap-3411	26	6	[	[	X
ap-3411	26	7	28	28	NUM
ap-3411	26	8	]	]	PUNCT
ap-3411	26	9	one	one	NUM
ap-3411	26	10	finds	find	VERB
ap-3411	26	11	the	the	DET
ap-3411	26	12	point	point	NOUN
ap-3411	26	13	and	and	CCONJ
ap-3411	26	14	generalized	generalized	ADJ
ap-3411	26	15	symmetries	symmetry	NOUN
ap-3411	26	16	for	for	ADP
ap-3411	26	17	the	the	DET
ap-3411	26	18	nonlinear	nonlinear	ADJ
ap-3411	26	19	first	first	ADJ
ap-3411	26	20	order	order	NOUN
ap-3411	26	21	wave	wave	NOUN
ap-3411	26	22	equation	equation	NOUN
ap-3411	26	23	ut	ut	PROPN
ap-3411	26	24	=	=	PROPN
ap-3411	26	25	uux	uux	PROPN
ap-3411	26	26	,	,	PUNCT
ap-3411	26	27	u	u	NOUN
ap-3411	26	28	=	=	PROPN
ap-3411	26	29	u(x	u(x	PROPN
ap-3411	26	30	,	,	PUNCT
ap-3411	26	31	t	t	PROPN
ap-3411	26	32	)	)	PUNCT
ap-3411	26	33	.	.	PUNCT
ap-3411	27	1	(	(	PUNCT
ap-3411	27	2	1.4	1.4	NUM
ap-3411	27	3	)	)	PUNCT
ap-3411	27	4	in	in	ADP
ap-3411	27	5	evolutionary	evolutionary	ADJ
ap-3411	27	6	form	form	NOUN
ap-3411	27	7	they	they	PRON
ap-3411	27	8	are	be	AUX
ap-3411	27	9	given	give	VERB
ap-3411	27	10	by	by	ADP
ap-3411	27	11	the	the	DET
ap-3411	27	12	characteristic	characteristic	ADJ
ap-3411	27	13	q	q	NOUN
ap-3411	27	14	=	=	PUNCT
ap-3411	27	15	uxf	uxf	ADJ
ap-3411	27	16	(	(	PUNCT
ap-3411	27	17	x+	x+	PROPN
ap-3411	27	18	tu	tu	PROPN
ap-3411	27	19	,	,	PUNCT
ap-3411	27	20	u	u	PROPN
ap-3411	27	21	,	,	PUNCT
ap-3411	27	22	t+	t+	VERB
ap-3411	27	23	1	1	NUM
ap-3411	27	24	ux	ux	PROPN
ap-3411	27	25	,	,	PUNCT
ap-3411	27	26	uxx	uxx	X
ap-3411	27	27	u3	u3	PROPN
ap-3411	27	28	x	x	X
ap-3411	27	29	)	)	PUNCT
ap-3411	27	30	,	,	PUNCT
ap-3411	27	31	(	(	PUNCT
ap-3411	27	32	1.5	1.5	NUM
ap-3411	27	33	)	)	PUNCT
ap-3411	27	34	where	where	SCONJ
ap-3411	27	35	the	the	DET
ap-3411	27	36	function	function	NOUN
ap-3411	27	37	f	f	PROPN
ap-3411	27	38	is	be	AUX
ap-3411	27	39	an	an	DET
ap-3411	27	40	arbitrary	arbitrary	ADJ
ap-3411	27	41	function	function	NOUN
ap-3411	27	42	of	of	ADP
ap-3411	27	43	its	its	PRON
ap-3411	27	44	arguments	argument	NOUN
ap-3411	27	45	.	.	PUNCT
ap-3411	28	1	in	in	ADP
ap-3411	28	2	particular	particular	ADJ
ap-3411	28	3	the	the	DET
ap-3411	28	4	last	last	ADJ
ap-3411	28	5	term	term	NOUN
ap-3411	28	6	corresponds	correspond	VERB
ap-3411	28	7	to	to	ADP
ap-3411	28	8	generalized	generalized	ADJ
ap-3411	28	9	symmetries	symmetry	NOUN
ap-3411	28	10	as	as	SCONJ
ap-3411	28	11	it	it	PRON
ap-3411	28	12	depends	depend	VERB
ap-3411	28	13	of	of	ADP
ap-3411	28	14	the	the	DET
ap-3411	28	15	second	second	ADJ
ap-3411	28	16	derivative	derivative	NOUN
ap-3411	28	17	of	of	ADP
ap-3411	28	18	the	the	DET
ap-3411	28	19	field	field	NOUN
ap-3411	28	20	.	.	PUNCT
ap-3411	29	1	for	for	ADP
ap-3411	29	2	the	the	DET
ap-3411	29	3	symmetries	symmetry	NOUN
ap-3411	29	4	of	of	ADP
ap-3411	29	5	hydrodynamictype	hydrodynamictype	ADJ
ap-3411	29	6	partial	partial	ADJ
ap-3411	29	7	differential	differential	NOUN
ap-3411	29	8	equations	equation	NOUN
ap-3411	29	9	see	see	VERB
ap-3411	29	10	[	[	X
ap-3411	29	11	11	11	NUM
ap-3411	29	12	]	]	PUNCT
ap-3411	29	13	.	.	PUNCT
ap-3411	30	1	results	result	NOUN
ap-3411	30	2	by	by	ADP
ap-3411	30	3	shabat	shabat	NOUN
ap-3411	30	4	and	and	CCONJ
ap-3411	30	5	zhiber	zhiber	NOUN
ap-3411	31	1	[	[	X
ap-3411	31	2	37	37	NUM
ap-3411	31	3	]	]	PUNCT
ap-3411	31	4	show	show	VERB
ap-3411	31	5	that	that	SCONJ
ap-3411	31	6	also	also	ADV
ap-3411	31	7	the	the	DET
ap-3411	31	8	liouville	liouville	NOUN
ap-3411	31	9	equation	equation	NOUN
ap-3411	31	10	,	,	PUNCT
ap-3411	31	11	being	be	AUX
ap-3411	31	12	darboux	darboux	VERB
ap-3411	31	13	integrable	integrable	ADJ
ap-3411	31	14	,	,	PUNCT
ap-3411	31	15	has	have	VERB
ap-3411	31	16	such	such	ADJ
ap-3411	31	17	kind	kind	NOUN
ap-3411	31	18	of	of	ADP
ap-3411	31	19	symmetries	symmetry	NOUN
ap-3411	31	20	:	:	PUNCT
ap-3411	31	21	q	q	X
ap-3411	31	22	=	=	PUNCT
ap-3411	31	23	(	(	PUNCT
ap-3411	31	24	dx	dx	PROPN
ap-3411	32	1	+	+	CCONJ
ap-3411	32	2	ux)f	ux)f	PROPN
ap-3411	32	3	(	(	PUNCT
ap-3411	32	4	w	w	PROPN
ap-3411	32	5	,	,	PUNCT
ap-3411	32	6	wx	wx	PROPN
ap-3411	32	7	,	,	PUNCT
ap-3411	32	8	.	.	PUNCT
ap-3411	32	9	.	.	PUNCT
ap-3411	32	10	.	.	PUNCT
ap-3411	33	1	,	,	PUNCT
ap-3411	33	2	wk1x	wk1x	PROPN
ap-3411	33	3	)	)	PUNCT
ap-3411	34	1	+	+	CCONJ
ap-3411	34	2	(	(	PUNCT
ap-3411	34	3	dt	dt	X
ap-3411	34	4	+	+	CCONJ
ap-3411	34	5	ut)g(w̄	ut)g(w̄	PROPN
ap-3411	34	6	,	,	PUNCT
ap-3411	34	7	w̄t	w̄t	PROPN
ap-3411	34	8	,	,	PUNCT
ap-3411	34	9	.	.	PUNCT
ap-3411	34	10	.	.	PUNCT
ap-3411	34	11	.	.	PUNCT
ap-3411	35	1	,	,	PUNCT
ap-3411	35	2	w̄k2	w̄k2	PROPN
ap-3411	35	3	t	t	PROPN
ap-3411	35	4	)	)	PUNCT
ap-3411	35	5	,	,	PUNCT
ap-3411	35	6	(	(	PUNCT
ap-3411	35	7	1.6	1.6	NUM
ap-3411	35	8	)	)	PUNCT
ap-3411	35	9	193	193	NUM
ap-3411	36	1	http://dx.doi.org/10.14311/ap.2016.56.0193	http://dx.doi.org/10.14311/ap.2016.56.0193	NUM
ap-3411	36	2	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3411	36	3	g.	g.	NOUN
ap-3411	36	4	gubbiotti	gubbiotti	PROPN
ap-3411	36	5	,	,	PUNCT
ap-3411	36	6	d.	d.	PROPN
ap-3411	36	7	levi	levi	PROPN
ap-3411	36	8	,	,	PUNCT
ap-3411	36	9	c.	c.	PROPN
ap-3411	36	10	scimiterna	scimiterna	PROPN
ap-3411	36	11	acta	acta	PROPN
ap-3411	36	12	polytechnica	polytechnica	PROPN
ap-3411	36	13	where	where	SCONJ
ap-3411	36	14	the	the	DET
ap-3411	36	15	operators	operator	NOUN
ap-3411	36	16	dx	dx	VERB
ap-3411	36	17	+	+	CCONJ
ap-3411	36	18	ux	ux	PROPN
ap-3411	36	19	and	and	CCONJ
ap-3411	36	20	dt	dt	PROPN
ap-3411	36	21	+	+	CCONJ
ap-3411	36	22	ut	ut	PROPN
ap-3411	36	23	are	be	AUX
ap-3411	36	24	the	the	DET
ap-3411	36	25	laplace	laplace	NOUN
ap-3411	36	26	operators	operator	NOUN
ap-3411	36	27	,	,	PUNCT
ap-3411	36	28	k1	k1	PROPN
ap-3411	36	29	and	and	CCONJ
ap-3411	36	30	k2	k2	PROPN
ap-3411	36	31	are	be	AUX
ap-3411	36	32	two	two	NUM
ap-3411	36	33	positive	positive	ADJ
ap-3411	36	34	integer	integer	NOUN
ap-3411	36	35	numbers	number	NOUN
ap-3411	36	36	,	,	PUNCT
ap-3411	36	37	f	f	PROPN
ap-3411	36	38	and	and	CCONJ
ap-3411	36	39	g	g	PROPN
ap-3411	36	40	are	be	AUX
ap-3411	36	41	two	two	NUM
ap-3411	36	42	arbitrary	arbitrary	ADJ
ap-3411	36	43	functions	function	NOUN
ap-3411	36	44	of	of	ADP
ap-3411	36	45	their	their	PRON
ap-3411	36	46	arguments	argument	NOUN
ap-3411	36	47	,	,	PUNCT
ap-3411	36	48	dx	dx	PROPN
ap-3411	36	49	and	and	CCONJ
ap-3411	36	50	dt	dt	PROPN
ap-3411	36	51	stands	stand	VERB
ap-3411	36	52	for	for	ADP
ap-3411	36	53	the	the	DET
ap-3411	36	54	total	total	ADJ
ap-3411	36	55	derivative	derivative	NOUN
ap-3411	36	56	with	with	ADP
ap-3411	36	57	respect	respect	NOUN
ap-3411	36	58	to	to	ADP
ap-3411	36	59	the	the	DET
ap-3411	36	60	x	x	NOUN
ap-3411	36	61	and	and	CCONJ
ap-3411	36	62	t	t	PROPN
ap-3411	36	63	variables	variable	NOUN
ap-3411	36	64	and	and	CCONJ
ap-3411	36	65	w	w	PROPN
ap-3411	36	66	=	=	PROPN
ap-3411	36	67	uxx	uxx	PROPN
ap-3411	37	1	−	−	PROPN
ap-3411	37	2	1	1	NUM
ap-3411	37	3	2u	2u	PROPN
ap-3411	37	4	2	2	NUM
ap-3411	37	5	x	x	NOUN
ap-3411	37	6	and	and	CCONJ
ap-3411	37	7	w̄	w̄	NOUN
ap-3411	37	8	=	=	SYM
ap-3411	37	9	utt	utt	ADJ
ap-3411	37	10	−	−	NOUN
ap-3411	37	11	1	1	NUM
ap-3411	37	12	2u	2u	NOUN
ap-3411	37	13	2	2	NUM
ap-3411	37	14	t	t	NOUN
ap-3411	37	15	are	be	AUX
ap-3411	37	16	the	the	DET
ap-3411	37	17	lowest	low	ADJ
ap-3411	37	18	order	order	NOUN
ap-3411	37	19	integrals	integral	NOUN
ap-3411	37	20	of	of	ADP
ap-3411	37	21	the	the	DET
ap-3411	37	22	liouville	liouville	NOUN
ap-3411	37	23	equation	equation	NOUN
ap-3411	37	24	in	in	ADP
ap-3411	37	25	the	the	DET
ap-3411	37	26	x	x	NOUN
ap-3411	37	27	and	and	CCONJ
ap-3411	37	28	t	t	PROPN
ap-3411	37	29	direction	direction	NOUN
ap-3411	37	30	.	.	PUNCT
ap-3411	38	1	here	here	ADV
ap-3411	38	2	and	and	CCONJ
ap-3411	38	3	in	in	ADP
ap-3411	38	4	the	the	DET
ap-3411	38	5	following	following	NOUN
ap-3411	38	6	by	by	ADP
ap-3411	38	7	wnx	wnx	ADV
ap-3411	38	8	we	we	PRON
ap-3411	38	9	mean	mean	VERB
ap-3411	38	10	the	the	DET
ap-3411	38	11	n	n	PROPN
ap-3411	38	12	times	time	NOUN
ap-3411	38	13	derivative	derivative	NOUN
ap-3411	38	14	of	of	ADP
ap-3411	38	15	the	the	DET
ap-3411	38	16	function	function	PROPN
ap-3411	38	17	w(x	w(x	PROPN
ap-3411	38	18	,	,	PUNCT
ap-3411	38	19	t	t	PROPN
ap-3411	38	20	)	)	PUNCT
ap-3411	38	21	with	with	ADP
ap-3411	38	22	respect	respect	NOUN
ap-3411	38	23	to	to	ADP
ap-3411	38	24	x.	x.	NOUN
ap-3411	39	1	so	so	SCONJ
ap-3411	39	2	the	the	DET
ap-3411	39	3	nonlinear	nonlinear	ADJ
ap-3411	39	4	wave	wave	NOUN
ap-3411	39	5	equation	equation	NOUN
ap-3411	39	6	(	(	PUNCT
ap-3411	39	7	1.4	1.4	NUM
ap-3411	39	8	)	)	PUNCT
ap-3411	39	9	as	as	ADV
ap-3411	39	10	well	well	ADV
ap-3411	39	11	as	as	ADP
ap-3411	39	12	the	the	DET
ap-3411	39	13	liouville	liouville	NOUN
ap-3411	39	14	equation	equation	NOUN
ap-3411	39	15	(	(	PUNCT
ap-3411	39	16	1.1	1.1	NUM
ap-3411	39	17	)	)	PUNCT
ap-3411	39	18	admit	admit	VERB
ap-3411	39	19	generalized	generalized	ADJ
ap-3411	39	20	symmetries	symmetry	NOUN
ap-3411	39	21	depending	depend	VERB
ap-3411	39	22	on	on	ADP
ap-3411	39	23	arbitrary	arbitrary	ADJ
ap-3411	39	24	functions	function	NOUN
ap-3411	39	25	.	.	PUNCT
ap-3411	40	1	then	then	ADV
ap-3411	40	2	medolaghi	medolaghi	PROPN
ap-3411	40	3	program	program	PROPN
ap-3411	40	4	could	could	AUX
ap-3411	40	5	be	be	AUX
ap-3411	40	6	extended	extend	VERB
ap-3411	40	7	to	to	ADP
ap-3411	40	8	the	the	DET
ap-3411	40	9	case	case	NOUN
ap-3411	40	10	of	of	ADP
ap-3411	40	11	generalized	generalized	ADJ
ap-3411	40	12	symmetries	symmetry	NOUN
ap-3411	40	13	.	.	PUNCT
ap-3411	41	1	we	we	PRON
ap-3411	41	2	here	here	ADV
ap-3411	41	3	present	present	VERB
ap-3411	41	4	some	some	DET
ap-3411	41	5	preliminary	preliminary	ADJ
ap-3411	41	6	ideas	idea	NOUN
ap-3411	41	7	on	on	ADP
ap-3411	41	8	a	a	DET
ap-3411	41	9	possible	possible	ADJ
ap-3411	41	10	solution	solution	NOUN
ap-3411	41	11	of	of	ADP
ap-3411	41	12	this	this	DET
ap-3411	41	13	program	program	NOUN
ap-3411	41	14	.	.	PUNCT
ap-3411	42	1	in	in	ADP
ap-3411	42	2	the	the	DET
ap-3411	42	3	following	follow	VERB
ap-3411	42	4	section	section	NOUN
ap-3411	42	5	we	we	PRON
ap-3411	42	6	will	will	AUX
ap-3411	42	7	present	present	VERB
ap-3411	42	8	some	some	DET
ap-3411	42	9	results	result	NOUN
ap-3411	42	10	on	on	ADP
ap-3411	42	11	the	the	DET
ap-3411	42	12	construction	construction	NOUN
ap-3411	42	13	of	of	ADP
ap-3411	42	14	pde	pde	NOUN
ap-3411	42	15	’s	’s	PART
ap-3411	42	16	presenting	present	VERB
ap-3411	42	17	generalized	generalized	ADJ
ap-3411	42	18	symmetries	symmetry	NOUN
ap-3411	42	19	depending	depend	VERB
ap-3411	42	20	on	on	ADP
ap-3411	42	21	arbitrary	arbitrary	ADJ
ap-3411	42	22	functions	function	NOUN
ap-3411	42	23	and	and	CCONJ
ap-3411	42	24	relate	relate	VERB
ap-3411	42	25	them	they	PRON
ap-3411	42	26	to	to	PART
ap-3411	42	27	darboux	darboux	VERB
ap-3411	42	28	integrable	integrable	ADJ
ap-3411	42	29	equations	equation	NOUN
ap-3411	42	30	.	.	PUNCT
ap-3411	43	1	then	then	ADV
ap-3411	43	2	in	in	ADP
ap-3411	43	3	section	section	NOUN
ap-3411	43	4	3	3	NUM
ap-3411	43	5	we	we	PRON
ap-3411	43	6	present	present	VERB
ap-3411	43	7	the	the	DET
ap-3411	43	8	counterpart	counterpart	NOUN
ap-3411	43	9	of	of	ADP
ap-3411	43	10	the	the	DET
ap-3411	43	11	previous	previous	ADJ
ap-3411	43	12	results	result	NOUN
ap-3411	43	13	in	in	ADP
ap-3411	43	14	the	the	DET
ap-3411	43	15	discrete	discrete	ADJ
ap-3411	43	16	case	case	NOUN
ap-3411	43	17	.	.	PUNCT
ap-3411	44	1	at	at	ADP
ap-3411	44	2	the	the	DET
ap-3411	44	3	end	end	NOUN
ap-3411	44	4	we	we	PRON
ap-3411	44	5	present	present	VERB
ap-3411	44	6	few	few	ADJ
ap-3411	44	7	conclusive	conclusive	ADJ
ap-3411	44	8	remarks	remark	NOUN
ap-3411	44	9	and	and	CCONJ
ap-3411	44	10	conjectures	conjecture	VERB
ap-3411	44	11	.	.	PUNCT
ap-3411	45	1	2	2	X
ap-3411	45	2	.	.	X
ap-3411	45	3	factorizable	factorizable	PROPN
ap-3411	45	4	differential	differential	PROPN
ap-3411	45	5	operators	operator	NOUN
ap-3411	45	6	,	,	PUNCT
ap-3411	45	7	darboux	darboux	VERB
ap-3411	45	8	integrable	integrable	ADJ
ap-3411	45	9	equations	equation	NOUN
ap-3411	45	10	and	and	CCONJ
ap-3411	45	11	symmetries	symmetry	NOUN
ap-3411	45	12	depending	depend	VERB
ap-3411	45	13	on	on	ADP
ap-3411	45	14	arbitrary	arbitrary	ADJ
ap-3411	45	15	functions	function	NOUN
ap-3411	45	16	.	.	PUNCT
ap-3411	46	1	the	the	DET
ap-3411	46	2	result	result	NOUN
ap-3411	46	3	(	(	PUNCT
ap-3411	46	4	1.5	1.5	NUM
ap-3411	46	5	)	)	PUNCT
ap-3411	46	6	can	can	AUX
ap-3411	46	7	be	be	AUX
ap-3411	46	8	in	in	ADP
ap-3411	46	9	principle	principle	NOUN
ap-3411	46	10	generalized	generalize	VERB
ap-3411	46	11	to	to	ADP
ap-3411	46	12	any	any	DET
ap-3411	46	13	differential	differential	ADJ
ap-3411	46	14	equation	equation	NOUN
ap-3411	46	15	of	of	ADP
ap-3411	46	16	the	the	DET
ap-3411	46	17	first	first	ADJ
ap-3411	46	18	order	order	NOUN
ap-3411	46	19	as	as	ADP
ap-3411	46	20	the	the	DET
ap-3411	46	21	equation	equation	NOUN
ap-3411	46	22	for	for	ADP
ap-3411	46	23	the	the	DET
ap-3411	46	24	symmetries	symmetry	NOUN
ap-3411	46	25	,	,	PUNCT
ap-3411	46	26	be	be	AUX
ap-3411	46	27	them	they	PRON
ap-3411	46	28	point	point	NOUN
ap-3411	46	29	or	or	CCONJ
ap-3411	46	30	generalized	generalized	ADJ
ap-3411	46	31	ones	one	NOUN
ap-3411	46	32	,	,	PUNCT
ap-3411	46	33	can	can	AUX
ap-3411	46	34	be	be	AUX
ap-3411	46	35	solved	solve	VERB
ap-3411	46	36	on	on	ADP
ap-3411	46	37	the	the	DET
ap-3411	46	38	characteristics	characteristic	NOUN
ap-3411	46	39	as	as	SCONJ
ap-3411	46	40	it	it	PRON
ap-3411	46	41	was	be	AUX
ap-3411	46	42	in	in	ADP
ap-3411	46	43	the	the	DET
ap-3411	46	44	case	case	NOUN
ap-3411	46	45	of	of	ADP
ap-3411	46	46	the	the	DET
ap-3411	46	47	hopf	hopf	ADJ
ap-3411	46	48	equation	equation	NOUN
ap-3411	46	49	(	(	PUNCT
ap-3411	46	50	1.4	1.4	NUM
ap-3411	46	51	)	)	PUNCT
ap-3411	46	52	.	.	PUNCT
ap-3411	47	1	let	let	VERB
ap-3411	47	2	consider	consider	VERB
ap-3411	47	3	,	,	PUNCT
ap-3411	47	4	with	with	ADP
ap-3411	47	5	no	no	DET
ap-3411	47	6	loss	loss	NOUN
ap-3411	47	7	of	of	ADP
ap-3411	47	8	generality	generality	NOUN
ap-3411	47	9	,	,	PUNCT
ap-3411	47	10	the	the	DET
ap-3411	47	11	example	example	NOUN
ap-3411	47	12	of	of	ADP
ap-3411	47	13	a	a	DET
ap-3411	47	14	general	general	ADJ
ap-3411	47	15	first	first	ADJ
ap-3411	47	16	order	order	NOUN
ap-3411	47	17	autonomous	autonomous	ADJ
ap-3411	47	18	equation	equation	NOUN
ap-3411	47	19	in	in	ADP
ap-3411	47	20	two	two	NUM
ap-3411	47	21	independent	independent	ADJ
ap-3411	47	22	variables	variable	NOUN
ap-3411	47	23	,	,	PUNCT
ap-3411	47	24	ut	ut	PROPN
ap-3411	47	25	=	=	SYM
ap-3411	47	26	f(u	f(u	PROPN
ap-3411	47	27	,	,	PUNCT
ap-3411	47	28	ux	ux	NOUN
ap-3411	47	29	)	)	PUNCT
ap-3411	47	30	,	,	PUNCT
ap-3411	47	31	u	u	NOUN
ap-3411	47	32	=	=	SYM
ap-3411	47	33	u(x	u(x	PROPN
ap-3411	47	34	,	,	PUNCT
ap-3411	47	35	t	t	PROPN
ap-3411	47	36	)	)	PUNCT
ap-3411	47	37	,	,	PUNCT
ap-3411	47	38	(	(	PUNCT
ap-3411	47	39	2.1	2.1	NUM
ap-3411	47	40	)	)	PUNCT
ap-3411	47	41	where	where	SCONJ
ap-3411	47	42	f	f	PROPN
ap-3411	47	43	is	be	AUX
ap-3411	47	44	an	an	DET
ap-3411	47	45	arbitrary	arbitrary	ADJ
ap-3411	47	46	function	function	NOUN
ap-3411	47	47	of	of	ADP
ap-3411	47	48	its	its	PRON
ap-3411	47	49	arguments	argument	NOUN
ap-3411	47	50	.	.	PUNCT
ap-3411	48	1	the	the	DET
ap-3411	48	2	symmetries	symmetry	NOUN
ap-3411	48	3	are	be	AUX
ap-3411	48	4	given	give	VERB
ap-3411	48	5	by	by	ADP
ap-3411	48	6	their	their	PRON
ap-3411	48	7	characteristics	characteristic	NOUN
ap-3411	48	8	q(x	q(x	PROPN
ap-3411	48	9	,	,	PUNCT
ap-3411	48	10	t	t	PROPN
ap-3411	48	11	,	,	PUNCT
ap-3411	48	12	u	u	NOUN
ap-3411	48	13	,	,	PUNCT
ap-3411	48	14	ux	ux	PROPN
ap-3411	48	15	,	,	PUNCT
ap-3411	48	16	.	.	PUNCT
ap-3411	48	17	.	.	PUNCT
ap-3411	48	18	.	.	PUNCT
ap-3411	49	1	,	,	PUNCT
ap-3411	49	2	ukx	ukx	PROPN
ap-3411	49	3	)	)	PUNCT
ap-3411	49	4	and	and	CCONJ
ap-3411	49	5	their	their	PRON
ap-3411	49	6	determining	determine	VERB
ap-3411	49	7	equations	equation	NOUN
ap-3411	49	8	are	be	AUX
ap-3411	49	9	given	give	VERB
ap-3411	49	10	by	by	ADP
ap-3411	49	11	dtq−	dtq−	PROPN
ap-3411	49	12	[	[	X
ap-3411	49	13	∂f	∂f	PROPN
ap-3411	49	14	∂u	∂u	PROPN
ap-3411	49	15	q+	q+	ADP
ap-3411	49	16	∂f	∂f	PROPN
ap-3411	49	17	∂ux	∂ux	ADJ
ap-3411	49	18	dxq	dxq	NOUN
ap-3411	49	19	]	]	PUNCT
ap-3411	49	20	∣∣∣∣	∣∣∣∣	NOUN
ap-3411	49	21	ut	ut	PROPN
ap-3411	49	22	=	=	PROPN
ap-3411	49	23	f	f	NOUN
ap-3411	49	24	=	=	SYM
ap-3411	49	25	0	0	PROPN
ap-3411	49	26	.	.	PUNCT
ap-3411	50	1	(	(	PUNCT
ap-3411	50	2	2.2	2.2	NUM
ap-3411	50	3	)	)	PUNCT
ap-3411	50	4	equation	equation	NOUN
ap-3411	50	5	(	(	PUNCT
ap-3411	50	6	2.2	2.2	NUM
ap-3411	50	7	)	)	PUNCT
ap-3411	50	8	is	be	AUX
ap-3411	50	9	a	a	DET
ap-3411	50	10	first	first	ADJ
ap-3411	50	11	order	order	NOUN
ap-3411	50	12	differential	differential	ADJ
ap-3411	50	13	equation	equation	NOUN
ap-3411	50	14	for	for	ADP
ap-3411	50	15	q	q	PROPN
ap-3411	50	16	which	which	PRON
ap-3411	50	17	can	can	AUX
ap-3411	50	18	be	be	AUX
ap-3411	50	19	solved	solve	VERB
ap-3411	50	20	on	on	ADP
ap-3411	50	21	the	the	DET
ap-3411	50	22	characteristics	characteristic	NOUN
ap-3411	50	23	and	and	CCONJ
ap-3411	50	24	whose	whose	DET
ap-3411	50	25	solutions	solution	NOUN
ap-3411	50	26	provide	provide	VERB
ap-3411	50	27	k	k	PROPN
ap-3411	51	1	+	+	CCONJ
ap-3411	51	2	2	2	NUM
ap-3411	51	3	symmetry	symmetry	NOUN
ap-3411	51	4	variables	variable	NOUN
ap-3411	51	5	.	.	PUNCT
ap-3411	52	1	then	then	ADV
ap-3411	52	2	,	,	PUNCT
ap-3411	52	3	as	as	ADP
ap-3411	52	4	in	in	ADP
ap-3411	52	5	the	the	DET
ap-3411	52	6	case	case	NOUN
ap-3411	52	7	of	of	ADP
ap-3411	52	8	(	(	PUNCT
ap-3411	52	9	1.5	1.5	NUM
ap-3411	52	10	)	)	PUNCT
ap-3411	52	11	,	,	PUNCT
ap-3411	52	12	the	the	DET
ap-3411	52	13	symmetries	symmetry	NOUN
ap-3411	52	14	of	of	ADP
ap-3411	52	15	(	(	PUNCT
ap-3411	52	16	2.1	2.1	NUM
ap-3411	52	17	)	)	PUNCT
ap-3411	52	18	are	be	AUX
ap-3411	52	19	given	give	VERB
ap-3411	52	20	by	by	ADP
ap-3411	52	21	arbitrary	arbitrary	ADJ
ap-3411	52	22	functions	function	NOUN
ap-3411	52	23	of	of	ADP
ap-3411	52	24	the	the	DET
ap-3411	52	25	k	k	PROPN
ap-3411	52	26	+	+	CCONJ
ap-3411	52	27	2	2	NUM
ap-3411	52	28	symmetry	symmetry	NOUN
ap-3411	52	29	variables	variable	NOUN
ap-3411	52	30	.	.	PUNCT
ap-3411	53	1	so	so	ADV
ap-3411	53	2	any	any	DET
ap-3411	53	3	first	first	ADJ
ap-3411	53	4	order	order	NOUN
ap-3411	53	5	pde	pde	NOUN
ap-3411	53	6	,	,	PUNCT
ap-3411	53	7	linear	linear	ADJ
ap-3411	53	8	or	or	CCONJ
ap-3411	53	9	nonlinear	nonlinear	ADJ
ap-3411	53	10	,	,	PUNCT
ap-3411	53	11	will	will	AUX
ap-3411	53	12	have	have	VERB
ap-3411	53	13	generically	generically	ADV
ap-3411	53	14	point	point	NOUN
ap-3411	53	15	and	and	CCONJ
ap-3411	53	16	generalized	generalized	ADJ
ap-3411	53	17	symmetries	symmetry	NOUN
ap-3411	53	18	depending	depend	VERB
ap-3411	53	19	on	on	ADP
ap-3411	53	20	arbitrary	arbitrary	ADJ
ap-3411	53	21	functions	function	NOUN
ap-3411	53	22	of	of	ADP
ap-3411	53	23	the	the	DET
ap-3411	53	24	symmetry	symmetry	NOUN
ap-3411	53	25	variables	variable	NOUN
ap-3411	53	26	.	.	PUNCT
ap-3411	54	1	we	we	PRON
ap-3411	54	2	can	can	AUX
ap-3411	54	3	easily	easily	ADV
ap-3411	54	4	show	show	VERB
ap-3411	54	5	an	an	DET
ap-3411	54	6	interesting	interesting	ADJ
ap-3411	54	7	consequence	consequence	NOUN
ap-3411	54	8	of	of	ADP
ap-3411	54	9	the	the	DET
ap-3411	54	10	existence	existence	NOUN
ap-3411	54	11	of	of	ADP
ap-3411	54	12	generalized	generalized	ADJ
ap-3411	54	13	symmetries	symmetry	NOUN
ap-3411	54	14	depending	depend	VERB
ap-3411	54	15	on	on	ADP
ap-3411	54	16	arbitrary	arbitrary	ADJ
ap-3411	54	17	functions	function	NOUN
ap-3411	54	18	.	.	PUNCT
ap-3411	55	1	for	for	ADP
ap-3411	55	2	the	the	DET
ap-3411	55	3	sake	sake	NOUN
ap-3411	55	4	of	of	ADP
ap-3411	55	5	concreteness	concreteness	NOUN
ap-3411	55	6	we	we	PRON
ap-3411	55	7	consider	consider	VERB
ap-3411	55	8	the	the	DET
ap-3411	55	9	symmetries	symmetry	NOUN
ap-3411	55	10	of	of	ADP
ap-3411	55	11	(	(	PUNCT
ap-3411	55	12	1.4	1.4	NUM
ap-3411	55	13	)	)	PUNCT
ap-3411	55	14	.	.	PUNCT
ap-3411	56	1	let	let	VERB
ap-3411	56	2	us	we	PRON
ap-3411	56	3	consider	consider	VERB
ap-3411	56	4	the	the	DET
ap-3411	56	5	subcase	subcase	NOUN
ap-3411	56	6	of	of	ADP
ap-3411	56	7	(	(	PUNCT
ap-3411	56	8	1.5	1.5	NUM
ap-3411	56	9	)	)	PUNCT
ap-3411	57	1	when	when	SCONJ
ap-3411	57	2	qf	qf	PROPN
ap-3411	57	3	=	=	PROPN
ap-3411	57	4	ux	ux	PROPN
ap-3411	57	5	[	[	PUNCT
ap-3411	57	6	f1(x+	f1(x+	PROPN
ap-3411	57	7	tu	tu	PROPN
ap-3411	57	8	)	)	PUNCT
ap-3411	58	1	+	+	CCONJ
ap-3411	58	2	f2	f2	PROPN
ap-3411	58	3	(	(	PUNCT
ap-3411	58	4	t+	t+	NOUN
ap-3411	58	5	1	1	NUM
ap-3411	58	6	ux	ux	ADJ
ap-3411	58	7	)	)	PUNCT
ap-3411	59	1	+	+	CCONJ
ap-3411	59	2	f3	f3	PROPN
ap-3411	59	3	(	(	PUNCT
ap-3411	59	4	uxx	uxx	NOUN
ap-3411	59	5	u3	u3	PROPN
ap-3411	59	6	x	x	X
ap-3411	59	7	)	)	PUNCT
ap-3411	59	8	]	]	PUNCT
ap-3411	59	9	,	,	PUNCT
ap-3411	59	10	(	(	PUNCT
ap-3411	59	11	2.3	2.3	NUM
ap-3411	59	12	)	)	PUNCT
ap-3411	59	13	i.e.	i.e.	X
ap-3411	59	14	,	,	PUNCT
ap-3411	59	15	the	the	DET
ap-3411	59	16	hopf	hopf	ADJ
ap-3411	59	17	equation	equation	NOUN
ap-3411	59	18	(	(	PUNCT
ap-3411	59	19	1.4	1.4	NUM
ap-3411	59	20	)	)	PUNCT
ap-3411	59	21	has	have	VERB
ap-3411	59	22	a	a	DET
ap-3411	59	23	symmetry	symmetry	NOUN
ap-3411	59	24	generator	generator	NOUN
ap-3411	59	25	of	of	ADP
ap-3411	59	26	the	the	DET
ap-3411	59	27	form	form	NOUN
ap-3411	59	28	:	:	PUNCT
ap-3411	59	29	x̂f	x̂f	X
ap-3411	59	30	=	=	SYM
ap-3411	59	31	qf∂u	qf∂u	NOUN
ap-3411	59	32	(	(	PUNCT
ap-3411	59	33	2.4	2.4	NUM
ap-3411	59	34	)	)	PUNCT
ap-3411	59	35	with	with	ADP
ap-3411	59	36	the	the	DET
ap-3411	59	37	functions	function	NOUN
ap-3411	59	38	fi	fi	NOUN
ap-3411	59	39	,	,	PUNCT
ap-3411	59	40	i	i	NOUN
ap-3411	59	41	=	=	NOUN
ap-3411	59	42	1	1	NUM
ap-3411	59	43	,	,	PUNCT
ap-3411	59	44	2	2	NUM
ap-3411	59	45	,	,	PUNCT
ap-3411	59	46	3	3	NUM
ap-3411	59	47	analytic	analytic	NOUN
ap-3411	59	48	in	in	ADP
ap-3411	59	49	their	their	PRON
ap-3411	59	50	argument	argument	NOUN
ap-3411	59	51	.	.	PUNCT
ap-3411	60	1	when	when	SCONJ
ap-3411	60	2	f2	f2	PROPN
ap-3411	60	3	and	and	CCONJ
ap-3411	60	4	f3	f3	PROPN
ap-3411	60	5	are	be	AUX
ap-3411	60	6	zero	zero	NUM
ap-3411	60	7	then	then	ADV
ap-3411	60	8	(	(	PUNCT
ap-3411	60	9	2.4	2.4	NUM
ap-3411	60	10	)	)	PUNCT
ap-3411	60	11	is	be	AUX
ap-3411	60	12	the	the	DET
ap-3411	60	13	infinitesimal	infinitesimal	ADJ
ap-3411	60	14	generator	generator	NOUN
ap-3411	60	15	of	of	ADP
ap-3411	60	16	point	point	NOUN
ap-3411	60	17	symmetries	symmetry	NOUN
ap-3411	60	18	depending	depend	VERB
ap-3411	60	19	on	on	ADP
ap-3411	60	20	an	an	DET
ap-3411	60	21	arbitrary	arbitrary	ADJ
ap-3411	60	22	function	function	NOUN
ap-3411	60	23	f1	f1	NOUN
ap-3411	60	24	;	;	PUNCT
ap-3411	60	25	when	when	SCONJ
ap-3411	60	26	f1	f1	NOUN
ap-3411	60	27	and	and	CCONJ
ap-3411	60	28	f3	f3	PROPN
ap-3411	60	29	are	be	AUX
ap-3411	60	30	zero	zero	NUM
ap-3411	60	31	then	then	ADV
ap-3411	60	32	(	(	PUNCT
ap-3411	60	33	2.4	2.4	NUM
ap-3411	60	34	)	)	PUNCT
ap-3411	60	35	is	be	AUX
ap-3411	60	36	the	the	DET
ap-3411	60	37	infinitesimal	infinitesimal	ADJ
ap-3411	60	38	generator	generator	NOUN
ap-3411	60	39	of	of	ADP
ap-3411	60	40	contact	contact	NOUN
ap-3411	60	41	symmetries	symmetry	NOUN
ap-3411	60	42	depending	depend	VERB
ap-3411	60	43	on	on	ADP
ap-3411	60	44	an	an	DET
ap-3411	60	45	arbitrary	arbitrary	ADJ
ap-3411	60	46	function	function	NOUN
ap-3411	60	47	f2	f2	NOUN
ap-3411	60	48	;	;	PUNCT
ap-3411	60	49	when	when	SCONJ
ap-3411	60	50	f1	f1	PROPN
ap-3411	60	51	and	and	CCONJ
ap-3411	60	52	f2	f2	PROPN
ap-3411	60	53	are	be	AUX
ap-3411	60	54	zero	zero	NUM
ap-3411	60	55	then	then	ADV
ap-3411	60	56	(	(	PUNCT
ap-3411	60	57	2.4	2.4	NUM
ap-3411	60	58	)	)	PUNCT
ap-3411	60	59	is	be	AUX
ap-3411	60	60	the	the	DET
ap-3411	60	61	infinitesimal	infinitesimal	ADJ
ap-3411	60	62	generator	generator	NOUN
ap-3411	60	63	of	of	ADP
ap-3411	60	64	generalized	generalized	ADJ
ap-3411	60	65	symmetries	symmetry	NOUN
ap-3411	60	66	depending	depend	VERB
ap-3411	60	67	on	on	ADP
ap-3411	60	68	an	an	DET
ap-3411	60	69	arbitrary	arbitrary	ADJ
ap-3411	60	70	function	function	NOUN
ap-3411	60	71	f3	f3	NOUN
ap-3411	60	72	.	.	PUNCT
ap-3411	61	1	if	if	SCONJ
ap-3411	61	2	we	we	PRON
ap-3411	61	3	take	take	VERB
ap-3411	61	4	two	two	NUM
ap-3411	61	5	of	of	ADP
ap-3411	61	6	such	such	ADJ
ap-3411	61	7	generators	generator	NOUN
ap-3411	61	8	,	,	PUNCT
ap-3411	61	9	x̂f	x̂f	NUM
ap-3411	61	10	and	and	CCONJ
ap-3411	61	11	x̂g	x̂g	PROPN
ap-3411	61	12	,	,	PUNCT
ap-3411	61	13	where	where	SCONJ
ap-3411	61	14	f	f	PROPN
ap-3411	61	15	and	and	CCONJ
ap-3411	61	16	g	g	PROPN
ap-3411	61	17	are	be	AUX
ap-3411	61	18	two	two	NUM
ap-3411	61	19	different	different	ADJ
ap-3411	61	20	functions	function	NOUN
ap-3411	61	21	of	of	ADP
ap-3411	61	22	the	the	DET
ap-3411	61	23	same	same	ADJ
ap-3411	61	24	argument	argument	NOUN
ap-3411	61	25	,	,	PUNCT
ap-3411	61	26	what	what	PRON
ap-3411	61	27	can	can	AUX
ap-3411	61	28	we	we	PRON
ap-3411	61	29	say	say	VERB
ap-3411	61	30	of	of	ADP
ap-3411	61	31	their	their	PRON
ap-3411	61	32	commutator	commutator	NOUN
ap-3411	61	33	?	?	PUNCT
ap-3411	62	1	it	it	PRON
ap-3411	62	2	has	have	AUX
ap-3411	62	3	been	be	AUX
ap-3411	62	4	proved	prove	VERB
ap-3411	62	5	by	by	ADP
ap-3411	62	6	bäcklund	bäcklund	NOUN
ap-3411	62	7	[	[	X
