id	sid	tid	token	lemma	pos
5138jd4900b	1	1	this	this	DET
5138jd4900b	1	2	thesis	thesis	NOUN
5138jd4900b	1	3	consists	consist	VERB
5138jd4900b	1	4	of	of	ADP
5138jd4900b	1	5	two	two	NUM
5138jd4900b	1	6	main	main	ADJ
5138jd4900b	1	7	topics	topic	NOUN
5138jd4900b	1	8	,	,	PUNCT
5138jd4900b	1	9	and	and	CCONJ
5138jd4900b	1	10	several	several	ADJ
5138jd4900b	1	11	parts	part	NOUN
5138jd4900b	1	12	contained	contain	VERB
5138jd4900b	1	13	within	within	ADP
5138jd4900b	1	14	the	the	DET
5138jd4900b	1	15	topics	topic	NOUN
5138jd4900b	1	16	.	.	PUNCT
5138jd4900b	2	1	the	the	DET
5138jd4900b	2	2	first	first	ADJ
5138jd4900b	2	3	topic	topic	NOUN
5138jd4900b	2	4	we	we	PRON
5138jd4900b	2	5	consider	consider	VERB
5138jd4900b	2	6	,	,	PUNCT
5138jd4900b	2	7	are	be	AUX
5138jd4900b	2	8	heat	heat	NOUN
5138jd4900b	2	9	(	(	PUNCT
5138jd4900b	2	10	or	or	CCONJ
5138jd4900b	2	11	diffusion	diffusion	NOUN
5138jd4900b	2	12	)	)	PUNCT
5138jd4900b	2	13	evolution	evolution	NOUN
5138jd4900b	2	14	equations	equation	NOUN
5138jd4900b	2	15	.	.	PUNCT
5138jd4900b	3	1	we	we	PRON
5138jd4900b	3	2	define	define	VERB
5138jd4900b	3	3	any	any	DET
5138jd4900b	3	4	evolution	evolution	NOUN
5138jd4900b	3	5	equation	equation	NOUN
5138jd4900b	3	6	as	as	ADP
5138jd4900b	3	7	a	a	DET
5138jd4900b	3	8	heat	heat	NOUN
5138jd4900b	3	9	type	type	NOUN
5138jd4900b	3	10	equation	equation	NOUN
5138jd4900b	3	11	if	if	SCONJ
5138jd4900b	3	12	it	it	PRON
5138jd4900b	3	13	can	can	AUX
5138jd4900b	3	14	be	be	AUX
5138jd4900b	3	15	written	write	VERB
5138jd4900b	3	16	in	in	ADP
5138jd4900b	3	17	the	the	DET
5138jd4900b	3	18	form	form	NOUN
5138jd4900b	3	19	$	$	SYM
5138jd4900b	3	20	p_t	p_t	X
5138jd4900b	3	21	u	u	PROPN
5138jd4900b	4	1	p_x^2	p_x^2	PROPN
5138jd4900b	4	2	u	u	PROPN
5138jd4900b	4	3	=	=	VERB
5138jd4900b	4	4	n(u)$	n(u)$	PROPN
5138jd4900b	4	5	,	,	PUNCT
5138jd4900b	4	6	where	where	SCONJ
5138jd4900b	4	7	$	$	SYM
5138jd4900b	4	8	n(u)$	n(u)$	NOUN
5138jd4900b	4	9	is	be	AUX
5138jd4900b	4	10	some	some	DET
5138jd4900b	4	11	nonlinear	nonlinear	ADJ
5138jd4900b	4	12	term	term	NOUN
5138jd4900b	4	13	.	.	PUNCT
5138jd4900b	5	1	the	the	DET
5138jd4900b	5	2	solutions	solution	NOUN
5138jd4900b	5	3	of	of	ADP
5138jd4900b	5	4	these	these	DET
5138jd4900b	5	5	equations	equation	NOUN
5138jd4900b	5	6	are	be	AUX
5138jd4900b	5	7	locally	locally	ADV
5138jd4900b	5	8	in	in	ADP
5138jd4900b	5	9	time	time	NOUN
5138jd4900b	5	10	characterized	characterize	VERB
5138jd4900b	5	11	by	by	ADP
5138jd4900b	5	12	the	the	DET
5138jd4900b	5	13	diffusion	diffusion	NOUN
5138jd4900b	5	14	,	,	PUNCT
5138jd4900b	5	15	and	and	CCONJ
5138jd4900b	5	16	their	their	PRON
5138jd4900b	5	17	analysis	analysis	NOUN
