id	sid	tid	token	lemma	pos
ap-3483	1	1	acta	acta	PROPN
ap-3483	1	2	polytechnica	polytechnica	PROPN
ap-3483	1	3	doi:10.14311	doi:10.14311	PROPN
ap-3483	1	4	/	/	SYM
ap-3483	1	5	ap.2016.56.0180	ap.2016.56.0180	PROPN
ap-3483	1	6	acta	acta	PROPN
ap-3483	1	7	polytechnica	polytechnica	PROPN
ap-3483	1	8	56(3):180–192	56(3):180–192	PROPN
ap-3483	1	9	,	,	PUNCT
ap-3483	1	10	2016	2016	NUM
ap-3483	1	11	©	©	PROPN
ap-3483	1	12	czech	czech	PROPN
ap-3483	1	13	technical	technical	PROPN
ap-3483	1	14	university	university	PROPN
ap-3483	1	15	in	in	ADP
ap-3483	1	16	prague	prague	PROPN
ap-3483	1	17	,	,	PUNCT
ap-3483	1	18	2016	2016	NUM
ap-3483	1	19	available	available	ADJ
ap-3483	1	20	online	online	ADV
ap-3483	1	21	at	at	ADP
ap-3483	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3483	1	23	on	on	ADP
ap-3483	1	24	immersion	immersion	NOUN
ap-3483	1	25	formulas	formula	NOUN
ap-3483	1	26	for	for	ADP
ap-3483	1	27	soliton	soliton	NOUN
ap-3483	1	28	surfaces	surface	NOUN
ap-3483	1	29	alfred	alfred	PROPN
ap-3483	1	30	michel	michel	PROPN
ap-3483	1	31	grundlanda	grundlanda	PROPN
ap-3483	1	32	,	,	PUNCT
ap-3483	1	33	b,∗	b,∗	PROPN
ap-3483	1	34	,	,	PUNCT
ap-3483	1	35	decio	decio	NOUN
ap-3483	1	36	levic	levic	PROPN
ap-3483	1	37	,	,	PUNCT
ap-3483	1	38	luigi	luigi	PROPN
ap-3483	1	39	martinad	martinad	PROPN
ap-3483	1	40	a	a	DET
ap-3483	1	41	centre	centre	NOUN
ap-3483	1	42	de	de	X
ap-3483	1	43	recherches	recherche	NOUN
ap-3483	1	44	mathématiques	mathématique	NOUN
ap-3483	1	45	,	,	PUNCT
ap-3483	1	46	université	université	PROPN
ap-3483	1	47	de	de	PROPN
ap-3483	1	48	montréal	montréal	PROPN
ap-3483	1	49	,	,	PUNCT
ap-3483	1	50	montréal	montréal	PROPN
ap-3483	1	51	cp	cp	PROPN
ap-3483	1	52	6128	6128	NUM
ap-3483	1	53	(	(	PUNCT
ap-3483	1	54	qc	qc	PROPN
ap-3483	1	55	)	)	PUNCT
ap-3483	1	56	h3c	h3c	PROPN
ap-3483	2	1	3j7	3j7	PROPN
ap-3483	2	2	,	,	PUNCT
ap-3483	2	3	canada	canada	PROPN
ap-3483	2	4	b	b	PROPN
ap-3483	2	5	department	department	PROPN
ap-3483	2	6	of	of	ADP
ap-3483	2	7	mathematics	mathematics	PROPN
ap-3483	2	8	and	and	CCONJ
ap-3483	2	9	computer	computer	NOUN
ap-3483	2	10	science	science	NOUN
ap-3483	2	11	,	,	PUNCT
ap-3483	2	12	université	université	PROPN
ap-3483	2	13	du	du	PROPN
ap-3483	2	14	québec	québec	PROPN
ap-3483	2	15	,	,	PUNCT
ap-3483	2	16	trois	trois	PROPN
ap-3483	2	17	-	-	PUNCT
ap-3483	2	18	rivières	rivières	PROPN
ap-3483	2	19	,	,	PUNCT
ap-3483	2	20	cp	cp	PROPN
ap-3483	2	21	500	500	NUM
ap-3483	2	22	(	(	PUNCT
ap-3483	2	23	qc	qc	PROPN
ap-3483	2	24	)	)	PUNCT
ap-3483	2	25	g9a	g9a	PROPN
ap-3483	2	26	5h7	5h7	NUM
ap-3483	2	27	,	,	PUNCT
ap-3483	2	28	canada	canada	PROPN
ap-3483	2	29	c	c	AUX
ap-3483	2	30	dipartimento	dipartimento	PROPN
ap-3483	2	31	di	di	X
ap-3483	2	32	mathematica	mathematica	PROPN
ap-3483	2	33	e	e	PROPN
ap-3483	2	34	fisica	fisica	PROPN
ap-3483	2	35	dell’università	dell’università	PROPN
ap-3483	2	36	roma	roma	PROPN
ap-3483	2	37	tre	tre	PROPN
ap-3483	2	38	,	,	PUNCT
ap-3483	2	39	sezione	sezione	PROPN
ap-3483	2	40	infn	infn	PROPN
ap-3483	2	41	di	di	PROPN
ap-3483	2	42	roma	roma	PROPN
ap-3483	2	43	tre	tre	PROPN
ap-3483	2	44	,	,	PUNCT
ap-3483	2	45	via	via	ADP
ap-3483	2	46	della	della	PROPN
ap-3483	2	47	vasca	vasca	PROPN
ap-3483	2	48	navale	navale	PROPN
ap-3483	2	49	84	84	NUM
ap-3483	2	50	,	,	PUNCT
ap-3483	2	51	roma	roma	PROPN
ap-3483	2	52	,	,	PUNCT
ap-3483	2	53	00146	00146	NUM
ap-3483	2	54	italy	italy	PROPN
ap-3483	2	55	d	d	X
ap-3483	2	56	dipartimento	dipartimento	ADP
ap-3483	2	57	di	di	X
ap-3483	2	58	mathematica	mathematica	PROPN
ap-3483	2	59	e	e	PROPN
ap-3483	2	60	fisica	fisica	PROPN
ap-3483	2	61	dell’università	dell’università	PROPN
ap-3483	2	62	del	del	PROPN
ap-3483	2	63	salento	salento	PROPN
ap-3483	2	64	,	,	PUNCT
ap-3483	2	65	sezione	sezione	PROPN
ap-3483	2	66	infn	infn	PROPN
ap-3483	2	67	di	di	PROPN
ap-3483	2	68	lecce	lecce	PROPN
ap-3483	2	69	,	,	PUNCT
ap-3483	2	70	via	via	ADP
ap-3483	2	71	arnesano	arnesano	PROPN
ap-3483	2	72	,	,	PUNCT
ap-3483	2	73	c.p	c.p	PROPN
ap-3483	2	74	.	.	PROPN
ap-3483	2	75	193	193	NUM
ap-3483	2	76	lecce	lecce	NOUN
ap-3483	2	77	,	,	PUNCT
ap-3483	2	78	73100	73100	NUM
ap-3483	2	79	italy	italy	PROPN
ap-3483	2	80	∗	∗	VERB
ap-3483	2	81	corresponding	correspond	VERB
ap-3483	2	82	author	author	NOUN
ap-3483	2	83	:	:	PUNCT
ap-3483	2	84	grundlan@crm.umontreal.ca	grundlan@crm.umontreal.ca	NOUN
ap-3483	2	85	abstract	abstract	NOUN
ap-3483	2	86	.	.	PUNCT
ap-3483	3	1	this	this	DET
ap-3483	3	2	paper	paper	NOUN
ap-3483	3	3	is	be	AUX
ap-3483	3	4	devoted	devote	VERB
ap-3483	3	5	to	to	ADP
ap-3483	3	6	a	a	DET
ap-3483	3	7	study	study	NOUN
ap-3483	3	8	of	of	ADP
ap-3483	3	9	the	the	DET
ap-3483	3	10	connections	connection	NOUN
ap-3483	3	11	between	between	ADP
ap-3483	3	12	three	three	NUM
ap-3483	3	13	different	different	ADJ
ap-3483	3	14	analytic	analytic	ADJ
ap-3483	3	15	descriptions	description	NOUN
ap-3483	3	16	for	for	ADP
ap-3483	3	17	the	the	DET
ap-3483	3	18	immersion	immersion	NOUN
ap-3483	3	19	functions	function	NOUN
ap-3483	3	20	of	of	ADP
ap-3483	3	21	2d	2d	NOUN
ap-3483	3	22	-	-	PUNCT
ap-3483	3	23	surfaces	surface	NOUN
ap-3483	3	24	corresponding	correspond	VERB
ap-3483	3	25	to	to	ADP
ap-3483	3	26	the	the	DET
ap-3483	3	27	following	follow	VERB
ap-3483	3	28	three	three	NUM
ap-3483	3	29	types	type	NOUN
ap-3483	3	30	of	of	ADP
ap-3483	3	31	symmetries	symmetry	NOUN
ap-3483	3	32	:	:	PUNCT
ap-3483	3	33	gauge	gauge	NOUN
ap-3483	3	34	symmetries	symmetry	NOUN
ap-3483	3	35	of	of	ADP
ap-3483	3	36	the	the	DET
ap-3483	3	37	linear	linear	PROPN
ap-3483	3	38	spectral	spectral	ADJ
ap-3483	3	39	problem	problem	NOUN
ap-3483	3	40	,	,	PUNCT
ap-3483	3	41	conformal	conformal	ADJ
ap-3483	3	42	transformations	transformation	NOUN
ap-3483	3	43	in	in	ADP
ap-3483	3	44	the	the	DET
ap-3483	3	45	spectral	spectral	ADJ
ap-3483	3	46	parameter	parameter	NOUN
ap-3483	3	47	and	and	CCONJ
ap-3483	3	48	generalized	generalized	ADJ
ap-3483	3	49	symmetries	symmetry	NOUN
ap-3483	3	50	of	of	ADP
ap-3483	3	51	the	the	DET
ap-3483	3	52	associated	associated	ADJ
ap-3483	3	53	integrable	integrable	ADJ
ap-3483	3	54	system	system	NOUN
ap-3483	3	55	.	.	PUNCT
ap-3483	4	1	after	after	ADP
ap-3483	4	2	a	a	DET
ap-3483	4	3	brief	brief	ADJ
ap-3483	4	4	exposition	exposition	NOUN
ap-3483	4	5	of	of	ADP
ap-3483	4	6	the	the	DET
ap-3483	4	7	theory	theory	NOUN
ap-3483	4	8	of	of	ADP
ap-3483	4	9	soliton	soliton	NOUN
ap-3483	4	10	surfaces	surface	NOUN
ap-3483	4	11	and	and	CCONJ
ap-3483	4	12	of	of	ADP
ap-3483	4	13	the	the	DET
ap-3483	4	14	main	main	ADJ
ap-3483	4	15	tool	tool	NOUN
ap-3483	4	16	used	use	VERB
ap-3483	4	17	to	to	PART
ap-3483	4	18	study	study	VERB
ap-3483	4	19	classical	classical	ADJ
ap-3483	4	20	and	and	CCONJ
ap-3483	4	21	generalized	generalized	ADJ
ap-3483	4	22	lie	lie	NOUN
ap-3483	4	23	symmetries	symmetry	NOUN
ap-3483	4	24	,	,	PUNCT
ap-3483	4	25	we	we	PRON
ap-3483	4	26	derive	derive	VERB
ap-3483	4	27	the	the	DET
ap-3483	4	28	necessary	necessary	ADJ
ap-3483	4	29	and	and	CCONJ
ap-3483	4	30	sufficient	sufficient	ADJ
ap-3483	4	31	conditions	condition	NOUN
ap-3483	4	32	under	under	ADP
ap-3483	4	33	which	which	PRON
ap-3483	4	34	the	the	DET
ap-3483	4	35	immersion	immersion	NOUN
ap-3483	4	36	formulas	formula	NOUN
ap-3483	4	37	associated	associate	VERB
ap-3483	4	38	with	with	ADP
ap-3483	4	39	these	these	DET
ap-3483	4	40	symmetries	symmetry	NOUN
ap-3483	4	41	are	be	AUX
ap-3483	4	42	linked	link	VERB
ap-3483	4	43	by	by	ADP
ap-3483	4	44	gauge	gauge	ADJ
ap-3483	4	45	transformations	transformation	NOUN
ap-3483	4	46	.	.	PUNCT
ap-3483	5	1	we	we	PRON
ap-3483	5	2	illustrate	illustrate	VERB
ap-3483	5	3	the	the	DET
ap-3483	5	4	theoretical	theoretical	ADJ
ap-3483	5	5	results	result	NOUN
ap-3483	5	6	by	by	ADP
ap-3483	5	7	examples	example	NOUN
ap-3483	5	8	involving	involve	VERB
ap-3483	5	9	the	the	DET
ap-3483	5	10	sigma	sigma	PROPN
ap-3483	5	11	model	model	NOUN
ap-3483	5	12	.	.	PUNCT
ap-3483	6	1	keywords	keyword	NOUN
ap-3483	6	2	:	:	PUNCT
ap-3483	6	3	integrable	integrable	ADJ
ap-3483	6	4	systems	system	NOUN
ap-3483	6	5	;	;	PUNCT
ap-3483	6	6	soliton	soliton	NOUN
ap-3483	6	7	surfaces	surface	NOUN
ap-3483	6	8	;	;	PUNCT
ap-3483	6	9	immersion	immersion	NOUN
ap-3483	6	10	formulas	formula	NOUN
ap-3483	6	11	;	;	PUNCT
ap-3483	6	12	generalized	generalized	ADJ
ap-3483	6	13	symmetries	symmetry	NOUN
ap-3483	6	14	.	.	PUNCT
ap-3483	7	1	ams	am	NOUN
ap-3483	7	2	mathematics	mathematics	PROPN
ap-3483	7	3	subject	subject	ADJ
ap-3483	7	4	classification	classification	NOUN
ap-3483	7	5	:	:	PUNCT
ap-3483	7	6	35q35	35q35	NUM
ap-3483	7	7	,	,	PUNCT
ap-3483	7	8	22e60	22e60	NUM
ap-3483	7	9	,	,	PUNCT
ap-3483	7	10	53a05	53a05	NUM
ap-3483	7	11	.	.	NOUN
ap-3483	8	1	1	1	NUM
ap-3483	8	2	.	.	X
ap-3483	8	3	introduction	introduction	NOUN
ap-3483	8	4	soliton	soliton	NOUN
ap-3483	8	5	surfaces	surface	NOUN
ap-3483	8	6	associated	associate	VERB
ap-3483	8	7	with	with	ADP
ap-3483	8	8	integrable	integrable	ADJ
ap-3483	8	9	systems	system	NOUN
ap-3483	8	10	have	have	AUX
ap-3483	8	11	been	be	AUX
ap-3483	8	12	shown	show	VERB
ap-3483	8	13	to	to	PART
ap-3483	8	14	play	play	VERB
ap-3483	8	15	an	an	DET
ap-3483	8	16	essential	essential	ADJ
ap-3483	8	17	role	role	NOUN
ap-3483	8	18	in	in	ADP
ap-3483	8	19	many	many	ADJ
ap-3483	8	20	problems	problem	NOUN
ap-3483	8	21	with	with	ADP
ap-3483	8	22	physical	physical	ADJ
ap-3483	8	23	applications	application	NOUN
ap-3483	8	24	(	(	PUNCT
ap-3483	8	25	see	see	VERB
ap-3483	8	26	e.g.	e.g.	ADV
ap-3483	8	27	[	[	X
ap-3483	8	28	2	2	NUM
ap-3483	8	29	,	,	PUNCT
ap-3483	8	30	5	5	NUM
ap-3483	8	31	–	–	PUNCT
ap-3483	8	32	9	9	NUM
ap-3483	8	33	,	,	PUNCT
ap-3483	8	34	11–13	11–13	NUM
ap-3483	8	35	,	,	PUNCT
ap-3483	8	36	15	15	NUM
ap-3483	8	37	,	,	PUNCT
ap-3483	8	38	19	19	NUM
ap-3483	8	39	,	,	PUNCT
ap-3483	8	40	29	29	NUM
ap-3483	8	41	,	,	PUNCT
ap-3483	8	42	30	30	NUM
ap-3483	8	43	,	,	PUNCT
ap-3483	8	44	33–35	33–35	NUM
ap-3483	8	45	]	]	PUNCT
ap-3483	8	46	)	)	PUNCT
ap-3483	8	47	.	.	PUNCT
ap-3483	9	1	we	we	PRON
ap-3483	9	2	say	say	VERB
ap-3483	9	3	that	that	SCONJ
ap-3483	9	4	a	a	DET
ap-3483	9	5	surface	surface	NOUN
ap-3483	9	6	is	be	AUX
ap-3483	9	7	integrable	integrable	ADJ
ap-3483	9	8	if	if	SCONJ
ap-3483	9	9	the	the	DET
ap-3483	9	10	gauss	gauss	ADJ
ap-3483	9	11	-	-	PUNCT
ap-3483	9	12	mainardi	mainardi	NOUN
ap-3483	9	13	-	-	PUNCT
ap-3483	9	14	codazzi	codazzi	NOUN
ap-3483	9	15	equations	equation	NOUN
ap-3483	9	16	corresponding	correspond	VERB
ap-3483	9	17	to	to	ADP
ap-3483	9	18	it	it	PRON
ap-3483	9	19	are	be	AUX
ap-3483	9	20	integrable	integrable	ADJ
ap-3483	9	21	,	,	PUNCT
ap-3483	9	22	i.e.	i.e.	X
ap-3483	9	23	if	if	SCONJ
ap-3483	9	24	they	they	PRON
ap-3483	9	25	can	can	AUX
ap-3483	9	26	be	be	AUX
ap-3483	9	27	represented	represent	VERB
ap-3483	9	28	as	as	ADP
ap-3483	9	29	the	the	DET
ap-3483	9	30	compatibility	compatibility	NOUN
ap-3483	9	31	conditions	condition	NOUN
ap-3483	9	32	for	for	ADP
ap-3483	9	33	some	some	DET
ap-3483	9	34	“	"	PUNCT
ap-3483	9	35	non	non	ADJ
ap-3483	9	36	-	-	ADJ
ap-3483	9	37	fake	fake	ADJ
ap-3483	9	38	”	"	PUNCT
ap-3483	9	39	linear	linear	PROPN
ap-3483	9	40	spectral	spectral	ADJ
ap-3483	9	41	problem	problem	NOUN
ap-3483	9	42	(	(	PUNCT
ap-3483	9	43	lsp	lsp	PROPN
ap-3483	9	44	)	)	PUNCT
ap-3483	10	1	[	[	X
ap-3483	10	2	2	2	NUM
ap-3483	10	3	,	,	PUNCT
ap-3483	10	4	3	3	NUM
ap-3483	10	5	,	,	PUNCT
ap-3483	10	6	5	5	NUM
ap-3483	10	7	,	,	PUNCT
ap-3483	10	8	17	17	NUM
ap-3483	10	9	,	,	PUNCT
ap-3483	10	10	18	18	NUM
ap-3483	10	11	,	,	PUNCT
ap-3483	10	12	21	21	NUM
ap-3483	10	13	,	,	PUNCT
ap-3483	10	14	22	22	NUM
ap-3483	10	15	,	,	PUNCT
ap-3483	10	16	24–26	24–26	NUM
ap-3483	10	17	,	,	PUNCT
ap-3483	10	18	31–35	31–35	NUM
ap-3483	10	19	]	]	PUNCT
ap-3483	10	20	.	.	PUNCT
ap-3483	11	1	the	the	DET
ap-3483	11	2	possibility	possibility	NOUN
ap-3483	11	3	of	of	ADP
ap-3483	11	4	using	use	VERB
ap-3483	11	5	an	an	DET
ap-3483	11	6	lsp	lsp	PROPN
ap-3483	11	7	to	to	PART
ap-3483	11	8	represent	represent	VERB
ap-3483	11	9	a	a	DET
ap-3483	11	10	moving	move	VERB
ap-3483	11	11	frame	frame	NOUN
ap-3483	11	12	on	on	ADP
ap-3483	11	13	the	the	DET
ap-3483	11	14	integrable	integrable	ADJ
ap-3483	11	15	surface	surface	NOUN
ap-3483	11	16	has	have	AUX
ap-3483	11	17	yielded	yield	VERB
ap-3483	11	18	many	many	ADJ
ap-3483	11	19	new	new	ADJ
ap-3483	11	20	results	result	NOUN
ap-3483	11	21	concerning	concern	VERB
ap-3483	11	22	the	the	DET
ap-3483	11	23	intrinsic	intrinsic	ADJ
ap-3483	11	24	geometric	geometric	ADJ
ap-3483	11	25	properties	property	NOUN
ap-3483	11	26	of	of	ADP
ap-3483	11	27	such	such	ADJ
ap-3483	11	28	surfaces	surface	NOUN
ap-3483	11	29	(	(	PUNCT
ap-3483	11	30	see	see	VERB
ap-3483	11	31	e.g.	e.g.	ADV
ap-3483	11	32	[	[	X
ap-3483	11	33	4	4	NUM
ap-3483	11	34	,	,	PUNCT
ap-3483	11	35	29	29	NUM
ap-3483	11	36	]	]	PUNCT
ap-3483	11	37	)	)	PUNCT
ap-3483	11	38	.	.	PUNCT
ap-3483	12	1	in	in	ADP
ap-3483	12	2	the	the	DET
ap-3483	12	3	present	present	ADJ
ap-3483	12	4	state	state	NOUN
ap-3483	12	5	of	of	ADP
ap-3483	12	6	development	development	NOUN
ap-3483	12	7	,	,	PUNCT
ap-3483	12	8	it	it	PRON
ap-3483	12	9	has	have	AUX
ap-3483	12	10	proved	prove	VERB
ap-3483	12	11	most	most	ADV
ap-3483	12	12	fruitful	fruitful	ADJ
ap-3483	12	13	to	to	PART
ap-3483	12	14	extend	extend	VERB
ap-3483	12	15	such	such	ADJ
ap-3483	12	16	characterizations	characterization	NOUN
ap-3483	12	17	of	of	ADP
ap-3483	12	18	soliton	soliton	NOUN
ap-3483	12	19	surfaces	surface	NOUN
ap-3483	12	20	via	via	ADP
ap-3483	12	21	their	their	PRON
ap-3483	12	22	immersion	immersion	NOUN
ap-3483	12	23	functions	function	NOUN
ap-3483	12	24	(	(	PUNCT
ap-3483	12	25	see	see	VERB
ap-3483	12	26	e.g.	e.g.	ADV
ap-3483	12	27	[	[	X
ap-3483	12	28	1	1	NUM
ap-3483	12	29	,	,	PUNCT
ap-3483	12	30	2	2	NUM
ap-3483	12	31	,	,	PUNCT
ap-3483	12	32	19	19	NUM
ap-3483	12	33	,	,	PUNCT
ap-3483	12	34	23	23	NUM
ap-3483	12	35	,	,	PUNCT
ap-3483	12	36	27	27	NUM
ap-3483	12	37	,	,	PUNCT
ap-3483	12	38	30	30	NUM
ap-3483	12	39	]	]	PUNCT
ap-3483	12	40	and	and	CCONJ
ap-3483	12	41	references	reference	NOUN
ap-3483	12	42	therein	therein	ADV
ap-3483	12	43	)	)	PUNCT
ap-3483	12	44	.	.	PUNCT
ap-3483	13	1	the	the	DET
ap-3483	13	2	construction	construction	NOUN
ap-3483	13	3	of	of	ADP
ap-3483	13	4	surfaces	surface	NOUN
ap-3483	13	5	related	relate	VERB
ap-3483	13	6	to	to	ADP
ap-3483	13	7	completely	completely	ADV
ap-3483	13	8	integrable	integrable	ADJ
ap-3483	13	9	models	model	NOUN
ap-3483	13	10	was	be	AUX
ap-3483	13	11	initiated	initiate	VERB
ap-3483	13	12	by	by	ADP
ap-3483	13	13	a.	a.	NOUN
ap-3483	13	14	sym	sym	PROPN
ap-3483	13	15	[	[	X
ap-3483	13	16	33–35	33–35	NUM
ap-3483	13	17	]	]	PUNCT
ap-3483	13	18	.	.	PUNCT
ap-3483	14	1	this	this	DET
ap-3483	14	2	construction	construction	NOUN
ap-3483	14	3	makes	make	VERB
ap-3483	14	4	use	use	NOUN
ap-3483	14	5	of	of	ADP
ap-3483	14	6	the	the	DET
ap-3483	14	7	conformal	conformal	ADJ
ap-3483	14	8	invariance	invariance	NOUN
ap-3483	14	9	of	of	ADP
ap-3483	14	10	the	the	DET
ap-3483	14	11	zero	zero	NUM
ap-3483	14	12	-	-	PUNCT
ap-3483	14	13	curvature	curvature	NOUN
ap-3483	14	14	representation	representation	NOUN
ap-3483	14	15	of	of	ADP
ap-3483	14	16	the	the	DET
ap-3483	14	17	system	system	NOUN
ap-3483	14	18	with	with	ADP
ap-3483	14	19	respect	respect	NOUN
ap-3483	14	20	to	to	ADP
ap-3483	14	21	the	the	DET
ap-3483	14	22	spectral	spectral	ADJ
ap-3483	14	23	parameter	parameter	NOUN
ap-3483	14	24	.	.	PUNCT
ap-3483	15	1	another	another	DET
ap-3483	15	2	approach	approach	NOUN
ap-3483	15	3	for	for	ADP
ap-3483	15	4	finding	find	VERB
ap-3483	15	5	such	such	ADJ
ap-3483	15	6	surfaces	surface	NOUN
ap-3483	15	7	has	have	AUX
ap-3483	15	8	been	be	AUX
ap-3483	15	9	formulated	formulate	VERB
ap-3483	15	10	by	by	ADP
ap-3483	15	11	j.	j.	PROPN
ap-3483	15	12	cieslinski	cieslinski	PROPN
ap-3483	15	13	and	and	CCONJ
ap-3483	15	14	a.	a.	PROPN
ap-3483	15	15	doliwa	doliwa	PROPN
ap-3483	16	1	[	[	X
ap-3483	16	2	5–7	5–7	X
ap-3483	16	3	]	]	PUNCT
ap-3483	16	4	using	use	VERB
ap-3483	16	5	gauge	gauge	NOUN
ap-3483	16	6	symmetries	symmetry	NOUN
ap-3483	16	7	of	of	ADP
ap-3483	16	8	the	the	DET
ap-3483	16	9	lsp	lsp	PROPN
ap-3483	16	10	.	.	PUNCT
ap-3483	17	1	a	a	DET
ap-3483	17	2	third	third	ADJ
ap-3483	17	3	approach	approach	NOUN
ap-3483	17	4	,	,	PUNCT
ap-3483	17	5	using	use	VERB
ap-3483	17	6	the	the	DET
ap-3483	17	7	lsp	lsp	PROPN
ap-3483	17	8	for	for	ADP
ap-3483	17	9	integrable	integrable	ADJ
ap-3483	17	10	systems	system	NOUN
ap-3483	17	11	and	and	CCONJ
ap-3483	17	12	their	their	PRON
ap-3483	17	13	symmetries	symmetry	NOUN
ap-3483	17	14	has	have	AUX
ap-3483	17	15	been	be	AUX
ap-3483	17	16	introduced	introduce	VERB
ap-3483	17	17	by	by	ADP
ap-3483	17	18	fokas	fokas	ADJ
ap-3483	17	19	and	and	CCONJ
ap-3483	17	20	gel’fand	gel’fand	VERB
ap-3483	17	21	[	[	X
ap-3483	17	22	8	8	NUM
ap-3483	17	23	,	,	PUNCT
ap-3483	17	24	9	9	NUM
ap-3483	17	25	]	]	PUNCT
ap-3483	17	26	,	,	PUNCT
ap-3483	17	27	to	to	PART
ap-3483	17	28	construct	construct	VERB
ap-3483	17	29	families	family	NOUN
ap-3483	17	30	of	of	ADP
ap-3483	17	31	soliton	soliton	NOUN
ap-3483	17	32	surfaces	surface	NOUN
ap-3483	17	33	.	.	PUNCT
ap-3483	18	1	most	most	ADV
ap-3483	18	2	recently	recently	ADV
ap-3483	18	3	,	,	PUNCT
ap-3483	18	4	in	in	ADP
ap-3483	18	5	a	a	DET
ap-3483	18	6	series	series	NOUN
ap-3483	18	7	of	of	ADP
ap-3483	18	8	papers	paper	NOUN
ap-3483	18	9	[	[	X
ap-3483	18	10	11–13	11–13	NUM
ap-3483	18	11	,	,	PUNCT
ap-3483	18	12	15	15	NUM
ap-3483	18	13	]	]	PUNCT
ap-3483	18	14	,	,	PUNCT
ap-3483	18	15	a	a	DET
ap-3483	18	16	reformulation	reformulation	NOUN
ap-3483	18	17	and	and	CCONJ
ap-3483	18	18	extension	extension	NOUN
ap-3483	18	19	of	of	ADP
ap-3483	18	20	the	the	DET
ap-3483	18	21	fokas	fokas	ADJ
ap-3483	18	22	-	-	PUNCT
ap-3483	18	23	gel’fand	gel’fand	NOUN
ap-3483	18	24	immersion	immersion	NOUN
ap-3483	18	25	formula	formula	NOUN
ap-3483	18	26	has	have	AUX
ap-3483	18	27	been	be	AUX
ap-3483	18	28	performed	perform	VERB
ap-3483	18	29	through	through	ADP
ap-3483	18	30	the	the	DET
ap-3483	18	31	formalism	formalism	NOUN
ap-3483	18	32	of	of	ADP
ap-3483	18	33	generalized	generalized	ADJ
ap-3483	18	34	vector	vector	NOUN
ap-3483	18	35	fields	field	NOUN
ap-3483	18	36	and	and	CCONJ
ap-3483	18	37	their	their	PRON
ap-3483	18	38	actions	action	NOUN
ap-3483	18	39	on	on	ADP
ap-3483	18	40	jet	jet	NOUN
ap-3483	18	41	spaces	space	NOUN
ap-3483	18	42	.	.	PUNCT
ap-3483	19	1	this	this	DET
ap-3483	19	2	extension	extension	NOUN
ap-3483	19	3	has	have	AUX
ap-3483	19	4	provided	provide	VERB
ap-3483	19	5	the	the	DET
ap-3483	19	6	necessary	necessary	ADJ
ap-3483	19	7	and	and	CCONJ
ap-3483	19	8	sufficient	sufficient	ADJ
ap-3483	19	9	conditions	condition	NOUN
ap-3483	19	10	for	for	ADP
ap-3483	19	11	the	the	DET
ap-3483	19	12	existence	existence	NOUN
ap-3483	19	13	of	of	ADP
ap-3483	19	14	soliton	soliton	NOUN
ap-3483	19	15	surfaces	surface	NOUN
ap-3483	19	16	in	in	ADP
ap-3483	19	17	terms	term	NOUN
ap-3483	19	18	of	of	ADP
ap-3483	19	19	the	the	DET
ap-3483	19	20	symmetries	symmetry	NOUN
ap-3483	19	21	of	of	ADP
ap-3483	19	22	the	the	DET
ap-3483	19	23	lsp	lsp	PROPN
ap-3483	19	24	and	and	CCONJ
ap-3483	19	25	integrable	integrable	ADJ
ap-3483	19	26	models	model	NOUN
ap-3483	19	27	.	.	PUNCT
ap-3483	20	1	the	the	DET
ap-3483	20	2	objective	objective	NOUN
ap-3483	20	3	of	of	ADP
ap-3483	20	4	this	this	DET
ap-3483	20	5	paper	paper	NOUN
ap-3483	20	6	is	be	AUX
ap-3483	20	7	to	to	PART
ap-3483	20	8	investigate	investigate	VERB
ap-3483	20	9	and	and	CCONJ
ap-3483	20	10	construct	construct	VERB
ap-3483	20	11	the	the	DET
ap-3483	20	12	relation	relation	NOUN
ap-3483	20	13	between	between	ADP
ap-3483	20	14	the	the	DET
ap-3483	20	15	three	three	NUM
ap-3483	20	16	approaches	approach	NOUN
ap-3483	20	17	concerning	concern	VERB
ap-3483	20	18	2d	2d	NOUN
ap-3483	20	19	-	-	PUNCT
ap-3483	20	20	soliton	soliton	NOUN
ap-3483	20	21	surfaces	surface	NOUN
ap-3483	20	22	associated	associate	VERB
ap-3483	20	23	with	with	ADP
ap-3483	20	24	integrable	integrable	ADJ
ap-3483	20	25	systems	system	NOUN
ap-3483	20	26	.	.	PUNCT
ap-3483	21	1	this	this	DET
ap-3483	21	2	paper	paper	NOUN
ap-3483	21	3	is	be	AUX
ap-3483	21	4	organized	organize	VERB
ap-3483	21	5	as	as	SCONJ
ap-3483	21	6	follows	follow	VERB
ap-3483	21	7	.	.	PUNCT
ap-3483	22	1	section	section	NOUN
ap-3483	22	2	2	2	NUM
ap-3483	22	3	contains	contain	VERB
ap-3483	22	4	a	a	DET
ap-3483	22	5	brief	brief	ADJ
ap-3483	22	6	summary	summary	NOUN
ap-3483	22	7	of	of	ADP
ap-3483	22	8	the	the	DET
ap-3483	22	9	results	result	NOUN
ap-3483	22	10	concerning	concern	VERB
ap-3483	22	11	the	the	DET
ap-3483	22	12	construction	construction	NOUN
ap-3483	22	13	of	of	ADP
ap-3483	22	14	soliton	soliton	NOUN
ap-3483	22	15	surfaces	surface	NOUN
ap-3483	22	16	and	and	CCONJ
ap-3483	22	17	symmetries	symmetry	NOUN
ap-3483	22	18	.	.	PUNCT
ap-3483	23	1	using	use	VERB
ap-3483	23	2	the	the	DET
ap-3483	23	3	sym	sym	NOUN
ap-3483	23	4	-	-	PUNCT
ap-3483	23	5	tafel	tafel	PROPN
ap-3483	23	6	(	(	PUNCT
ap-3483	23	7	st	st	NOUN
ap-3483	23	8	)	)	PUNCT
ap-3483	23	9	formula	formula	NOUN
ap-3483	23	10	,	,	PUNCT
ap-3483	23	11	we	we	PRON
ap-3483	23	12	get	get	VERB
ap-3483	23	13	the	the	DET
ap-3483	23	14	surface	surface	NOUN
ap-3483	23	15	by	by	ADP
ap-3483	23	16	differentiating	differentiate	VERB
ap-3483	23	17	the	the	DET
ap-3483	23	18	solution	solution	NOUN
ap-3483	23	19	of	of	ADP
ap-3483	23	20	the	the	DET
ap-3483	23	21	lsp	lsp	PROPN
ap-3483	23	22	with	with	ADP
ap-3483	23	23	respect	respect	NOUN
ap-3483	23	24	to	to	ADP
ap-3483	23	25	the	the	DET
ap-3483	23	26	spectral	spectral	ADJ
ap-3483	23	27	parameter	parameter	NOUN
ap-3483	23	28	.	.	PUNCT
ap-3483	24	1	through	through	ADP
ap-3483	24	2	the	the	DET
ap-3483	24	3	cieslinskidoliwa	cieslinskidoliwa	NOUN
ap-3483	24	4	(	(	PUNCT
ap-3483	24	5	cd	cd	PROPN
ap-3483	24	6	)	)	PUNCT
ap-3483	24	7	formula	formula	NOUN
ap-3483	24	8	we	we	PRON
ap-3483	24	9	apply	apply	VERB
ap-3483	24	10	a	a	DET
ap-3483	24	11	gauge	gauge	ADJ
ap-3483	24	12	transformation	transformation	NOUN
ap-3483	24	13	and	and	CCONJ
ap-3483	24	14	through	through	ADP
ap-3483	24	15	the	the	DET
ap-3483	24	16	fokas	fokas	ADJ
ap-3483	24	17	-	-	PUNCT
ap-3483	24	18	gel’fand	gel’fand	NOUN
ap-3483	24	19	(	(	PUNCT
ap-3483	24	20	fg	fg	NOUN
ap-3483	24	21	)	)	PUNCT
ap-3483	24	22	formula	formula	NOUN
ap-3483	24	23	we	we	PRON
ap-3483	24	24	consider	consider	VERB
ap-3483	24	25	the	the	DET
ap-3483	24	26	generalized	generalized	ADJ
ap-3483	24	27	symmetries	symmetry	NOUN
ap-3483	24	28	of	of	ADP
ap-3483	24	29	the	the	DET
ap-3483	24	30	associated	associated	ADJ
ap-3483	24	31	integrable	integrable	ADJ
ap-3483	24	32	equation	equation	NOUN
ap-3483	24	33	.	.	PUNCT
ap-3483	25	1	in	in	ADP
ap-3483	25	2	section	section	NOUN
ap-3483	25	3	3	3	NUM
ap-3483	25	4	we	we	PRON
ap-3483	25	5	demonstrate	demonstrate	VERB
ap-3483	25	6	that	that	SCONJ
ap-3483	25	7	the	the	DET
ap-3483	25	8	immersion	immersion	NOUN
ap-3483	25	9	problem	problem	NOUN
ap-3483	25	10	can	can	AUX
ap-3483	25	11	be	be	AUX
ap-3483	25	12	mapped	map	VERB
ap-3483	25	13	through	through	ADP
ap-3483	25	14	a	a	DET
ap-3483	25	15	gauge	gauge	NOUN
ap-3483	25	16	to	to	ADP
ap-3483	25	17	any	any	PRON
ap-3483	25	18	of	of	ADP
ap-3483	25	19	the	the	DET
ap-3483	25	20	three	three	NUM
ap-3483	25	21	immersion	immersion	NOUN
ap-3483	25	22	formulas	formula	NOUN
ap-3483	25	23	listed	list	VERB
ap-3483	25	24	above	above	ADV
ap-3483	25	25	and	and	CCONJ
ap-3483	25	26	we	we	PRON
ap-3483	25	27	show	show	VERB
ap-3483	25	28	that	that	SCONJ
ap-3483	25	29	these	these	DET
ap-3483	25	30	formulas	formula	NOUN
ap-3483	25	31	correspond	correspond	VERB
ap-3483	25	32	to	to	ADP
ap-3483	25	33	possibly	possibly	ADV
ap-3483	25	34	different	different	ADJ
ap-3483	25	35	parametrizations	parametrization	NOUN
ap-3483	25	36	of	of	ADP
ap-3483	25	37	the	the	DET
ap-3483	25	38	same	same	ADJ
ap-3483	25	39	surface	surface	NOUN
ap-3483	25	40	.	.	PUNCT
ap-3483	26	1	then	then	ADV
ap-3483	26	2	,	,	PUNCT
ap-3483	26	3	in	in	ADP
ap-3483	26	4	section	section	NOUN
ap-3483	26	5	4	4	NUM
ap-3483	26	6	,	,	PUNCT
ap-3483	26	7	we	we	PRON
ap-3483	26	8	apply	apply	VERB
ap-3483	26	9	the	the	DET
ap-3483	26	10	results	result	NOUN
ap-3483	26	11	on	on	ADP
ap-3483	26	12	the	the	DET
ap-3483	26	13	example	example	NOUN
ap-3483	26	14	of	of	ADP
ap-3483	26	15	the	the	DET
ap-3483	26	16	sigma	sigma	PROPN
ap-3483	26	17	model	model	PROPN
ap-3483	26	18	.	.	PUNCT
ap-3483	27	1	section	section	NOUN
ap-3483	27	2	5	5	NUM
ap-3483	27	3	contains	contain	VERB
ap-3483	27	4	the	the	DET
ap-3483	27	5	concluding	concluding	NOUN
ap-3483	27	6	remarks	remark	NOUN
ap-3483	27	7	.	.	PUNCT
ap-3483	28	1	180	180	NUM
ap-3483	28	2	http://dx.doi.org/10.14311/ap.2016.56.0180	http://dx.doi.org/10.14311/ap.2016.56.0180	NOUN
ap-3483	28	3	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3483	28	4	vol	vol	NOUN
ap-3483	28	5	.	.	PUNCT
ap-3483	29	1	56	56	NUM
ap-3483	29	2	no	no	NOUN
ap-3483	29	3	.	.	PUNCT
ap-3483	30	1	3/2016	3/2016	NUM
ap-3483	30	2	on	on	ADP
ap-3483	30	3	immersion	immersion	NOUN
ap-3483	30	4	formulas	formula	NOUN
ap-3483	30	5	for	for	ADP
ap-3483	30	6	soliton	soliton	NOUN
ap-3483	30	7	surfaces	surface	NOUN
ap-3483	30	8	2	2	NUM
ap-3483	30	9	.	.	X
ap-3483	31	1	summary	summary	NOUN
ap-3483	31	2	of	of	ADP
ap-3483	31	3	results	result	NOUN
ap-3483	31	4	on	on	ADP
ap-3483	31	5	the	the	DET
ap-3483	31	6	construction	construction	NOUN
ap-3483	31	7	of	of	ADP
ap-3483	31	8	soliton	soliton	NOUN
ap-3483	31	9	surfaces	surface	NOUN
ap-3483	31	10	in	in	ADP
ap-3483	31	11	this	this	DET
ap-3483	31	12	section	section	NOUN
ap-3483	31	13	we	we	PRON
ap-3483	31	14	recall	recall	VERB
ap-3483	31	15	the	the	DET
ap-3483	31	16	main	main	ADJ
ap-3483	31	17	tools	tool	NOUN
ap-3483	31	18	used	use	VERB
ap-3483	31	19	to	to	PART
ap-3483	31	20	study	study	VERB
ap-3483	31	21	symmetries	symmetry	NOUN
ap-3483	31	22	suitable	suitable	ADJ
ap-3483	31	23	for	for	ADP
ap-3483	31	24	the	the	DET
ap-3483	31	25	use	use	NOUN
ap-3483	31	26	of	of	ADP
ap-3483	31	27	fokas	fokas	ADJ
ap-3483	31	28	-	-	PUNCT
ap-3483	31	29	gel’fand	gel’fand	NOUN
ap-3483	31	30	formulas	formula	NOUN
ap-3483	31	31	for	for	ADP
ap-3483	31	32	the	the	DET
ap-3483	31	33	construction	construction	NOUN
ap-3483	31	34	of	of	ADP
ap-3483	31	35	2d	2d	NUM
ap-3483	31	36	surfaces	surface	NOUN
ap-3483	31	37	.	.	PUNCT
ap-3483	32	1	we	we	PRON
ap-3483	32	2	make	make	VERB
ap-3483	32	3	use	use	NOUN
ap-3483	32	4	of	of	ADP
ap-3483	32	5	the	the	DET
ap-3483	32	6	formalism	formalism	NOUN
ap-3483	32	7	of	of	ADP
ap-3483	32	8	vector	vector	NOUN
ap-3483	32	9	fields	field	NOUN
ap-3483	32	10	and	and	CCONJ
ap-3483	32	11	their	their	PRON
ap-3483	32	12	prolongations	prolongation	NOUN
ap-3483	32	13	as	as	SCONJ
ap-3483	32	14	presented	present	VERB
ap-3483	32	15	in	in	ADP
ap-3483	32	16	[	[	X
ap-3483	32	17	29	29	NUM
ap-3483	32	18	]	]	PUNCT
ap-3483	32	19	.	.	PUNCT
ap-3483	33	1	more	more	ADV
ap-3483	33	2	specifically	specifically	ADV
ap-3483	33	3	,	,	PUNCT
ap-3483	33	4	we	we	PRON
ap-3483	33	5	rewrite	rewrite	VERB
ap-3483	33	6	the	the	DET
ap-3483	33	7	formula	formula	NOUN
ap-3483	33	8	for	for	ADP
ap-3483	33	9	the	the	DET
ap-3483	33	10	immersion	immersion	NOUN
ap-3483	33	11	functions	function	NOUN
ap-3483	33	12	of	of	ADP
ap-3483	33	13	2d	2d	NOUN
ap-3483	33	14	surfaces	surface	NOUN
ap-3483	33	15	in	in	ADP
ap-3483	33	16	terms	term	NOUN
ap-3483	33	17	of	of	ADP
ap-3483	33	18	the	the	DET
ap-3483	33	19	prolongation	prolongation	NOUN
ap-3483	33	20	formalism	formalism	NOUN
ap-3483	33	21	of	of	ADP
ap-3483	33	22	the	the	DET
ap-3483	33	23	vector	vector	NOUN
ap-3483	33	24	fields	field	NOUN
ap-3483	33	25	instead	instead	ADV
ap-3483	33	26	of	of	ADP
ap-3483	33	27	the	the	DET
ap-3483	33	28	fréchet	fréchet	NOUN
ap-3483	33	29	derivatives	derivative	NOUN
ap-3483	33	30	.	.	PUNCT
ap-3483	34	1	2.1	2.1	NUM
ap-3483	34	2	.	.	PUNCT
ap-3483	35	1	classical	classical	ADJ
ap-3483	35	2	and	and	CCONJ
ap-3483	35	3	generalized	generalized	ADJ
ap-3483	35	4	lie	lie	NOUN
ap-3483	35	5	symmetries	symmetry	NOUN
ap-3483	35	6	letx	letx	NOUN
ap-3483	35	7	(	(	PUNCT
ap-3483	35	8	with	with	ADP
ap-3483	35	9	coordinates	coordinate	NOUN
ap-3483	35	10	xα	xα	PROPN
ap-3483	35	11	,	,	PUNCT
ap-3483	35	12	α	α	NOUN
ap-3483	35	13	=	=	SYM
ap-3483	35	14	1	1	NUM
ap-3483	35	15	,	,	PUNCT
ap-3483	35	16	.	.	PUNCT
ap-3483	35	17	.	.	PUNCT
ap-3483	35	18	.	.	PUNCT
ap-3483	36	1	,	,	PUNCT
ap-3483	36	2	p	p	X
ap-3483	36	3	)	)	PUNCT
ap-3483	36	4	and	and	CCONJ
ap-3483	36	5	u	u	X
ap-3483	36	6	(	(	PUNCT
ap-3483	36	7	with	with	ADP
ap-3483	36	8	coordinates	coordinate	NOUN
ap-3483	36	9	uk	uk	PROPN
ap-3483	36	10	,	,	PUNCT
ap-3483	36	11	k	k	PROPN
ap-3483	36	12	=	=	SYM
ap-3483	36	13	1	1	NUM
ap-3483	36	14	,	,	PUNCT
ap-3483	36	15	.	.	PUNCT
ap-3483	36	16	.	.	PUNCT
ap-3483	36	17	.	.	PUNCT
ap-3483	37	1	,	,	PUNCT
ap-3483	37	2	q	q	X
ap-3483	37	3	)	)	PUNCT
ap-3483	37	4	be	be	AUX
ap-3483	37	5	differential	differential	ADJ
ap-3483	37	6	manifolds	manifold	NOUN
ap-3483	37	7	representing	represent	VERB
ap-3483	37	8	spaces	space	NOUN
ap-3483	37	9	of	of	ADP
ap-3483	37	10	independent	independent	ADJ
ap-3483	37	11	and	and	CCONJ
ap-3483	37	12	dependent	dependent	ADJ
ap-3483	37	13	variables	variable	NOUN
ap-3483	37	14	,	,	PUNCT
ap-3483	37	15	respectively	respectively	ADV
ap-3483	37	16	.	.	PUNCT
ap-3483	38	1	let	let	VERB
ap-3483	38	2	jn	jn	PROPN
ap-3483	38	3	=	=	PROPN
ap-3483	38	4	jn(x	jn(x	NUM
ap-3483	38	5	×	×	PROPN
ap-3483	38	6	u	u	NOUN
ap-3483	38	7	)	)	PUNCT
ap-3483	38	8	denote	denote	VERB
ap-3483	38	9	the	the	DET
ap-3483	38	10	n	n	CCONJ
ap-3483	38	11	-	-	PUNCT
ap-3483	38	12	jet	jet	NOUN
ap-3483	38	13	space	space	NOUN
ap-3483	38	14	over	over	ADP
ap-3483	38	15	x	x	SYM
ap-3483	38	16	×	×	PROPN
ap-3483	38	17	u	u	NOUN
ap-3483	38	18	.	.	PUNCT
ap-3483	39	1	the	the	DET
ap-3483	39	2	coordinates	coordinate	NOUN
ap-3483	39	3	of	of	ADP
ap-3483	39	4	jn	jn	PROPN
ap-3483	39	5	are	be	AUX
ap-3483	39	6	given	give	VERB
ap-3483	39	7	by	by	ADP
ap-3483	39	8	xα	xα	PROPN
ap-3483	39	9	,	,	PUNCT
ap-3483	39	10	uk	uk	PROPN
ap-3483	39	11	and	and	CCONJ
ap-3483	39	12	ukj	ukj	PROPN
ap-3483	39	13	=	=	NOUN
ap-3483	39	14	∂nuk	∂nuk	NUM
ap-3483	39	15	∂xj1	∂xj1	PROPN
ap-3483	39	16	...	...	PUNCT
ap-3483	39	17	∂xjn	∂xjn	X
ap-3483	39	18	where	where	SCONJ
ap-3483	39	19	j	j	PROPN
ap-3483	39	20	=	=	PRON
ap-3483	39	21	(	(	PUNCT
ap-3483	39	22	j1	j1	PROPN
ap-3483	39	23	,	,	PUNCT
ap-3483	39	24	.	.	PUNCT
ap-3483	39	25	.	.	PUNCT
ap-3483	39	26	.	.	PUNCT
ap-3483	40	1	,	,	PUNCT
ap-3483	40	2	jn	jn	PROPN
ap-3483	40	3	)	)	PUNCT
ap-3483	40	4	is	be	AUX
ap-3483	40	5	a	a	DET
ap-3483	40	6	symmetric	symmetric	ADJ
ap-3483	40	7	multi	multi	NOUN
ap-3483	40	8	-	-	NOUN
ap-3483	40	9	index	index	NOUN
ap-3483	40	10	.	.	PUNCT
ap-3483	41	1	we	we	PRON
ap-3483	41	2	denote	denote	VERB
ap-3483	41	3	these	these	DET
ap-3483	41	4	coordinates	coordinate	NOUN
ap-3483	41	5	by	by	ADP
ap-3483	41	6	x	x	PROPN
ap-3483	41	7	and	and	CCONJ
ap-3483	41	8	u(n	u(n	PROPN
ap-3483	41	9	)	)	PUNCT
ap-3483	41	10	.	.	PUNCT
ap-3483	42	1	on	on	ADP
ap-3483	42	2	jn	jn	PROPN
ap-3483	42	3	we	we	PRON
ap-3483	42	4	can	can	AUX
ap-3483	42	5	define	define	VERB
ap-3483	42	6	a	a	DET
ap-3483	42	7	system	system	NOUN
ap-3483	42	8	of	of	ADP
ap-3483	42	9	partial	partial	ADJ
ap-3483	42	10	differential	differential	ADJ
ap-3483	42	11	equations	equation	NOUN
ap-3483	42	12	(	(	PUNCT
ap-3483	42	13	pdes	pde	NOUN
ap-3483	42	14	)	)	PUNCT
ap-3483	42	15	in	in	ADP
ap-3483	42	16	p	p	NOUN
ap-3483	42	17	independent	independent	ADJ
ap-3483	42	18	and	and	CCONJ
ap-3483	42	19	q	q	NOUN
ap-3483	42	20	dependent	dependent	ADJ
ap-3483	42	21	variables	variable	NOUN
ap-3483	42	22	given	give	VERB
ap-3483	42	23	by	by	ADP
ap-3483	42	24	m	m	PROPN
ap-3483	42	25	equations	equation	NOUN
ap-3483	42	26	of	of	ADP
ap-3483	42	27	the	the	DET
ap-3483	42	28	form	form	NOUN
ap-3483	42	29	ωµ(x	ωµ(x	NUM
ap-3483	42	30	,	,	PUNCT
ap-3483	42	31	u(n	u(n	PROPN
ap-3483	42	32	)	)	PUNCT
ap-3483	42	33	)	)	PUNCT
ap-3483	43	1	=	=	SYM
ap-3483	43	2	0	0	NUM
ap-3483	43	3	,	,	PUNCT
ap-3483	43	4	µ	µ	X
ap-3483	43	5	=	=	SYM
ap-3483	43	6	1	1	NUM
ap-3483	43	7	,	,	PUNCT
ap-3483	43	8	.	.	PUNCT
ap-3483	43	9	.	.	PUNCT
ap-3483	43	10	.	.	PUNCT
ap-3483	44	1	,	,	PUNCT
ap-3483	44	2	m.	m.	NOUN
ap-3483	44	3	(	(	PUNCT
ap-3483	44	4	2.1	2.1	NUM
ap-3483	44	5	)	)	PUNCT
ap-3483	44	6	we	we	PRON
ap-3483	44	7	consider	consider	VERB
ap-3483	44	8	a	a	DET
ap-3483	44	9	vector	vector	NOUN
ap-3483	44	10	field	field	NOUN
ap-3483	44	11	v	v	ADP
ap-3483	44	12	tangent	tangent	NOUN
ap-3483	44	13	to	to	ADP
ap-3483	44	14	j0	j0	PROPN
ap-3483	44	15	=	=	PUNCT
ap-3483	44	16	x	x	SYM
ap-3483	44	17	×u	×u	NUM
ap-3483	44	18	v	v	NOUN
ap-3483	44	19	=	=	SYM
ap-3483	44	20	ξα(x	ξα(x	NOUN
ap-3483	44	21	,	,	PUNCT
ap-3483	44	22	u)∂α	u)∂α	PROPN
ap-3483	44	23	+	+	CCONJ
ap-3483	44	24	ϕk(x	ϕk(x	NOUN
ap-3483	44	25	,	,	PUNCT
ap-3483	44	26	u)∂k	u)∂k	PROPN
ap-3483	44	27	,	,	PUNCT
ap-3483	44	28	(	(	PUNCT
ap-3483	44	29	2.2	2.2	NUM
ap-3483	44	30	)	)	PUNCT
ap-3483	44	31	where	where	SCONJ
ap-3483	44	32	∂α	∂α	PROPN
ap-3483	44	33	=	=	SYM
ap-3483	44	34	∂/∂xα	∂/∂xα	NOUN
ap-3483	44	35	,	,	PUNCT
ap-3483	44	36	∂k	∂k	X
ap-3483	44	37	=	=	PUNCT
ap-3483	44	38	∂/∂uk	∂/∂uk	PROPN
ap-3483	45	1	and	and	CCONJ
ap-3483	45	2	we	we	PRON
ap-3483	45	3	adopt	adopt	VERB
ap-3483	45	4	the	the	DET
ap-3483	45	5	summation	summation	NOUN
ap-3483	45	6	convention	convention	NOUN
ap-3483	45	7	over	over	ADP
ap-3483	45	8	repeated	repeat	VERB
ap-3483	45	9	indices	index	NOUN
ap-3483	45	10	.	.	PUNCT
ap-3483	46	1	such	such	DET
ap-3483	46	2	a	a	DET
ap-3483	46	3	field	field	NOUN
ap-3483	46	4	defines	define	VERB
ap-3483	46	5	vector	vector	NOUN
ap-3483	46	6	fields	field	NOUN
ap-3483	46	7	,	,	PUNCT
ap-3483	46	8	pr(n	pr(n	NUM
ap-3483	46	9	)	)	PUNCT
ap-3483	46	10	v	v	NOUN
ap-3483	46	11	on	on	ADP
ap-3483	46	12	jn	jn	PROPN
ap-3483	47	1	[	[	X
ap-3483	47	2	29	29	NUM
ap-3483	47	3	]	]	SYM
ap-3483	47	4	pr(n	pr(n	NUM
ap-3483	47	5	)	)	PUNCT
ap-3483	47	6	v	v	NOUN
ap-3483	47	7	=	=	PUNCT
ap-3483	47	8	ξα∂α	ξα∂α	ADP
ap-3483	47	9	+	+	NUM
ap-3483	47	10	ϕkj	ϕkj	PROPN
ap-3483	47	11	∂	∂	NOUN
ap-3483	47	12	∂ukj	∂ukj	NOUN
ap-3483	47	13	.	.	PUNCT
ap-3483	48	1	(	(	PUNCT
ap-3483	48	2	2.3	2.3	NUM
ap-3483	48	3	)	)	PUNCT
ap-3483	48	4	the	the	DET
ap-3483	48	5	functions	function	NOUN
ap-3483	48	6	ϕkj	ϕkj	NOUN
ap-3483	48	7	are	be	AUX
ap-3483	48	8	given	give	VERB
ap-3483	48	9	by	by	ADP
ap-3483	48	10	ϕkj	ϕkj	NOUN
ap-3483	48	11	=	=	SYM
ap-3483	48	12	djr	djr	NOUN
ap-3483	48	13	k	k	PROPN
ap-3483	48	14	+	+	CCONJ
ap-3483	48	15	ξαukj	ξαukj	ADJ
ap-3483	48	16	,	,	PUNCT
ap-3483	48	17	α	α	NOUN
ap-3483	48	18	,	,	PUNCT
ap-3483	48	19	rk	rk	NOUN
ap-3483	48	20	=	=	NOUN
ap-3483	48	21	ϕk	ϕk	NOUN
ap-3483	49	1	−	−	PROPN
ap-3483	49	2	ξαukα	ξαukα	ADJ
ap-3483	49	3	,	,	PUNCT
ap-3483	49	4	(	(	PUNCT
ap-3483	49	5	2.4	2.4	NUM
ap-3483	49	6	)	)	PUNCT
ap-3483	49	7	where	where	SCONJ
ap-3483	49	8	the	the	DET
ap-3483	49	9	operators	operator	NOUN
ap-3483	49	10	dj	dj	VERB
ap-3483	49	11	correspond	correspond	VERB
ap-3483	49	12	to	to	ADP
ap-3483	49	13	multiple	multiple	ADJ
ap-3483	49	14	total	total	ADJ
ap-3483	49	15	derivatives	derivative	NOUN
ap-3483	49	16	,	,	PUNCT
ap-3483	49	17	each	each	PRON
ap-3483	49	18	of	of	ADP
ap-3483	49	19	which	which	PRON
ap-3483	49	20	is	be	AUX
ap-3483	49	21	a	a	DET
ap-3483	49	22	combination	combination	NOUN
ap-3483	49	23	of	of	ADP
ap-3483	49	24	total	total	ADJ
ap-3483	49	25	derivatives	derivative	NOUN
ap-3483	49	26	of	of	ADP
ap-3483	49	27	the	the	DET
ap-3483	49	28	form	form	NOUN
ap-3483	49	29	dα	dα	X
ap-3483	49	30	=	=	PUNCT
ap-3483	49	31	∂α	∂α	PROPN
ap-3483	49	32	+	+	CCONJ
ap-3483	49	33	ukj	ukj	ADJ
ap-3483	49	34	,	,	PUNCT
ap-3483	49	35	α	α	PROPN
ap-3483	49	36	∂	∂	NOUN
ap-3483	49	37	∂ukj	∂ukj	X
ap-3483	49	38	,	,	PUNCT
ap-3483	49	39	α	α	PROPN
ap-3483	49	40	=	=	SYM
ap-3483	49	41	1	1	NUM
ap-3483	49	42	,	,	PUNCT
ap-3483	49	43	.	.	PUNCT
ap-3483	49	44	.	.	PUNCT
ap-3483	49	45	.	.	PUNCT
ap-3483	50	1	,	,	PUNCT
ap-3483	50	2	p	p	X
ap-3483	50	3	(	(	PUNCT
ap-3483	50	4	2.5	2.5	NUM
ap-3483	50	5	)	)	PUNCT
ap-3483	50	6	and	and	CCONJ
ap-3483	50	7	rk	rk	PRON
ap-3483	50	8	are	be	AUX
ap-3483	50	9	the	the	DET
ap-3483	50	10	so	so	ADV
ap-3483	50	11	-	-	PUNCT
ap-3483	50	12	called	call	VERB
ap-3483	50	13	characteristics	characteristic	NOUN
ap-3483	50	14	of	of	ADP
ap-3483	50	15	the	the	DET
ap-3483	50	16	vector	vector	NOUN
ap-3483	50	17	field	field	NOUN
ap-3483	50	18	v.	v.	CCONJ
ap-3483	50	19	in	in	ADP
ap-3483	50	20	the	the	DET
ap-3483	50	21	following	following	NOUN
ap-3483	50	22	,	,	PUNCT
ap-3483	50	23	the	the	DET
ap-3483	50	24	representation	representation	NOUN
ap-3483	50	25	of	of	ADP
ap-3483	50	26	v	v	NOUN
ap-3483	50	27	can	can	AUX
ap-3483	50	28	be	be	AUX
ap-3483	50	29	written	write	VERB
ap-3483	50	30	equivalently	equivalently	ADV
ap-3483	50	31	as	as	ADP
ap-3483	50	32	v	v	NOUN
ap-3483	50	33	=	=	SYM
ap-3483	50	34	ξαdα	ξαdα	NOUN
ap-3483	50	35	+	+	CCONJ
ap-3483	50	36	ωr	ωr	ADJ
ap-3483	50	37	,	,	PUNCT
ap-3483	50	38	ωr	ωr	X
ap-3483	50	39	=	=	PUNCT
ap-3483	50	40	rk	rk	PROPN
ap-3483	50	41	∂	∂	NOUN
ap-3483	50	42	∂uk	∂uk	PROPN
ap-3483	50	43	.	.	PUNCT
ap-3483	51	1	(	(	PUNCT
ap-3483	51	2	2.6	2.6	NUM
ap-3483	51	3	)	)	PUNCT
ap-3483	51	4	one	one	PRON
ap-3483	51	5	says	say	VERB
ap-3483	51	6	that	that	SCONJ
ap-3483	51	7	the	the	DET
ap-3483	51	8	vector	vector	NOUN
ap-3483	51	9	field	field	NOUN
ap-3483	51	10	v	v	NOUN
ap-3483	51	11	is	be	AUX
ap-3483	51	12	a	a	DET
ap-3483	51	13	classical	classical	ADJ
ap-3483	51	14	lie	lie	NOUN
ap-3483	51	15	point	point	NOUN
ap-3483	51	16	symmetry	symmetry	NOUN
ap-3483	51	17	of	of	ADP
ap-3483	51	18	a	a	DET
ap-3483	51	19	nondegenerate	nondegenerate	ADJ
ap-3483	51	20	system	system	NOUN
ap-3483	51	21	of	of	ADP
ap-3483	51	22	pdes	pde	NOUN
ap-3483	51	23	(	(	PUNCT
ap-3483	51	24	2.1	2.1	NUM
ap-3483	51	25	)	)	PUNCT
ap-3483	52	1	if	if	SCONJ
ap-3483	52	2	and	and	CCONJ
ap-3483	52	3	only	only	ADV
ap-3483	52	4	if	if	SCONJ
ap-3483	52	5	its	its	PRON
ap-3483	52	6	n	n	CCONJ
ap-3483	52	7	-	-	PUNCT
ap-3483	52	8	th	th	VERB
ap-3483	52	9	prolongation	prolongation	NOUN
ap-3483	52	10	of	of	ADP
ap-3483	52	11	v	v	NOUN
ap-3483	52	12	is	be	AUX
ap-3483	52	13	such	such	DET
ap-3483	52	14	that	that	PRON
ap-3483	52	15	pr(n	pr(n	NUM
ap-3483	52	16	)	)	PUNCT
ap-3483	52	17	vωµ(x	vωµ(x	PROPN
ap-3483	52	18	,	,	PUNCT
ap-3483	52	19	u(n	u(n	PROPN
ap-3483	52	20	)	)	PUNCT
ap-3483	52	21	)	)	PUNCT
ap-3483	53	1	=	=	SYM
ap-3483	53	2	0	0	NUM
ap-3483	53	3	,	,	PUNCT
ap-3483	53	4	µ	µ	X
ap-3483	53	5	=	=	SYM
ap-3483	53	6	1	1	NUM
ap-3483	53	7	,	,	PUNCT
ap-3483	53	8	.	.	PUNCT
ap-3483	53	9	.	.	PUNCT
ap-3483	53	10	.	.	PUNCT
ap-3483	54	1	,	,	PUNCT
ap-3483	54	2	m	m	PROPN
ap-3483	54	3	(	(	PUNCT
ap-3483	54	4	2.7	2.7	NUM
ap-3483	54	5	)	)	PUNCT
ap-3483	55	1	whenever	whenever	SCONJ
ap-3483	55	2	ωµ(x	ωµ(x	X
ap-3483	55	3	,	,	PUNCT
ap-3483	55	4	u(n	u(n	PROPN
ap-3483	55	5	)	)	PUNCT
ap-3483	55	6	)	)	PUNCT
ap-3483	56	1	=	=	SYM
ap-3483	56	2	0	0	NUM
ap-3483	56	3	,	,	PUNCT
ap-3483	56	4	µ	µ	X
ap-3483	56	5	=	=	SYM
ap-3483	56	6	1	1	NUM
ap-3483	56	7	,	,	PUNCT
ap-3483	56	8	.	.	PUNCT
ap-3483	56	9	.	.	PUNCT
ap-3483	56	10	.	.	PUNCT
ap-3483	57	1	,	,	PUNCT
ap-3483	57	2	m	m	NOUN
ap-3483	57	3	are	be	AUX
ap-3483	57	4	satisfied	satisfied	ADJ
ap-3483	57	5	.	.	PUNCT
ap-3483	58	1	by	by	ADP
ap-3483	58	2	a	a	DET
ap-3483	58	3	totally	totally	ADV
ap-3483	58	4	non	non	ADJ
ap-3483	58	5	-	-	ADJ
ap-3483	58	6	degenerate	degenerate	ADJ
ap-3483	58	7	system	system	NOUN
ap-3483	58	8	we	we	PRON
ap-3483	58	9	mean	mean	VERB
ap-3483	58	10	a	a	DET
ap-3483	58	11	system	system	NOUN
ap-3483	58	12	for	for	ADP
ap-3483	58	13	which	which	PRON
ap-3483	58	14	all	all	DET
ap-3483	58	15	their	their	PRON
ap-3483	58	16	prolongations	prolongation	NOUN
ap-3483	58	17	have	have	VERB
ap-3483	58	18	maximal	maximal	ADJ
ap-3483	58	19	rank	rank	NOUN
ap-3483	58	20	and	and	CCONJ
ap-3483	58	21	are	be	AUX
ap-3483	58	22	locally	locally	ADV
ap-3483	58	23	solvable	solvable	ADJ
ap-3483	58	24	[	[	X
ap-3483	58	25	29	29	NUM
ap-3483	58	26	]	]	PUNCT
ap-3483	58	27	.	.	PUNCT
ap-3483	59	1	it	it	PRON
ap-3483	59	2	follows	follow	VERB
ap-3483	59	3	from	from	ADP
ap-3483	59	4	the	the	DET
ap-3483	59	5	wellknown	wellknown	ADJ
ap-3483	59	6	properties	property	NOUN
ap-3483	59	7	of	of	ADP
ap-3483	59	8	the	the	DET
ap-3483	59	9	symmetries	symmetry	NOUN
ap-3483	59	10	of	of	ADP
ap-3483	59	11	a	a	DET
ap-3483	59	12	differential	differential	ADJ
ap-3483	59	13	system	system	NOUN
ap-3483	59	14	that	that	PRON
ap-3483	59	15	the	the	DET
ap-3483	59	16	commutator	commutator	NOUN
ap-3483	59	17	of	of	ADP
ap-3483	59	18	two	two	NUM
ap-3483	59	19	symmetries	symmetry	NOUN
ap-3483	59	20	is	be	AUX
ap-3483	59	21	again	again	ADV
ap-3483	59	22	a	a	DET
ap-3483	59	23	symmetry	symmetry	NOUN
ap-3483	59	24	.	.	PUNCT
ap-3483	60	1	thus	thus	ADV
ap-3483	60	2	,	,	PUNCT
ap-3483	60	3	such	such	ADJ
ap-3483	60	4	symmetries	symmetry	NOUN
ap-3483	60	5	form	form	VERB
ap-3483	60	6	a	a	DET
ap-3483	60	7	lie	lie	NOUN
ap-3483	60	8	algebra	algebra	VERB
ap-3483	60	9	g	g	NOUN
ap-3483	60	10	,	,	PUNCT
ap-3483	60	11	which	which	PRON
ap-3483	60	12	locally	locally	ADV
ap-3483	60	13	defines	define	VERB
ap-3483	60	14	an	an	DET
ap-3483	60	15	action	action	NOUN
ap-3483	60	16	of	of	ADP
ap-3483	60	17	a	a	DET
ap-3483	60	18	lie	lie	NOUN
ap-3483	60	19	group	group	NOUN
ap-3483	60	20	g	g	PROPN
ap-3483	60	21	on	on	ADP
ap-3483	60	22	j0	j0	PROPN
ap-3483	60	23	.	.	PUNCT
ap-3483	61	1	every	every	DET
ap-3483	61	2	solution	solution	NOUN
ap-3483	61	3	of	of	ADP
ap-3483	61	4	(	(	PUNCT
ap-3483	61	5	2.1	2.1	NUM
ap-3483	61	6	)	)	PUNCT
ap-3483	61	7	can	can	AUX
ap-3483	61	8	be	be	AUX
ap-3483	61	9	represented	represent	VERB
ap-3483	61	10	by	by	ADP
ap-3483	61	11	its	its	PRON
ap-3483	61	12	graph	graph	NOUN
ap-3483	61	13	,	,	PUNCT
ap-3483	61	14	uk	uk	PROPN
ap-3483	61	15	=	=	PRON
ap-3483	61	16	θk(x	θk(x	X
ap-3483	61	17	)	)	PUNCT
ap-3483	61	18	,	,	PUNCT
ap-3483	61	19	which	which	PRON
ap-3483	61	20	is	be	AUX
ap-3483	61	21	a	a	DET
ap-3483	61	22	section	section	NOUN
ap-3483	61	23	of	of	ADP
ap-3483	61	24	j0	j0	PROPN
ap-3483	61	25	.	.	PUNCT
ap-3483	62	1	the	the	DET
ap-3483	62	2	symmetry	symmetry	NOUN
ap-3483	62	3	group	group	NOUN
ap-3483	62	4	g	g	PROPN
ap-3483	62	5	transforms	transform	VERB
ap-3483	62	6	solutions	solution	NOUN
ap-3483	62	7	into	into	ADP
ap-3483	62	8	solutions	solution	NOUN
ap-3483	62	9	.	.	PUNCT
ap-3483	63	1	this	this	PRON
ap-3483	63	2	means	mean	VERB
ap-3483	63	3	that	that	SCONJ
ap-3483	63	4	a	a	DET
ap-3483	63	5	graph	graph	NOUN
ap-3483	63	6	corresponding	correspond	VERB
ap-3483	63	7	to	to	ADP
ap-3483	63	8	one	one	NUM
ap-3483	63	9	solution	solution	NOUN
ap-3483	63	10	is	be	AUX
ap-3483	63	11	transformed	transform	VERB
ap-3483	63	12	into	into	ADP
ap-3483	63	13	a	a	DET
ap-3483	63	14	graph	graph	NOUN
ap-3483	63	15	associated	associate	VERB
ap-3483	63	16	with	with	ADP
ap-3483	63	17	another	another	DET
ap-3483	63	18	solution	solution	NOUN
ap-3483	63	19	.	.	PUNCT
ap-3483	64	1	if	if	SCONJ
ap-3483	64	2	the	the	DET
ap-3483	64	3	graph	graph	NOUN
ap-3483	64	4	is	be	AUX
ap-3483	64	5	preserved	preserve	VERB
ap-3483	64	6	by	by	ADP
ap-3483	64	7	the	the	DET
ap-3483	64	8	group	group	NOUN
ap-3483	64	9	g	g	NOUN
ap-3483	64	10	or	or	CCONJ
ap-3483	64	11	equivalently	equivalently	ADV
ap-3483	64	12	,	,	PUNCT
ap-3483	64	13	if	if	SCONJ
ap-3483	64	14	the	the	DET
ap-3483	64	15	vector	vector	NOUN
ap-3483	64	16	fields	field	VERB
ap-3483	64	17	v	v	NOUN
ap-3483	64	18	from	from	ADP
ap-3483	64	19	the	the	DET
ap-3483	64	20	algebra	algebra	NOUN
ap-3483	64	21	g	g	NOUN
