id	sid	tid	token	lemma	pos
ap-5513	1	1	acta	acta	PROPN
ap-5513	1	2	polytechnica	polytechnica	PROPN
ap-5513	1	3	doi:10.14311	doi:10.14311	PROPN
ap-5513	1	4	/	/	SYM
ap-5513	1	5	ap.2020.60.0098	ap.2020.60.0098	PROPN
ap-5513	1	6	acta	acta	PROPN
ap-5513	1	7	polytechnica	polytechnica	PROPN
ap-5513	1	8	60(2):98–110	60(2):98–110	PROPN
ap-5513	1	9	,	,	PUNCT
ap-5513	1	10	2020	2020	NUM
ap-5513	1	11	©	©	PROPN
ap-5513	1	12	czech	czech	PROPN
ap-5513	1	13	technical	technical	PROPN
ap-5513	1	14	university	university	PROPN
ap-5513	1	15	in	in	ADP
ap-5513	1	16	prague	prague	PROPN
ap-5513	1	17	,	,	PUNCT
ap-5513	1	18	2020	2020	NUM
ap-5513	1	19	available	available	ADJ
ap-5513	1	20	online	online	ADV
ap-5513	1	21	at	at	ADP
ap-5513	1	22	https://ojs.cvut.cz/ojs/index.php/ap	https://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-5513	1	23	similarity	similarity	NOUN
ap-5513	1	24	solutions	solution	NOUN
ap-5513	1	25	and	and	CCONJ
ap-5513	1	26	conservation	conservation	NOUN
ap-5513	1	27	laws	law	NOUN
ap-5513	1	28	for	for	ADP
ap-5513	1	29	the	the	DET
ap-5513	1	30	beam	beam	NOUN
ap-5513	1	31	equations	equation	NOUN
ap-5513	1	32	:	:	PUNCT
ap-5513	1	33	a	a	DET
ap-5513	1	34	complete	complete	ADJ
ap-5513	1	35	study	study	NOUN
ap-5513	1	36	amlan	amlan	NOUN
ap-5513	1	37	kanti	kanti	NOUN
ap-5513	1	38	haldera,∗	haldera,∗	NOUN
ap-5513	1	39	,	,	PUNCT
ap-5513	1	40	andronikos	andronikos	ADJ
ap-5513	1	41	paliathanasisb	paliathanasisb	NOUN
ap-5513	1	42	,	,	PUNCT
ap-5513	1	43	c	c	PROPN
ap-5513	1	44	,	,	PUNCT
ap-5513	1	45	peter	peter	PROPN
ap-5513	1	46	gavin	gavin	PROPN
ap-5513	1	47	lawrence	lawrence	PROPN
ap-5513	1	48	leachc	leachc	PROPN
ap-5513	1	49	,	,	PUNCT
ap-5513	1	50	d	d	PROPN
ap-5513	1	51	a	a	DET
ap-5513	1	52	pondicherry	pondicherry	PROPN
ap-5513	1	53	university	university	NOUN
ap-5513	1	54	,	,	PUNCT
ap-5513	1	55	department	department	NOUN
ap-5513	1	56	of	of	ADP
ap-5513	1	57	mathematics	mathematic	NOUN
ap-5513	1	58	,	,	PUNCT
ap-5513	1	59	605014	605014	NUM
ap-5513	1	60	kalapet	kalapet	PROPN
ap-5513	1	61	,	,	PUNCT
ap-5513	1	62	india	india	PROPN
ap-5513	1	63	b	b	PROPN
ap-5513	1	64	universidad	universidad	PROPN
ap-5513	1	65	austral	austral	PROPN
ap-5513	1	66	de	de	X
ap-5513	1	67	chile	chile	PROPN
ap-5513	1	68	,	,	PUNCT
ap-5513	1	69	instituto	instituto	PROPN
ap-5513	1	70	de	de	PROPN
ap-5513	1	71	ciencias	ciencias	PROPN
ap-5513	1	72	físicas	físicas	PROPN
ap-5513	1	73	y	y	PROPN
ap-5513	1	74	matemáticas	matemáticas	PROPN
ap-5513	1	75	,	,	PUNCT
ap-5513	1	76	valdivia	valdivia	PROPN
ap-5513	1	77	,	,	PUNCT
ap-5513	1	78	chile	chile	PROPN
ap-5513	1	79	c	c	PROPN
ap-5513	1	80	durban	durban	PROPN
ap-5513	1	81	university	university	PROPN
ap-5513	1	82	of	of	ADP
ap-5513	1	83	technology	technology	PROPN
ap-5513	1	84	,	,	PUNCT
ap-5513	1	85	institute	institute	NOUN
ap-5513	1	86	for	for	ADP
ap-5513	1	87	systems	system	NOUN
ap-5513	1	88	science	science	NOUN
ap-5513	1	89	,	,	PUNCT
ap-5513	1	90	durban	durban	PROPN
ap-5513	1	91	4000	4000	NUM
ap-5513	1	92	,	,	PUNCT
ap-5513	1	93	republic	republic	NOUN
ap-5513	1	94	of	of	ADP
ap-5513	1	95	south	south	PROPN
ap-5513	1	96	africa	africa	PROPN
ap-5513	2	1	d	d	PROPN
ap-5513	2	2	university	university	PROPN
ap-5513	2	3	of	of	ADP
ap-5513	2	4	kwazulu	kwazulu	PROPN
ap-5513	2	5	-	-	PUNCT
ap-5513	2	6	natal	natal	ADJ
ap-5513	2	7	,	,	PUNCT
ap-5513	2	8	school	school	NOUN
ap-5513	2	9	of	of	ADP
ap-5513	2	10	mathematics	mathematic	NOUN
ap-5513	2	11	,	,	PUNCT
ap-5513	2	12	statistics	statistic	NOUN
ap-5513	2	13	and	and	CCONJ
ap-5513	2	14	computer	computer	NOUN
ap-5513	2	15	science	science	NOUN
ap-5513	2	16	,	,	PUNCT
ap-5513	2	17	durban	durban	PROPN
ap-5513	2	18	,	,	PUNCT
ap-5513	2	19	south	south	PROPN
ap-5513	2	20	africa	africa	PROPN
ap-5513	2	21	∗	∗	VERB
ap-5513	2	22	corresponding	correspond	VERB
ap-5513	2	23	author	author	NOUN
ap-5513	2	24	:	:	PUNCT
ap-5513	2	25	amlan91.res@pondiuni.edu.in	amlan91.res@pondiuni.edu.in	PROPN
ap-5513	2	26	abstract	abstract	NOUN
ap-5513	2	27	.	.	PUNCT
ap-5513	3	1	we	we	PRON
ap-5513	3	2	study	study	VERB
ap-5513	3	3	the	the	DET
ap-5513	3	4	similarity	similarity	NOUN
ap-5513	3	5	solutions	solution	NOUN
ap-5513	3	6	and	and	CCONJ
ap-5513	3	7	we	we	PRON
ap-5513	3	8	determine	determine	VERB
ap-5513	3	9	the	the	DET
ap-5513	3	10	conservation	conservation	NOUN
ap-5513	3	11	laws	law	NOUN
ap-5513	3	12	of	of	ADP
ap-5513	3	13	various	various	ADJ
ap-5513	3	14	forms	form	NOUN
ap-5513	3	15	of	of	ADP
ap-5513	3	16	beam	beam	NOUN
ap-5513	3	17	equations	equation	NOUN
ap-5513	3	18	,	,	PUNCT
ap-5513	3	19	such	such	ADJ
ap-5513	3	20	as	as	ADP
ap-5513	3	21	euler	euler	NOUN
ap-5513	3	22	-	-	PUNCT
ap-5513	3	23	bernoulli	bernoulli	PROPN
ap-5513	3	24	,	,	PUNCT
ap-5513	3	25	rayleigh	rayleigh	PROPN
ap-5513	3	26	and	and	CCONJ
ap-5513	3	27	timoshenko	timoshenko	NOUN
ap-5513	3	28	-	-	PUNCT
ap-5513	3	29	prescott	prescott	NOUN
ap-5513	3	30	.	.	PUNCT
ap-5513	4	1	the	the	DET
ap-5513	4	2	travelling	travel	VERB
ap-5513	4	3	-	-	PUNCT
ap-5513	4	4	wave	wave	NOUN
ap-5513	4	5	reduction	reduction	NOUN
ap-5513	4	6	leads	lead	VERB
ap-5513	4	7	to	to	AUX
ap-5513	4	8	solvable	solvable	VERB
ap-5513	4	9	fourth	fourth	ADJ
ap-5513	4	10	-	-	PUNCT
ap-5513	4	11	order	order	NOUN
ap-5513	4	12	odes	ode	VERB
ap-5513	4	13	for	for	ADP
ap-5513	4	14	all	all	DET
ap-5513	4	15	the	the	DET
ap-5513	4	16	forms	form	NOUN
ap-5513	4	17	.	.	PUNCT
ap-5513	5	1	in	in	ADP
ap-5513	5	2	addition	addition	NOUN
ap-5513	5	3	,	,	PUNCT
ap-5513	5	4	the	the	DET
ap-5513	5	5	reduction	reduction	NOUN
ap-5513	5	6	based	base	VERB
ap-5513	5	7	on	on	ADP
ap-5513	5	8	the	the	DET
ap-5513	5	9	scaling	scaling	ADJ
ap-5513	5	10	symmetry	symmetry	NOUN
ap-5513	5	11	for	for	ADP
ap-5513	5	12	the	the	DET
ap-5513	5	13	euler	euler	NOUN
ap-5513	5	14	-	-	PUNCT
ap-5513	5	15	bernoulli	bernoulli	PROPN
ap-5513	5	16	form	form	NOUN
ap-5513	5	17	leads	lead	VERB
ap-5513	5	18	to	to	ADP
ap-5513	5	19	certain	certain	ADJ
ap-5513	5	20	odes	ode	NOUN
ap-5513	5	21	for	for	ADP
ap-5513	5	22	which	which	PRON
ap-5513	5	23	there	there	PRON
ap-5513	5	24	exists	exist	VERB
ap-5513	5	25	zero	zero	NUM
ap-5513	5	26	symmetries	symmetry	NOUN
ap-5513	5	27	.	.	PUNCT
ap-5513	6	1	therefore	therefore	ADV
ap-5513	6	2	,	,	PUNCT
ap-5513	6	3	we	we	PRON
ap-5513	6	4	conduct	conduct	VERB
ap-5513	6	5	the	the	DET
ap-5513	6	6	singularity	singularity	NOUN
ap-5513	6	7	analysis	analysis	NOUN
ap-5513	6	8	to	to	PART
ap-5513	6	9	ascertain	ascertain	VERB
ap-5513	6	10	the	the	DET
ap-5513	6	11	integrability	integrability	NOUN
ap-5513	6	12	.	.	PUNCT
ap-5513	7	1	we	we	PRON
ap-5513	7	2	study	study	VERB
ap-5513	7	3	two	two	NUM
ap-5513	7	4	reduced	reduce	VERB
ap-5513	7	5	odes	ode	NOUN
ap-5513	7	6	of	of	ADP
ap-5513	7	7	second	second	ADJ
ap-5513	7	8	and	and	CCONJ
ap-5513	7	9	third	third	ADJ
ap-5513	7	10	orders	order	NOUN
ap-5513	7	11	.	.	PUNCT
ap-5513	8	1	the	the	DET
ap-5513	8	2	reduced	reduced	ADJ
ap-5513	8	3	second	second	ADJ
ap-5513	8	4	-	-	PUNCT
ap-5513	8	5	order	order	NOUN
ap-5513	8	6	ode	ode	NOUN
ap-5513	8	7	is	be	AUX
ap-5513	8	8	a	a	DET
ap-5513	8	9	perturbed	perturb	VERB
ap-5513	8	10	form	form	NOUN
ap-5513	8	11	of	of	ADP
ap-5513	8	12	painlevé	painlevé	NOUN
ap-5513	8	13	-	-	PUNCT
ap-5513	8	14	ince	ince	NOUN
ap-5513	8	15	equation	equation	NOUN
ap-5513	8	16	,	,	PUNCT
ap-5513	8	17	which	which	PRON
ap-5513	8	18	is	be	AUX
ap-5513	8	19	integrable	integrable	ADJ
ap-5513	8	20	and	and	CCONJ
ap-5513	8	21	the	the	DET
ap-5513	8	22	third	third	ADJ
ap-5513	8	23	-	-	PUNCT
ap-5513	8	24	order	order	NOUN
ap-5513	8	25	ode	ode	NOUN
ap-5513	8	26	falls	fall	NOUN
ap-5513	8	27	into	into	ADP
ap-5513	8	28	the	the	DET
ap-5513	8	29	category	category	NOUN
ap-5513	8	30	of	of	ADP
ap-5513	8	31	equations	equation	NOUN
ap-5513	8	32	studied	study	VERB
ap-5513	8	33	by	by	ADP
ap-5513	8	34	chazy	chazy	PROPN
ap-5513	8	35	,	,	PUNCT
ap-5513	8	36	bureau	bureau	NOUN
ap-5513	8	37	and	and	CCONJ
ap-5513	8	38	cosgrove	cosgrove	PROPN
ap-5513	8	39	.	.	PUNCT
ap-5513	9	1	moreover	moreover	ADV
ap-5513	9	2	,	,	PUNCT
ap-5513	9	3	we	we	PRON
ap-5513	9	4	derived	derive	VERB
ap-5513	9	5	the	the	DET
ap-5513	9	6	symmetries	symmetry	NOUN
ap-5513	9	7	and	and	CCONJ
ap-5513	9	8	its	its	PRON
ap-5513	9	9	corresponding	correspond	VERB
ap-5513	9	10	reductions	reduction	NOUN
ap-5513	9	11	and	and	CCONJ
ap-5513	9	12	conservation	conservation	NOUN
ap-5513	9	13	laws	law	NOUN
ap-5513	9	14	for	for	ADP
ap-5513	9	15	the	the	DET
ap-5513	9	16	forced	force	VERB
ap-5513	9	17	form	form	NOUN
ap-5513	9	18	of	of	ADP
ap-5513	9	19	the	the	DET
ap-5513	9	20	abovementioned	abovementioned	ADJ
ap-5513	9	21	beam	beam	NOUN
ap-5513	9	22	forms	form	NOUN
ap-5513	9	23	.	.	PUNCT
ap-5513	10	1	the	the	DET
ap-5513	10	2	lie	lie	NOUN
ap-5513	10	3	algebra	algebra	NOUN
ap-5513	10	4	is	be	AUX
ap-5513	10	5	mentioned	mention	VERB
ap-5513	10	6	explicitly	explicitly	ADV
ap-5513	10	7	for	for	ADP
ap-5513	10	8	all	all	DET
ap-5513	10	9	the	the	DET
ap-5513	10	10	cases	case	NOUN
ap-5513	10	11	.	.	PUNCT
ap-5513	11	1	keywords	keyword	NOUN
ap-5513	11	2	:	:	PUNCT
ap-5513	11	3	symmetry	symmetry	NOUN
ap-5513	11	4	analysis	analysis	NOUN
ap-5513	11	5	,	,	PUNCT
ap-5513	11	6	singularity	singularity	NOUN
ap-5513	11	7	analysis	analysis	NOUN
ap-5513	11	8	,	,	PUNCT
ap-5513	11	9	conservation	conservation	NOUN
ap-5513	11	10	laws	law	NOUN
ap-5513	11	11	,	,	PUNCT
ap-5513	11	12	beam	beam	NOUN
ap-5513	11	13	equation	equation	NOUN
ap-5513	11	14	.	.	PUNCT
ap-5513	12	1	1	1	X
ap-5513	12	2	.	.	X
ap-5513	12	3	introduction	introduction	NOUN
ap-5513	12	4	there	there	PRON
ap-5513	12	5	are	be	VERB
ap-5513	12	6	basically	basically	ADV
ap-5513	12	7	two	two	NUM
ap-5513	12	8	types	type	NOUN
ap-5513	12	9	of	of	ADP
ap-5513	12	10	beams	beam	NOUN
ap-5513	12	11	.	.	PUNCT
ap-5513	13	1	one	one	NUM
ap-5513	13	2	type	type	NOUN
ap-5513	13	3	is	be	AUX
ap-5513	13	4	supported	support	VERB
ap-5513	13	5	at	at	ADP
ap-5513	13	6	both	both	DET
ap-5513	13	7	ends	end	NOUN
ap-5513	13	8	and	and	CCONJ
ap-5513	13	9	the	the	DET
ap-5513	13	10	other	other	ADJ
ap-5513	13	11	type	type	NOUN
ap-5513	13	12	is	be	AUX
ap-5513	13	13	supported	support	VERB
ap-5513	13	14	at	at	ADP
ap-5513	13	15	only	only	ADV
ap-5513	13	16	one	one	NUM
ap-5513	13	17	end	end	NOUN
ap-5513	13	18	.	.	PUNCT
ap-5513	14	1	it	it	PRON
ap-5513	14	2	is	be	AUX
ap-5513	14	3	a	a	DET
ap-5513	14	4	cantilever	cantilever	NOUN
ap-5513	14	5	.	.	PUNCT
ap-5513	15	1	the	the	DET
ap-5513	15	2	latter	latter	ADJ
ap-5513	15	3	is	be	AUX
ap-5513	15	4	of	of	ADP
ap-5513	15	5	greater	great	ADJ
ap-5513	15	6	mathematical	mathematical	ADJ
ap-5513	15	7	and	and	CCONJ
ap-5513	15	8	physical	physical	ADJ
ap-5513	15	9	interest	interest	NOUN
ap-5513	15	10	for	for	ADP
ap-5513	15	11	the	the	DET
ap-5513	15	12	free	free	ADJ
ap-5513	15	13	end	end	NOUN
ap-5513	15	14	can	can	AUX
ap-5513	15	15	vibrate	vibrate	VERB
ap-5513	15	16	.	.	PUNCT
ap-5513	16	1	this	this	PRON
ap-5513	16	2	causes	cause	VERB
ap-5513	16	3	stresses	stress	NOUN
ap-5513	16	4	in	in	ADP
ap-5513	16	5	the	the	DET
ap-5513	16	6	beam	beam	NOUN
ap-5513	16	7	.	.	PUNCT
ap-5513	17	1	the	the	DET
ap-5513	17	2	first	first	ADJ
ap-5513	17	3	mathematical	mathematical	ADJ
ap-5513	17	4	description	description	NOUN
ap-5513	17	5	was	be	AUX
ap-5513	17	6	made	make	VERB
ap-5513	17	7	by	by	ADP
ap-5513	17	8	leonhard	leonhard	PROPN
ap-5513	17	9	euler	euler	PROPN
ap-5513	17	10	and	and	CCONJ
ap-5513	17	11	daniel	daniel	PROPN
ap-5513	17	12	bernoulli	bernoulli	PROPN
ap-5513	17	13	around	around	ADP
ap-5513	17	14	1750	1750	NUM
ap-5513	17	15	,	,	PUNCT
ap-5513	17	16	but	but	CCONJ
ap-5513	17	17	there	there	PRON
ap-5513	17	18	were	be	VERB
ap-5513	17	19	some	some	DET
ap-5513	17	20	earlier	early	ADJ
ap-5513	17	21	attempts	attempt	NOUN
ap-5513	17	22	by	by	ADP
ap-5513	17	23	leonardo	leonardo	PROPN
ap-5513	17	24	da	da	PROPN
ap-5513	17	25	vinci	vinci	PROPN
ap-5513	17	26	and	and	CCONJ
ap-5513	17	27	galileo	galileo	PROPN
ap-5513	17	28	galilei	galilei	NOUN
ap-5513	17	29	who	who	PRON
ap-5513	17	30	were	be	AUX
ap-5513	17	31	more	more	ADJ
ap-5513	17	32	than	than	ADP
ap-5513	17	33	a	a	DET
ap-5513	17	34	little	little	ADJ
ap-5513	17	35	hampered	hamper	VERB
ap-5513	17	36	by	by	ADP
ap-5513	17	37	no	no	DET
ap-5513	17	38	knowledge	knowledge	NOUN
ap-5513	17	39	of	of	ADP
ap-5513	17	40	differential	differential	ADJ
ap-5513	17	41	equations	equation	NOUN
ap-5513	17	42	.	.	PUNCT
ap-5513	18	1	jacob	jacob	PROPN
ap-5513	18	2	bernoulli	bernoulli	PROPN
ap-5513	18	3	laid	lay	VERB
ap-5513	18	4	the	the	DET
ap-5513	18	5	groundwork	groundwork	NOUN
ap-5513	18	6	for	for	ADP
ap-5513	18	7	the	the	DET
ap-5513	18	8	development	development	NOUN
ap-5513	18	9	of	of	ADP
ap-5513	18	10	leonhard	leonhard	PROPN
ap-5513	18	11	euler	euler	PROPN
ap-5513	18	12	and	and	CCONJ
ap-5513	18	13	daniel	daniel	PROPN
ap-5513	18	14	bernoulli	bernoulli	PROPN
ap-5513	18	15	.	.	PUNCT
ap-5513	19	1	in	in	ADP
ap-5513	19	2	1894	1894	NUM
ap-5513	19	3	,	,	PUNCT
ap-5513	19	4	the	the	DET
ap-5513	19	5	polymath	polymath	NOUN
ap-5513	19	6	lord	lord	PROPN
ap-5513	19	7	rayleigh	rayleigh	PROPN
ap-5513	19	8	proposed	propose	VERB
ap-5513	19	9	an	an	DET
ap-5513	19	10	improvement	improvement	NOUN
ap-5513	19	11	to	to	ADP
ap-5513	19	12	the	the	DET
ap-5513	19	13	euler	euler	VERB
ap-5513	19	14	-	-	PUNCT
ap-5513	19	15	bernoulli	bernoulli	PROPN
ap-5513	19	16	model	model	NOUN
ap-5513	19	17	by	by	ADP
ap-5513	19	18	including	include	VERB
ap-5513	19	19	a	a	DET
ap-5513	19	20	term	term	NOUN
ap-5513	19	21	related	relate	VERB
ap-5513	19	22	to	to	ADP
ap-5513	19	23	rotational	rotational	ADJ
ap-5513	19	24	stress	stress	NOUN
ap-5513	19	25	.	.	PUNCT
ap-5513	20	1	in	in	ADP
ap-5513	20	2	1921	1921	NUM
ap-5513	20	3	,	,	PUNCT
ap-5513	20	4	timoshenko	timoshenko	NOUN
ap-5513	20	5	introduced	introduce	VERB
ap-5513	20	6	considerable	considerable	ADJ
ap-5513	20	7	improvements	improvement	NOUN
ap-5513	20	8	in	in	ADP
ap-5513	20	9	what	what	PRON
ap-5513	20	10	is	be	AUX
ap-5513	20	11	now	now	ADV
ap-5513	20	12	termed	term	VERB
ap-5513	20	13	the	the	DET
ap-5513	20	14	timoshenko	timoshenko	ADJ
ap-5513	20	15	-	-	PUNCT
ap-5513	20	16	prescott	prescott	NOUN
ap-5513	20	17	model	model	NOUN
ap-5513	20	18	.	.	PUNCT
ap-5513	21	1	there	there	PRON
ap-5513	21	2	has	have	AUX
ap-5513	21	3	been	be	AUX
ap-5513	21	4	a	a	DET
ap-5513	21	5	considerable	considerable	ADJ
ap-5513	21	6	experimental	experimental	ADJ
ap-5513	21	7	and	and	CCONJ
ap-5513	21	8	numerical	numerical	ADJ
ap-5513	21	9	work	work	NOUN
ap-5513	21	10	devoted	devote	VERB
ap-5513	21	11	to	to	ADP
ap-5513	21	12	the	the	DET
ap-5513	21	13	comparison	comparison	NOUN
ap-5513	21	14	of	of	ADP
ap-5513	21	15	predictions	prediction	NOUN
ap-5513	21	16	of	of	ADP
ap-5513	21	17	the	the	DET
ap-5513	21	18	theories	theory	NOUN
ap-5513	21	19	and	and	CCONJ
ap-5513	21	20	experimental	experimental	ADJ
ap-5513	21	21	results	result	NOUN
ap-5513	21	22	.	.	PUNCT
ap-5513	22	1	it	it	PRON
ap-5513	22	2	should	should	AUX
ap-5513	22	3	be	be	AUX
ap-5513	22	4	emphasised	emphasise	VERB
ap-5513	22	5	that	that	SCONJ
ap-5513	22	6	the	the	DET
ap-5513	22	7	infinitesimal	infinitesimal	ADJ
ap-5513	22	8	theory	theory	NOUN
ap-5513	22	9	of	of	ADP
ap-5513	22	10	elasticity	elasticity	NOUN
ap-5513	22	11	is	be	AUX
ap-5513	22	12	three	three	NUM
ap-5513	22	13	-	-	PUNCT
ap-5513	22	14	dimensional	dimensional	ADJ
ap-5513	22	15	and	and	CCONJ
ap-5513	22	16	that	that	SCONJ
ap-5513	22	17	the	the	DET
ap-5513	22	18	three	three	NUM
ap-5513	22	19	models	model	NOUN
ap-5513	22	20	mentioned	mention	VERB
ap-5513	22	21	above	above	ADV
ap-5513	22	22	are	be	AUX
ap-5513	22	23	linear	linear	NOUN
ap-5513	22	24	models	model	NOUN
ap-5513	22	25	.	.	PUNCT
ap-5513	23	1	they	they	PRON
ap-5513	23	2	make	make	VERB
ap-5513	23	3	for	for	ADP
ap-5513	23	4	easier	easy	ADJ
ap-5513	23	5	mathematics	mathematic	NOUN
ap-5513	23	6	,	,	PUNCT
ap-5513	23	7	but	but	CCONJ
ap-5513	23	8	there	there	PRON
ap-5513	23	9	is	be	VERB
ap-5513	23	10	a	a	DET
ap-5513	23	11	price	price	NOUN
ap-5513	23	12	to	to	PART
ap-5513	23	13	pay	pay	VERB
ap-5513	23	14	.	.	PUNCT
ap-5513	24	1	curiously	curiously	ADV
ap-5513	24	2	,	,	PUNCT
ap-5513	24	3	the	the	DET
ap-5513	24	4	simplest	simple	ADJ
ap-5513	24	5	model	model	NOUN
ap-5513	24	6	,	,	PUNCT
ap-5513	24	7	that	that	PRON
ap-5513	24	8	of	of	ADP
ap-5513	24	9	euler	euler	NOUN
ap-5513	24	10	-	-	PUNCT
ap-5513	24	11	bernoulli	bernoulli	PROPN
ap-5513	24	12	,	,	PUNCT
ap-5513	24	13	still	still	ADV
ap-5513	24	14	finds	find	VERB
ap-5513	24	15	favour	favour	PRON
ap-5513	24	16	amongst	amongst	ADP
ap-5513	24	17	some	some	DET
ap-5513	24	18	practitioners	practitioner	NOUN
ap-5513	24	19	.	.	PUNCT
ap-5513	25	1	some	some	PRON
ap-5513	25	2	of	of	ADP
ap-5513	25	3	the	the	DET
ap-5513	25	4	experimental	experimental	ADJ
ap-5513	25	5	work	work	NOUN
ap-5513	25	6	[	[	X
ap-5513	25	7	1	1	X
ap-5513	25	8	]	]	PUNCT
ap-5513	25	9	undertaken	undertake	VERB
ap-5513	25	10	to	to	PART
ap-5513	25	11	compare	compare	VERB
ap-5513	25	12	reality	reality	NOUN
ap-5513	25	13	with	with	ADP
ap-5513	25	14	theoretical	theoretical	ADJ
ap-5513	25	15	prediction	prediction	NOUN
ap-5513	25	16	tries	try	VERB
ap-5513	25	17	to	to	PART
ap-5513	25	18	make	make	VERB
ap-5513	25	19	the	the	DET
ap-5513	25	20	experiment	experiment	NOUN
ap-5513	25	21	as	as	ADV
ap-5513	25	22	close	close	ADV
ap-5513	25	23	to	to	ADP
ap-5513	25	24	a	a	DET
ap-5513	25	25	one	one	NUM
ap-5513	25	26	-	-	PUNCT
ap-5513	25	27	dimensional	dimensional	ADJ
ap-5513	25	28	model	model	NOUN
ap-5513	25	29	as	as	ADP
ap-5513	25	30	possible	possible	ADJ
ap-5513	25	31	.	.	PUNCT
ap-5513	26	1	one	one	NUM
ap-5513	26	2	of	of	ADP
ap-5513	26	3	the	the	DET
ap-5513	26	4	more	more	ADV
ap-5513	26	5	interesting	interesting	ADJ
ap-5513	26	6	studies	study	NOUN
ap-5513	26	7	is	be	AUX
ap-5513	26	8	the	the	DET
ap-5513	26	9	propagation	propagation	NOUN
ap-5513	26	10	of	of	ADP
ap-5513	26	11	shock	shock	NOUN
ap-5513	26	12	waves	wave	NOUN
ap-5513	26	13	along	along	ADP
ap-5513	26	14	the	the	DET
ap-5513	26	15	beam	beam	NOUN
ap-5513	26	16	.	.	PUNCT
ap-5513	27	1	this	this	PRON
ap-5513	27	2	involves	involve	VERB
ap-5513	27	3	firing	fire	VERB
ap-5513	27	4	a	a	DET
ap-5513	27	5	bullet	bullet	NOUN
ap-5513	27	6	into	into	ADP
ap-5513	27	7	the	the	DET
ap-5513	27	8	fixed	fixed	ADJ
ap-5513	27	9	end	end	NOUN
ap-5513	27	10	of	of	ADP
ap-5513	27	11	the	the	DET
ap-5513	27	12	cantilever	cantilever	NOUN
ap-5513	27	13	which	which	PRON
ap-5513	27	14	is	be	AUX
ap-5513	27	15	of	of	ADP
ap-5513	27	16	a	a	DET
ap-5513	27	17	small	small	ADJ
ap-5513	27	18	diameter	diameter	NOUN
ap-5513	27	19	–	–	PUNCT
ap-5513	27	20	25	25	NUM
ap-5513	27	21	mm	mm	NOUN
ap-5513	27	22	–	–	PUNCT
ap-5513	27	23	to	to	PART
ap-5513	27	24	emulate	emulate	VERB
ap-5513	27	25	a	a	DET
ap-5513	27	26	uniform	uniform	ADJ
ap-5513	27	27	boundary	boundary	ADJ
ap-5513	27	28	condition	condition	NOUN
ap-5513	27	29	at	at	ADP
ap-5513	27	30	the	the	DET
ap-5513	27	31	fixed	fixed	ADJ
ap-5513	27	32	end	end	NOUN
ap-5513	27	33	of	of	ADP
ap-5513	27	34	the	the	DET
ap-5513	27	35	beam	beam	NOUN
ap-5513	27	36	.	.	PUNCT
ap-5513	28	1	the	the	DET
ap-5513	28	2	literature	literature	NOUN
ap-5513	28	3	devoted	devote	VERB
ap-5513	28	4	to	to	ADP
ap-5513	28	5	the	the	DET
ap-5513	28	6	theory	theory	NOUN
ap-5513	28	7	and	and	CCONJ
ap-5513	28	8	practice	practice	NOUN
ap-5513	28	9	of	of	ADP
ap-5513	28	10	beams	beam	NOUN
ap-5513	28	11	is	be	AUX
ap-5513	28	12	extensive	extensive	ADJ
ap-5513	28	13	both	both	CCONJ
ap-5513	28	14	in	in	ADP
ap-5513	28	15	time	time	NOUN
ap-5513	28	16	and	and	CCONJ
ap-5513	28	17	space	space	NOUN
ap-5513	28	18	.	.	PUNCT
ap-5513	29	1	a	a	DET
ap-5513	29	2	fairly	fairly	ADV
ap-5513	29	3	recent	recent	ADJ
ap-5513	29	4	paper	paper	NOUN
ap-5513	29	5	by	by	ADP
ap-5513	29	6	labuschagne	labuschagne	NOUN
ap-5513	29	7	[	[	X
ap-5513	29	8	2	2	X
ap-5513	29	9	]	]	PUNCT
ap-5513	29	10	is	be	AUX
ap-5513	29	11	very	very	ADV
ap-5513	29	12	good	good	ADJ
ap-5513	29	13	in	in	ADP
ap-5513	29	14	its	its	PRON
ap-5513	29	15	historical	historical	ADJ
ap-5513	29	16	aspects	aspect	NOUN
ap-5513	29	17	as	as	ADV
ap-5513	29	18	well	well	ADV
ap-5513	29	19	as	as	ADP
ap-5513	29	20	being	be	AUX
ap-5513	29	21	clearly	clearly	ADV
ap-5513	29	22	written	write	VERB
ap-5513	29	23	.	.	PUNCT
ap-5513	30	1	earlier	early	ADJ
ap-5513	30	2	papers	paper	NOUN
ap-5513	30	3	in	in	ADP
ap-5513	30	4	addition	addition	NOUN
ap-5513	30	5	to	to	ADP
ap-5513	30	6	that	that	PRON
ap-5513	30	7	of	of	ADP
ap-5513	30	8	davies	davy	NOUN
ap-5513	30	9	cited	cite	VERB
ap-5513	30	10	above	above	ADV
ap-5513	30	11	are	be	AUX
ap-5513	30	12	by	by	ADP
ap-5513	30	13	hudson	hudson	PROPN
ap-5513	31	1	[	[	X
ap-5513	31	2	3	3	NUM
ap-5513	31	3	]	]	PUNCT
ap-5513	31	4	and	and	CCONJ
ap-5513	31	5	bancroft	bancroft	PROPN
ap-5513	32	1	[	[	X
ap-5513	32	2	4	4	NUM
ap-5513	32	3	]	]	PUNCT
ap-5513	32	4	.	.	PUNCT
ap-5513	33	1	an	an	DET
ap-5513	33	2	interesting	interesting	ADJ
ap-5513	33	3	feature	feature	NOUN
ap-5513	33	4	is	be	AUX
ap-5513	33	5	that	that	SCONJ
ap-5513	33	6	the	the	DET
ap-5513	33	7	beams	beam	NOUN
ap-5513	33	8	are	be	AUX
ap-5513	33	9	taken	take	VERB
ap-5513	33	10	to	to	PART
ap-5513	33	11	be	be	AUX
ap-5513	33	12	cylindrical	cylindrical	ADJ
ap-5513	33	13	in	in	ADP
ap-5513	33	14	shape	shape	NOUN
ap-5513	33	15	even	even	ADV
ap-5513	33	16	though	though	SCONJ
ap-5513	33	17	the	the	DET
ap-5513	33	18	beams	beam	NOUN
ap-5513	33	19	one	one	PRON
ap-5513	33	20	sees	see	VERB
ap-5513	33	21	in	in	ADP
ap-5513	33	22	buildings	building	NOUN
ap-5513	33	23	are	be	AUX
ap-5513	33	24	anything	anything	PRON
ap-5513	33	25	but	but	ADV
ap-5513	33	26	cylindrical	cylindrical	ADJ
ap-5513	33	27	with	with	ADP
ap-5513	33	28	some	some	DET
ap-5513	33	29	exceptions	exception	NOUN
ap-5513	33	30	to	to	PART
ap-5513	33	31	be	be	AUX
ap-5513	33	32	found	find	VERB
ap-5513	33	33	in	in	ADP
ap-5513	33	34	beamed	beamed	ADJ
ap-5513	33	35	structures	structure	NOUN
ap-5513	33	36	of	of	ADP
ap-5513	33	37	the	the	DET
ap-5513	33	38	nineteenth	nineteenth	ADJ
ap-5513	33	39	century	century	NOUN
ap-5513	33	40	.	.	PUNCT
ap-5513	34	1	one	one	NUM
ap-5513	34	2	assumes	assume	VERB
ap-5513	34	3	that	that	SCONJ
ap-5513	34	4	this	this	PRON
ap-5513	34	5	makes	make	VERB
ap-5513	34	6	the	the	DET
ap-5513	34	7	analysis	analysis	NOUN
ap-5513	34	8	simpler	simple	ADJ
ap-5513	34	9	due	due	ADP
ap-5513	34	10	to	to	ADP
ap-5513	34	11	the	the	DET
ap-5513	34	12	radial	radial	ADJ
ap-5513	34	13	symmetry	symmetry	NOUN
ap-5513	34	14	.	.	PUNCT
ap-5513	35	1	even	even	ADV
ap-5513	35	2	a	a	DET
ap-5513	35	3	square	square	ADJ
ap-5513	35	4	cross	cross	NOUN
ap-5513	35	5	-	-	NOUN
ap-5513	35	6	section	section	NOUN
ap-5513	35	7	would	would	AUX
ap-5513	35	8	significantly	significantly	ADV
ap-5513	35	9	complicate	complicate	VERB
ap-5513	35	10	the	the	DET
ap-5513	35	11	mathematics	mathematic	NOUN
ap-5513	35	12	.	.	PUNCT
ap-5513	36	1	98	98	NUM
ap-5513	36	2	https://doi.org/10.14311/ap.2020.60.0098	https://doi.org/10.14311/ap.2020.60.0098	PRON
ap-5513	36	3	https://ojs.cvut.cz/ojs/index.php/ap	https://ojs.cvut.cz/ojs/index.php/ap	NUM
ap-5513	36	4	vol	vol	NOUN
ap-5513	36	5	.	.	PUNCT
ap-5513	37	1	60	60	NUM
ap-5513	37	2	no	no	NOUN
ap-5513	37	3	.	.	PUNCT
ap-5513	38	1	2/2020	2/2020	NUM
ap-5513	38	2	similarity	similarity	NOUN
ap-5513	38	3	solutions	solution	NOUN
ap-5513	38	4	and	and	CCONJ
ap-5513	38	5	conservation	conservation	NOUN
ap-5513	38	6	laws	law	NOUN
ap-5513	38	7	for	for	ADP
ap-5513	38	8	the	the	DET
ap-5513	38	9	beam	beam	NOUN
ap-5513	38	10	equations	equation	NOUN
ap-5513	38	11	.	.	PUNCT
ap-5513	38	12	.	.	PUNCT
ap-5513	39	1	.	.	PUNCT
ap-5513	40	1	in	in	ADP
ap-5513	40	2	this	this	DET
ap-5513	40	3	work	work	NOUN
ap-5513	40	4	,	,	PUNCT
ap-5513	40	5	we	we	PRON
ap-5513	40	6	study	study	VERB
ap-5513	40	7	the	the	DET
ap-5513	40	8	algebraic	algebraic	ADJ
ap-5513	40	9	properties	property	NOUN
ap-5513	40	10	of	of	ADP
ap-5513	40	11	the	the	DET
ap-5513	40	12	euler	euler	PROPN
ap-5513	40	13	-	-	PUNCT
ap-5513	40	14	bernoulli	bernoulli	PROPN
ap-5513	40	15	,	,	PUNCT
ap-5513	40	16	the	the	DET
ap-5513	40	17	rayleigh	rayleigh	PROPN
ap-5513	40	18	and	and	CCONJ
ap-5513	40	19	of	of	ADP
ap-5513	40	20	the	the	DET
ap-5513	40	21	timoshenkoprescott	timoshenkoprescott	NOUN
ap-5513	40	22	according	accord	VERB
ap-5513	40	23	to	to	ADP
ap-5513	40	24	the	the	DET
ap-5513	40	25	admitted	admit	VERB
ap-5513	40	26	lie	lie	NOUN
ap-5513	40	27	point	point	NOUN
ap-5513	40	28	symmetries	symmetry	NOUN
ap-5513	40	29	,	,	PUNCT
ap-5513	40	30	for	for	ADP
ap-5513	40	31	the	the	DET
ap-5513	40	32	source	source	NOUN
ap-5513	40	33	-	-	PUNCT
ap-5513	40	34	free	free	ADJ
ap-5513	40	35	equation	equation	NOUN
ap-5513	40	36	as	as	ADP
ap-5513	40	37	also	also	ADV
ap-5513	40	38	in	in	ADP
ap-5513	40	39	the	the	DET
ap-5513	40	40	case	case	NOUN
ap-5513	40	41	where	where	SCONJ
ap-5513	40	42	a	a	DET
ap-5513	40	43	homogeneous	homogeneous	ADJ
ap-5513	40	44	source	source	NOUN
ap-5513	40	45	term	term	NOUN
ap-5513	40	46	exists	exist	VERB
ap-5513	40	47	.	.	PUNCT
ap-5513	41	1	the	the	DET
ap-5513	41	2	application	application	NOUN
ap-5513	41	3	of	of	ADP
ap-5513	41	4	the	the	DET
ap-5513	41	5	symmetry	symmetry	NOUN
ap-5513	41	6	analysis	analysis	NOUN
ap-5513	41	7	for	for	ADP
ap-5513	41	8	the	the	DET
ap-5513	41	9	euler	euler	NOUN
ap-5513	41	10	-	-	PUNCT
ap-5513	41	11	bernoulli	bernoulli	NOUN
ap-5513	41	12	equation	equation	NOUN
ap-5513	41	13	is	be	AUX
ap-5513	41	14	not	not	PART
ap-5513	41	15	new	new	ADJ
ap-5513	41	16	,	,	PUNCT
ap-5513	41	17	there	there	PRON
ap-5513	41	18	are	be	VERB
ap-5513	41	19	various	various	ADJ
ap-5513	41	20	studies	study	NOUN
ap-5513	41	21	in	in	ADP
ap-5513	41	22	the	the	DET
ap-5513	41	23	literature	literature	NOUN
ap-5513	41	24	[	[	X
ap-5513	41	25	5–9	5–9	X
ap-5513	41	26	]	]	X
ap-5513	41	27	,	,	PUNCT
ap-5513	41	28	however	however	ADV
ap-5513	41	29	in	in	ADP
ap-5513	41	30	this	this	DET
ap-5513	41	31	paper	paper	NOUN
ap-5513	41	32	,	,	PUNCT