ap-3411	62	8	17	17	NUM
ap-3411	62	9	]	]	PUNCT
ap-3411	62	10	that	that	SCONJ
ap-3411	62	11	as	as	ADV
ap-3411	62	12	soon	soon	ADV
ap-3411	62	13	as	as	SCONJ
ap-3411	62	14	the	the	DET
ap-3411	62	15	characteristic	characteristic	ADJ
ap-3411	62	16	q	q	NOUN
ap-3411	62	17	depends	depend	VERB
ap-3411	62	18	on	on	ADP
ap-3411	62	19	derivatives	derivative	NOUN
ap-3411	62	20	of	of	ADP
ap-3411	62	21	order	order	NOUN
ap-3411	62	22	higher	high	ADJ
ap-3411	62	23	than	than	ADP
ap-3411	62	24	the	the	DET
ap-3411	62	25	first	first	ADJ
ap-3411	62	26	one	one	NUM
ap-3411	62	27	,	,	PUNCT
ap-3411	62	28	the	the	DET
ap-3411	62	29	symmetry	symmetry	NOUN
ap-3411	62	30	group	group	NOUN
ap-3411	62	31	is	be	AUX
ap-3411	62	32	infinite	infinite	ADJ
ap-3411	62	33	.	.	PUNCT
ap-3411	63	1	the	the	DET
ap-3411	63	2	last	last	ADJ
ap-3411	63	3	symmetry	symmetry	NOUN
ap-3411	63	4	group	group	NOUN
ap-3411	63	5	which	which	PRON
ap-3411	63	6	can	can	AUX
ap-3411	63	7	be	be	AUX
ap-3411	63	8	finite	finite	NOUN
ap-3411	63	9	is	be	AUX
ap-3411	63	10	the	the	DET
ap-3411	63	11	one	one	NUM
ap-3411	63	12	of	of	ADP
ap-3411	63	13	the	the	DET
ap-3411	63	14	contact	contact	NOUN
ap-3411	63	15	symmetries	symmetry	NOUN
ap-3411	63	16	,	,	PUNCT
ap-3411	63	17	if	if	SCONJ
ap-3411	63	18	no	no	DET
ap-3411	63	19	arbitrary	arbitrary	ADJ
ap-3411	63	20	function	function	NOUN
ap-3411	63	21	is	be	AUX
ap-3411	63	22	present	present	ADJ
ap-3411	63	23	.	.	PUNCT
ap-3411	64	1	as	as	SCONJ
ap-3411	64	2	was	be	AUX
ap-3411	64	3	shown	show	VERB
ap-3411	64	4	in	in	ADP
ap-3411	64	5	the	the	DET
ap-3411	64	6	case	case	NOUN
ap-3411	64	7	of	of	ADP
ap-3411	64	8	the	the	DET
ap-3411	64	9	liouville	liouville	NOUN
ap-3411	64	10	equation	equation	NOUN
ap-3411	64	11	the	the	DET
ap-3411	64	12	presence	presence	NOUN
ap-3411	64	13	of	of	ADP
ap-3411	64	14	a	a	DET
ap-3411	64	15	symmetry	symmetry	NOUN
ap-3411	64	16	generator	generator	NOUN
ap-3411	64	17	of	of	ADP
ap-3411	64	18	point	point	NOUN
ap-3411	64	19	symmetries	symmetry	NOUN
ap-3411	64	20	depending	depend	VERB
ap-3411	64	21	on	on	ADP
ap-3411	64	22	an	an	DET
ap-3411	64	23	arbitrary	arbitrary	ADJ
ap-3411	64	24	function	function	NOUN
ap-3411	64	25	provide	provide	VERB
ap-3411	64	26	an	an	DET
ap-3411	64	27	infinite	infinite	ADJ
ap-3411	64	28	dimensional	dimensional	ADJ
ap-3411	64	29	lie	lie	NOUN
ap-3411	64	30	algebra	algebra	NOUN
ap-3411	64	31	of	of	ADP
ap-3411	64	32	point	point	NOUN
ap-3411	64	33	symmetries	symmetry	NOUN
ap-3411	64	34	.	.	PUNCT
ap-3411	65	1	let	let	VERB
ap-3411	65	2	us	we	PRON
ap-3411	65	3	carry	carry	VERB
ap-3411	65	4	out	out	ADP
ap-3411	65	5	the	the	DET
ap-3411	65	6	the	the	DET
ap-3411	65	7	commutation	commutation	NOUN
ap-3411	65	8	of	of	ADP
ap-3411	65	9	x̂f	x̂f	NUM
ap-3411	65	10	and	and	CCONJ
ap-3411	65	11	x̂g	x̂g	PROPN
ap-3411	65	12	,	,	PUNCT
ap-3411	65	13	for	for	ADP
ap-3411	65	14	f	f	PROPN
ap-3411	65	15	and	and	CCONJ
ap-3411	65	16	g	g	NOUN
ap-3411	65	17	equal	equal	ADJ
ap-3411	65	18	to	to	ADP
ap-3411	65	19	f1	f1	NOUN
ap-3411	65	20	we	we	PRON
ap-3411	65	21	get	get	VERB
ap-3411	65	22	:	:	PUNCT
ap-3411	65	23	[	[	PUNCT
ap-3411	65	24	x̂f1	x̂f1	NOUN
ap-3411	65	25	,	,	PUNCT
ap-3411	65	26	x̂g1	x̂g1	PROPN
ap-3411	65	27	]	]	PUNCT
ap-3411	66	1	=	=	PUNCT
ap-3411	66	2	x̂f1g′	x̂f1g′	PROPN
ap-3411	67	1	1−f	1−f	NUM
ap-3411	67	2	′	′	NUM
ap-3411	67	3	1g1	1g1	NUM
ap-3411	67	4	,	,	PUNCT
ap-3411	67	5	(	(	PUNCT
ap-3411	67	6	2.5	2.5	NUM
ap-3411	67	7	)	)	PUNCT
ap-3411	67	8	equal	equal	ADJ
ap-3411	67	9	to	to	ADP
ap-3411	67	10	f2	f2	PROPN
ap-3411	67	11	we	we	PRON
ap-3411	67	12	get	get	VERB
ap-3411	67	13	:	:	PUNCT
ap-3411	67	14	[	[	PUNCT
ap-3411	67	15	x̂f2	x̂f2	PROPN
ap-3411	67	16	,	,	PUNCT
ap-3411	67	17	x̂g2	x̂g2	PROPN
ap-3411	67	18	]	]	PUNCT
ap-3411	68	1	=	=	PUNCT
ap-3411	68	2	0	0	NUM
ap-3411	68	3	,	,	PUNCT
ap-3411	68	4	(	(	PUNCT
ap-3411	68	5	2.6	2.6	NUM
ap-3411	68	6	)	)	PUNCT
ap-3411	68	7	194	194	NUM
ap-3411	68	8	vol	vol	NOUN
ap-3411	68	9	.	.	PUNCT
ap-3411	69	1	56	56	NUM
ap-3411	69	2	no	no	NOUN
ap-3411	69	3	.	.	PUNCT
ap-3411	70	1	3/2016	3/2016	NUM
ap-3411	70	2	on	on	ADP
ap-3411	70	3	pde	pde	NOUN
ap-3411	70	4	and	and	CCONJ
ap-3411	70	5	p∆e	p∆e	NOUN
ap-3411	70	6	with	with	ADP
ap-3411	70	7	symmetries	symmetry	NOUN
ap-3411	70	8	depending	depend	VERB
ap-3411	70	9	on	on	ADP
ap-3411	70	10	arbitrary	arbitrary	ADJ
ap-3411	70	11	functions	function	NOUN
ap-3411	70	12	and	and	CCONJ
ap-3411	70	13	equal	equal	ADJ
ap-3411	70	14	to	to	ADP
ap-3411	70	15	f3	f3	PROPN
ap-3411	70	16	we	we	PRON
ap-3411	70	17	get	get	VERB
ap-3411	70	18	:	:	PUNCT
ap-3411	70	19	[	[	PUNCT
ap-3411	70	20	x̂f3	x̂f3	NOUN
ap-3411	70	21	,	,	PUNCT
ap-3411	70	22	x̂g3	x̂g3	PROPN
ap-3411	70	23	]	]	PUNCT
ap-3411	71	1	=	=	PUNCT
ap-3411	72	1	[	[	X
ap-3411	72	2	f	f	X
ap-3411	72	3	′′3	′′3	NOUN
ap-3411	72	4	g′3	g′3	VERB
ap-3411	72	5	−	−	PROPN
ap-3411	72	6	f	f	PROPN
ap-3411	72	7	′3g′′3	′3g′′3	PROPN
ap-3411	72	8	]	]	PUNCT
ap-3411	72	9	(	(	PUNCT
ap-3411	72	10	uxxxux	uxxxux	ADJ
ap-3411	72	11	−	−	PROPN
ap-3411	72	12	3u2	3u2	NUM
ap-3411	72	13	xx)2	xx)2	PROPN
ap-3411	72	14	u9	u9	PROPN
ap-3411	72	15	x	x	PROPN
ap-3411	72	16	∂u	∂u	PROPN
ap-3411	72	17	.	.	PUNCT
ap-3411	73	1	(	(	PUNCT
ap-3411	73	2	2.7	2.7	NUM
ap-3411	73	3	)	)	PUNCT
ap-3411	73	4	the	the	DET
ap-3411	73	5	algebra	algebra	NOUN
ap-3411	73	6	(	(	PUNCT
ap-3411	73	7	2.5	2.5	NUM
ap-3411	73	8	)	)	PUNCT
ap-3411	73	9	turn	turn	VERB
ap-3411	73	10	out	out	ADP
ap-3411	73	11	to	to	PART
ap-3411	73	12	be	be	AUX
ap-3411	73	13	a	a	DET
ap-3411	73	14	virasoro	virasoro	NOUN
ap-3411	73	15	algebra	algebra	NOUN
ap-3411	73	16	of	of	ADP
ap-3411	73	17	lie	lie	NOUN
ap-3411	73	18	point	point	NOUN
ap-3411	73	19	symmetries	symmetry	NOUN
ap-3411	73	20	.	.	PUNCT
ap-3411	74	1	the	the	DET
ap-3411	74	2	infinitesimal	infinitesimal	ADJ
ap-3411	74	3	generators	generator	NOUN
ap-3411	74	4	of	of	ADP
ap-3411	74	5	the	the	DET
ap-3411	74	6	contact	contact	NOUN
ap-3411	74	7	symmetries	symmetry	NOUN
ap-3411	74	8	(	(	PUNCT
ap-3411	74	9	2.6	2.6	NUM
ap-3411	74	10	)	)	PUNCT
ap-3411	74	11	commute	commute	NOUN
ap-3411	74	12	but	but	CCONJ
ap-3411	74	13	the	the	DET
ap-3411	74	14	infinitesimal	infinitesimal	ADJ
ap-3411	74	15	generator	generator	NOUN
ap-3411	74	16	depending	depend	VERB
ap-3411	74	17	on	on	ADP
ap-3411	74	18	an	an	DET
ap-3411	74	19	arbitrary	arbitrary	ADJ
ap-3411	74	20	function	function	NOUN
ap-3411	74	21	of	of	ADP
ap-3411	74	22	the	the	DET
ap-3411	74	23	generalized	generalized	ADJ
ap-3411	74	24	symmetry	symmetry	NOUN
ap-3411	74	25	take	take	VERB
ap-3411	74	26	the	the	DET
ap-3411	74	27	form	form	NOUN
ap-3411	74	28	of	of	ADP
ap-3411	74	29	a	a	DET
ap-3411	74	30	master	master	NOUN
ap-3411	74	31	symmetry	symmetry	NOUN
ap-3411	74	32	as	as	SCONJ
ap-3411	74	33	the	the	DET
ap-3411	74	34	commutator	commutator	NOUN
ap-3411	74	35	of	of	ADP
ap-3411	74	36	two	two	NUM
ap-3411	74	37	such	such	ADJ
ap-3411	74	38	symmetries	symmetry	NOUN
ap-3411	74	39	provide	provide	VERB
ap-3411	74	40	a	a	DET
ap-3411	74	41	symmetry	symmetry	NOUN
ap-3411	74	42	of	of	ADP
ap-3411	74	43	higher	high	ADJ
ap-3411	74	44	order	order	NOUN
ap-3411	74	45	(	(	PUNCT
ap-3411	74	46	2.7	2.7	NUM
ap-3411	74	47	)	)	PUNCT
ap-3411	74	48	.	.	PUNCT
ap-3411	75	1	the	the	DET
ap-3411	75	2	existence	existence	NOUN
ap-3411	75	3	of	of	ADP
ap-3411	75	4	arbitrary	arbitrary	ADJ
ap-3411	75	5	functions	function	NOUN
ap-3411	75	6	of	of	ADP
ap-3411	75	7	generalized	generalized	ADJ
ap-3411	75	8	symmetries	symmetry	NOUN
ap-3411	75	9	is	be	AUX
ap-3411	75	10	not	not	PART
ap-3411	75	11	limited	limit	VERB
ap-3411	75	12	to	to	ADP
ap-3411	75	13	the	the	DET
ap-3411	75	14	case	case	NOUN
ap-3411	75	15	of	of	ADP
ap-3411	75	16	first	first	ADJ
ap-3411	75	17	order	order	NOUN
ap-3411	75	18	differential	differential	ADJ
ap-3411	75	19	equations	equation	NOUN
ap-3411	75	20	.	.	PUNCT
ap-3411	76	1	it	it	PRON
ap-3411	76	2	can	can	AUX
ap-3411	76	3	easily	easily	ADV
ap-3411	76	4	extended	extend	VERB
ap-3411	76	5	to	to	ADP
ap-3411	76	6	higher	high	ADJ
ap-3411	76	7	order	order	NOUN
ap-3411	76	8	pde	pde	NOUN
ap-3411	76	9	’s	’s	ADV
ap-3411	76	10	when	when	SCONJ
ap-3411	76	11	the	the	DET
ap-3411	76	12	differential	differential	ADJ
ap-3411	76	13	operator	operator	NOUN
ap-3411	76	14	which	which	PRON
ap-3411	76	15	define	define	VERB
ap-3411	76	16	the	the	DET
ap-3411	76	17	equation	equation	NOUN
ap-3411	76	18	is	be	AUX
ap-3411	76	19	factorizable	factorizable	ADJ
ap-3411	76	20	.	.	PUNCT
ap-3411	77	1	few	few	ADJ
ap-3411	77	2	authors	author	NOUN
ap-3411	77	3	[	[	X
ap-3411	77	4	18	18	NUM
ap-3411	77	5	,	,	PUNCT
ap-3411	77	6	34	34	NUM
ap-3411	77	7	]	]	PUNCT
ap-3411	77	8	showed	show	VERB
ap-3411	77	9	through	through	ADP
ap-3411	77	10	the	the	DET
ap-3411	77	11	laplace	laplace	NOUN
ap-3411	77	12	cascade	cascade	NOUN
ap-3411	77	13	method	method	NOUN
ap-3411	77	14	that	that	PRON
ap-3411	77	15	factorizable	factorizable	ADJ
ap-3411	77	16	linear	linear	PROPN
ap-3411	77	17	pde	pde	PROPN
ap-3411	77	18	’s	’s	PART
ap-3411	77	19	are	be	AUX
ap-3411	77	20	darboux	darboux	VERB
ap-3411	77	21	integrable	integrable	ADJ
ap-3411	77	22	if	if	SCONJ
ap-3411	77	23	the	the	DET
ap-3411	77	24	cascade	cascade	NOUN
ap-3411	77	25	terminates	terminate	VERB
ap-3411	77	26	.	.	PUNCT
ap-3411	78	1	we	we	PRON
ap-3411	78	2	can	can	AUX
ap-3411	78	3	show	show	VERB
ap-3411	78	4	that	that	SCONJ
ap-3411	78	5	a	a	DET
ap-3411	78	6	factorizable	factorizable	ADJ
ap-3411	78	7	pde	pde	NOUN
ap-3411	78	8	admits	admit	VERB
ap-3411	78	9	as	as	ADP
ap-3411	78	10	a	a	DET
ap-3411	78	11	subclass	subclass	NOUN
ap-3411	78	12	of	of	ADP
ap-3411	78	13	symmetries	symmetry	NOUN
ap-3411	78	14	the	the	DET
ap-3411	78	15	symmetries	symmetry	NOUN
ap-3411	78	16	of	of	ADP
ap-3411	78	17	its	its	PRON
ap-3411	78	18	first	first	ADJ
ap-3411	78	19	order	order	NOUN
ap-3411	78	20	pde	pde	NOUN
ap-3411	78	21	.	.	PUNCT
ap-3411	79	1	as	as	ADP
ap-3411	79	2	an	an	DET
ap-3411	79	3	example	example	NOUN
ap-3411	79	4	let	let	VERB
ap-3411	79	5	us	we	PRON
ap-3411	79	6	consider	consider	VERB
ap-3411	79	7	the	the	DET
ap-3411	79	8	case	case	NOUN
ap-3411	79	9	of	of	ADP
ap-3411	79	10	second	second	ADJ
ap-3411	79	11	order	order	NOUN
ap-3411	79	12	factorizable	factorizable	PROPN
ap-3411	79	13	pde	pde	PROPN
ap-3411	79	14	’s	’s	PART
ap-3411	79	15	.	.	PUNCT
ap-3411	80	1	let	let	VERB
ap-3411	80	2	us	we	PRON
ap-3411	80	3	consider	consider	VERB
ap-3411	80	4	the	the	DET
ap-3411	80	5	second	second	ADJ
ap-3411	80	6	order	order	NOUN
ap-3411	80	7	autonomous	autonomous	ADJ
ap-3411	80	8	partial	partial	ADJ
ap-3411	80	9	differential	differential	NOUN
ap-3411	80	10	equation	equation	NOUN
ap-3411	80	11	for	for	ADP
ap-3411	80	12	one	one	NUM
ap-3411	80	13	dependent	dependent	ADJ
ap-3411	80	14	variable	variable	ADJ
ap-3411	80	15	u	u	NOUN
ap-3411	80	16	in	in	ADP
ap-3411	80	17	the	the	DET
ap-3411	80	18	two	two	NUM
ap-3411	80	19	independent	independent	ADJ
ap-3411	80	20	variables	variable	NOUN
ap-3411	80	21	x	x	PUNCT
ap-3411	80	22	and	and	CCONJ
ap-3411	81	1	t	t	PROPN
ap-3411	81	2	e1	e1	NOUN
ap-3411	81	3	=	=	SYM
ap-3411	81	4	utt	utt	PROPN
ap-3411	82	1	+	+	PUNCT
ap-3411	82	2	[	[	PUNCT
ap-3411	82	3	g(u	g(u	PROPN
ap-3411	82	4	,	,	PUNCT
ap-3411	82	5	ux)−	ux)−	PROPN
ap-3411	82	6	f(u	f(u	PROPN
ap-3411	82	7	,	,	PUNCT
ap-3411	82	8	ux)ux	ux)ux	PROPN
ap-3411	82	9	]	]	PUNCT
ap-3411	82	10	uxt	uxt	NOUN
ap-3411	82	11	−	−	PROPN
ap-3411	82	12	f(u	f(u	PROPN
ap-3411	82	13	,	,	PUNCT
ap-3411	82	14	ux)ux	ux)ux	PROPN
ap-3411	82	15	g(u	g(u	PROPN
ap-3411	82	16	,	,	PUNCT
ap-3411	82	17	ux)uxx	ux)uxx	PROPN
ap-3411	82	18	−	−	PROPN
ap-3411	82	19	f(u	f(u	PROPN
ap-3411	82	20	,	,	PUNCT
ap-3411	82	21	ux)u	ux)u	PROPN
ap-3411	82	22	[	[	PUNCT
ap-3411	82	23	ut	ut	PROPN
ap-3411	82	24	−	−	PROPN
ap-3411	82	25	g(u	g(u	PROPN
ap-3411	82	26	,	,	PUNCT
ap-3411	82	27	ux)ux	ux)ux	PROPN
ap-3411	82	28	]	]	PUNCT
ap-3411	82	29	=	=	PUNCT
ap-3411	82	30	0	0	NUM
ap-3411	82	31	,	,	PUNCT
ap-3411	82	32	(	(	PUNCT
ap-3411	82	33	2.8	2.8	NUM
ap-3411	82	34	)	)	PUNCT
ap-3411	82	35	where	where	SCONJ
ap-3411	82	36	f	f	PROPN
ap-3411	82	37	and	and	CCONJ
ap-3411	82	38	g	g	PROPN
ap-3411	82	39	are	be	AUX
ap-3411	82	40	two	two	NUM
ap-3411	82	41	arbitrary	arbitrary	ADJ
ap-3411	82	42	functions	function	NOUN
ap-3411	82	43	of	of	ADP
ap-3411	82	44	their	their	PRON
ap-3411	82	45	arguments	argument	NOUN
ap-3411	82	46	.	.	PUNCT
ap-3411	83	1	defining	define	VERB
ap-3411	83	2	the	the	DET
ap-3411	83	3	first	first	ADJ
ap-3411	83	4	order	order	NOUN
ap-3411	83	5	autonomous	autonomous	ADJ
ap-3411	83	6	pde	pde	NOUN
ap-3411	83	7	for	for	ADP
ap-3411	83	8	u	u	NOUN
ap-3411	83	9	=	=	PROPN
ap-3411	83	10	u(x	u(x	PROPN
ap-3411	83	11	,	,	PUNCT
ap-3411	83	12	t	t	PROPN
ap-3411	83	13	)	)	PUNCT
ap-3411	83	14	,	,	PUNCT
ap-3411	83	15	e0	e0	PROPN
ap-3411	83	16	=	=	SYM
ap-3411	83	17	ut	ut	PROPN
ap-3411	83	18	−	−	PROPN
ap-3411	83	19	f(u	f(u	PROPN
ap-3411	83	20	,	,	PUNCT
ap-3411	83	21	ux	ux	NOUN
ap-3411	83	22	)	)	PUNCT
ap-3411	83	23	=	=	SYM
ap-3411	83	24	0	0	NUM
ap-3411	83	25	,	,	PUNCT
ap-3411	83	26	(	(	PUNCT
ap-3411	83	27	2.9	2.9	NUM
ap-3411	83	28	)	)	PUNCT
ap-3411	83	29	(	(	PUNCT
ap-3411	83	30	2.8	2.8	NUM
ap-3411	83	31	)	)	PUNCT
ap-3411	83	32	is	be	AUX
ap-3411	83	33	factorizable	factorizable	ADJ
ap-3411	83	34	as	as	ADP
ap-3411	83	35	:	:	PUNCT
ap-3411	83	36	e1	e1	NOUN
ap-3411	83	37	=	=	SYM
ap-3411	84	1	[	[	PUNCT
ap-3411	84	2	∂t	∂t	PROPN
ap-3411	84	3	+	+	CCONJ
ap-3411	84	4	g(u	g(u	PROPN
ap-3411	84	5	,	,	PUNCT
ap-3411	84	6	ux)∂x	ux)∂x	PROPN
ap-3411	84	7	]	]	PUNCT
ap-3411	84	8	e0	e0	PROPN
ap-3411	84	9	=	=	PUNCT
ap-3411	84	10	0	0	X
ap-3411	84	11	.	.	PUNCT
ap-3411	85	1	(	(	PUNCT
ap-3411	85	2	2.10	2.10	NUM
ap-3411	85	3	)	)	PUNCT
ap-3411	85	4	the	the	DET
ap-3411	85	5	symmetries	symmetry	NOUN
ap-3411	85	6	of	of	ADP
ap-3411	85	7	e0	e0	PROPN
ap-3411	85	8	are	be	AUX
ap-3411	85	9	given	give	VERB
ap-3411	85	10	by	by	ADP
ap-3411	85	11	the	the	DET
ap-3411	85	12	infinitesimal	infinitesimal	ADJ
ap-3411	85	13	generator	generator	NOUN
ap-3411	85	14	x̂	x̂	PUNCT
ap-3411	86	1	=	=	SYM
ap-3411	86	2	q0(x	q0(x	PROPN
ap-3411	86	3	,	,	PUNCT
ap-3411	86	4	t	t	PROPN
ap-3411	86	5	,	,	PUNCT
ap-3411	86	6	u	u	NOUN
ap-3411	86	7	,	,	PUNCT
ap-3411	86	8	ux	ux	PROPN
ap-3411	86	9	,	,	PUNCT
ap-3411	86	10	ut	ut	PROPN
ap-3411	86	11	,	,	PUNCT
ap-3411	86	12	uxx	uxx	PROPN
ap-3411	86	13	,	,	PUNCT
ap-3411	86	14	.	.	PUNCT
ap-3411	86	15	.	.	PUNCT
ap-3411	86	16	.	.	PUNCT
ap-3411	86	17	)	)	PUNCT
ap-3411	87	1	∂u	∂u	PROPN
ap-3411	87	2	(	(	PUNCT
ap-3411	87	3	2.11	2.11	NUM
ap-3411	87	4	)	)	PUNCT
ap-3411	87	5	and	and	CCONJ
ap-3411	87	6	the	the	DET
ap-3411	87	7	determining	determine	VERB
ap-3411	87	8	equation	equation	NOUN
ap-3411	87	9	is	be	AUX
ap-3411	87	10	written	write	VERB
ap-3411	87	11	as	as	ADP
ap-3411	87	12	dtq0	dtq0	PROPN
ap-3411	87	13	−	−	PROPN
ap-3411	87	14	f(u	f(u	PROPN
ap-3411	87	15	,	,	PUNCT
ap-3411	87	16	ux)uq0	ux)uq0	PROPN
ap-3411	87	17	−	−	PROPN
ap-3411	87	18	f(u	f(u	PROPN
ap-3411	87	19	,	,	PUNCT
ap-3411	87	20	ux)uxdxq0	ux)uxdxq0	ADJ
ap-3411	87	21	∣∣∣	∣∣∣	ADJ
ap-3411	87	22	e0=0	e0=0	PROPN
ap-3411	87	23	=	=	SYM
ap-3411	87	24	0	0	NUM
ap-3411	87	25	,	,	PUNCT
ap-3411	87	26	(	(	PUNCT
ap-3411	87	27	2.12	2.12	NUM
ap-3411	87	28	)	)	PUNCT
ap-3411	87	29	where	where	SCONJ
ap-3411	87	30	dtq0	dtq0	NOUN
ap-3411	87	31	and	and	CCONJ
ap-3411	87	32	dxq0	dxq0	PROPN
ap-3411	87	33	are	be	AUX
ap-3411	87	34	the	the	DET
ap-3411	87	35	coefficient	coefficient	NOUN
ap-3411	87	36	of	of	ADP
ap-3411	87	37	the	the	DET
ap-3411	87	38	prolongation	prolongation	NOUN
ap-3411	87	39	of	of	ADP
ap-3411	87	40	x̂	x̂	NOUN
ap-3411	87	41	with	with	ADP
ap-3411	87	42	respect	respect	NOUN
ap-3411	87	43	to	to	ADP
ap-3411	87	44	ut	ut	PROPN
ap-3411	87	45	and	and	CCONJ
ap-3411	87	46	ux	ux	PROPN
ap-3411	87	47	.	.	PUNCT
ap-3411	88	1	the	the	DET
ap-3411	88	2	determining	determine	VERB
ap-3411	88	3	equation	equation	NOUN
ap-3411	88	4	for	for	ADP
ap-3411	88	5	the	the	DET
ap-3411	88	6	symmetries	symmetry	NOUN
ap-3411	88	7	of	of	ADP
ap-3411	88	8	e1	e1	NOUN
ap-3411	88	9	=	=	NOUN
ap-3411	88	10	0	0	NUM
ap-3411	88	11	of	of	ADP
ap-3411	88	12	infinitesimal	infinitesimal	ADJ
ap-3411	88	13	generator	generator	NOUN
ap-3411	88	14	ŷ	ŷ	NUM
ap-3411	88	15	=	=	SYM
ap-3411	89	1	q1(x	q1(x	PROPN
ap-3411	89	2	,	,	PUNCT
ap-3411	89	3	t	t	PROPN
ap-3411	89	4	,	,	PUNCT
ap-3411	89	5	u	u	NOUN
ap-3411	89	6	,	,	PUNCT
ap-3411	89	7	ux	ux	PROPN
ap-3411	89	8	,	,	PUNCT
ap-3411	89	9	ut	ut	PROPN
ap-3411	89	10	,	,	PUNCT
ap-3411	89	11	uxx	uxx	PROPN
ap-3411	89	12	,	,	PUNCT
ap-3411	89	13	.	.	PUNCT
ap-3411	89	14	.	.	PUNCT
ap-3411	89	15	.	.	PUNCT
ap-3411	90	1	)	)	PUNCT
ap-3411	91	1	∂u	∂u	PROPN
ap-3411	91	2	(	(	PUNCT
ap-3411	91	3	2.13	2.13	NUM
ap-3411	91	4	)	)	PUNCT
ap-3411	91	5	is	be	AUX
ap-3411	91	6	given	give	VERB
ap-3411	91	7	by	by	ADP
ap-3411	91	8	pr	pr	NOUN
ap-3411	91	9	ŷ	ŷ	PUNCT
ap-3411	91	10	e1	e1	VERB
ap-3411	91	11	∣∣∣	∣∣∣	NOUN
ap-3411	91	12	e1=0	e1=0	PROPN
ap-3411	91	13	=	=	NOUN
ap-3411	92	1	0	0	X
ap-3411	92	2	.	.	PUNCT
ap-3411	93	1	(	(	PUNCT
ap-3411	93	2	2.14	2.14	NUM
ap-3411	93	3	)	)	PUNCT
ap-3411	93	4	the	the	DET
ap-3411	93	5	explicit	explicit	ADJ
ap-3411	93	6	expression	expression	NOUN
ap-3411	93	7	of	of	ADP
ap-3411	93	8	(	(	PUNCT
ap-3411	93	9	2.14	2.14	NUM
ap-3411	93	10	)	)	PUNCT
ap-3411	93	11	is	be	AUX
ap-3411	93	12	long	long	ADJ
ap-3411	93	13	as	as	SCONJ
ap-3411	93	14	it	it	PRON
ap-3411	93	15	involves	involve	VERB
ap-3411	93	16	the	the	DET
ap-3411	93	17	application	application	NOUN
ap-3411	93	18	of	of	ADP
ap-3411	93	19	the	the	DET
ap-3411	93	20	second	second	ADJ
ap-3411	93	21	prolongation	prolongation	NOUN
ap-3411	93	22	of	of	ADP
ap-3411	93	23	ŷ	ŷ	NUM
ap-3411	93	24	.	.	PUNCT
ap-3411	94	1	so	so	ADV
ap-3411	94	2	we	we	PRON
ap-3411	94	3	do	do	AUX
ap-3411	94	4	not	not	PART
ap-3411	94	5	write	write	VERB
ap-3411	94	6	it	it	PRON
ap-3411	94	7	down	down	ADP
ap-3411	94	8	here	here	ADV
ap-3411	94	9	.	.	PUNCT
ap-3411	95	1	by	by	ADP
ap-3411	95	2	direct	direct	ADJ
ap-3411	95	3	calculation	calculation	NOUN
ap-3411	95	4	it	it	PRON
ap-3411	95	5	is	be	AUX
ap-3411	95	6	easy	easy	ADJ
ap-3411	95	7	to	to	PART
ap-3411	95	8	show	show	VERB
ap-3411	95	9	that	that	SCONJ
ap-3411	95	10	(	(	PUNCT
ap-3411	95	11	2.14	2.14	NUM
ap-3411	95	12	)	)	PUNCT
ap-3411	95	13	is	be	AUX
ap-3411	95	14	satisfied	satisfied	ADJ
ap-3411	95	15	by	by	ADP
ap-3411	95	16	the	the	DET
ap-3411	95	17	solution	solution	NOUN
ap-3411	95	18	of	of	ADP
ap-3411	95	19	(	(	PUNCT
ap-3411	95	20	2.12	2.12	NUM
ap-3411	95	21	)	)	PUNCT
ap-3411	95	22	.	.	PUNCT
ap-3411	96	1	this	this	PRON
ap-3411	96	2	shows	show	VERB
ap-3411	96	3	that	that	SCONJ
ap-3411	96	4	the	the	DET
ap-3411	96	5	symmetries	symmetry	NOUN
ap-3411	96	6	of	of	ADP
ap-3411	96	7	the	the	DET
ap-3411	96	8	second	second	ADJ
ap-3411	96	9	order	order	NOUN
ap-3411	96	10	autonomous	autonomous	ADJ
ap-3411	96	11	factorizable	factorizable	ADJ
ap-3411	96	12	pde	pde	NOUN
ap-3411	96	13	e1	e1	PROPN
ap-3411	96	14	=	=	SYM
ap-3411	96	15	0	0	NUM
ap-3411	96	16	contain	contain	VERB
ap-3411	96	17	those	those	PRON
ap-3411	96	18	of	of	ADP
ap-3411	96	19	e0	e0	PROPN
ap-3411	96	20	=	=	PROPN
ap-3411	96	21	0	0	X
ap-3411	96	22	.	.	PUNCT
ap-3411	97	1	so	so	ADV
ap-3411	97	2	e1	e1	PROPN
ap-3411	97	3	=	=	SYM
ap-3411	97	4	0	0	NUM
ap-3411	97	5	can	can	AUX
ap-3411	97	6	have	have	VERB
ap-3411	97	7	arbitrary	arbitrary	ADJ
ap-3411	97	8	function	function	NOUN
ap-3411	97	9	dependent	dependent	ADJ
ap-3411	97	10	generalized	generalized	ADJ
ap-3411	97	11	symmetries	symmetry	NOUN
ap-3411	97	12	as	as	ADP
ap-3411	97	13	e0	e0	PROPN
ap-3411	97	14	=	=	SYM
ap-3411	97	15	0	0	PROPN
ap-3411	97	16	does	do	VERB
ap-3411	97	17	.	.	PUNCT
ap-3411	98	1	this	this	DET
ap-3411	98	2	proof	proof	NOUN
ap-3411	98	3	can	can	AUX
ap-3411	98	4	be	be	AUX
ap-3411	98	5	extended	extend	VERB
ap-3411	98	6	to	to	ADP
ap-3411	98	7	pde	pde	NOUN
ap-3411	98	8	’s	’s	ADV
ap-3411	98	9	of	of	ADP
ap-3411	98	10	any	any	DET
ap-3411	98	11	order	order	NOUN
ap-3411	98	12	and	and	CCONJ
ap-3411	98	13	of	of	ADP
ap-3411	98	14	any	any	DET
ap-3411	98	15	number	number	NOUN
ap-3411	98	16	of	of	ADP
ap-3411	98	17	variables	variable	NOUN
ap-3411	98	18	.	.	PUNCT
ap-3411	99	1	the	the	DET
ap-3411	99	2	relation	relation	NOUN
ap-3411	99	3	of	of	ADP
ap-3411	99	4	this	this	DET
ap-3411	99	5	factorization	factorization	NOUN
ap-3411	99	6	to	to	ADP
ap-3411	99	7	laplace	laplace	NOUN
ap-3411	99	8	cascade	cascade	NOUN
ap-3411	99	9	method	method	NOUN
ap-3411	99	10	and	and	CCONJ
ap-3411	99	11	darboux	darboux	VERB
ap-3411	99	12	integrability	integrability	NOUN
ap-3411	99	13	is	be	AUX
ap-3411	99	14	still	still	ADV
ap-3411	99	15	to	to	PART
ap-3411	99	16	be	be	AUX
ap-3411	99	17	understood	understand	VERB
ap-3411	99	18	.	.	PUNCT
ap-3411	100	1	3	3	X
ap-3411	100	2	.	.	X
ap-3411	100	3	discrete	discrete	ADJ
ap-3411	100	4	equations	equation	NOUN
ap-3411	100	5	with	with	ADP
ap-3411	100	6	generalized	generalized	ADJ
ap-3411	100	7	symmetries	symmetry	NOUN
ap-3411	100	8	depending	depend	VERB
ap-3411	100	9	on	on	ADP
ap-3411	100	10	an	an	DET
ap-3411	100	11	arbitrary	arbitrary	ADJ
ap-3411	100	12	function	function	NOUN
ap-3411	100	13	.	.	PUNCT
ap-3411	101	1	partial	partial	ADJ
ap-3411	101	2	difference	difference	NOUN
ap-3411	101	3	equations	equation	NOUN
ap-3411	101	4	(	(	PUNCT
ap-3411	101	5	p∆e	p∆e	NOUN
ap-3411	101	6	’s	’s	PART
ap-3411	101	7	)	)	PUNCT
ap-3411	101	8	can	can	AUX
ap-3411	101	9	have	have	VERB
ap-3411	101	10	symmetries	symmetry	NOUN
ap-3411	101	11	depending	depend	VERB
ap-3411	101	12	on	on	ADP
ap-3411	101	13	arbitrary	arbitrary	ADJ
ap-3411	101	14	functions	function	NOUN
ap-3411	101	15	.	.	PUNCT
ap-3411	102	1	the	the	DET
ap-3411	102	2	presence	presence	NOUN
ap-3411	102	3	of	of	ADP
ap-3411	102	4	arbitrary	arbitrary	ADJ
ap-3411	102	5	functions	function	NOUN
ap-3411	102	6	of	of	ADP
ap-3411	102	7	point	point	NOUN
ap-3411	102	8	symmetries	symmetry	NOUN
ap-3411	102	9	has	have	AUX
ap-3411	102	10	been	be	AUX
ap-3411	102	11	shown	show	VERB
ap-3411	102	12	to	to	PART
ap-3411	102	13	appear	appear	VERB
ap-3411	102	14	,	,	PUNCT
ap-3411	102	15	as	as	ADP
ap-3411	102	16	in	in	ADP
ap-3411	102	17	the	the	DET
ap-3411	102	18	continuous	continuous	ADJ
ap-3411	102	19	case	case	NOUN
ap-3411	102	20	[	[	X
ap-3411	102	21	3	3	NUM
ap-3411	102	22	,	,	PUNCT
ap-3411	102	23	11	11	NUM
ap-3411	102	24	,	,	PUNCT
ap-3411	102	25	17	17	NUM
ap-3411	102	26	,	,	PUNCT
ap-3411	102	27	31	31	NUM
ap-3411	102	28	]	]	PUNCT
ap-3411	102	29	,	,	PUNCT
ap-3411	102	30	when	when	SCONJ
ap-3411	102	31	the	the	DET
ap-3411	102	32	p∆e	p∆e	NOUN
ap-3411	102	33	is	be	AUX
ap-3411	102	34	linearizable	linearizable	ADJ
ap-3411	102	35	[	[	X
ap-3411	102	36	21	21	NUM
ap-3411	102	37	]	]	PUNCT
ap-3411	102	38	.	.	PUNCT
ap-3411	103	1	here	here	ADV
ap-3411	103	2	we	we	PRON
ap-3411	103	3	show	show	VERB
ap-3411	103	4	on	on	ADP
ap-3411	103	5	some	some	DET
ap-3411	103	6	examples	example	NOUN
ap-3411	103	7	that	that	SCONJ
ap-3411	103	8	one	one	PRON
ap-3411	103	9	can	can	AUX
ap-3411	103	10	find	find	VERB
ap-3411	103	11	p∆e	p∆e	NOUN
ap-3411	103	12	’s	’s	PART
ap-3411	103	13	which	which	PRON
ap-3411	103	14	have	have	VERB
ap-3411	103	15	arbitrary	arbitrary	ADJ
ap-3411	103	16	functions	function	NOUN
ap-3411	103	17	of	of	ADP
ap-3411	103	18	generalized	generalized	ADJ
ap-3411	103	19	symmetries	symmetry	NOUN
ap-3411	103	20	.	.	PUNCT
ap-3411	104	1	when	when	SCONJ
ap-3411	104	2	they	they	PRON
ap-3411	104	3	appear	appear	VERB
ap-3411	104	4	the	the	DET
ap-3411	104	5	system	system	NOUN
ap-3411	104	6	is	be	AUX
ap-3411	104	7	usually	usually	ADV
ap-3411	104	8	linearizable	linearizable	ADJ
ap-3411	104	9	but	but	CCONJ
ap-3411	104	10	a	a	DET
ap-3411	104	11	complete	complete	ADJ
ap-3411	104	12	theory	theory	NOUN
ap-3411	104	13	in	in	ADP
ap-3411	104	14	this	this	DET
ap-3411	104	15	case	case	NOUN
ap-3411	104	16	is	be	AUX
ap-3411	104	17	absent	absent	ADJ
ap-3411	104	18	.	.	PUNCT
ap-3411	105	1	we	we	PRON
ap-3411	105	2	have	have	VERB
ap-3411	105	3	some	some	DET
ap-3411	105	4	results	result	NOUN
ap-3411	105	5	on	on	ADP
ap-3411	105	6	darboux	darboux	VERB
ap-3411	105	7	integrable	integrable	ADJ
ap-3411	105	8	discrete	discrete	ADJ
ap-3411	105	9	equations	equation	NOUN
ap-3411	105	10	[	[	X
ap-3411	105	11	2	2	NUM
ap-3411	105	12	,	,	PUNCT
ap-3411	105	13	9	9	NUM
ap-3411	105	14	,	,	PUNCT
ap-3411	105	15	10	10	NUM
ap-3411	105	16	,	,	PUNCT
ap-3411	105	17	32	32	NUM
ap-3411	105	18	,	,	PUNCT
ap-3411	105	19	33	33	NUM
ap-3411	105	20	,	,	PUNCT
ap-3411	105	21	35	35	NUM
ap-3411	105	22	]	]	PUNCT
ap-3411	105	23	which	which	PRON
ap-3411	105	24	correspond	correspond	VERB
ap-3411	105	25	to	to	ADP
ap-3411	105	26	p∆e	p∆e	NOUN
ap-3411	105	27	’s	’s	PART
ap-3411	105	28	which	which	PRON
ap-3411	105	29	have	have	VERB
ap-3411	105	30	two	two	NUM
ap-3411	105	31	distinct	distinct	ADJ
ap-3411	105	32	conserved	conserve	VERB
ap-3411	105	33	quantities	quantity	NOUN
ap-3411	105	34	in	in	ADP
ap-3411	105	35	the	the	DET
ap-3411	105	36	two	two	NUM
ap-3411	105	37	different	different	ADJ
ap-3411	105	38	directions	direction	NOUN
ap-3411	105	39	of	of	ADP
ap-3411	105	40	the	the	DET
ap-3411	105	41	discrete	discrete	ADJ