ap-3483	64	22	are	be	AUX
ap-3483	64	23	tangent	tangent	ADJ
ap-3483	64	24	to	to	ADP
ap-3483	64	25	the	the	DET
ap-3483	64	26	graph	graph	NOUN
ap-3483	64	27	,	,	PUNCT
ap-3483	64	28	then	then	ADV
ap-3483	64	29	the	the	DET
ap-3483	64	30	related	related	ADJ
ap-3483	64	31	solution	solution	NOUN
ap-3483	64	32	is	be	AUX
ap-3483	64	33	said	say	VERB
ap-3483	64	34	to	to	PART
ap-3483	64	35	be	be	AUX
ap-3483	64	36	g	g	NOUN
ap-3483	64	37	-	-	PUNCT
ap-3483	64	38	invariant	invariant	ADJ
ap-3483	64	39	.	.	PUNCT
ap-3483	65	1	invariant	invariant	ADJ
ap-3483	65	2	solutions	solution	NOUN
ap-3483	65	3	satisfy	satisfy	VERB
ap-3483	65	4	,	,	PUNCT
ap-3483	65	5	in	in	ADP
ap-3483	65	6	addition	addition	NOUN
ap-3483	65	7	to	to	ADP
ap-3483	65	8	the	the	DET
ap-3483	65	9	equations	equation	NOUN
ap-3483	65	10	(	(	PUNCT
ap-3483	65	11	2.1	2.1	NUM
ap-3483	65	12	)	)	PUNCT
ap-3483	65	13	,	,	PUNCT
ap-3483	65	14	the	the	DET
ap-3483	65	15	characteristic	characteristic	ADJ
ap-3483	65	16	equations	equation	NOUN
ap-3483	65	17	equated	equate	VERB
ap-3483	65	18	to	to	ADP
ap-3483	65	19	zero	zero	NUM
ap-3483	65	20	ϕka(x	ϕka(x	NOUN
ap-3483	65	21	,	,	PUNCT
ap-3483	65	22	θ)−	θ)−	PROPN
ap-3483	65	23	ξαa	ξαa	X
ap-3483	65	24	(	(	PUNCT
ap-3483	65	25	x	x	NOUN
ap-3483	65	26	,	,	PUNCT
ap-3483	65	27	θ)θk	θ)θk	PROPN
ap-3483	65	28	,	,	PUNCT
ap-3483	65	29	α	α	NOUN
ap-3483	65	30	=	=	SYM
ap-3483	65	31	0	0	NUM
ap-3483	65	32	,	,	PUNCT
ap-3483	65	33	a	a	DET
ap-3483	65	34	=	=	NOUN
ap-3483	65	35	1	1	NUM
ap-3483	65	36	,	,	PUNCT
ap-3483	65	37	.	.	PUNCT
ap-3483	65	38	.	.	PUNCT
ap-3483	66	1	.	.	PUNCT
ap-3483	67	1	,	,	PUNCT
ap-3483	67	2	r	r	NOUN
ap-3483	67	3	,	,	PUNCT
ap-3483	67	4	(	(	PUNCT
ap-3483	67	5	2.8	2.8	NUM
ap-3483	67	6	)	)	PUNCT
ap-3483	67	7	where	where	SCONJ
ap-3483	67	8	the	the	DET
ap-3483	67	9	index	index	NOUN
ap-3483	67	10	a	a	DET
ap-3483	67	11	runs	run	NOUN
ap-3483	67	12	over	over	ADP
ap-3483	67	13	the	the	DET
ap-3483	67	14	generators	generator	NOUN
ap-3483	67	15	of	of	ADP
ap-3483	67	16	g.	g.	PROPN
ap-3483	68	1	it	it	PRON
ap-3483	68	2	may	may	AUX
ap-3483	68	3	happen	happen	VERB
ap-3483	68	4	that	that	SCONJ
ap-3483	68	5	invariant	invariant	ADJ
ap-3483	68	6	solutions	solution	NOUN
ap-3483	68	7	are	be	AUX
ap-3483	68	8	restricted	restrict	VERB
ap-3483	68	9	in	in	ADP
ap-3483	68	10	number	number	NOUN
ap-3483	68	11	or	or	CCONJ
ap-3483	68	12	trivial	trivial	ADJ
ap-3483	68	13	if	if	SCONJ
ap-3483	68	14	the	the	DET
ap-3483	68	15	full	full	ADJ
ap-3483	68	16	symmetry	symmetry	NOUN
ap-3483	68	17	group	group	NOUN
ap-3483	68	18	is	be	AUX
ap-3483	68	19	small	small	ADJ
ap-3483	68	20	.	.	PUNCT
ap-3483	69	1	to	to	PART
ap-3483	69	2	extend	extend	VERB
ap-3483	69	3	the	the	DET
ap-3483	69	4	number	number	NOUN
ap-3483	69	5	of	of	ADP
ap-3483	69	6	symmetries	symmetry	NOUN
ap-3483	69	7	,	,	PUNCT
ap-3483	69	8	and	and	CCONJ
ap-3483	69	9	thus	thus	ADV
ap-3483	69	10	of	of	ADP
ap-3483	69	11	solutions	solution	NOUN
ap-3483	69	12	,	,	PUNCT
ap-3483	69	13	one	one	NUM
ap-3483	69	14	looks	look	VERB
ap-3483	69	15	for	for	ADP
ap-3483	69	16	generalized	generalized	ADJ
ap-3483	69	17	symmetries	symmetry	NOUN
ap-3483	69	18	.	.	PUNCT
ap-3483	70	1	they	they	PRON
ap-3483	70	2	exist	exist	VERB
ap-3483	70	3	only	only	ADV
ap-3483	70	4	if	if	SCONJ
ap-3483	70	5	the	the	DET
ap-3483	70	6	nonlinear	nonlinear	ADJ
ap-3483	70	7	equation	equation	NOUN
ap-3483	70	8	(	(	PUNCT
ap-3483	70	9	2.1	2.1	NUM
ap-3483	70	10	)	)	PUNCT
ap-3483	70	11	is	be	AUX
ap-3483	70	12	integrable	integrable	ADJ
ap-3483	70	13	[	[	X
ap-3483	70	14	28	28	NUM
ap-3483	70	15	]	]	PUNCT
ap-3483	70	16	,	,	PUNCT
ap-3483	70	17	i.e.	i.e.	X
ap-3483	70	18	it	it	PRON
ap-3483	70	19	has	have	AUX
ap-3483	70	20	been	be	AUX
ap-3483	70	21	obtained	obtain	VERB
ap-3483	70	22	as	as	ADP
ap-3483	70	23	the	the	DET
ap-3483	70	24	compatibility	compatibility	NOUN
ap-3483	70	25	of	of	ADP
ap-3483	70	26	a	a	DET
ap-3483	70	27	lax	lax	ADJ
ap-3483	70	28	pair	pair	NOUN
ap-3483	70	29	(	(	PUNCT
ap-3483	70	30	see	see	VERB
ap-3483	70	31	(	(	PUNCT
ap-3483	70	32	2.13	2.13	NUM
ap-3483	70	33	)	)	PUNCT
ap-3483	70	34	and	and	CCONJ
ap-3483	70	35	in	in	ADP
ap-3483	70	36	the	the	DET
ap-3483	70	37	following	following	NOUN
ap-3483	70	38	)	)	PUNCT
ap-3483	70	39	.	.	PUNCT
ap-3483	71	1	a	a	DET
ap-3483	71	2	generalized	generalize	VERB
ap-3483	71	3	vector	vector	NOUN
ap-3483	71	4	field	field	NOUN
ap-3483	71	5	is	be	AUX
ap-3483	71	6	expressed	express	VERB
ap-3483	71	7	in	in	ADP
ap-3483	71	8	terms	term	NOUN
ap-3483	71	9	of	of	ADP
ap-3483	71	10	the	the	DET
ap-3483	71	11	characteristics	characteristic	NOUN
ap-3483	71	12	ωr	ωr	VERB
ap-3483	71	13	=	=	PUNCT
ap-3483	71	14	rk[u	rk[u	PROPN
ap-3483	71	15	]	]	X
ap-3483	71	16	∂	∂	NUM
ap-3483	71	17	∂uk	∂uk	NOUN
ap-3483	71	18	,	,	PUNCT
ap-3483	71	19	(	(	PUNCT
ap-3483	71	20	2.9	2.9	NUM
ap-3483	71	21	)	)	PUNCT
ap-3483	72	1	where	where	SCONJ
ap-3483	72	2	[	[	X
ap-3483	72	3	u	u	X
ap-3483	72	4	]	]	X
ap-3483	72	5	=	=	SYM
ap-3483	72	6	(	(	PUNCT
ap-3483	72	7	x	x	X
ap-3483	72	8	,	,	PUNCT
ap-3483	72	9	u(n	u(n	PROPN
ap-3483	72	10	)	)	PUNCT
ap-3483	72	11	)	)	PUNCT
ap-3483	73	1	∈	∈	PROPN
ap-3483	74	1	jn	jn	PROPN
ap-3483	74	2	.	.	PUNCT
ap-3483	75	1	the	the	DET
ap-3483	75	2	prolongation	prolongation	NOUN
ap-3483	75	3	of	of	ADP
ap-3483	75	4	an	an	DET
ap-3483	75	5	evolutionary	evolutionary	ADJ
ap-3483	75	6	vector	vector	NOUN
ap-3483	75	7	field	field	NOUN
ap-3483	75	8	ωr	ωr	NOUN
ap-3483	75	9	is	be	AUX
ap-3483	75	10	given	give	VERB
ap-3483	75	11	by	by	ADP
ap-3483	75	12	prωr	prωr	NOUN
ap-3483	75	13	=	=	SYM
ap-3483	76	1	ωr	ωr	PROPN
ap-3483	77	1	+	+	PROPN
ap-3483	77	2	djr	djr	PROPN
ap-3483	77	3	k	k	PROPN
ap-3483	77	4	∂	∂	NOUN
ap-3483	77	5	∂ukj	∂ukj	X
ap-3483	77	6	.	.	PUNCT
ap-3483	78	1	(	(	PUNCT
ap-3483	78	2	2.10	2.10	NUM
ap-3483	78	3	)	)	PUNCT
ap-3483	78	4	a	a	DET
ap-3483	78	5	vector	vector	NOUN
ap-3483	78	6	field	field	NOUN
ap-3483	78	7	ωr	ωr	NOUN
ap-3483	78	8	is	be	AUX
ap-3483	78	9	a	a	DET
ap-3483	78	10	generalized	generalized	ADJ
ap-3483	78	11	symmetry	symmetry	NOUN
ap-3483	78	12	of	of	ADP
ap-3483	78	13	a	a	DET
ap-3483	78	14	nondegenerated	nondegenerated	ADJ
ap-3483	78	15	system	system	NOUN
ap-3483	78	16	of	of	ADP
ap-3483	78	17	pdes	pde	NOUN
ap-3483	78	18	(	(	PUNCT
ap-3483	78	19	2.1	2.1	NUM
ap-3483	78	20	)	)	PUNCT
ap-3483	78	21	if	if	SCONJ
ap-3483	78	22	and	and	CCONJ
ap-3483	78	23	only	only	ADV
ap-3483	78	24	if	if	SCONJ
ap-3483	78	25	[	[	X
ap-3483	78	26	29	29	NUM
ap-3483	78	27	]	]	X
ap-3483	78	28	prωrωµ(x	prωrωµ(x	NOUN
ap-3483	78	29	,	,	PUNCT
ap-3483	78	30	u(n	u(n	PROPN
ap-3483	78	31	)	)	PUNCT
ap-3483	78	32	)	)	PUNCT
ap-3483	79	1	=	=	SYM
ap-3483	79	2	0	0	NUM
ap-3483	79	3	,	,	PUNCT
ap-3483	79	4	(	(	PUNCT
ap-3483	79	5	2.11	2.11	NUM
ap-3483	79	6	)	)	PUNCT
ap-3483	79	7	whenever	whenever	SCONJ
ap-3483	79	8	ω(x	ω(x	X
ap-3483	79	9	,	,	PUNCT
ap-3483	79	10	u(n	u(n	PROPN
ap-3483	79	11	)	)	PUNCT
ap-3483	79	12	)	)	PUNCT
ap-3483	80	1	=	=	SYM
ap-3483	80	2	0	0	NUM
ap-3483	80	3	and	and	CCONJ
ap-3483	80	4	its	its	PRON
ap-3483	80	5	differential	differential	ADJ
ap-3483	80	6	consequences	consequence	NOUN
ap-3483	80	7	are	be	AUX
ap-3483	80	8	satisfied	satisfied	ADJ
ap-3483	80	9	.	.	PUNCT
ap-3483	81	1	2.2	2.2	NUM
ap-3483	81	2	.	.	PUNCT
ap-3483	82	1	the	the	DET
ap-3483	82	2	immersion	immersion	NOUN
ap-3483	82	3	formulas	formula	NOUN
ap-3483	82	4	for	for	ADP
ap-3483	82	5	soliton	soliton	NOUN
ap-3483	82	6	surfaces	surface	NOUN
ap-3483	82	7	in	in	ADP
ap-3483	82	8	order	order	NOUN
ap-3483	82	9	to	to	PART
ap-3483	82	10	analyse	analyse	VERB
ap-3483	82	11	the	the	DET
ap-3483	82	12	fokas	fokas	ADJ
ap-3483	82	13	-	-	PUNCT
ap-3483	82	14	gel’fand	gel’fand	NOUN
ap-3483	82	15	immersion	immersion	NOUN
ap-3483	82	16	formula	formula	NOUN
ap-3483	82	17	for	for	ADP
ap-3483	82	18	a	a	DET
ap-3483	82	19	surface	surface	NOUN
ap-3483	82	20	in	in	ADP
ap-3483	82	21	2d	2d	NOUN
ap-3483	82	22	,	,	PUNCT
ap-3483	82	23	we	we	PRON
ap-3483	82	24	briefly	briefly	ADV
ap-3483	82	25	summarize	summarize	VERB
ap-3483	82	26	the	the	DET
ap-3483	82	27	results	result	NOUN
ap-3483	82	28	obtained	obtain	VERB
ap-3483	82	29	in	in	ADP
ap-3483	82	30	[	[	X
ap-3483	82	31	2	2	NUM
ap-3483	82	32	,	,	PUNCT
ap-3483	82	33	5–9	5–9	NUM
ap-3483	82	34	,	,	PUNCT
ap-3483	82	35	11–13	11–13	NUM
ap-3483	82	36	,	,	PUNCT
ap-3483	82	37	15	15	NUM
ap-3483	82	38	,	,	PUNCT
ap-3483	82	39	33–35	33–35	NUM
ap-3483	82	40	]	]	PUNCT
ap-3483	82	41	.	.	PUNCT
ap-3483	83	1	let	let	VERB
ap-3483	83	2	us	we	PRON
ap-3483	83	3	consider	consider	VERB
ap-3483	83	4	an	an	DET
ap-3483	83	5	integrable	integrable	ADJ
ap-3483	83	6	system	system	NOUN
ap-3483	83	7	of	of	ADP
ap-3483	83	8	partial	partial	ADJ
ap-3483	83	9	differential	differential	ADJ
ap-3483	83	10	equations	equation	NOUN
ap-3483	83	11	(	(	PUNCT
ap-3483	83	12	pdes	pde	NOUN
ap-3483	83	13	)	)	PUNCT
ap-3483	83	14	in	in	ADP
ap-3483	83	15	two	two	NUM
ap-3483	83	16	independent	independent	ADJ
ap-3483	83	17	variables	variable	NOUN
ap-3483	83	18	x1	x1	PROPN
ap-3483	83	19	,	,	PUNCT
ap-3483	83	20	x2	x2	PROPN
ap-3483	83	21	and	and	CCONJ
ap-3483	83	22	m	m	PROPN
ap-3483	83	23	dependent	dependent	ADJ
ap-3483	83	24	variables	variable	NOUN
ap-3483	83	25	uk(x1	uk(x1	ADJ
ap-3483	83	26	,	,	PUNCT
ap-3483	83	27	x2	x2	PROPN
ap-3483	83	28	)	)	PUNCT
ap-3483	83	29	written	write	VERB
ap-3483	83	30	as	as	ADP
ap-3483	83	31	ω[u	ω[u	NOUN
ap-3483	83	32	]	]	X
ap-3483	83	33	=	=	SYM
ap-3483	83	34	0	0	X
ap-3483	83	35	.	.	PUNCT
ap-3483	84	1	(	(	PUNCT
ap-3483	84	2	2.12	2.12	NUM
ap-3483	84	3	)	)	PUNCT
ap-3483	84	4	181	181	NUM
ap-3483	84	5	a.	a.	NOUN
ap-3483	84	6	m.	m.	NOUN
ap-3483	84	7	grundland	grundland	PROPN
ap-3483	84	8	,	,	PUNCT
ap-3483	84	9	d.	d.	PROPN
ap-3483	84	10	levi	levi	PROPN
ap-3483	84	11	,	,	PUNCT
ap-3483	84	12	l.	l.	PROPN
ap-3483	84	13	martina	martina	PROPN
ap-3483	84	14	acta	acta	PROPN
ap-3483	84	15	polytechnica	polytechnica	PROPN
ap-3483	84	16	suppose	suppose	VERB
ap-3483	84	17	that	that	SCONJ
ap-3483	84	18	the	the	DET
ap-3483	84	19	system	system	NOUN
ap-3483	84	20	(	(	PUNCT
ap-3483	84	21	2.12	2.12	NUM
ap-3483	84	22	)	)	PUNCT
ap-3483	84	23	is	be	AUX
ap-3483	84	24	obtained	obtain	VERB
ap-3483	84	25	as	as	ADP
ap-3483	84	26	the	the	DET
ap-3483	84	27	compatibility	compatibility	NOUN
ap-3483	84	28	of	of	ADP
ap-3483	84	29	a	a	DET
ap-3483	84	30	matrix	matrix	NOUN
ap-3483	84	31	lsp	lsp	NOUN
ap-3483	84	32	written	write	VERB
ap-3483	84	33	in	in	ADP
ap-3483	84	34	the	the	DET
ap-3483	84	35	form	form	NOUN
ap-3483	84	36	[	[	X
ap-3483	84	37	33	33	NUM
ap-3483	84	38	]	]	SYM
ap-3483	84	39	∂αφ(x1	∂αφ(x1	PROPN
ap-3483	84	40	,	,	PUNCT
ap-3483	84	41	x2	x2	PROPN
ap-3483	84	42	,	,	PUNCT
ap-3483	84	43	λ)−	λ)−	PROPN
ap-3483	84	44	uα([u	uα([u	PROPN
ap-3483	84	45	]	]	PUNCT
ap-3483	84	46	,	,	PUNCT
ap-3483	84	47	λ)φ(x1	λ)φ(x1	ADP
ap-3483	84	48	,	,	PUNCT
ap-3483	84	49	x2	x2	PROPN
ap-3483	84	50	,	,	PUNCT
ap-3483	84	51	λ	λ	X
ap-3483	84	52	)	)	PUNCT
ap-3483	84	53	=	=	SYM
ap-3483	84	54	0	0	NUM
ap-3483	84	55	,	,	PUNCT
ap-3483	84	56	α	α	NOUN
ap-3483	84	57	=	=	SYM
ap-3483	84	58	1	1	NUM
ap-3483	84	59	,	,	PUNCT
ap-3483	84	60	2	2	NUM
ap-3483	84	61	.	.	PUNCT
ap-3483	84	62	(	(	PUNCT
ap-3483	84	63	2.13	2.13	NUM
ap-3483	84	64	)	)	PUNCT
ap-3483	84	65	in	in	ADP
ap-3483	84	66	what	what	PRON
ap-3483	84	67	follows	follow	VERB
ap-3483	84	68	,	,	PUNCT
ap-3483	84	69	the	the	DET
ap-3483	84	70	potential	potential	ADJ
ap-3483	84	71	matrices	matrix	NOUN
ap-3483	84	72	uα	uα	PROPN
ap-3483	84	73	can	can	AUX
ap-3483	84	74	be	be	AUX
ap-3483	84	75	defined	define	VERB
ap-3483	84	76	on	on	ADP
ap-3483	84	77	the	the	DET
ap-3483	84	78	extended	extended	ADJ
ap-3483	84	79	jet	jet	NOUN
ap-3483	84	80	space	space	NOUN
ap-3483	84	81	n	n	NOUN
ap-3483	84	82	=	=	SYM
ap-3483	84	83	(	(	PUNCT
ap-3483	84	84	jn	jn	PROPN
ap-3483	84	85	,	,	PUNCT
ap-3483	84	86	λ	λ	PROPN
ap-3483	84	87	)	)	PUNCT
ap-3483	84	88	,	,	PUNCT
ap-3483	84	89	where	where	SCONJ
ap-3483	84	90	λ	λ	PROPN
ap-3483	84	91	is	be	AUX
ap-3483	84	92	the	the	DET
ap-3483	84	93	spectral	spectral	ADJ
ap-3483	84	94	parameter	parameter	NOUN
ap-3483	84	95	.	.	PUNCT
ap-3483	85	1	the	the	DET
ap-3483	85	2	compatibility	compatibility	NOUN
ap-3483	85	3	condition	condition	NOUN
ap-3483	85	4	of	of	ADP
ap-3483	85	5	the	the	DET
ap-3483	85	6	lsp	lsp	PROPN
ap-3483	85	7	(	(	PUNCT
ap-3483	85	8	2.13	2.13	NUM
ap-3483	85	9	)	)	PUNCT
ap-3483	85	10	,	,	PUNCT
ap-3483	85	11	often	often	ADV
ap-3483	85	12	called	call	VERB
ap-3483	85	13	the	the	DET
ap-3483	85	14	zero	zero	NUM
ap-3483	85	15	-	-	PUNCT
ap-3483	85	16	curvature	curvature	NOUN
ap-3483	85	17	condition	condition	NOUN
ap-3483	85	18	(	(	PUNCT
ap-3483	85	19	zcc	zcc	PROPN
ap-3483	85	20	)	)	PUNCT
ap-3483	85	21	d2u1	d2u1	X
ap-3483	86	1	−d1u2	−d1u2	NOUN
ap-3483	86	2	+	+	NUM
ap-3483	86	3	[	[	X
ap-3483	86	4	u1	u1	NOUN
ap-3483	86	5	,	,	PUNCT
ap-3483	86	6	u2	u2	NOUN
ap-3483	86	7	]	]	PUNCT
ap-3483	86	8	=	=	SYM
ap-3483	86	9	0	0	NUM
ap-3483	86	10	,	,	PUNCT
ap-3483	86	11	(	(	PUNCT
ap-3483	86	12	2.14	2.14	NUM
ap-3483	86	13	)	)	PUNCT
ap-3483	86	14	which	which	PRON
ap-3483	86	15	is	be	AUX
ap-3483	86	16	assumed	assume	VERB
ap-3483	86	17	to	to	PART
ap-3483	86	18	be	be	AUX
ap-3483	86	19	valid	valid	ADJ
ap-3483	86	20	for	for	ADP
ap-3483	86	21	all	all	DET
ap-3483	86	22	values	value	NOUN
ap-3483	86	23	of	of	ADP
ap-3483	86	24	λ	λ	NOUN
ap-3483	86	25	,	,	PUNCT
ap-3483	86	26	implies	imply	VERB
ap-3483	86	27	(	(	PUNCT
ap-3483	86	28	2.12	2.12	NUM
ap-3483	86	29	)	)	PUNCT
ap-3483	86	30	.	.	PUNCT
ap-3483	87	1	the	the	DET
ap-3483	87	2	bracket	bracket	NOUN
ap-3483	87	3	in	in	ADP
ap-3483	87	4	(	(	PUNCT
ap-3483	87	5	2.14	2.14	NUM
ap-3483	87	6	)	)	PUNCT
ap-3483	87	7	denotes	denote	VERB
ap-3483	87	8	the	the	DET
ap-3483	87	9	lie	lie	NOUN
ap-3483	87	10	algebra	algebra	NOUN
ap-3483	87	11	commutator	commutator	NOUN
ap-3483	87	12	.	.	PUNCT
ap-3483	88	1	equation	equation	NOUN
ap-3483	88	2	(	(	PUNCT
ap-3483	88	3	2.14	2.14	NUM
ap-3483	88	4	)	)	PUNCT
ap-3483	88	5	provides	provide	VERB
ap-3483	88	6	a	a	DET
ap-3483	88	7	representation	representation	NOUN
ap-3483	88	8	for	for	ADP
ap-3483	88	9	the	the	DET
ap-3483	88	10	initial	initial	ADJ
ap-3483	88	11	system	system	NOUN
ap-3483	88	12	(	(	PUNCT
ap-3483	88	13	2.12	2.12	NUM
ap-3483	88	14	)	)	PUNCT
ap-3483	88	15	under	under	ADP
ap-3483	88	16	consideration	consideration	NOUN
ap-3483	88	17	.	.	PUNCT
ap-3483	89	1	the	the	DET
ap-3483	89	2	m	m	ADJ
ap-3483	89	3	-	-	ADJ
ap-3483	89	4	dimensional	dimensional	ADJ
ap-3483	89	5	matrix	matrix	NOUN
ap-3483	89	6	functions	function	NOUN
ap-3483	89	7	uα	uα	PART
ap-3483	89	8	take	take	VERB
ap-3483	89	9	values	value	NOUN
ap-3483	89	10	in	in	ADP
ap-3483	89	11	some	some	DET
ap-3483	89	12	semisimple	semisimple	NOUN
ap-3483	89	13	lie	lie	NOUN
ap-3483	89	14	algebra	algebra	NOUN
ap-3483	89	15	g	g	PROPN
ap-3483	89	16	and	and	CCONJ
ap-3483	89	17	the	the	DET
ap-3483	89	18	wavefunction	wavefunction	NOUN
ap-3483	89	19	φ	φ	PROPN
ap-3483	89	20	takes	take	VERB
ap-3483	89	21	values	value	NOUN
ap-3483	89	22	in	in	ADP
ap-3483	89	23	the	the	DET
ap-3483	89	24	corresponding	correspond	VERB
ap-3483	89	25	lie	lie	NOUN
ap-3483	89	26	group	group	NOUN
ap-3483	90	1	g.	g.	PROPN
ap-3483	91	1	we	we	PRON
ap-3483	91	2	can	can	AUX
ap-3483	91	3	say	say	VERB
ap-3483	91	4	that	that	SCONJ
ap-3483	91	5	,	,	PUNCT
ap-3483	91	6	as	as	ADV
ap-3483	91	7	long	long	ADV
ap-3483	91	8	as	as	SCONJ
ap-3483	91	9	the	the	DET
ap-3483	91	10	potential	potential	ADJ
ap-3483	91	11	matrices	matrix	NOUN
ap-3483	91	12	uα([u	uα([u	PROPN
ap-3483	91	13	]	]	PUNCT
ap-3483	91	14	,	,	PUNCT
ap-3483	91	15	λ	λ	NOUN
ap-3483	91	16	)	)	PUNCT
ap-3483	91	17	satisfy	satisfy	VERB
ap-3483	91	18	the	the	DET
ap-3483	91	19	zcc	zcc	NOUN
ap-3483	91	20	(	(	PUNCT
ap-3483	91	21	2.14	2.14	NUM
ap-3483	91	22	)	)	PUNCT
ap-3483	91	23	,	,	PUNCT
ap-3483	91	24	there	there	PRON
ap-3483	91	25	exists	exist	VERB
ap-3483	91	26	a	a	DET
ap-3483	91	27	group	group	NOUN
ap-3483	91	28	-	-	PUNCT
ap-3483	91	29	valued	value	VERB
ap-3483	91	30	function	function	NOUN
ap-3483	91	31	φ	φ	NUM
ap-3483	91	32	which	which	PRON
ap-3483	91	33	satisfies	satisfy	VERB
ap-3483	91	34	(	(	PUNCT
ap-3483	91	35	2.13	2.13	NUM
ap-3483	91	36	)	)	PUNCT
ap-3483	91	37	.	.	PUNCT
ap-3483	92	1	there	there	PRON
ap-3483	92	2	exists	exist	VERB
ap-3483	92	3	a	a	DET
ap-3483	92	4	subclass	subclass	NOUN
ap-3483	92	5	of	of	ADP
ap-3483	92	6	φ	φ	NUM
ap-3483	92	7	which	which	PRON
ap-3483	92	8	can	can	AUX
ap-3483	92	9	be	be	AUX
ap-3483	92	10	defined	define	VERB
ap-3483	92	11	formally	formally	ADV
ap-3483	92	12	on	on	ADP
ap-3483	92	13	the	the	DET
ap-3483	92	14	extended	extended	ADJ
ap-3483	92	15	jet	jet	NOUN
ap-3483	92	16	space	space	NOUN
ap-3483	92	17	n	n	NOUN
ap-3483	92	18	.	.	PUNCT
ap-3483	93	1	for	for	ADP
ap-3483	93	2	φ	φ	NUM
ap-3483	93	3	belonging	belong	VERB
ap-3483	93	4	to	to	ADP
ap-3483	93	5	this	this	DET
ap-3483	93	6	subclass	subclass	NOUN
ap-3483	93	7	we	we	PRON
ap-3483	93	8	can	can	AUX
ap-3483	93	9	write	write	VERB
ap-3483	93	10	formally	formally	ADV
ap-3483	93	11	φ	φ	PROPN
ap-3483	93	12	=	=	SYM
ap-3483	93	13	φ([u	φ([u	PROPN
ap-3483	93	14	]	]	PUNCT
ap-3483	93	15	,	,	PUNCT
ap-3483	93	16	λ	λ	NOUN
ap-3483	93	17	)	)	PUNCT
ap-3483	93	18	∈	∈	PROPN
ap-3483	93	19	g	g	NOUN
ap-3483	93	20	,	,	PUNCT
ap-3483	93	21	meaning	mean	VERB
ap-3483	93	22	that	that	SCONJ
ap-3483	93	23	φ	φ	PROPN
ap-3483	93	24	depends	depend	VERB
ap-3483	93	25	functionally	functionally	ADV
ap-3483	93	26	on	on	ADP
ap-3483	93	27	[	[	X
ap-3483	93	28	u	u	X
ap-3483	93	29	]	]	X
ap-3483	93	30	and	and	CCONJ
ap-3483	93	31	meromorphically	meromorphically	ADV
ap-3483	93	32	in	in	ADP
ap-3483	93	33	λ	λ	PROPN
ap-3483	93	34	.	.	PUNCT
ap-3483	94	1	when	when	SCONJ
ap-3483	94	2	φ	φ	PROPN
ap-3483	94	3	=	=	SYM
ap-3483	94	4	φ([u	φ([u	PROPN
ap-3483	94	5	]	]	PUNCT
ap-3483	94	6	,	,	PUNCT
ap-3483	94	7	λ	λ	PROPN
ap-3483	94	8	)	)	PUNCT
ap-3483	94	9	the	the	DET
ap-3483	94	10	lsp	lsp	PROPN
ap-3483	94	11	(	(	PUNCT
ap-3483	94	12	2.13	2.13	NUM
ap-3483	94	13	)	)	PUNCT
ap-3483	94	14	can	can	AUX
ap-3483	94	15	be	be	AUX
ap-3483	94	16	written	write	VERB
ap-3483	94	17	as	as	ADP
ap-3483	94	18	λα([u	λα([u	PROPN
ap-3483	94	19	]	]	PUNCT
ap-3483	94	20	,	,	PUNCT
ap-3483	94	21	λ	λ	NOUN
ap-3483	94	22	)	)	PUNCT
ap-3483	94	23	≡	≡	PROPN
ap-3483	94	24	dαφ([u	dαφ([u	NOUN
ap-3483	94	25	]	]	PUNCT
ap-3483	94	26	,	,	PUNCT
ap-3483	94	27	λ)−	λ)−	PROPN
ap-3483	94	28	uα([u	uα([u	PROPN
ap-3483	94	29	]	]	X
ap-3483	94	30	,	,	PUNCT
ap-3483	94	31	λ)φ([u	λ)φ([u	NOUN
ap-3483	94	32	]	]	X
ap-3483	94	33	,	,	PUNCT
ap-3483	94	34	λ	λ	NOUN
ap-3483	94	35	)	)	PUNCT
ap-3483	94	36	=	=	SYM
ap-3483	94	37	0	0	NUM
ap-3483	94	38	,	,	PUNCT
ap-3483	94	39	α	α	NOUN
ap-3483	94	40	=	=	SYM
ap-3483	94	41	1	1	NUM
ap-3483	94	42	,	,	PUNCT
ap-3483	94	43	2	2	NUM
ap-3483	94	44	,	,	PUNCT
ap-3483	94	45	(	(	PUNCT
ap-3483	94	46	2.15	2.15	NUM
ap-3483	94	47	)	)	PUNCT
ap-3483	94	48	which	which	PRON
ap-3483	94	49	is	be	AUX
ap-3483	94	50	a	a	DET
ap-3483	94	51	convenient	convenient	ADJ
ap-3483	94	52	form	form	NOUN
ap-3483	94	53	for	for	ADP
ap-3483	94	54	the	the	DET
ap-3483	94	55	analysis	analysis	NOUN
ap-3483	94	56	we	we	PRON
ap-3483	94	57	carry	carry	VERB
ap-3483	94	58	out	out	ADP
ap-3483	94	59	in	in	ADP
ap-3483	94	60	the	the	DET
ap-3483	94	61	following	following	NOUN
ap-3483	94	62	.	.	PUNCT
ap-3483	95	1	in	in	ADP
ap-3483	95	2	reference	reference	NOUN
ap-3483	95	3	[	[	X
ap-3483	95	4	9	9	NUM
ap-3483	95	5	]	]	PUNCT
ap-3483	95	6	,	,	PUNCT
ap-3483	95	7	the	the	DET
ap-3483	95	8	authors	author	NOUN
ap-3483	95	9	looked	look	VERB
ap-3483	95	10	for	for	ADP
ap-3483	95	11	a	a	DET
ap-3483	95	12	simultaneous	simultaneous	ADJ
ap-3483	95	13	infinitesimal	infinitesimal	ADJ
ap-3483	95	14	deformation	deformation	NOUN
ap-3483	95	15	of	of	ADP
ap-3483	95	16	the	the	DET
ap-3483	95	17	associated	associated	ADJ
ap-3483	95	18	lsp	lsp	PROPN
ap-3483	95	19	(	(	PUNCT
ap-3483	95	20	2.15	2.15	NUM
ap-3483	95	21	)	)	PUNCT
ap-3483	95	22	which	which	PRON
ap-3483	95	23	preserves	preserve	VERB
ap-3483	95	24	the	the	DET
ap-3483	95	25	zcc	zcc	NOUN
ap-3483	95	26	(	(	PUNCT
ap-3483	95	27	2.14)ũ1	2.14)ũ1	NOUN
ap-3483	95	28	ũ2	ũ2	PROPN
ap-3483	95	29	φ̃	φ̃	PROPN
ap-3483	95	30			PROPN
ap-3483	95	31	=	=	SYM
ap-3483	95	32	u1	u1	NOUN
ap-3483	95	33	u2	u2	PROPN
ap-3483	95	34	φ	φ	PROPN
ap-3483	95	35	+	+	PROPN
ap-3483	95	36	ε	ε	PROPN
ap-3483	95	37	a1	a1	X
ap-3483	95	38	a2	a2	PROPN
ap-3483	95	39	ψ	ψ	PROPN
ap-3483	95	40	+o(ε2	+o(ε2	NUM
ap-3483	95	41	)	)	PUNCT
ap-3483	95	42	,	,	PUNCT
ap-3483	95	43	(	(	PUNCT
ap-3483	95	44	2.16	2.16	NUM
ap-3483	95	45	)	)	PUNCT
ap-3483	95	46	where	where	SCONJ
ap-3483	95	47	the	the	DET
ap-3483	95	48	matrices	matrix	NOUN
ap-3483	95	49	ũ1	ũ1	NOUN
ap-3483	95	50	,	,	PUNCT
ap-3483	95	51	ũ2	ũ2	PROPN
ap-3483	95	52	,	,	PUNCT
ap-3483	95	53	a1	a1	NOUN
ap-3483	95	54	and	and	CCONJ
ap-3483	95	55	a2	a2	PROPN
ap-3483	95	56	take	take	VERB
ap-3483	95	57	values	value	NOUN
ap-3483	95	58	in	in	ADP
ap-3483	95	59	the	the	DET
ap-3483	95	60	lie	lie	NOUN
ap-3483	95	61	algebra	algebra	VERB
ap-3483	95	62	g	g	NOUN
ap-3483	95	63	,	,	PUNCT
ap-3483	95	64	while	while	SCONJ
ap-3483	95	65	φ̃	φ̃	PROPN
ap-3483	95	66	and	and	CCONJ
ap-3483	95	67	ψ	ψ	PROPN
ap-3483	95	68	belong	belong	VERB
ap-3483	95	69	to	to	ADP
ap-3483	95	70	the	the	DET
ap-3483	95	71	corresponding	correspond	VERB
ap-3483	95	72	lie	lie	NOUN
ap-3483	95	73	group	group	NOUN
ap-3483	95	74	g.	g.	PROPN
ap-3483	96	1	the	the	DET
ap-3483	96	2	parameter	parameter	PROPN
ap-3483	96	3	λ	λ	PROPN
ap-3483	96	4	is	be	AUX
ap-3483	96	5	left	leave	VERB
ap-3483	96	6	invariant	invariant	ADJ
ap-3483	96	7	under	under	ADP
ap-3483	96	8	the	the	DET
ap-3483	96	9	transformation	transformation	NOUN
ap-3483	96	10	(	(	PUNCT
ap-3483	96	11	2.16	2.16	NUM
ap-3483	96	12	)	)	PUNCT
ap-3483	96	13	and	and	CCONJ
ap-3483	96	14	0	0	NUM
ap-3483	96	15	<	<	X
ap-3483	96	16	ε	ε	PROPN
ap-3483	96	17	�	�	PROPN
ap-3483	96	18	1	1	NUM
ap-3483	96	19	.	.	PUNCT
ap-3483	97	1	the	the	DET
ap-3483	97	2	corresponding	correspond	VERB
ap-3483	97	3	infinitesimal	infinitesimal	ADJ
ap-3483	97	4	generator	generator	NOUN
ap-3483	97	5	formally	formally	ADV
ap-3483	97	6	takes	take	VERB
ap-3483	97	7	the	the	DET
ap-3483	97	8	evolutionary	evolutionary	ADJ
ap-3483	97	9	form	form	NOUN
ap-3483	97	10	x̂e	x̂e	PRON
ap-3483	98	1	=	=	PUNCT
ap-3483	98	2	a1∂u1	a1∂u1	NOUN
ap-3483	98	3	+	+	ADJ
ap-3483	98	4	a2∂u2	a2∂u2	NOUN
ap-3483	98	5	+	+	CCONJ
ap-3483	98	6	ψ∂φ	ψ∂φ	PROPN
ap-3483	98	7	.	.	PUNCT
ap-3483	99	1	(	(	PUNCT
ap-3483	99	2	2.17	2.17	NUM
ap-3483	99	3	)	)	PUNCT
ap-3483	99	4	equation	equation	NOUN
ap-3483	99	5	(	(	PUNCT
ap-3483	99	6	2.17	2.17	NUM
ap-3483	99	7	)	)	PUNCT
ap-3483	99	8	can	can	AUX
ap-3483	99	9	be	be	AUX
ap-3483	99	10	written	write	VERB
ap-3483	99	11	as	as	ADP
ap-3483	99	12	x̂ε	x̂ε	PROPN
ap-3483	99	13	=	=	SYM
ap-3483	99	14	a1j∂uj	a1j∂uj	PROPN
ap-3483	99	15	1	1	NUM
ap-3483	100	1	+	+	NOUN
ap-3483	100	2	a2j∂uj	a2j∂uj	PROPN
ap-3483	100	3	2	2	NUM
ap-3483	100	4	+	+	CCONJ
ap-3483	100	5	ψj∂φj	ψj∂φj	PROPN
ap-3483	100	6	,	,	PUNCT
ap-3483	100	7	(	(	PUNCT
ap-3483	100	8	2.18	2.18	NUM
ap-3483	100	9	)	)	PUNCT
ap-3483	100	10	where	where	SCONJ
ap-3483	100	11	we	we	PRON
ap-3483	100	12	decompose	decompose	VERB
ap-3483	100	13	the	the	DET
ap-3483	100	14	matrix	matrix	NOUN
ap-3483	100	15	functions	function	NOUN
ap-3483	100	16	a1	a1	NOUN
ap-3483	100	17	and	and	CCONJ
ap-3483	100	18	a2	a2	PROPN
ap-3483	100	19	in	in	ADP
ap-3483	100	20	the	the	DET
ap-3483	100	21	basis	basis	NOUN
ap-3483	100	22	ej	ej	NOUN
ap-3483	100	23	,	,	PUNCT
ap-3483	100	24	j	j	PROPN
ap-3483	100	25	=	=	SYM
ap-3483	100	26	1	1	NUM
ap-3483	100	27	,	,	PUNCT
ap-3483	100	28	.	.	PUNCT
ap-3483	100	29	.	.	PUNCT
ap-3483	101	1	.	.	PUNCT
ap-3483	102	1	,	,	PUNCT
ap-3483	102	2	s	s	VERB
ap-3483	102	3	for	for	SCONJ
ap-3483	102	4	the	the	DET
ap-3483	102	5	lie	lie	NOUN
ap-3483	102	6	algebra	algebra	NOUN
ap-3483	102	7	g	g	PRON
ap-3483	102	8	uα	uα	PROPN
ap-3483	102	9	=	=	PUNCT
ap-3483	102	10	u	u	PROPN
ap-3483	102	11	jαej	jαej	VERB
ap-3483	102	12	∈	∈	PROPN
ap-3483	102	13	g	g	PROPN
ap-3483	102	14	,	,	PUNCT
ap-3483	102	15	[	[	X
ap-3483	102	16	ei	ei	X
ap-3483	102	17	,	,	PUNCT
ap-3483	102	18	ej	ej	X
ap-3483	102	19	]	]	X
ap-3483	102	20	=	=	PUNCT
ap-3483	102	21	ckijek	ckijek	NOUN
ap-3483	102	22	,	,	PUNCT
ap-3483	102	23	(	(	PUNCT
ap-3483	102	24	2.19	2.19	NUM
ap-3483	102	25	)	)	PUNCT
ap-3483	102	26	where	where	SCONJ
ap-3483	102	27	[	[	PUNCT
ap-3483	102	28	,	,	PUNCT
ap-3483	102	29	]	]	X
ap-3483	102	30	is	be	AUX
ap-3483	102	31	the	the	DET
ap-3483	102	32	lie	lie	NOUN
ap-3483	102	33	algebra	algebra	NOUN
ap-3483	102	34	commutator	commutator	NOUN
ap-3483	102	35	and	and	CCONJ
ap-3483	102	36	ckij	ckij	PROPN
ap-3483	102	37	are	be	AUX
ap-3483	102	38	the	the	DET
ap-3483	102	39	structural	structural	ADJ
ap-3483	102	40	constants	constant	NOUN
ap-3483	102	41	of	of	ADP
ap-3483	102	42	g.	g.	PROPN
ap-3483	102	43	since	since	SCONJ
ap-3483	102	44	this	this	DET
ap-3483	102	45	generator	generator	NOUN
ap-3483	102	46	x̂e	x̂e	PRON
ap-3483	102	47	does	do	AUX
ap-3483	102	48	not	not	PART
ap-3483	102	49	transform	transform	VERB
ap-3483	102	50	λ	λ	PRON
ap-3483	102	51	,	,	PUNCT
ap-3483	102	52	these	these	DET
ap-3483	102	53	symmetries	symmetry	NOUN
ap-3483	102	54	preserve	preserve	VERB
ap-3483	102	55	the	the	DET
ap-3483	102	56	singularity	singularity	NOUN
ap-3483	102	57	structure	structure	NOUN
ap-3483	102	58	of	of	ADP
ap-3483	102	59	the	the	DET
ap-3483	102	60	potential	potential	ADJ
ap-3483	102	61	matrices	matrix	NOUN
ap-3483	102	62	uα	uα	NOUN
ap-3483	102	63	in	in	ADP
ap-3483	102	64	the	the	DET
ap-3483	102	65	spectral	spectral	ADJ
ap-3483	102	66	parameter	parameter	PROPN
ap-3483	102	67	λ	λ	PROPN
ap-3483	102	68	.	.	PUNCT
ap-3483	103	1	the	the	DET
ap-3483	103	2	infinitesimal	infinitesimal	ADJ
ap-3483	103	3	deformation	deformation	NOUN
ap-3483	103	4	of	of	ADP
ap-3483	103	5	the	the	DET
ap-3483	103	6	lsp	lsp	PROPN
ap-3483	103	7	(	(	PUNCT
ap-3483	103	8	2.13	2.13	NUM
ap-3483	103	9	)	)	PUNCT
ap-3483	103	10	and	and	CCONJ
ap-3483	103	11	the	the	DET
ap-3483	103	12	zcc	zcc	NOUN
ap-3483	103	13	(	(	PUNCT
ap-3483	103	14	2.14	2.14	NUM
ap-3483	103	15	)	)	PUNCT
ap-3483	103	16	under	under	ADP
ap-3483	103	17	the	the	DET
ap-3483	103	18	infinitesimal	infinitesimal	ADJ
ap-3483	103	19	transformation	transformation	NOUN
ap-3483	103	20	(	(	PUNCT
ap-3483	103	21	2.16	2.16	NUM
ap-3483	103	22	)	)	PUNCT
ap-3483	103	23	requires	require	VERB
ap-3483	103	24	that	that	SCONJ
ap-3483	103	25	the	the	DET
ap-3483	103	26	matrix	matrix	NOUN
ap-3483	103	27	functions	function	NOUN
ap-3483	103	28	uα	uα	NOUN
ap-3483	103	29	and	and	CCONJ
ap-3483	103	30	ψ	ψ	X
ap-3483	103	31	satisfy	satisfy	NOUN
ap-3483	103	32	,	,	PUNCT
ap-3483	103	33	at	at	ADP
ap-3483	103	34	first	first	ADJ
ap-3483	103	35	order	order	NOUN
ap-3483	103	36	in	in	ADP
ap-3483	103	37	ε	ε	PROPN
ap-3483	103	38	,	,	PUNCT
ap-3483	103	39	the	the	DET
ap-3483	103	40	equations	equation	NOUN
ap-3483	103	41	dαψ	dαψ	VERB
ap-3483	103	42	=	=	SYM
ap-3483	103	43	uαψ	uαψ	NOUN
ap-3483	104	1	+	+	NOUN
ap-3483	104	2	aαφ	aαφ	NOUN
ap-3483	104	3	,	,	PUNCT
ap-3483	105	1	α	α	NOUN
ap-3483	105	2	=	=	SYM
ap-3483	105	3	1	1	NUM
ap-3483	105	4	,	,	PUNCT
ap-3483	105	5	2	2	NUM
ap-3483	105	6	(	(	PUNCT
ap-3483	105	7	2.20	2.20	NUM
ap-3483	105	8	)	)	PUNCT
ap-3483	105	9	and	and	CCONJ
ap-3483	105	10	d2a1	d2a1	ADP
ap-3483	106	1	−d1a2	−d1a2	INTJ
ap-3483	106	2	+	+	NUM
ap-3483	106	3	[	[	X
ap-3483	106	4	a1	a1	NOUN
ap-3483	106	5	,	,	PUNCT
ap-3483	106	6	u2	u2	NOUN
ap-3483	106	7	]	]	PUNCT
ap-3483	106	8	+	+	CCONJ
ap-3483	106	9	[	[	X
ap-3483	106	10	u1	u1	NOUN
ap-3483	106	11	,	,	PUNCT
ap-3483	106	12	a2	a2	PROPN
ap-3483	106	13	]	]	X
ap-3483	106	14	=	=	SYM
ap-3483	106	15	0	0	NUM
ap-3483	106	16	,	,	PUNCT
ap-3483	106	17	(	(	PUNCT
ap-3483	106	18	2.21	2.21	NUM
ap-3483	106	19	)	)	PUNCT
ap-3483	106	20	the	the	DET
ap-3483	106	21	equation	equation	NOUN
ap-3483	106	22	(	(	PUNCT
ap-3483	106	23	2.21	2.21	NUM
ap-3483	106	24	)	)	PUNCT
ap-3483	106	25	coincides	coincide	VERB
ap-3483	106	26	with	with	ADP
ap-3483	106	27	the	the	DET
ap-3483	106	28	compatibility	compatibility	NOUN
ap-3483	106	29	condition	condition	NOUN
ap-3483	106	30	for	for	ADP
ap-3483	106	31	(	(	PUNCT
ap-3483	106	32	2.20	2.20	NUM
ap-3483	106	33	)	)	PUNCT
ap-3483	106	34	.	.	PUNCT
ap-3483	107	1	for	for	ADP
ap-3483	107	2	the	the	DET
ap-3483	107	3	given	give	VERB
ap-3483	107	4	matrix	matrix	NOUN
ap-3483	107	5	functions	function	NOUN
ap-3483	107	6	uα	uα	PROPN
ap-3483	107	7	,	,	PUNCT
ap-3483	107	8	aα	aα	NOUN
ap-3483	107	9	∈	∈	PROPN
ap-3483	107	10	g	g	PROPN
ap-3483	107	11	and	and	CCONJ
ap-3483	107	12	φ	φ	PROPN
ap-3483	107	13	∈	∈	PROPN
ap-3483	107	14	g	g	PROPN
ap-3483	107	15	satisfying	satisfy	VERB
ap-3483	107	16	equations	equation	NOUN
ap-3483	107	17	(	(	PUNCT
ap-3483	107	18	2.14	2.14	NUM
ap-3483	107	19	)	)	PUNCT
ap-3483	107	20	,	,	PUNCT
ap-3483	107	21	(	(	PUNCT
ap-3483	107	22	2.15	2.15	NUM
ap-3483	107	23	)	)	PUNCT
ap-3483	107	24	and	and	CCONJ
ap-3483	107	25	(	(	PUNCT
ap-3483	107	26	2.21	2.21	NUM
ap-3483	107	27	)	)	PUNCT
ap-3483	107	28	,	,	PUNCT
ap-3483	107	29	an	an	DET
ap-3483	107	30	infinitesimal	infinitesimal	ADJ
ap-3483	107	31	symmetry	symmetry	NOUN
ap-3483	107	32	of	of	ADP
ap-3483	107	33	the	the	DET
ap-3483	107	34	matrix	matrix	NOUN
ap-3483	107	35	system	system	NOUN
ap-3483	107	36	of	of	ADP
ap-3483	107	37	the	the	DET
ap-3483	107	38	integrable	integrable	ADJ
ap-3483	107	39	pdes	pde	NOUN
ap-3483	107	40	(	(	PUNCT
ap-3483	107	41	2.12	2.12	NUM
ap-3483	107	42	)	)	PUNCT
ap-3483	107	43	allows	allow	VERB
ap-3483	107	44	us	we	PRON
ap-3483	107	45	to	to	PART
ap-3483	107	46	generate	generate	VERB
ap-3483	107	47	a	a	DET
ap-3483	107	48	2d	2d	NUM
ap-3483	107	49	-	-	PUNCT
ap-3483	107	50	surface	surface	NOUN
ap-3483	107	51	immersed	immerse	VERB
ap-3483	107	52	in	in	ADP
ap-3483	107	53	the	the	DET
ap-3483	107	54	lie	lie	NOUN
ap-3483	107	55	algebra	algebra	NOUN
ap-3483	107	56	g.	g.	NOUN
ap-3483	107	57	according	accord	VERB
ap-3483	107	58	to	to	ADP
ap-3483	107	59	[	[	X
ap-3483	107	60	8	8	NUM
ap-3483	107	61	]	]	PUNCT
ap-3483	107	62	this	this	DET
ap-3483	107	63	result	result	NOUN
ap-3483	107	64	is	be	AUX
ap-3483	107	65	formulated	formulate	VERB
ap-3483	107	66	as	as	SCONJ
ap-3483	107	67	follows	follow	NOUN
ap-3483	107	68	.	.	PUNCT
ap-3483	108	1	theorem	theorem	NOUN
ap-3483	108	2	1	1	NUM
ap-3483	108	3	.	.	PUNCT
ap-3483	109	1	if	if	SCONJ
ap-3483	109	2	the	the	DET
ap-3483	109	3	matrix	matrix	NOUN
ap-3483	109	4	functions	function	NOUN
ap-3483	109	5	uα	uα	PROPN
ap-3483	109	6	∈	∈	PROPN
ap-3483	109	7	g	g	PROPN
ap-3483	109	8	,	,	PUNCT
ap-3483	109	9	α	α	NOUN
ap-3483	109	10	=	=	SYM
ap-3483	109	11	1	1	NUM
ap-3483	109	12	,	,	PUNCT
ap-3483	109	13	2	2	NUM
ap-3483	109	14	and	and	CCONJ
ap-3483	109	15	φ	φ	NUM
ap-3483	109	16	∈	∈	PROPN
ap-3483	109	17	g	g	PROPN
ap-3483	109	18	of	of	ADP
ap-3483	109	19	the	the	DET
ap-3483	109	20	lsp	lsp	PROPN
ap-3483	109	21	(	(	PUNCT
ap-3483	109	22	2.15	2.15	NUM
ap-3483	109	23	)	)	PUNCT
ap-3483	109	24	satisfy	satisfy	VERB
ap-3483	109	25	the	the	DET
ap-3483	109	26	zcc	zcc	NOUN
ap-3483	109	27	(	(	PUNCT
ap-3483	109	28	2.14	2.14	NUM
ap-3483	109	29	)	)	PUNCT
ap-3483	109	30	and	and	CCONJ
ap-3483	109	31	aα	aα	NOUN
ap-3483	109	32	∈	∈	PROPN
ap-3483	109	33	g	g	NOUN
ap-3483	109	34	are	be	AUX
ap-3483	109	35	linearly	linearly	ADV
ap-3483	109	36	independent	independent	ADJ
ap-3483	109	37	matrix	matrix	NOUN
ap-3483	109	38	functions	function	NOUN
ap-3483	109	39	which	which	PRON
ap-3483	109	40	satisfy	satisfy	VERB
ap-3483	109	41	(	(	PUNCT
ap-3483	109	42	2.21	2.21	NUM
ap-3483	109	43	)	)	PUNCT
ap-3483	109	44	and	and	CCONJ
ap-3483	109	45	φ	φ	NUM
ap-3483	109	46	∈	∈	PROPN
ap-3483	109	47	g	g	PROPN
ap-3483	109	48	satisfies	satisfy	VERB
ap-3483	109	49	the	the	DET
ap-3483	109	50	lsp	lsp	PROPN
ap-3483	109	51	(	(	PUNCT
ap-3483	109	52	2.15	2.15	NUM
ap-3483	109	53	)	)	PUNCT
ap-3483	109	54	,	,	PUNCT
ap-3483	109	55	then	then	ADV
ap-3483	109	56	there	there	PRON
ap-3483	109	57	exists	exist	VERB
ap-3483	109	58	(	(	PUNCT
ap-3483	109	59	up	up	ADP
ap-3483	109	60	to	to	PART
ap-3483	109	61	affine	affine	VERB
ap-3483	109	62	transformations	transformation	NOUN
ap-3483	109	63	)	)	PUNCT
ap-3483	109	64	a	a	DET
ap-3483	109	65	2d	2d	NOUN
ap-3483	109	66	-	-	PUNCT
ap-3483	109	67	surface	surface	NOUN
ap-3483	109	68	with	with	ADP
ap-3483	109	69	a	a	DET
ap-3483	109	70	g	g	ADV
ap-3483	109	71	-	-	PUNCT
ap-3483	109	72	valued	value	VERB
ap-3483	109	73	immersion	immersion	NOUN
ap-3483	109	74	function	function	NOUN
ap-3483	109	75	f	f	NOUN
ap-3483	109	76	(	(	PUNCT
ap-3483	109	77	[	[	X
ap-3483	109	78	u	u	X
ap-3483	109	79	]	]	X
ap-3483	109	80	,	,	PUNCT
ap-3483	109	81	λ	λ	NOUN
ap-3483	109	82	)	)	PUNCT
ap-3483	109	83	such	such	ADJ
ap-3483	109	84	that	that	SCONJ
ap-3483	109	85	the	the	DET
ap-3483	109	86	tangent	tangent	NOUN
ap-3483	109	87	vectors	vector	NOUN
ap-3483	109	88	to	to	ADP
ap-3483	109	89	this	this	DET
ap-3483	109	90	surface	surface	NOUN
ap-3483	109	91	are	be	AUX
ap-3483	109	92	given	give	VERB
ap-3483	109	93	by	by	ADP
ap-3483	109	94	dαf	dαf	NOUN
ap-3483	109	95	(	(	PUNCT
ap-3483	109	96	[	[	X
ap-3483	109	97	u	u	X
ap-3483	109	98	]	]	X
ap-3483	109	99	,	,	PUNCT
ap-3483	109	100	λ	λ	NOUN
ap-3483	109	101	)	)	PUNCT
ap-3483	109	102	=	=	SYM
ap-3483	109	103	φ−1aα([u	φ−1aα([u	PROPN
ap-3483	109	104	]	]	PUNCT
ap-3483	109	105	,	,	PUNCT
ap-3483	109	106	λ)φ	λ)φ	ADJ
ap-3483	109	107	,	,	PUNCT
ap-3483	109	108	α	α	NOUN
ap-3483	109	109	=	=	SYM
ap-3483	109	110	1	1	NUM
ap-3483	109	111	,	,	PUNCT
ap-3483	109	112	2	2	NUM
ap-3483	109	113	.	.	PUNCT
ap-3483	109	114	(	(	PUNCT
ap-3483	109	115	2.22	2.22	NUM
ap-3483	109	116	)	)	PUNCT
ap-3483	109	117	proof	proof	NOUN
ap-3483	109	118	.	.	PUNCT
ap-3483	110	1	the	the	DET
ap-3483	110	2	compatibility	compatibility	NOUN
ap-3483	110	3	condition	condition	NOUN
ap-3483	110	4	of	of	ADP
ap-3483	110	5	(	(	PUNCT
ap-3483	110	6	2.22	2.22	NUM
ap-3483	110	7	)	)	PUNCT
ap-3483	110	8	coincides	coincide	VERB
ap-3483	110	9	with	with	ADP
ap-3483	110	10	(	(	PUNCT
ap-3483	110	11	2.21	2.21	NUM
ap-3483	110	12	)	)	PUNCT
ap-3483	110	13	.	.	PUNCT
ap-3483	111	1	so	so	ADV
ap-3483	111	2	an	an	DET
ap-3483	111	3	immersion	immersion	NOUN
ap-3483	111	4	function	function	NOUN
ap-3483	111	5	f	f	NOUN
ap-3483	111	6	(	(	PUNCT
ap-3483	111	7	[	[	X
ap-3483	111	8	u	u	X
ap-3483	111	9	]	]	X
ap-3483	111	10	,	,	PUNCT
ap-3483	111	11	λ	λ	NOUN
ap-3483	111	12	)	)	PUNCT
ap-3483	111	13	exists	exist	VERB
ap-3483	111	14	and	and	CCONJ
ap-3483	111	15	can	can	AUX
ap-3483	111	16	be	be	AUX
ap-3483	111	17	assumed	assume	VERB
ap-3483	111	18	to	to	PART
ap-3483	111	19	take	take	VERB
ap-3483	111	20	its	its	PRON
ap-3483	111	21	values	value	NOUN
ap-3483	111	22	in	in	ADP
ap-3483	111	23	the	the	DET
ap-3483	111	24	lie	lie	NOUN
ap-3483	111	25	algebra	algebra	NOUN
ap-3483	111	26	g.	g.	PROPN
ap-3483	112	1	if	if	SCONJ
ap-3483	112	2	we	we	PRON
ap-3483	112	3	define	define	VERB
ap-3483	112	4	the	the	DET
ap-3483	112	5	matrix	matrix	NOUN
ap-3483	112	6	function	function	NOUN
ap-3483	112	7	ψ	ψ	NOUN
ap-3483	112	8	=	=	X
ap-3483	112	9	φf	φf	NOUN
ap-3483	112	10	,	,	PUNCT
ap-3483	112	11	(	(	PUNCT
ap-3483	112	12	2.23	2.23	NUM
ap-3483	112	13	)	)	PUNCT
ap-3483	112	14	then	then	ADV
ap-3483	112	15	,	,	PUNCT
ap-3483	112	16	using	use	VERB
ap-3483	112	17	(	(	PUNCT
ap-3483	112	18	2.22	2.22	NUM
ap-3483	112	19	)	)	PUNCT
ap-3483	112	20	,	,	PUNCT
ap-3483	112	21	the	the	DET
ap-3483	112	22	function	function	NOUN
ap-3483	112	23	ψ	ψ	X
ap-3483	112	24	satisfies	satisfie	NOUN
ap-3483	112	25	(	(	PUNCT
ap-3483	112	26	2.20	2.20	NUM
ap-3483	112	27	)	)	PUNCT
ap-3483	112	28	.	.	PUNCT
ap-3483	113	1	hence	hence	ADV
ap-3483	113	2	,	,	PUNCT
ap-3483	113	3	since	since	SCONJ
ap-3483	113	4	f	f	PROPN
ap-3483	113	5	=	=	SYM
ap-3483	113	6	φ−1ψ	φ−1ψ	NOUN
ap-3483	113	7	,	,	PUNCT
ap-3483	113	8	the	the	DET
ap-3483	113	9	formula	formula	NOUN
ap-3483	113	10	φ̃	φ̃	PROPN
ap-3483	113	11	=	=	SYM
ap-3483	113	12	φ	φ	PROPN
ap-3483	113	13	+	+	X
ap-3483	113	14	εψ	εψ	PROPN
ap-3483	113	15	=	=	PUNCT
ap-3483	113	16	φ(i	φ(i	PROPN
ap-3483	113	17	+	+	CCONJ
ap-3483	113	18	εf	εf	PROPN
ap-3483	113	19	)	)	PUNCT
ap-3483	113	20	implies	imply	VERB
ap-3483	113	21	that	that	SCONJ
ap-3483	113	22	φ̃	φ̃	PROPN
ap-3483	113	23	is	be	AUX
ap-3483	113	24	in	in	ADP
ap-3483	113	25	the	the	DET
ap-3483	113	26	lie	lie	NOUN
ap-3483	113	27	group	group	NOUN
ap-3483	113	28	g.	g.	PROPN
ap-3483	114	1	the	the	DET
ap-3483	114	2	immersion	immersion	NOUN
ap-3483	114	3	function	function	NOUN
ap-3483	114	4	f	f	NOUN
ap-3483	114	5	=	=	PUNCT
ap-3483	114	6	(	(	PUNCT
ap-3483	114	7	φ−1([u	φ−1([u	PROPN
ap-3483	114	8	]	]	PUNCT
ap-3483	114	9	,	,	PUNCT
ap-3483	114	10	λ)dφ̃([u	λ)dφ̃([u	PROPN
ap-3483	114	11	]	]	X
ap-3483	114	12	,	,	PUNCT
ap-3483	114	13	λ	λ	PROPN
ap-3483	114	14	,	,	PUNCT
ap-3483	114	15	ε	ε	PROPN
ap-3483	114	16	)	)	PUNCT
ap-3483	114	17	dε	dε	VERB
ap-3483	114	18	)	)	PUNCT
ap-3483	114	19	∣∣∣∣	∣∣∣∣	NOUN
ap-3483	114	20	ε=0	ε=0	X
ap-3483	114	21	(	(	PUNCT
ap-3483	114	22	2.24	2.24	NUM
ap-3483	114	23	)	)	PUNCT
ap-3483	114	24	is	be	AUX
ap-3483	114	25	an	an	DET
ap-3483	114	26	element	element	NOUN
ap-3483	114	27	of	of	ADP
ap-3483	114	28	the	the	DET
ap-3483	114	29	lie	lie	NOUN
ap-3483	114	30	algebra	algebra	NOUN
ap-3483	114	31	g.	g.	PROPN
ap-3483	115	1	this	this	PRON
ap-3483	115	2	shows	show	VERB
ap-3483	115	3	that	that	SCONJ
ap-3483	115	4	we	we	PRON
ap-3483	115	5	have	have	AUX
ap-3483	115	6	constructed	construct	VERB
ap-3483	115	7	an	an	DET
ap-3483	115	8	appropriate	appropriate	ADJ
ap-3483	115	9	infinitesimal	infinitesimal	ADJ
ap-3483	115	10	deformation	deformation	NOUN
ap-3483	115	11	of	of	ADP
ap-3483	115	12	the	the	DET
ap-3483	115	13	wavefunction	wavefunction	NOUN
ap-3483	115	14	φ	φ	PROPN
ap-3483	115	15	.	.	PUNCT
ap-3483	116	1	in	in	ADP
ap-3483	116	2	[	[	X
ap-3483	116	3	5	5	NUM
ap-3483	116	4	,	,	PUNCT
ap-3483	116	5	33	33	NUM
ap-3483	116	6	]	]	PUNCT
ap-3483	117	1	it	it	PRON
ap-3483	117	2	was	be	AUX
ap-3483	117	3	shown	show	VERB
ap-3483	117	4	that	that	SCONJ
ap-3483	117	5	the	the	DET
ap-3483	117	6	admissible	admissible	ADJ
ap-3483	117	7	symmetries	symmetry	NOUN
ap-3483	117	8	of	of	ADP
ap-3483	117	9	the	the	DET
ap-3483	117	10	zcc	zcc	NOUN
ap-3483	117	11	(	(	PUNCT
ap-3483	117	12	2.14	2.14	NUM
ap-3483	117	13	)	)	PUNCT
ap-3483	117	14	include	include	VERB
ap-3483	117	15	a	a	DET
ap-3483	117	16	conformal	conformal	ADJ
ap-3483	117	17	transformation	transformation	NOUN
ap-3483	117	18	of	of	ADP
ap-3483	117	19	the	the	DET
ap-3483	117	20	spectral	spectral	ADJ
ap-3483	117	21	parameter	parameter	PROPN
ap-3483	117	22	λ	λ	PROPN
ap-3483	117	23	,	,	PUNCT
ap-3483	117	24	a	a	DET
ap-3483	117	25	gauge	gauge	ADJ
ap-3483	117	26	transformation	transformation	NOUN
ap-3483	117	27	of	of	ADP
ap-3483	117	28	the	the	DET
ap-3483	117	29	wavefunction	wavefunction	NOUN
ap-3483	117	30	φ	φ	PROPN
ap-3483	117	31	in	in	ADP
ap-3483	117	32	the	the	DET
ap-3483	117	33	lsp	lsp	PROPN
ap-3483	117	34	(	(	PUNCT
ap-3483	117	35	2.13	2.13	NUM
ap-3483	117	36	)	)	PUNCT
ap-3483	117	37	and	and	CCONJ
ap-3483	117	38	generalized	generalized	ADJ
ap-3483	117	39	symmetries	symmetry	NOUN
ap-3483	117	40	of	of	ADP
ap-3483	117	41	the	the	DET
ap-3483	117	42	integrable	integrable	ADJ
ap-3483	117	43	system	system	NOUN
ap-3483	117	44	(	(	PUNCT
ap-3483	117	45	2.12	2.12	NUM
ap-3483	117	46	)	)	PUNCT
ap-3483	117	47	.	.	PUNCT
ap-3483	118	1	all	all	DET
ap-3483	118	2	these	these	DET
ap-3483	118	3	symmetries	symmetry	NOUN
ap-3483	118	4	can	can	AUX
ap-3483	118	5	be	be	AUX
ap-3483	118	6	used	use	VERB
ap-3483	118	7	to	to	PART
ap-3483	118	8	determine	determine	VERB
ap-3483	118	9	explicitly	explicitly	ADV
ap-3483	118	10	a	a	DET
ap-3483	118	11	g	g	ADV
ap-3483	118	12	-	-	PUNCT
ap-3483	118	13	valued	value	VERB
ap-3483	118	14	immersion	immersion	NOUN
ap-3483	118	15	function	function	NOUN
ap-3483	118	16	f	f	PROPN
ap-3483	118	17	of	of	ADP
ap-3483	118	18	a	a	DET
ap-3483	118	19	2dsurface	2dsurface	NUM
ap-3483	118	20	.	.	PUNCT
ap-3483	119	1	thus	thus	ADV
ap-3483	119	2	,	,	PUNCT
ap-3483	119	3	a	a	DET
ap-3483	119	4	generalization	generalization	NOUN
ap-3483	119	5	of	of	ADP
ap-3483	119	6	the	the	DET
ap-3483	119	7	fg	fg	PROPN
ap-3483	119	8	formula	formula	NOUN
ap-3483	119	9	for	for	ADP
ap-3483	119	10	immersion	immersion	NOUN
ap-3483	119	11	can	can	AUX
ap-3483	119	12	be	be	AUX
ap-3483	119	13	formulated	formulate	VERB
ap-3483	119	14	as	as	SCONJ
ap-3483	119	15	follows	follow	VERB
ap-3483	119	16	[	[	X
ap-3483	119	17	9	9	NUM
ap-3483	119	18	,	,	PUNCT
ap-3483	119	19	11	11	NUM
ap-3483	119	20	]	]	PUNCT
ap-3483	119	21	.	.	PUNCT
ap-3483	120	1	182	182	NUM
ap-3483	120	2	vol	vol	NOUN
ap-3483	120	3	.	.	PUNCT
ap-3483	121	1	56	56	NUM
ap-3483	121	2	no	no	NOUN
ap-3483	121	3	.	.	PUNCT
ap-3483	122	1	3/2016	3/2016	NUM
ap-3483	122	2	on	on	ADP
ap-3483	122	3	immersion	immersion	NOUN
ap-3483	122	4	formulas	formula	NOUN
ap-3483	122	5	for	for	ADP
ap-3483	122	6	soliton	soliton	NOUN
ap-3483	122	7	surfaces	surface	NOUN
ap-3483	122	8	theorem	theorem	VERB
ap-3483	122	9	2	2	NUM
ap-3483	122	10	.	.	PUNCT
ap-3483	123	1	let	let	VERB
ap-3483	123	2	the	the	DET
ap-3483	123	3	set	set	NOUN
ap-3483	123	4	of	of	ADP
ap-3483	123	5	scalar	scalar	ADJ
ap-3483	123	6	functions	function	NOUN
ap-3483	123	7	{	{	PUNCT
ap-3483	123	8	uk	uk	PROPN
ap-3483	123	9	}	}	PUNCT
ap-3483	123	10	satisfy	satisfy	VERB
ap-3483	123	11	a	a	DET
ap-3483	123	12	system	system	NOUN
ap-3483	123	13	of	of	ADP
ap-3483	123	14	integrable	integrable	ADJ
ap-3483	123	15	pdes	pde	NOUN
ap-3483	123	16	ω[u	ω[u	PROPN
ap-3483	123	17	]	]	X
ap-3483	123	18	=	=	SYM
ap-3483	123	19	0	0	X
ap-3483	123	20	.	.	PUNCT
ap-3483	124	1	let	let	AUX
ap-3483	124	2	the	the	DET
ap-3483	124	3	g	g	NOUN
ap-3483	124	4	-	-	PUNCT
ap-3483	124	5	valued	value	VERB
ap-3483	124	6	function	function	NOUN
ap-3483	124	7	φ([u	φ([u	PROPN
ap-3483	124	8	]	]	PUNCT
ap-3483	124	9	,	,	PUNCT
ap-3483	124	10	λ	λ	NOUN
ap-3483	124	11	)	)	PUNCT
ap-3483	124	12	satisfy	satisfy	VERB
ap-3483	124	13	the	the	DET
ap-3483	124	14	lsp	lsp	PROPN
ap-3483	124	15	(	(	PUNCT
ap-3483	124	16	2.15	2.15	NUM
ap-3483	124	17	)	)	PUNCT
ap-3483	124	18	of	of	ADP
ap-3483	124	19	gvalued	gvalue	VERB
ap-3483	124	20	potentials	potential	VERB
ap-3483	124	21	uα([u	uα([u	PROPN
ap-3483	124	22	]	]	PUNCT
ap-3483	124	23	,	,	PUNCT
ap-3483	124	24	λ	λ	PROPN
ap-3483	124	25	)	)	PUNCT
ap-3483	124	26	.	.	PUNCT
ap-3483	125	1	let	let	VERB
ap-3483	125	2	us	we	PRON
ap-3483	125	3	define	define	VERB
ap-3483	125	4	the	the	DET
ap-3483	125	5	linearly	linearly	ADV
ap-3483	125	6	independent	independent	ADJ
ap-3483	125	7	g	g	NOUN
ap-3483	125	8	-	-	PUNCT
ap-3483	125	9	valued	value	VERB
ap-3483	125	10	matrix	matrix	NOUN
ap-3483	125	11	functions	function	NOUN
ap-3483	125	12	aα([u	aα([u	PROPN
ap-3483	125	13	]	]	X
ap-3483	125	14	,	,	PUNCT
ap-3483	125	15	λ	λ	X
ap-3483	125	16	)	)	PUNCT
ap-3483	125	17	(	(	PUNCT
ap-3483	125	18	α	α	NOUN
ap-3483	125	19	=	=	SYM
ap-3483	125	20	1	1	NUM
ap-3483	125	21	,	,	PUNCT
ap-3483	125	22	2	2	NUM
ap-3483	125	23	)	)	PUNCT
ap-3483	125	24	by	by	ADP
ap-3483	125	25	the	the	DET
ap-3483	125	26	equations	equation	NOUN
ap-3483	125	27	aα([u	aα([u	PROPN
ap-3483	125	28	]	]	X
ap-3483	125	29	,	,	PUNCT
ap-3483	125	30	λ	λ	NOUN
ap-3483	125	31	)	)	PUNCT
ap-3483	125	32	=	=	X
ap-3483	125	33	β(λ)dλuα	β(λ)dλuα	X
ap-3483	126	1	+	+	CCONJ
ap-3483	126	2	(	(	PUNCT
ap-3483	126	3	dαs	dαs	X
ap-3483	126	4	+	+	CCONJ
ap-3483	127	1	[	[	X
ap-3483	127	2	s	s	X
ap-3483	127	3	,	,	PUNCT
ap-3483	127	4	uα	uα	NOUN
ap-3483	127	5	]	]	X
ap-3483	127	6	)	)	PUNCT
ap-3483	128	1	+	+	CCONJ