ap-5513	41	33	we	we	PRON
ap-5513	41	34	obtained	obtain	VERB
ap-5513	41	35	some	some	DET
ap-5513	41	36	new	new	ADJ
ap-5513	41	37	results	result	NOUN
ap-5513	41	38	,	,	PUNCT
ap-5513	41	39	as	as	ADP
ap-5513	41	40	the	the	DET
ap-5513	41	41	reduction	reduction	NOUN
ap-5513	41	42	of	of	ADP
ap-5513	41	43	the	the	DET
ap-5513	41	44	euler	euler	NOUN
ap-5513	41	45	-	-	PUNCT
ap-5513	41	46	bernoulli	bernoulli	PROPN
ap-5513	41	47	form	form	NOUN
ap-5513	41	48	to	to	ADP
ap-5513	41	49	a	a	DET
ap-5513	41	50	perturbed	perturb	VERB
ap-5513	41	51	form	form	NOUN
ap-5513	41	52	of	of	ADP
ap-5513	41	53	painlevé	painlevé	NOUN
ap-5513	41	54	-	-	NOUN
ap-5513	41	55	ince	ince	NOUN
ap-5513	41	56	[	[	X
ap-5513	41	57	10	10	NUM
ap-5513	41	58	]	]	PUNCT
ap-5513	41	59	equation	equation	NOUN
ap-5513	41	60	,	,	PUNCT
ap-5513	41	61	which	which	PRON
ap-5513	41	62	is	be	AUX
ap-5513	41	63	integrable	integrable	ADJ
ap-5513	41	64	and	and	CCONJ
ap-5513	41	65	the	the	DET
ap-5513	41	66	third	third	ADJ
ap-5513	41	67	-	-	PUNCT
ap-5513	41	68	order	order	NOUN
ap-5513	41	69	ode	ode	NOUN
ap-5513	41	70	,	,	PUNCT
ap-5513	41	71	which	which	PRON
ap-5513	41	72	falls	fall	VERB
ap-5513	41	73	into	into	ADP
ap-5513	41	74	the	the	DET
ap-5513	41	75	category	category	NOUN
ap-5513	41	76	of	of	ADP
ap-5513	41	77	equations	equation	NOUN
ap-5513	41	78	studied	study	VERB
ap-5513	41	79	by	by	ADP
ap-5513	41	80	chazy	chazy	PROPN
ap-5513	41	81	,	,	PUNCT
ap-5513	41	82	bureau	bureau	NOUN
ap-5513	41	83	and	and	CCONJ
ap-5513	41	84	cosgrove	cosgrove	PROPN
ap-5513	41	85	.	.	PUNCT
ap-5513	42	1	also	also	ADV
ap-5513	42	2	,	,	PUNCT
ap-5513	42	3	we	we	PRON
ap-5513	42	4	show	show	VERB
ap-5513	42	5	that	that	SCONJ
ap-5513	42	6	the	the	DET
ap-5513	42	7	three	three	NUM
ap-5513	42	8	beam	beam	NOUN
ap-5513	42	9	equations	equation	NOUN
ap-5513	42	10	of	of	ADP
ap-5513	42	11	our	our	PRON
ap-5513	42	12	study	study	NOUN
ap-5513	42	13	admit	admit	VERB
ap-5513	42	14	the	the	DET
ap-5513	42	15	same	same	ADJ
ap-5513	42	16	travelling	travelling	ADJ
ap-5513	42	17	-	-	PUNCT
ap-5513	42	18	wave	wave	NOUN
ap-5513	42	19	solution	solution	NOUN
ap-5513	42	20	.	.	PUNCT
ap-5513	43	1	certain	certain	ADJ
ap-5513	43	2	phenomenal	phenomenal	ADJ
ap-5513	43	3	works	work	NOUN
ap-5513	43	4	were	be	AUX
ap-5513	43	5	recently	recently	ADV
ap-5513	43	6	done	do	VERB
ap-5513	43	7	for	for	ADP
ap-5513	43	8	the	the	DET
ap-5513	43	9	static	static	PROPN
ap-5513	43	10	euler	euler	PROPN
ap-5513	43	11	-	-	PUNCT
ap-5513	43	12	bernoulli	bernoulli	NOUN
ap-5513	43	13	equation	equation	NOUN
ap-5513	43	14	by	by	ADP
ap-5513	43	15	ruiz	ruiz	NOUN
ap-5513	44	1	[	[	X
ap-5513	44	2	11	11	NUM
ap-5513	44	3	]	]	PUNCT
ap-5513	44	4	and	and	CCONJ
ap-5513	44	5	da	da	PROPN
ap-5513	44	6	silva	silva	PROPN
ap-5513	44	7	pl	pl	PROPN
ap-5513	45	1	[	[	X
ap-5513	45	2	12	12	NUM
ap-5513	45	3	]	]	PUNCT
ap-5513	45	4	.	.	PUNCT
ap-5513	46	1	in	in	ADP
ap-5513	46	2	ruiz	ruiz	NOUN
ap-5513	46	3	[	[	X
ap-5513	46	4	11	11	NUM
ap-5513	46	5	]	]	PUNCT
ap-5513	46	6	,	,	PUNCT
ap-5513	46	7	the	the	DET
ap-5513	46	8	euler	euler	PROPN
ap-5513	46	9	-	-	PUNCT
ap-5513	46	10	bernoulli	bernoulli	NOUN
ap-5513	46	11	equation	equation	NOUN
ap-5513	46	12	with	with	ADP
ap-5513	46	13	an	an	DET
ap-5513	46	14	external	external	ADJ
ap-5513	46	15	agent	agent	NOUN
ap-5513	46	16	is	be	AUX
ap-5513	46	17	studied	study	VERB
ap-5513	46	18	with	with	ADP
ap-5513	46	19	respect	respect	NOUN
ap-5513	46	20	to	to	ADP
ap-5513	46	21	the	the	DET
ap-5513	46	22	joint	joint	ADJ
ap-5513	46	23	invariants	invariant	NOUN
ap-5513	46	24	of	of	ADP
ap-5513	46	25	the	the	DET
ap-5513	46	26	algebra	algebra	NOUN
ap-5513	46	27	and	and	CCONJ
ap-5513	46	28	complete	complete	ADJ
ap-5513	46	29	solutions	solution	NOUN
ap-5513	46	30	are	be	AUX
ap-5513	46	31	specified	specify	VERB
ap-5513	46	32	whereas	whereas	SCONJ
ap-5513	46	33	in	in	ADP
ap-5513	46	34	[	[	X
ap-5513	46	35	12	12	NUM
ap-5513	46	36	]	]	PUNCT
ap-5513	46	37	,	,	PUNCT
ap-5513	46	38	for	for	ADP
ap-5513	46	39	the	the	DET
ap-5513	46	40	static	static	PROPN
ap-5513	46	41	euler	euler	PROPN
ap-5513	46	42	-	-	PUNCT
ap-5513	46	43	bernoulli	bernoulli	NOUN
ap-5513	46	44	equation	equation	NOUN
ap-5513	46	45	with	with	ADP
ap-5513	46	46	specific	specific	ADJ
ap-5513	46	47	nonlinear	nonlinear	ADJ
ap-5513	46	48	term	term	NOUN
ap-5513	46	49	,	,	PUNCT
ap-5513	46	50	it	it	PRON
ap-5513	46	51	was	be	AUX
ap-5513	46	52	found	find	VERB
ap-5513	46	53	that	that	SCONJ
ap-5513	46	54	the	the	DET
ap-5513	46	55	algebraic	algebraic	ADJ
ap-5513	46	56	structure	structure	NOUN
ap-5513	46	57	of	of	ADP
ap-5513	46	58	lie	lie	NOUN
ap-5513	46	59	point	point	NOUN
ap-5513	46	60	symmetries	symmetry	NOUN
ap-5513	46	61	is	be	AUX
ap-5513	46	62	similar	similar	ADJ
ap-5513	46	63	to	to	ADP
ap-5513	46	64	that	that	PRON
ap-5513	46	65	of	of	ADP
ap-5513	46	66	the	the	DET
ap-5513	46	67	noether	noether	ADJ
ap-5513	46	68	symmetries	symmetry	NOUN
ap-5513	46	69	.	.	PUNCT
ap-5513	47	1	it	it	PRON
ap-5513	47	2	is	be	AUX
ap-5513	47	3	worthwhile	worthwhile	ADJ
ap-5513	47	4	to	to	PART
ap-5513	47	5	mention	mention	VERB
ap-5513	47	6	the	the	DET
ap-5513	47	7	paper	paper	NOUN
ap-5513	47	8	of	of	ADP
ap-5513	47	9	freire	freire	PROPN
ap-5513	47	10	il	il	PROPN
ap-5513	48	1	[	[	X
ap-5513	48	2	13	13	NUM
ap-5513	48	3	]	]	PUNCT
ap-5513	48	4	where	where	SCONJ
ap-5513	48	5	the	the	DET
ap-5513	48	6	lane	lane	NOUN
ap-5513	48	7	-	-	PUNCT
ap-5513	48	8	emden	emden	NOUN
ap-5513	48	9	system	system	NOUN
ap-5513	48	10	is	be	AUX
ap-5513	48	11	reduced	reduce	VERB
ap-5513	48	12	to	to	ADP
ap-5513	48	13	the	the	DET
ap-5513	48	14	emden	emden	ADJ
ap-5513	48	15	-	-	PUNCT
ap-5513	48	16	fowler	fowler	PROPN
ap-5513	48	17	equations	equation	NOUN
ap-5513	48	18	and	and	CCONJ
ap-5513	48	19	,	,	PUNCT
ap-5513	48	20	correspondingly	correspondingly	ADV
ap-5513	48	21	,	,	PUNCT
ap-5513	48	22	the	the	DET
ap-5513	48	23	solutions	solution	NOUN
ap-5513	48	24	of	of	ADP
ap-5513	48	25	the	the	DET
ap-5513	48	26	system	system	NOUN
ap-5513	48	27	have	have	AUX
ap-5513	48	28	been	be	AUX
ap-5513	48	29	studied	study	VERB
ap-5513	48	30	with	with	ADP
ap-5513	48	31	the	the	DET
ap-5513	48	32	aid	aid	NOUN
ap-5513	48	33	of	of	ADP
ap-5513	48	34	the	the	DET
ap-5513	48	35	point	point	NOUN
ap-5513	48	36	symmetries	symmetry	NOUN
ap-5513	48	37	.	.	PUNCT
ap-5513	49	1	to	to	PART
ap-5513	49	2	elaborate	elaborate	VERB
ap-5513	49	3	the	the	DET
ap-5513	49	4	above	above	ADJ
ap-5513	49	5	mentioned	mention	VERB
ap-5513	49	6	works	work	NOUN
ap-5513	49	7	,	,	PUNCT
ap-5513	49	8	we	we	PRON
ap-5513	49	9	focus	focus	VERB
ap-5513	49	10	on	on	ADP
ap-5513	49	11	the	the	DET
ap-5513	49	12	more	more	ADV
ap-5513	49	13	general	general	ADJ
ap-5513	49	14	euler	euler	VERB
ap-5513	49	15	-	-	PUNCT
ap-5513	49	16	bernoulli	bernoulli	NOUN
ap-5513	49	17	equation	equation	NOUN
ap-5513	49	18	with	with	ADP
ap-5513	49	19	and	and	CCONJ
ap-5513	49	20	without	without	ADP
ap-5513	49	21	the	the	DET
ap-5513	49	22	external	external	ADJ
ap-5513	49	23	forcing	force	VERB
ap-5513	49	24	term	term	NOUN
ap-5513	49	25	and	and	CCONJ
ap-5513	49	26	compute	compute	VERB
ap-5513	49	27	its	its	PRON
ap-5513	49	28	solution	solution	NOUN
ap-5513	49	29	using	use	VERB
ap-5513	49	30	the	the	DET
ap-5513	49	31	point	point	NOUN
ap-5513	49	32	symmetries	symmetry	NOUN
ap-5513	49	33	.	.	PUNCT
ap-5513	50	1	it	it	PRON
ap-5513	50	2	is	be	AUX
ap-5513	50	3	also	also	ADV
ap-5513	50	4	our	our	PRON
ap-5513	50	5	intuition	intuition	NOUN
ap-5513	50	6	that	that	SCONJ
ap-5513	50	7	the	the	DET
ap-5513	50	8	point	point	NOUN
ap-5513	50	9	symmetries	symmetry	NOUN
ap-5513	50	10	of	of	ADP
ap-5513	50	11	the	the	DET
ap-5513	50	12	form	form	NOUN
ap-5513	50	13	of	of	ADP
ap-5513	50	14	euler	euler	NOUN
ap-5513	50	15	-	-	PUNCT
ap-5513	50	16	bernoulli	bernoulli	NOUN
ap-5513	50	17	under	under	ADP
ap-5513	50	18	consideration	consideration	NOUN
ap-5513	50	19	do	do	AUX
ap-5513	50	20	possess	possess	VERB
ap-5513	50	21	some	some	DET
ap-5513	50	22	similarities	similarity	NOUN
ap-5513	50	23	with	with	ADP
ap-5513	50	24	the	the	DET
ap-5513	50	25	noether	noether	ADJ
ap-5513	50	26	symmetries	symmetry	NOUN
ap-5513	50	27	to	to	PART
ap-5513	50	28	follow	follow	VERB
ap-5513	50	29	the	the	DET
ap-5513	50	30	results	result	NOUN
ap-5513	50	31	of	of	ADP
ap-5513	50	32	the	the	DET
ap-5513	50	33	above	above	ADJ
ap-5513	50	34	mentioned	mention	VERB
ap-5513	50	35	work	work	NOUN
ap-5513	50	36	.	.	PUNCT
ap-5513	51	1	this	this	DET
ap-5513	51	2	paper	paper	NOUN
ap-5513	51	3	is	be	AUX
ap-5513	51	4	structured	structure	VERB
ap-5513	51	5	in	in	ADP
ap-5513	51	6	the	the	DET
ap-5513	51	7	following	following	ADJ
ap-5513	51	8	way	way	NOUN
ap-5513	51	9	:	:	PUNCT
ap-5513	51	10	in	in	ADP
ap-5513	51	11	section	section	NOUN
ap-5513	51	12	2	2	NUM
ap-5513	51	13	,	,	PUNCT
ap-5513	51	14	we	we	PRON
ap-5513	51	15	mention	mention	VERB
ap-5513	51	16	the	the	DET
ap-5513	51	17	lie	lie	NOUN
ap-5513	51	18	point	point	NOUN
ap-5513	51	19	symmetries	symmetry	NOUN
ap-5513	51	20	and	and	CCONJ
ap-5513	51	21	the	the	DET
ap-5513	51	22	corresponding	corresponding	ADJ
ap-5513	51	23	algebra	algebra	NOUN
ap-5513	51	24	.	.	PUNCT
ap-5513	52	1	in	in	ADP
ap-5513	52	2	section	section	NOUN
ap-5513	52	3	3	3	NUM
ap-5513	52	4	,	,	PUNCT
ap-5513	52	5	we	we	PRON
ap-5513	52	6	discuss	discuss	VERB
ap-5513	52	7	the	the	DET
ap-5513	52	8	travelling	travel	VERB
ap-5513	52	9	-	-	PUNCT
ap-5513	52	10	wave	wave	NOUN
ap-5513	52	11	solutions	solution	NOUN
ap-5513	52	12	for	for	ADP
ap-5513	52	13	all	all	DET
ap-5513	52	14	the	the	DET
ap-5513	52	15	beam	beam	NOUN
ap-5513	52	16	forms	form	NOUN
ap-5513	52	17	and	and	CCONJ
ap-5513	52	18	further	further	ADJ
ap-5513	52	19	reductions	reduction	NOUN
ap-5513	52	20	of	of	ADP
ap-5513	52	21	euler	euler	NOUN
ap-5513	52	22	-	-	PUNCT
ap-5513	52	23	bernoulli	bernoulli	NOUN
ap-5513	52	24	form	form	NOUN
ap-5513	52	25	using	use	VERB
ap-5513	52	26	the	the	DET
ap-5513	52	27	scaling	scale	VERB
ap-5513	52	28	symmetries	symmetry	NOUN
ap-5513	52	29	.	.	PUNCT
ap-5513	53	1	in	in	ADP
ap-5513	53	2	section	section	NOUN
ap-5513	53	3	4	4	NUM
ap-5513	53	4	,	,	PUNCT
ap-5513	53	5	we	we	PRON
ap-5513	53	6	study	study	VERB
ap-5513	53	7	the	the	DET
ap-5513	53	8	forced	force	VERB
ap-5513	53	9	forms	form	NOUN
ap-5513	53	10	of	of	ADP
ap-5513	53	11	the	the	DET
ap-5513	53	12	beam	beam	NOUN
ap-5513	53	13	equations	equation	NOUN
ap-5513	53	14	.	.	PUNCT
ap-5513	54	1	section	section	NOUN
ap-5513	54	2	5	5	NUM
ap-5513	54	3	is	be	AUX
ap-5513	54	4	devoted	devote	VERB
ap-5513	54	5	to	to	ADP
ap-5513	54	6	the	the	DET
ap-5513	54	7	singularity	singularity	NOUN
ap-5513	54	8	analysis	analysis	NOUN
ap-5513	54	9	of	of	ADP
ap-5513	54	10	a	a	DET
ap-5513	54	11	third	third	ADJ
ap-5513	54	12	-	-	PUNCT
ap-5513	54	13	order	order	NOUN
ap-5513	54	14	equation	equation	NOUN
ap-5513	54	15	,	,	PUNCT
ap-5513	54	16	which	which	PRON
ap-5513	54	17	is	be	AUX
ap-5513	54	18	obtained	obtain	VERB
ap-5513	54	19	by	by	ADP
ap-5513	54	20	the	the	DET
ap-5513	54	21	reduction	reduction	NOUN
ap-5513	54	22	of	of	ADP
ap-5513	54	23	euler	euler	NOUN
ap-5513	54	24	-	-	PUNCT
ap-5513	54	25	bernoulli	bernoulli	NOUN
ap-5513	54	26	equation	equation	NOUN
ap-5513	54	27	by	by	ADP
ap-5513	54	28	using	use	VERB
ap-5513	54	29	the	the	DET
ap-5513	54	30	scaling	scale	VERB
ap-5513	54	31	symmetry	symmetry	NOUN
ap-5513	54	32	.	.	PUNCT
ap-5513	55	1	conservation	conservation	NOUN
ap-5513	55	2	laws	law	NOUN
ap-5513	55	3	for	for	ADP
ap-5513	55	4	the	the	DET
ap-5513	55	5	three	three	NUM
ap-5513	55	6	beam	beam	NOUN
ap-5513	55	7	equations	equation	NOUN
ap-5513	55	8	are	be	AUX
ap-5513	55	9	derived	derive	VERB
ap-5513	55	10	in	in	ADP
ap-5513	55	11	section	section	NOUN
ap-5513	55	12	6	6	NUM
ap-5513	55	13	.	.	PUNCT
ap-5513	56	1	the	the	DET
ap-5513	56	2	conclusion	conclusion	NOUN
ap-5513	56	3	and	and	CCONJ
ap-5513	56	4	appropriate	appropriate	ADJ
ap-5513	56	5	references	reference	NOUN
ap-5513	56	6	are	be	AUX
ap-5513	56	7	mentioned	mention	VERB
ap-5513	56	8	henceforth	henceforth	ADV
ap-5513	56	9	.	.	PUNCT
ap-5513	57	1	2	2	X
ap-5513	57	2	.	.	NUM
ap-5513	57	3	lie	lie	NOUN
ap-5513	57	4	symmetry	symmetry	NOUN
ap-5513	57	5	analysis	analysis	NOUN
ap-5513	57	6	for	for	ADP
ap-5513	57	7	the	the	DET
ap-5513	57	8	convenience	convenience	NOUN
ap-5513	57	9	of	of	ADP
ap-5513	57	10	the	the	DET
ap-5513	57	11	reader	reader	NOUN
ap-5513	57	12	,	,	PUNCT
ap-5513	57	13	we	we	PRON
ap-5513	57	14	give	give	VERB
ap-5513	57	15	a	a	DET
ap-5513	57	16	briefly	briefly	NOUN
ap-5513	57	17	discussion	discussion	NOUN
ap-5513	57	18	in	in	ADP
ap-5513	57	19	the	the	DET
ap-5513	57	20	theory	theory	NOUN
ap-5513	57	21	of	of	ADP
ap-5513	57	22	lie	lie	NOUN
ap-5513	57	23	point	point	NOUN
ap-5513	57	24	symmetries	symmetry	NOUN
ap-5513	57	25	.	.	PUNCT
ap-5513	58	1	in	in	ADP
ap-5513	58	2	particular	particular	ADJ
ap-5513	58	3	,	,	PUNCT
ap-5513	58	4	we	we	PRON
ap-5513	58	5	present	present	VERB
ap-5513	58	6	the	the	DET
ap-5513	58	7	basic	basic	ADJ
ap-5513	58	8	definitions	definition	NOUN
ap-5513	58	9	and	and	CCONJ
ap-5513	58	10	main	main	ADJ
ap-5513	58	11	steps	step	NOUN
ap-5513	58	12	for	for	ADP
ap-5513	58	13	the	the	DET
ap-5513	58	14	determination	determination	NOUN
ap-5513	58	15	of	of	ADP
ap-5513	58	16	lie	lie	NOUN
ap-5513	58	17	point	point	NOUN
ap-5513	58	18	symmetries	symmetry	NOUN
ap-5513	58	19	for	for	ADP
ap-5513	58	20	a	a	DET
ap-5513	58	21	give	give	NOUN
ap-5513	58	22	differential	differential	ADJ
ap-5513	58	23	equation	equation	NOUN
ap-5513	58	24	.	.	PUNCT
ap-5513	59	1	consider	consider	VERB
ap-5513	59	2	ha	ha	INTJ
ap-5513	59	3	(	(	PUNCT
ap-5513	59	4	t	t	PROPN
ap-5513	59	5	,	,	PUNCT
ap-5513	59	6	x	x	X
ap-5513	59	7	,	,	PUNCT
ap-5513	59	8	u	u	NOUN
ap-5513	59	9	,	,	PUNCT
ap-5513	59	10	u	u	NOUN
ap-5513	59	11	,	,	PUNCT
ap-5513	59	12	i	i	NOUN
ap-5513	59	13	)	)	PUNCT
ap-5513	59	14	=	=	SYM
ap-5513	59	15	0	0	PUNCT
ap-5513	59	16	to	to	PART
ap-5513	59	17	be	be	AUX
ap-5513	59	18	a	a	DET
ap-5513	59	19	set	set	NOUN
ap-5513	59	20	of	of	ADP
ap-5513	59	21	differential	differential	ADJ
ap-5513	59	22	equations	equation	NOUN
ap-5513	59	23	and	and	CCONJ
ap-5513	59	24	u	u	NOUN
ap-5513	59	25	,	,	PUNCT
ap-5513	59	26	i	i	PRON
ap-5513	59	27	=	=	SYM
ap-5513	59	28	∂u	∂u	PROPN
ap-5513	59	29	∂yi	∂yi	PROPN
ap-5513	59	30	in	in	ADP
ap-5513	59	31	which	which	PRON
ap-5513	59	32	yi	yi	NOUN
ap-5513	59	33	=	=	SYM
ap-5513	59	34	(	(	PUNCT
ap-5513	59	35	t	t	PROPN
ap-5513	59	36	,	,	PUNCT
ap-5513	59	37	x	x	NOUN
ap-5513	59	38	)	)	PUNCT
ap-5513	59	39	.	.	PUNCT
ap-5513	60	1	then	then	ADV
ap-5513	60	2	,	,	PUNCT
ap-5513	60	3	under	under	ADP
ap-5513	60	4	the	the	DET
ap-5513	60	5	action	action	NOUN
ap-5513	60	6	of	of	ADP
ap-5513	60	7	the	the	DET
ap-5513	60	8	infinitesimal	infinitesimal	ADJ
ap-5513	60	9	one	one	NUM
ap-5513	60	10	-	-	PUNCT
ap-5513	60	11	parameter	parameter	NOUN
ap-5513	60	12	point	point	NOUN
ap-5513	60	13	transformation	transformation	NOUN
ap-5513	60	14	t′	t′	X
ap-5513	60	15	=	=	SYM
ap-5513	60	16	t	t	PROPN
ap-5513	60	17	(	(	PUNCT
ap-5513	60	18	t	t	PROPN
ap-5513	60	19	,	,	PUNCT
ap-5513	60	20	x	x	X
ap-5513	60	21	,	,	PUNCT
ap-5513	60	22	u	u	NOUN
ap-5513	60	23	;	;	PUNCT
ap-5513	60	24	ε	ε	PROPN
ap-5513	60	25	)	)	PUNCT
ap-5513	60	26	,	,	PUNCT
ap-5513	60	27	(	(	PUNCT
ap-5513	60	28	1	1	X
ap-5513	60	29	)	)	PUNCT
ap-5513	60	30	x′	x′	X
ap-5513	61	1	=	=	PUNCT
ap-5513	61	2	x	x	X
ap-5513	61	3	(	(	PUNCT
ap-5513	61	4	t	t	PROPN
ap-5513	61	5	,	,	PUNCT
ap-5513	61	6	x	x	X
ap-5513	61	7	,	,	PUNCT
ap-5513	61	8	u	u	NOUN
ap-5513	61	9	;	;	PUNCT
ap-5513	61	10	ε	ε	PROPN
ap-5513	61	11	)	)	PUNCT
ap-5513	61	12	,	,	PUNCT
ap-5513	61	13	(	(	PUNCT
ap-5513	61	14	2	2	X
ap-5513	61	15	)	)	PUNCT
ap-5513	61	16	u	u	NOUN
ap-5513	61	17	′a	′a	NOUN
ap-5513	61	18	=	=	SYM
ap-5513	61	19	ua	ua	PROPN
ap-5513	61	20	(	(	PUNCT
ap-5513	61	21	t	t	PROPN
ap-5513	61	22	,	,	PUNCT
ap-5513	61	23	x	x	X
ap-5513	61	24	,	,	PUNCT
ap-5513	61	25	u	u	NOUN
ap-5513	61	26	;	;	PUNCT
ap-5513	61	27	ε	ε	PROPN
ap-5513	61	28	)	)	PUNCT
ap-5513	61	29	,	,	PUNCT
ap-5513	61	30	(	(	PUNCT
ap-5513	61	31	3	3	X
ap-5513	61	32	)	)	PUNCT
ap-5513	61	33	in	in	ADP
ap-5513	61	34	which	which	PRON
ap-5513	61	35	ε	ε	PROPN
ap-5513	61	36	is	be	AUX
ap-5513	61	37	an	an	DET
ap-5513	61	38	infinitesimal	infinitesimal	ADJ
ap-5513	61	39	parameter	parameter	NOUN
ap-5513	61	40	,	,	PUNCT
ap-5513	61	41	the	the	DET
ap-5513	61	42	set	set	NOUN
ap-5513	61	43	of	of	ADP
ap-5513	61	44	differential	differential	ADJ
ap-5513	61	45	equations	equation	NOUN
ap-5513	61	46	ha	ha	INTJ
ap-5513	61	47	is	be	AUX
ap-5513	61	48	invariant	invariant	ADJ
ap-5513	61	49	if	if	SCONJ
ap-5513	61	50	and	and	CCONJ
ap-5513	61	51	only	only	ADV
ap-5513	61	52	if	if	SCONJ
ap-5513	61	53	,	,	PUNCT
ap-5513	61	54	ha	ha	INTJ
ap-5513	61	55	(	(	PUNCT
ap-5513	61	56	t′	t′	NUM
ap-5513	61	57	,	,	PUNCT
ap-5513	61	58	x′	x′	NUM
ap-5513	61	59	,	,	PUNCT
ap-5513	61	60	u′	u′	X
ap-5513	61	61	)	)	PUNCT
ap-5513	62	1	=	=	PUNCT
ap-5513	62	2	ha	ha	INTJ
ap-5513	62	3	(	(	PUNCT
ap-5513	62	4	t	t	PROPN
ap-5513	62	5	,	,	PUNCT
ap-5513	62	6	x	x	NOUN
ap-5513	62	7	,	,	PUNCT
ap-5513	62	8	u	u	NOUN
ap-5513	62	9	)	)	PUNCT
ap-5513	62	10	,	,	PUNCT
ap-5513	62	11	(	(	PUNCT
ap-5513	62	12	4	4	NUM
ap-5513	62	13	)	)	PUNCT
ap-5513	62	14	or	or	CCONJ
ap-5513	62	15	equivalently	equivalently	ADV
ap-5513	62	16	lim	lim	PROPN
ap-5513	62	17	ε→0	ε→0	NOUN
ap-5513	62	18	ha	ha	INTJ
ap-5513	62	19	(	(	PUNCT
ap-5513	62	20	t′	t′	NUM
ap-5513	62	21	,	,	PUNCT
ap-5513	62	22	x′	x′	NUM
ap-5513	62	23	,	,	PUNCT
ap-5513	62	24	u′	u′	PROPN
ap-5513	62	25	;	;	PUNCT
ap-5513	62	26	ε)−ha	ε)−ha	PROPN
ap-5513	62	27	(	(	PUNCT
ap-5513	62	28	t	t	PROPN
ap-5513	62	29	,	,	PUNCT
ap-5513	62	30	x	x	NOUN
ap-5513	62	31	,	,	PUNCT
ap-5513	62	32	u	u	NOUN
ap-5513	62	33	)	)	PUNCT
ap-5513	62	34	ε	ε	PROPN
ap-5513	62	35	=	=	SYM
ap-5513	62	36	0	0	PROPN
ap-5513	62	37	.	.	PUNCT
ap-5513	63	1	(	(	PUNCT
ap-5513	63	2	5	5	X
ap-5513	63	3	)	)	PUNCT
ap-5513	63	4	the	the	DET
ap-5513	63	5	latter	latter	ADJ
ap-5513	63	6	expression	expression	NOUN
ap-5513	63	7	is	be	AUX
ap-5513	63	8	the	the	DET
ap-5513	63	9	definition	definition	NOUN
ap-5513	63	10	of	of	ADP
ap-5513	63	11	the	the	DET
ap-5513	63	12	lie	lie	NOUN
ap-5513	63	13	derivative	derivative	ADJ
ap-5513	63	14	l	l	NOUN
ap-5513	63	15	of	of	ADP
ap-5513	63	16	ha	ha	INTJ
ap-5513	63	17	along	along	ADP
ap-5513	63	18	the	the	DET
ap-5513	63	19	direction	direction	NOUN
ap-5513	63	20	γ	γ	X
ap-5513	63	21	=	=	SYM
ap-5513	63	22	∂t′	∂t′	ADJ
ap-5513	63	23	∂ε	∂ε	PROPN
ap-5513	63	24	∂t	∂t	PROPN
ap-5513	63	25	+	+	CCONJ
ap-5513	63	26	∂x′	∂x′	VERB
ap-5513	63	27	∂ε	∂ε	VERB
ap-5513	63	28	∂x	∂x	NOUN
ap-5513	63	29	+	+	CCONJ
ap-5513	63	30	∂u′	∂u′	PROPN
ap-5513	63	31	∂ε	∂ε	PROPN
ap-5513	63	32	∂u	∂u	PROPN
ap-5513	63	33	.	.	PUNCT
ap-5513	64	1	(	(	PUNCT
ap-5513	64	2	6	6	NUM
ap-5513	64	3	)	)	PUNCT
ap-5513	64	4	hence	hence	ADV
ap-5513	64	5	,	,	PUNCT
ap-5513	64	6	we	we	PRON
ap-5513	64	7	shall	shall	AUX
ap-5513	64	8	say	say	VERB
ap-5513	64	9	that	that	SCONJ
ap-5513	64	10	the	the	DET
ap-5513	64	11	vector	vector	NOUN
ap-5513	64	12	field	field	NOUN
ap-5513	64	13	γ	γ	PROPN
ap-5513	64	14	will	will	AUX
ap-5513	64	15	be	be	AUX
ap-5513	64	16	a	a	DET
ap-5513	64	17	lie	lie	NOUN
ap-5513	64	18	point	point	NOUN
ap-5513	64	19	symmetry	symmetry	NOUN
ap-5513	64	20	for	for	ADP
ap-5513	64	21	the	the	DET
ap-5513	64	22	set	set	NOUN
ap-5513	64	23	of	of	ADP
ap-5513	64	24	differential	differential	ADJ
ap-5513	64	25	equations	equation	NOUN
ap-5513	64	26	ha	ha	INTJ
ap-5513	64	27	if	if	SCONJ
ap-5513	64	28	and	and	CCONJ
ap-5513	64	29	only	only	ADV
ap-5513	64	30	if	if	SCONJ
ap-5513	64	31	the	the	DET
ap-5513	64	32	following	follow	VERB
ap-5513	64	33	condition	condition	NOUN
ap-5513	64	34	is	be	AUX
ap-5513	64	35	true	true	ADJ
ap-5513	64	36	lγ	lγ	ADP
ap-5513	64	37	(	(	PUNCT
ap-5513	64	38	ha	ha	INTJ
ap-5513	64	39	)	)	PUNCT
ap-5513	65	1	=	=	SYM
ap-5513	65	2	0	0	X
ap-5513	65	3	.	.	PUNCT
ap-5513	66	1	(	(	PUNCT
ap-5513	66	2	7	7	X
ap-5513	66	3	)	)	PUNCT
ap-5513	66	4	in	in	ADP
ap-5513	66	5	other	other	ADJ
ap-5513	66	6	words	word	NOUN
ap-5513	66	7	,	,	PUNCT
ap-5513	66	8	the	the	DET
ap-5513	66	9	operator	operator	NOUN
ap-5513	66	10	γ	γ	PROPN
ap-5513	66	11	can	can	AUX
ap-5513	66	12	be	be	AUX
ap-5513	66	13	considered	consider	VERB
ap-5513	66	14	to	to	PART
ap-5513	66	15	be	be	AUX
ap-5513	66	16	symmetry	symmetry	NOUN
ap-5513	66	17	provided	provide	VERB
ap-5513	66	18	γ[n]ha	γ[n]ha	PROPN
ap-5513	66	19	=	=	SYM
ap-5513	66	20	0	0	NUM
ap-5513	66	21	,	,	PUNCT
ap-5513	66	22	99	99	NUM
ap-5513	66	23	a.	a.	NOUN
ap-5513	66	24	k.	k.	PROPN
ap-5513	66	25	halder	halder	PROPN
ap-5513	66	26	,	,	PUNCT
ap-5513	66	27	a.	a.	NOUN
ap-5513	66	28	paliathanasis	paliathanasis	NOUN
ap-5513	66	29	,	,	PUNCT
ap-5513	66	30	p.	p.	NOUN
ap-5513	66	31	g.	g.	PROPN
ap-5513	66	32	l.	l.	PROPN
ap-5513	66	33	leach	leach	PROPN
ap-5513	66	34	acta	acta	PROPN
ap-5513	66	35	polytechnica	polytechnica	PROPN
ap-5513	66	36	whenever	whenever	SCONJ
ap-5513	66	37	ha(t	ha(t	NOUN
ap-5513	66	38	,	,	PUNCT
ap-5513	66	39	x	x	NOUN
ap-5513	66	40	,	,	PUNCT
ap-5513	66	41	u	u	NOUN
ap-5513	66	42	,	,	PUNCT
ap-5513	66	43	u	u	NOUN
ap-5513	66	44	,	,	PUNCT
ap-5513	66	45	i	i	PRON
ap-5513	66	46	)	)	PUNCT
ap-5513	66	47	=	=	SYM
ap-5513	66	48	0	0	NUM
ap-5513	66	49	and	and	CCONJ
ap-5513	66	50	γ[n	γ[n	NUM
ap-5513	66	51	]	]	X
ap-5513	66	52	denotes	denote	VERB
ap-5513	66	53	the	the	DET
ap-5513	66	54	n	n	ADV
ap-5513	66	55	-	-	PUNCT
ap-5513	66	56	th	th	VERB
ap-5513	66	57	prolongation	prolongation	NOUN
ap-5513	66	58	of	of	ADP
ap-5513	66	59	the	the	DET
ap-5513	66	60	specified	specify	VERB
ap-5513	66	61	operator	operator	NOUN
ap-5513	66	62	in	in	ADP
ap-5513	66	63	its	its	PRON
ap-5513	66	64	defined	define	VERB
ap-5513	66	65	space	space	NOUN
ap-5513	66	66	.	.	PUNCT
ap-5513	67	1	the	the	DET
ap-5513	67	2	set	set	NOUN
ap-5513	67	3	of	of	ADP
ap-5513	67	4	all	all	DET
ap-5513	67	5	such	such	ADJ
ap-5513	67	6	operators	operator	NOUN
ap-5513	67	7	can	can	AUX
ap-5513	67	8	be	be	AUX
ap-5513	67	9	denoted	denote	VERB
ap-5513	67	10	by	by	ADP
ap-5513	67	11	g	g	PROPN
ap-5513	67	12	,	,	PUNCT
ap-5513	67	13	which	which	PRON
ap-5513	67	14	can	can	AUX
ap-5513	67	15	be	be	AUX
ap-5513	67	16	regarded	regard	VERB
ap-5513	67	17	as	as	ADP
ap-5513	67	18	the	the	DET
ap-5513	67	19	symmetry	symmetry	NOUN
ap-5513	67	20	group	group	NOUN
ap-5513	67	21	for	for	ADP
ap-5513	67	22	the	the	DET
ap-5513	67	23	set	set	NOUN
ap-5513	67	24	of	of	ADP
ap-5513	67	25	differential	differential	ADJ
ap-5513	67	26	equations	equation	NOUN
ap-5513	67	27	ha(t	ha(t	NOUN
ap-5513	67	28	,	,	PUNCT
ap-5513	67	29	x	x	X
ap-5513	67	30	,	,	PUNCT
ap-5513	67	31	u	u	NOUN
ap-5513	67	32	,	,	PUNCT
ap-5513	67	33	u	u	NOUN
ap-5513	67	34	,	,	PUNCT
ap-5513	67	35	i	i	PRON
ap-5513	67	36	)	)	PUNCT
ap-5513	68	1	=	=	PUNCT
ap-5513	68	2	0	0	PUNCT
ap-5513	69	1	[	[	X
ap-5513	69	2	14–16	14–16	NUM
ap-5513	69	3	]	]	SYM
ap-5513	69	4	.	.	PUNCT
ap-5513	70	1	2.1	2.1	NUM
ap-5513	70	2	.	.	PUNCT
ap-5513	71	1	the	the	DET
ap-5513	71	2	euler	euler	PROPN
ap-5513	71	3	-	-	PUNCT
ap-5513	71	4	bernoulli	bernoulli	NOUN
ap-5513	71	5	equation	equation	NOUN
ap-5513	71	6	.	.	PUNCT
ap-5513	72	1	the	the	DET
ap-5513	72	2	euler	euler	PROPN
ap-5513	72	3	-	-	PUNCT
ap-5513	72	4	bernoulli	bernoulli	PROPN
ap-5513	72	5	form	form	NOUN
ap-5513	72	6	of	of	ADP
ap-5513	72	7	the	the	DET
ap-5513	72	8	beam	beam	NOUN
ap-5513	72	9	equation	equation	NOUN
ap-5513	72	10	is	be	AUX
ap-5513	72	11	[	[	X
ap-5513	72	12	1	1	NUM
ap-5513	72	13	,	,	PUNCT
ap-5513	72	14	17	17	NUM
ap-5513	72	15	]	]	PUNCT
ap-5513	72	16	,	,	PUNCT
ap-5513	72	17	αβuxxxx	αβuxxxx	NOUN
ap-5513	72	18	+	+	CCONJ
ap-5513	72	19	utt	utt	ADJ
ap-5513	72	20	=	=	SYM
ap-5513	72	21	0	0	PROPN
ap-5513	72	22	.	.	PUNCT
ap-5513	73	1	(	(	PUNCT
ap-5513	73	2	8)	8)	NUM
ap-5513	73	3	the	the	DET
ap-5513	73	4	lie	lie	NOUN
ap-5513	73	5	point	point	NOUN
ap-5513	73	6	symmetries	symmetry	NOUN
ap-5513	73	7	are	be	AUX
ap-5513	73	8	γ1a	γ1a	PROPN
ap-5513	73	9	=	=	SYM
ap-5513	73	10	∂x	∂x	PROPN
ap-5513	73	11	,	,	PUNCT
ap-5513	73	12	γ2a	γ2a	NOUN
ap-5513	73	13	=	=	SYM
ap-5513	73	14	∂t	∂t	PROPN
ap-5513	73	15	,	,	PUNCT
ap-5513	73	16	γ3a	γ3a	VERB
ap-5513	73	17	=	=	NOUN
ap-5513	73	18	u∂u	u∂u	NOUN
ap-5513	73	19	,	,	PUNCT
ap-5513	73	20	γ4a	γ4a	PROPN
ap-5513	73	21	=	=	SYM
ap-5513	73	22	2t∂t	2t∂t	PROPN
ap-5513	74	1	+	+	CCONJ
ap-5513	74	2	x∂x	x∂x	NUM
ap-5513	74	3	,	,	PUNCT
ap-5513	74	4	γ5a	γ5a	ADP
ap-5513	74	5	=	=	SYM
ap-5513	74	6	a(t	a(t	PROPN
ap-5513	74	7	,	,	PUNCT
ap-5513	74	8	x)∂u	x)∂u	PROPN
ap-5513	74	9	,	,	PUNCT
ap-5513	74	10	where	where	SCONJ
ap-5513	74	11	a(t	a(t	NOUN
ap-5513	74	12	,	,	PUNCT
ap-5513	74	13	x	x	NOUN
ap-5513	74	14	)	)	PUNCT
ap-5513	74	15	satisfies	satisfy	VERB
ap-5513	74	16	the	the	DET
ap-5513	74	17	euler	euler	PROPN
ap-5513	74	18	-	-	PUNCT
ap-5513	74	19	bernoulli	bernoulli	PROPN
ap-5513	74	20	form	form	NOUN
ap-5513	74	21	of	of	ADP
ap-5513	74	22	the	the	DET
ap-5513	74	23	beam	beam	NOUN
ap-5513	74	24	equation	equation	NOUN
ap-5513	74	25	.	.	PUNCT
ap-5513	75	1	the	the	DET
ap-5513	75	2	lie	lie	NOUN
ap-5513	75	3	algebra	algebra	NOUN
ap-5513	75	4	is	be	AUX
ap-5513	75	5	(	(	PUNCT
ap-5513	75	6	a3,3	a3,3	ADV
ap-5513	75	7	⊕a1)⊕s∞a1	⊕a1)⊕s∞a1	PROPN
ap-5513	75	8	,	,	PUNCT
ap-5513	75	9	according	accord	VERB
ap-5513	75	10	to	to	ADP
ap-5513	75	11	the	the	DET
ap-5513	75	12	morozov	morozov	NOUN
ap-5513	75	13	-	-	PUNCT
ap-5513	75	14	mubarakzyanov	mubarakzyanov	NOUN
ap-5513	75	15	classificatin	classificatin	ADJ
ap-5513	75	16	scheme	scheme	NOUN
ap-5513	76	1	[	[	X
ap-5513	76	2	18–21	18–21	NUM
ap-5513	76	3	]	]	X
ap-5513	76	4	.	.	PUNCT
ap-5513	77	1	1	1	NUM
ap-5513	77	2	2.2	2.2	NUM
ap-5513	77	3	.	.	PUNCT
ap-5513	78	1	the	the	DET
ap-5513	78	2	rayleigh	rayleigh	PROPN
ap-5513	78	3	equation	equation	NOUN
ap-5513	78	4	.	.	PUNCT
ap-5513	79	1	the	the	DET
ap-5513	79	2	rayleigh	rayleigh	PROPN
ap-5513	79	3	form	form	NOUN
ap-5513	79	4	of	of	ADP
ap-5513	79	5	the	the	DET
ap-5513	79	6	beam	beam	NOUN