ap-3411	105	42	plane	plane	NOUN
ap-3411	105	43	.	.	PUNCT
ap-3411	106	1	the	the	DET
ap-3411	106	2	complete	complete	ADJ
ap-3411	106	3	classification	classification	NOUN
ap-3411	106	4	of	of	ADP
ap-3411	106	5	darboux	darboux	VERB
ap-3411	106	6	integrable	integrable	ADJ
ap-3411	106	7	equations	equation	NOUN
ap-3411	106	8	on	on	ADP
ap-3411	106	9	the	the	DET
ap-3411	106	10	lattice	lattice	NOUN
ap-3411	106	11	is	be	AUX
ap-3411	106	12	absent	absent	ADJ
ap-3411	106	13	and	and	CCONJ
ap-3411	106	14	only	only	ADV
ap-3411	106	15	195	195	NUM
ap-3411	106	16	g.	g.	NOUN
ap-3411	106	17	gubbiotti	gubbiotti	PROPN
ap-3411	106	18	,	,	PUNCT
ap-3411	106	19	d.	d.	PROPN
ap-3411	106	20	levi	levi	PROPN
ap-3411	106	21	,	,	PUNCT
ap-3411	106	22	c.	c.	PROPN
ap-3411	106	23	scimiterna	scimiterna	PROPN
ap-3411	106	24	acta	acta	PROPN
ap-3411	106	25	polytechnica	polytechnica	PROPN
ap-3411	106	26	some	some	DET
ap-3411	106	27	simple	simple	ADJ
ap-3411	106	28	classes	class	NOUN
ap-3411	106	29	are	be	AUX
ap-3411	106	30	worked	work	VERB
ap-3411	106	31	out	out	ADP
ap-3411	106	32	in	in	ADP
ap-3411	106	33	the	the	DET
ap-3411	106	34	references	reference	NOUN
ap-3411	106	35	mentioned	mention	VERB
ap-3411	106	36	above	above	ADV
ap-3411	106	37	.	.	PUNCT
ap-3411	107	1	darboux	darboux	VERB
ap-3411	107	2	integrable	integrable	ADJ
ap-3411	107	3	equations	equation	NOUN
ap-3411	107	4	turn	turn	VERB
ap-3411	107	5	out	out	ADP
ap-3411	107	6	to	to	PART
ap-3411	107	7	be	be	AUX
ap-3411	107	8	linearizable	linearizable	ADJ
ap-3411	107	9	but	but	CCONJ
ap-3411	107	10	the	the	DET
ap-3411	107	11	other	other	ADJ
ap-3411	107	12	way	way	NOUN
ap-3411	107	13	around	around	ADV
ap-3411	107	14	may	may	AUX
ap-3411	107	15	not	not	PART
ap-3411	107	16	be	be	AUX
ap-3411	107	17	true	true	ADJ
ap-3411	107	18	.	.	PUNCT
ap-3411	108	1	here	here	ADV
ap-3411	108	2	in	in	ADP
ap-3411	108	3	the	the	DET
ap-3411	108	4	following	following	NOUN
ap-3411	108	5	we	we	PRON
ap-3411	108	6	presents	present	VERB
ap-3411	108	7	three	three	NUM
ap-3411	108	8	linearizable	linearizable	ADJ
ap-3411	108	9	p∆e	p∆e	NOUN
ap-3411	108	10	’s	’s	PART
ap-3411	108	11	[	[	X
ap-3411	108	12	13	13	NUM
ap-3411	108	13	,	,	PUNCT
ap-3411	108	14	14	14	NUM
ap-3411	108	15	]	]	PUNCT
ap-3411	108	16	which	which	PRON
ap-3411	108	17	have	have	VERB
ap-3411	108	18	arbitrary	arbitrary	ADJ
ap-3411	108	19	functions	function	NOUN
ap-3411	108	20	of	of	ADP
ap-3411	108	21	generalized	generalized	ADJ
ap-3411	108	22	symmetries	symmetry	NOUN
ap-3411	108	23	.	.	PUNCT
ap-3411	109	1	then	then	ADV
ap-3411	109	2	,	,	PUNCT
ap-3411	109	3	in	in	ADP
ap-3411	109	4	a	a	DET
ap-3411	109	5	subsection	subsection	NOUN
ap-3411	109	6	,	,	PUNCT
ap-3411	109	7	we	we	PRON
ap-3411	109	8	present	present	VERB
ap-3411	109	9	the	the	DET
ap-3411	109	10	case	case	NOUN
ap-3411	109	11	of	of	ADP
ap-3411	109	12	the	the	DET
ap-3411	109	13	completely	completely	ADV
ap-3411	109	14	discrete	discrete	ADJ
ap-3411	109	15	liouville	liouville	NOUN
ap-3411	109	16	equations	equation	NOUN
ap-3411	109	17	.	.	PUNCT
ap-3411	110	1	the	the	DET
ap-3411	110	2	first	first	ADJ
ap-3411	110	3	two	two	NUM
ap-3411	110	4	equations	equation	NOUN
ap-3411	110	5	are	be	AUX
ap-3411	110	6	quad	quad	NOUN
ap-3411	110	7	graph	graph	NOUN
ap-3411	110	8	equations	equation	NOUN
ap-3411	110	9	which	which	PRON
ap-3411	110	10	do	do	AUX
ap-3411	110	11	not	not	PART
ap-3411	110	12	possess	possess	VERB
ap-3411	110	13	the	the	DET
ap-3411	110	14	tetrahedron	tetrahedron	NOUN
ap-3411	110	15	property	property	NOUN
ap-3411	110	16	.	.	PUNCT
ap-3411	111	1	they	they	PRON
ap-3411	111	2	turn	turn	VERB
ap-3411	111	3	out	out	ADP
ap-3411	111	4	to	to	PART
ap-3411	111	5	be	be	AUX
ap-3411	111	6	linearazable	linearazable	ADJ
ap-3411	111	7	and	and	CCONJ
ap-3411	111	8	have	have	VERB
ap-3411	111	9	generalized	generalized	ADJ
ap-3411	111	10	symmetries	symmetry	NOUN
ap-3411	111	11	of	of	ADP
ap-3411	111	12	any	any	DET
ap-3411	111	13	order	order	NOUN
ap-3411	111	14	[	[	X
ap-3411	111	15	14	14	NUM
ap-3411	111	16	]	]	PUNCT
ap-3411	111	17	.	.	PUNCT
ap-3411	112	1	then	then	ADV
ap-3411	112	2	we	we	PRON
ap-3411	112	3	consider	consider	VERB
ap-3411	112	4	an	an	DET
ap-3411	112	5	equation	equation	NOUN
ap-3411	112	6	of	of	ADP
ap-3411	112	7	the	the	DET
ap-3411	112	8	boll	boll	NOUN
ap-3411	112	9	classification	classification	NOUN
ap-3411	112	10	,	,	PUNCT
ap-3411	112	11	th(ε	th(ε	NOUN
ap-3411	112	12	)	)	PUNCT
ap-3411	112	13	1	1	NUM
ap-3411	112	14	,	,	PUNCT
ap-3411	112	15	which	which	PRON
ap-3411	112	16	is	be	AUX
ap-3411	112	17	non	non	X
ap-3411	112	18	autonomous	autonomous	ADJ
ap-3411	112	19	,	,	PUNCT
ap-3411	112	20	linearizable	linearizable	ADJ
ap-3411	112	21	and	and	CCONJ
ap-3411	112	22	has	have	VERB
ap-3411	112	23	three	three	NUM
ap-3411	112	24	-	-	PUNCT
ap-3411	112	25	point	point	NOUN
ap-3411	112	26	generalized	generalize	VERB
ap-3411	112	27	symmetries	symmetry	NOUN
ap-3411	112	28	[	[	X
ap-3411	112	29	4	4	NUM
ap-3411	112	30	,	,	PUNCT
ap-3411	112	31	13	13	NUM
ap-3411	112	32	]	]	PUNCT
ap-3411	112	33	.	.	PUNCT
ap-3411	113	1	the	the	DET
ap-3411	113	2	three	three	NUM
ap-3411	113	3	equations	equation	NOUN
ap-3411	113	4	are	be	AUX
ap-3411	113	5	:	:	PUNCT
ap-3411	113	6	(	(	PUNCT
ap-3411	113	7	1	1	NUM
ap-3411	113	8	.	.	PUNCT
ap-3411	113	9	)	)	PUNCT
ap-3411	114	1	the	the	DET
ap-3411	114	2	first	first	ADJ
ap-3411	114	3	equation	equation	NOUN
ap-3411	114	4	belongs	belong	VERB
ap-3411	114	5	to	to	ADP
ap-3411	114	6	the	the	DET
ap-3411	114	7	classification	classification	NOUN
ap-3411	114	8	of	of	ADP
ap-3411	114	9	compatible	compatible	ADJ
ap-3411	114	10	equations	equation	NOUN
ap-3411	114	11	around	around	ADP
ap-3411	114	12	the	the	DET
ap-3411	114	13	cube	cube	NOUN
ap-3411	114	14	with	with	ADP
ap-3411	114	15	no	no	DET
ap-3411	114	16	tetrahedron	tetrahedron	NOUN
ap-3411	114	17	property	property	NOUN
ap-3411	114	18	presented	present	VERB
ap-3411	114	19	by	by	ADP
ap-3411	114	20	hietarinta	hietarinta	NOUN
ap-3411	114	21	in	in	ADP
ap-3411	114	22	[	[	X
ap-3411	114	23	14	14	NUM
ap-3411	114	24	]	]	X
ap-3411	114	25	:	:	PUNCT
ap-3411	114	26	vm+1,nvm	vm+1,nvm	NOUN
ap-3411	114	27	,	,	PUNCT
ap-3411	114	28	n+1	n+1	PROPN
ap-3411	114	29	+	+	PROPN
ap-3411	114	30	vm	vm	PROPN
ap-3411	114	31	,	,	PUNCT
ap-3411	114	32	nvm+1,n+1	nvm+1,n+1	NOUN
ap-3411	114	33	=	=	SYM
ap-3411	114	34	0	0	PROPN
ap-3411	114	35	.	.	PUNCT
ap-3411	115	1	(	(	PUNCT
ap-3411	115	2	3.1	3.1	NUM
ap-3411	115	3	)	)	PUNCT
ap-3411	115	4	the	the	DET
ap-3411	115	5	three	three	NUM
ap-3411	115	6	-	-	PUNCT
ap-3411	115	7	point	point	NOUN
ap-3411	115	8	symmetries	symmetry	NOUN
ap-3411	115	9	in	in	ADP
ap-3411	115	10	the	the	DET
ap-3411	115	11	m	m	NOUN
ap-3411	115	12	-	-	NOUN
ap-3411	115	13	direction	direction	NOUN
ap-3411	115	14	of	of	ADP
ap-3411	115	15	(	(	PUNCT
ap-3411	115	16	3.1	3.1	NUM
ap-3411	115	17	)	)	PUNCT
ap-3411	115	18	are	be	AUX
ap-3411	115	19	given	give	VERB
ap-3411	115	20	by	by	ADP
ap-3411	115	21	the	the	DET
ap-3411	115	22	characteristic	characteristic	PROPN
ap-3411	115	23	qm	qm	PROPN
ap-3411	115	24	,	,	PUNCT
ap-3411	115	25	n	n	PROPN
ap-3411	115	26	=	=	SYM
ap-3411	115	27	vm	vm	PROPN
ap-3411	115	28	,	,	PUNCT
ap-3411	115	29	nf	nf	INTJ
ap-3411	115	30	(	(	PUNCT
ap-3411	115	31	(	(	PUNCT
ap-3411	115	32	−1)n	−1)n	PROPN
ap-3411	115	33	vm+1,n	vm+1,n	PROPN
ap-3411	115	34	vm	vm	PROPN
ap-3411	115	35	,	,	PUNCT
ap-3411	115	36	n	n	PRON
ap-3411	115	37	,	,	PUNCT
ap-3411	115	38	(	(	PUNCT
ap-3411	115	39	−1)n	−1)n	PROPN
ap-3411	115	40	vm	vm	PROPN
ap-3411	115	41	,	,	PUNCT
ap-3411	115	42	n	n	PRON
ap-3411	115	43	vm−1,n	vm−1,n	NOUN
ap-3411	115	44	)	)	PUNCT
ap-3411	115	45	.	.	PUNCT
ap-3411	116	1	(	(	PUNCT
ap-3411	116	2	3.2	3.2	NUM
ap-3411	116	3	)	)	PUNCT
ap-3411	116	4	as	as	ADP
ap-3411	116	5	(	(	PUNCT
ap-3411	116	6	3.1	3.1	NUM
ap-3411	116	7	)	)	PUNCT
ap-3411	116	8	is	be	AUX
ap-3411	116	9	symmetric	symmetric	ADJ
ap-3411	116	10	in	in	ADP
ap-3411	116	11	the	the	DET
ap-3411	116	12	exchange	exchange	NOUN
ap-3411	116	13	of	of	ADP
ap-3411	116	14	n	n	PROPN
ap-3411	116	15	and	and	CCONJ
ap-3411	116	16	m	m	VERB
ap-3411	116	17	the	the	DET
ap-3411	116	18	generalized	generalized	ADJ
ap-3411	116	19	symmetry	symmetry	NOUN
ap-3411	116	20	(	(	PUNCT
ap-3411	116	21	3.2	3.2	NUM
ap-3411	116	22	)	)	PUNCT
ap-3411	116	23	is	be	AUX
ap-3411	116	24	valid	valid	ADJ
ap-3411	116	25	also	also	ADV
ap-3411	116	26	in	in	ADP
ap-3411	116	27	the	the	DET
ap-3411	116	28	direction	direction	NOUN
ap-3411	116	29	n	n	CCONJ
ap-3411	116	30	with	with	ADP
ap-3411	116	31	the	the	DET
ap-3411	116	32	role	role	NOUN
ap-3411	116	33	of	of	ADP
ap-3411	116	34	n	n	NUM
ap-3411	116	35	and	and	CCONJ
ap-3411	116	36	m	m	AUX
ap-3411	116	37	interchanged	interchange	VERB
ap-3411	116	38	.	.	PUNCT
ap-3411	117	1	we	we	PRON
ap-3411	117	2	can	can	AUX
ap-3411	117	3	easily	easily	ADV
ap-3411	117	4	find	find	VERB
ap-3411	117	5	two	two	NUM
ap-3411	117	6	conserved	conserved	ADJ
ap-3411	117	7	quantities	quantity	NOUN
ap-3411	117	8	w1	w1	NOUN
ap-3411	117	9	=	=	SYM
ap-3411	117	10	(	(	PUNCT
ap-3411	117	11	−1)n	−1)n	PROPN
ap-3411	117	12	vm+1,n	vm+1,n	PROPN
ap-3411	117	13	vm	vm	PROPN
ap-3411	117	14	,	,	PUNCT
ap-3411	117	15	n	n	PRON
ap-3411	117	16	,	,	PUNCT
ap-3411	117	17	w2	w2	NOUN
ap-3411	117	18	=	=	SYM
ap-3411	117	19	(	(	PUNCT
ap-3411	117	20	−1)m	−1)m	PROPN
ap-3411	117	21	vm	vm	PROPN
ap-3411	117	22	,	,	PUNCT
ap-3411	117	23	n+1	n+1	PROPN
ap-3411	117	24	vm	vm	PROPN
ap-3411	117	25	,	,	PUNCT
ap-3411	117	26	n	n	PROPN
ap-3411	117	27	(	(	PUNCT
ap-3411	117	28	3.3	3.3	NUM
ap-3411	117	29	)	)	PUNCT
ap-3411	117	30	such	such	ADJ
ap-3411	117	31	that	that	SCONJ
ap-3411	117	32	(	(	PUNCT
ap-3411	117	33	t2	t2	NOUN
ap-3411	117	34	−	−	PROPN
ap-3411	117	35	1)w1	1)w1	NUM
ap-3411	117	36	=	=	SYM
ap-3411	117	37	0	0	NUM
ap-3411	117	38	,	,	PUNCT
ap-3411	117	39	t1hm	t1hm	X
ap-3411	117	40	,	,	PUNCT
ap-3411	117	41	n	n	NOUN
ap-3411	117	42	=	=	NOUN
ap-3411	117	43	hm+1,n	hm+1,n	NOUN
ap-3411	117	44	,	,	PUNCT
ap-3411	117	45	(	(	PUNCT
ap-3411	117	46	t1	t1	NOUN
ap-3411	117	47	−	−	PROPN
ap-3411	117	48	1)w2	1)w2	PROPN
ap-3411	117	49	=	=	SYM
ap-3411	117	50	0	0	NUM
ap-3411	117	51	,	,	PUNCT
ap-3411	117	52	t2hm	t2hm	NOUN
ap-3411	117	53	,	,	PUNCT
ap-3411	117	54	n	n	NOUN
ap-3411	117	55	=	=	SYM
ap-3411	117	56	hm	hm	INTJ
ap-3411	117	57	,	,	PUNCT
ap-3411	117	58	n+1	n+1	PROPN
ap-3411	117	59	.	.	PUNCT
ap-3411	117	60	(	(	PUNCT
ap-3411	117	61	3.4	3.4	NUM
ap-3411	117	62	)	)	PUNCT
ap-3411	117	63	then	then	ADV
ap-3411	117	64	(	(	PUNCT
ap-3411	117	65	3.1	3.1	NUM
ap-3411	117	66	)	)	PUNCT
ap-3411	117	67	is	be	AUX
ap-3411	117	68	darboux	darboux	VERB
ap-3411	117	69	integrable	integrable	ADJ
ap-3411	117	70	equation	equation	NOUN
ap-3411	117	71	and	and	CCONJ
ap-3411	117	72	(	(	PUNCT
ap-3411	117	73	3.2	3.2	NUM
ap-3411	117	74	)	)	PUNCT
ap-3411	117	75	is	be	AUX
ap-3411	117	76	just	just	ADV
ap-3411	117	77	the	the	DET
ap-3411	117	78	three	three	NUM
ap-3411	117	79	-	-	PUNCT
ap-3411	117	80	point	point	NOUN
ap-3411	117	81	subcase	subcase	NOUN
ap-3411	117	82	of	of	ADP
ap-3411	117	83	a	a	DET
ap-3411	117	84	general	general	ADJ
ap-3411	117	85	characteristic	characteristic	NOUN
ap-3411	117	86	in	in	ADP
ap-3411	117	87	the	the	DET
ap-3411	117	88	m	m	PROPN
ap-3411	117	89	direction	direction	NOUN
ap-3411	117	90	qm	qm	PROPN
ap-3411	117	91	,	,	PUNCT
ap-3411	117	92	n	n	PROPN
ap-3411	117	93	=	=	SYM
ap-3411	117	94	vm	vm	PROPN
ap-3411	117	95	,	,	PUNCT
ap-3411	117	96	nf	nf	INTJ
ap-3411	117	97	(	(	PUNCT
ap-3411	117	98	(	(	PUNCT
ap-3411	117	99	−1)nt−n1	−1)nt−n1	PROPN
ap-3411	117	100	vm+1,n	vm+1,n	PROPN
ap-3411	117	101	vm	vm	PROPN
ap-3411	117	102	,	,	PUNCT
ap-3411	117	103	n	n	CCONJ
ap-3411	117	104	,	,	PUNCT
ap-3411	117	105	.	.	PUNCT
ap-3411	117	106	.	.	PUNCT
ap-3411	117	107	.	.	PUNCT
ap-3411	118	1	,	,	PUNCT
ap-3411	118	2	(	(	PUNCT
ap-3411	118	3	−1)ntm1	−1)ntm1	NUM
ap-3411	118	4	vm+1,n	vm+1,n	PROPN
ap-3411	118	5	vm	vm	PROPN
ap-3411	118	6	,	,	PUNCT
ap-3411	118	7	n	n	PROPN
ap-3411	118	8	)	)	PUNCT
ap-3411	118	9	,	,	PUNCT
ap-3411	118	10	(	(	PUNCT
ap-3411	118	11	3.5	3.5	NUM
ap-3411	118	12	)	)	PUNCT
ap-3411	118	13	with	with	ADP
ap-3411	118	14	n	n	PRON
ap-3411	118	15	and	and	CCONJ
ap-3411	118	16	m	m	VERB
ap-3411	118	17	two	two	NUM
ap-3411	118	18	positive	positive	ADJ
ap-3411	118	19	arbitrary	arbitrary	ADJ
ap-3411	118	20	integers	integer	NOUN
ap-3411	118	21	such	such	ADJ
ap-3411	118	22	that	that	SCONJ
ap-3411	118	23	the	the	DET
ap-3411	118	24	number	number	NOUN
ap-3411	118	25	of	of	ADP
ap-3411	118	26	points	point	NOUN
ap-3411	118	27	involved	involve	VERB
ap-3411	118	28	in	in	ADP
ap-3411	118	29	the	the	DET
ap-3411	118	30	symmetry	symmetry	NOUN
ap-3411	118	31	is	be	AUX
ap-3411	118	32	given	give	VERB
ap-3411	118	33	by	by	ADP
ap-3411	118	34	n	n	PROPN
ap-3411	118	35	+	+	NOUN
ap-3411	118	36	m	m	PROPN
ap-3411	118	37	+	+	ADJ
ap-3411	118	38	2	2	NUM
ap-3411	118	39	.	.	PUNCT
ap-3411	118	40	a	a	DET
ap-3411	118	41	similar	similar	ADJ
ap-3411	118	42	characteristic	characteristic	NOUN
ap-3411	118	43	exists	exist	VERB
ap-3411	118	44	also	also	ADV
ap-3411	118	45	in	in	ADP
ap-3411	118	46	the	the	DET
ap-3411	118	47	n	n	NUM
ap-3411	118	48	direction	direction	NOUN
ap-3411	118	49	with	with	ADP
ap-3411	118	50	the	the	DET
ap-3411	118	51	role	role	NOUN
ap-3411	118	52	of	of	ADP
ap-3411	118	53	n	n	NUM
ap-3411	118	54	and	and	CCONJ
ap-3411	118	55	m	m	AUX
ap-3411	118	56	interchanged	interchange	VERB
ap-3411	118	57	.	.	PUNCT
ap-3411	119	1	equation	equation	NOUN
ap-3411	119	2	(	(	PUNCT
ap-3411	119	3	3.1	3.1	NUM
ap-3411	119	4	)	)	PUNCT
ap-3411	119	5	is	be	AUX
ap-3411	119	6	linearizable	linearizable	ADJ
ap-3411	119	7	in	in	ADP
ap-3411	119	8	three	three	NUM
ap-3411	119	9	ways	way	NOUN
ap-3411	119	10	:	:	PUNCT
ap-3411	119	11	•	•	NOUN
ap-3411	119	12	by	by	ADP
ap-3411	119	13	the	the	DET
ap-3411	119	14	point	point	NOUN
ap-3411	119	15	transformation	transformation	NOUN
ap-3411	119	16	v0,0	v0,0	NOUN
ap-3411	119	17	.=	.=	PROPN
ap-3411	119	18	ex0,0	ex0,0	NOUN
ap-3411	119	19	,	,	PUNCT
ap-3411	119	20	so	so	SCONJ
ap-3411	119	21	that	that	SCONJ
ap-3411	119	22	x0,0	x0,0	NOUN
ap-3411	119	23	=	=	PRON
ap-3411	119	24	log	log	VERB
ap-3411	119	25	v0,0	v0,0	NOUN
ap-3411	119	26	(	(	PUNCT
ap-3411	119	27	without	without	ADP
ap-3411	119	28	loss	loss	NOUN
ap-3411	119	29	of	of	ADP
ap-3411	119	30	generality	generality	NOUN
ap-3411	119	31	,	,	PUNCT
ap-3411	119	32	log	log	NOUN
ap-3411	119	33	can	can	AUX
ap-3411	119	34	be	be	AUX
ap-3411	119	35	always	always	ADV
ap-3411	119	36	taken	take	VERB
ap-3411	119	37	to	to	PART
ap-3411	119	38	stand	stand	VERB
ap-3411	119	39	for	for	ADP
ap-3411	119	40	the	the	DET
ap-3411	119	41	principal	principal	ADJ
ap-3411	119	42	value	value	NOUN
ap-3411	119	43	of	of	ADP
ap-3411	119	44	the	the	DET
ap-3411	119	45	complex	complex	ADJ
ap-3411	119	46	logarithm	logarithm	NOUN
ap-3411	119	47	)	)	PUNCT
ap-3411	119	48	,	,	PUNCT
ap-3411	119	49	is	be	AUX
ap-3411	119	50	transformed	transform	VERB
ap-3411	119	51	into	into	ADP
ap-3411	119	52	the	the	DET
ap-3411	119	53	linear	linear	ADJ
ap-3411	119	54	equation	equation	NOUN
ap-3411	119	55	x0,0	x0,0	PROPN
ap-3411	120	1	−	−	PROPN
ap-3411	120	2	x1,0	x1,0	PROPN
ap-3411	120	3	−	−	PROPN
ap-3411	120	4	x0,1	x0,1	PROPN
ap-3411	121	1	+	+	NUM
ap-3411	121	2	x1,1	x1,1	PROPN
ap-3411	122	1	=	=	PUNCT
ap-3411	122	2	iπ	iπ	NOUN
ap-3411	122	3	.	.	NOUN
ap-3411	122	4	•	•	NUM
ap-3411	122	5	by	by	ADP
ap-3411	122	6	the	the	DET
ap-3411	122	7	hopf	hopf	ADJ
ap-3411	122	8	–	–	PUNCT
ap-3411	122	9	cole	cole	NOUN
ap-3411	122	10	transformation	transformation	NOUN
ap-3411	122	11	v1,0	v1,0	PROPN
ap-3411	122	12	/	/	SYM
ap-3411	122	13	v0,0	v0,0	NOUN
ap-3411	122	14	.=	.=	PROPN
ap-3411	122	15	w0,0	w0,0	NOUN
ap-3411	122	16	(	(	PUNCT
ap-3411	122	17	v0,0	v0,0	NOUN
ap-3411	122	18	6=	6=	NUM
ap-3411	122	19	0	0	NUM
ap-3411	122	20	)	)	PUNCT
ap-3411	122	21	into	into	ADP
ap-3411	122	22	the	the	DET
ap-3411	122	23	ordinary	ordinary	ADJ
ap-3411	122	24	difference	difference	NOUN
ap-3411	122	25	equation	equation	NOUN
ap-3411	122	26	w0,1	w0,1	PROPN
ap-3411	122	27	+	+	PROPN
ap-3411	122	28	w0,0	w0,0	NOUN
ap-3411	122	29	=	=	SYM
ap-3411	122	30	0	0	NUM
ap-3411	122	31	.	.	NOUN
ap-3411	122	32	•	•	NUM
ap-3411	122	33	by	by	ADP
ap-3411	122	34	the	the	DET
ap-3411	122	35	hopf	hopf	ADJ
ap-3411	122	36	–	–	PUNCT
ap-3411	122	37	cole	cole	NOUN
ap-3411	122	38	transformation	transformation	NOUN
ap-3411	122	39	v0,1	v0,1	NOUN
ap-3411	122	40	/	/	SYM
ap-3411	122	41	v0,0	v0,0	NOUN
ap-3411	122	42	.=	.=	PUNCT
ap-3411	123	1	t0,0	t0,0	NOUN
ap-3411	123	2	(	(	PUNCT
ap-3411	123	3	v0,0	v0,0	NOUN
ap-3411	123	4	6=	6=	NUM
ap-3411	123	5	0	0	NUM
ap-3411	123	6	)	)	PUNCT
ap-3411	123	7	into	into	ADP
ap-3411	123	8	the	the	DET
ap-3411	123	9	ordinary	ordinary	ADJ
ap-3411	123	10	difference	difference	NOUN
ap-3411	123	11	equation	equation	NOUN
ap-3411	123	12	t1,0	t1,0	NOUN
ap-3411	123	13	+	+	NUM
ap-3411	123	14	t0,0	t0,0	NOUN
ap-3411	123	15	=	=	SYM
ap-3411	123	16	0	0	NUM
ap-3411	123	17	.	.	PUNCT
ap-3411	124	1	(	(	PUNCT
ap-3411	124	2	2	2	NUM
ap-3411	124	3	.	.	PUNCT
ap-3411	124	4	)	)	PUNCT
ap-3411	125	1	a	a	DET
ap-3411	125	2	second	second	ADJ
ap-3411	125	3	equation	equation	NOUN
ap-3411	125	4	which	which	PRON
ap-3411	125	5	belongs	belong	VERB
ap-3411	125	6	to	to	ADP
ap-3411	125	7	the	the	DET
ap-3411	125	8	classification	classification	NOUN
ap-3411	125	9	of	of	ADP
ap-3411	125	10	equations	equation	NOUN
ap-3411	125	11	compatible	compatible	ADJ
ap-3411	125	12	around	around	ADP
ap-3411	125	13	the	the	DET
ap-3411	125	14	cube	cube	NOUN
ap-3411	125	15	with	with	ADP
ap-3411	125	16	no	no	DET
ap-3411	125	17	tetrahedron	tetrahedron	NOUN
ap-3411	125	18	property	property	NOUN
ap-3411	125	19	presented	present	VERB
ap-3411	125	20	by	by	ADP
ap-3411	125	21	hietarinta	hietarinta	NOUN
ap-3411	125	22	in	in	ADP
ap-3411	125	23	[	[	X
ap-3411	125	24	14	14	NUM
ap-3411	125	25	]	]	PUNCT
ap-3411	125	26	is	be	AUX
ap-3411	125	27	:	:	PUNCT
ap-3411	125	28	vm	vm	PROPN
ap-3411	125	29	,	,	PUNCT
ap-3411	125	30	n	n	PROPN
ap-3411	125	31	+	+	NUM
ap-3411	125	32	vm+1,n	vm+1,n	PROPN
ap-3411	125	33	+	+	CCONJ
ap-3411	125	34	vm	vm	PROPN
ap-3411	125	35	,	,	PUNCT
ap-3411	125	36	n+1	n+1	PROPN
ap-3411	125	37	+	+	NUM
ap-3411	125	38	vm+1,n+1	vm+1,n+1	NOUN
ap-3411	125	39	+	+	CCONJ
ap-3411	125	40	vm+1,nvm	vm+1,nvm	NOUN
ap-3411	125	41	,	,	PUNCT
ap-3411	125	42	n+1vm+1,n+1	n+1vm+1,n+1	X
ap-3411	125	43	+	+	CCONJ
ap-3411	125	44	vm	vm	PROPN
ap-3411	125	45	,	,	PUNCT
ap-3411	125	46	n	n	CCONJ
ap-3411	125	47	[	[	PUNCT
ap-3411	125	48	vm+1,nvm	vm+1,nvm	NOUN
ap-3411	125	49	,	,	PUNCT
ap-3411	125	50	n+1	n+1	PROPN
ap-3411	125	51	+	+	NUM
ap-3411	125	52	vm+1,nvm+1,n+1	vm+1,nvm+1,n+1	X
ap-3411	125	53	+	+	CCONJ
ap-3411	125	54	vm	vm	PROPN
ap-3411	125	55	,	,	PUNCT
ap-3411	125	56	n+1vm+1,n+1	n+1vm+1,n+1	X
ap-3411	125	57	]	]	PUNCT
ap-3411	125	58	=	=	SYM
ap-3411	125	59	0	0	NUM
ap-3411	125	60	,	,	PUNCT
ap-3411	125	61	(	(	PUNCT
ap-3411	125	62	3.6	3.6	NUM
ap-3411	125	63	)	)	PUNCT
ap-3411	125	64	whose	whose	DET
ap-3411	125	65	three	three	NUM
ap-3411	125	66	-	-	PUNCT
ap-3411	125	67	point	point	NOUN
ap-3411	125	68	symmetries	symmetry	NOUN
ap-3411	125	69	in	in	ADP
ap-3411	125	70	the	the	DET
ap-3411	125	71	m	m	NOUN
ap-3411	125	72	-	-	NOUN
ap-3411	125	73	direction	direction	NOUN
ap-3411	125	74	are	be	AUX
ap-3411	125	75	given	give	VERB
ap-3411	125	76	by	by	ADP
ap-3411	125	77	qm	qm	PROPN
ap-3411	125	78	,	,	PUNCT
ap-3411	125	79	n	n	PROPN
ap-3411	125	80	=	=	SYM
ap-3411	125	81	(	(	PUNCT
ap-3411	125	82	−1)n(1−	−1)n(1−	X
ap-3411	125	83	v2	v2	NOUN
ap-3411	125	84	m	m	NOUN
ap-3411	125	85	,	,	PUNCT
ap-3411	125	86	n)k	n)k	ADV
ap-3411	125	87	(	(	PUNCT
ap-3411	125	88	(	(	PUNCT
ap-3411	125	89	(	(	PUNCT
ap-3411	125	90	1−	1−	NUM
ap-3411	125	91	vm	vm	PROPN
ap-3411	125	92	,	,	PUNCT
ap-3411	125	93	n)(1−	n)(1−	ADJ
ap-3411	125	94	vm−1,n	vm−1,n	NOUN
ap-3411	125	95	)	)	PUNCT
ap-3411	125	96	(	(	PUNCT
ap-3411	125	97	1	1	NUM
ap-3411	125	98	+	+	CCONJ
ap-3411	125	99	vm	vm	PROPN
ap-3411	125	100	,	,	PUNCT
ap-3411	125	101	n)(1	n)(1	X
ap-3411	125	102	+	+	CCONJ
ap-3411	125	103	vm−1,n	vm−1,n	NOUN
ap-3411	125	104	)	)	PUNCT
ap-3411	125	105	)	)	PUNCT
ap-3411	125	106	(	(	PUNCT
ap-3411	125	107	−1)n	−1)n	NOUN
ap-3411	125	108	,	,	PUNCT
ap-3411	125	109	(	(	PUNCT
ap-3411	125	110	(	(	PUNCT
ap-3411	125	111	1−	1−	NUM
ap-3411	125	112	vm	vm	PROPN
ap-3411	125	113	,	,	PUNCT
ap-3411	125	114	n)(1−	n)(1−	ADJ
ap-3411	125	115	vm+1,n	vm+1,n	PROPN
ap-3411	125	116	)	)	PUNCT
ap-3411	125	117	(	(	PUNCT
ap-3411	125	118	1	1	NUM
ap-3411	125	119	+	+	CCONJ
ap-3411	125	120	vm	vm	PROPN
ap-3411	125	121	,	,	PUNCT
ap-3411	125	122	n)(1	n)(1	PROPN
ap-3411	125	123	+	+	NUM
ap-3411	125	124	vm+1,n	vm+1,n	PROPN
ap-3411	125	125	)	)	PUNCT
ap-3411	125	126	)	)	PUNCT
ap-3411	125	127	(	(	PUNCT
ap-3411	125	128	−1)n	−1)n	NOUN
ap-3411	125	129	)	)	PUNCT
ap-3411	125	130	.	.	PUNCT
ap-3411	126	1	(	(	PUNCT
ap-3411	126	2	3.7	3.7	NUM
ap-3411	126	3	)	)	PUNCT
ap-3411	126	4	equation	equation	NOUN
ap-3411	126	5	(	(	PUNCT
ap-3411	126	6	3.6	3.6	NUM
ap-3411	126	7	)	)	PUNCT
ap-3411	126	8	admits	admit	VERB
ap-3411	126	9	a	a	DET
ap-3411	126	10	fourfold	fourfold	ADJ
ap-3411	126	11	discrete	discrete	ADJ
ap-3411	126	12	symmetry	symmetry	NOUN
ap-3411	126	13	given	give	VERB
ap-3411	126	14	by	by	ADP
ap-3411	126	15	v0,0	v0,0	NOUN
ap-3411	126	16	→	→	SYM
ap-3411	126	17	v	v	PROPN
ap-3411	126	18	(	(	PUNCT
ap-3411	126	19	ε	ε	PROPN
ap-3411	126	20	)	)	PUNCT
ap-3411	126	21	0,0	0,0	NOUN
ap-3411	126	22	.=	.=	VERB
ap-3411	127	1	(	(	PUNCT
ap-3411	127	2	1	1	NUM
ap-3411	127	3	+	+	NUM
ap-3411	127	4	ε)v0,0	ε)v0,0	NOUN
ap-3411	127	5	+	+	CCONJ
ap-3411	127	6	1−	1−	NUM
ap-3411	127	7	ε	ε	X
ap-3411	127	8	(	(	PUNCT
ap-3411	127	9	1−	1−	NUM
ap-3411	127	10	ε)v0,0	ε)v0,0	NOUN
ap-3411	127	11	+	+	CCONJ
ap-3411	127	12	1	1	NUM
ap-3411	127	13	+	+	CCONJ
ap-3411	127	14	ε	ε	PROPN
ap-3411	127	15	,	,	PUNCT
ap-3411	127	16	(	(	PUNCT
ap-3411	127	17	3.8	3.8	NUM
ap-3411	127	18	)	)	PUNCT
ap-3411	127	19	196	196	NUM
ap-3411	127	20	vol	vol	NOUN
ap-3411	127	21	.	.	PUNCT
ap-3411	128	1	56	56	NUM
ap-3411	128	2	no	no	NOUN
ap-3411	128	3	.	.	PUNCT
ap-3411	129	1	3/2016	3/2016	NUM
ap-3411	129	2	on	on	ADP
ap-3411	129	3	pde	pde	NOUN
ap-3411	129	4	and	and	CCONJ
ap-3411	129	5	p∆e	p∆e	NOUN
ap-3411	129	6	with	with	ADP
ap-3411	129	7	symmetries	symmetry	NOUN
ap-3411	129	8	depending	depend	VERB
ap-3411	129	9	on	on	ADP
ap-3411	129	10	arbitrary	arbitrary	ADJ
ap-3411	129	11	functions	function	NOUN
ap-3411	129	12	where	where	SCONJ
ap-3411	129	13	ε	ε	PROPN
ap-3411	129	14	is	be	AUX
ap-3411	129	15	one	one	NUM
ap-3411	129	16	of	of	ADP
ap-3411	129	17	the	the	DET
ap-3411	129	18	four	four	NUM
ap-3411	129	19	quartic	quartic	ADJ
ap-3411	129	20	roots	root	NOUN
ap-3411	129	21	of	of	ADP
ap-3411	129	22	unity	unity	NOUN
ap-3411	129	23	,	,	PUNCT
ap-3411	129	24	ε	ε	PROPN
ap-3411	129	25	=	=	PUNCT
ap-3411	129	26	(	(	PUNCT
ap-3411	129	27	±i,±1	±i,±1	NUM
ap-3411	129	28	)	)	PUNCT
ap-3411	129	29	.	.	PUNCT
ap-3411	130	1	equation	equation	NOUN
ap-3411	130	2	(	(	PUNCT
ap-3411	130	3	3.6	3.6	NUM
ap-3411	130	4	)	)	PUNCT
ap-3411	130	5	is	be	AUX
ap-3411	130	6	symmetric	symmetric	ADJ
ap-3411	130	7	in	in	ADP
ap-3411	130	8	the	the	DET
ap-3411	130	9	exchange	exchange	NOUN
ap-3411	130	10	of	of	ADP
ap-3411	130	11	n	n	PROPN
ap-3411	130	12	and	and	CCONJ
ap-3411	130	13	m	m	PROPN
ap-3411	130	14	and	and	CCONJ
ap-3411	130	15	consequently	consequently	ADV
ap-3411	130	16	the	the	DET
ap-3411	130	17	generalized	generalized	ADJ
ap-3411	130	18	symmetry	symmetry	NOUN
ap-3411	130	19	(	(	PUNCT
ap-3411	130	20	3.7	3.7	NUM
ap-3411	130	21	)	)	PUNCT
ap-3411	130	22	is	be	AUX
ap-3411	130	23	valid	valid	ADJ
ap-3411	130	24	also	also	ADV
ap-3411	130	25	in	in	ADP
ap-3411	130	26	the	the	DET
ap-3411	130	27	direction	direction	NOUN
ap-3411	130	28	n	n	ADP
ap-3411	130	29	interchanging	interchange	VERB
ap-3411	130	30	the	the	DET
ap-3411	130	31	role	role	NOUN
ap-3411	130	32	of	of	ADP
ap-3411	130	33	n	n	PROPN
ap-3411	130	34	and	and	CCONJ
ap-3411	130	35	m.	m.	NOUN
ap-3411	130	36	it	it	PRON
ap-3411	130	37	is	be	AUX
ap-3411	130	38	not	not	PART
ap-3411	130	39	contained	contain	VERB
ap-3411	130	40	in	in	ADP
ap-3411	130	41	the	the	DET
ap-3411	130	42	lists	list	NOUN
ap-3411	130	43	of	of	ADP
ap-3411	130	44	darboux	darboux	VERB
ap-3411	130	45	integrable	integrable	ADJ
ap-3411	130	46	discrete	discrete	ADJ
ap-3411	130	47	equations	equation	NOUN
ap-3411	131	1	[	[	X
ap-3411	131	2	9	9	NUM
ap-3411	131	3	]	]	PUNCT
ap-3411	131	4	and	and	CCONJ
ap-3411	131	5	[	[	X
ap-3411	131	6	32	32	NUM
ap-3411	131	7	]	]	PUNCT
ap-3411	131	8	,	,	PUNCT
ap-3411	131	9	however	however	ADV
ap-3411	131	10	we	we	PRON
ap-3411	131	11	can	can	AUX
ap-3411	131	12	prove	prove	VERB
ap-3411	131	13	that	that	SCONJ
ap-3411	131	14	it	it	PRON
ap-3411	131	15	is	be	AUX
ap-3411	131	16	darboux	darboux	VERB
ap-3411	131	17	integrable	integrable	ADJ
ap-3411	131	18	as	as	SCONJ
ap-3411	131	19	it	it	PRON
ap-3411	131	20	admits	admit	VERB
ap-3411	131	21	the	the	DET
ap-3411	131	22	following	follow	VERB
ap-3411	131	23	integrals	integral	NOUN
ap-3411	131	24	which	which	PRON
ap-3411	131	25	satisfy	satisfy	VERB