ap-3483	128	2	prωruα	prωruα	ADJ
ap-3483	128	3	+	+	CCONJ
ap-3483	128	4	(	(	PUNCT
ap-3483	128	5	prωr(dαφ−	prωr(dαφ−	X
ap-3483	128	6	uαφ	uαφ	ADJ
ap-3483	128	7	)	)	PUNCT
ap-3483	128	8	)	)	PUNCT
ap-3483	129	1	φ−1	φ−1	PROPN
ap-3483	129	2	.	.	PUNCT
ap-3483	130	1	(	(	PUNCT
ap-3483	130	2	2.25	2.25	NUM
ap-3483	130	3	)	)	PUNCT
ap-3483	130	4	here	here	ADV
ap-3483	130	5	β(λ	β(λ	NOUN
ap-3483	130	6	)	)	PUNCT
ap-3483	130	7	is	be	AUX
ap-3483	130	8	an	an	DET
ap-3483	130	9	arbitrary	arbitrary	ADJ
ap-3483	130	10	scalar	scalar	ADJ
ap-3483	130	11	function	function	NOUN
ap-3483	130	12	of	of	ADP
ap-3483	130	13	λ	λ	PROPN
ap-3483	130	14	,	,	PUNCT
ap-3483	130	15	s	s	PART
ap-3483	130	16	=	=	SYM
ap-3483	130	17	s([u	s([u	PROPN
ap-3483	130	18	]	]	PUNCT
ap-3483	130	19	,	,	PUNCT
ap-3483	130	20	λ	λ	X
ap-3483	130	21	)	)	PUNCT
ap-3483	130	22	is	be	AUX
ap-3483	130	23	an	an	DET
ap-3483	130	24	arbitrary	arbitrary	ADJ
ap-3483	130	25	g	g	NOUN
ap-3483	130	26	-	-	PUNCT
ap-3483	130	27	valued	value	VERB
ap-3483	130	28	matrix	matrix	NOUN
ap-3483	130	29	function	function	NOUN
ap-3483	130	30	defined	define	VERB
ap-3483	130	31	on	on	ADP
ap-3483	130	32	the	the	DET
ap-3483	130	33	jet	jet	NOUN
ap-3483	130	34	space	space	NOUN
ap-3483	130	35	n	n	NOUN
ap-3483	130	36	,	,	PUNCT
ap-3483	130	37	ωr	ωr	X
ap-3483	130	38	=	=	PUNCT
ap-3483	130	39	rk[u]∂uk	rk[u]∂uk	PROPN
ap-3483	130	40	is	be	AUX
ap-3483	130	41	the	the	DET
ap-3483	130	42	vector	vector	NOUN
ap-3483	130	43	field	field	NOUN
ap-3483	130	44	,	,	PUNCT
ap-3483	130	45	written	write	VERB
ap-3483	130	46	in	in	ADP
ap-3483	130	47	evolutionary	evolutionary	ADJ
ap-3483	130	48	form	form	NOUN
ap-3483	130	49	,	,	PUNCT
ap-3483	130	50	of	of	ADP
ap-3483	130	51	the	the	DET
ap-3483	130	52	generalized	generalized	ADJ
ap-3483	130	53	symmetries	symmetry	NOUN
ap-3483	130	54	of	of	ADP
ap-3483	130	55	the	the	DET
ap-3483	130	56	integrable	integrable	ADJ
ap-3483	130	57	pdes	pde	NOUN
ap-3483	130	58	ω[u	ω[u	PROPN
ap-3483	130	59	]	]	X
ap-3483	130	60	=	=	SYM
ap-3483	130	61	0	0	NUM
ap-3483	130	62	given	give	VERB
ap-3483	130	63	by	by	ADP
ap-3483	130	64	the	the	DET
ap-3483	130	65	zcc	zcc	NOUN
ap-3483	130	66	(	(	PUNCT
ap-3483	130	67	2.14	2.14	NUM
ap-3483	130	68	)	)	PUNCT
ap-3483	130	69	.	.	PUNCT
ap-3483	131	1	then	then	ADV
ap-3483	131	2	there	there	PRON
ap-3483	131	3	exists	exist	VERB
ap-3483	131	4	a	a	DET
ap-3483	131	5	2d	2d	NOUN
ap-3483	131	6	-	-	PUNCT
ap-3483	131	7	surface	surface	NOUN
ap-3483	131	8	with	with	ADP
ap-3483	131	9	immersion	immersion	NOUN
ap-3483	131	10	function	function	NOUN
ap-3483	131	11	f	f	NOUN
ap-3483	131	12	(	(	PUNCT
ap-3483	131	13	[	[	X
ap-3483	131	14	u	u	X
ap-3483	131	15	]	]	X
ap-3483	131	16	,	,	PUNCT
ap-3483	131	17	λ	λ	NOUN
ap-3483	131	18	)	)	PUNCT
ap-3483	131	19	in	in	ADP
ap-3483	131	20	the	the	DET
ap-3483	131	21	lie	lie	NOUN
ap-3483	131	22	algebra	algebra	NOUN
ap-3483	131	23	g	g	NOUN
ap-3483	131	24	given	give	VERB
ap-3483	131	25	by	by	ADP
ap-3483	131	26	the	the	DET
ap-3483	131	27	formula	formula	NOUN
ap-3483	131	28	(	(	PUNCT
ap-3483	131	29	up	up	ADP
ap-3483	131	30	to	to	ADP
ap-3483	131	31	an	an	DET
ap-3483	131	32	additive	additive	ADJ
ap-3483	131	33	g	g	ADV
ap-3483	131	34	-	-	PUNCT
ap-3483	131	35	valued	value	VERB
ap-3483	131	36	constant	constant	ADJ
ap-3483	131	37	)	)	PUNCT
ap-3483	131	38	f	f	NOUN
ap-3483	131	39	(	(	PUNCT
ap-3483	131	40	[	[	X
ap-3483	131	41	u	u	X
ap-3483	131	42	]	]	X
ap-3483	131	43	,	,	PUNCT
ap-3483	131	44	λ	λ	NOUN
ap-3483	131	45	)	)	PUNCT
ap-3483	131	46	=	=	SYM
ap-3483	131	47	φ−1	φ−1	PROPN
ap-3483	131	48	(	(	PUNCT
ap-3483	131	49	β(λ)dλφ	β(λ)dλφ	NOUN
ap-3483	131	50	+	+	CCONJ
ap-3483	131	51	sφ	sφ	PROPN
ap-3483	131	52	+	+	NUM
ap-3483	131	53	prωrφ	prωrφ	NOUN
ap-3483	131	54	)	)	PUNCT
ap-3483	131	55	.	.	PUNCT
ap-3483	132	1	(	(	PUNCT
ap-3483	132	2	2.26	2.26	NUM
ap-3483	132	3	)	)	PUNCT
ap-3483	132	4	the	the	DET
ap-3483	132	5	integrated	integrate	VERB
ap-3483	132	6	form	form	NOUN
ap-3483	132	7	of	of	ADP
ap-3483	132	8	the	the	DET
ap-3483	132	9	surface	surface	NOUN
ap-3483	132	10	(	(	PUNCT
ap-3483	132	11	2.26	2.26	NUM
ap-3483	132	12	)	)	PUNCT
ap-3483	132	13	defines	define	VERB
ap-3483	132	14	a	a	DET
ap-3483	132	15	mapping	mapping	NOUN
ap-3483	132	16	f	f	NOUN
ap-3483	132	17	:	:	PUNCT
ap-3483	132	18	n	n	X
ap-3483	132	19	→	→	SYM
ap-3483	132	20	g	g	PROPN
ap-3483	132	21	and	and	CCONJ
ap-3483	132	22	we	we	PRON
ap-3483	132	23	will	will	AUX
ap-3483	132	24	refer	refer	VERB
ap-3483	132	25	to	to	ADP
ap-3483	132	26	it	it	PRON
ap-3483	132	27	as	as	ADP
ap-3483	132	28	the	the	DET
ap-3483	132	29	st	st	PROPN
ap-3483	132	30	immersion	immersion	NOUN
ap-3483	132	31	formula	formula	NOUN
ap-3483	132	32	(	(	PUNCT
ap-3483	132	33	when	when	SCONJ
ap-3483	132	34	s	s	VERB
ap-3483	132	35	=	=	SYM
ap-3483	132	36	0	0	NUM
ap-3483	132	37	,	,	PUNCT
ap-3483	132	38	ωr	ωr	ADV
ap-3483	132	39	=	=	SYM
ap-3483	132	40	0	0	NUM
ap-3483	132	41	)	)	PUNCT
ap-3483	133	1	[	[	X
ap-3483	133	2	33–35	33–35	NUM
ap-3483	133	3	]	]	X
ap-3483	133	4	fst	fst	NOUN
ap-3483	133	5	(	(	PUNCT
ap-3483	133	6	[	[	X
ap-3483	133	7	u	u	X
ap-3483	133	8	]	]	X
ap-3483	133	9	,	,	PUNCT
ap-3483	133	10	λ	λ	NOUN
ap-3483	133	11	)	)	PUNCT
ap-3483	133	12	=	=	SYM
ap-3483	133	13	β(λ)φ−1(dλφ	β(λ)φ−1(dλφ	X
ap-3483	133	14	)	)	PUNCT
ap-3483	133	15	∈	∈	PROPN
ap-3483	133	16	g	g	NOUN
ap-3483	133	17	,	,	PUNCT
ap-3483	133	18	(	(	PUNCT
ap-3483	133	19	2.27	2.27	NUM
ap-3483	133	20	)	)	PUNCT
ap-3483	133	21	the	the	DET
ap-3483	133	22	cd	cd	PROPN
ap-3483	133	23	immersion	immersion	NOUN
ap-3483	133	24	formula	formula	NOUN
ap-3483	133	25	(	(	PUNCT
ap-3483	133	26	when	when	SCONJ
ap-3483	133	27	β	β	X
ap-3483	133	28	=	=	PUNCT
ap-3483	133	29	ωr	ωr	PROPN
ap-3483	133	30	=	=	NOUN
ap-3483	133	31	0	0	NUM
ap-3483	133	32	)	)	PUNCT
ap-3483	134	1	[	[	X
ap-3483	134	2	5–7	5–7	X
ap-3483	134	3	]	]	X
ap-3483	134	4	fcd([u	fcd([u	NOUN
ap-3483	134	5	]	]	PUNCT
ap-3483	134	6	,	,	PUNCT
ap-3483	134	7	λ	λ	NOUN
ap-3483	134	8	)	)	PUNCT
ap-3483	134	9	=	=	PUNCT
ap-3483	135	1	φ−1s([u	φ−1s([u	PROPN
ap-3483	135	2	]	]	PUNCT
ap-3483	135	3	,	,	PUNCT
ap-3483	135	4	λ)φ	λ)φ	ADJ
ap-3483	135	5	∈	∈	PROPN
ap-3483	135	6	g	g	NOUN
ap-3483	135	7	,	,	PUNCT
ap-3483	135	8	(	(	PUNCT
ap-3483	135	9	2.28	2.28	NUM
ap-3483	135	10	)	)	PUNCT
ap-3483	135	11	or	or	CCONJ
ap-3483	135	12	the	the	DET
ap-3483	135	13	fg	fg	PROPN
ap-3483	135	14	immersion	immersion	NOUN
ap-3483	135	15	formula	formula	NOUN
ap-3483	135	16	(	(	PUNCT
ap-3483	135	17	when	when	SCONJ
ap-3483	135	18	β	β	X
ap-3483	135	19	=	=	SYM
ap-3483	135	20	0	0	NUM
ap-3483	135	21	,	,	PUNCT
ap-3483	135	22	s	s	NOUN
ap-3483	135	23	=	=	NOUN
ap-3483	135	24	0	0	NUM
ap-3483	135	25	)	)	PUNCT
ap-3483	136	1	[	[	X
ap-3483	136	2	8	8	NUM
ap-3483	136	3	,	,	PUNCT
ap-3483	136	4	9	9	NUM
ap-3483	136	5	]	]	PUNCT
ap-3483	136	6	ffg([u	ffg([u	NOUN
ap-3483	136	7	]	]	PUNCT
ap-3483	136	8	,	,	PUNCT
ap-3483	136	9	λ	λ	NOUN
ap-3483	136	10	)	)	PUNCT
ap-3483	136	11	=	=	SYM
ap-3483	136	12	φ−1(prωrφ	φ−1(prωrφ	X
ap-3483	136	13	)	)	PUNCT
ap-3483	136	14	∈	∈	PROPN
ap-3483	136	15	g.	g.	NOUN
ap-3483	136	16	(	(	PUNCT
ap-3483	136	17	2.29	2.29	NUM
ap-3483	136	18	)	)	PUNCT
ap-3483	136	19	2.3	2.3	NUM
ap-3483	136	20	.	.	PUNCT
ap-3483	137	1	application	application	NOUN
ap-3483	137	2	of	of	ADP
ap-3483	137	3	the	the	DET
ap-3483	137	4	method	method	NOUN
ap-3483	137	5	the	the	DET
ap-3483	137	6	construction	construction	NOUN
ap-3483	137	7	of	of	ADP
ap-3483	137	8	soliton	soliton	NOUN
ap-3483	137	9	surfaces	surface	NOUN
ap-3483	137	10	requires	require	VERB
ap-3483	137	11	three	three	NUM
ap-3483	137	12	elements	element	NOUN
ap-3483	137	13	for	for	ADP
ap-3483	137	14	an	an	DET
ap-3483	137	15	explicit	explicit	ADJ
ap-3483	137	16	representation	representation	NOUN
ap-3483	137	17	of	of	ADP
ap-3483	137	18	the	the	DET
ap-3483	137	19	immersion	immersion	NOUN
ap-3483	137	20	function	function	NOUN
ap-3483	138	1	f	f	PROPN
ap-3483	138	2	∈	∈	PROPN
ap-3483	138	3	g	g	PROPN
ap-3483	138	4	:	:	PUNCT
ap-3483	138	5	(	(	PUNCT
ap-3483	138	6	1	1	NUM
ap-3483	138	7	.	.	PUNCT
ap-3483	138	8	)	)	PUNCT
ap-3483	139	1	an	an	DET
ap-3483	139	2	lsp	lsp	PROPN
ap-3483	139	3	(	(	PUNCT
ap-3483	139	4	2.13	2.13	NUM
ap-3483	139	5	)	)	PUNCT
ap-3483	139	6	for	for	ADP
ap-3483	139	7	the	the	DET
ap-3483	139	8	integrable	integrable	ADJ
ap-3483	139	9	pde	pde	NOUN
ap-3483	139	10	.	.	PUNCT
ap-3483	140	1	(	(	PUNCT
ap-3483	140	2	2	2	NUM
ap-3483	140	3	.	.	PUNCT
ap-3483	140	4	)	)	PUNCT
ap-3483	141	1	a	a	DET
ap-3483	141	2	generalized	generalized	ADJ
ap-3483	141	3	symmetry	symmetry	NOUN
ap-3483	141	4	ωr	ωr	NUM
ap-3483	141	5	of	of	ADP
ap-3483	141	6	the	the	DET
ap-3483	141	7	integrable	integrable	ADJ
ap-3483	141	8	pde	pde	NOUN
ap-3483	141	9	.	.	PUNCT
ap-3483	142	1	(	(	PUNCT
ap-3483	142	2	3	3	NUM
ap-3483	142	3	.	.	PUNCT
ap-3483	142	4	)	)	PUNCT
ap-3483	143	1	a	a	DET
ap-3483	143	2	solution	solution	NOUN
ap-3483	143	3	φ	φ	NUM
ap-3483	143	4	of	of	ADP
ap-3483	143	5	the	the	DET
ap-3483	143	6	lsp	lsp	PROPN
ap-3483	143	7	associated	associate	VERB
ap-3483	143	8	with	with	ADP
ap-3483	143	9	the	the	DET
ap-3483	143	10	soliton	soliton	NOUN
ap-3483	143	11	solution	solution	NOUN
ap-3483	143	12	of	of	ADP
ap-3483	143	13	the	the	DET
ap-3483	143	14	integrable	integrable	ADJ
ap-3483	143	15	pde	pde	NOUN
ap-3483	143	16	.	.	PUNCT
ap-3483	144	1	note	note	VERB
ap-3483	144	2	that	that	DET
ap-3483	144	3	item	item	NOUN
ap-3483	144	4	(	(	PUNCT
ap-3483	144	5	1	1	NUM
ap-3483	144	6	.	.	PUNCT
ap-3483	144	7	)	)	PUNCT
ap-3483	144	8	is	be	AUX
ap-3483	144	9	always	always	ADV
ap-3483	144	10	required	require	VERB
ap-3483	144	11	.	.	PUNCT
ap-3483	145	1	in	in	ADP
ap-3483	145	2	its	its	PRON
ap-3483	145	3	presence	presence	NOUN
ap-3483	145	4	,	,	PUNCT
ap-3483	145	5	even	even	ADV
ap-3483	145	6	without	without	ADP
ap-3483	145	7	one	one	NUM
ap-3483	145	8	of	of	ADP
ap-3483	145	9	the	the	DET
ap-3483	145	10	remaining	remain	VERB
ap-3483	145	11	two	two	NUM
ap-3483	145	12	objects	object	NOUN
ap-3483	145	13	,	,	PUNCT
ap-3483	145	14	we	we	PRON
ap-3483	145	15	can	can	AUX
ap-3483	145	16	obtain	obtain	VERB
ap-3483	145	17	an	an	DET
ap-3483	145	18	immersion	immersion	NOUN
ap-3483	145	19	function	function	NOUN
ap-3483	145	20	f	f	PROPN
ap-3483	145	21	.	.	PUNCT
ap-3483	146	1	when	when	SCONJ
ap-3483	146	2	a	a	DET
ap-3483	146	3	solution	solution	NOUN
ap-3483	146	4	φ	φ	NUM
ap-3483	146	5	of	of	ADP
ap-3483	146	6	the	the	DET
ap-3483	146	7	lsp	lsp	PROPN
ap-3483	146	8	is	be	AUX
ap-3483	146	9	unknown	unknown	ADJ
ap-3483	146	10	,	,	PUNCT
ap-3483	146	11	the	the	DET
ap-3483	146	12	geometry	geometry	NOUN
ap-3483	146	13	of	of	ADP
ap-3483	146	14	the	the	DET
ap-3483	146	15	surface	surface	NOUN
ap-3483	146	16	f	f	PROPN
ap-3483	146	17	can	can	AUX
ap-3483	146	18	be	be	AUX
ap-3483	146	19	obtained	obtain	VERB
ap-3483	146	20	using	use	VERB
ap-3483	146	21	the	the	DET
ap-3483	146	22	non	non	ADJ
ap-3483	146	23	-	-	ADJ
ap-3483	146	24	degenerate	degenerate	ADJ
ap-3483	146	25	killing	killing	NOUN
ap-3483	146	26	form	form	NOUN
ap-3483	146	27	on	on	ADP
ap-3483	146	28	the	the	DET
ap-3483	146	29	lie	lie	NOUN
ap-3483	146	30	algebra	algebra	NOUN
ap-3483	146	31	g.	g.	VERB
ap-3483	146	32	the	the	DET
ap-3483	146	33	2d	2d	NOUN
ap-3483	146	34	-	-	PUNCT
ap-3483	146	35	surface	surface	NOUN
ap-3483	146	36	with	with	ADP
ap-3483	146	37	the	the	DET
ap-3483	146	38	immersion	immersion	NOUN
ap-3483	146	39	function	function	NOUN
ap-3483	146	40	f	f	PROPN
ap-3483	146	41	can	can	AUX
ap-3483	146	42	be	be	AUX
ap-3483	146	43	interpreted	interpret	VERB
ap-3483	146	44	as	as	ADP
ap-3483	146	45	a	a	DET
ap-3483	146	46	pseudo	pseudo	NOUN
ap-3483	146	47	-	-	ADJ
ap-3483	146	48	riemannian	riemannian	ADJ
ap-3483	146	49	manifold	manifold	NOUN
ap-3483	146	50	.	.	PUNCT
ap-3483	147	1	when	when	SCONJ
ap-3483	147	2	the	the	DET
ap-3483	147	3	generalized	generalized	ADJ
ap-3483	147	4	symmetries	symmetry	NOUN
ap-3483	147	5	ωr	ωr	VERB
ap-3483	147	6	of	of	ADP
ap-3483	147	7	the	the	DET
ap-3483	147	8	integrable	integrable	ADJ
ap-3483	147	9	pde	pde	NOUN
ap-3483	147	10	are	be	AUX
ap-3483	147	11	unknown	unknown	ADJ
ap-3483	147	12	but	but	CCONJ
ap-3483	147	13	we	we	PRON
ap-3483	147	14	know	know	VERB
ap-3483	147	15	a	a	DET
ap-3483	147	16	solution	solution	NOUN
ap-3483	147	17	φ	φ	NUM
ap-3483	147	18	of	of	ADP
ap-3483	147	19	the	the	DET
ap-3483	147	20	lsp	lsp	PROPN
ap-3483	147	21	then	then	ADV
ap-3483	147	22	we	we	PRON
ap-3483	147	23	can	can	AUX
ap-3483	147	24	define	define	VERB
ap-3483	147	25	the	the	DET
ap-3483	147	26	2d	2d	NOUN
ap-3483	147	27	-	-	PUNCT
ap-3483	147	28	soliton	soliton	NOUN
ap-3483	147	29	surface	surface	NOUN
ap-3483	147	30	using	use	VERB
ap-3483	147	31	the	the	DET
ap-3483	147	32	gauge	gauge	ADJ
ap-3483	147	33	transformation	transformation	NOUN
ap-3483	147	34	and	and	CCONJ
ap-3483	147	35	the	the	DET
ap-3483	147	36	λ	λ	NOUN
ap-3483	147	37	-	-	NOUN
ap-3483	147	38	invariance	invariance	NOUN
ap-3483	147	39	of	of	ADP
ap-3483	147	40	the	the	DET
ap-3483	147	41	zcc	zcc	NOUN
ap-3483	148	1	f	f	X
ap-3483	148	2	=	=	PUNCT
ap-3483	148	3	φ−1(β(λ)dλφ	φ−1(β(λ)dλφ	PROPN
ap-3483	148	4	+	+	NUM
ap-3483	148	5	sφ	sφ	PROPN
ap-3483	148	6	)	)	PUNCT
ap-3483	148	7	,	,	PUNCT
ap-3483	148	8	(	(	PUNCT
ap-3483	148	9	2.30	2.30	NUM
ap-3483	148	10	)	)	PUNCT
ap-3483	148	11	where	where	SCONJ
ap-3483	148	12	β(λ	β(λ	NOUN
ap-3483	148	13	)	)	PUNCT
ap-3483	148	14	is	be	AUX
ap-3483	148	15	an	an	DET
ap-3483	148	16	arbitrary	arbitrary	ADJ
ap-3483	148	17	scalar	scalar	ADJ
ap-3483	148	18	function	function	NOUN
ap-3483	148	19	of	of	ADP
ap-3483	148	20	λ	λ	PROPN
ap-3483	148	21	and	and	CCONJ
ap-3483	148	22	s	s	VERB
ap-3483	148	23	is	be	AUX
ap-3483	148	24	an	an	DET
ap-3483	148	25	arbitrary	arbitrary	ADJ
ap-3483	148	26	g	g	NOUN
ap-3483	148	27	-	-	PUNCT
ap-3483	148	28	valued	value	VERB
ap-3483	148	29	matrix	matrix	NOUN
ap-3483	148	30	function	function	NOUN
ap-3483	148	31	defined	define	VERB
ap-3483	148	32	on	on	ADP
ap-3483	148	33	the	the	DET
ap-3483	148	34	extended	extended	ADJ
ap-3483	148	35	jet	jet	NOUN
ap-3483	148	36	space	space	NOUN
ap-3483	148	37	n	n	NOUN
ap-3483	148	38	.	.	PUNCT
ap-3483	149	1	equation	equation	NOUN
ap-3483	149	2	(	(	PUNCT
ap-3483	149	3	2.30	2.30	NUM
ap-3483	149	4	)	)	PUNCT
ap-3483	149	5	is	be	AUX
ap-3483	149	6	consistent	consistent	ADJ
ap-3483	149	7	with	with	ADP
ap-3483	149	8	the	the	DET
ap-3483	149	9	tangent	tangent	NOUN
ap-3483	150	1	vectors	vector	NOUN
ap-3483	150	2	dαf	dαf	VERB
ap-3483	150	3	=	=	SYM
ap-3483	150	4	β(λ)φ−1(dλuα	β(λ)φ−1(dλuα	X
ap-3483	150	5	)	)	PUNCT
ap-3483	151	1	+	+	CCONJ
ap-3483	151	2	φ−1(dαs	φ−1(dαs	X
ap-3483	152	1	+	+	PUNCT
ap-3483	152	2	[	[	X
ap-3483	152	3	s	s	X
ap-3483	152	4	,	,	PUNCT
ap-3483	152	5	uα])φ	uα])φ	NOUN
ap-3483	152	6	.	.	PUNCT
ap-3483	153	1	(	(	PUNCT
ap-3483	153	2	2.31	2.31	NUM
ap-3483	153	3	)	)	PUNCT
ap-3483	153	4	in	in	ADP
ap-3483	153	5	all	all	DET
ap-3483	153	6	cases	case	NOUN
ap-3483	153	7	,	,	PUNCT
ap-3483	153	8	the	the	DET
ap-3483	153	9	tangent	tangent	NOUN
ap-3483	153	10	vectors	vector	NOUN
ap-3483	153	11	,	,	PUNCT
ap-3483	153	12	given	give	VERB
ap-3483	153	13	by	by	ADP
ap-3483	153	14	(	(	PUNCT
ap-3483	153	15	2.22	2.22	NUM
ap-3483	153	16	)	)	PUNCT
ap-3483	153	17	,	,	PUNCT
ap-3483	153	18	and	and	CCONJ
ap-3483	153	19	the	the	DET
ap-3483	153	20	unit	unit	NOUN
ap-3483	153	21	normal	normal	ADJ
ap-3483	153	22	vector	vector	NOUN
ap-3483	153	23	to	to	ADP
ap-3483	153	24	a	a	DET
ap-3483	153	25	2d	2d	NUM
ap-3483	153	26	-	-	PUNCT
ap-3483	153	27	surface	surface	NOUN
ap-3483	153	28	expressed	express	VERB
ap-3483	153	29	in	in	ADP
ap-3483	153	30	terms	term	NOUN
ap-3483	153	31	of	of	ADP
ap-3483	153	32	matrices	matrix	NOUN
ap-3483	153	33	are	be	AUX
ap-3483	153	34	dαf	dαf	NOUN
ap-3483	153	35	=	=	PUNCT
ap-3483	153	36	φ−1aαφ	φ−1aαφ	PROPN
ap-3483	153	37	∈	∈	PROPN
ap-3483	153	38	g	g	NOUN
ap-3483	153	39	,	,	PUNCT
ap-3483	153	40	n	n	NOUN
ap-3483	153	41	=	=	SYM
ap-3483	153	42	φ−1[a1	φ−1[a1	PROPN
ap-3483	153	43	,	,	PUNCT
ap-3483	153	44	a2]φ	a2]φ	X
ap-3483	153	45	(	(	PUNCT
ap-3483	153	46	1	1	NUM
ap-3483	153	47	2	2	NUM
ap-3483	153	48	tr[a1	tr[a1	PROPN
ap-3483	153	49	,	,	PUNCT
ap-3483	153	50	a2]2)1/2	a2]2)1/2	PROPN
ap-3483	153	51	∈	∈	PROPN
ap-3483	153	52	g	g	NOUN
ap-3483	153	53	,	,	PUNCT
ap-3483	153	54	(	(	PUNCT
ap-3483	153	55	2.32	2.32	NUM
ap-3483	153	56	)	)	PUNCT
ap-3483	153	57	where	where	SCONJ
ap-3483	153	58	the	the	DET
ap-3483	153	59	g	g	NOUN
ap-3483	153	60	-	-	PUNCT
ap-3483	153	61	valued	value	VERB
ap-3483	153	62	matrices	matrix	NOUN
ap-3483	153	63	aα	aα	NOUN
ap-3483	153	64	are	be	AUX
ap-3483	153	65	given	give	VERB
ap-3483	153	66	by	by	ADP
ap-3483	153	67	(	(	PUNCT
ap-3483	153	68	2.25	2.25	NUM
ap-3483	153	69	)	)	PUNCT
ap-3483	153	70	.	.	PUNCT
ap-3483	154	1	the	the	DET
ap-3483	154	2	first	first	ADJ
ap-3483	154	3	and	and	CCONJ
ap-3483	154	4	second	second	ADJ
ap-3483	154	5	fundamental	fundamental	ADJ
ap-3483	154	6	forms	form	NOUN
ap-3483	154	7	are	be	AUX
ap-3483	154	8	given	give	VERB
ap-3483	154	9	by	by	ADP
ap-3483	154	10	i	i	PRON
ap-3483	154	11	=	=	NOUN
ap-3483	154	12	gijdxidxj	gijdxidxj	ADJ
ap-3483	154	13	,	,	PUNCT
ap-3483	154	14	ii	ii	PROPN
ap-3483	154	15	=	=	SYM
ap-3483	154	16	bijdxidxj	bijdxidxj	PROPN
ap-3483	154	17	,	,	PUNCT
ap-3483	154	18	i	i	PRON
ap-3483	154	19	=	=	NOUN
ap-3483	154	20	1	1	NUM
ap-3483	154	21	,	,	PUNCT
ap-3483	154	22	2	2	NUM
ap-3483	154	23	,	,	PUNCT
ap-3483	154	24	(	(	PUNCT
ap-3483	154	25	2.33	2.33	NUM
ap-3483	154	26	)	)	PUNCT
ap-3483	154	27	where	where	SCONJ
ap-3483	154	28	gij	gij	NOUN
ap-3483	154	29	=	=	SYM
ap-3483	154	30	ε	ε	PROPN
ap-3483	154	31	2	2	NUM
ap-3483	154	32	tr(aiaj	tr(aiaj	NOUN
ap-3483	154	33	)	)	PUNCT
ap-3483	154	34	,	,	PUNCT
ap-3483	154	35	bij	bij	NOUN
ap-3483	154	36	=	=	SYM
ap-3483	154	37	ε	ε	PROPN
ap-3483	154	38	2	2	NUM
ap-3483	154	39	tr	tr	VERB
ap-3483	154	40	(	(	PUNCT
ap-3483	154	41	(	(	PUNCT
ap-3483	154	42	djai	djai	VERB
ap-3483	154	43	+	+	SYM
ap-3483	155	1	[	[	X
ap-3483	155	2	ai	ai	ADP
ap-3483	155	3	,	,	PUNCT
ap-3483	155	4	uj	uj	PROPN
ap-3483	155	5	]	]	PUNCT
ap-3483	155	6	)	)	PUNCT
ap-3483	155	7	n	n	CCONJ
ap-3483	155	8	)	)	PUNCT
ap-3483	155	9	,	,	PUNCT
ap-3483	155	10	ε	ε	PROPN
ap-3483	155	11	=	=	SYM
ap-3483	155	12	±1	±1	VERB
ap-3483	155	13	.	.	PUNCT
ap-3483	156	1	(	(	PUNCT
ap-3483	156	2	2.34	2.34	NUM
ap-3483	156	3	)	)	PUNCT
ap-3483	156	4	this	this	PRON
ap-3483	156	5	gives	give	VERB
ap-3483	156	6	the	the	DET
ap-3483	156	7	following	follow	VERB
ap-3483	156	8	expressions	expression	NOUN
ap-3483	156	9	for	for	ADP
ap-3483	156	10	the	the	DET
ap-3483	156	11	mean	mean	ADJ
ap-3483	156	12	and	and	CCONJ
ap-3483	156	13	gaussian	gaussian	ADJ
ap-3483	156	14	curvatures	curvature	NOUN
ap-3483	156	15	h	h	NOUN
ap-3483	156	16	=	=	SYM
ap-3483	156	17	1	1	NUM
ap-3483	156	18	∆	∆	X
ap-3483	156	19	(	(	PUNCT
ap-3483	156	20	tr(a2	tr(a2	NOUN
ap-3483	156	21	2	2	X
ap-3483	156	22	)	)	PUNCT
ap-3483	156	23	tr	tr	PUNCT
ap-3483	156	24	(	(	PUNCT
ap-3483	156	25	(	(	PUNCT
ap-3483	156	26	d1a1	d1a1	X
ap-3483	156	27	+	+	PUNCT
ap-3483	156	28	[	[	X
ap-3483	156	29	a1	a1	NOUN
ap-3483	156	30	,	,	PUNCT
ap-3483	156	31	u1])n	u1])n	NOUN
ap-3483	156	32	)	)	PUNCT
ap-3483	156	33	−	−	PROPN
ap-3483	156	34	8	8	NUM
ap-3483	156	35	tr(a1a2	tr(a1a2	NOUN
ap-3483	156	36	)	)	PUNCT
ap-3483	156	37	tr	tr	PUNCT
ap-3483	156	38	(	(	PUNCT
ap-3483	156	39	(	(	PUNCT
ap-3483	156	40	d2a1	d2a1	ADP
ap-3483	156	41	+	+	PUNCT
ap-3483	157	1	[	[	X
ap-3483	157	2	a1	a1	NOUN
ap-3483	157	3	,	,	PUNCT
ap-3483	157	4	u2])n	u2])n	NOUN
ap-3483	157	5	)	)	PUNCT
ap-3483	158	1	+	+	CCONJ
ap-3483	158	2	tr(a2	tr(a2	NOUN
ap-3483	158	3	1	1	X
ap-3483	158	4	)	)	PUNCT
ap-3483	158	5	tr	tr	VERB
ap-3483	158	6	(	(	PUNCT
ap-3483	158	7	(	(	PUNCT
ap-3483	158	8	d2a2	d2a2	X
ap-3483	158	9	+	+	NUM
ap-3483	158	10	[	[	X
ap-3483	158	11	a2	a2	NOUN
ap-3483	158	12	,	,	PUNCT
ap-3483	158	13	u2])n	u2])n	NOUN
ap-3483	158	14	)	)	PUNCT
ap-3483	158	15	)	)	PUNCT
ap-3483	158	16	,	,	PUNCT
ap-3483	158	17	k	k	PROPN
ap-3483	158	18	=	=	SYM
ap-3483	158	19	1	1	NUM
ap-3483	158	20	∆	∆	PROPN
ap-3483	158	21	(	(	PUNCT
ap-3483	158	22	tr	tr	VERB
ap-3483	158	23	(	(	PUNCT
ap-3483	158	24	(	(	PUNCT
ap-3483	158	25	d1a1	d1a1	X
ap-3483	158	26	+	+	PUNCT
ap-3483	158	27	[	[	X
ap-3483	158	28	a1	a1	NOUN
ap-3483	158	29	,	,	PUNCT
ap-3483	158	30	u1])n	u1])n	NOUN
ap-3483	158	31	)	)	PUNCT
ap-3483	158	32	·	·	PUNCT
ap-3483	158	33	tr	tr	VERB
ap-3483	158	34	(	(	PUNCT
ap-3483	158	35	(	(	PUNCT
ap-3483	158	36	d2a2	d2a2	X
ap-3483	158	37	+	+	NUM
ap-3483	158	38	[	[	X
ap-3483	158	39	a2	a2	NOUN
ap-3483	158	40	,	,	PUNCT
ap-3483	158	41	u2])n	u2])n	NOUN
ap-3483	158	42	)	)	PUNCT
ap-3483	158	43	−	−	ADP
ap-3483	158	44	2	2	NUM
ap-3483	158	45	tr2((d2a1	tr2((d2a1	NOUN
ap-3483	158	46	+	+	CCONJ
ap-3483	159	1	[	[	X
ap-3483	159	2	a1	a1	NOUN
ap-3483	159	3	,	,	PUNCT
ap-3483	159	4	u2])n	u2])n	NOUN
ap-3483	159	5	)	)	PUNCT
ap-3483	159	6	)	)	PUNCT
ap-3483	159	7	,	,	PUNCT
ap-3483	159	8	∆	∆	PROPN
ap-3483	159	9	=	=	SYM
ap-3483	159	10	tr(a2	tr(a2	NOUN
ap-3483	159	11	1	1	X
ap-3483	159	12	)	)	PUNCT
ap-3483	159	13	tr(a2	tr(a2	NOUN
ap-3483	159	14	2)−	2)−	NUM
ap-3483	159	15	4	4	NUM
ap-3483	159	16	tr(a1a2	tr(a1a2	NOUN
ap-3483	159	17	)	)	PUNCT
ap-3483	159	18	,	,	PUNCT
ap-3483	159	19	(	(	PUNCT
ap-3483	159	20	2.35	2.35	NUM
ap-3483	159	21	)	)	PUNCT
ap-3483	159	22	which	which	PRON
ap-3483	159	23	are	be	AUX
ap-3483	159	24	expressible	expressible	ADJ
ap-3483	159	25	in	in	ADP
ap-3483	159	26	terms	term	NOUN
ap-3483	159	27	of	of	ADP
ap-3483	159	28	uα	uα	PROPN
ap-3483	159	29	and	and	CCONJ
ap-3483	159	30	aα	aα	NOUN
ap-3483	159	31	only	only	ADV
ap-3483	159	32	.	.	PUNCT
ap-3483	160	1	the	the	DET
ap-3483	160	2	study	study	NOUN
ap-3483	160	3	of	of	ADP
ap-3483	160	4	soliton	soliton	NOUN
ap-3483	160	5	surfaces	surface	NOUN
ap-3483	160	6	defined	define	VERB
ap-3483	160	7	via	via	ADP
ap-3483	160	8	the	the	DET
ap-3483	160	9	fg	fg	PROPN
ap-3483	160	10	formula	formula	NOUN
ap-3483	160	11	for	for	ADP
ap-3483	160	12	immersion	immersion	NOUN
ap-3483	160	13	provides	provide	VERB
ap-3483	160	14	a	a	DET
ap-3483	160	15	unique	unique	ADJ
ap-3483	160	16	mechanism	mechanism	NOUN
ap-3483	160	17	for	for	ADP
ap-3483	160	18	studying	study	VERB
ap-3483	160	19	the	the	DET
ap-3483	160	20	relationship	relationship	NOUN
ap-3483	160	21	between	between	ADP
ap-3483	160	22	these	these	DET
ap-3483	160	23	various	various	ADJ
ap-3483	160	24	characteristics	characteristic	NOUN
ap-3483	160	25	of	of	ADP
ap-3483	160	26	integrable	integrable	ADJ
ap-3483	160	27	systems	system	NOUN
ap-3483	160	28	.	.	PUNCT
ap-3483	161	1	for	for	ADP
ap-3483	161	2	example	example	NOUN
ap-3483	161	3	,	,	PUNCT
ap-3483	161	4	do	do	AUX
ap-3483	161	5	the	the	DET
ap-3483	161	6	infinite	infinite	ADJ
ap-3483	161	7	families	family	NOUN
ap-3483	161	8	of	of	ADP
ap-3483	161	9	conservation	conservation	NOUN
ap-3483	161	10	laws	law	NOUN
ap-3483	161	11	have	have	VERB
ap-3483	161	12	a	a	DET
ap-3483	161	13	geometric	geometric	ADJ
ap-3483	161	14	characterization	characterization	NOUN
ap-3483	161	15	?	?	PUNCT
ap-3483	162	1	what	what	PRON
ap-3483	162	2	is	be	AUX
ap-3483	162	3	the	the	DET
ap-3483	162	4	geometry	geometry	NOUN
ap-3483	162	5	behind	behind	ADP
ap-3483	162	6	the	the	DET
ap-3483	162	7	hamiltonian	hamiltonian	ADJ
ap-3483	162	8	structure	structure	NOUN
ap-3483	162	9	?	?	PUNCT
ap-3483	163	1	is	be	AUX
ap-3483	163	2	there	there	PRON
ap-3483	163	3	a	a	DET
ap-3483	163	4	geometric	geometric	ADJ
ap-3483	163	5	interpretation	interpretation	NOUN
ap-3483	163	6	of	of	ADP
ap-3483	163	7	the	the	DET
ap-3483	163	8	family	family	NOUN
ap-3483	163	9	of	of	ADP
ap-3483	163	10	surfaces	surface	NOUN
ap-3483	163	11	and	and	CCONJ
ap-3483	163	12	frames	frame	NOUN
ap-3483	163	13	associated	associate	VERB
ap-3483	163	14	with	with	ADP
ap-3483	163	15	the	the	DET
ap-3483	163	16	spectral	spectral	ADJ
ap-3483	163	17	parameter	parameter	NOUN
ap-3483	163	18	?	?	PUNCT
ap-3483	164	1	these	these	DET
ap-3483	164	2	answers	answer	NOUN
ap-3483	164	3	will	will	AUX
ap-3483	164	4	not	not	PART
ap-3483	164	5	only	only	ADV
ap-3483	164	6	serve	serve	VERB
ap-3483	164	7	to	to	PART
ap-3483	164	8	construct	construct	VERB
ap-3483	164	9	surfaces	surface	NOUN
ap-3483	164	10	with	with	ADP
ap-3483	164	11	interesting	interesting	ADJ
ap-3483	164	12	geometric	geometric	ADJ
ap-3483	164	13	quantities	quantity	NOUN
ap-3483	164	14	but	but	CCONJ
ap-3483	164	15	can	can	AUX
ap-3483	164	16	also	also	ADV
ap-3483	164	17	help	help	VERB
ap-3483	164	18	to	to	PART
ap-3483	164	19	clarify	clarify	VERB
ap-3483	164	20	some	some	DET
ap-3483	164	21	problems	problem	NOUN
ap-3483	164	22	in	in	ADP
ap-3483	164	23	the	the	DET
ap-3483	164	24	theory	theory	NOUN
ap-3483	164	25	of	of	ADP
ap-3483	164	26	integrable	integrable	ADJ
ap-3483	164	27	system	system	NOUN
ap-3483	164	28	.	.	PUNCT
ap-3483	165	1	following	follow	VERB
ap-3483	165	2	the	the	DET
ap-3483	165	3	three	three	NUM
ap-3483	165	4	terms	term	NOUN
ap-3483	165	5	in	in	ADP
ap-3483	165	6	(	(	PUNCT
ap-3483	165	7	2.26	2.26	NUM
ap-3483	165	8	)	)	PUNCT
ap-3483	165	9	for	for	ADP
ap-3483	165	10	the	the	DET
ap-3483	165	11	immersion	immersion	NOUN
ap-3483	165	12	of	of	ADP
ap-3483	165	13	2d	2d	NOUN
ap-3483	165	14	-	-	PUNCT
ap-3483	165	15	soliton	soliton	NOUN
ap-3483	165	16	surfaces	surface	NOUN
ap-3483	165	17	in	in	ADP
ap-3483	165	18	lie	lie	NOUN
ap-3483	165	19	algebras	algebra	NOUN
ap-3483	165	20	,	,	PUNCT
ap-3483	165	21	we	we	PRON
ap-3483	165	22	now	now	ADV
ap-3483	165	23	show	show	VERB
ap-3483	165	24	that	that	SCONJ
ap-3483	165	25	there	there	PRON
ap-3483	165	26	exists	exist	VERB
ap-3483	165	27	a	a	DET
ap-3483	165	28	relation	relation	NOUN
ap-3483	165	29	between	between	ADP
ap-3483	165	30	the	the	DET
ap-3483	165	31	symtafel	symtafel	NOUN
ap-3483	165	32	,	,	PUNCT
ap-3483	165	33	the	the	DET
ap-3483	165	34	cieslinski	cieslinski	PROPN
ap-3483	165	35	-	-	PUNCT
ap-3483	165	36	doliwa	doliwa	PROPN
ap-3483	165	37	and	and	CCONJ
ap-3483	165	38	the	the	DET
ap-3483	165	39	fokas	fokas	ADJ
ap-3483	165	40	-	-	PUNCT
ap-3483	165	41	gel’fand	gel’fand	NOUN
ap-3483	165	42	formulas	formula	NOUN
ap-3483	165	43	.	.	PUNCT
ap-3483	166	1	183	183	NUM
ap-3483	166	2	a.	a.	NOUN
ap-3483	166	3	m.	m.	NOUN
ap-3483	166	4	grundland	grundland	PROPN
ap-3483	166	5	,	,	PUNCT
ap-3483	166	6	d.	d.	PROPN
ap-3483	166	7	levi	levi	PROPN
ap-3483	166	8	,	,	PUNCT
ap-3483	166	9	l.	l.	PROPN
ap-3483	166	10	martina	martina	PROPN
ap-3483	166	11	acta	acta	PROPN
ap-3483	166	12	polytechnica	polytechnica	PROPN
ap-3483	166	13	3	3	X
ap-3483	166	14	.	.	PUNCT
ap-3483	167	1	mapping	mapping	NOUN
ap-3483	167	2	between	between	ADP
ap-3483	167	3	the	the	DET
ap-3483	167	4	sym	sym	NOUN
ap-3483	167	5	-	-	PUNCT
ap-3483	167	6	tafel	tafel	PROPN
ap-3483	167	7	,	,	PUNCT
ap-3483	167	8	the	the	DET
ap-3483	167	9	cieslinski	cieslinski	PROPN
ap-3483	167	10	-	-	PUNCT
ap-3483	167	11	doliwa	doliwa	PROPN
ap-3483	167	12	and	and	CCONJ
ap-3483	167	13	the	the	DET
ap-3483	167	14	fokas	fokas	ADJ
ap-3483	167	15	-	-	PUNCT
ap-3483	167	16	gel’fand	gel’fand	NOUN
ap-3483	167	17	immersion	immersion	NOUN
ap-3483	167	18	formulas	formula	VERB
ap-3483	167	19	3.1	3.1	NUM
ap-3483	167	20	.	.	PUNCT
ap-3483	168	1	λ	λ	NOUN
ap-3483	168	2	-	-	ADJ
ap-3483	168	3	conformal	conformal	ADJ
ap-3483	168	4	symmetries	symmetry	NOUN
ap-3483	168	5	and	and	CCONJ
ap-3483	168	6	gauge	gauge	ADJ
ap-3483	168	7	transformations	transformation	NOUN
ap-3483	168	8	in	in	ADP
ap-3483	168	9	this	this	DET
ap-3483	168	10	subsection	subsection	NOUN
ap-3483	168	11	we	we	PRON
ap-3483	168	12	show	show	VERB
ap-3483	168	13	that	that	SCONJ
ap-3483	168	14	the	the	DET
ap-3483	168	15	st	st	PROPN
ap-3483	168	16	immersion	immersion	NOUN
ap-3483	168	17	formula	formula	NOUN
ap-3483	168	18	can	can	AUX
ap-3483	168	19	always	always	ADV
ap-3483	168	20	be	be	AUX
ap-3483	168	21	represented	represent	VERB
ap-3483	168	22	by	by	ADP
ap-3483	168	23	a	a	DET
ap-3483	168	24	gauge	gauge	ADJ
ap-3483	168	25	transformation	transformation	NOUN
ap-3483	168	26	through	through	ADP
ap-3483	168	27	the	the	DET
ap-3483	168	28	cd	cd	PROPN
ap-3483	168	29	formula	formula	NOUN
ap-3483	168	30	for	for	ADP
ap-3483	168	31	immersion	immersion	NOUN
ap-3483	168	32	.	.	PUNCT
ap-3483	169	1	the	the	DET
ap-3483	169	2	converse	converse	NOUN
ap-3483	169	3	statement	statement	NOUN
ap-3483	169	4	is	be	AUX
ap-3483	169	5	also	also	ADV
ap-3483	169	6	true	true	ADJ
ap-3483	169	7	:	:	PUNCT
ap-3483	169	8	from	from	ADP
ap-3483	169	9	a	a	DET
ap-3483	169	10	specific	specific	ADJ
ap-3483	169	11	gauge	gauge	NOUN
ap-3483	169	12	it	it	PRON
ap-3483	169	13	is	be	AUX
ap-3483	169	14	always	always	ADV
ap-3483	169	15	possible	possible	ADJ
ap-3483	169	16	to	to	PART
ap-3483	169	17	determine	determine	VERB
ap-3483	169	18	the	the	DET
ap-3483	169	19	st	st	PROPN
ap-3483	169	20	immersion	immersion	NOUN
ap-3483	169	21	formula	formula	NOUN
ap-3483	169	22	for	for	ADP
ap-3483	169	23	soliton	soliton	NOUN
ap-3483	169	24	surfaces	surface	NOUN
ap-3483	169	25	.	.	PUNCT
ap-3483	170	1	proposition	proposition	NOUN
ap-3483	170	2	1	1	NUM
ap-3483	170	3	.	.	PUNCT
ap-3483	171	1	a	a	DET
ap-3483	171	2	symmetry	symmetry	NOUN
ap-3483	171	3	of	of	ADP
ap-3483	171	4	the	the	DET
ap-3483	171	5	zcc	zcc	NOUN
ap-3483	171	6	(	(	PUNCT
ap-3483	171	7	2.14	2.14	NUM
ap-3483	171	8	)	)	PUNCT
ap-3483	171	9	of	of	ADP
ap-3483	171	10	the	the	DET
ap-3483	171	11	lsp	lsp	PROPN
ap-3483	171	12	associated	associate	VERB
ap-3483	171	13	with	with	ADP
ap-3483	171	14	an	an	DET
ap-3483	171	15	integrable	integrable	ADJ
ap-3483	171	16	system	system	NOUN
ap-3483	171	17	ω[u	ω[u	NOUN
ap-3483	171	18	]	]	X
ap-3483	171	19	=	=	SYM
ap-3483	171	20	0	0	NUM
ap-3483	171	21	is	be	AUX
ap-3483	171	22	a	a	DET
ap-3483	171	23	λ	λ	NOUN
ap-3483	171	24	-	-	ADJ
ap-3483	171	25	conformal	conformal	ADJ
ap-3483	171	26	symmetry	symmetry	NOUN
ap-3483	171	27	if	if	SCONJ
ap-3483	172	1	and	and	CCONJ
ap-3483	172	2	only	only	ADV
ap-3483	172	3	if	if	SCONJ
ap-3483	172	4	there	there	PRON
ap-3483	172	5	exists	exist	VERB
ap-3483	172	6	a	a	DET
ap-3483	172	7	g	g	NOUN
ap-3483	172	8	-	-	PUNCT
ap-3483	172	9	valued	value	VERB
ap-3483	172	10	matrix	matrix	NOUN
ap-3483	172	11	function	function	NOUN
ap-3483	172	12	s1	s1	NOUN
ap-3483	172	13	=	=	SYM
ap-3483	172	14	s1([u	s1([u	PROPN
ap-3483	172	15	]	]	PUNCT
ap-3483	172	16	,	,	PUNCT
ap-3483	172	17	λ	λ	PROPN
ap-3483	172	18	)	)	PUNCT
ap-3483	172	19	which	which	PRON
ap-3483	172	20	is	be	AUX
ap-3483	172	21	a	a	DET
ap-3483	172	22	solution	solution	NOUN
ap-3483	172	23	of	of	ADP
ap-3483	172	24	the	the	DET
ap-3483	172	25	system	system	NOUN
ap-3483	172	26	of	of	ADP
ap-3483	172	27	differential	differential	ADJ
ap-3483	172	28	equations	equation	NOUN
ap-3483	172	29	dαs1	dαs1	VERB
ap-3483	172	30	+	+	PUNCT
ap-3483	173	1	[	[	X
ap-3483	173	2	s1	s1	NOUN
ap-3483	173	3	,	,	PUNCT
ap-3483	173	4	uα	uα	X
ap-3483	173	5	]	]	X
ap-3483	173	6	=	=	SYM
ap-3483	173	7	β(λ)dλuα	β(λ)dλuα	NUM
ap-3483	173	8	,	,	PUNCT
ap-3483	173	9	α	α	NOUN
ap-3483	173	10	=	=	SYM
ap-3483	173	11	1	1	NUM
ap-3483	173	12	,	,	PUNCT
ap-3483	173	13	2	2	NUM
ap-3483	173	14	.	.	PUNCT
ap-3483	173	15	(	(	PUNCT
ap-3483	173	16	3.1	3.1	NUM
ap-3483	173	17	)	)	PUNCT
ap-3483	173	18	proof	proof	NOUN
ap-3483	173	19	.	.	PUNCT
ap-3483	174	1	first	first	ADV
ap-3483	174	2	we	we	PRON
ap-3483	174	3	show	show	VERB
ap-3483	174	4	that	that	SCONJ
ap-3483	174	5	for	for	ADP
ap-3483	174	6	any	any	DET
ap-3483	174	7	λ	λ	NOUN
ap-3483	174	8	-	-	ADJ
ap-3483	174	9	conformal	conformal	ADJ
ap-3483	174	10	symmetry	symmetry	NOUN
ap-3483	174	11	of	of	ADP
ap-3483	174	12	the	the	DET
ap-3483	174	13	zcc	zcc	NOUN
ap-3483	174	14	of	of	ADP
ap-3483	174	15	the	the	DET
ap-3483	174	16	lsp	lsp	PROPN
ap-3483	174	17	associated	associate	VERB
ap-3483	174	18	with	with	ADP
ap-3483	174	19	the	the	DET
ap-3483	174	20	integrable	integrable	ADJ
ap-3483	174	21	system	system	NOUN
ap-3483	174	22	ω[u	ω[u	NOUN
ap-3483	174	23	]	]	X
ap-3483	174	24	=	=	SYM
ap-3483	174	25	0	0	NUM
ap-3483	174	26	,	,	PUNCT
ap-3483	174	27	there	there	PRON
ap-3483	174	28	exists	exist	VERB
ap-3483	174	29	a	a	DET
ap-3483	174	30	g	g	NOUN
ap-3483	174	31	-	-	PUNCT
ap-3483	174	32	valued	value	VERB
ap-3483	174	33	matrix	matrix	NOUN
ap-3483	174	34	function	function	NOUN
ap-3483	174	35	s1	s1	NOUN
ap-3483	174	36	=	=	SYM
ap-3483	174	37	s1([u	s1([u	PROPN
ap-3483	174	38	]	]	PUNCT
ap-3483	174	39	,	,	PUNCT
ap-3483	174	40	λ	λ	PROPN
ap-3483	174	41	)	)	PUNCT
ap-3483	174	42	which	which	PRON
ap-3483	174	43	is	be	AUX
ap-3483	174	44	a	a	DET
ap-3483	174	45	solution	solution	NOUN
ap-3483	174	46	of	of	ADP
ap-3483	174	47	the	the	DET
ap-3483	174	48	system	system	NOUN
ap-3483	174	49	of	of	ADP
ap-3483	174	50	differential	differential	ADJ
ap-3483	174	51	equations	equation	NOUN
ap-3483	174	52	(	(	PUNCT
ap-3483	174	53	3.1	3.1	NUM
ap-3483	174	54	)	)	PUNCT
ap-3483	174	55	.	.	PUNCT
ap-3483	175	1	indeed	indeed	ADV
ap-3483	175	2	,	,	PUNCT
ap-3483	175	3	the	the	DET
ap-3483	175	4	linearly	linearly	ADV
ap-3483	175	5	independent	independent	ADJ
ap-3483	175	6	g	g	NOUN
ap-3483	175	7	-	-	PUNCT
ap-3483	175	8	valued	value	VERB
ap-3483	175	9	matrix	matrix	NOUN
ap-3483	175	10	functions	function	NOUN
ap-3483	175	11	aα([u	aα([u	PROPN
ap-3483	175	12	]	]	X
ap-3483	175	13	,	,	PUNCT
ap-3483	175	14	λ	λ	NOUN
ap-3483	175	15	)	)	PUNCT
ap-3483	175	16	=	=	PUNCT
ap-3483	176	1	β(λ)dλuα([u	β(λ)dλuα([u	PROPN
ap-3483	176	2	]	]	X
ap-3483	176	3	,	,	PUNCT
ap-3483	176	4	λ	λ	PROPN
ap-3483	176	5	)	)	PUNCT
ap-3483	176	6	,	,	PUNCT
ap-3483	176	7	(	(	PUNCT
ap-3483	176	8	3.2	3.2	NUM
ap-3483	176	9	)	)	PUNCT
ap-3483	176	10	associated	associate	VERB
ap-3483	176	11	with	with	ADP
ap-3483	176	12	the	the	DET
ap-3483	176	13	λ	λ	NOUN
ap-3483	176	14	-	-	ADJ
ap-3483	176	15	conformal	conformal	ADJ
ap-3483	176	16	symmetry	symmetry	NOUN
ap-3483	176	17	of	of	ADP
ap-3483	176	18	the	the	DET
ap-3483	176	19	zcc	zcc	NOUN
ap-3483	176	20	(	(	PUNCT
ap-3483	176	21	2.14	2.14	NUM
ap-3483	176	22	)	)	PUNCT
ap-3483	176	23	satisfy	satisfy	VERB
ap-3483	176	24	the	the	DET
ap-3483	176	25	infinitesimal	infinitesimal	ADJ
ap-3483	176	26	deformation	deformation	NOUN
ap-3483	176	27	of	of	ADP
ap-3483	176	28	the	the	DET
ap-3483	176	29	zcc	zcc	NOUN
ap-3483	176	30	(	(	PUNCT
ap-3483	176	31	2.21	2.21	NUM
ap-3483	176	32	)	)	PUNCT
ap-3483	176	33	and	and	CCONJ
ap-3483	176	34	the	the	DET
ap-3483	176	35	corresponding	correspond	VERB
ap-3483	176	36	st	st	PROPN
ap-3483	176	37	immersion	immersion	NOUN
ap-3483	176	38	function	function	NOUN
ap-3483	176	39	is	be	AUX
ap-3483	176	40	fst	fst	NOUN
ap-3483	176	41	(	(	PUNCT
ap-3483	176	42	[	[	X
ap-3483	176	43	u	u	X
ap-3483	176	44	]	]	X
ap-3483	176	45	,	,	PUNCT
ap-3483	176	46	λ	λ	NOUN
ap-3483	176	47	)	)	PUNCT
ap-3483	176	48	=	=	PUNCT
ap-3483	176	49	β(λ)φ−1dλφ	β(λ)φ−1dλφ	X
ap-3483	176	50	∈	∈	PROPN
ap-3483	176	51	g	g	PROPN
ap-3483	176	52	,	,	PUNCT
ap-3483	176	53	(	(	PUNCT
ap-3483	176	54	3.3	3.3	NUM
ap-3483	176	55	)	)	PUNCT
ap-3483	176	56	with	with	ADP
ap-3483	176	57	linearly	linearly	ADV
ap-3483	176	58	independent	independent	ADJ
ap-3483	176	59	tangent	tangent	NOUN
ap-3483	176	60	vectors	vector	NOUN
ap-3483	176	61	dαf	dαf	VERB
ap-3483	176	62	st	st	PROPN
ap-3483	176	63	=	=	SYM
ap-3483	176	64	β(λ)φ−1(dλuα)φ	β(λ)φ−1(dλuα)φ	PROPN
ap-3483	176	65	,	,	PUNCT
ap-3483	176	66	α	α	NOUN
ap-3483	176	67	=	=	SYM
ap-3483	176	68	1	1	NUM
ap-3483	176	69	,	,	PUNCT
ap-3483	176	70	2	2	NUM
ap-3483	176	71	.	.	PUNCT
ap-3483	176	72	(	(	PUNCT
ap-3483	176	73	3.4	3.4	NUM
ap-3483	176	74	)	)	PUNCT
ap-3483	176	75	on	on	ADP
ap-3483	176	76	the	the	DET
ap-3483	176	77	other	other	ADJ
ap-3483	176	78	hand	hand	NOUN
ap-3483	176	79	any	any	DET
ap-3483	176	80	g	g	NOUN
ap-3483	176	81	-	-	PUNCT
ap-3483	176	82	valued	value	VERB
ap-3483	176	83	matrix	matrix	NOUN
ap-3483	176	84	function	function	NOUN
ap-3483	176	85	can	can	AUX
ap-3483	176	86	be	be	AUX
ap-3483	176	87	written	write	VERB
ap-3483	176	88	as	as	ADP
ap-3483	176	89	the	the	DET
ap-3483	176	90	adjoint	adjoint	PROPN
ap-3483	176	91	group	group	NOUN
ap-3483	176	92	action	action	NOUN
ap-3483	176	93	on	on	ADP
ap-3483	176	94	its	its	PRON
ap-3483	176	95	lie	lie	NOUN
ap-3483	176	96	algebra	algebra	NOUN
ap-3483	176	97	.	.	PUNCT
ap-3483	177	1	this	this	PRON
ap-3483	177	2	implies	imply	VERB
ap-3483	177	3	the	the	DET
ap-3483	177	4	existence	existence	NOUN
ap-3483	177	5	of	of	ADP
ap-3483	177	6	a	a	DET
ap-3483	177	7	g	g	NOUN
ap-3483	177	8	-	-	PUNCT
ap-3483	177	9	valued	value	VERB
ap-3483	177	10	matrix	matrix	NOUN
ap-3483	177	11	function	function	NOUN
ap-3483	177	12	s1([u	s1([u	PROPN
ap-3483	177	13	]	]	PUNCT
ap-3483	177	14	,	,	PUNCT
ap-3483	177	15	λ	λ	PROPN
ap-3483	177	16	)	)	PUNCT
ap-3483	177	17	for	for	ADP
ap-3483	177	18	which	which	PRON
ap-3483	177	19	the	the	DET
ap-3483	177	20	st	st	PROPN
ap-3483	177	21	immersion	immersion	NOUN
ap-3483	177	22	formula	formula	NOUN
ap-3483	177	23	(	(	PUNCT
ap-3483	177	24	3.3	3.3	NUM
ap-3483	177	25	)	)	PUNCT
ap-3483	177	26	is	be	AUX
ap-3483	177	27	the	the	DET
ap-3483	177	28	cd	cd	PROPN
ap-3483	177	29	formula	formula	NOUN
ap-3483	177	30	,	,	PUNCT
ap-3483	177	31	i.e.	i.e.	X
ap-3483	177	32	fcd([u	fcd([u	PROPN
ap-3483	177	33	]	]	PUNCT
ap-3483	177	34	,	,	PUNCT
ap-3483	177	35	λ	λ	NOUN
ap-3483	177	36	)	)	PUNCT
ap-3483	177	37	=	=	SYM
ap-3483	177	38	φ−1s1([u	φ−1s1([u	PROPN
ap-3483	177	39	]	]	PUNCT
ap-3483	177	40	,	,	PUNCT
ap-3483	177	41	λ)φ	λ)φ	ADJ
ap-3483	177	42	∈	∈	PROPN
ap-3483	177	43	g	g	NOUN
ap-3483	177	44	,	,	PUNCT
ap-3483	177	45	(	(	PUNCT
ap-3483	177	46	3.5	3.5	NUM
ap-3483	177	47	)	)	PUNCT
ap-3483	177	48	whose	whose	DET
ap-3483	177	49	tangent	tangent	NOUN
ap-3483	177	50	vectors	vector	NOUN
ap-3483	177	51	are	be	AUX
ap-3483	177	52	found	find	VERB
ap-3483	177	53	to	to	PART
ap-3483	177	54	be	be	AUX
ap-3483	177	55	dαf	dαf	NOUN
ap-3483	177	56	cd	cd	NOUN
ap-3483	177	57	=	=	PUNCT
ap-3483	177	58	φ−1(dαs1	φ−1(dαs1	X
ap-3483	178	1	+	+	PUNCT
ap-3483	178	2	[	[	X
ap-3483	178	3	s1	s1	NOUN
ap-3483	178	4	,	,	PUNCT
ap-3483	178	5	uα	uα	PROPN
ap-3483	178	6	]	]	PUNCT
ap-3483	178	7	)	)	PUNCT
ap-3483	178	8	φ	φ	PROPN
ap-3483	178	9	,	,	PUNCT
ap-3483	178	10	α	α	NOUN
ap-3483	178	11	=	=	SYM
ap-3483	178	12	1	1	NUM
ap-3483	178	13	,	,	PUNCT
ap-3483	178	14	2	2	NUM
ap-3483	178	15	.	.	PUNCT
ap-3483	178	16	(	(	PUNCT
ap-3483	178	17	3.6	3.6	NUM
ap-3483	178	18	)	)	PUNCT
ap-3483	178	19	by	by	ADP
ap-3483	178	20	comparing	compare	VERB
ap-3483	178	21	the	the	DET
ap-3483	178	22	tangent	tangent	ADJ
ap-3483	178	23	vectors	vector	NOUN
ap-3483	178	24	(	(	PUNCT
ap-3483	178	25	3.4	3.4	NUM
ap-3483	178	26	)	)	PUNCT
ap-3483	178	27	and	and	CCONJ
ap-3483	178	28	(	(	PUNCT
ap-3483	178	29	3.6	3.6	NUM
ap-3483	178	30	)	)	PUNCT
ap-3483	178	31	we	we	PRON
ap-3483	178	32	obtain	obtain	VERB
ap-3483	178	33	(	(	PUNCT
ap-3483	178	34	3.1	3.1	NUM
ap-3483	178	35	)	)	PUNCT
ap-3483	178	36	.	.	PUNCT
ap-3483	179	1	it	it	PRON
ap-3483	179	2	remains	remain	VERB
ap-3483	179	3	to	to	PART
ap-3483	179	4	show	show	VERB
ap-3483	179	5	that	that	SCONJ
ap-3483	179	6	the	the	DET
ap-3483	179	7	system	system	NOUN
ap-3483	179	8	(	(	PUNCT
ap-3483	179	9	3.1	3.1	NUM
ap-3483	179	10	)	)	PUNCT
ap-3483	179	11	is	be	AUX
ap-3483	179	12	a	a	DET
ap-3483	179	13	solvable	solvable	ADJ
ap-3483	179	14	one	one	NUM
ap-3483	179	15	.	.	PUNCT
ap-3483	180	1	indeed	indeed	ADV
ap-3483	180	2	,	,	PUNCT
ap-3483	180	3	from	from	ADP
ap-3483	180	4	the	the	DET
ap-3483	180	5	compatibility	compatibility	NOUN
ap-3483	180	6	condition	condition	NOUN
ap-3483	180	7	of	of	ADP
ap-3483	180	8	(	(	PUNCT
ap-3483	180	9	3.1	3.1	NUM
ap-3483	180	10	)	)	PUNCT
ap-3483	180	11	we	we	PRON
ap-3483	180	12	get	get	VERB
ap-3483	180	13	β(λ)d2(dλu1)−	β(λ)d2(dλu1)−	PROPN
ap-3483	180	14	β(λ)d1(dλu2	β(λ)d1(dλu2	NUM
ap-3483	180	15	)	)	PUNCT
ap-3483	180	16	−	−	PROPN
ap-3483	181	1	[	[	PUNCT
ap-3483	181	2	β(λ)dλu2	β(λ)dλu2	NOUN
ap-3483	181	3	−	−	ADP
ap-3483	181	4	[	[	X
ap-3483	181	5	s1	s1	NOUN
ap-3483	181	6	,	,	PUNCT
ap-3483	181	7	u2	u2	NOUN
ap-3483	181	8	]	]	PUNCT
ap-3483	181	9	,	,	PUNCT
ap-3483	181	10	u1	u1	NOUN
ap-3483	181	11	]	]	PUNCT
ap-3483	181	12	−	−	PUNCT
ap-3483	182	1	[	[	X
ap-3483	182	2	s1	s1	NOUN
ap-3483	182	3	,	,	PUNCT
ap-3483	182	4	d2u1	d2u1	X
ap-3483	182	5	]	]	X
ap-3483	183	1	+	+	CCONJ
ap-3483	183	2	[	[	PUNCT
ap-3483	183	3	β(λ)dλu1	β(λ)dλu1	ADP
ap-3483	183	4	−	−	PROPN
ap-3483	183	5	[	[	X
ap-3483	183	6	s1	s1	NOUN
ap-3483	183	7	,	,	PUNCT
ap-3483	183	8	u1	u1	NOUN
ap-3483	183	9	]	]	PUNCT
ap-3483	183	10	,	,	PUNCT
ap-3483	183	11	u2	u2	PROPN
ap-3483	183	12	]	]	PUNCT
ap-3483	183	13	+	+	CCONJ
ap-3483	183	14	[	[	X
ap-3483	183	15	s1	s1	NOUN
ap-3483	183	16	,	,	PUNCT
ap-3483	183	17	d1u2	d1u2	X
ap-3483	183	18	]	]	X
ap-3483	183	19	=	=	SYM
ap-3483	183	20	0	0	NUM
ap-3483	183	21	,	,	PUNCT
ap-3483	183	22	(	(	PUNCT
ap-3483	183	23	3.7	3.7	NUM
ap-3483	183	24	)	)	PUNCT
ap-3483	183	25	which	which	PRON
ap-3483	183	26	has	have	VERB
ap-3483	183	27	to	to	PART
ap-3483	183	28	be	be	AUX
ap-3483	183	29	satisfied	satisfied	ADJ
ap-3483	183	30	whenever	whenever	SCONJ
ap-3483	183	31	(	(	PUNCT
ap-3483	183	32	3.1	3.1	NUM
ap-3483	183	33	)	)	PUNCT
ap-3483	183	34	holds	hold	VERB
ap-3483	183	35	.	.	PUNCT
ap-3483	184	1	using	use	VERB
ap-3483	184	2	the	the	DET
ap-3483	184	3	zcc	zcc	NOUN
ap-3483	184	4	(	(	PUNCT
ap-3483	184	5	2.14	2.14	NUM
ap-3483	184	6	)	)	PUNCT
ap-3483	184	7	and	and	CCONJ
ap-3483	184	8	the	the	DET
ap-3483	184	9	jacobi	jacobi	PROPN
ap-3483	184	10	identity	identity	NOUN
ap-3483	184	11	it	it	PRON
ap-3483	184	12	is	be	AUX
ap-3483	184	13	easy	easy	ADJ
ap-3483	184	14	to	to	PART
ap-3483	184	15	show	show	VERB
ap-3483	184	16	that	that	SCONJ
ap-3483	184	17	(	(	PUNCT
ap-3483	184	18	3.7	3.7	NUM
ap-3483	184	19	)	)	PUNCT
ap-3483	184	20	is	be	AUX
ap-3483	184	21	identically	identically	ADV
ap-3483	184	22	satisfied	satisfied	ADJ
ap-3483	184	23	.	.	PUNCT
ap-3483	185	1	so	so	ADV
ap-3483	185	2	if	if	SCONJ
ap-3483	185	3	we	we	PRON
ap-3483	185	4	can	can	AUX
ap-3483	185	5	find	find	VERB
ap-3483	185	6	a	a	DET
ap-3483	185	7	gauge	gauge	NOUN
ap-3483	185	8	s1([u	s1([u	NOUN
ap-3483	185	9	]	]	PUNCT
ap-3483	185	10	,	,	PUNCT
ap-3483	185	11	λ	λ	X
ap-3483	185	12	)	)	PUNCT
ap-3483	185	13	which	which	PRON
ap-3483	185	14	satisfies	satisfy	VERB
ap-3483	185	15	(	(	PUNCT
ap-3483	185	16	3.1	3.1	NUM
ap-3483	185	17	)	)	PUNCT
ap-3483	185	18	,	,	PUNCT
ap-3483	185	19	then	then	ADV
ap-3483	185	20	the	the	DET
ap-3483	185	21	st	st	PROPN
ap-3483	185	22	immersion	immersion	NOUN
ap-3483	185	23	formula	formula	NOUN
ap-3483	185	24	(	(	PUNCT
ap-3483	185	25	3.3	3.3	NUM
ap-3483	185	26	)	)	PUNCT
ap-3483	185	27	can	can	AUX
ap-3483	185	28	always	always	ADV
ap-3483	185	29	be	be	AUX
ap-3483	185	30	represented	represent	VERB
ap-3483	185	31	by	by	ADP
ap-3483	185	32	a	a	DET
ap-3483	185	33	gauge	gauge	NOUN
ap-3483	185	34	.	.	PUNCT
ap-3483	186	1	conversely	conversely	ADV
ap-3483	186	2	,	,	PUNCT
ap-3483	186	3	we	we	PRON
ap-3483	186	4	show	show	VERB
ap-3483	186	5	that	that	SCONJ
ap-3483	186	6	for	for	ADP
ap-3483	186	7	any	any	DET
ap-3483	186	8	g	g	NOUN
ap-3483	186	9	-	-	PUNCT
ap-3483	186	10	valued	value	VERB
ap-3483	186	11	matrix	matrix	NOUN
ap-3483	186	12	function	function	NOUN
ap-3483	186	13	s1	s1	NOUN
ap-3483	186	14	defined	define	VERB
ap-3483	186	15	as	as	ADP
ap-3483	186	16	a	a	DET
ap-3483	186	17	solution	solution	NOUN
ap-3483	186	18	of	of	ADP
ap-3483	186	19	the	the	DET
ap-3483	186	20	system	system	NOUN
ap-3483	186	21	of	of	ADP
ap-3483	186	22	pdes	pde	NOUN
ap-3483	186	23	(	(	PUNCT
ap-3483	186	24	3.1	3.1	NUM
ap-3483	186	25	)	)	PUNCT
ap-3483	186	26	,	,	PUNCT
ap-3483	186	27	there	there	PRON
ap-3483	186	28	exists	exist	VERB
ap-3483	186	29	a	a	DET
ap-3483	186	30	λ	λ	NOUN
ap-3483	186	31	-	-	ADJ