5138jd4900b	5	18	should	should	AUX
5138jd4900b	5	19	take	take	VERB
5138jd4900b	5	20	this	this	DET
5138jd4900b	5	21	term	term	NOUN
5138jd4900b	5	22	into	into	ADP
5138jd4900b	5	23	account	account	NOUN
5138jd4900b	5	24	.	.	PUNCT
5138jd4900b	6	1	therefore	therefore	ADV
5138jd4900b	6	2	,	,	PUNCT
5138jd4900b	6	3	the	the	DET
5138jd4900b	6	4	techniques	technique	NOUN
5138jd4900b	6	5	we	we	PRON
5138jd4900b	6	6	employ	employ	VERB
5138jd4900b	6	7	to	to	PART
5138jd4900b	6	8	study	study	VERB
5138jd4900b	6	9	these	these	DET
5138jd4900b	6	10	equations	equation	NOUN
5138jd4900b	6	11	are	be	AUX
5138jd4900b	6	12	fundamentally	fundamentally	ADV
5138jd4900b	6	13	different	different	ADJ
5138jd4900b	6	14	from	from	ADP
5138jd4900b	6	15	techniques	technique	NOUN
5138jd4900b	6	16	we	we	PRON
5138jd4900b	6	17	use	use	VERB
5138jd4900b	6	18	to	to	PART
5138jd4900b	6	19	study	study	VERB
5138jd4900b	6	20	other	other	ADJ
5138jd4900b	6	21	evolution	evolution	NOUN
5138jd4900b	6	22	partial	partial	ADJ
5138jd4900b	6	23	differential	differential	ADJ
5138jd4900b	6	24	equations	equation	NOUN
5138jd4900b	6	25	(	(	PUNCT
5138jd4900b	6	26	pde	pde	NOUN
5138jd4900b	6	27	's	's	PART
5138jd4900b	6	28	)	)	PUNCT
5138jd4900b	6	29	.	.	PUNCT
5138jd4900b	7	1	there	there	PRON
5138jd4900b	7	2	are	be	VERB
5138jd4900b	7	3	many	many	ADJ
5138jd4900b	7	4	interesting	interesting	ADJ
5138jd4900b	7	5	phenomenon	phenomenon	NOUN
5138jd4900b	7	6	which	which	PRON
5138jd4900b	7	7	can	can	AUX
5138jd4900b	7	8	be	be	AUX
5138jd4900b	7	9	modeled	model	VERB
5138jd4900b	7	10	by	by	ADP
5138jd4900b	7	11	nonlinear	nonlinear	ADJ
5138jd4900b	7	12	diffusion	diffusion	NOUN
5138jd4900b	7	13	equations	equation	NOUN
5138jd4900b	7	14	.	.	PUNCT
5138jd4900b	8	1	most	most	ADV
5138jd4900b	8	2	notably	notably	ADV
5138jd4900b	8	3	,	,	PUNCT
5138jd4900b	8	4	we	we	PRON
5138jd4900b	8	5	consider	consider	VERB
5138jd4900b	8	6	two	two	NUM
5138jd4900b	8	7	applications	application	NOUN
5138jd4900b	8	8	in	in	ADP
5138jd4900b	8	9	this	this	DET
5138jd4900b	8	10	thesis	thesis	NOUN
5138jd4900b	8	11	,	,	PUNCT
5138jd4900b	8	12	the	the	DET
5138jd4900b	8	13	generalized	generalized	ADJ
5138jd4900b	8	14	burgers	burger	NOUN
5138jd4900b	8	15	equation	equation	NOUN
5138jd4900b	8	16	and	and	CCONJ
5138jd4900b	8	17	the	the	DET
5138jd4900b	8	18	nonlinear	nonlinear	ADJ
5138jd4900b	8	19	financial	financial	ADJ
5138jd4900b	8	20	diffusion	diffusion	NOUN
5138jd4900b	8	21	equation	equation	NOUN
5138jd4900b	8	22	.	.	PUNCT
5138jd4900b	9	1	the	the	DET
5138jd4900b	9	2	first	first	ADJ
5138jd4900b	9	3	aforementioned	aforementioned	ADJ
5138jd4900b	9	4	equation	equation	NOUN
5138jd4900b	9	5	is	be	AUX