ap-3411	131	26	(	(	PUNCT
ap-3411	131	27	3.4	3.4	NUM
ap-3411	131	28	):	):	PUNCT
ap-3411	131	29	w1	w1	NOUN
ap-3411	131	30	=	=	SYM
ap-3411	131	31	(	(	PUNCT
ap-3411	131	32	(	(	PUNCT
ap-3411	131	33	1−	1−	NUM
ap-3411	131	34	vm	vm	PROPN
ap-3411	131	35	,	,	PUNCT
ap-3411	131	36	n)(1−	n)(1−	ADJ
ap-3411	131	37	vm+1,n	vm+1,n	PROPN
ap-3411	131	38	)	)	PUNCT
ap-3411	131	39	(	(	PUNCT
ap-3411	131	40	1	1	NUM
ap-3411	131	41	+	+	CCONJ
ap-3411	131	42	vm	vm	PROPN
ap-3411	131	43	,	,	PUNCT
ap-3411	131	44	n)(1	n)(1	PROPN
ap-3411	131	45	+	+	NUM
ap-3411	131	46	vm+1,n	vm+1,n	PROPN
ap-3411	131	47	)	)	PUNCT
ap-3411	131	48	)	)	PUNCT
ap-3411	132	1	(	(	PUNCT
ap-3411	132	2	−1)n	−1)n	NOUN
ap-3411	132	3	,	,	PUNCT
ap-3411	132	4	w2	w2	NOUN
ap-3411	132	5	=	=	SYM
ap-3411	132	6	(	(	PUNCT
ap-3411	132	7	(	(	PUNCT
ap-3411	132	8	1−	1−	NUM
ap-3411	132	9	vm	vm	PROPN
ap-3411	132	10	,	,	PUNCT
ap-3411	132	11	n)(1−	n)(1−	PROPN
ap-3411	132	12	vm	vm	PROPN
ap-3411	132	13	,	,	PUNCT
ap-3411	132	14	n+1	n+1	PROPN
ap-3411	132	15	)	)	PUNCT
ap-3411	132	16	(	(	PUNCT
ap-3411	132	17	1	1	NUM
ap-3411	132	18	+	+	CCONJ
ap-3411	132	19	vm	vm	PROPN
ap-3411	132	20	,	,	PUNCT
ap-3411	132	21	n)(1	n)(1	X
ap-3411	132	22	+	+	CCONJ
ap-3411	132	23	vm	vm	PROPN
ap-3411	132	24	,	,	PUNCT
ap-3411	132	25	n+1	n+1	PROPN
ap-3411	132	26	)	)	PUNCT
ap-3411	132	27	)	)	PUNCT
ap-3411	133	1	(	(	PUNCT
ap-3411	133	2	−1)m	−1)m	PROPN
ap-3411	133	3	.	.	PUNCT
ap-3411	134	1	(	(	PUNCT
ap-3411	134	2	3.9	3.9	NUM
ap-3411	134	3	)	)	PUNCT
ap-3411	134	4	the	the	DET
ap-3411	134	5	symmetry	symmetry	NOUN
ap-3411	134	6	characteristic	characteristic	ADJ
ap-3411	134	7	(	(	PUNCT
ap-3411	134	8	3.7	3.7	NUM
ap-3411	134	9	)	)	PUNCT
ap-3411	134	10	is	be	AUX
ap-3411	134	11	nothing	nothing	PRON
ap-3411	134	12	but	but	SCONJ
ap-3411	134	13	the	the	DET
ap-3411	134	14	reduction	reduction	NOUN
ap-3411	134	15	to	to	ADP
ap-3411	134	16	three	three	NUM
ap-3411	134	17	-	-	PUNCT
ap-3411	134	18	point	point	NOUN
ap-3411	134	19	of	of	ADP
ap-3411	134	20	a	a	DET
ap-3411	134	21	general	general	ADJ
ap-3411	134	22	case	case	NOUN
ap-3411	134	23	depending	depend	VERB
ap-3411	134	24	on	on	ADP
ap-3411	134	25	n	n	DET
ap-3411	134	26	+	+	NOUN
ap-3411	134	27	m	m	VERB
ap-3411	134	28	+	+	ADJ
ap-3411	134	29	2	2	NUM
ap-3411	134	30	points	point	NOUN
ap-3411	134	31	with	with	ADP
ap-3411	134	32	n	n	NOUN
ap-3411	134	33	and	and	CCONJ
ap-3411	134	34	m	m	PRON
ap-3411	134	35	arbitrary	arbitrary	ADJ
ap-3411	134	36	positive	positive	ADJ
ap-3411	134	37	integers	integer	NOUN
ap-3411	134	38	,	,	PUNCT
ap-3411	134	39	qm	qm	PROPN
ap-3411	134	40	,	,	PUNCT
ap-3411	134	41	n	n	PROPN
ap-3411	134	42	=	=	SYM
ap-3411	134	43	(	(	PUNCT
ap-3411	134	44	−1)n(1−	−1)n(1−	X
ap-3411	134	45	v2	v2	NOUN
ap-3411	134	46	m	m	NOUN
ap-3411	134	47	,	,	PUNCT
ap-3411	134	48	n)k	n)k	ADV
ap-3411	134	49	(	(	PUNCT
ap-3411	134	50	t−n1	t−n1	NOUN
ap-3411	134	51	(	(	PUNCT
ap-3411	134	52	(	(	PUNCT
ap-3411	134	53	1−	1−	NUM
ap-3411	134	54	vm	vm	PROPN
ap-3411	134	55	,	,	PUNCT
ap-3411	134	56	n)(1−	n)(1−	ADJ
ap-3411	134	57	vm−1,n	vm−1,n	NOUN
ap-3411	134	58	)	)	PUNCT
ap-3411	134	59	(	(	PUNCT
ap-3411	134	60	1	1	NUM
ap-3411	134	61	+	+	CCONJ
ap-3411	134	62	vm	vm	PROPN
ap-3411	134	63	,	,	PUNCT
ap-3411	134	64	n)(1	n)(1	X
ap-3411	134	65	+	+	CCONJ
ap-3411	134	66	vm−1,n	vm−1,n	NOUN
ap-3411	134	67	)	)	PUNCT
ap-3411	134	68	)	)	PUNCT
ap-3411	134	69	(	(	PUNCT
ap-3411	134	70	−1)n	−1)n	NOUN
ap-3411	134	71	,	,	PUNCT
ap-3411	134	72	.	.	PUNCT
ap-3411	134	73	.	.	PUNCT
ap-3411	134	74	.	.	PUNCT
ap-3411	135	1	,	,	PUNCT
ap-3411	135	2	tm1	tm1	PROPN
ap-3411	135	3	(	(	PUNCT
ap-3411	135	4	(	(	PUNCT
ap-3411	135	5	1−	1−	NUM
ap-3411	135	6	vm	vm	PROPN
ap-3411	135	7	,	,	PUNCT
ap-3411	135	8	n)(1−	n)(1−	ADJ
ap-3411	135	9	vm−1,n	vm−1,n	NOUN
ap-3411	135	10	)	)	PUNCT
ap-3411	135	11	(	(	PUNCT
ap-3411	135	12	1	1	NUM
ap-3411	135	13	+	+	CCONJ
ap-3411	135	14	vm	vm	PROPN
ap-3411	135	15	,	,	PUNCT
ap-3411	135	16	n)(1	n)(1	X
ap-3411	135	17	+	+	CCONJ
ap-3411	135	18	vm−1,n	vm−1,n	NOUN
ap-3411	135	19	)	)	PUNCT
ap-3411	135	20	)	)	PUNCT
ap-3411	135	21	(	(	PUNCT
ap-3411	135	22	−1)n	−1)n	NOUN
ap-3411	135	23	)	)	PUNCT
ap-3411	135	24	.	.	PUNCT
ap-3411	136	1	(	(	PUNCT
ap-3411	136	2	3.10	3.10	NUM
ap-3411	136	3	)	)	PUNCT
ap-3411	136	4	a	a	DET
ap-3411	136	5	similar	similar	ADJ
ap-3411	136	6	characteristic	characteristic	NOUN
ap-3411	136	7	exists	exist	VERB
ap-3411	136	8	also	also	ADV
ap-3411	136	9	in	in	ADP
ap-3411	136	10	the	the	DET
ap-3411	136	11	n	n	NUM
ap-3411	136	12	direction	direction	NOUN
ap-3411	136	13	with	with	ADP
ap-3411	136	14	the	the	DET
ap-3411	136	15	role	role	NOUN
ap-3411	136	16	of	of	ADP
ap-3411	136	17	n	n	NUM
ap-3411	136	18	and	and	CCONJ
ap-3411	136	19	m	m	AUX
ap-3411	136	20	interchanged	interchange	VERB
ap-3411	136	21	.	.	PUNCT
ap-3411	137	1	equation	equation	NOUN
ap-3411	137	2	(	(	PUNCT
ap-3411	137	3	3.6	3.6	NUM
ap-3411	137	4	)	)	PUNCT
ap-3411	137	5	is	be	AUX
ap-3411	137	6	linearizable	linearizable	ADJ
ap-3411	137	7	by	by	ADP
ap-3411	137	8	the	the	DET
ap-3411	137	9	point	point	NOUN
ap-3411	137	10	transformation	transformation	NOUN
ap-3411	137	11	:	:	PUNCT
ap-3411	137	12	vm	vm	PROPN
ap-3411	137	13	,	,	PUNCT
ap-3411	137	14	n	n	PROPN
ap-3411	137	15	.=	.=	NOUN
ap-3411	138	1	1	1	NUM
ap-3411	138	2	+	+	CCONJ
ap-3411	138	3	exm	exm	NOUN
ap-3411	138	4	,	,	PUNCT
ap-3411	138	5	n	n	PROPN
ap-3411	138	6	1−	1−	NUM
ap-3411	138	7	exm	exm	NOUN
ap-3411	138	8	,	,	PUNCT
ap-3411	138	9	n	n	PROPN
ap-3411	138	10	(	(	PUNCT
ap-3411	138	11	3.11	3.11	NUM
ap-3411	138	12	)	)	PUNCT
ap-3411	138	13	into	into	ADP
ap-3411	138	14	the	the	DET
ap-3411	138	15	linear	linear	ADJ
ap-3411	138	16	equation	equation	NOUN
ap-3411	138	17	xm	xm	PROPN
ap-3411	138	18	,	,	PUNCT
ap-3411	138	19	n	n	PROPN
ap-3411	138	20	+	+	CCONJ
ap-3411	138	21	xm+1,n	xm+1,n	NOUN
ap-3411	139	1	+	+	CCONJ
ap-3411	139	2	xm	xm	PROPN
ap-3411	139	3	,	,	PUNCT
ap-3411	139	4	n+1	n+1	PROPN
ap-3411	139	5	+	+	NUM
ap-3411	139	6	xm+1,n+1	xm+1,n+1	PUNCT
ap-3411	139	7	=	=	SYM
ap-3411	139	8	2izπ	2izπ	PROPN
ap-3411	139	9	,	,	PUNCT
ap-3411	139	10	(	(	PUNCT
ap-3411	139	11	3.12	3.12	NUM
ap-3411	139	12	)	)	PUNCT
ap-3411	139	13	where	where	SCONJ
ap-3411	139	14	z	z	NOUN
ap-3411	139	15	=	=	SYM
ap-3411	139	16	−1	−1	NOUN
ap-3411	139	17	,	,	PUNCT
ap-3411	139	18	0	0	NUM
ap-3411	139	19	,	,	PUNCT
ap-3411	139	20	1	1	NUM
ap-3411	139	21	,	,	PUNCT
ap-3411	139	22	2	2	NUM
ap-3411	139	23	.	.	PUNCT
ap-3411	140	1	the	the	DET
ap-3411	140	2	indeterminacy	indeterminacy	NOUN
ap-3411	140	3	of	of	ADP
ap-3411	140	4	the	the	DET
ap-3411	140	5	inhomogeneous	inhomogeneous	ADJ
ap-3411	140	6	term	term	NOUN
ap-3411	140	7	of	of	ADP
ap-3411	140	8	(	(	PUNCT
ap-3411	140	9	3.12	3.12	NUM
ap-3411	140	10	)	)	PUNCT
ap-3411	140	11	takes	take	VERB
ap-3411	140	12	into	into	ADP
ap-3411	140	13	account	account	NOUN
ap-3411	140	14	the	the	DET
ap-3411	140	15	fourfold	fourfold	ADJ
ap-3411	140	16	discrete	discrete	ADJ
ap-3411	140	17	symmetry	symmetry	NOUN
ap-3411	140	18	(	(	PUNCT
ap-3411	140	19	3.8	3.8	NUM
ap-3411	140	20	)	)	PUNCT
ap-3411	140	21	of	of	ADP
ap-3411	140	22	(	(	PUNCT
ap-3411	140	23	3.6	3.6	NUM
ap-3411	140	24	)	)	PUNCT
ap-3411	140	25	.	.	PUNCT
ap-3411	141	1	it	it	PRON
ap-3411	141	2	is	be	AUX
ap-3411	141	3	worth	worth	ADJ
ap-3411	141	4	while	while	SCONJ
ap-3411	141	5	to	to	PART
ap-3411	141	6	notice	notice	VERB
ap-3411	141	7	that	that	SCONJ
ap-3411	141	8	inverting	inverting	NOUN
ap-3411	141	9	(	(	PUNCT
ap-3411	141	10	3.11	3.11	NUM
ap-3411	141	11	)	)	PUNCT
ap-3411	141	12	we	we	PRON
ap-3411	141	13	get	get	VERB
ap-3411	141	14	x0,0	x0,0	NOUN
ap-3411	141	15	=	=	PRON
ap-3411	141	16	log	log	VERB
ap-3411	141	17	v0,0−1	v0,0−1	PROPN
ap-3411	141	18	v0,0	v0,0	NOUN
ap-3411	141	19	+	+	NOUN
ap-3411	141	20	1	1	NUM
ap-3411	141	21	,	,	PUNCT
ap-3411	141	22	where	where	SCONJ
ap-3411	141	23	without	without	ADP
ap-3411	141	24	loss	loss	NOUN
ap-3411	141	25	of	of	ADP
ap-3411	141	26	generality	generality	NOUN
ap-3411	141	27	,	,	PUNCT
ap-3411	141	28	the	the	DET
ap-3411	141	29	function	function	NOUN
ap-3411	141	30	log	log	NOUN
ap-3411	141	31	can	can	AUX
ap-3411	141	32	always	always	ADV
ap-3411	141	33	be	be	AUX
ap-3411	141	34	taken	take	VERB
ap-3411	141	35	as	as	ADP
ap-3411	141	36	the	the	DET
ap-3411	141	37	principal	principal	ADJ
ap-3411	141	38	value	value	NOUN
ap-3411	141	39	of	of	ADP
ap-3411	141	40	the	the	DET
ap-3411	141	41	complex	complex	ADJ
ap-3411	141	42	logarithm	logarithm	NOUN
ap-3411	141	43	[	[	X
ap-3411	141	44	30	30	NUM
ap-3411	141	45	]	]	PUNCT
ap-3411	141	46	.	.	PUNCT
ap-3411	142	1	other	other	ADJ
ap-3411	142	2	two	two	NUM
ap-3411	142	3	linearizations	linearization	NOUN
ap-3411	142	4	,	,	PUNCT
ap-3411	142	5	similar	similar	ADJ
ap-3411	142	6	to	to	ADP
ap-3411	142	7	those	those	PRON
ap-3411	142	8	showed	show	VERB
ap-3411	142	9	for	for	ADP
ap-3411	142	10	(	(	PUNCT
ap-3411	142	11	3.1	3.1	NUM
ap-3411	142	12	)	)	PUNCT
ap-3411	142	13	,	,	PUNCT
ap-3411	142	14	are	be	AUX
ap-3411	142	15	also	also	ADV
ap-3411	142	16	present	present	ADJ
ap-3411	142	17	here	here	ADV
ap-3411	142	18	.	.	PUNCT
ap-3411	143	1	(	(	PUNCT
ap-3411	143	2	3	3	NUM
ap-3411	143	3	.	.	NUM
ap-3411	143	4	)	)	PUNCT
ap-3411	144	1	th	th	X
ap-3411	144	2	(	(	PUNCT
ap-3411	144	3	ε	ε	PROPN
ap-3411	144	4	)	)	PUNCT
ap-3411	144	5	1	1	NUM
ap-3411	144	6	is	be	AUX
ap-3411	144	7	:	:	PUNCT
ap-3411	144	8	(	(	PUNCT
ap-3411	144	9	xm	xm	PROPN
ap-3411	144	10	,	,	PUNCT
ap-3411	144	11	n	n	CCONJ
ap-3411	144	12	−	−	PROPN
ap-3411	144	13	xm+1,n)(xm	xm+1,n)(xm	NOUN
ap-3411	144	14	,	,	PUNCT
ap-3411	144	15	n+1	n+1	PROPN
ap-3411	144	16	−	−	PROPN
ap-3411	144	17	xm+1,n+1)−	xm+1,n+1)−	PROPN
ap-3411	145	1	ε2α2	ε2α2	PROPN
ap-3411	145	2	(	(	PUNCT
ap-3411	145	3	f	f	X
ap-3411	145	4	(	(	PUNCT
ap-3411	145	5	+	+	NOUN
ap-3411	145	6	)	)	PUNCT
ap-3411	145	7	n	n	PRON
ap-3411	145	8	xm	xm	NOUN
ap-3411	145	9	,	,	PUNCT
ap-3411	145	10	n+1xm+1,n+1	n+1xm+1,n+1	X
ap-3411	145	11	+	+	CCONJ
ap-3411	145	12	f	f	X
ap-3411	145	13	(	(	PUNCT
ap-3411	145	14	−	−	NOUN
ap-3411	145	15	)	)	PUNCT
ap-3411	145	16	n	n	NOUN
ap-3411	145	17	xm	xm	NOUN
ap-3411	145	18	,	,	PUNCT
ap-3411	145	19	nxm+1,n	nxm+1,n	X
ap-3411	145	20	)	)	PUNCT
ap-3411	145	21	−	−	ADP
ap-3411	146	1	α2	α2	ADJ
ap-3411	146	2	=	=	SYM
ap-3411	146	3	0	0	NUM
ap-3411	146	4	.	.	PUNCT
ap-3411	147	1	(	(	PUNCT
ap-3411	147	2	3.13	3.13	NUM
ap-3411	147	3	)	)	PUNCT
ap-3411	147	4	where	where	SCONJ
ap-3411	147	5	f	f	PROPN
ap-3411	147	6	(	(	PUNCT
ap-3411	147	7	±	±	PROPN
ap-3411	147	8	)	)	PUNCT
ap-3411	147	9	n	n	NOUN
ap-3411	147	10	=	=	SYM
ap-3411	147	11	1±(−1)n	1±(−1)n	PROPN
ap-3411	147	12	2	2	NUM
ap-3411	147	13	and	and	CCONJ
ap-3411	147	14	ε	ε	PROPN
ap-3411	147	15	and	and	CCONJ
ap-3411	147	16	α2	α2	PROPN
ap-3411	147	17	are	be	AUX
ap-3411	147	18	arbitrary	arbitrary	ADJ
ap-3411	147	19	constants	constant	NOUN
ap-3411	147	20	.	.	PUNCT
ap-3411	148	1	equation	equation	NOUN
ap-3411	148	2	(	(	PUNCT
ap-3411	148	3	3.13	3.13	NUM
ap-3411	148	4	)	)	PUNCT
ap-3411	148	5	is	be	AUX
ap-3411	148	6	darboux	darboux	VERB
ap-3411	148	7	integrable	integrable	ADJ
ap-3411	148	8	,	,	PUNCT
ap-3411	148	9	as	as	SCONJ
ap-3411	148	10	we	we	PRON
ap-3411	148	11	can	can	AUX
ap-3411	148	12	find	find	VERB
ap-3411	148	13	two	two	NUM
ap-3411	148	14	integrals	integral	NOUN
ap-3411	148	15	in	in	ADP
ap-3411	148	16	the	the	DET
ap-3411	148	17	m	m	NOUN
ap-3411	148	18	and	and	CCONJ
ap-3411	148	19	n	n	NUM
ap-3411	148	20	directions	direction	NOUN
ap-3411	148	21	which	which	PRON
ap-3411	148	22	satisfy	satisfy	VERB
ap-3411	148	23	(	(	PUNCT
ap-3411	148	24	3.4	3.4	NUM
ap-3411	148	25	)	)	PUNCT
ap-3411	148	26	.	.	PUNCT
ap-3411	149	1	the	the	DET
ap-3411	149	2	m	m	ADJ
ap-3411	149	3	-	-	ADJ
ap-3411	149	4	integral	integral	ADJ
ap-3411	149	5	being	be	AUX
ap-3411	149	6	given	give	VERB
ap-3411	149	7	by	by	ADP
ap-3411	149	8	w2	w2	NOUN
ap-3411	149	9	.=	.=	PROPN
ap-3411	150	1	a2f	a2f	PROPN
ap-3411	150	2	(	(	PUNCT
ap-3411	150	3	+	+	NOUN
ap-3411	150	4	)	)	PUNCT
ap-3411	150	5	n	n	CCONJ
ap-3411	150	6	s+	s+	NUM
ap-3411	150	7	b2f	b2f	PRON
ap-3411	150	8	(	(	PUNCT
ap-3411	150	9	−	−	NOUN
ap-3411	150	10	)	)	PUNCT
ap-3411	150	11	n	n	PROPN
ap-3411	150	12	(	(	PUNCT
ap-3411	150	13	t2	t2	PROPN
ap-3411	150	14	+	+	CCONJ
ap-3411	150	15	1)u	1)u	NUM
ap-3411	150	16	,	,	PUNCT
ap-3411	150	17	s	s	PART
ap-3411	150	18	.=	.=	NOUN
ap-3411	151	1	xm	xm	PROPN
ap-3411	151	2	,	,	PUNCT
ap-3411	151	3	n+1	n+1	PROPN
ap-3411	151	4	−	−	PROPN
ap-3411	151	5	xm	xm	PROPN
ap-3411	151	6	,	,	PUNCT
ap-3411	151	7	n−1	n−1	PROPN
ap-3411	151	8	1	1	NUM
ap-3411	151	9	+	+	CCONJ
ap-3411	151	10	ε2xm	ε2xm	PROPN
ap-3411	151	11	,	,	PUNCT
ap-3411	151	12	n+1xm	n+1xm	NOUN
ap-3411	151	13	,	,	PUNCT
ap-3411	151	14	n−1	n−1	PROPN
ap-3411	151	15	,	,	PUNCT
ap-3411	151	16	u	u	PROPN
ap-3411	151	17	.=	.=	PROPN
ap-3411	151	18	xm	xm	PROPN
ap-3411	151	19	,	,	PUNCT
ap-3411	151	20	n	n	CCONJ
ap-3411	151	21	−	−	PROPN
ap-3411	151	22	xm	xm	PROPN
ap-3411	151	23	,	,	PUNCT
ap-3411	151	24	n−1	n−1	PROPN
ap-3411	151	25	,	,	PUNCT
ap-3411	151	26	(	(	PUNCT
ap-3411	151	27	3.14	3.14	NUM
ap-3411	151	28	)	)	PUNCT
ap-3411	151	29	where	where	SCONJ
ap-3411	151	30	a2	a2	PROPN
ap-3411	151	31	and	and	CCONJ
ap-3411	151	32	b2	b2	NOUN
ap-3411	151	33	are	be	AUX
ap-3411	151	34	two	two	NUM
ap-3411	151	35	arbitrary	arbitrary	ADJ
ap-3411	151	36	constants	constant	NOUN
ap-3411	151	37	.	.	PUNCT
ap-3411	152	1	the	the	DET
ap-3411	152	2	n	n	NUM
ap-3411	152	3	direction	direction	NOUN
ap-3411	152	4	integral	integral	ADJ
ap-3411	152	5	is	be	AUX
ap-3411	152	6	different	different	ADJ
ap-3411	152	7	,	,	PUNCT
ap-3411	152	8	as	as	ADP
ap-3411	152	9	th(ε	th(ε	NOUN
ap-3411	152	10	)	)	PUNCT
ap-3411	152	11	1	1	NUM
ap-3411	152	12	is	be	AUX
ap-3411	152	13	not	not	PART
ap-3411	152	14	symmetric	symmetric	ADJ
ap-3411	152	15	in	in	ADP
ap-3411	152	16	the	the	DET
ap-3411	152	17	exchange	exchange	NOUN
ap-3411	152	18	of	of	ADP
ap-3411	152	19	n	n	PROPN
ap-3411	152	20	and	and	CCONJ
ap-3411	152	21	m	m	PROPN
ap-3411	152	22	,	,	PUNCT
ap-3411	152	23	and	and	CCONJ
ap-3411	152	24	is	be	AUX
ap-3411	152	25	given	give	VERB
ap-3411	152	26	by	by	ADP
ap-3411	152	27	w1	w1	NOUN
ap-3411	152	28	.=	.=	PROPN
ap-3411	153	1	f	f	X
ap-3411	153	2	(	(	PUNCT
ap-3411	153	3	+	+	NOUN
ap-3411	153	4	)	)	PUNCT
ap-3411	153	5	n	n	PRON
ap-3411	153	6	α2	α2	NOUN
ap-3411	153	7	v	v	ADP
ap-3411	153	8	+	+	CCONJ
ap-3411	153	9	f	f	X
ap-3411	153	10	(	(	PUNCT
ap-3411	153	11	−	−	NOUN
ap-3411	153	12	)	)	PUNCT
ap-3411	153	13	n	n	PRON
ap-3411	153	14	t	t	PROPN
ap-3411	153	15	,	,	PUNCT
ap-3411	153	16	t	t	PROPN
ap-3411	153	17	.=	.=	PROPN
ap-3411	153	18	xm	xm	PROPN
ap-3411	153	19	,	,	PUNCT
ap-3411	153	20	n	n	CCONJ
ap-3411	153	21	−	−	PROPN
ap-3411	153	22	xm−1,n	xm−1,n	PROPN
ap-3411	153	23	1	1	NUM
ap-3411	153	24	+	+	CCONJ
ap-3411	153	25	ε2xm−1,nxm	ε2xm−1,nxm	NOUN
ap-3411	153	26	,	,	PUNCT
ap-3411	153	27	n	n	CCONJ
ap-3411	153	28	,	,	PUNCT
ap-3411	153	29	v	v	X
ap-3411	153	30	.=	.=	PROPN
ap-3411	153	31	xm	xm	PROPN
ap-3411	153	32	,	,	PUNCT
ap-3411	153	33	n	n	CCONJ
ap-3411	153	34	−	−	PROPN
ap-3411	153	35	xm−1,n	xm−1,n	PROPN
ap-3411	153	36	.	.	PUNCT
ap-3411	154	1	(	(	PUNCT
ap-3411	154	2	3.15	3.15	NUM
ap-3411	154	3	)	)	PUNCT
ap-3411	154	4	equations	equation	NOUN
ap-3411	154	5	(	(	PUNCT
ap-3411	154	6	3.14	3.14	NUM
ap-3411	154	7	)	)	PUNCT
ap-3411	154	8	and	and	CCONJ
ap-3411	154	9	(	(	PUNCT
ap-3411	154	10	3.15	3.15	NUM
ap-3411	154	11	)	)	PUNCT
ap-3411	154	12	are	be	AUX
ap-3411	154	13	effectively	effectively	ADV
ap-3411	154	14	four	four	NUM
ap-3411	154	15	integrals	integral	NOUN
ap-3411	154	16	as	as	ADP
ap-3411	154	17	ai	ai	NOUN
ap-3411	154	18	and	and	CCONJ
ap-3411	154	19	bi	bi	ADJ
ap-3411	154	20	,	,	PUNCT
ap-3411	154	21	i	i	NOUN
ap-3411	154	22	=	=	NOUN
ap-3411	154	23	1	1	NUM
ap-3411	154	24	,	,	PUNCT
ap-3411	154	25	2	2	NUM
ap-3411	154	26	are	be	AUX
ap-3411	154	27	independent	independent	ADJ
ap-3411	154	28	constants	constant	NOUN
ap-3411	154	29	.	.	PUNCT
ap-3411	155	1	in	in	ADP
ap-3411	155	2	[	[	X
ap-3411	155	3	12	12	NUM
ap-3411	155	4	]	]	PUNCT
ap-3411	155	5	we	we	PRON
ap-3411	155	6	constructed	construct	VERB
ap-3411	155	7	its	its	PRON
ap-3411	155	8	three	three	NUM
ap-3411	155	9	-	-	PUNCT
ap-3411	155	10	point	point	NOUN
ap-3411	155	11	generalized	generalize	VERB
ap-3411	155	12	symmetries	symmetry	NOUN
ap-3411	155	13	along	along	ADP
ap-3411	155	14	the	the	DET
ap-3411	155	15	direction	direction	NOUN
ap-3411	155	16	m	m	PROPN
ap-3411	155	17	:	:	PUNCT
ap-3411	155	18	qm	qm	PROPN
ap-3411	155	19	,	,	PUNCT
ap-3411	155	20	n	n	PROPN
ap-3411	155	21	=	=	SYM
ap-3411	155	22	f	f	X
ap-3411	155	23	(	(	PUNCT
ap-3411	155	24	+	+	NOUN
ap-3411	155	25	)	)	PUNCT
ap-3411	155	26	n	n	CCONJ
ap-3411	155	27	(	(	PUNCT
ap-3411	155	28	α2(v2	α2(v2	NUM
ap-3411	155	29	+	+	CCONJ
ap-3411	155	30	ε2α2	ε2α2	NOUN
ap-3411	155	31	2	2	X
ap-3411	155	32	)	)	PUNCT
ap-3411	155	33	(	(	PUNCT
ap-3411	155	34	v̄	v̄	NOUN
ap-3411	155	35	−	−	NOUN
ap-3411	155	36	v)(v̄	v)(v̄	NOUN
ap-3411	155	37	+	+	CCONJ
ap-3411	156	1	v)bm	v)bm	PROPN
ap-3411	156	2	(	(	PUNCT
ap-3411	156	3	α2	α2	PROPN
ap-3411	156	4	v̄	v̄	PROPN
ap-3411	156	5	)	)	PUNCT
ap-3411	157	1	−	−	PROPN
ap-3411	157	2	α2(v̄	α2(v̄	NUM
ap-3411	158	1	2	2	NUM
ap-3411	158	2	+	+	CCONJ
ap-3411	158	3	ε2α2	ε2α2	NOUN
ap-3411	158	4	2	2	X
ap-3411	158	5	)	)	PUNCT
ap-3411	158	6	(	(	PUNCT
ap-3411	158	7	v̄	v̄	NOUN
ap-3411	158	8	−	−	NOUN
ap-3411	158	9	v)(v̄	v)(v̄	NOUN
ap-3411	158	10	+	+	CCONJ
ap-3411	158	11	v)bm−1	v)bm−1	PROPN
ap-3411	158	12	(	(	PUNCT
ap-3411	158	13	α2	α2	NOUN
ap-3411	158	14	v	v	NOUN
ap-3411	158	15	)	)	PUNCT
ap-3411	159	1	+	+	CCONJ
ap-3411	159	2	(	(	PUNCT
ap-3411	159	3	xm	xm	PROPN
ap-3411	159	4	,	,	PUNCT
ap-3411	159	5	n	n	PRON
ap-3411	159	6	−	−	PROPN
ap-3411	159	7	(	(	PUNCT
ap-3411	159	8	v̄	v̄	NOUN
ap-3411	159	9	2+ε2α2	2+ε2α2	NUM
ap-3411	159	10	2)v	2)v	NUM
ap-3411	159	11	(	(	PUNCT
ap-3411	159	12	v̄−v)(v̄+v	v̄−v)(v̄+v	PROPN
ap-3411	159	13	)	)	PUNCT
ap-3411	159	14	)	)	PUNCT
ap-3411	160	1	ω	ω	PROPN
ap-3411	161	1	+	+	CCONJ
ap-3411	161	2	γn	γn	NOUN
ap-3411	161	3	)	)	PUNCT
ap-3411	162	1	+	+	CCONJ
ap-3411	162	2	f	f	X
ap-3411	162	3	(	(	PUNCT
ap-3411	162	4	−	−	NOUN
ap-3411	162	5	)	)	PUNCT
ap-3411	162	6	n	n	PROPN
ap-3411	162	7	(	(	PUNCT
ap-3411	162	8	t̄2t2	t̄2t2	NOUN
ap-3411	162	9	(	(	PUNCT
ap-3411	162	10	t̄−	t̄−	NUM
ap-3411	162	11	t)(t̄+	t)(t̄+	NOUN
ap-3411	162	12	t	t	NOUN
ap-3411	162	13	)	)	PUNCT
ap-3411	162	14	(	(	PUNCT
ap-3411	162	15	bm(t̄)−bm−1(t))−	bm(t̄)−bm−1(t))−	ADP
ap-3411	162	16	t̄2	t̄2	NOUN
ap-3411	162	17	t	t	NOUN
ap-3411	162	18	(	(	PUNCT
ap-3411	162	19	t̄−	t̄−	NOUN
ap-3411	162	20	t)(t̄+	t)(t̄+	NOUN
ap-3411	162	21	t	t	PROPN
ap-3411	162	22	)	)	PUNCT
ap-3411	162	23	ω	ω	PROPN
ap-3411	162	24	+	+	CCONJ
ap-3411	162	25	δn	δn	NOUN
ap-3411	162	26	)	)	PUNCT
ap-3411	162	27	(	(	PUNCT
ap-3411	162	28	1	1	NUM
ap-3411	162	29	+	+	CCONJ
ap-3411	162	30	ε2x2	ε2x2	NOUN
ap-3411	162	31	m	m	NOUN
ap-3411	162	32	,	,	PUNCT
ap-3411	162	33	n	n	CCONJ
ap-3411	162	34	)	)	PUNCT
ap-3411	162	35	,	,	PUNCT
ap-3411	162	36	(	(	PUNCT
ap-3411	162	37	3.16	3.16	NUM
ap-3411	162	38	)	)	PUNCT
ap-3411	162	39	where	where	SCONJ
ap-3411	162	40	bm(y	bm(y	PUNCT
ap-3411	162	41	)	)	PUNCT
ap-3411	162	42	,	,	PUNCT
ap-3411	162	43	γn	γn	NOUN
ap-3411	162	44	and	and	CCONJ
ap-3411	162	45	δn	δn	NOUN
ap-3411	162	46	are	be	AUX
ap-3411	162	47	generic	generic	ADJ
ap-3411	162	48	functions	function	NOUN
ap-3411	162	49	of	of	ADP
ap-3411	162	50	their	their	PRON
ap-3411	162	51	arguments	argument	NOUN
ap-3411	162	52	,	,	PUNCT
ap-3411	162	53	ω	ω	PROPN
ap-3411	162	54	is	be	AUX
ap-3411	162	55	an	an	DET
ap-3411	162	56	arbitrary	arbitrary	ADJ
ap-3411	162	57	constant	constant	ADJ
ap-3411	162	58	and	and	CCONJ
ap-3411	162	59	v̄	v̄	NOUN
ap-3411	162	60	=	=	SYM
ap-3411	163	1	t1v	t1v	X
ap-3411	163	2	and	and	CCONJ
ap-3411	163	3	t̄	t̄	PROPN
ap-3411	163	4	=	=	SYM
ap-3411	163	5	t1	t1	PROPN
ap-3411	163	6	t.	t.	PROPN
ap-3411	163	7	let	let	VERB
ap-3411	163	8	us	we	PRON
ap-3411	163	9	note	note	VERB
ap-3411	163	10	that	that	SCONJ
ap-3411	163	11	any	any	DET
ap-3411	163	12	free	free	ADJ
ap-3411	163	13	function	function	NOUN
ap-3411	163	14	and	and	CCONJ
ap-3411	163	15	free	free	ADJ
ap-3411	163	16	parameter	parameter	NOUN
ap-3411	163	17	may	may	AUX
ap-3411	163	18	eventually	eventually	ADV
ap-3411	163	19	depend	depend	VERB
ap-3411	163	20	on	on	ADP
ap-3411	163	21	α2	α2	ADJ
ap-3411	163	22	and	and	CCONJ
ap-3411	163	23	ε	ε	PROPN
ap-3411	163	24	.	.	PUNCT
ap-3411	164	1	it	it	PRON
ap-3411	164	2	is	be	AUX
ap-3411	164	3	possible	possible	ADJ
ap-3411	164	4	to	to	PART
ap-3411	164	5	demonstrate	demonstrate	VERB
ap-3411	164	6	that	that	SCONJ
ap-3411	164	7	,	,	PUNCT
ap-3411	164	8	as	as	ADV
ap-3411	164	9	long	long	ADV
ap-3411	164	10	as	as	ADP
ap-3411	164	11	ε	ε	PROPN
ap-3411	164	12	6=	6=	PROPN
ap-3411	164	13	0	0	NUM
ap-3411	164	14	,	,	PUNCT
ap-3411	164	15	no	no	PRON
ap-3411	164	16	n−independent	n−independent	NOUN
ap-3411	164	17	reduction	reduction	NOUN
ap-3411	164	18	of	of	ADP
ap-3411	164	19	the	the	DET
ap-3411	164	20	above	above	ADJ
ap-3411	164	21	symmetry	symmetry	NOUN
ap-3411	164	22	exists	exist	VERB
ap-3411	164	23	.	.	PUNCT
ap-3411	165	1	if	if	SCONJ
ap-3411	165	2	in	in	ADP
ap-3411	165	3	(	(	PUNCT
ap-3411	165	4	3.16	3.16	NUM
ap-3411	165	5	)	)	PUNCT
ap-3411	165	6	the	the	DET
ap-3411	165	7	functions	function	NOUN
ap-3411	165	8	bm−1	bm−1	NOUN
ap-3411	165	9	appearing	appear	VERB
ap-3411	165	10	in	in	ADP
ap-3411	165	11	it	it	PRON
ap-3411	165	12	will	will	AUX
ap-3411	165	13	depend	depend	VERB
ap-3411	165	14	on	on	ADP
ap-3411	165	15	the	the	DET
ap-3411	165	16	variables	variable	NOUN
ap-3411	165	17	t	t	PROPN
ap-3411	165	18	p1w1	p1w1	X
ap-3411	165	19	,	,	PUNCT
ap-3411	165	20	.	.	PUNCT
ap-3411	165	21	.	.	PUNCT
ap-3411	165	22	.	.	PUNCT
ap-3411	166	1	,	,	PUNCT
ap-3411	166	2	t	t	PROPN
ap-3411	166	3	p+n	p+n	ADJ
ap-3411	166	4	1	1	NUM
ap-3411	166	5	w1	w1	NOUN
ap-3411	166	6	197	197	NUM
ap-3411	166	7	g.	g.	NOUN
ap-3411	166	8	gubbiotti	gubbiotti	PROPN
ap-3411	166	9	,	,	PUNCT
ap-3411	166	10	d.	d.	PROPN
ap-3411	166	11	levi	levi	PROPN
ap-3411	166	12	,	,	PUNCT
ap-3411	166	13	c.	c.	PROPN
ap-3411	166	14	scimiterna	scimiterna	PROPN
ap-3411	166	15	acta	acta	PROPN
ap-3411	166	16	polytechnica	polytechnica	PROPN
ap-3411	166	17	and	and	CCONJ
ap-3411	166	18	consequently	consequently	ADV
ap-3411	166	19	bm	bm	PROPN
ap-3411	166	20	on	on	ADP
ap-3411	166	21	t	t	PROPN
ap-3411	166	22	p+1	p+1	PROPN
ap-3411	166	23	1	1	NUM
ap-3411	166	24	w1	w1	NOUN
ap-3411	166	25	,	,	PUNCT
ap-3411	166	26	.	.	PUNCT
ap-3411	166	27	.	.	PUNCT
ap-3411	166	28	.	.	PUNCT
ap-3411	167	1	,	,	PUNCT
ap-3411	167	2	t	t	X
ap-3411	167	3	p+1+n	p+1+n	DET
ap-3411	167	4	1	1	NUM
ap-3411	167	5	w1	w1	NOUN
ap-3411	167	6	,	,	PUNCT
ap-3411	167	7	one	one	PRON
ap-3411	167	8	obtains	obtain	VERB
ap-3411	167	9	the	the	DET
ap-3411	167	10	generalized	generalized	ADJ
ap-3411	167	11	symmetries	symmetry	NOUN
ap-3411	167	12	for	for	ADP
ap-3411	167	13	(	(	PUNCT
ap-3411	167	14	3.13	3.13	NUM
ap-3411	167	15	)	)	PUNCT
ap-3411	167	16	in	in	ADP
ap-3411	167	17	the	the	DET
ap-3411	167	18	direction	direction	NOUN
ap-3411	167	19	m	m	VERB
ap-3411	167	20	at	at	ADP
ap-3411	167	21	all	all	DET
ap-3411	167	22	order	order	NOUN
ap-3411	167	23	.	.	PUNCT
ap-3411	168	1	the	the	DET
ap-3411	168	2	three	three	NUM
ap-3411	168	3	-	-	PUNCT
ap-3411	168	4	point	point	NOUN
ap-3411	168	5	generalized	generalized	ADJ
ap-3411	168	6	symmetry	symmetry	NOUN
ap-3411	168	7	along	along	ADP
ap-3411	168	8	the	the	DET
ap-3411	168	9	direction	direction	NOUN
ap-3411	168	10	n	n	NOUN
ap-3411	168	11	is	be	AUX
ap-3411	168	12	different	different	ADJ
ap-3411	168	13	as	as	SCONJ
ap-3411	168	14	the	the	DET
ap-3411	168	15	equation	equation	NOUN
ap-3411	168	16	is	be	AUX
ap-3411	168	17	not	not	PART
ap-3411	168	18	symmetric	symmetric	ADJ
ap-3411	168	19	.	.	PUNCT
ap-3411	169	1	it	it	PRON
ap-3411	169	2	is	be	AUX
ap-3411	169	3	:	:	PUNCT
ap-3411	169	4	qm	qm	PROPN
ap-3411	169	5	,	,	PUNCT
ap-3411	169	6	n	n	PROPN
ap-3411	169	7	=	=	SYM
ap-3411	169	8	f	f	X
ap-3411	169	9	(	(	PUNCT
ap-3411	169	10	+	+	NOUN
ap-3411	169	11	)	)	PUNCT
ap-3411	169	12	n	n	CCONJ
ap-3411	169	13	(	(	PUNCT
ap-3411	169	14	bn(s	bn(s	X
ap-3411	169	15	)	)	PUNCT
ap-3411	169	16	+	+	NUM
ap-3411	169	17	κn	κn	NOUN
ap-3411	169	18	)	)	PUNCT
ap-3411	170	1	+	+	CCONJ
ap-3411	170	2	f	f	X
ap-3411	170	3	(	(	PUNCT
ap-3411	170	4	−	−	NOUN
ap-3411	170	5	)	)	PUNCT
ap-3411	170	6	n	n	CCONJ
ap-3411	170	7	(	(	PUNCT
ap-3411	170	8	1	1	NUM
ap-3411	170	9	+	+	CCONJ
ap-3411	170	10	ε2x2	ε2x2	PROPN
ap-3411	170	11	m	m	ADJ
ap-3411	170	12	,	,	PUNCT
ap-3411	170	13	n)(cn(ū+	n)(cn(ū+	NOUN
ap-3411	170	14	u	u	NOUN
ap-3411	170	15	)	)	PUNCT
ap-3411	170	16	+	+	CCONJ
ap-3411	170	17	λn	λn	NOUN
ap-3411	170	18	)	)	PUNCT
ap-3411	170	19	,	,	PUNCT
ap-3411	170	20	(	(	PUNCT
ap-3411	170	21	3.17	3.17	NUM
ap-3411	170	22	)	)	PUNCT
ap-3411	170	23	where	where	SCONJ
ap-3411	170	24	bn(y	bn(y	NUM
ap-3411	170	25	)	)	PUNCT
ap-3411	170	26	and	and	CCONJ
ap-3411	170	27	cn(y	cn(y	NUM
ap-3411	170	28	)	)	PUNCT
ap-3411	170	29	are	be	AUX
ap-3411	170	30	arbitrary	arbitrary	ADJ
ap-3411	170	31	functions	function	NOUN
ap-3411	170	32	of	of	ADP
ap-3411	170	33	their	their	PRON