ap-5513	79	7	equation	equation	NOUN
ap-5513	79	8	is	be	AUX
ap-5513	79	9	[	[	X
ap-5513	79	10	1	1	NUM
ap-5513	79	11	,	,	PUNCT
ap-5513	79	12	17	17	NUM
ap-5513	79	13	]	]	PUNCT
ap-5513	79	14	,	,	PUNCT
ap-5513	79	15	αβuxxxx	αβuxxxx	NOUN
ap-5513	79	16	+	+	CCONJ
ap-5513	79	17	utt	utt	ADJ
ap-5513	79	18	−	−	NOUN
ap-5513	79	19	βuxxtt	βuxxtt	NOUN
ap-5513	79	20	=	=	NOUN
ap-5513	79	21	0	0	X
ap-5513	79	22	.	.	PUNCT
ap-5513	80	1	(	(	PUNCT
ap-5513	80	2	9	9	X
ap-5513	80	3	)	)	PUNCT
ap-5513	80	4	the	the	DET
ap-5513	80	5	lie	lie	NOUN
ap-5513	80	6	point	point	NOUN
ap-5513	80	7	symmetries	symmetry	NOUN
ap-5513	80	8	are	be	AUX
ap-5513	80	9	γ1b	γ1b	PROPN
ap-5513	80	10	=	=	SYM
ap-5513	80	11	∂t	∂t	PROPN
ap-5513	80	12	,	,	PUNCT
ap-5513	80	13	γ2b	γ2b	PROPN
ap-5513	80	14	=	=	SYM
ap-5513	80	15	∂x	∂x	PROPN
ap-5513	80	16	,	,	PUNCT
ap-5513	80	17	γ3b	γ3b	NOUN
ap-5513	80	18	=	=	NOUN
ap-5513	80	19	u∂u	u∂u	NOUN
ap-5513	80	20	,	,	PUNCT
ap-5513	80	21	γ4b	γ4b	NUM
ap-5513	80	22	=	=	SYM
ap-5513	80	23	b(t	b(t	PROPN
ap-5513	80	24	,	,	PUNCT
ap-5513	80	25	x)∂u	x)∂u	PROPN
ap-5513	80	26	,	,	PUNCT
ap-5513	80	27	where	where	SCONJ
ap-5513	80	28	b(t	b(t	NOUN
ap-5513	80	29	,	,	PUNCT
ap-5513	80	30	x	x	PRON
ap-5513	80	31	)	)	PUNCT
ap-5513	80	32	satisfies	satisfy	VERB
ap-5513	80	33	the	the	DET
ap-5513	80	34	rayleigh	rayleigh	PROPN
ap-5513	80	35	form	form	NOUN
ap-5513	80	36	of	of	ADP
ap-5513	80	37	the	the	DET
ap-5513	80	38	beam	beam	NOUN
ap-5513	80	39	equation	equation	NOUN
ap-5513	80	40	.	.	PUNCT
ap-5513	81	1	consequently	consequently	ADV
ap-5513	81	2	,	,	PUNCT
ap-5513	81	3	the	the	DET
ap-5513	81	4	admitted	admit	VERB
ap-5513	81	5	lie	lie	NOUN
ap-5513	81	6	algebra	algebra	NOUN
ap-5513	81	7	is	be	AUX
ap-5513	81	8	a3	a3	NOUN
ap-5513	81	9	⊕s∞a1	⊕s∞a1	NOUN
ap-5513	81	10	.	.	PUNCT
ap-5513	82	1	2.3	2.3	NUM
ap-5513	82	2	.	.	PUNCT
ap-5513	83	1	the	the	DET
ap-5513	83	2	timoshenko	timoshenko	NOUN
ap-5513	83	3	-	-	PUNCT
ap-5513	83	4	prescott	prescott	NOUN
ap-5513	83	5	equation	equation	NOUN
ap-5513	83	6	.	.	PUNCT
ap-5513	84	1	the	the	DET
ap-5513	84	2	timoshenko	timoshenko	NOUN
ap-5513	84	3	and	and	CCONJ
ap-5513	84	4	prescott	prescott	NOUN
ap-5513	84	5	form	form	NOUN
ap-5513	84	6	of	of	ADP
ap-5513	84	7	the	the	DET
ap-5513	84	8	beam	beam	NOUN
ap-5513	84	9	equation	equation	NOUN
ap-5513	84	10	is	be	AUX
ap-5513	84	11	[	[	X
ap-5513	84	12	1	1	NUM
ap-5513	84	13	,	,	PUNCT
ap-5513	84	14	24	24	NUM
ap-5513	84	15	]	]	PUNCT
ap-5513	84	16	,	,	PUNCT
ap-5513	84	17	αβuxxxx	αβuxxxx	NOUN
ap-5513	84	18	+	+	CCONJ
ap-5513	84	19	utt	utt	ADJ
ap-5513	84	20	−	−	NOUN
ap-5513	84	21	β(1	β(1	PROPN
ap-5513	84	22	+	+	NUM
ap-5513	84	23	ε)uxxtt	ε)uxxtt	NOUN
ap-5513	84	24	+	+	CCONJ
ap-5513	84	25	εβutttt	εβutttt	NOUN
ap-5513	84	26	α	α	NOUN
ap-5513	84	27	=	=	SYM
ap-5513	84	28	0	0	PROPN
ap-5513	84	29	.	.	PUNCT
ap-5513	85	1	(	(	PUNCT
ap-5513	85	2	10	10	NUM
ap-5513	85	3	)	)	PUNCT
ap-5513	85	4	the	the	DET
ap-5513	85	5	lie	lie	NOUN
ap-5513	85	6	point	point	NOUN
ap-5513	85	7	symmetries	symmetry	NOUN
ap-5513	85	8	are	be	AUX
ap-5513	85	9	γ1c	γ1c	NOUN
ap-5513	85	10	=	=	PUNCT
ap-5513	85	11	∂t	∂t	PROPN
ap-5513	85	12	,	,	PUNCT
ap-5513	85	13	γ2c	γ2c	NOUN
ap-5513	85	14	=	=	SYM
ap-5513	85	15	∂x	∂x	PROPN
ap-5513	85	16	,	,	PUNCT
ap-5513	85	17	γ3c	γ3c	PROPN
ap-5513	85	18	=	=	SYM
ap-5513	85	19	u∂u	u∂u	NOUN
ap-5513	85	20	,	,	PUNCT
ap-5513	85	21	γ4c	γ4c	PROPN
ap-5513	85	22	=	=	SYM
ap-5513	85	23	c(t	c(t	PROPN
ap-5513	85	24	,	,	PUNCT
ap-5513	85	25	x)∂u	x)∂u	PROPN
ap-5513	85	26	,	,	PUNCT
ap-5513	85	27	where	where	SCONJ
ap-5513	85	28	c(t	c(t	PROPN
ap-5513	85	29	,	,	PUNCT
ap-5513	85	30	x	x	NOUN
ap-5513	85	31	)	)	PUNCT
ap-5513	85	32	satisfies	satisfy	VERB
ap-5513	85	33	the	the	DET
ap-5513	85	34	timoshenko	timoshenko	NOUN
ap-5513	85	35	and	and	CCONJ
ap-5513	85	36	prescott	prescott	NOUN
ap-5513	85	37	form	form	NOUN
ap-5513	85	38	of	of	ADP
ap-5513	85	39	the	the	DET
ap-5513	85	40	beam	beam	NOUN
ap-5513	85	41	equation	equation	NOUN
ap-5513	85	42	.	.	PUNCT
ap-5513	86	1	hence	hence	ADV
ap-5513	86	2	,	,	PUNCT
ap-5513	86	3	the	the	DET
ap-5513	86	4	admitted	admit	VERB
ap-5513	86	5	lie	lie	NOUN
ap-5513	86	6	algebra	algebra	NOUN
ap-5513	86	7	is	be	AUX
ap-5513	86	8	a3	a3	NOUN
ap-5513	86	9	⊕s∞a1	⊕s∞a1	NOUN
ap-5513	86	10	.	.	PUNCT
ap-5513	87	1	therefore	therefore	ADV
ap-5513	87	2	,	,	PUNCT
ap-5513	87	3	we	we	PRON
ap-5513	87	4	can	can	AUX
ap-5513	87	5	say	say	VERB
ap-5513	87	6	that	that	SCONJ
ap-5513	87	7	the	the	DET
ap-5513	87	8	timoshenko	timoshenko	ADJ
ap-5513	87	9	-	-	PUNCT
ap-5513	87	10	prescott	prescott	NOUN
ap-5513	87	11	equation	equation	NOUN
ap-5513	87	12	and	and	CCONJ
ap-5513	87	13	the	the	DET
ap-5513	87	14	rayleigh	rayleigh	PROPN
ap-5513	87	15	equation	equation	NOUN
ap-5513	87	16	are	be	AUX
ap-5513	87	17	algebraic	algebraic	ADV
ap-5513	87	18	equivalent	equivalent	ADJ
ap-5513	87	19	,	,	PUNCT
ap-5513	87	20	but	but	CCONJ
ap-5513	87	21	different	different	ADJ
ap-5513	87	22	with	with	ADP
ap-5513	87	23	the	the	DET
ap-5513	87	24	euler	euler	VERB
ap-5513	87	25	-	-	PUNCT
ap-5513	87	26	bernoulli	bernoulli	NOUN
ap-5513	87	27	equation	equation	NOUN
ap-5513	87	28	as	as	SCONJ
ap-5513	87	29	it	it	PRON
ap-5513	87	30	admits	admit	VERB
ap-5513	87	31	a	a	DET
ap-5513	87	32	higher	higher	ADV
ap-5513	87	33	-	-	PUNCT
ap-5513	87	34	dimensional	dimensional	ADJ
ap-5513	87	35	lie	lie	NOUN
ap-5513	87	36	algebra	algebra	NOUN
ap-5513	87	37	.	.	PUNCT
ap-5513	88	1	we	we	PRON
ap-5513	88	2	proceed	proceed	VERB
ap-5513	88	3	our	our	PRON
ap-5513	88	4	analysis	analysis	NOUN
ap-5513	88	5	by	by	ADP
ap-5513	88	6	applying	apply	VERB
ap-5513	88	7	the	the	DET
ap-5513	88	8	lie	lie	NOUN
ap-5513	88	9	point	point	NOUN
ap-5513	88	10	symmetries	symmetry	NOUN
ap-5513	88	11	to	to	PART
ap-5513	88	12	determine	determine	VERB
ap-5513	88	13	similarity	similarity	NOUN
ap-5513	88	14	solutions	solution	NOUN
ap-5513	88	15	for	for	ADP
ap-5513	88	16	the	the	DET
ap-5513	88	17	three	three	NUM
ap-5513	88	18	equations	equation	NOUN
ap-5513	88	19	of	of	ADP
ap-5513	88	20	our	our	PRON
ap-5513	88	21	study	study	NOUN
ap-5513	88	22	.	.	PUNCT
ap-5513	89	1	1we	1we	ADJ
ap-5513	89	2	use	use	VERB
ap-5513	89	3	the	the	DET
ap-5513	89	4	sym	sym	NOUN
ap-5513	89	5	package	package	NOUN
ap-5513	89	6	developed	develop	VERB
ap-5513	89	7	by	by	ADP
ap-5513	89	8	prof.stelios	prof.stelios	PROPN
ap-5513	89	9	dimas	dima	NOUN
ap-5513	90	1	[	[	X
ap-5513	90	2	22	22	NUM
ap-5513	90	3	,	,	PUNCT
ap-5513	90	4	23	23	NUM
ap-5513	90	5	]	]	PUNCT
ap-5513	90	6	.	.	PUNCT
ap-5513	91	1	100	100	NUM
ap-5513	91	2	vol	vol	NOUN
ap-5513	91	3	.	.	PUNCT
ap-5513	92	1	60	60	NUM
ap-5513	92	2	no	no	NOUN
ap-5513	92	3	.	.	PUNCT
ap-5513	93	1	2/2020	2/2020	NUM
ap-5513	93	2	similarity	similarity	NOUN
ap-5513	93	3	solutions	solution	NOUN
ap-5513	93	4	and	and	CCONJ
ap-5513	93	5	conservation	conservation	NOUN
ap-5513	93	6	laws	law	NOUN
ap-5513	93	7	for	for	ADP
ap-5513	93	8	the	the	DET
ap-5513	93	9	beam	beam	NOUN
ap-5513	93	10	equations	equation	NOUN
ap-5513	93	11	.	.	PUNCT
ap-5513	93	12	.	.	PUNCT
ap-5513	94	1	.	.	PUNCT
ap-5513	95	1	3	3	X
ap-5513	95	2	.	.	X
ap-5513	95	3	the	the	DET
ap-5513	95	4	travelling	travel	VERB
ap-5513	95	5	-	-	PUNCT
ap-5513	95	6	wave	wave	NOUN
ap-5513	95	7	solution	solution	NOUN
ap-5513	95	8	the	the	DET
ap-5513	95	9	travelling	travel	VERB
ap-5513	95	10	-	-	PUNCT
ap-5513	95	11	wave	wave	NOUN
ap-5513	95	12	solution	solution	NOUN
ap-5513	95	13	for	for	ADP
ap-5513	95	14	eq	eq	NOUN
ap-5513	95	15	(	(	PUNCT
ap-5513	95	16	8)	8)	NUM
ap-5513	95	17	,	,	PUNCT
ap-5513	95	18	with	with	ADP
ap-5513	95	19	respect	respect	NOUN
ap-5513	95	20	to	to	ADP
ap-5513	95	21	γ2a	γ2a	PROPN
ap-5513	95	22	+	+	CCONJ
ap-5513	95	23	cγ1a	cγ1a	PROPN
ap-5513	95	24	,	,	PUNCT
ap-5513	95	25	where	where	SCONJ
ap-5513	95	26	c	c	X
ap-5513	95	27	,	,	PUNCT
ap-5513	95	28	denotes	denote	VERB
ap-5513	95	29	the	the	DET
ap-5513	95	30	frequency	frequency	NOUN
ap-5513	95	31	,	,	PUNCT
ap-5513	95	32	leads	lead	VERB
ap-5513	95	33	to	to	ADP
ap-5513	95	34	the	the	DET
ap-5513	95	35	fourth	fourth	ADJ
ap-5513	95	36	order	order	NOUN
ap-5513	95	37	equation	equation	NOUN
ap-5513	95	38	,	,	PUNCT
ap-5513	95	39	c2v′′(s	c2v′′(	VERB
ap-5513	95	40	)	)	PUNCT
ap-5513	96	1	+	+	CCONJ
ap-5513	96	2	αβv′′′′(s	αβv′′′′(s	PROPN
ap-5513	96	3	)	)	PUNCT
ap-5513	97	1	=	=	SYM
ap-5513	97	2	0	0	NUM
ap-5513	97	3	,	,	PUNCT
ap-5513	97	4	(	(	PUNCT
ap-5513	97	5	11	11	NUM
ap-5513	97	6	)	)	PUNCT
ap-5513	97	7	where	where	SCONJ
ap-5513	97	8	s	s	VERB
ap-5513	97	9	=	=	SYM
ap-5513	97	10	x−	x−	PROPN
ap-5513	97	11	ct	ct	PROPN
ap-5513	97	12	,	,	PUNCT
ap-5513	97	13	v(s	v(s	PROPN
ap-5513	97	14	)	)	PUNCT
ap-5513	97	15	=	=	SYM
ap-5513	97	16	u(x	u(x	PROPN
ap-5513	97	17	,	,	PUNCT
ap-5513	97	18	t	t	PROPN
ap-5513	97	19	)	)	PUNCT
ap-5513	97	20	.	.	PUNCT
ap-5513	98	1	the	the	DET
ap-5513	98	2	lie	lie	NOUN
ap-5513	98	3	point	point	NOUN
ap-5513	98	4	symmetries	symmetry	NOUN
ap-5513	98	5	of	of	ADP
ap-5513	98	6	equation	equation	NOUN
ap-5513	98	7	(	(	PUNCT
ap-5513	98	8	11	11	NUM
ap-5513	98	9	)	)	PUNCT
ap-5513	98	10	are	be	AUX
ap-5513	98	11	γ1d	γ1d	NOUN
ap-5513	98	12	=	=	SYM
ap-5513	98	13	∂s	∂s	PROPN
ap-5513	98	14	,	,	PUNCT
ap-5513	98	15	γ2d	γ2d	PROPN
ap-5513	98	16	=	=	SYM
ap-5513	98	17	∂v	∂v	PROPN
ap-5513	98	18	,	,	PUNCT
ap-5513	98	19	γ3d	γ3d	NOUN
ap-5513	98	20	=	=	SYM
ap-5513	98	21	s∂v	s∂v	ADJ
ap-5513	98	22	,	,	PUNCT
ap-5513	98	23	γ4d	γ4d	PROPN
ap-5513	98	24	=	=	SYM
ap-5513	98	25	v∂v	v∂v	NOUN
ap-5513	98	26	,	,	PUNCT
ap-5513	98	27	γ5d	γ5d	NOUN
ap-5513	98	28	=	=	PUNCT
ap-5513	98	29	sin	sin	NOUN
ap-5513	98	30	cs√	cs√	NOUN
ap-5513	98	31	αβ	αβ	INTJ
ap-5513	98	32	∂v	∂v	PROPN
ap-5513	98	33	,	,	PUNCT
ap-5513	98	34	γ6d	γ6d	PROPN
ap-5513	98	35	=	=	SYM
ap-5513	98	36	cos	cos	PROPN
ap-5513	98	37	cs√	cs√	PROPN
ap-5513	99	1	αβ	αβ	INTJ
ap-5513	99	2	∂v	∂v	PROPN
ap-5513	99	3	.	.	PUNCT
ap-5513	100	1	the	the	DET
ap-5513	100	2	reduced	reduce	VERB
ap-5513	100	3	form	form	NOUN
ap-5513	100	4	has	have	VERB
ap-5513	100	5	six	six	NUM
ap-5513	100	6	symmetries	symmetry	NOUN
ap-5513	100	7	and	and	CCONJ
ap-5513	100	8	hence	hence	ADV
ap-5513	100	9	linearisable	linearisable	ADJ
ap-5513	100	10	,	,	PUNCT
ap-5513	100	11	the	the	DET
ap-5513	100	12	solution	solution	NOUN
ap-5513	100	13	for	for	ADP
ap-5513	100	14	the	the	DET
ap-5513	100	15	fourth	fourth	ADJ
ap-5513	100	16	-	-	PUNCT
ap-5513	100	17	order	order	NOUN
ap-5513	100	18	equation	equation	NOUN
ap-5513	100	19	can	can	AUX
ap-5513	100	20	be	be	AUX
ap-5513	100	21	given	give	VERB
ap-5513	100	22	as	as	ADP
ap-5513	100	23	,	,	PUNCT
ap-5513	100	24	v(s	v(s	PROPN
ap-5513	100	25	)	)	PUNCT
ap-5513	101	1	=	=	SYM
ap-5513	101	2	c0	c0	PROPN
ap-5513	101	3	+	+	CCONJ
ap-5513	101	4	c1s+	c1s+	PROPN
ap-5513	101	5	c2	c2	PROPN
ap-5513	101	6	sin	sin	NOUN
ap-5513	101	7	cs√	cs√	PUNCT
ap-5513	102	1	αβ	αβ	INTJ
ap-5513	103	1	+	+	CCONJ
ap-5513	103	2	c3	c3	PROPN
ap-5513	103	3	cos	cos	PROPN
ap-5513	103	4	cs√	cs√	PROPN
ap-5513	104	1	αβ	αβ	INTJ
ap-5513	104	2	,	,	PUNCT
ap-5513	104	3	where	where	SCONJ
ap-5513	104	4	ci	ci	NOUN
ap-5513	104	5	,	,	PUNCT
ap-5513	104	6	i	i	NOUN
ap-5513	104	7	=	=	NOUN
ap-5513	104	8	0	0	NUM
ap-5513	104	9	,	,	PUNCT
ap-5513	104	10	1	1	NUM
ap-5513	104	11	,	,	PUNCT
ap-5513	104	12	2	2	NUM
ap-5513	104	13	,	,	PUNCT
ap-5513	104	14	3	3	NUM
ap-5513	104	15	are	be	AUX
ap-5513	104	16	arbitrary	arbitrary	ADJ
ap-5513	104	17	constants	constant	NOUN
ap-5513	104	18	.	.	PUNCT
ap-5513	105	1	corresponding	correspond	VERB
ap-5513	105	2	,	,	PUNCT
ap-5513	105	3	to	to	PART
ap-5513	105	4	which	which	PRON
ap-5513	105	5	the	the	DET
ap-5513	105	6	solution	solution	NOUN
ap-5513	105	7	for	for	ADP
ap-5513	105	8	euler	euler	NOUN
ap-5513	105	9	-	-	PUNCT
ap-5513	105	10	bernoulli	bernoulli	PROPN
ap-5513	105	11	form	form	NOUN
ap-5513	105	12	of	of	ADP
ap-5513	105	13	beam	beam	NOUN
ap-5513	105	14	can	can	AUX
ap-5513	105	15	be	be	AUX
ap-5513	105	16	given	give	VERB
ap-5513	105	17	as	as	ADP
ap-5513	105	18	u(x	u(x	NOUN
ap-5513	105	19	,	,	PUNCT
ap-5513	105	20	t	t	NOUN
ap-5513	105	21	)	)	PUNCT
ap-5513	106	1	=	=	SYM
ap-5513	106	2	c0	c0	NOUN
ap-5513	106	3	+	+	CCONJ
ap-5513	106	4	c1(x−	c1(x−	NOUN
ap-5513	106	5	ct	ct	NOUN
ap-5513	106	6	)	)	PUNCT
ap-5513	107	1	+	+	CCONJ
ap-5513	107	2	c2	c2	PROPN
ap-5513	107	3	sin	sin	NOUN
ap-5513	107	4	c(x−	c(x−	PROPN
ap-5513	107	5	ct)√	ct)√	PROPN
ap-5513	107	6	αβ	αβ	INTJ
ap-5513	107	7	+	+	CCONJ
ap-5513	107	8	c3	c3	PROPN
ap-5513	107	9	cos	cos	PROPN
ap-5513	107	10	c(x−	c(x−	PROPN
ap-5513	107	11	ct)√	ct)√	PROPN
ap-5513	107	12	αβ	αβ	INTJ
ap-5513	107	13	.	.	PUNCT
ap-5513	108	1	3.1	3.1	NUM
ap-5513	108	2	.	.	PUNCT
ap-5513	109	1	further	further	ADJ
ap-5513	109	2	reduction	reduction	NOUN
ap-5513	109	3	of	of	ADP
ap-5513	109	4	the	the	DET
ap-5513	109	5	euler	euler	NOUN
ap-5513	109	6	-	-	PUNCT
ap-5513	109	7	bernoulli	bernoulli	NOUN
ap-5513	109	8	equation	equation	NOUN
ap-5513	109	9	.	.	PUNCT
ap-5513	110	1	the	the	DET
ap-5513	110	2	reduction	reduction	NOUN
ap-5513	110	3	with	with	ADP
ap-5513	110	4	respect	respect	NOUN
ap-5513	110	5	to	to	ADP
ap-5513	110	6	γ3a	γ3a	ADJ
ap-5513	110	7	and	and	CCONJ
ap-5513	110	8	γ4a	γ4a	NOUN
ap-5513	110	9	,	,	PUNCT
ap-5513	110	10	leads	lead	VERB
ap-5513	110	11	to	to	ADP
ap-5513	110	12	fourth	fourth	ADJ
ap-5513	110	13	-	-	PUNCT
ap-5513	110	14	order	order	NOUN
ap-5513	110	15	odes	ode	NOUN
ap-5513	110	16	.	.	PUNCT
ap-5513	111	1	for	for	ADP
ap-5513	111	2	the	the	DET
ap-5513	111	3	similarity	similarity	NOUN
ap-5513	111	4	variables	variable	NOUN
ap-5513	111	5	with	with	ADP
ap-5513	111	6	respect	respect	NOUN
ap-5513	111	7	to	to	ADP
ap-5513	111	8	2γ3a+γ4a	2γ3a+γ4a	NOUN
ap-5513	111	9	,	,	PUNCT
ap-5513	111	10	s	s	PART
ap-5513	111	11	=	=	SYM
ap-5513	111	12	t	t	X
ap-5513	111	13	x2	x2	PROPN
ap-5513	111	14	,	,	PUNCT
ap-5513	111	15	u(t	u(t	NOUN
ap-5513	111	16	,	,	PUNCT
ap-5513	111	17	x	x	NOUN
ap-5513	111	18	)	)	PUNCT
ap-5513	111	19	=	=	SYM
ap-5513	111	20	tv(s	tv(s	NUM
ap-5513	111	21	)	)	PUNCT
ap-5513	111	22	,	,	PUNCT
ap-5513	111	23	the	the	DET
ap-5513	111	24	reduced	reduce	VERB
ap-5513	111	25	ode	ode	NOUN
ap-5513	111	26	is	be	AUX
ap-5513	111	27	(	(	PUNCT
ap-5513	111	28	2	2	NUM
ap-5513	111	29	αβ	αβ	NOUN
ap-5513	111	30	+	+	NOUN
ap-5513	111	31	120s2	120s2	NUM
ap-5513	111	32	)	)	PUNCT
ap-5513	111	33	v′	v′	NOUN
ap-5513	112	1	+	+	CCONJ
ap-5513	112	2	(	(	PUNCT
ap-5513	112	3	s+	s+	X
ap-5513	112	4	300s3	300s3	NUM
ap-5513	112	5	)	)	PUNCT
ap-5513	112	6	v′′	v′′	NOUN
ap-5513	112	7	+	+	CCONJ
ap-5513	112	8	144s4v′′′	144s4v′′′	NUM
ap-5513	112	9	+	+	CCONJ
ap-5513	112	10	16s5v′′′′	16s5v′′′′	NUM
ap-5513	112	11	=	=	SYM
ap-5513	112	12	0	0	X
ap-5513	112	13	.	.	PUNCT
ap-5513	113	1	the	the	DET
ap-5513	113	2	latter	latter	ADJ
ap-5513	113	3	equation	equation	NOUN
ap-5513	113	4	is	be	AUX
ap-5513	113	5	solvable	solvable	ADJ
ap-5513	113	6	.	.	PUNCT
ap-5513	114	1	we	we	PRON
ap-5513	114	2	continue	continue	VERB
ap-5513	114	3	by	by	ADP
ap-5513	114	4	considering	consider	VERB
ap-5513	114	5	the	the	DET
ap-5513	114	6	similarity	similarity	NOUN
ap-5513	114	7	variable	variable	ADJ
ap-5513	114	8	u(t	u(t	NOUN
ap-5513	114	9	,	,	PUNCT
ap-5513	114	10	x	x	NOUN
ap-5513	114	11	)	)	PUNCT
ap-5513	114	12	=	=	SYM
ap-5513	114	13	xv(s	xv(s	NUM
ap-5513	114	14	)	)	PUNCT
ap-5513	114	15	,	,	PUNCT
ap-5513	114	16	with	with	SCONJ
ap-5513	114	17	respect	respect	NOUN
ap-5513	114	18	to	to	ADP
ap-5513	114	19	γ3a+γ4a	γ3a+γ4a	PROPN
ap-5513	114	20	for	for	ADP
ap-5513	114	21	s	s	VERB
ap-5513	114	22	being	be	AUX
ap-5513	114	23	same	same	ADJ
ap-5513	114	24	as	as	ADP
ap-5513	114	25	above	above	ADJ
ap-5513	114	26	leads	lead	VERB
ap-5513	114	27	to	to	ADP
ap-5513	114	28	the	the	DET
ap-5513	114	29	fourth	fourth	ADJ
ap-5513	114	30	-	-	PUNCT
ap-5513	114	31	order	order	NOUN
ap-5513	114	32	ode	ode	ADJ
ap-5513	114	33	,	,	PUNCT
ap-5513	114	34	24sv′	24sv′	NUM
ap-5513	114	35	+	+	CCONJ
ap-5513	114	36	(	(	PUNCT
ap-5513	114	37	1	1	NUM
ap-5513	114	38	αβ	αβ	NOUN
ap-5513	114	39	+	+	CCONJ
ap-5513	114	40	156s2	156s2	NUM
ap-5513	114	41	)	)	PUNCT
ap-5513	114	42	v′′	v′′	NOUN
ap-5513	114	43	+	+	CCONJ
ap-5513	115	1	16s3	16s3	NUM
ap-5513	115	2	(	(	PUNCT
ap-5513	115	3	7v′′′	7v′′′	NUM
ap-5513	115	4	+	+	CCONJ
ap-5513	115	5	sv′′′′	sv′′′′	NOUN
ap-5513	115	6	)	)	PUNCT
ap-5513	116	1	=	=	SYM
ap-5513	116	2	0	0	X
ap-5513	116	3	.	.	PUNCT
ap-5513	117	1	(	(	PUNCT
ap-5513	117	2	12	12	NUM
ap-5513	117	3	)	)	PUNCT
ap-5513	117	4	the	the	DET
ap-5513	117	5	equation	equation	NOUN
ap-5513	117	6	has	have	VERB
ap-5513	117	7	a	a	DET
ap-5513	117	8	total	total	NOUN
ap-5513	117	9	of	of	ADP
ap-5513	117	10	five	five	NUM
ap-5513	117	11	lie	lie	NOUN
ap-5513	117	12	point	point	NOUN
ap-5513	117	13	symmetries	symmetry	NOUN
ap-5513	117	14	with	with	ADP
ap-5513	117	15	∂v	∂v	PROPN
ap-5513	117	16	,	,	PUNCT
ap-5513	117	17	v∂v	v∂v	NOUN
ap-5513	117	18	are	be	AUX
ap-5513	117	19	the	the	DET
ap-5513	117	20	two	two	NUM
ap-5513	117	21	simpler	simple	ADJ
ap-5513	117	22	symmetries	symmetry	NOUN
ap-5513	117	23	,	,	PUNCT
ap-5513	117	24	the	the	DET
ap-5513	117	25	other	other	ADJ
ap-5513	117	26	three	three	NUM
ap-5513	117	27	are	be	AUX
ap-5513	117	28	in	in	ADP
ap-5513	117	29	terms	term	NOUN
ap-5513	117	30	of	of	ADP
ap-5513	117	31	hypergeometric	hypergeometric	ADJ
ap-5513	117	32	functions	function	NOUN
ap-5513	117	33	,	,	PUNCT
ap-5513	117	34	which	which	PRON
ap-5513	117	35	is	be	AUX
ap-5513	117	36	complicated	complicate	VERB
ap-5513	117	37	enough	enough	ADV
ap-5513	117	38	to	to	PART
ap-5513	117	39	be	be	AUX
ap-5513	117	40	mentioned	mention	VERB
ap-5513	117	41	here	here	ADV
ap-5513	117	42	.	.	PUNCT
ap-5513	118	1	we	we	PRON
ap-5513	118	2	apply	apply	VERB
ap-5513	118	3	∂v	∂v	PROPN
ap-5513	118	4	to	to	PART
ap-5513	118	5	perform	perform	VERB
ap-5513	118	6	the	the	DET
ap-5513	118	7	reduction	reduction	NOUN
ap-5513	118	8	.	.	PUNCT
ap-5513	119	1	the	the	DET
ap-5513	119	2	new	new	ADJ
ap-5513	119	3	invariant	invariant	ADJ
ap-5513	119	4	functions	function	NOUN
ap-5513	119	5	are	be	AUX
ap-5513	119	6	s	s	NOUN
ap-5513	119	7	=	=	ADJ
ap-5513	119	8	h	h	NOUN
ap-5513	119	9	and	and	CCONJ
ap-5513	119	10	g(h	g(h	NUM
ap-5513	119	11	)	)	PUNCT
ap-5513	120	1	=	=	SYM
ap-5513	120	2	v′(s	v′(s	PROPN
ap-5513	120	3	)	)	PUNCT
ap-5513	120	4	,	,	PUNCT
ap-5513	120	5	hence	hence	ADV
ap-5513	120	6	,	,	PUNCT
ap-5513	120	7	the	the	DET
ap-5513	120	8	reduced	reduce	VERB
ap-5513	120	9	equation	equation	NOUN
ap-5513	120	10	is	be	AUX
ap-5513	120	11	a	a	DET
ap-5513	120	12	third	third	ADJ
ap-5513	120	13	-	-	PUNCT
ap-5513	120	14	order	order	NOUN
ap-5513	120	15	ode	ode	ADJ
ap-5513	120	16	,	,	PUNCT
ap-5513	120	17	g′′′(h	g′′′(h	PROPN
ap-5513	120	18	)	)	PUNCT
ap-5513	120	19	=	=	SYM
ap-5513	120	20	−7g′′(h	−7g′′(h	ADJ
ap-5513	120	21	)	)	PUNCT
ap-5513	120	22	h	h	NOUN
ap-5513	121	1	−	−	PROPN
ap-5513	122	1	(	(	PUNCT
ap-5513	122	2	39	39	NUM
ap-5513	122	3	4h2	4h2	NUM
ap-5513	123	1	+	+	CCONJ
ap-5513	123	2	1	1	NUM
ap-5513	123	3	16h4αβ	16h4αβ	NUM
ap-5513	123	4	)	)	PUNCT
ap-5513	123	5	g′(h)−	g′(h)−	NOUN
ap-5513	123	6	3g(h	3g(h	NUM
ap-5513	123	7	)	)	PUNCT
ap-5513	123	8	2h3	2h3	NUM
ap-5513	123	9	.	.	PUNCT
ap-5513	124	1	(	(	PUNCT
ap-5513	124	2	13	13	NUM
ap-5513	124	3	)	)	PUNCT
ap-5513	124	4	101	101	NUM
ap-5513	124	5	a.	a.	NOUN
ap-5513	124	6	k.	k.	PROPN
ap-5513	124	7	halder	halder	PROPN
ap-5513	124	8	,	,	PUNCT
ap-5513	124	9	a.	a.	NOUN
ap-5513	124	10	paliathanasis	paliathanasis	NOUN
ap-5513	124	11	,	,	PUNCT
ap-5513	124	12	p.	p.	NOUN
ap-5513	124	13	g.	g.	PROPN
ap-5513	124	14	l.	l.	PROPN
ap-5513	124	15	leach	leach	PROPN
ap-5513	124	16	acta	acta	PROPN
ap-5513	124	17	polytechnica	polytechnica	PROPN
ap-5513	124	18	the	the	DET
ap-5513	124	19	latter	latter	ADJ
ap-5513	124	20	equation	equation	NOUN
ap-5513	124	21	admits	admit	VERB
ap-5513	124	22	four	four	NUM
ap-5513	124	23	lie	lie	NOUN
ap-5513	124	24	point	point	NOUN
ap-5513	124	25	symmetries	symmetry	NOUN
ap-5513	124	26	.	.	PUNCT
ap-5513	125	1	the	the	PRON
ap-5513	125	2	simpler	simple	ADJ
ap-5513	125	3	one	one	NUM
ap-5513	125	4	being	be	AUX
ap-5513	125	5	g∂g	g∂g	NOUN
ap-5513	125	6	,	,	PUNCT
ap-5513	125	7	the	the	DET
ap-5513	125	8	other	other	ADJ
ap-5513	125	9	three	three	NUM
ap-5513	125	10	are	be	AUX
ap-5513	125	11	hyperbolic	hyperbolic	ADJ
ap-5513	125	12	functions	function	NOUN
ap-5513	125	13	of	of	ADP
ap-5513	125	14	sin	sin	NOUN
ap-5513	125	15	h	h	NOUN
ap-5513	125	16	,	,	PUNCT
ap-5513	125	17	cosh	cosh	NOUN
ap-5513	125	18	and	and	CCONJ
ap-5513	125	19	hypergeometric	hypergeometric	ADJ
ap-5513	125	20	function	function	NOUN
ap-5513	125	21	respectively	respectively	ADV
ap-5513	125	22	.	.	PUNCT
ap-5513	126	1	we	we	PRON
ap-5513	126	2	consider	consider	VERB
ap-5513	126	3	g∂g	g∂g	NOUN
ap-5513	126	4	,	,	PUNCT
ap-5513	126	5	to	to	PART
ap-5513	126	6	do	do	VERB
ap-5513	126	7	the	the	DET
ap-5513	126	8	reduction	reduction	NOUN
ap-5513	126	9	.	.	PUNCT
ap-5513	127	1	the	the	DET
ap-5513	127	2	subsequent	subsequent	ADJ
ap-5513	127	3	second	second	ADJ
ap-5513	127	4	-	-	PUNCT
ap-5513	127	5	order	order	NOUN
ap-5513	127	6	equation	equation	NOUN
ap-5513	127	7	is	be	AUX
ap-5513	127	8	,	,	PUNCT
ap-5513	127	9	m′′(n	m′′(n	ADJ
ap-5513	127	10	)	)	PUNCT
ap-5513	127	11	=	=	SYM
ap-5513	127	12	(	(	PUNCT
ap-5513	127	13	−3m(n)−	−3m(n)−	PROPN
ap-5513	127	14	7	7	NUM
ap-5513	127	15	n	n	NOUN
ap-5513	127	16	)	)	PUNCT
ap-5513	127	17	m′(n)−m(n)3	m′(n)−m(n)3	PROPN
ap-5513	127	18	−	−	PROPN
ap-5513	127	19	7m(n)2	7m(n)2	PROPN
ap-5513	127	20	n	n	NUM
ap-5513	127	21	−	−	PROPN
ap-5513	127	22	(	(	PUNCT
ap-5513	127	23	39	39	NUM
ap-5513	127	24	4n2	4n2	NUM
ap-5513	128	1	+	+	CCONJ
ap-5513	128	2	1	1	NUM
ap-5513	128	3	16n4αβ	16n4αβ	NUM
ap-5513	128	4	)	)	PUNCT
ap-5513	129	1	m(n)−	m(n)−	NOUN
ap-5513	129	2	3	3	NUM
ap-5513	129	3	2n3	2n3	NUM
ap-5513	129	4	,	,	PUNCT
ap-5513	129	5	(	(	PUNCT
ap-5513	129	6	14	14	NUM
ap-5513	129	7	)	)	PUNCT
ap-5513	129	8	where	where	SCONJ
ap-5513	129	9	n	n	NOUN
ap-5513	129	10	=	=	SYM
ap-5513	129	11	h	h	NOUN
ap-5513	129	12	and	and	CCONJ
ap-5513	129	13	m(n	m(n	PROPN
ap-5513	129	14	)	)	PUNCT
ap-5513	129	15	=	=	PUNCT
ap-5513	130	1	g′(h	g′(h	X
ap-5513	130	2	)	)	PUNCT
ap-5513	130	3	g(h	g(h	NUM
ap-5513	130	4	)	)	PUNCT
ap-5513	130	5	.	.	PUNCT
ap-5513	131	1	this	this	PRON
ap-5513	131	2	is	be	AUX
ap-5513	131	3	the	the	DET
ap-5513	131	4	perturbed	perturb	VERB
ap-5513	131	5	form	form	NOUN
ap-5513	131	6	of	of	ADP
ap-5513	131	7	painlevé	painlevé	NOUN
ap-5513	131	8	-	-	PUNCT
ap-5513	131	9	ince	ince	NOUN
ap-5513	131	10	equation	equation	NOUN
ap-5513	131	11	and	and	CCONJ
ap-5513	131	12	the	the	DET
ap-5513	131	13	singularity	singularity	NOUN
ap-5513	131	14	analysis	analysis	NOUN
ap-5513	131	15	of	of	ADP
ap-5513	131	16	this	this	DET
ap-5513	131	17	equation	equation	NOUN
ap-5513	131	18	shows	show	VERB
ap-5513	131	19	that	that	SCONJ
ap-5513	131	20	it	it	PRON
ap-5513	131	21	is	be	AUX
ap-5513	131	22	integrable	integrable	ADJ
ap-5513	131	23	.	.	PUNCT
ap-5513	132	1	in	in	ADP
ap-5513	132	2	our	our	PRON
ap-5513	132	3	subsequent	subsequent	ADJ
ap-5513	132	4	paper	paper	NOUN
ap-5513	132	5	,	,	PUNCT
ap-5513	132	6	we	we	PRON
ap-5513	132	7	look	look	VERB
ap-5513	132	8	at	at	ADP
ap-5513	132	9	the	the	DET
ap-5513	132	10	analysis	analysis	NOUN
ap-5513	132	11	and	and	CCONJ
ap-5513	132	12	discuss	discuss	VERB
ap-5513	132	13	it	it	PRON
ap-5513	132	14	elaborately	elaborately	ADV
ap-5513	132	15	.	.	PUNCT
ap-5513	133	1	the	the	DET
ap-5513	133	2	reduction	reduction	NOUN
ap-5513	133	3	of	of	ADP
ap-5513	133	4	(	(	PUNCT
ap-5513	133	5	12	12	NUM
ap-5513	133	6	)	)	PUNCT
ap-5513	133	7	with	with	ADP
ap-5513	133	8	respect	respect	NOUN
ap-5513	133	9	to	to	ADP
ap-5513	133	10	v∂v	v∂v	NOUN
ap-5513	133	11	,	,	PUNCT
ap-5513	133	12	leads	lead	VERB
ap-5513	133	13	to	to	ADP
ap-5513	133	14	a	a	DET
ap-5513	133	15	third	third	ADJ
ap-5513	133	16	-	-	PUNCT
ap-5513	133	17	order	order	NOUN
ap-5513	133	18	equation	equation	NOUN
ap-5513	133	19	with	with	ADP
ap-5513	133	20	zero	zero	NUM
ap-5513	133	21	symmetries	symmetry	NOUN
ap-5513	133	22	,	,	PUNCT
ap-5513	133	23	g′′′(h	g′′′(h	PROPN
ap-5513	133	24	)	)	PUNCT
ap-5513	133	25	=	=	PUNCT
ap-5513	134	1	(	(	PUNCT
ap-5513	134	2	−4g(h)−	−4g(h)−	NUM
ap-5513	134	3	7	7	NUM
ap-5513	134	4	h	h	NOUN
ap-5513	134	5	)	)	PUNCT
ap-5513	134	6	g′′(h)−	g′′(h)−	NOUN
ap-5513	134	7	3g′2	3g′2	NUM
ap-5513	135	1	−	−	PROPN
ap-5513	135	2	(	(	PUNCT
ap-5513	135	3	6g(h)2	6g(h)2	NOUN
ap-5513	135	4	+	+	CCONJ
ap-5513	135	5	21g(h	21g(h	NUM
ap-5513	135	6	)	)	PUNCT
ap-5513	135	7	h	h	NOUN
ap-5513	136	1	+	+	CCONJ
ap-5513	136	2	39	39	NUM
ap-5513	136	3	4h2	4h2	NUM
ap-5513	136	4	+	+	CCONJ
ap-5513	136	5	1	1	NUM
ap-5513	136	6	16h4αβ	16h4αβ	NUM
ap-5513	136	7	)	)	PUNCT
ap-5513	136	8	g′(h	g′(h	PUNCT
ap-5513	136	9	)	)	PUNCT
ap-5513	136	10	−g(h)4	−g(h)4	NOUN
ap-5513	136	11	−	−	PROPN
ap-5513	136	12	7g(h)3	7g(h)3	NUM
ap-5513	136	13	h	h	NOUN
ap-5513	137	1	−	−	PROPN
ap-5513	138	1	(	(	PUNCT
ap-5513	138	2	39	39	NUM
ap-5513	138	3	4h2	4h2	NUM
ap-5513	139	1	+	+	CCONJ
ap-5513	139	2	1	1	NUM
ap-5513	139	3	16h4αβ	16h4αβ	NUM
ap-5513	139	4	)	)	PUNCT
ap-5513	140	1	g(h)2	g(h)2	PROPN
ap-5513	140	2	−	−	PROPN
ap-5513	140	3	3g(h	3g(h	NUM
ap-5513	140	4	)	)	PUNCT
ap-5513	140	5	2h3	2h3	NUM
ap-5513	140	6	,	,	PUNCT
ap-5513	140	7	(	(	PUNCT
ap-5513	140	8	15	15	NUM
ap-5513	140	9	)	)	PUNCT
ap-5513	140	10	where	where	SCONJ
ap-5513	140	11	h	h	NOUN
ap-5513	140	12	=	=	SYM
ap-5513	140	13	s	s	X
ap-5513	140	14	and	and	CCONJ
ap-5513	140	15	g(h	g(h	NUM
ap-5513	140	16	)	)	PUNCT
ap-5513	141	1	=	=	SYM
ap-5513	141	2	v′(s	v′(s	X
ap-5513	141	3	)	)	PUNCT
ap-5513	141	4	v(s	v(s	PROPN
ap-5513	141	5	)	)	PUNCT
ap-5513	141	6	.	.	PUNCT
ap-5513	142	1	this	this	DET
ap-5513	142	2	equation	equation	NOUN
ap-5513	142	3	is	be	AUX
ap-5513	142	4	integrable	integrable	ADJ
ap-5513	142	5	as	as	SCONJ
ap-5513	142	6	ascertained	ascertain	VERB
ap-5513	142	7	by	by	ADP
ap-5513	142	8	the	the	DET
ap-5513	142	9	singularity	singularity	NOUN
ap-5513	142	10	analysis	analysis	NOUN
ap-5513	142	11	,	,	PUNCT
ap-5513	142	12	the	the	DET
ap-5513	142	13	calculations	calculation	NOUN