ap-3483	186	32	conformal	conformal	ADJ
ap-3483	186	33	symmetry	symmetry	NOUN
ap-3483	186	34	of	of	ADP
ap-3483	186	35	the	the	DET
ap-3483	186	36	zcc	zcc	NOUN
ap-3483	186	37	of	of	ADP
ap-3483	186	38	the	the	DET
ap-3483	186	39	lsp	lsp	PROPN
ap-3483	186	40	associated	associate	VERB
ap-3483	186	41	with	with	ADP
ap-3483	186	42	the	the	DET
ap-3483	186	43	integrable	integrable	ADJ
ap-3483	186	44	system	system	NOUN
ap-3483	186	45	ω[u	ω[u	NOUN
ap-3483	186	46	]	]	X
ap-3483	186	47	=	=	SYM
ap-3483	186	48	0	0	X
ap-3483	186	49	.	.	PUNCT
ap-3483	186	50	indeed	indeed	ADV
ap-3483	186	51	,	,	PUNCT
ap-3483	186	52	comparing	compare	VERB
ap-3483	186	53	the	the	DET
ap-3483	186	54	immersion	immersion	NOUN
ap-3483	186	55	formulas	formula	NOUN
ap-3483	186	56	(	(	PUNCT
ap-3483	186	57	3.3	3.3	NUM
ap-3483	186	58	)	)	PUNCT
ap-3483	186	59	with	with	ADP
ap-3483	186	60	(	(	PUNCT
ap-3483	186	61	3.5	3.5	NUM
ap-3483	186	62	)	)	PUNCT
ap-3483	186	63	we	we	PRON
ap-3483	186	64	find	find	VERB
ap-3483	186	65	a	a	DET
ap-3483	186	66	linear	linear	ADJ
ap-3483	186	67	matrix	matrix	NOUN
ap-3483	186	68	equation	equation	NOUN
ap-3483	186	69	for	for	ADP
ap-3483	186	70	the	the	DET
ap-3483	186	71	wavefunction	wavefunction	NOUN
ap-3483	186	72	φ	φ	PROPN
ap-3483	186	73	β(λ)dλφ	β(λ)dλφ	PROPN
ap-3483	186	74	=	=	SYM
ap-3483	186	75	s1([u	s1([u	PROPN
ap-3483	186	76	]	]	X
ap-3483	186	77	,	,	PUNCT
ap-3483	186	78	λ)φ	λ)φ	X
ap-3483	186	79	.	.	PUNCT
ap-3483	187	1	(	(	PUNCT
ap-3483	187	2	3.8	3.8	NUM
ap-3483	187	3	)	)	PUNCT
ap-3483	187	4	if	if	SCONJ
ap-3483	187	5	the	the	DET
ap-3483	187	6	gauge	gauge	NOUN
ap-3483	187	7	function	function	NOUN
ap-3483	187	8	s1([u	s1([u	PROPN
ap-3483	187	9	]	]	PUNCT
ap-3483	187	10	,	,	PUNCT
ap-3483	187	11	λ	λ	X
ap-3483	187	12	)	)	PUNCT
ap-3483	187	13	is	be	AUX
ap-3483	187	14	known	know	VERB
ap-3483	187	15	,	,	PUNCT
ap-3483	187	16	by	by	ADP
ap-3483	187	17	solving	solve	VERB
ap-3483	187	18	(	(	PUNCT
ap-3483	187	19	3.8	3.8	NUM
ap-3483	187	20	)	)	PUNCT
ap-3483	187	21	we	we	PRON
ap-3483	187	22	can	can	AUX
ap-3483	187	23	determine	determine	VERB
ap-3483	187	24	the	the	DET
ap-3483	187	25	wavefunction	wavefunction	NOUN
ap-3483	187	26	φ	φ	PROPN
ap-3483	187	27	and	and	CCONJ
ap-3483	187	28	consequently	consequently	ADV
ap-3483	187	29	obtain	obtain	VERB
ap-3483	187	30	the	the	DET
ap-3483	187	31	st	st	PROPN
ap-3483	187	32	immersion	immersion	NOUN
ap-3483	187	33	formula	formula	NOUN
ap-3483	187	34	for	for	ADP
ap-3483	187	35	2d	2d	NOUN
ap-3483	187	36	-	-	PUNCT
ap-3483	187	37	soliton	soliton	NOUN
ap-3483	187	38	surfaces	surface	NOUN
ap-3483	187	39	.	.	PUNCT
ap-3483	188	1	therefore	therefore	ADV
ap-3483	188	2	,	,	PUNCT
ap-3483	188	3	the	the	DET
ap-3483	188	4	st	st	PROPN
ap-3483	188	5	formula	formula	NOUN
ap-3483	188	6	for	for	ADP
ap-3483	188	7	immersion	immersion	NOUN
ap-3483	188	8	(	(	PUNCT
ap-3483	188	9	2.27	2.27	NUM
ap-3483	188	10	)	)	PUNCT
ap-3483	188	11	is	be	AUX
ap-3483	188	12	equivalent	equivalent	ADJ
ap-3483	188	13	to	to	ADP
ap-3483	188	14	the	the	DET
ap-3483	188	15	cd	cd	PROPN
ap-3483	188	16	immersion	immersion	NOUN
ap-3483	188	17	formula	formula	NOUN
ap-3483	188	18	(	(	PUNCT
ap-3483	188	19	2.28	2.28	NUM
ap-3483	188	20	)	)	PUNCT
ap-3483	188	21	for	for	ADP
ap-3483	188	22	the	the	DET
ap-3483	188	23	gauge	gauge	NOUN
ap-3483	188	24	s1	s1	NOUN
ap-3483	188	25	,	,	PUNCT
ap-3483	188	26	which	which	PRON
ap-3483	188	27	satisfies	satisfy	VERB
ap-3483	188	28	differential	differential	ADJ
ap-3483	188	29	equation	equation	NOUN
ap-3483	188	30	(	(	PUNCT
ap-3483	188	31	3.1	3.1	NUM
ap-3483	188	32	)	)	PUNCT
ap-3483	188	33	.	.	PUNCT
ap-3483	189	1	3.2	3.2	NUM
ap-3483	189	2	.	.	PUNCT
ap-3483	190	1	generalized	generalize	VERB
ap-3483	190	2	symmetries	symmetry	NOUN
ap-3483	190	3	and	and	CCONJ
ap-3483	190	4	gauge	gauge	ADJ
ap-3483	190	5	transformations	transformation	NOUN
ap-3483	190	6	in	in	ADP
ap-3483	190	7	this	this	DET
ap-3483	190	8	subsection	subsection	NOUN
ap-3483	190	9	we	we	PRON
ap-3483	190	10	discuss	discuss	VERB
ap-3483	190	11	the	the	DET
ap-3483	190	12	links	link	NOUN
ap-3483	190	13	between	between	ADP
ap-3483	190	14	gauge	gauge	NOUN
ap-3483	190	15	transformations	transformation	NOUN
ap-3483	190	16	and	and	CCONJ
ap-3483	190	17	generalized	generalized	ADJ
ap-3483	190	18	symmetries	symmetry	NOUN
ap-3483	190	19	of	of	ADP
ap-3483	190	20	the	the	DET
ap-3483	190	21	zcc	zcc	NOUN
ap-3483	190	22	associated	associate	VERB
ap-3483	190	23	with	with	ADP
ap-3483	190	24	the	the	DET
ap-3483	190	25	integrable	integrable	ADJ
ap-3483	190	26	partial	partial	ADJ
ap-3483	190	27	differential	differential	NOUN
ap-3483	190	28	system	system	NOUN
ap-3483	190	29	ω[u	ω[u	NOUN
ap-3483	190	30	]	]	X
ap-3483	190	31	=	=	SYM
ap-3483	190	32	0	0	X
ap-3483	190	33	.	.	PUNCT
ap-3483	191	1	we	we	PRON
ap-3483	191	2	show	show	VERB
ap-3483	191	3	that	that	SCONJ
ap-3483	191	4	the	the	DET
ap-3483	191	5	immersion	immersion	NOUN
ap-3483	191	6	formula	formula	NOUN
ap-3483	191	7	associated	associate	VERB
ap-3483	191	8	with	with	ADP
ap-3483	191	9	the	the	DET
ap-3483	191	10	generalized	generalized	ADJ
ap-3483	191	11	symmetries	symmetry	NOUN
ap-3483	191	12	(	(	PUNCT
ap-3483	191	13	2.29	2.29	NUM
ap-3483	191	14	)	)	PUNCT
ap-3483	191	15	can	can	AUX
ap-3483	191	16	always	always	ADV
ap-3483	191	17	be	be	AUX
ap-3483	191	18	obtained	obtain	VERB
ap-3483	191	19	by	by	ADP
ap-3483	191	20	a	a	DET
ap-3483	191	21	gauge	gauge	ADJ
ap-3483	191	22	transformation	transformation	NOUN
ap-3483	191	23	and	and	CCONJ
ap-3483	191	24	the	the	DET
ap-3483	191	25	converse	converse	NOUN
ap-3483	191	26	statement	statement	NOUN
ap-3483	191	27	is	be	AUX
ap-3483	191	28	also	also	ADV
ap-3483	191	29	true	true	ADJ
ap-3483	191	30	.	.	PUNCT
ap-3483	192	1	proposition	proposition	NOUN
ap-3483	192	2	2	2	NUM
ap-3483	192	3	.	.	PUNCT
ap-3483	193	1	a	a	DET
ap-3483	193	2	vector	vector	NOUN
ap-3483	193	3	field	field	NOUN
ap-3483	193	4	ωr	ωr	NOUN
ap-3483	193	5	is	be	AUX
ap-3483	193	6	a	a	DET
ap-3483	193	7	generalized	generalized	ADJ
ap-3483	193	8	symmetry	symmetry	NOUN
ap-3483	193	9	of	of	ADP
ap-3483	193	10	the	the	DET
ap-3483	193	11	zcc	zcc	NOUN
ap-3483	193	12	(	(	PUNCT
ap-3483	193	13	2.14	2.14	NUM
ap-3483	193	14	)	)	PUNCT
ap-3483	193	15	of	of	ADP
ap-3483	193	16	the	the	DET
ap-3483	193	17	lsp	lsp	PROPN
ap-3483	193	18	associated	associate	VERB
ap-3483	193	19	with	with	ADP
ap-3483	193	20	an	an	DET
ap-3483	193	21	integrable	integrable	ADJ
ap-3483	193	22	system	system	NOUN
ap-3483	193	23	ω[u	ω[u	NOUN
ap-3483	193	24	]	]	X
ap-3483	193	25	=	=	SYM
ap-3483	193	26	0	0	PUNCT
ap-3483	194	1	if	if	SCONJ
ap-3483	194	2	and	and	CCONJ
ap-3483	194	3	only	only	ADV
ap-3483	194	4	if	if	SCONJ
ap-3483	194	5	there	there	PRON
ap-3483	194	6	exists	exist	VERB
ap-3483	194	7	a	a	DET
ap-3483	194	8	g	g	NOUN
ap-3483	194	9	-	-	PUNCT
ap-3483	194	10	valued	value	VERB
ap-3483	194	11	matrix	matrix	NOUN
ap-3483	194	12	function	function	NOUN
ap-3483	194	13	(	(	PUNCT
ap-3483	194	14	gauge	gauge	NOUN
ap-3483	194	15	)	)	PUNCT
ap-3483	194	16	s2	s2	NOUN
ap-3483	194	17	=	=	PUNCT
ap-3483	194	18	s2([u	s2([u	NOUN
ap-3483	194	19	]	]	PUNCT
ap-3483	194	20	,	,	PUNCT
ap-3483	194	21	λ	λ	PROPN
ap-3483	194	22	)	)	PUNCT
ap-3483	194	23	which	which	PRON
ap-3483	194	24	is	be	AUX
ap-3483	194	25	a	a	DET
ap-3483	194	26	solution	solution	NOUN
ap-3483	194	27	of	of	ADP
ap-3483	194	28	the	the	DET
ap-3483	194	29	system	system	NOUN
ap-3483	194	30	of	of	ADP
ap-3483	194	31	differential	differential	ADJ
ap-3483	194	32	equations	equation	NOUN
ap-3483	194	33	dαs2	dαs2	VERB
ap-3483	194	34	+	+	CCONJ
ap-3483	195	1	[	[	X
ap-3483	195	2	s2	s2	NOUN
ap-3483	195	3	,	,	PUNCT
ap-3483	195	4	uα	uα	X
ap-3483	195	5	]	]	X
ap-3483	195	6	=	=	SYM
ap-3483	195	7	prωruα	prωruα	NOUN
ap-3483	195	8	+	+	CCONJ
ap-3483	195	9	(	(	PUNCT
ap-3483	195	10	prωr(dαφ−	prωr(dαφ−	X
ap-3483	195	11	uαφ	uαφ	ADJ
ap-3483	195	12	)	)	PUNCT
ap-3483	195	13	)	)	PUNCT
ap-3483	196	1	φ−1	φ−1	PROPN
ap-3483	196	2	.	.	PUNCT
ap-3483	197	1	(	(	PUNCT
ap-3483	197	2	3.9	3.9	NUM
ap-3483	197	3	)	)	PUNCT
ap-3483	197	4	proof	proof	NOUN
ap-3483	197	5	.	.	PUNCT
ap-3483	198	1	first	first	ADV
ap-3483	198	2	we	we	PRON
ap-3483	198	3	demonstrate	demonstrate	VERB
ap-3483	198	4	that	that	SCONJ
ap-3483	198	5	for	for	ADP
ap-3483	198	6	every	every	DET
ap-3483	198	7	infinitesimal	infinitesimal	ADJ
ap-3483	198	8	generator	generator	NOUN
ap-3483	198	9	ωr	ωr	ADP
ap-3483	198	10	which	which	PRON
ap-3483	198	11	is	be	AUX
ap-3483	198	12	a	a	DET
ap-3483	198	13	generalized	generalized	ADJ
ap-3483	198	14	symmetry	symmetry	NOUN
ap-3483	198	15	of	of	ADP
ap-3483	198	16	the	the	DET
ap-3483	198	17	zcc	zcc	NOUN
ap-3483	198	18	(	(	PUNCT
ap-3483	198	19	2.14	2.14	NUM
ap-3483	198	20	)	)	PUNCT
ap-3483	198	21	,	,	PUNCT
ap-3483	198	22	there	there	PRON
ap-3483	198	23	exists	exist	VERB
ap-3483	198	24	a	a	DET
ap-3483	198	25	g	g	NOUN
ap-3483	198	26	-	-	PUNCT
ap-3483	198	27	valued	value	VERB
ap-3483	198	28	matrix	matrix	NOUN
ap-3483	198	29	function	function	NOUN
ap-3483	198	30	(	(	PUNCT
ap-3483	198	31	gauge	gauge	NOUN
ap-3483	198	32	)	)	PUNCT
ap-3483	198	33	s2	s2	NOUN
ap-3483	198	34	=	=	PUNCT
ap-3483	198	35	s2([u	s2([u	NOUN
ap-3483	198	36	]	]	PUNCT
ap-3483	198	37	,	,	PUNCT
ap-3483	198	38	λ	λ	PROPN
ap-3483	198	39	)	)	PUNCT
ap-3483	198	40	which	which	PRON
ap-3483	198	41	is	be	AUX
ap-3483	198	42	a	a	DET
ap-3483	198	43	solution	solution	NOUN
ap-3483	198	44	of	of	ADP
ap-3483	198	45	the	the	DET
ap-3483	198	46	system	system	NOUN
ap-3483	198	47	of	of	ADP
ap-3483	198	48	differential	differential	ADJ
ap-3483	198	49	equations	equation	NOUN
ap-3483	198	50	(	(	PUNCT
ap-3483	198	51	3.9	3.9	NUM
ap-3483	198	52	)	)	PUNCT
ap-3483	198	53	.	.	PUNCT
ap-3483	199	1	indeed	indeed	ADV
ap-3483	199	2	an	an	DET
ap-3483	199	3	evolutionary	evolutionary	ADJ
ap-3483	199	4	vector	vector	NOUN
ap-3483	199	5	field	field	NOUN
ap-3483	199	6	ωr	ωr	NOUN
ap-3483	199	7	is	be	AUX
ap-3483	199	8	a	a	DET
ap-3483	199	9	generalized	generalized	ADJ
ap-3483	199	10	symmetry	symmetry	NOUN
ap-3483	199	11	of	of	ADP
ap-3483	199	12	the	the	DET
ap-3483	199	13	zcc	zcc	NOUN
ap-3483	199	14	(	(	PUNCT
ap-3483	199	15	2.14	2.14	NUM
ap-3483	199	16	)	)	PUNCT
ap-3483	199	17	if	if	SCONJ
ap-3483	199	18	and	and	CCONJ
ap-3483	199	19	only	only	ADV
ap-3483	199	20	if	if	SCONJ
ap-3483	199	21	prωr	prωr	PROPN
ap-3483	199	22	(	(	PUNCT
ap-3483	199	23	d2u1	d2u1	X
ap-3483	199	24	−d1u2	−d1u2	NOUN
ap-3483	199	25	+	+	NUM
ap-3483	199	26	[	[	X
ap-3483	199	27	u1	u1	NOUN
ap-3483	199	28	,	,	PUNCT
ap-3483	199	29	u2	u2	NOUN
ap-3483	199	30	]	]	PUNCT
ap-3483	199	31	)	)	PUNCT
ap-3483	200	1	=	=	SYM
ap-3483	200	2	0	0	NUM
ap-3483	200	3	,	,	PUNCT
ap-3483	200	4	(	(	PUNCT
ap-3483	200	5	3.10	3.10	NUM
ap-3483	200	6	)	)	PUNCT
ap-3483	200	7	whenever	whenever	SCONJ
ap-3483	200	8	the	the	DET
ap-3483	200	9	zcc	zcc	NOUN
ap-3483	200	10	(	(	PUNCT
ap-3483	200	11	2.14	2.14	NUM
ap-3483	200	12	)	)	PUNCT
ap-3483	200	13	holds	hold	VERB
ap-3483	200	14	.	.	PUNCT
ap-3483	201	1	equation	equation	NOUN
ap-3483	201	2	(	(	PUNCT
ap-3483	201	3	3.10	3.10	NUM
ap-3483	201	4	)	)	PUNCT
ap-3483	201	5	is	be	AUX
ap-3483	201	6	equivalent	equivalent	ADJ
ap-3483	201	7	to	to	ADP
ap-3483	201	8	the	the	DET
ap-3483	201	9	infinitesimal	infinitesimal	ADJ
ap-3483	201	10	deformation	deformation	NOUN
ap-3483	201	11	of	of	ADP
ap-3483	201	12	the	the	DET
ap-3483	201	13	zcc	zcc	NOUN
ap-3483	201	14	(	(	PUNCT
ap-3483	201	15	2.14	2.14	NUM
ap-3483	201	16	)	)	PUNCT
ap-3483	201	17	given	give	VERB
ap-3483	201	18	by	by	ADP
ap-3483	201	19	(	(	PUNCT
ap-3483	201	20	2.21	2.21	NUM
ap-3483	201	21	)	)	PUNCT
ap-3483	201	22	,	,	PUNCT
ap-3483	201	23	with	with	ADP
ap-3483	201	24	linearly	linearly	ADV
ap-3483	201	25	independent	independent	ADJ
ap-3483	201	26	gvalued	gvalue	VERB
ap-3483	201	27	matrix	matrix	NOUN
ap-3483	201	28	functions	function	NOUN
ap-3483	201	29	aα([u	aα([u	PROPN
ap-3483	201	30	]	]	X
ap-3483	201	31	,	,	PUNCT
ap-3483	201	32	λ	λ	NOUN
ap-3483	201	33	)	)	PUNCT
ap-3483	201	34	=	=	VERB
ap-3483	202	1	prωruα	prωruα	VERB
ap-3483	202	2	+	+	CCONJ
ap-3483	202	3	(	(	PUNCT
ap-3483	202	4	prωr(dαφ−	prωr(dαφ−	X
ap-3483	202	5	uαφ	uαφ	ADJ
ap-3483	202	6	)	)	PUNCT
ap-3483	202	7	)	)	PUNCT
ap-3483	203	1	φ−1	φ−1	PROPN
ap-3483	203	2	,	,	PUNCT
ap-3483	203	3	α	α	NOUN
ap-3483	203	4	=	=	SYM
ap-3483	203	5	1	1	NUM
ap-3483	203	6	,	,	PUNCT
ap-3483	203	7	2	2	NUM
ap-3483	203	8	.	.	PUNCT
ap-3483	203	9	(	(	PUNCT
ap-3483	203	10	3.11	3.11	NUM
ap-3483	203	11	)	)	PUNCT
ap-3483	203	12	184	184	NUM
ap-3483	203	13	vol	vol	NOUN
ap-3483	203	14	.	.	PUNCT
ap-3483	204	1	56	56	NUM
ap-3483	204	2	no	no	NOUN
ap-3483	204	3	.	.	PUNCT
ap-3483	205	1	3/2016	3/2016	NUM
ap-3483	205	2	on	on	ADP
ap-3483	205	3	immersion	immersion	NOUN
ap-3483	205	4	formulas	formula	NOUN
ap-3483	205	5	for	for	ADP
ap-3483	205	6	soliton	soliton	NOUN
ap-3483	205	7	surfaces	surface	NOUN
ap-3483	205	8	in	in	ADP
ap-3483	205	9	the	the	DET
ap-3483	205	10	derivation	derivation	NOUN
ap-3483	205	11	of	of	ADP
ap-3483	205	12	(	(	PUNCT
ap-3483	205	13	3.11	3.11	NUM
ap-3483	205	14	)	)	PUNCT
ap-3483	205	15	we	we	PRON
ap-3483	205	16	use	use	VERB
ap-3483	205	17	the	the	DET
ap-3483	205	18	fact	fact	NOUN
ap-3483	205	19	that	that	SCONJ
ap-3483	205	20	the	the	DET
ap-3483	205	21	total	total	ADJ
ap-3483	205	22	derivatives	derivative	NOUN
ap-3483	205	23	dα	dα	AUX
ap-3483	205	24	commute	commute	VERB
ap-3483	205	25	with	with	ADP
ap-3483	205	26	the	the	DET
ap-3483	205	27	prolongation	prolongation	NOUN
ap-3483	205	28	of	of	ADP
ap-3483	205	29	a	a	DET
ap-3483	205	30	vector	vector	NOUN
ap-3483	205	31	field	field	NOUN
ap-3483	205	32	ωr	ωr	VERB
ap-3483	205	33	written	write	VERB
ap-3483	205	34	in	in	ADP
ap-3483	205	35	the	the	DET
ap-3483	205	36	evolutionary	evolutionary	ADJ
ap-3483	205	37	form	form	NOUN
ap-3483	205	38	[	[	X
ap-3483	205	39	29	29	NUM
ap-3483	205	40	]	]	X
ap-3483	206	1	[	[	X
ap-3483	206	2	dα	dα	NOUN
ap-3483	206	3	,	,	PUNCT
ap-3483	206	4	prωr	prωr	NOUN
ap-3483	206	5	]	]	PUNCT
ap-3483	206	6	=	=	SYM
ap-3483	206	7	0	0	NUM
ap-3483	206	8	,	,	PUNCT
ap-3483	206	9	α	α	NOUN
ap-3483	206	10	=	=	SYM
ap-3483	206	11	1	1	NUM
ap-3483	206	12	,	,	PUNCT
ap-3483	206	13	2	2	NUM
ap-3483	206	14	.	.	PUNCT
ap-3483	206	15	(	(	PUNCT
ap-3483	206	16	3.12	3.12	NUM
ap-3483	206	17	)	)	PUNCT
ap-3483	206	18	using	use	VERB
ap-3483	206	19	the	the	DET
ap-3483	206	20	lsp	lsp	PROPN
ap-3483	206	21	(	(	PUNCT
ap-3483	206	22	2.15	2.15	NUM
ap-3483	206	23	)	)	PUNCT
ap-3483	206	24	,	,	PUNCT
ap-3483	206	25	equation	equation	NOUN
ap-3483	206	26	(	(	PUNCT
ap-3483	206	27	3.11	3.11	NUM
ap-3483	206	28	)	)	PUNCT
ap-3483	206	29	can	can	AUX
ap-3483	206	30	be	be	AUX
ap-3483	206	31	written	write	VERB
ap-3483	206	32	in	in	ADP
ap-3483	206	33	the	the	DET
ap-3483	206	34	equivalent	equivalent	ADJ
ap-3483	206	35	form	form	NOUN
ap-3483	206	36	aα([u	aα([u	PROPN
ap-3483	206	37	]	]	PUNCT
ap-3483	206	38	,	,	PUNCT
ap-3483	206	39	λ	λ	NOUN
ap-3483	206	40	)	)	PUNCT
ap-3483	206	41	=	=	SYM
ap-3483	206	42	[	[	PUNCT
ap-3483	206	43	−uα(prωrφ	−uα(prωrφ	NOUN
ap-3483	206	44	)	)	PUNCT
ap-3483	206	45	+	+	CCONJ
ap-3483	206	46	prωr(dαφ	prωr(dαφ	NOUN
ap-3483	206	47	)	)	PUNCT
ap-3483	206	48	]	]	PUNCT
ap-3483	207	1	φ−1	φ−1	PROPN
ap-3483	207	2	.	.	PUNCT
ap-3483	208	1	α	α	X
ap-3483	208	2	=	=	SYM
ap-3483	208	3	1	1	NUM
ap-3483	208	4	,	,	PUNCT
ap-3483	208	5	2	2	NUM
ap-3483	208	6	(	(	PUNCT
ap-3483	208	7	3.13	3.13	NUM
ap-3483	208	8	)	)	PUNCT
ap-3483	208	9	substituting	substitute	VERB
ap-3483	208	10	(	(	PUNCT
ap-3483	208	11	3.13	3.13	NUM
ap-3483	208	12	)	)	PUNCT
ap-3483	208	13	into	into	ADP
ap-3483	208	14	(	(	PUNCT
ap-3483	208	15	2.21	2.21	NUM
ap-3483	208	16	)	)	PUNCT
ap-3483	208	17	we	we	PRON
ap-3483	208	18	obtain	obtain	VERB
ap-3483	208	19	(	(	PUNCT
ap-3483	208	20	−d2u1	−d2u1	X
ap-3483	208	21	+	+	NOUN
ap-3483	208	22	d1u2	d1u2	NOUN
ap-3483	208	23	−	−	NOUN
ap-3483	209	1	[	[	X
ap-3483	209	2	u1	u1	NOUN
ap-3483	209	3	,	,	PUNCT
ap-3483	209	4	u2	u2	PROPN
ap-3483	209	5	]	]	PUNCT
ap-3483	209	6	)	)	PUNCT
ap-3483	209	7	(	(	PUNCT
ap-3483	209	8	prωrφ)φ−1	prωrφ)φ−1	NOUN
ap-3483	209	9	=	=	SYM
ap-3483	209	10	0	0	NUM
ap-3483	209	11	,	,	PUNCT
ap-3483	209	12	which	which	PRON
ap-3483	209	13	is	be	AUX
ap-3483	209	14	satisfied	satisfied	ADJ
ap-3483	209	15	identically	identically	ADV
ap-3483	209	16	whenever	whenever	SCONJ
ap-3483	209	17	the	the	DET
ap-3483	209	18	zcc	zcc	NOUN
ap-3483	209	19	(	(	PUNCT
ap-3483	209	20	2.14	2.14	NUM
ap-3483	209	21	)	)	PUNCT
ap-3483	209	22	holds	hold	VERB
ap-3483	209	23	.	.	PUNCT
ap-3483	210	1	an	an	DET
ap-3483	210	2	integrated	integrate	VERB
ap-3483	210	3	form	form	NOUN
ap-3483	210	4	of	of	ADP
ap-3483	210	5	the	the	DET
ap-3483	210	6	immersion	immersion	NOUN
ap-3483	210	7	function	function	NOUN
ap-3483	210	8	ffg([u	ffg([u	NOUN
ap-3483	210	9	]	]	PUNCT
ap-3483	210	10	,	,	PUNCT
ap-3483	210	11	λ	λ	NOUN
ap-3483	210	12	)	)	PUNCT
ap-3483	210	13	of	of	ADP
ap-3483	210	14	a	a	DET
ap-3483	210	15	2d	2d	NUM
ap-3483	210	16	-	-	PUNCT
ap-3483	210	17	surface	surface	NOUN
ap-3483	210	18	associated	associate	VERB
ap-3483	210	19	with	with	ADP
ap-3483	210	20	a	a	DET
ap-3483	210	21	generalized	generalized	ADJ
ap-3483	210	22	symmetry	symmetry	NOUN
ap-3483	210	23	ωr	ωr	NOUN
ap-3483	210	24	of	of	ADP
ap-3483	210	25	the	the	DET
ap-3483	210	26	zcc	zcc	NOUN
ap-3483	210	27	(	(	PUNCT
ap-3483	210	28	2.14	2.14	NUM
ap-3483	210	29	)	)	PUNCT
ap-3483	210	30	and	and	CCONJ
ap-3483	210	31	the	the	DET
ap-3483	210	32	tangent	tangent	NOUN
ap-3483	210	33	vectors	vector	NOUN
ap-3483	210	34	(	(	PUNCT
ap-3483	210	35	2.22	2.22	NUM
ap-3483	210	36	)	)	PUNCT
ap-3483	210	37	is	be	AUX
ap-3483	210	38	given	give	VERB
ap-3483	210	39	by	by	ADP
ap-3483	210	40	the	the	DET
ap-3483	210	41	fg	fg	PROPN
ap-3483	210	42	formula	formula	NOUN
ap-3483	210	43	ffg([u	ffg([u	NOUN
ap-3483	210	44	]	]	PUNCT
ap-3483	210	45	,	,	PUNCT
ap-3483	210	46	λ	λ	NOUN
ap-3483	210	47	)	)	PUNCT
ap-3483	210	48	=	=	SYM
ap-3483	210	49	φ−1(prωrφ	φ−1(prωrφ	X
ap-3483	210	50	)	)	PUNCT
ap-3483	210	51	∈	∈	PROPN
ap-3483	210	52	g.	g.	NOUN
ap-3483	210	53	(	(	PUNCT
ap-3483	210	54	3.14	3.14	NUM
ap-3483	210	55	)	)	PUNCT
ap-3483	210	56	the	the	DET
ap-3483	210	57	fact	fact	NOUN
ap-3483	210	58	that	that	SCONJ
ap-3483	210	59	any	any	DET
ap-3483	210	60	g	g	NOUN
ap-3483	210	61	-	-	PUNCT
ap-3483	210	62	valued	value	VERB
ap-3483	210	63	matrix	matrix	NOUN
ap-3483	210	64	function	function	NOUN
ap-3483	210	65	can	can	AUX
ap-3483	210	66	be	be	AUX
ap-3483	210	67	written	write	VERB
ap-3483	210	68	under	under	ADP
ap-3483	210	69	the	the	DET
ap-3483	210	70	adjoint	adjoint	PROPN
ap-3483	210	71	group	group	NOUN
ap-3483	210	72	action	action	NOUN
ap-3483	210	73	implies	imply	VERB
ap-3483	210	74	that	that	SCONJ
ap-3483	210	75	there	there	PRON
ap-3483	210	76	exists	exist	VERB
ap-3483	210	77	a	a	DET
ap-3483	210	78	g	g	NOUN
ap-3483	210	79	-	-	PUNCT
ap-3483	210	80	valued	value	VERB
ap-3483	210	81	gauge	gauge	NOUN
ap-3483	210	82	s2	s2	PROPN
ap-3483	210	83	,	,	PUNCT
ap-3483	210	84	such	such	ADJ
ap-3483	210	85	that	that	SCONJ
ap-3483	210	86	(	(	PUNCT
ap-3483	210	87	3.5	3.5	NUM
ap-3483	210	88	)	)	PUNCT
ap-3483	210	89	holds	hold	VERB
ap-3483	210	90	for	for	ADP
ap-3483	210	91	the	the	DET
ap-3483	210	92	cd	cd	PROPN
ap-3483	210	93	immersion	immersion	NOUN
ap-3483	210	94	function	function	NOUN
ap-3483	210	95	and	and	CCONJ
ap-3483	210	96	its	its	PRON
ap-3483	210	97	tangent	tangent	NOUN
ap-3483	210	98	vectors	vector	NOUN
ap-3483	210	99	dαf	dαf	PROPN
ap-3483	210	100	cd	cd	PROPN
ap-3483	210	101	given	give	VERB
ap-3483	210	102	by	by	ADP
ap-3483	210	103	(	(	PUNCT
ap-3483	210	104	3.6	3.6	NUM
ap-3483	210	105	)	)	PUNCT
ap-3483	210	106	.	.	PUNCT
ap-3483	211	1	comparing	compare	VERB
ap-3483	211	2	equations	equation	NOUN
ap-3483	211	3	(	(	PUNCT
ap-3483	211	4	2.22	2.22	NUM
ap-3483	211	5	)	)	PUNCT
ap-3483	211	6	and	and	CCONJ
ap-3483	211	7	(	(	PUNCT
ap-3483	211	8	3.11	3.11	NUM
ap-3483	211	9	)	)	PUNCT
ap-3483	211	10	with	with	ADP
ap-3483	211	11	(	(	PUNCT
ap-3483	211	12	3.6	3.6	NUM
ap-3483	211	13	)	)	PUNCT
ap-3483	211	14	we	we	PRON
ap-3483	211	15	get	get	VERB
ap-3483	211	16	(	(	PUNCT
ap-3483	211	17	3.9	3.9	NUM
ap-3483	211	18	)	)	PUNCT
ap-3483	211	19	.	.	PUNCT
ap-3483	212	1	let	let	VERB
ap-3483	212	2	us	we	PRON
ap-3483	212	3	show	show	VERB
ap-3483	212	4	that	that	SCONJ
ap-3483	212	5	the	the	DET
ap-3483	212	6	system	system	NOUN
ap-3483	212	7	(	(	PUNCT
ap-3483	212	8	3.9	3.9	NUM
ap-3483	212	9	)	)	PUNCT
ap-3483	212	10	always	always	ADV
ap-3483	212	11	possesses	possess	VERB
ap-3483	212	12	a	a	DET
ap-3483	212	13	solution	solution	NOUN
ap-3483	212	14	.	.	PUNCT
ap-3483	213	1	the	the	DET
ap-3483	213	2	compatibility	compatibility	NOUN
ap-3483	213	3	condition	condition	NOUN
ap-3483	213	4	of	of	ADP
ap-3483	213	5	(	(	PUNCT
ap-3483	213	6	3.9	3.9	NUM
ap-3483	213	7	)	)	PUNCT
ap-3483	213	8	,	,	PUNCT
ap-3483	213	9	whenever	whenever	SCONJ
ap-3483	213	10	(	(	PUNCT
ap-3483	213	11	3.9	3.9	NUM
ap-3483	213	12	)	)	PUNCT
ap-3483	213	13	and	and	CCONJ
ap-3483	213	14	(	(	PUNCT
ap-3483	213	15	2.21	2.21	NUM
ap-3483	213	16	)	)	PUNCT
ap-3483	213	17	hold	hold	NOUN
ap-3483	213	18	,	,	PUNCT
ap-3483	213	19	implies	imply	VERB
ap-3483	213	20	the	the	DET
ap-3483	213	21	relation	relation	NOUN
ap-3483	213	22	[	[	X
ap-3483	213	23	s2	s2	PROPN
ap-3483	213	24	,	,	PUNCT
ap-3483	213	25	d2u1	d2u1	X
ap-3483	213	26	−d1u2	−d1u2	X
ap-3483	213	27	]	]	X
ap-3483	213	28	+	+	CCONJ
ap-3483	213	29	[	[	PUNCT
ap-3483	213	30	[	[	X
ap-3483	213	31	s2	s2	NOUN
ap-3483	213	32	,	,	PUNCT
ap-3483	213	33	u1	u1	NOUN
ap-3483	213	34	]	]	PUNCT
ap-3483	213	35	,	,	PUNCT
ap-3483	213	36	u2	u2	PROPN
ap-3483	213	37	]	]	PUNCT
ap-3483	213	38	−	−	PROPN
ap-3483	214	1	[	[	PUNCT
ap-3483	214	2	[	[	X
ap-3483	214	3	s2	s2	NOUN
ap-3483	214	4	,	,	PUNCT
ap-3483	214	5	u2	u2	NOUN
ap-3483	214	6	]	]	PUNCT
ap-3483	214	7	,	,	PUNCT
ap-3483	214	8	u1	u1	NOUN
ap-3483	214	9	]	]	PUNCT
ap-3483	214	10	=	=	SYM
ap-3483	214	11	0	0	NUM
ap-3483	214	12	,	,	PUNCT
ap-3483	214	13	(	(	PUNCT
ap-3483	214	14	3.15	3.15	NUM
ap-3483	214	15	)	)	PUNCT
ap-3483	214	16	which	which	PRON
ap-3483	214	17	is	be	AUX
ap-3483	214	18	identically	identically	ADV
ap-3483	214	19	satisfied	satisfied	ADJ
ap-3483	214	20	in	in	ADP
ap-3483	214	21	view	view	NOUN
ap-3483	214	22	of	of	ADP
ap-3483	214	23	the	the	DET
ap-3483	214	24	zcc	zcc	NOUN
ap-3483	214	25	(	(	PUNCT
ap-3483	214	26	2.14	2.14	NUM
ap-3483	214	27	)	)	PUNCT
ap-3483	214	28	and	and	CCONJ
ap-3483	214	29	the	the	DET
ap-3483	214	30	jacobi	jacobi	PROPN
ap-3483	214	31	identity	identity	NOUN
ap-3483	214	32	.	.	PUNCT
ap-3483	215	1	so	so	ADV
ap-3483	215	2	,	,	PUNCT
ap-3483	215	3	if	if	SCONJ
ap-3483	215	4	we	we	PRON
ap-3483	215	5	can	can	AUX
ap-3483	215	6	find	find	VERB
ap-3483	215	7	a	a	DET
ap-3483	215	8	gauge	gauge	ADJ
ap-3483	215	9	function	function	NOUN
ap-3483	215	10	s2([u	s2([u	NOUN
ap-3483	215	11	]	]	PUNCT
ap-3483	215	12	,	,	PUNCT
ap-3483	215	13	λ	λ	PROPN
ap-3483	215	14	)	)	PUNCT
ap-3483	215	15	which	which	PRON
ap-3483	215	16	satisfies	satisfy	VERB
ap-3483	215	17	(	(	PUNCT
ap-3483	215	18	3.9	3.9	NUM
ap-3483	215	19	)	)	PUNCT
ap-3483	215	20	,	,	PUNCT
ap-3483	215	21	then	then	ADV
ap-3483	215	22	the	the	DET
ap-3483	215	23	fg	fg	PROPN
ap-3483	215	24	formula	formula	NOUN
ap-3483	215	25	(	(	PUNCT
ap-3483	215	26	3.14	3.14	NUM
ap-3483	215	27	)	)	PUNCT
ap-3483	215	28	can	can	AUX
ap-3483	215	29	always	always	ADV
ap-3483	215	30	be	be	AUX
ap-3483	215	31	represented	represent	VERB
ap-3483	215	32	by	by	ADP
ap-3483	215	33	a	a	DET
ap-3483	215	34	gauge	gauge	ADJ
ap-3483	215	35	transformation	transformation	NOUN
ap-3483	215	36	.	.	PUNCT
ap-3483	216	1	the	the	DET
ap-3483	216	2	converse	converse	NOUN
ap-3483	216	3	statement	statement	NOUN
ap-3483	216	4	is	be	AUX
ap-3483	216	5	also	also	ADV
ap-3483	216	6	true	true	ADJ
ap-3483	216	7	.	.	PUNCT
ap-3483	217	1	we	we	PRON
ap-3483	217	2	show	show	VERB
ap-3483	217	3	that	that	SCONJ
ap-3483	217	4	for	for	ADP
ap-3483	217	5	any	any	DET
ap-3483	217	6	g	g	NOUN
ap-3483	217	7	-	-	PUNCT
ap-3483	217	8	valued	value	VERB
ap-3483	217	9	matrix	matrix	NOUN
ap-3483	217	10	function	function	NOUN
ap-3483	217	11	s2	s2	NOUN
ap-3483	217	12	defined	define	VERB
ap-3483	217	13	as	as	ADP
ap-3483	217	14	a	a	DET
ap-3483	217	15	solution	solution	NOUN
ap-3483	217	16	of	of	ADP
ap-3483	217	17	the	the	DET
ap-3483	217	18	system	system	NOUN
ap-3483	217	19	of	of	ADP
ap-3483	217	20	pdes	pde	NOUN
ap-3483	217	21	(	(	PUNCT
ap-3483	217	22	3.9	3.9	NUM
ap-3483	217	23	)	)	PUNCT
ap-3483	217	24	,	,	PUNCT
ap-3483	217	25	there	there	PRON
ap-3483	217	26	exists	exist	VERB
ap-3483	217	27	a	a	DET
ap-3483	217	28	generalized	generalized	ADJ
ap-3483	217	29	symmetry	symmetry	NOUN
ap-3483	217	30	ωr	ωr	NOUN
ap-3483	217	31	of	of	ADP
ap-3483	217	32	the	the	DET
ap-3483	217	33	zcc	zcc	NOUN
ap-3483	217	34	of	of	ADP
ap-3483	217	35	the	the	DET
ap-3483	217	36	lsp	lsp	PROPN
ap-3483	217	37	associated	associate	VERB
ap-3483	217	38	with	with	ADP
ap-3483	217	39	ω[u	ω[u	NUM
ap-3483	217	40	]	]	X
ap-3483	217	41	=	=	SYM
ap-3483	217	42	0	0	X
ap-3483	217	43	.	.	PUNCT
ap-3483	218	1	indeed	indeed	ADV
ap-3483	218	2	,	,	PUNCT
ap-3483	218	3	let	let	VERB
ap-3483	218	4	the	the	DET
ap-3483	218	5	lsp	lsp	PROPN
ap-3483	218	6	of	of	ADP
ap-3483	218	7	ω[u	ω[u	PROPN
ap-3483	218	8	]	]	X
ap-3483	218	9	=	=	SYM
ap-3483	218	10	0	0	NUM
ap-3483	218	11	admit	admit	VERB
ap-3483	218	12	a	a	DET
ap-3483	218	13	gauge	gauge	NOUN
ap-3483	218	14	symmetry	symmetry	NOUN
ap-3483	218	15	.	.	PUNCT
ap-3483	219	1	if	if	SCONJ
ap-3483	219	2	the	the	DET
ap-3483	219	3	gauge	gauge	ADJ
ap-3483	219	4	s2([u	s2([u	NOUN
ap-3483	219	5	]	]	PUNCT
ap-3483	219	6	,	,	PUNCT
ap-3483	219	7	λ	λ	X
ap-3483	219	8	)	)	PUNCT
ap-3483	219	9	is	be	AUX
ap-3483	219	10	given	give	VERB
ap-3483	219	11	,	,	PUNCT
ap-3483	219	12	then	then	ADV
ap-3483	219	13	the	the	DET
ap-3483	219	14	immersion	immersion	NOUN
ap-3483	219	15	function	function	NOUN
ap-3483	219	16	fcd	fcd	NOUN
ap-3483	219	17	of	of	ADP
ap-3483	219	18	a	a	DET
ap-3483	219	19	2d	2d	NOUN
ap-3483	219	20	-	-	PUNCT
ap-3483	219	21	surface	surface	NOUN
ap-3483	219	22	can	can	AUX
ap-3483	219	23	be	be	AUX
ap-3483	219	24	integrated	integrate	VERB
ap-3483	219	25	explicitly	explicitly	ADV
ap-3483	219	26	[	[	X
ap-3483	219	27	5–7	5–7	X
ap-3483	219	28	]	]	X
ap-3483	219	29	fcd([u	fcd([u	NOUN
ap-3483	219	30	]	]	PUNCT
ap-3483	219	31	,	,	PUNCT
ap-3483	219	32	λ	λ	X
ap-3483	219	33	)	)	PUNCT
ap-3483	219	34	=	=	PUNCT
ap-3483	219	35	φ−1s2([u	φ−1s2([u	PROPN
ap-3483	219	36	]	]	PUNCT
ap-3483	219	37	,	,	PUNCT
ap-3483	219	38	λ)φ	λ)φ	ADJ
ap-3483	219	39	∈	∈	PROPN
ap-3483	219	40	g	g	NOUN
ap-3483	219	41	,	,	PUNCT
ap-3483	219	42	(	(	PUNCT
ap-3483	219	43	3.16	3.16	NUM
ap-3483	219	44	)	)	PUNCT
ap-3483	219	45	whenever	whenever	SCONJ
ap-3483	219	46	the	the	DET
ap-3483	219	47	tangent	tangent	NOUN
ap-3483	219	48	vectors	vector	VERB
ap-3483	219	49	dαf	dαf	NOUN
ap-3483	219	50	cd	cd	PROPN
ap-3483	219	51	=	=	PUNCT
ap-3483	219	52	φ−1(dαs2	φ−1(dαs2	X
ap-3483	220	1	+	+	PUNCT
ap-3483	220	2	[	[	X
ap-3483	220	3	s2	s2	NOUN
ap-3483	220	4	,	,	PUNCT
ap-3483	220	5	uα	uα	NOUN
ap-3483	220	6	]	]	PUNCT
ap-3483	220	7	)	)	PUNCT
ap-3483	220	8	φ	φ	X
ap-3483	220	9	.	.	PUNCT
ap-3483	221	1	(	(	PUNCT
ap-3483	221	2	3.17	3.17	NUM
ap-3483	221	3	)	)	PUNCT
ap-3483	221	4	are	be	AUX
ap-3483	221	5	linearly	linearly	ADV
ap-3483	221	6	independent	independent	ADJ
ap-3483	221	7	.	.	PUNCT
ap-3483	222	1	it	it	PRON
ap-3483	222	2	is	be	AUX
ap-3483	222	3	straightforward	straightforward	ADJ
ap-3483	222	4	to	to	PART
ap-3483	222	5	verify	verify	VERB
ap-3483	222	6	that	that	SCONJ
ap-3483	222	7	the	the	DET
ap-3483	222	8	characteristics	characteristic	NOUN
ap-3483	222	9	of	of	ADP
ap-3483	222	10	a	a	DET
ap-3483	222	11	generalized	generalized	ADJ
ap-3483	222	12	vector	vector	NOUN
ap-3483	222	13	field	field	NOUN
ap-3483	222	14	ωsr	ωsr	NOUN
ap-3483	222	15	,	,	PUNCT
ap-3483	222	16	written	write	VERB
ap-3483	222	17	in	in	ADP
ap-3483	222	18	evalutionary	evalutionary	ADJ
ap-3483	222	19	form	form	NOUN
ap-3483	222	20	,	,	PUNCT
ap-3483	222	21	associated	associate	VERB
ap-3483	222	22	with	with	ADP
ap-3483	222	23	a	a	DET
ap-3483	222	24	gauge	gauge	NOUN
ap-3483	222	25	symmetry	symmetry	NOUN
ap-3483	222	26	s2	s2	PROPN
ap-3483	222	27	,	,	PUNCT
ap-3483	222	28	can	can	AUX
ap-3483	222	29	be	be	AUX
ap-3483	222	30	expressed	express	VERB
ap-3483	222	31	as	as	ADP
ap-3483	222	32	aα	aα	NOUN
ap-3483	222	33	=	=	NOUN
ap-3483	222	34	dαs2	dαs2	NOUN
ap-3483	222	35	+	+	CCONJ
ap-3483	223	1	[	[	X
ap-3483	223	2	s2	s2	NOUN
ap-3483	223	3	,	,	PUNCT
ap-3483	223	4	uα	uα	X
ap-3483	223	5	]	]	X
ap-3483	223	6	∈	∈	PROPN
ap-3483	223	7	g.	g.	NOUN
ap-3483	223	8	(	(	PUNCT
ap-3483	223	9	3.18	3.18	NUM
ap-3483	223	10	)	)	PUNCT
ap-3483	223	11	the	the	DET
ap-3483	223	12	matrices	matrix	NOUN
ap-3483	223	13	aα	aα	NOUN
ap-3483	223	14	identically	identically	ADV
ap-3483	223	15	satisfy	satisfy	VERB
ap-3483	223	16	the	the	DET
ap-3483	223	17	determining	determine	VERB
ap-3483	223	18	equations	equation	NOUN
ap-3483	223	19	(	(	PUNCT
ap-3483	223	20	2.21	2.21	NUM
ap-3483	223	21	)	)	PUNCT
ap-3483	223	22	which	which	PRON
ap-3483	223	23	are	be	AUX
ap-3483	223	24	required	require	VERB
ap-3483	223	25	for	for	SCONJ
ap-3483	223	26	ωsr	ωsr	PROPN
ap-3483	223	27	to	to	PART
ap-3483	223	28	be	be	AUX
ap-3483	223	29	a	a	DET
ap-3483	223	30	generalized	generalized	ADJ
ap-3483	223	31	symmetry	symmetry	NOUN
ap-3483	223	32	of	of	ADP
ap-3483	223	33	the	the	DET
ap-3483	223	34	zcc	zcc	NOUN
ap-3483	223	35	ω[u	ω[u	NOUN
ap-3483	223	36	]	]	X
ap-3483	223	37	=	=	SYM
ap-3483	223	38	0	0	PUNCT
ap-3483	224	1	d2a1	d2a1	VERB
ap-3483	224	2	−d1a2	−d1a2	INTJ
ap-3483	224	3	+	+	NUM
ap-3483	224	4	[	[	X
ap-3483	224	5	a1	a1	NOUN
ap-3483	224	6	,	,	PUNCT
ap-3483	224	7	u2	u2	NOUN
ap-3483	224	8	]	]	PUNCT
ap-3483	224	9	+	+	CCONJ
ap-3483	224	10	[	[	X
ap-3483	224	11	u1	u1	NOUN
ap-3483	224	12	,	,	PUNCT
ap-3483	224	13	a2	a2	PROPN
ap-3483	224	14	]	]	PUNCT
ap-3483	224	15	=	=	SYM
ap-3483	224	16	prωsr	prωsr	NOUN
ap-3483	224	17	(	(	PUNCT
ap-3483	224	18	d2u1	d2u1	X
ap-3483	224	19	−d1u2	−d1u2	NOUN
ap-3483	224	20	+	+	NUM
ap-3483	224	21	[	[	X
ap-3483	224	22	u1	u1	NOUN
ap-3483	224	23	,	,	PUNCT
ap-3483	224	24	u2	u2	NOUN
ap-3483	224	25	]	]	PUNCT
ap-3483	224	26	)	)	PUNCT
ap-3483	225	1	=	=	SYM
ap-3483	225	2	0	0	NUM
ap-3483	225	3	,	,	PUNCT
ap-3483	225	4	(	(	PUNCT
ap-3483	225	5	3.19	3.19	NUM
ap-3483	225	6	)	)	PUNCT
ap-3483	225	7	whenever	whenever	SCONJ
ap-3483	225	8	ω[u	ω[u	ADP
ap-3483	225	9	]	]	X
ap-3483	225	10	=	=	SYM
ap-3483	225	11	0	0	NUM
ap-3483	225	12	holds	hold	NOUN
ap-3483	225	13	.	.	PUNCT
ap-3483	226	1	hence	hence	ADV
ap-3483	226	2	,	,	PUNCT
ap-3483	226	3	the	the	DET
ap-3483	226	4	vector	vector	NOUN
ap-3483	226	5	field	field	NOUN
ap-3483	226	6	ωsr	ωsr	PROPN
ap-3483	226	7	associated	associate	VERB
ap-3483	226	8	with	with	ADP
ap-3483	226	9	a	a	DET
ap-3483	226	10	gauge	gauge	NOUN
ap-3483	226	11	symmetry	symmetry	NOUN
ap-3483	226	12	s2	s2	NOUN
ap-3483	226	13	is	be	AUX
ap-3483	226	14	given	give	VERB
ap-3483	226	15	by	by	ADP
ap-3483	226	16	ωsr	ωsr	PROPN
ap-3483	226	17	=	=	SYM
ap-3483	226	18	(	(	PUNCT
ap-3483	226	19	dαs2	dαs2	NOUN
ap-3483	226	20	+	+	CCONJ
ap-3483	227	1	[	[	X
ap-3483	227	2	s2	s2	NOUN
ap-3483	227	3	,	,	PUNCT
ap-3483	227	4	uα	uα	NOUN
ap-3483	227	5	]	]	PUNCT
ap-3483	227	6	)	)	PUNCT
ap-3483	227	7	j	j	PROPN
ap-3483	227	8	∂	∂	NOUN
ap-3483	227	9	∂u	∂u	PROPN
ap-3483	227	10	jα	jα	NOUN
ap-3483	227	11	,	,	PUNCT
ap-3483	227	12	(	(	PUNCT
ap-3483	227	13	3.20	3.20	NUM
ap-3483	227	14	)	)	PUNCT
ap-3483	227	15	where	where	SCONJ
ap-3483	227	16	we	we	PRON
ap-3483	227	17	have	have	AUX
ap-3483	227	18	decomposed	decompose	VERB
ap-3483	227	19	the	the	DET
ap-3483	227	20	matrix	matrix	NOUN
ap-3483	227	21	functions	function	NOUN
ap-3483	227	22	aα	aα	NOUN
ap-3483	227	23	and	and	CCONJ
ap-3483	227	24	uα	uα	PROPN
ap-3483	227	25	in	in	ADP
ap-3483	227	26	the	the	DET
ap-3483	227	27	basis	basis	NOUN
ap-3483	227	28	{	{	PUNCT
ap-3483	227	29	ej}n1	ej}n1	VERB
ap-3483	227	30	for	for	ADP
ap-3483	227	31	the	the	DET
ap-3483	227	32	lie	lie	NOUN
ap-3483	227	33	algebra	algebra	VERB
ap-3483	227	34	uα	uα	NOUN
ap-3483	227	35	=	=	SYM
ap-3483	227	36	u	u	PROPN
ap-3483	227	37	jαej	jαej	VERB
ap-3483	227	38	∈	∈	PROPN
ap-3483	227	39	g	g	PROPN
ap-3483	227	40	,	,	PUNCT
ap-3483	227	41	dαs2	dαs2	NOUN
ap-3483	227	42	+	+	CCONJ
ap-3483	228	1	[	[	X
ap-3483	228	2	s2	s2	NOUN
ap-3483	228	3	,	,	PUNCT
ap-3483	228	4	uα	uα	X
ap-3483	228	5	]	]	X
ap-3483	228	6	=	=	SYM
ap-3483	228	7	(	(	PUNCT
ap-3483	228	8	dαs2	dαs2	NOUN
ap-3483	228	9	+	+	CCONJ
ap-3483	229	1	[	[	X
ap-3483	229	2	s2	s2	NOUN
ap-3483	229	3	,	,	PUNCT
ap-3483	229	4	uα	uα	NOUN
ap-3483	229	5	]	]	PUNCT
ap-3483	229	6	)	)	PUNCT
ap-3483	229	7	j	j	PROPN
ap-3483	229	8	ej	ej	INTJ
ap-3483	229	9	.	.	PUNCT
ap-3483	230	1	(	(	PUNCT
ap-3483	230	2	3.21	3.21	NUM
ap-3483	230	3	)	)	PUNCT
ap-3483	230	4	hence	hence	ADV
ap-3483	230	5	,	,	PUNCT
ap-3483	230	6	for	for	ADP
ap-3483	230	7	any	any	DET
ap-3483	230	8	smooth	smooth	ADJ
ap-3483	230	9	g	g	NOUN
ap-3483	230	10	-	-	PUNCT
ap-3483	230	11	valued	value	VERB
ap-3483	230	12	gauge	gauge	NOUN
ap-3483	230	13	s2([u	s2([u	NOUN
ap-3483	230	14	]	]	PUNCT
ap-3483	230	15	,	,	PUNCT
ap-3483	230	16	λ	λ	PROPN
ap-3483	230	17	)	)	PUNCT
ap-3483	230	18	there	there	PRON
ap-3483	230	19	exists	exist	VERB
ap-3483	230	20	a	a	DET
ap-3483	230	21	generalized	generalized	ADJ
ap-3483	230	22	symmetry	symmetry	NOUN
ap-3483	230	23	ωsr	ωsr	NUM
ap-3483	230	24	of	of	ADP
ap-3483	230	25	the	the	DET
ap-3483	230	26	zcc	zcc	NOUN
ap-3483	230	27	(	(	PUNCT
ap-3483	230	28	2.14	2.14	NUM
ap-3483	230	29	)	)	PUNCT
ap-3483	230	30	and	and	CCONJ
ap-3483	230	31	the	the	DET
ap-3483	230	32	converse	converse	NOUN
ap-3483	230	33	statement	statement	NOUN
ap-3483	230	34	holds	hold	VERB
ap-3483	230	35	as	as	ADV
ap-3483	230	36	well	well	ADV
ap-3483	230	37	.	.	PUNCT
ap-3483	231	1	comparing	compare	VERB
ap-3483	231	2	the	the	DET
ap-3483	231	3	fg	fg	PROPN
ap-3483	231	4	formula	formula	NOUN
ap-3483	231	5	for	for	ADP
ap-3483	231	6	immersion	immersion	NOUN
ap-3483	231	7	(	(	PUNCT
ap-3483	231	8	3.14	3.14	NUM
ap-3483	231	9	)	)	PUNCT
ap-3483	231	10	with	with	ADP
ap-3483	231	11	the	the	DET
ap-3483	231	12	cd	cd	PROPN
ap-3483	231	13	immersion	immersion	NOUN
ap-3483	231	14	formula	formula	NOUN
ap-3483	231	15	(	(	PUNCT
ap-3483	231	16	3.5	3.5	NUM
ap-3483	231	17	)	)	PUNCT
ap-3483	231	18	we	we	PRON
ap-3483	231	19	find	find	VERB
ap-3483	231	20	the	the	DET
ap-3483	231	21	gauge	gauge	ADJ
ap-3483	231	22	s2	s2	NOUN
ap-3483	231	23	=	=	SYM
ap-3483	231	24	(	(	PUNCT
ap-3483	231	25	prωrφ)φ−1	prωrφ)φ−1	PROPN
ap-3483	231	26	.	.	PUNCT
ap-3483	232	1	(	(	PUNCT
ap-3483	232	2	3.22	3.22	NUM
ap-3483	232	3	)	)	PUNCT
ap-3483	232	4	hence	hence	ADV
ap-3483	232	5	the	the	DET
ap-3483	232	6	fg	fg	PROPN
ap-3483	232	7	formula	formula	NOUN
ap-3483	232	8	for	for	ADP
ap-3483	232	9	immersion	immersion	NOUN
ap-3483	232	10	(	(	PUNCT
ap-3483	232	11	2.29	2.29	NUM
ap-3483	232	12	)	)	PUNCT
ap-3483	232	13	is	be	AUX
ap-3483	232	14	equivalent	equivalent	ADJ
ap-3483	232	15	to	to	ADP
ap-3483	232	16	the	the	DET
ap-3483	232	17	cd	cd	PROPN
ap-3483	232	18	immersion	immersion	NOUN
ap-3483	232	19	formula	formula	NOUN
ap-3483	232	20	(	(	PUNCT
ap-3483	232	21	2.28	2.28	NUM
ap-3483	232	22	)	)	PUNCT
ap-3483	232	23	for	for	ADP
ap-3483	232	24	the	the	DET
ap-3483	232	25	gauge	gauge	ADJ
ap-3483	232	26	s2	s2	NOUN
ap-3483	232	27	satisfying	satisfying	NOUN
ap-3483	232	28	(	(	PUNCT
ap-3483	232	29	3.9	3.9	NUM
ap-3483	232	30	)	)	PUNCT
ap-3483	232	31	.	.	PUNCT
ap-3483	233	1	3.3	3.3	NUM
ap-3483	233	2	.	.	PUNCT
ap-3483	234	1	the	the	DET
ap-3483	234	2	sym	sym	PROPN
ap-3483	234	3	-	-	PUNCT
ap-3483	234	4	tafel	tafel	NOUN
ap-3483	234	5	immersion	immersion	NOUN
ap-3483	234	6	formula	formula	NOUN
ap-3483	234	7	versus	versus	ADP
ap-3483	234	8	the	the	DET
ap-3483	234	9	fokas	fokas	ADJ
ap-3483	234	10	-	-	PUNCT
ap-3483	234	11	gel’fand	gel’fand	NOUN
ap-3483	234	12	immersion	immersion	NOUN
ap-3483	234	13	formula	formula	NOUN
ap-3483	234	14	under	under	ADP
ap-3483	234	15	the	the	DET
ap-3483	234	16	assumptions	assumption	NOUN
ap-3483	234	17	of	of	ADP
ap-3483	234	18	propositions	proposition	NOUN
ap-3483	234	19	1	1	NUM
ap-3483	234	20	and	and	CCONJ
ap-3483	234	21	2	2	NUM
ap-3483	234	22	,	,	PUNCT
ap-3483	234	23	we	we	PRON
ap-3483	234	24	have	have	VERB
ap-3483	234	25	the	the	DET
ap-3483	234	26	following	follow	VERB
ap-3483	234	27	result	result	NOUN
ap-3483	234	28	.	.	PUNCT
ap-3483	235	1	proposition	proposition	NOUN
ap-3483	235	2	3	3	X
ap-3483	235	3	.	.	PUNCT
ap-3483	236	1	let	let	VERB
ap-3483	236	2	s1	s1	NOUN
ap-3483	236	3	and	and	CCONJ
ap-3483	236	4	s2	s2	PROPN
ap-3483	236	5	be	be	AUX
ap-3483	236	6	the	the	DET
ap-3483	236	7	two	two	NUM
ap-3483	236	8	g	g	ADV
ap-3483	236	9	-	-	PUNCT
ap-3483	236	10	valued	value	VERB
ap-3483	236	11	matrix	matrix	NOUN
ap-3483	236	12	functions	function	NOUN
ap-3483	236	13	determined	determine	VERB
ap-3483	236	14	in	in	ADP
ap-3483	236	15	propositions	proposition	NOUN
ap-3483	236	16	1	1	NUM
ap-3483	236	17	and	and	CCONJ
ap-3483	236	18	2	2	NUM
ap-3483	236	19	,	,	PUNCT
ap-3483	236	20	respectively	respectively	ADV
ap-3483	236	21	in	in	ADP
ap-3483	236	22	terms	term	NOUN
ap-3483	236	23	of	of	ADP
ap-3483	236	24	a	a	DET
ap-3483	236	25	λ	λ	NOUN
ap-3483	236	26	-	-	ADJ
ap-3483	236	27	conformal	conformal	ADJ
ap-3483	236	28	symmetry	symmetry	NOUN
ap-3483	236	29	and	and	CCONJ
ap-3483	236	30	a	a	DET
ap-3483	236	31	generalized	generalized	ADJ
ap-3483	236	32	symmetry	symmetry	NOUN
ap-3483	236	33	of	of	ADP
ap-3483	236	34	the	the	DET
ap-3483	236	35	zcc	zcc	NOUN
ap-3483	236	36	(	(	PUNCT
ap-3483	236	37	2.14	2.14	NUM
ap-3483	236	38	)	)	PUNCT
ap-3483	236	39	of	of	ADP
ap-3483	236	40	the	the	DET
ap-3483	236	41	lsp	lsp	PROPN
ap-3483	236	42	associated	associate	VERB
ap-3483	236	43	with	with	ADP
ap-3483	236	44	an	an	DET
ap-3483	236	45	integrable	integrable	ADJ
ap-3483	236	46	system	system	NOUN
ap-3483	236	47	ω[u	ω[u	NOUN
ap-3483	236	48	]	]	X
ap-3483	236	49	=	=	SYM
ap-3483	237	1	0	0	X
ap-3483	237	2	.	.	PUNCT
ap-3483	238	1	if	if	SCONJ
ap-3483	238	2	the	the	DET
ap-3483	238	3	gauge	gauge	ADJ
ap-3483	238	4	s2	s2	NOUN
ap-3483	238	5	is	be	AUX
ap-3483	238	6	a	a	DET
ap-3483	238	7	non	non	ADJ
ap-3483	238	8	-	-	ADJ
ap-3483	238	9	singular	singular	ADJ
ap-3483	238	10	matrix	matrix	NOUN
ap-3483	238	11	then	then	ADV
ap-3483	238	12	there	there	PRON
ap-3483	238	13	exists	exist	VERB
ap-3483	238	14	a	a	DET
ap-3483	238	15	matrix	matrix	NOUN
ap-3483	238	16	m	m	NOUN
ap-3483	238	17	=	=	SYM
ap-3483	238	18	s1s	s1s	ADJ
ap-3483	238	19	−1	−1	NOUN
ap-3483	238	20	2	2	NUM
ap-3483	238	21	such	such	ADJ
ap-3483	238	22	that	that	PRON
ap-3483	238	23	β(λ)(dλφ	β(λ)(dλφ	PROPN
ap-3483	238	24	)	)	PUNCT
ap-3483	238	25	=	=	SYM
ap-3483	238	26	m(prωrφ	m(prωrφ	NOUN
ap-3483	238	27	)	)	PUNCT
ap-3483	238	28	.	.	PUNCT
ap-3483	239	1	(	(	PUNCT
ap-3483	239	2	3.23	3.23	NUM
ap-3483	239	3	)	)	PUNCT
ap-3483	239	4	the	the	DET
ap-3483	239	5	matrix	matrix	NOUN
ap-3483	239	6	m	m	VERB
ap-3483	239	7	defines	define	VERB
ap-3483	239	8	a	a	DET
ap-3483	239	9	mapping	mapping	NOUN
ap-3483	239	10	from	from	ADP
ap-3483	239	11	the	the	DET
ap-3483	239	12	fg	fg	PROPN
ap-3483	239	13	immersion	immersion	NOUN
ap-3483	239	14	formula	formula	NOUN
ap-3483	239	15	(	(	PUNCT
ap-3483	239	16	3.14	3.14	NUM
ap-3483	239	17	)	)	PUNCT
ap-3483	239	18	to	to	ADP
ap-3483	239	19	the	the	DET
ap-3483	239	20	st	st	PROPN
ap-3483	239	21	immersion	immersion	NOUN
ap-3483	239	22	formula	formula	NOUN
ap-3483	239	23	(	(	PUNCT
ap-3483	239	24	3.3	3.3	NUM
ap-3483	239	25	)	)	PUNCT
ap-3483	239	26	.	.	PUNCT
ap-3483	240	1	alternatively	alternatively	ADV
ap-3483	240	2	,	,	PUNCT
ap-3483	240	3	if	if	SCONJ
ap-3483	240	4	the	the	DET
ap-3483	240	5	gauge	gauge	NOUN
ap-3483	240	6	s1	s1	NOUN
ap-3483	240	7	is	be	AUX
ap-3483	240	8	a	a	DET
ap-3483	240	9	non	non	ADJ
ap-3483	240	10	-	-	ADJ
ap-3483	240	11	singular	singular	ADJ
ap-3483	240	12	matrix	matrix	NOUN
ap-3483	240	13	then	then	ADV
ap-3483	240	14	there	there	PRON
ap-3483	240	15	exists	exist	VERB
ap-3483	240	16	a	a	DET
ap-3483	240	17	matrix	matrix	NOUN
ap-3483	240	18	m−1	m−1	PROPN
ap-3483	240	19	such	such	ADJ
ap-3483	240	20	that	that	SCONJ
ap-3483	240	21	(	(	PUNCT
ap-3483	240	22	prωrφ	prωrφ	PROPN
ap-3483	240	23	)	)	PUNCT
ap-3483	240	24	=	=	SYM
ap-3483	240	25	m−1β(λ)(dλφ	m−1β(λ)(dλφ	PROPN
ap-3483	240	26	)	)	PUNCT
ap-3483	240	27	.	.	PUNCT
ap-3483	241	1	(	(	PUNCT
ap-3483	241	2	3.24	3.24	NUM
ap-3483	241	3	)	)	PUNCT
ap-3483	241	4	the	the	DET
ap-3483	241	5	matrix	matrix	NOUN
ap-3483	241	6	m−1	m−1	PROPN
ap-3483	241	7	defines	define	VERB
ap-3483	241	8	a	a	DET
ap-3483	241	9	mapping	mapping	NOUN
ap-3483	241	10	from	from	ADP
ap-3483	241	11	the	the	DET
ap-3483	241	12	st	st	PROPN
ap-3483	241	13	immersion	immersion	NOUN
ap-3483	241	14	formula	formula	NOUN
ap-3483	241	15	(	(	PUNCT
ap-3483	241	16	3.3	3.3	NUM
ap-3483	241	17	)	)	PUNCT
ap-3483	241	18	to	to	ADP
ap-3483	241	19	the	the	DET
ap-3483	241	20	fg	fg	PROPN
ap-3483	241	21	immersion	immersion	NOUN
ap-3483	241	22	formula	formula	NOUN
ap-3483	241	23	(	(	PUNCT
ap-3483	241	24	3.14	3.14	NUM
ap-3483	241	25	)	)	PUNCT
ap-3483	241	26	.	.	PUNCT
ap-3483	242	1	185	185	NUM
ap-3483	242	2	a.	a.	NOUN
ap-3483	242	3	m.	m.	NOUN
ap-3483	242	4	grundland	grundland	PROPN
ap-3483	242	5	,	,	PUNCT
ap-3483	242	6	d.	d.	PROPN
ap-3483	242	7	levi	levi	PROPN
ap-3483	242	8	,	,	PUNCT
ap-3483	242	9	l.	l.	PROPN
ap-3483	242	10	martina	martina	PROPN
ap-3483	242	11	acta	acta	PROPN
ap-3483	242	12	polytechnica	polytechnica	PROPN
ap-3483	242	13	fst	fst	PROPN
ap-3483	242	14	=	=	PUNCT
ap-3483	242	15	β(λ)φ−1(dλφ	β(λ)φ−1(dλφ	PROPN
ap-3483	242	16	)	)	PUNCT
ap-3483	242	17	∈	∈	PROPN
ap-3483	242	18	g	g	PROPN
ap-3483	242	19	φ	φ	PROPN
ap-3483	242	20	∈	∈	PROPN
ap-3483	242	21	g	g	PROPN
ap-3483	242	22	ffg	ffg	PROPN
ap-3483	242	23	=	=	SYM
ap-3483	242	24	φ−1(prωrφ	φ−1(prωrφ	ADJ
ap-3483	242	25	)	)	PUNCT
ap-3483	242	26	∈	∈	PROPN
ap-3483	242	27	g	g	PROPN
ap-3483	242	28	s2	s2	PROPN
ap-3483	242	29	◦	◦	NOUN
ap-3483	242	30	s−1	s−1	PROPN
ap-3483	242	31	1	1	NUM
ap-3483	242	32	s1∈g	s1∈g	NOUN
ap-3483	242	33	s2∈g	s2∈g	PROPN
ap-3483	242	34	s1	s1	PROPN
ap-3483	242	35	◦	◦	NOUN
ap-3483	242	36	s−1	s−1	PROPN
ap-3483	242	37	2	2	NUM
ap-3483	242	38	figure	figure	NOUN
ap-3483	242	39	1	1	NUM
ap-3483	242	40	.	.	PUNCT
ap-3483	242	41	representation	representation	NOUN
ap-3483	242	42	of	of	ADP
ap-3483	242	43	the	the	DET
ap-3483	242	44	relations	relation	NOUN
ap-3483	242	45	between	between	ADP
ap-3483	242	46	the	the	DET
ap-3483	242	47	wavefunction	wavefunction	NOUN
ap-3483	242	48	φ	φ	PROPN
ap-3483	242	49	∈	∈	PROPN
ap-3483	242	50	g	g	PROPN
ap-3483	242	51	and	and	CCONJ
ap-3483	242	52	the	the	DET
ap-3483	242	53	g	g	NOUN
ap-3483	242	54	-	-	PUNCT
ap-3483	242	55	valued	value	VERB
ap-3483	242	56	st	st	PROPN
ap-3483	242	57	and	and	CCONJ
ap-3483	242	58	fg	fg	PROPN
ap-3483	242	59	formulas	formula	NOUN
ap-3483	242	60	for	for	ADP
ap-3483	242	61	immersions	immersion	NOUN
ap-3483	242	62	of	of	ADP
ap-3483	242	63	2d	2d	NOUN
ap-3483	242	64	-	-	PUNCT
ap-3483	242	65	soliton	soliton	NOUN
ap-3483	242	66	surfaces	surface	NOUN
ap-3483	242	67	.	.	PUNCT
ap-3483	243	1	proof	proof	NOUN
ap-3483	243	2	.	.	PUNCT
ap-3483	244	1	equation	equation	NOUN
ap-3483	244	2	(	(	PUNCT
ap-3483	244	3	3.23	3.23	NUM
ap-3483	244	4	)	)	PUNCT
ap-3483	244	5	or	or	CCONJ
ap-3483	244	6	(	(	PUNCT
ap-3483	244	7	3.24	3.24	NUM
ap-3483	244	8	)	)	PUNCT
ap-3483	244	9	is	be	AUX
ap-3483	244	10	obtained	obtain	VERB
ap-3483	244	11	by	by	ADP
ap-3483	244	12	eliminating	eliminate	VERB