ap-3411	170	34	argument	argument	NOUN
ap-3411	170	35	and	and	CCONJ
ap-3411	170	36	of	of	ADP
ap-3411	170	37	the	the	DET
ap-3411	170	38	lattice	lattice	PROPN
ap-3411	170	39	variable	variable	PROPN
ap-3411	170	40	n	n	CCONJ
ap-3411	170	41	,	,	PUNCT
ap-3411	170	42	ū	ū	NOUN
ap-3411	170	43	=	=	PUNCT
ap-3411	170	44	t2u	t2u	PROPN
ap-3411	170	45	and	and	CCONJ
ap-3411	170	46	κn	κn	NOUN
ap-3411	170	47	and	and	CCONJ
ap-3411	170	48	λn	λn	PROPN
ap-3411	170	49	are	be	AUX
ap-3411	170	50	arbitrary	arbitrary	ADJ
ap-3411	170	51	functions	function	NOUN
ap-3411	170	52	of	of	ADP
ap-3411	170	53	the	the	DET
ap-3411	170	54	lattice	lattice	PROPN
ap-3411	170	55	variable	variable	PROPN
ap-3411	170	56	n.	n.	NOUN
ap-3411	170	57	due	due	ADP
ap-3411	170	58	to	to	ADP
ap-3411	170	59	the	the	DET
ap-3411	170	60	complexity	complexity	NOUN
ap-3411	170	61	of	of	ADP
ap-3411	170	62	the	the	DET
ap-3411	170	63	three	three	NUM
ap-3411	170	64	-	-	PUNCT
ap-3411	170	65	point	point	NOUN
ap-3411	170	66	generalized	generalized	ADJ
ap-3411	170	67	symmetries	symmetry	NOUN
ap-3411	170	68	we	we	PRON
ap-3411	170	69	are	be	AUX
ap-3411	170	70	not	not	PART
ap-3411	170	71	able	able	ADJ
ap-3411	170	72	,	,	PUNCT
ap-3411	170	73	in	in	ADP
ap-3411	170	74	this	this	DET
ap-3411	170	75	case	case	NOUN
ap-3411	170	76	,	,	PUNCT
ap-3411	170	77	to	to	PART
ap-3411	170	78	evince	evince	VERB
ap-3411	170	79	the	the	DET
ap-3411	170	80	laplace	laplace	NOUN
ap-3411	170	81	operators	operator	NOUN
ap-3411	170	82	and	and	CCONJ
ap-3411	170	83	thus	thus	ADV
ap-3411	170	84	write	write	VERB
ap-3411	170	85	the	the	DET
ap-3411	170	86	generalized	generalized	ADJ
ap-3411	170	87	symmetries	symmetry	NOUN
ap-3411	170	88	depending	depend	VERB
ap-3411	170	89	on	on	ADP
ap-3411	170	90	an	an	DET
ap-3411	170	91	arbitrary	arbitrary	ADJ
ap-3411	170	92	function	function	NOUN
ap-3411	170	93	for	for	ADP
ap-3411	170	94	any	any	DET
ap-3411	170	95	number	number	NOUN
ap-3411	170	96	of	of	ADP
ap-3411	170	97	points	point	NOUN
ap-3411	170	98	.	.	PUNCT
ap-3411	171	1	as	as	ADP
ap-3411	171	2	in	in	ADP
ap-3411	171	3	the	the	DET
ap-3411	171	4	case	case	NOUN
ap-3411	171	5	of	of	ADP
ap-3411	171	6	pde	pde	PROPN
ap-3411	171	7	’s	’	VERB
ap-3411	171	8	presented	present	VERB
ap-3411	171	9	in	in	ADP
ap-3411	171	10	the	the	DET
ap-3411	171	11	previous	previous	ADJ
ap-3411	171	12	section	section	NOUN
ap-3411	171	13	also	also	ADV
ap-3411	171	14	here	here	ADV
ap-3411	171	15	the	the	DET
ap-3411	171	16	generalized	generalized	ADJ
ap-3411	171	17	symmetry	symmetry	NOUN
ap-3411	171	18	depending	depend	VERB
ap-3411	171	19	on	on	ADP
ap-3411	171	20	an	an	DET
ap-3411	171	21	arbitrary	arbitrary	ADJ
ap-3411	171	22	function	function	NOUN
ap-3411	171	23	play	play	VERB
ap-3411	171	24	the	the	DET
ap-3411	171	25	role	role	NOUN
ap-3411	171	26	of	of	ADP
ap-3411	171	27	a	a	DET
ap-3411	171	28	master	master	NOUN
ap-3411	171	29	symmetry	symmetry	NOUN
ap-3411	171	30	.	.	PUNCT
ap-3411	172	1	let	let	VERB
ap-3411	172	2	us	we	PRON
ap-3411	172	3	consider	consider	VERB
ap-3411	172	4	,	,	PUNCT
ap-3411	172	5	as	as	ADP
ap-3411	172	6	an	an	DET
ap-3411	172	7	example	example	NOUN
ap-3411	172	8	,	,	PUNCT
ap-3411	172	9	the	the	DET
ap-3411	172	10	commutation	commutation	NOUN
ap-3411	172	11	of	of	ADP
ap-3411	172	12	two	two	NUM
ap-3411	172	13	generalized	generalized	ADJ
ap-3411	172	14	symmetries	symmetry	NOUN
ap-3411	172	15	of	of	ADP
ap-3411	172	16	(	(	PUNCT
ap-3411	172	17	3.1	3.1	NUM
ap-3411	172	18	)	)	PUNCT
ap-3411	172	19	of	of	ADP
ap-3411	172	20	infinitesimal	infinitesimal	ADJ
ap-3411	172	21	generators	generator	NOUN
ap-3411	172	22	x̂fm	x̂fm	PUNCT
ap-3411	173	1	=	=	PUNCT
ap-3411	173	2	vmfm∂vm	vmfm∂vm	INTJ
ap-3411	173	3	and	and	CCONJ
ap-3411	173	4	x̂gm	x̂gm	PROPN
ap-3411	174	1	=	=	PUNCT
ap-3411	174	2	vmgm∂vm	vmgm∂vm	NOUN
ap-3411	174	3	characterized	characterize	VERB
ap-3411	174	4	by	by	ADP
ap-3411	174	5	the	the	DET
ap-3411	174	6	arbitrary	arbitrary	ADJ
ap-3411	174	7	functions	function	NOUN
ap-3411	174	8	fm	fm	NOUN
ap-3411	174	9	=	=	SYM
ap-3411	174	10	f	f	PROPN
ap-3411	174	11	(	(	PUNCT
ap-3411	174	12	(	(	PUNCT
ap-3411	174	13	−1)n	−1)n	PROPN
ap-3411	174	14	vm+1	vm+1	PROPN
ap-3411	174	15	vm	vm	PROPN
ap-3411	174	16	)	)	PUNCT
ap-3411	174	17	and	and	CCONJ
ap-3411	174	18	gm	gm	PROPN
ap-3411	174	19	=	=	SYM
ap-3411	174	20	g	g	PROPN
ap-3411	174	21	(	(	PUNCT
ap-3411	174	22	(	(	PUNCT
ap-3411	174	23	−1)n	−1)n	PROPN
ap-3411	174	24	vm+1	vm+1	PROPN
ap-3411	174	25	vm	vm	PROPN
ap-3411	174	26	)	)	PUNCT
ap-3411	174	27	corresponding	correspond	VERB
ap-3411	174	28	to	to	ADP
ap-3411	174	29	(	(	PUNCT
ap-3411	174	30	3.5	3.5	NUM
ap-3411	174	31	)	)	PUNCT
ap-3411	174	32	with	with	ADP
ap-3411	174	33	n	n	NOUN
ap-3411	174	34	=	=	SYM
ap-3411	174	35	m	m	NOUN
ap-3411	174	36	=	=	NOUN
ap-3411	174	37	0	0	X
ap-3411	174	38	.	.	PUNCT
ap-3411	175	1	we	we	PRON
ap-3411	175	2	have	have	VERB
ap-3411	175	3	:	:	PUNCT
ap-3411	175	4	[	[	PUNCT
ap-3411	175	5	x̂fm	x̂fm	X
ap-3411	175	6	,	,	PUNCT
ap-3411	175	7	x̂gm	x̂gm	PROPN
ap-3411	175	8	]	]	PUNCT
ap-3411	176	1	=	=	PUNCT
ap-3411	176	2	(	(	PUNCT
ap-3411	176	3	−1)nvm+1hm∂vm	−1)nvm+1hm∂vm	NOUN
ap-3411	176	4	.	.	PUNCT
ap-3411	177	1	(	(	PUNCT
ap-3411	177	2	3.18	3.18	NUM
ap-3411	177	3	)	)	PUNCT
ap-3411	177	4	where	where	SCONJ
ap-3411	177	5	hm	hm	INTJ
ap-3411	178	1	=	=	PUNCT
ap-3411	179	1	[	[	X
ap-3411	179	2	∆fmg′m	∆fmg′m	NOUN
ap-3411	179	3	−∆gmf	−∆gmf	NOUN
ap-3411	179	4	′m	′m	PROPN
ap-3411	179	5	]	]	PUNCT
ap-3411	179	6	.	.	PUNCT
ap-3411	180	1	(	(	PUNCT
ap-3411	180	2	3.19	3.19	NUM
ap-3411	180	3	)	)	PUNCT
ap-3411	180	4	in	in	ADP
ap-3411	180	5	(	(	PUNCT
ap-3411	180	6	3.19	3.19	NUM
ap-3411	180	7	)	)	PUNCT
ap-3411	180	8	,	,	PUNCT
ap-3411	180	9	f	f	PROPN
ap-3411	180	10	′m	′m	PROPN
ap-3411	180	11	means	mean	VERB
ap-3411	180	12	the	the	DET
ap-3411	180	13	derivative	derivative	NOUN
ap-3411	180	14	of	of	ADP
ap-3411	180	15	fm	fm	PROPN
ap-3411	180	16	with	with	ADP
ap-3411	180	17	respect	respect	NOUN
ap-3411	180	18	to	to	ADP
ap-3411	180	19	its	its	PRON
ap-3411	180	20	argument	argument	NOUN
ap-3411	180	21	and	and	CCONJ
ap-3411	180	22	the	the	DET
ap-3411	180	23	operator	operator	NOUN
ap-3411	180	24	∆	∆	PROPN
ap-3411	180	25	is	be	AUX
ap-3411	180	26	such	such	ADJ
ap-3411	180	27	that	that	SCONJ
ap-3411	180	28	∆fm	∆fm	PROPN
ap-3411	180	29	=	=	SYM
ap-3411	181	1	fm+1	fm+1	NUM
ap-3411	181	2	−	−	PROPN
ap-3411	181	3	fm	fm	NOUN
ap-3411	181	4	.	.	PUNCT
ap-3411	182	1	the	the	DET
ap-3411	182	2	function	function	NOUN
ap-3411	182	3	hm	hm	INTJ
ap-3411	182	4	depends	depend	VERB
ap-3411	182	5	on	on	ADP
ap-3411	182	6	more	more	ADJ
ap-3411	182	7	points	point	NOUN
ap-3411	182	8	than	than	ADP
ap-3411	182	9	the	the	DET
ap-3411	182	10	functions	function	NOUN
ap-3411	182	11	fm	fm	PROPN
ap-3411	182	12	and	and	CCONJ
ap-3411	182	13	gm	gm	PROPN
ap-3411	182	14	and	and	CCONJ
ap-3411	182	15	so	so	ADV
ap-3411	182	16	the	the	DET
ap-3411	182	17	generator	generator	NOUN
ap-3411	182	18	x̂fm	x̂fm	PROPN
ap-3411	182	19	plays	play	VERB
ap-3411	182	20	the	the	DET
ap-3411	182	21	role	role	NOUN
ap-3411	182	22	of	of	ADP
ap-3411	182	23	a	a	DET
ap-3411	182	24	master	master	NOUN
ap-3411	182	25	symmetry	symmetry	NOUN
ap-3411	182	26	.	.	PUNCT
ap-3411	183	1	3.1	3.1	NUM
ap-3411	183	2	.	.	PUNCT
ap-3411	184	1	the	the	DET
ap-3411	184	2	discrete	discrete	ADJ
ap-3411	184	3	algebraic	algebraic	ADJ
ap-3411	184	4	liouville	liouville	NOUN
ap-3411	184	5	equations	equation	NOUN
ap-3411	184	6	among	among	ADP
ap-3411	184	7	the	the	DET
ap-3411	184	8	many	many	ADJ
ap-3411	184	9	different	different	ADJ
ap-3411	184	10	completely	completely	ADV
ap-3411	184	11	discrete	discrete	ADJ
ap-3411	184	12	liouville	liouville	NOUN
ap-3411	184	13	equations	equation	NOUN
ap-3411	184	14	which	which	PRON
ap-3411	184	15	go	go	VERB
ap-3411	184	16	in	in	ADP
ap-3411	184	17	the	the	DET
ap-3411	184	18	continuous	continuous	ADJ
ap-3411	184	19	limit	limit	NOUN
ap-3411	184	20	in	in	ADP
ap-3411	184	21	the	the	DET
ap-3411	184	22	algebraic	algebraic	ADJ
ap-3411	184	23	liouville	liouville	NOUN
ap-3411	184	24	equation	equation	NOUN
ap-3411	184	25	vvxy	vvxy	VERB
ap-3411	184	26	−	−	PROPN
ap-3411	184	27	vxvy	vxvy	PROPN
ap-3411	184	28	=	=	SYM
ap-3411	184	29	v3	v3	PROPN
ap-3411	184	30	,	,	PUNCT
ap-3411	184	31	(	(	PUNCT
ap-3411	184	32	3.20	3.20	NUM
ap-3411	184	33	)	)	PUNCT
ap-3411	184	34	obtained	obtain	VERB
ap-3411	184	35	from	from	ADP
ap-3411	184	36	(	(	PUNCT
ap-3411	184	37	1.1	1.1	NUM
ap-3411	184	38	)	)	PUNCT
ap-3411	184	39	by	by	ADP
ap-3411	184	40	setting	set	VERB
ap-3411	184	41	v	v	ADP
ap-3411	184	42	=	=	SYM
ap-3411	184	43	eu	eu	PROPN
ap-3411	184	44	,	,	PUNCT
ap-3411	184	45	let	let	VERB
ap-3411	184	46	’s	’s	NOUN
ap-3411	184	47	mention	mention	VERB
ap-3411	184	48	the	the	DET
ap-3411	184	49	following	follow	VERB
ap-3411	184	50	four	four	NUM
ap-3411	184	51	:	:	PUNCT
ap-3411	184	52	•	•	ADP
ap-3411	184	53	the	the	DET
ap-3411	184	54	tzitzeica	tzitzeica	NOUN
ap-3411	184	55	-	-	PUNCT
ap-3411	184	56	liouville	liouville	NOUN
ap-3411	184	57	equation	equation	NOUN
ap-3411	184	58	,	,	PUNCT
ap-3411	184	59	given	give	VERB
ap-3411	184	60	in	in	ADP
ap-3411	184	61	[	[	X
ap-3411	184	62	1	1	NUM
ap-3411	184	63	]	]	X
ap-3411	184	64	:	:	PUNCT
ap-3411	184	65	hm	hm	INTJ
ap-3411	184	66	,	,	PUNCT
ap-3411	184	67	nhm+1,n+1(hm+1,n	nhm+1,n+1(hm+1,n	PROPN
ap-3411	184	68	−	−	PROPN
ap-3411	184	69	1)(hm	1)(hm	NUM
ap-3411	184	70	,	,	PUNCT
ap-3411	184	71	n+1	n+1	PROPN
ap-3411	184	72	−	−	PROPN
ap-3411	184	73	1)−	1)−	PROPN
ap-3411	184	74	(	(	PUNCT
ap-3411	184	75	hm	hm	INTJ
ap-3411	184	76	,	,	PUNCT
ap-3411	184	77	n	n	CCONJ
ap-3411	184	78	−	−	PROPN
ap-3411	184	79	1)(hm+1,n+1	1)(hm+1,n+1	NOUN
ap-3411	184	80	−	−	PROPN
ap-3411	184	81	1	1	NUM
ap-3411	184	82	)	)	PUNCT
ap-3411	184	83	=	=	SYM
ap-3411	184	84	0	0	NUM
ap-3411	184	85	;	;	PUNCT
ap-3411	184	86	•	•	ADP
ap-3411	184	87	the	the	DET
ap-3411	184	88	potential	potential	ADJ
ap-3411	184	89	hirota	hirota	NOUN
ap-3411	184	90	-	-	PUNCT
ap-3411	184	91	liouville	liouville	NOUN
ap-3411	184	92	equation	equation	NOUN
ap-3411	184	93	,	,	PUNCT
ap-3411	184	94	given	give	VERB
ap-3411	184	95	in	in	ADP
ap-3411	184	96	[	[	X
ap-3411	184	97	15	15	NUM
ap-3411	184	98	,	,	PUNCT
ap-3411	184	99	33	33	NUM
ap-3411	184	100	]	]	PUNCT
ap-3411	184	101	:	:	PUNCT
ap-3411	184	102	vm	vm	PROPN
ap-3411	184	103	,	,	PUNCT
ap-3411	184	104	nvm+1,n+1	nvm+1,n+1	PROPN
ap-3411	184	105	−	−	PROPN
ap-3411	184	106	vm+1,nvm	vm+1,nvm	NOUN
ap-3411	184	107	,	,	PUNCT
ap-3411	184	108	n+1	n+1	PROPN
ap-3411	184	109	+	+	NUM
ap-3411	184	110	1	1	NUM
ap-3411	184	111	=	=	SYM
ap-3411	184	112	0	0	NUM
ap-3411	184	113	;	;	PUNCT
ap-3411	184	114	•	•	NUM
ap-3411	184	115	the	the	DET
ap-3411	184	116	hirota	hirota	NOUN
ap-3411	184	117	-	-	PUNCT
ap-3411	184	118	liouville	liouville	NOUN
ap-3411	184	119	equation	equation	NOUN
ap-3411	184	120	,	,	PUNCT
ap-3411	184	121	given	give	VERB
ap-3411	184	122	in	in	ADP
ap-3411	184	123	[	[	X
ap-3411	184	124	16	16	NUM
ap-3411	184	125	,	,	PUNCT
ap-3411	184	126	33	33	NUM
ap-3411	184	127	]	]	PUNCT
ap-3411	184	128	:	:	PUNCT
ap-3411	184	129	um	um	INTJ
ap-3411	184	130	,	,	PUNCT
ap-3411	184	131	num+1,n+1	num+1,n+1	NOUN
ap-3411	184	132	−	−	PROPN
ap-3411	184	133	(	(	PUNCT
ap-3411	184	134	um+1,n	um+1,n	NOUN
ap-3411	184	135	−	−	PROPN
ap-3411	184	136	1)(um	1)(um	NUM
ap-3411	184	137	,	,	PUNCT
ap-3411	184	138	n+1	n+1	PROPN
ap-3411	184	139	−	−	PROPN
ap-3411	184	140	1	1	NUM
ap-3411	184	141	)	)	PUNCT
ap-3411	184	142	=	=	SYM
ap-3411	184	143	0	0	NUM
ap-3411	184	144	;	;	PUNCT
ap-3411	184	145	•	•	ADP
ap-3411	184	146	the	the	DET
ap-3411	184	147	adler	adler	NOUN
ap-3411	184	148	-	-	PUNCT
ap-3411	184	149	startsev	startsev	PROPN
ap-3411	184	150	liouville	liouville	NOUN
ap-3411	184	151	equation	equation	NOUN
ap-3411	184	152	,	,	PUNCT
ap-3411	184	153	given	give	VERB
ap-3411	184	154	in	in	ADP
ap-3411	184	155	[	[	X
ap-3411	184	156	2	2	NUM
ap-3411	184	157	]	]	SYM
ap-3411	184	158	:	:	PUNCT
ap-3411	184	159	tm	tm	PROPN
ap-3411	184	160	,	,	PUNCT
ap-3411	184	161	ntm+1,n+1	ntm+1,n+1	PROPN
ap-3411	184	162	(	(	PUNCT
ap-3411	184	163	1	1	NUM
ap-3411	184	164	+	+	SYM
ap-3411	184	165	1	1	NUM
ap-3411	184	166	tm+1,n	tm+1,n	NOUN
ap-3411	184	167	)	)	PUNCT
ap-3411	184	168	(	(	PUNCT
ap-3411	184	169	1	1	NUM
ap-3411	184	170	+	+	SYM
ap-3411	184	171	1	1	NUM
ap-3411	184	172	tm	tm	NOUN
ap-3411	184	173	,	,	PUNCT
ap-3411	184	174	n+1	n+1	NUM
ap-3411	184	175	)	)	PUNCT
ap-3411	184	176	−	−	PROPN
ap-3411	185	1	1	1	NUM
ap-3411	185	2	=	=	SYM
ap-3411	185	3	0	0	NUM
ap-3411	185	4	.	.	PUNCT
ap-3411	186	1	(	(	PUNCT
ap-3411	186	2	3.21	3.21	NUM
ap-3411	186	3	)	)	PUNCT
ap-3411	186	4	these	these	DET
ap-3411	186	5	p∆e	p∆e	NOUN
ap-3411	186	6	’s	’s	PART
ap-3411	186	7	can	can	AUX
ap-3411	186	8	be	be	AUX
ap-3411	186	9	transformed	transform	VERB
ap-3411	186	10	one	one	NUM
ap-3411	186	11	into	into	ADP
ap-3411	186	12	the	the	DET
ap-3411	186	13	other	other	ADJ
ap-3411	186	14	by	by	ADP
ap-3411	186	15	the	the	DET
ap-3411	186	16	following	follow	VERB
ap-3411	186	17	transformations	transformation	NOUN
ap-3411	186	18	:	:	PUNCT
ap-3411	186	19	um	um	INTJ
ap-3411	186	20	,	,	PUNCT
ap-3411	186	21	n	n	NOUN
ap-3411	186	22	=	=	SYM
ap-3411	186	23	hm	hm	PROPN
ap-3411	186	24	,	,	PUNCT
ap-3411	186	25	n	n	X
ap-3411	186	26	hm	hm	INTJ
ap-3411	186	27	,	,	PUNCT
ap-3411	186	28	n	n	PROPN
ap-3411	186	29	−	−	PROPN
ap-3411	186	30	1	1	NUM
ap-3411	186	31	,	,	PUNCT
ap-3411	186	32	hm	hm	INTJ
ap-3411	186	33	,	,	PUNCT
ap-3411	186	34	n	n	PROPN
ap-3411	186	35	6=	6=	PROPN
ap-3411	186	36	1	1	NUM
ap-3411	186	37	,	,	PUNCT
ap-3411	186	38	um	um	INTJ
ap-3411	186	39	,	,	PUNCT
ap-3411	186	40	n	n	NOUN
ap-3411	186	41	=	=	NOUN
ap-3411	186	42	vm+1,nvm	vm+1,nvm	NOUN
ap-3411	186	43	,	,	PUNCT
ap-3411	186	44	n+1	n+1	PROPN
ap-3411	186	45	,	,	PUNCT
ap-3411	186	46	um	um	INTJ
ap-3411	186	47	,	,	PUNCT
ap-3411	186	48	n	n	NOUN
ap-3411	186	49	=	=	SYM
ap-3411	186	50	−	−	PROPN
ap-3411	186	51	1	1	NUM
ap-3411	186	52	tm	tm	NOUN
ap-3411	186	53	,	,	PUNCT
ap-3411	186	54	n	n	NOUN
ap-3411	186	55	.	.	PUNCT
ap-3411	187	1	(	(	PUNCT
ap-3411	187	2	3.22	3.22	NUM
ap-3411	187	3	)	)	PUNCT
ap-3411	187	4	the	the	DET
ap-3411	187	5	generalized	generalized	ADJ
ap-3411	187	6	symmetries	symmetry	NOUN
ap-3411	187	7	of	of	ADP
ap-3411	187	8	(	(	PUNCT
ap-3411	187	9	3.21	3.21	NUM
ap-3411	187	10	)	)	PUNCT
ap-3411	187	11	along	along	ADP
ap-3411	187	12	the	the	DET
ap-3411	187	13	direction	direction	NOUN
ap-3411	187	14	m	m	VERB
ap-3411	187	15	are	be	AUX
ap-3411	187	16	given	give	VERB
ap-3411	187	17	for	for	ADP
ap-3411	187	18	all	all	PRON
ap-3411	187	19	p	p	NOUN
ap-3411	187	20	∈	∈	PROPN
ap-3411	187	21	z	z	NOUN
ap-3411	187	22	and	and	CCONJ
ap-3411	187	23	n	n	CCONJ
ap-3411	187	24	∈	∈	PROPN
ap-3411	187	25	n0	n0	PROPN
ap-3411	187	26	by	by	ADP
ap-3411	187	27	dtm	dtm	PROPN
ap-3411	187	28	,	,	PUNCT
ap-3411	187	29	n	n	PRON
ap-3411	187	30	dε	dε	VERB
ap-3411	187	31	=	=	SYM
ap-3411	187	32	−(1	−(1	PROPN
ap-3411	187	33	+	+	CCONJ
ap-3411	187	34	tm	tm	PROPN
ap-3411	187	35	,	,	PUNCT
ap-3411	187	36	n)(t1	n)(t1	PROPN
ap-3411	187	37	−	−	PROPN
ap-3411	187	38	1	1	X
ap-3411	187	39	)	)	PUNCT
ap-3411	187	40	(	(	PUNCT
ap-3411	187	41	1	1	NUM
ap-3411	187	42	+	+	CCONJ
ap-3411	187	43	tm	tm	PROPN
ap-3411	187	44	,	,	PUNCT
ap-3411	187	45	n(1	n(1	PROPN
ap-3411	187	46	+	+	CCONJ
ap-3411	187	47	tm−1,n	tm−1,n	NOUN
ap-3411	187	48	)	)	PUNCT
ap-3411	187	49	tm−1,n	tm−1,n	PUNCT
ap-3411	187	50	)	)	PUNCT
ap-3411	187	51	−1	−1	NOUN
ap-3411	187	52	tm	tm	NOUN
ap-3411	187	53	,	,	PUNCT
ap-3411	187	54	nf(t	nf(t	VERB
ap-3411	187	55	p1w1	p1w1	X
ap-3411	187	56	,	,	PUNCT
ap-3411	187	57	.	.	PUNCT
ap-3411	187	58	.	.	PUNCT
ap-3411	187	59	.	.	PUNCT
ap-3411	188	1	,	,	PUNCT
ap-3411	188	2	t	t	PROPN
ap-3411	188	3	p+n	p+n	ADJ
ap-3411	188	4	1	1	NUM
ap-3411	188	5	w1	w1	NOUN
ap-3411	188	6	)	)	PUNCT
ap-3411	188	7	,	,	PUNCT
ap-3411	188	8	(	(	PUNCT
ap-3411	188	9	3.23	3.23	NUM
ap-3411	188	10	)	)	PUNCT
ap-3411	188	11	where	where	SCONJ
ap-3411	188	12	ε	ε	PROPN
ap-3411	188	13	is	be	AUX
ap-3411	188	14	the	the	DET
ap-3411	188	15	group	group	NOUN
ap-3411	188	16	parameter	parameter	NOUN
ap-3411	188	17	,	,	PUNCT
ap-3411	188	18	f(x	f(x	PROPN
ap-3411	188	19	,	,	PUNCT
ap-3411	188	20	y	y	PROPN
ap-3411	188	21	,	,	PUNCT
ap-3411	188	22	.	.	PUNCT
ap-3411	188	23	.	.	PUNCT
ap-3411	189	1	.	.	PUNCT
ap-3411	190	1	,	,	PUNCT
ap-3411	190	2	z	z	X
ap-3411	190	3	)	)	PUNCT
ap-3411	190	4	is	be	AUX
ap-3411	190	5	an	an	DET
ap-3411	190	6	arbitrary	arbitrary	ADJ
ap-3411	190	7	function	function	NOUN
ap-3411	190	8	of	of	ADP
ap-3411	190	9	its	its	PRON
ap-3411	190	10	arguments	argument	NOUN
ap-3411	190	11	and	and	CCONJ
ap-3411	190	12	w1	w1	NOUN
ap-3411	190	13	is	be	AUX
ap-3411	190	14	the	the	DET
ap-3411	190	15	darboux	darboux	VERB
ap-3411	190	16	integral	integral	ADJ
ap-3411	190	17	of	of	ADP
ap-3411	190	18	the	the	DET
ap-3411	190	19	liouville	liouville	NOUN
ap-3411	190	20	equation	equation	NOUN
ap-3411	190	21	(	(	PUNCT
ap-3411	190	22	3.21	3.21	NUM
ap-3411	190	23	)	)	PUNCT
ap-3411	190	24	along	along	ADP
ap-3411	190	25	the	the	DET
ap-3411	190	26	direction	direction	NOUN
ap-3411	190	27	n	n	CCONJ
ap-3411	190	28	,	,	PUNCT
ap-3411	190	29	given	give	VERB
ap-3411	190	30	in	in	ADP
ap-3411	190	31	[	[	X
ap-3411	190	32	2	2	NUM
ap-3411	190	33	]	]	PUNCT
ap-3411	190	34	by	by	ADP
ap-3411	190	35	w1	w1	NOUN
ap-3411	191	1	=	=	SYM
ap-3411	191	2	(	(	PUNCT
ap-3411	191	3	1	1	NUM
ap-3411	191	4	+	+	CCONJ
ap-3411	191	5	tm	tm	PROPN
ap-3411	191	6	,	,	PUNCT
ap-3411	191	7	n(1	n(1	PROPN
ap-3411	191	8	+	+	CCONJ
ap-3411	191	9	tm−1,n	tm−1,n	NOUN
ap-3411	191	10	)	)	PUNCT
ap-3411	191	11	tm−1,n	tm−1,n	NOUN
ap-3411	191	12	)	)	PUNCT
ap-3411	191	13	(	(	PUNCT
ap-3411	191	14	1	1	NUM
ap-3411	191	15	+	+	CCONJ
ap-3411	191	16	tm	tm	NOUN
ap-3411	191	17	,	,	PUNCT
ap-3411	191	18	n	n	NOUN
ap-3411	191	19	tm+1,n(1	tm+1,n(1	NOUN
ap-3411	192	1	+	+	CCONJ
ap-3411	192	2	tm	tm	PROPN
ap-3411	192	3	,	,	PUNCT
ap-3411	192	4	n	n	CCONJ
ap-3411	192	5	)	)	PUNCT
ap-3411	192	6	)	)	PUNCT
ap-3411	192	7	,	,	PUNCT
ap-3411	192	8	198	198	NUM
ap-3411	192	9	vol	vol	NOUN
ap-3411	192	10	.	.	PUNCT
ap-3411	193	1	56	56	NUM
ap-3411	193	2	no	no	NOUN
ap-3411	193	3	.	.	PUNCT
ap-3411	194	1	3/2016	3/2016	NUM
ap-3411	194	2	on	on	ADP
ap-3411	194	3	pde	pde	NOUN
ap-3411	194	4	and	and	CCONJ
ap-3411	194	5	p∆e	p∆e	NOUN
ap-3411	194	6	with	with	ADP
ap-3411	194	7	symmetries	symmetry	NOUN
ap-3411	194	8	depending	depend	VERB
ap-3411	194	9	on	on	ADP
ap-3411	194	10	arbitrary	arbitrary	ADJ
ap-3411	194	11	functions	function	NOUN
ap-3411	194	12	satisfying	satisfy	VERB
ap-3411	194	13	(	(	PUNCT
ap-3411	194	14	3.4	3.4	NUM
ap-3411	194	15	)	)	PUNCT
ap-3411	194	16	.	.	PUNCT
ap-3411	195	1	equation	equation	NOUN
ap-3411	195	2	(	(	PUNCT
ap-3411	195	3	3.23	3.23	NUM
ap-3411	195	4	)	)	PUNCT
ap-3411	195	5	is	be	AUX
ap-3411	195	6	the	the	DET
ap-3411	195	7	equivalent	equivalent	NOUN
ap-3411	195	8	of	of	ADP
ap-3411	195	9	formula	formula	NOUN
ap-3411	195	10	(	(	PUNCT
ap-3411	195	11	1.6	1.6	NUM
ap-3411	195	12	)	)	PUNCT
ap-3411	195	13	introduced	introduce	VERB
ap-3411	195	14	by	by	ADP
ap-3411	195	15	zhiber	zhiber	PROPN
ap-3411	195	16	and	and	CCONJ
ap-3411	195	17	shabat	shabat	PROPN
ap-3411	195	18	for	for	ADP
ap-3411	195	19	the	the	DET
ap-3411	195	20	continuous	continuous	ADJ
ap-3411	195	21	liouville	liouville	NOUN
ap-3411	195	22	equation	equation	NOUN
ap-3411	195	23	.	.	PUNCT
ap-3411	196	1	choosing	choose	VERB
ap-3411	196	2	p	p	NOUN
ap-3411	196	3	=	=	PUNCT
ap-3411	196	4	−1	−1	NOUN
ap-3411	196	5	and	and	CCONJ
ap-3411	196	6	n	n	NOUN
ap-3411	196	7	=	=	SYM
ap-3411	196	8	1	1	NUM
ap-3411	196	9	in	in	ADP
ap-3411	196	10	(	(	PUNCT
ap-3411	196	11	3.23	3.23	NUM
ap-3411	196	12	)	)	PUNCT
ap-3411	196	13	we	we	PRON
ap-3411	196	14	obtain	obtain	VERB
ap-3411	196	15	the	the	DET
ap-3411	196	16	most	most	ADV
ap-3411	196	17	general	general	ADJ
ap-3411	196	18	generalized	generalized	ADJ
ap-3411	196	19	symmetry	symmetry	NOUN
ap-3411	196	20	depending	depend	VERB
ap-3411	196	21	at	at	ADP
ap-3411	196	22	most	most	ADJ
ap-3411	196	23	on	on	ADP
ap-3411	196	24	the	the	DET
ap-3411	196	25	five	five	NUM
ap-3411	196	26	points	point	NOUN
ap-3411	196	27	tm−2,n	tm−2,n	ADP
ap-3411	196	28	,	,	PUNCT
ap-3411	196	29	tm−1,n	tm−1,n	PROPN
ap-3411	196	30	,	,	PUNCT
ap-3411	196	31	tm	tm	NOUN
ap-3411	196	32	,	,	PUNCT
ap-3411	196	33	n	n	CCONJ
ap-3411	196	34	,	,	PUNCT
ap-3411	196	35	tm+1,n	tm+1,n	PROPN
ap-3411	196	36	and	and	CCONJ
ap-3411	196	37	tm+2,n	tm+2,n	PROPN
ap-3411	196	38	dtm	dtm	PROPN
ap-3411	196	39	,	,	PUNCT
ap-3411	196	40	n	n	PRON
ap-3411	196	41	dε	dε	VERB
ap-3411	196	42	=	=	SYM
ap-3411	196	43	−(1	−(1	PROPN
ap-3411	197	1	+	+	CCONJ
ap-3411	197	2	tm	tm	PROPN
ap-3411	197	3	,	,	PUNCT
ap-3411	197	4	n)(t1	n)(t1	PROPN
ap-3411	197	5	−	−	PROPN
ap-3411	197	6	1	1	X
ap-3411	197	7	)	)	PUNCT
ap-3411	197	8	(	(	PUNCT
ap-3411	197	9	1	1	NUM
ap-3411	197	10	+	+	CCONJ
ap-3411	197	11	tm	tm	PROPN
ap-3411	197	12	,	,	PUNCT
ap-3411	197	13	n(1	n(1	PROPN
ap-3411	197	14	+	+	CCONJ
ap-3411	197	15	tm−1,n	tm−1,n	NOUN
ap-3411	197	16	)	)	PUNCT
ap-3411	197	17	tm−1,n	tm−1,n	PUNCT
ap-3411	197	18	)	)	PUNCT
ap-3411	197	19	−1	−1	NOUN
ap-3411	197	20	tm	tm	PROPN
ap-3411	197	21	,	,	PUNCT
ap-3411	197	22	ng(t−1	ng(t−1	PROPN
ap-3411	197	23	1	1	NUM
ap-3411	197	24	w1,w1	w1,w1	PROPN
ap-3411	197	25	)	)	PUNCT
ap-3411	197	26	.	.	PUNCT
ap-3411	198	1	(	(	PUNCT
ap-3411	198	2	3.24	3.24	NUM
ap-3411	198	3	)	)	PUNCT
ap-3411	198	4	if	if	SCONJ
ap-3411	198	5	∂xg(x	∂xg(x	ADV
ap-3411	198	6	,	,	PUNCT
ap-3411	198	7	y	y	NOUN
ap-3411	198	8	)	)	PUNCT
ap-3411	198	9	6=	6=	ADP
ap-3411	198	10	0	0	NUM
ap-3411	198	11	and	and	CCONJ
ap-3411	198	12	∂yg(x	∂yg(x	NOUN
ap-3411	198	13	,	,	PUNCT
ap-3411	198	14	y	y	NOUN
ap-3411	198	15	)	)	PUNCT
ap-3411	198	16	6=	6=	ADP
ap-3411	198	17	0	0	NUM
ap-3411	198	18	,	,	PUNCT
ap-3411	198	19	then	then	ADV
ap-3411	198	20	we	we	PRON
ap-3411	198	21	get	get	VERB
ap-3411	198	22	a	a	DET
ap-3411	198	23	five	five	NUM
ap-3411	198	24	-	-	PUNCT
ap-3411	198	25	point	point	NOUN
ap-3411	198	26	symmetry	symmetry	NOUN
ap-3411	198	27	;	;	PUNCT
ap-3411	198	28	if	if	SCONJ
ap-3411	198	29	∂xg(x	∂xg(x	ADV
ap-3411	198	30	,	,	PUNCT
ap-3411	198	31	y	y	NOUN
ap-3411	198	32	)	)	PUNCT
ap-3411	198	33	=	=	SYM
ap-3411	198	34	0	0	NUM
ap-3411	198	35	and	and	CCONJ
ap-3411	198	36	∂yg(x	∂yg(x	NOUN
ap-3411	198	37	,	,	PUNCT
ap-3411	198	38	y	y	NOUN
ap-3411	198	39	)	)	PUNCT
ap-3411	198	40	6=	6=	ADP
ap-3411	198	41	0	0	NUM
ap-3411	198	42	,	,	PUNCT
ap-3411	198	43	then	then	ADV
ap-3411	198	44	we	we	PRON
ap-3411	198	45	get	get	VERB
ap-3411	198	46	a	a	DET
ap-3411	198	47	four	four	NUM
ap-3411	198	48	-	-	PUNCT
ap-3411	198	49	point	point	NOUN
ap-3411	198	50	symmetry	symmetry	NOUN
ap-3411	198	51	depending	depend	VERB
ap-3411	198	52	on	on	ADP
ap-3411	198	53	the	the	DET
ap-3411	198	54	asymmetric	asymmetric	ADJ
ap-3411	198	55	set	set	NOUN
ap-3411	198	56	tm−1,n	tm−1,n	NOUN
ap-3411	198	57	,	,	PUNCT
ap-3411	198	58	tm	tm	NOUN
ap-3411	198	59	,	,	PUNCT
ap-3411	198	60	n	n	CCONJ
ap-3411	198	61	,	,	PUNCT
ap-3411	198	62	tm+1,n	tm+1,n	PROPN
ap-3411	198	63	and	and	CCONJ
ap-3411	198	64	tm+2,n	tm+2,n	PROPN
ap-3411	198	65	;	;	PUNCT
ap-3411	198	66	if	if	SCONJ
ap-3411	198	67	∂xg(x	∂xg(x	ADV
ap-3411	198	68	,	,	PUNCT
ap-3411	198	69	y	y	NOUN
ap-3411	198	70	)	)	PUNCT
ap-3411	198	71	6=	6=	ADP
ap-3411	198	72	0	0	NUM
ap-3411	198	73	and	and	CCONJ
ap-3411	198	74	∂yg(x	∂yg(x	NOUN
ap-3411	198	75	,	,	PUNCT
ap-3411	198	76	y	y	NOUN
ap-3411	198	77	)	)	PUNCT
ap-3411	198	78	=	=	SYM
ap-3411	198	79	0	0	NUM
ap-3411	198	80	,	,	PUNCT
ap-3411	198	81	then	then	ADV
ap-3411	198	82	we	we	PRON
ap-3411	198	83	get	get	VERB
ap-3411	198	84	a	a	DET
ap-3411	198	85	four	four	NUM
ap-3411	198	86	-	-	PUNCT
ap-3411	198	87	point	point	NOUN
ap-3411	198	88	symmetry	symmetry	NOUN
ap-3411	198	89	depending	depend	VERB
ap-3411	198	90	on	on	ADP
ap-3411	198	91	the	the	DET
ap-3411	198	92	asymmetric	asymmetric	ADJ
ap-3411	198	93	set	set	NOUN
ap-3411	198	94	tm−2,n	tm−2,n	NOUN
ap-3411	198	95	,	,	PUNCT
ap-3411	198	96	tm−1,n	tm−1,n	PROPN
ap-3411	198	97	,	,	PUNCT
ap-3411	198	98	tm	tm	NOUN
ap-3411	198	99	,	,	PUNCT
ap-3411	198	100	n	n	NOUN
ap-3411	198	101	and	and	CCONJ
ap-3411	198	102	tm+1,n	tm+1,n	PROPN
ap-3411	198	103	;	;	PUNCT
ap-3411	198	104	finally	finally	ADV
ap-3411	198	105	if	if	SCONJ
ap-3411	198	106	g	g	NOUN
ap-3411	198	107	=	=	NOUN
ap-3411	198	108	1	1	NUM
ap-3411	198	109	we	we	PRON
ap-3411	198	110	get	get	VERB
ap-3411	198	111	the	the	DET
ap-3411	198	112	three	three	NUM
ap-3411	198	113	-	-	PUNCT
ap-3411	198	114	point	point	NOUN
ap-3411	198	115	symmetry	symmetry	NOUN
ap-3411	198	116	dtm	dtm	PROPN
ap-3411	198	117	,	,	PUNCT
ap-3411	198	118	n	n	PRON
ap-3411	198	119	dε	dε	VERB
ap-3411	198	120	=	=	SYM
ap-3411	198	121	−(1	−(1	PROPN
ap-3411	199	1	+	+	CCONJ
ap-3411	199	2	tm	tm	PROPN
ap-3411	199	3	,	,	PUNCT
ap-3411	199	4	n)(t1	n)(t1	PROPN
ap-3411	199	5	−	−	PROPN
ap-3411	199	6	1	1	X
ap-3411	199	7	)	)	PUNCT
ap-3411	199	8	(	(	PUNCT
ap-3411	199	9	1	1	NUM
ap-3411	199	10	+	+	CCONJ
ap-3411	199	11	tm	tm	PROPN
ap-3411	199	12	,	,	PUNCT
ap-3411	199	13	n(1	n(1	PROPN
ap-3411	199	14	+	+	CCONJ
ap-3411	199	15	tm−1,n	tm−1,n	NOUN