5138jd4900b	9	6	a	a	DET
5138jd4900b	9	7	mathematical	mathematical	ADJ
5138jd4900b	9	8	generalization	generalization	NOUN
5138jd4900b	9	9	of	of	ADP
5138jd4900b	9	10	burgers	burger	NOUN
5138jd4900b	9	11	equation	equation	NOUN
5138jd4900b	9	12	,	,	PUNCT
5138jd4900b	9	13	which	which	PRON
5138jd4900b	9	14	we	we	PRON
5138jd4900b	9	15	consider	consider	VERB
5138jd4900b	9	16	to	to	PART
5138jd4900b	9	17	illustrate	illustrate	VERB
5138jd4900b	9	18	some	some	PRON
5138jd4900b	9	19	of	of	ADP
5138jd4900b	9	20	the	the	DET
5138jd4900b	9	21	techniques	technique	NOUN
5138jd4900b	9	22	used	use	VERB
5138jd4900b	9	23	in	in	ADP
5138jd4900b	9	24	the	the	DET
5138jd4900b	9	25	study	study	NOUN
5138jd4900b	9	26	of	of	ADP
5138jd4900b	9	27	this	this	DET
5138jd4900b	9	28	type	type	NOUN
5138jd4900b	9	29	of	of	ADP
5138jd4900b	9	30	equations	equation	NOUN
5138jd4900b	9	31	.	.	PUNCT
5138jd4900b	10	1	the	the	DET
5138jd4900b	10	2	second	second	ADJ
5138jd4900b	10	3	equation	equation	NOUN
5138jd4900b	10	4	has	have	AUX
5138jd4900b	10	5	been	be	AUX
5138jd4900b	10	6	derived	derive	VERB
5138jd4900b	10	7	to	to	PART
5138jd4900b	10	8	model	model	VERB
5138jd4900b	10	9	an	an	DET
5138jd4900b	10	10	investment	investment	NOUN
5138jd4900b	10	11	strategy	strategy	NOUN
5138jd4900b	10	12	for	for	ADP
5138jd4900b	10	13	a	a	DET
5138jd4900b	10	14	retirement	retirement	NOUN
5138jd4900b	10	15	portfolio	portfolio	NOUN
5138jd4900b	10	16	.	.	PUNCT
5138jd4900b	11	1	the	the	DET
5138jd4900b	11	2	second	second	ADJ
5138jd4900b	11	3	main	main	ADJ
5138jd4900b	11	4	topic	topic	NOUN
5138jd4900b	11	5	we	we	PRON
5138jd4900b	11	6	consider	consider	VERB
5138jd4900b	11	7	are	be	AUX
5138jd4900b	11	8	camassa	camassa	ADJ
5138jd4900b	11	9	--	--	PUNCT
5138jd4900b	11	10	holm	holm	NOUN
5138jd4900b	11	11	type	type	NOUN
5138jd4900b	11	12	equations	equation	NOUN
5138jd4900b	11	13	.	.	PUNCT
5138jd4900b	12	1	these	these	DET
5138jd4900b	12	2	equations	equation	NOUN
5138jd4900b	12	3	are	be	AUX
5138jd4900b	12	4	of	of	ADP
5138jd4900b	12	5	the	the	DET
5138jd4900b	12	6	form	form	NOUN
5138jd4900b	12	7	$	$	SYM
5138jd4900b	12	8	p_t	p_t	X
5138jd4900b	12	9	u	u	PROPN
5138jd4900b	13	1	+	+	CCONJ
5138jd4900b	13	2	u	u	NOUN
5138jd4900b	13	3	^k	^k	PROPN
5138jd4900b	13	4	p_x	p_x	PUNCT
5138jd4900b	13	5	u	u	PROPN
5138jd4900b	13	6	+	+	PROPN
5138jd4900b	13	7	f(u	f(u	NOUN
5138jd4900b	13	8	)	)	PUNCT
5138jd4900b	13	9	=	=	PROPN
5138jd4900b	13	10	0	0	NUM
5138jd4900b	13	11	$	$	NUM
5138jd4900b	13	12	,	,	PUNCT
5138jd4900b	13	13	where	where	SCONJ
5138jd4900b	13	14	$	$	SYM
5138jd4900b	13	15	f(cdot)$	f(cdot)$	PROPN
5138jd4900b	13	16	is	be	AUX
5138jd4900b	13	17	a	a	DET
5138jd4900b	13	18	nonlocal	nonlocal	ADJ