ap-3483	244	13	the	the	DET
ap-3483	244	14	wavefunction	wavefunction	NOUN
ap-3483	244	15	φ	φ	PROPN
ap-3483	244	16	from	from	ADP
ap-3483	244	17	the	the	DET
ap-3483	244	18	right	right	ADJ
ap-3483	244	19	-	-	PUNCT
ap-3483	244	20	hand	hand	NOUN
ap-3483	244	21	side	side	NOUN
ap-3483	244	22	of	of	ADP
ap-3483	244	23	equations	equation	NOUN
ap-3483	244	24	(	(	PUNCT
ap-3483	244	25	3.8	3.8	NUM
ap-3483	244	26	)	)	PUNCT
ap-3483	244	27	and	and	CCONJ
ap-3483	244	28	prωrφ	prωrφ	NOUN
ap-3483	244	29	=	=	SYM
ap-3483	244	30	s2φ	s2φ	NOUN
ap-3483	244	31	,	,	PUNCT
ap-3483	244	32	(	(	PUNCT
ap-3483	244	33	3.25	3.25	NUM
ap-3483	244	34	)	)	PUNCT
ap-3483	244	35	respectively	respectively	ADV
ap-3483	244	36	.	.	PUNCT
ap-3483	245	1	so	so	ADV
ap-3483	245	2	the	the	DET
ap-3483	245	3	link	link	NOUN
ap-3483	245	4	between	between	ADP
ap-3483	245	5	the	the	DET
ap-3483	245	6	immersion	immersion	NOUN
ap-3483	245	7	functions	function	NOUN
ap-3483	245	8	fst	fst	NOUN
ap-3483	245	9	and	and	CCONJ
ap-3483	245	10	ffg	ffg	PROPN
ap-3483	245	11	exists	exist	VERB
ap-3483	245	12	,	,	PUNCT
ap-3483	245	13	up	up	ADP
ap-3483	245	14	to	to	ADP
ap-3483	245	15	a	a	DET
ap-3483	245	16	g	g	ADV
ap-3483	245	17	-	-	PUNCT
ap-3483	245	18	valued	value	VERB
ap-3483	245	19	gauge	gauge	NOUN
ap-3483	245	20	function	function	NOUN
ap-3483	245	21	.	.	PUNCT
ap-3483	246	1	it	it	PRON
ap-3483	246	2	should	should	AUX
ap-3483	246	3	be	be	AUX
ap-3483	246	4	noted	note	VERB
ap-3483	246	5	that	that	SCONJ
ap-3483	246	6	in	in	ADP
ap-3483	246	7	order	order	NOUN
ap-3483	246	8	to	to	PART
ap-3483	246	9	recover	recover	VERB
ap-3483	246	10	soliton	soliton	NOUN
ap-3483	246	11	surfaces	surface	NOUN
ap-3483	246	12	,	,	PUNCT
ap-3483	246	13	we	we	PRON
ap-3483	246	14	have	have	VERB
ap-3483	246	15	to	to	PART
ap-3483	246	16	perform	perform	VERB
ap-3483	246	17	an	an	DET
ap-3483	246	18	integration	integration	NOUN
ap-3483	246	19	with	with	ADP
ap-3483	246	20	respect	respect	NOUN
ap-3483	246	21	to	to	ADP
ap-3483	246	22	the	the	DET
ap-3483	246	23	curvilinear	curvilinear	PROPN
ap-3483	246	24	coordinates	coordinate	NOUN
ap-3483	246	25	in	in	ADP
ap-3483	246	26	the	the	DET
ap-3483	246	27	case	case	NOUN
ap-3483	246	28	of	of	ADP
ap-3483	246	29	the	the	DET
ap-3483	246	30	fg	fg	PROPN
ap-3483	246	31	formula	formula	NOUN
ap-3483	246	32	.	.	PUNCT
ap-3483	247	1	alternatively	alternatively	ADV
ap-3483	247	2	,	,	PUNCT
ap-3483	247	3	by	by	ADP
ap-3483	247	4	using	use	VERB
ap-3483	247	5	the	the	DET
ap-3483	247	6	st	st	PROPN
ap-3483	247	7	immersion	immersion	NOUN
ap-3483	247	8	formula	formula	NOUN
ap-3483	247	9	,	,	PUNCT
ap-3483	247	10	we	we	PRON
ap-3483	247	11	obtain	obtain	VERB
ap-3483	247	12	the	the	DET
ap-3483	247	13	same	same	ADJ
ap-3483	247	14	soliton	soliton	NOUN
ap-3483	247	15	surface	surface	NOUN
ap-3483	247	16	by	by	ADP
ap-3483	247	17	differentiating	differentiate	VERB
ap-3483	247	18	the	the	DET
ap-3483	247	19	wavefunction	wavefunction	NOUN
ap-3483	247	20	φ	φ	PROPN
ap-3483	247	21	with	with	ADP
ap-3483	247	22	respect	respect	NOUN
ap-3483	247	23	to	to	ADP
ap-3483	247	24	the	the	DET
ap-3483	247	25	spectral	spectral	ADJ
ap-3483	247	26	parameter	parameter	PROPN
ap-3483	247	27	λ	λ	PROPN
ap-3483	247	28	.	.	PUNCT
ap-3483	248	1	the	the	DET
ap-3483	248	2	connection	connection	NOUN
ap-3483	248	3	between	between	ADP
ap-3483	248	4	the	the	DET
ap-3483	248	5	fg	fg	PROPN
ap-3483	248	6	and	and	CCONJ
ap-3483	248	7	st	st	PROPN
ap-3483	248	8	approaches	approach	NOUN
ap-3483	248	9	for	for	ADP
ap-3483	248	10	determining	determine	VERB
ap-3483	248	11	the	the	DET
ap-3483	248	12	immersion	immersion	NOUN
ap-3483	248	13	functions	function	NOUN
ap-3483	248	14	fst	fst	NOUN
ap-3483	248	15	and	and	CCONJ
ap-3483	248	16	ffg	ffg	PROPN
ap-3483	248	17	of	of	ADP
ap-3483	248	18	2d	2d	NOUN
ap-3483	248	19	-	-	PUNCT
ap-3483	248	20	surfaces	surface	NOUN
ap-3483	248	21	is	be	AUX
ap-3483	248	22	obtained	obtain	VERB
ap-3483	248	23	through	through	ADP
ap-3483	248	24	the	the	DET
ap-3483	248	25	gauge	gauge	NOUN
ap-3483	248	26	matrix	matrix	NOUN
ap-3483	248	27	functions	function	NOUN
ap-3483	248	28	m	m	VERB
ap-3483	248	29	or	or	CCONJ
ap-3483	248	30	m−1	m−1	PROPN
ap-3483	248	31	from	from	ADP
ap-3483	248	32	the	the	DET
ap-3483	248	33	equation	equation	NOUN
ap-3483	248	34	(	(	PUNCT
ap-3483	248	35	3.23	3.23	NUM
ap-3483	248	36	)	)	PUNCT
ap-3483	248	37	or	or	CCONJ
ap-3483	248	38	(	(	PUNCT
ap-3483	248	39	3.24	3.24	NUM
ap-3483	248	40	)	)	PUNCT
ap-3483	248	41	,	,	PUNCT
ap-3483	248	42	respectively	respectively	ADV
ap-3483	248	43	(	(	PUNCT
ap-3483	248	44	see	see	VERB
ap-3483	248	45	fig	fig	NOUN
ap-3483	248	46	.	.	PUNCT
ap-3483	249	1	1	1	NUM
ap-3483	249	2	)	)	PUNCT
ap-3483	249	3	.	.	PUNCT
ap-3483	250	1	we	we	PRON
ap-3483	250	2	can	can	AUX
ap-3483	250	3	also	also	ADV
ap-3483	250	4	write	write	VERB
ap-3483	250	5	direct	direct	ADJ
ap-3483	250	6	equations	equation	NOUN
ap-3483	250	7	relating	relate	VERB
ap-3483	250	8	the	the	DET
ap-3483	250	9	generalized	generalized	ADJ
ap-3483	250	10	symmetries	symmetry	NOUN
ap-3483	250	11	ωr	ωr	VERB
ap-3483	250	12	with	with	ADP
ap-3483	250	13	the	the	DET
ap-3483	250	14	sym	sym	NOUN
ap-3483	250	15	-	-	PUNCT
ap-3483	250	16	tafel	tafel	NOUN
ap-3483	250	17	λconformal	λconformal	ADJ
ap-3483	250	18	symmetry	symmetry	NOUN
ap-3483	250	19	for	for	ADP
ap-3483	250	20	the	the	DET
ap-3483	250	21	zcc	zcc	NOUN
ap-3483	250	22	(	(	PUNCT
ap-3483	250	23	2.14	2.14	NUM
ap-3483	250	24	)	)	PUNCT
ap-3483	250	25	,	,	PUNCT
ap-3483	250	26	eliminating	eliminate	VERB
ap-3483	250	27	the	the	DET
ap-3483	250	28	gauge	gauge	ADJ
ap-3483	250	29	s2([u	s2([u	NOUN
ap-3483	250	30	]	]	PUNCT
ap-3483	250	31	,	,	PUNCT
ap-3483	250	32	λ	λ	NOUN
ap-3483	250	33	)	)	PUNCT
ap-3483	250	34	in	in	ADP
ap-3483	250	35	(	(	PUNCT
ap-3483	250	36	3.9	3.9	NUM
ap-3483	250	37	)	)	PUNCT
ap-3483	250	38	by	by	ADP
ap-3483	250	39	using	use	VERB
ap-3483	250	40	(	(	PUNCT
ap-3483	250	41	3.8	3.8	NUM
ap-3483	250	42	)	)	PUNCT
ap-3483	250	43	.	.	PUNCT
ap-3483	251	1	so	so	ADV
ap-3483	251	2	we	we	PRON
ap-3483	251	3	get	get	VERB
ap-3483	251	4	β(λ)(dλφ)uα	β(λ)(dλφ)uα	NOUN
ap-3483	251	5	−	−	NOUN
ap-3483	251	6	β(λ)φuαφ−1(dλφ	β(λ)φuαφ−1(dλφ	NOUN
ap-3483	251	7	)	)	PUNCT
ap-3483	252	1	+	+	CCONJ
ap-3483	253	1	β(λ)(dλuα)φ	β(λ)(dλuα)φ	PROPN
ap-3483	253	2	+	+	NUM
ap-3483	253	3	φ	φ	PROPN
ap-3483	253	4	[	[	PUNCT
ap-3483	253	5	−prωr(dαφ	−prωr(dαφ	PROPN
ap-3483	253	6	)	)	PUNCT
ap-3483	253	7	+	+	CCONJ
ap-3483	253	8	uα(prωrφ	uα(prωrφ	NOUN
ap-3483	253	9	)	)	PUNCT
ap-3483	253	10	]	]	PUNCT
ap-3483	254	1	φ−1	φ−1	PROPN
ap-3483	254	2	=	=	SYM
ap-3483	254	3	0	0	X
ap-3483	254	4	.	.	PUNCT
ap-3483	255	1	(	(	PUNCT
ap-3483	255	2	3.26	3.26	NUM
ap-3483	255	3	)	)	PUNCT
ap-3483	255	4	however	however	ADV
ap-3483	255	5	,	,	PUNCT
ap-3483	255	6	equations	equation	NOUN
ap-3483	255	7	(	(	PUNCT
ap-3483	255	8	3.26	3.26	NUM
ap-3483	255	9	)	)	PUNCT
ap-3483	255	10	are	be	AUX
ap-3483	255	11	nonlinear	nonlinear	ADJ
ap-3483	255	12	differential	differential	ADJ
ap-3483	255	13	equations	equation	NOUN
ap-3483	255	14	for	for	ADP
ap-3483	255	15	the	the	DET
ap-3483	255	16	wavefunction	wavefunction	NOUN
ap-3483	255	17	φ	φ	PROPN
ap-3483	255	18	,	,	PUNCT
ap-3483	255	19	which	which	PRON
ap-3483	255	20	in	in	ADP
ap-3483	255	21	general	general	ADJ
ap-3483	255	22	are	be	AUX
ap-3483	255	23	not	not	PART
ap-3483	255	24	easy	easy	ADJ
ap-3483	255	25	to	to	PART
ap-3483	255	26	solve	solve	VERB
ap-3483	255	27	.	.	PUNCT
ap-3483	256	1	to	to	PART
ap-3483	256	2	conclude	conclude	VERB
ap-3483	256	3	,	,	PUNCT
ap-3483	256	4	in	in	ADP
ap-3483	256	5	all	all	DET
ap-3483	256	6	three	three	NUM
ap-3483	256	7	cases	case	NOUN
ap-3483	256	8	we	we	PRON
ap-3483	256	9	give	give	VERB
ap-3483	256	10	explicit	explicit	ADJ
ap-3483	256	11	expressions	expression	NOUN
ap-3483	256	12	for	for	ADP
ap-3483	256	13	2d	2d	NOUN
ap-3483	256	14	-	-	PUNCT
ap-3483	256	15	soliton	soliton	NOUN
ap-3483	256	16	surfaces	surface	NOUN
ap-3483	256	17	immersed	immerse	VERB
ap-3483	256	18	in	in	ADP
ap-3483	256	19	the	the	DET
ap-3483	256	20	lie	lie	NOUN
ap-3483	256	21	algebra	algebra	NOUN
ap-3483	256	22	g	g	PROPN
ap-3483	256	23	and	and	CCONJ
ap-3483	256	24	demonstrate	demonstrate	VERB
ap-3483	256	25	that	that	SCONJ
ap-3483	256	26	one	one	NUM
ap-3483	256	27	such	such	ADJ
ap-3483	256	28	surface	surface	NOUN
ap-3483	256	29	can	can	AUX
ap-3483	256	30	be	be	AUX
ap-3483	256	31	transformed	transform	VERB
ap-3483	256	32	to	to	ADP
ap-3483	256	33	another	another	DET
ap-3483	256	34	one	one	NOUN
ap-3483	256	35	through	through	ADP
ap-3483	256	36	a	a	DET
ap-3483	256	37	gauge	gauge	NOUN
ap-3483	256	38	.	.	PUNCT
ap-3483	257	1	4	4	X
ap-3483	257	2	.	.	X
ap-3483	257	3	the	the	DET
ap-3483	257	4	sigma	sigma	PROPN
ap-3483	257	5	model	model	NOUN
ap-3483	257	6	and	and	CCONJ
ap-3483	257	7	soliton	soliton	NOUN
ap-3483	257	8	surfaces	surface	NOUN
ap-3483	257	9	for	for	ADP
ap-3483	257	10	the	the	DET
ap-3483	257	11	sake	sake	NOUN
ap-3483	257	12	of	of	ADP
ap-3483	257	13	generality	generality	NOUN
ap-3483	257	14	we	we	PRON
ap-3483	257	15	start	start	VERB
ap-3483	257	16	by	by	ADP
ap-3483	257	17	considering	consider	VERB
ap-3483	257	18	the	the	DET
ap-3483	257	19	general	general	ADJ
ap-3483	257	20	cpn−1	cpn−1	PROPN
ap-3483	257	21	model	model	NOUN
ap-3483	257	22	.	.	PUNCT
ap-3483	258	1	the	the	DET
ap-3483	258	2	problem	problem	NOUN
ap-3483	258	3	of	of	ADP
ap-3483	258	4	constructing	construct	VERB
ap-3483	258	5	integrable	integrable	ADJ
ap-3483	258	6	surfaces	surface	NOUN
ap-3483	258	7	associated	associate	VERB
ap-3483	258	8	with	with	ADP
ap-3483	258	9	the	the	DET
ap-3483	258	10	cpn−1	cpn−1	PROPN
ap-3483	258	11	models	model	NOUN
ap-3483	258	12	and	and	CCONJ
ap-3483	258	13	their	their	PRON
ap-3483	258	14	deformations	deformation	NOUN
ap-3483	258	15	under	under	ADP
ap-3483	258	16	various	various	ADJ
ap-3483	258	17	types	type	NOUN
ap-3483	258	18	of	of	ADP
ap-3483	258	19	dynamics	dynamic	NOUN
ap-3483	258	20	have	have	AUX
ap-3483	258	21	generated	generate	VERB
ap-3483	258	22	a	a	DET
ap-3483	258	23	great	great	ADJ
ap-3483	258	24	deal	deal	NOUN
ap-3483	258	25	of	of	ADP
ap-3483	258	26	interest	interest	NOUN
ap-3483	258	27	over	over	ADP
ap-3483	258	28	the	the	DET
ap-3483	258	29	past	past	ADJ
ap-3483	258	30	decades	decade	NOUN
ap-3483	258	31	[	[	X
ap-3483	258	32	1	1	NUM
ap-3483	258	33	,	,	PUNCT
ap-3483	258	34	23	23	NUM
ap-3483	258	35	,	,	PUNCT
ap-3483	258	36	37	37	NUM
ap-3483	258	37	]	]	PUNCT
ap-3483	258	38	.	.	PUNCT
ap-3483	259	1	the	the	DET
ap-3483	259	2	most	most	ADV
ap-3483	259	3	fruitful	fruitful	ADJ
ap-3483	259	4	approach	approach	NOUN
ap-3483	259	5	to	to	ADP
ap-3483	259	6	the	the	DET
ap-3483	259	7	study	study	NOUN
ap-3483	259	8	of	of	ADP
ap-3483	259	9	general	general	ADJ
ap-3483	259	10	properties	property	NOUN
ap-3483	259	11	of	of	ADP
ap-3483	259	12	this	this	DET
ap-3483	259	13	model	model	NOUN
ap-3483	259	14	has	have	AUX
ap-3483	259	15	been	be	AUX
ap-3483	259	16	formulated	formulate	VERB
ap-3483	259	17	through	through	ADP
ap-3483	259	18	descriptions	description	NOUN
ap-3483	259	19	of	of	ADP
ap-3483	259	20	the	the	DET
ap-3483	259	21	model	model	NOUN
ap-3483	259	22	in	in	ADP
ap-3483	259	23	terms	term	NOUN
ap-3483	259	24	of	of	ADP
ap-3483	259	25	rank	rank	NOUN
ap-3483	259	26	-	-	PUNCT
ap-3483	259	27	one	one	NUM
ap-3483	259	28	hermitian	hermitian	ADJ
ap-3483	259	29	projectors	projector	NOUN
ap-3483	259	30	.	.	PUNCT
ap-3483	260	1	a	a	DET
ap-3483	260	2	matrix	matrix	NOUN
ap-3483	260	3	p	p	X
ap-3483	260	4	(	(	PUNCT
ap-3483	260	5	z	z	NOUN
ap-3483	260	6	,	,	PUNCT
ap-3483	260	7	z̄	z̄	PRON
ap-3483	260	8	)	)	PUNCT
ap-3483	260	9	is	be	AUX
ap-3483	260	10	said	say	VERB
ap-3483	260	11	to	to	PART
ap-3483	260	12	be	be	AUX
ap-3483	260	13	a	a	DET
ap-3483	260	14	rank	rank	NOUN
ap-3483	260	15	-	-	PUNCT
ap-3483	260	16	one	one	NUM
ap-3483	260	17	hermitian	hermitian	ADJ
ap-3483	260	18	projector	projector	NOUN
ap-3483	260	19	if	if	SCONJ
ap-3483	260	20	p	p	NOUN
ap-3483	260	21	2	2	NUM
ap-3483	260	22	=	=	SYM
ap-3483	260	23	p	p	NOUN
ap-3483	260	24	,	,	PUNCT
ap-3483	260	25	p	p	X
ap-3483	260	26	=	=	X
ap-3483	260	27	p	p	PROPN
ap-3483	260	28	†	†	PROPN
ap-3483	260	29	,	,	PUNCT
ap-3483	260	30	trp	trp	PROPN
ap-3483	260	31	=	=	PROPN
ap-3483	261	1	1	1	X
ap-3483	261	2	.	.	PUNCT
ap-3483	261	3	(	(	PUNCT
ap-3483	261	4	4.1	4.1	NUM
ap-3483	261	5	)	)	PUNCT
ap-3483	261	6	the	the	DET
ap-3483	261	7	target	target	NOUN
ap-3483	261	8	space	space	NOUN
ap-3483	261	9	of	of	ADP
ap-3483	261	10	the	the	DET
ap-3483	261	11	projector	projector	NOUN
ap-3483	261	12	p	p	NOUN
ap-3483	261	13	is	be	AUX
ap-3483	261	14	determined	determine	VERB
ap-3483	261	15	by	by	ADP
ap-3483	261	16	a	a	DET
ap-3483	261	17	complex	complex	ADJ
ap-3483	261	18	line	line	NOUN
ap-3483	261	19	in	in	ADP
ap-3483	261	20	cn	cn	PROPN
ap-3483	261	21	,	,	PUNCT
ap-3483	261	22	i.e.	i.e.	X
ap-3483	261	23	by	by	ADP
ap-3483	261	24	a	a	DET
ap-3483	261	25	one	one	NUM
ap-3483	261	26	-	-	PUNCT
ap-3483	261	27	dimensional	dimensional	ADJ
ap-3483	261	28	vector	vector	NOUN
ap-3483	261	29	function	function	NOUN
ap-3483	261	30	f(z	f(z	PROPN
ap-3483	261	31	,	,	PUNCT
ap-3483	261	32	z̄	z̄	NOUN
ap-3483	261	33	)	)	PUNCT
ap-3483	261	34	given	give	VERB
ap-3483	261	35	by	by	ADP
ap-3483	261	36	p	p	NOUN
ap-3483	261	37	=	=	PUNCT
ap-3483	261	38	f	f	PROPN
ap-3483	261	39	⊗	⊗	PROPN
ap-3483	261	40	f†	f†	ADJ
ap-3483	261	41	f†f	f†f	NUM
ap-3483	261	42	,	,	PUNCT
ap-3483	261	43	(	(	PUNCT
ap-3483	261	44	4.2	4.2	NUM
ap-3483	261	45	)	)	PUNCT
ap-3483	261	46	where	where	SCONJ
ap-3483	261	47	f	f	PROPN
ap-3483	261	48	is	be	AUX
ap-3483	261	49	the	the	DET
ap-3483	261	50	mapping	mapping	NOUN
ap-3483	261	51	c	c	NOUN
ap-3483	261	52	⊇	⊇	PROPN
ap-3483	261	53	ω	ω	PROPN
ap-3483	261	54	3	3	NUM
ap-3483	261	55	z	z	NOUN
ap-3483	261	56	=	=	PUNCT
ap-3483	261	57	x	x	PROPN
ap-3483	262	1	+	+	CCONJ
ap-3483	263	1	iy	iy	PROPN
ap-3483	263	2	7→	7→	NUM
ap-3483	263	3	f	f	NOUN
ap-3483	263	4	=	=	SYM
ap-3483	263	5	(	(	PUNCT
ap-3483	263	6	f0	f0	PROPN
ap-3483	263	7	,	,	PUNCT
ap-3483	263	8	f1	f1	NOUN
ap-3483	263	9	,	,	PUNCT
ap-3483	263	10	.	.	PUNCT
ap-3483	263	11	.	.	PUNCT
ap-3483	263	12	.	.	PUNCT
ap-3483	264	1	,	,	PUNCT
ap-3483	264	2	fn−1)cn\{0	fn−1)cn\{0	PROPN
ap-3483	264	3	}	}	PUNCT
ap-3483	264	4	.	.	PUNCT
ap-3483	265	1	equation	equation	NOUN
ap-3483	265	2	(	(	PUNCT
ap-3483	265	3	4.2	4.2	NUM
ap-3483	265	4	)	)	PUNCT
ap-3483	265	5	gives	give	VERB
ap-3483	265	6	an	an	DET
ap-3483	265	7	isomorphism	isomorphism	NOUN
ap-3483	265	8	between	between	ADP
ap-3483	265	9	the	the	DET
ap-3483	265	10	equivalence	equivalence	NOUN
ap-3483	265	11	classes	class	NOUN
ap-3483	265	12	of	of	ADP
ap-3483	265	13	the	the	DET
ap-3483	265	14	cpn−1	cpn−1	PROPN
ap-3483	265	15	model	model	NOUN
ap-3483	265	16	and	and	CCONJ
ap-3483	265	17	the	the	DET
ap-3483	265	18	set	set	NOUN
ap-3483	265	19	of	of	ADP
ap-3483	265	20	rank	rank	NOUN
ap-3483	265	21	-	-	PUNCT
ap-3483	265	22	one	one	NUM
ap-3483	265	23	hermitian	hermitian	ADJ
ap-3483	265	24	projectors	projector	NOUN
ap-3483	265	25	p	p	NOUN
ap-3483	265	26	.	.	PUNCT
ap-3483	266	1	the	the	DET
ap-3483	266	2	equations	equation	NOUN
ap-3483	266	3	of	of	ADP
ap-3483	266	4	motion	motion	NOUN
ap-3483	266	5	ω(p	ω(p	NOUN
ap-3483	266	6	)	)	PUNCT
ap-3483	266	7	=	=	PUNCT
ap-3483	267	1	[	[	X
ap-3483	267	2	∂+∂−p	∂+∂−p	NOUN
ap-3483	267	3	,	,	PUNCT
ap-3483	267	4	p	p	X
ap-3483	267	5	]	]	X
ap-3483	267	6	=	=	SYM
ap-3483	267	7	0	0	NUM
ap-3483	267	8	,	,	PUNCT
ap-3483	267	9	∂±	∂±	PROPN
ap-3483	267	10	=	=	NOUN
ap-3483	267	11	1	1	NUM
ap-3483	267	12	2(∂1	2(∂1	NUM
ap-3483	267	13	±	±	NUM
ap-3483	267	14	i∂2	i∂2	NOUN
ap-3483	267	15	)	)	PUNCT
ap-3483	267	16	,	,	PUNCT
ap-3483	267	17	∂1	∂1	ADJ
ap-3483	267	18	=	=	SYM
ap-3483	267	19	∂x	∂x	PROPN
ap-3483	267	20	,	,	PUNCT
ap-3483	267	21	∂2	∂2	NOUN
ap-3483	267	22	=	=	SYM
ap-3483	267	23	∂y	∂y	PROPN
ap-3483	267	24	(	(	PUNCT
ap-3483	267	25	4.3	4.3	NUM
ap-3483	267	26	)	)	PUNCT
ap-3483	267	27	and	and	CCONJ
ap-3483	267	28	other	other	ADJ
ap-3483	267	29	properties	property	NOUN
ap-3483	267	30	of	of	ADP
ap-3483	267	31	the	the	DET
ap-3483	267	32	model	model	NOUN
ap-3483	267	33	take	take	VERB
ap-3483	267	34	a	a	DET
ap-3483	267	35	compact	compact	ADJ
ap-3483	267	36	form	form	NOUN
ap-3483	267	37	when	when	SCONJ
ap-3483	267	38	the	the	DET
ap-3483	267	39	model	model	NOUN
ap-3483	267	40	is	be	AUX
ap-3483	267	41	written	write	VERB
ap-3483	267	42	in	in	ADP
ap-3483	267	43	terms	term	NOUN
ap-3483	267	44	of	of	ADP
ap-3483	267	45	the	the	DET
ap-3483	267	46	projector	projector	NOUN
ap-3483	267	47	.	.	PUNCT
ap-3483	268	1	now	now	ADV
ap-3483	268	2	we	we	PRON
ap-3483	268	3	present	present	VERB
ap-3483	268	4	some	some	DET
ap-3483	268	5	examples	example	NOUN
ap-3483	268	6	which	which	PRON
ap-3483	268	7	illustrate	illustrate	VERB
ap-3483	268	8	the	the	DET
ap-3483	268	9	theoretical	theoretical	ADJ
ap-3483	268	10	considerations	consideration	NOUN
ap-3483	268	11	presented	present	VERB
ap-3483	268	12	in	in	ADP
ap-3483	268	13	the	the	DET
ap-3483	268	14	previous	previous	ADJ
ap-3483	268	15	section	section	NOUN
ap-3483	268	16	.	.	PUNCT
ap-3483	269	1	our	our	PRON
ap-3483	269	2	first	first	ADJ
ap-3483	269	3	example	example	NOUN
ap-3483	269	4	shows	show	VERB
ap-3483	269	5	that	that	SCONJ
ap-3483	269	6	the	the	DET
ap-3483	269	7	integrated	integrate	VERB
ap-3483	269	8	form	form	NOUN
ap-3483	269	9	of	of	ADP
ap-3483	269	10	the	the	DET
ap-3483	269	11	surface	surface	NOUN
ap-3483	269	12	associated	associate	VERB
ap-3483	269	13	with	with	ADP
ap-3483	269	14	the	the	DET
ap-3483	269	15	cpn−1	cpn−1	PROPN
ap-3483	269	16	model	model	NOUN
ap-3483	269	17	admits	admit	VERB
ap-3483	269	18	conformal	conformal	ADJ
ap-3483	269	19	symmetries	symmetry	NOUN
ap-3483	269	20	which	which	PRON
ap-3483	269	21	depend	depend	VERB
ap-3483	269	22	on	on	ADP
ap-3483	269	23	two	two	NUM
ap-3483	269	24	arbitrary	arbitrary	ADJ
ap-3483	269	25	functions	function	NOUN
ap-3483	269	26	of	of	ADP
ap-3483	269	27	one	one	NUM
ap-3483	269	28	complex	complex	ADJ
ap-3483	269	29	variable	variable	NOUN
ap-3483	269	30	.	.	PUNCT
ap-3483	270	1	this	this	DET
ap-3483	270	2	model	model	NOUN
ap-3483	270	3	is	be	AUX
ap-3483	270	4	defined	define	VERB
ap-3483	270	5	on	on	ADP
ap-3483	270	6	the	the	DET
ap-3483	270	7	riemann	riemann	PROPN
ap-3483	270	8	sphere	sphere	PROPN
ap-3483	270	9	s2	s2	PROPN
ap-3483	270	10	=	=	SYM
ap-3483	270	11	c∪{∞	c∪{∞	PROPN
ap-3483	270	12	}	}	PUNCT
ap-3483	270	13	and	and	CCONJ
ap-3483	270	14	its	its	PRON
ap-3483	270	15	action	action	NOUN
ap-3483	270	16	functional	functional	ADJ
ap-3483	270	17	is	be	AUX
ap-3483	270	18	finite	finite	ADJ
ap-3483	270	19	[	[	X
ap-3483	270	20	37	37	NUM
ap-3483	270	21	]	]	PUNCT
ap-3483	270	22	.	.	PUNCT
ap-3483	271	1	an	an	DET
ap-3483	271	2	entire	entire	ADJ
ap-3483	271	3	class	class	NOUN
ap-3483	271	4	of	of	ADP
ap-3483	271	5	solutions	solution	NOUN
ap-3483	271	6	of	of	ADP
ap-3483	271	7	(	(	PUNCT
ap-3483	271	8	4.3	4.3	NUM
ap-3483	271	9	)	)	PUNCT
ap-3483	271	10	is	be	AUX
ap-3483	271	11	obtained	obtain	VERB
ap-3483	271	12	by	by	ADP
ap-3483	271	13	acting	act	VERB
ap-3483	271	14	on	on	ADP
ap-3483	271	15	the	the	DET
ap-3483	271	16	holomorphic	holomorphic	ADJ
ap-3483	271	17	(	(	PUNCT
ap-3483	271	18	or	or	CCONJ
ap-3483	271	19	anti	anti	ADJ
ap-3483	271	20	-	-	ADJ
ap-3483	271	21	holomorphic	holomorphic	ADJ
ap-3483	271	22	)	)	PUNCT
ap-3483	271	23	solution	solution	NOUN
ap-3483	271	24	p	p	X
ap-3483	272	1	[	[	X
ap-3483	272	2	10	10	NUM
ap-3483	272	3	]	]	PUNCT
ap-3483	272	4	with	with	ADP
ap-3483	272	5	raising	raise	VERB
ap-3483	272	6	and	and	CCONJ
ap-3483	272	7	lowering	lower	VERB
ap-3483	272	8	operators	operator	NOUN
ap-3483	272	9	.	.	PUNCT
ap-3483	273	1	these	these	DET
ap-3483	273	2	operators	operator	NOUN
ap-3483	273	3	are	be	AUX
ap-3483	273	4	given	give	VERB
ap-3483	273	5	by	by	ADP
ap-3483	273	6	π±(p	π±(p	NOUN
ap-3483	273	7	)	)	PUNCT
ap-3483	273	8	=	=	PUNCT
ap-3483	273	9			PUNCT
ap-3483	273	10	(	(	PUNCT
ap-3483	273	11	∂±p	∂±p	NOUN
ap-3483	273	12	)	)	PUNCT
ap-3483	273	13	p	p	NOUN
ap-3483	273	14	(	(	PUNCT
ap-3483	273	15	∂∓p	∂∓p	NOUN
ap-3483	273	16	)	)	PUNCT
ap-3483	273	17	tr(∂±pp∂∓p	tr(∂±pp∂∓p	NOUN
ap-3483	273	18	)	)	PUNCT
ap-3483	273	19	for	for	ADP
ap-3483	273	20	(	(	PUNCT
ap-3483	273	21	∂±p	∂±p	X
ap-3483	273	22	)	)	PUNCT
ap-3483	273	23	p	p	NOUN
ap-3483	273	24	(	(	PUNCT
ap-3483	273	25	∂∓p	∂∓p	NOUN
ap-3483	273	26	)	)	PUNCT
ap-3483	273	27	6=	6=	ADP
ap-3483	273	28	0	0	NUM
ap-3483	273	29	,	,	PUNCT
ap-3483	273	30	0	0	NUM
ap-3483	273	31	for	for	ADP
ap-3483	273	32	(	(	PUNCT
ap-3483	273	33	∂±p	∂±p	X
ap-3483	273	34	)	)	PUNCT
ap-3483	273	35	p	p	NOUN
ap-3483	273	36	(	(	PUNCT
ap-3483	273	37	∂∓p	∂∓p	NOUN
ap-3483	273	38	)	)	PUNCT
ap-3483	273	39	=	=	SYM
ap-3483	273	40	0	0	NUM
ap-3483	273	41	,	,	PUNCT
ap-3483	273	42	π−(pk	π−(pk	X
ap-3483	273	43	)	)	PUNCT
ap-3483	273	44	=	=	SYM
ap-3483	273	45	pk−1	pk−1	PROPN
ap-3483	273	46	,	,	PUNCT
ap-3483	273	47	π+(pk	π+(pk	NOUN
ap-3483	273	48	)	)	PUNCT
ap-3483	273	49	=	=	PUNCT
ap-3483	273	50	pk+1	pk+1	X
ap-3483	273	51	.	.	PUNCT
ap-3483	274	1	(	(	PUNCT
ap-3483	274	2	4.4	4.4	NUM
ap-3483	274	3	)	)	PUNCT
ap-3483	274	4	the	the	DET
ap-3483	274	5	set	set	NOUN
ap-3483	274	6	of	of	ADP
ap-3483	274	7	n	n	PRON
ap-3483	274	8	rank-1	rank-1	NUM
ap-3483	274	9	projectors	projector	NOUN
ap-3483	274	10	{	{	PUNCT
ap-3483	274	11	p0	p0	NOUN
ap-3483	274	12	,	,	PUNCT
ap-3483	274	13	.	.	PUNCT
ap-3483	274	14	.	.	PUNCT
ap-3483	275	1	.	.	PUNCT
ap-3483	276	1	,	,	PUNCT
ap-3483	276	2	pn−1	pn−1	ADJ
ap-3483	276	3	}	}	PUNCT
ap-3483	276	4	acts	act	VERB
ap-3483	276	5	on	on	ADP
ap-3483	276	6	orthogonal	orthogonal	ADJ
ap-3483	276	7	complements	complement	NOUN
ap-3483	276	8	of	of	ADP
ap-3483	276	9	one	one	NUM
ap-3483	276	10	-	-	PUNCT
ap-3483	276	11	dimensional	dimensional	ADJ
ap-3483	276	12	subspaces	subspace	NOUN
ap-3483	276	13	in	in	ADP
ap-3483	276	14	cn	cn	PROPN
ap-3483	276	15	and	and	CCONJ
ap-3483	276	16	satisfy	satisfy	VERB
ap-3483	276	17	the	the	DET
ap-3483	276	18	orthogonality	orthogonality	NOUN
ap-3483	276	19	and	and	CCONJ
ap-3483	276	20	completeness	completeness	NOUN
ap-3483	276	21	relations	relation	NOUN
ap-3483	276	22	pjpk	pjpk	NOUN
ap-3483	276	23	=	=	NOUN
ap-3483	276	24	δjkpj	δjkpj	NOUN
ap-3483	276	25	,	,	PUNCT
ap-3483	276	26	(	(	PUNCT
ap-3483	276	27	no	no	DET
ap-3483	276	28	summation	summation	NOUN
ap-3483	276	29	)	)	PUNCT
ap-3483	276	30	and	and	CCONJ
ap-3483	276	31	n−1∑	n−1∑	PROPN
ap-3483	276	32	j=0	j=0	PROPN
ap-3483	276	33	pj	pj	PROPN
ap-3483	276	34	=	=	PUNCT
ap-3483	276	35	in	in	ADP
ap-3483	276	36	,	,	PUNCT
ap-3483	276	37	(	(	PUNCT
ap-3483	276	38	4.5	4.5	NUM
ap-3483	276	39	)	)	PUNCT
ap-3483	276	40	where	where	SCONJ
ap-3483	276	41	in	in	ADP
ap-3483	276	42	is	be	AUX
ap-3483	276	43	the	the	DET
ap-3483	276	44	n	n	ADV
ap-3483	276	45	×n	×n	ADJ
ap-3483	276	46	identity	identity	NOUN
ap-3483	276	47	matrix	matrix	NOUN
ap-3483	276	48	on	on	ADP
ap-3483	276	49	cn	cn	PROPN
ap-3483	276	50	.	.	PUNCT
ap-3483	277	1	these	these	DET
ap-3483	277	2	projectors	projector	NOUN
ap-3483	277	3	provide	provide	VERB
ap-3483	277	4	a	a	DET
ap-3483	277	5	basis	basis	NOUN
ap-3483	277	6	of	of	ADP
ap-3483	277	7	commuting	commute	VERB
ap-3483	277	8	elements	element	NOUN
ap-3483	277	9	in	in	ADP
ap-3483	277	10	the	the	DET
ap-3483	277	11	space	space	NOUN
ap-3483	277	12	of	of	ADP
ap-3483	277	13	the	the	DET
ap-3483	277	14	hermitian	hermitian	ADJ
ap-3483	277	15	matrices	matrix	NOUN
ap-3483	277	16	on	on	ADP
ap-3483	277	17	cn	cn	PROPN
ap-3483	277	18	and	and	CCONJ
ap-3483	277	19	satisfy	satisfy	VERB
ap-3483	277	20	the	the	DET
ap-3483	277	21	euler	euler	PROPN
ap-3483	277	22	-	-	PUNCT
ap-3483	277	23	lagrange	lagrange	NOUN
ap-3483	277	24	equation	equation	NOUN
ap-3483	277	25	(	(	PUNCT
ap-3483	277	26	written	write	VERB
ap-3483	277	27	in	in	ADP
ap-3483	277	28	the	the	DET
ap-3483	277	29	form	form	NOUN
ap-3483	277	30	of	of	ADP
ap-3483	277	31	a	a	DET
ap-3483	277	32	conservation	conservation	NOUN
ap-3483	277	33	law	law	NOUN
ap-3483	277	34	)	)	PUNCT
ap-3483	277	35	∂[∂̄pk	∂[∂̄pk	NOUN
ap-3483	277	36	,	,	PUNCT
ap-3483	277	37	pk	pk	NOUN
ap-3483	277	38	]	]	X
ap-3483	277	39	+	+	NOUN
ap-3483	277	40	∂̄[∂pk	∂̄[∂pk	PROPN
ap-3483	277	41	,	,	PUNCT
ap-3483	277	42	pk	pk	NOUN
ap-3483	277	43	]	]	X
ap-3483	277	44	=	=	SYM
ap-3483	277	45	0	0	NUM
ap-3483	277	46	,	,	PUNCT
ap-3483	277	47	k	k	NOUN
ap-3483	277	48	=	=	SYM
ap-3483	277	49	0	0	NUM
ap-3483	277	50	,	,	PUNCT
ap-3483	277	51	1	1	NUM
ap-3483	277	52	,	,	PUNCT
ap-3483	277	53	.	.	PUNCT
ap-3483	277	54	.	.	PUNCT
ap-3483	278	1	.	.	PUNCT
ap-3483	279	1	,	,	PUNCT
ap-3483	280	1	n	n	CCONJ
ap-3483	280	2	−	−	PROPN
ap-3483	280	3	1	1	NUM
ap-3483	280	4	,	,	PUNCT
ap-3483	280	5	(	(	PUNCT
ap-3483	280	6	4.6	4.6	NUM
ap-3483	280	7	)	)	PUNCT
ap-3483	280	8	where	where	SCONJ
ap-3483	280	9	∂	∂	NOUN
ap-3483	280	10	=	=	SYM
ap-3483	280	11	1	1	NUM
ap-3483	280	12	2	2	NUM
ap-3483	280	13	(	(	PUNCT
ap-3483	280	14	∂x	∂x	PROPN
ap-3483	280	15	−	−	PROPN
ap-3483	280	16	i∂y	i∂y	NOUN
ap-3483	280	17	)	)	PUNCT
ap-3483	280	18	and	and	CCONJ
ap-3483	280	19	∂̄	∂̄	X
ap-3483	280	20	=	=	SYM
ap-3483	280	21	1	1	NUM
ap-3483	280	22	2	2	NUM
ap-3483	280	23	(	(	PUNCT
ap-3483	280	24	∂x	∂x	PROPN
ap-3483	280	25	+	+	NUM
ap-3483	280	26	i∂y	i∂y	NUM
ap-3483	280	27	)	)	PUNCT
ap-3483	280	28	.	.	PUNCT
ap-3483	281	1	for	for	ADP
ap-3483	281	2	a	a	DET
ap-3483	281	3	given	give	VERB
ap-3483	281	4	set	set	NOUN
ap-3483	281	5	of	of	ADP
ap-3483	281	6	rank-1	rank-1	NUM
ap-3483	281	7	projector	projector	NOUN
ap-3483	281	8	solutions	solution	NOUN
ap-3483	281	9	pk	pk	NOUN
ap-3483	281	10	of	of	ADP
ap-3483	281	11	(	(	PUNCT
ap-3483	281	12	4.6	4.6	NUM
ap-3483	281	13	)	)	PUNCT
ap-3483	281	14	186	186	NUM
ap-3483	281	15	vol	vol	NOUN
ap-3483	281	16	.	.	PUNCT
ap-3483	282	1	56	56	NUM
ap-3483	282	2	no	no	NOUN
ap-3483	282	3	.	.	PUNCT
ap-3483	283	1	3/2016	3/2016	NUM
ap-3483	283	2	on	on	ADP
ap-3483	283	3	immersion	immersion	NOUN
ap-3483	283	4	formulas	formula	NOUN
ap-3483	283	5	for	for	ADP
ap-3483	283	6	soliton	soliton	NOUN
ap-3483	283	7	surfaces	surface	NOUN
ap-3483	283	8	the	the	DET
ap-3483	283	9	su(n)-valued	su(n)-value	VERB
ap-3483	283	10	generalized	generalize	VERB
ap-3483	283	11	weierstrass	weierstrass	NOUN
ap-3483	283	12	formula	formula	NOUN
ap-3483	283	13	for	for	ADP
ap-3483	283	14	immersion	immersion	NOUN
ap-3483	283	15	(	(	PUNCT
ap-3483	283	16	gwfi	gwfi	NOUN
ap-3483	283	17	)	)	PUNCT
ap-3483	284	1	[	[	X
ap-3483	284	2	20	20	NUM
ap-3483	284	3	]	]	SYM
ap-3483	284	4	fk(z	fk(z	NUM
ap-3483	284	5	,	,	PUNCT
ap-3483	284	6	z̄	z̄	NOUN
ap-3483	284	7	)	)	PUNCT
ap-3483	285	1	=	=	VERB
ap-3483	286	1	i	i	PRON
ap-3483	286	2	∫	∫	VERB
ap-3483	286	3	γ	γ	X
ap-3483	286	4	(	(	PUNCT
ap-3483	286	5	−[∂pk	−[∂pk	NOUN
ap-3483	286	6	,	,	PUNCT
ap-3483	286	7	pk]dz	pk]dz	NOUN
ap-3483	286	8	+	+	CCONJ
ap-3483	287	1	[	[	X
ap-3483	287	2	∂̄pk	∂̄pk	PROPN
ap-3483	287	3	,	,	PUNCT
ap-3483	287	4	pk]dz̄	pk]dz̄	NOUN
ap-3483	287	5	)	)	PUNCT
ap-3483	287	6	,	,	PUNCT
ap-3483	287	7	k	k	PROPN
ap-3483	287	8	=	=	SYM
ap-3483	287	9	0	0	NUM
ap-3483	287	10	,	,	PUNCT
ap-3483	287	11	1	1	NUM
ap-3483	287	12	,	,	PUNCT
ap-3483	287	13	.	.	PUNCT
ap-3483	287	14	.	.	PUNCT
ap-3483	288	1	.	.	PUNCT
ap-3483	289	1	,	,	PUNCT
ap-3483	289	2	n	n	CCONJ
ap-3483	289	3	−	−	PROPN
ap-3483	289	4	1	1	NUM
ap-3483	289	5	(	(	PUNCT
ap-3483	289	6	4.7	4.7	NUM
ap-3483	289	7	)	)	PUNCT
ap-3483	289	8	(	(	PUNCT
ap-3483	289	9	where	where	SCONJ
ap-3483	289	10	γ	γ	PROPN
ap-3483	289	11	is	be	AUX
ap-3483	289	12	a	a	DET
ap-3483	289	13	curve	curve	NOUN
ap-3483	289	14	locally	locally	ADV
ap-3483	289	15	independent	independent	ADJ
ap-3483	289	16	of	of	ADP
ap-3483	289	17	the	the	DET
ap-3483	289	18	trajectory	trajectory	NOUN
ap-3483	289	19	in	in	ADP
ap-3483	289	20	c	c	NOUN
ap-3483	289	21	)	)	PUNCT
ap-3483	289	22	can	can	AUX
ap-3483	289	23	be	be	AUX
ap-3483	289	24	explicitly	explicitly	ADV
ap-3483	289	25	integrated	integrate	VERB
ap-3483	289	26	[	[	PUNCT
ap-3483	289	27	10	10	NUM
ap-3483	289	28	]	]	SYM
ap-3483	289	29	fk(z	fk(z	NUM
ap-3483	289	30	,	,	PUNCT
ap-3483	289	31	z̄	z̄	NOUN
ap-3483	289	32	)	)	PUNCT
ap-3483	290	1	=	=	SYM
ap-3483	290	2	−i	−i	NOUN
ap-3483	290	3	(	(	PUNCT
ap-3483	290	4	pk	pk	NOUN
ap-3483	290	5	+	+	CCONJ
ap-3483	290	6	2	2	NUM
ap-3483	290	7	k−1∑	k−1∑	PROPN
ap-3483	290	8	j=0	j=0	PROPN
ap-3483	290	9	pj	pj	PROPN
ap-3483	290	10	)	)	PUNCT
ap-3483	291	1	+	+	CCONJ
ap-3483	291	2	1	1	NUM
ap-3483	291	3	+	+	NUM
ap-3483	291	4	2k	2k	NUM
ap-3483	291	5	n	n	CCONJ
ap-3483	291	6	in	in	ADV
ap-3483	291	7	.	.	PUNCT
ap-3483	292	1	(	(	PUNCT
ap-3483	292	2	4.8	4.8	NUM
ap-3483	292	3	)	)	PUNCT
ap-3483	292	4	the	the	DET
ap-3483	292	5	immersion	immersion	NOUN
ap-3483	292	6	functions	function	NOUN
ap-3483	292	7	fk	fk	INTJ
ap-3483	292	8	satisfy	satisfy	VERB
ap-3483	292	9	the	the	DET
ap-3483	292	10	algebraic	algebraic	ADJ
ap-3483	292	11	conditions	condition	NOUN
ap-3483	293	1	[	[	X
ap-3483	293	2	fk	fk	INTJ
ap-3483	293	3	−	−	PROPN
ap-3483	293	4	ickin	ickin	X
ap-3483	293	5	]	]	PUNCT
ap-3483	294	1	[	[	X
ap-3483	294	2	fk	fk	INTJ
ap-3483	294	3	−	−	PROPN
ap-3483	294	4	i(ck−1)in	i(ck−1)in	NOUN
ap-3483	294	5	]	]	X
ap-3483	294	6	[	[	X
ap-3483	294	7	fk	fk	INTJ
ap-3483	294	8	−	−	NOUN
ap-3483	294	9	i(ck−2)in	i(ck−2)in	NOUN
ap-3483	294	10	]	]	PUNCT
ap-3483	294	11	=	=	PUNCT
ap-3483	294	12	0	0	NUM
ap-3483	294	13	,	,	PUNCT
ap-3483	294	14	0	0	PUNCT
ap-3483	294	15	<	<	X
ap-3483	294	16	k	k	X
ap-3483	294	17	<	<	X
ap-3483	294	18	n	n	CCONJ
ap-3483	294	19	−	−	PROPN
ap-3483	294	20	1	1	NUM
ap-3483	294	21	,	,	PUNCT
ap-3483	294	22	[	[	X
ap-3483	294	23	f0	f0	ADP
ap-3483	294	24	−	−	NOUN
ap-3483	294	25	ic0	ic0	ADP
ap-3483	294	26	in	in	ADP
ap-3483	294	27	]	]	PUNCT
ap-3483	294	28	[	[	X
ap-3483	294	29	f0	f0	X
ap-3483	294	30	−	−	PROPN
ap-3483	294	31	i(c0	i(c0	NOUN
ap-3483	295	1	−	−	PROPN
ap-3483	296	1	1)in	1)in	NUM
ap-3483	296	2	]	]	PUNCT
ap-3483	297	1	=	=	PUNCT
ap-3483	297	2	0	0	NUM
ap-3483	297	3	,	,	PUNCT
ap-3483	297	4	[	[	X
ap-3483	297	5	fn−1	fn−1	ADJ
ap-3483	297	6	+	+	CCONJ
ap-3483	297	7	ic0	ic0	ADP
ap-3483	297	8	in	in	ADV
ap-3483	297	9	]	]	PUNCT
ap-3483	297	10	[	[	X
ap-3483	297	11	fn−1	fn−1	PROPN
ap-3483	297	12	+	+	NUM
ap-3483	297	13	i(c0	i(c0	NOUN
ap-3483	297	14	−	−	PROPN
ap-3483	298	1	1)in	1)in	NUM
ap-3483	298	2	]	]	PUNCT
ap-3483	299	1	=	=	SYM
ap-3483	299	2	0	0	NUM
ap-3483	299	3	,	,	PUNCT
ap-3483	299	4	n−1∑	n−1∑	PROPN
ap-3483	299	5	j=0	j=0	PROPN
ap-3483	299	6	(	(	PUNCT
ap-3483	299	7	−1)jfj	−1)jfj	PROPN
ap-3483	299	8	=	=	SYM
ap-3483	299	9	0	0	PROPN
ap-3483	299	10	,	,	PUNCT
ap-3483	299	11	ck	ck	NOUN
ap-3483	299	12	=	=	SYM
ap-3483	299	13	1	1	NUM
ap-3483	299	14	n	n	CCONJ
ap-3483	299	15	(	(	PUNCT
ap-3483	299	16	1	1	NUM
ap-3483	299	17	+	+	NUM
ap-3483	299	18	2k	2k	NUM
ap-3483	299	19	)	)	PUNCT
ap-3483	299	20	.	.	PUNCT
ap-3483	300	1	(	(	PUNCT
ap-3483	300	2	4.9	4.9	NUM
ap-3483	300	3	)	)	PUNCT
ap-3483	300	4	the	the	DET
ap-3483	300	5	lsp	lsp	PROPN
ap-3483	300	6	associated	associate	VERB
ap-3483	300	7	with	with	ADP
ap-3483	300	8	(	(	PUNCT
ap-3483	300	9	4.6	4.6	NUM
ap-3483	300	10	)	)	PUNCT
ap-3483	300	11	is	be	AUX
ap-3483	300	12	given	give	VERB
ap-3483	300	13	by	by	ADP
ap-3483	300	14	[	[	X
ap-3483	300	15	27	27	NUM
ap-3483	300	16	,	,	PUNCT
ap-3483	300	17	36	36	NUM
ap-3483	300	18	]	]	PUNCT
ap-3483	300	19	∂αφk	∂αφk	VERB
ap-3483	301	1	=	=	NOUN
ap-3483	301	2	uαkφk	uαkφk	NOUN
ap-3483	301	3	,	,	PUNCT
ap-3483	301	4	uαk	uαk	ADP
ap-3483	301	5	=	=	SYM
ap-3483	301	6	2	2	NUM
ap-3483	301	7	1±	1±	NUM
ap-3483	301	8	λ	λ	X
ap-3483	301	9	[	[	X
ap-3483	301	10	∂αpk	∂αpk	X
ap-3483	301	11	,	,	PUNCT
ap-3483	301	12	pk	pk	NOUN
ap-3483	301	13	]	]	X
ap-3483	301	14	,	,	PUNCT
ap-3483	301	15	(	(	PUNCT
ap-3483	301	16	u1k)†	u1k)†	PROPN
ap-3483	301	17	=	=	SYM
ap-3483	301	18	−u2k	−u2k	NOUN
ap-3483	301	19	,	,	PUNCT
ap-3483	301	20	(	(	PUNCT
ap-3483	301	21	4.10	4.10	NUM
ap-3483	301	22	)	)	PUNCT
ap-3483	301	23	(	(	PUNCT
ap-3483	301	24	where	where	SCONJ
ap-3483	301	25	α	α	NOUN
ap-3483	301	26	=	=	SYM
ap-3483	301	27	1	1	NUM
ap-3483	301	28	,	,	PUNCT
ap-3483	301	29	2	2	NUM
ap-3483	301	30	stands	stand	VERB
ap-3483	301	31	for	for	ADP
ap-3483	301	32	±	±	NUM
ap-3483	301	33	)	)	PUNCT
ap-3483	301	34	with	with	ADP
ap-3483	301	35	soliton	soliton	NOUN
ap-3483	301	36	solution	solution	NOUN
ap-3483	301	37	φk	φk	ADP
ap-3483	301	38	=	=	PUNCT
ap-3483	301	39	φk([p	φk([p	PROPN
ap-3483	301	40	]	]	PUNCT
ap-3483	301	41	,	,	PUNCT
ap-3483	301	42	λ	λ	NOUN
ap-3483	301	43	)	)	PUNCT
ap-3483	301	44	∈	∈	PROPN
ap-3483	301	45	su(n	su(n	NOUN
ap-3483	301	46	)	)	PUNCT
ap-3483	301	47	which	which	PRON
ap-3483	301	48	goes	go	VERB
ap-3483	301	49	to	to	ADP
ap-3483	301	50	in	in	ADP
ap-3483	301	51	as	as	ADP
ap-3483	301	52	λ→∞	λ→∞	X
ap-3483	301	53	[	[	X
ap-3483	301	54	36	36	NUM
ap-3483	301	55	,	,	PUNCT
ap-3483	301	56	37	37	NUM
ap-3483	301	57	]	]	PUNCT
ap-3483	301	58	φk	φk	ADP
ap-3483	301	59	=	=	PUNCT
ap-3483	301	60	in	in	ADP
ap-3483	301	61	+	+	ADJ
ap-3483	301	62	4λ	4λ	NOUN
ap-3483	301	63	(	(	PUNCT
ap-3483	301	64	1−	1−	NUM
ap-3483	301	65	λ)2	λ)2	NOUN
ap-3483	301	66	k−1∑	k−1∑	PROPN
ap-3483	301	67	j=0	j=0	PROPN
ap-3483	301	68	pj	pj	PROPN
ap-3483	301	69	−	−	PROPN
ap-3483	301	70	2	2	NUM
ap-3483	301	71	1−	1−	NUM
ap-3483	301	72	λpk	λpk	NOUN
ap-3483	301	73	,	,	PUNCT
ap-3483	301	74	φ−1	φ−1	PROPN
ap-3483	301	75	k	k	PROPN
ap-3483	302	1	=	=	PUNCT
ap-3483	302	2	in	in	ADP
ap-3483	302	3	−	−	PROPN
ap-3483	302	4	4λ	4λ	NOUN
ap-3483	302	5	(	(	PUNCT
ap-3483	302	6	1	1	NUM
ap-3483	302	7	+	+	CCONJ
ap-3483	302	8	λ)2	λ)2	PROPN
ap-3483	302	9	k−1∑	k−1∑	PROPN
ap-3483	302	10	j=0	j=0	PROPN
ap-3483	302	11	pj	pj	PROPN
ap-3483	302	12	−	−	NUM
ap-3483	302	13	2	2	NUM
ap-3483	302	14	1	1	NUM
ap-3483	302	15	+	+	NUM
ap-3483	302	16	λ	λ	PROPN
ap-3483	302	17	pk	pk	NOUN
ap-3483	302	18	,	,	PUNCT
ap-3483	302	19	λ	λ	X
ap-3483	302	20	=	=	VERB
ap-3483	302	21	it	it	PRON
ap-3483	302	22	,	,	PUNCT
ap-3483	302	23	t	t	PROPN
ap-3483	302	24	∈	∈	PROPN
ap-3483	302	25	r.	r.	PROPN
ap-3483	302	26	(	(	PUNCT
ap-3483	302	27	4.11	4.11	NUM
ap-3483	302	28	)	)	PUNCT
ap-3483	302	29	the	the	DET
ap-3483	302	30	recurrence	recurrence	NOUN
ap-3483	302	31	relation	relation	NOUN
ap-3483	302	32	(	(	PUNCT
ap-3483	302	33	4.4	4.4	NUM
ap-3483	302	34	)	)	PUNCT
ap-3483	302	35	is	be	AUX
ap-3483	302	36	expressed	express	VERB
ap-3483	302	37	in	in	ADP
ap-3483	302	38	terms	term	NOUN
ap-3483	302	39	of	of	ADP
ap-3483	302	40	rank-1	rank-1	NUM
ap-3483	302	41	projectors	projector	NOUN
ap-3483	302	42	pk	pk	NOUN
ap-3483	302	43	,	,	PUNCT
ap-3483	302	44	without	without	ADP
ap-3483	302	45	any	any	DET
ap-3483	302	46	reference	reference	NOUN
ap-3483	302	47	to	to	ADP
ap-3483	302	48	the	the	DET
ap-3483	302	49	sequence	sequence	NOUN
ap-3483	302	50	of	of	ADP
ap-3483	302	51	functions	function	NOUN
ap-3483	302	52	fk	fk	INTJ
ap-3483	302	53	as	as	ADP
ap-3483	302	54	in	in	ADP
ap-3483	302	55	(	(	PUNCT
ap-3483	302	56	4.2	4.2	NUM
ap-3483	302	57	)	)	PUNCT
ap-3483	302	58	.	.	PUNCT
ap-3483	303	1	for	for	ADP
ap-3483	303	2	the	the	DET
ap-3483	303	3	sake	sake	NOUN
ap-3483	303	4	of	of	ADP
ap-3483	303	5	simplicity	simplicity	NOUN
ap-3483	303	6	,	,	PUNCT
ap-3483	303	7	in	in	ADP
ap-3483	303	8	this	this	DET
ap-3483	303	9	section	section	NOUN
ap-3483	303	10	,	,	PUNCT
ap-3483	303	11	we	we	PRON
ap-3483	303	12	drop	drop	VERB
ap-3483	303	13	the	the	DET
ap-3483	303	14	index	index	NOUN
ap-3483	303	15	k	k	PROPN
ap-3483	303	16	attributed	attribute	VERB
ap-3483	303	17	to	to	ADP
ap-3483	303	18	the	the	DET
ap-3483	303	19	n	n	PROPN
ap-3483	303	20	projectors	projector	NOUN
ap-3483	303	21	pk	pk	NOUN
ap-3483	303	22	.	.	PUNCT
ap-3483	304	1	it	it	PRON
ap-3483	304	2	is	be	AUX
ap-3483	304	3	convenient	convenient	ADJ
ap-3483	304	4	for	for	SCONJ
ap-3483	304	5	computational	computational	ADJ
ap-3483	304	6	purposes	purpose	NOUN
ap-3483	304	7	to	to	PART
ap-3483	304	8	express	express	VERB
ap-3483	304	9	the	the	DET
ap-3483	304	10	cpn−1	cpn−1	PROPN
ap-3483	304	11	model	model	NOUN
ap-3483	304	12	in	in	ADP
ap-3483	304	13	terms	term	NOUN
ap-3483	304	14	of	of	ADP
ap-3483	304	15	the	the	DET
ap-3483	304	16	matrix	matrix	NOUN
ap-3483	304	17	θ	θ	PROPN
ap-3483	304	18	≡	≡	PROPN
ap-3483	305	1	i	i	PRON
ap-3483	305	2	(	(	PUNCT
ap-3483	305	3	p	p	NOUN
ap-3483	305	4	−	−	PROPN
ap-3483	305	5	1	1	NUM
ap-3483	305	6	n	n	NOUN
ap-3483	305	7	in	in	ADP
ap-3483	305	8	)	)	PUNCT
ap-3483	305	9	=	=	PUNCT
ap-3483	305	10	θses	θse	VERB
ap-3483	305	11	∈	∈	NOUN
ap-3483	305	12	su(n	su(n	NOUN
ap-3483	305	13	)	)	PUNCT
ap-3483	305	14	,	,	PUNCT
ap-3483	306	1	[	[	X
ap-3483	306	2	ej	ej	X
ap-3483	306	3	,	,	PUNCT
ap-3483	306	4	el	el	PROPN
ap-3483	306	5	]	]	X
ap-3483	306	6	=	=	SYM
ap-3483	306	7	csjles	csjle	NOUN
ap-3483	306	8	,	,	PUNCT
ap-3483	306	9	j	j	NOUN
ap-3483	306	10	,	,	PUNCT
ap-3483	306	11	l	l	PROPN
ap-3483	306	12	,	,	PUNCT
ap-3483	306	13	s	s	PART
ap-3483	306	14	=	=	NOUN
ap-3483	306	15	1	1	NUM
ap-3483	306	16	,	,	PUNCT
ap-3483	306	17	.	.	PUNCT
ap-3483	306	18	.	.	PUNCT
ap-3483	307	1	.	.	PUNCT
ap-3483	308	1	,	,	PUNCT
ap-3483	308	2	n2	n2	ADJ
ap-3483	308	3	−	−	PROPN
ap-3483	308	4	1	1	NUM
ap-3483	308	5	,	,	PUNCT
ap-3483	308	6	(	(	PUNCT
ap-3483	308	7	4.12	4.12	NUM
ap-3483	308	8	)	)	PUNCT
ap-3483	308	9	where	where	SCONJ
ap-3483	308	10	csjl	csjl	NOUN
ap-3483	308	11	are	be	AUX
ap-3483	308	12	the	the	DET
ap-3483	308	13	structural	structural	ADJ
ap-3483	308	14	constants	constant	NOUN
ap-3483	308	15	of	of	ADP
ap-3483	308	16	g	g	PROPN
ap-3483	308	17	and	and	CCONJ
ap-3483	308	18	es	es	PRON
ap-3483	308	19	is	be	AUX
ap-3483	308	20	the	the	DET
ap-3483	308	21	basis	basis	NOUN
ap-3483	308	22	element	element	NOUN
ap-3483	308	23	for	for	ADP
ap-3483	308	24	the	the	DET
ap-3483	308	25	su(n	su(n	NOUN
ap-3483	308	26	)	)	PUNCT
ap-3483	308	27	algebra	algebra	NOUN
ap-3483	308	28	.	.	PUNCT
ap-3483	309	1	due	due	ADP
ap-3483	309	2	to	to	ADP
ap-3483	309	3	the	the	DET
ap-3483	309	4	indempotency	indempotency	NOUN
ap-3483	309	5	of	of	ADP
ap-3483	309	6	the	the	DET
ap-3483	309	7	projector	projector	NOUN
ap-3483	309	8	p	p	NOUN
ap-3483	309	9	we	we	PRON
ap-3483	309	10	get	get	VERB
ap-3483	309	11	the	the	DET
ap-3483	309	12	following	follow	VERB
ap-3483	309	13	algebraic	algebraic	ADJ
ap-3483	309	14	restriction	restriction	NOUN
ap-3483	309	15	on	on	ADP
ap-3483	309	16	θ	θ	PROPN
ap-3483	309	17	:	:	PUNCT
ap-3483	309	18	θ	θ	X
ap-3483	309	19	·	·	PUNCT
ap-3483	309	20	θ	θ	X
ap-3483	310	1	=	=	PUNCT
ap-3483	310	2	−i2−n	−i2−n	PROPN
ap-3483	310	3	n	n	NUM
ap-3483	310	4	θ	θ	NOUN
ap-3483	310	5	+	+	CCONJ
ap-3483	310	6	1−n	1−n	NUM
ap-3483	310	7	n2	n2	NOUN
ap-3483	310	8	in	in	ADP
ap-3483	310	9	⇐	⇐	ADJ
ap-3483	310	10	⇒	⇒	NOUN
ap-3483	310	11	p	p	X
ap-3483	310	12	2	2	NUM
ap-3483	310	13	=	=	SYM
ap-3483	310	14	p.	p.	NOUN
ap-3483	310	15	(	(	PUNCT
ap-3483	310	16	4.13	4.13	NUM
ap-3483	310	17	)	)	PUNCT
ap-3483	310	18	the	the	DET
ap-3483	310	19	equations	equation	NOUN
ap-3483	310	20	of	of	ADP
ap-3483	310	21	motion	motion	NOUN
ap-3483	310	22	in	in	ADP
ap-3483	310	23	terms	term	NOUN
ap-3483	310	24	of	of	ADP
ap-3483	310	25	the	the	DET
ap-3483	310	26	matrix	matrix	NOUN
ap-3483	310	27	θ	θ	NOUN
ap-3483	310	28	are	be	AUX
ap-3483	310	29	ωj	ωj	ADP
ap-3483	310	30	[	[	X
ap-3483	310	31	θ	θ	X
ap-3483	310	32	]	]	X
ap-3483	310	33	=	=	X
ap-3483	310	34	[	[	PUNCT
ap-3483	310	35	(	(	PUNCT
ap-3483	310	36	∂2	∂2	NOUN
ap-3483	310	37	1	1	NUM
ap-3483	310	38	+	+	CCONJ
ap-3483	310	39	∂2	∂2	PROPN
ap-3483	310	40	2)θ	2)θ	NOUN
ap-3483	310	41	,	,	PUNCT
ap-3483	310	42	θ	θ	PROPN
ap-3483	310	43	]	]	X
ap-3483	310	44	j	j	X
ap-3483	310	45	=	=	SYM
ap-3483	310	46	0	0	PROPN
ap-3483	310	47	,	,	PUNCT
ap-3483	310	48	j	j	PROPN
ap-3483	310	49	=	=	SYM
ap-3483	310	50	1	1	NUM
ap-3483	310	51	,	,	PUNCT
ap-3483	310	52	.	.	PUNCT
ap-3483	310	53	.	.	PUNCT
ap-3483	310	54	.	.	PUNCT
ap-3483	311	1	,	,	PUNCT
ap-3483	311	2	n2	n2	ADJ
ap-3483	311	3	−	−	PROPN
ap-3483	311	4	1	1	NUM
ap-3483	311	5	(	(	PUNCT
ap-3483	311	6	4.14	4.14	NUM
ap-3483	311	7	)	)	PUNCT
ap-3483	312	1	where	where	SCONJ
ap-3483	312	2	[	[	X
ap-3483	312	3	·	·	PUNCT
ap-3483	312	4	,	,	PUNCT
ap-3483	312	5	·	·	PUNCT
ap-3483	312	6	]	]	X
ap-3483	312	7	j	j	PROPN
ap-3483	312	8	denotes	denote	VERB
ap-3483	312	9	the	the	DET
ap-3483	312	10	coefficients	coefficient	NOUN
ap-3483	312	11	of	of	ADP
ap-3483	312	12	the	the	DET
ap-3483	312	13	commutator	commutator	NOUN
ap-3483	312	14	with	with	ADP
ap-3483	312	15	respect	respect	NOUN
ap-3483	312	16	to	to	ADP
ap-3483	312	17	the	the	DET
ap-3483	312	18	jth	jth	PROPN
ap-3483	312	19	basis	basis	NOUN
ap-3483	312	20	element	element	NOUN
ap-3483	312	21	ej	ej	PROPN
ap-3483	312	22	for	for	ADP
ap-3483	312	23	the	the	DET
ap-3483	312	24	su(n	su(n	NOUN
ap-3483	312	25	)	)	PUNCT
ap-3483	312	26	algebra	algebra	NOUN
ap-3483	312	27	.	.	PUNCT
ap-3483	313	1	the	the	DET
ap-3483	313	2	potential	potential	ADJ
ap-3483	313	3	matrices	matrix	NOUN
ap-3483	313	4	uα	uα	X
ap-3483	313	5	in	in	ADP
ap-3483	313	6	terms	term	NOUN
ap-3483	313	7	of	of	ADP
ap-3483	313	8	θ	θ	PROPN
ap-3483	313	9	are	be	AUX
ap-3483	313	10	u1	u1	NOUN
ap-3483	313	11	=	=	SYM
ap-3483	313	12	−2	−2	PROPN
ap-3483	313	13	1−	1−	NUM
ap-3483	313	14	λ2	λ2	NOUN
ap-3483	313	15	(	(	PUNCT
ap-3483	313	16	[	[	X
ap-3483	313	17	∂1θ	∂1θ	NOUN
ap-3483	313	18	,	,	PUNCT
ap-3483	313	19	θ]−	θ]−	ADP
ap-3483	313	20	iλ[∂2θ	iλ[∂2θ	ADJ
ap-3483	313	21	,	,	PUNCT
ap-3483	313	22	θ	θ	NOUN
ap-3483	313	23	]	]	PUNCT
ap-3483	313	24	)	)	PUNCT
ap-3483	313	25	,	,	PUNCT
ap-3483	313	26	u2	u2	NOUN
ap-3483	313	27	=	=	PUNCT
ap-3483	313	28	−2	−2	PROPN
ap-3483	313	29	1−	1−	NUM
ap-3483	313	30	λ2	λ2	NOUN
ap-3483	313	31	(	(	PUNCT
ap-3483	313	32	iλ[∂1θ	iλ[∂1θ	PROPN
ap-3483	313	33	,	,	PUNCT
ap-3483	313	34	θ	θ	X
ap-3483	313	35	]	]	PUNCT
ap-3483	314	1	+	+	CCONJ
ap-3483	314	2	[	[	X
ap-3483	314	3	∂2θ	∂2θ	NOUN
ap-3483	314	4	,	,	PUNCT
ap-3483	314	5	θ	θ	X
ap-3483	314	6	]	]	PUNCT
ap-3483	314	7	)	)	PUNCT
ap-3483	314	8	,	,	PUNCT
ap-3483	314	9	λ	λ	X
ap-3483	314	10	=	=	VERB
ap-3483	314	11	it	it	PRON
ap-3483	314	12	,	,	PUNCT
ap-3483	314	13	t	t	PROPN
ap-3483	314	14	∈	∈	PROPN
ap-3483	314	15	r.	r.	PROPN
ap-3483	314	16	(	(	PUNCT
ap-3483	314	17	4.15	4.15	NUM
ap-3483	314	18	)	)	PUNCT
ap-3483	314	19	the	the	DET
ap-3483	314	20	wavefunction	wavefunction	NOUN
ap-3483	314	21	φ	φ	PROPN
ap-3483	314	22	in	in	ADP
ap-3483	314	23	terms	term	NOUN
ap-3483	314	24	of	of	ADP
ap-3483	314	25	θ	θ	PROPN
ap-3483	314	26	is	be	AUX
ap-3483	314	27	φ([θ	φ([θ	NOUN
ap-3483	314	28	]	]	X
ap-3483	314	29	,	,	PUNCT
ap-3483	314	30	λ	λ	NOUN
ap-3483	314	31	)	)	PUNCT
ap-3483	314	32	=	=	NOUN
ap-3483	314	33	in	in	ADP
ap-3483	314	34	+	+	ADJ
ap-3483	314	35	4λ	4λ	NOUN
ap-3483	314	36	(	(	PUNCT
ap-3483	314	37	1−	1−	NUM
ap-3483	314	38	λ)2	λ)2	NOUN
ap-3483	314	39	k−1∑	k−1∑	PROPN
ap-3483	314	40	j=0	j=0	PROPN
ap-3483	314	41	πj	πj	VERB
ap-3483	314	42	−(θ	−(θ	NOUN
ap-3483	314	43	)	)	PUNCT
ap-3483	315	1	−	−	PROPN
ap-3483	315	2	2	2	NUM
ap-3483	316	1	1−	1−	NUM
ap-3483	316	2	λ	λ	X
ap-3483	316	3	(	(	PUNCT
ap-3483	316	4	1	1	NUM
ap-3483	316	5	n	n	NOUN
ap-3483	316	6	in	in	ADP
ap-3483	316	7	−	−	PROPN
ap-3483	316	8	iθ	iθ	NOUN
ap-3483	316	9	)	)	PUNCT
ap-3483	316	10	∈	∈	PROPN
ap-3483	316	11	su	su	PROPN
ap-3483	316	12	(	(	PUNCT
ap-3483	316	13	n	n	CCONJ
ap-3483	316	14	)	)	PUNCT
ap-3483	316	15	,	,	PUNCT
ap-3483	316	16	(	(	PUNCT
ap-3483	316	17	4.16	4.16	NUM
ap-3483	316	18	)	)	PUNCT
ap-3483	316	19	where	where	SCONJ
ap-3483	316	20	π±	π±	PRON
ap-3483	316	21	are	be	AUX
ap-3483	316	22	the	the	DET
ap-3483	316	23	raising	raising	NOUN
ap-3483	316	24	and	and	CCONJ
ap-3483	316	25	lowering	lower	VERB
ap-3483	316	26	operators	operator	NOUN
ap-3483	316	27	acting	act	VERB
ap-3483	316	28	on	on	ADP