ap-3411	199	16	)	)	PUNCT
ap-3411	199	17	tm−1,n	tm−1,n	PUNCT
ap-3411	199	18	)	)	PUNCT
ap-3411	200	1	−1	−1	NOUN
ap-3411	200	2	tm	tm	PROPN
ap-3411	200	3	,	,	PUNCT
ap-3411	200	4	n	n	CCONJ
ap-3411	200	5	,	,	PUNCT
ap-3411	200	6	(	(	PUNCT
ap-3411	200	7	3.25	3.25	NUM
ap-3411	200	8	)	)	PUNCT
ap-3411	200	9	which	which	PRON
ap-3411	200	10	does	do	AUX
ap-3411	200	11	n’t	not	PART
ap-3411	200	12	depend	depend	VERB
ap-3411	200	13	on	on	ADP
ap-3411	200	14	any	any	DET
ap-3411	200	15	arbitrary	arbitrary	ADJ
ap-3411	200	16	function	function	NOUN
ap-3411	200	17	.	.	PUNCT
ap-3411	201	1	as	as	SCONJ
ap-3411	201	2	it	it	PRON
ap-3411	201	3	is	be	AUX
ap-3411	201	4	evident	evident	ADJ
ap-3411	201	5	from	from	ADP
ap-3411	201	6	(	(	PUNCT
ap-3411	201	7	3.23	3.23	NUM
ap-3411	201	8	)	)	PUNCT
ap-3411	201	9	there	there	PRON
ap-3411	201	10	is	be	VERB
ap-3411	201	11	no	no	DET
ap-3411	201	12	way	way	NOUN
ap-3411	201	13	that	that	PRON
ap-3411	201	14	we	we	PRON
ap-3411	201	15	can	can	AUX
ap-3411	201	16	get	get	VERB
ap-3411	201	17	a	a	DET
ap-3411	201	18	lie	lie	NOUN
ap-3411	201	19	point	point	NOUN
ap-3411	201	20	symmetry	symmetry	NOUN
ap-3411	201	21	in	in	ADP
ap-3411	201	22	agreement	agreement	NOUN
ap-3411	201	23	with	with	ADP
ap-3411	201	24	the	the	DET
ap-3411	201	25	results	result	NOUN
ap-3411	201	26	presented	present	VERB
ap-3411	201	27	in	in	ADP
ap-3411	201	28	[	[	X
ap-3411	201	29	19	19	NUM
ap-3411	201	30	,	,	PUNCT
ap-3411	201	31	20	20	NUM
ap-3411	201	32	]	]	PUNCT
ap-3411	201	33	.	.	PUNCT
ap-3411	202	1	the	the	DET
ap-3411	202	2	lowest	low	ADJ
ap-3411	202	3	possible	possible	ADJ
ap-3411	202	4	symmetry	symmetry	NOUN
ap-3411	202	5	is	be	AUX
ap-3411	202	6	a	a	DET
ap-3411	202	7	generalized	generalized	ADJ
ap-3411	202	8	symmetry	symmetry	NOUN
ap-3411	202	9	depending	depend	VERB
ap-3411	202	10	on	on	ADP
ap-3411	202	11	three	three	NUM
ap-3411	202	12	points	point	NOUN
ap-3411	202	13	(	(	PUNCT
ap-3411	202	14	3.25	3.25	NUM
ap-3411	202	15	)	)	PUNCT
ap-3411	202	16	.	.	PUNCT
ap-3411	203	1	equation	equation	NOUN
ap-3411	203	2	(	(	PUNCT
ap-3411	203	3	3.21	3.21	NUM
ap-3411	203	4	)	)	PUNCT
ap-3411	203	5	is	be	AUX
ap-3411	203	6	symmetric	symmetric	ADJ
ap-3411	203	7	in	in	ADP
ap-3411	203	8	the	the	DET
ap-3411	203	9	exchange	exchange	NOUN
ap-3411	203	10	of	of	ADP
ap-3411	203	11	the	the	DET
ap-3411	203	12	m	m	NOUN
ap-3411	203	13	and	and	CCONJ
ap-3411	203	14	n	n	NOUN
ap-3411	203	15	indices	index	NOUN
ap-3411	203	16	.	.	PUNCT
ap-3411	204	1	so	so	ADV
ap-3411	204	2	the	the	DET
ap-3411	204	3	symmetries	symmetry	NOUN
ap-3411	204	4	in	in	ADP
ap-3411	204	5	the	the	DET
ap-3411	204	6	n	n	PRON
ap-3411	204	7	directions	direction	NOUN
ap-3411	204	8	are	be	AUX
ap-3411	204	9	trivially	trivially	ADV
ap-3411	204	10	given	give	VERB
ap-3411	204	11	by	by	ADP
ap-3411	204	12	(	(	PUNCT
ap-3411	204	13	3.23	3.23	NUM
ap-3411	204	14	)	)	PUNCT
ap-3411	204	15	with	with	ADP
ap-3411	204	16	t1	t1	NOUN
ap-3411	204	17	substituted	substitute	VERB
ap-3411	204	18	by	by	ADP
ap-3411	204	19	t2	t2	PROPN
ap-3411	204	20	and	and	CCONJ
ap-3411	204	21	the	the	DET
ap-3411	204	22	shifts	shift	NOUN
ap-3411	204	23	in	in	ADP
ap-3411	204	24	m	m	AUX
ap-3411	204	25	substituted	substitute	VERB
ap-3411	204	26	by	by	ADP
ap-3411	204	27	shifts	shift	NOUN
ap-3411	204	28	in	in	ADP
ap-3411	204	29	n.	n.	PROPN
ap-3411	204	30	4	4	NUM
ap-3411	204	31	.	.	PUNCT
ap-3411	204	32	conclusive	conclusive	ADJ
ap-3411	204	33	remarks	remark	NOUN
ap-3411	204	34	in	in	ADP
ap-3411	204	35	this	this	DET
ap-3411	204	36	note	note	NOUN
ap-3411	204	37	we	we	PRON
ap-3411	204	38	presented	present	VERB
ap-3411	204	39	a	a	DET
ap-3411	204	40	set	set	NOUN
ap-3411	204	41	of	of	ADP
ap-3411	204	42	results	result	NOUN
ap-3411	204	43	partially	partially	ADV
ap-3411	204	44	distributed	distribute	VERB
ap-3411	204	45	in	in	ADP
ap-3411	204	46	a	a	DET
ap-3411	204	47	series	series	NOUN
ap-3411	204	48	of	of	ADP
ap-3411	204	49	articles	article	NOUN
ap-3411	204	50	of	of	ADP
ap-3411	204	51	different	different	ADJ
ap-3411	204	52	authors	author	NOUN
ap-3411	204	53	concerning	concern	VERB
ap-3411	204	54	the	the	DET
ap-3411	204	55	presence	presence	NOUN
ap-3411	204	56	of	of	ADP
ap-3411	204	57	symmetries	symmetry	NOUN
ap-3411	204	58	depending	depend	VERB
ap-3411	204	59	on	on	ADP
ap-3411	204	60	arbitrary	arbitrary	ADJ
ap-3411	204	61	functions	function	NOUN
ap-3411	204	62	both	both	CCONJ
ap-3411	204	63	in	in	ADP
ap-3411	204	64	the	the	DET
ap-3411	204	65	continuous	continuous	ADJ
ap-3411	204	66	and	and	CCONJ
ap-3411	204	67	in	in	ADP
ap-3411	204	68	the	the	DET
ap-3411	204	69	discrete	discrete	ADJ
ap-3411	204	70	setting	setting	NOUN
ap-3411	204	71	.	.	PUNCT
ap-3411	205	1	few	few	ADJ
ap-3411	205	2	of	of	ADP
ap-3411	205	3	the	the	DET
ap-3411	205	4	words	word	NOUN
ap-3411	205	5	associated	associate	VERB
ap-3411	205	6	to	to	ADP
ap-3411	205	7	these	these	DET
ap-3411	205	8	systems	system	NOUN
ap-3411	205	9	are	be	AUX
ap-3411	205	10	darboux	darboux	VERB
ap-3411	205	11	integrable	integrable	ADJ
ap-3411	205	12	systems	system	NOUN
ap-3411	205	13	,	,	PUNCT
ap-3411	205	14	linearizable	linearizable	ADJ
ap-3411	205	15	systems	system	NOUN
ap-3411	205	16	,	,	PUNCT
ap-3411	205	17	factorizable	factorizable	NOUN
ap-3411	205	18	differential	differential	NOUN
ap-3411	205	19	operators	operator	NOUN
ap-3411	205	20	but	but	CCONJ
ap-3411	205	21	not	not	PART
ap-3411	205	22	all	all	PRON
ap-3411	205	23	necessarily	necessarily	ADV
ap-3411	205	24	proved	prove	VERB
ap-3411	205	25	to	to	PART
ap-3411	205	26	be	be	AUX
ap-3411	205	27	connected	connect	VERB
ap-3411	205	28	to	to	ADP
ap-3411	205	29	the	the	DET
ap-3411	205	30	presence	presence	NOUN
ap-3411	205	31	of	of	ADP
ap-3411	205	32	symmetries	symmetry	NOUN
ap-3411	205	33	depending	depend	VERB
ap-3411	205	34	on	on	ADP
ap-3411	205	35	arbitrary	arbitrary	ADJ
ap-3411	205	36	functions	function	NOUN
ap-3411	205	37	.	.	PUNCT
ap-3411	206	1	darboux	darboux	VERB
ap-3411	206	2	integrable	integrable	ADJ
ap-3411	206	3	systems	system	NOUN
ap-3411	206	4	in	in	ADP
ap-3411	206	5	two	two	NUM
ap-3411	206	6	independent	independent	ADJ
ap-3411	206	7	variables	variable	NOUN
ap-3411	206	8	are	be	AUX
ap-3411	206	9	systems	system	NOUN
ap-3411	206	10	,	,	PUNCT
ap-3411	206	11	studied	study	VERB
ap-3411	206	12	primarily	primarily	ADV
ap-3411	206	13	by	by	ADP
ap-3411	206	14	g.	g.	PROPN
ap-3411	206	15	darboux	darboux	NOUN
ap-3411	206	16	,	,	PUNCT
ap-3411	206	17	characterized	characterize	VERB
ap-3411	206	18	by	by	ADP
ap-3411	206	19	the	the	DET
ap-3411	206	20	presence	presence	NOUN
ap-3411	206	21	of	of	ADP
ap-3411	206	22	at	at	ADV
ap-3411	206	23	least	least	ADJ
ap-3411	206	24	a	a	DET
ap-3411	206	25	couple	couple	NOUN
ap-3411	206	26	of	of	ADP
ap-3411	206	27	conserved	conserved	ADJ
ap-3411	206	28	quantities	quantity	NOUN
ap-3411	206	29	in	in	ADP
ap-3411	206	30	the	the	DET
ap-3411	206	31	two	two	NUM
ap-3411	206	32	independent	independent	ADJ
ap-3411	206	33	variables	variable	NOUN
ap-3411	206	34	.	.	PUNCT
ap-3411	207	1	as	as	ADV
ap-3411	207	2	far	far	ADV
ap-3411	207	3	as	as	SCONJ
ap-3411	207	4	it	it	PRON
ap-3411	207	5	is	be	AUX
ap-3411	207	6	known	know	VERB
ap-3411	207	7	in	in	ADP
ap-3411	207	8	the	the	DET
ap-3411	207	9	literature	literature	NOUN
ap-3411	207	10	darboux	darboux	VERB
ap-3411	207	11	integrable	integrable	ADJ
ap-3411	207	12	systems	system	NOUN
ap-3411	207	13	are	be	AUX
ap-3411	207	14	linearizable	linearizable	ADJ
ap-3411	207	15	and	and	CCONJ
ap-3411	207	16	the	the	DET
ap-3411	207	17	primary	primary	ADJ
ap-3411	207	18	example	example	NOUN
ap-3411	207	19	is	be	AUX
ap-3411	207	20	the	the	DET
ap-3411	207	21	liouville	liouville	NOUN
ap-3411	207	22	equation	equation	NOUN
ap-3411	207	23	(	(	PUNCT
ap-3411	207	24	1.1	1.1	NUM
ap-3411	207	25	)	)	PUNCT
ap-3411	207	26	which	which	PRON
ap-3411	207	27	has	have	AUX
ap-3411	207	28	also	also	ADV
ap-3411	207	29	arbitrary	arbitrary	ADJ
ap-3411	207	30	function	function	NOUN
ap-3411	207	31	dependent	dependent	ADJ
ap-3411	207	32	symmetries	symmetry	NOUN
ap-3411	207	33	,	,	PUNCT
ap-3411	207	34	both	both	PRON
ap-3411	207	35	point	point	VERB
ap-3411	207	36	and	and	CCONJ
ap-3411	207	37	generalized	generalize	VERB
ap-3411	208	1	[	[	PUNCT
ap-3411	208	2	38	38	NUM
ap-3411	208	3	]	]	PUNCT
ap-3411	208	4	.	.	PUNCT
ap-3411	209	1	here	here	ADV
ap-3411	209	2	we	we	PRON
ap-3411	209	3	showed	show	VERB
ap-3411	209	4	that	that	SCONJ
ap-3411	209	5	generically	generically	ADV
ap-3411	209	6	first	first	ADJ
ap-3411	209	7	order	order	NOUN
ap-3411	209	8	pde	pde	NOUN
ap-3411	209	9	’s	’s	PART
ap-3411	209	10	have	have	VERB
ap-3411	209	11	symmetries	symmetry	NOUN
ap-3411	209	12	depending	depend	VERB
ap-3411	209	13	on	on	ADP
ap-3411	209	14	arbitrary	arbitrary	ADJ
ap-3411	209	15	functions	function	NOUN
ap-3411	209	16	as	as	SCONJ
ap-3411	209	17	the	the	DET
ap-3411	209	18	symmetry	symmetry	NOUN
ap-3411	209	19	determining	determine	VERB
ap-3411	209	20	equations	equation	NOUN
ap-3411	209	21	are	be	AUX
ap-3411	209	22	characterized	characterize	VERB
ap-3411	209	23	by	by	ADP
ap-3411	209	24	just	just	ADV
ap-3411	209	25	first	first	ADJ
ap-3411	209	26	order	order	NOUN
ap-3411	209	27	pde	pde	NOUN
ap-3411	209	28	’s	’s	NOUN
ap-3411	209	29	which	which	PRON
ap-3411	209	30	can	can	AUX
ap-3411	209	31	be	be	AUX
ap-3411	209	32	solved	solve	VERB
ap-3411	209	33	on	on	ADP
ap-3411	209	34	the	the	DET
ap-3411	209	35	characteristics	characteristic	NOUN
ap-3411	209	36	in	in	ADP
ap-3411	209	37	term	term	NOUN
ap-3411	209	38	of	of	ADP
ap-3411	209	39	arbitrary	arbitrary	ADJ
ap-3411	209	40	functions	function	NOUN
ap-3411	209	41	of	of	ADP
ap-3411	209	42	the	the	DET
ap-3411	209	43	symmetry	symmetry	NOUN
ap-3411	209	44	variables	variable	NOUN
ap-3411	209	45	.	.	PUNCT
ap-3411	210	1	these	these	DET
ap-3411	210	2	same	same	ADJ
ap-3411	210	3	symmetries	symmetry	NOUN
ap-3411	210	4	can	can	AUX
ap-3411	210	5	be	be	AUX
ap-3411	210	6	found	find	VERB
ap-3411	210	7	in	in	ADP
ap-3411	210	8	pde	pde	NOUN
ap-3411	210	9	’s	’s	ADV
ap-3411	210	10	of	of	ADP
ap-3411	210	11	higher	high	ADJ
ap-3411	210	12	order	order	NOUN
ap-3411	210	13	when	when	SCONJ
ap-3411	210	14	the	the	DET
ap-3411	210	15	differential	differential	ADJ
ap-3411	210	16	operator	operator	NOUN
ap-3411	210	17	is	be	AUX
ap-3411	210	18	factorized	factorize	VERB
ap-3411	210	19	in	in	ADP
ap-3411	210	20	the	the	DET
ap-3411	210	21	product	product	NOUN
ap-3411	210	22	of	of	ADP
ap-3411	210	23	lower	low	ADJ
ap-3411	210	24	order	order	NOUN
ap-3411	210	25	ones	one	NOUN
ap-3411	210	26	which	which	PRON
ap-3411	210	27	,	,	PUNCT
ap-3411	210	28	at	at	ADP
ap-3411	210	29	the	the	DET
ap-3411	210	30	bottom	bottom	NOUN
ap-3411	210	31	,	,	PUNCT
ap-3411	210	32	is	be	AUX
ap-3411	210	33	just	just	ADV
ap-3411	210	34	a	a	DET
ap-3411	210	35	first	first	ADJ
ap-3411	210	36	order	order	NOUN
ap-3411	210	37	one	one	NUM
ap-3411	210	38	.	.	PUNCT
ap-3411	211	1	tsarev	tsarev	VERB
ap-3411	211	2	in	in	ADP
ap-3411	211	3	[	[	X
ap-3411	211	4	34	34	NUM
ap-3411	211	5	]	]	PUNCT
ap-3411	211	6	correlate	correlate	VERB
ap-3411	211	7	darboux	darboux	VERB
ap-3411	211	8	integrable	integrable	ADJ
ap-3411	211	9	systems	system	NOUN
ap-3411	211	10	with	with	ADP
ap-3411	211	11	factorizable	factorizable	PROPN
ap-3411	211	12	differential	differential	PROPN
ap-3411	211	13	operators	operator	NOUN
ap-3411	211	14	.	.	PUNCT
ap-3411	212	1	the	the	DET
ap-3411	212	2	situation	situation	NOUN
ap-3411	212	3	is	be	AUX
ap-3411	212	4	less	less	ADV
ap-3411	212	5	clear	clear	ADJ
ap-3411	212	6	in	in	ADP
ap-3411	212	7	the	the	DET
ap-3411	212	8	discrete	discrete	ADJ
ap-3411	212	9	setting	setting	NOUN
ap-3411	212	10	.	.	PUNCT
ap-3411	213	1	the	the	DET
ap-3411	213	2	classification	classification	NOUN
ap-3411	213	3	of	of	ADP
ap-3411	213	4	darboux	darboux	VERB
ap-3411	213	5	integrable	integrable	ADJ
ap-3411	213	6	systems	system	NOUN
ap-3411	213	7	is	be	AUX
ap-3411	213	8	not	not	PART
ap-3411	213	9	complete	complete	ADJ
ap-3411	213	10	for	for	SCONJ
ap-3411	213	11	p∆e	p∆e	NOUN
ap-3411	213	12	’s	’	VERB
ap-3411	213	13	even	even	ADV
ap-3411	213	14	on	on	ADP
ap-3411	213	15	the	the	DET
ap-3411	213	16	square	square	ADJ
ap-3411	213	17	graph	graph	NOUN
ap-3411	213	18	.	.	PUNCT
ap-3411	214	1	few	few	ADJ
ap-3411	214	2	results	result	NOUN
ap-3411	214	3	[	[	X
ap-3411	214	4	2	2	NUM
ap-3411	214	5	,	,	PUNCT
ap-3411	214	6	35	35	NUM
ap-3411	214	7	]	]	PUNCT
ap-3411	214	8	are	be	AUX
ap-3411	214	9	known	know	VERB
ap-3411	214	10	on	on	ADP
ap-3411	214	11	factorizable	factorizable	ADJ
ap-3411	214	12	difference	difference	NOUN
ap-3411	214	13	operators	operator	NOUN
ap-3411	214	14	in	in	ADP
ap-3411	214	15	the	the	DET
ap-3411	214	16	framework	framework	NOUN
ap-3411	214	17	of	of	ADP
ap-3411	214	18	darboux	darboux	VERB
ap-3411	214	19	integrable	integrable	ADJ
ap-3411	214	20	systems	system	NOUN
ap-3411	214	21	and	and	CCONJ
ap-3411	214	22	symmetries	symmetry	NOUN
ap-3411	214	23	.	.	PUNCT
ap-3411	215	1	nothing	nothing	PRON
ap-3411	215	2	has	have	AUX
ap-3411	215	3	been	be	AUX
ap-3411	215	4	done	do	VERB
ap-3411	215	5	up	up	ADP
ap-3411	215	6	to	to	ADP
ap-3411	215	7	now	now	ADV
ap-3411	215	8	to	to	PART
ap-3411	215	9	characterize	characterize	VERB
ap-3411	215	10	partial	partial	ADJ
ap-3411	215	11	difference	difference	NOUN
ap-3411	215	12	equations	equation	NOUN
ap-3411	215	13	whose	whose	DET
ap-3411	215	14	symmetries	symmetry	NOUN
ap-3411	215	15	are	be	AUX
ap-3411	215	16	written	write	VERB
ap-3411	215	17	in	in	ADP
ap-3411	215	18	term	term	NOUN
ap-3411	215	19	of	of	ADP
ap-3411	215	20	arbitrary	arbitrary	ADJ
ap-3411	215	21	functions	function	NOUN
ap-3411	215	22	of	of	ADP
ap-3411	215	23	symmetry	symmetry	NOUN
ap-3411	215	24	variables	variable	NOUN
ap-3411	215	25	.	.	PUNCT
ap-3411	216	1	moreover	moreover	ADV
ap-3411	216	2	,	,	PUNCT
ap-3411	216	3	let	let	VERB
ap-3411	216	4	us	we	PRON
ap-3411	216	5	notice	notice	VERB
ap-3411	216	6	that	that	SCONJ
ap-3411	216	7	the	the	DET
ap-3411	216	8	generalized	generalized	ADJ
ap-3411	216	9	symmetries	symmetry	NOUN
ap-3411	216	10	we	we	PRON
ap-3411	216	11	obtain	obtain	VERB
ap-3411	216	12	for	for	ADP
ap-3411	216	13	darboux	darboux	VERB
ap-3411	216	14	integrable	integrable	ADJ
ap-3411	216	15	equations	equation	NOUN
ap-3411	216	16	as	as	ADP
ap-3411	216	17	(	(	PUNCT
ap-3411	216	18	3.5	3.5	NUM
ap-3411	216	19	)	)	PUNCT
ap-3411	216	20	,	,	PUNCT
ap-3411	216	21	(	(	PUNCT
ap-3411	216	22	3.10	3.10	NUM
ap-3411	216	23	)	)	PUNCT
ap-3411	216	24	and	and	CCONJ
ap-3411	216	25	(	(	PUNCT
ap-3411	216	26	3.23	3.23	NUM
ap-3411	216	27	)	)	PUNCT
ap-3411	216	28	do	do	AUX
ap-3411	216	29	not	not	PART
ap-3411	216	30	define	define	VERB
ap-3411	216	31	,	,	PUNCT
ap-3411	216	32	in	in	ADP
ap-3411	216	33	general	general	ADJ
ap-3411	216	34	,	,	PUNCT
ap-3411	216	35	s	s	NOUN
ap-3411	216	36	-	-	PUNCT
ap-3411	216	37	integrable	integrable	ADJ
ap-3411	216	38	differential	differential	ADJ
ap-3411	216	39	difference	difference	NOUN
ap-3411	216	40	equations	equation	NOUN
ap-3411	216	41	.	.	PUNCT
ap-3411	217	1	indeed	indeed	ADV
ap-3411	217	2	these	these	DET
ap-3411	217	3	symmetries	symmetry	NOUN
ap-3411	217	4	do	do	AUX
ap-3411	217	5	not	not	PART
ap-3411	217	6	always	always	ADV
ap-3411	217	7	satisfy	satisfy	VERB
ap-3411	217	8	the	the	DET
ap-3411	217	9	necessary	necessary	ADJ
ap-3411	217	10	condition	condition	NOUN
ap-3411	217	11	for	for	ADP
ap-3411	217	12	the	the	DET
ap-3411	217	13	s	s	NOUN
ap-3411	217	14	-	-	NOUN
ap-3411	217	15	integrability	integrability	NOUN
ap-3411	217	16	,	,	PUNCT
ap-3411	217	17	that	that	SCONJ
ap-3411	217	18	the	the	DET
ap-3411	217	19	highest	high	ADJ
ap-3411	217	20	order	order	NOUN
ap-3411	217	21	shift	shift	NOUN
ap-3411	217	22	in	in	ADP
ap-3411	217	23	the	the	DET
ap-3411	217	24	lattice	lattice	NOUN
ap-3411	217	25	variable	variable	NOUN
ap-3411	217	26	is	be	AUX
ap-3411	217	27	the	the	DET
ap-3411	217	28	opposite	opposite	NOUN
ap-3411	217	29	of	of	ADP
ap-3411	217	30	the	the	DET
ap-3411	217	31	lowest	low	ADJ
ap-3411	217	32	one	one	NUM
ap-3411	218	1	[	[	X
ap-3411	218	2	23	23	NUM
ap-3411	218	3	,	,	PUNCT
ap-3411	218	4	36	36	NUM
ap-3411	218	5	]	]	PUNCT
ap-3411	218	6	.	.	PUNCT
ap-3411	219	1	as	as	ADP
ap-3411	219	2	a	a	DET
ap-3411	219	3	result	result	NOUN
ap-3411	219	4	of	of	ADP
ap-3411	219	5	this	this	DET
ap-3411	219	6	note	note	NOUN
ap-3411	219	7	we	we	PRON
ap-3411	219	8	can	can	AUX
ap-3411	219	9	conjecture	conjecture	VERB
ap-3411	219	10	the	the	DET
ap-3411	219	11	following	follow	VERB
ap-3411	219	12	theorem	theorem	NOUN
ap-3411	219	13	:	:	PUNCT
ap-3411	219	14	theorem	theorem	NOUN
ap-3411	219	15	1	1	NUM
ap-3411	219	16	.	.	NOUN
ap-3411	219	17	necessary	necessary	ADJ
ap-3411	219	18	and	and	CCONJ
ap-3411	219	19	sufficient	sufficient	ADJ
ap-3411	219	20	conditions	condition	NOUN
ap-3411	219	21	for	for	ADP
ap-3411	219	22	a	a	DET
ap-3411	219	23	pde	pde	NOUN
ap-3411	219	24	and	and	CCONJ
ap-3411	219	25	a	a	DET
ap-3411	219	26	p∆e	p∆e	NOUN
ap-3411	219	27	to	to	PART
ap-3411	219	28	have	have	VERB
ap-3411	219	29	symmetries	symmetry	NOUN
ap-3411	219	30	,	,	PUNCT
ap-3411	219	31	possibly	possibly	ADV
ap-3411	219	32	point	point	VERB
ap-3411	219	33	but	but	CCONJ
ap-3411	219	34	surely	surely	ADV
ap-3411	219	35	generalized	generalize	VERB
ap-3411	219	36	,	,	PUNCT
ap-3411	219	37	depending	depend	VERB
ap-3411	219	38	on	on	ADP
ap-3411	219	39	arbitrary	arbitrary	ADJ
ap-3411	219	40	functions	function	NOUN
ap-3411	219	41	is	be	AUX
ap-3411	219	42	that	that	SCONJ
ap-3411	219	43	the	the	DET
ap-3411	219	44	system	system	NOUN
ap-3411	219	45	be	be	AUX
ap-3411	219	46	darboux	darboux	VERB
ap-3411	219	47	integrable	integrable	ADJ
ap-3411	219	48	.	.	PUNCT
ap-3411	220	1	some	some	PRON
ap-3411	220	2	of	of	ADP
ap-3411	220	3	the	the	DET
ap-3411	220	4	results	result	NOUN
ap-3411	220	5	presented	present	VERB
ap-3411	220	6	here	here	ADV
ap-3411	220	7	are	be	AUX
ap-3411	220	8	new	new	ADJ
ap-3411	220	9	and	and	CCONJ
ap-3411	220	10	never	never	ADV
ap-3411	220	11	presented	present	VERB
ap-3411	220	12	anywhere	anywhere	ADV
ap-3411	220	13	.	.	PUNCT
ap-3411	221	1	among	among	ADP
ap-3411	221	2	them	they	PRON
ap-3411	221	3	let	let	VERB
ap-3411	221	4	us	we	PRON
ap-3411	221	5	mention	mention	VERB
ap-3411	221	6	the	the	DET
ap-3411	221	7	structure	structure	NOUN
ap-3411	221	8	of	of	ADP
ap-3411	221	9	the	the	DET
ap-3411	221	10	lie	lie	NOUN
ap-3411	221	11	algebra	algebra	NOUN
ap-3411	221	12	of	of	ADP
ap-3411	221	13	the	the	DET
ap-3411	221	14	symmetries	symmetry	NOUN
ap-3411	221	15	of	of	ADP
ap-3411	221	16	the	the	DET
ap-3411	221	17	hopf	hopf	ADJ
ap-3411	221	18	equation	equation	NOUN
ap-3411	221	19	,	,	PUNCT
ap-3411	221	20	the	the	DET
ap-3411	221	21	fact	fact	NOUN
ap-3411	221	22	that	that	SCONJ
ap-3411	221	23	both	both	PRON
ap-3411	221	24	for	for	ADP
ap-3411	221	25	pde	pde	NOUN
ap-3411	221	26	’s	’s	PART
ap-3411	221	27	and	and	CCONJ
ap-3411	221	28	p∆e	p∆e	NOUN
ap-3411	221	29	’s	’s	PART
ap-3411	221	30	generalized	generalized	ADJ
ap-3411	221	31	symmetries	symmetry	NOUN
ap-3411	221	32	characterized	characterize	VERB
ap-3411	221	33	by	by	ADP
ap-3411	221	34	arbitrary	arbitrary	ADJ
ap-3411	221	35	functions	function	NOUN
ap-3411	221	36	provide	provide	VERB
ap-3411	221	37	master	master	NOUN
ap-3411	221	38	symmetries	symmetry	NOUN
ap-3411	221	39	.	.	PUNCT
ap-3411	222	1	moreover	moreover	ADV
ap-3411	222	2	the	the	DET
ap-3411	222	3	calculations	calculation	NOUN
ap-3411	222	4	of	of	ADP
ap-3411	222	5	the	the	DET
ap-3411	222	6	generalized	generalized	ADJ
ap-3411	222	7	symmetries	symmetry	NOUN
ap-3411	222	8	,	,	PUNCT
ap-3411	222	9	the	the	DET
ap-3411	222	10	darboux	darboux	NOUN
ap-3411	222	11	integrals	integral	NOUN
ap-3411	222	12	and	and	CCONJ
ap-3411	222	13	the	the	DET
ap-3411	222	14	linearizing	linearize	VERB
ap-3411	222	15	transformation	transformation	NOUN
ap-3411	222	16	for	for	ADP
ap-3411	222	17	the	the	DET
ap-3411	222	18	two	two	NUM
ap-3411	222	19	nonlinear	nonlinear	NOUN
ap-3411	222	20	quad	quad	NOUN
ap-3411	222	21	graph	graph	NOUN
ap-3411	222	22	equations	equation	NOUN
ap-3411	222	23	introduced	introduce	VERB
ap-3411	222	24	by	by	ADP
ap-3411	222	25	hietarinta	hietarinta	NOUN
ap-3411	222	26	are	be	AUX
ap-3411	222	27	new	new	ADJ
ap-3411	222	28	here	here	ADV
ap-3411	222	29	as	as	ADV
ap-3411	222	30	well	well	ADV
ap-3411	222	31	as	as	ADP
ap-3411	222	32	the	the	DET
ap-3411	222	33	generalized	generalized	ADJ
ap-3411	222	34	symmetries	symmetry	NOUN
ap-3411	222	35	for	for	ADP
ap-3411	222	36	the	the	DET
ap-3411	222	37	completely	completely	ADV
ap-3411	222	38	discrete	discrete	ADJ
ap-3411	222	39	liouville	liouville	NOUN
ap-3411	222	40	equation	equation	NOUN
ap-3411	222	41	and	and	CCONJ
ap-3411	222	42	the	the	DET
ap-3411	222	43	darboux	darboux	VERB
ap-3411	222	44	integrals	integral	NOUN
ap-3411	222	45	for	for	ADP
ap-3411	222	46	th(ε	th(ε	NOUN
ap-3411	222	47	)	)	PUNCT
ap-3411	222	48	1	1	NUM
ap-3411	222	49	.	.	PUNCT
ap-3411	223	1	acknowledgements	acknowledgement	NOUN
ap-3411	223	2	cs	cs	PROPN
ap-3411	223	3	and	and	CCONJ
ap-3411	223	4	dl	dl	PROPN
ap-3411	223	5	have	have	AUX
ap-3411	223	6	been	be	AUX
ap-3411	223	7	partly	partly	ADV
ap-3411	223	8	supported	support	VERB
ap-3411	223	9	by	by	ADP
ap-3411	223	10	the	the	DET
ap-3411	223	11	italian	italian	PROPN
ap-3411	223	12	ministry	ministry	PROPN
ap-3411	223	13	of	of	ADP
ap-3411	223	14	education	education	PROPN
ap-3411	223	15	and	and	CCONJ
ap-3411	223	16	research	research	NOUN
ap-3411	223	17	,	,	PUNCT
ap-3411	223	18	2010	2010	NUM
ap-3411	223	19	prin	prin	NOUN
ap-3411	223	20	continuous	continuous	ADJ
ap-3411	223	21	and	and	CCONJ
ap-3411	223	22	discrete	discrete	ADJ
ap-3411	223	23	nonlinear	nonlinear	ADJ
ap-3411	223	24	integrable	integrable	ADJ
ap-3411	223	25	evolutions	evolution	NOUN
ap-3411	223	26	:	:	PUNCT
ap-3411	223	27	from	from	ADP
ap-3411	223	28	water	water	NOUN
ap-3411	223	29	waves	wave	NOUN
ap-3411	223	30	to	to	ADP
ap-3411	223	31	symplectic	symplectic	ADJ
ap-3411	223	32	maps	map	NOUN
ap-3411	223	33	.	.	PUNCT
ap-3411	224	1	gg	gg	NOUN
ap-3411	224	2	and	and	CCONJ
ap-3411	224	3	dl	dl	PROPN
ap-3411	224	4	are	be	AUX
ap-3411	224	5	supported	support	VERB
ap-3411	224	6	by	by	ADP
ap-3411	224	7	infn	infn	PROPN
ap-3411	224	8	is	be	AUX
ap-3411	224	9	-	-	PUNCT
ap-3411	224	10	csn4	csn4	ADJ
ap-3411	224	11	mathematical	mathematical	ADJ
ap-3411	224	12	methods	method	NOUN
ap-3411	224	13	of	of	ADP
ap-3411	224	14	nonlinear	nonlinear	ADJ
ap-3411	224	15	physics	physic	NOUN
ap-3411	224	16	.	.	PUNCT
ap-3411	225	1	199	199	NUM
ap-3411	225	2	g.	g.	NOUN
ap-3411	225	3	gubbiotti	gubbiotti	PROPN
ap-3411	225	4	,	,	PUNCT
ap-3411	225	5	d.	d.	PROPN
ap-3411	225	6	levi	levi	PROPN
ap-3411	225	7	,	,	PUNCT
ap-3411	225	8	c.	c.	PROPN
ap-3411	225	9	scimiterna	scimiterna	PROPN
ap-3411	225	10	acta	acta	PROPN
ap-3411	225	11	polytechnica	polytechnica	PROPN
ap-3411	225	12	references	reference	NOUN
ap-3411	225	13	[	[	X
ap-3411	225	14	1	1	X
ap-3411	225	15	]	]	PUNCT
ap-3411	225	16	v.	v.	PROPN
ap-3411	225	17	e.	e.	PROPN
ap-3411	225	18	adler	adler	PROPN
ap-3411	225	19	on	on	ADP
ap-3411	225	20	a	a	DET
ap-3411	225	21	discrete	discrete	ADJ
ap-3411	225	22	analog	analog	NOUN
ap-3411	225	23	of	of	ADP
ap-3411	225	24	the	the	DET
ap-3411	225	25	tzitzeica	tzitzeica	PROPN
ap-3411	225	26	equation	equation	NOUN
ap-3411	225	27	,	,	PUNCT
ap-3411	225	28	preprint	preprint	NOUN
ap-3411	225	29	arxiv:1103.5139v1	arxiv:1103.5139v1	NOUN
ap-3411	225	30	,	,	PUNCT
ap-3411	225	31	march	march	PROPN
ap-3411	225	32	26th	26th	NUM
ap-3411	225	33	,	,	PUNCT
ap-3411	225	34	2011	2011	NUM
ap-3411	225	35	.	.	PUNCT
ap-3411	226	1	[	[	X
ap-3411	226	2	2	2	X
ap-3411	226	3	]	]	PUNCT
ap-3411	226	4	v.	v.	PROPN
ap-3411	226	5	e.	e.	PROPN
ap-3411	226	6	adler	adler	PROPN
ap-3411	226	7	and	and	CCONJ
ap-3411	226	8	s.	s.	PROPN
ap-3411	226	9	ya	ya	PROPN
ap-3411	226	10	.	.	PROPN
ap-3411	226	11	startsev	startsev	PROPN
ap-3411	226	12	,	,	PUNCT
ap-3411	226	13	discrete	discrete	ADJ
ap-3411	226	14	analogues	analogue	NOUN
ap-3411	226	15	of	of	ADP
ap-3411	226	16	the	the	DET
ap-3411	226	17	liouville	liouville	NOUN
ap-3411	226	18	equation	equation	NOUN
ap-3411	226	19	,	,	PUNCT
ap-3411	226	20	theor	theor	PROPN
ap-3411	226	21	.	.	PUNCT
ap-3411	226	22	math	math	NOUN
ap-3411	226	23	.	.	PUNCT
ap-3411	227	1	phys	phy	NOUN
ap-3411	227	2	.	.	PUNCT
ap-3411	227	3	,	,	PUNCT
ap-3411	227	4	121	121	NUM
ap-3411	227	5	(	(	PUNCT
ap-3411	227	6	1999	1999	NUM
ap-3411	227	7	)	)	PUNCT
ap-3411	227	8	1484–1495	1484–1495	NUM
ap-3411	227	9	,	,	PUNCT
ap-3411	227	10	doi:10.1007	doi:10.1007	NOUN
ap-3411	227	11	/	/	SYM
ap-3411	227	12	bf02557219	bf02557219	PROPN
ap-3411	228	1	[	[	X
ap-3411	228	2	3	3	X
ap-3411	228	3	]	]	X
ap-3411	228	4	g.	g.	PROPN
ap-3411	228	5	bluman	bluman	PROPN
ap-3411	228	6	and	and	CCONJ
ap-3411	228	7	s.	s.	PROPN
ap-3411	228	8	kumey	kumey	PROPN
ap-3411	228	9	,	,	PUNCT
ap-3411	228	10	symmetries	symmetry	NOUN
ap-3411	228	11	and	and	CCONJ
ap-3411	228	12	differential	differential	ADJ
ap-3411	228	13	equations	equation	NOUN
ap-3411	228	14	,	,	PUNCT
ap-3411	228	15	springer	springer	NOUN
ap-3411	228	16	–	–	PUNCT
ap-3411	228	17	verlag	verlag	PROPN