5138jd4900b	13	19	,	,	PUNCT
5138jd4900b	13	20	nonlinear	nonlinear	ADJ
5138jd4900b	13	21	operator	operator	NOUN
5138jd4900b	13	22	.	.	PUNCT
5138jd4900b	14	1	equations	equation	NOUN
5138jd4900b	14	2	of	of	ADP
5138jd4900b	14	3	this	this	DET
5138jd4900b	14	4	form	form	NOUN
5138jd4900b	14	5	exhibit	exhibit	VERB
5138jd4900b	14	6	some	some	DET
5138jd4900b	14	7	interesting	interesting	ADJ
5138jd4900b	14	8	mathematical	mathematical	ADJ
5138jd4900b	14	9	properties	property	NOUN
5138jd4900b	14	10	,	,	PUNCT
5138jd4900b	14	11	including	include	VERB
5138jd4900b	14	12	non	non	ADJ
5138jd4900b	14	13	-	-	ADJ
5138jd4900b	14	14	smooth	smooth	ADJ
5138jd4900b	14	15	solutions	solution	NOUN
5138jd4900b	14	16	.	.	PUNCT
5138jd4900b	15	1	this	this	PRON
5138jd4900b	15	2	is	be	AUX
5138jd4900b	15	3	in	in	ADP
5138jd4900b	15	4	sharp	sharp	ADJ
5138jd4900b	15	5	contrast	contrast	NOUN
5138jd4900b	15	6	to	to	ADP
5138jd4900b	15	7	diffusive	diffusive	ADJ
5138jd4900b	15	8	equations	equation	NOUN
5138jd4900b	15	9	,	,	PUNCT
5138jd4900b	15	10	whose	whose	DET
5138jd4900b	15	11	solutions	solution	NOUN
5138jd4900b	15	12	are	be	AUX
5138jd4900b	15	13	often	often	ADV
5138jd4900b	15	14	characterized	characterize	VERB
5138jd4900b	15	15	by	by	ADP
5138jd4900b	15	16	a	a	DET
5138jd4900b	15	17	gaussian	gaussian	ADJ
5138jd4900b	15	18	-	-	PUNCT
5138jd4900b	15	19	like	like	ADJ
5138jd4900b	15	20	shape	shape	NOUN
5138jd4900b	15	21	.	.	PUNCT
5138jd4900b	16	1	to	to	PART
5138jd4900b	16	2	study	study	VERB
5138jd4900b	16	3	properties	property	NOUN
5138jd4900b	16	4	of	of	ADP
5138jd4900b	16	5	these	these	DET
5138jd4900b	16	6	equations	equation	NOUN
5138jd4900b	16	7	,	,	PUNCT
5138jd4900b	16	8	we	we	PRON
5138jd4900b	16	9	must	must	AUX
5138jd4900b	16	10	use	use	VERB
5138jd4900b	16	11	very	very	ADV
5138jd4900b	16	12	different	different	ADJ
5138jd4900b	16	13	tools	tool	NOUN
5138jd4900b	16	14	from	from	ADP
5138jd4900b	16	15	the	the	DET
5138jd4900b	16	16	area	area	NOUN
5138jd4900b	16	17	of	of	ADP
5138jd4900b	16	18	analysis	analysis	NOUN
5138jd4900b	16	19	,	,	PUNCT
5138jd4900b	16	20	as	as	SCONJ
5138jd4900b	16	21	the	the	DET
5138jd4900b	16	22	techniques	technique	NOUN
5138jd4900b	16	23	which	which	PRON
5138jd4900b	16	24	we	we	PRON
5138jd4900b	16	25	employ	employ	VERB
5138jd4900b	16	26	for	for	ADP
5138jd4900b	16	27	the	the	DET
5138jd4900b	16	28	heat	heat	NOUN
5138jd4900b	16	29	--	--	PUNCT
5138jd4900b	16	30	type	type	NOUN
5138jd4900b	16	31	equations	equation	NOUN
5138jd4900b	16	32	do	do	AUX
5138jd4900b	16	33	not	not	PART
5138jd4900b	16	34	apply	apply	VERB
5138jd4900b	16	35	.	.	PUNCT
5138jd4900b	17	1	when	when	SCONJ