ap-3483	316	29	the	the	DET
ap-3483	316	30	elements	element	NOUN
ap-3483	316	31	θ	θ	PROPN
ap-3483	316	32	of	of	ADP
ap-3483	316	33	the	the	DET
ap-3483	316	34	algebra	algebra	NOUN
ap-3483	316	35	su(n	su(n	NOUN
ap-3483	316	36	)	)	PUNCT
ap-3483	316	37	π−(θk	π−(θk	NOUN
ap-3483	316	38	)	)	PUNCT
ap-3483	316	39	=	=	SYM
ap-3483	316	40	θk−1	θk−1	PROPN
ap-3483	316	41	,	,	PUNCT
ap-3483	316	42	π+(θk	π+(θk	PROPN
ap-3483	316	43	)	)	PUNCT
ap-3483	316	44	=	=	PUNCT
ap-3483	316	45	θk+1	θk+1	X
ap-3483	316	46	.	.	X
ap-3483	316	47	(	(	PUNCT
ap-3483	316	48	4.17	4.17	NUM
ap-3483	316	49	)	)	PUNCT
ap-3483	316	50	in	in	ADP
ap-3483	316	51	what	what	PRON
ap-3483	316	52	follows	follow	VERB
ap-3483	316	53	,	,	PUNCT
ap-3483	316	54	we	we	PRON
ap-3483	316	55	use	use	VERB
ap-3483	316	56	the	the	DET
ap-3483	316	57	simplified	simplified	ADJ
ap-3483	316	58	notation	notation	NOUN
ap-3483	316	59	of	of	ADP
ap-3483	316	60	π±(θk	π±(θk	PROPN
ap-3483	316	61	)	)	PUNCT
ap-3483	316	62	by	by	ADP
ap-3483	316	63	π±(θ	π±(θ	PROPN
ap-3483	316	64	)	)	PUNCT
ap-3483	316	65	,	,	PUNCT
ap-3483	316	66	where	where	SCONJ
ap-3483	316	67	the	the	DET
ap-3483	316	68	index	index	NOUN
ap-3483	316	69	k	k	PROPN
ap-3483	316	70	is	be	AUX
ap-3483	316	71	suppressed	suppress	VERB
ap-3483	316	72	.	.	PUNCT
ap-3483	317	1	the	the	DET
ap-3483	317	2	operators	operator	NOUN
ap-3483	317	3	(	(	PUNCT
ap-3483	317	4	4.17	4.17	NUM
ap-3483	317	5	)	)	PUNCT
ap-3483	317	6	are	be	AUX
ap-3483	317	7	written	write	VERB
ap-3483	317	8	explicitly	explicitly	ADV
ap-3483	317	9	as	as	ADP
ap-3483	317	10	π−(θ	π−(θ	NOUN
ap-3483	317	11	)	)	PUNCT
ap-3483	317	12	=	=	PUNCT
ap-3483	318	1	∂̄θ(e	∂̄θ(e	PROPN
ap-3483	318	2	−	−	PROPN
ap-3483	318	3	iθ)∂θ	iθ)∂θ	NOUN
ap-3483	318	4	tr(∂̄θ(e	tr(∂̄θ(e	NOUN
ap-3483	318	5	−	−	PROPN
ap-3483	318	6	iθ)∂θ	iθ)∂θ	NOUN
ap-3483	318	7	)	)	PUNCT
ap-3483	318	8	,	,	PUNCT
ap-3483	318	9	π+(θ	π+(θ	NOUN
ap-3483	318	10	)	)	PUNCT
ap-3483	318	11	=	=	SYM
ap-3483	319	1	∂θ(e	∂θ(e	NOUN
ap-3483	319	2	−	−	NOUN
ap-3483	319	3	iθ)∂̄θ	iθ)∂̄θ	NOUN
ap-3483	319	4	tr(∂θ(e	tr(∂θ(e	ADJ
ap-3483	319	5	−	−	NOUN
ap-3483	319	6	iθ)∂̄θ	iθ)∂̄θ	NOUN
ap-3483	319	7	)	)	PUNCT
ap-3483	319	8	,	,	PUNCT
ap-3483	320	1	e	e	X
ap-3483	320	2	=	=	SYM
ap-3483	320	3	1	1	NUM
ap-3483	320	4	n	n	CCONJ
ap-3483	320	5	in	in	ADV
ap-3483	320	6	,	,	PUNCT
ap-3483	320	7	(	(	PUNCT
ap-3483	320	8	4.18	4.18	NUM
ap-3483	320	9	)	)	PUNCT
ap-3483	320	10	where	where	SCONJ
ap-3483	320	11	the	the	DET
ap-3483	320	12	traces	trace	NOUN
ap-3483	320	13	in	in	ADP
ap-3483	320	14	the	the	DET
ap-3483	320	15	denominators	denominator	NOUN
ap-3483	320	16	are	be	AUX
ap-3483	320	17	different	different	ADJ
ap-3483	320	18	from	from	ADP
ap-3483	320	19	zero	zero	NUM
ap-3483	320	20	unless	unless	SCONJ
ap-3483	320	21	the	the	DET
ap-3483	320	22	whole	whole	ADJ
ap-3483	320	23	matrix	matrix	NOUN
ap-3483	320	24	is	be	AUX
ap-3483	320	25	zero	zero	NUM
ap-3483	320	26	.	.	PUNCT
ap-3483	321	1	for	for	ADP
ap-3483	321	2	any	any	DET
ap-3483	321	3	functions	function	NOUN
ap-3483	321	4	f	f	PROPN
ap-3483	321	5	and	and	CCONJ
ap-3483	321	6	g	g	PROPN
ap-3483	321	7	of	of	ADP
ap-3483	321	8	one	one	NUM
ap-3483	321	9	variable	variable	NOUN
ap-3483	321	10	,	,	PUNCT
ap-3483	321	11	the	the	DET
ap-3483	321	12	equations	equation	NOUN
ap-3483	321	13	of	of	ADP
ap-3483	321	14	motion	motion	NOUN
ap-3483	321	15	(	(	PUNCT
ap-3483	321	16	4.14	4.14	NUM
ap-3483	321	17	)	)	PUNCT
ap-3483	321	18	and	and	CCONJ
ap-3483	321	19	their	their	PRON
ap-3483	321	20	lsp	lsp	PROPN
ap-3483	321	21	(	(	PUNCT
ap-3483	321	22	2.15	2.15	NUM
ap-3483	321	23	)	)	PUNCT
ap-3483	321	24	(	(	PUNCT
ap-3483	321	25	with	with	ADP
ap-3483	321	26	the	the	DET
ap-3483	321	27	potential	potential	ADJ
ap-3483	321	28	matrices	matrix	NOUN
ap-3483	321	29	(	(	PUNCT
ap-3483	321	30	4.15	4.15	NUM
ap-3483	321	31	)	)	PUNCT
ap-3483	321	32	)	)	PUNCT
ap-3483	321	33	admit	admit	VERB
ap-3483	321	34	the	the	DET
ap-3483	321	35	conformal	conformal	ADJ
ap-3483	321	36	symmetries	symmetry	NOUN
ap-3483	321	37	ωci	ωci	NOUN
ap-3483	321	38	=	=	PUNCT
ap-3483	321	39	[	[	PUNCT
ap-3483	321	40	f(x)∂1θ	f(x)∂1θ	NUM
ap-3483	321	41	j	j	PROPN
ap-3483	321	42	+	+	CCONJ
ap-3483	321	43	g(y)∂2θ	g(y)∂2θ	PROPN
ap-3483	321	44	j	j	PROPN
ap-3483	321	45	]	]	PUNCT
ap-3483	321	46	∂	∂	NUM
ap-3483	321	47	∂θj	∂θj	NOUN
ap-3483	321	48	,	,	PUNCT
ap-3483	321	49	i	i	PRON
ap-3483	321	50	=	=	NOUN
ap-3483	321	51	1	1	NUM
ap-3483	321	52	,	,	PUNCT
ap-3483	321	53	2	2	NUM
ap-3483	321	54	.	.	PUNCT
ap-3483	321	55	(	(	PUNCT
ap-3483	321	56	4.19	4.19	NUM
ap-3483	321	57	)	)	PUNCT
ap-3483	321	58	the	the	DET
ap-3483	321	59	vector	vector	NOUN
ap-3483	321	60	fields	field	NOUN
ap-3483	321	61	ωci	ωci	NOUN
ap-3483	321	62	are	be	AUX
ap-3483	321	63	related	relate	VERB
ap-3483	321	64	to	to	ADP
ap-3483	321	65	the	the	DET
ap-3483	321	66	fields	field	NOUN
ap-3483	321	67	ηci	ηci	VERB
ap-3483	321	68	defined	define	VERB
ap-3483	321	69	on	on	ADP
ap-3483	321	70	the	the	DET
ap-3483	321	71	jet	jet	NOUN
ap-3483	321	72	spacem	spacem	NOUN
ap-3483	321	73	=	=	PUNCT
ap-3483	322	1	[	[	X
ap-3483	322	2	(	(	PUNCT
ap-3483	322	3	φ	φ	PROPN
ap-3483	322	4	,	,	PUNCT
ap-3483	322	5	uα	uα	PROPN
ap-3483	322	6	)	)	PUNCT
ap-3483	322	7	]	]	PUNCT
ap-3483	322	8	ηci	ηci	PROPN
ap-3483	322	9	=	=	SYM
ap-3483	322	10	(	(	PUNCT
ap-3483	322	11	∂iφj	∂iφj	NOUN
ap-3483	322	12	)	)	PUNCT
ap-3483	322	13	∂	∂	NUM
ap-3483	322	14	∂φj	∂φj	PROPN
ap-3483	322	15	+	+	CCONJ
ap-3483	322	16	(	(	PUNCT
ap-3483	322	17	∂iu	∂iu	PROPN
ap-3483	322	18	jα	jα	PROPN
ap-3483	322	19	)	)	PUNCT
ap-3483	322	20	∂	∂	NOUN
ap-3483	322	21	∂u	∂u	PROPN
ap-3483	322	22	jα	jα	NOUN
ap-3483	322	23	,	,	PUNCT
ap-3483	322	24	i	i	PRON
ap-3483	322	25	=	=	NOUN
ap-3483	322	26	1	1	NUM
ap-3483	322	27	,	,	PUNCT
ap-3483	322	28	2	2	NUM
ap-3483	322	29	,	,	PUNCT
ap-3483	322	30	(	(	PUNCT
ap-3483	322	31	4.20	4.20	NUM
ap-3483	322	32	)	)	PUNCT
ap-3483	322	33	which	which	PRON
ap-3483	322	34	are	be	AUX
ap-3483	322	35	conformal	conformal	ADJ
ap-3483	322	36	symmetries	symmetry	NOUN
ap-3483	322	37	of	of	ADP
ap-3483	322	38	the	the	DET
ap-3483	322	39	lsp	lsp	PROPN
ap-3483	322	40	(	(	PUNCT
ap-3483	322	41	2.15	2.15	NUM
ap-3483	322	42	)	)	PUNCT
ap-3483	322	43	.	.	PUNCT
ap-3483	323	1	the	the	DET
ap-3483	323	2	integrated	integrate	VERB
ap-3483	323	3	form	form	NOUN
ap-3483	323	4	of	of	ADP
ap-3483	323	5	the	the	DET
ap-3483	323	6	surface	surface	NOUN
ap-3483	323	7	is	be	AUX
ap-3483	323	8	given	give	VERB
ap-3483	323	9	by	by	ADP
ap-3483	323	10	the	the	DET
ap-3483	323	11	fg	fg	PROPN
ap-3483	323	12	formula	formula	NOUN
ap-3483	323	13	[	[	X
ap-3483	323	14	15	15	NUM
ap-3483	323	15	]	]	X
ap-3483	323	16	ffg	ffg	X
ap-3483	323	17	=	=	SYM
ap-3483	323	18	φ−1(f(x)u1	φ−1(f(x)u1	NOUN
ap-3483	323	19	+	+	NUM
ap-3483	323	20	g(y)u2	g(y)u2	NOUN
ap-3483	323	21	)	)	PUNCT
ap-3483	323	22	φ	φ	PROPN
ap-3483	323	23	∈	∈	PROPN
ap-3483	323	24	su(n	su(n	PROPN
ap-3483	323	25	)	)	PUNCT
ap-3483	323	26	.	.	PUNCT
ap-3483	324	1	(	(	PUNCT
ap-3483	324	2	4.21	4.21	NUM
ap-3483	324	3	)	)	PUNCT
ap-3483	324	4	4.1	4.1	NUM
ap-3483	324	5	.	.	PUNCT
ap-3483	325	1	soliton	soliton	NOUN
ap-3483	325	2	surfaces	surface	NOUN
ap-3483	325	3	associated	associate	VERB
ap-3483	325	4	with	with	ADP
ap-3483	325	5	the	the	DET
ap-3483	325	6	cp	cp	PROPN
ap-3483	325	7	1	1	PROPN
ap-3483	325	8	sigma	sigma	PROPN
ap-3483	325	9	model	model	NOUN
ap-3483	325	10	we	we	PRON
ap-3483	325	11	give	give	VERB
ap-3483	325	12	a	a	DET
ap-3483	325	13	simple	simple	ADJ
ap-3483	325	14	example	example	NOUN
ap-3483	325	15	to	to	PART
ap-3483	325	16	illustrate	illustrate	VERB
ap-3483	325	17	the	the	DET
ap-3483	325	18	construction	construction	NOUN
ap-3483	325	19	of	of	ADP
ap-3483	325	20	2d	2d	NOUN
ap-3483	325	21	-	-	PUNCT
ap-3483	325	22	soliton	soliton	NOUN
ap-3483	325	23	surfaces	surface	NOUN
ap-3483	325	24	associated	associate	VERB
ap-3483	325	25	with	with	ADP
ap-3483	325	26	the	the	DET
ap-3483	325	27	cp	cp	PROPN
ap-3483	325	28	1	1	NUM
ap-3483	325	29	187	187	NUM
ap-3483	325	30	a.	a.	NOUN
ap-3483	325	31	m.	m.	NOUN
ap-3483	325	32	grundland	grundland	PROPN
ap-3483	325	33	,	,	PUNCT
ap-3483	325	34	d.	d.	PROPN
ap-3483	325	35	levi	levi	PROPN
ap-3483	325	36	,	,	PUNCT
ap-3483	325	37	l.	l.	PROPN
ap-3483	325	38	martina	martina	PROPN
ap-3483	325	39	acta	acta	PROPN
ap-3483	325	40	polytechnica	polytechnica	PROPN
ap-3483	325	41	model	model	NOUN
ap-3483	325	42	(	(	PUNCT
ap-3483	325	43	n	n	NOUN
ap-3483	325	44	=	=	SYM
ap-3483	325	45	2	2	NUM
ap-3483	325	46	)	)	PUNCT
ap-3483	325	47	introduced	introduce	VERB
ap-3483	325	48	in	in	ADP
ap-3483	325	49	previous	previous	ADJ
ap-3483	325	50	section	section	NOUN
ap-3483	325	51	.	.	PUNCT
ap-3483	326	1	the	the	DET
ap-3483	326	2	only	only	ADJ
ap-3483	326	3	solutions	solution	NOUN
ap-3483	326	4	with	with	ADP
ap-3483	326	5	finite	finite	ADJ
ap-3483	326	6	action	action	NOUN
ap-3483	326	7	of	of	ADP
ap-3483	326	8	the	the	DET
ap-3483	326	9	cp	cp	PROPN
ap-3483	326	10	1	1	NUM
ap-3483	326	11	model	model	NOUN
ap-3483	326	12	are	be	AUX
ap-3483	326	13	holomorphic	holomorphic	ADJ
ap-3483	326	14	and	and	CCONJ
ap-3483	326	15	antiholomorphic	antiholomorphic	ADJ
ap-3483	326	16	projectors	projector	NOUN
ap-3483	326	17	[	[	X
ap-3483	326	18	37	37	NUM
ap-3483	326	19	]	]	PUNCT
ap-3483	326	20	.	.	PUNCT
ap-3483	327	1	the	the	DET
ap-3483	327	2	rank	rank	NOUN
ap-3483	327	3	-	-	PUNCT
ap-3483	327	4	one	one	NUM
ap-3483	327	5	hermitian	hermitian	ADJ
ap-3483	327	6	projectors	projector	NOUN
ap-3483	327	7	(	(	PUNCT
ap-3483	327	8	i.e.	i.e.	X
ap-3483	327	9	holomorphic	holomorphic	ADJ
ap-3483	327	10	p0	p0	NOUN
ap-3483	327	11	and	and	CCONJ
ap-3483	327	12	antiholomorphic	antiholomorphic	ADJ
ap-3483	327	13	p1	p1	NOUN
ap-3483	327	14	)	)	PUNCT
ap-3483	327	15	based	base	VERB
ap-3483	327	16	on	on	ADP
ap-3483	327	17	the	the	DET
ap-3483	327	18	veronese	veronese	ADJ
ap-3483	327	19	sequence	sequence	NOUN
ap-3483	327	20	f0	f0	PROPN
ap-3483	327	21	=	=	PUNCT
ap-3483	327	22	(	(	PUNCT
ap-3483	327	23	1	1	NUM
ap-3483	327	24	,	,	PUNCT
ap-3483	327	25	z	z	NOUN
ap-3483	327	26	)	)	PUNCT
ap-3483	327	27	,	,	PUNCT
ap-3483	327	28	take	take	VERB
ap-3483	327	29	the	the	DET
ap-3483	327	30	form	form	NOUN
ap-3483	327	31	p0	p0	NOUN
ap-3483	327	32	=	=	SYM
ap-3483	327	33	f0	f0	PROPN
ap-3483	327	34	⊗	⊗	PROPN
ap-3483	327	35	f†0	f†0	PROPN
ap-3483	327	36	f†0f0	f†0f0	NOUN
ap-3483	327	37	=	=	SYM
ap-3483	327	38	1	1	NUM
ap-3483	327	39	1	1	NUM
ap-3483	327	40	+	+	NUM
ap-3483	327	41	|z|2	|z|2	NOUN
ap-3483	327	42	(	(	PUNCT
ap-3483	327	43	1	1	NUM
ap-3483	327	44	z̄	z̄	NOUN
ap-3483	327	45	z	z	PROPN
ap-3483	327	46	|z|2	|z|2	PROPN
ap-3483	327	47	)	)	PUNCT
ap-3483	327	48	,	,	PUNCT
ap-3483	327	49	p1	p1	PROPN
ap-3483	327	50	=	=	SYM
ap-3483	327	51	f1	f1	PROPN
ap-3483	327	52	⊗	⊗	PROPN
ap-3483	327	53	f†1	f†1	NOUN
ap-3483	327	54	f†1f1	f†1f1	X
ap-3483	327	55	=	=	SYM
ap-3483	328	1	1	1	NUM
ap-3483	328	2	1	1	NUM
ap-3483	328	3	+	+	NUM
ap-3483	328	4	|z|2	|z|2	NOUN
ap-3483	328	5	(	(	PUNCT
ap-3483	328	6	|z|2	|z|2	NOUN
ap-3483	328	7	−z̄	−z̄	NOUN
ap-3483	328	8	−z	−z	NOUN
ap-3483	328	9	1	1	NUM
ap-3483	328	10	)	)	PUNCT
ap-3483	328	11	,	,	PUNCT
ap-3483	328	12	(	(	PUNCT
ap-3483	328	13	4.22	4.22	NUM
ap-3483	328	14	)	)	PUNCT
ap-3483	328	15	where	where	SCONJ
ap-3483	328	16	f1	f1	NOUN
ap-3483	328	17	=	=	SYM
ap-3483	328	18	(	(	PUNCT
ap-3483	328	19	i2	i2	PROPN
ap-3483	328	20	−	−	PROPN
ap-3483	328	21	p0)∂f0	p0)∂f0	NUM
ap-3483	328	22	.	.	PUNCT
ap-3483	329	1	the	the	DET
ap-3483	329	2	corresponding	corresponding	ADJ
ap-3483	329	3	integrated	integrate	VERB
ap-3483	329	4	forms	form	NOUN
ap-3483	329	5	of	of	ADP
ap-3483	329	6	the	the	DET
ap-3483	329	7	surfaces	surface	NOUN
ap-3483	329	8	are	be	AUX
ap-3483	329	9	given	give	VERB
ap-3483	329	10	by	by	ADP
ap-3483	329	11	the	the	DET
ap-3483	329	12	gwfi	gwfi	NOUN
ap-3483	329	13	(	(	PUNCT
ap-3483	329	14	4.8	4.8	NUM
ap-3483	329	15	)	)	PUNCT
ap-3483	329	16	f0	f0	PROPN
ap-3483	329	17	=	=	SYM
ap-3483	329	18	i(1	i(1	PROPN
ap-3483	329	19	2	2	NUM
ap-3483	329	20	i2	i2	NOUN
ap-3483	329	21	−	−	PROPN
ap-3483	329	22	p0	p0	NOUN
ap-3483	329	23	)	)	PUNCT
ap-3483	330	1	=	=	SYM
ap-3483	330	2	i	i	PRON
ap-3483	330	3	1	1	NUM
ap-3483	330	4	+	+	NUM
ap-3483	330	5	|z|2	|z|2	NOUN
ap-3483	330	6	(	(	PUNCT
ap-3483	330	7	1	1	NUM
ap-3483	330	8	2	2	NUM
ap-3483	330	9	(	(	PUNCT
ap-3483	330	10	|z|2	|z|2	NOUN
ap-3483	330	11	−	−	NOUN
ap-3483	330	12	1	1	X
ap-3483	330	13	)	)	PUNCT
ap-3483	330	14	−z̄	−z̄	NOUN
ap-3483	330	15	−z	−z	NOUN
ap-3483	330	16	1	1	NUM
ap-3483	330	17	2	2	NUM
ap-3483	330	18	(	(	PUNCT
ap-3483	330	19	1−	1−	NUM
ap-3483	330	20	|z|2	|z|2	PROPN
ap-3483	330	21	)	)	PUNCT
ap-3483	330	22	)	)	PUNCT
ap-3483	331	1	∈	∈	PROPN
ap-3483	331	2	su(2	su(2	NOUN
ap-3483	331	3	)	)	PUNCT
ap-3483	331	4	,	,	PUNCT
ap-3483	331	5	f1	f1	NOUN
ap-3483	331	6	=	=	SYM
ap-3483	331	7	−i(p1	−i(p1	PROPN
ap-3483	331	8	+	+	CCONJ
ap-3483	331	9	2p0	2p0	NUM
ap-3483	331	10	)	)	PUNCT
ap-3483	332	1	+	+	NUM
ap-3483	332	2	3i	3i	NUM
ap-3483	332	3	2	2	NUM
ap-3483	332	4	i2	i2	NOUN
ap-3483	332	5	=	=	SYM
ap-3483	332	6	f0	f0	PROPN
ap-3483	332	7	.	.	PUNCT
ap-3483	333	1	(	(	PUNCT
ap-3483	333	2	4.23	4.23	NUM
ap-3483	333	3	)	)	PUNCT
ap-3483	333	4	from	from	ADP
ap-3483	333	5	equation	equation	NOUN
ap-3483	333	6	(	(	PUNCT
ap-3483	333	7	4.10	4.10	NUM
ap-3483	333	8	)	)	PUNCT
ap-3483	333	9	the	the	DET
ap-3483	333	10	potential	potential	ADJ
ap-3483	333	11	matrices	matrix	NOUN
ap-3483	333	12	uαk	uαk	ADP
ap-3483	333	13	become	become	VERB
ap-3483	333	14	u10	u10	NOUN
ap-3483	333	15	=	=	SYM
ap-3483	333	16	u11	u11	PROPN
ap-3483	333	17	=	=	SYM
ap-3483	333	18	2	2	NUM
ap-3483	333	19	(	(	PUNCT
ap-3483	333	20	λ+	λ+	NUM
ap-3483	333	21	1)(1	1)(1	NUM
ap-3483	333	22	+	+	CCONJ
ap-3483	333	23	|z|2)2	|z|2)2	NOUN
ap-3483	333	24	(	(	PUNCT
ap-3483	333	25	−z̄	−z̄	NOUN
ap-3483	333	26	−z̄2	−z̄2	PROPN
ap-3483	333	27	1	1	NUM
ap-3483	333	28	z̄	z̄	PROPN
ap-3483	333	29	)	)	PUNCT
ap-3483	333	30	,	,	PUNCT
ap-3483	333	31	u20	u20	NUM
ap-3483	333	32	=	=	SYM
ap-3483	333	33	u21	u21	PROPN
ap-3483	333	34	=	=	SYM
ap-3483	333	35	2	2	NUM
ap-3483	333	36	(	(	PUNCT
ap-3483	333	37	λ−	λ−	PROPN
ap-3483	333	38	1)(1	1)(1	NUM
ap-3483	333	39	+	+	CCONJ
ap-3483	333	40	|z|2)2	|z|2)2	PROPN
ap-3483	333	41	(	(	PUNCT
ap-3483	333	42	−z	−z	NOUN
ap-3483	333	43	1	1	NUM
ap-3483	333	44	−z2	−z2	NOUN
ap-3483	333	45	z	z	PROPN
ap-3483	333	46	)	)	PUNCT
ap-3483	333	47	,	,	PUNCT
ap-3483	334	1	λ	λ	X
ap-3483	334	2	=	=	VERB
ap-3483	334	3	it	it	PRON
ap-3483	334	4	,	,	PUNCT
ap-3483	334	5	t	t	PROPN
ap-3483	334	6	∈	∈	PROPN
ap-3483	334	7	r.	r.	PROPN
ap-3483	334	8	(	(	PUNCT
ap-3483	334	9	4.24	4.24	NUM
ap-3483	334	10	)	)	PUNCT
ap-3483	334	11	the	the	DET
ap-3483	334	12	su(2)-valued	su(2)-value	VERB
ap-3483	334	13	soliton	soliton	NOUN
ap-3483	334	14	wavefunctions	wavefunction	NOUN
ap-3483	334	15	φk	φk	ADP
ap-3483	334	16	in	in	ADP
ap-3483	334	17	the	the	DET
ap-3483	334	18	lsp	lsp	PROPN
ap-3483	334	19	(	(	PUNCT
ap-3483	334	20	4.10	4.10	NUM
ap-3483	334	21	)	)	PUNCT
ap-3483	334	22	for	for	ADP
ap-3483	334	23	the	the	DET
ap-3483	334	24	cp	cp	PROPN
ap-3483	334	25	1	1	NUM
ap-3483	334	26	model	model	NOUN
ap-3483	334	27	have	have	VERB
ap-3483	334	28	the	the	DET
ap-3483	334	29	form	form	NOUN
ap-3483	334	30	φ0	φ0	NOUN
ap-3483	334	31	=	=	NOUN
ap-3483	334	32	1	1	NUM
ap-3483	334	33	1	1	NUM
ap-3483	334	34	+	+	NUM
ap-3483	334	35	|z|2	|z|2	NOUN
ap-3483	334	36	(	(	PUNCT
ap-3483	334	37	−i+t+(i+t)|z|2	−i+t+(i+t)|z|2	X
ap-3483	334	38	t−i	t−i	NOUN
ap-3483	334	39	−2iz̄	−2iz̄	PROPN
ap-3483	334	40	t−i	t−i	NOUN
ap-3483	334	41	−2iz	−2iz	ADP
ap-3483	334	42	t+i	t+i	PROPN
ap-3483	334	43	i+t+(t−i)|z|2	i+t+(t−i)|z|2	ADP
ap-3483	334	44	t+i	t+i	NOUN
ap-3483	334	45	)	)	PUNCT
ap-3483	334	46	,	,	PUNCT
ap-3483	334	47	φ1	φ1	NOUN
ap-3483	334	48	=	=	SYM
ap-3483	335	1	1	1	NUM
ap-3483	335	2	1	1	NUM
ap-3483	335	3	+	+	NUM
ap-3483	335	4	|z|2	|z|2	NOUN
ap-3483	335	5	(	(	PUNCT
ap-3483	335	6	1+t2+(t+i)2|z|2	1+t2+(t+i)2|z|2	NUM
ap-3483	335	7	(	(	PUNCT
ap-3483	335	8	t−i)2	t−i)2	NOUN
ap-3483	335	9	2(1−it)z̄	2(1−it)z̄	NUM
ap-3483	335	10	(	(	PUNCT
ap-3483	335	11	t−i)2	t−i)2	NOUN
ap-3483	335	12	−2i(t−i)z	−2i(t−i)z	X
ap-3483	335	13	(	(	PUNCT
ap-3483	335	14	t+i)2	t+i)2	PROPN
ap-3483	335	15	1+t2+(t−i)2|z|2	1+t2+(t−i)2|z|2	NUM
ap-3483	335	16	(	(	PUNCT
ap-3483	335	17	t+i)2	t+i)2	PROPN
ap-3483	335	18	)	)	PUNCT
ap-3483	335	19	.	.	PUNCT
ap-3483	336	1	(	(	PUNCT
ap-3483	336	2	4.25	4.25	NUM
ap-3483	336	3	)	)	PUNCT
ap-3483	336	4	let	let	VERB
ap-3483	336	5	us	we	PRON
ap-3483	336	6	now	now	ADV
ap-3483	336	7	consider	consider	VERB
ap-3483	336	8	separately	separately	ADV
ap-3483	336	9	four	four	NUM
ap-3483	336	10	different	different	ADJ
ap-3483	336	11	analytic	analytic	ADJ
ap-3483	336	12	descriptions	description	NOUN
ap-3483	336	13	for	for	ADP
ap-3483	336	14	the	the	DET
ap-3483	336	15	immersion	immersion	NOUN
ap-3483	336	16	functions	function	NOUN
ap-3483	336	17	of	of	ADP
ap-3483	336	18	2dsoliton	2dsoliton	NUM
ap-3483	336	19	surfaces	surface	NOUN
ap-3483	336	20	in	in	ADP
ap-3483	336	21	lie	lie	NOUN
ap-3483	336	22	algebras	algebra	NOUN
ap-3483	336	23	which	which	PRON
ap-3483	336	24	are	be	AUX
ap-3483	336	25	related	relate	VERB
ap-3483	336	26	to	to	ADP
ap-3483	336	27	four	four	NUM
ap-3483	336	28	different	different	ADJ
ap-3483	336	29	types	type	NOUN
ap-3483	336	30	of	of	ADP
ap-3483	336	31	symmetries	symmetry	NOUN
ap-3483	336	32	.	.	PUNCT
ap-3483	337	1	i.	i.	PROPN
ap-3483	337	2	the	the	DET
ap-3483	337	3	zcc	zcc	NOUN
ap-3483	337	4	(	(	PUNCT
ap-3483	337	5	2.14	2.14	NUM
ap-3483	337	6	)	)	PUNCT
ap-3483	337	7	of	of	ADP
ap-3483	337	8	the	the	DET
ap-3483	337	9	cp	cp	PROPN
ap-3483	337	10	1	1	NUM
ap-3483	337	11	model	model	NOUN
ap-3483	337	12	admits	admit	VERB
ap-3483	337	13	a	a	DET
ap-3483	337	14	conformal	conformal	ADJ
ap-3483	337	15	symmetry	symmetry	NOUN
ap-3483	337	16	in	in	ADP
ap-3483	337	17	the	the	DET
ap-3483	337	18	spectral	spectral	ADJ
ap-3483	337	19	parameter	parameter	PROPN
ap-3483	337	20	λ	λ	PROPN
ap-3483	337	21	.	.	PUNCT
ap-3483	338	1	the	the	DET
ap-3483	338	2	tangent	tangent	NOUN
ap-3483	338	3	vectors	vector	NOUN
ap-3483	338	4	dαf	dαf	PROPN
ap-3483	338	5	st	st	PROPN
ap-3483	338	6	k	k	PROPN
ap-3483	338	7	associated	associate	VERB
ap-3483	338	8	with	with	ADP
ap-3483	338	9	this	this	DET
ap-3483	338	10	symmetry	symmetry	NOUN
ap-3483	338	11	are	be	AUX
ap-3483	338	12	given	give	VERB
ap-3483	338	13	by	by	ADP
ap-3483	338	14	dαf	dαf	NOUN
ap-3483	338	15	st	st	PROPN
ap-3483	338	16	k	k	PROPN
ap-3483	338	17	=	=	PUNCT
ap-3483	338	18	φ−1	φ−1	PROPN
ap-3483	338	19	k	k	PROPN
ap-3483	338	20	(	(	PUNCT
ap-3483	338	21	dλuαk)φk	dλuαk)φk	PROPN
ap-3483	338	22	,	,	PUNCT
ap-3483	338	23	α	α	X
ap-3483	338	24	,	,	PUNCT
ap-3483	338	25	k	k	PROPN
ap-3483	338	26	=	=	SYM
ap-3483	338	27	1	1	NUM
ap-3483	338	28	,	,	PUNCT
ap-3483	338	29	2	2	NUM
ap-3483	338	30	and	and	CCONJ
ap-3483	338	31	are	be	AUX
ap-3483	338	32	linearly	linearly	ADV
ap-3483	338	33	independent	independent	ADJ
ap-3483	338	34	.	.	PUNCT
ap-3483	339	1	the	the	DET
ap-3483	339	2	integrated	integrate	VERB
ap-3483	339	3	forms	form	NOUN
ap-3483	339	4	of	of	ADP
ap-3483	339	5	the	the	DET
ap-3483	339	6	2d	2d	NOUN
ap-3483	339	7	-	-	PUNCT
ap-3483	339	8	surfaces	surface	NOUN
ap-3483	339	9	in	in	ADP
ap-3483	339	10	su(2	su(2	NOUN
ap-3483	339	11	)	)	PUNCT
ap-3483	339	12	are	be	AUX
ap-3483	339	13	given	give	VERB
ap-3483	339	14	by	by	ADP
ap-3483	339	15	the	the	DET
ap-3483	339	16	st	st	PROPN
ap-3483	339	17	formulas	formula	NOUN
ap-3483	339	18	(	(	PUNCT
ap-3483	339	19	2.27	2.27	NUM
ap-3483	339	20	)	)	PUNCT
ap-3483	339	21	fst0	fst0	NOUN
ap-3483	339	22	=	=	SYM
ap-3483	339	23	φ−1	φ−1	PROPN
ap-3483	339	24	0	0	PUNCT
ap-3483	339	25	(	(	PUNCT
ap-3483	339	26	dλφ0	dλφ0	NOUN
ap-3483	339	27	)	)	PUNCT
ap-3483	339	28	=	=	SYM
ap-3483	339	29	2i	2i	NUM
ap-3483	339	30	(	(	PUNCT
ap-3483	339	31	1	1	NUM
ap-3483	339	32	+	+	NUM
ap-3483	339	33	t2)2(1	t2)2(1	NOUN
ap-3483	339	34	+	+	CCONJ
ap-3483	339	35	|z|2)2	|z|2)2	NOUN
ap-3483	339	36	·	·	PUNCT
ap-3483	339	37	(	(	PUNCT
ap-3483	339	38	−|z|2[t2	−|z|2[t2	NOUN
ap-3483	339	39	−	−	NOUN
ap-3483	339	40	3	3	NUM
ap-3483	339	41	+	+	NOUN
ap-3483	339	42	|z|2(1	|z|2(1	NOUN
ap-3483	339	43	+	+	CCONJ
ap-3483	339	44	t2	t2	NOUN
ap-3483	339	45	)	)	PUNCT
ap-3483	339	46	]	]	PUNCT
ap-3483	340	1	z[(t−	z[(t−	X
ap-3483	340	2	i)2	i)2	PROPN
ap-3483	340	3	+	+	CCONJ
ap-3483	340	4	|z|2(3−	|z|2(3−	PROPN
ap-3483	340	5	2it+	2it+	PROPN
ap-3483	340	6	t2	t2	NOUN
ap-3483	340	7	)	)	PUNCT
ap-3483	340	8	]	]	PUNCT
ap-3483	341	1	z̄[(t+	z̄[(t+	PROPN
ap-3483	341	2	i)2	i)2	ADJ
ap-3483	341	3	+	+	CCONJ
ap-3483	341	4	|z|2(3	|z|2(3	NOUN
ap-3483	341	5	+	+	CCONJ
ap-3483	341	6	2it+	2it+	PROPN
ap-3483	341	7	t2	t2	NOUN
ap-3483	341	8	)	)	PUNCT
ap-3483	341	9	]	]	PUNCT
ap-3483	341	10	|z|2[t2	|z|2[t2	NOUN
ap-3483	342	1	−	−	NOUN
ap-3483	342	2	3	3	NUM
ap-3483	343	1	+	+	NUM
ap-3483	343	2	|z|2(t2	|z|2(t2	NOUN
ap-3483	343	3	+	+	CCONJ
ap-3483	343	4	1	1	NUM
ap-3483	343	5	)	)	PUNCT
ap-3483	343	6	]	]	PUNCT
ap-3483	343	7	)	)	PUNCT
ap-3483	343	8	,	,	PUNCT
ap-3483	343	9	fst1	fst1	NOUN
ap-3483	343	10	=	=	SYM
ap-3483	343	11	φ−1	φ−1	PROPN
ap-3483	343	12	1	1	NUM
ap-3483	343	13	(	(	PUNCT
ap-3483	343	14	dλφ1	dλφ1	PROPN
ap-3483	343	15	)	)	PUNCT
ap-3483	344	1	=	=	SYM
ap-3483	344	2	2i	2i	NUM
ap-3483	344	3	(	(	PUNCT
ap-3483	344	4	1	1	NUM
ap-3483	344	5	+	+	NUM
ap-3483	344	6	t2)2(1	t2)2(1	NOUN
ap-3483	344	7	+	+	CCONJ
ap-3483	344	8	|z|2)2	|z|2)2	NOUN
ap-3483	344	9	·	·	PUNCT
ap-3483	344	10	(	(	PUNCT
ap-3483	344	11	−[(t2	−[(t2	NOUN
ap-3483	344	12	+	+	NUM
ap-3483	344	13	1)(1	1)(1	NUM
ap-3483	344	14	+	+	CCONJ
ap-3483	344	15	2|z|4	2|z|4	NUM
ap-3483	344	16	)	)	PUNCT
ap-3483	344	17	+	+	NOUN
ap-3483	344	18	3|z|2(t2	3|z|2(t2	NUM
ap-3483	344	19	−	−	NOUN
ap-3483	344	20	3	3	NUM
ap-3483	344	21	)	)	PUNCT
ap-3483	344	22	]	]	PUNCT
ap-3483	344	23	z[t2	z[t2	NOUN
ap-3483	345	1	−	−	PROPN
ap-3483	345	2	6it−	6it−	NUM
ap-3483	345	3	5	5	NUM
ap-3483	345	4	+	+	CCONJ
ap-3483	345	5	|z|2(7	|z|2(7	NOUN
ap-3483	345	6	+	+	CCONJ
ap-3483	345	7	t2	t2	PROPN
ap-3483	345	8	−	−	PROPN
ap-3483	345	9	6it	6it	NOUN
ap-3483	345	10	)	)	PUNCT
ap-3483	345	11	]	]	PUNCT
ap-3483	346	1	z̄[6it−	z̄[6it−	NOUN
ap-3483	346	2	5	5	NUM
ap-3483	347	1	+	+	CCONJ
ap-3483	347	2	t2	t2	NOUN
ap-3483	347	3	+	+	CCONJ
ap-3483	347	4	|z|2(7	|z|2(7	NOUN
ap-3483	347	5	+	+	CCONJ
ap-3483	347	6	6it+	6it+	PROPN
ap-3483	347	7	t2	t2	NOUN
ap-3483	347	8	)	)	PUNCT
ap-3483	347	9	]	]	PUNCT
ap-3483	347	10	(	(	PUNCT
ap-3483	347	11	t2	t2	NOUN
ap-3483	347	12	+	+	CCONJ
ap-3483	347	13	1)(1	1)(1	NUM
ap-3483	347	14	+	+	CCONJ
ap-3483	347	15	2|z|4	2|z|4	NUM
ap-3483	347	16	)	)	PUNCT
ap-3483	347	17	+	+	NOUN
ap-3483	347	18	3|z|2(t2	3|z|2(t2	NUM
ap-3483	347	19	−	−	NOUN
ap-3483	347	20	3	3	NUM
ap-3483	347	21	)	)	PUNCT
ap-3483	347	22	)	)	PUNCT
ap-3483	347	23	,	,	PUNCT
ap-3483	347	24	(	(	PUNCT
ap-3483	347	25	4.26	4.26	NUM
ap-3483	347	26	)	)	PUNCT
ap-3483	347	27	where	where	SCONJ
ap-3483	347	28	,	,	PUNCT
ap-3483	347	29	without	without	ADP
ap-3483	347	30	loss	loss	NOUN
ap-3483	347	31	of	of	ADP
ap-3483	347	32	generality	generality	NOUN
ap-3483	347	33	,	,	PUNCT
ap-3483	347	34	we	we	PRON
ap-3483	347	35	can	can	AUX
ap-3483	347	36	put	put	VERB
ap-3483	347	37	β(λ	β(λ	NOUN
ap-3483	347	38	)	)	PUNCT
ap-3483	347	39	=	=	SYM
ap-3483	347	40	1	1	NUM
ap-3483	347	41	in	in	ADP
ap-3483	347	42	the	the	DET
ap-3483	347	43	expression	expression	NOUN
ap-3483	347	44	(	(	PUNCT
ap-3483	347	45	2.27	2.27	NUM
ap-3483	347	46	)	)	PUNCT
ap-3483	347	47	.	.	PUNCT
ap-3483	348	1	the	the	DET
ap-3483	348	2	surfaces	surface	NOUN
ap-3483	348	3	fstk	fstk	ADJ
ap-3483	348	4	satisfy	satisfy	NOUN
ap-3483	348	5	(	(	PUNCT
ap-3483	348	6	fstk	fstk	ADJ
ap-3483	348	7	)	)	PUNCT
ap-3483	348	8	2	2	NUM
ap-3483	348	9	+	+	CCONJ
ap-3483	348	10	1	1	NUM
ap-3483	348	11	4	4	NUM
ap-3483	348	12	i2	i2	NOUN
ap-3483	348	13	=	=	SYM
ap-3483	348	14	0	0	NUM
ap-3483	348	15	,	,	PUNCT
ap-3483	348	16	for	for	ADP
ap-3483	348	17	k	k	PROPN
ap-3483	348	18	=	=	SYM
ap-3483	348	19	0	0	NUM
ap-3483	348	20	,	,	PUNCT
ap-3483	348	21	1	1	NUM
ap-3483	348	22	and	and	CCONJ
ap-3483	348	23	have	have	VERB
ap-3483	348	24	positive	positive	ADJ
ap-3483	348	25	constant	constant	ADJ
ap-3483	348	26	gaussian	gaussian	NOUN
ap-3483	348	27	and	and	CCONJ
ap-3483	348	28	mean	mean	ADJ
ap-3483	348	29	curvatures	curvature	NOUN
ap-3483	348	30	.	.	PUNCT
ap-3483	349	1	hence	hence	ADV
ap-3483	349	2	,	,	PUNCT
ap-3483	349	3	they	they	PRON
ap-3483	349	4	are	be	AUX
ap-3483	349	5	spheres	sphere	NOUN
ap-3483	349	6	(	(	PUNCT
ap-3483	349	7	see	see	VERB
ap-3483	349	8	fig	fig	NOUN
ap-3483	349	9	.	.	PUNCT
ap-3483	350	1	2a	2a	NUM
ap-3483	350	2	)	)	PUNCT
ap-3483	350	3	k0	k0	PROPN
ap-3483	350	4	=	=	PROPN
ap-3483	350	5	k1	k1	PROPN
ap-3483	350	6	=	=	SYM
ap-3483	350	7	4	4	NUM
ap-3483	350	8	,	,	PUNCT
ap-3483	350	9	h0	h0	NOUN
ap-3483	350	10	=	=	PUNCT
ap-3483	350	11	h1	h1	PROPN
ap-3483	350	12	=	=	ADJ
ap-3483	350	13	4	4	NUM
ap-3483	350	14	.	.	PUNCT
ap-3483	350	15	(	(	PUNCT
ap-3483	350	16	4.27	4.27	NUM
ap-3483	350	17	)	)	PUNCT
ap-3483	350	18	the	the	DET
ap-3483	350	19	surfaces	surface	NOUN
ap-3483	350	20	fstk	fstk	ADJ
ap-3483	350	21	in	in	ADP
ap-3483	350	22	cartesian	cartesian	ADJ
ap-3483	350	23	coordinates	coordinate	NOUN
ap-3483	350	24	(	(	PUNCT
ap-3483	350	25	x	x	X
ap-3483	350	26	,	,	PUNCT
ap-3483	350	27	y	y	NOUN
ap-3483	350	28	)	)	PUNCT
ap-3483	350	29	take	take	VERB
ap-3483	350	30	the	the	DET
ap-3483	350	31	form	form	NOUN
ap-3483	350	32	for	for	ADP
ap-3483	350	33	z	z	NOUN
ap-3483	350	34	=	=	SYM
ap-3483	350	35	x+	x+	PROPN
ap-3483	350	36	iy	iy	PROPN
ap-3483	350	37	fstk	fstk	NOUN
ap-3483	350	38	=	=	PUNCT
ap-3483	350	39	{	{	PUNCT
ap-3483	350	40	x	x	SYM
ap-3483	350	41	1	1	NUM
ap-3483	351	1	+	+	NUM
ap-3483	351	2	x2	x2	PROPN
ap-3483	352	1	+	+	CCONJ
ap-3483	352	2	y2	y2	INTJ
ap-3483	352	3	,	,	PUNCT
ap-3483	352	4	y	y	PROPN
ap-3483	352	5	1	1	NUM
ap-3483	352	6	+	+	CCONJ
ap-3483	352	7	x2	x2	PROPN
ap-3483	353	1	+	+	CCONJ
ap-3483	353	2	y2	y2	PROPN
ap-3483	353	3	,	,	PUNCT
ap-3483	353	4	1−	1−	NUM
ap-3483	353	5	x2	x2	INTJ
ap-3483	354	1	−	−	PROPN
ap-3483	354	2	y2	y2	NOUN
ap-3483	354	3	2(1	2(1	NUM
ap-3483	355	1	+	+	CCONJ
ap-3483	355	2	x2	x2	PROPN
ap-3483	356	1	+	+	CCONJ
ap-3483	356	2	y2	y2	NOUN
ap-3483	356	3	)	)	PUNCT
ap-3483	356	4	}	}	PUNCT
ap-3483	357	1	(	(	PUNCT
ap-3483	357	2	4.28	4.28	X
ap-3483	357	3	)	)	PUNCT
ap-3483	357	4	the	the	DET
ap-3483	357	5	su(2)-valued	su(2)-value	VERB
ap-3483	357	6	gauges	gauge	NOUN
ap-3483	357	7	sstk	sstk	NOUN
ap-3483	357	8	associated	associate	VERB
ap-3483	357	9	with	with	ADP
ap-3483	357	10	the	the	DET
ap-3483	357	11	st	st	PROPN
ap-3483	357	12	immersion	immersion	PROPN
ap-3483	357	13	functions	function	NOUN
ap-3483	357	14	fstk	fstk	ADJ
ap-3483	357	15	(	(	PUNCT
ap-3483	357	16	4.26	4.26	NUM
ap-3483	357	17	)	)	PUNCT
ap-3483	357	18	take	take	VERB
ap-3483	357	19	the	the	DET
ap-3483	357	20	form	form	NOUN
ap-3483	357	21	sst0	sst0	NOUN
ap-3483	357	22	=	=	SYM
ap-3483	357	23	(	(	PUNCT
ap-3483	357	24	dλφ0)φ−1	dλφ0)φ−1	PROPN
ap-3483	357	25	0	0	PUNCT
ap-3483	358	1	=	=	SYM
ap-3483	358	2	2i	2i	NUM
ap-3483	358	3	1	1	NUM
ap-3483	358	4	+	+	NUM
ap-3483	358	5	|z|2	|z|2	NOUN
ap-3483	358	6	(	(	PUNCT
ap-3483	358	7	−|z|2	−|z|2	PROPN
ap-3483	358	8	t2	t2	PROPN
ap-3483	358	9	+	+	PROPN
ap-3483	358	10	1	1	NUM
ap-3483	358	11	z̄	z̄	X
ap-3483	358	12	(	(	PUNCT
ap-3483	358	13	t−i)2	t−i)2	PROPN
ap-3483	358	14	z	z	NOUN
ap-3483	358	15	(	(	PUNCT
ap-3483	358	16	t+i)2	t+i)2	PROPN
ap-3483	358	17	|z|2	|z|2	PROPN
ap-3483	358	18	t2	t2	NOUN
ap-3483	358	19	+	+	PROPN
ap-3483	358	20	1	1	NUM
ap-3483	358	21	)	)	PUNCT
ap-3483	358	22	,	,	PUNCT
ap-3483	358	23	sst1	sst1	NOUN
ap-3483	358	24	=	=	SYM
ap-3483	358	25	(	(	PUNCT
ap-3483	358	26	dλφ1)φ−1	dλφ1)φ−1	NOUN
ap-3483	358	27	1	1	NUM
ap-3483	358	28	=	=	SYM
ap-3483	358	29	2i	2i	NUM
ap-3483	358	30	1	1	NUM
ap-3483	358	31	+	+	NUM
ap-3483	358	32	|z|2	|z|2	NOUN
ap-3483	358	33	(	(	PUNCT
ap-3483	358	34	−(1	−(1	ADJ
ap-3483	358	35	+	+	ADJ
ap-3483	358	36	2|z|2	2|z|2	NOUN
ap-3483	358	37	)	)	PUNCT
ap-3483	358	38	t2	t2	NOUN
ap-3483	358	39	+	+	PROPN
ap-3483	358	40	1	1	NUM
ap-3483	358	41	z̄(t+i)2	z̄(t+i)2	NOUN
ap-3483	358	42	(	(	PUNCT
ap-3483	358	43	t−i)4	t−i)4	NUM
ap-3483	358	44	z(t−i)2	z(t−i)2	PROPN
ap-3483	358	45	(	(	PUNCT
ap-3483	358	46	t+i)4	t+i)4	PROPN
ap-3483	358	47	1	1	NUM
ap-3483	358	48	+	+	NUM
ap-3483	358	49	2|z|2	2|z|2	NUM
ap-3483	358	50	t2	t2	NOUN
ap-3483	358	51	+	+	NOUN
ap-3483	358	52	1	1	NUM
ap-3483	358	53	)	)	PUNCT
ap-3483	358	54	,	,	PUNCT
ap-3483	358	55	detsstk	detsstk	ADJ
ap-3483	358	56	6=	6=	ADP
ap-3483	358	57	0	0	NUM
ap-3483	358	58	,	,	PUNCT
ap-3483	358	59	trsstk	trsstk	PROPN
ap-3483	358	60	=	=	NOUN
ap-3483	358	61	0	0	PROPN
ap-3483	358	62	.	.	PUNCT
ap-3483	359	1	(	(	PUNCT
ap-3483	359	2	4.29	4.29	NUM
ap-3483	359	3	)	)	PUNCT
ap-3483	359	4	ii	ii	PROPN
ap-3483	359	5	.	.	PUNCT
ap-3483	360	1	the	the	DET
ap-3483	360	2	surfaces	surface	NOUN
ap-3483	360	3	f	f	PROPN
ap-3483	360	4	gk	gk	PROPN
ap-3483	360	5	∈	∈	PROPN
ap-3483	360	6	su(2	su(2	NOUN
ap-3483	360	7	)	)	PUNCT
ap-3483	360	8	associated	associate	VERB
ap-3483	360	9	with	with	ADP
ap-3483	360	10	the	the	DET
ap-3483	360	11	scaling	scale	VERB
ap-3483	360	12	symmetries	symmetry	NOUN
ap-3483	360	13	of	of	ADP
ap-3483	360	14	the	the	DET
ap-3483	360	15	zcc	zcc	NOUN
ap-3483	360	16	(	(	PUNCT
ap-3483	360	17	2.14	2.14	NUM
ap-3483	360	18	)	)	PUNCT
ap-3483	360	19	associated	associate	VERB
ap-3483	360	20	with	with	ADP
ap-3483	360	21	equations	equation	NOUN
ap-3483	360	22	of	of	ADP
ap-3483	360	23	the	the	DET
ap-3483	360	24	cp	cp	PROPN
ap-3483	360	25	1	1	NUM
ap-3483	360	26	model	model	NOUN
ap-3483	360	27	(	(	PUNCT
ap-3483	360	28	4.6	4.6	NUM
ap-3483	360	29	)	)	PUNCT
ap-3483	360	30	ωgk	ωgk	NOUN
ap-3483	360	31	=	=	SYM
ap-3483	360	32	(	(	PUNCT
ap-3483	360	33	d1(zu1k	d1(zu1k	PROPN
ap-3483	360	34	)	)	PUNCT
ap-3483	360	35	+	+	CCONJ
ap-3483	360	36	z̄(d2u1k	z̄(d2u1k	PROPN
ap-3483	360	37	)	)	PUNCT
ap-3483	360	38	)	)	PUNCT
ap-3483	360	39	∂	∂	NUM
ap-3483	361	1	∂θ1	∂θ1	NOUN
ap-3483	361	2	+	+	CCONJ
ap-3483	361	3	(	(	PUNCT
ap-3483	361	4	z(d1u2k	z(d1u2k	PROPN
ap-3483	361	5	)	)	PUNCT
ap-3483	361	6	+	+	NOUN
ap-3483	361	7	d2(z̄u2k	d2(z̄u2k	NOUN
ap-3483	361	8	)	)	PUNCT
ap-3483	361	9	)	)	PUNCT
ap-3483	361	10	∂	∂	NUM
ap-3483	362	1	∂θ2	∂θ2	NOUN
ap-3483	362	2	,	,	PUNCT
ap-3483	362	3	(	(	PUNCT
ap-3483	362	4	4.30	4.30	NUM
ap-3483	362	5	)	)	PUNCT
ap-3483	362	6	have	have	VERB
ap-3483	362	7	the	the	DET
ap-3483	362	8	integrated	integrate	VERB
ap-3483	362	9	form	form	NOUN
ap-3483	362	10	[	[	X
ap-3483	362	11	14	14	NUM
ap-3483	362	12	]	]	X
ap-3483	362	13	f	f	PROPN
ap-3483	362	14	gk	gk	PROPN
ap-3483	362	15	=	=	PUNCT
ap-3483	362	16	φ−1	φ−1	PROPN
ap-3483	362	17	k	k	NOUN
ap-3483	362	18	(	(	PUNCT
ap-3483	362	19	zu1k	zu1k	PROPN
ap-3483	362	20	+	+	NUM
ap-3483	362	21	z̄u2k)φk	z̄u2k)φk	NOUN
ap-3483	362	22	,	,	PUNCT
ap-3483	362	23	k	k	PROPN
ap-3483	362	24	=	=	SYM
ap-3483	362	25	0	0	NUM
ap-3483	362	26	,	,	PUNCT
ap-3483	362	27	1	1	NUM
ap-3483	362	28	(	(	PUNCT
ap-3483	362	29	4.31	4.31	NUM
ap-3483	362	30	)	)	PUNCT
ap-3483	362	31	where	where	SCONJ
ap-3483	362	32	θ1	θ1	NOUN
ap-3483	362	33	and	and	CCONJ
ap-3483	362	34	θ2	θ2	PROPN
ap-3483	362	35	are	be	AUX
ap-3483	362	36	complex	complex	ADV
ap-3483	362	37	-	-	PUNCT
ap-3483	362	38	valued	value	VERB
ap-3483	362	39	functions	function	NOUN
ap-3483	362	40	determined	determine	VERB
ap-3483	362	41	from	from	ADP
ap-3483	362	42	the	the	DET
ap-3483	362	43	su(2	su(2	NOUN
ap-3483	362	44	)	)	PUNCT
ap-3483	362	45	lie	lie	NOUN
ap-3483	362	46	algebra	algebra	NOUN
ap-3483	362	47	(	(	PUNCT
ap-3483	362	48	4.12	4.12	NUM
ap-3483	362	49	)	)	PUNCT
ap-3483	362	50	.	.	PUNCT
ap-3483	363	1	the	the	DET
ap-3483	363	2	surfaces	surface	NOUN
ap-3483	363	3	f	f	X
ap-3483	363	4	gk	gk	PROPN
ap-3483	363	5	also	also	ADV
ap-3483	363	6	have	have	VERB
ap-3483	363	7	constant	constant	ADJ
ap-3483	363	8	positive	positive	ADJ
ap-3483	363	9	curvatures	curvature	NOUN
ap-3483	363	10	k0	k0	PROPN
ap-3483	363	11	=	=	PROPN
ap-3483	363	12	k1	k1	PROPN
ap-3483	363	13	=	=	SYM
ap-3483	363	14	−4λ2	−4λ2	NUM
ap-3483	363	15	,	,	PUNCT
ap-3483	363	16	h0	h0	NOUN
ap-3483	363	17	=	=	PUNCT
ap-3483	363	18	h1	h1	PROPN
ap-3483	363	19	=	=	SYM
ap-3483	363	20	−4iλ	−4iλ	PROPN
ap-3483	363	21	,	,	PUNCT
ap-3483	363	22	iλ	iλ	PROPN
ap-3483	363	23	∈	∈	PROPN
ap-3483	363	24	r.	r.	PROPN
ap-3483	363	25	(	(	PUNCT
ap-3483	363	26	4.32	4.32	NUM
ap-3483	363	27	)	)	PUNCT
ap-3483	363	28	188	188	NUM
ap-3483	363	29	vol	vol	NOUN
ap-3483	363	30	.	.	PUNCT
ap-3483	364	1	56	56	NUM
ap-3483	364	2	no	no	NOUN
ap-3483	364	3	.	.	PUNCT
ap-3483	365	1	3/2016	3/2016	NUM
ap-3483	365	2	on	on	ADP
ap-3483	365	3	immersion	immersion	NOUN
ap-3483	365	4	formulas	formula	NOUN
ap-3483	365	5	for	for	ADP
ap-3483	365	6	soliton	soliton	NOUN
ap-3483	365	7	surfaces	surface	NOUN
ap-3483	365	8	the	the	DET
ap-3483	365	9	surfaces	surface	NOUN
ap-3483	366	1	f	f	X
ap-3483	366	2	gk	gk	NOUN
ap-3483	366	3	are	be	AUX
ap-3483	366	4	not	not	PART
ap-3483	366	5	spheres	sphere	NOUN
ap-3483	366	6	(	(	PUNCT
ap-3483	366	7	as	as	ADP
ap-3483	366	8	in	in	ADP
ap-3483	366	9	the	the	DET
ap-3483	366	10	previous	previous	ADJ
ap-3483	366	11	cases	case	NOUN
ap-3483	366	12	(	(	PUNCT
ap-3483	366	13	4.27	4.27	NUM
ap-3483	366	14	)	)	PUNCT
ap-3483	366	15	)	)	PUNCT
ap-3483	366	16	since	since	SCONJ
ap-3483	366	17	they	they	PRON
ap-3483	366	18	have	have	VERB
ap-3483	366	19	boundaries	boundary	NOUN
ap-3483	366	20	(	(	PUNCT
ap-3483	366	21	see	see	VERB
ap-3483	366	22	fig	fig	NOUN
ap-3483	366	23	.	.	PUNCT
ap-3483	366	24	2b	2b	NUM
ap-3483	366	25	)	)	PUNCT
ap-3483	366	26	.	.	PUNCT
ap-3483	367	1	the	the	DET
ap-3483	367	2	surfaces	surface	NOUN
ap-3483	367	3	f	f	X
ap-3483	367	4	gk	gk	NOUN
ap-3483	367	5	can	can	AUX
ap-3483	367	6	be	be	AUX
ap-3483	367	7	given	give	VERB
ap-3483	367	8	in	in	ADP
ap-3483	367	9	the	the	DET
ap-3483	367	10	parametric	parametric	ADJ
ap-3483	367	11	form	form	NOUN
ap-3483	367	12	f	f	PROPN
ap-3483	367	13	gk	gk	PROPN
ap-3483	367	14	=	=	PUNCT
ap-3483	367	15	(	(	PUNCT
ap-3483	367	16	x3	x3	ADJ
ap-3483	367	17	−	−	PROPN
ap-3483	367	18	2x2y	2x2y	NOUN
ap-3483	367	19	+	+	CCONJ
ap-3483	367	20	x(y2	x(y2	PROPN
ap-3483	367	21	−	−	PROPN
ap-3483	368	1	1)−	1)−	PROPN
ap-3483	368	2	2y(1	2y(1	NUM
ap-3483	368	3	+	+	NUM
ap-3483	368	4	y2	y2	NOUN
ap-3483	368	5	)	)	PUNCT
ap-3483	368	6	(	(	PUNCT
ap-3483	368	7	1	1	NUM
ap-3483	368	8	+	+	NUM
ap-3483	368	9	x2	x2	PROPN
ap-3483	369	1	+	+	CCONJ
ap-3483	369	2	y2)2	y2)2	PRON
ap-3483	369	3	,	,	PUNCT
ap-3483	369	4	−	−	PROPN
ap-3483	369	5	2x3	2x3	NUM
ap-3483	369	6	+	+	NUM
ap-3483	369	7	x2y	x2y	X
ap-3483	370	1	+	+	CCONJ
ap-3483	370	2	y(y2	y(y2	ADJ
ap-3483	370	3	−	−	NOUN
ap-3483	370	4	1	1	NUM
ap-3483	370	5	)	)	PUNCT
ap-3483	371	1	+	+	NUM
ap-3483	371	2	2x(1	2x(1	NUM
ap-3483	371	3	+	+	CCONJ
ap-3483	371	4	y2	y2	NUM
ap-3483	371	5	)	)	PUNCT
ap-3483	371	6	(	(	PUNCT
ap-3483	371	7	1	1	NUM
ap-3483	371	8	+	+	NUM
ap-3483	371	9	x2	x2	PROPN
ap-3483	372	1	+	+	CCONJ
ap-3483	372	2	y2)2	y2)2	PRON
ap-3483	372	3	,	,	PUNCT
ap-3483	372	4	2(x2	2(x2	NUM
ap-3483	372	5	+	+	CCONJ
ap-3483	372	6	y2	y2	NOUN
ap-3483	372	7	)	)	PUNCT
ap-3483	372	8	(	(	PUNCT
ap-3483	372	9	1	1	NUM
ap-3483	372	10	+	+	NUM
ap-3483	372	11	x2	x2	PROPN
ap-3483	373	1	+	+	CCONJ
ap-3483	373	2	y2)2	y2)2	PRON
ap-3483	373	3	)	)	PUNCT
ap-3483	373	4	.	.	PUNCT
ap-3483	374	1	(	(	PUNCT
ap-3483	374	2	4.33	4.33	NUM
ap-3483	374	3	)	)	PUNCT
ap-3483	374	4	the	the	DET
ap-3483	374	5	su(2)-valued	su(2)-value	VERB
ap-3483	374	6	gauges	gauge	NOUN
ap-3483	374	7	sgk	sgk	NOUN
ap-3483	374	8	=	=	SYM
ap-3483	374	9	(	(	PUNCT
ap-3483	374	10	prωgφk)φ−1	prωgφk)φ−1	NUM
ap-3483	374	11	k	k	PROPN
ap-3483	374	12	associated	associate	VERB
ap-3483	374	13	with	with	ADP
ap-3483	374	14	the	the	DET
ap-3483	374	15	scaling	scaling	ADJ
ap-3483	374	16	symmetries	symmetry	NOUN
ap-3483	374	17	ωgk	ωgk	NOUN
ap-3483	374	18	are	be	AUX
ap-3483	374	19	given	give	VERB
ap-3483	374	20	by	by	ADP
ap-3483	374	21	sg0	sg0	NOUN
ap-3483	374	22	=	=	SYM
ap-3483	374	23	sg1	sg1	NOUN
ap-3483	374	24	=	=	SYM
ap-3483	374	25	2	2	NUM
ap-3483	374	26	(	(	PUNCT
ap-3483	374	27	t2	t2	NOUN
ap-3483	374	28	+	+	CCONJ
ap-3483	374	29	1)(1	1)(1	NUM
ap-3483	374	30	+	+	CCONJ
ap-3483	374	31	|z|2)2	|z|2)2	NOUN
ap-3483	374	32	·	·	PUNCT
ap-3483	374	33	(	(	PUNCT
ap-3483	374	34	2it|z|2	2it|z|2	NUM
ap-3483	374	35	iz̄[i−	iz̄[i−	NOUN
ap-3483	374	36	t+	t+	NUM
ap-3483	374	37	|z|2(t+	|z|2(t+	PROPN
ap-3483	374	38	i	i	NOUN
ap-3483	374	39	)	)	PUNCT
ap-3483	374	40	]	]	PUNCT
ap-3483	375	1	z[1−	z[1−	PROPN
ap-3483	375	2	it+	it+	INTJ
ap-3483	375	3	|z|2(1	|z|2(1	PROPN
ap-3483	375	4	+	+	CCONJ
ap-3483	375	5	it	it	PRON
ap-3483	375	6	)	)	PUNCT
ap-3483	375	7	]	]	PUNCT
ap-3483	375	8	−2it|z|2	−2it|z|2	X
ap-3483	375	9	)	)	PUNCT
ap-3483	375	10	,	,	PUNCT
ap-3483	375	11	(	(	PUNCT
ap-3483	375	12	4.34	4.34	NUM
ap-3483	375	13	)	)	PUNCT
ap-3483	375	14	where	where	SCONJ
ap-3483	375	15	detsgk	detsgk	NOUN
ap-3483	375	16	6=	6=	PRON
ap-3483	375	17	0	0	NUM
ap-3483	375	18	.	.	X
ap-3483	375	19	iii	iii	X
ap-3483	375	20	.	.	PUNCT
ap-3483	376	1	in	in	ADP
ap-3483	376	2	the	the	DET
ap-3483	376	3	case	case	NOUN
ap-3483	376	4	of	of	ADP
ap-3483	376	5	surfaces	surface	NOUN
ap-3483	376	6	associated	associate	VERB
ap-3483	376	7	with	with	ADP
ap-3483	376	8	the	the	DET
ap-3483	376	9	conformal	conformal	ADJ
ap-3483	376	10	symmetries	symmetry	NOUN
ap-3483	376	11	ωck	ωck	PROPN
ap-3483	376	12	=	=	SYM
ap-3483	376	13	−gk(z)∂	−gk(z)∂	PROPN
ap-3483	376	14	−	−	PROPN
ap-3483	376	15	ḡk(z̄)∂̄	ḡk(z̄)∂̄	PROPN
ap-3483	376	16	,	,	PUNCT
ap-3483	376	17	(	(	PUNCT
ap-3483	376	18	4.35	4.35	NUM
ap-3483	376	19	)	)	PUNCT
ap-3483	376	20	where	where	SCONJ
ap-3483	376	21	for	for	ADP
ap-3483	376	22	simplicity	simplicity	NOUN
ap-3483	376	23	we	we	PRON
ap-3483	376	24	have	have	AUX
ap-3483	376	25	assumed	assume	VERB
ap-3483	376	26	that	that	SCONJ
ap-3483	376	27	gk(z	gk(z	NOUN
ap-3483	376	28	)	)	PUNCT
ap-3483	376	29	=	=	SYM
ap-3483	377	1	1	1	NUM
ap-3483	377	2	+	+	CCONJ
ap-3483	377	3	i	i	PRON
ap-3483	377	4	,	,	PUNCT
ap-3483	377	5	the	the	DET
ap-3483	377	6	su(2)-valued	su(2)-value	VERB
ap-3483	377	7	immersion	immersion	NOUN
ap-3483	377	8	functions	function	NOUN
ap-3483	377	9	f	f	X
ap-3483	377	10	ck	ck	INTJ
ap-3483	377	11	are	be	AUX
ap-3483	377	12	given	give	VERB
ap-3483	377	13	by	by	ADP
ap-3483	377	14	[	[	X
ap-3483	377	15	12	12	NUM
ap-3483	377	16	]	]	X
ap-3483	377	17	f	f	X
ap-3483	377	18	ck	ck	NOUN
ap-3483	377	19	=	=	SYM
ap-3483	377	20	φ−1	φ−1	PROPN
ap-3483	377	21	k	k	X
ap-3483	377	22	(	(	PUNCT
ap-3483	377	23	u1k	u1k	PROPN
ap-3483	377	24	+	+	SYM
ap-3483	377	25	u2k)φk	u2k)φk	ADJ
ap-3483	377	26	,	,	PUNCT
ap-3483	377	27	(	(	PUNCT
ap-3483	377	28	4.36	4.36	NUM
ap-3483	377	29	)	)	PUNCT
ap-3483	378	1	where	where	SCONJ
ap-3483	378	2	u10	u10	PROPN
ap-3483	378	3	+	+	CCONJ
ap-3483	378	4	u20	u20	PROPN
ap-3483	378	5	=	=	SYM
ap-3483	378	6	u11	u11	PROPN
ap-3483	378	7	+	+	CCONJ
ap-3483	378	8	u21	u21	PROPN
ap-3483	378	9	=	=	SYM
ap-3483	378	10	2	2	NUM
ap-3483	378	11	(	(	PUNCT
ap-3483	378	12	t2	t2	NOUN
ap-3483	378	13	+	+	CCONJ
ap-3483	378	14	1)(1	1)(1	NUM
ap-3483	378	15	+	+	CCONJ
ap-3483	378	16	|z|2)2	|z|2)2	NOUN
ap-3483	378	17	·	·	PUNCT
ap-3483	378	18	(	(	PUNCT
ap-3483	378	19	2z	2z	NOUN
ap-3483	378	20	+	+	CCONJ
ap-3483	378	21	i(t+	i(t+	ADJ
ap-3483	378	22	i)(z	i)(z	NOUN
ap-3483	378	23	+	+	PUNCT
ap-3483	378	24	z̄	z̄	X
ap-3483	378	25	)	)	PUNCT
ap-3483	378	26	−1−	−1−	PROPN
ap-3483	378	27	it+	it+	PROPN
ap-3483	378	28	iz̄2(t+	iz̄2(t+	PROPN
ap-3483	378	29	i	i	PROPN
ap-3483	378	30	)	)	PUNCT
ap-3483	378	31	1	1	NUM
ap-3483	379	1	+	+	PUNCT
ap-3483	379	2	z2	z2	NOUN
ap-3483	379	3	+	+	CCONJ
ap-3483	379	4	it(z2	it(z2	PRON
ap-3483	379	5	−	−	PROPN
ap-3483	379	6	1	1	NUM
ap-3483	379	7	)	)	PUNCT
ap-3483	379	8	−[2z	−[2z	NOUN
ap-3483	380	1	+	+	X
ap-3483	380	2	i(t+	i(t+	ADJ
ap-3483	380	3	i)(z	i)(z	NOUN
ap-3483	381	1	+	+	PUNCT
ap-3483	381	2	z̄	z̄	NOUN
ap-3483	381	3	)	)	PUNCT
ap-3483	381	4	]	]	PUNCT
ap-3483	381	5	)	)	PUNCT
ap-3483	381	6	.	.	PUNCT
ap-3483	382	1	(	(	PUNCT
ap-3483	382	2	4.37	4.37	NUM
ap-3483	382	3	)	)	PUNCT
ap-3483	382	4	by	by	ADP
ap-3483	382	5	further	further	ADJ
ap-3483	382	6	computation	computation	NOUN
ap-3483	382	7	it	it	PRON
ap-3483	382	8	can	can	AUX
ap-3483	382	9	be	be	AUX
ap-3483	382	10	verified	verify	VERB
ap-3483	382	11	that	that	SCONJ
ap-3483	382	12	the	the	DET
ap-3483	382	13	gaussian	gaussian	ADJ
ap-3483	382	14	curvature	curvature	NOUN
ap-3483	382	15	and	and	CCONJ
ap-3483	382	16	the	the	DET
ap-3483	382	17	mean	mean	ADJ
ap-3483	382	18	curvature	curvature	NOUN
ap-3483	382	19	corresponding	correspond	VERB
ap-3483	382	20	to	to	ADP
ap-3483	382	21	the	the	DET
ap-3483	382	22	surfaces	surface	NOUN
ap-3483	382	23	f	f	X
ap-3483	382	24	ck	ck	INTJ
ap-3483	382	25	are	be	AUX
ap-3483	382	26	not	not	PART
ap-3483	382	27	constant	constant	ADJ
ap-3483	382	28	for	for	ADP
ap-3483	382	29	any	any	DET
ap-3483	382	30	value	value	NOUN
ap-3483	382	31	of	of	ADP
ap-3483	382	32	λ	λ	PROPN
ap-3483	382	33	.	.	PUNCT
ap-3483	383	1	the	the	DET
ap-3483	383	2	fact	fact	NOUN
ap-3483	383	3	that	that	SCONJ
ap-3483	383	4	the	the	DET
ap-3483	383	5	surfaces	surface	NOUN
ap-3483	383	6	f	f	X
ap-3483	383	7	ck	ck	INTJ
ap-3483	383	8	have	have	AUX
ap-3483	383	9	the	the	DET
ap-3483	383	10	euler	euler	VERB
ap-3483	383	11	-	-	PUNCT
ap-3483	383	12	poincaré	poincaré	PROPN
ap-3483	383	13	characters	character	NOUN
ap-3483	383	14	[	[	X
ap-3483	383	15	10	10	NUM
ap-3483	383	16	]	]	X
ap-3483	383	17	χk	χk	NOUN
ap-3483	383	18	=	=	SYM
ap-3483	383	19	−1	−1	NOUN
ap-3483	383	20	π	π	X
ap-3483	383	21	∫∫	∫∫	PROPN
ap-3483	383	22	s2	s2	VERB
ap-3483	383	23	∂∂̄	∂∂̄	ADJ
ap-3483	383	24	ln	ln	NOUN
ap-3483	384	1	[	[	X
ap-3483	384	2	tr(∂pk	tr(∂pk	NOUN
ap-3483	384	3	·	·	PUNCT
ap-3483	384	4	∂̄pk)]dx1dx2	∂̄pk)]dx1dx2	PROPN
ap-3483	384	5	(	(	PUNCT
ap-3483	384	6	4.38	4.38	NUM
ap-3483	384	7	)	)	PUNCT
ap-3483	384	8	equal	equal	ADJ
ap-3483	384	9	to	to	ADP
ap-3483	384	10	2	2	NUM
ap-3483	384	11	and	and	CCONJ
ap-3483	384	12	positive	positive	ADJ
ap-3483	384	13	gaussian	gaussian	NOUN
ap-3483	384	14	curvature	curvature	NOUN
ap-3483	384	15	k	k	PROPN
ap-3483	384	16	>	>	X
ap-3483	384	17	0	0	NUM
ap-3483	384	18	means	mean	VERB
ap-3483	384	19	that	that	SCONJ
ap-3483	384	20	the	the	DET
ap-3483	384	21	surfaces	surface	NOUN
ap-3483	385	1	f	f	X
ap-3483	385	2	ck	ck	INTJ
ap-3483	385	3	are	be	AUX
ap-3483	385	4	homeomorphic	homeomorphic	ADJ
ap-3483	385	5	to	to	ADP
ap-3483	385	6	ovaloids	ovaloid	NOUN
ap-3483	385	7	(	(	PUNCT
ap-3483	385	8	see	see	VERB
ap-3483	385	9	fig	fig	NOUN
ap-3483	385	10	.	.	PUNCT
ap-3483	386	1	2c	2c	NUM
ap-3483	386	2	)	)	PUNCT
ap-3483	386	3	.	.	PUNCT
ap-3483	387	1	the	the	DET
ap-3483	387	2	surfaces	surface	NOUN
ap-3483	388	1	f	f	X
ap-3483	388	2	ck	ck	INTJ
ap-3483	388	3	associated	associate	VERB
ap-3483	388	4	with	with	ADP
ap-3483	388	5	the	the	DET
ap-3483	388	6	conformal	conformal	ADJ
ap-3483	388	7	symmetries	symmetry	NOUN
ap-3483	388	8	ωck	ωck	PROPN
ap-3483	388	9	are	be	AUX
ap-3483	388	10	cardioid	cardioid	NOUN
ap-3483	388	11	surfaces	surface	NOUN
ap-3483	388	12	which	which	PRON
ap-3483	388	13	can	can	AUX
ap-3483	388	14	be	be	AUX
ap-3483	388	15	parametrized	parametrize	VERB
ap-3483	388	16	as	as	SCONJ
ap-3483	388	17	follows	follow	VERB
ap-3483	388	18	f	f	NOUN
ap-3483	388	19	ck	ck	NOUN
ap-3483	389	1	=	=	PRON
ap-3483	389	2	(	(	PUNCT
ap-3483	389	3	x2	x2	INTJ
ap-3483	389	4	−	−	PROPN
ap-3483	389	5	1−	1−	NUM
ap-3483	389	6	4xy	4xy	NOUN
ap-3483	389	7	−	−	PROPN
ap-3483	390	1	y2	y2	INTJ
ap-3483	390	2	(	(	PUNCT
ap-3483	390	3	1	1	NUM
ap-3483	390	4	+	+	NUM
ap-3483	390	5	x2	x2	PROPN
ap-3483	391	1	+	+	CCONJ