ap-5513	142	14	of	of	ADP
ap-5513	142	15	which	which	PRON
ap-5513	142	16	are	be	AUX
ap-5513	142	17	mentioned	mention	VERB
ap-5513	142	18	in	in	ADP
ap-5513	142	19	a	a	DET
ap-5513	142	20	following	follow	VERB
ap-5513	142	21	section	section	NOUN
ap-5513	142	22	.	.	PUNCT
ap-5513	143	1	3.2	3.2	NUM
ap-5513	143	2	.	.	PUNCT
ap-5513	144	1	the	the	DET
ap-5513	144	2	travelling	travel	VERB
ap-5513	144	3	wave	wave	NOUN
ap-5513	144	4	solution	solution	NOUN
ap-5513	144	5	for	for	ADP
ap-5513	144	6	the	the	DET
ap-5513	144	7	rayleigh	rayleigh	PROPN
ap-5513	144	8	equation	equation	NOUN
ap-5513	144	9	.	.	PUNCT
ap-5513	145	1	the	the	DET
ap-5513	145	2	reduction	reduction	NOUN
ap-5513	145	3	using	use	VERB
ap-5513	145	4	γ1b	γ1b	NOUN
ap-5513	145	5	+	+	PUNCT
ap-5513	145	6	cγ2b	cγ2b	NOUN
ap-5513	145	7	leads	lead	VERB
ap-5513	145	8	to	to	ADP
ap-5513	145	9	the	the	DET
ap-5513	145	10	fourth	fourth	ADJ
ap-5513	145	11	-	-	PUNCT
ap-5513	145	12	order	order	NOUN
ap-5513	145	13	equation	equation	NOUN
ap-5513	145	14	which	which	PRON
ap-5513	145	15	is	be	AUX
ap-5513	145	16	maximally	maximally	ADV
ap-5513	145	17	symmetric	symmetric	ADJ
ap-5513	145	18	,	,	PUNCT
ap-5513	145	19	where	where	SCONJ
ap-5513	145	20	c	c	PROPN
ap-5513	145	21	is	be	AUX
ap-5513	145	22	the	the	DET
ap-5513	145	23	frequency	frequency	NOUN
ap-5513	145	24	.	.	PUNCT
ap-5513	146	1	the	the	DET
ap-5513	146	2	definition	definition	NOUN
ap-5513	146	3	of	of	ADP
ap-5513	146	4	similarity	similarity	NOUN
ap-5513	146	5	variables	variable	NOUN
ap-5513	146	6	s	s	PART
ap-5513	146	7	and	and	CCONJ
ap-5513	146	8	v(s	v(s	NUM
ap-5513	146	9	)	)	PUNCT
ap-5513	146	10	is	be	AUX
ap-5513	146	11	similar	similar	ADJ
ap-5513	146	12	to	to	ADP
ap-5513	146	13	that	that	PRON
ap-5513	146	14	of	of	ADP
ap-5513	146	15	the	the	DET
ap-5513	146	16	previous	previous	ADJ
ap-5513	146	17	case	case	NOUN
ap-5513	146	18	.	.	PUNCT
ap-5513	147	1	(	(	PUNCT
ap-5513	147	2	1−	1−	NUM
ap-5513	147	3	βc2	βc2	NOUN
ap-5513	147	4	)	)	PUNCT
ap-5513	147	5	v′′′′(s	v′′′′(s	PROPN
ap-5513	147	6	)	)	PUNCT
ap-5513	147	7	+	+	CCONJ
ap-5513	147	8	c2v′′(s	c2v′′(	VERB
ap-5513	147	9	)	)	PUNCT
ap-5513	147	10	=	=	SYM
ap-5513	147	11	0	0	NUM
ap-5513	147	12	,	,	PUNCT
ap-5513	147	13	(	(	PUNCT
ap-5513	147	14	16	16	NUM
ap-5513	147	15	)	)	PUNCT
ap-5513	147	16	which	which	PRON
ap-5513	147	17	is	be	AUX
ap-5513	147	18	in	in	ADP
ap-5513	147	19	the	the	DET
ap-5513	147	20	form	form	NOUN
ap-5513	147	21	of	of	ADP
ap-5513	147	22	equation	equation	NOUN
ap-5513	147	23	(	(	PUNCT
ap-5513	147	24	11	11	NUM
ap-5513	147	25	)	)	PUNCT
ap-5513	147	26	.	.	PUNCT
ap-5513	148	1	3.3	3.3	NUM
ap-5513	148	2	.	.	PUNCT
ap-5513	149	1	the	the	DET
ap-5513	149	2	travelling	travel	VERB
ap-5513	149	3	-	-	PUNCT
ap-5513	149	4	wave	wave	NOUN
ap-5513	149	5	solution	solution	NOUN
ap-5513	149	6	for	for	ADP
ap-5513	149	7	the	the	DET
ap-5513	149	8	timoshenko	timoshenko	ADJ
ap-5513	149	9	-	-	PUNCT
ap-5513	149	10	prescott	prescott	NOUN
ap-5513	149	11	equation	equation	NOUN
ap-5513	149	12	.	.	PUNCT
ap-5513	150	1	in	in	ADP
ap-5513	150	2	a	a	DET
ap-5513	150	3	similar	similar	ADJ
ap-5513	150	4	way	way	NOUN
ap-5513	150	5	,	,	PUNCT
ap-5513	150	6	the	the	DET
ap-5513	150	7	application	application	NOUN
ap-5513	150	8	of	of	ADP
ap-5513	150	9	the	the	DET
ap-5513	150	10	generic	generic	ADJ
ap-5513	150	11	symmetry	symmetry	NOUN
ap-5513	150	12	vector	vector	NOUN
ap-5513	150	13	,	,	PUNCT
ap-5513	150	14	γ1c	γ1c	PROPN
ap-5513	151	1	+	+	NUM
ap-5513	151	2	cγ2c	cγ2c	PROPN
ap-5513	151	3	,	,	PUNCT
ap-5513	151	4	in	in	ADP
ap-5513	151	5	(	(	PUNCT
ap-5513	151	6	10	10	NUM
ap-5513	151	7	)	)	PUNCT
ap-5513	151	8	provides	provide	VERB
ap-5513	151	9	the	the	DET
ap-5513	151	10	fourth	fourth	ADJ
ap-5513	151	11	-	-	PUNCT
ap-5513	151	12	order	order	NOUN
ap-5513	151	13	ode	ode	NOUN
ap-5513	151	14	,	,	PUNCT
ap-5513	151	15	(	(	PUNCT
ap-5513	151	16	α2β	α2β	PROPN
ap-5513	151	17	−	−	PROPN
ap-5513	151	18	βc2a−	βc2a−	VERB
ap-5513	151	19	αβc2ε+	αβc2ε+	NOUN
ap-5513	151	20	c4εβ	c4εβ	X
ap-5513	151	21	)	)	PUNCT
ap-5513	152	1	v′′′′(s	v′′′′(s	ADP
ap-5513	152	2	)	)	PUNCT
ap-5513	152	3	+	+	NUM
ap-5513	152	4	ac2v′′	ac2v′′	NUM
ap-5513	152	5	(	(	PUNCT
ap-5513	152	6	s	s	X
ap-5513	152	7	)	)	PUNCT
ap-5513	152	8	=	=	SYM
ap-5513	152	9	0	0	NUM
ap-5513	152	10	,	,	PUNCT
ap-5513	152	11	(	(	PUNCT
ap-5513	152	12	17	17	NUM
ap-5513	152	13	)	)	PUNCT
ap-5513	152	14	which	which	PRON
ap-5513	152	15	is	be	AUX
ap-5513	152	16	again	again	ADV
ap-5513	152	17	in	in	ADP
ap-5513	152	18	the	the	DET
ap-5513	152	19	form	form	NOUN
ap-5513	152	20	of	of	ADP
ap-5513	152	21	(	(	PUNCT
ap-5513	152	22	11	11	NUM
ap-5513	152	23	)	)	PUNCT
ap-5513	152	24	.	.	PUNCT
ap-5513	153	1	consequently	consequently	ADV
ap-5513	153	2	,	,	PUNCT
ap-5513	153	3	we	we	PRON
ap-5513	153	4	conclude	conclude	VERB
ap-5513	153	5	that	that	SCONJ
ap-5513	153	6	the	the	DET
ap-5513	153	7	three	three	NUM
ap-5513	153	8	different	different	ADJ
ap-5513	153	9	beam	beam	NOUN
ap-5513	153	10	equations	equation	NOUN
ap-5513	153	11	provide	provide	VERB
ap-5513	153	12	the	the	DET
ap-5513	153	13	same	same	ADJ
ap-5513	153	14	travel	travel	NOUN
ap-5513	153	15	-	-	PUNCT
ap-5513	153	16	wave	wave	NOUN
ap-5513	153	17	solutions	solution	NOUN
ap-5513	153	18	.	.	PUNCT
ap-5513	154	1	we	we	PRON
ap-5513	154	2	continue	continue	VERB
ap-5513	154	3	our	our	PRON
ap-5513	154	4	analysis	analysis	NOUN
ap-5513	154	5	by	by	ADP
ap-5513	154	6	assuming	assume	VERB
ap-5513	154	7	the	the	DET
ap-5513	154	8	existence	existence	NOUN
ap-5513	154	9	of	of	ADP
ap-5513	154	10	a	a	DET
ap-5513	154	11	source	source	NOUN
ap-5513	154	12	term	term	NOUN
ap-5513	154	13	f	f	PROPN
ap-5513	154	14	(	(	PUNCT
ap-5513	154	15	u	u	NOUN
ap-5513	154	16	)	)	PUNCT
ap-5513	154	17	in	in	ADP
ap-5513	154	18	the	the	DET
ap-5513	154	19	beam	beam	NOUN
ap-5513	154	20	equations	equation	NOUN
ap-5513	154	21	.	.	PUNCT
ap-5513	155	1	4	4	X
ap-5513	155	2	.	.	X
ap-5513	155	3	symmetry	symmetry	NOUN
ap-5513	155	4	analysis	analysis	NOUN
ap-5513	155	5	with	with	ADP
ap-5513	155	6	a	a	DET
ap-5513	155	7	source	source	NOUN
ap-5513	155	8	term	term	NOUN
ap-5513	155	9	in	in	ADP
ap-5513	155	10	this	this	DET
ap-5513	155	11	section	section	NOUN
ap-5513	155	12	,	,	PUNCT
ap-5513	155	13	we	we	PRON
ap-5513	155	14	study	study	VERB
ap-5513	155	15	the	the	DET
ap-5513	155	16	impact	impact	NOUN
ap-5513	155	17	of	of	ADP
ap-5513	155	18	the	the	DET
ap-5513	155	19	forcing	force	VERB
ap-5513	155	20	-	-	PUNCT
ap-5513	155	21	source	source	NOUN
ap-5513	155	22	term	term	NOUN
ap-5513	155	23	f(u	f(u	PROPN
ap-5513	155	24	)	)	PUNCT
ap-5513	155	25	in	in	ADP
ap-5513	155	26	the	the	DET
ap-5513	155	27	rhs	rhs	PROPN
ap-5513	155	28	of	of	ADP
ap-5513	155	29	the	the	DET
ap-5513	155	30	euler	euler	PROPN
ap-5513	155	31	-	-	PUNCT
ap-5513	155	32	bernoulli	bernoulli	PROPN
ap-5513	155	33	,	,	PUNCT
ap-5513	155	34	rayleigh	rayleigh	PROPN
ap-5513	155	35	and	and	CCONJ
ap-5513	155	36	timoshenko	timoshenko	NOUN
ap-5513	155	37	-	-	PUNCT
ap-5513	155	38	prescott	prescott	NOUN
ap-5513	155	39	beam	beam	NOUN
ap-5513	155	40	equations	equation	NOUN
ap-5513	155	41	.	.	PUNCT
ap-5513	156	1	4.1	4.1	NUM
ap-5513	156	2	.	.	X
ap-5513	156	3	euler	euler	NOUN
ap-5513	156	4	-	-	PUNCT
ap-5513	156	5	bernoulli	bernoulli	PROPN
ap-5513	156	6	.	.	PUNCT
ap-5513	157	1	the	the	DET
ap-5513	157	2	lie	lie	NOUN
ap-5513	157	3	symmetry	symmetry	NOUN
ap-5513	157	4	analysis	analysis	NOUN
ap-5513	157	5	for	for	ADP
ap-5513	157	6	the	the	DET
ap-5513	157	7	euler	euler	PROPN
ap-5513	157	8	-	-	PUNCT
ap-5513	157	9	bernoulli	bernoulli	NOUN
ap-5513	157	10	equation	equation	NOUN
ap-5513	157	11	(	(	PUNCT
ap-5513	157	12	8)	8)	NUM
ap-5513	157	13	with	with	ADP
ap-5513	157	14	the	the	DET
ap-5513	157	15	forced	force	VERB
ap-5513	157	16	term	term	NOUN
ap-5513	157	17	f(u	f(u	PROPN
ap-5513	157	18	)	)	PUNCT
ap-5513	157	19	,	,	PUNCT
ap-5513	157	20	leads	lead	VERB
ap-5513	157	21	to	to	ADP
ap-5513	157	22	the	the	DET
ap-5513	157	23	following	follow	VERB
ap-5513	157	24	possible	possible	ADJ
ap-5513	157	25	cases	case	NOUN
ap-5513	157	26	for	for	ADP
ap-5513	157	27	the	the	DET
ap-5513	157	28	forcing	force	VERB
ap-5513	157	29	term	term	NOUN
ap-5513	157	30	f1	f1	NOUN
ap-5513	157	31	(	(	PUNCT
ap-5513	157	32	u	u	NOUN
ap-5513	157	33	)	)	PUNCT
ap-5513	157	34	=	=	PUNCT
ap-5513	157	35	au+	au+	PROPN
ap-5513	157	36	b	b	PROPN
ap-5513	157	37	,	,	PUNCT
ap-5513	157	38	(	(	PUNCT
ap-5513	157	39	18	18	NUM
ap-5513	157	40	)	)	PUNCT
ap-5513	157	41	f2	f2	PROPN
ap-5513	157	42	(	(	PUNCT
ap-5513	157	43	u	u	NOUN
ap-5513	157	44	)	)	PUNCT
ap-5513	157	45	=	=	SYM
ap-5513	157	46	(	(	PUNCT
ap-5513	157	47	au+	au+	PROPN
ap-5513	157	48	b)n	b)n	NOUN
ap-5513	157	49	,	,	PUNCT
ap-5513	157	50	(	(	PUNCT
ap-5513	157	51	19	19	NUM
ap-5513	157	52	)	)	PUNCT
ap-5513	157	53	f3	f3	PROPN
ap-5513	157	54	(	(	PUNCT
ap-5513	157	55	u	u	NOUN
ap-5513	157	56	)	)	PUNCT
ap-5513	157	57	=	=	SYM
ap-5513	158	1	eau+b	eau+b	PROPN
ap-5513	158	2	,	,	PUNCT
ap-5513	158	3	(	(	PUNCT
ap-5513	158	4	20	20	NUM
ap-5513	158	5	)	)	PUNCT
ap-5513	158	6	f4	f4	PROPN
ap-5513	158	7	(	(	PUNCT
ap-5513	158	8	u	u	NOUN
ap-5513	158	9	)	)	PUNCT
ap-5513	158	10	=	=	SYM
ap-5513	158	11	arbitrary	arbitrary	ADJ
ap-5513	158	12	.	.	PUNCT
ap-5513	159	1	(	(	PUNCT
ap-5513	159	2	21	21	NUM
ap-5513	159	3	)	)	PUNCT
ap-5513	159	4	for	for	ADP
ap-5513	159	5	f1(u	f1(u	NOUN
ap-5513	159	6	)	)	PUNCT
ap-5513	159	7	,	,	PUNCT
ap-5513	159	8	the	the	DET
ap-5513	159	9	admitted	admit	VERB
ap-5513	159	10	lie	lie	NOUN
ap-5513	159	11	point	point	NOUN
ap-5513	159	12	symmetries	symmetry	NOUN
ap-5513	159	13	for	for	ADP
ap-5513	159	14	the	the	DET
ap-5513	159	15	euler	euler	PROPN
ap-5513	159	16	-	-	PUNCT
ap-5513	159	17	bernoulli	bernoulli	PROPN
ap-5513	159	18	equation	equation	NOUN
ap-5513	159	19	are	be	AUX
ap-5513	159	20	,	,	PUNCT
ap-5513	159	21	γf1	γf1	ADP
ap-5513	159	22	1	1	NUM
ap-5513	159	23	=	=	SYM
ap-5513	159	24	∂t	∂t	PROPN
ap-5513	159	25	,	,	PUNCT
ap-5513	159	26	γf1	γf1	ADP
ap-5513	159	27	2	2	NUM
ap-5513	159	28	=	=	SYM
ap-5513	159	29	∂x	∂x	PROPN
ap-5513	159	30	,	,	PUNCT
ap-5513	159	31	γf1	γf1	ADP
ap-5513	159	32	3	3	NUM
ap-5513	159	33	=	=	SYM
ap-5513	159	34	u∂u	u∂u	NOUN
ap-5513	159	35	,	,	PUNCT
ap-5513	159	36	γf1	γf1	ADP
ap-5513	159	37	∞	∞	PROPN
ap-5513	160	1	=	=	SYM
ap-5513	160	2	b	b	PROPN
ap-5513	160	3	(	(	PUNCT
ap-5513	160	4	t	t	PROPN
ap-5513	160	5	,	,	PUNCT
ap-5513	160	6	x	x	NOUN
ap-5513	160	7	)	)	PUNCT
ap-5513	160	8	∂u	∂u	PROPN
ap-5513	160	9	,	,	PUNCT
ap-5513	160	10	102	102	NUM
ap-5513	160	11	vol	vol	NOUN
ap-5513	160	12	.	.	PUNCT
ap-5513	161	1	60	60	NUM
ap-5513	162	1	no	no	NOUN
ap-5513	162	2	.	.	PUNCT
ap-5513	163	1	2/2020	2/2020	NUM
ap-5513	163	2	similarity	similarity	NOUN
ap-5513	163	3	solutions	solution	NOUN
ap-5513	163	4	and	and	CCONJ
ap-5513	163	5	conservation	conservation	NOUN
ap-5513	163	6	laws	law	NOUN
ap-5513	163	7	for	for	ADP
ap-5513	163	8	the	the	DET
ap-5513	163	9	beam	beam	NOUN
ap-5513	163	10	equations	equation	NOUN
ap-5513	163	11	.	.	PUNCT
ap-5513	163	12	.	.	PUNCT
ap-5513	163	13	.	.	PUNCT
ap-5513	164	1	where	where	SCONJ
ap-5513	164	2	they	they	PRON
ap-5513	164	3	form	form	VERB
ap-5513	164	4	the	the	DET
ap-5513	164	5	3a1	3a1	NUM
ap-5513	164	6	lie	lie	NOUN
ap-5513	164	7	algebra	algebra	NOUN
ap-5513	164	8	and	and	CCONJ
ap-5513	164	9	b	b	PROPN
ap-5513	164	10	(	(	PUNCT
ap-5513	164	11	t	t	PROPN
ap-5513	164	12	,	,	PUNCT
ap-5513	164	13	x	x	X
ap-5513	164	14	)	)	PUNCT
ap-5513	164	15	is	be	AUX
ap-5513	164	16	a	a	DET
ap-5513	164	17	solution	solution	NOUN
ap-5513	164	18	of	of	ADP
ap-5513	164	19	the	the	DET
ap-5513	164	20	original	original	ADJ
ap-5513	164	21	equation	equation	NOUN
ap-5513	164	22	.	.	PUNCT
ap-5513	165	1	for	for	ADP
ap-5513	165	2	the	the	DET
ap-5513	165	3	source	source	NOUN
ap-5513	165	4	f2	f2	PROPN
ap-5513	165	5	(	(	PUNCT
ap-5513	165	6	u	u	NOUN
ap-5513	165	7	)	)	PUNCT
ap-5513	165	8	,	,	PUNCT
ap-5513	165	9	the	the	DET
ap-5513	165	10	admitted	admit	VERB
ap-5513	165	11	lie	lie	NOUN
ap-5513	165	12	point	point	NOUN
ap-5513	165	13	symmetries	symmetry	NOUN
ap-5513	165	14	are	be	AUX
ap-5513	165	15	,	,	PUNCT
ap-5513	165	16	γf2	γf2	INTJ
ap-5513	165	17	1	1	X
ap-5513	165	18	=	=	SYM
ap-5513	165	19	∂t	∂t	PROPN
ap-5513	165	20	,	,	PUNCT
ap-5513	165	21	γf2	γf2	PROPN
ap-5513	165	22	2	2	X
ap-5513	165	23	=	=	SYM
ap-5513	165	24	∂x	∂x	PROPN
ap-5513	165	25	,	,	PUNCT
ap-5513	165	26	γf2	γf2	INTJ
ap-5513	165	27	3	3	NUM
ap-5513	165	28	=	=	SYM
ap-5513	165	29	2	2	NUM
ap-5513	165	30	(	(	PUNCT
ap-5513	165	31	n−	n−	NOUN
ap-5513	165	32	1	1	NUM
ap-5513	165	33	)	)	PUNCT
ap-5513	165	34	t∂t	t∂t	NOUN
ap-5513	166	1	+	+	CCONJ
ap-5513	166	2	(	(	PUNCT
ap-5513	166	3	n−	n−	NOUN
ap-5513	166	4	1)x∂x	1)x∂x	NUM
ap-5513	166	5	−	−	NOUN
ap-5513	166	6	4	4	NUM
ap-5513	166	7	(	(	PUNCT
ap-5513	166	8	u+	u+	NUM
ap-5513	166	9	b	b	PROPN
ap-5513	166	10	a	a	PRON
ap-5513	166	11	)	)	PUNCT
ap-5513	166	12	∂u	∂u	PROPN
ap-5513	166	13	,	,	PUNCT
ap-5513	166	14	which	which	PRON
ap-5513	166	15	they	they	PRON
ap-5513	166	16	form	form	VERB
ap-5513	166	17	the	the	DET
ap-5513	166	18	2a1	2a1	NUM
ap-5513	166	19	⊕s	⊕s	NOUN
ap-5513	166	20	a1	a1	NOUN
ap-5513	166	21	lie	lie	NOUN
ap-5513	166	22	algebra	algebra	NOUN
ap-5513	166	23	.	.	PUNCT
ap-5513	167	1	for	for	ADP
ap-5513	167	2	f3	f3	PROPN
ap-5513	167	3	(	(	PUNCT
ap-5513	167	4	u	u	NOUN
ap-5513	167	5	)	)	PUNCT
ap-5513	167	6	the	the	DET
ap-5513	167	7	admitted	admit	VERB
ap-5513	167	8	lie	lie	NOUN
ap-5513	167	9	point	point	NOUN
ap-5513	167	10	symmetries	symmetry	NOUN
ap-5513	167	11	are	be	AUX
ap-5513	167	12	,	,	PUNCT
ap-5513	167	13	γf3	γf3	PROPN
ap-5513	167	14	1	1	NUM
ap-5513	167	15	=	=	SYM
ap-5513	167	16	∂t	∂t	PROPN
ap-5513	167	17	,	,	PUNCT
ap-5513	167	18	γf3	γf3	PROPN
ap-5513	167	19	2	2	NUM
ap-5513	167	20	=	=	SYM
ap-5513	167	21	∂x	∂x	PROPN
ap-5513	167	22	,	,	PUNCT
ap-5513	167	23	γf3	γf3	PROPN
ap-5513	167	24	3	3	NUM
ap-5513	167	25	=	=	SYM
ap-5513	167	26	2t∂t	2t∂t	PROPN
ap-5513	168	1	+	+	CCONJ
ap-5513	168	2	x∂x	x∂x	NUM
ap-5513	168	3	−	−	VERB
ap-5513	168	4	4	4	NUM
ap-5513	168	5	a	a	DET
ap-5513	168	6	∂u	∂u	PROPN
ap-5513	168	7	,	,	PUNCT
ap-5513	168	8	where	where	SCONJ
ap-5513	168	9	the	the	DET
ap-5513	168	10	corresponding	correspond	VERB
ap-5513	168	11	lie	lie	NOUN
ap-5513	168	12	algebra	algebra	NOUN
ap-5513	168	13	is	be	AUX
ap-5513	168	14	the	the	DET
ap-5513	168	15	2a1	2a1	NUM
ap-5513	168	16	⊕s	⊕s	NOUN
ap-5513	168	17	a1	a1	NOUN
ap-5513	168	18	.	.	PUNCT
ap-5513	169	1	finally	finally	ADV
ap-5513	169	2	,	,	PUNCT
ap-5513	169	3	for	for	ADP
ap-5513	169	4	the	the	DET
ap-5513	169	5	arbitrary	arbitrary	ADJ
ap-5513	169	6	functional	functional	ADJ
ap-5513	169	7	form	form	NOUN
ap-5513	169	8	of	of	ADP
ap-5513	169	9	f	f	PROPN
ap-5513	169	10	(	(	PUNCT
ap-5513	169	11	u	u	NOUN
ap-5513	169	12	)	)	PUNCT
ap-5513	169	13	,	,	PUNCT
ap-5513	169	14	the	the	DET
ap-5513	169	15	admitted	admit	VERB
ap-5513	169	16	lie	lie	NOUN
ap-5513	169	17	point	point	NOUN
ap-5513	169	18	symmetries	symmetry	NOUN
ap-5513	169	19	are	be	AUX
ap-5513	169	20	the	the	DET
ap-5513	169	21	only	only	ADJ
ap-5513	169	22	two	two	NUM
ap-5513	169	23	symmetry	symmetry	NOUN
ap-5513	169	24	vectors	vector	NOUN
ap-5513	169	25	,	,	PUNCT
ap-5513	169	26	γf4	γf4	NOUN
ap-5513	169	27	1	1	NUM
ap-5513	169	28	=	=	SYM
ap-5513	169	29	∂t	∂t	PROPN
ap-5513	169	30	,	,	PUNCT
ap-5513	169	31	γf4	γf4	NOUN
ap-5513	169	32	2	2	NUM
ap-5513	169	33	=	=	SYM
ap-5513	169	34	∂x	∂x	PROPN
ap-5513	169	35	,	,	PUNCT
ap-5513	169	36	which	which	PRON
ap-5513	169	37	form	form	VERB
ap-5513	169	38	the	the	DET
ap-5513	169	39	2a1	2a1	NUM
ap-5513	169	40	lie	lie	NOUN
ap-5513	169	41	algebra	algebra	NOUN
ap-5513	169	42	and	and	CCONJ
ap-5513	169	43	provide	provide	VERB
ap-5513	169	44	the	the	DET
ap-5513	169	45	travelling	travel	VERB
ap-5513	169	46	-	-	PUNCT
ap-5513	169	47	wave	wave	NOUN
ap-5513	169	48	solution	solution	NOUN
ap-5513	169	49	.	.	PUNCT
ap-5513	170	1	4.2	4.2	NUM
ap-5513	170	2	.	.	PUNCT
ap-5513	171	1	rayleigh	rayleigh	PROPN
ap-5513	171	2	and	and	CCONJ
ap-5513	171	3	timoshenko	timoshenko	NOUN
ap-5513	171	4	-	-	PUNCT
ap-5513	171	5	prescott	prescott	NOUN
ap-5513	171	6	equations	equation	NOUN
ap-5513	171	7	.	.	PUNCT
ap-5513	172	1	for	for	ADP
ap-5513	172	2	the	the	DET
ap-5513	172	3	other	other	ADJ
ap-5513	172	4	two	two	NUM
ap-5513	172	5	beam	beam	NOUN
ap-5513	172	6	equations	equation	NOUN
ap-5513	172	7	,	,	PUNCT
ap-5513	172	8	namely	namely	ADV
ap-5513	172	9	the	the	DET
ap-5513	172	10	rayleigh	rayleigh	PROPN
ap-5513	172	11	and	and	CCONJ
ap-5513	172	12	timoshenko	timoshenko	NOUN
ap-5513	172	13	-	-	PUNCT
ap-5513	172	14	prescott	prescott	NOUN
ap-5513	172	15	equations	equation	NOUN
ap-5513	172	16	with	with	ADP
ap-5513	172	17	a	a	DET
ap-5513	172	18	source	source	NOUN
ap-5513	172	19	term	term	NOUN
ap-5513	172	20	,	,	PUNCT
ap-5513	172	21	we	we	PRON
ap-5513	172	22	find	find	VERB
ap-5513	172	23	that	that	SCONJ
ap-5513	172	24	,	,	PUNCT
ap-5513	172	25	for	for	ADP
ap-5513	172	26	a	a	DET
ap-5513	172	27	linear	linear	ADJ
ap-5513	172	28	function	function	NOUN
ap-5513	172	29	f	f	PROPN
ap-5513	172	30	=	=	PROPN
ap-5513	172	31	f1	f1	PROPN
ap-5513	172	32	(	(	PUNCT
ap-5513	172	33	u	u	NOUN
ap-5513	172	34	)	)	PUNCT
ap-5513	172	35	,	,	PUNCT
ap-5513	172	36	the	the	DET
ap-5513	172	37	two	two	NUM
ap-5513	172	38	equations	equation	NOUN
ap-5513	172	39	admit	admit	VERB
ap-5513	172	40	the	the	DET
ap-5513	172	41	same	same	ADJ
ap-5513	172	42	lie	lie	NOUN
ap-5513	172	43	point	point	NOUN
ap-5513	172	44	symmetries	symmetry	NOUN
ap-5513	172	45	with	with	ADP
ap-5513	172	46	the	the	DET
ap-5513	172	47	force	force	NOUN
ap-5513	172	48	-	-	PUNCT
ap-5513	172	49	free	free	ADJ
ap-5513	172	50	case	case	NOUN
ap-5513	172	51	,	,	PUNCT
ap-5513	172	52	while	while	SCONJ
ap-5513	172	53	for	for	ADP
ap-5513	172	54	arbitrary	arbitrary	ADJ
ap-5513	172	55	function	function	NOUN
ap-5513	172	56	f	f	PROPN
ap-5513	172	57	(	(	PUNCT
ap-5513	172	58	u	u	NOUN
ap-5513	172	59	)	)	PUNCT
ap-5513	172	60	=	=	SYM
ap-5513	172	61	f4	f4	X
ap-5513	172	62	(	(	PUNCT
ap-5513	172	63	u	u	NOUN
ap-5513	172	64	)	)	PUNCT
ap-5513	172	65	,	,	PUNCT
ap-5513	172	66	admit	admit	VERB
ap-5513	172	67	only	only	ADV
ap-5513	172	68	two	two	NUM
ap-5513	172	69	lie	lie	NOUN
ap-5513	172	70	point	point	NOUN
ap-5513	172	71	symmetries	symmetry	NOUN
ap-5513	172	72	,	,	PUNCT
ap-5513	172	73	the	the	DET
ap-5513	172	74	vector	vector	NOUN
ap-5513	172	75	fields	field	NOUN
ap-5513	172	76	γf4	γf4	NOUN
ap-5513	172	77	1	1	NUM
ap-5513	172	78	,	,	PUNCT
ap-5513	172	79	γf4	γf4	NOUN
ap-5513	172	80	2	2	NUM
ap-5513	172	81	which	which	PRON
ap-5513	172	82	provide	provide	VERB
ap-5513	172	83	travelling	travelling	ADJ
ap-5513	172	84	-	-	PUNCT
ap-5513	172	85	wave	wave	NOUN
ap-5513	172	86	solutions	solution	NOUN
ap-5513	172	87	.	.	PUNCT
ap-5513	173	1	4.3	4.3	NUM
ap-5513	173	2	.	.	PUNCT
ap-5513	173	3	symmetry	symmetry	NOUN
ap-5513	173	4	classification	classification	NOUN
ap-5513	173	5	of	of	ADP
ap-5513	173	6	ode	ode	PROPN
ap-5513	173	7	.	.	PUNCT
ap-5513	174	1	we	we	PRON
ap-5513	174	2	show	show	VERB
ap-5513	174	3	the	the	DET
ap-5513	174	4	reduction	reduction	NOUN
ap-5513	174	5	with	with	ADP
ap-5513	174	6	the	the	DET
ap-5513	174	7	lie	lie	NOUN
ap-5513	174	8	point	point	NOUN
ap-5513	174	9	symmetries	symmetry	NOUN
ap-5513	174	10	,	,	PUNCT
ap-5513	174	11	γf4	γf4	NOUN
ap-5513	174	12	1	1	NUM
ap-5513	174	13	+	+	NUM
ap-5513	174	14	cγf4	cγf4	NOUN
ap-5513	174	15	2	2	NUM
ap-5513	174	16	,	,	PUNCT
ap-5513	174	17	because	because	SCONJ
ap-5513	174	18	the	the	DET
ap-5513	174	19	three	three	NUM
ap-5513	174	20	beam	beam	NOUN
ap-5513	174	21	equations	equation	NOUN
ap-5513	174	22	of	of	ADP
ap-5513	174	23	our	our	PRON
ap-5513	174	24	consideration	consideration	NOUN
ap-5513	174	25	provide	provide	VERB
ap-5513	174	26	the	the	DET
ap-5513	174	27	same	same	ADJ
ap-5513	174	28	fourth	fourth	ADJ
ap-5513	174	29	-	-	PUNCT
ap-5513	174	30	order	order	NOUN
ap-5513	174	31	ode	ode	NOUN
ap-5513	174	32	,	,	PUNCT
ap-5513	174	33	which	which	PRON
ap-5513	174	34	now	now	ADV
ap-5513	174	35	,	,	PUNCT
ap-5513	174	36	with	with	ADP
ap-5513	174	37	a	a	DET
ap-5513	174	38	source	source	NOUN
ap-5513	174	39	term	term	NOUN
ap-5513	174	40	,	,	PUNCT
ap-5513	174	41	takes	take	VERB
ap-5513	174	42	the	the	DET
ap-5513	174	43	following	follow	VERB
ap-5513	174	44	form	form	NOUN
ap-5513	174	45	,	,	PUNCT
ap-5513	174	46	v′′′′	v′′′′	PROPN
ap-5513	174	47	+	+	NUM
ap-5513	174	48	c2v′′	c2v′′	NOUN
ap-5513	174	49	=	=	SYM
ap-5513	174	50	f	f	X
ap-5513	174	51	(	(	PUNCT
ap-5513	174	52	v	v	NOUN
ap-5513	174	53	)	)	PUNCT
ap-5513	174	54	,	,	PUNCT
ap-5513	174	55	(	(	PUNCT
ap-5513	174	56	22	22	X
ap-5513	174	57	)	)	PUNCT
ap-5513	174	58	we	we	PRON
ap-5513	174	59	perform	perform	VERB
ap-5513	174	60	the	the	DET
ap-5513	174	61	symmetry	symmetry	NOUN
ap-5513	174	62	classification	classification	NOUN
ap-5513	174	63	of	of	ADP
ap-5513	174	64	the	the	DET
ap-5513	174	65	latter	latter	ADJ
ap-5513	174	66	differential	differential	NOUN
ap-5513	174	67	equation	equation	NOUN
ap-5513	174	68	and	and	CCONJ
ap-5513	174	69	we	we	PRON
ap-5513	174	70	find	find	VERB
ap-5513	174	71	that	that	SCONJ
ap-5513	174	72	,	,	PUNCT
ap-5513	174	73	for	for	ADP
ap-5513	174	74	the	the	DET
ap-5513	174	75	arbitrary	arbitrary	ADJ
ap-5513	174	76	function	function	NOUN
ap-5513	174	77	f	f	PROPN
ap-5513	174	78	(	(	PUNCT
ap-5513	174	79	v	v	NOUN
ap-5513	174	80	)	)	PUNCT
ap-5513	174	81	,	,	PUNCT
ap-5513	174	82	the	the	DET
ap-5513	174	83	latter	latter	ADJ
ap-5513	174	84	equation	equation	NOUN
ap-5513	174	85	admits	admit	VERB
ap-5513	174	86	only	only	ADV
ap-5513	174	87	the	the	DET
ap-5513	174	88	autonomous	autonomous	ADJ
ap-5513	174	89	symmetry	symmetry	NOUN
ap-5513	174	90	vector	vector	NOUN
ap-5513	174	91	∂v	∂v	PROPN
ap-5513	174	92	.	.	PUNCT
ap-5513	175	1	however	however	ADV
ap-5513	175	2	,	,	PUNCT
ap-5513	175	3	for	for	ADP
ap-5513	175	4	a	a	DET
ap-5513	175	5	constant	constant	ADJ
ap-5513	175	6	source	source	NOUN
ap-5513	175	7	f	f	PROPN
ap-5513	175	8	(	(	PUNCT
ap-5513	175	9	v	v	NOUN
ap-5513	175	10	)	)	PUNCT
ap-5513	175	11	=	=	SYM
ap-5513	175	12	a0	a0	PROPN
ap-5513	175	13	,	,	PUNCT
ap-5513	175	14	the	the	DET
ap-5513	175	15	lie	lie	NOUN
ap-5513	175	16	point	point	NOUN
ap-5513	175	17	symmetries	symmetry	NOUN
ap-5513	175	18	are	be	AUX
ap-5513	175	19	,	,	PUNCT
ap-5513	175	20	∂s	∂s	PROPN
ap-5513	175	21	,	,	PUNCT
ap-5513	175	22	∂v	∂v	PROPN
ap-5513	175	23	,	,	PUNCT
ap-5513	175	24	s∂v	s∂v	ADJ
ap-5513	175	25	,	,	PUNCT
ap-5513	175	26	(	(	PUNCT
ap-5513	175	27	2c2v	2c2v	NOUN
ap-5513	175	28	−	−	PROPN
ap-5513	175	29	a0s	a0s	PROPN
ap-5513	175	30	2	2	NUM
ap-5513	175	31	)	)	PUNCT
ap-5513	175	32	∂v	∂v	PROPN
ap-5513	175	33	,	,	PUNCT
ap-5513	175	34	cos	cos	PROPN
ap-5513	175	35	(	(	PUNCT
ap-5513	175	36	cs	cs	PROPN
ap-5513	175	37	)	)	PUNCT
ap-5513	175	38	∂v	∂v	PROPN
ap-5513	175	39	,	,	PUNCT
ap-5513	175	40	sin	sin	NOUN
ap-5513	175	41	(	(	PUNCT
ap-5513	175	42	cs	cs	PROPN
ap-5513	175	43	)	)	PUNCT
ap-5513	175	44	∂v	∂v	PROPN
ap-5513	175	45	,	,	PUNCT
ap-5513	175	46	where	where	SCONJ
ap-5513	175	47	the	the	DET
ap-5513	175	48	generic	generic	ADJ
ap-5513	175	49	solution	solution	NOUN
ap-5513	175	50	of	of	ADP
ap-5513	175	51	equation	equation	NOUN
ap-5513	175	52	(	(	PUNCT
ap-5513	175	53	22	22	NUM
ap-5513	175	54	)	)	PUNCT
ap-5513	175	55	is	be	AUX
ap-5513	175	56	,	,	PUNCT
ap-5513	175	57	v	v	INTJ
ap-5513	175	58	(	(	PUNCT
ap-5513	175	59	s	s	NOUN
ap-5513	175	60	)	)	PUNCT
ap-5513	175	61	=	=	SYM
ap-5513	175	62	v1	v1	NOUN
ap-5513	175	63	sin	sin	NOUN
ap-5513	175	64	(	(	PUNCT
ap-5513	175	65	cs	cs	PROPN
ap-5513	175	66	)	)	PUNCT
ap-5513	175	67	+	+	CCONJ
ap-5513	175	68	v2	v2	PROPN
ap-5513	175	69	cos	cos	PROPN
ap-5513	175	70	(	(	PUNCT
ap-5513	175	71	cs	cs	PROPN
ap-5513	175	72	)	)	PUNCT
ap-5513	175	73	+	+	CCONJ
ap-5513	175	74	v3s+	v3s+	PROPN
ap-5513	175	75	v4	v4	NOUN
ap-5513	175	76	+	+	CCONJ
ap-5513	175	77	a0	a0	PROPN
ap-5513	175	78	2c2	2c2	NUM
ap-5513	175	79	s	s	PART
ap-5513	175	80	2	2	NUM
ap-5513	175	81	.	.	PUNCT
ap-5513	176	1	(	(	PUNCT
ap-5513	176	2	23	23	NUM
ap-5513	176	3	)	)	PUNCT
ap-5513	176	4	on	on	ADP
ap-5513	176	5	the	the	DET
ap-5513	176	6	other	other	ADJ
ap-5513	176	7	hand	hand	NOUN
ap-5513	176	8	,	,	PUNCT
ap-5513	176	9	for	for	ADP
ap-5513	176	10	f	f	PROPN
ap-5513	176	11	(	(	PUNCT
ap-5513	176	12	v	v	NOUN
ap-5513	176	13	)	)	PUNCT
ap-5513	176	14	=	=	PUNCT
ap-5513	177	1	a1v	a1v	PROPN
ap-5513	177	2	+	+	SYM
ap-5513	177	3	a0	a0	NOUN
ap-5513	177	4	,	,	PUNCT
ap-5513	177	5	equation	equation	NOUN
ap-5513	177	6	(	(	PUNCT
ap-5513	177	7	22	22	NUM
ap-5513	177	8	)	)	PUNCT
ap-5513	177	9	admits	admit	VERB
ap-5513	177	10	the	the	DET
ap-5513	177	11	six	six	NUM
ap-5513	177	12	lie	lie	NOUN
ap-5513	177	13	point	point	NOUN
ap-5513	177	14	symmetries	symmetry	NOUN
ap-5513	177	15	,	,	PUNCT
ap-5513	177	16	∂s	∂s	PROPN
ap-5513	177	17	,	,	PUNCT
ap-5513	177	18	(	(	PUNCT
ap-5513	177	19	a1v	a1v	PROPN
ap-5513	177	20	+	+	SYM
ap-5513	177	21	a0	a0	PROPN
ap-5513	177	22	)	)	PUNCT
ap-5513	177	23	∂v	∂v	PROPN
ap-5513	177	24	,	,	PUNCT
ap-5513	177	25	exp	exp	NOUN
ap-5513	177	26	(	(	PUNCT
ap-5513	177	27	±i	±i	PRON
ap-5513	177	28	√	√	PROPN
ap-5513	177	29	2c2	2c2	NUM
ap-5513	177	30	+	+	CCONJ
ap-5513	177	31	2	2	NUM
ap-5513	177	32	√	√	NOUN
ap-5513	177	33	c4	c4	NOUN
ap-5513	177	34	+	+	CCONJ
ap-5513	177	35	4a1	4a1	NUM
ap-5513	177	36	2	2	NUM
ap-5513	177	37	s	s	PART
ap-5513	177	38	)	)	PUNCT
ap-5513	177	39	∂v	∂v	PROPN
ap-5513	177	40	,	,	PUNCT
ap-5513	177	41	exp	exp	NOUN
ap-5513	177	42	(	(	PUNCT
ap-5513	177	43	±i	±i	PRON
ap-5513	177	44	√	√	PROPN
ap-5513	177	45	2c2	2c2	NUM
ap-5513	177	46	−	−	ADP
ap-5513	177	47	2	2	NUM
ap-5513	177	48	√	√	NOUN
ap-5513	177	49	c4	c4	NOUN
ap-5513	177	50	+	+	CCONJ
ap-5513	177	51	4a1	4a1	NUM
ap-5513	177	52	2	2	NUM
ap-5513	177	53	s	s	PART
ap-5513	177	54	)	)	PUNCT
ap-5513	177	55	∂v	∂v	PROPN
ap-5513	177	56	,	,	PUNCT
ap-5513	177	57	where	where	SCONJ
ap-5513	177	58	the	the	DET
ap-5513	177	59	generic	generic	ADJ
ap-5513	177	60	solution	solution	NOUN