5138jd4900b	17	2	studying	study	VERB
5138jd4900b	17	3	differential	differential	ADJ
5138jd4900b	17	4	equations	equation	NOUN
5138jd4900b	17	5	,	,	PUNCT
5138jd4900b	17	6	it	it	PRON
5138jd4900b	17	7	is	be	AUX
5138jd4900b	17	8	often	often	ADV
5138jd4900b	17	9	advantageous	advantageous	ADJ
5138jd4900b	17	10	to	to	PART
5138jd4900b	17	11	use	use	VERB
5138jd4900b	17	12	numerical	numerical	ADJ
5138jd4900b	17	13	techniques	technique	NOUN
5138jd4900b	17	14	to	to	PART
5138jd4900b	17	15	give	give	VERB
5138jd4900b	17	16	us	we	PRON
5138jd4900b	17	17	insight	insight	NOUN
5138jd4900b	17	18	into	into	ADP
5138jd4900b	17	19	the	the	DET
5138jd4900b	17	20	properties	property	NOUN
5138jd4900b	17	21	of	of	ADP
5138jd4900b	17	22	the	the	DET
5138jd4900b	17	23	solutions	solution	NOUN
5138jd4900b	17	24	.	.	PUNCT
5138jd4900b	18	1	solving	solve	VERB
5138jd4900b	18	2	an	an	DET
5138jd4900b	18	3	equation	equation	NOUN
5138jd4900b	18	4	numerically	numerically	ADV
5138jd4900b	18	5	may	may	AUX
5138jd4900b	18	6	indicate	indicate	VERB
5138jd4900b	18	7	that	that	SCONJ
5138jd4900b	18	8	the	the	DET
5138jd4900b	18	9	solution	solution	NOUN
5138jd4900b	18	10	exists	exist	VERB
5138jd4900b	18	11	for	for	ADP
5138jd4900b	18	12	a	a	DET
5138jd4900b	18	13	long	long	ADJ
5138jd4900b	18	14	period	period	NOUN
5138jd4900b	18	15	of	of	ADP
5138jd4900b	18	16	time	time	NOUN
5138jd4900b	18	17	,	,	PUNCT
5138jd4900b	18	18	or	or	CCONJ
5138jd4900b	18	19	it	it	PRON
5138jd4900b	18	20	may	may	AUX
5138jd4900b	18	21	allow	allow	VERB
5138jd4900b	18	22	us	we	PRON
5138jd4900b	18	23	to	to	PART
5138jd4900b	18	24	test	test	VERB
5138jd4900b	18	25	for	for	ADP
5138jd4900b	18	26	some	some	DET
5138jd4900b	18	27	types	type	NOUN
5138jd4900b	18	28	of	of	ADP
5138jd4900b	18	29	initial	initial	ADJ
5138jd4900b	18	30	data	datum	NOUN
5138jd4900b	18	31	which	which	PRON
5138jd4900b	18	32	lead	lead	VERB
5138jd4900b	18	33	to	to	ADP
5138jd4900b	18	34	blow	blow	VERB
5138jd4900b	18	35	-	-	PUNCT
5138jd4900b	18	36	up	up	NOUN
5138jd4900b	18	37	of	of	ADP
5138jd4900b	18	38	the	the	DET
5138jd4900b	18	39	solution	solution	NOUN
5138jd4900b	18	40	.	.	PUNCT
5138jd4900b	19	1	for	for	ADP
5138jd4900b	19	2	example	example	NOUN
5138jd4900b	19	3	as	as	ADP
5138jd4900b	19	4	in	in	ADP
5138jd4900b	19	5	the	the	DET
5138jd4900b	19	6	case	case	NOUN
5138jd4900b	19	7	of	of	ADP
5138jd4900b	19	8	burgers	burger	NOUN
5138jd4900b	19	9	equation	equation	NOUN
5138jd4900b	19	10	,	,	PUNCT
5138jd4900b	19	11	we	we	PRON
5138jd4900b	19	12	may	may	AUX
5138jd4900b	19	13	find	find	VERB
5138jd4900b	19	14	that	that	SCONJ
5138jd4900b	19	15	particular	particular	ADJ
5138jd4900b	19	16	profiles	profile	NOUN
5138jd4900b	19	17	lead	lead	VERB