ap-3411	228	18	,	,	PUNCT
ap-3411	228	19	new	new	PROPN
ap-3411	228	20	york	york	PROPN
ap-3411	228	21	,	,	PUNCT
ap-3411	228	22	1989	1989	NUM
ap-3411	228	23	,	,	PUNCT
ap-3411	228	24	doi:10.1007/978	doi:10.1007/978	PROPN
ap-3411	228	25	-	-	PUNCT
ap-3411	228	26	1	1	NUM
ap-3411	228	27	-	-	PUNCT
ap-3411	228	28	4757	4757	NUM
ap-3411	228	29	-	-	SYM
ap-3411	228	30	4307	4307	NUM
ap-3411	228	31	-	-	SYM
ap-3411	228	32	4	4	NUM
ap-3411	228	33	[	[	SYM
ap-3411	228	34	4	4	NUM
ap-3411	228	35	]	]	PUNCT
ap-3411	228	36	r.	r.	PROPN
ap-3411	228	37	boll	boll	PROPN
ap-3411	228	38	,	,	PUNCT
ap-3411	228	39	classification	classification	NOUN
ap-3411	228	40	and	and	CCONJ
ap-3411	228	41	lagrangian	lagrangian	ADJ
ap-3411	228	42	structure	structure	NOUN
ap-3411	228	43	od	od	PROPN
ap-3411	228	44	3d	3d	NUM
ap-3411	228	45	consistent	consistent	ADJ
ap-3411	228	46	quad	quad	ADJ
ap-3411	228	47	-	-	PUNCT
ap-3411	228	48	equations	equation	NOUN
ap-3411	228	49	,	,	PUNCT
ap-3411	228	50	ph	ph	PROPN
ap-3411	228	51	.	.	PROPN
ap-3411	228	52	d.	d.	PROPN
ap-3411	228	53	dissertation	dissertation	PROPN
ap-3411	228	54	(	(	PUNCT
ap-3411	228	55	2012	2012	NUM
ap-3411	228	56	)	)	PUNCT
ap-3411	228	57	.	.	PUNCT
ap-3411	229	1	[	[	X
ap-3411	229	2	5	5	X
ap-3411	229	3	]	]	PUNCT
ap-3411	229	4	f.	f.	PROPN
ap-3411	229	5	calogero	calogero	PROPN
ap-3411	229	6	and	and	CCONJ
ap-3411	229	7	w.	w.	PROPN
ap-3411	229	8	eckhaus	eckhaus	PROPN
ap-3411	229	9	,	,	PUNCT
ap-3411	229	10	nonlinear	nonlinear	ADJ
ap-3411	229	11	evolution	evolution	NOUN
ap-3411	229	12	equations	equation	NOUN
ap-3411	229	13	,	,	PUNCT
ap-3411	229	14	rescalings	rescaling	NOUN
ap-3411	229	15	,	,	PUNCT
ap-3411	229	16	model	model	NOUN
ap-3411	229	17	pdes	pde	NOUN
ap-3411	229	18	and	and	CCONJ
ap-3411	229	19	their	their	PRON
ap-3411	229	20	integrability	integrability	NOUN
ap-3411	229	21	.	.	PUNCT
ap-3411	230	1	i	i	PRON
ap-3411	230	2	&	&	CCONJ
ap-3411	230	3	ii	ii	PROPN
ap-3411	230	4	.	.	PUNCT
ap-3411	230	5	inv	inv	PROPN
ap-3411	230	6	.	.	PUNCT
ap-3411	231	1	probl	probl	NOUN
ap-3411	231	2	.	.	PUNCT
ap-3411	232	1	3	3	NUM
ap-3411	232	2	(	(	PUNCT
ap-3411	232	3	1987	1987	NUM
ap-3411	232	4	)	)	PUNCT
ap-3411	233	1	229–262	229–262	NUM
ap-3411	233	2	,	,	PUNCT
ap-3411	233	3	doi:10.1088/0266	doi:10.1088/0266	NOUN
ap-3411	233	4	-	-	PUNCT
ap-3411	233	5	5611/3/2/008	5611/3/2/008	NUM
ap-3411	233	6	&	&	CCONJ
ap-3411	233	7	4	4	NUM
ap-3411	233	8	(	(	PUNCT
ap-3411	233	9	1988	1988	NUM
ap-3411	233	10	)	)	PUNCT
ap-3411	233	11	11–33	11–33	NUM
ap-3411	233	12	,	,	PUNCT
ap-3411	233	13	doi:10.1088/0266	doi:10.1088/0266	NOUN
ap-3411	233	14	-	-	PUNCT
ap-3411	233	15	5611/4/1/005	5611/4/1/005	NUM
ap-3411	233	16	[	[	X
ap-3411	233	17	6	6	NUM
ap-3411	233	18	]	]	PUNCT
ap-3411	233	19	b.	b.	PROPN
ap-3411	233	20	champagne	champagne	PROPN
ap-3411	233	21	and	and	CCONJ
ap-3411	233	22	p.	p.	PROPN
ap-3411	233	23	winternitz	winternitz	PROPN
ap-3411	233	24	,	,	PUNCT
ap-3411	233	25	on	on	ADP
ap-3411	233	26	the	the	DET
ap-3411	233	27	infinite	infinite	ADJ
ap-3411	233	28	-	-	PUNCT
ap-3411	233	29	dimensional	dimensional	ADJ
ap-3411	233	30	symmetry	symmetry	NOUN
ap-3411	233	31	group	group	NOUN
ap-3411	233	32	of	of	ADP
ap-3411	233	33	the	the	DET
ap-3411	233	34	davey	davey	NOUN
ap-3411	233	35	-	-	PUNCT
ap-3411	233	36	stewartson	stewartson	NOUN
ap-3411	233	37	equantions	equantion	NOUN
ap-3411	233	38	,	,	PUNCT
ap-3411	233	39	j.	j.	PROPN
ap-3411	233	40	math	math	PROPN
ap-3411	233	41	.	.	PUNCT
ap-3411	234	1	phys	phy	NOUN
ap-3411	234	2	,	,	PUNCT
ap-3411	234	3	29	29	NUM
ap-3411	234	4	(	(	PUNCT
ap-3411	234	5	1988	1988	NUM
ap-3411	234	6	)	)	PUNCT
ap-3411	234	7	1–8	1–8	NUM
ap-3411	234	8	,	,	PUNCT
ap-3411	234	9	doi:10.1063/1.528173	doi:10.1063/1.528173	ADJ
ap-3411	234	10	[	[	X
ap-3411	234	11	7	7	NUM
ap-3411	234	12	]	]	X
ap-3411	234	13	d.	d.	PROPN
ap-3411	234	14	david	david	PROPN
ap-3411	234	15	,	,	PUNCT
ap-3411	234	16	n.	n.	PROPN
ap-3411	234	17	kamran	kamran	PROPN
ap-3411	234	18	,	,	PUNCT
ap-3411	234	19	d.	d.	PROPN
ap-3411	234	20	levi	levi	PROPN
ap-3411	234	21	and	and	CCONJ
ap-3411	234	22	p.	p.	PROPN
ap-3411	234	23	winternitz	winternitz	PROPN
ap-3411	234	24	,	,	PUNCT
ap-3411	234	25	subalgebras	subalgebras	PROPN
ap-3411	234	26	of	of	ADP
ap-3411	234	27	loop	loop	NOUN
ap-3411	234	28	algebras	algebra	NOUN
ap-3411	234	29	and	and	CCONJ
ap-3411	234	30	symmetries	symmetry	NOUN
ap-3411	234	31	of	of	ADP
ap-3411	234	32	the	the	DET
ap-3411	234	33	kadomtsev	kadomtsev	ADJ
ap-3411	234	34	-	-	PUNCT
ap-3411	234	35	petviashvili	petviashvili	NOUN
ap-3411	234	36	equation	equation	NOUN
ap-3411	234	37	,	,	PUNCT
ap-3411	234	38	phys	phy	NOUN
ap-3411	234	39	.	.	PUNCT
ap-3411	235	1	rev	rev	PROPN
ap-3411	235	2	.	.	PROPN
ap-3411	235	3	lett	lett	PROPN
ap-3411	235	4	.	.	PUNCT
ap-3411	236	1	55	55	NUM
ap-3411	236	2	(	(	PUNCT
ap-3411	236	3	1985	1985	NUM
ap-3411	236	4	)	)	PUNCT
ap-3411	236	5	2111–2113	2111–2113	NUM
ap-3411	236	6	,	,	PUNCT
ap-3411	236	7	doi:10.1103	doi:10.1103	X
ap-3411	236	8	/	/	SYM
ap-3411	236	9	physrevlett.55.2111	physrevlett.55.2111	NOUN
ap-3411	236	10	[	[	X
ap-3411	236	11	8	8	NUM
ap-3411	236	12	]	]	X
ap-3411	236	13	d.	d.	PROPN
ap-3411	236	14	david	david	PROPN
ap-3411	236	15	,	,	PUNCT
ap-3411	236	16	n.	n.	PROPN
ap-3411	236	17	kamran	kamran	PROPN
ap-3411	236	18	,	,	PUNCT
ap-3411	236	19	d.	d.	PROPN
ap-3411	236	20	levi	levi	PROPN
ap-3411	236	21	and	and	CCONJ
ap-3411	236	22	p.	p.	PROPN
ap-3411	236	23	winternitz	winternitz	PROPN
ap-3411	236	24	,	,	PUNCT
ap-3411	236	25	symmetry	symmetry	NOUN
ap-3411	236	26	reduction	reduction	NOUN
ap-3411	236	27	for	for	ADP
ap-3411	236	28	the	the	DET
ap-3411	236	29	kadomtsev	kadomtsev	ADJ
ap-3411	236	30	–	–	PUNCT
ap-3411	236	31	petviashvili	petviashvili	NOUN
ap-3411	236	32	equation	equation	NOUN
ap-3411	236	33	using	use	VERB
ap-3411	236	34	a	a	DET
ap-3411	236	35	loop	loop	NOUN
ap-3411	236	36	algebra	algebra	NOUN
ap-3411	236	37	,	,	PUNCT
ap-3411	236	38	j.	j.	PROPN
ap-3411	236	39	math	math	PROPN
ap-3411	236	40	.	.	PUNCT
ap-3411	237	1	phys	phy	NOUN
ap-3411	237	2	.	.	PUNCT
ap-3411	238	1	27	27	NUM
ap-3411	238	2	(	(	PUNCT
ap-3411	238	3	1986	1986	NUM
ap-3411	238	4	)	)	PUNCT
ap-3411	238	5	1225–1237	1225–1237	NUM
ap-3411	238	6	,	,	PUNCT
ap-3411	238	7	doi:10.1063/1.527129	doi:10.1063/1.527129	VERB
ap-3411	238	8	[	[	X
ap-3411	238	9	9	9	NUM
ap-3411	238	10	]	]	PUNCT
ap-3411	238	11	r.	r.	PROPN
ap-3411	238	12	n.	n.	PROPN
ap-3411	238	13	garifullin	garifullin	PROPN
ap-3411	238	14	and	and	CCONJ
ap-3411	238	15	r.	r.	PROPN
ap-3411	238	16	i.	i.	PROPN
ap-3411	238	17	yamilov	yamilov	PROPN
ap-3411	238	18	,	,	PUNCT
ap-3411	238	19	generalized	generalized	ADJ
ap-3411	238	20	symmetry	symmetry	NOUN
ap-3411	238	21	classification	classification	NOUN
ap-3411	238	22	of	of	ADP
ap-3411	238	23	discrete	discrete	ADJ
ap-3411	238	24	equations	equation	NOUN
ap-3411	238	25	of	of	ADP
ap-3411	238	26	a	a	DET
ap-3411	238	27	class	class	NOUN
ap-3411	238	28	depending	depend	VERB
ap-3411	238	29	on	on	ADP
ap-3411	238	30	twelve	twelve	NUM
ap-3411	238	31	parameters	parameter	NOUN
ap-3411	238	32	,	,	PUNCT
ap-3411	238	33	j.	j.	PROPN
ap-3411	238	34	phys	phys	PROPN
ap-3411	238	35	.	.	PUNCT
ap-3411	239	1	a	a	DET
ap-3411	239	2	:	:	PUNCT
ap-3411	239	3	math	math	NOUN
ap-3411	239	4	.	.	PUNCT
ap-3411	240	1	theor	theor	PROPN
ap-3411	240	2	.	.	PUNCT
ap-3411	241	1	45	45	NUM
ap-3411	241	2	(	(	PUNCT
ap-3411	241	3	2012	2012	NUM
ap-3411	241	4	)	)	PUNCT
ap-3411	241	5	345205	345205	NUM
ap-3411	241	6	(	(	PUNCT
ap-3411	241	7	23	23	NUM
ap-3411	241	8	pp	pp	NOUN
ap-3411	241	9	.	.	PUNCT
ap-3411	241	10	)	)	PUNCT
ap-3411	241	11	,	,	PUNCT
ap-3411	241	12	doi:10.1088/1751	doi:10.1088/1751	NOUN
ap-3411	241	13	-	-	SYM
ap-3411	241	14	8113/45/34/345205	8113/45/34/345205	NUM
ap-3411	241	15	[	[	X
ap-3411	241	16	10	10	NUM
ap-3411	241	17	]	]	X
ap-3411	241	18	r.	r.	PROPN
ap-3411	241	19	n.	n.	PROPN
ap-3411	241	20	garifullin	garifullin	PROPN
ap-3411	241	21	,	,	PUNCT
ap-3411	241	22	r.	r.	PROPN
ap-3411	241	23	i.	i.	PROPN
ap-3411	241	24	yamilov	yamilov	PROPN
ap-3411	241	25	,	,	PUNCT
ap-3411	241	26	examples	example	NOUN
ap-3411	241	27	of	of	ADP
ap-3411	241	28	darboux	darboux	VERB
ap-3411	241	29	integrable	integrable	ADJ
ap-3411	241	30	discrete	discrete	ADJ
ap-3411	241	31	equations	equation	NOUN
ap-3411	241	32	possessing	possess	VERB
ap-3411	241	33	first	first	ADJ
ap-3411	241	34	integrals	integral	NOUN
ap-3411	241	35	of	of	ADP
ap-3411	241	36	an	an	DET
ap-3411	241	37	arbitrarily	arbitrarily	ADV
ap-3411	241	38	high	high	ADJ
ap-3411	241	39	minimal	minimal	ADJ
ap-3411	241	40	order	order	NOUN
ap-3411	241	41	,	,	PUNCT
ap-3411	241	42	ufimsk	ufimsk	PROPN
ap-3411	241	43	.	.	PUNCT
ap-3411	242	1	mat	mat	PROPN
ap-3411	242	2	.	.	PUNCT
ap-3411	243	1	zh	zh	PROPN
ap-3411	243	2	.	.	PROPN
ap-3411	243	3	,	,	PUNCT
ap-3411	243	4	4	4	NUM
ap-3411	243	5	(	(	PUNCT
ap-3411	243	6	2012	2012	NUM
ap-3411	243	7	)	)	PUNCT
ap-3411	243	8	,	,	PUNCT
ap-3411	243	9	174–180	174–180	NUM
ap-3411	243	10	.	.	PUNCT
ap-3411	244	1	[	[	X
ap-3411	244	2	11	11	NUM
ap-3411	244	3	]	]	PUNCT
ap-3411	244	4	a.	a.	NOUN
ap-3411	244	5	m.	m.	PROPN
ap-3411	244	6	grundland	grundland	PROPN
ap-3411	244	7	,	,	PUNCT
ap-3411	244	8	m.	m.	PROPN
ap-3411	244	9	b.	b.	PROPN
ap-3411	244	10	sheftel	sheftel	PROPN
ap-3411	244	11	and	and	CCONJ
ap-3411	244	12	p.	p.	PROPN
ap-3411	244	13	winternitz	winternitz	PROPN
ap-3411	244	14	,	,	PUNCT
ap-3411	244	15	invariant	invariant	ADJ
ap-3411	244	16	solutions	solution	NOUN
ap-3411	244	17	of	of	ADP
ap-3411	244	18	hydrodynamic	hydrodynamic	ADJ
ap-3411	244	19	-	-	PUNCT
ap-3411	244	20	type	type	NOUN
ap-3411	244	21	equations	equation	NOUN
ap-3411	244	22	,	,	PUNCT
ap-3411	244	23	j.	j.	PROPN
ap-3411	244	24	phys	phys	PROPN
ap-3411	244	25	.	.	PUNCT
ap-3411	245	1	a	a	DET
ap-3411	245	2	:	:	PUNCT
ap-3411	245	3	math	math	NOUN
ap-3411	245	4	.	.	PUNCT
ap-3411	246	1	gen	gen	PROPN
ap-3411	246	2	.	.	PROPN
ap-3411	246	3	33	33	NUM
ap-3411	246	4	(	(	PUNCT
ap-3411	246	5	2000	2000	NUM
ap-3411	246	6	)	)	PUNCT
ap-3411	246	7	8193	8193	NUM
ap-3411	246	8	-	-	SYM
ap-3411	246	9	8215	8215	NUM
ap-3411	246	10	,	,	PUNCT
ap-3411	246	11	doi:10.1088/0305	doi:10.1088/0305	ADJ
ap-3411	246	12	-	-	PUNCT
ap-3411	246	13	4470/33/46/304	4470/33/46/304	PROPN
ap-3411	247	1	[	[	X
ap-3411	247	2	12	12	NUM
ap-3411	247	3	]	]	X
ap-3411	247	4	g.	g.	PROPN
ap-3411	247	5	gubbiotti	gubbiotti	PROPN
ap-3411	247	6	,	,	PUNCT
ap-3411	247	7	c.	c.	PROPN
ap-3411	247	8	scimiterna	scimiterna	PROPN
ap-3411	247	9	and	and	CCONJ
ap-3411	247	10	d.	d.	PROPN
ap-3411	247	11	levi	levi	PROPN
ap-3411	247	12	,	,	PUNCT
ap-3411	247	13	linearizability	linearizability	NOUN
ap-3411	247	14	and	and	CCONJ
ap-3411	247	15	fake	fake	ADJ
ap-3411	247	16	lax	lax	ADJ
ap-3411	247	17	pair	pair	NOUN
ap-3411	247	18	for	for	ADP
ap-3411	247	19	a	a	DET
ap-3411	247	20	consistent	consistent	NOUN
ap-3411	247	21	around	around	ADP
ap-3411	247	22	the	the	DET
ap-3411	247	23	cube	cube	NOUN
ap-3411	247	24	nonlinear	nonlinear	ADJ
ap-3411	247	25	non	non	ADJ
ap-3411	247	26	-	-	ADJ
ap-3411	247	27	autonomous	autonomous	ADJ
ap-3411	247	28	quad	quad	ADJ
ap-3411	247	29	-	-	PUNCT
ap-3411	247	30	graph	graph	NOUN
ap-3411	247	31	equation	equation	NOUN
ap-3411	247	32	,	,	PUNCT
ap-3411	247	33	arxiv:1510.01527	arxiv:1510.01527	NOUN
ap-3411	247	34	,	,	PUNCT
ap-3411	247	35	submitted	submit	VERB
ap-3411	247	36	to	to	ADP
ap-3411	247	37	theor	theor	PROPN
ap-3411	247	38	.	.	PUNCT
ap-3411	247	39	math	math	NOUN
ap-3411	247	40	.	.	PUNCT
ap-3411	248	1	phys	phy	NOUN
ap-3411	248	2	.	.	PUNCT
ap-3411	248	3	.	.	PUNCT
ap-3411	249	1	[	[	X
ap-3411	249	2	13	13	NUM
ap-3411	249	3	]	]	X
ap-3411	249	4	g.	g.	PROPN
ap-3411	249	5	gubbiotti	gubbiotti	PROPN
ap-3411	249	6	,	,	PUNCT
ap-3411	249	7	c.	c.	PROPN
ap-3411	249	8	scimiterna	scimiterna	PROPN
ap-3411	249	9	and	and	CCONJ
ap-3411	249	10	d.	d.	PROPN
ap-3411	249	11	levi	levi	PROPN
ap-3411	249	12	,	,	PUNCT
ap-3411	249	13	the	the	DET
ap-3411	249	14	non	non	PROPN
ap-3411	249	15	autonomous	autonomous	ADJ
ap-3411	249	16	ydkn	ydkn	PROPN
ap-3411	249	17	equation	equation	NOUN
ap-3411	249	18	and	and	CCONJ
ap-3411	249	19	generalized	generalized	ADJ
ap-3411	249	20	symmetries	symmetry	NOUN
ap-3411	249	21	of	of	ADP
ap-3411	249	22	boll	boll	PROPN
ap-3411	249	23	equations	equation	NOUN
ap-3411	249	24	,	,	PUNCT
ap-3411	249	25	arxiv:1510.07175	arxiv:1510.07175	PROPN
ap-3411	249	26	,	,	PUNCT
ap-3411	249	27	submitted	submit	VERB
ap-3411	249	28	to	to	ADP
ap-3411	249	29	j.	j.	PROPN
ap-3411	249	30	phys	phys	PROPN
ap-3411	249	31	.	.	PUNCT
ap-3411	250	1	a.	a.	NOUN
ap-3411	251	1	[	[	X
ap-3411	251	2	14	14	NUM
ap-3411	251	3	]	]	PUNCT
ap-3411	251	4	j.	j.	PROPN
ap-3411	251	5	hietarinta	hietarinta	PROPN
ap-3411	251	6	,	,	PUNCT
ap-3411	251	7	searching	search	VERB
ap-3411	251	8	for	for	ADP
ap-3411	251	9	cac	cac	PROPN
ap-3411	251	10	-	-	PUNCT
ap-3411	251	11	maps	maps	PROPN
ap-3411	251	12	,	,	PUNCT
ap-3411	251	13	j.	j.	PROPN
ap-3411	251	14	nonlinear	nonlinear	PROPN
ap-3411	251	15	math	math	PROPN
ap-3411	251	16	.	.	PUNCT
ap-3411	252	1	phys	phy	NOUN
ap-3411	252	2	.	.	PUNCT
ap-3411	253	1	12	12	NUM
ap-3411	253	2	suppl	suppl	ADJ
ap-3411	253	3	.	.	PUNCT
ap-3411	253	4	2	2	NUM
ap-3411	253	5	(	(	PUNCT
ap-3411	253	6	2005	2005	NUM
ap-3411	253	7	)	)	PUNCT
ap-3411	253	8	223–230	223–230	NUM
ap-3411	253	9	,	,	PUNCT
ap-3411	253	10	doi:10.2991	doi:10.2991	NOUN
ap-3411	253	11	/	/	SYM
ap-3411	253	12	jnmp.2005.12.s2.16	jnmp.2005.12.s2.16	PROPN
ap-3411	254	1	[	[	X
ap-3411	254	2	15	15	NUM
ap-3411	254	3	]	]	X
ap-3411	254	4	r.	r.	PROPN
ap-3411	254	5	hirota	hirota	PROPN
ap-3411	254	6	,	,	PUNCT
ap-3411	254	7	nonlinear	nonlinear	ADJ
ap-3411	254	8	partial	partial	ADJ
ap-3411	254	9	difference	difference	NOUN
ap-3411	254	10	equations	equation	NOUN
ap-3411	254	11	.	.	PUNCT
ap-3411	255	1	v.	v.	ADP
ap-3411	255	2	nonlinear	nonlinear	ADJ
ap-3411	255	3	equations	equation	NOUN
ap-3411	255	4	reducible	reducible	ADJ
ap-3411	255	5	to	to	ADP
ap-3411	255	6	linear	linear	PROPN
ap-3411	255	7	equations	equation	NOUN
ap-3411	255	8	,	,	PUNCT
ap-3411	255	9	j.	j.	PROPN
ap-3411	255	10	phys	phys	PROPN
ap-3411	255	11	.	.	PUNCT
ap-3411	256	1	soc	soc	PROPN
ap-3411	256	2	.	.	PUNCT
ap-3411	257	1	japan	japan	PROPN
ap-3411	257	2	46	46	NUM
ap-3411	257	3	(	(	PUNCT
ap-3411	257	4	1979	1979	NUM
ap-3411	257	5	)	)	PUNCT
ap-3411	257	6	312	312	NUM
ap-3411	257	7	-	-	NUM
ap-3411	257	8	319	319	NUM
ap-3411	257	9	,	,	PUNCT
ap-3411	257	10	doi:10.1143	doi:10.1143	NOUN
ap-3411	257	11	/	/	SYM
ap-3411	257	12	jpsj.46.312	jpsj.46.312	PROPN
ap-3411	258	1	[	[	X
ap-3411	258	2	16	16	NUM
ap-3411	258	3	]	]	X
ap-3411	258	4	r.	r.	PROPN
ap-3411	258	5	hirota	hirota	PROPN
ap-3411	258	6	,	,	PUNCT
ap-3411	258	7	discrete	discrete	VERB
ap-3411	258	8	two	two	NUM
ap-3411	258	9	-	-	PUNCT
ap-3411	258	10	dimensional	dimensional	ADJ
ap-3411	258	11	toda	toda	NOUN
ap-3411	258	12	molecule	molecule	NOUN
ap-3411	258	13	equation	equation	NOUN
ap-3411	258	14	,	,	PUNCT
ap-3411	258	15	j.	j.	PROPN
ap-3411	258	16	phys	phys	PROPN
ap-3411	258	17	.	.	PUNCT
ap-3411	259	1	soc	soc	PROPN
ap-3411	259	2	.	.	PUNCT
ap-3411	260	1	japan	japan	PROPN
ap-3411	260	2	56	56	NUM
ap-3411	260	3	(	(	PUNCT
ap-3411	260	4	1987	1987	NUM
ap-3411	260	5	)	)	PUNCT
ap-3411	260	6	4285	4285	NUM
ap-3411	260	7	-	-	SYM
ap-3411	260	8	4288	4288	NUM
ap-3411	260	9	,	,	PUNCT
ap-3411	260	10	doi:10.1143	doi:10.1143	NOUN
ap-3411	260	11	/	/	SYM
ap-3411	260	12	jpsj.56.4285	jpsj.56.4285	PROPN
ap-3411	261	1	[	[	X
ap-3411	261	2	17	17	NUM
ap-3411	261	3	]	]	X
ap-3411	261	4	n.	n.	PROPN
ap-3411	261	5	h.	h.	PROPN
ap-3411	261	6	ibragimov	ibragimov	PROPN
ap-3411	261	7	,	,	PUNCT
ap-3411	261	8	transformation	transformation	NOUN
ap-3411	261	9	groups	group	NOUN
ap-3411	261	10	applied	apply	VERB
ap-3411	261	11	to	to	ADP
ap-3411	261	12	mathematical	mathematical	ADJ
ap-3411	261	13	physics	physics	PROPN
ap-3411	261	14	,	,	PUNCT
ap-3411	261	15	nauka	nauka	PROPN
ap-3411	261	16	,	,	PUNCT
ap-3411	261	17	moscow	moscow	PROPN
ap-3411	261	18	,	,	PUNCT
ap-3411	261	19	1983	1983	NUM
ap-3411	261	20	(	(	PUNCT
ap-3411	261	21	english	english	ADJ
ap-3411	261	22	translation	translation	NOUN
ap-3411	261	23	by	by	ADP
ap-3411	261	24	reidel	reidel	PROPN
ap-3411	261	25	,	,	PUNCT
ap-3411	261	26	dordrecht	dordrecht	PROPN
ap-3411	261	27	,	,	PUNCT
ap-3411	261	28	1985	1985	NUM
ap-3411	261	29	)	)	PUNCT
ap-3411	261	30	,	,	PUNCT
ap-3411	261	31	doi:10.1007/978	doi:10.1007/978	PROPN
ap-3411	261	32	-	-	PUNCT
ap-3411	261	33	94	94	NUM
ap-3411	261	34	-	-	PUNCT
ap-3411	261	35	009	009	NUM
ap-3411	261	36	-	-	PUNCT
ap-3411	261	37	5243	5243	NUM
ap-3411	261	38	-	-	SYM
ap-3411	261	39	0	0	PUNCT
ap-3411	262	1	[	[	X
ap-3411	262	2	18	18	NUM
ap-3411	262	3	]	]	PUNCT
ap-3411	262	4	m.	m.	NOUN
ap-3411	262	5	juráš	juráš	PROPN
ap-3411	262	6	and	and	CCONJ
ap-3411	262	7	i.	i.	PROPN
ap-3411	262	8	m.	m.	PROPN
ap-3411	262	9	anderson	anderson	PROPN
ap-3411	262	10	,	,	PUNCT
ap-3411	262	11	generalized	generalized	ADJ
ap-3411	262	12	laplace	laplace	NOUN
ap-3411	262	13	invariants	invariant	NOUN
ap-3411	262	14	and	and	CCONJ
ap-3411	262	15	the	the	DET
ap-3411	262	16	method	method	NOUN
ap-3411	262	17	of	of	ADP
ap-3411	262	18	darboux	darboux	NOUN
ap-3411	262	19	,	,	PUNCT
ap-3411	262	20	duke	duke	PROPN
ap-3411	262	21	math	math	PROPN
ap-3411	262	22	.	.	PUNCT
ap-3411	263	1	j.	j.	PROPN
ap-3411	263	2	89	89	NUM
ap-3411	263	3	(	(	PUNCT
ap-3411	263	4	1997	1997	NUM
ap-3411	263	5	)	)	PUNCT
ap-3411	263	6	351–375	351–375	NUM
ap-3411	263	7	,	,	PUNCT
ap-3411	263	8	doi:10.1215	doi:10.1215	NOUN
ap-3411	263	9	/	/	SYM
ap-3411	263	10	s0012	s0012	NOUN
ap-3411	263	11	-	-	PUNCT
ap-3411	263	12	7094	7094	NUM
ap-3411	263	13	-	-	PUNCT
ap-3411	263	14	97	97	NUM
ap-3411	263	15	-	-	PUNCT
ap-3411	263	16	08916	08916	NUM
ap-3411	263	17	-	-	PUNCT
ap-3411	263	18	x	x	PUNCT
ap-3411	264	1	[	[	X
ap-3411	264	2	19	19	NUM
ap-3411	264	3	]	]	X
ap-3411	264	4	d.	d.	PROPN
ap-3411	264	5	levi	levi	PROPN
ap-3411	264	6	,	,	PUNCT
ap-3411	264	7	l.	l.	PROPN
ap-3411	264	8	martina	martina	PROPN
ap-3411	264	9	and	and	CCONJ
ap-3411	264	10	p.	p.	PROPN
ap-3411	264	11	winternitz	winternitz	PROPN
ap-3411	264	12	,	,	PUNCT
ap-3411	264	13	lie	lie	NOUN
ap-3411	264	14	-	-	PUNCT
ap-3411	264	15	point	point	NOUN
ap-3411	264	16	symmetries	symmetry	NOUN
ap-3411	264	17	of	of	ADP
ap-3411	264	18	the	the	DET
ap-3411	264	19	discrete	discrete	ADJ
ap-3411	264	20	liouville	liouville	NOUN
ap-3411	264	21	equation	equation	NOUN
ap-3411	264	22	,	,	PUNCT
ap-3411	264	23	j.	j.	PROPN
ap-3411	264	24	phys	phys	PROPN
ap-3411	264	25	.	.	PUNCT
ap-3411	265	1	a	a	DET
ap-3411	265	2	:	:	PUNCT
ap-3411	265	3	math	math	NOUN
ap-3411	265	4	.	.	PUNCT
ap-3411	266	1	theor	theor	PROPN
ap-3411	266	2	.	.	PUNCT
ap-3411	267	1	48	48	NUM
ap-3411	267	2	(	(	PUNCT
ap-3411	267	3	2015	2015	NUM
ap-3411	267	4	)	)	PUNCT
ap-3411	267	5	025204	025204	NUM
ap-3411	267	6	(	(	PUNCT
ap-3411	267	7	18	18	NUM
ap-3411	267	8	pp	pp	NUM
ap-3411	267	9	.	.	PUNCT
ap-3411	267	10	)	)	PUNCT
ap-3411	267	11	,	,	PUNCT
ap-3411	267	12	doi:10.1088/1751	doi:10.1088/1751	AUX
ap-3411	267	13	-	-	PUNCT
ap-3411	267	14	8113/48/2/025204	8113/48/2/025204	NUM
ap-3411	267	15	arxiv:1407.4043	arxiv:1407.4043	NOUN
ap-3411	267	16	[	[	X
ap-3411	267	17	20	20	NUM
ap-3411	267	18	]	]	X
ap-3411	267	19	d.	d.	PROPN
ap-3411	267	20	levi	levi	PROPN
ap-3411	267	21	,	,	PUNCT
ap-3411	267	22	l.	l.	PROPN
ap-3411	267	23	martina	martina	PROPN
ap-3411	267	24	and	and	CCONJ
ap-3411	267	25	p.	p.	PROPN
ap-3411	267	26	winternitz	winternitz	PROPN
ap-3411	267	27	,	,	PUNCT
ap-3411	267	28	structure	structure	NOUN
ap-3411	267	29	preserving	preserve	VERB
ap-3411	267	30	discretizations	discretization	NOUN
ap-3411	267	31	of	of	ADP
ap-3411	267	32	the	the	DET
ap-3411	267	33	liouville	liouville	NOUN
ap-3411	267	34	equation	equation	NOUN
ap-3411	267	35	and	and	CCONJ
ap-3411	267	36	their	their	PRON
ap-3411	267	37	numerical	numerical	ADJ
ap-3411	267	38	tests	test	NOUN
ap-3411	267	39	,	,	PUNCT
ap-3411	267	40	sigma	sigma	NOUN
ap-3411	267	41	11	11	NUM
ap-3411	267	42	(	(	PUNCT
ap-3411	267	43	2015	2015	NUM
ap-3411	267	44	)	)	PUNCT
ap-3411	267	45	080	080	NUM
ap-3411	267	46	(	(	PUNCT
ap-3411	267	47	20	20	NUM
ap-3411	267	48	pp	pp	NUM
ap-3411	267	49	.	.	PUNCT
ap-3411	267	50	)	)	PUNCT
ap-3411	267	51	,	,	PUNCT
ap-3411	267	52	doi:10.3842	doi:10.3842	NOUN
ap-3411	267	53	/	/	SYM
ap-3411	267	54	sigma.2015.080	sigma.2015.080	NOUN
ap-3411	267	55	arxiv:1504.01953v2	arxiv:1504.01953v2	PROPN
ap-3411	267	56	[	[	X
ap-3411	267	57	21	21	NUM
ap-3411	267	58	]	]	X
ap-3411	267	59	d.	d.	PROPN
ap-3411	267	60	levi	levi	PROPN
ap-3411	267	61	and	and	CCONJ
ap-3411	267	62	c.	c.	PROPN
ap-3411	267	63	scimiterna	scimiterna	PROPN
ap-3411	267	64	,	,	PUNCT
ap-3411	267	65	linearization	linearization	NOUN
ap-3411	267	66	through	through	ADP
ap-3411	267	67	symmetries	symmetry	NOUN
ap-3411	267	68	for	for	ADP
ap-3411	267	69	discrete	discrete	ADJ
ap-3411	267	70	equations	equation	NOUN
ap-3411	267	71	,	,	PUNCT
ap-3411	267	72	j.	j.	PROPN
ap-3411	267	73	phys	phys	PROPN
ap-3411	267	74	.	.	PUNCT
ap-3411	268	1	a	a	DET
ap-3411	268	2	:	:	PUNCT
ap-3411	268	3	math	math	NOUN
ap-3411	268	4	.	.	PUNCT
ap-3411	269	1	theor	theor	PROPN
ap-3411	269	2	.	.	PUNCT
ap-3411	270	1	46	46	NUM
ap-3411	270	2	(	(	PUNCT
ap-3411	270	3	2013	2013	NUM
ap-3411	270	4	)	)	PUNCT
ap-3411	270	5	325204	325204	NUM
ap-3411	270	6	(	(	PUNCT
ap-3411	270	7	18	18	NUM
ap-3411	270	8	pp	pp	NUM
ap-3411	270	9	)	)	PUNCT
ap-3411	270	10	,	,	PUNCT
ap-3411	270	11	doi:10.1088/1751	doi:10.1088/1751	NOUN
ap-3411	270	12	-	-	PUNCT
ap-3411	270	13	8113/46/32/325204	8113/46/32/325204	PROPN
ap-3411	271	1	[	[	X
ap-3411	271	2	22	22	NUM
ap-3411	271	3	]	]	X
ap-3411	271	4	d.	d.	PROPN
ap-3411	271	5	levi	levi	PROPN
ap-3411	271	6	and	and	CCONJ
ap-3411	271	7	p.	p.	PROPN
ap-3411	271	8	winternitz	winternitz	PROPN
ap-3411	271	9	,	,	PUNCT
ap-3411	271	10	continuous	continuous	ADJ
ap-3411	271	11	symmetries	symmetry	NOUN
ap-3411	271	12	of	of	ADP
ap-3411	271	13	discrete	discrete	ADJ
ap-3411	271	14	equations	equation	NOUN
ap-3411	271	15	,	,	PUNCT
ap-3411	271	16	phys	phy	NOUN
ap-3411	271	17	.	.	PUNCT
ap-3411	272	1	lett	lett	PROPN
ap-3411	272	2	.	.	PUNCT
ap-3411	273	1	a	a	DET
ap-3411	273	2	152	152	NUM
ap-3411	273	3	(	(	PUNCT
ap-3411	273	4	1991	1991	NUM
ap-3411	273	5	)	)	PUNCT
ap-3411	273	6	335–338	335–338	NUM
ap-3411	273	7	,	,	PUNCT
ap-3411	273	8	doi:10.1016/0375	doi:10.1016/0375	ADJ
ap-3411	273	9	-	-	PUNCT
ap-3411	273	10	9601(91)90733	9601(91)90733	NUM
ap-3411	273	11	-	-	PUNCT
ap-3411	273	12	o	o	NOUN
ap-3411	274	1	[	[	X
ap-3411	274	2	23	23	NUM
ap-3411	274	3	]	]	X
ap-3411	274	4	d.	d.	PROPN
ap-3411	274	5	levi	levi	PROPN
ap-3411	274	6	and	and	CCONJ
ap-3411	274	7	r.	r.	PROPN
ap-3411	274	8	i.	i.	PROPN
ap-3411	274	9	yamilov	yamilov	PROPN
ap-3411	274	10	,	,	PUNCT
ap-3411	274	11	conditions	condition	NOUN
ap-3411	274	12	for	for	ADP
ap-3411	274	13	the	the	DET
ap-3411	274	14	existence	existence	NOUN
ap-3411	274	15	of	of	ADP
ap-3411	274	16	higher	high	ADJ
ap-3411	274	17	symmetries	symmetry	NOUN
ap-3411	274	18	of	of	ADP
ap-3411	274	19	evolutionary	evolutionary	ADJ
ap-3411	274	20	equations	equation	NOUN
ap-3411	274	21	on	on	ADP
ap-3411	274	22	the	the	DET
ap-3411	274	23	lattice	lattice	NOUN
ap-3411	274	24	,	,	PUNCT
ap-3411	274	25	j.	j.	PROPN
ap-3411	274	26	math	math	PROPN
ap-3411	274	27	.	.	PUNCT
ap-3411	275	1	phys	phy	NOUN
ap-3411	275	2	.	.	PUNCT
ap-3411	276	1	38	38	NUM
ap-3411	276	2	(	(	PUNCT
ap-3411	276	3	1997	1997	NUM
ap-3411	276	4	)	)	PUNCT
ap-3411	276	5	6648–6674	6648–6674	NOUN
ap-3411	276	6	,	,	PUNCT
ap-3411	276	7	doi:10.1063/1.532230	doi:10.1063/1.532230	PROPN
ap-3411	277	1	[	[	X
ap-3411	277	2	24	24	NUM
ap-3411	277	3	]	]	PUNCT
ap-3411	277	4	s.	s.	PROPN
ap-3411	277	5	lie	lie	PROPN
ap-3411	277	6	,	,	PUNCT
ap-3411	277	7	über	über	PROPN
ap-3411	277	8	gruppen	gruppen	PROPN
ap-3411	277	9	von	von	PROPN
ap-3411	277	10	transformationen	transformationen	PROPN
ap-3411	277	11	,	,	PUNCT
ap-3411	277	12	gottinger	gottinger	ADP
ap-3411	277	13	nachrichten	nachrichten	NOUN
ap-3411	277	14	1874	1874	NUM
ap-3411	277	15	(	(	PUNCT
ap-3411	277	16	1874	1874	NUM
ap-3411	277	17	)	)	PUNCT
ap-3411	278	1	529–542	529–542	NUM
ap-3411	278	2	.	.	PUNCT
ap-3411	279	1	[	[	X
ap-3411	279	2	25	25	NUM
ap-3411	279	3	]	]	X
ap-3411	279	4	s.	s.	PROPN
ap-3411	279	5	lie	lie	PROPN
ap-3411	279	6	,	,	PUNCT
ap-3411	279	7	articles	article	NOUN
ap-3411	279	8	published	publish	VERB
ap-3411	279	9	mostly	mostly	ADV
ap-3411	279	10	in	in	ADP
ap-3411	279	11	the	the	DET
ap-3411	279	12	norwegian	norwegian	ADJ
ap-3411	279	13	archive	archive	NOUN
ap-3411	279	14	and	and	CCONJ
ap-3411	279	15	reproduced	reproduce	VERB
ap-3411	279	16	in	in	ADP
ap-3411	279	17	the	the	DET
ap-3411	279	18	essential	essential	ADJ
ap-3411	279	19	part	part	NOUN
ap-3411	279	20	in	in	ADP
ap-3411	279	21	:	:	PUNCT
ap-3411	279	22	allgemeine	allgemeine	PROPN
ap-3411	279	23	theorie	theorie	PROPN
ap-3411	279	24	der	der	PROPN
ap-3411	279	25	partiellen	partiellen	PROPN
ap-3411	279	26	differentialgleichungen	differentialgleichungen	PROPN
ap-3411	279	27	erster	erster	NOUN