ap-5513	177	61	of	of	ADP
ap-5513	177	62	(	(	PUNCT
ap-5513	177	63	22	22	NUM
ap-5513	177	64	)	)	PUNCT
ap-5513	177	65	is	be	AUX
ap-5513	177	66	,	,	PUNCT
ap-5513	177	67	v	v	INTJ
ap-5513	177	68	(	(	PUNCT
ap-5513	177	69	s	s	NOUN
ap-5513	177	70	)	)	PUNCT
ap-5513	177	71	=	=	SYM
ap-5513	177	72	v1	v1	NOUN
ap-5513	177	73	exp	exp	NOUN
ap-5513	177	74	(	(	PUNCT
ap-5513	177	75	i	i	PRON
ap-5513	177	76	√	√	VERB
ap-5513	177	77	2c2	2c2	NUM
ap-5513	178	1	+	+	CCONJ
ap-5513	178	2	2	2	NUM
ap-5513	178	3	√	√	NOUN
ap-5513	178	4	c4	c4	NOUN
ap-5513	178	5	+	+	CCONJ
ap-5513	178	6	4a1	4a1	NUM
ap-5513	178	7	2	2	NUM
ap-5513	178	8	s	s	NOUN
ap-5513	178	9	)	)	PUNCT
ap-5513	179	1	+	+	CCONJ
ap-5513	179	2	v2	v2	NOUN
ap-5513	179	3	exp	exp	NOUN
ap-5513	179	4	(	(	PUNCT
ap-5513	179	5	−i	−i	PROPN
ap-5513	179	6	√	√	PROPN
ap-5513	179	7	2c2	2c2	NUM
ap-5513	179	8	+	+	CCONJ
ap-5513	179	9	2	2	NUM
ap-5513	179	10	√	√	NOUN
ap-5513	179	11	c4	c4	NOUN
ap-5513	179	12	+	+	CCONJ
ap-5513	179	13	4a1	4a1	NUM
ap-5513	179	14	2	2	NUM
ap-5513	179	15	s	s	NOUN
ap-5513	179	16	)	)	PUNCT
ap-5513	179	17	+	+	CCONJ
ap-5513	180	1	+	+	PROPN
ap-5513	180	2	v3	v3	PROPN
ap-5513	180	3	exp	exp	NOUN
ap-5513	180	4	(	(	PUNCT
ap-5513	180	5	+	+	NOUN
ap-5513	180	6	i	i	NOUN
ap-5513	180	7	√	√	VERB
ap-5513	180	8	2c2	2c2	NUM
ap-5513	180	9	−	−	NOUN
ap-5513	180	10	2	2	NUM
ap-5513	180	11	√	√	NOUN
ap-5513	180	12	c4	c4	NOUN
ap-5513	180	13	+	+	CCONJ
ap-5513	180	14	4a1	4a1	NUM
ap-5513	180	15	2	2	NUM
ap-5513	180	16	s	s	NOUN
ap-5513	180	17	)	)	PUNCT
ap-5513	180	18	+	+	NUM
ap-5513	180	19	v4	v4	NOUN
ap-5513	180	20	exp	exp	NOUN
ap-5513	180	21	(	(	PUNCT
ap-5513	180	22	−i	−i	PROPN
ap-5513	180	23	√	√	PROPN
ap-5513	180	24	2c2	2c2	NUM
ap-5513	180	25	−	−	NOUN
ap-5513	180	26	2	2	NUM
ap-5513	180	27	√	√	NOUN
ap-5513	180	28	c4	c4	NOUN
ap-5513	180	29	+	+	CCONJ
ap-5513	180	30	4a1	4a1	NUM
ap-5513	180	31	2	2	NUM
ap-5513	180	32	s	s	NOUN
ap-5513	180	33	)	)	PUNCT
ap-5513	180	34	.	.	PUNCT
ap-5513	181	1	(	(	PUNCT
ap-5513	181	2	24	24	NUM
ap-5513	181	3	)	)	PUNCT
ap-5513	181	4	103	103	NUM
ap-5513	181	5	a.	a.	NOUN
ap-5513	181	6	k.	k.	PROPN
ap-5513	181	7	halder	halder	PROPN
ap-5513	181	8	,	,	PUNCT
ap-5513	181	9	a.	a.	NOUN
ap-5513	181	10	paliathanasis	paliathanasis	NOUN
ap-5513	181	11	,	,	PUNCT
ap-5513	181	12	p.	p.	NOUN
ap-5513	181	13	g.	g.	PROPN
ap-5513	181	14	l.	l.	PROPN
ap-5513	181	15	leach	leach	PROPN
ap-5513	181	16	acta	acta	PROPN
ap-5513	181	17	polytechnica	polytechnica	PROPN
ap-5513	181	18	4.4	4.4	NUM
ap-5513	181	19	.	.	PUNCT
ap-5513	182	1	scaling	scale	VERB
ap-5513	182	2	solutions	solution	NOUN
ap-5513	182	3	for	for	ADP
ap-5513	182	4	the	the	DET
ap-5513	182	5	forced	force	VERB
ap-5513	182	6	euler	euler	PROPN
ap-5513	182	7	-	-	PUNCT
ap-5513	182	8	bernoulli	bernoulli	NOUN
ap-5513	182	9	equation	equation	NOUN
ap-5513	182	10	.	.	PUNCT
ap-5513	183	1	we	we	PRON
ap-5513	183	2	continue	continue	VERB
ap-5513	183	3	by	by	ADP
ap-5513	183	4	presenting	present	VERB
ap-5513	183	5	the	the	DET
ap-5513	183	6	reduction	reduction	NOUN
ap-5513	183	7	with	with	ADP
ap-5513	183	8	the	the	DET
ap-5513	183	9	scaling	scale	VERB
ap-5513	183	10	symmetries	symmetry	NOUN
ap-5513	183	11	for	for	ADP
ap-5513	183	12	the	the	DET
ap-5513	183	13	euler	euler	PROPN
ap-5513	183	14	-	-	PUNCT
ap-5513	183	15	bernoulli	bernoulli	NOUN
ap-5513	183	16	equation	equation	NOUN
ap-5513	183	17	for	for	ADP
ap-5513	183	18	the	the	DET
ap-5513	183	19	power	power	NOUN
ap-5513	183	20	-	-	PUNCT
ap-5513	183	21	law	law	NOUN
ap-5513	183	22	and	and	CCONJ
ap-5513	183	23	the	the	DET
ap-5513	183	24	exponential	exponential	ADJ
ap-5513	183	25	sources	source	NOUN
ap-5513	183	26	f2	f2	PROPN
ap-5513	183	27	(	(	PUNCT
ap-5513	183	28	u	u	NOUN
ap-5513	183	29	)	)	PUNCT
ap-5513	183	30	and	and	CCONJ
ap-5513	183	31	f3	f3	PROPN
ap-5513	183	32	(	(	PUNCT
ap-5513	183	33	u	u	NOUN
ap-5513	183	34	)	)	PUNCT
ap-5513	183	35	.	.	PUNCT
ap-5513	184	1	for	for	ADP
ap-5513	184	2	simplicity	simplicity	NOUN
ap-5513	184	3	and	and	CCONJ
ap-5513	184	4	without	without	ADP
ap-5513	184	5	a	a	DET
ap-5513	184	6	loss	loss	NOUN
ap-5513	184	7	of	of	ADP
ap-5513	184	8	generality	generality	NOUN
ap-5513	184	9	,	,	PUNCT
ap-5513	184	10	we	we	PRON
ap-5513	184	11	select	select	VERB
ap-5513	184	12	b	b	NOUN
ap-5513	184	13	=	=	NOUN
ap-5513	184	14	0	0	PROPN
ap-5513	184	15	.	.	PUNCT
ap-5513	185	1	for	for	ADP
ap-5513	185	2	the	the	DET
ap-5513	185	3	power	power	NOUN
ap-5513	185	4	-	-	PUNCT
ap-5513	185	5	law	law	NOUN
ap-5513	185	6	source	source	NOUN
ap-5513	185	7	f2	f2	PROPN
ap-5513	185	8	(	(	PUNCT
ap-5513	185	9	u	u	NOUN
ap-5513	185	10	)	)	PUNCT
ap-5513	185	11	=	=	SYM
ap-5513	185	12	aun	aun	PROPN
ap-5513	185	13	,	,	PUNCT
ap-5513	185	14	the	the	DET
ap-5513	185	15	application	application	NOUN
ap-5513	185	16	of	of	ADP
ap-5513	185	17	the	the	DET
ap-5513	185	18	lie	lie	NOUN
ap-5513	185	19	point	point	NOUN
ap-5513	185	20	symmetry	symmetry	NOUN
ap-5513	185	21	γf2	γf2	X
ap-5513	185	22	3	3	NUM
ap-5513	185	23	provides	provide	VERB
ap-5513	185	24	the	the	DET
ap-5513	185	25	reduced	reduced	ADJ
ap-5513	185	26	fourth	fourth	ADJ
ap-5513	185	27	-	-	PUNCT
ap-5513	185	28	order	order	NOUN
ap-5513	185	29	ode	ode	PROPN
ap-5513	185	30	,	,	PUNCT
ap-5513	185	31	4αβv′′′′	4αβv′′′′	PROPN
ap-5513	185	32	+	+	CCONJ
ap-5513	185	33	s2v′′	s2v′′	VERB
ap-5513	185	34	+	+	CCONJ
ap-5513	185	35	3n+	3n+	NUM
ap-5513	185	36	5	5	NUM
ap-5513	185	37	n−	n−	NOUN
ap-5513	185	38	1	1	NUM
ap-5513	185	39	sv	sv	NOUN
ap-5513	185	40	′	′	NUM
ap-5513	186	1	+	+	CCONJ
ap-5513	186	2	8(1	8(1	NOUN
ap-5513	186	3	+	+	CCONJ
ap-5513	186	4	n)v	n)v	NOUN
ap-5513	186	5	(	(	PUNCT
ap-5513	186	6	n−	n−	NOUN
ap-5513	186	7	1)2	1)2	NUM
ap-5513	186	8	−	−	NOUN
ap-5513	186	9	4avn	4avn	NUM
ap-5513	186	10	=	=	SYM
ap-5513	186	11	0	0	NUM
ap-5513	186	12	,	,	PUNCT
ap-5513	186	13	(	(	PUNCT
ap-5513	186	14	25	25	NUM
ap-5513	186	15	)	)	PUNCT
ap-5513	186	16	in	in	ADP
ap-5513	186	17	which	which	PRON
ap-5513	186	18	s	s	VERB
ap-5513	186	19	=	=	SYM
ap-5513	186	20	x√	x√	PROPN
ap-5513	186	21	t	t	NOUN
ap-5513	186	22	and	and	CCONJ
ap-5513	186	23	u	u	PROPN
ap-5513	186	24	(	(	PUNCT
ap-5513	186	25	t	t	PROPN
ap-5513	186	26	,	,	PUNCT
ap-5513	186	27	x	x	NOUN
ap-5513	186	28	)	)	PUNCT
ap-5513	186	29	=	=	SYM
ap-5513	186	30	v	v	X
ap-5513	186	31	(	(	PUNCT
ap-5513	186	32	s	s	NOUN
ap-5513	186	33	)	)	PUNCT
ap-5513	186	34	t	t	NOUN
ap-5513	186	35	2	2	NUM
ap-5513	186	36	n−1	n−1	PROPN
ap-5513	186	37	.	.	PUNCT
ap-5513	187	1	for	for	ADP
ap-5513	187	2	the	the	DET
ap-5513	187	3	exponential	exponential	ADJ
ap-5513	187	4	source	source	NOUN
ap-5513	187	5	f3	f3	PROPN
ap-5513	187	6	(	(	PUNCT
ap-5513	187	7	u	u	NOUN
ap-5513	187	8	)	)	PUNCT
ap-5513	187	9	=	=	SYM
ap-5513	187	10	eau	eau	PROPN
ap-5513	187	11	,	,	PUNCT
ap-5513	187	12	the	the	DET
ap-5513	187	13	reduced	reduce	VERB
ap-5513	187	14	equation	equation	NOUN
ap-5513	187	15	given	give	VERB
ap-5513	187	16	by	by	ADP
ap-5513	187	17	the	the	DET
ap-5513	187	18	scaling	scaling	NOUN
ap-5513	187	19	symmetry	symmetry	NOUN
ap-5513	187	20	is	be	AUX
ap-5513	187	21	,	,	PUNCT
ap-5513	187	22	4αβv′′′′	4αβv′′′′	PROPN
ap-5513	188	1	+	+	CCONJ
ap-5513	188	2	s2v′′	s2v′′	VERB
ap-5513	188	3	+	+	CCONJ
ap-5513	188	4	3sav′	3sav′	NUM
ap-5513	188	5	+	+	CCONJ
ap-5513	188	6	4aeav	4aeav	NUM
ap-5513	188	7	+	+	CCONJ
ap-5513	188	8	8	8	NUM
ap-5513	188	9	=	=	SYM
ap-5513	188	10	0	0	NUM
ap-5513	188	11	,	,	PUNCT
ap-5513	188	12	(	(	PUNCT
ap-5513	188	13	26	26	NUM
ap-5513	188	14	)	)	PUNCT
ap-5513	188	15	where	where	SCONJ
ap-5513	188	16	now	now	ADV
ap-5513	188	17	s	s	VERB
ap-5513	188	18	=	=	SYM
ap-5513	188	19	x√	x√	PROPN
ap-5513	188	20	t	t	NOUN
ap-5513	188	21	and	and	CCONJ
ap-5513	188	22	u	u	PROPN
ap-5513	188	23	(	(	PUNCT
ap-5513	188	24	t	t	PROPN
ap-5513	188	25	,	,	PUNCT
ap-5513	188	26	x	x	NOUN
ap-5513	188	27	)	)	PUNCT
ap-5513	189	1	=	=	SYM
ap-5513	189	2	−	−	PROPN
ap-5513	189	3	2	2	NUM
ap-5513	189	4	a	a	DET
ap-5513	189	5	ln	ln	ADJ
ap-5513	189	6	(	(	PUNCT
ap-5513	189	7	t	t	NOUN
ap-5513	189	8	)	)	PUNCT
ap-5513	190	1	+	+	X
ap-5513	190	2	v	v	X
ap-5513	190	3	(	(	PUNCT
ap-5513	190	4	s	s	NOUN
ap-5513	190	5	)	)	PUNCT
ap-5513	190	6	.	.	PUNCT
ap-5513	191	1	5	5	X
ap-5513	191	2	.	.	X
ap-5513	191	3	singularity	singularity	NOUN
ap-5513	191	4	analysis	analysis	NOUN
ap-5513	191	5	the	the	DET
ap-5513	191	6	third	third	ADJ
ap-5513	191	7	-	-	PUNCT
ap-5513	191	8	order	order	NOUN
ap-5513	191	9	ode	ode	NOUN
ap-5513	191	10	that	that	SCONJ
ap-5513	191	11	we	we	PRON
ap-5513	191	12	apply	apply	VERB
ap-5513	191	13	the	the	DET
ap-5513	191	14	singularity	singularity	NOUN
ap-5513	191	15	analysis	analysis	NOUN
ap-5513	191	16	to	to	ADP
ap-5513	191	17	is	be	AUX
ap-5513	191	18	(	(	PUNCT
ap-5513	191	19	15	15	NUM
ap-5513	191	20	)	)	PUNCT
ap-5513	191	21	or	or	CCONJ
ap-5513	191	22	24νxy(x	24νxy(x	NUM
ap-5513	191	23	)	)	PUNCT
ap-5513	192	1	+	+	CCONJ
ap-5513	192	2	y(x)2	y(x)2	NOUN
ap-5513	192	3	+	+	CCONJ
ap-5513	192	4	156νx2y(x)2	156νx2y(x)2	NOUN
ap-5513	192	5	+	+	CCONJ
ap-5513	192	6	112νx3y(x)3	112νx3y(x)3	NUM
ap-5513	192	7	+	+	CCONJ
ap-5513	192	8	16νx4y(x)4	16νx4y(x)4	NUM
ap-5513	192	9	+	+	CCONJ
ap-5513	192	10	y′(x	y′(x	NOUN
ap-5513	192	11	)	)	PUNCT
ap-5513	192	12	+	+	NUM
ap-5513	192	13	156νx2y′(x	156νx2y′(x	X
ap-5513	192	14	)	)	PUNCT
ap-5513	192	15	+336νx3y(x)y′(x	+336νx3y(x)y′(x	NOUN
ap-5513	192	16	)	)	PUNCT
ap-5513	193	1	+	+	NUM
ap-5513	193	2	+96νx4y(x)2y′(x	+96νx4y(x)2y′(x	NOUN
ap-5513	193	3	)	)	PUNCT
ap-5513	194	1	+	+	CCONJ
ap-5513	194	2	48νx4y′2(x	48νx4y′2(x	NOUN
ap-5513	194	3	)	)	PUNCT
ap-5513	195	1	+	+	CCONJ
ap-5513	195	2	112νx3y′′(x	112νx3y′′(x	X
ap-5513	195	3	)	)	PUNCT
ap-5513	195	4	+64νx4y(x)y′′(x	+64νx4y(x)y′′(x	NOUN
ap-5513	195	5	)	)	PUNCT
ap-5513	196	1	+	+	NUM
ap-5513	197	1	16νx4y′′′(x	16νx4y′′′(x	X
ap-5513	197	2	)	)	PUNCT
ap-5513	197	3	=	=	SYM
ap-5513	197	4	0	0	NUM
ap-5513	197	5	,	,	PUNCT
ap-5513	197	6	(	(	PUNCT
ap-5513	197	7	27	27	NUM
ap-5513	197	8	)	)	PUNCT
ap-5513	198	1	where	where	SCONJ
ap-5513	198	2	g	g	PROPN
ap-5513	198	3	(	(	PUNCT
ap-5513	198	4	h	h	NOUN
ap-5513	198	5	)	)	PUNCT
ap-5513	198	6	=	=	SYM
ap-5513	198	7	y	y	PROPN
ap-5513	198	8	(	(	PUNCT
ap-5513	198	9	x	x	NOUN
ap-5513	198	10	)	)	PUNCT
ap-5513	198	11	,	,	PUNCT
ap-5513	198	12	h	h	NOUN
ap-5513	198	13	=	=	PUNCT
ap-5513	198	14	x	x	PROPN
ap-5513	198	15	and	and	CCONJ
ap-5513	198	16	αβ	αβ	INTJ
ap-5513	198	17	=	=	NOUN
ap-5513	198	18	v.	v.	CCONJ
ap-5513	198	19	we	we	PRON
ap-5513	198	20	apply	apply	VERB
ap-5513	198	21	the	the	DET
ap-5513	198	22	ars	ar	NOUN
ap-5513	198	23	algorithm	algorithm	NOUN
ap-5513	198	24	[	[	X
ap-5513	198	25	25–27	25–27	NUM
ap-5513	198	26	]	]	X
ap-5513	198	27	and	and	CCONJ
ap-5513	198	28	we	we	PRON
ap-5513	198	29	make	make	VERB
ap-5513	198	30	the	the	DET
ap-5513	198	31	usual	usual	ADJ
ap-5513	198	32	substitution	substitution	NOUN
ap-5513	198	33	to	to	PART
ap-5513	198	34	obtain	obtain	VERB
ap-5513	198	35	the	the	DET
ap-5513	198	36	leading	lead	VERB
ap-5513	198	37	-	-	PUNCT
ap-5513	198	38	order	order	NOUN
ap-5513	198	39	behaviour	behaviour	NOUN
ap-5513	199	1	[	[	X
ap-5513	199	2	28	28	NUM
ap-5513	199	3	]	]	PUNCT
ap-5513	199	4	,	,	PUNCT
ap-5513	199	5	y	y	PROPN
ap-5513	199	6	→	→	SYM
ap-5513	199	7	a(x−	a(x−	NOUN
ap-5513	199	8	x0)p	x0)p	NOUN
ap-5513	199	9	,	,	PUNCT
ap-5513	199	10	(	(	PUNCT
ap-5513	199	11	28	28	NUM
ap-5513	199	12	)	)	PUNCT
ap-5513	199	13	which	which	PRON
ap-5513	199	14	provides	provide	VERB
ap-5513	199	15	32aνpx4(x−	32aνpx4(x−	NUM
ap-5513	199	16	x0)−3+p	x0)−3+p	PROPN
ap-5513	199	17	−	−	PROPN
ap-5513	199	18	48aνp2x4(x−	48aνp2x4(x−	NUM
ap-5513	199	19	x0)−3+p	x0)−3+p	PROPN
ap-5513	199	20	+	+	CCONJ
ap-5513	199	21	16aνp3x4(x−	16aνp3x4(x−	NUM
ap-5513	199	22	x0)−3+p	x0)−3+p	PROPN
ap-5513	199	23	−	−	PROPN
ap-5513	199	24	112aνpx3(x−	112aνpx3(x−	PROPN
ap-5513	199	25	x0)−2+p	x0)−2+p	PROPN
ap-5513	199	26	+112aνp2x3(x−	+112aνp2x3(x−	PROPN
ap-5513	199	27	x0)−2+p	x0)−2+p	PROPN
ap-5513	199	28	+	+	CCONJ
ap-5513	199	29	ap(x−	ap(x−	PROPN
ap-5513	199	30	x0)−1+p	x0)−1+p	NOUN
ap-5513	199	31	+	+	CCONJ
ap-5513	199	32	156aνpx2(x−	156aνpx2(x−	NUM
ap-5513	199	33	x0)−1+p	x0)−1+p	NOUN
ap-5513	199	34	+	+	CCONJ
ap-5513	199	35	24aνx(x−	24aνx(x−	PROPN
ap-5513	199	36	x0)p	x0)p	PROPN
ap-5513	199	37	+	+	PROPN
ap-5513	199	38	a2(x−	a2(x−	X
ap-5513	199	39	x0)2p	x0)2p	PROPN
ap-5513	200	1	+	+	PROPN
ap-5513	201	1	156a2νx2(x−	156a2νx2(x−	NUM
ap-5513	201	2	x0)2p	x0)2p	PUNCT
ap-5513	202	1	+	+	CCONJ
ap-5513	203	1	112a3νx3(x−	112a3νx3(x−	NUM
ap-5513	203	2	x0)3p	x0)3p	NOUN
ap-5513	204	1	+	+	CCONJ
ap-5513	204	2	16a4νx4(x−	16a4νx4(x−	NUM
ap-5513	204	3	x0)4p	x0)4p	PROPN
ap-5513	204	4	−64a2νpx4(x−	−64a2νpx4(x−	PROPN
ap-5513	204	5	x0)−2	x0)−2	X
ap-5513	205	1	+	+	ADJ
ap-5513	205	2	2p	2p	NUM
ap-5513	205	3	+	+	CCONJ
ap-5513	205	4	112a2νp2x4(x−	112a2νp2x4(x−	NUM
ap-5513	205	5	x0)−2	x0)−2	X
ap-5513	205	6	+	+	NOUN
ap-5513	205	7	2p	2p	NOUN
ap-5513	205	8	+	+	CCONJ
ap-5513	205	9	336a2νpx3(x−	336a2νpx3(x−	NUM
ap-5513	205	10	x0)−1	x0)−1	NOUN
ap-5513	205	11	+	+	NOUN
ap-5513	205	12	2p	2p	NOUN
ap-5513	205	13	+96a3νpx4(x−	+96a3νpx4(x−	NUM
ap-5513	205	14	x0)−1	x0)−1	NOUN
ap-5513	205	15	+	+	NOUN
ap-5513	205	16	3p	3p	NUM
ap-5513	205	17	=	=	SYM
ap-5513	205	18	0	0	NUM
ap-5513	205	19	.	.	PUNCT
ap-5513	206	1	(	(	PUNCT
ap-5513	206	2	29	29	NUM
ap-5513	206	3	)	)	PUNCT
ap-5513	206	4	from	from	ADP
ap-5513	206	5	the	the	DET
ap-5513	206	6	latter	latter	ADJ
ap-5513	206	7	,	,	PUNCT
ap-5513	206	8	it	it	PRON
ap-5513	206	9	is	be	AUX
ap-5513	206	10	evident	evident	ADJ
ap-5513	206	11	that	that	SCONJ
ap-5513	206	12	p→	p→	NOUN
ap-5513	206	13	−1	−1	NOUN
ap-5513	206	14	.	.	PUNCT
ap-5513	207	1	hence	hence	ADV
ap-5513	207	2	,	,	PUNCT
ap-5513	207	3	−	−	PROPN
ap-5513	207	4	96aνx4	96aνx4	PROPN
ap-5513	207	5	(	(	PUNCT
ap-5513	207	6	x−	x−	PROPN
ap-5513	207	7	x0)4	x0)4	PROPN
ap-5513	208	1	+	+	CCONJ
ap-5513	208	2	176a2νx4	176a2νx4	PROPN
ap-5513	208	3	(	(	PUNCT
ap-5513	208	4	x−	x−	PROPN
ap-5513	208	5	x0)4	x0)4	X
ap-5513	209	1	−	−	PROPN
ap-5513	209	2	96a3νx4	96a3νx4	PROPN
ap-5513	209	3	(	(	PUNCT
ap-5513	209	4	x−	x−	PROPN
ap-5513	209	5	x0)4	x0)4	PROPN
ap-5513	210	1	+	+	NUM
ap-5513	210	2	16a4νx4	16a4νx4	NUM
ap-5513	210	3	(	(	PUNCT
ap-5513	210	4	x−	x−	PROPN
ap-5513	210	5	x0)4	x0)4	PROPN
ap-5513	211	1	+	+	CCONJ
ap-5513	211	2	224aνx3	224aνx3	NUM
ap-5513	211	3	(	(	PUNCT
ap-5513	211	4	x−	x−	PROPN
ap-5513	211	5	x0)3	x0)3	PROPN
ap-5513	211	6	−336a2νx3	−336a2νx3	PROPN
ap-5513	211	7	(	(	PUNCT
ap-5513	211	8	x−	x−	PROPN
ap-5513	211	9	x0)3	x0)3	PROPN
ap-5513	212	1	+	+	CCONJ
ap-5513	213	1	112a3νx3	112a3νx3	NUM
ap-5513	213	2	(	(	PUNCT
ap-5513	213	3	x−	x−	PROPN
ap-5513	213	4	x0)3	x0)3	PROPN
ap-5513	213	5	−	−	PROPN
ap-5513	213	6	a	a	PRON
ap-5513	213	7	(	(	PUNCT
ap-5513	213	8	x−	x−	PROPN
ap-5513	213	9	x0)2	x0)2	PROPN
ap-5513	213	10	(	(	PUNCT
ap-5513	213	11	30	30	NUM
ap-5513	213	12	)	)	PUNCT
ap-5513	213	13	+	+	NUM
ap-5513	213	14	a2	a2	PROPN
ap-5513	213	15	(	(	PUNCT
ap-5513	213	16	x−	x−	PROPN
ap-5513	213	17	x0)2	x0)2	PROPN
ap-5513	214	1	−	−	PROPN
ap-5513	214	2	156aνx2	156aνx2	NUM
ap-5513	214	3	(	(	PUNCT
ap-5513	214	4	x−	x−	PROPN
ap-5513	214	5	x0)2	x0)2	PROPN
ap-5513	215	1	+	+	CCONJ
ap-5513	215	2	156a2νx2	156a2νx2	NUM
ap-5513	215	3	(	(	PUNCT
ap-5513	215	4	x−	x−	PROPN
ap-5513	215	5	x0)2	x0)2	PROPN
ap-5513	216	1	+	+	NUM
ap-5513	216	2	24aνx	24aνx	ADJ
ap-5513	216	3	x−	x−	PROPN
ap-5513	216	4	x0	x0	PROPN
ap-5513	216	5	.	.	PUNCT
ap-5513	217	1	we	we	PRON
ap-5513	217	2	extract	extract	VERB
ap-5513	217	3	the	the	DET
ap-5513	217	4	obvious	obvious	ADJ
ap-5513	217	5	dominant	dominant	ADJ
ap-5513	217	6	terms	term	NOUN
ap-5513	217	7	,	,	PUNCT
ap-5513	217	8	−	−	PROPN
ap-5513	217	9	96aνx4	96aνx4	PROPN
ap-5513	217	10	(	(	PUNCT
ap-5513	217	11	x−	x−	PROPN
ap-5513	217	12	x0)4	x0)4	PROPN
ap-5513	218	1	+	+	CCONJ
ap-5513	218	2	176a2νx4	176a2νx4	PROPN
ap-5513	218	3	(	(	PUNCT
ap-5513	218	4	x−	x−	PROPN
ap-5513	218	5	x0)4	x0)4	X
ap-5513	219	1	−	−	PROPN
ap-5513	219	2	96a3νx4	96a3νx4	PROPN
ap-5513	219	3	(	(	PUNCT
ap-5513	219	4	x−	x−	PROPN
ap-5513	219	5	x0)4	x0)4	PROPN
ap-5513	220	1	+	+	NUM
ap-5513	220	2	16a4νx4	16a4νx4	NUM
ap-5513	220	3	(	(	PUNCT
ap-5513	220	4	x−	x−	PROPN
ap-5513	220	5	x0)4	x0)4	PROPN
ap-5513	220	6	,	,	PUNCT
ap-5513	220	7	(	(	PUNCT
ap-5513	220	8	31	31	NUM
ap-5513	220	9	)	)	PUNCT
ap-5513	220	10	and	and	CCONJ
ap-5513	220	11	solve	solve	VERB
ap-5513	220	12	for	for	ADP
ap-5513	220	13	a	a	PRON
ap-5513	220	14	,	,	PUNCT
ap-5513	220	15	(	(	PUNCT
ap-5513	220	16	−3	−3	PROPN
ap-5513	220	17	+	+	NUM
ap-5513	220	18	a)(−2	a)(−2	PROPN
ap-5513	220	19	+	+	CCONJ
ap-5513	220	20	a)(−1	a)(−1	PROPN
ap-5513	220	21	+	+	CCONJ
ap-5513	220	22	a)a	a)a	X
ap-5513	220	23	=	=	SYM
ap-5513	220	24	0	0	NUM
ap-5513	220	25	,	,	PUNCT
ap-5513	220	26	(	(	PUNCT
ap-5513	220	27	32	32	NUM
ap-5513	220	28	)	)	PUNCT
ap-5513	220	29	104	104	NUM
ap-5513	220	30	vol	vol	NOUN
ap-5513	220	31	.	.	PUNCT
ap-5513	221	1	60	60	NUM
ap-5513	221	2	no	no	NOUN
ap-5513	221	3	.	.	PUNCT
ap-5513	222	1	2/2020	2/2020	NUM
ap-5513	222	2	similarity	similarity	NOUN
ap-5513	222	3	solutions	solution	NOUN
ap-5513	222	4	and	and	CCONJ
ap-5513	222	5	conservation	conservation	NOUN
ap-5513	222	6	laws	law	NOUN
ap-5513	222	7	for	for	ADP
ap-5513	222	8	the	the	DET
ap-5513	222	9	beam	beam	NOUN
ap-5513	222	10	equations	equation	NOUN
ap-5513	222	11	.	.	PUNCT
ap-5513	222	12	.	.	PUNCT
ap-5513	222	13	.	.	PUNCT
ap-5513	223	1	to	to	PART
ap-5513	223	2	obtain	obtain	VERB
ap-5513	223	3	,	,	PUNCT
ap-5513	223	4	a→	a→	X
ap-5513	223	5	0	0	NUM
ap-5513	223	6	,	,	PUNCT
ap-5513	223	7	a→	a→	X
ap-5513	223	8	1	1	NUM
ap-5513	223	9	,	,	PUNCT
ap-5513	223	10	a→	a→	X
ap-5513	223	11	2	2	NUM
ap-5513	223	12	,	,	PUNCT
ap-5513	223	13	a→	a→	AUX
ap-5513	223	14	3	3	NUM
ap-5513	223	15	.	.	PUNCT
ap-5513	224	1	(	(	PUNCT
ap-5513	224	2	33	33	NUM
ap-5513	224	3	)	)	PUNCT
ap-5513	224	4	in	in	ADP
ap-5513	224	5	order	order	NOUN
ap-5513	224	6	to	to	PART
ap-5513	224	7	find	find	VERB
ap-5513	224	8	the	the	DET
ap-5513	224	9	resonances	resonance	NOUN
ap-5513	224	10	,	,	PUNCT
ap-5513	224	11	we	we	PRON
ap-5513	224	12	substitute	substitute	VERB
ap-5513	224	13	,	,	PUNCT
ap-5513	224	14	y	y	PROPN
ap-5513	224	15	→	→	SYM
ap-5513	224	16	a(x−	a(x−	NOUN
ap-5513	224	17	x0)−1	x0)−1	X
ap-5513	224	18	+	+	NOUN
ap-5513	224	19	m(x−	m(x−	NOUN
ap-5513	224	20	x0)−1+s	x0)−1+s	NOUN
ap-5513	224	21	,	,	PUNCT
ap-5513	224	22	(	(	PUNCT
ap-5513	224	23	34	34	NUM
ap-5513	224	24	)	)	PUNCT
ap-5513	224	25	and	and	CCONJ
ap-5513	224	26	we	we	PRON
ap-5513	224	27	linearize	linearize	VERB
ap-5513	224	28	around	around	ADP
ap-5513	224	29	m.	m.	NOUN
ap-5513	224	30	then	then	ADV
ap-5513	224	31	,	,	PUNCT
ap-5513	224	32	the	the	DET
ap-5513	224	33	usual	usual	ADJ
ap-5513	224	34	x→	x→	PUNCT
ap-5513	225	1	z	z	PROPN
ap-5513	226	1	+	+	CCONJ
ap-5513	226	2	x0	x0	PROPN
ap-5513	226	3	,	,	PUNCT
ap-5513	226	4	simplify	simplify	VERB
ap-5513	226	5	the	the	DET
ap-5513	226	6	calculations	calculation	NOUN
ap-5513	226	7	and	and	CCONJ
ap-5513	226	8	provide	provide	VERB
ap-5513	226	9	the	the	DET
ap-5513	226	10	dominant	dominant	ADJ
ap-5513	226	11	terms	term	NOUN
ap-5513	226	12	factor	factor	NOUN
ap-5513	226	13	as	as	ADP
ap-5513	226	14	,	,	PUNCT
ap-5513	226	15	16ν(−3	16ν(−3	NUM
ap-5513	226	16	+	+	NUM
ap-5513	226	17	2a+	2a+	NUM
ap-5513	226	18	s	s	NOUN
ap-5513	226	19	)	)	PUNCT
ap-5513	226	20	(	(	PUNCT
ap-5513	226	21	2−	2−	NUM
ap-5513	226	22	6a+	6a+	NUM
ap-5513	226	23	2a2	2a2	NUM
ap-5513	226	24	−	−	PROPN
ap-5513	226	25	3s+	3s+	NUM
ap-5513	226	26	2as+	2as+	PROPN
ap-5513	226	27	s2)x4	s2)x4	VERB
ap-5513	226	28	0z	0z	NOUN
ap-5513	226	29	−4+s	−4+	NOUN
ap-5513	226	30	,	,	PUNCT
ap-5513	226	31	(	(	PUNCT
ap-5513	226	32	35	35	NUM
ap-5513	226	33	)	)	PUNCT
ap-5513	226	34	and	and	CCONJ
ap-5513	226	35	for	for	ADP
ap-5513	226	36	the	the	DET
ap-5513	226	37	three	three	NUM
ap-5513	226	38	values	value	NOUN
ap-5513	226	39	of	of	ADP
ap-5513	226	40	a	a	PRON
ap-5513	226	41	,	,	PUNCT
ap-5513	226	42	we	we	PRON
ap-5513	226	43	obtain	obtain	VERB
ap-5513	226	44	the	the	DET
ap-5513	226	45	three	three	NUM
ap-5513	226	46	sets	set	NOUN
ap-5513	226	47	of	of	ADP
ap-5513	226	48	resonances	resonance	NOUN
ap-5513	226	49	,	,	PUNCT
ap-5513	226	50	for	for	ADP
ap-5513	226	51	each	each	DET
ap-5513	226	52	value	value	NOUN
ap-5513	226	53	of	of	ADP
ap-5513	226	54	the	the	DET
ap-5513	226	55	coefficient	coefficient	NOUN
ap-5513	226	56	term	term	NOUN
ap-5513	226	57	a	a	PRON
ap-5513	226	58	:	:	PUNCT
ap-5513	226	59	a	a	PRON
ap-5513	226	60	=	=	SYM
ap-5513	226	61	1	1	NUM
ap-5513	226	62	:	:	PUNCT
ap-5513	226	63	s→	s→	X
ap-5513	226	64	−1	−1	NOUN
ap-5513	226	65	,	,	PUNCT
ap-5513	226	66	s→	s→	PROPN
ap-5513	226	67	1	1	NUM
ap-5513	226	68	,	,	PUNCT
ap-5513	226	69	s→	s→	X
ap-5513	226	70	2	2	NUM
ap-5513	226	71	,	,	PUNCT
ap-5513	226	72	a	a	DET
ap-5513	226	73	=	=	SYM
ap-5513	226	74	2	2	NUM
ap-5513	226	75	:	:	PUNCT
ap-5513	226	76	s→	s→	X
ap-5513	226	77	−2	−2	PROPN
ap-5513	226	78	,	,	PUNCT
ap-5513	226	79	s→	s→	X
ap-5513	226	80	−1	−1	NOUN
ap-5513	226	81	,	,	PUNCT
ap-5513	226	82	s→	s→	PROPN
ap-5513	226	83	1	1	NUM
ap-5513	226	84	,	,	PUNCT
ap-5513	226	85	and	and	CCONJ
ap-5513	226	86	a	a	PRON
ap-5513	226	87	=	=	SYM
ap-5513	226	88	3	3	NUM
ap-5513	226	89	:	:	PUNCT
ap-5513	226	90	s→	s→	X
ap-5513	227	1	−3	−3	PROPN
ap-5513	227	2	,	,	PUNCT
ap-5513	227	3	s→	s→	PROPN
ap-5513	227	4	−2	−2	NOUN
ap-5513	227	5	,	,	PUNCT
ap-5513	227	6	s→	s→	X
ap-5513	227	7	−1	−1	NOUN
ap-5513	227	8	.	.	PUNCT
ap-5513	228	1	for	for	ADP
ap-5513	228	2	a	a	DET
ap-5513	228	3	=	=	SYM
ap-5513	228	4	1	1	NUM
ap-5513	228	5	,	,	PUNCT
ap-5513	228	6	the	the	DET
ap-5513	228	7	solution	solution	NOUN
ap-5513	228	8	is	be	AUX
ap-5513	228	9	expressed	express	VERB
ap-5513	228	10	in	in	ADP
ap-5513	228	11	terms	term	NOUN
ap-5513	228	12	of	of	ADP
ap-5513	228	13	a	a	DET
ap-5513	228	14	right	right	ADJ
ap-5513	228	15	painlevé	painlevé	NOUN
ap-5513	228	16	series	series	NOUN
ap-5513	228	17	,	,	PUNCT
ap-5513	228	18	for	for	ADP
ap-5513	228	19	a	a	DET
ap-5513	228	20	=	=	SYM
ap-5513	228	21	3	3	NUM
ap-5513	228	22	,	,	PUNCT
ap-5513	228	23	in	in	ADP
ap-5513	228	24	terms	term	NOUN
ap-5513	228	25	of	of	ADP
ap-5513	228	26	a	a	DET
ap-5513	228	27	left	left	ADJ
ap-5513	228	28	painlevé	painlevé	NOUN
ap-5513	228	29	series	series	NOUN
ap-5513	228	30	and	and	CCONJ
ap-5513	228	31	for	for	ADP
ap-5513	228	32	a	a	DET
ap-5513	228	33	=	=	SYM
ap-5513	228	34	2	2	NUM
ap-5513	228	35	,	,	PUNCT
ap-5513	228	36	in	in	ADP
ap-5513	228	37	terms	term	NOUN
ap-5513	228	38	of	of	ADP
ap-5513	228	39	a	a	DET
ap-5513	228	40	mixed	mixed	ADJ
ap-5513	228	41	painlevé	painlevé	NOUN
ap-5513	228	42	series	series	NOUN
ap-5513	228	43	.	.	PUNCT
ap-5513	229	1	we	we	PRON
ap-5513	229	2	commence	commence	VERB
ap-5513	229	3	the	the	DET
ap-5513	229	4	consistency	consistency	NOUN
ap-5513	229	5	test	test	NOUN
ap-5513	229	6	.	.	PUNCT
ap-5513	230	1	for	for	ADP
ap-5513	230	2	the	the	DET
ap-5513	230	3	right	right	ADJ
ap-5513	230	4	painlevé	painlevé	PROPN
ap-5513	230	5	series	series	PROPN
ap-5513	230	6	,	,	PUNCT
ap-5513	230	7	we	we	PRON
ap-5513	230	8	write	write	VERB
ap-5513	230	9	y	y	PROPN
ap-5513	230	10	→	→	PUNCT
ap-5513	230	11	(	(	PUNCT
ap-5513	230	12	x−	x−	PROPN
ap-5513	230	13	x0)−1	x0)−1	X
ap-5513	231	1	+	+	CCONJ
ap-5513	231	2	f0	f0	PROPN
ap-5513	231	3	+	+	CCONJ
ap-5513	231	4	f1(x−	f1(x−	X
ap-5513	231	5	x0	x0	NUM
ap-5513	231	6	)	)	PUNCT
ap-5513	232	1	+	+	NUM
ap-5513	232	2	f2(x−	f2(x−	NOUN
ap-5513	232	3	x0)2	x0)2	PUNCT
ap-5513	233	1	+	+	CCONJ
ap-5513	233	2	f3(x−	f3(x−	PRON
ap-5513	233	3	x0)3	x0)3	X
ap-5513	233	4	+	+	CCONJ
ap-5513	233	5	...	...	PUNCT
ap-5513	233	6	(	(	PUNCT
ap-5513	233	7	36	36	NUM
ap-5513	233	8	)	)	PUNCT
ap-5513	233	9	where	where	SCONJ
ap-5513	233	10	f0	f0	PROPN
ap-5513	233	11	and	and	CCONJ
ap-5513	233	12	f1	f1	NOUN
ap-5513	233	13	are	be	AUX
ap-5513	233	14	the	the	DET
ap-5513	233	15	second	second	ADJ
ap-5513	233	16	and	and	CCONJ
ap-5513	233	17	third	third	ADJ
ap-5513	233	18	constants	constant	NOUN
ap-5513	233	19	of	of	ADP
ap-5513	233	20	integration	integration	NOUN
ap-5513	233	21	.	.	PUNCT
ap-5513	234	1	the	the	DET
ap-5513	234	2	output	output	NOUN
ap-5513	234	3	is	be	AUX
ap-5513	234	4	enormous	enormous	ADJ
ap-5513	234	5	and	and	CCONJ
ap-5513	234	6	hence	hence	ADV
ap-5513	234	7	omitted	omit	VERB
ap-5513	234	8	.	.	PUNCT
ap-5513	235	1	the	the	DET
ap-5513	235	2	substitution	substitution	NOUN
ap-5513	235	3	x→	x→	PUNCT
ap-5513	236	1	z	z	NOUN
ap-5513	237	1	+	+	CCONJ
ap-5513	237	2	x0	x0	PROPN
ap-5513	237	3	,	,	PUNCT
ap-5513	237	4	just	just	ADV
ap-5513	237	5	makes	make	VERB
ap-5513	237	6	it	it	PRON
ap-5513	237	7	easier	easy	ADJ
ap-5513	237	8	to	to	PART
ap-5513	237	9	collect	collect	VERB
ap-5513	237	10	as	as	ADP
ap-5513	237	11	powers	power	NOUN
ap-5513	237	12	.	.	PUNCT
ap-5513	238	1	the	the	DET
ap-5513	238	2	terms	term	NOUN
ap-5513	238	3	in	in	ADP
ap-5513	238	4	z−1	z−1	PROPN
ap-5513	238	5	are	be	AUX
ap-5513	238	6	,	,	PUNCT
ap-5513	238	7	2f0	2f0	NUM
ap-5513	238	8	z	z	NOUN
ap-5513	238	9	+	+	NOUN
ap-5513	238	10	24νx0	24νx0	X
ap-5513	238	11	z	z	NOUN
ap-5513	238	12	+	+	NOUN
ap-5513	238	13	312f0νx	312f0νx	NUM
ap-5513	238	14	2	2	NUM
ap-5513	238	15	0	0	NUM
ap-5513	238	16	z	z	NOUN
ap-5513	238	17	+	+	NUM
ap-5513	238	18	336f	336f	NOUN
ap-5513	238	19	2	2	NUM
ap-5513	238	20	0	0	NUM
ap-5513	238	21	νx	νx	NOUN
ap-5513	238	22	3	3	NUM
ap-5513	238	23	0	0	SYM
ap-5513	238	24	z	z	NOUN
ap-5513	238	25	+	+	NOUN
ap-5513	238	26	336f1νx	336f1νx	NUM
ap-5513	238	27	3	3	NUM
ap-5513	238	28	0	0	SYM
ap-5513	238	29	z	z	NOUN
ap-5513	238	30	+	+	X
ap-5513	238	31	+64f	+64f	NUM
ap-5513	238	32	3	3	NUM
ap-5513	238	33	0	0	NUM
ap-5513	238	34	νx	νx	NUM
ap-5513	238	35	4	4	NUM
ap-5513	238	36	0	0	NUM
ap-5513	238	37	z	z	NOUN
ap-5513	238	38	+	+	NOUN
ap-5513	238	39	192f0f1νx	192f0f1νx	NUM
ap-5513	238	40	4	4	NUM
ap-5513	238	41	0	0	NUM
ap-5513	238	42	z	z	NOUN
ap-5513	239	1	+	+	CCONJ
ap-5513	239	2	128f2νx	128f2νx	NUM
ap-5513	239	3	4	4	NUM
ap-5513	239	4	0	0	NUM
ap-5513	239	5	z	z	NOUN
ap-5513	240	1	+	+	NOUN
ap-5513	240	2	......	......	PUNCT