ap-3483	391	2	y2)2	y2)2	NOUN
ap-3483	391	3	,	,	PUNCT
ap-3483	391	4	−2(1	−2(1	NOUN
ap-3483	391	5	+	+	CCONJ
ap-3483	391	6	x2	x2	PROPN
ap-3483	392	1	+	+	CCONJ
ap-3483	392	2	xy	xy	PROPN
ap-3483	392	3	−	−	PROPN
ap-3483	392	4	y2	y2	PROPN
ap-3483	392	5	)	)	PUNCT
ap-3483	392	6	(	(	PUNCT
ap-3483	392	7	1	1	X
ap-3483	392	8	+	+	NUM
ap-3483	392	9	x2	x2	PROPN
ap-3483	393	1	+	+	CCONJ
ap-3483	393	2	y2)2	y2)2	PRON
ap-3483	393	3	,	,	PUNCT
ap-3483	393	4	2(2x−	2(2x−	NUM
ap-3483	393	5	y	y	NOUN
ap-3483	393	6	)	)	PUNCT
ap-3483	393	7	(	(	PUNCT
ap-3483	393	8	1	1	NUM
ap-3483	393	9	+	+	NUM
ap-3483	393	10	x2	x2	PROPN
ap-3483	393	11	+	+	CCONJ
ap-3483	393	12	y2)2	y2)2	NOUN
ap-3483	393	13	)	)	PUNCT
ap-3483	393	14	(	(	PUNCT
ap-3483	393	15	4.39	4.39	NUM
ap-3483	393	16	)	)	PUNCT
ap-3483	393	17	the	the	DET
ap-3483	393	18	su(2)-valued	su(2)-value	VERB
ap-3483	393	19	gauges	gauge	NOUN
ap-3483	393	20	sck	sck	PROPN
ap-3483	393	21	associated	associate	VERB
ap-3483	393	22	with	with	ADP
ap-3483	393	23	the	the	DET
ap-3483	393	24	conformal	conformal	ADJ
ap-3483	393	25	symmetries	symmetry	NOUN
ap-3483	393	26	ωcktake	ωcktake	VERB
ap-3483	393	27	the	the	DET
ap-3483	393	28	form	form	NOUN
ap-3483	393	29	sc0	sc0	NOUN
ap-3483	393	30	=	=	SYM
ap-3483	393	31	(	(	PUNCT
ap-3483	393	32	prωcφ0)φ−1	prωcφ0)φ−1	X
ap-3483	393	33	0	0	NUM
ap-3483	393	34	=	=	SYM
ap-3483	393	35	2	2	NUM
ap-3483	393	36	(	(	PUNCT
ap-3483	393	37	1	1	NUM
ap-3483	393	38	+	+	CCONJ
ap-3483	393	39	|z|2)2	|z|2)2	NOUN
ap-3483	393	40	·	·	PUNCT
ap-3483	393	41	(	(	PUNCT
ap-3483	393	42	−i(1−i)(t−i)z+(1+i)(1−it)z̄	−i(1−i)(t−i)z+(1+i)(1−it)z̄	VERB
ap-3483	393	43	t2	t2	NOUN
ap-3483	393	44	+	+	NOUN
ap-3483	393	45	1	1	NUM
ap-3483	393	46	i(1+i)(t+i)−(1−i)z2(t−i	i(1+i)(t+i)−(1−i)z2(t−i	NOUN
ap-3483	393	47	)	)	PUNCT
ap-3483	393	48	(	(	PUNCT
ap-3483	393	49	t+i)2	t+i)2	PROPN
ap-3483	393	50	(	(	PUNCT
ap-3483	393	51	1−i)(1+it)+(1+i)(1−it)z̄2	1−i)(1+it)+(1+i)(1−it)z̄2	NUM
ap-3483	393	52	(	(	PUNCT
ap-3483	393	53	t−i)2	t−i)2	PROPN
ap-3483	393	54	(	(	PUNCT
ap-3483	393	55	1−i)(1+it)z+i(1+i)(t+i)z̄	1−i)(1+it)z+i(1+i)(t+i)z̄	NUM
ap-3483	393	56	t2	t2	NOUN
ap-3483	393	57	+	+	PROPN
ap-3483	393	58	1	1	NUM
ap-3483	393	59	)	)	PUNCT
ap-3483	393	60	,	,	PUNCT
ap-3483	393	61	sc1	sc1	NOUN
ap-3483	393	62	=	=	SYM
ap-3483	393	63	(	(	PUNCT
ap-3483	393	64	prωcφ1)φ−1	prωcφ1)φ−1	ADV
ap-3483	393	65	1	1	NUM
ap-3483	393	66	=	=	SYM
ap-3483	393	67	2	2	NUM
ap-3483	393	68	(	(	PUNCT
ap-3483	393	69	1	1	NUM
ap-3483	393	70	+	+	CCONJ
ap-3483	393	71	|z|2)2	|z|2)2	NOUN
ap-3483	393	72	·	·	PUNCT
ap-3483	393	73	(	(	PUNCT
ap-3483	393	74	−i(1−i)(t−i)z+(1+i)(1−it)z̄	−i(1−i)(t−i)z+(1+i)(1−it)z̄	VERB
ap-3483	393	75	t2	t2	NOUN
ap-3483	393	76	+	+	NOUN
ap-3483	393	77	1	1	NUM
ap-3483	393	78	i(t−i)2[(1+i)(t+i)−(1−i)(t−i)z2	i(t−i)2[(1+i)(t+i)−(1−i)(t−i)z2	NOUN
ap-3483	393	79	]	]	PUNCT
ap-3483	393	80	(	(	PUNCT
ap-3483	393	81	t+i)4	t+i)4	X
ap-3483	393	82	(	(	PUNCT
ap-3483	393	83	t+i)2[(1−i)(1+it)+(1+i)(1−it)z̄2	t+i)2[(1−i)(1+it)+(1+i)(1−it)z̄2	PROPN
ap-3483	393	84	]	]	X
ap-3483	393	85	(	(	PUNCT
ap-3483	393	86	t−i)4	t−i)4	NUM
ap-3483	393	87	(	(	PUNCT
ap-3483	393	88	1−i)(1+it)z+i(1+i)(t+i)z̄	1−i)(1+it)z+i(1+i)(t+i)z̄	NUM
ap-3483	393	89	t2	t2	NOUN
ap-3483	393	90	+	+	NOUN
ap-3483	393	91	1	1	NUM
ap-3483	393	92	)	)	PUNCT
ap-3483	393	93	,	,	PUNCT
ap-3483	393	94	(	(	PUNCT
ap-3483	393	95	4.40	4.40	NUM
ap-3483	393	96	)	)	PUNCT
ap-3483	394	1	where	where	SCONJ
ap-3483	394	2	detsck	detsck	VERB
ap-3483	394	3	6=	6=	PRON
ap-3483	394	4	0	0	NUM
ap-3483	394	5	.	.	X
ap-3483	394	6	iv	iv	X
ap-3483	394	7	.	.	PUNCT
ap-3483	395	1	if	if	SCONJ
ap-3483	395	2	the	the	DET
ap-3483	395	3	generalized	generalized	ADJ
ap-3483	395	4	symmetries	symmetry	NOUN
ap-3483	395	5	of	of	ADP
ap-3483	395	6	the	the	DET
ap-3483	395	7	cp	cp	PROPN
ap-3483	395	8	1	1	NUM
ap-3483	395	9	model	model	NOUN
ap-3483	395	10	(	(	PUNCT
ap-3483	395	11	4.6	4.6	NUM
ap-3483	395	12	)	)	PUNCT
ap-3483	395	13	are	be	AUX
ap-3483	395	14	written	write	VERB
ap-3483	395	15	in	in	ADP
ap-3483	395	16	the	the	DET
ap-3483	395	17	evolutionary	evolutionary	ADJ
ap-3483	395	18	form	form	NOUN
ap-3483	395	19	ωrk	ωrk	VERB
ap-3483	395	20	=	=	SYM
ap-3483	395	21	(	(	PUNCT
ap-3483	395	22	d2	d2	PROPN
ap-3483	395	23	1u1k	1u1k	PROPN
ap-3483	395	24	+	+	PROPN
ap-3483	395	25	d2	d2	PROPN
ap-3483	395	26	2u1k	2u1k	PROPN
ap-3483	396	1	+	+	CCONJ
ap-3483	397	1	[	[	X
ap-3483	397	2	d1u1k	d1u1k	NUM
ap-3483	397	3	,	,	PUNCT
ap-3483	397	4	u1k	u1k	PROPN
ap-3483	397	5	]	]	X
ap-3483	398	1	+	+	PROPN
ap-3483	398	2	[	[	X
ap-3483	398	3	d2u1k	d2u1k	NUM
ap-3483	398	4	,	,	PUNCT
ap-3483	398	5	u1k	u1k	PROPN
ap-3483	398	6	]	]	PUNCT
ap-3483	398	7	)	)	PUNCT
ap-3483	398	8	∂	∂	NOUN
ap-3483	399	1	∂θ1	∂θ1	NOUN
ap-3483	399	2	+	+	CCONJ
ap-3483	399	3	(	(	PUNCT
ap-3483	399	4	d2	d2	PROPN
ap-3483	399	5	1u2k+d2	1u2k+d2	PROPN
ap-3483	399	6	2u2k+[d2u2k	2u2k+[d2u2k	NOUN
ap-3483	399	7	,	,	PUNCT
ap-3483	399	8	u2k	u2k	X
ap-3483	399	9	]	]	X
ap-3483	399	10	+	+	CCONJ
ap-3483	400	1	[	[	X
ap-3483	400	2	d1u2k	d1u2k	NOUN
ap-3483	400	3	,	,	PUNCT
ap-3483	400	4	u2k	u2k	X
ap-3483	400	5	]	]	PUNCT
ap-3483	400	6	)	)	PUNCT
ap-3483	400	7	∂	∂	PUNCT
ap-3483	400	8	∂θ2	∂θ2	NOUN
ap-3483	400	9	,	,	PUNCT
ap-3483	400	10	k	k	NOUN
ap-3483	400	11	=	=	SYM
ap-3483	400	12	1	1	NUM
ap-3483	400	13	,	,	PUNCT
ap-3483	400	14	2	2	NUM
ap-3483	400	15	(	(	PUNCT
ap-3483	400	16	4.41	4.41	NUM
ap-3483	400	17	)	)	PUNCT
ap-3483	400	18	(	(	PUNCT
ap-3483	400	19	where	where	SCONJ
ap-3483	400	20	θ1	θ1	NOUN
ap-3483	400	21	and	and	CCONJ
ap-3483	400	22	θ2	θ2	PROPN
ap-3483	400	23	are	be	AUX
ap-3483	400	24	complex	complex	ADV
ap-3483	400	25	-	-	PUNCT
ap-3483	400	26	valued	value	VERB
ap-3483	400	27	functions	function	NOUN
ap-3483	400	28	obtained	obtain	VERB
ap-3483	400	29	from	from	ADP
ap-3483	400	30	(	(	PUNCT
ap-3483	400	31	4.12	4.12	NUM
ap-3483	400	32	)	)	PUNCT
ap-3483	400	33	)	)	PUNCT
ap-3483	401	1	then	then	ADV
ap-3483	401	2	the	the	DET
ap-3483	401	3	su(2)-valued	su(2)-value	VERB
ap-3483	401	4	integrated	integrate	VERB
ap-3483	401	5	form	form	NOUN
ap-3483	401	6	of	of	ADP
ap-3483	401	7	the	the	DET
ap-3483	401	8	immersion	immersion	NOUN
ap-3483	401	9	becomes	become	VERB
ap-3483	401	10	[	[	X
ap-3483	401	11	14	14	NUM
ap-3483	401	12	]	]	PUNCT
ap-3483	401	13	ffgk	ffgk	NOUN
ap-3483	401	14	=	=	PUNCT
ap-3483	401	15	φ−1(prωrk	φ−1(prωrk	PROPN
ap-3483	401	16	φk	φk	ADP
ap-3483	401	17	)	)	PUNCT
ap-3483	401	18	=	=	SYM
ap-3483	401	19	φ−1	φ−1	PROPN
ap-3483	401	20	k	k	X
ap-3483	401	21	(	(	PUNCT
ap-3483	401	22	d1u1k	d1u1k	X
ap-3483	401	23	+	+	ADJ
ap-3483	401	24	d2u2k)φk	d2u2k)φk	PROPN
ap-3483	401	25	.	.	PUNCT
ap-3483	402	1	(	(	PUNCT
ap-3483	402	2	4.42	4.42	NUM
ap-3483	402	3	)	)	PUNCT
ap-3483	402	4	the	the	DET
ap-3483	402	5	tangent	tangent	NOUN
ap-3483	402	6	vectors	vector	NOUN
ap-3483	402	7	to	to	ADP
ap-3483	402	8	this	this	DET
ap-3483	402	9	surface	surface	NOUN
ap-3483	402	10	are	be	AUX
ap-3483	402	11	given	give	VERB
ap-3483	402	12	by	by	ADP
ap-3483	402	13	d1f	d1f	NOUN
ap-3483	402	14	fg	fg	PROPN
ap-3483	402	15	k	k	PROPN
ap-3483	402	16	=	=	PUNCT
ap-3483	402	17	φ−1	φ−1	PROPN
ap-3483	402	18	k	k	PROPN
ap-3483	402	19	(	(	PUNCT
ap-3483	402	20	prωrk	prωrk	PROPN
ap-3483	402	21	u1k)φk	u1k)φk	ADJ
ap-3483	402	22	=	=	PUNCT
ap-3483	402	23	φ−1	φ−1	PROPN
ap-3483	402	24	k	k	PROPN
ap-3483	402	25	(	(	PUNCT
ap-3483	402	26	d2	d2	PROPN
ap-3483	402	27	1u1k	1u1k	PROPN
ap-3483	402	28	+	+	PROPN
ap-3483	402	29	d2	d2	PROPN
ap-3483	402	30	2u1k	2u1k	PROPN
ap-3483	403	1	+	+	PROPN
ap-3483	404	1	[	[	X
ap-3483	404	2	d1u1k	d1u1k	ADJ
ap-3483	404	3	,	,	PUNCT
ap-3483	404	4	u1k	u1k	PROPN
ap-3483	404	5	]	]	X
ap-3483	405	1	+	+	CCONJ
ap-3483	405	2	[	[	X
ap-3483	405	3	d2u1k	d2u1k	NUM
ap-3483	405	4	,	,	PUNCT
ap-3483	405	5	u1k])φk	u1k])φk	PROPN
ap-3483	405	6	,	,	PUNCT
ap-3483	405	7	d2f	d2f	PROPN
ap-3483	405	8	fg	fg	PROPN
ap-3483	405	9	k	k	PROPN
ap-3483	405	10	=	=	PUNCT
ap-3483	405	11	φ−1	φ−1	PROPN
ap-3483	405	12	k	k	PROPN
ap-3483	405	13	(	(	PUNCT
ap-3483	405	14	prωrk	prωrk	PROPN
ap-3483	405	15	u2k)φk	u2k)φk	PROPN
ap-3483	405	16	=	=	PUNCT
ap-3483	405	17	φ−1	φ−1	PROPN
ap-3483	405	18	k	k	PROPN
ap-3483	405	19	(	(	PUNCT
ap-3483	405	20	d2	d2	PROPN
ap-3483	405	21	1u2k	1u2k	PROPN
ap-3483	405	22	+	+	ADJ
ap-3483	405	23	d2	d2	PROPN
ap-3483	405	24	2u2k	2u2k	NOUN
ap-3483	405	25	+	+	PROPN
ap-3483	405	26	[	[	X
ap-3483	405	27	d2u2k	d2u2k	NOUN
ap-3483	405	28	,	,	PUNCT
ap-3483	405	29	u2k	u2k	X
ap-3483	405	30	]	]	X
ap-3483	405	31	+	+	CCONJ
ap-3483	405	32	[	[	X
ap-3483	405	33	d1u2k	d1u2k	NOUN
ap-3483	405	34	,	,	PUNCT
ap-3483	405	35	u2k])φk	u2k])φk	PROPN
ap-3483	405	36	.	.	PUNCT
ap-3483	405	37	(	(	PUNCT
ap-3483	405	38	4.43	4.43	NUM
ap-3483	405	39	)	)	PUNCT
ap-3483	405	40	the	the	DET
ap-3483	405	41	surfaces	surface	NOUN
ap-3483	405	42	ffgk	ffgk	NOUN
ap-3483	405	43	also	also	ADV
ap-3483	405	44	have	have	VERB
ap-3483	405	45	positive	positive	ADJ
ap-3483	405	46	gaussian	gaussian	ADJ
ap-3483	405	47	curvatures	curvature	NOUN
ap-3483	405	48	k	k	NOUN
ap-3483	405	49	>	>	PUNCT
ap-3483	405	50	0	0	PUNCT
ap-3483	405	51	and	and	CCONJ
ap-3483	405	52	the	the	DET
ap-3483	405	53	euler	euler	PROPN
ap-3483	405	54	-	-	PUNCT
ap-3483	405	55	poincaré	poincaré	PROPN
ap-3483	405	56	characters	character	NOUN
ap-3483	405	57	are	be	AUX
ap-3483	405	58	equal	equal	ADJ
ap-3483	405	59	to	to	ADP
ap-3483	405	60	2	2	NUM
ap-3483	405	61	.	.	PUNCT
ap-3483	406	1	in	in	ADP
ap-3483	406	2	the	the	DET
ap-3483	406	3	parametrization	parametrization	NOUN
ap-3483	406	4	x	x	X
ap-3483	406	5	,	,	PUNCT
ap-3483	406	6	y	y	PROPN
ap-3483	406	7	,	,	PUNCT
ap-3483	406	8	the	the	DET
ap-3483	406	9	surfaces	surface	NOUN
ap-3483	406	10	ffgk	ffgk	NOUN
ap-3483	406	11	take	take	VERB
ap-3483	406	12	the	the	DET
ap-3483	406	13	form	form	NOUN
ap-3483	406	14	ffgk	ffgk	NOUN
ap-3483	406	15	=	=	PUNCT
ap-3483	406	16	(	(	PUNCT
ap-3483	406	17	−x	−x	NOUN
ap-3483	406	18	3	3	NUM
ap-3483	406	19	−	−	PRON
ap-3483	406	20	6x2y	6x2y	NOUN
ap-3483	406	21	−	−	NOUN
ap-3483	406	22	x(1	x(1	PROPN
ap-3483	406	23	+	+	CCONJ
ap-3483	406	24	3y2	3y2	NUM
ap-3483	406	25	)	)	PUNCT
ap-3483	407	1	+	+	CCONJ
ap-3483	407	2	2y(1	2y(1	NUM
ap-3483	407	3	+	+	NUM
ap-3483	407	4	y2	y2	NOUN
ap-3483	407	5	)	)	PUNCT
ap-3483	407	6	(	(	PUNCT
ap-3483	407	7	1	1	X
ap-3483	407	8	+	+	NUM
ap-3483	407	9	x2	x2	PROPN
ap-3483	408	1	+	+	CCONJ
ap-3483	408	2	y2)3	y2)3	NUM
ap-3483	408	3	,	,	PUNCT
ap-3483	408	4	2x3	2x3	NUM
ap-3483	408	5	+	+	CCONJ
ap-3483	408	6	y	y	NOUN
ap-3483	408	7	+	+	NOUN
ap-3483	408	8	3x2y	3x2y	NUM
ap-3483	408	9	−	−	NOUN
ap-3483	408	10	y3	y3	NOUN
ap-3483	408	11	+	+	NUM
ap-3483	408	12	x(2−	x(2−	PROPN
ap-3483	408	13	6y2	6y2	NUM
ap-3483	408	14	)	)	PUNCT
ap-3483	408	15	(	(	PUNCT
ap-3483	408	16	1	1	NUM
ap-3483	408	17	+	+	NUM
ap-3483	408	18	x2	x2	PROPN
ap-3483	409	1	+	+	CCONJ
ap-3483	409	2	y2)3	y2)3	X
ap-3483	409	3	,	,	PUNCT
ap-3483	409	4	−	−	PROPN
ap-3483	409	5	2(x2	2(x2	NOUN
ap-3483	410	1	−	−	NOUN
ap-3483	410	2	4xy	4xy	ADJ
ap-3483	410	3	−	−	PROPN
ap-3483	410	4	y2	y2	PROPN
ap-3483	410	5	)	)	PUNCT
ap-3483	410	6	(	(	PUNCT
ap-3483	410	7	1	1	X
ap-3483	410	8	+	+	NUM
ap-3483	410	9	x2	x2	PROPN
ap-3483	411	1	+	+	CCONJ
ap-3483	411	2	y2)3	y2)3	X
ap-3483	411	3	)	)	PUNCT
ap-3483	411	4	(	(	PUNCT
ap-3483	411	5	4.44	4.44	NUM
ap-3483	411	6	)	)	PUNCT
ap-3483	411	7	and	and	CCONJ
ap-3483	411	8	they	they	PRON
ap-3483	411	9	are	be	AUX
ap-3483	411	10	homeomorphic	homeomorphic	ADJ
ap-3483	411	11	to	to	ADP
ap-3483	411	12	ovaloids	ovaloid	NOUN
ap-3483	411	13	.	.	PUNCT
ap-3483	412	1	the	the	DET
ap-3483	412	2	su(2)-valued	su(2)-value	VERB
ap-3483	412	3	gauges	gauge	NOUN
ap-3483	412	4	sfgk	sfgk	NOUN
ap-3483	412	5	associated	associate	VERB
ap-3483	412	6	with	with	ADP
ap-3483	412	7	the	the	DET
ap-3483	412	8	generalized	generalized	ADJ
ap-3483	412	9	symmetry	symmetry	NOUN
ap-3483	412	10	ωrk	ωrk	AUX
ap-3483	412	11	take	take	VERB
ap-3483	412	12	the	the	DET
ap-3483	412	13	form	form	NOUN
ap-3483	412	14	sfgk	sfgk	NOUN
ap-3483	412	15	=	=	SYM
ap-3483	412	16	(	(	PUNCT
ap-3483	412	17	prωrk	prωrk	PROPN
ap-3483	412	18	φk)φ−1	φk)φ−1	PROPN
ap-3483	412	19	k	k	X
ap-3483	413	1	=	=	PUNCT
ap-3483	413	2	d1u1k	d1u1k	X
ap-3483	413	3	+	+	NOUN
ap-3483	413	4	d2u2k	d2u2k	X
ap-3483	413	5	.	.	PUNCT
ap-3483	414	1	(	(	PUNCT
ap-3483	414	2	4.45	4.45	NUM
ap-3483	414	3	)	)	PUNCT
ap-3483	414	4	189	189	NUM
ap-3483	414	5	a.	a.	NOUN
ap-3483	414	6	m.	m.	NOUN
ap-3483	414	7	grundland	grundland	PROPN
ap-3483	414	8	,	,	PUNCT
ap-3483	414	9	d.	d.	PROPN
ap-3483	414	10	levi	levi	PROPN
ap-3483	414	11	,	,	PUNCT
ap-3483	414	12	l.	l.	PROPN
ap-3483	414	13	martina	martina	PROPN
ap-3483	414	14	acta	acta	PROPN
ap-3483	414	15	polytechnica	polytechnica	PROPN
ap-3483	414	16	under	under	ADP
ap-3483	414	17	the	the	DET
ap-3483	414	18	assumption	assumption	NOUN
ap-3483	414	19	that	that	SCONJ
ap-3483	414	20	pk	pk	NOUN
ap-3483	414	21	are	be	AUX
ap-3483	414	22	holomorphic	holomorphic	ADJ
ap-3483	414	23	or	or	CCONJ
ap-3483	414	24	antiholomorphic	antiholomorphic	ADJ
ap-3483	414	25	projectors	projector	NOUN
ap-3483	414	26	(	(	PUNCT
ap-3483	414	27	4.22	4.22	NUM
ap-3483	414	28	)	)	PUNCT
ap-3483	414	29	the	the	DET
ap-3483	414	30	gauges	gauge	NOUN
ap-3483	414	31	sfgk	sfgk	NOUN
ap-3483	414	32	take	take	VERB
ap-3483	414	33	the	the	DET
ap-3483	414	34	form	form	NOUN
ap-3483	414	35	sfg0	sfg0	NOUN
ap-3483	414	36	=	=	SYM
ap-3483	414	37	sfg1	sfg1	PROPN
ap-3483	414	38	=	=	SYM
ap-3483	414	39	4	4	NUM
ap-3483	414	40	(	(	PUNCT
ap-3483	414	41	t2	t2	NOUN
ap-3483	414	42	+	+	CCONJ
ap-3483	414	43	1)(1	1)(1	NUM
ap-3483	414	44	+	+	CCONJ
ap-3483	414	45	|z|2)3	|z|2)3	PROPN
ap-3483	414	46	·	·	PUNCT
ap-3483	414	47	(	(	PUNCT
ap-3483	414	48	−z2(1	−z2(1	NOUN
ap-3483	414	49	+	+	CCONJ
ap-3483	414	50	it	it	PRON
ap-3483	414	51	)	)	PUNCT
ap-3483	415	1	+	+	CCONJ
ap-3483	415	2	z̄2(1−	z̄2(1−	VERB
ap-3483	415	3	it	it	PRON
ap-3483	415	4	)	)	PUNCT
ap-3483	415	5	z̄3(1−	z̄3(1−	NOUN
ap-3483	415	6	it	it	PRON
ap-3483	415	7	)	)	PUNCT
ap-3483	416	1	+	+	CCONJ
ap-3483	416	2	z(it+	z(it+	PROPN
ap-3483	416	3	1	1	NUM
ap-3483	416	4	)	)	PUNCT
ap-3483	416	5	−iz3(t−	−iz3(t−	PUNCT
ap-3483	417	1	i	i	NOUN
ap-3483	417	2	)	)	PUNCT
ap-3483	418	1	+	+	CCONJ
ap-3483	418	2	iz̄(t+	iz̄(t+	PROPN
ap-3483	418	3	i	i	NOUN
ap-3483	418	4	)	)	PUNCT
ap-3483	418	5	z2(1	z2(1	NOUN
ap-3483	418	6	+	+	CCONJ
ap-3483	418	7	it)−	it)−	PRON
ap-3483	418	8	z̄2(1−	z̄2(1−	VERB
ap-3483	418	9	it	it	PRON
ap-3483	418	10	)	)	PUNCT
ap-3483	418	11	)	)	PUNCT
ap-3483	418	12	,	,	PUNCT
ap-3483	418	13	(	(	PUNCT
ap-3483	418	14	4.46	4.46	NUM
ap-3483	418	15	)	)	PUNCT
ap-3483	418	16	where	where	SCONJ
ap-3483	418	17	detsfgk	detsfgk	NOUN
ap-3483	418	18	6=	6=	ADP
ap-3483	418	19	0	0	NUM
ap-3483	418	20	.	.	PUNCT
ap-3483	419	1	hence	hence	ADV
ap-3483	419	2	the	the	DET
ap-3483	419	3	mappings	mapping	NOUN
ap-3483	419	4	mk	mk	NOUN
ap-3483	419	5	=	=	SYM
ap-3483	419	6	sstk	sstk	ADJ
ap-3483	419	7	(	(	PUNCT
ap-3483	419	8	sfgk	sfgk	NOUN
ap-3483	419	9	)	)	PUNCT
ap-3483	419	10	−1	−1	NOUN
ap-3483	419	11	from	from	ADP
ap-3483	419	12	the	the	DET
ap-3483	419	13	fg	fg	PROPN
ap-3483	419	14	immersion	immersion	NOUN
ap-3483	419	15	formulas	formula	NOUN
ap-3483	419	16	to	to	ADP
ap-3483	419	17	the	the	DET
ap-3483	419	18	st	st	PROPN
ap-3483	419	19	immersion	immersion	NOUN
ap-3483	419	20	formulas	formula	NOUN
ap-3483	419	21	are	be	AUX
ap-3483	419	22	given	give	VERB
ap-3483	419	23	by	by	ADP
ap-3483	419	24	m0	m0	PROPN
ap-3483	419	25	=	=	SYM
ap-3483	419	26	sst0	sst0	PROPN
ap-3483	419	27	(	(	PUNCT
ap-3483	419	28	sfg0	sfg0	PROPN
ap-3483	419	29	)	)	PUNCT
ap-3483	419	30	−1	−1	NOUN
ap-3483	420	1	=	=	SYM
ap-3483	420	2	1	1	NUM
ap-3483	420	3	2(t2	2(t2	NUM
ap-3483	420	4	+	+	CCONJ
ap-3483	420	5	1	1	NUM
ap-3483	420	6	)	)	PUNCT
ap-3483	420	7	·	·	PUNCT
ap-3483	420	8	(	(	PUNCT
ap-3483	420	9	−2iz3(t−i)+z̄[(t+i)2+|z|2(t2	−2iz3(t−i)+z̄[(t+i)2+|z|2(t2	NUM
ap-3483	420	10	+	+	NOUN
ap-3483	420	11	1	1	NUM
ap-3483	420	12	)	)	PUNCT
ap-3483	420	13	]	]	PUNCT
ap-3483	420	14	z(t−i	z(t−i	NOUN
ap-3483	420	15	)	)	PUNCT
ap-3483	420	16	−	−	PROPN
ap-3483	421	1	[	[	X
ap-3483	421	2	z3(1+t2)+2z̄(1−it)+z(t−i)2	z3(1+t2)+2z̄(1−it)+z(t−i)2	X
ap-3483	421	3	]	]	X
ap-3483	421	4	t+i	t+i	X
ap-3483	421	5	z[(t+i)2+(t2	z[(t+i)2+(t2	PROPN
ap-3483	421	6	+	+	PROPN
ap-3483	421	7	1)|z|2	1)|z|2	NUM
ap-3483	421	8	+	+	NOUN
ap-3483	421	9	2(1+it	2(1+it	NOUN
ap-3483	421	10	)	)	PUNCT
ap-3483	421	11	]	]	PUNCT
ap-3483	421	12	t−i	t−i	NOUN
ap-3483	421	13	z(t−i)2+|z|2z(t2	z(t−i)2+|z|2z(t2	NOUN
ap-3483	421	14	+	+	PROPN
ap-3483	421	15	1)+2iz̄3(t+i	1)+2iz̄3(t+i	NUM
ap-3483	421	16	)	)	PUNCT
ap-3483	421	17	z̄(t+i	z̄(t+i	NOUN
ap-3483	421	18	)	)	PUNCT
ap-3483	421	19	)	)	PUNCT
ap-3483	421	20	,	,	PUNCT
ap-3483	421	21	m1	m1	PROPN
ap-3483	421	22	=	=	SYM
ap-3483	421	23	sst1	sst1	PROPN
ap-3483	421	24	(	(	PUNCT
ap-3483	421	25	sfg1	sfg1	PROPN
ap-3483	421	26	)	)	PUNCT
ap-3483	421	27	−1	−1	NOUN
ap-3483	422	1	=	=	SYM
ap-3483	422	2	i	i	PRON
ap-3483	422	3	2|z|2	2|z|2	NUM
ap-3483	422	4	(	(	PUNCT
ap-3483	422	5	−(1	−(1	ADJ
ap-3483	422	6	+	+	ADJ
ap-3483	422	7	2|z|2	2|z|2	NOUN
ap-3483	422	8	)	)	PUNCT
ap-3483	422	9	t2	t2	NOUN
ap-3483	422	10	+	+	PROPN
ap-3483	422	11	1	1	NUM
ap-3483	422	12	(	(	PUNCT
ap-3483	422	13	i+t)2z̄	i+t)2z̄	X
ap-3483	422	14	(	(	PUNCT
ap-3483	422	15	t−i)4	t−i)4	NUM
ap-3483	422	16	z(t−i)2	z(t−i)2	NOUN
ap-3483	422	17	(	(	PUNCT
ap-3483	422	18	t+i)4	t+i)4	PROPN
ap-3483	422	19	1	1	NUM
ap-3483	422	20	+	+	NUM
ap-3483	422	21	2|z|2	2|z|2	NUM
ap-3483	422	22	t2	t2	NOUN
ap-3483	422	23	+	+	NOUN
ap-3483	422	24	1	1	NUM
ap-3483	422	25	)	)	PUNCT
ap-3483	422	26	·	·	PUNCT
ap-3483	423	1	(	(	PUNCT
ap-3483	423	2	z2(it+	z2(it+	PROPN
ap-3483	423	3	1	1	NUM
ap-3483	423	4	)	)	PUNCT
ap-3483	423	5	+	+	NUM
ap-3483	423	6	z̄2(it−	z̄2(it−	NUM
ap-3483	423	7	1	1	NUM
ap-3483	423	8	)	)	PUNCT
ap-3483	423	9	−z(it+	−z(it+	NUM
ap-3483	423	10	1	1	NUM
ap-3483	423	11	)	)	PUNCT
ap-3483	423	12	+	+	NUM
ap-3483	423	13	z̄3(it−	z̄3(it−	NUM
ap-3483	423	14	1	1	NUM
ap-3483	423	15	)	)	PUNCT
ap-3483	423	16	z3(it+	z3(it+	PROPN
ap-3483	423	17	1	1	NUM
ap-3483	423	18	)	)	PUNCT
ap-3483	423	19	+	+	CCONJ
ap-3483	423	20	(	(	PUNCT
ap-3483	423	21	1−	1−	NUM
ap-3483	423	22	it)z̄	it)z̄	NOUN
ap-3483	423	23	−z2(1	−z2(1	NOUN
ap-3483	423	24	+	+	CCONJ
ap-3483	423	25	it	it	PRON
ap-3483	423	26	)	)	PUNCT
ap-3483	424	1	+	+	CCONJ
ap-3483	424	2	(	(	PUNCT
ap-3483	424	3	1−	1−	NUM
ap-3483	424	4	it)z̄2	it)z̄2	ADJ
ap-3483	424	5	)	)	PUNCT
ap-3483	424	6	,	,	PUNCT
ap-3483	424	7	(	(	PUNCT
ap-3483	424	8	4.47	4.47	NUM
ap-3483	424	9	)	)	PUNCT
ap-3483	425	1	where	where	SCONJ
ap-3483	425	2	detmk	detmk	NOUN
ap-3483	425	3	6=	6=	PROPN
ap-3483	425	4	0	0	NUM
ap-3483	425	5	.	.	PUNCT
ap-3483	426	1	conversely	conversely	ADV
ap-3483	426	2	,	,	PUNCT
ap-3483	426	3	the	the	PRON
ap-3483	426	4	gauges	gauge	VERB
ap-3483	426	5	m−1	m−1	PROPN
ap-3483	426	6	k	k	PROPN
ap-3483	426	7	=	=	PROPN
ap-3483	426	8	sfgk	sfgk	NOUN
ap-3483	426	9	(	(	PUNCT
ap-3483	426	10	sstk	sstk	ADJ
ap-3483	426	11	)	)	PUNCT
ap-3483	426	12	−1	−1	NOUN
ap-3483	426	13	do	do	AUX
ap-3483	426	14	exist	exist	VERB
ap-3483	426	15	.	.	PUNCT
ap-3483	427	1	hence	hence	ADV
ap-3483	427	2	there	there	PRON
ap-3483	427	3	exist	exist	VERB
ap-3483	427	4	mappings	mapping	NOUN
ap-3483	427	5	from	from	ADP
ap-3483	427	6	the	the	DET
ap-3483	427	7	st	st	PROPN
ap-3483	427	8	immersion	immersion	NOUN
ap-3483	427	9	formulas	formula	NOUN
ap-3483	427	10	to	to	ADP
ap-3483	427	11	the	the	DET
ap-3483	427	12	fg	fg	PROPN
ap-3483	427	13	immersion	immersion	NOUN
ap-3483	427	14	formulas	formula	VERB
ap-3483	427	15	m−1	m−1	PROPN
ap-3483	427	16	0	0	NUM
ap-3483	428	1	=	=	SYM
ap-3483	428	2	sfg0	sfg0	PROPN
ap-3483	428	3	(	(	PUNCT
ap-3483	428	4	sst0	sst0	PROPN
ap-3483	428	5	)	)	PUNCT
ap-3483	428	6	−1	−1	NOUN
ap-3483	428	7	=	=	SYM
ap-3483	428	8	2	2	NUM
ap-3483	428	9	(	(	PUNCT
ap-3483	428	10	1	1	NUM
ap-3483	428	11	+	+	NUM
ap-3483	428	12	|z|2)3	|z|2)3	PROPN
ap-3483	428	13	(	(	PUNCT
ap-3483	428	14	m11	m11	PROPN
ap-3483	428	15	m12	m12	PROPN
ap-3483	428	16	m21	m21	PROPN
ap-3483	428	17	m22	m22	PROPN
ap-3483	428	18	)	)	PUNCT
ap-3483	428	19	,	,	PUNCT
ap-3483	428	20	(	(	PUNCT
ap-3483	428	21	4.48	4.48	NUM
ap-3483	428	22	)	)	PUNCT
ap-3483	428	23	where	where	SCONJ
ap-3483	428	24	m11	m11	NOUN
ap-3483	428	25	=	=	SYM
ap-3483	428	26	(	(	PUNCT
ap-3483	428	27	t−	t−	PROPN
ap-3483	428	28	i)2z	i)2z	X
ap-3483	428	29	+	+	CCONJ
ap-3483	428	30	(	(	PUNCT
ap-3483	428	31	1	1	NUM
ap-3483	428	32	+	+	CCONJ
ap-3483	428	33	t2)|z|2z	t2)|z|2z	ADJ
ap-3483	428	34	+	+	CCONJ
ap-3483	428	35	2(it−	2(it−	NUM
ap-3483	428	36	1)z̄3	1)z̄3	NUM
ap-3483	428	37	(	(	PUNCT
ap-3483	428	38	i+	i+	NOUN
ap-3483	428	39	t)z̄	t)z̄	NOUN
ap-3483	428	40	,	,	PUNCT
ap-3483	428	41	m12	m12	PROPN
ap-3483	428	42	=	=	SYM
ap-3483	428	43	2(1	2(1	NUM
ap-3483	428	44	+	+	CCONJ
ap-3483	428	45	it)z2	it)z2	NOUN
ap-3483	428	46	+	+	CCONJ
ap-3483	428	47	(	(	PUNCT
ap-3483	428	48	i+	i+	NOUN
ap-3483	428	49	t)2z̄2	t)2z̄2	PROPN
ap-3483	428	50	+	+	CCONJ
ap-3483	428	51	(	(	PUNCT
ap-3483	428	52	1	1	NUM
ap-3483	428	53	+	+	NUM
ap-3483	428	54	t2)|z|2z̄2	t2)|z|2z̄2	PROPN
ap-3483	428	55	(	(	PUNCT
ap-3483	428	56	i−	i−	PROPN
ap-3483	428	57	t)z	t)z	NOUN
ap-3483	428	58	,	,	PUNCT
ap-3483	428	59	m21	m21	X
ap-3483	428	60	=	=	SYM
ap-3483	428	61	(	(	PUNCT
ap-3483	428	62	t−	t−	PROPN
ap-3483	428	63	i)2z2	i)2z2	X
ap-3483	428	64	+	+	CCONJ
ap-3483	428	65	(	(	PUNCT
ap-3483	428	66	1	1	NUM
ap-3483	428	67	+	+	CCONJ
ap-3483	428	68	t2)|z|2z2	t2)|z|2z2	ADJ
ap-3483	428	69	+	+	CCONJ
ap-3483	428	70	2(1−	2(1−	X
ap-3483	428	71	it)z̄2	it)z̄2	ADJ
ap-3483	428	72	(	(	PUNCT
ap-3483	428	73	i+	i+	NUM
ap-3483	428	74	t)z̄	t)z̄	NOUN
ap-3483	428	75	,	,	PUNCT
ap-3483	428	76	m22	m22	PROPN
ap-3483	428	77	=	=	PUNCT
ap-3483	428	78	−2(1	−2(1	NOUN
ap-3483	428	79	+	+	CCONJ
ap-3483	428	80	it)z3	it)z3	PROPN
ap-3483	429	1	+	+	CCONJ
ap-3483	429	2	(	(	PUNCT
ap-3483	429	3	i+	i+	NOUN
ap-3483	429	4	t)2z̄	t)2z̄	X
ap-3483	429	5	+	+	CCONJ
ap-3483	429	6	(	(	PUNCT
ap-3483	429	7	1	1	NUM
ap-3483	429	8	+	+	NUM
ap-3483	429	9	t2)|z|2z̄	t2)|z|2z̄	NOUN
ap-3483	429	10	(	(	PUNCT
ap-3483	429	11	t−	t−	PROPN
ap-3483	429	12	i)z	i)z	ADJ
ap-3483	429	13	,	,	PUNCT
ap-3483	429	14	and	and	CCONJ
ap-3483	429	15	m−1	m−1	PROPN
ap-3483	429	16	1	1	NUM
ap-3483	429	17	=	=	NOUN
ap-3483	429	18	sfg1	sfg1	PROPN
ap-3483	429	19	(	(	PUNCT
ap-3483	429	20	sst1	sst1	NOUN
ap-3483	429	21	)	)	PUNCT
ap-3483	429	22	−1	−1	NOUN
ap-3483	429	23	=	=	SYM
ap-3483	429	24	2	2	NUM
ap-3483	429	25	(	(	PUNCT
ap-3483	429	26	t2	t2	NOUN
ap-3483	429	27	+	+	CCONJ
ap-3483	429	28	1)(1	1)(1	NUM
ap-3483	429	29	+	+	CCONJ
ap-3483	429	30	|z|2)3(1	|z|2)3(1	ADV
ap-3483	429	31	+	+	NUM
ap-3483	429	32	4|z|2	4|z|2	X
ap-3483	429	33	)	)	PUNCT
ap-3483	429	34	·	·	PUNCT
ap-3483	430	1	(	(	PUNCT
ap-3483	430	2	−z2(1	−z2(1	NOUN
ap-3483	430	3	+	+	CCONJ
ap-3483	430	4	it	it	PRON
ap-3483	430	5	)	)	PUNCT
ap-3483	431	1	+	+	CCONJ
ap-3483	431	2	z̄2(1−	z̄2(1−	VERB
ap-3483	431	3	it	it	PRON
ap-3483	431	4	)	)	PUNCT
ap-3483	431	5	z̄3(1−	z̄3(1−	NOUN
ap-3483	431	6	it	it	PRON
ap-3483	431	7	)	)	PUNCT
ap-3483	432	1	+	+	CCONJ
ap-3483	432	2	z(1	z(1	PROPN
ap-3483	433	1	+	+	CCONJ
ap-3483	433	2	it	it	PRON
ap-3483	433	3	)	)	PUNCT
ap-3483	433	4	−z3(1	−z3(1	PROPN
ap-3483	434	1	+	+	CCONJ
ap-3483	434	2	it	it	PRON
ap-3483	434	3	)	)	PUNCT
ap-3483	435	1	+	+	CCONJ
ap-3483	435	2	z̄(it−	z̄(it−	PROPN
ap-3483	435	3	1	1	NUM
ap-3483	435	4	)	)	PUNCT
ap-3483	435	5	z2(1	z2(1	NOUN
ap-3483	435	6	+	+	CCONJ
ap-3483	435	7	it)−	it)−	PRON
ap-3483	435	8	z̄2(1−	z̄2(1−	VERB
ap-3483	435	9	it	it	PRON
ap-3483	435	10	)	)	PUNCT
ap-3483	435	11	)	)	PUNCT
ap-3483	435	12	·	·	PUNCT
ap-3483	436	1	(	(	PUNCT
ap-3483	436	2	(	(	PUNCT
ap-3483	436	3	1	1	NUM
ap-3483	436	4	+	+	NUM
ap-3483	436	5	2|z|2)(1	2|z|2)(1	PRON
ap-3483	436	6	+	+	CCONJ
ap-3483	436	7	it)(i+	it)(i+	PROPN
ap-3483	436	8	t	t	PROPN
ap-3483	436	9	)	)	PUNCT
ap-3483	436	10	−iz̄(i+t)4	−iz̄(i+t)4	PROPN
ap-3483	436	11	(	(	PUNCT
ap-3483	436	12	t−i)2	t−i)2	VERB
ap-3483	436	13	−iz(t−i)4	−iz(t−i)4	NOUN
ap-3483	436	14	(	(	PUNCT
ap-3483	436	15	i+t)2	i+t)2	PROPN
ap-3483	436	16	(	(	PUNCT
ap-3483	436	17	1	1	NUM
ap-3483	436	18	+	+	NUM
ap-3483	436	19	2|z|2)(1−	2|z|2)(1−	NUM
ap-3483	436	20	it)(−i+	it)(−i+	VERB
ap-3483	436	21	t	t	PROPN
ap-3483	436	22	)	)	PUNCT
ap-3483	436	23	)	)	PUNCT
ap-3483	436	24	.	.	PUNCT
ap-3483	437	1	(	(	PUNCT
ap-3483	437	2	4.49	4.49	NUM
ap-3483	437	3	)	)	PUNCT
ap-3483	437	4	(	(	PUNCT
ap-3483	437	5	a	a	X
ap-3483	437	6	)	)	PUNCT
ap-3483	437	7	(	(	PUNCT
ap-3483	437	8	b	b	X
ap-3483	437	9	)	)	PUNCT
ap-3483	437	10	(	(	PUNCT
ap-3483	437	11	c	c	X
ap-3483	437	12	)	)	PUNCT
ap-3483	437	13	(	(	PUNCT
ap-3483	437	14	d	d	X
ap-3483	437	15	)	)	PUNCT
ap-3483	437	16	figure	figure	NOUN
ap-3483	437	17	2	2	NUM
ap-3483	437	18	.	.	PUNCT
ap-3483	437	19	surfaces	surface	NOUN
ap-3483	437	20	fst	fst	PROPN
ap-3483	437	21	0	0	PUNCT
ap-3483	438	1	in	in	ADP
ap-3483	438	2	(	(	PUNCT
ap-3483	438	3	a	a	X
ap-3483	438	4	)	)	PUNCT
ap-3483	438	5	,	,	PUNCT
ap-3483	438	6	f	f	PROPN
ap-3483	438	7	g	g	PROPN
ap-3483	438	8	0	0	NUM
ap-3483	438	9	in	in	ADP
ap-3483	438	10	(	(	PUNCT
ap-3483	438	11	b	b	NOUN
ap-3483	438	12	)	)	PUNCT
ap-3483	438	13	,	,	PUNCT
ap-3483	438	14	f	f	PROPN
ap-3483	438	15	c	c	NOUN
ap-3483	438	16	0	0	NUM
ap-3483	438	17	in	in	ADP
ap-3483	438	18	(	(	PUNCT
ap-3483	438	19	c	c	NOUN
ap-3483	438	20	)	)	PUNCT
ap-3483	438	21	and	and	CCONJ
ap-3483	438	22	ff	ff	VERB
ap-3483	438	23	g	g	NOUN
ap-3483	438	24	0	0	NUM
ap-3483	438	25	in	in	ADP
ap-3483	438	26	(	(	PUNCT
ap-3483	438	27	d	d	NOUN
ap-3483	438	28	)	)	PUNCT
ap-3483	438	29	for	for	ADP
ap-3483	438	30	k	k	PROPN
ap-3483	438	31	=	=	SYM
ap-3483	438	32	0	0	NUM
ap-3483	438	33	,	,	PUNCT
ap-3483	438	34	1	1	NUM
ap-3483	438	35	and	and	CCONJ
ap-3483	438	36	λ	λ	X
ap-3483	438	37	=	=	SYM
ap-3483	438	38	i/2	i/2	PROPN
ap-3483	438	39	,	,	PUNCT
ap-3483	438	40	and	and	CCONJ
ap-3483	438	41	ξ±	ξ±	NUM
ap-3483	438	42	=	=	SYM
ap-3483	438	43	x	x	SYM
ap-3483	438	44	±	±	NUM
ap-3483	438	45	iy	iy	PROPN
ap-3483	438	46	with	with	ADP
ap-3483	438	47	x	x	PROPN
ap-3483	438	48	,	,	PUNCT
ap-3483	438	49	y	y	PROPN
ap-3483	438	50	∈	∈	PROPN
ap-3483	439	1	[	[	X
ap-3483	439	2	−5	−5	NOUN
ap-3483	439	3	,	,	PUNCT
ap-3483	439	4	5	5	NUM
ap-3483	439	5	]	]	PUNCT
ap-3483	439	6	.	.	PUNCT
ap-3483	440	1	the	the	DET
ap-3483	440	2	axes	axis	NOUN
ap-3483	440	3	indicate	indicate	VERB
ap-3483	440	4	the	the	DET
ap-3483	440	5	components	component	NOUN
ap-3483	440	6	of	of	ADP
ap-3483	440	7	the	the	DET
ap-3483	440	8	immersion	immersion	NOUN
ap-3483	440	9	function	function	NOUN
ap-3483	440	10	in	in	ADP
ap-3483	440	11	the	the	DET
ap-3483	440	12	basis	basis	NOUN
ap-3483	440	13	for	for	ADP
ap-3483	440	14	su(2	su(2	NOUN
ap-3483	440	15	)	)	PUNCT
ap-3483	440	16	,	,	PUNCT
ap-3483	440	17	e1	e1	NOUN
ap-3483	440	18	=	=	SYM
ap-3483	440	19	(	(	PUNCT
ap-3483	440	20	0	0	NUM
ap-3483	440	21	i	i	PRON
ap-3483	440	22	i	i	VERB
ap-3483	440	23	0	0	NUM
ap-3483	440	24	)	)	PUNCT
ap-3483	440	25	,	,	PUNCT
ap-3483	440	26	e2	e2	PROPN
ap-3483	440	27	=	=	PUNCT
ap-3483	440	28	(	(	PUNCT
ap-3483	440	29	0	0	NUM
ap-3483	440	30	−1	−1	NOUN
ap-3483	440	31	1	1	NUM
ap-3483	440	32	0	0	NUM
ap-3483	440	33	)	)	PUNCT
ap-3483	440	34	,	,	PUNCT
ap-3483	440	35	e3	e3	NOUN
ap-3483	440	36	=	=	SYM
ap-3483	440	37	(	(	PUNCT
ap-3483	440	38	i	i	NOUN
ap-3483	440	39	0	0	NUM
ap-3483	440	40	0	0	NUM
ap-3483	440	41	−i	−i	NOUN
ap-3483	440	42	)	)	PUNCT
ap-3483	440	43	.	.	PUNCT
ap-3483	441	1	5	5	X
ap-3483	441	2	.	.	X
ap-3483	441	3	concluding	conclude	VERB
ap-3483	441	4	remarks	remark	NOUN
ap-3483	441	5	in	in	ADP
ap-3483	441	6	this	this	DET
ap-3483	441	7	paper	paper	NOUN
ap-3483	441	8	we	we	PRON
ap-3483	441	9	have	have	AUX
ap-3483	441	10	shown	show	VERB
ap-3483	441	11	how	how	SCONJ
ap-3483	441	12	three	three	NUM
ap-3483	441	13	different	different	ADJ
ap-3483	441	14	analytic	analytic	ADJ
ap-3483	441	15	descriptions	description	NOUN
ap-3483	441	16	for	for	ADP
ap-3483	441	17	the	the	DET
ap-3483	441	18	immersion	immersion	NOUN
ap-3483	441	19	function	function	NOUN
ap-3483	441	20	of	of	ADP
ap-3483	441	21	2d	2d	NOUN
ap-3483	441	22	-	-	PUNCT
ap-3483	441	23	soliton	soliton	NOUN
ap-3483	441	24	surfaces	surface	NOUN
ap-3483	441	25	can	can	AUX
ap-3483	441	26	be	be	AUX
ap-3483	441	27	related	relate	VERB
ap-3483	441	28	through	through	ADP
ap-3483	441	29	different	different	ADJ
ap-3483	441	30	g	g	NOUN
ap-3483	441	31	-	-	PUNCT
ap-3483	441	32	valued	value	VERB
ap-3483	441	33	gauge	gauge	NOUN
ap-3483	441	34	transformations	transformation	NOUN
ap-3483	441	35	.	.	PUNCT
ap-3483	442	1	the	the	DET
ap-3483	442	2	existence	existence	NOUN
ap-3483	442	3	of	of	ADP
ap-3483	442	4	such	such	ADJ
ap-3483	442	5	gauges	gauge	NOUN
ap-3483	442	6	is	be	AUX
ap-3483	442	7	demonstrated	demonstrate	VERB
ap-3483	442	8	by	by	ADP
ap-3483	442	9	reducing	reduce	VERB
ap-3483	442	10	the	the	DET
ap-3483	442	11	problem	problem	NOUN
ap-3483	442	12	to	to	ADP
ap-3483	442	13	that	that	PRON
ap-3483	442	14	of	of	ADP
ap-3483	442	15	mappings	mapping	NOUN
ap-3483	442	16	between	between	ADP
ap-3483	442	17	different	different	ADJ
ap-3483	442	18	forms	form	NOUN
ap-3483	442	19	of	of	ADP
ap-3483	442	20	the	the	DET
ap-3483	442	21	immersion	immersion	NOUN
ap-3483	442	22	formulas	formula	NOUN
ap-3483	442	23	for	for	ADP
ap-3483	442	24	three	three	NUM
ap-3483	442	25	types	type	NOUN
ap-3483	442	26	of	of	ADP
ap-3483	442	27	symmetries	symmetry	NOUN
ap-3483	442	28	:	:	PUNCT
ap-3483	442	29	conformal	conformal	ADJ
ap-3483	442	30	transformations	transformation	NOUN
ap-3483	442	31	in	in	ADP
ap-3483	442	32	the	the	DET
ap-3483	442	33	spectral	spectral	ADJ
ap-3483	442	34	parameter	parameter	NOUN
ap-3483	442	35	,	,	PUNCT
ap-3483	442	36	gauge	gauge	ADJ
ap-3483	442	37	symmetries	symmetry	NOUN
ap-3483	442	38	of	of	ADP
ap-3483	442	39	the	the	DET
ap-3483	442	40	lsp	lsp	PROPN
ap-3483	442	41	and	and	CCONJ
ap-3483	442	42	generalized	generalized	ADJ
ap-3483	442	43	symmetries	symmetry	NOUN
ap-3483	442	44	of	of	ADP
ap-3483	442	45	the	the	DET
ap-3483	442	46	integrable	integrable	ADJ
ap-3483	442	47	systems	system	NOUN
ap-3483	442	48	.	.	PUNCT
ap-3483	443	1	we	we	PRON
ap-3483	443	2	have	have	AUX
ap-3483	443	3	investigated	investigate	VERB
ap-3483	443	4	the	the	DET
ap-3483	443	5	geometric	geometric	ADJ
ap-3483	443	6	consequences	consequence	NOUN
ap-3483	443	7	of	of	ADP
ap-3483	443	8	these	these	DET
ap-3483	443	9	mappings	mapping	NOUN
ap-3483	443	10	and	and	CCONJ
ap-3483	443	11	rephrased	rephrase	VERB
ap-3483	443	12	them	they	PRON
ap-3483	443	13	as	as	ADP
ap-3483	443	14	requirements	requirement	NOUN
ap-3483	443	15	for	for	ADP
ap-3483	443	16	the	the	DET
ap-3483	443	17	existence	existence	NOUN
ap-3483	443	18	of	of	ADP
ap-3483	443	19	the	the	DET
ap-3483	443	20	corresponding	correspond	VERB
ap-3483	443	21	vector	vector	NOUN
ap-3483	443	22	fields	field	NOUN
ap-3483	443	23	and	and	CCONJ
ap-3483	443	24	their	their	PRON
ap-3483	443	25	prolongations	prolongation	NOUN
ap-3483	443	26	acting	act	VERB
ap-3483	443	27	on	on	ADP
ap-3483	443	28	a	a	DET
ap-3483	443	29	solution	solution	NOUN
ap-3483	443	30	φ	φ	NUM
ap-3483	443	31	of	of	ADP
ap-3483	443	32	the	the	DET
ap-3483	443	33	associated	associated	ADJ
ap-3483	443	34	lsp	lsp	PROPN
ap-3483	443	35	for	for	ADP
ap-3483	443	36	an	an	DET
ap-3483	443	37	integrable	integrable	ADJ
ap-3483	443	38	pde	pde	NOUN
ap-3483	443	39	.	.	PUNCT
ap-3483	444	1	the	the	DET
ap-3483	444	2	explicit	explicit	ADJ
ap-3483	444	3	expressions	expression	NOUN
ap-3483	444	4	for	for	ADP
ap-3483	444	5	these	these	DET
ap-3483	444	6	relations	relation	NOUN
ap-3483	444	7	,	,	PUNCT
ap-3483	444	8	which	which	PRON
ap-3483	444	9	we	we	PRON
ap-3483	444	10	have	have	AUX
ap-3483	444	11	established	establish	VERB
ap-3483	444	12	,	,	PUNCT
ap-3483	444	13	have	have	AUX
ap-3483	444	14	provided	provide	VERB
ap-3483	444	15	us	we	PRON
ap-3483	444	16	with	with	ADP
ap-3483	444	17	a	a	DET
ap-3483	444	18	tool	tool	NOUN
ap-3483	444	19	for	for	ADP
ap-3483	444	20	distinguishing	distinguish	VERB
ap-3483	444	21	between	between	ADP
ap-3483	444	22	the	the	DET
ap-3483	444	23	cases	case	NOUN
ap-3483	444	24	in	in	ADP
ap-3483	444	25	which	which	PRON
ap-3483	444	26	soliton	soliton	NOUN
ap-3483	444	27	surfaces	surface	NOUN
ap-3483	444	28	can	can	AUX
ap-3483	444	29	be	be	AUX
ap-3483	444	30	or	or	CCONJ
ap-3483	444	31	can	can	AUX
ap-3483	444	32	not	not	PART
ap-3483	444	33	be	be	AUX
ap-3483	444	34	related	relate	VERB
ap-3483	444	35	among	among	ADP
ap-3483	444	36	them	they	PRON
ap-3483	444	37	,	,	PUNCT
ap-3483	444	38	see	see	VERB
ap-3483	444	39	proposition	proposition	NOUN
ap-3483	444	40	3	3	X
ap-3483	444	41	.	.	PUNCT
ap-3483	445	1	the	the	DET
ap-3483	445	2	task	task	NOUN
ap-3483	445	3	of	of	ADP
ap-3483	445	4	finding	find	VERB
ap-3483	445	5	an	an	DET
ap-3483	445	6	increasing	increase	VERB
ap-3483	445	7	number	number	NOUN
ap-3483	445	8	of	of	ADP
ap-3483	445	9	soliton	soliton	NOUN
ap-3483	445	10	surfaces	surface	NOUN
ap-3483	445	11	associated	associate	VERB
ap-3483	445	12	with	with	ADP
ap-3483	445	13	integrable	integrable	ADJ
ap-3483	445	14	systems	system	NOUN
ap-3483	445	15	is	be	AUX
ap-3483	445	16	related	relate	VERB
ap-3483	445	17	to	to	ADP
ap-3483	445	18	the	the	DET
ap-3483	445	19	symmetry	symmetry	NOUN
ap-3483	445	20	properties	property	NOUN
ap-3483	445	21	of	of	ADP
ap-3483	445	22	these	these	DET
ap-3483	445	23	systems	system	NOUN
ap-3483	445	24	.	.	PUNCT
ap-3483	446	1	the	the	DET
ap-3483	446	2	construction	construction	NOUN
ap-3483	446	3	of	of	ADP
ap-3483	446	4	soliton	soliton	NOUN
ap-3483	446	5	surfaces	surface	NOUN
ap-3483	446	6	started	start	VERB
ap-3483	446	7	with	with	ADP
ap-3483	446	8	the	the	DET
ap-3483	446	9	contribution	contribution	NOUN
ap-3483	446	10	of	of	ADP
ap-3483	446	11	sym	sym	PROPN
ap-3483	446	12	[	[	X
ap-3483	446	13	33	33	NUM
ap-3483	446	14	,	,	PUNCT
ap-3483	446	15	34	34	NUM
ap-3483	446	16	]	]	PUNCT
ap-3483	446	17	and	and	CCONJ
ap-3483	446	18	tafel	tafel	X
ap-3483	446	19	[	[	X
ap-3483	446	20	35	35	NUM
ap-3483	446	21	]	]	PUNCT
ap-3483	446	22	providing	provide	VERB
ap-3483	446	23	a	a	DET
ap-3483	446	24	formula	formula	NOUN
ap-3483	446	25	for	for	ADP
ap-3483	446	26	the	the	DET
ap-3483	446	27	immersion	immersion	NOUN
ap-3483	446	28	of	of	ADP
ap-3483	446	29	integrable	integrable	ADJ
ap-3483	446	30	surfaces	surface	NOUN
ap-3483	446	31	which	which	PRON
ap-3483	446	32	are	be	AUX
ap-3483	446	33	extensively	extensively	ADV
ap-3483	446	34	used	use	VERB
ap-3483	446	35	in	in	ADP
ap-3483	446	36	the	the	DET
ap-3483	446	37	literature	literature	NOUN
ap-3483	446	38	(	(	PUNCT
ap-3483	446	39	see	see	VERB
ap-3483	446	40	e.g.	e.g.	ADV
ap-3483	446	41	190	190	NUM
ap-3483	446	42	vol	vol	NOUN
ap-3483	446	43	.	.	PUNCT
ap-3483	447	1	56	56	NUM
ap-3483	447	2	no	no	NOUN
ap-3483	447	3	.	.	PUNCT
ap-3483	448	1	3/2016	3/2016	NUM
ap-3483	448	2	on	on	ADP
ap-3483	448	3	immersion	immersion	NOUN
ap-3483	448	4	formulas	formula	NOUN
ap-3483	448	5	for	for	ADP
ap-3483	448	6	soliton	soliton	NOUN
ap-3483	448	7	surfaces	surface	NOUN
ap-3483	448	8	[	[	X
ap-3483	448	9	2	2	NUM
ap-3483	448	10	,	,	PUNCT
ap-3483	448	11	5–16	5–16	NOUN
ap-3483	448	12	,	,	PUNCT
ap-3483	448	13	30	30	NUM
ap-3483	448	14	,	,	PUNCT
ap-3483	448	15	33–35	33–35	NUM
ap-3483	448	16	]	]	PUNCT
ap-3483	448	17	)	)	PUNCT
ap-3483	448	18	.	.	PUNCT
ap-3483	449	1	in	in	ADP
ap-3483	449	2	this	this	DET
ap-3483	449	3	paper	paper	NOUN
ap-3483	449	4	we	we	PRON
ap-3483	449	5	have	have	AUX
ap-3483	449	6	addressed	address	VERB
ap-3483	449	7	the	the	DET
ap-3483	449	8	question	question	NOUN
ap-3483	449	9	and	and	CCONJ
ap-3483	449	10	formulated	formulate	VERB
ap-3483	449	11	easily	easily	ADV
ap-3483	449	12	verifiable	verifiable	ADJ
ap-3483	449	13	conditions	condition	NOUN
ap-3483	449	14	which	which	PRON
ap-3483	449	15	ensure	ensure	VERB
ap-3483	449	16	that	that	SCONJ
ap-3483	449	17	the	the	DET
ap-3483	449	18	st	st	PROPN
ap-3483	449	19	formula	formula	NOUN
ap-3483	449	20	produces	produce	VERB
ap-3483	449	21	a	a	DET
ap-3483	449	22	desired	desire	VERB
ap-3483	449	23	result	result	NOUN
ap-3483	449	24	.	.	PUNCT
ap-3483	450	1	this	this	DET
ap-3483	450	2	advance	advance	NOUN
ap-3483	450	3	can	can	AUX
ap-3483	450	4	assist	assist	VERB
ap-3483	450	5	future	future	ADJ
ap-3483	450	6	studies	study	NOUN
ap-3483	450	7	of	of	ADP
ap-3483	450	8	2d	2d	NOUN
ap-3483	450	9	-	-	PUNCT
ap-3483	450	10	soliton	soliton	NOUN
ap-3483	450	11	surfaces	surface	NOUN
ap-3483	450	12	with	with	ADP
ap-3483	450	13	integrable	integrable	ADJ
ap-3483	450	14	models	model	NOUN
ap-3483	450	15	,	,	PUNCT
ap-3483	450	16	which	which	PRON
ap-3483	450	17	can	can	AUX
ap-3483	450	18	describe	describe	VERB
ap-3483	450	19	more	more	ADV
ap-3483	450	20	diverse	diverse	ADJ
ap-3483	450	21	types	type	NOUN
ap-3483	450	22	of	of	ADP
ap-3483	450	23	surfaces	surface	NOUN
ap-3483	450	24	than	than	ADP
ap-3483	450	25	the	the	DET
ap-3483	450	26	ones	one	NOUN
ap-3483	450	27	discussed	discuss	VERB
ap-3483	450	28	in	in	ADP
ap-3483	450	29	three	three	NUM
ap-3483	450	30	-	-	PUNCT
ap-3483	450	31	dimensional	dimensional	ADJ
ap-3483	450	32	euclidean	euclidean	ADJ
ap-3483	450	33	space	space	NOUN
ap-3483	450	34	for	for	ADP
ap-3483	450	35	the	the	DET
ap-3483	450	36	cp	cp	PROPN
ap-3483	450	37	1	1	PROPN
ap-3483	450	38	sigma	sigma	PROPN
ap-3483	450	39	model	model	NOUN
ap-3483	450	40	.	.	PUNCT
ap-3483	451	1	it	it	PRON
ap-3483	451	2	may	may	AUX
ap-3483	451	3	be	be	AUX
ap-3483	451	4	worthwhile	worthwhile	ADJ
ap-3483	451	5	to	to	PART
ap-3483	451	6	extend	extend	VERB
ap-3483	451	7	the	the	DET
ap-3483	451	8	investigation	investigation	NOUN
ap-3483	451	9	of	of	ADP
ap-3483	451	10	soliton	soliton	NOUN
ap-3483	451	11	surfaces	surface	NOUN
ap-3483	451	12	to	to	ADP
ap-3483	451	13	the	the	DET
ap-3483	451	14	case	case	NOUN
ap-3483	451	15	of	of	ADP
ap-3483	451	16	the	the	DET
ap-3483	451	17	sigma	sigma	PROPN
ap-3483	451	18	models	model	NOUN
ap-3483	451	19	defined	define	VERB
ap-3483	451	20	on	on	ADP
ap-3483	451	21	other	other	ADJ
ap-3483	451	22	homogeneous	homogeneous	ADJ
ap-3483	451	23	spaces	space	NOUN
ap-3483	451	24	via	via	ADP
ap-3483	451	25	grassmann	grassmann	NOUN
ap-3483	451	26	models	model	NOUN
ap-3483	451	27	and	and	CCONJ
ap-3483	451	28	possibly	possibly	ADV
ap-3483	451	29	to	to	ADP
ap-3483	451	30	models	model	NOUN
ap-3483	451	31	associated	associate	VERB
ap-3483	451	32	with	with	ADP
ap-3483	451	33	octonion	octonion	NOUN
ap-3483	451	34	geometry	geometry	NOUN
ap-3483	451	35	.	.	PUNCT
ap-3483	452	1	this	this	DET
ap-3483	452	2	case	case	NOUN
ap-3483	452	3	could	could	AUX
ap-3483	452	4	lead	lead	VERB
ap-3483	452	5	to	to	ADP
ap-3483	452	6	different	different	ADJ
ap-3483	452	7	classes	class	NOUN
ap-3483	452	8	and	and	CCONJ
ap-3483	452	9	types	type	NOUN
ap-3483	452	10	of	of	ADP
ap-3483	452	11	surfaces	surface	NOUN
ap-3483	452	12	than	than	ADP
ap-3483	452	13	those	those	PRON
ap-3483	452	14	studied	study	VERB
ap-3483	452	15	in	in	ADP
ap-3483	452	16	this	this	DET
ap-3483	452	17	paper	paper	NOUN
ap-3483	452	18	.	.	PUNCT
ap-3483	453	1	this	this	DET
ap-3483	453	2	task	task	NOUN
ap-3483	453	3	will	will	AUX
ap-3483	453	4	be	be	AUX
ap-3483	453	5	explored	explore	VERB
ap-3483	453	6	in	in	ADP
ap-3483	453	7	a	a	DET
ap-3483	453	8	future	future	ADJ
ap-3483	453	9	work	work	NOUN
ap-3483	453	10	.	.	PUNCT
ap-3483	454	1	acknowledgements	acknowledgement	NOUN
ap-3483	454	2	amg	amg	PROPN
ap-3483	454	3	has	have	AUX
ap-3483	454	4	been	be	AUX
ap-3483	454	5	partially	partially	ADV
ap-3483	454	6	supported	support	VERB
ap-3483	454	7	by	by	ADP
ap-3483	454	8	a	a	DET
ap-3483	454	9	research	research	NOUN
ap-3483	454	10	grant	grant	NOUN
ap-3483	454	11	from	from	ADP
ap-3483	454	12	nserc	nserc	NOUN
ap-3483	454	13	of	of	ADP
ap-3483	454	14	canada	canada	PROPN
ap-3483	454	15	and	and	CCONJ
ap-3483	454	16	would	would	AUX
ap-3483	454	17	also	also	ADV
ap-3483	454	18	like	like	VERB
ap-3483	454	19	to	to	PART
ap-3483	454	20	thank	thank	VERB
ap-3483	454	21	the	the	DET
ap-3483	454	22	dipartimento	dipartimento	PROPN
ap-3483	454	23	di	di	X
ap-3483	454	24	mathematica	mathematica	PROPN
ap-3483	454	25	e	e	PROPN
ap-3483	454	26	fisica	fisica	PROPN
ap-3483	454	27	of	of	ADP
ap-3483	454	28	the	the	DET
ap-3483	454	29	universitá	universitá	PROPN
ap-3483	454	30	roma	roma	PROPN
ap-3483	454	31	tre	tre	PROPN
ap-3483	454	32	and	and	CCONJ
ap-3483	454	33	the	the	DET
ap-3483	454	34	dipartimento	dipartimento	PROPN
ap-3483	454	35	di	di	X
ap-3483	454	36	mathematica	mathematica	PROPN
ap-3483	454	37	e	e	PROPN
ap-3483	454	38	fisica	fisica	PROPN
ap-3483	454	39	of	of	ADP
ap-3483	454	40	universitá	universitá	PROPN
ap-3483	454	41	del	del	PROPN
ap-3483	454	42	salento	salento	PROPN
ap-3483	454	43	for	for	ADP
ap-3483	454	44	its	its	PRON
ap-3483	454	45	warm	warm	ADJ
ap-3483	454	46	hospitality	hospitality	NOUN
ap-3483	454	47	.	.	PUNCT
ap-3483	455	1	dl	dl	PROPN
ap-3483	455	2	has	have	AUX
ap-3483	455	3	been	be	AUX
ap-3483	455	4	partly	partly	ADV
ap-3483	455	5	supported	support	VERB
ap-3483	455	6	by	by	ADP
ap-3483	455	7	the	the	DET
ap-3483	455	8	italian	italian	PROPN
ap-3483	455	9	ministry	ministry	PROPN
ap-3483	455	10	of	of	ADP
ap-3483	455	11	education	education	PROPN
ap-3483	455	12	and	and	CCONJ
ap-3483	455	13	research	research	NOUN
ap-3483	455	14	,	,	PUNCT
ap-3483	455	15	2010	2010	NUM
ap-3483	455	16	prin	prin	NOUN
ap-3483	455	17	continuous	continuous	ADJ
ap-3483	455	18	and	and	CCONJ
ap-3483	455	19	discrete	discrete	ADJ
ap-3483	455	20	nonlinear	nonlinear	ADJ
ap-3483	455	21	integrable	integrable	ADJ
ap-3483	455	22	evolutions	evolution	NOUN
ap-3483	455	23	:	:	PUNCT
ap-3483	455	24	from	from	ADP
ap-3483	455	25	water	water	NOUN
ap-3483	455	26	waves	wave	NOUN
ap-3483	455	27	to	to	ADP
ap-3483	455	28	symplectic	symplectic	ADJ
ap-3483	455	29	maps	map	NOUN
ap-3483	455	30	.	.	PUNCT
ap-3483	456	1	lm	lm	PROPN
ap-3483	456	2	has	have	AUX
ap-3483	456	3	been	be	AUX
ap-3483	456	4	partly	partly	ADV
ap-3483	456	5	supported	support	VERB
ap-3483	456	6	by	by	ADP
ap-3483	456	7	the	the	DET
ap-3483	456	8	italian	italian	PROPN
ap-3483	456	9	ministry	ministry	PROPN
ap-3483	456	10	of	of	ADP
ap-3483	456	11	education	education	PROPN
ap-3483	456	12	and	and	CCONJ
ap-3483	456	13	research	research	NOUN
ap-3483	456	14	,	,	PUNCT
ap-3483	456	15	2011	2011	NUM
ap-3483	456	16	prin	prin	PROPN
ap-3483	456	17	teorie	teorie	PROPN
ap-3483	456	18	geometriche	geometriche	PROPN
ap-3483	456	19	e	e	PROPN
ap-3483	456	20	analitiche	analitiche	PROPN
ap-3483	456	21	dei	dei	X
ap-3483	456	22	sistemi	sistemi	X
ap-3483	456	23	hamiltoniani	hamiltoniani	PROPN
ap-3483	456	24	in	in	ADP
ap-3483	456	25	dimensioni	dimensioni	PROPN
ap-3483	456	26	finite	finite	PROPN
ap-3483	456	27	e	e	X
ap-3483	456	28	infinite	infinite	VERB
ap-3483	456	29	.	.	PUNCT
ap-3483	457	1	dl	dl	PROPN
ap-3483	458	1	and	and	CCONJ
ap-3483	458	2	lm	lm	INTJ
ap-3483	458	3	are	be	AUX
ap-3483	458	4	also	also	ADV
ap-3483	458	5	supported	support	VERB
ap-3483	458	6	by	by	ADP
ap-3483	458	7	infn	infn	PROPN
ap-3483	458	8	is	be	AUX
ap-3483	458	9	-	-	PUNCT
ap-3483	458	10	csn4	csn4	ADJ
ap-3483	458	11	mathematical	mathematical	ADJ
ap-3483	458	12	methods	method	NOUN
ap-3483	458	13	of	of	ADP
ap-3483	458	14	nonlinear	nonlinear	ADJ
ap-3483	458	15	physics	physic	NOUN
ap-3483	458	16	.	.	PUNCT
ap-3483	459	1	references	reference	NOUN
ap-3483	459	2	[	[	X
ap-3483	459	3	1	1	X
ap-3483	459	4	]	]	X
ap-3483	459	5	babelon	babelon	PROPN
ap-3483	459	6	o	o	PROPN
ap-3483	459	7	,	,	PUNCT
ap-3483	459	8	bernard	bernard	PROPN
ap-3483	459	9	d	d	PROPN
ap-3483	459	10	and	and	CCONJ
ap-3483	459	11	talon	talon	PROPN
ap-3483	459	12	m	m	PROPN
ap-3483	459	13	2006	2006	NUM