5138jd4900b	19	18	to	to	ADP
5138jd4900b	19	19	blow	blow	VERB
5138jd4900b	19	20	-	-	PUNCT
5138jd4900b	19	21	up	up	NOUN
5138jd4900b	19	22	.	.	PUNCT
5138jd4900b	20	1	these	these	DET
5138jd4900b	20	2	insights	insight	NOUN
5138jd4900b	20	3	may	may	AUX
5138jd4900b	20	4	tell	tell	VERB
5138jd4900b	20	5	us	we	PRON
5138jd4900b	20	6	how	how	SCONJ
5138jd4900b	20	7	we	we	PRON
5138jd4900b	20	8	should	should	AUX
5138jd4900b	20	9	frame	frame	VERB
5138jd4900b	20	10	the	the	DET
5138jd4900b	20	11	mathematical	mathematical	ADJ
5138jd4900b	20	12	questions	question	NOUN
5138jd4900b	20	13	we	we	PRON
5138jd4900b	20	14	are	be	AUX
5138jd4900b	20	15	interested	interested	ADJ
5138jd4900b	20	16	in	in	ADP
5138jd4900b	20	17	answering	answer	VERB
5138jd4900b	20	18	.	.	PUNCT
5138jd4900b	21	1	it	it	PRON
5138jd4900b	21	2	also	also	ADV
5138jd4900b	21	3	is	be	AUX
5138jd4900b	21	4	frequently	frequently	ADV
5138jd4900b	21	5	the	the	DET
5138jd4900b	21	6	case	case	NOUN
5138jd4900b	21	7	that	that	SCONJ
5138jd4900b	21	8	exact	exact	ADJ
5138jd4900b	21	9	solutions	solution	NOUN
5138jd4900b	21	10	can	can	AUX
5138jd4900b	21	11	not	not	PART
5138jd4900b	21	12	be	be	AUX
5138jd4900b	21	13	written	write	VERB
5138jd4900b	21	14	down	down	ADP
5138jd4900b	21	15	for	for	ADP
5138jd4900b	21	16	interesting	interesting	ADJ
5138jd4900b	21	17	initial	initial	ADJ
5138jd4900b	21	18	data	datum	NOUN
5138jd4900b	21	19	.	.	PUNCT
5138jd4900b	22	1	therefore	therefore	ADV
5138jd4900b	22	2	,	,	PUNCT
5138jd4900b	22	3	numerical	numerical	ADJ
5138jd4900b	22	4	methods	method	NOUN
5138jd4900b	22	5	allow	allow	VERB
5138jd4900b	22	6	us	we	PRON
5138jd4900b	22	7	to	to	PART
5138jd4900b	22	8	calculate	calculate	VERB
5138jd4900b	22	9	solutions	solution	NOUN
5138jd4900b	22	10	within	within	ADP
5138jd4900b	22	11	machine	machine	NOUN
5138jd4900b	22	12	precision	precision	NOUN
5138jd4900b	22	13	,	,	PUNCT
5138jd4900b	22	14	and	and	CCONJ
5138jd4900b	22	15	make	make	VERB
5138jd4900b	22	16	the	the	DET
5138jd4900b	22	17	same	same	ADJ
5138jd4900b	22	18	conclusions	conclusion	NOUN
5138jd4900b	22	19	we	we	PRON
5138jd4900b	22	20	would	would	AUX
5138jd4900b	22	21	have	have	AUX
5138jd4900b	22	22	made	make	VERB
5138jd4900b	22	23	had	have	AUX
5138jd4900b	22	24	we	we	PRON
5138jd4900b	22	25	had	have	VERB
5138jd4900b	22	26	a	a	DET
5138jd4900b	22	27	formulaic	formulaic	ADJ
5138jd4900b	22	28	solution	solution	NOUN
5138jd4900b	22	29	.	.	PUNCT
5138jd4900b	23	1	we	we	PRON
5138jd4900b	23	2	illustrate	illustrate	VERB
5138jd4900b	23	3	some	some	PRON
5138jd4900b	23	4	of	of	ADP
5138jd4900b	23	5	these	these	DET
5138jd4900b	23	6	numerical	numerical	ADJ