ap-5513	241	1	=	=	SYM
ap-5513	241	2	0	0	X
ap-5513	241	3	.	.	PUNCT
ap-5513	242	1	(	(	PUNCT
ap-5513	242	2	37	37	NUM
ap-5513	242	3	)	)	PUNCT
ap-5513	242	4	this	this	PRON
ap-5513	242	5	is	be	AUX
ap-5513	242	6	solved	solve	VERB
ap-5513	242	7	to	to	PART
ap-5513	242	8	give	give	VERB
ap-5513	242	9	,	,	PUNCT
ap-5513	242	10	64νx4	64νx4	NUM
ap-5513	242	11	0f2	0f2	PUNCT
ap-5513	243	1	→	→	SYM
ap-5513	243	2	−f0	−f0	PROPN
ap-5513	243	3	−	−	PROPN
ap-5513	243	4	12νx0	12νx0	NOUN
ap-5513	244	1	−	−	NOUN
ap-5513	244	2	156f0νx	156f0νx	NUM
ap-5513	244	3	2	2	NUM
ap-5513	244	4	0	0	NUM
ap-5513	245	1	−	−	PROPN
ap-5513	246	1	168f	168f	NUM
ap-5513	246	2	2	2	NUM
ap-5513	246	3	0	0	NUM
ap-5513	246	4	νx	νx	NOUN
ap-5513	246	5	3	3	NUM
ap-5513	246	6	0	0	NUM
ap-5513	247	1	+	+	CCONJ
ap-5513	247	2	−168f1νx	−168f1νx	NOUN
ap-5513	247	3	3	3	NUM
ap-5513	247	4	0	0	NUM
ap-5513	247	5	−	−	PROPN
ap-5513	248	1	32a3	32a3	NUM
ap-5513	248	2	0νx	0νx	ADJ
ap-5513	248	3	4	4	NUM
ap-5513	248	4	0	0	NUM
ap-5513	248	5	−	−	NOUN
ap-5513	248	6	96f0f1νx	96f0f1νx	NUM
ap-5513	248	7	4	4	NUM
ap-5513	248	8	0	0	NUM
ap-5513	248	9	.	.	PUNCT
ap-5513	249	1	(	(	PUNCT
ap-5513	249	2	38	38	NUM
ap-5513	249	3	)	)	PUNCT
ap-5513	249	4	the	the	DET
ap-5513	249	5	expression	expression	NOUN
ap-5513	249	6	for	for	ADP
ap-5513	249	7	f2	f2	PROPN
ap-5513	249	8	is	be	AUX
ap-5513	249	9	substituted	substitute	VERB
ap-5513	249	10	into	into	ADP
ap-5513	249	11	the	the	DET
ap-5513	249	12	major	major	ADJ
ap-5513	249	13	output	output	NOUN
ap-5513	249	14	,	,	PUNCT
ap-5513	249	15	−7f	−7f	PROPN
ap-5513	249	16	2	2	NUM
ap-5513	249	17	0	0	NUM
ap-5513	249	18	+	+	CCONJ
ap-5513	249	19	3f1	3f1	NUM
ap-5513	249	20	−	−	NOUN
ap-5513	249	21	240ν	240ν	NOUN
ap-5513	249	22	−	−	PROPN
ap-5513	250	1	22f0	22f0	NUM
ap-5513	250	2	x0	x0	NUM
ap-5513	250	3	−	−	PROPN
ap-5513	250	4	2880f0νx0	2880f0νx0	NUM
ap-5513	250	5	−	−	NOUN
ap-5513	250	6	3780f	3780f	NUM
ap-5513	250	7	2	2	NUM
ap-5513	250	8	0	0	NUM
ap-5513	250	9	νx	νx	NOUN
ap-5513	250	10	2	2	NUM
ap-5513	250	11	0	0	NUM
ap-5513	250	12	−	−	NOUN
ap-5513	250	13	2220f1νx	2220f1νx	NUM
ap-5513	251	1	2	2	NUM
ap-5513	251	2	0	0	NUM
ap-5513	252	1	+	+	NUM
ap-5513	252	2	−1680f	−1680f	NOUN
ap-5513	252	3	3	3	NUM
ap-5513	252	4	0	0	NUM
ap-5513	252	5	νx	νx	NUM
ap-5513	252	6	3	3	NUM
ap-5513	252	7	0	0	NUM
ap-5513	252	8	−	−	PROPN
ap-5513	252	9	1680f0f1νx	1680f0f1νx	NOUN
ap-5513	252	10	3	3	NUM
ap-5513	252	11	0	0	NUM
ap-5513	252	12	−	−	PROPN
ap-5513	252	13	240f	240f	PROPN
ap-5513	252	14	4	4	NUM
ap-5513	252	15	0	0	NUM
ap-5513	252	16	νx	νx	NUM
ap-5513	252	17	4	4	NUM
ap-5513	252	18	0	0	NUM
ap-5513	252	19	+	+	CCONJ
ap-5513	252	20	−480f	−480f	NOUN
ap-5513	252	21	2	2	NUM
ap-5513	252	22	0f1νx	0f1νx	NUM
ap-5513	252	23	4	4	NUM
ap-5513	252	24	0	0	NUM
ap-5513	252	25	+	+	NUM
ap-5513	252	26	240f	240f	NUM
ap-5513	252	27	2	2	NUM
ap-5513	252	28	1	1	NUM
ap-5513	252	29	νx	νx	NUM
ap-5513	252	30	4	4	NUM
ap-5513	252	31	0	0	NUM
ap-5513	252	32	+	+	CCONJ
ap-5513	252	33	480f3νx	480f3νx	NUM
ap-5513	252	34	4	4	NUM
ap-5513	252	35	0	0	NUM
ap-5513	252	36	=	=	SYM
ap-5513	252	37	0	0	NUM
ap-5513	252	38	,	,	PUNCT
ap-5513	252	39	(	(	PUNCT
ap-5513	252	40	39	39	NUM
ap-5513	252	41	)	)	PUNCT
ap-5513	252	42	and	and	CCONJ
ap-5513	252	43	the	the	DET
ap-5513	252	44	coefficient	coefficient	NOUN
ap-5513	252	45	of	of	ADP
ap-5513	252	46	the	the	DET
ap-5513	252	47	constant	constant	ADJ
ap-5513	252	48	term	term	NOUN
ap-5513	252	49	is	be	AUX
ap-5513	252	50	solved	solve	VERB
ap-5513	252	51	to	to	PART
ap-5513	252	52	give	give	VERB
ap-5513	252	53	f3	f3	PROPN
ap-5513	252	54	as	as	ADP
ap-5513	252	55	,	,	PUNCT
ap-5513	252	56	480νx5	480νx5	NUM
ap-5513	252	57	0f3	0f3	NUM
ap-5513	252	58	=	=	SYM
ap-5513	253	1	22f0	22f0	NUM
ap-5513	253	2	+	+	NUM
ap-5513	253	3	7f	7f	X
ap-5513	253	4	2	2	NUM
ap-5513	253	5	0	0	NUM
ap-5513	253	6	x0	x0	NUM
ap-5513	253	7	−	−	PROPN
ap-5513	253	8	3f1x0	3f1x0	NUM
ap-5513	253	9	+	+	CCONJ
ap-5513	253	10	240νx0	240νx0	NUM
ap-5513	254	1	+	+	CCONJ
ap-5513	254	2	2880f0νx	2880f0νx	NUM
ap-5513	254	3	2	2	NUM
ap-5513	254	4	0	0	NUM
ap-5513	255	1	+	+	CCONJ
ap-5513	255	2	3780f	3780f	NUM
ap-5513	255	3	2	2	NUM
ap-5513	255	4	0	0	NUM
ap-5513	255	5	νx	νx	NUM
ap-5513	255	6	3	3	NUM
ap-5513	255	7	0	0	NUM
ap-5513	255	8	+2220f1νx	+2220f1νx	ADJ
ap-5513	255	9	3	3	NUM
ap-5513	255	10	0	0	NUM
ap-5513	256	1	+	+	NUM
ap-5513	256	2	1680f	1680f	NUM
ap-5513	256	3	3	3	NUM
ap-5513	256	4	0	0	NUM
ap-5513	256	5	νx	νx	NUM
ap-5513	256	6	4	4	NUM
ap-5513	256	7	0	0	NUM
ap-5513	256	8	+	+	CCONJ
ap-5513	256	9	1680f0f1νx	1680f0f1νx	NUM
ap-5513	256	10	4	4	NUM
ap-5513	256	11	0	0	NUM
ap-5513	256	12	+	+	NUM
ap-5513	256	13	240f	240f	NUM
ap-5513	256	14	4	4	NUM
ap-5513	256	15	0	0	NUM
ap-5513	256	16	νx	νx	NOUN
ap-5513	256	17	5	5	NUM
ap-5513	256	18	0	0	NUM
ap-5513	256	19	+	+	CCONJ
ap-5513	256	20	480f	480f	PROPN
ap-5513	256	21	2	2	NUM
ap-5513	256	22	0f1νx	0f1νx	NUM
ap-5513	257	1	5	5	NUM
ap-5513	257	2	0	0	NUM
ap-5513	257	3	−	−	PROPN
ap-5513	257	4	240f	240f	NOUN
ap-5513	257	5	2	2	NUM
ap-5513	257	6	1	1	NUM
ap-5513	257	7	νx	νx	NOUN
ap-5513	257	8	5	5	NUM
ap-5513	257	9	0	0	NUM
ap-5513	257	10	.	.	PUNCT
ap-5513	258	1	(	(	PUNCT
ap-5513	258	2	40	40	NUM
ap-5513	258	3	)	)	PUNCT
ap-5513	258	4	thus	thus	ADV
ap-5513	258	5	,	,	PUNCT
ap-5513	258	6	there	there	PRON
ap-5513	258	7	is	be	VERB
ap-5513	258	8	not	not	PART
ap-5513	258	9	a	a	DET
ap-5513	258	10	problem	problem	NOUN
ap-5513	258	11	with	with	ADP
ap-5513	258	12	the	the	DET
ap-5513	258	13	determination	determination	NOUN
ap-5513	258	14	of	of	ADP
ap-5513	258	15	the	the	DET
ap-5513	258	16	coefficients	coefficient	NOUN
ap-5513	258	17	of	of	ADP
ap-5513	258	18	the	the	DET
ap-5513	258	19	terms	term	NOUN
ap-5513	258	20	in	in	ADP
ap-5513	258	21	the	the	DET
ap-5513	258	22	right	right	ADJ
ap-5513	258	23	painlevé	painlevé	PROPN
ap-5513	258	24	series	series	PROPN
ap-5513	258	25	.	.	PUNCT
ap-5513	259	1	as	as	SCONJ
ap-5513	259	2	certain	certain	ADJ
ap-5513	259	3	terms	term	NOUN
ap-5513	259	4	in	in	ADP
ap-5513	259	5	the	the	DET
ap-5513	259	6	third	third	ADJ
ap-5513	259	7	-	-	PUNCT
ap-5513	259	8	order	order	NOUN
ap-5513	259	9	ode	ode	NOUN
ap-5513	259	10	are	be	AUX
ap-5513	259	11	less	less	ADV
ap-5513	259	12	dominant	dominant	ADJ
ap-5513	259	13	,	,	PUNCT
ap-5513	259	14	there	there	PRON
ap-5513	259	15	can	can	AUX
ap-5513	259	16	not	not	PART
ap-5513	259	17	be	be	AUX
ap-5513	259	18	a	a	DET
ap-5513	259	19	left	left	ADJ
ap-5513	259	20	painlevé	painlevé	NOUN
ap-5513	259	21	series	series	NOUN
ap-5513	259	22	.	.	PUNCT
ap-5513	260	1	the	the	DET
ap-5513	260	2	possibility	possibility	NOUN
ap-5513	260	3	of	of	ADP
ap-5513	260	4	the	the	DET
ap-5513	260	5	existence	existence	NOUN
ap-5513	260	6	of	of	ADP
ap-5513	260	7	a	a	DET
ap-5513	260	8	mixed	mixed	ADJ
ap-5513	260	9	painlevé	painlevé	NOUN
ap-5513	260	10	series	series	NOUN
ap-5513	260	11	is	be	AUX
ap-5513	260	12	moot	moot	ADJ
ap-5513	260	13	due	due	ADP
ap-5513	260	14	to	to	ADP
ap-5513	260	15	the	the	DET
ap-5513	260	16	practical	practical	ADJ
ap-5513	260	17	difficulty	difficulty	NOUN
ap-5513	260	18	of	of	ADP
ap-5513	260	19	calculating	calculate	VERB
ap-5513	260	20	coefficients	coefficient	NOUN
ap-5513	260	21	.	.	PUNCT
ap-5513	261	1	consequently	consequently	ADV
ap-5513	261	2	,	,	PUNCT
ap-5513	261	3	equation	equation	NOUN
ap-5513	261	4	(	(	PUNCT
ap-5513	261	5	15	15	NUM
ap-5513	261	6	)	)	PUNCT
ap-5513	261	7	is	be	AUX
ap-5513	261	8	integrable	integrable	ADJ
ap-5513	261	9	according	accord	VERB
ap-5513	261	10	to	to	ADP
ap-5513	261	11	the	the	DET
ap-5513	261	12	painlevé	painlevé	NOUN
ap-5513	261	13	test	test	NOUN
ap-5513	261	14	105	105	NUM
ap-5513	261	15	a.	a.	NOUN
ap-5513	261	16	k.	k.	PROPN
ap-5513	261	17	halder	halder	PROPN
ap-5513	261	18	,	,	PUNCT
ap-5513	261	19	a.	a.	NOUN
ap-5513	261	20	paliathanasis	paliathanasis	NOUN
ap-5513	261	21	,	,	PUNCT
ap-5513	261	22	p.	p.	NOUN
ap-5513	261	23	g.	g.	PROPN
ap-5513	261	24	l.	l.	PROPN
ap-5513	261	25	leach	leach	PROPN
ap-5513	261	26	acta	acta	PROPN
ap-5513	261	27	polytechnica	polytechnica	PROPN
ap-5513	261	28	6	6	NUM
ap-5513	261	29	.	.	PUNCT
ap-5513	262	1	conservation	conservation	NOUN
ap-5513	262	2	laws	law	NOUN
ap-5513	262	3	the	the	DET
ap-5513	262	4	ibragimov	ibragimov	NOUN
ap-5513	262	5	’s	’s	PART
ap-5513	262	6	theory	theory	NOUN
ap-5513	262	7	of	of	ADP
ap-5513	262	8	nonlinear	nonlinear	ADJ
ap-5513	262	9	self	self	NOUN
ap-5513	262	10	-	-	PUNCT
ap-5513	262	11	adjointness	adjointness	NOUN
ap-5513	262	12	details	detail	NOUN
ap-5513	262	13	the	the	DET
ap-5513	262	14	construction	construction	NOUN
ap-5513	262	15	of	of	ADP
ap-5513	262	16	conservation	conservation	NOUN
ap-5513	262	17	laws	law	NOUN
ap-5513	262	18	for	for	ADP
ap-5513	262	19	a	a	DET
ap-5513	262	20	scalar	scalar	ADJ
ap-5513	262	21	pde[29–31	pde[29–31	NOUN
ap-5513	262	22	]	]	PUNCT
ap-5513	262	23	.	.	PUNCT
ap-5513	263	1	our	our	PRON
ap-5513	263	2	first	first	ADJ
ap-5513	263	3	step	step	NOUN
ap-5513	263	4	is	be	AUX
ap-5513	263	5	to	to	PART
ap-5513	263	6	verify	verify	VERB
ap-5513	263	7	the	the	DET
ap-5513	263	8	self	self	NOUN
ap-5513	263	9	-	-	PUNCT
ap-5513	263	10	adjointness	adjointness	NOUN
ap-5513	263	11	condition	condition	NOUN
ap-5513	263	12	on	on	ADP
ap-5513	263	13	the	the	DET
ap-5513	263	14	various	various	ADJ
ap-5513	263	15	forms	form	NOUN
ap-5513	263	16	of	of	ADP
ap-5513	263	17	beams	beam	NOUN
ap-5513	263	18	and	and	CCONJ
ap-5513	263	19	later	later	ADV
ap-5513	263	20	on	on	ADV
ap-5513	263	21	,	,	PUNCT
ap-5513	263	22	compute	compute	VERB
ap-5513	263	23	the	the	DET
ap-5513	263	24	conservation	conservation	NOUN
ap-5513	263	25	laws	law	NOUN
ap-5513	263	26	.	.	PUNCT
ap-5513	264	1	the	the	DET
ap-5513	264	2	preliminaries	preliminary	NOUN
ap-5513	264	3	can	can	AUX
ap-5513	264	4	be	be	AUX
ap-5513	264	5	easily	easily	ADV
ap-5513	264	6	accessed	access	VERB
ap-5513	264	7	from[29	from[29	NOUN
ap-5513	264	8	]	]	PUNCT
ap-5513	264	9	.	.	PUNCT
ap-5513	265	1	the	the	DET
ap-5513	265	2	main	main	ADJ
ap-5513	265	3	motivation	motivation	NOUN
ap-5513	265	4	behind	behind	ADP
ap-5513	265	5	using	use	VERB
ap-5513	265	6	the	the	DET
ap-5513	265	7	ibragimov	ibragimov	NOUN
ap-5513	265	8	’s	’s	PART
ap-5513	265	9	approach	approach	NOUN
ap-5513	265	10	is	be	AUX
ap-5513	265	11	to	to	PART
ap-5513	265	12	obtain	obtain	VERB
ap-5513	265	13	the	the	DET
ap-5513	265	14	conservation	conservation	NOUN
ap-5513	265	15	laws	law	NOUN
ap-5513	265	16	to	to	PART
ap-5513	265	17	deduce	deduce	VERB
ap-5513	265	18	certain	certain	ADJ
ap-5513	265	19	special	special	ADJ
ap-5513	265	20	solutions	solution	NOUN
ap-5513	265	21	for	for	ADP
ap-5513	265	22	the	the	DET
ap-5513	265	23	beam	beam	NOUN
ap-5513	265	24	equations	equation	NOUN
ap-5513	265	25	following	follow	VERB
ap-5513	265	26	the	the	DET
ap-5513	265	27	methodology	methodology	NOUN
ap-5513	265	28	specified	specify	VERB
ap-5513	265	29	by	by	ADP
ap-5513	265	30	cimpoiasu	cimpoiasu	PROPN
ap-5513	265	31	[	[	X
ap-5513	265	32	32	32	NUM
ap-5513	265	33	]	]	PUNCT
ap-5513	265	34	,	,	PUNCT
ap-5513	265	35	where	where	SCONJ
ap-5513	265	36	the	the	DET
ap-5513	265	37	author	author	NOUN
ap-5513	265	38	have	have	AUX
ap-5513	265	39	used	use	VERB
ap-5513	265	40	the	the	DET
ap-5513	265	41	nonlinear	nonlinear	ADJ
ap-5513	265	42	self	self	NOUN
ap-5513	265	43	-	-	PUNCT
ap-5513	265	44	adjointness	adjointness	NOUN
ap-5513	265	45	method	method	NOUN
ap-5513	265	46	to	to	PART
ap-5513	265	47	compute	compute	VERB
ap-5513	265	48	solutions	solution	NOUN
ap-5513	265	49	for	for	ADP
ap-5513	265	50	the	the	DET
ap-5513	265	51	rossby	rossby	ADJ
ap-5513	265	52	waves	wave	NOUN
ap-5513	265	53	.	.	PUNCT
ap-5513	266	1	the	the	DET
ap-5513	266	2	noether	noether	PROPN
ap-5513	266	3	’s	’s	PART
ap-5513	266	4	theorem	theorem	NOUN
ap-5513	266	5	can	can	AUX
ap-5513	266	6	be	be	AUX
ap-5513	266	7	easily	easily	ADV
ap-5513	266	8	applied	apply	VERB
ap-5513	266	9	to	to	PART
ap-5513	266	10	obtain	obtain	VERB
ap-5513	266	11	the	the	DET
ap-5513	266	12	conserved	conserved	ADJ
ap-5513	266	13	terms	term	NOUN
ap-5513	266	14	but	but	CCONJ
ap-5513	266	15	it	it	PRON
ap-5513	266	16	is	be	AUX
ap-5513	266	17	our	our	PRON
ap-5513	266	18	intuition	intuition	NOUN
ap-5513	266	19	that	that	SCONJ
ap-5513	266	20	the	the	DET
ap-5513	266	21	non	non	ADJ
ap-5513	266	22	-	-	ADJ
ap-5513	266	23	local	local	ADJ
ap-5513	266	24	conserved	conserved	ADJ
ap-5513	266	25	terms	term	NOUN
ap-5513	266	26	as	as	SCONJ
ap-5513	266	27	obtained	obtain	VERB
ap-5513	266	28	using	use	VERB
ap-5513	266	29	the	the	DET
ap-5513	266	30	ibragimov	ibragimov	NOUN
ap-5513	266	31	’s	’s	PART
ap-5513	266	32	method	method	NOUN
ap-5513	266	33	can	can	AUX
ap-5513	266	34	contribute	contribute	VERB
ap-5513	266	35	in	in	ADP
ap-5513	266	36	obtaining	obtain	VERB
ap-5513	266	37	new	new	ADJ
ap-5513	266	38	solutions	solution	NOUN
ap-5513	266	39	in	in	ADP
ap-5513	266	40	a	a	DET
ap-5513	266	41	different	different	ADJ
ap-5513	266	42	subspace	subspace	NOUN
ap-5513	266	43	of	of	ADP
ap-5513	266	44	the	the	DET
ap-5513	266	45	complex	complex	ADJ
ap-5513	266	46	plane	plane	NOUN
ap-5513	266	47	.	.	PUNCT
ap-5513	267	1	the	the	DET
ap-5513	267	2	main	main	ADJ
ap-5513	267	3	objective	objective	NOUN
ap-5513	267	4	is	be	AUX
ap-5513	267	5	to	to	PART
ap-5513	267	6	deduce	deduce	VERB
ap-5513	267	7	new	new	ADJ
ap-5513	267	8	solutions	solution	NOUN
ap-5513	267	9	using	use	VERB
ap-5513	267	10	the	the	DET
ap-5513	267	11	point	point	NOUN
ap-5513	267	12	symmetries	symmetry	NOUN
ap-5513	267	13	,	,	PUNCT
ap-5513	267	14	singularities	singularity	NOUN
ap-5513	267	15	and	and	CCONJ
ap-5513	267	16	conservation	conservation	NOUN
ap-5513	267	17	laws	law	NOUN
ap-5513	267	18	.	.	PUNCT
ap-5513	268	1	for	for	ADP
ap-5513	268	2	instance	instance	NOUN
ap-5513	268	3	,	,	PUNCT
ap-5513	268	4	the	the	DET
ap-5513	268	5	euler	euler	PROPN
ap-5513	268	6	-	-	PUNCT
ap-5513	268	7	bernoulli	bernoulli	NOUN
ap-5513	268	8	equation	equation	NOUN
ap-5513	268	9	does	do	AUX
ap-5513	268	10	imply	imply	VERB
ap-5513	268	11	the	the	DET
ap-5513	268	12	existence	existence	NOUN
ap-5513	268	13	of	of	ADP
ap-5513	268	14	series	series	NOUN
ap-5513	268	15	type	type	NOUN
ap-5513	268	16	solutions	solution	NOUN
ap-5513	268	17	through	through	ADP
ap-5513	268	18	the	the	DET
ap-5513	268	19	method	method	NOUN
ap-5513	268	20	of	of	ADP
ap-5513	268	21	singularity	singularity	NOUN
ap-5513	268	22	analysis	analysis	NOUN
ap-5513	268	23	as	as	SCONJ
ap-5513	268	24	mentioned	mention	VERB
ap-5513	268	25	in	in	ADP
ap-5513	268	26	section	section	NOUN
ap-5513	268	27	5	5	NUM
ap-5513	268	28	for	for	ADP
ap-5513	268	29	equation	equation	NOUN
ap-5513	268	30	(	(	PUNCT
ap-5513	268	31	15	15	NUM
ap-5513	268	32	)	)	PUNCT
ap-5513	268	33	.	.	PUNCT
ap-5513	269	1	let	let	VERB
ap-5513	269	2	the	the	DET
ap-5513	269	3	scalar	scalar	ADJ
ap-5513	269	4	pde	pde	NOUN
ap-5513	269	5	admit	admit	VERB
ap-5513	269	6	the	the	DET
ap-5513	269	7	following	follow	VERB
ap-5513	269	8	generators	generator	NOUN
ap-5513	269	9	of	of	ADP
ap-5513	269	10	the	the	DET
ap-5513	269	11	infinitesimal	infinitesimal	ADJ
ap-5513	269	12	transformation	transformation	NOUN
ap-5513	269	13	,	,	PUNCT
ap-5513	269	14	v	v	NOUN
ap-5513	269	15	=	=	SYM
ap-5513	269	16	ξi(x	ξi(x	X
ap-5513	269	17	,	,	PUNCT
ap-5513	269	18	u	u	NOUN
ap-5513	269	19	,	,	PUNCT
ap-5513	269	20	ui	ui	PROPN
ap-5513	269	21	,	,	PUNCT
ap-5513	269	22	..	..	PUNCT
ap-5513	269	23	)	)	PUNCT
ap-5513	270	1	∂	∂	NUM
ap-5513	270	2	∂xi	∂xi	NOUN
ap-5513	270	3	+	+	CCONJ
ap-5513	270	4	η(x	η(x	PROPN
ap-5513	270	5	,	,	PUNCT
ap-5513	270	6	u	u	NOUN
ap-5513	270	7	,	,	PUNCT
ap-5513	270	8	ui	ui	PROPN
ap-5513	270	9	,	,	PUNCT
ap-5513	270	10	...	...	PUNCT
ap-5513	270	11	)	)	PUNCT
ap-5513	270	12	∂	∂	NUM
ap-5513	270	13	∂u	∂u	PROPN
ap-5513	270	14	.	.	PUNCT
ap-5513	271	1	(	(	PUNCT
ap-5513	271	2	41	41	NUM
ap-5513	271	3	)	)	PUNCT
ap-5513	271	4	then	then	ADV
ap-5513	271	5	the	the	DET
ap-5513	271	6	scalar	scalar	ADJ
ap-5513	271	7	pde	pde	NOUN
ap-5513	271	8	and	and	CCONJ
ap-5513	271	9	its	its	PRON
ap-5513	271	10	adjoint	adjoint	NOUN
ap-5513	271	11	equation	equation	NOUN
ap-5513	271	12	,	,	PUNCT
ap-5513	271	13	as	as	SCONJ
ap-5513	271	14	defined	define	VERB
ap-5513	271	15	above	above	ADV
ap-5513	271	16	,	,	PUNCT
ap-5513	271	17	admits	admit	VERB
ap-5513	271	18	the	the	DET
ap-5513	271	19	conservation	conservation	NOUN
ap-5513	271	20	law	law	NOUN
ap-5513	271	21	ci	ci	NOUN
ap-5513	272	1	=	=	PUNCT
ap-5513	272	2	ξil	ξil	VERB
ap-5513	273	1	+	+	PROPN
ap-5513	273	2	w	w	NOUN
ap-5513	273	3	(	(	PUNCT
ap-5513	273	4	∂l	∂l	NOUN
ap-5513	273	5	∂ui	∂ui	PROPN
ap-5513	273	6	−dj	−dj	NOUN
ap-5513	274	1	(	(	PUNCT
ap-5513	274	2	∂l	∂l	VERB
ap-5513	274	3	∂uij	∂uij	PRON
ap-5513	274	4	)	)	PUNCT
ap-5513	275	1	+	+	ADP
ap-5513	275	2	djdk	djdk	ADJ
ap-5513	275	3	(	(	PUNCT
ap-5513	275	4	∂l	∂l	PROPN
ap-5513	275	5	∂uijk	∂uijk	NOUN
ap-5513	275	6	)	)	PUNCT
ap-5513	275	7	−	−	PROPN
ap-5513	275	8	...	...	PUNCT
ap-5513	275	9	)	)	PUNCT
ap-5513	276	1	+	+	ADJ
ap-5513	276	2	dj(w	dj(w	NUM
ap-5513	276	3	)	)	PUNCT
ap-5513	277	1	(	(	PUNCT
ap-5513	277	2	∂l	∂l	X
ap-5513	277	3	∂uij	∂uij	PRON
ap-5513	277	4	−dk	−dk	INTJ
ap-5513	277	5	(	(	PUNCT
ap-5513	277	6	∂l	∂l	PROPN
ap-5513	277	7	∂uij	∂uij	PRON
ap-5513	277	8	)	)	PUNCT
ap-5513	278	1	+	+	CCONJ
ap-5513	278	2	...	...	PUNCT
ap-5513	278	3	)	)	PUNCT
ap-5513	279	1	+	+	ADV
ap-5513	279	2	djdk(w	djdk(w	NOUN
ap-5513	279	3	)	)	PUNCT
ap-5513	279	4	(	(	PUNCT
ap-5513	279	5	∂l	∂l	X
ap-5513	279	6	∂uijk	∂uijk	X
ap-5513	279	7	−	−	NOUN
ap-5513	279	8	...	...	PUNCT
ap-5513	279	9	)	)	PUNCT
ap-5513	279	10	,	,	PUNCT
ap-5513	279	11	where	where	SCONJ
ap-5513	279	12	w	w	NOUN
ap-5513	279	13	=	=	SYM
ap-5513	279	14	η	η	PROPN
ap-5513	279	15	−	−	PROPN
ap-5513	279	16	ξiui	ξiui	NOUN
ap-5513	279	17	and	and	CCONJ
ap-5513	279	18	l	l	NOUN
ap-5513	279	19	denotes	denote	NOUN
ap-5513	279	20	the	the	DET
ap-5513	279	21	lagarangian	lagarangian	NOUN
ap-5513	279	22	of	of	ADP
ap-5513	279	23	the	the	DET
ap-5513	279	24	corresponding	corresponding	ADJ
ap-5513	279	25	form	form	NOUN
ap-5513	279	26	of	of	ADP
ap-5513	279	27	the	the	DET
ap-5513	279	28	beam	beam	NOUN
ap-5513	279	29	equation	equation	NOUN
ap-5513	279	30	.	.	PUNCT
ap-5513	280	1	for	for	ADP
ap-5513	280	2	the	the	DET
ap-5513	280	3	euler	euler	PROPN
ap-5513	280	4	-	-	PUNCT
ap-5513	280	5	bernoulli	bernoulli	PROPN
ap-5513	280	6	,	,	PUNCT
ap-5513	280	7	rayleigh	rayleigh	PROPN
ap-5513	280	8	and	and	CCONJ
ap-5513	280	9	timshenko	timshenko	ADJ
ap-5513	280	10	-	-	PUNCT
ap-5513	280	11	prescott	prescott	NOUN
ap-5513	280	12	forms	form	NOUN
ap-5513	280	13	the	the	DET
ap-5513	280	14	lagarangians	lagarangian	NOUN
ap-5513	280	15	are	be	AUX
ap-5513	280	16	as	as	SCONJ
ap-5513	280	17	follows	follow	VERB
ap-5513	280	18	l	l	NOUN
ap-5513	280	19	=	=	SYM
ap-5513	281	1	q(t	q(t	PROPN
ap-5513	281	2	,	,	PUNCT
ap-5513	281	3	x)(utt	x)(utt	PROPN
ap-5513	281	4	+	+	NUM
ap-5513	281	5	αβuxxxx	αβuxxxx	NOUN
ap-5513	281	6	)	)	PUNCT
ap-5513	281	7	,	,	PUNCT
ap-5513	281	8	l	l	X
ap-5513	281	9	=	=	PUNCT
ap-5513	282	1	q(t	q(t	PROPN
ap-5513	282	2	,	,	PUNCT
ap-5513	282	3	x)(αβuxxxx	x)(αβuxxxx	PROPN
ap-5513	282	4	+	+	CCONJ
ap-5513	282	5	utt	utt	ADJ
ap-5513	282	6	−	−	PROPN
ap-5513	282	7	βuxxtt	βuxxtt	NOUN
ap-5513	282	8	)	)	PUNCT
ap-5513	282	9	,	,	PUNCT
ap-5513	282	10	l	l	NOUN
ap-5513	282	11	=	=	PUNCT
ap-5513	283	1	q(t	q(t	PROPN
ap-5513	283	2	,	,	PUNCT
ap-5513	283	3	x)(αβuxxxx	x)(αβuxxxx	PROPN
ap-5513	283	4	+	+	NUM
ap-5513	283	5	utt	utt	ADJ
ap-5513	283	6	−	−	NOUN
ap-5513	283	7	β(1	β(1	PROPN
ap-5513	283	8	+	+	NUM
ap-5513	283	9	ε)uxxtt	ε)uxxtt	NOUN
ap-5513	283	10	+	+	CCONJ
ap-5513	283	11	εβutttt	εβutttt	NOUN
ap-5513	283	12	α	α	NOUN
ap-5513	283	13	)	)	PUNCT
ap-5513	283	14	,	,	PUNCT
ap-5513	283	15	where	where	SCONJ
ap-5513	283	16	q(t	q(t	NOUN
ap-5513	283	17	,	,	PUNCT
ap-5513	283	18	x	x	PRON
ap-5513	283	19	)	)	PUNCT
ap-5513	283	20	is	be	AUX
ap-5513	283	21	the	the	DET
ap-5513	283	22	new	new	ADJ
ap-5513	283	23	dependent	dependent	ADJ
ap-5513	283	24	variable	variable	NOUN
ap-5513	283	25	.	.	PUNCT
ap-5513	284	1	to	to	PART
ap-5513	284	2	verify	verify	VERB
ap-5513	284	3	the	the	DET
ap-5513	284	4	non	non	ADJ
ap-5513	284	5	-	-	ADJ
ap-5513	284	6	linear	linear	ADJ
ap-5513	284	7	self	self	NOUN
ap-5513	284	8	adjointness	adjointness	NOUN
ap-5513	284	9	,	,	PUNCT
ap-5513	284	10	the	the	DET
ap-5513	284	11	substitution	substitution	NOUN
ap-5513	284	12	of	of	ADP
ap-5513	284	13	q(t	q(t	PROPN
ap-5513	284	14	,	,	PUNCT
ap-5513	284	15	x	x	NOUN
ap-5513	284	16	)	)	PUNCT
ap-5513	284	17	=	=	SYM
ap-5513	284	18	φ(t	φ(t	PROPN
ap-5513	284	19	,	,	PUNCT
ap-5513	284	20	x	x	X
ap-5513	284	21	,	,	PUNCT
ap-5513	284	22	u	u	NOUN
ap-5513	284	23	)	)	PUNCT
ap-5513	284	24	,	,	PUNCT
ap-5513	284	25	to	to	ADP
ap-5513	284	26	the	the	DET
ap-5513	284	27	adjoint	adjoint	NOUN
ap-5513	284	28	equation	equation	NOUN
ap-5513	284	29	of	of	ADP
ap-5513	284	30	(	(	PUNCT
ap-5513	284	31	8)	8)	NUM
ap-5513	284	32	,	,	PUNCT
ap-5513	284	33	(	(	PUNCT
ap-5513	284	34	9	9	NUM
ap-5513	284	35	)	)	PUNCT
ap-5513	284	36	and	and	CCONJ
ap-5513	284	37	(	(	PUNCT
ap-5513	284	38	10	10	NUM
ap-5513	284	39	)	)	PUNCT
ap-5513	284	40	must	must	AUX
ap-5513	284	41	satisfy	satisfy	VERB
ap-5513	284	42	for	for	ADP
ap-5513	284	43	all	all	DET
ap-5513	284	44	solutions	solution	NOUN
ap-5513	284	45	u	u	NOUN
ap-5513	284	46	of	of	ADP
ap-5513	284	47	those	those	DET
ap-5513	284	48	equations	equation	NOUN
ap-5513	284	49	.	.	PUNCT
ap-5513	285	1	the	the	DET
ap-5513	285	2	possible	possible	ADJ
ap-5513	285	3	values	value	NOUN
ap-5513	285	4	of	of	ADP
ap-5513	285	5	φ(t	φ(t	PROPN
ap-5513	285	6	,	,	PUNCT
ap-5513	285	7	x	x	X
ap-5513	285	8	,	,	PUNCT
ap-5513	285	9	u	u	NOUN
ap-5513	285	10	)	)	PUNCT
ap-5513	285	11	is	be	AUX
ap-5513	285	12	a	a	DET
ap-5513	285	13	constant	constant	ADJ
ap-5513	285	14	term	term	NOUN
ap-5513	285	15	,	,	PUNCT
ap-5513	285	16	let	let	VERB
ap-5513	285	17	us	we	PRON
ap-5513	285	18	say	say	VERB
ap-5513	285	19	,	,	PUNCT
ap-5513	285	20	a0	a0	PROPN
ap-5513	285	21	and	and	CCONJ
ap-5513	285	22	a1u(t	a1u(t	PROPN
ap-5513	285	23	,	,	PUNCT
ap-5513	285	24	x	x	NOUN
ap-5513	285	25	)	)	PUNCT
ap-5513	285	26	+	+	NUM
ap-5513	285	27	a2	a2	NOUN
ap-5513	285	28	,	,	PUNCT
ap-5513	285	29	where	where	SCONJ
ap-5513	285	30	a1	a1	NOUN
ap-5513	285	31	and	and	CCONJ
ap-5513	285	32	a2	a2	PROPN
ap-5513	285	33	are	be	AUX
ap-5513	285	34	arbitrary	arbitrary	ADJ
ap-5513	285	35	constants	constant	NOUN
ap-5513	285	36	.	.	PUNCT
ap-5513	286	1	a	a	DET
ap-5513	286	2	complete	complete	ADJ
ap-5513	286	3	description	description	NOUN
ap-5513	286	4	of	of	ADP
ap-5513	286	5	this	this	DET
ap-5513	286	6	method	method	NOUN
ap-5513	286	7	can	can	AUX
ap-5513	286	8	be	be	AUX
ap-5513	286	9	obtained	obtain	VERB
ap-5513	286	10	from	from	ADP
ap-5513	286	11	[	[	X
ap-5513	286	12	29	29	NUM
ap-5513	286	13	]	]	PUNCT
ap-5513	286	14	.	.	PUNCT
ap-5513	287	1	6.1	6.1	NUM
ap-5513	287	2	.	.	PUNCT
ap-5513	288	1	conservation	conservation	NOUN
ap-5513	288	2	laws	law	NOUN
ap-5513	288	3	for	for	ADP
ap-5513	288	4	the	the	DET
ap-5513	288	5	various	various	ADJ
ap-5513	288	6	form	form	NOUN
ap-5513	288	7	of	of	ADP
ap-5513	288	8	beam	beam	NOUN
ap-5513	288	9	.	.	PUNCT
ap-5513	289	1	with	with	ADP
ap-5513	289	2	respect	respect	NOUN
ap-5513	289	3	to	to	ADP
ap-5513	289	4	each	each	PRON
ap-5513	289	5	of	of	ADP
ap-5513	289	6	the	the	DET
ap-5513	289	7	symmetries	symmetry	NOUN
ap-5513	289	8	in	in	ADP
ap-5513	289	9	(	(	PUNCT
ap-5513	289	10	8)	8)	NUM
ap-5513	289	11	,	,	PUNCT
ap-5513	289	12	we	we	PRON
ap-5513	289	13	compute	compute	VERB
ap-5513	289	14	the	the	DET
ap-5513	289	15	nonzero	nonzero	NOUN
ap-5513	289	16	conservation	conservation	NOUN
ap-5513	289	17	laws	law	NOUN
ap-5513	289	18	.	.	PUNCT
ap-5513	290	1	for	for	ADP
ap-5513	290	2	γ1a	γ1a	PROPN
ap-5513	290	3	,	,	PUNCT
ap-5513	290	4	the	the	DET
ap-5513	290	5	conservation	conservation	NOUN
ap-5513	290	6	components	component	NOUN
ap-5513	290	7	are	be	AUX
ap-5513	290	8	ct	ct	NOUN
ap-5513	290	9	=	=	PUNCT
ap-5513	290	10	uxφt	uxφt	NOUN
ap-5513	290	11	−	−	PROPN
ap-5513	290	12	uxtφ(t	uxtφ(t	PROPN
ap-5513	290	13	,	,	PUNCT
ap-5513	290	14	x	x	X
ap-5513	290	15	,	,	PUNCT
ap-5513	290	16	u	u	NOUN
ap-5513	290	17	)	)	PUNCT
ap-5513	290	18	,	,	PUNCT
ap-5513	290	19	cx	cx	PROPN
ap-5513	290	20	=	=	SYM
ap-5513	290	21	φ(t	φ(t	PROPN
ap-5513	290	22	,	,	PUNCT
ap-5513	290	23	x	x	X
ap-5513	290	24	,	,	PUNCT
ap-5513	290	25	u)(utt	u)(utt	ADJ
ap-5513	290	26	+	+	CCONJ
ap-5513	290	27	αβuxxxx	αβuxxxx	NOUN
ap-5513	290	28	)	)	PUNCT
ap-5513	290	29	+	+	CCONJ
ap-5513	290	30	αβuxφxxxx	αβuxφxxxx	ADJ
ap-5513	290	31	−	−	NOUN
ap-5513	290	32	αβuxxφxx	αβuxxφxx	NOUN
ap-5513	290	33	+	+	CCONJ
ap-5513	290	34	αβφxuxxx	αβφxuxxx	PROPN
ap-5513	290	35	−	−	PROPN
ap-5513	290	36	uxxxxφ(t	uxxxxφ(t	PROPN
ap-5513	290	37	,	,	PUNCT
ap-5513	290	38	x	x	NOUN
ap-5513	290	39	,	,	PUNCT
ap-5513	290	40	u	u	NOUN
ap-5513	290	41	)	)	PUNCT
ap-5513	290	42	.	.	PUNCT
ap-5513	291	1	(	(	PUNCT
ap-5513	291	2	42	42	NUM
ap-5513	291	3	)	)	PUNCT
ap-5513	291	4	for	for	ADP
ap-5513	291	5	γ2a	γ2a	NOUN
ap-5513	291	6	,	,	PUNCT
ap-5513	291	7	ct	ct	PROPN
ap-5513	291	8	=	=	SYM
ap-5513	291	9	φ(t	φ(t	PROPN
ap-5513	291	10	,	,	PUNCT
ap-5513	291	11	x	x	X
ap-5513	291	12	,	,	PUNCT
ap-5513	291	13	u)(utt	u)(utt	ADJ
ap-5513	291	14	+	+	CCONJ
ap-5513	291	15	αβuxxxx	αβuxxxx	NOUN
ap-5513	291	16	)	)	PUNCT
ap-5513	291	17	+	+	CCONJ
ap-5513	291	18	utφt	utφt	ADJ
ap-5513	291	19	−	−	PROPN
ap-5513	291	20	uttφ(t	uttφ(t	PROPN
ap-5513	291	21	,	,	PUNCT
ap-5513	291	22	x	x	NOUN
ap-5513	291	23	,	,	PUNCT
ap-5513	291	24	u	u	NOUN
ap-5513	291	25	)	)	PUNCT
ap-5513	291	26	,	,	PUNCT
ap-5513	291	27	cx	cx	PROPN
ap-5513	291	28	=	=	SYM
ap-5513	292	1	αβ(utφxxx	αβ(utφxxx	NUM
ap-5513	292	2	−	−	NOUN
ap-5513	292	3	uxtφxx	uxtφxx	PROPN
ap-5513	292	4	−	−	PROPN
ap-5513	292	5	uxxtφx	uxxtφx	ADJ
ap-5513	292	6	−	−	NOUN
ap-5513	292	7	uxxxtφ(t	uxxxtφ(t	PROPN
ap-5513	292	8	,	,	PUNCT
ap-5513	292	9	x	x	NOUN
ap-5513	292	10	,	,	PUNCT
ap-5513	292	11	u	u	NOUN