ap-3483	459	14	introduction	introduction	NOUN
ap-3483	459	15	to	to	ADP
ap-3483	459	16	classical	classical	ADJ
ap-3483	459	17	integrable	integrable	ADJ
ap-3483	459	18	systems	system	NOUN
ap-3483	459	19	(	(	PUNCT
ap-3483	459	20	cambridge	cambridge	PROPN
ap-3483	459	21	monographs	monograph	NOUN
ap-3483	459	22	on	on	ADP
ap-3483	459	23	mathematical	mathematical	ADJ
ap-3483	459	24	physics	physics	NOUN
ap-3483	459	25	)	)	PUNCT
ap-3483	459	26	(	(	PUNCT
ap-3483	459	27	cambridge	cambridge	PROPN
ap-3483	459	28	:	:	PUNCT
ap-3483	459	29	cambridge	cambridge	PROPN
ap-3483	459	30	university	university	PROPN
ap-3483	459	31	press	press	PROPN
ap-3483	459	32	)	)	PUNCT
ap-3483	459	33	doi:10.1017	doi:10.1017	NOUN
ap-3483	459	34	/	/	SYM
ap-3483	459	35	cbo9780511535024	cbo9780511535024	NOUN
ap-3483	459	36	[	[	X
ap-3483	459	37	2	2	NUM
ap-3483	459	38	]	]	X
ap-3483	459	39	bobenko	bobenko	NOUN
ap-3483	459	40	ai	ai	NOUN
ap-3483	459	41	(	(	PUNCT
ap-3483	459	42	1994	1994	NUM
ap-3483	459	43	)	)	PUNCT
ap-3483	459	44	surfaces	surface	NOUN
ap-3483	459	45	in	in	ADP
ap-3483	459	46	terms	term	NOUN
ap-3483	459	47	of	of	ADP
ap-3483	459	48	2	2	NUM
ap-3483	459	49	by	by	ADP
ap-3483	459	50	2	2	NUM
ap-3483	459	51	matrices	matrix	NOUN
ap-3483	459	52	.	.	PUNCT
ap-3483	460	1	old	old	ADJ
ap-3483	460	2	and	and	CCONJ
ap-3483	460	3	new	new	ADJ
ap-3483	460	4	integrable	integrable	ADJ
ap-3483	460	5	cases	case	NOUN
ap-3483	460	6	in	in	ADP
ap-3483	460	7	harmonic	harmonic	ADJ
ap-3483	460	8	maps	map	NOUN
ap-3483	460	9	and	and	CCONJ
ap-3483	460	10	integrable	integrable	ADJ
ap-3483	460	11	systems	system	NOUN
ap-3483	460	12	,	,	PUNCT
ap-3483	460	13	eds	ed	NOUN
ap-3483	460	14	fordy	fordy	VERB
ap-3483	460	15	a	a	DET
ap-3483	460	16	,	,	PUNCT
ap-3483	460	17	wood	wood	NOUN
ap-3483	460	18	j	j	PROPN
ap-3483	460	19	(	(	PUNCT
ap-3483	460	20	braunschwieg	braunschwieg	NOUN
ap-3483	460	21	,	,	PUNCT
ap-3483	460	22	vieweg	vieweg	NOUN
ap-3483	460	23	)	)	PUNCT
ap-3483	460	24	doi:10.1007/978	doi:10.1007/978	PROPN
ap-3483	460	25	-	-	PUNCT
ap-3483	460	26	3	3	NUM
ap-3483	460	27	-	-	PUNCT
ap-3483	460	28	663	663	NUM
ap-3483	460	29	-	-	PUNCT
ap-3483	460	30	14092	14092	NUM
ap-3483	460	31	-	-	SYM
ap-3483	460	32	4_5	4_5	NUM
ap-3483	461	1	[	[	X
ap-3483	461	2	3	3	X
ap-3483	461	3	]	]	SYM
ap-3483	461	4	calogero	calogero	PROPN
ap-3483	461	5	f	f	PROPN
ap-3483	461	6	and	and	CCONJ
ap-3483	461	7	nucci	nucci	PROPN
ap-3483	461	8	mc	mc	PROPN
ap-3483	461	9	,	,	PUNCT
ap-3483	461	10	lax	lax	ADJ
ap-3483	461	11	pairs	pair	NOUN
ap-3483	461	12	galore	galore	NOUN
ap-3483	461	13	,	,	PUNCT
ap-3483	461	14	j.	j.	PROPN
ap-3483	461	15	math	math	PROPN
ap-3483	461	16	.	.	PUNCT
ap-3483	462	1	phys	phy	NOUN
ap-3483	462	2	.	.	PUNCT
ap-3483	462	3	,	,	PUNCT
ap-3483	462	4	32	32	NUM
ap-3483	462	5	72–74	72–74	NUM
ap-3483	462	6	(	(	PUNCT
ap-3483	462	7	1991	1991	NUM
ap-3483	462	8	)	)	PUNCT
ap-3483	462	9	doi:10.1063/1.529096	doi:10.1063/1.529096	NOUN
ap-3483	463	1	[	[	X
ap-3483	463	2	4	4	X
ap-3483	463	3	]	]	X
ap-3483	463	4	cartan	cartan	PROPN
ap-3483	463	5	e	e	X
ap-3483	463	6	1953	1953	NUM
ap-3483	463	7	sur	sur	X
ap-3483	463	8	la	la	PROPN
ap-3483	463	9	structure	structure	PROPN
ap-3483	463	10	des	des	X
ap-3483	463	11	groupes	groupes	PROPN
ap-3483	463	12	infinis	infinis	PROPN
ap-3483	463	13	de	de	X
ap-3483	463	14	transformation	transformation	PROPN
ap-3483	463	15	chapitre	chapitre	PROPN
ap-3483	463	16	i.	i.	PROPN
ap-3483	463	17	les	les	PROPN
ap-3483	463	18	systèmes	systèmes	PROPN
ap-3483	463	19	différentiels	différentiel	NOUN
ap-3483	463	20	en	en	ADP
ap-3483	463	21	involution	involution	PROPN
ap-3483	463	22	(	(	PUNCT
ap-3483	463	23	paris	paris	PROPN
ap-3483	463	24	,	,	PUNCT
ap-3483	463	25	gauthier	gauthier	NOUN
ap-3483	463	26	-	-	PUNCT
ap-3483	463	27	villars	villar	NOUN
ap-3483	463	28	)	)	PUNCT
ap-3483	463	29	.	.	PUNCT
ap-3483	464	1	[	[	X
ap-3483	464	2	5	5	NUM
ap-3483	464	3	]	]	PUNCT
ap-3483	464	4	cieśliński	cieśliński	NOUN
ap-3483	464	5	j	j	PROPN
ap-3483	464	6	1997	1997	NUM
ap-3483	464	7	a	a	DET
ap-3483	464	8	generalized	generalized	ADJ
ap-3483	464	9	formula	formula	NOUN
ap-3483	464	10	for	for	ADP
ap-3483	464	11	integrable	integrable	ADJ
ap-3483	464	12	classes	class	NOUN
ap-3483	464	13	of	of	ADP
ap-3483	464	14	surfaces	surface	NOUN
ap-3483	464	15	in	in	ADP
ap-3483	464	16	lie	lie	NOUN
ap-3483	464	17	algebras	algebras	PROPN
ap-3483	464	18	journal	journal	PROPN
ap-3483	464	19	of	of	ADP
ap-3483	464	20	mathematical	mathematical	ADJ
ap-3483	464	21	physics	physics	NOUN
ap-3483	464	22	38	38	NUM
ap-3483	464	23	4255–4272	4255–4272	NUM
ap-3483	464	24	,	,	PUNCT
ap-3483	464	25	doi:10.1063/1.532093	doi:10.1063/1.532093	NOUN
ap-3483	464	26	[	[	X
ap-3483	464	27	6	6	NUM
ap-3483	464	28	]	]	PUNCT
ap-3483	464	29	cieslinski	cieslinski	PROPN
ap-3483	464	30	j	j	PROPN
ap-3483	464	31	2007	2007	NUM
ap-3483	464	32	pseudospherical	pseudospherical	ADJ
ap-3483	464	33	surfaces	surface	NOUN
ap-3483	464	34	on	on	ADP
ap-3483	464	35	time	time	NOUN
ap-3483	464	36	scales	scale	NOUN
ap-3483	464	37	:	:	PUNCT
ap-3483	464	38	a	a	DET
ap-3483	464	39	geometric	geometric	ADJ
ap-3483	464	40	deformation	deformation	NOUN
ap-3483	464	41	and	and	CCONJ
ap-3483	464	42	the	the	DET
ap-3483	464	43	spectral	spectral	ADJ
ap-3483	464	44	approach	approach	NOUN
ap-3483	464	45	j.	j.	PROPN
ap-3483	464	46	phys	phys	PROPN
ap-3483	464	47	.	.	PUNCT
ap-3483	465	1	a	a	DET
ap-3483	465	2	:	:	PUNCT
ap-3483	465	3	math	math	NOUN
ap-3483	465	4	.	.	PUNCT
ap-3483	466	1	theor	theor	PROPN
ap-3483	466	2	.	.	PUNCT
ap-3483	467	1	40	40	NUM
ap-3483	467	2	12525	12525	NUM
ap-3483	467	3	-	-	SYM
ap-3483	467	4	38	38	NUM
ap-3483	467	5	,	,	PUNCT
ap-3483	467	6	doi:10.1088/1751	doi:10.1088/1751	NOUN
ap-3483	467	7	-	-	PUNCT
ap-3483	467	8	8113/40/42	8113/40/42	NUM
ap-3483	467	9	/	/	SYM
ap-3483	467	10	s02	s02	NOUN
ap-3483	467	11	[	[	X
ap-3483	467	12	7	7	NUM
ap-3483	467	13	]	]	PUNCT
ap-3483	467	14	doliwa	doliwa	NOUN
ap-3483	467	15	a	a	PRON
ap-3483	467	16	and	and	CCONJ
ap-3483	467	17	sym	sym	PROPN
ap-3483	467	18	a	a	DET
ap-3483	467	19	1992	1992	NUM
ap-3483	467	20	constant	constant	ADJ
ap-3483	467	21	mean	mean	NOUN
ap-3483	467	22	curvature	curvature	NOUN
ap-3483	467	23	surfaces	surface	NOUN
ap-3483	467	24	in	in	ADP
ap-3483	467	25	e3	e3	NOUN
ap-3483	467	26	as	as	ADP
ap-3483	467	27	an	an	DET
ap-3483	467	28	example	example	NOUN
ap-3483	467	29	of	of	ADP
ap-3483	467	30	soliton	soliton	NOUN
ap-3483	467	31	surfaces	surface	NOUN
ap-3483	467	32	,	,	PUNCT
ap-3483	467	33	nonlinear	nonlinear	ADJ
ap-3483	467	34	evolution	evolution	NOUN
ap-3483	467	35	equations	equation	NOUN
ap-3483	467	36	and	and	CCONJ
ap-3483	467	37	dynamical	dynamical	ADJ
ap-3483	467	38	systems	system	NOUN
ap-3483	467	39	(	(	PUNCT
ap-3483	467	40	boiti	boiti	NOUN
ap-3483	467	41	m	m	PROPN
ap-3483	467	42	,	,	PUNCT
ap-3483	467	43	martina	martina	PROPN
ap-3483	467	44	l	l	PROPN
ap-3483	467	45	and	and	CCONJ
ap-3483	467	46	pempinelli	pempinelli	PROPN
ap-3483	467	47	f	f	PROPN
ap-3483	467	48	,	,	PUNCT
ap-3483	467	49	eds	ed	NOUN
ap-3483	467	50	,	,	PUNCT
ap-3483	467	51	world	world	NOUN
ap-3483	467	52	scientific	scientific	PROPN
ap-3483	467	53	,	,	PUNCT
ap-3483	467	54	singapore	singapore	PROPN
ap-3483	467	55	,	,	PUNCT
ap-3483	467	56	pp	pp	ADV
ap-3483	467	57	111	111	NUM
ap-3483	467	58	-	-	SYM
ap-3483	467	59	7	7	NUM
ap-3483	467	60	)	)	PUNCT
ap-3483	468	1	[	[	X
ap-3483	468	2	8	8	NUM
ap-3483	468	3	]	]	X
ap-3483	468	4	fokas	foka	VERB
ap-3483	468	5	a	a	DET
ap-3483	468	6	s	s	NOUN
ap-3483	468	7	and	and	CCONJ
ap-3483	468	8	gel’fand	gel’fand	VERB
ap-3483	468	9	i	i	PRON
ap-3483	468	10	m	m	VERB
ap-3483	468	11	1996	1996	NUM
ap-3483	468	12	surfaces	surface	NOUN
ap-3483	468	13	on	on	ADP
ap-3483	468	14	lie	lie	NOUN
ap-3483	468	15	groups	group	NOUN
ap-3483	468	16	,	,	PUNCT
ap-3483	468	17	on	on	ADP
ap-3483	468	18	lie	lie	NOUN
ap-3483	468	19	algebras	algebra	NOUN
ap-3483	468	20	,	,	PUNCT
ap-3483	468	21	and	and	CCONJ
ap-3483	468	22	their	their	PRON
ap-3483	468	23	integrability	integrability	NOUN
ap-3483	468	24	comm	comm	NOUN
ap-3483	468	25	.	.	PUNCT
ap-3483	469	1	math	math	NOUN
ap-3483	469	2	.	.	PUNCT
ap-3483	470	1	phys	phy	NOUN
ap-3483	470	2	.	.	PUNCT
ap-3483	471	1	177	177	NUM
ap-3483	471	2	203–220	203–220	NUM
ap-3483	471	3	[	[	PUNCT
ap-3483	471	4	9	9	NUM
ap-3483	471	5	]	]	X
ap-3483	471	6	fokas	foka	VERB
ap-3483	471	7	a	a	DET
ap-3483	471	8	s	s	PROPN
ap-3483	471	9	,	,	PUNCT
ap-3483	471	10	gel’fand	gel’fand	VERB
ap-3483	471	11	i	i	PRON
ap-3483	471	12	m	m	PROPN
ap-3483	471	13	,	,	PUNCT
ap-3483	471	14	finkel	finkel	PROPN
ap-3483	471	15	f	f	PROPN
ap-3483	471	16	and	and	CCONJ
ap-3483	471	17	liu	liu	PROPN
ap-3483	471	18	q	q	PROPN
ap-3483	471	19	m	m	PROPN
ap-3483	471	20	2000	2000	NUM
ap-3483	471	21	a	a	DET
ap-3483	471	22	formula	formula	NOUN
ap-3483	471	23	for	for	ADP
ap-3483	471	24	constructing	construct	VERB
ap-3483	471	25	infinitely	infinitely	ADV
ap-3483	471	26	many	many	ADJ
ap-3483	471	27	surfaces	surface	NOUN
ap-3483	471	28	on	on	ADP
ap-3483	471	29	lie	lie	NOUN
ap-3483	471	30	algebras	algebra	NOUN
ap-3483	471	31	and	and	CCONJ
ap-3483	471	32	integrable	integrable	ADJ
ap-3483	471	33	equations	equation	NOUN
ap-3483	471	34	sel	sel	PROPN
ap-3483	471	35	.	.	PUNCT
ap-3483	471	36	math	math	NOUN
ap-3483	471	37	.	.	PUNCT
ap-3483	472	1	6	6	NUM
ap-3483	472	2	347–375	347–375	NUM
ap-3483	472	3	doi:10.1007	doi:10.1007	NOUN
ap-3483	472	4	/	/	SYM
ap-3483	472	5	pl00001392	pl00001392	PROPN
ap-3483	472	6	[	[	X
ap-3483	472	7	10	10	NUM
ap-3483	472	8	]	]	X
ap-3483	472	9	goldstein	goldstein	PROPN
ap-3483	472	10	p	p	PROPN
ap-3483	472	11	p	p	PROPN
ap-3483	472	12	and	and	CCONJ
ap-3483	472	13	grundland	grundland	NOUN
ap-3483	472	14	a	a	DET
ap-3483	472	15	m	m	ADJ
ap-3483	472	16	2010	2010	NUM
ap-3483	472	17	invariant	invariant	ADJ
ap-3483	472	18	recurrence	recurrence	NOUN
ap-3483	472	19	relations	relation	NOUN
ap-3483	472	20	for	for	ADP
ap-3483	472	21	cpn−1	cpn−1	PROPN
ap-3483	472	22	models	model	NOUN
ap-3483	472	23	j.	j.	PROPN
ap-3483	472	24	phys	phys	PROPN
ap-3483	472	25	.	.	PUNCT
ap-3483	473	1	a	a	DET
ap-3483	473	2	:	:	PUNCT
ap-3483	473	3	math	math	PROPN
ap-3483	473	4	theor	theor	PROPN
ap-3483	473	5	.	.	PROPN
ap-3483	474	1	43	43	NUM
ap-3483	474	2	,	,	PUNCT
ap-3483	474	3	265206	265206	NUM
ap-3483	474	4	(	(	PUNCT
ap-3483	474	5	18pp	18pp	ADJ
ap-3483	474	6	)	)	PUNCT
ap-3483	474	7	,	,	PUNCT
ap-3483	474	8	doi:10.1088/1751	doi:10.1088/1751	NOUN
ap-3483	474	9	-	-	PUNCT
ap-3483	474	10	8113/43/26/265206	8113/43/26/265206	NOUN
ap-3483	474	11	[	[	X
ap-3483	474	12	11	11	NUM
ap-3483	474	13	]	]	X
ap-3483	474	14	grundland	grundland	NOUN
ap-3483	474	15	am	be	AUX
ap-3483	474	16	2016	2016	NUM
ap-3483	474	17	soliton	soliton	NOUN
ap-3483	474	18	surfaces	surface	NOUN
ap-3483	474	19	in	in	ADP
ap-3483	474	20	generalized	generalized	ADJ
ap-3483	474	21	symmetry	symmetry	NOUN
ap-3483	474	22	approach	approach	NOUN
ap-3483	474	23	j.	j.	PROPN
ap-3483	474	24	theor	theor	PROPN
ap-3483	474	25	.	.	PUNCT
ap-3483	475	1	math	math	NOUN
ap-3483	475	2	.	.	PUNCT
ap-3483	476	1	phys	phy	NOUN
ap-3483	476	2	.	.	PUNCT
ap-3483	477	1	(	(	PUNCT
ap-3483	477	2	accepted	accept	VERB
ap-3483	477	3	.	.	PUNCT
ap-3483	477	4	)	)	PUNCT
ap-3483	478	1	[	[	X
ap-3483	478	2	12	12	NUM
ap-3483	478	3	]	]	PUNCT
ap-3483	478	4	grundland	grundland	NOUN
ap-3483	478	5	a	a	DET
ap-3483	478	6	m	m	NOUN
ap-3483	478	7	and	and	CCONJ
ap-3483	478	8	post	post	PROPN
ap-3483	478	9	s	s	PROPN
ap-3483	478	10	2011	2011	NUM
ap-3483	478	11	soliton	soliton	NOUN
ap-3483	478	12	surfaces	surface	NOUN
ap-3483	478	13	associated	associate	VERB
ap-3483	478	14	with	with	ADP
ap-3483	478	15	generalized	generalized	ADJ
ap-3483	478	16	symmetries	symmetry	NOUN
ap-3483	478	17	of	of	ADP
ap-3483	478	18	integrable	integrable	ADJ
ap-3483	478	19	equations	equation	NOUN
ap-3483	478	20	j.	j.	PROPN
ap-3483	478	21	phys	phys	PROPN
ap-3483	478	22	.	.	PUNCT
ap-3483	479	1	a.	a.	NOUN
ap-3483	479	2	:	:	PUNCT
ap-3483	479	3	math	math	NOUN
ap-3483	479	4	.	.	PUNCT
ap-3483	480	1	theor.44	theor.44	NOUN
ap-3483	480	2	165203	165203	NUM
ap-3483	480	3	(	(	PUNCT
ap-3483	480	4	31pp	31pp	NOUN
ap-3483	480	5	)	)	PUNCT
ap-3483	480	6	doi:10.1088/1751	doi:10.1088/1751	NOUN
ap-3483	480	7	-	-	PUNCT
ap-3483	480	8	8113/44/16/165203	8113/44/16/165203	PROPN
ap-3483	480	9	[	[	X
ap-3483	480	10	13	13	NUM
ap-3483	480	11	]	]	PUNCT
ap-3483	480	12	grundland	grundland	NOUN
ap-3483	480	13	a	a	DET
ap-3483	480	14	m	m	NOUN
ap-3483	480	15	and	and	CCONJ
ap-3483	480	16	post	post	PROPN
ap-3483	480	17	s	s	PART
ap-3483	480	18	2012	2012	NUM
ap-3483	480	19	surfaces	surface	NOUN
ap-3483	480	20	immersed	immerse	VERB
ap-3483	480	21	in	in	ADP
ap-3483	480	22	lie	lie	NOUN
ap-3483	480	23	algebras	algebras	PROPN
ap-3483	480	24	associated	associate	VERB
ap-3483	480	25	with	with	ADP
ap-3483	480	26	elliptic	elliptic	ADJ
ap-3483	480	27	integrals	integral	NOUN
ap-3483	480	28	j	j	PROPN
ap-3483	480	29	phys	phy	NOUN
ap-3483	480	30	a	a	PRON
ap-3483	480	31	:	:	PUNCT
ap-3483	480	32	math	math	NOUN
ap-3483	480	33	theor	theor	PROPN
ap-3483	480	34	45	45	NUM
ap-3483	480	35	,	,	PUNCT
ap-3483	480	36	015204	015204	NUM
ap-3483	480	37	(	(	PUNCT
ap-3483	480	38	20pp	20pp	ADJ
ap-3483	480	39	)	)	PUNCT
ap-3483	480	40	,	,	PUNCT
ap-3483	480	41	doi:10.1088/1751	doi:10.1088/1751	NOUN
ap-3483	480	42	-	-	SYM
ap-3483	480	43	8113/45/1/015204	8113/45/1/015204	NUM
ap-3483	481	1	[	[	X
ap-3483	481	2	14	14	NUM
ap-3483	481	3	]	]	X
ap-3483	481	4	grundland	grundland	NOUN
ap-3483	481	5	am	be	AUX
ap-3483	481	6	and	and	CCONJ
ap-3483	481	7	post	post	VERB
ap-3483	481	8	s	s	PART
ap-3483	481	9	2012	2012	NUM
ap-3483	481	10	soliton	soliton	NOUN
ap-3483	481	11	surfaces	surface	NOUN
ap-3483	481	12	associated	associate	VERB
ap-3483	481	13	with	with	ADP
ap-3483	481	14	cpn−1	cpn−1	PROPN
ap-3483	481	15	sigma	sigma	PROPN
ap-3483	481	16	models	model	VERB
ap-3483	481	17	j.	j.	PROPN
ap-3483	481	18	phys	phys	PROPN
ap-3483	481	19	.	.	PUNCT
ap-3483	482	1	conf	conf	PROPN
ap-3483	482	2	.	.	PUNCT
ap-3483	483	1	series	series	PROPN
ap-3483	483	2	380	380	NUM
ap-3483	483	3	,	,	PUNCT
ap-3483	483	4	012023	012023	NUM
ap-3483	483	5	pp	pp	ADP
ap-3483	483	6	1	1	NUM
ap-3483	483	7	-	-	SYM
ap-3483	483	8	14	14	NUM
ap-3483	483	9	,	,	PUNCT
ap-3483	483	10	doi:10.1088/1742	doi:10.1088/1742	NOUN
ap-3483	483	11	-	-	PUNCT
ap-3483	483	12	6596/380/1/012023	6596/380/1/012023	NUM
ap-3483	484	1	[	[	X
ap-3483	484	2	15	15	NUM
ap-3483	484	3	]	]	X
ap-3483	484	4	grundland	grundland	NOUN
ap-3483	484	5	am	be	AUX
ap-3483	484	6	,	,	PUNCT
ap-3483	484	7	post	post	NOUN
ap-3483	484	8	s	s	NOUN
ap-3483	484	9	and	and	CCONJ
ap-3483	484	10	riglioni	riglioni	ADJ
ap-3483	484	11	d	d	SYM
ap-3483	484	12	2014	2014	NUM
ap-3483	484	13	soliton	soliton	NOUN
ap-3483	484	14	surfaces	surface	NOUN
ap-3483	484	15	and	and	CCONJ
ap-3483	484	16	generalized	generalized	ADJ
ap-3483	484	17	symmetries	symmetry	NOUN
ap-3483	484	18	of	of	ADP
ap-3483	484	19	integrable	integrable	ADJ
ap-3483	484	20	systems	system	NOUN
ap-3483	484	21	j.	j.	PROPN
ap-3483	484	22	phys	phys	PROPN
ap-3483	484	23	.	.	PUNCT
ap-3483	485	1	a.	a.	NOUN
ap-3483	485	2	:	:	PUNCT
ap-3483	485	3	math	math	NOUN
ap-3483	485	4	.	.	PUNCT
ap-3483	486	1	theor.47	theor.47	NOUN
ap-3483	486	2	015201	015201	NUM
ap-3483	486	3	(	(	PUNCT
ap-3483	486	4	14pp	14pp	NOUN
ap-3483	486	5	)	)	PUNCT
ap-3483	486	6	doi:10.1088/1751	doi:10.1088/1751	ADV
ap-3483	486	7	-	-	PUNCT
ap-3483	486	8	8113/47/1/015201	8113/47/1/015201	NUM
ap-3483	486	9	[	[	SYM
ap-3483	486	10	16	16	NUM
ap-3483	486	11	]	]	X
ap-3483	486	12	grundland	grundland	NOUN
ap-3483	486	13	am	be	AUX
ap-3483	486	14	and	and	CCONJ
ap-3483	486	15	yurdusen	yurdusen	VERB
ap-3483	486	16	i	i	PRON
ap-3483	486	17	2009	2009	NUM
ap-3483	486	18	on	on	ADP
ap-3483	486	19	analytic	analytic	ADJ
ap-3483	486	20	descriptions	description	NOUN
ap-3483	486	21	of	of	ADP
ap-3483	486	22	two	two	NUM
ap-3483	486	23	-	-	PUNCT
ap-3483	486	24	dimensional	dimensional	ADJ
ap-3483	486	25	surfaces	surface	NOUN
ap-3483	486	26	associated	associate	VERB
ap-3483	486	27	with	with	ADP
ap-3483	486	28	the	the	DET
ap-3483	486	29	cpn−1	cpn−1	PROPN
ap-3483	486	30	sigma	sigma	PROPN
ap-3483	486	31	model	model	PROPN
ap-3483	486	32	,	,	PUNCT
ap-3483	486	33	j.	j.	PROPN
ap-3483	486	34	phys	phys	PROPN
ap-3483	486	35	.	.	PUNCT
ap-3483	487	1	a	a	DET
ap-3483	487	2	:	:	PUNCT
ap-3483	487	3	math	math	NOUN
ap-3483	487	4	.	.	PUNCT
ap-3483	488	1	theor	theor	PROPN
ap-3483	488	2	.	.	PUNCT
ap-3483	489	1	42	42	NUM
ap-3483	489	2	172001	172001	NUM
ap-3483	489	3	doi:10.1088/1751	doi:10.1088/1751	ADV
ap-3483	489	4	-	-	PUNCT
ap-3483	489	5	8113/42/17/172001	8113/42/17/172001	VERB
ap-3483	489	6	[	[	X
ap-3483	489	7	17	17	NUM
ap-3483	489	8	]	]	PUNCT
ap-3483	489	9	gubbiotti	gubbiotti	NOUN
ap-3483	489	10	g	g	NOUN
ap-3483	489	11	,	,	PUNCT
ap-3483	489	12	scimiterna	scimiterna	NOUN
ap-3483	489	13	c	c	PROPN
ap-3483	489	14	and	and	CCONJ
ap-3483	489	15	levi	levi	PROPN
ap-3483	489	16	d	d	PROPN
ap-3483	489	17	2016	2016	NUM
ap-3483	489	18	linearizability	linearizability	NOUN
ap-3483	489	19	and	and	CCONJ
ap-3483	489	20	fake	fake	ADJ
ap-3483	489	21	lax	lax	ADJ
ap-3483	489	22	pair	pair	NOUN
ap-3483	489	23	for	for	ADP
ap-3483	489	24	a	a	DET
ap-3483	489	25	consistent	consistent	NOUN
ap-3483	489	26	around	around	ADP
ap-3483	489	27	the	the	DET
ap-3483	489	28	cube	cube	NOUN
ap-3483	489	29	nonlinear	nonlinear	ADJ
ap-3483	489	30	non	non	ADJ
ap-3483	489	31	–	–	PROPN
ap-3483	489	32	autonomous	autonomous	ADJ
ap-3483	489	33	quad	quad	ADJ
ap-3483	489	34	–	–	PUNCT
ap-3483	489	35	graph	graph	NOUN
ap-3483	489	36	equation	equation	NOUN
ap-3483	489	37	,	,	PUNCT
ap-3483	489	38	teor	teor	PROPN
ap-3483	489	39	.	.	PUNCT
ap-3483	489	40	math	math	PROPN
ap-3483	489	41	.	.	PUNCT
ap-3483	490	1	phys	phy	NOUN
ap-3483	490	2	.	.	PUNCT
ap-3483	490	3	,	,	PUNCT
ap-3483	490	4	in	in	ADP
ap-3483	490	5	press	press	NOUN
ap-3483	490	6	.	.	PUNCT
ap-3483	491	1	[	[	X
ap-3483	491	2	18	18	NUM
ap-3483	491	3	]	]	X
ap-3483	491	4	hay	hay	PROPN
ap-3483	491	5	m	m	PROPN
ap-3483	491	6	and	and	CCONJ
ap-3483	491	7	butler	butler	PROPN
ap-3483	491	8	s	s	PROPN
ap-3483	491	9	,	,	PUNCT
ap-3483	491	10	simple	simple	ADJ
ap-3483	491	11	identification	identification	NOUN
ap-3483	491	12	of	of	ADP
ap-3483	491	13	fake	fake	ADJ
ap-3483	491	14	lax	lax	ADJ
ap-3483	491	15	pair	pair	NOUN
ap-3483	491	16	,	,	PUNCT
ap-3483	491	17	arxiv:1311.2406v1	arxiv:1311.2406v1	NOUN
ap-3483	491	18	.	.	PUNCT
ap-3483	492	1	[	[	X
ap-3483	492	2	19	19	NUM
ap-3483	492	3	]	]	X
ap-3483	492	4	helein	helein	NOUN
ap-3483	492	5	f	f	PROPN
ap-3483	492	6	2001	2001	NUM
ap-3483	492	7	constant	constant	ADJ
ap-3483	492	8	mean	mean	NOUN
ap-3483	492	9	curvature	curvature	NOUN
ap-3483	492	10	surfaces	surface	NOUN
ap-3483	492	11	,	,	PUNCT
ap-3483	492	12	harmonic	harmonic	ADJ
ap-3483	492	13	maps	map	NOUN
ap-3483	492	14	and	and	CCONJ
ap-3483	492	15	integrable	integrable	ADJ
ap-3483	492	16	systems	system	NOUN
ap-3483	492	17	(	(	PUNCT
ap-3483	492	18	lectures	lecture	NOUN
ap-3483	492	19	in	in	ADP
ap-3483	492	20	mathematics	mathematic	NOUN
ap-3483	492	21	)	)	PUNCT
ap-3483	492	22	(	(	PUNCT
ap-3483	492	23	boston	boston	PROPN
ap-3483	492	24	,	,	PUNCT
ap-3483	492	25	ma	ma	PROPN
ap-3483	492	26	:	:	PUNCT
ap-3483	492	27	birkhauser	birkhauser	NOUN
ap-3483	492	28	)	)	PUNCT
ap-3483	492	29	,	,	PUNCT
ap-3483	492	30	doi:10.1007/978	doi:10.1007/978	PROPN
ap-3483	492	31	-	-	PUNCT
ap-3483	492	32	3	3	NUM
ap-3483	492	33	-	-	PUNCT
ap-3483	492	34	0348	0348	NUM
ap-3483	492	35	-	-	PUNCT
ap-3483	492	36	8330	8330	NUM
ap-3483	492	37	-	-	SYM
ap-3483	492	38	6	6	NUM
ap-3483	492	39	[	[	SYM
ap-3483	492	40	20	20	NUM
ap-3483	492	41	]	]	PUNCT
ap-3483	492	42	konopelchenko	konopelchenko	PROPN
ap-3483	492	43	b	b	PROPN
ap-3483	492	44	g	g	PROPN
ap-3483	492	45	,	,	PUNCT
ap-3483	492	46	1996	1996	NUM
ap-3483	492	47	induced	induce	VERB
ap-3483	492	48	surfaces	surface	NOUN
ap-3483	492	49	and	and	CCONJ
ap-3483	492	50	their	their	PRON
ap-3483	492	51	integrable	integrable	ADJ
ap-3483	492	52	dynamics	dynamic	NOUN
ap-3483	492	53	.	.	PUNCT
ap-3483	493	1	stud	stud	PROPN
ap-3483	493	2	.	.	PUNCT
ap-3483	494	1	appl	appl	PROPN
ap-3483	494	2	.	.	PROPN
ap-3483	494	3	math	math	NOUN
ap-3483	494	4	.	.	PUNCT
ap-3483	495	1	96	96	NUM
ap-3483	495	2	,	,	PUNCT
ap-3483	495	3	9–51	9–51	NOUN
ap-3483	495	4	,	,	PUNCT
ap-3483	495	5	doi:10.1002	doi:10.1002	NOUN
ap-3483	495	6	/	/	SYM
ap-3483	495	7	sapm19969619	sapm19969619	PROPN
ap-3483	496	1	[	[	X
ap-3483	496	2	21	21	NUM
ap-3483	496	3	]	]	X
ap-3483	496	4	levi	levi	PROPN
ap-3483	496	5	d	d	PROPN
ap-3483	496	6	,	,	PUNCT
ap-3483	496	7	sym	sym	PROPN
ap-3483	496	8	a	a	PROPN
ap-3483	496	9	and	and	CCONJ
ap-3483	496	10	tu	tu	PROPN
ap-3483	496	11	gz	gz	PROPN
ap-3483	496	12	,	,	PUNCT
ap-3483	496	13	a	a	DET
ap-3483	496	14	working	work	VERB
ap-3483	496	15	algorithm	algorithm	NOUN
ap-3483	496	16	to	to	PART
ap-3483	496	17	isolate	isolate	VERB
ap-3483	496	18	integrable	integrable	ADJ
ap-3483	496	19	surfaces	surface	NOUN
ap-3483	496	20	in	in	ADP
ap-3483	496	21	e3	e3	NOUN
ap-3483	496	22	,	,	PUNCT
ap-3483	496	23	preprint	preprint	VERB
ap-3483	496	24	df	df	PROPN
ap-3483	496	25	infn	infn	PROPN
ap-3483	496	26	761	761	NUM
ap-3483	496	27	,	,	PUNCT
ap-3483	496	28	roma	roma	PROPN
ap-3483	496	29	oct	oct	PROPN
ap-3483	496	30	.	.	PROPN
ap-3483	496	31	10th	10th	NUM
ap-3483	496	32	,	,	PUNCT
ap-3483	496	33	1990	1990	NUM
ap-3483	496	34	,	,	PUNCT
ap-3483	496	35	doi:10.1016/0375	doi:10.1016/0375	PROPN
ap-3483	496	36	-	-	SYM
ap-3483	496	37	9601(90)90897	9601(90)90897	NUM
ap-3483	496	38	-	-	PUNCT
ap-3483	496	39	w	w	NOUN
ap-3483	497	1	[	[	X
ap-3483	497	2	22	22	NUM
ap-3483	497	3	]	]	X
ap-3483	497	4	li	li	PROPN
ap-3483	497	5	yq	yq	PROPN
ap-3483	497	6	,	,	PUNCT
ap-3483	497	7	li	li	PROPN
ap-3483	497	8	b	b	PROPN
ap-3483	497	9	and	and	CCONJ
ap-3483	497	10	lou	lou	PROPN
ap-3483	497	11	sy	sy	PROPN
ap-3483	497	12	,	,	PUNCT
ap-3483	497	13	constraints	constraint	NOUN
ap-3483	497	14	for	for	ADP
ap-3483	497	15	evolution	evolution	NOUN
ap-3483	497	16	equations	equation	NOUN
ap-3483	497	17	with	with	ADP
ap-3483	497	18	some	some	DET
ap-3483	497	19	special	special	ADJ
ap-3483	497	20	forms	form	NOUN
ap-3483	497	21	of	of	ADP
ap-3483	497	22	lax	lax	ADJ
ap-3483	497	23	pairs	pair	NOUN
ap-3483	497	24	and	and	CCONJ
ap-3483	497	25	distinguishing	distinguish	VERB
ap-3483	497	26	lax	lax	ADJ
ap-3483	497	27	pairs	pair	NOUN
ap-3483	497	28	by	by	ADP
ap-3483	497	29	available	available	ADJ
ap-3483	497	30	constraints	constraint	NOUN
ap-3483	497	31	,	,	PUNCT
ap-3483	497	32	arxiv:1008.1375v2	arxiv:1008.1375v2	ADJ
ap-3483	497	33	.	.	PUNCT
ap-3483	498	1	[	[	X
ap-3483	498	2	23	23	NUM
ap-3483	498	3	]	]	X
ap-3483	498	4	manton	manton	PROPN
ap-3483	498	5	n	n	PROPN
ap-3483	498	6	and	and	CCONJ
ap-3483	498	7	sutcliffe	sutcliffe	PROPN
ap-3483	498	8	p	p	PROPN
ap-3483	498	9	2004	2004	NUM
ap-3483	498	10	topological	topological	ADJ
ap-3483	498	11	solitons	soliton	NOUN
ap-3483	498	12	(	(	PUNCT
ap-3483	498	13	cambridge	cambridge	NOUN
ap-3483	498	14	monographs	monograph	NOUN
ap-3483	498	15	on	on	ADP
ap-3483	498	16	mathematical	mathematical	ADJ
ap-3483	498	17	physics	physics	NOUN
ap-3483	498	18	)	)	PUNCT
ap-3483	498	19	(	(	PUNCT
ap-3483	498	20	cambridge	cambridge	PROPN
ap-3483	498	21	:	:	PUNCT
ap-3483	498	22	cambridge	cambridge	PROPN
ap-3483	498	23	university	university	PROPN
ap-3483	498	24	press	press	PROPN
ap-3483	498	25	)	)	PUNCT
ap-3483	498	26	,	,	PUNCT
ap-3483	498	27	doi:10.1017	doi:10.1017	X
ap-3483	498	28	/	/	SYM
ap-3483	498	29	cbo9780511617034	cbo9780511617034	ADJ
ap-3483	498	30	191	191	NUM
ap-3483	498	31	http://dx.doi.org/10.1017/cbo9780511535024	http://dx.doi.org/10.1017/cbo9780511535024	NOUN
ap-3483	498	32	http://dx.doi.org/10.1007/978-3-663-14092-4_5	http://dx.doi.org/10.1007/978-3-663-14092-4_5	PROPN
ap-3483	498	33	http://dx.doi.org/10.1063/1.529096	http://dx.doi.org/10.1063/1.529096	NOUN
ap-3483	498	34	http://dx.doi.org/10.1063/1.532093	http://dx.doi.org/10.1063/1.532093	ADP
ap-3483	498	35	http://dx.doi.org/10.1088/1751-8113/40/42/s02	http://dx.doi.org/10.1088/1751-8113/40/42/s02	PROPN
ap-3483	498	36	http://dx.doi.org/10.1007/pl00001392	http://dx.doi.org/10.1007/pl00001392	NOUN
ap-3483	498	37	http://dx.doi.org/10.1088/1751-8113/43/26/265206	http://dx.doi.org/10.1088/1751-8113/43/26/265206	ADP
ap-3483	498	38	http://dx.doi.org/10.1088/1751-8113/44/16/165203	http://dx.doi.org/10.1088/1751-8113/44/16/165203	X
ap-3483	498	39	http://dx.doi.org/10.1088/1751-8113/45/1/015204	http://dx.doi.org/10.1088/1751-8113/45/1/015204	NOUN
ap-3483	498	40	http://dx.doi.org/10.1088/1742-6596/380/1/012023	http://dx.doi.org/10.1088/1742-6596/380/1/012023	PROPN
ap-3483	498	41	http://dx.doi.org/10.1088/1751-8113/47/1/015201	http://dx.doi.org/10.1088/1751-8113/47/1/015201	PROPN
ap-3483	498	42	http://dx.doi.org/10.1088/1751-8113/42/17/172001	http://dx.doi.org/10.1088/1751-8113/42/17/172001	X
ap-3483	498	43	http://arxiv.org/abs/1311.2406v1	http://arxiv.org/abs/1311.2406v1	PRON
ap-3483	498	44	http://dx.doi.org/10.1007/978-3-0348-8330-6	http://dx.doi.org/10.1007/978-3-0348-8330-6	PUNCT
ap-3483	498	45	http://dx.doi.org/10.1002/sapm19969619	http://dx.doi.org/10.1002/sapm19969619	PROPN
ap-3483	498	46	http://dx.doi.org/10.1016/0375-9601(90)90897-w	http://dx.doi.org/10.1016/0375-9601(90)90897-w	ADP
ap-3483	498	47	http://arxiv.org/abs/1008.1375v2	http://arxiv.org/abs/1008.1375v2	PROPN
ap-3483	498	48	http://dx.doi.org/10.1017/cbo9780511617034	http://dx.doi.org/10.1017/cbo9780511617034	NOUN
ap-3483	498	49	a.	a.	NOUN
ap-3483	498	50	m.	m.	NOUN
ap-3483	498	51	grundland	grundland	PROPN
ap-3483	498	52	,	,	PUNCT
ap-3483	498	53	d.	d.	PROPN
ap-3483	498	54	levi	levi	PROPN
ap-3483	498	55	,	,	PUNCT
ap-3483	498	56	l.	l.	PROPN
ap-3483	498	57	martina	martina	PROPN
ap-3483	498	58	acta	acta	PROPN
ap-3483	498	59	polytechnica	polytechnica	PROPN
ap-3483	498	60	[	[	X
ap-3483	498	61	24	24	NUM
ap-3483	498	62	]	]	X
ap-3483	498	63	marvan	marvan	NOUN
ap-3483	498	64	m	m	PROPN
ap-3483	498	65	2002	2002	NUM
ap-3483	498	66	on	on	ADP
ap-3483	498	67	the	the	DET
ap-3483	498	68	horizontal	horizontal	ADJ
ap-3483	498	69	gauge	gauge	NOUN
ap-3483	498	70	cohomology	cohomology	NOUN
ap-3483	498	71	and	and	CCONJ
ap-3483	498	72	nonremovability	nonremovability	NOUN
ap-3483	498	73	of	of	ADP
ap-3483	498	74	the	the	DET
ap-3483	498	75	spectral	spectral	ADJ
ap-3483	498	76	parameter	parameter	NOUN
ap-3483	498	77	,	,	PUNCT
ap-3483	498	78	acta	acta	PROPN
ap-3483	498	79	appl	appl	PROPN
ap-3483	498	80	.	.	PUNCT
ap-3483	498	81	math	math	NOUN
ap-3483	498	82	.	.	PUNCT
ap-3483	499	1	72	72	NUM
ap-3483	499	2	51–65	51–65	NUM
ap-3483	499	3	,	,	PUNCT
ap-3483	499	4	doi:10.1023	doi:10.1023	NOUN
ap-3483	499	5	/	/	SYM
ap-3483	499	6	a:1015218422059	a:1015218422059	NOUN
ap-3483	500	1	[	[	X
ap-3483	500	2	25	25	NUM
ap-3483	500	3	]	]	X
ap-3483	500	4	marvan	marvan	PROPN
ap-3483	500	5	m	m	PROPN
ap-3483	500	6	2004	2004	NUM
ap-3483	500	7	reducibility	reducibility	NOUN
ap-3483	500	8	of	of	ADP
ap-3483	500	9	zero	zero	NUM
ap-3483	500	10	curvature	curvature	NOUN
ap-3483	500	11	representations	representation	NOUN
ap-3483	500	12	with	with	ADP
ap-3483	500	13	application	application	NOUN
ap-3483	500	14	to	to	ADP
ap-3483	500	15	recursion	recursion	NOUN
ap-3483	500	16	operators	operator	NOUN
ap-3483	500	17	,	,	PUNCT
ap-3483	500	18	acta	acta	PROPN
ap-3483	500	19	appl	appl	PROPN
ap-3483	500	20	.	.	PROPN
ap-3483	500	21	math	math	NOUN
ap-3483	500	22	.	.	PUNCT
ap-3483	501	1	83	83	NUM
ap-3483	501	2	39–68	39–68	NUM
ap-3483	501	3	,	,	PUNCT
ap-3483	501	4	doi:10.1023	doi:10.1023	NOUN
ap-3483	501	5	/	/	SYM
ap-3483	502	1	b	b	NOUN
ap-3483	502	2	:	:	PUNCT
ap-3483	502	3	acap.0000035588.67805.0b	acap.0000035588.67805.0b	X
ap-3483	503	1	[	[	X
ap-3483	503	2	26	26	NUM
ap-3483	503	3	]	]	X
ap-3483	503	4	marvan	marvan	NOUN
ap-3483	503	5	m	m	PROPN
ap-3483	503	6	2010	2010	NUM
ap-3483	503	7	on	on	ADP
ap-3483	503	8	the	the	DET
ap-3483	503	9	spectral	spectral	ADJ
ap-3483	503	10	parameter	parameter	PROPN
ap-3483	503	11	problem	problem	NOUN
ap-3483	503	12	,	,	PUNCT
ap-3483	503	13	acta	acta	PROPN
ap-3483	503	14	appl	appl	PROPN
ap-3483	503	15	.	.	PROPN
ap-3483	503	16	math	math	NOUN
ap-3483	503	17	.	.	PUNCT
ap-3483	504	1	109	109	NUM
ap-3483	504	2	239–255	239–255	NUM
ap-3483	504	3	,	,	PUNCT
ap-3483	504	4	doi:10.1007	doi:10.1007	NOUN
ap-3483	504	5	/	/	SYM
ap-3483	504	6	s10440	s10440	NOUN
ap-3483	504	7	-	-	PUNCT
ap-3483	504	8	009	009	NUM
ap-3483	504	9	-	-	PUNCT
ap-3483	504	10	9450	9450	NUM
ap-3483	504	11	-	-	SYM
ap-3483	504	12	4	4	NUM
ap-3483	504	13	[	[	SYM
ap-3483	504	14	27	27	NUM
ap-3483	504	15	]	]	X
ap-3483	504	16	mikhailov	mikhailov	PROPN
ap-3483	504	17	av	av	PROPN
ap-3483	504	18	1986	1986	NUM
ap-3483	504	19	integrable	integrable	ADJ
ap-3483	504	20	magnetic	magnetic	ADJ
ap-3483	504	21	models	model	NOUN
ap-3483	504	22	soliton	soliton	NOUN
ap-3483	504	23	(	(	PUNCT
ap-3483	504	24	modern	modern	ADJ
ap-3483	504	25	problems	problem	NOUN
ap-3483	504	26	in	in	ADP
ap-3483	504	27	condensed	condense	VERB
ap-3483	504	28	matter	matter	NOUN
ap-3483	504	29	vol	vol	NOUN
ap-3483	504	30	17	17	NUM
ap-3483	504	31	)	)	PUNCT
ap-3483	504	32	ed	ed	NOUN
ap-3483	504	33	s	s	NOUN
ap-3483	504	34	e	e	NOUN
ap-3483	504	35	trullinger	trullinger	NOUN
ap-3483	504	36	et	et	PROPN
ap-3483	504	37	al	al	PROPN
ap-3483	504	38	(	(	PUNCT
ap-3483	504	39	amsterdam	amsterdam	PROPN
ap-3483	504	40	:	:	PUNCT
ap-3483	504	41	north	north	NOUN
ap-3483	504	42	-	-	PUNCT
ap-3483	504	43	holland	holland	PROPN
ap-3483	504	44	)	)	PUNCT
ap-3483	504	45	pp	pp	ADP
ap-3483	504	46	623	623	NUM
ap-3483	504	47	-	-	SYM
ap-3483	504	48	90	90	NUM
ap-3483	504	49	[	[	SYM
ap-3483	504	50	28	28	NUM
ap-3483	504	51	]	]	X
ap-3483	504	52	mikhailov	mikhailov	PROPN
ap-3483	504	53	a	a	DET
ap-3483	504	54	v	v	NOUN
ap-3483	504	55	,	,	PUNCT
ap-3483	504	56	shabat	shabat	PROPN
ap-3483	504	57	a	a	DET
ap-3483	504	58	b	b	PROPN
ap-3483	504	59	and	and	CCONJ
ap-3483	504	60	sokolov	sokolov	ADJ
ap-3483	504	61	v	v	NUM
ap-3483	504	62	v	v	ADP
ap-3483	504	63	1991	1991	NUM
ap-3483	504	64	the	the	DET
ap-3483	504	65	symmetry	symmetry	NOUN
ap-3483	504	66	approach	approach	NOUN
ap-3483	504	67	to	to	ADP
ap-3483	504	68	classification	classification	NOUN
ap-3483	504	69	of	of	ADP
ap-3483	504	70	integrable	integrable	ADJ
ap-3483	504	71	equations	equation	NOUN
ap-3483	504	72	,	,	PUNCT
ap-3483	504	73	in	in	ADP
ap-3483	504	74	nonlinear	nonlinear	ADJ
ap-3483	504	75	dynamics	dynamic	NOUN
ap-3483	504	76	,	,	PUNCT
ap-3483	504	77	ed	ed	PROPN
ap-3483	504	78	zakharov	zakharov	PROPN
ap-3483	504	79	v	v	PROPN
ap-3483	504	80	e	e	PROPN
ap-3483	504	81	,	,	PUNCT
ap-3483	504	82	springer	springer	NOUN
ap-3483	504	83	,	,	PUNCT
ap-3483	504	84	pp	pp	ADV
ap-3483	504	85	115	115	NUM
ap-3483	504	86	-	-	SYM
ap-3483	504	87	184	184	NUM
ap-3483	504	88	.	.	PUNCT
ap-3483	505	1	[	[	X
ap-3483	505	2	29	29	NUM
ap-3483	505	3	]	]	X
ap-3483	505	4	olver	olver	NOUN
ap-3483	505	5	p	p	X
ap-3483	505	6	j	j	PROPN
ap-3483	505	7	1993	1993	NUM
ap-3483	505	8	applications	application	NOUN
ap-3483	505	9	of	of	ADP
ap-3483	505	10	lie	lie	NOUN
ap-3483	505	11	groups	group	NOUN
ap-3483	505	12	to	to	PART
ap-3483	505	13	differential	differential	VERB
ap-3483	505	14	equations	equation	NOUN
ap-3483	505	15	,	,	PUNCT
ap-3483	505	16	2nd	2nd	ADJ
ap-3483	505	17	edn	edn	NOUN
ap-3483	505	18	.	.	PUNCT
ap-3483	506	1	(	(	PUNCT
ap-3483	506	2	new	new	PROPN
ap-3483	506	3	york	york	PROPN
ap-3483	506	4	,	,	PUNCT
ap-3483	506	5	springer	springer	NOUN
ap-3483	506	6	)	)	PUNCT
ap-3483	506	7	.	.	PUNCT
ap-3483	507	1	doi:10.1007/978	doi:10.1007/978	ADJ
ap-3483	507	2	-	-	PUNCT
ap-3483	507	3	1	1	NUM
ap-3483	507	4	-	-	PUNCT
ap-3483	507	5	4612	4612	NUM
ap-3483	507	6	-	-	SYM
ap-3483	507	7	4350	4350	NUM
ap-3483	507	8	-	-	SYM
ap-3483	507	9	2	2	NUM
ap-3483	507	10	[	[	SYM
ap-3483	507	11	30	30	NUM
ap-3483	507	12	]	]	X
ap-3483	507	13	rogers	rogers	PROPN
ap-3483	507	14	c	c	PROPN
ap-3483	507	15	and	and	CCONJ
ap-3483	507	16	schief	schief	PROPN
ap-3483	507	17	wk	wk	NOUN
ap-3483	507	18	2000	2000	NUM
ap-3483	507	19	backlund	backlund	PROPN
ap-3483	507	20	and	and	CCONJ
ap-3483	507	21	darboux	darboux	ADJ
ap-3483	507	22	transformations	transformation	NOUN
ap-3483	507	23	.	.	PUNCT
ap-3483	508	1	geometry	geometry	NOUN
ap-3483	508	2	and	and	CCONJ
ap-3483	508	3	modern	modern	ADJ
ap-3483	508	4	applications	application	NOUN
ap-3483	508	5	in	in	ADP
ap-3483	508	6	soliton	soliton	NOUN
ap-3483	508	7	theory	theory	NOUN
ap-3483	508	8	(	(	PUNCT
ap-3483	508	9	cambridge	cambridge	PROPN
ap-3483	508	10	:	:	PUNCT
ap-3483	508	11	cambridge	cambridge	PROPN
ap-3483	508	12	university	university	PROPN
ap-3483	508	13	press	press	PROPN
ap-3483	508	14	)	)	PUNCT
ap-3483	508	15	.	.	PUNCT
ap-3483	509	1	doi:10.1017	doi:10.1017	PROPN
ap-3483	509	2	/	/	SYM
ap-3483	509	3	cbo9780511606359	cbo9780511606359	PROPN
ap-3483	510	1	[	[	X
ap-3483	510	2	31	31	NUM
ap-3483	510	3	]	]	X
ap-3483	510	4	sakovich	sakovich	PROPN
ap-3483	510	5	s	s	PROPN
ap-3483	510	6	yu	yu	PROPN
ap-3483	510	7	,	,	PUNCT
ap-3483	510	8	true	true	ADJ
ap-3483	510	9	and	and	CCONJ
ap-3483	510	10	fake	fake	ADJ
ap-3483	510	11	lax	lax	ADJ
ap-3483	510	12	pairs	pair	NOUN
ap-3483	510	13	:	:	PUNCT
ap-3483	510	14	how	how	SCONJ
ap-3483	510	15	to	to	PART
ap-3483	510	16	distinguish	distinguish	VERB
ap-3483	510	17	them	they	PRON
ap-3483	510	18	,	,	PUNCT
ap-3483	510	19	arxiv	arxiv	PROPN
ap-3483	510	20	:	:	PUNCT
ap-3483	510	21	nlin.si/0112027	nlin.si/0112027	ADJ
ap-3483	510	22	.	.	PUNCT
ap-3483	511	1	[	[	X
ap-3483	511	2	32	32	NUM
ap-3483	511	3	]	]	X
ap-3483	511	4	sakovich	sakovich	PROPN
ap-3483	511	5	s	s	PROPN
ap-3483	511	6	yu	yu	PROPN
ap-3483	511	7	,	,	PUNCT
ap-3483	511	8	cyclic	cyclic	ADJ
ap-3483	511	9	bases	basis	NOUN
ap-3483	511	10	of	of	ADP
ap-3483	511	11	zero	zero	NUM
ap-3483	511	12	-	-	PUNCT
ap-3483	511	13	curvature	curvature	NOUN
ap-3483	511	14	representations	representation	NOUN
ap-3483	511	15	:	:	PUNCT
ap-3483	511	16	five	five	NUM
ap-3483	511	17	illustrations	illustration	NOUN
ap-3483	511	18	to	to	ADP
ap-3483	511	19	one	one	NUM
ap-3483	511	20	concept	concept	NOUN
ap-3483	511	21	,	,	PUNCT
ap-3483	511	22	arxiv	arxiv	PROPN
ap-3483	511	23	:	:	PUNCT
ap-3483	511	24	nlin/0212019v1	nlin/0212019v1	NUM
ap-3483	511	25	.	.	PUNCT
ap-3483	512	1	[	[	X
ap-3483	512	2	33	33	NUM
ap-3483	512	3	]	]	PUNCT
ap-3483	512	4	sym	sym	NOUN
ap-3483	512	5	a	a	PRON
ap-3483	512	6	,	,	PUNCT
ap-3483	512	7	1982	1982	NUM
ap-3483	512	8	soliton	soliton	NOUN
ap-3483	512	9	surfaces	surface	NOUN
ap-3483	512	10	.	.	PUNCT
ap-3483	513	1	lett	lett	PROPN
ap-3483	513	2	.	.	PUNCT
ap-3483	514	1	nuovo	nuovo	PROPN
ap-3483	514	2	cimento	cimento	PROPN
ap-3483	514	3	33	33	NUM
ap-3483	514	4	,	,	PUNCT
ap-3483	514	5	394	394	NUM
ap-3483	514	6	-	-	SYM
ap-3483	514	7	400	400	NUM
ap-3483	514	8	.	.	PUNCT
ap-3483	515	1	[	[	X
ap-3483	515	2	34	34	NUM
ap-3483	515	3	]	]	PUNCT
ap-3483	515	4	sym	sym	NOUN
ap-3483	515	5	a	a	ADP
ap-3483	515	6	,	,	PUNCT
ap-3483	515	7	1995	1995	NUM
ap-3483	515	8	soliton	soliton	NOUN
ap-3483	515	9	surfaces	surface	NOUN
ap-3483	515	10	and	and	CCONJ
ap-3483	515	11	their	their	PRON
ap-3483	515	12	applications	application	NOUN
ap-3483	515	13	(	(	PUNCT
ap-3483	515	14	soliton	soliton	NOUN
ap-3483	515	15	geometry	geometry	NOUN
ap-3483	515	16	from	from	ADP
ap-3483	515	17	spectral	spectral	ADJ
ap-3483	515	18	problems	problem	NOUN
ap-3483	515	19	)	)	PUNCT
ap-3483	515	20	geometric	geometric	ADJ
ap-3483	515	21	aspect	aspect	NOUN
ap-3483	515	22	of	of	ADP
ap-3483	515	23	the	the	DET
ap-3483	515	24	einstein	einstein	ADJ
ap-3483	515	25	equation	equation	NOUN
ap-3483	515	26	and	and	CCONJ
ap-3483	515	27	integrable	integrable	ADJ
ap-3483	515	28	systems	system	NOUN
ap-3483	515	29	(	(	PUNCT
ap-3483	515	30	lectures	lecture	VERB
ap-3483	515	31	notes	note	NOUN
ap-3483	515	32	in	in	ADP
ap-3483	515	33	physics	physics	NOUN
ap-3483	515	34	vol	vol	NOUN
ap-3483	515	35	239	239	NUM
ap-3483	515	36	)	)	PUNCT
ap-3483	515	37	ed	ed	NOUN
ap-3483	515	38	r	r	NOUN
ap-3483	515	39	martini	martini	NOUN
ap-3483	515	40	(	(	PUNCT
ap-3483	515	41	berlin	berlin	NOUN
ap-3483	515	42	:	:	PUNCT
ap-3483	515	43	springer	springer	NOUN
ap-3483	515	44	)	)	PUNCT
ap-3483	515	45	pp	pp	ADP
ap-3483	515	46	154	154	NUM
ap-3483	515	47	-	-	SYM
ap-3483	515	48	231	231	NUM
ap-3483	515	49	.	.	PUNCT
ap-3483	516	1	doi:10.1007/3	doi:10.1007/3	PROPN
ap-3483	516	2	-	-	PUNCT
ap-3483	516	3	540	540	NUM
ap-3483	516	4	-	-	PUNCT
ap-3483	516	5	16039	16039	NUM
ap-3483	516	6	-	-	PUNCT
ap-3483	516	7	6_6	6_6	PROPN
ap-3483	516	8	[	[	X
ap-3483	516	9	35	35	NUM
ap-3483	516	10	]	]	PUNCT
ap-3483	516	11	tafel	tafel	PROPN
ap-3483	516	12	j	j	PROPN
ap-3483	516	13	1995	1995	NUM
ap-3483	516	14	surfaces	surface	NOUN
ap-3483	516	15	in	in	ADP
ap-3483	516	16	r3	r3	PROPN
ap-3483	516	17	with	with	ADP
ap-3483	516	18	prescribed	prescribed	ADJ
ap-3483	516	19	curvature	curvature	NOUN
ap-3483	516	20	j.	j.	PROPN
ap-3483	516	21	geom	geom	PROPN
ap-3483	516	22	.	.	PUNCT
ap-3483	517	1	phys	phy	NOUN
ap-3483	517	2	.	.	PUNCT
ap-3483	518	1	17	17	NUM
ap-3483	518	2	381	381	NUM
ap-3483	518	3	-	-	SYM
ap-3483	518	4	90	90	NUM
ap-3483	518	5	.	.	PUNCT
ap-3483	518	6	doi:10.1016/0393	doi:10.1016/0393	PROPN
ap-3483	518	7	-	-	PUNCT
ap-3483	518	8	0440(94)00054	0440(94)00054	NUM
ap-3483	518	9	-	-	SYM
ap-3483	518	10	9	9	NUM
ap-3483	519	1	[	[	SYM
ap-3483	519	2	36	36	NUM
ap-3483	519	3	]	]	X
ap-3483	519	4	zakharov	zakharov	PROPN
ap-3483	519	5	v	v	NOUN
ap-3483	519	6	e	e	NOUN
ap-3483	519	7	and	and	CCONJ
ap-3483	519	8	mikhailov	mikhailov	PROPN
ap-3483	519	9	a	a	DET
ap-3483	519	10	v	v	ADJ
ap-3483	519	11	1979	1979	NUM
ap-3483	519	12	relativistically	relativistically	ADV
ap-3483	519	13	invariant	invariant	ADJ
ap-3483	519	14	two	two	NUM
ap-3483	519	15	-	-	PUNCT
ap-3483	519	16	dimensional	dimensional	ADJ
ap-3483	519	17	models	model	NOUN
ap-3483	519	18	of	of	ADP
ap-3483	519	19	field	field	NOUN
ap-3483	519	20	theory	theory	NOUN
ap-3483	519	21	which	which	PRON
ap-3483	519	22	are	be	AUX
ap-3483	519	23	integrable	integrable	ADJ
ap-3483	519	24	by	by	ADP
ap-3483	519	25	means	mean	NOUN
ap-3483	519	26	of	of	ADP
ap-3483	519	27	the	the	DET
ap-3483	519	28	inverse	inverse	NOUN
ap-3483	519	29	scattering	scattering	NOUN
ap-3483	519	30	problem	problem	NOUN
ap-3483	519	31	method	method	NOUN
ap-3483	519	32	sov	sov	NOUN
ap-3483	519	33	.	.	PUNCT
ap-3483	520	1	phys	phy	NOUN
ap-3483	520	2	.	.	PUNCT
ap-3483	521	1	–	–	PUNCT
ap-3483	521	2	jetp	jetp	VERB
ap-3483	521	3	47	47	NUM
ap-3483	521	4	1017–49	1017–49	NUM
ap-3483	522	1	[	[	X
ap-3483	522	2	37	37	NUM
ap-3483	522	3	]	]	X
ap-3483	522	4	zakrzewski	zakrzewski	PROPN
ap-3483	522	5	w	w	PROPN
ap-3483	522	6	1989	1989	NUM
ap-3483	522	7	low	low	ADJ
ap-3483	522	8	dimensional	dimensional	ADJ
ap-3483	522	9	sigma	sigma	NOUN
ap-3483	522	10	models	model	NOUN
ap-3483	522	11	(	(	PUNCT
ap-3483	522	12	bristol	bristol	NOUN
ap-3483	522	13	:	:	PUNCT
ap-3483	522	14	hilger	hilger	NOUN
ap-3483	522	15	)	)	PUNCT
ap-3483	522	16	.	.	PUNCT
ap-3483	523	1	192	192	NUM
ap-3483	523	2	http://dx.doi.org/10.1023/a:1015218422059	http://dx.doi.org/10.1023/a:1015218422059	ADP
ap-3483	523	3	http://dx.doi.org/10.1023/b:acap.0000035588.67805.0b	http://dx.doi.org/10.1023/b:acap.0000035588.67805.0b	PROPN
ap-3483	523	4	http://dx.doi.org/10.1007/s10440-009-9450-4	http://dx.doi.org/10.1007/s10440-009-9450-4	X
ap-3483	523	5	http://dx.doi.org/10.1007/978-1-4612-4350-2	http://dx.doi.org/10.1007/978-1-4612-4350-2	NOUN
ap-3483	523	6	http://dx.doi.org/10.1017/cbo9780511606359	http://dx.doi.org/10.1017/cbo9780511606359	PUNCT
ap-3483	523	7	http://arxiv.org/abs/nlin.si/0112027	http://arxiv.org/abs/nlin.si/0112027	PROPN
ap-3483	523	8	http://arxiv.org/abs/nlin/0212019v1	http://arxiv.org/abs/nlin/0212019v1	PROPN
ap-3483	523	9	http://dx.doi.org/10.1007/3-540-16039-6_6	http://dx.doi.org/10.1007/3-540-16039-6_6	VERB
ap-3483	523	10	http://dx.doi.org/10.1016/0393-0440(94)00054-9	http://dx.doi.org/10.1016/0393-0440(94)00054-9	ADJ
ap-3483	523	11	acta	acta	PROPN
ap-3483	523	12	polytechnica	polytechnica	PROPN
ap-3483	523	13	56(3):180–192	56(3):180–192	PROPN
ap-3483	523	14	,	,	PUNCT
ap-3483	523	15	2016	2016	NUM
ap-3483	523	16	1	1	NUM
ap-3483	523	17	introduction	introduction	NOUN
ap-3483	523	18	2	2	NUM
ap-3483	523	19	summary	summary	NOUN
ap-3483	523	20	of	of	ADP
ap-3483	523	21	results	result	NOUN
ap-3483	523	22	on	on	ADP
ap-3483	523	23	the	the	DET
ap-3483	523	24	construction	construction	NOUN
ap-3483	523	25	of	of	ADP
ap-3483	523	26	soliton	soliton	NOUN
ap-3483	523	27	surfaces	surface	NOUN
ap-3483	523	28	2.1	2.1	NUM
ap-3483	523	29	classical	classical	ADJ
ap-3483	523	30	and	and	CCONJ
ap-3483	523	31	generalized	generalized	ADJ
ap-3483	523	32	lie	lie	NOUN
ap-3483	523	33	symmetries	symmetry	NOUN
ap-3483	523	34	2.2	2.2	NUM
ap-3483	523	35	the	the	DET
ap-3483	523	36	immersion	immersion	NOUN
ap-3483	523	37	formulas	formula	NOUN
ap-3483	523	38	for	for	ADP
ap-3483	523	39	soliton	soliton	NOUN
ap-3483	523	40	surfaces	surface	NOUN
ap-3483	523	41	2.3	2.3	NUM
ap-3483	523	42	application	application	NOUN
ap-3483	523	43	of	of	ADP
ap-3483	523	44	the	the	DET
ap-3483	523	45	method	method	NOUN
ap-3483	523	46	3	3	NUM
ap-3483	523	47	mapping	mapping	NOUN
ap-3483	523	48	between	between	ADP
ap-3483	523	49	the	the	DET
ap-3483	523	50	sym	sym	NOUN
ap-3483	523	51	-	-	PUNCT
ap-3483	523	52	tafel	tafel	PROPN
ap-3483	523	53	,	,	PUNCT
ap-3483	523	54	the	the	DET
ap-3483	523	55	cieslinski	cieslinski	PROPN
ap-3483	523	56	-	-	PUNCT
ap-3483	523	57	doliwa	doliwa	PROPN
ap-3483	523	58	and	and	CCONJ
ap-3483	523	59	the	the	DET
ap-3483	523	60	fokas	fokas	ADJ
ap-3483	523	61	-	-	PUNCT
ap-3483	523	62	gel'fand	gel'fand	NOUN
ap-3483	523	63	immersion	immersion	NOUN
ap-3483	523	64	formulas	formula	VERB
ap-3483	523	65	3.1	3.1	NUM
ap-3483	523	66	lambda	lambda	ADJ
ap-3483	523	67	-	-	PUNCT
ap-3483	523	68	conformal	conformal	ADJ
ap-3483	523	69	symmetries	symmetry	NOUN
ap-3483	523	70	and	and	CCONJ
ap-3483	523	71	gauge	gauge	ADJ
ap-3483	523	72	transformations	transformation	NOUN
ap-3483	523	73	3.2	3.2	NUM
ap-3483	523	74	generalized	generalized	ADJ
ap-3483	523	75	symmetries	symmetry	NOUN
ap-3483	523	76	and	and	CCONJ
ap-3483	523	77	gauge	gauge	ADJ
ap-3483	523	78	transformations	transformation	NOUN
ap-3483	523	79	3.3	3.3	NUM
ap-3483	523	80	the	the	DET
ap-3483	523	81	sym	sym	NOUN
ap-3483	523	82	-	-	PUNCT
ap-3483	523	83	tafel	tafel	NOUN
ap-3483	523	84	immersion	immersion	NOUN
ap-3483	523	85	formula	formula	NOUN
ap-3483	523	86	versus	versus	ADP
ap-3483	523	87	the	the	DET
ap-3483	523	88	fokas	fokas	ADJ
ap-3483	523	89	-	-	PUNCT
ap-3483	523	90	gel'fand	gel'fand	NOUN
ap-3483	523	91	immersion	immersion	NOUN
ap-3483	523	92	formula	formula	NOUN
ap-3483	523	93	4	4	NUM
ap-3483	523	94	the	the	DET
ap-3483	523	95	sigma	sigma	PROPN
ap-3483	523	96	model	model	NOUN
ap-3483	523	97	and	and	CCONJ
ap-3483	523	98	soliton	soliton	NOUN
ap-3483	523	99	surfaces	surface	NOUN
ap-3483	523	100	4.1	4.1	NUM
ap-3483	523	101	soliton	soliton	NOUN
ap-3483	523	102	surfaces	surface	NOUN
ap-3483	523	103	associated	associate	VERB
ap-3483	523	104	with	with	ADP
ap-3483	523	105	the	the	DET
ap-3483	523	106	cp1	cp1	PROPN
ap-3483	523	107	sigma	sigma	PROPN
ap-3483	523	108	model	model	NOUN
ap-3483	523	109	5	5	NUM
ap-3483	523	110	concluding	conclude	VERB
ap-3483	523	111	remarks	remark	NOUN
ap-3483	523	112	acknowledgements	acknowledgement	NOUN
ap-3483	523	113	references	reference	NOUN