5138jd4900b	23	7	methods	method	NOUN
5138jd4900b	23	8	by	by	ADP
5138jd4900b	23	9	examining	examine	VERB
5138jd4900b	23	10	an	an	DET
5138jd4900b	23	11	equation	equation	NOUN
5138jd4900b	23	12	derived	derive	VERB
5138jd4900b	23	13	in	in	ADP
5138jd4900b	23	14	financial	financial	ADJ
5138jd4900b	23	15	mathematics	mathematic	NOUN
5138jd4900b	23	16	.	.	PUNCT
5138jd4900b	24	1	this	this	DET
5138jd4900b	24	2	thesis	thesis	NOUN
5138jd4900b	24	3	begins	begin	VERB
5138jd4900b	24	4	with	with	ADP
5138jd4900b	24	5	a	a	DET
5138jd4900b	24	6	introduction	introduction	NOUN
5138jd4900b	24	7	to	to	ADP
5138jd4900b	24	8	heat	heat	NOUN
5138jd4900b	24	9	equations	equation	NOUN
5138jd4900b	24	10	,	,	PUNCT
5138jd4900b	24	11	by	by	ADP
5138jd4900b	24	12	studying	study	VERB
5138jd4900b	24	13	the	the	DET
5138jd4900b	24	14	historical	historical	ADJ
5138jd4900b	24	15	advances	advance	NOUN
5138jd4900b	24	16	leading	lead	VERB
5138jd4900b	24	17	up	up	ADP
5138jd4900b	24	18	to	to	ADP
5138jd4900b	24	19	fourier	fourier	NOUN
5138jd4900b	24	20	and	and	CCONJ
5138jd4900b	24	21	several	several	ADJ
5138jd4900b	24	22	advances	advance	NOUN
5138jd4900b	24	23	and	and	CCONJ
5138jd4900b	24	24	applications	application	NOUN
5138jd4900b	24	25	of	of	ADP
5138jd4900b	24	26	his	his	PRON
5138jd4900b	24	27	ideas	idea	NOUN
5138jd4900b	24	28	.	.	PUNCT
5138jd4900b	25	1	it	it	PRON
5138jd4900b	25	2	is	be	AUX
5138jd4900b	25	3	important	important	ADJ
5138jd4900b	25	4	to	to	PART
5138jd4900b	25	5	understand	understand	VERB
5138jd4900b	25	6	how	how	SCONJ
5138jd4900b	25	7	fourier	fourier	NOUN
5138jd4900b	25	8	developed	develop	VERB
5138jd4900b	25	9	his	his	PRON
5138jd4900b	25	10	work	work	NOUN
5138jd4900b	25	11	,	,	PUNCT
5138jd4900b	25	12	and	and	CCONJ
5138jd4900b	25	13	why	why	SCONJ
5138jd4900b	25	14	it	it	PRON
5138jd4900b	25	15	was	be	AUX
5138jd4900b	25	16	so	so	ADV
5138jd4900b	25	17	important	important	ADJ
5138jd4900b	25	18	at	at	ADP
5138jd4900b	25	19	the	the	DET
5138jd4900b	25	20	time	time	NOUN
5138jd4900b	25	21	.	.	PUNCT
5138jd4900b	26	1	we	we	PRON
5138jd4900b	26	2	then	then	ADV
5138jd4900b	26	3	explore	explore	VERB
5138jd4900b	26	4	some	some	PRON
5138jd4900b	26	5	of	of	ADP
5138jd4900b	26	6	the	the	DET
5138jd4900b	26	7	classical	classical	ADJ
5138jd4900b	26	8	results	result	NOUN
5138jd4900b	26	9	related	relate	VERB
5138jd4900b	26	10	to	to	ADP
5138jd4900b	26	11	the	the	DET
5138jd4900b	26	12	heat	heat	NOUN
5138jd4900b	26	13	equation	equation	NOUN
5138jd4900b	26	14	before	before	ADP
5138jd4900b	26	15	moving	move	VERB
5138jd4900b	26	16	on	on	ADP
5138jd4900b	26	17	to	to	ADP
5138jd4900b	26	18	the	the	DET
5138jd4900b	26	19	most	most	ADV
5138jd4900b	26	20	famous	famous	ADJ