ap-5513	292	12	)	)	PUNCT
ap-5513	292	13	)	)	PUNCT
ap-5513	292	14	.	.	PUNCT
ap-5513	293	1	(	(	PUNCT
ap-5513	293	2	43	43	NUM
ap-5513	293	3	)	)	PUNCT
ap-5513	293	4	106	106	NUM
ap-5513	293	5	vol	vol	NOUN
ap-5513	293	6	.	.	PUNCT
ap-5513	294	1	60	60	NUM
ap-5513	294	2	no	no	NOUN
ap-5513	294	3	.	.	PUNCT
ap-5513	295	1	2/2020	2/2020	NUM
ap-5513	295	2	similarity	similarity	NOUN
ap-5513	295	3	solutions	solution	NOUN
ap-5513	295	4	and	and	CCONJ
ap-5513	295	5	conservation	conservation	NOUN
ap-5513	295	6	laws	law	NOUN
ap-5513	295	7	for	for	ADP
ap-5513	295	8	the	the	DET
ap-5513	295	9	beam	beam	NOUN
ap-5513	295	10	equations	equation	NOUN
ap-5513	295	11	.	.	PUNCT
ap-5513	295	12	.	.	PUNCT
ap-5513	295	13	.	.	PUNCT
ap-5513	296	1	for	for	ADP
ap-5513	296	2	γ3a	γ3a	VERB
ap-5513	296	3	,	,	PUNCT
ap-5513	296	4	ct	ct	NUM
ap-5513	296	5	=	=	SYM
ap-5513	296	6	−	−	PROPN
ap-5513	296	7	uφt	uφt	NOUN
ap-5513	296	8	+	+	CCONJ
ap-5513	296	9	utφ(t	utφ(t	PROPN
ap-5513	296	10	,	,	PUNCT
ap-5513	296	11	x	x	NOUN
ap-5513	296	12	,	,	PUNCT
ap-5513	296	13	u	u	NOUN
ap-5513	296	14	)	)	PUNCT
ap-5513	296	15	,	,	PUNCT
ap-5513	296	16	cx	cx	PROPN
ap-5513	296	17	=	=	PUNCT
ap-5513	297	1	αβ(uxφxx	αβ(uxφxx	PROPN
ap-5513	297	2	−	−	PROPN
ap-5513	297	3	uφxxx	uφxxx	ADJ
ap-5513	297	4	+	+	CCONJ
ap-5513	297	5	uxxφx	uxxφx	ADJ
ap-5513	297	6	+	+	CCONJ
ap-5513	297	7	uxxxx	uxxxx	ADJ
ap-5513	297	8	)	)	PUNCT
ap-5513	297	9	.	.	PUNCT
ap-5513	298	1	(	(	PUNCT
ap-5513	298	2	44	44	NUM
ap-5513	298	3	)	)	PUNCT
ap-5513	298	4	for	for	ADP
ap-5513	298	5	γ4a	γ4a	NOUN
ap-5513	298	6	,	,	PUNCT
ap-5513	298	7	ct	ct	PROPN
ap-5513	298	8	=	=	SYM
ap-5513	298	9	2t(φ(t	2t(φ(t	NUM
ap-5513	298	10	,	,	PUNCT
ap-5513	298	11	x	x	X
ap-5513	298	12	,	,	PUNCT
ap-5513	298	13	u)(utt	u)(utt	ADJ
ap-5513	298	14	+	+	CCONJ
ap-5513	298	15	αβuxxxx	αβuxxxx	NOUN
ap-5513	298	16	)	)	PUNCT
ap-5513	298	17	)	)	PUNCT
ap-5513	299	1	+	+	PUNCT
ap-5513	299	2	φt(2tut	φt(2tut	PUNCT
ap-5513	300	1	+	+	CCONJ
ap-5513	300	2	xux)−	xux)−	PROPN
ap-5513	300	3	φ(t	φ(t	PROPN
ap-5513	300	4	,	,	PUNCT
ap-5513	300	5	x	x	X
ap-5513	300	6	,	,	PUNCT
ap-5513	300	7	u)(2tutt	u)(2tutt	X
ap-5513	300	8	+	+	NUM
ap-5513	300	9	2ut	2ut	NOUN
ap-5513	300	10	+	+	CCONJ
ap-5513	300	11	xuxt	xuxt	PROPN
ap-5513	300	12	)	)	PUNCT
ap-5513	300	13	,	,	PUNCT
ap-5513	300	14	cx	cx	PROPN
ap-5513	300	15	=	=	PUNCT
ap-5513	300	16	x(φ(t	x(φ(t	PROPN
ap-5513	300	17	,	,	PUNCT
ap-5513	300	18	x	x	X
ap-5513	300	19	,	,	PUNCT
ap-5513	300	20	u)(utt	u)(utt	ADJ
ap-5513	300	21	+	+	CCONJ
ap-5513	300	22	αβuxxxx	αβuxxxx	NOUN
ap-5513	300	23	)	)	PUNCT
ap-5513	300	24	)	)	PUNCT
ap-5513	301	1	+	+	CCONJ
ap-5513	302	1	αβφxxx(2tut	αβφxxx(2tut	PUNCT
ap-5513	303	1	+	+	CCONJ
ap-5513	303	2	xux)−	xux)−	PROPN
ap-5513	303	3	αβφxx(2tuxt	αβφxx(2tuxt	NOUN
ap-5513	303	4	+	+	CCONJ
ap-5513	303	5	xuxx	xuxx	NOUN
ap-5513	303	6	+	+	CCONJ
ap-5513	303	7	ux	ux	ADJ
ap-5513	303	8	)	)	PUNCT
ap-5513	303	9	+	+	NUM
ap-5513	303	10	αβφx(2tuxxt	αβφx(2tuxxt	NOUN
ap-5513	303	11	+	+	CCONJ
ap-5513	303	12	xuxxx	xuxxx	PROPN
ap-5513	304	1	+	+	CCONJ
ap-5513	304	2	2uxx)−	2uxx)−	NUM
ap-5513	304	3	αβφ(t	αβφ(t	NUM
ap-5513	304	4	,	,	PUNCT
ap-5513	304	5	x	x	PRON
ap-5513	304	6	,	,	PUNCT
ap-5513	304	7	u)(2tuxxxt	u)(2tuxxxt	PUNCT
ap-5513	304	8	+	+	SYM
ap-5513	304	9	xuxxxx	xuxxxx	NOUN
ap-5513	304	10	+	+	NUM
ap-5513	304	11	3uxxx	3uxxx	NUM
ap-5513	304	12	)	)	PUNCT
ap-5513	304	13	.	.	PUNCT
ap-5513	305	1	(	(	PUNCT
ap-5513	305	2	45	45	NUM
ap-5513	305	3	)	)	PUNCT
ap-5513	305	4	f0r	f0r	NOUN
ap-5513	305	5	γ5a	γ5a	NOUN
ap-5513	305	6	,	,	PUNCT
ap-5513	305	7	ct	ct	NUM
ap-5513	305	8	=	=	SYM
ap-5513	305	9	−	−	NOUN
ap-5513	305	10	a(t	a(t	NOUN
ap-5513	305	11	,	,	PUNCT
ap-5513	305	12	x)φt	x)φt	PROPN
ap-5513	305	13	+	+	CCONJ
ap-5513	305	14	atφ(t	atφ(t	PROPN
ap-5513	305	15	,	,	PUNCT
ap-5513	305	16	x	x	NOUN
ap-5513	305	17	,	,	PUNCT
ap-5513	305	18	u	u	NOUN
ap-5513	305	19	)	)	PUNCT
ap-5513	305	20	,	,	PUNCT
ap-5513	305	21	cx	cx	PROPN
ap-5513	305	22	=	=	PUNCT
ap-5513	305	23	−	−	PROPN
ap-5513	305	24	αβa(t	αβa(t	PROPN
ap-5513	305	25	,	,	PUNCT
ap-5513	305	26	x)φxxx	x)φxxx	PROPN
ap-5513	306	1	+	+	CCONJ
ap-5513	306	2	αβaxφxx	αβaxφxx	PROPN
ap-5513	306	3	−	−	PROPN
ap-5513	306	4	αβaxxφx	αβaxxφx	PROPN
ap-5513	306	5	+	+	CCONJ
ap-5513	306	6	φ(t	φ(t	PROPN
ap-5513	306	7	,	,	PUNCT
ap-5513	306	8	x	x	NOUN
ap-5513	306	9	,	,	PUNCT
ap-5513	306	10	u)axxx	u)axxx	PROPN
ap-5513	306	11	.	.	PUNCT
ap-5513	307	1	(	(	PUNCT
ap-5513	307	2	46	46	NUM
ap-5513	307	3	)	)	PUNCT
ap-5513	307	4	next	next	ADV
ap-5513	307	5	,	,	PUNCT
ap-5513	307	6	we	we	PRON
ap-5513	307	7	compute	compute	VERB
ap-5513	307	8	the	the	DET
ap-5513	307	9	conservation	conservation	NOUN
ap-5513	307	10	laws	law	NOUN
ap-5513	307	11	of	of	ADP
ap-5513	307	12	equation	equation	NOUN
ap-5513	307	13	(	(	PUNCT
ap-5513	307	14	9	9	NUM
ap-5513	307	15	)	)	PUNCT
ap-5513	307	16	,	,	PUNCT
ap-5513	307	17	with	with	ADP
ap-5513	307	18	respect	respect	NOUN
ap-5513	307	19	to	to	ADP
ap-5513	307	20	its	its	PRON
ap-5513	307	21	symmetries	symmetry	NOUN
ap-5513	307	22	.	.	PUNCT
ap-5513	308	1	γ1b	γ1b	PRON
ap-5513	308	2	leads	lead	VERB
ap-5513	308	3	to	to	ADP
ap-5513	308	4	the	the	DET
ap-5513	308	5	following	following	ADJ
ap-5513	308	6	conserved	conserved	ADJ
ap-5513	308	7	components	component	NOUN
ap-5513	308	8	,	,	PUNCT
ap-5513	308	9	ct	ct	PROPN
ap-5513	308	10	=	=	SYM
ap-5513	308	11	φ(t	φ(t	PROPN
ap-5513	308	12	,	,	PUNCT
ap-5513	308	13	x	x	X
ap-5513	308	14	,	,	PUNCT
ap-5513	308	15	u)(αβuxxxx	u)(αβuxxxx	PROPN
ap-5513	308	16	+	+	CCONJ
ap-5513	308	17	utt	utt	ADJ
ap-5513	308	18	−	−	NOUN
ap-5513	308	19	βuxxtt	βuxxtt	NOUN
ap-5513	308	20	)	)	PUNCT
ap-5513	309	1	+	+	CCONJ
ap-5513	309	2	utφt	utφt	ADJ
ap-5513	309	3	−	−	PROPN
ap-5513	309	4	φ(t	φ(t	PROPN
ap-5513	309	5	,	,	PUNCT
ap-5513	309	6	x	x	NOUN
ap-5513	309	7	,	,	PUNCT
ap-5513	309	8	u)utt	u)utt	PROPN
ap-5513	309	9	,	,	PUNCT
ap-5513	309	10	cx	cx	NOUN
ap-5513	309	11	=	=	SYM
ap-5513	309	12	αβ(utφxxx	αβ(utφxxx	PROPN
ap-5513	309	13	−	−	NOUN
ap-5513	309	14	uxtφxx	uxtφxx	NOUN
ap-5513	309	15	+	+	CCONJ
ap-5513	309	16	uxxtφx	uxxtφx	ADJ
ap-5513	309	17	−	−	PROPN
ap-5513	309	18	uxxxtφ(t	uxxxtφ(t	PROPN
ap-5513	309	19	,	,	PUNCT
ap-5513	309	20	x	x	NOUN
ap-5513	309	21	,	,	PUNCT
ap-5513	309	22	u	u	NOUN
ap-5513	309	23	)	)	PUNCT
ap-5513	309	24	)	)	PUNCT
ap-5513	309	25	.	.	PUNCT
ap-5513	310	1	(	(	PUNCT
ap-5513	310	2	47	47	NUM
ap-5513	310	3	)	)	PUNCT
ap-5513	310	4	for	for	ADP
ap-5513	310	5	γ2b	γ2b	PROPN
ap-5513	310	6	,	,	PUNCT
ap-5513	310	7	ct	ct	PROPN
ap-5513	310	8	=	=	PROPN
ap-5513	310	9	uxφt	uxφt	NOUN
ap-5513	310	10	−	−	PROPN
ap-5513	310	11	uxtφ(t	uxtφ(t	PROPN
ap-5513	310	12	,	,	PUNCT
ap-5513	310	13	x	x	X
ap-5513	310	14	,	,	PUNCT
ap-5513	310	15	u	u	NOUN
ap-5513	310	16	)	)	PUNCT
ap-5513	310	17	,	,	PUNCT
ap-5513	310	18	cx	cx	PROPN
ap-5513	310	19	=	=	SYM
ap-5513	310	20	φ(t	φ(t	PROPN
ap-5513	310	21	,	,	PUNCT
ap-5513	310	22	x	x	X
ap-5513	310	23	,	,	PUNCT
ap-5513	310	24	u)(αβuxxxx	u)(αβuxxxx	PROPN
ap-5513	310	25	+	+	CCONJ
ap-5513	310	26	utt	utt	ADJ
ap-5513	310	27	−	−	NOUN
ap-5513	310	28	βuxxtt	βuxxtt	NOUN
ap-5513	310	29	)	)	PUNCT
ap-5513	311	1	+	+	CCONJ
ap-5513	311	2	αβ(uxφxxx	αβ(uxφxxx	ADV
ap-5513	311	3	−	−	PROPN
ap-5513	311	4	uxxφxx	uxxφxx	ADJ
ap-5513	311	5	+	+	CCONJ
ap-5513	311	6	uxxxφx	uxxxφx	ADJ
ap-5513	311	7	−	−	PROPN
ap-5513	311	8	φ(t	φ(t	PROPN
ap-5513	311	9	,	,	PUNCT
ap-5513	311	10	x	x	NOUN
ap-5513	311	11	,	,	PUNCT
ap-5513	311	12	u)uxxxx	u)uxxxx	NOUN
ap-5513	311	13	)	)	PUNCT
ap-5513	311	14	.	.	PUNCT
ap-5513	312	1	(	(	PUNCT
ap-5513	312	2	48	48	NUM
ap-5513	312	3	)	)	PUNCT
ap-5513	312	4	for	for	ADP
ap-5513	312	5	γ3b	γ3b	NOUN
ap-5513	312	6	,	,	PUNCT
ap-5513	312	7	ct	ct	PROPN
ap-5513	312	8	=	=	SYM
ap-5513	312	9	utφ(t	utφ(t	PROPN
ap-5513	312	10	,	,	PUNCT
ap-5513	312	11	x	x	PRON
ap-5513	312	12	,	,	PUNCT
ap-5513	312	13	u)−	u)−	PROPN
ap-5513	312	14	uφt	uφt	PROPN
ap-5513	312	15	,	,	PUNCT
ap-5513	312	16	cx	cx	PROPN
ap-5513	313	1	=	=	PUNCT
ap-5513	314	1	αβ(uxφxx	αβ(uxφxx	PROPN
ap-5513	314	2	−	−	ADP
ap-5513	314	3	uφxxx	uφxxx	ADJ
ap-5513	314	4	−	−	NOUN
ap-5513	314	5	uxxφx	uxxφx	ADJ
ap-5513	314	6	+	+	CCONJ
ap-5513	314	7	uxxxφ(t	uxxxφ(t	ADJ
ap-5513	314	8	,	,	PUNCT
ap-5513	314	9	x	x	NOUN
ap-5513	314	10	,	,	PUNCT
ap-5513	314	11	u	u	NOUN
ap-5513	314	12	)	)	PUNCT
ap-5513	314	13	)	)	PUNCT
ap-5513	314	14	.	.	PUNCT
ap-5513	315	1	(	(	PUNCT
ap-5513	315	2	49	49	NUM
ap-5513	315	3	)	)	PUNCT
ap-5513	315	4	for	for	ADP
ap-5513	315	5	γ4b	γ4b	PROPN
ap-5513	315	6	,	,	PUNCT
ap-5513	315	7	ct	ct	PROPN
ap-5513	315	8	=	=	SYM
ap-5513	315	9	btφ(t	btφ(t	PROPN
ap-5513	315	10	,	,	PUNCT
ap-5513	315	11	x	x	PRON
ap-5513	315	12	,	,	PUNCT
ap-5513	315	13	u)−	u)−	PROPN
ap-5513	315	14	b(t	b(t	PROPN
ap-5513	315	15	,	,	PUNCT
ap-5513	315	16	x)φt	x)φt	PROPN
ap-5513	315	17	,	,	PUNCT
ap-5513	315	18	cx	cx	PROPN
ap-5513	315	19	=	=	PUNCT
ap-5513	316	1	αβ(bxφxx	αβ(bxφxx	PROPN
ap-5513	316	2	−	−	PROPN
ap-5513	316	3	b(t	b(t	PROPN
ap-5513	316	4	,	,	PUNCT
ap-5513	316	5	x)φxxx	x)φxxx	PROPN
ap-5513	316	6	−	−	PROPN
ap-5513	316	7	bxxφx	bxxφx	VERB
ap-5513	316	8	+	+	CCONJ
ap-5513	316	9	bxxxφ(t	bxxxφ(t	NOUN
ap-5513	316	10	,	,	PUNCT
ap-5513	316	11	x	x	NOUN
ap-5513	316	12	,	,	PUNCT
ap-5513	316	13	u	u	NOUN
ap-5513	316	14	)	)	PUNCT
ap-5513	316	15	)	)	PUNCT
ap-5513	316	16	.	.	PUNCT
ap-5513	317	1	(	(	PUNCT
ap-5513	317	2	50	50	NUM
ap-5513	317	3	)	)	PUNCT
ap-5513	317	4	for	for	ADP
ap-5513	317	5	the	the	DET
ap-5513	317	6	timoshenko	timoshenko	ADJ
ap-5513	317	7	-	-	PUNCT
ap-5513	317	8	prescott	prescott	NOUN
ap-5513	317	9	form	form	NOUN
ap-5513	317	10	of	of	ADP
ap-5513	317	11	the	the	DET
ap-5513	317	12	beam	beam	NOUN
ap-5513	317	13	(	(	PUNCT
ap-5513	317	14	10	10	NUM
ap-5513	317	15	)	)	PUNCT
ap-5513	317	16	,	,	PUNCT
ap-5513	317	17	the	the	DET
ap-5513	317	18	conserved	conserved	ADJ
ap-5513	317	19	components	component	NOUN
ap-5513	317	20	are	be	AUX
ap-5513	317	21	as	as	SCONJ
ap-5513	317	22	follows	follow	VERB
ap-5513	317	23	:	:	PUNCT
ap-5513	317	24	for	for	ADP
ap-5513	317	25	γ1c	γ1c	PROPN
ap-5513	317	26	,	,	PUNCT
ap-5513	317	27	ct	ct	PROPN
ap-5513	317	28	=	=	SYM
ap-5513	317	29	φ(t	φ(t	PROPN
ap-5513	317	30	,	,	PUNCT
ap-5513	317	31	x	x	X
ap-5513	317	32	,	,	PUNCT
ap-5513	317	33	u	u	NOUN
ap-5513	317	34	)	)	PUNCT
ap-5513	317	35	(	(	PUNCT
ap-5513	317	36	αβuxxxx	αβuxxxx	NOUN
ap-5513	317	37	+	+	CCONJ
ap-5513	317	38	utt	utt	ADJ
ap-5513	317	39	−	−	NOUN
ap-5513	317	40	β(1	β(1	PROPN
ap-5513	317	41	+	+	NUM
ap-5513	317	42	ε)uxxtt	ε)uxxtt	NOUN
ap-5513	317	43	+	+	CCONJ
ap-5513	317	44	εβutttt	εβutttt	NOUN
ap-5513	317	45	α	α	NOUN
ap-5513	317	46	)	)	PUNCT
ap-5513	318	1	+	+	CCONJ
ap-5513	318	2	ut	ut	PROPN
ap-5513	318	3	(	(	PUNCT
ap-5513	318	4	φt	φt	ADP
ap-5513	318	5	+	+	CCONJ
ap-5513	318	6	εβφttt	εβφttt	NOUN
ap-5513	318	7	α	α	NOUN
ap-5513	318	8	)	)	PUNCT
ap-5513	318	9	−	−	PROPN
ap-5513	318	10	utt	utt	PROPN
ap-5513	318	11	(	(	PUNCT
ap-5513	318	12	φ(t	φ(t	PROPN
ap-5513	318	13	,	,	PUNCT
ap-5513	318	14	x	x	X
ap-5513	318	15	,	,	PUNCT
ap-5513	318	16	u	u	NOUN
ap-5513	318	17	)	)	PUNCT
ap-5513	318	18	+	+	NUM
ap-5513	318	19	εβφtt	εβφtt	NOUN
ap-5513	318	20	α	α	NOUN
ap-5513	318	21	)	)	PUNCT
ap-5513	319	1	+	+	CCONJ
ap-5513	319	2	uttt	uttt	ADJ
ap-5513	319	3	εβφt	εβφt	NOUN
ap-5513	319	4	α	α	NOUN
ap-5513	319	5	−	−	PROPN
ap-5513	319	6	utttt	utttt	NOUN
ap-5513	319	7	εβφ(t	εβφ(t	PROPN
ap-5513	319	8	,	,	PUNCT
ap-5513	319	9	x	x	NOUN
ap-5513	319	10	,	,	PUNCT
ap-5513	319	11	u	u	NOUN
ap-5513	319	12	)	)	PUNCT
ap-5513	319	13	α	α	PROPN
ap-5513	319	14	,	,	PUNCT
ap-5513	319	15	cx	cx	PROPN
ap-5513	319	16	=	=	SYM
ap-5513	319	17	αβ(utφxxx	αβ(utφxxx	NUM
ap-5513	319	18	−	−	NOUN
ap-5513	319	19	uxtφxx	uxtφxx	NOUN
ap-5513	319	20	+	+	CCONJ
ap-5513	319	21	uxxtφx	uxxtφx	ADJ
ap-5513	319	22	−	−	PROPN
ap-5513	319	23	uxxxtφ(t	uxxxtφ(t	PROPN
ap-5513	319	24	,	,	PUNCT
ap-5513	319	25	x	x	NOUN
ap-5513	319	26	,	,	PUNCT
ap-5513	319	27	u	u	NOUN
ap-5513	319	28	)	)	PUNCT
ap-5513	319	29	)	)	PUNCT
ap-5513	319	30	.	.	PUNCT
ap-5513	320	1	(	(	PUNCT
ap-5513	320	2	51	51	NUM
ap-5513	320	3	)	)	PUNCT
ap-5513	320	4	107	107	NUM
ap-5513	320	5	a.	a.	NOUN
ap-5513	320	6	k.	k.	PROPN
ap-5513	320	7	halder	halder	PROPN
ap-5513	320	8	,	,	PUNCT
ap-5513	320	9	a.	a.	NOUN
ap-5513	320	10	paliathanasis	paliathanasis	NOUN
ap-5513	320	11	,	,	PUNCT
ap-5513	320	12	p.	p.	NOUN
ap-5513	320	13	g.	g.	PROPN
ap-5513	320	14	l.	l.	PROPN
ap-5513	320	15	leach	leach	PROPN
ap-5513	320	16	acta	acta	PROPN
ap-5513	320	17	polytechnica	polytechnica	PROPN
ap-5513	320	18	for	for	ADP
ap-5513	320	19	γ2c	γ2c	NOUN
ap-5513	320	20	,	,	PUNCT
ap-5513	320	21	ct	ct	PROPN
ap-5513	320	22	=	=	SYM
ap-5513	320	23	ux	ux	PROPN
ap-5513	320	24	(	(	PUNCT
ap-5513	320	25	φt	φt	NOUN
ap-5513	320	26	+	+	CCONJ
ap-5513	320	27	φtttεβ	φtttεβ	ADV
ap-5513	320	28	α	α	NOUN
ap-5513	320	29	)	)	PUNCT
ap-5513	320	30	−	−	PROPN
ap-5513	320	31	uxt	uxt	NOUN
ap-5513	320	32	(	(	PUNCT
ap-5513	320	33	φ(t	φ(t	PROPN
ap-5513	320	34	,	,	PUNCT
ap-5513	320	35	x	x	X
ap-5513	320	36	,	,	PUNCT
ap-5513	320	37	u	u	NOUN
ap-5513	320	38	)	)	PUNCT
ap-5513	320	39	+	+	CCONJ
ap-5513	320	40	φttεβ	φttεβ	ADJ
ap-5513	320	41	α	α	NOUN
ap-5513	320	42	)	)	PUNCT
ap-5513	321	1	+	+	CCONJ
ap-5513	321	2	uxtt	uxtt	ADJ
ap-5513	321	3	φtεβ	φtεβ	NOUN
ap-5513	321	4	α	α	NOUN
ap-5513	321	5	−	−	PROPN
ap-5513	321	6	uxttt	uxttt	PROPN
ap-5513	321	7	εβ	εβ	PROPN
ap-5513	321	8	α	α	PROPN
ap-5513	321	9	,	,	PUNCT
ap-5513	321	10	cx	cx	PROPN
ap-5513	321	11	=	=	SYM
ap-5513	321	12	φ(t	φ(t	PROPN
ap-5513	321	13	,	,	PUNCT
ap-5513	321	14	x	x	X
ap-5513	321	15	,	,	PUNCT
ap-5513	321	16	u	u	NOUN
ap-5513	321	17	)	)	PUNCT
ap-5513	321	18	(	(	PUNCT
ap-5513	321	19	αβuxxxx	αβuxxxx	NOUN
ap-5513	321	20	+	+	CCONJ
ap-5513	321	21	utt	utt	ADJ
ap-5513	321	22	−	−	NOUN
ap-5513	321	23	β(1	β(1	PROPN
ap-5513	321	24	+	+	NUM
ap-5513	321	25	ε)uxxtt	ε)uxxtt	NOUN
ap-5513	321	26	+	+	CCONJ
ap-5513	321	27	εβutttt	εβutttt	NOUN
ap-5513	321	28	α	α	NOUN
ap-5513	321	29	)	)	PUNCT
ap-5513	322	1	+	+	CCONJ
ap-5513	322	2	αβ(uxφxxx	αβ(uxφxxx	ADV
ap-5513	322	3	−	−	PROPN
ap-5513	322	4	uxxφxx	uxxφxx	ADJ
ap-5513	322	5	+	+	CCONJ
ap-5513	322	6	uxxxφx	uxxxφx	ADJ
ap-5513	322	7	−	−	PROPN
ap-5513	322	8	φ(t	φ(t	PROPN
ap-5513	322	9	,	,	PUNCT
ap-5513	322	10	x	x	NOUN
ap-5513	322	11	,	,	PUNCT
ap-5513	322	12	u)uxxxx	u)uxxxx	NOUN
ap-5513	322	13	)	)	PUNCT
ap-5513	322	14	.	.	PUNCT
ap-5513	323	1	(	(	PUNCT
ap-5513	323	2	52	52	NUM
ap-5513	323	3	)	)	PUNCT
ap-5513	323	4	for	for	ADP
ap-5513	323	5	γ3c	γ3c	PROPN
ap-5513	323	6	,	,	PUNCT
ap-5513	323	7	ct	ct	NUM
ap-5513	323	8	=	=	SYM
ap-5513	323	9	−	−	PROPN
ap-5513	323	10	u	u	NOUN
ap-5513	323	11	(	(	PUNCT
ap-5513	323	12	φt	φt	ADP
ap-5513	323	13	+	+	CCONJ
ap-5513	323	14	εβφttt	εβφttt	NOUN
ap-5513	323	15	α	α	NOUN
ap-5513	323	16	)	)	PUNCT
ap-5513	324	1	+	+	CCONJ
ap-5513	324	2	ut	ut	PROPN
ap-5513	324	3	(	(	PUNCT
ap-5513	324	4	φ(t	φ(t	PROPN
ap-5513	324	5	,	,	PUNCT
ap-5513	324	6	x	x	X
ap-5513	324	7	,	,	PUNCT
ap-5513	324	8	u	u	NOUN
ap-5513	324	9	)	)	PUNCT
ap-5513	324	10	+	+	CCONJ
ap-5513	324	11	εβφtt	εβφtt	ADJ
ap-5513	324	12	α	α	NOUN
ap-5513	324	13	)	)	PUNCT
ap-5513	324	14	−	−	PROPN
ap-5513	324	15	utt	utt	ADJ
ap-5513	324	16	εβφt	εβφt	NOUN
ap-5513	324	17	α	α	NOUN
ap-5513	324	18	+	+	CCONJ
ap-5513	324	19	uttt	uttt	PROPN
ap-5513	324	20	εβφ(t	εβφ(t	PROPN
ap-5513	324	21	,	,	PUNCT
ap-5513	324	22	x	x	NOUN
ap-5513	324	23	,	,	PUNCT
ap-5513	324	24	u	u	NOUN
ap-5513	324	25	)	)	PUNCT
ap-5513	324	26	α	α	PROPN
ap-5513	324	27	,	,	PUNCT
ap-5513	324	28	cx	cx	PROPN
ap-5513	324	29	=	=	PUNCT
ap-5513	325	1	αβ(uxφxx	αβ(uxφxx	PROPN
ap-5513	325	2	−	−	ADP
ap-5513	325	3	uφxxx	uφxxx	ADJ
ap-5513	325	4	−	−	NOUN
ap-5513	325	5	uxxφx	uxxφx	ADJ
ap-5513	325	6	+	+	CCONJ
ap-5513	325	7	uxxxφ(t	uxxxφ(t	ADJ
ap-5513	325	8	,	,	PUNCT
ap-5513	325	9	x	x	NOUN
ap-5513	325	10	,	,	PUNCT
ap-5513	325	11	u	u	NOUN
ap-5513	325	12	)	)	PUNCT
ap-5513	325	13	)	)	PUNCT
ap-5513	325	14	.	.	PUNCT
ap-5513	326	1	(	(	PUNCT
ap-5513	326	2	53	53	NUM
ap-5513	326	3	)	)	PUNCT
ap-5513	326	4	for	for	ADP
ap-5513	326	5	γ4c	γ4c	PROPN
ap-5513	326	6	,	,	PUNCT
ap-5513	326	7	ct	ct	PROPN
ap-5513	326	8	=	=	PUNCT
ap-5513	326	9	−	−	PROPN
ap-5513	326	10	c(t	c(t	PROPN
ap-5513	326	11	,	,	PUNCT
ap-5513	326	12	x	x	NOUN
ap-5513	326	13	)	)	PUNCT
ap-5513	326	14	(	(	PUNCT
ap-5513	326	15	φt	φt	ADP
ap-5513	326	16	+	+	CCONJ
ap-5513	326	17	εβφttt	εβφttt	NOUN
ap-5513	326	18	α	α	NOUN
ap-5513	326	19	)	)	PUNCT
ap-5513	327	1	+	+	CCONJ
ap-5513	327	2	ct	ct	PROPN
ap-5513	327	3	(	(	PUNCT
ap-5513	327	4	φ(t	φ(t	PROPN
ap-5513	327	5	,	,	PUNCT
ap-5513	327	6	x	x	X
ap-5513	327	7	,	,	PUNCT
ap-5513	327	8	u	u	NOUN
ap-5513	327	9	)	)	PUNCT
ap-5513	327	10	+	+	CCONJ
ap-5513	327	11	εβφtt	εβφtt	ADJ
ap-5513	327	12	α	α	NOUN
ap-5513	327	13	)	)	PUNCT
ap-5513	327	14	−	−	PROPN
ap-5513	328	1	ctt	ctt	PROPN
ap-5513	328	2	εβφt	εβφt	PROPN
ap-5513	328	3	α	α	PROPN
ap-5513	329	1	+	+	CCONJ
ap-5513	329	2	cttt	cttt	PROPN
ap-5513	329	3	εβφ(t	εβφ(t	PROPN
ap-5513	329	4	,	,	PUNCT
ap-5513	329	5	x	x	NOUN
ap-5513	329	6	,	,	PUNCT
ap-5513	329	7	u	u	NOUN
ap-5513	329	8	)	)	PUNCT
ap-5513	329	9	α	α	PROPN
ap-5513	329	10	,	,	PUNCT
ap-5513	329	11	cx	cx	PROPN
ap-5513	329	12	=	=	PUNCT
ap-5513	329	13	αβ(cxφxx	αβ(cxφxx	PROPN
ap-5513	330	1	−	−	PROPN
ap-5513	330	2	c(t	c(t	PROPN
ap-5513	330	3	,	,	PUNCT
ap-5513	330	4	x)φxxx	x)φxxx	PUNCT
ap-5513	330	5	−	−	PROPN
ap-5513	331	1	cxxφx	cxxφx	PROPN
ap-5513	331	2	+	+	CCONJ
ap-5513	331	3	cxxxφ(t	cxxxφ(t	ADJ
ap-5513	331	4	,	,	PUNCT
ap-5513	331	5	x	x	NOUN
ap-5513	331	6	,	,	PUNCT
ap-5513	331	7	u	u	NOUN
ap-5513	331	8	)	)	PUNCT
ap-5513	331	9	)	)	PUNCT
ap-5513	331	10	.	.	PUNCT
ap-5513	332	1	(	(	PUNCT
ap-5513	332	2	54	54	NUM
ap-5513	332	3	)	)	PUNCT
ap-5513	332	4	7	7	NUM
ap-5513	332	5	.	.	PUNCT
ap-5513	332	6	conclusion	conclusion	NOUN
ap-5513	332	7	in	in	ADP
ap-5513	332	8	this	this	DET
ap-5513	332	9	work	work	NOUN
ap-5513	332	10	,	,	PUNCT
ap-5513	332	11	we	we	PRON
ap-5513	332	12	focused	focus	VERB
ap-5513	332	13	on	on	ADP
ap-5513	332	14	the	the	DET
ap-5513	332	15	algebraic	algebraic	ADJ
ap-5513	332	16	properties	property	NOUN
ap-5513	332	17	for	for	ADP
ap-5513	332	18	three	three	NUM
ap-5513	332	19	different	different	ADJ
ap-5513	332	20	forms	form	NOUN
ap-5513	332	21	of	of	ADP
ap-5513	332	22	the	the	DET
ap-5513	332	23	beam	beam	NOUN
ap-5513	332	24	equations	equation	NOUN
ap-5513	332	25	with	with	ADP
ap-5513	332	26	or	or	CCONJ
ap-5513	332	27	without	without	ADP
ap-5513	332	28	a	a	DET
ap-5513	332	29	source	source	NOUN
ap-5513	332	30	.	.	PUNCT
ap-5513	333	1	for	for	ADP
ap-5513	333	2	the	the	DET
ap-5513	333	3	source	source	NOUN
ap-5513	333	4	free	free	ADJ
ap-5513	333	5	equations	equation	NOUN
ap-5513	333	6	,	,	PUNCT
ap-5513	333	7	we	we	PRON
ap-5513	333	8	found	find	VERB
ap-5513	333	9	that	that	SCONJ
ap-5513	333	10	the	the	DET
ap-5513	333	11	euler	euler	PROPN
ap-5513	333	12	-	-	PUNCT
ap-5513	333	13	bernoulli	bernoulli	NOUN
ap-5513	333	14	equation	equation	NOUN
ap-5513	333	15	is	be	AUX
ap-5513	333	16	invariant	invariant	ADJ
ap-5513	333	17	under	under	ADP
ap-5513	333	18	the	the	DET
ap-5513	333	19	lie	lie	NOUN
ap-5513	333	20	algebra	algebra	NOUN
ap-5513	333	21	(	(	PUNCT
ap-5513	333	22	a3,3	a3,3	ADV
ap-5513	333	23	⊕a1)⊕s∞a1	⊕a1)⊕s∞a1	ADJ
ap-5513	333	24	,	,	PUNCT
ap-5513	333	25	while	while	SCONJ
ap-5513	333	26	,	,	PUNCT
ap-5513	333	27	the	the	DET
ap-5513	333	28	rayleigh	rayleigh	PROPN
ap-5513	333	29	and	and	CCONJ
ap-5513	333	30	timoshenko	timoshenko	NOUN
ap-5513	333	31	-	-	PUNCT
ap-5513	333	32	prescott	prescott	NOUN
ap-5513	333	33	equations	equation	NOUN
ap-5513	333	34	are	be	AUX
ap-5513	333	35	invariant	invariant	ADJ
ap-5513	333	36	under	under	ADP
ap-5513	333	37	the	the	DET
ap-5513	333	38	lie	lie	NOUN
ap-5513	333	39	algebra	algebra	NOUN
ap-5513	333	40	a3	a3	NOUN
ap-5513	333	41	⊕s∞a1	⊕s∞a1	NOUN
ap-5513	333	42	.	.	PUNCT
ap-5513	334	1	in	in	ADP
ap-5513	334	2	the	the	DET
ap-5513	334	3	case	case	NOUN
ap-5513	334	4	of	of	ADP
ap-5513	334	5	an	an	DET
ap-5513	334	6	isotropic	isotropic	ADJ
ap-5513	334	7	source	source	NOUN
ap-5513	334	8	f	f	PROPN
ap-5513	334	9	(	(	PUNCT
ap-5513	334	10	u	u	NOUN
ap-5513	334	11	)	)	PUNCT
ap-5513	334	12	,	,	PUNCT
ap-5513	334	13	we	we	PRON
ap-5513	334	14	found	find	VERB
ap-5513	334	15	that	that	SCONJ
ap-5513	334	16	the	the	DET
ap-5513	334	17	euler	euler	PROPN
ap-5513	334	18	-	-	PUNCT
ap-5513	334	19	bernoulli	bernoulli	PROPN
ap-5513	334	20	,	,	PUNCT
ap-5513	334	21	rayleigh	rayleigh	PROPN
ap-5513	334	22	and	and	CCONJ
ap-5513	334	23	timoshenko	timoshenko	NOUN
ap-5513	334	24	-	-	PUNCT
ap-5513	334	25	prescott	prescott	NOUN
ap-5513	334	26	equations	equation	NOUN
ap-5513	334	27	are	be	AUX
ap-5513	334	28	invariant	invariant	ADJ
ap-5513	334	29	under	under	ADP
ap-5513	334	30	the	the	DET
ap-5513	334	31	lie	lie	NOUN
ap-5513	334	32	algebra	algebra	NOUN
ap-5513	334	33	2a1	2a1	NUM
ap-5513	334	34	for	for	ADP
ap-5513	334	35	an	an	DET
ap-5513	334	36	arbitrary	arbitrary	ADJ
ap-5513	334	37	source	source	NOUN
ap-5513	334	38	f	f	PROPN
ap-5513	334	39	(	(	PUNCT
ap-5513	334	40	u	u	NOUN
ap-5513	334	41	)	)	PUNCT
ap-5513	334	42	.	.	PUNCT
ap-5513	335	1	moreover	moreover	ADV
ap-5513	335	2	,	,	PUNCT
ap-5513	335	3	for	for	ADP
ap-5513	335	4	the	the	DET
ap-5513	335	5	euler	euler	PROPN
ap-5513	335	6	-	-	PUNCT
ap-5513	335	7	bernoulli	bernoulli	PROPN
ap-5513	335	8	beam	beam	PROPN
ap-5513	335	9	equations	equation	NOUN
ap-5513	335	10	,	,	PUNCT
ap-5513	335	11	the	the	DET
ap-5513	335	12	admitted	admit	VERB
ap-5513	335	13	lie	lie	NOUN
ap-5513	335	14	algebras	algebra	NOUN
ap-5513	335	15	are	be	AUX
ap-5513	335	16	a3	a3	NOUN
ap-5513	335	17	⊕s∞a1	⊕s∞a1	PROPN
ap-5513	335	18	for	for	ADP
ap-5513	335	19	linear	linear	PROPN
ap-5513	335	20	f	f	PROPN
ap-5513	335	21	(	(	PUNCT
ap-5513	335	22	u	u	NOUN
ap-5513	335	23	)	)	PUNCT
ap-5513	335	24	=	=	PUNCT
ap-5513	335	25	au+	au+	PROPN
ap-5513	335	26	b	b	PROPN
ap-5513	335	27	,	,	PUNCT
ap-5513	335	28	2a1	2a1	NUM
ap-5513	335	29	⊕s	⊕s	NOUN
ap-5513	335	30	a1	a1	NOUN
ap-5513	335	31	for	for	ADP
ap-5513	335	32	exponential	exponential	NOUN
ap-5513	335	33	or	or	CCONJ
ap-5513	335	34	power	power	NOUN
ap-5513	335	35	-	-	PUNCT
ap-5513	335	36	law	law	NOUN
ap-5513	335	37	functional	functional	ADJ
ap-5513	335	38	form	form	NOUN
ap-5513	335	39	.	.	PUNCT
ap-5513	336	1	for	for	ADP
ap-5513	336	2	the	the	DET
ap-5513	336	3	other	other	ADJ
ap-5513	336	4	two	two	NUM
ap-5513	336	5	beam	beam	NOUN
ap-5513	336	6	equations	equation	NOUN
ap-5513	336	7	,	,	PUNCT
ap-5513	336	8	there	there	PRON
ap-5513	336	9	are	be	VERB
ap-5513	336	10	no	no	DET
ap-5513	336	11	specific	specific	ADJ
ap-5513	336	12	functional	functional	ADJ
ap-5513	336	13	forms	form	NOUN
ap-5513	336	14	of	of	ADP
ap-5513	336	15	f	f	PROPN
ap-5513	336	16	(	(	PUNCT
ap-5513	336	17	u	u	NOUN
ap-5513	336	18	)	)	PUNCT
ap-5513	336	19	,	,	PUNCT
ap-5513	336	20	where	where	SCONJ
ap-5513	336	21	the	the	DET
ap-5513	336	22	equations	equation	NOUN
ap-5513	336	23	admit	admit	VERB
ap-5513	336	24	different	different	ADJ
ap-5513	336	25	algebras	algebra	NOUN
ap-5513	336	26	.	.	PUNCT
ap-5513	337	1	therefore	therefore	ADV
ap-5513	337	2	,	,	PUNCT
ap-5513	337	3	for	for	ADP
ap-5513	337	4	the	the	DET
ap-5513	337	5	source	source	NOUN
ap-5513	337	6	-	-	PUNCT
ap-5513	337	7	free	free	ADJ
ap-5513	337	8	equations	equation	NOUN
ap-5513	337	9	,	,	PUNCT
ap-5513	337	10	we	we	PRON
ap-5513	337	11	derived	derive	VERB
ap-5513	337	12	the	the	DET
ap-5513	337	13	conservation	conservation	NOUN
ap-5513	337	14	laws	law	NOUN
ap-5513	337	15	by	by	ADP
ap-5513	337	16	applying	apply	VERB
ap-5513	337	17	the	the	DET
ap-5513	337	18	ibragimov	ibragimov	NOUN
ap-5513	337	19	’s	’s	PART
ap-5513	337	20	method	method	NOUN
ap-5513	337	21	.	.	PUNCT
ap-5513	338	1	we	we	PRON
ap-5513	338	2	applied	apply	VERB
ap-5513	338	3	the	the	DET
ap-5513	338	4	lie	lie	NOUN
ap-5513	338	5	point	point	NOUN
ap-5513	338	6	symmetries	symmetry	NOUN
ap-5513	338	7	to	to	PART
ap-5513	338	8	reduce	reduce	VERB
ap-5513	338	9	the	the	DET
ap-5513	338	10	pdes	pde	NOUN
ap-5513	338	11	and	and	CCONJ
ap-5513	338	12	we	we	PRON
ap-5513	338	13	proved	prove	VERB
ap-5513	338	14	that	that	SCONJ
ap-5513	338	15	the	the	DET
ap-5513	338	16	three	three	NUM
ap-5513	338	17	beam	beam	NOUN
ap-5513	338	18	equations	equation	NOUN
ap-5513	338	19	provide	provide	VERB
ap-5513	338	20	exactly	exactly	ADV
ap-5513	338	21	the	the	DET
ap-5513	338	22	same	same	ADJ
ap-5513	338	23	travelling	travelling	ADJ
ap-5513	338	24	-	-	PUNCT
ap-5513	338	25	wave	wave	NOUN
ap-5513	338	26	solutions	solution	NOUN
ap-5513	338	27	.	.	PUNCT
ap-5513	339	1	the	the	DET
ap-5513	339	2	most	most	ADV
ap-5513	339	3	important	important	ADJ
ap-5513	339	4	result	result	NOUN
ap-5513	339	5	of	of	ADP
ap-5513	339	6	our	our	PRON
ap-5513	339	7	paper	paper	NOUN
ap-5513	339	8	is	be	AUX
ap-5513	339	9	the	the	DET
ap-5513	339	10	reduction	reduction	NOUN
ap-5513	339	11	of	of	ADP
ap-5513	339	12	euler	euler	NOUN
ap-5513	339	13	-	-	PUNCT
ap-5513	339	14	bernoulli	bernoulli	NOUN
ap-5513	339	15	equation	equation	NOUN
ap-5513	339	16	to	to	ADP
ap-5513	339	17	a	a	DET
ap-5513	339	18	second	second	ADJ
ap-5513	339	19	-	-	PUNCT
ap-5513	339	20	order	order	NOUN
ap-5513	339	21	equation	equation	NOUN
ap-5513	339	22	,	,	PUNCT
ap-5513	339	23	of	of	ADP
ap-5513	339	24	the	the	DET
ap-5513	339	25	form	form	NOUN
ap-5513	339	26	of	of	ADP
ap-5513	339	27	perturbed	perturb	VERB
ap-5513	339	28	painlevé	painlevé	PROPN
ap-5513	339	29	-	-	PUNCT
ap-5513	339	30	ince	ince	NOUN
ap-5513	339	31	equation	equation	NOUN
ap-5513	339	32	and	and	CCONJ
ap-5513	339	33	to	to	ADP
ap-5513	339	34	a	a	DET
ap-5513	339	35	third	third	ADJ
ap-5513	339	36	-	-	PUNCT
ap-5513	339	37	order	order	NOUN
ap-5513	339	38	equation	equation	NOUN
ap-5513	339	39	,	,	PUNCT
ap-5513	339	40	which	which	PRON
ap-5513	339	41	was	be	AUX
ap-5513	339	42	studied	study	VERB
ap-5513	339	43	by	by	ADP
ap-5513	339	44	chazy	chazy	PROPN
ap-5513	339	45	,	,	PUNCT
ap-5513	339	46	bureau	bureau	NOUN
ap-5513	339	47	and	and	CCONJ
ap-5513	339	48	cosgrove	cosgrove	PROPN
ap-5513	339	49	.	.	PUNCT
ap-5513	340	1	one	one	NUM