ap-3411	279	28	ordnung	ordnung	ADJ
ap-3411	279	29	math	math	NOUN
ap-3411	279	30	.	.	PUNCT
ap-3411	280	1	ann	ann	PROPN
ap-3411	280	2	.	.	PROPN
ap-3411	281	1	9	9	NUM
ap-3411	281	2	(	(	PUNCT
ap-3411	281	3	1875	1875	NUM
ap-3411	281	4	)	)	PUNCT
ap-3411	282	1	245–296	245–296	NUM
ap-3411	282	2	,	,	PUNCT
ap-3411	282	3	doi:10.1007	doi:10.1007	NOUN
ap-3411	282	4	/	/	SYM
ap-3411	282	5	bf01443377	bf01443377	NOUN
ap-3411	282	6	;	;	PUNCT
ap-3411	282	7	theorie	theorie	PROPN
ap-3411	282	8	der	der	PROPN
ap-3411	282	9	transformationsgruppen	transformationsgruppen	VERB
ap-3411	282	10	i	i	PROPN
ap-3411	282	11	,	,	PUNCT
ap-3411	282	12	math	math	NOUN
ap-3411	282	13	.	.	PUNCT
ap-3411	283	1	ann	ann	PROPN
ap-3411	283	2	.	.	PROPN
ap-3411	284	1	16	16	NUM
ap-3411	284	2	(	(	PUNCT
ap-3411	284	3	1880	1880	NUM
ap-3411	284	4	)	)	PUNCT
ap-3411	284	5	,	,	PUNCT
ap-3411	284	6	441–528	441–528	NUM
ap-3411	284	7	,	,	PUNCT
ap-3411	284	8	doi:10.1007	doi:10.1007	NOUN
ap-3411	284	9	/	/	SYM
ap-3411	284	10	bf01446218	bf01446218	NOUN
ap-3411	284	11	;	;	PUNCT
ap-3411	284	12	allgemeine	allgemeine	PROPN
ap-3411	284	13	untersuchungen	untersuchungen	PROPN
ap-3411	284	14	über	über	PROPN
ap-3411	284	15	differentialgleichungen	differentialgleichungen	PROPN
ap-3411	284	16	,	,	PUNCT
ap-3411	284	17	die	die	VERB
ap-3411	284	18	eine	eine	PROPN
ap-3411	284	19	continuirliche	continuirliche	PROPN
ap-3411	284	20	,	,	PUNCT
ap-3411	284	21	endliche	endliche	NOUN
ap-3411	284	22	gruppe	gruppe	PROPN
ap-3411	284	23	gestatten	gestatten	VERB
ap-3411	284	24	,	,	PUNCT
ap-3411	284	25	math	math	NOUN
ap-3411	284	26	.	.	PUNCT
ap-3411	285	1	ann	ann	PROPN
ap-3411	285	2	.	.	PROPN
ap-3411	286	1	25	25	NUM
ap-3411	286	2	(	(	PUNCT
ap-3411	286	3	1885	1885	NUM
ap-3411	286	4	)	)	PUNCT
ap-3411	287	1	71–151	71–151	NUM
ap-3411	287	2	,	,	PUNCT
ap-3411	287	3	doi:10.1007	doi:10.1007	NOUN
ap-3411	287	4	/	/	SYM
ap-3411	287	5	bf01446421	bf01446421	PROPN
ap-3411	287	6	;	;	PUNCT
ap-3411	287	7	classification	classification	NOUN
ap-3411	287	8	und	und	NOUN
ap-3411	287	9	integration	integration	NOUN
ap-3411	287	10	von	von	PROPN
ap-3411	287	11	gewöhnlichen	gewöhnlichen	PROPN
ap-3411	287	12	differentialgleichungen	differentialgleichungen	PROPN
ap-3411	287	13	zwischen	zwischen	PROPN
ap-3411	287	14	xy	xy	PROPN
ap-3411	287	15	,	,	PUNCT
ap-3411	287	16	die	die	VERB
ap-3411	287	17	eine	eine	PROPN
ap-3411	287	18	gruppe	gruppe	PROPN
ap-3411	287	19	von	von	PROPN
ap-3411	287	20	transformationen	transformationen	PROPN
ap-3411	287	21	gestatten	gestatten	NOUN
ap-3411	287	22	,	,	PUNCT
ap-3411	287	23	math	math	NOUN
ap-3411	287	24	.	.	PUNCT
ap-3411	288	1	ann	ann	PROPN
ap-3411	288	2	.	.	PROPN
ap-3411	289	1	32	32	NUM
ap-3411	289	2	(	(	PUNCT
ap-3411	289	3	1888	1888	NUM
ap-3411	289	4	)	)	PUNCT
ap-3411	290	1	213–281	213–281	NUM
ap-3411	290	2	,	,	PUNCT
ap-3411	290	3	doi:10.1007	doi:10.1007	NOUN
ap-3411	290	4	/	/	SYM
ap-3411	290	5	bf01444068	bf01444068	PROPN
ap-3411	291	1	[	[	X
ap-3411	291	2	26	26	NUM
ap-3411	291	3	]	]	X
ap-3411	291	4	l.	l.	PROPN
ap-3411	291	5	martina	martina	PROPN
ap-3411	291	6	and	and	CCONJ
ap-3411	291	7	p.	p.	PROPN
ap-3411	291	8	winternitz	winternitz	PROPN
ap-3411	291	9	,	,	PUNCT
ap-3411	291	10	analysis	analysis	NOUN
ap-3411	291	11	and	and	CCONJ
ap-3411	291	12	applications	application	NOUN
ap-3411	291	13	of	of	ADP
ap-3411	291	14	the	the	DET
ap-3411	291	15	symmetry	symmetry	NOUN
ap-3411	291	16	group	group	NOUN
ap-3411	291	17	of	of	ADP
ap-3411	291	18	the	the	DET
ap-3411	291	19	multidimensional	multidimensional	ADJ
ap-3411	291	20	three	three	NUM
ap-3411	291	21	wave	wave	NOUN
ap-3411	291	22	resonant	resonant	NOUN
ap-3411	291	23	interaction	interaction	NOUN
ap-3411	291	24	problem	problem	NOUN
ap-3411	291	25	,	,	PUNCT
ap-3411	291	26	ann	ann	PROPN
ap-3411	291	27	.	.	PUNCT
ap-3411	291	28	physics	physics	PROPN
ap-3411	291	29	196	196	NUM
ap-3411	291	30	(	(	PUNCT
ap-3411	291	31	1989	1989	NUM
ap-3411	291	32	)	)	PUNCT
ap-3411	291	33	231–277	231–277	NUM
ap-3411	291	34	,	,	PUNCT
ap-3411	291	35	doi:10.1016/0003	doi:10.1016/0003	NOUN
ap-3411	291	36	-	-	PUNCT
ap-3411	291	37	4916(89)90178	4916(89)90178	NUM
ap-3411	291	38	-	-	SYM
ap-3411	291	39	4	4	NUM
ap-3411	291	40	200	200	NUM
ap-3411	291	41	http://arxiv.org/abs/1103.5139v1	http://arxiv.org/abs/1103.5139v1	SYM
ap-3411	291	42	http://dx.doi.org/10.1007/bf02557219	http://dx.doi.org/10.1007/bf02557219	ADJ
ap-3411	291	43	http://dx.doi.org/10.1007/978-1-4757-4307-4	http://dx.doi.org/10.1007/978-1-4757-4307-4	ADJ
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ap-3411	291	46	http://dx.doi.org/10.1063/1.528173	http://dx.doi.org/10.1063/1.528173	PROPN
ap-3411	291	47	http://dx.doi.org/10.1103/physrevlett.55.2111	http://dx.doi.org/10.1103/physrevlett.55.2111	PROPN
ap-3411	291	48	http://dx.doi.org/10.1063/1.527129	http://dx.doi.org/10.1063/1.527129	PROPN
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ap-3411	291	50	http://dx.doi.org/10.1088/0305-4470/33/46/304	http://dx.doi.org/10.1088/0305-4470/33/46/304	PROPN
ap-3411	291	51	http://arxiv.org/abs/1510.01527	http://arxiv.org/abs/1510.01527	PROPN
ap-3411	291	52	http://arxiv.org/abs/1510.07175	http://arxiv.org/abs/1510.07175	PROPN
ap-3411	291	53	http://dx.doi.org/10.2991/jnmp.2005.12.s2.16	http://dx.doi.org/10.2991/jnmp.2005.12.s2.16	PROPN
ap-3411	291	54	http://dx.doi.org/10.1143/jpsj.46.312	http://dx.doi.org/10.1143/jpsj.46.312	PROPN
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ap-3411	291	56	http://dx.doi.org/10.1007/978-94-009-5243-0	http://dx.doi.org/10.1007/978-94-009-5243-0	PROPN
ap-3411	291	57	http://dx.doi.org/10.1215/s0012-7094-97-08916-x	http://dx.doi.org/10.1215/s0012-7094-97-08916-x	PROPN
ap-3411	291	58	http://dx.doi.org/10.1088/1751-8113/48/2/025204	http://dx.doi.org/10.1088/1751-8113/48/2/025204	PROPN
ap-3411	291	59	http://arxiv.org/abs/1407.4043	http://arxiv.org/abs/1407.4043	NOUN
ap-3411	291	60	http://dx.doi.org/10.3842/sigma.2015.080	http://dx.doi.org/10.3842/sigma.2015.080	NOUN
ap-3411	291	61	http://arxiv.org/abs/1504.01953v2	http://arxiv.org/abs/1504.01953v2	PROPN
ap-3411	291	62	http://dx.doi.org/10.1088/1751-8113/46/32/325204	http://dx.doi.org/10.1088/1751-8113/46/32/325204	NOUN
ap-3411	292	1	http://dx.doi.org/10.1016/0375-9601(91)90733-o	http://dx.doi.org/10.1016/0375-9601(91)90733-o	NOUN
ap-3411	292	2	http://dx.doi.org/10.1063/1.532230	http://dx.doi.org/10.1063/1.532230	X
ap-3411	292	3	http://dx.doi.org/10.1007/bf01443377	http://dx.doi.org/10.1007/bf01443377	PUNCT
ap-3411	292	4	http://dx.doi.org/10.1007/bf01446218	http://dx.doi.org/10.1007/bf01446218	INTJ
ap-3411	293	1	http://dx.doi.org/10.1007/bf01446421	http://dx.doi.org/10.1007/bf01446421	NOUN
ap-3411	293	2	http://dx.doi.org/10.1007/bf01444068	http://dx.doi.org/10.1007/bf01444068	INTJ
ap-3411	293	3	http://dx.doi.org/10.1016/0003-4916(89)90178-4	http://dx.doi.org/10.1016/0003-4916(89)90178-4	X
ap-3411	293	4	vol	vol	NOUN
ap-3411	293	5	.	.	PUNCT
ap-3411	294	1	56	56	NUM
ap-3411	294	2	no	no	NOUN
ap-3411	294	3	.	.	PUNCT
ap-3411	295	1	3/2016	3/2016	NUM
ap-3411	295	2	on	on	ADP
ap-3411	295	3	pde	pde	NOUN
ap-3411	295	4	and	and	CCONJ
ap-3411	295	5	p∆e	p∆e	NOUN
ap-3411	295	6	with	with	ADP
ap-3411	295	7	symmetries	symmetry	NOUN
ap-3411	295	8	depending	depend	VERB
ap-3411	295	9	on	on	ADP
ap-3411	295	10	arbitrary	arbitrary	ADJ
ap-3411	295	11	functions	function	NOUN
ap-3411	295	12	[	[	X
ap-3411	295	13	27	27	NUM
ap-3411	295	14	]	]	X
ap-3411	295	15	p.	p.	PROPN
ap-3411	295	16	medolaghi	medolaghi	PROPN
ap-3411	295	17	,	,	PUNCT
ap-3411	295	18	classificazione	classificazione	PROPN
ap-3411	295	19	delle	delle	NOUN
ap-3411	295	20	equazioni	equazioni	PROPN
ap-3411	295	21	alle	alle	PROPN
ap-3411	295	22	derivate	derivate	PROPN
ap-3411	295	23	parziali	parziali	PROPN
ap-3411	295	24	del	del	PROPN
ap-3411	295	25	secondo	secondo	PROPN
ap-3411	295	26	ordine	ordine	PROPN
ap-3411	295	27	,	,	PUNCT
ap-3411	295	28	che	che	PROPN
ap-3411	295	29	ammettono	ammettono	PROPN
ap-3411	295	30	un	un	PROPN
ap-3411	295	31	gruppo	gruppo	PROPN
ap-3411	295	32	infinito	infinito	PROPN
ap-3411	295	33	di	di	PROPN
ap-3411	295	34	trasformazioni	trasformazioni	PROPN
ap-3411	295	35	puntuali	puntuali	PROPN
ap-3411	295	36	,	,	PUNCT
ap-3411	295	37	ann	ann	PROPN
ap-3411	295	38	.	.	PROPN
ap-3411	295	39	mat	mat	PROPN
ap-3411	295	40	.	.	PUNCT
ap-3411	295	41	pura	pura	NOUN
ap-3411	295	42	appl	appl	NOUN
ap-3411	295	43	.	.	PROPN
ap-3411	295	44	1	1	NUM
ap-3411	295	45	(	(	PUNCT
ap-3411	295	46	1898	1898	NUM
ap-3411	295	47	)	)	PUNCT
ap-3411	296	1	229–263	229–263	NUM
ap-3411	296	2	,	,	PUNCT
ap-3411	296	3	doi:10.1007	doi:10.1007	NOUN
ap-3411	296	4	/	/	SYM
ap-3411	296	5	bf02419192	bf02419192	PROPN
ap-3411	297	1	[	[	X
ap-3411	297	2	28	28	NUM
ap-3411	297	3	]	]	X
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ap-3411	297	5	j.	j.	PROPN
ap-3411	297	6	olver	olver	PROPN
ap-3411	297	7	,	,	PUNCT
ap-3411	297	8	applications	application	NOUN
ap-3411	297	9	of	of	ADP
ap-3411	297	10	lie	lie	NOUN
ap-3411	297	11	groups	group	NOUN
ap-3411	297	12	to	to	ADP
ap-3411	297	13	differeial	differeial	ADJ
ap-3411	297	14	equations	equation	NOUN
ap-3411	297	15	,	,	PUNCT
ap-3411	297	16	(	(	PUNCT
ap-3411	297	17	second	second	ADJ
ap-3411	297	18	edition	edition	NOUN
ap-3411	297	19	)	)	PUNCT
ap-3411	297	20	,	,	PUNCT
ap-3411	297	21	springer	springer	NOUN
ap-3411	297	22	,	,	PUNCT
ap-3411	297	23	new	new	PROPN
ap-3411	297	24	york	york	PROPN
ap-3411	297	25	,	,	PUNCT
ap-3411	297	26	1993	1993	NUM
ap-3411	297	27	,	,	PUNCT
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ap-3411	297	29	-	-	PUNCT
ap-3411	297	30	1	1	NUM
ap-3411	297	31	-	-	PUNCT
ap-3411	297	32	4612	4612	NUM
ap-3411	297	33	-	-	SYM
ap-3411	297	34	4350	4350	NUM
ap-3411	297	35	-	-	SYM
ap-3411	297	36	2	2	NUM
ap-3411	297	37	[	[	X
ap-3411	297	38	29	29	NUM
ap-3411	297	39	]	]	X
ap-3411	297	40	f.	f.	PROPN
ap-3411	297	41	schwarz	schwarz	PROPN
ap-3411	297	42	,	,	PUNCT
ap-3411	297	43	symmetries	symmetry	NOUN
ap-3411	297	44	of	of	ADP
ap-3411	297	45	the	the	DET
ap-3411	297	46	two	two	NUM
ap-3411	297	47	-	-	PUNCT
ap-3411	297	48	dimensional	dimensional	ADJ
ap-3411	297	49	korteweg	korteweg	NOUN
ap-3411	297	50	-	-	PUNCT
ap-3411	297	51	devries	devries	PROPN
ap-3411	297	52	equation	equation	NOUN
ap-3411	297	53	,	,	PUNCT
ap-3411	297	54	j.	j.	PROPN
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ap-3411	298	2	.	.	PUNCT
ap-3411	299	1	jpn	jpn	PROPN
ap-3411	299	2	.	.	PROPN
ap-3411	300	1	51	51	NUM
ap-3411	300	2	(	(	PUNCT
ap-3411	300	3	1982	1982	NUM
ap-3411	300	4	)	)	PUNCT
ap-3411	300	5	2387–2389	2387–2389	NUM
ap-3411	300	6	,	,	PUNCT
ap-3411	300	7	doi:10.1143	doi:10.1143	NOUN
ap-3411	300	8	/	/	SYM
ap-3411	300	9	jpsj.51.2387	jpsj.51.2387	NOUN
ap-3411	301	1	[	[	X
ap-3411	301	2	30	30	NUM
ap-3411	301	3	]	]	X
ap-3411	301	4	c.	c.	NOUN
ap-3411	301	5	scimiterna	scimiterna	PROPN
ap-3411	301	6	and	and	CCONJ
ap-3411	301	7	d.	d.	PROPN
ap-3411	301	8	levi	levi	PROPN
ap-3411	301	9	,	,	PUNCT
ap-3411	301	10	classification	classification	NOUN
ap-3411	301	11	of	of	ADP
ap-3411	301	12	discrete	discrete	ADJ
ap-3411	301	13	equations	equation	NOUN
ap-3411	301	14	linearizable	linearizable	ADJ
ap-3411	301	15	by	by	ADP
ap-3411	301	16	point	point	NOUN
ap-3411	301	17	transformation	transformation	NOUN
ap-3411	301	18	on	on	ADP
ap-3411	301	19	a	a	DET
ap-3411	301	20	square	square	ADJ
ap-3411	301	21	lattice	lattice	NOUN
ap-3411	301	22	,	,	PUNCT
ap-3411	301	23	front	front	NOUN
ap-3411	301	24	.	.	PUNCT
ap-3411	301	25	math	math	NOUN
ap-3411	301	26	.	.	PUNCT
ap-3411	302	1	china	china	PROPN
ap-3411	302	2	8	8	NUM
ap-3411	302	3	(	(	PUNCT
ap-3411	302	4	2013	2013	NUM
ap-3411	302	5	)	)	PUNCT
ap-3411	302	6	1067–1076	1067–1076	NUM
ap-3411	302	7	,	,	PUNCT
ap-3411	302	8	doi:10.1007	doi:10.1007	ADJ
ap-3411	302	9	/	/	SYM
ap-3411	302	10	s11464	s11464	PROPN
ap-3411	302	11	-	-	PUNCT
ap-3411	302	12	013	013	NUM
ap-3411	302	13	-	-	PUNCT
ap-3411	302	14	0280	0280	NUM
ap-3411	302	15	-	-	SYM
ap-3411	302	16	3	3	NUM
ap-3411	302	17	[	[	X
ap-3411	302	18	31	31	NUM
ap-3411	302	19	]	]	PUNCT
ap-3411	302	20	m.	m.	PROPN
ap-3411	302	21	b.	b.	PROPN
ap-3411	302	22	sheftel	sheftel	PROPN
ap-3411	302	23	,	,	PUNCT
ap-3411	302	24	symmetry	symmetry	NOUN
ap-3411	302	25	group	group	NOUN
ap-3411	302	26	analysis	analysis	NOUN
ap-3411	302	27	and	and	CCONJ
ap-3411	302	28	invariant	invariant	ADJ
ap-3411	302	29	solutions	solution	NOUN
ap-3411	302	30	of	of	ADP
ap-3411	302	31	hydrodynamic	hydrodynamic	ADJ
ap-3411	302	32	-	-	PUNCT
ap-3411	302	33	type	type	NOUN
ap-3411	302	34	systems	system	NOUN
ap-3411	302	35	,	,	PUNCT
ap-3411	302	36	int	int	NOUN
ap-3411	302	37	.	.	PUNCT
ap-3411	303	1	j.	j.	PROPN
ap-3411	303	2	math	math	PROPN
ap-3411	303	3	.	.	PUNCT
ap-3411	304	1	math	math	NOUN
ap-3411	304	2	.	.	PUNCT
ap-3411	305	1	sci	sci	PROPN
ap-3411	305	2	.	.	PROPN
ap-3411	305	3	2004	2004	NUM
ap-3411	305	4	(	(	PUNCT
ap-3411	305	5	2004	2004	NUM
ap-3411	305	6	)	)	PUNCT
ap-3411	305	7	,	,	PUNCT
ap-3411	305	8	487–534	487–534	NUM
ap-3411	305	9	,	,	PUNCT
ap-3411	305	10	doi:10.1155	doi:10.1155	NOUN
ap-3411	305	11	/	/	SYM
ap-3411	305	12	s0161171204206147	s0161171204206147	PROPN
ap-3411	306	1	[	[	X
ap-3411	306	2	32	32	NUM
ap-3411	306	3	]	]	PUNCT
ap-3411	306	4	s.	s.	PROPN
ap-3411	306	5	ya	ya	PROPN
ap-3411	306	6	.	.	PROPN
ap-3411	306	7	startsev	startsev	PROPN
ap-3411	306	8	,	,	PUNCT
ap-3411	306	9	darboux	darboux	VERB
ap-3411	306	10	integrable	integrable	ADJ
ap-3411	306	11	discrete	discrete	ADJ
ap-3411	306	12	equations	equation	NOUN
ap-3411	306	13	possessing	possess	VERB
ap-3411	306	14	an	an	DET
ap-3411	306	15	autonomous	autonomous	ADJ
ap-3411	306	16	first	first	ADJ
ap-3411	306	17	-	-	PUNCT
ap-3411	306	18	order	order	NOUN
ap-3411	306	19	integral	integral	ADJ
ap-3411	306	20	,	,	PUNCT
ap-3411	306	21	j.	j.	PROPN
ap-3411	306	22	phys	phys	PROPN
ap-3411	306	23	.	.	PUNCT
ap-3411	307	1	a	a	DET
ap-3411	307	2	:	:	PUNCT
ap-3411	307	3	math	math	NOUN
ap-3411	307	4	.	.	PUNCT
ap-3411	308	1	theor	theor	PROPN
ap-3411	308	2	.	.	PUNCT
ap-3411	309	1	47	47	NUM
ap-3411	309	2	(	(	PUNCT
ap-3411	309	3	2014	2014	NUM
ap-3411	309	4	)	)	PUNCT
ap-3411	309	5	105204	105204	NUM
ap-3411	309	6	(	(	PUNCT
ap-3411	309	7	16pp	16pp	NUM
ap-3411	309	8	)	)	PUNCT
ap-3411	309	9	,	,	PUNCT
ap-3411	309	10	doi:10.1088/1751	doi:10.1088/1751	NOUN
ap-3411	309	11	-	-	PUNCT
ap-3411	309	12	8113/47/10/105204	8113/47/10/105204	NUM
ap-3411	309	13	[	[	X
ap-3411	309	14	33	33	NUM
ap-3411	309	15	]	]	PUNCT
ap-3411	309	16	s.	s.	PROPN
ap-3411	309	17	ya	ya	PROPN
ap-3411	309	18	.	.	PROPN
ap-3411	309	19	startsev	startsev	PROPN
ap-3411	309	20	,	,	PUNCT
ap-3411	309	21	non	non	ADJ
ap-3411	309	22	-	-	ADJ
ap-3411	309	23	point	point	ADJ
ap-3411	309	24	invertible	invertible	ADJ
ap-3411	309	25	transformations	transformation	NOUN
ap-3411	309	26	and	and	CCONJ
ap-3411	309	27	integrability	integrability	NOUN
ap-3411	309	28	of	of	ADP
ap-3411	309	29	partial	partial	ADJ
ap-3411	309	30	difference	difference	NOUN
ap-3411	309	31	equations	equation	NOUN
ap-3411	309	32	,	,	PUNCT
ap-3411	309	33	sigma	sigma	NOUN
ap-3411	309	34	10	10	NUM
ap-3411	309	35	(	(	PUNCT
ap-3411	309	36	2014	2014	NUM
ap-3411	309	37	)	)	PUNCT
ap-3411	309	38	066	066	NUM
ap-3411	309	39	(	(	PUNCT
ap-3411	309	40	13	13	NUM
ap-3411	309	41	pp	pp	NUM
ap-3411	309	42	.	.	PUNCT
ap-3411	309	43	)	)	PUNCT
ap-3411	310	1	,	,	PUNCT
ap-3411	310	2	doi:10.3842	doi:10.3842	PROPN
ap-3411	310	3	/	/	SYM
ap-3411	310	4	sigma.2014.066	sigma.2014.066	PROPN
ap-3411	310	5	[	[	X
ap-3411	310	6	34	34	NUM
ap-3411	310	7	]	]	PUNCT
ap-3411	310	8	s.	s.	PROPN
ap-3411	310	9	p.	p.	PROPN
ap-3411	310	10	tsarev	tsarev	PROPN
ap-3411	310	11	,	,	PUNCT
ap-3411	310	12	factoring	factor	VERB
ap-3411	310	13	linear	linear	ADJ
ap-3411	310	14	partial	partial	ADJ
ap-3411	310	15	differential	differential	NOUN
ap-3411	310	16	operators	operator	NOUN
ap-3411	310	17	and	and	CCONJ
ap-3411	310	18	the	the	DET
ap-3411	310	19	darboux	darboux	VERB
ap-3411	310	20	method	method	NOUN
ap-3411	310	21	for	for	ADP
ap-3411	310	22	integrating	integrate	VERB
ap-3411	310	23	nonlinear	nonlinear	ADJ
ap-3411	310	24	partial	partial	ADJ
ap-3411	310	25	differential	differential	NOUN
ap-3411	310	26	equations	equation	NOUN
ap-3411	310	27	,	,	PUNCT
ap-3411	310	28	teoret	teoret	PROPN
ap-3411	310	29	.	.	PUNCT
ap-3411	311	1	mat	mat	PROPN
ap-3411	311	2	.	.	PUNCT
ap-3411	311	3	fiz	fiz	PROPN
ap-3411	311	4	.	.	PUNCT
ap-3411	312	1	122	122	NUM
ap-3411	312	2	(	(	PUNCT
ap-3411	312	3	2000	2000	NUM
ap-3411	312	4	)	)	PUNCT
ap-3411	312	5	,	,	PUNCT
ap-3411	313	1	144–160	144–160	NUM
ap-3411	313	2	;	;	PUNCT
ap-3411	313	3	english	english	PROPN
ap-3411	313	4	transl	transl	PROPN
ap-3411	313	5	.	.	PUNCT
ap-3411	313	6	,	,	PUNCT
ap-3411	313	7	theoret	theoret	PROPN
ap-3411	313	8	.	.	PUNCT
ap-3411	314	1	math	math	NOUN
ap-3411	314	2	.	.	PUNCT
ap-3411	315	1	phys	phy	NOUN
ap-3411	315	2	.	.	PUNCT
ap-3411	316	1	122	122	NUM
ap-3411	316	2	(	(	PUNCT
ap-3411	316	3	2000	2000	NUM
ap-3411	316	4	)	)	PUNCT
ap-3411	316	5	,	,	PUNCT
ap-3411	316	6	121–133	121–133	NUM
ap-3411	316	7	,	,	PUNCT
ap-3411	316	8	doi:10.1007	doi:10.1007	NOUN
ap-3411	316	9	/	/	SYM
ap-3411	316	10	bf02551175	bf02551175	PROPN
ap-3411	317	1	[	[	X
ap-3411	317	2	35	35	NUM
ap-3411	317	3	]	]	X
ap-3411	317	4	v.	v.	PROPN
ap-3411	317	5	l.	l.	PROPN
ap-3411	317	6	vereshchagin	vereshchagin	PROPN
ap-3411	317	7	,	,	PUNCT
ap-3411	317	8	darboux	darboux	VERB
ap-3411	317	9	-	-	PUNCT
ap-3411	317	10	integrable	integrable	ADJ
ap-3411	317	11	discrete	discrete	ADJ
ap-3411	317	12	systems	system	NOUN
ap-3411	317	13	,	,	PUNCT
ap-3411	317	14	theor	theor	PROPN
ap-3411	317	15	.	.	PUNCT
ap-3411	317	16	math	math	NOUN
ap-3411	317	17	.	.	PUNCT
ap-3411	318	1	phys	phy	NOUN
ap-3411	318	2	.	.	PUNCT
ap-3411	318	3	,	,	PUNCT
ap-3411	318	4	156	156	NUM
ap-3411	318	5	(	(	PUNCT
ap-3411	318	6	2008	2008	NUM
ap-3411	318	7	)	)	PUNCT
ap-3411	318	8	1142–1153	1142–1153	NUM
ap-3411	318	9	,	,	PUNCT
ap-3411	318	10	doi:10.1007	doi:10.1007	ADJ
ap-3411	318	11	/	/	SYM
ap-3411	318	12	s11232	s11232	NOUN
ap-3411	318	13	-	-	PUNCT
ap-3411	318	14	008	008	NUM
ap-3411	318	15	-	-	PUNCT
ap-3411	318	16	0084	0084	NUM
ap-3411	318	17	-	-	PUNCT
ap-3411	318	18	x	x	SYM
ap-3411	319	1	[	[	X
ap-3411	319	2	36	36	NUM
ap-3411	319	3	]	]	PUNCT
ap-3411	319	4	r.	r.	PROPN
ap-3411	319	5	i.	i.	PROPN
ap-3411	319	6	yamilov	yamilov	PROPN
ap-3411	319	7	,	,	PUNCT
ap-3411	319	8	symmetries	symmetry	NOUN
ap-3411	319	9	as	as	ADP
ap-3411	319	10	integrability	integrability	NOUN
ap-3411	319	11	criteria	criterion	NOUN
ap-3411	319	12	for	for	ADP
ap-3411	319	13	differential	differential	ADJ
ap-3411	319	14	difference	difference	NOUN
ap-3411	319	15	equations	equation	NOUN
ap-3411	319	16	,	,	PUNCT
ap-3411	319	17	j.	j.	PROPN
ap-3411	319	18	phys	phys	PROPN
ap-3411	319	19	.	.	PUNCT
ap-3411	320	1	a	a	DET
ap-3411	320	2	:	:	PUNCT
ap-3411	320	3	math	math	NOUN
ap-3411	320	4	.	.	PUNCT
ap-3411	321	1	gen	gen	PROPN
ap-3411	321	2	.	.	PROPN
ap-3411	321	3	39	39	NUM
ap-3411	321	4	(	(	PUNCT
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ap-3411	321	6	)	)	PUNCT
ap-3411	321	7	r541	r541	PROPN
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ap-3411	321	9	r623	r623	NUM
ap-3411	321	10	,	,	PUNCT
ap-3411	321	11	doi:10.1088/0305	doi:10.1088/0305	ADJ
ap-3411	321	12	-	-	PUNCT
ap-3411	321	13	4470/39/45	4470/39/45	NUM
ap-3411	321	14	/	/	SYM
ap-3411	321	15	r01	r01	PROPN
ap-3411	321	16	[	[	X
ap-3411	321	17	37	37	NUM
ap-3411	321	18	]	]	PUNCT
ap-3411	321	19	a.	a.	NOUN
ap-3411	321	20	v.	v.	ADP
ap-3411	321	21	zhiber	zhiber	PROPN
ap-3411	321	22	and	and	CCONJ
ap-3411	321	23	a.	a.	PROPN
ap-3411	321	24	b.	b.	PROPN
ap-3411	321	25	shabat	shabat	PROPN
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ap-3411	321	27	klein	klein	PROPN
ap-3411	321	28	–	–	PUNCT
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ap-3411	321	31	with	with	ADP
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ap-3411	321	33	nontrivial	nontrivial	ADJ
ap-3411	321	34	group	group	NOUN
ap-3411	321	35	,	,	PUNCT
ap-3411	321	36	dokl	dokl	NOUN
ap-3411	321	37	.	.	PUNCT
ap-3411	322	1	akad	akad	PROPN
ap-3411	322	2	.	.	PUNCT
ap-3411	323	1	nauk	nauk	PROPN
ap-3411	323	2	sssr	sssr	NOUN
ap-3411	323	3	247	247	NUM
ap-3411	323	4	(	(	PUNCT
ap-3411	323	5	1979	1979	NUM
ap-3411	323	6	)	)	PUNCT
ap-3411	323	7	,	,	PUNCT
ap-3411	323	8	1103–1107	1103–1107	NUM
ap-3411	323	9	;	;	PUNCT
ap-3411	323	10	english	english	PROPN
ap-3411	323	11	transl	transl	PROPN
ap-3411	323	12	.	.	PUNCT
ap-3411	324	1	,	,	PUNCT
ap-3411	324	2	soviet	soviet	ADJ
ap-3411	324	3	phys	phy	NOUN
ap-3411	324	4	.	.	PUNCT
ap-3411	325	1	dokl	dokl	NOUN
ap-3411	325	2	.	.	PUNCT
ap-3411	326	1	24	24	NUM
ap-3411	326	2	(	(	PUNCT
ap-3411	326	3	1979	1979	NUM
ap-3411	326	4	)	)	PUNCT
ap-3411	326	5	,	,	PUNCT
ap-3411	326	6	607–609	607–609	NUM
ap-3411	326	7	.	.	PUNCT
ap-3411	327	1	[	[	X
ap-3411	327	2	38	38	NUM
ap-3411	327	3	]	]	PUNCT
ap-3411	327	4	a.	a.	NOUN
ap-3411	327	5	v.	v.	ADP
ap-3411	327	6	zhiber	zhiber	NOUN
ap-3411	327	7	and	and	CCONJ
ap-3411	327	8	v.	v.	PROPN
ap-3411	327	9	v.	v.	PROPN
ap-3411	327	10	sokolov	sokolov	PROPN
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ap-3411	327	13	integrable	integrable	ADJ
ap-3411	327	14	hyperbolic	hyperbolic	ADJ
ap-3411	327	15	equations	equation	NOUN
ap-3411	327	16	of	of	ADP
ap-3411	327	17	liouville	liouville	NOUN
ap-3411	327	18	type	type	NOUN
ap-3411	327	19	,	,	PUNCT
ap-3411	327	20	uspekhi	uspekhi	PROPN
ap-3411	327	21	mat	mat	PROPN
ap-3411	327	22	.	.	PUNCT
ap-3411	328	1	nauk	nauk	PROPN
ap-3411	328	2	56	56	NUM
ap-3411	328	3	(	(	PUNCT
ap-3411	328	4	2001	2001	NUM
ap-3411	328	5	)	)	PUNCT
ap-3411	328	6	63–106	63–106	NOUN
ap-3411	328	7	;	;	PUNCT
ap-3411	328	8	english	english	PROPN
ap-3411	328	9	transl	transl	PROPN
ap-3411	328	10	.	.	PUNCT
ap-3411	328	11	,	,	PUNCT
ap-3411	328	12	russian	russian	ADJ
ap-3411	328	13	math	math	NOUN
ap-3411	328	14	.	.	PUNCT
ap-3411	329	1	surveys	survey	NOUN
ap-3411	329	2	56	56	NUM
ap-3411	329	3	(	(	PUNCT
ap-3411	329	4	2001	2001	NUM
ap-3411	329	5	)	)	PUNCT
ap-3411	329	6	61–101	61–101	PROPN
ap-3411	329	7	,	,	PUNCT
ap-3411	329	8	doi:10.1070	doi:10.1070	ADP
ap-3411	329	9	/	/	SYM
ap-3411	329	10	rm2001v056n01abeh000357	rm2001v056n01abeh000357	PROPN
ap-3411	329	11	201	201	NUM
ap-3411	329	12	http://dx.doi.org/10.1007/bf02419192	http://dx.doi.org/10.1007/bf02419192	NOUN
ap-3411	329	13	http://dx.doi.org/10.1007/978-1-4612-4350-2	http://dx.doi.org/10.1007/978-1-4612-4350-2	VERB
ap-3411	329	14	http://dx.doi.org/10.1143/jpsj.51.2387	http://dx.doi.org/10.1143/jpsj.51.2387	PROPN
ap-3411	329	15	http://dx.doi.org/10.1007/s11464-013-0280-3	http://dx.doi.org/10.1007/s11464-013-0280-3	NOUN
ap-3411	329	16	http://dx.doi.org/10.1155/s0161171204206147	http://dx.doi.org/10.1155/s0161171204206147	NOUN
ap-3411	329	17	http://dx.doi.org/10.1088/1751-8113/47/10/105204	http://dx.doi.org/10.1088/1751-8113/47/10/105204	NOUN
ap-3411	329	18	http://dx.doi.org/10.3842/sigma.2014.066	http://dx.doi.org/10.3842/sigma.2014.066	NOUN
ap-3411	329	19	http://dx.doi.org/10.1007/bf02551175	http://dx.doi.org/10.1007/bf02551175	X
ap-3411	329	20	http://dx.doi.org/10.1007/s11232-008-0084-x	http://dx.doi.org/10.1007/s11232-008-0084-x	CCONJ
ap-3411	329	21	http://dx.doi.org/10.1088/0305-4470/39/45/r01	http://dx.doi.org/10.1088/0305-4470/39/45/r01	PROPN
ap-3411	329	22	http://dx.doi.org/10.1070/rm2001v056n01abeh000357	http://dx.doi.org/10.1070/rm2001v056n01abeh000357	PROPN
ap-3411	329	23	acta	acta	PROPN
ap-3411	329	24	polytechnica	polytechnica	PROPN
ap-3411	329	25	56(3):193–201	56(3):193–201	PROPN
ap-3411	329	26	,	,	PUNCT
ap-3411	329	27	2016	2016	NUM
ap-3411	329	28	1	1	NUM
ap-3411	329	29	introduction	introduction	NOUN
ap-3411	329	30	2	2	NUM
ap-3411	329	31	factorizable	factorizable	NOUN
ap-3411	329	32	differential	differential	NOUN
ap-3411	329	33	operators	operator	NOUN
ap-3411	329	34	,	,	PUNCT
ap-3411	329	35	darboux	darboux	VERB
ap-3411	329	36	integrable	integrable	ADJ
ap-3411	329	37	equations	equation	NOUN
ap-3411	329	38	and	and	CCONJ
ap-3411	329	39	symmetries	symmetry	NOUN
ap-3411	329	40	depending	depend	VERB
ap-3411	329	41	on	on	ADP
ap-3411	329	42	arbitrary	arbitrary	ADJ
ap-3411	329	43	functions	function	NOUN
ap-3411	329	44	.	.	PUNCT
ap-3411	330	1	3	3	NUM
ap-3411	330	2	discrete	discrete	ADJ
ap-3411	330	3	equations	equation	NOUN
ap-3411	330	4	with	with	ADP
ap-3411	330	5	generalized	generalized	ADJ
ap-3411	330	6	symmetries	symmetry	NOUN
ap-3411	330	7	depending	depend	VERB
ap-3411	330	8	on	on	ADP
ap-3411	330	9	an	an	DET
ap-3411	330	10	arbitrary	arbitrary	ADJ
ap-3411	330	11	function	function	NOUN
ap-3411	330	12	.	.	PUNCT
ap-3411	331	1	3.1	3.1	NUM
ap-3411	331	2	the	the	DET
ap-3411	331	3	discrete	discrete	ADJ
ap-3411	331	4	algebraic	algebraic	ADJ
ap-3411	331	5	liouville	liouville	NOUN
ap-3411	331	6	equations	equation	NOUN
ap-3411	331	7	4	4	NUM
ap-3411	331	8	conclusive	conclusive	ADJ
ap-3411	331	9	remarks	remark	NOUN
ap-3411	331	10	acknowledgements	acknowledgement	NOUN
ap-3411	331	11	references	reference	NOUN