5138jd4900b	26	21	nonlinear	nonlinear	ADJ
5138jd4900b	26	22	heat	heat	NOUN
5138jd4900b	26	23	--	--	PUNCT
5138jd4900b	26	24	type	type	NOUN
5138jd4900b	26	25	equation	equation	NOUN
5138jd4900b	26	26	,	,	PUNCT
5138jd4900b	26	27	the	the	DET
5138jd4900b	26	28	navier	navier	NOUN
5138jd4900b	26	29	--	--	PUNCT
5138jd4900b	26	30	stokes	stoke	NOUN
5138jd4900b	26	31	equation	equation	NOUN
5138jd4900b	26	32	,	,	PUNCT
5138jd4900b	26	33	and	and	CCONJ
5138jd4900b	26	34	explore	explore	VERB
5138jd4900b	26	35	several	several	ADJ
5138jd4900b	26	36	particular	particular	ADJ
5138jd4900b	26	37	solutions	solution	NOUN
5138jd4900b	26	38	.	.	PUNCT
5138jd4900b	27	1	the	the	DET
5138jd4900b	27	2	second	second	ADJ
5138jd4900b	27	3	section	section	NOUN
5138jd4900b	27	4	of	of	ADP
5138jd4900b	27	5	the	the	DET
5138jd4900b	27	6	document	document	NOUN
5138jd4900b	27	7	presents	present	VERB
5138jd4900b	27	8	the	the	DET
5138jd4900b	27	9	generalized	generalize	VERB
5138jd4900b	27	10	burgers	burger	NOUN
5138jd4900b	27	11	equation	equation	NOUN
5138jd4900b	27	12	,	,	PUNCT
5138jd4900b	27	13	and	and	CCONJ
5138jd4900b	27	14	contains	contain	VERB
5138jd4900b	27	15	our	our	PRON
5138jd4900b	27	16	main	main	ADJ
5138jd4900b	27	17	results	result	NOUN
5138jd4900b	27	18	contained	contain	VERB
5138jd4900b	27	19	within	within	ADP
5138jd4900b	27	20	this	this	DET
5138jd4900b	27	21	thesis	thesis	NOUN
5138jd4900b	27	22	.	.	PUNCT
5138jd4900b	28	1	the	the	DET
5138jd4900b	28	2	third	third	ADJ
5138jd4900b	28	3	section	section	NOUN
5138jd4900b	28	4	presents	present	VERB
5138jd4900b	28	5	our	our	PRON
5138jd4900b	28	6	results	result	NOUN
5138jd4900b	28	7	related	relate	VERB
5138jd4900b	28	8	to	to	ADP
5138jd4900b	28	9	a	a	DET
5138jd4900b	28	10	camassa	camassa	ADJ
5138jd4900b	28	11	--	--	PUNCT
5138jd4900b	28	12	holm	holm	NOUN
5138jd4900b	28	13	type	type	NOUN
5138jd4900b	28	14	equation	equation	NOUN
5138jd4900b	28	15	,	,	PUNCT
5138jd4900b	28	16	and	and	CCONJ
5138jd4900b	28	17	we	we	PRON
5138jd4900b	28	18	conclude	conclude	VERB
5138jd4900b	28	19	the	the	DET
5138jd4900b	28	20	thesis	thesis	NOUN
5138jd4900b	28	21	by	by	ADP
5138jd4900b	28	22	presenting	present	VERB
5138jd4900b	28	23	some	some	DET
5138jd4900b	28	24	numerical	numerical	ADJ
5138jd4900b	28	25	methods	method	NOUN
5138jd4900b	28	26	for	for	ADP
5138jd4900b	28	27	a	a	DET
5138jd4900b	28	28	nonlinear	nonlinear	ADJ
5138jd4900b	28	29	heat	heat	NOUN
5138jd4900b	28	30	equation	equation	NOUN
5138jd4900b	28	31	derived	derive	VERB
5138jd4900b	28	32	from	from	ADP
5138jd4900b	28	33	financial	financial	ADJ
5138jd4900b	28	34	mathematics	mathematic	NOUN
5138jd4900b	28	35	.	.	PUNCT