ap-5513	340	2	of	of	ADP
ap-5513	340	3	our	our	PRON
ap-5513	340	4	subsequent	subsequent	ADJ
ap-5513	340	5	papers	paper	NOUN
ap-5513	340	6	will	will	AUX
ap-5513	340	7	be	be	AUX
ap-5513	340	8	on	on	ADP
ap-5513	340	9	the	the	DET
ap-5513	340	10	singularity	singularity	NOUN
ap-5513	340	11	analysis	analysis	NOUN
ap-5513	340	12	of	of	ADP
ap-5513	340	13	the	the	DET
ap-5513	340	14	perturbed	perturb	VERB
ap-5513	340	15	painlevé	painlevé	NOUN
ap-5513	340	16	-	-	PUNCT
ap-5513	340	17	ince	ince	NOUN
ap-5513	340	18	equation	equation	NOUN
ap-5513	340	19	.	.	PUNCT
ap-5513	341	1	moreover	moreover	ADV
ap-5513	341	2	,	,	PUNCT
ap-5513	341	3	our	our	PRON
ap-5513	341	4	future	future	ADJ
ap-5513	341	5	work	work	NOUN
ap-5513	341	6	also	also	ADV
ap-5513	341	7	includes	include	VERB
ap-5513	341	8	deriving	derive	VERB
ap-5513	341	9	further	further	ADJ
ap-5513	341	10	solutions	solution	NOUN
ap-5513	341	11	of	of	ADP
ap-5513	341	12	the	the	DET
ap-5513	341	13	different	different	ADJ
ap-5513	341	14	forms	form	NOUN
ap-5513	341	15	of	of	ADP
ap-5513	341	16	beams	beam	NOUN
ap-5513	341	17	using	use	VERB
ap-5513	341	18	conservation	conservation	NOUN
ap-5513	341	19	laws	law	NOUN
ap-5513	341	20	.	.	PUNCT
ap-5513	342	1	acknowledgements	acknowledgement	NOUN
ap-5513	342	2	akh	akh	PROPN
ap-5513	342	3	expresses	express	VERB
ap-5513	342	4	grateful	grateful	ADJ
ap-5513	342	5	thanks	thank	NOUN
ap-5513	342	6	to	to	ADP
ap-5513	342	7	ugc	ugc	PROPN
ap-5513	342	8	(	(	PUNCT
ap-5513	342	9	india	india	PROPN
ap-5513	342	10	)	)	PUNCT
ap-5513	342	11	nfsc	nfsc	PROPN
ap-5513	342	12	,	,	PUNCT
ap-5513	342	13	award	award	NOUN
ap-5513	342	14	no	no	INTJ
ap-5513	342	15	.	.	PUNCT
ap-5513	343	1	f1	f1	PROPN
ap-5513	343	2	-	-	PUNCT
ap-5513	343	3	17.1/201718	17.1/201718	NUM
ap-5513	343	4	/	/	SYM
ap-5513	343	5	rgnf-2017	rgnf-2017	NOUN
ap-5513	343	6	-	-	PUNCT
ap-5513	343	7	18	18	NUM
ap-5513	343	8	-	-	PUNCT
ap-5513	343	9	sc	sc	NOUN
ap-5513	343	10	-	-	NOUN
ap-5513	343	11	ori-39488	ori-39488	NOUN
ap-5513	343	12	for	for	ADP
ap-5513	343	13	financial	financial	ADJ
ap-5513	343	14	support	support	NOUN
ap-5513	343	15	and	and	CCONJ
ap-5513	343	16	late	late	ADJ
ap-5513	343	17	prof	prof	PROPN
ap-5513	343	18	.	.	PUNCT
ap-5513	344	1	k.m.tamizhmani	k.m.tamizhmani	PROPN
ap-5513	344	2	for	for	ADP
ap-5513	344	3	the	the	DET
ap-5513	344	4	discussions	discussion	NOUN
ap-5513	344	5	that	that	PRON
ap-5513	344	6	formed	form	VERB
ap-5513	344	7	the	the	DET
ap-5513	344	8	basis	basis	NOUN
ap-5513	344	9	of	of	ADP
ap-5513	344	10	this	this	DET
ap-5513	344	11	work	work	NOUN
ap-5513	344	12	.	.	PUNCT
ap-5513	345	1	pgll	pgll	PROPN
ap-5513	345	2	acknowledges	acknowledge	VERB
ap-5513	345	3	the	the	DET
ap-5513	345	4	support	support	NOUN
ap-5513	345	5	of	of	ADP
ap-5513	345	6	the	the	DET
ap-5513	345	7	national	national	PROPN
ap-5513	345	8	research	research	PROPN
ap-5513	345	9	foundation	foundation	PROPN
ap-5513	345	10	of	of	ADP
ap-5513	345	11	south	south	PROPN
ap-5513	345	12	africa	africa	PROPN
ap-5513	345	13	,	,	PUNCT
ap-5513	345	14	the	the	DET
ap-5513	345	15	university	university	NOUN
ap-5513	345	16	of	of	ADP
ap-5513	345	17	kwazulu	kwazulu	PROPN
ap-5513	345	18	-	-	PUNCT
ap-5513	345	19	natal	natal	NOUN
ap-5513	345	20	and	and	CCONJ
ap-5513	345	21	the	the	DET
ap-5513	345	22	durban	durban	PROPN
ap-5513	345	23	university	university	PROPN
ap-5513	345	24	of	of	ADP
ap-5513	345	25	technology	technology	NOUN
ap-5513	345	26	and	and	CCONJ
ap-5513	345	27	thanks	thank	NOUN
ap-5513	345	28	the	the	DET
ap-5513	345	29	department	department	NOUN
ap-5513	345	30	of	of	ADP
ap-5513	345	31	mathematics	mathematics	PROPN
ap-5513	345	32	,	,	PUNCT
ap-5513	345	33	pondicherry	pondicherry	PROPN
ap-5513	345	34	university	university	NOUN
ap-5513	345	35	,	,	PUNCT
ap-5513	345	36	for	for	ADP
ap-5513	345	37	gracious	gracious	ADJ
ap-5513	345	38	hospitality	hospitality	NOUN
ap-5513	345	39	.	.	PUNCT
ap-5513	346	1	references	reference	NOUN
ap-5513	346	2	[	[	X
ap-5513	346	3	1	1	NUM
ap-5513	346	4	]	]	X
ap-5513	346	5	r.	r.	PROPN
ap-5513	346	6	m.	m.	PROPN
ap-5513	346	7	davies	davies	PROPN
ap-5513	346	8	,	,	PUNCT
ap-5513	346	9	g.	g.	PROPN
ap-5513	346	10	i.	i.	PROPN
ap-5513	346	11	taylor	taylor	PROPN
ap-5513	346	12	.	.	PUNCT
ap-5513	347	1	a	a	DET
ap-5513	347	2	critical	critical	ADJ
ap-5513	347	3	study	study	NOUN
ap-5513	347	4	of	of	ADP
ap-5513	347	5	the	the	DET
ap-5513	347	6	hopkinson	hopkinson	PROPN
ap-5513	347	7	pressure	pressure	NOUN
ap-5513	347	8	bar	bar	NOUN
ap-5513	347	9	.	.	PUNCT
ap-5513	348	1	philosophical	philosophical	ADJ
ap-5513	348	2	transactions	transaction	NOUN
ap-5513	348	3	of	of	ADP
ap-5513	348	4	the	the	DET
ap-5513	348	5	royal	royal	ADJ
ap-5513	348	6	society	society	NOUN
ap-5513	348	7	of	of	ADP
ap-5513	348	8	london	london	PROPN
ap-5513	348	9	series	series	PROPN
ap-5513	348	10	a	a	PRON
ap-5513	348	11	,	,	PUNCT
ap-5513	348	12	mathematical	mathematical	ADJ
ap-5513	348	13	and	and	CCONJ
ap-5513	348	14	physical	physical	ADJ
ap-5513	348	15	sciences	science	NOUN
ap-5513	348	16	240(821):375	240(821):375	ADJ
ap-5513	348	17	–	–	PUNCT
ap-5513	348	18	457	457	NUM
ap-5513	348	19	,	,	PUNCT
ap-5513	348	20	1948	1948	NUM
ap-5513	348	21	.	.	PUNCT
ap-5513	349	1	doi:10.1098	doi:10.1098	PROPN
ap-5513	349	2	/	/	SYM
ap-5513	349	3	rsta.1948.0001	rsta.1948.0001	PROPN
ap-5513	349	4	.	.	PUNCT
ap-5513	350	1	[	[	X
ap-5513	350	2	2	2	NUM
ap-5513	350	3	]	]	PUNCT
ap-5513	350	4	a.	a.	NOUN
ap-5513	350	5	labuschagne	labuschagne	PROPN
ap-5513	350	6	,	,	PUNCT
ap-5513	350	7	n.	n.	PROPN
ap-5513	350	8	van	van	PROPN
ap-5513	350	9	rensburg	rensburg	PROPN
ap-5513	350	10	,	,	PUNCT
ap-5513	350	11	a.	a.	PROPN
ap-5513	350	12	van	van	PROPN
ap-5513	350	13	der	der	PROPN
ap-5513	350	14	merwe	merwe	PROPN
ap-5513	350	15	.	.	PROPN
ap-5513	350	16	comparison	comparison	NOUN
ap-5513	350	17	of	of	ADP
ap-5513	350	18	linear	linear	PROPN
ap-5513	350	19	beam	beam	NOUN
ap-5513	350	20	theories	theory	NOUN
ap-5513	350	21	.	.	PUNCT
ap-5513	351	1	mathematical	mathematical	ADJ
ap-5513	351	2	and	and	CCONJ
ap-5513	351	3	computer	computer	NOUN
ap-5513	351	4	modelling	model	VERB
ap-5513	351	5	49(1):20	49(1):20	NUM
ap-5513	351	6	–	–	PUNCT
ap-5513	351	7	30	30	NUM
ap-5513	351	8	,	,	PUNCT
ap-5513	351	9	2009	2009	NUM
ap-5513	351	10	.	.	PUNCT
ap-5513	352	1	doi:10.1016	doi:10.1016	PROPN
ap-5513	352	2	/	/	SYM
ap-5513	352	3	j.mcm.2008.06.006	j.mcm.2008.06.006	PROPN
ap-5513	352	4	.	.	PUNCT
ap-5513	353	1	108	108	NUM
ap-5513	353	2	http://dx.doi.org/10.1098/rsta.1948.0001	http://dx.doi.org/10.1098/rsta.1948.0001	NOUN
ap-5513	353	3	http://dx.doi.org/10.1016/j.mcm.2008.06.006	http://dx.doi.org/10.1016/j.mcm.2008.06.006	ADJ
ap-5513	353	4	vol	vol	NOUN
ap-5513	353	5	.	.	PUNCT
ap-5513	354	1	60	60	NUM
ap-5513	354	2	no	no	NOUN
ap-5513	354	3	.	.	PUNCT
ap-5513	355	1	2/2020	2/2020	NUM
ap-5513	355	2	similarity	similarity	NOUN
ap-5513	355	3	solutions	solution	NOUN
ap-5513	355	4	and	and	CCONJ
ap-5513	355	5	conservation	conservation	NOUN
ap-5513	355	6	laws	law	NOUN
ap-5513	355	7	for	for	ADP
ap-5513	355	8	the	the	DET
ap-5513	355	9	beam	beam	NOUN
ap-5513	355	10	equations	equation	NOUN
ap-5513	355	11	.	.	PUNCT
ap-5513	355	12	.	.	PUNCT
ap-5513	355	13	.	.	PUNCT
ap-5513	356	1	[	[	X
ap-5513	356	2	3	3	X
ap-5513	356	3	]	]	X
ap-5513	356	4	g.	g.	PROPN
ap-5513	356	5	e.	e.	PROPN
ap-5513	356	6	hudson	hudson	PROPN
ap-5513	356	7	.	.	PUNCT
ap-5513	357	1	dispersion	dispersion	NOUN
ap-5513	357	2	of	of	ADP
ap-5513	357	3	elastic	elastic	ADJ
ap-5513	357	4	waves	wave	NOUN
ap-5513	357	5	in	in	ADP
ap-5513	357	6	solid	solid	ADJ
ap-5513	357	7	circular	circular	ADJ
ap-5513	357	8	cylinders	cylinder	NOUN
ap-5513	357	9	.	.	PUNCT
ap-5513	358	1	physical	physical	ADJ
ap-5513	358	2	review	review	NOUN
ap-5513	358	3	63:46	63:46	NUM
ap-5513	358	4	–	–	PUNCT
ap-5513	358	5	51	51	NUM
ap-5513	358	6	,	,	PUNCT
ap-5513	358	7	1943	1943	NUM
ap-5513	358	8	.	.	PUNCT
ap-5513	359	1	doi:10.1103	doi:10.1103	PROPN
ap-5513	359	2	/	/	SYM
ap-5513	359	3	physrev.63.46	physrev.63.46	PROPN
ap-5513	359	4	.	.	PUNCT
ap-5513	360	1	[	[	X
ap-5513	360	2	4	4	X
ap-5513	360	3	]	]	X
ap-5513	360	4	d.	d.	PROPN
ap-5513	360	5	bancroft	bancroft	PROPN
ap-5513	360	6	.	.	PUNCT
ap-5513	361	1	the	the	DET
ap-5513	361	2	velocity	velocity	NOUN
ap-5513	361	3	of	of	ADP
ap-5513	361	4	longitudinal	longitudinal	ADJ
ap-5513	361	5	waves	wave	NOUN
ap-5513	361	6	in	in	ADP
ap-5513	361	7	cylindrical	cylindrical	ADJ
ap-5513	361	8	bars	bar	NOUN
ap-5513	361	9	.	.	PUNCT
ap-5513	362	1	physical	physical	ADJ
ap-5513	362	2	review	review	NOUN
ap-5513	362	3	59:588	59:588	NUM
ap-5513	362	4	–	–	PUNCT
ap-5513	362	5	593	593	NUM
ap-5513	362	6	,	,	PUNCT
ap-5513	362	7	1941	1941	NUM
ap-5513	362	8	.	.	PUNCT
ap-5513	363	1	doi:10.1103	doi:10.1103	NOUN
ap-5513	363	2	/	/	SYM
ap-5513	363	3	physrev.59.588	physrev.59.588	NOUN
ap-5513	363	4	.	.	PUNCT
ap-5513	364	1	[	[	X
ap-5513	364	2	5	5	NUM
ap-5513	364	3	]	]	PUNCT
ap-5513	364	4	a.	a.	NOUN
ap-5513	364	5	h.	h.	PROPN
ap-5513	364	6	bokhari	bokhari	PROPN
ap-5513	364	7	,	,	PUNCT
ap-5513	364	8	f.	f.	PROPN
ap-5513	364	9	m.	m.	PROPN
ap-5513	364	10	mahomed	mahome	VERB
ap-5513	364	11	,	,	PUNCT
ap-5513	364	12	f.	f.	PROPN
ap-5513	364	13	d.	d.	PROPN
ap-5513	364	14	zaman	zaman	PROPN
ap-5513	364	15	.	.	PUNCT
ap-5513	365	1	symmetries	symmetry	NOUN
ap-5513	365	2	and	and	CCONJ
ap-5513	365	3	integrability	integrability	NOUN
ap-5513	365	4	of	of	ADP
ap-5513	365	5	a	a	DET
ap-5513	365	6	fourth	fourth	ADJ
ap-5513	365	7	-	-	PUNCT
ap-5513	365	8	order	order	NOUN
ap-5513	365	9	euler	euler	NOUN
ap-5513	365	10	–	–	PUNCT
ap-5513	365	11	bernoulli	bernoulli	PROPN
ap-5513	365	12	beam	beam	NOUN
ap-5513	365	13	equation	equation	NOUN
ap-5513	365	14	.	.	PUNCT
ap-5513	366	1	journal	journal	PROPN
ap-5513	366	2	of	of	ADP
ap-5513	366	3	mathematical	mathematical	ADJ
ap-5513	366	4	physics	physics	PROPN
ap-5513	366	5	51(5):053517	51(5):053517	PROPN
ap-5513	366	6	,	,	PUNCT
ap-5513	366	7	2010	2010	NUM
ap-5513	366	8	.	.	PUNCT
ap-5513	367	1	doi:10.1063/1.3377045	doi:10.1063/1.3377045	ADJ
ap-5513	367	2	.	.	PUNCT
ap-5513	368	1	[	[	X
ap-5513	368	2	6	6	NUM
ap-5513	368	3	]	]	PUNCT
ap-5513	368	4	a.	a.	NOUN
ap-5513	368	5	fatima	fatima	PROPN
ap-5513	368	6	,	,	PUNCT
ap-5513	368	7	f.	f.	PROPN
ap-5513	368	8	m.	m.	PROPN
ap-5513	368	9	mahomed	mahome	VERB
ap-5513	368	10	,	,	PUNCT
ap-5513	368	11	c.	c.	PROPN
ap-5513	368	12	m.	m.	PROPN
ap-5513	368	13	khalique	khalique	PROPN
ap-5513	368	14	.	.	PUNCT
ap-5513	369	1	noether	noether	ADJ
ap-5513	369	2	symmetries	symmetry	NOUN
ap-5513	369	3	and	and	CCONJ
ap-5513	369	4	exact	exact	ADJ
ap-5513	369	5	solutions	solution	NOUN
ap-5513	369	6	of	of	ADP
ap-5513	369	7	an	an	DET
ap-5513	369	8	euler	euler	NOUN
ap-5513	369	9	–	–	PUNCT
ap-5513	369	10	bernoulli	bernoulli	PROPN
ap-5513	369	11	beam	beam	PROPN
ap-5513	369	12	model	model	PROPN
ap-5513	369	13	.	.	PUNCT
ap-5513	370	1	international	international	ADJ
ap-5513	370	2	journal	journal	PROPN
ap-5513	370	3	of	of	ADP
ap-5513	370	4	modern	modern	ADJ
ap-5513	370	5	physics	physics	PROPN
ap-5513	370	6	b	b	PROPN
ap-5513	370	7	30(28	30(28	NUM
ap-5513	370	8	-	-	SYM
ap-5513	370	9	29):1640011	29):1640011	NUM
ap-5513	370	10	,	,	PUNCT
ap-5513	370	11	2016	2016	NUM
ap-5513	370	12	.	.	PUNCT
ap-5513	371	1	doi:10.1142	doi:10.1142	VERB
ap-5513	371	2	/	/	SYM
ap-5513	371	3	s0217979216400117	s0217979216400117	NOUN
ap-5513	371	4	.	.	PUNCT
ap-5513	372	1	[	[	X
ap-5513	372	2	7	7	X
ap-5513	372	3	]	]	X
ap-5513	372	4	d.	d.	PROPN
ap-5513	372	5	huang	huang	PROPN
ap-5513	372	6	,	,	PUNCT
ap-5513	372	7	x.	x.	PROPN
ap-5513	372	8	li	li	PROPN
ap-5513	372	9	,	,	PUNCT
ap-5513	372	10	s.	s.	PROPN
ap-5513	372	11	yu	yu	PROPN
ap-5513	372	12	.	.	PROPN
ap-5513	372	13	lie	lie	PROPN
ap-5513	372	14	symmetry	symmetry	NOUN
ap-5513	372	15	classification	classification	NOUN
ap-5513	372	16	of	of	ADP
ap-5513	372	17	the	the	DET
ap-5513	372	18	generalized	generalized	ADJ
ap-5513	372	19	nonlinear	nonlinear	ADJ
ap-5513	372	20	beam	beam	NOUN
ap-5513	372	21	equation	equation	NOUN
ap-5513	372	22	.	.	PUNCT
ap-5513	373	1	symmetry	symmetry	PROPN
ap-5513	373	2	9:115	9:115	PROPN
ap-5513	373	3	,	,	PUNCT
ap-5513	373	4	2017	2017	NUM
ap-5513	373	5	.	.	PUNCT
ap-5513	374	1	doi:10.3390	doi:10.3390	NOUN
ap-5513	374	2	/	/	SYM
ap-5513	374	3	sym9070115	sym9070115	NOUN
ap-5513	374	4	.	.	PUNCT
ap-5513	375	1	[	[	X
ap-5513	375	2	8	8	NUM
ap-5513	375	3	]	]	X
ap-5513	375	4	c.	c.	PROPN
ap-5513	375	5	wafo	wafo	PROPN
ap-5513	375	6	soh	soh	PROPN
ap-5513	375	7	.	.	PUNCT
ap-5513	375	8	euler	euler	PROPN
ap-5513	375	9	–	–	PUNCT
ap-5513	375	10	bernoulli	bernoulli	NOUN
ap-5513	375	11	beams	beam	NOUN
ap-5513	375	12	from	from	ADP
ap-5513	375	13	a	a	DET
ap-5513	375	14	symmetry	symmetry	NOUN
ap-5513	375	15	standpoint	standpoint	NOUN
ap-5513	375	16	-	-	PUNCT
ap-5513	375	17	characterization	characterization	NOUN
ap-5513	375	18	of	of	ADP
ap-5513	375	19	equivalent	equivalent	ADJ
ap-5513	375	20	equations	equation	NOUN
ap-5513	375	21	.	.	PUNCT
ap-5513	376	1	journal	journal	PROPN
ap-5513	376	2	of	of	ADP
ap-5513	376	3	mathematical	mathematical	ADJ
ap-5513	376	4	analysis	analysis	NOUN
ap-5513	376	5	and	and	CCONJ
ap-5513	376	6	applications	application	NOUN
ap-5513	376	7	345(1):387	345(1):387	NUM
ap-5513	376	8	–	–	PUNCT
ap-5513	376	9	395	395	NUM
ap-5513	376	10	,	,	PUNCT
ap-5513	376	11	2008	2008	NUM
ap-5513	376	12	.	.	PUNCT
ap-5513	377	1	doi:10.1016	doi:10.1016	PROPN
ap-5513	377	2	/	/	SYM
ap-5513	377	3	j.jmaa.2008.04.023	j.jmaa.2008.04.023	PROPN
ap-5513	377	4	.	.	PUNCT
ap-5513	378	1	[	[	X
ap-5513	378	2	9	9	NUM
ap-5513	378	3	]	]	PUNCT
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ap-5513	378	6	.	.	PUNCT
ap-5513	379	1	the	the	DET
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ap-5513	379	3	of	of	ADP
ap-5513	379	4	symmetric	symmetric	ADJ
ap-5513	379	5	positive	positive	ADJ
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ap-5513	379	9	-	-	PUNCT
ap-5513	379	10	order	order	NOUN
ap-5513	379	11	elastic	elastic	ADJ
ap-5513	379	12	beam	beam	NOUN
ap-5513	379	13	equations	equation	NOUN
ap-5513	379	14	.	.	PUNCT
ap-5513	380	1	symmetry	symmetry	NOUN
ap-5513	380	2	11:121	11:121	NUM
ap-5513	380	3	,	,	PUNCT
ap-5513	380	4	2019	2019	NUM
ap-5513	380	5	.	.	PUNCT
ap-5513	381	1	doi:10.3390	doi:10.3390	NOUN
ap-5513	381	2	/	/	SYM
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ap-5513	381	4	.	.	PUNCT
ap-5513	382	1	[	[	X
ap-5513	382	2	10	10	NUM
ap-5513	382	3	]	]	X
ap-5513	382	4	e.	e.	PROPN
ap-5513	382	5	l.	l.	PROPN
ap-5513	382	6	ince	ince	PROPN
ap-5513	382	7	.	.	PUNCT
ap-5513	383	1	ordinary	ordinary	ADJ
ap-5513	383	2	differential	differential	ADJ
ap-5513	383	3	equations	equation	NOUN
ap-5513	383	4	.	.	PUNCT
ap-5513	384	1	longmans	longmans	PROPN
ap-5513	384	2	green	green	PROPN
ap-5513	384	3	&	&	CCONJ
ap-5513	384	4	co	co	PROPN
ap-5513	384	5	,	,	PUNCT
ap-5513	384	6	london	london	PROPN
ap-5513	384	7	,	,	PUNCT
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ap-5513	384	9	.	.	PUNCT
ap-5513	385	1	[	[	X
ap-5513	385	2	11	11	NUM
ap-5513	385	3	]	]	PUNCT
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ap-5513	385	12	.	.	PUNCT
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ap-5513	386	2	general	general	ADJ
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ap-5513	386	4	and	and	CCONJ
ap-5513	386	5	first	first	ADJ
ap-5513	386	6	integrals	integral	NOUN
ap-5513	386	7	of	of	ADP
ap-5513	386	8	a	a	DET
ap-5513	386	9	remarkable	remarkable	ADJ
ap-5513	386	10	static	static	ADJ
ap-5513	386	11	euler	euler	NOUN
ap-5513	386	12	-	-	PUNCT
ap-5513	386	13	bernoulli	bernoulli	PROPN
ap-5513	386	14	beam	beam	NOUN
ap-5513	386	15	equation	equation	NOUN
ap-5513	386	16	.	.	PUNCT
ap-5513	387	1	communications	communication	NOUN
ap-5513	387	2	in	in	ADP
ap-5513	387	3	nonlinear	nonlinear	ADJ
ap-5513	387	4	science	science	NOUN
ap-5513	387	5	and	and	CCONJ
ap-5513	387	6	numerical	numerical	PROPN
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ap-5513	387	8	69:261	69:261	PROPN
ap-5513	387	9	–	–	PUNCT
ap-5513	387	10	169	169	NUM
ap-5513	387	11	,	,	PUNCT
ap-5513	387	12	2018	2018	NUM
ap-5513	387	13	.	.	PUNCT
ap-5513	388	1	doi:10.1016	doi:10.1016	PROPN
ap-5513	388	2	/	/	SYM
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ap-5513	388	4	.	.	PUNCT
ap-5513	389	1	[	[	X
ap-5513	389	2	12	12	NUM
ap-5513	389	3	]	]	X
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ap-5513	389	5	da	da	PROPN
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ap-5513	389	10	.	.	PUNCT
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ap-5513	390	4	a	a	DET
ap-5513	390	5	class	class	NOUN
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ap-5513	390	8	even	even	ADJ
ap-5513	390	9	-	-	PUNCT
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ap-5513	390	11	ordinary	ordinary	ADJ
ap-5513	390	12	differential	differential	ADJ
ap-5513	390	13	equations	equation	NOUN
ap-5513	390	14	.	.	PUNCT
ap-5513	391	1	i	i	PRON
ap-5513	391	2	m	m	VERB
ap-5513	391	3	a	a	DET
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ap-5513	391	5	of	of	ADP
ap-5513	391	6	applied	apply	VERB
ap-5513	391	7	mathematics	mathematic	NOUN
ap-5513	391	8	80:1739	80:1739	NUM
ap-5513	391	9	–	–	PUNCT
ap-5513	391	10	1758	1758	NUM
ap-5513	391	11	,	,	PUNCT
ap-5513	391	12	2015	2015	NUM
ap-5513	391	13	.	.	PUNCT
ap-5513	392	1	doi:10.1093	doi:10.1093	NOUN
ap-5513	392	2	/	/	SYM
ap-5513	392	3	imamat	imamat	NOUN
ap-5513	392	4	/	/	SYM
ap-5513	392	5	hxv014	hxv014	PROPN
ap-5513	392	6	.	.	PUNCT
ap-5513	393	1	[	[	X
ap-5513	393	2	13	13	NUM
ap-5513	393	3	]	]	SYM
ap-5513	393	4	i.	i.	PROPN
ap-5513	393	5	l.	l.	PROPN
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ap-5513	393	7	,	,	PUNCT
ap-5513	393	8	p.	p.	PROPN
ap-5513	393	9	l.	l.	PROPN
ap-5513	393	10	da	da	PROPN
ap-5513	393	11	silva	silva	PROPN
ap-5513	393	12	,	,	PUNCT
ap-5513	393	13	m.	m.	NOUN
ap-5513	393	14	torrisi	torrisi	VERB
ap-5513	393	15	.	.	PUNCT
ap-5513	394	1	lie	lie	NOUN
ap-5513	394	2	and	and	CCONJ
ap-5513	394	3	noether	noether	ADJ
ap-5513	394	4	symmetries	symmetry	NOUN
ap-5513	394	5	for	for	ADP
ap-5513	394	6	a	a	DET
ap-5513	394	7	class	class	NOUN
ap-5513	394	8	of	of	ADP
ap-5513	394	9	fourth	fourth	ADJ
ap-5513	394	10	-	-	PUNCT
ap-5513	394	11	order	order	NOUN
ap-5513	394	12	emden	emden	ADJ
ap-5513	394	13	–	–	PUNCT
ap-5513	394	14	fowler	fowler	PROPN
ap-5513	394	15	equations	equation	NOUN
ap-5513	394	16	.	.	PUNCT
ap-5513	395	1	journal	journal	PROPN
ap-5513	395	2	of	of	ADP
ap-5513	395	3	physics	physics	PROPN
ap-5513	395	4	a	a	PRON
ap-5513	395	5	:	:	PUNCT
ap-5513	395	6	mathematical	mathematical	ADJ
ap-5513	395	7	and	and	CCONJ
ap-5513	395	8	theoretical	theoretical	ADJ
ap-5513	395	9	46(24):245206	46(24):245206	NUM
ap-5513	395	10	,	,	PUNCT
ap-5513	395	11	2013	2013	NUM
ap-5513	395	12	.	.	PUNCT
ap-5513	396	1	doi:10.1088/1751	doi:10.1088/1751	NOUN
ap-5513	396	2	-	-	PUNCT
ap-5513	396	3	8113/46/24/245206	8113/46/24/245206	NUM
ap-5513	396	4	.	.	PUNCT
ap-5513	397	1	[	[	X
ap-5513	397	2	14	14	NUM
ap-5513	397	3	]	]	X
ap-5513	397	4	w.	w.	PROPN
ap-5513	397	5	bluman	bluman	PROPN
ap-5513	397	6	,	,	PUNCT
ap-5513	397	7	s.	s.	PROPN
ap-5513	397	8	kumei	kumei	PROPN
ap-5513	397	9	.	.	PUNCT
ap-5513	398	1	symmetries	symmetry	NOUN
ap-5513	398	2	and	and	CCONJ
ap-5513	398	3	differential	differential	ADJ
ap-5513	398	4	equations	equation	NOUN
ap-5513	398	5	.	.	PUNCT
ap-5513	399	1	springer	springer	NOUN
ap-5513	399	2	,	,	PUNCT
ap-5513	399	3	new	new	PROPN
ap-5513	399	4	york	york	PROPN
ap-5513	399	5	,	,	PUNCT
ap-5513	399	6	1989	1989	NUM
ap-5513	399	7	.	.	PUNCT
ap-5513	400	1	doi:10.1007/978	doi:10.1007/978	ADJ
ap-5513	400	2	-	-	PUNCT
ap-5513	400	3	1	1	NUM
ap-5513	400	4	-	-	PUNCT
ap-5513	400	5	4757	4757	NUM
ap-5513	400	6	-	-	SYM
ap-5513	400	7	4307	4307	NUM
ap-5513	400	8	-	-	SYM
ap-5513	400	9	4	4	NUM
ap-5513	400	10	.	.	PUNCT
ap-5513	401	1	[	[	X
ap-5513	401	2	15	15	NUM
ap-5513	401	3	]	]	X
ap-5513	401	4	y.	y.	PROPN
ap-5513	401	5	n.	n.	PROPN
ap-5513	401	6	grigoriev	grigoriev	PROPN
ap-5513	401	7	,	,	PUNCT
ap-5513	401	8	v.	v.	PROPN
ap-5513	401	9	f.	f.	PROPN
ap-5513	401	10	kovalev	kovalev	PROPN
ap-5513	401	11	,	,	PUNCT
ap-5513	401	12	s.	s.	PROPN
ap-5513	401	13	meleshko	meleshko	VERB
ap-5513	401	14	,	,	PUNCT
ap-5513	401	15	n.	n.	NOUN
ap-5513	401	16	ibragimov	ibragimov	NOUN
ap-5513	401	17	.	.	PUNCT
ap-5513	402	1	symmetries	symmetry	NOUN
ap-5513	402	2	of	of	ADP
ap-5513	402	3	integro	integro	PROPN
ap-5513	402	4	-	-	PUNCT
ap-5513	402	5	differential	differential	NOUN
ap-5513	402	6	equations	equation	NOUN
ap-5513	402	7	:	:	PUNCT
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ap-5513	402	9	applications	application	NOUN
ap-5513	402	10	in	in	ADP
ap-5513	402	11	mechanics	mechanic	NOUN
ap-5513	402	12	and	and	CCONJ
ap-5513	402	13	plasma	plasma	NOUN
ap-5513	402	14	physics	physic	NOUN
ap-5513	402	15	.	.	PUNCT
ap-5513	403	1	springer	springer	PROPN
ap-5513	403	2	dordrecht	dordrecht	PROPN
ap-5513	403	3	,	,	PUNCT
ap-5513	403	4	2010	2010	NUM
ap-5513	403	5	.	.	PUNCT
ap-5513	404	1	[	[	X
ap-5513	404	2	16	16	NUM
ap-5513	404	3	]	]	PUNCT
ap-5513	404	4	p.	p.	PROPN
ap-5513	404	5	j.	j.	PROPN
ap-5513	404	6	olver	olver	PROPN
ap-5513	404	7	.	.	PUNCT
ap-5513	405	1	applications	application	NOUN
ap-5513	405	2	of	of	ADP
ap-5513	405	3	lie	lie	NOUN
ap-5513	405	4	groups	group	NOUN
ap-5513	405	5	to	to	PART
ap-5513	405	6	differential	differential	VERB
ap-5513	405	7	equations	equation	NOUN
ap-5513	405	8	.	.	PUNCT
ap-5513	406	1	springer	springer	NOUN
ap-5513	406	2	science	science	PROPN
ap-5513	406	3	&	&	CCONJ
ap-5513	406	4	business	business	NOUN
ap-5513	406	5	media	medium	NOUN
ap-5513	406	6	,	,	PUNCT
ap-5513	406	7	new	new	PROPN
ap-5513	406	8	york	york	PROPN
ap-5513	406	9	,	,	PUNCT
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ap-5513	406	11	.	.	PUNCT
ap-5513	407	1	[	[	X
ap-5513	407	2	17	17	NUM
ap-5513	407	3	]	]	X
ap-5513	407	4	j.	j.	PROPN
ap-5513	407	5	m.	m.	PROPN
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ap-5513	407	7	,	,	PUNCT
ap-5513	407	8	s.	s.	PROPN
ap-5513	407	9	p.	p.	PROPN
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ap-5513	407	11	.	.	PUNCT
ap-5513	408	1	mechanics	mechanic	NOUN
ap-5513	408	2	of	of	ADP
ap-5513	408	3	materials	material	NOUN
ap-5513	408	4	.	.	PUNCT
ap-5513	409	1	pws	pws	PROPN
ap-5513	409	2	-	-	PUNCT
ap-5513	409	3	kent	kent	PROPN
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ap-5513	409	5	company	company	NOUN
ap-5513	409	6	,	,	PUNCT
ap-5513	409	7	1997	1997	NUM
ap-5513	409	8	.	.	PUNCT
ap-5513	410	1	[	[	X
ap-5513	410	2	18	18	NUM
ap-5513	410	3	]	]	X
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ap-5513	410	5	v.	v.	ADP
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ap-5513	410	7	.	.	PUNCT
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ap-5513	411	2	of	of	ADP
ap-5513	411	3	six	six	NUM
ap-5513	411	4	-	-	PUNCT
ap-5513	411	5	dimensional	dimensional	ADJ
ap-5513	411	6	nilpotent	nilpotent	ADJ
ap-5513	411	7	lie	lie	NOUN
ap-5513	411	8	algebras	algebra	NOUN
ap-5513	411	9	.	.	PUNCT
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ap-5513	412	6	5:161	5:161	PROPN
ap-5513	412	7	–	–	PUNCT
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ap-5513	412	9	,	,	PUNCT
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ap-5513	412	11	.	.	PUNCT
ap-5513	413	1	[	[	X
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ap-5513	413	7	.	.	PUNCT
ap-5513	414	1	on	on	ADP
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ap-5513	414	3	lie	lie	NOUN
ap-5513	414	4	algebras	algebra	NOUN
ap-5513	414	5	.	.	PUNCT
ap-5513	415	1	izvestia	izvestia	PROPN
ap-5513	415	2	vysshikh	vysshikh	PROPN
ap-5513	415	3	uchebn	uchebn	NOUN
ap-5513	415	4	zavendenĭı	zavendenĭı	PROPN
ap-5513	415	5	matematika	matematika	X
ap-5513	415	6	34:99	34:99	NUM
ap-5513	415	7	–	–	PUNCT
ap-5513	415	8	106	106	NUM
ap-5513	415	9	,	,	PUNCT
ap-5513	415	10	1963	1963	NUM
ap-5513	415	11	.	.	PUNCT
ap-5513	416	1	[	[	X
ap-5513	416	2	20	20	NUM
ap-5513	416	3	]	]	X
ap-5513	416	4	g.	g.	PROPN
ap-5513	416	5	m.	m.	PROPN
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ap-5513	416	7	.	.	PUNCT
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ap-5513	417	2	of	of	ADP
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ap-5513	417	6	five	five	NUM
ap-5513	417	7	-	-	PUNCT
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ap-5513	417	9	lie	lie	NOUN
ap-5513	417	10	algebras	algebra	NOUN
ap-5513	417	11	.	.	PUNCT
ap-5513	418	1	izvestia	izvestia	PROPN
ap-5513	418	2	vysshikh	vysshikh	PROPN
ap-5513	418	3	uchebn	uchebn	NOUN
ap-5513	418	4	zavendenĭı	zavendenĭı	PROPN
ap-5513	418	5	matematika	matematika	X
ap-5513	418	6	32:114	32:114	NUM
ap-5513	418	7	–	–	PUNCT
ap-5513	418	8	123	123	NUM
ap-5513	418	9	,	,	PUNCT
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ap-5513	418	11	.	.	PUNCT
ap-5513	419	1	[	[	X
ap-5513	419	2	21	21	NUM
ap-5513	419	3	]	]	X
ap-5513	419	4	g.	g.	PROPN
ap-5513	419	5	m.	m.	PROPN
ap-5513	419	6	mubarakzyanov	mubarakzyanov	PROPN
ap-5513	419	7	.	.	PUNCT
ap-5513	420	1	classification	classification	NOUN
ap-5513	420	2	of	of	ADP
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ap-5513	420	4	six	six	NUM
ap-5513	420	5	-	-	PUNCT
ap-5513	420	6	dimensional	dimensional	ADJ
ap-5513	420	7	lie	lie	NOUN
ap-5513	420	8	algebras	algebra	NOUN
ap-5513	420	9	with	with	ADP
ap-5513	420	10	one	one	NUM
ap-5513	420	11	nilpotent	nilpotent	ADJ
ap-5513	420	12	base	base	NOUN
ap-5513	420	13	element	element	NOUN
ap-5513	420	14	.	.	PUNCT
ap-5513	421	1	izvestia	izvestia	PROPN
ap-5513	421	2	vysshikh	vysshikh	NOUN
ap-5513	421	3	uchebn	uchebn	NOUN
ap-5513	421	4	zavendenĭı	zavendenĭı	PROPN
ap-5513	421	5	matematika	matematika	PROPN
ap-5513	421	6	35:104	35:104	PROPN
ap-5513	421	7	–	–	PUNCT
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ap-5513	421	9	,	,	PUNCT
ap-5513	421	10	1963	1963	NUM
ap-5513	421	11	.	.	PUNCT
ap-5513	422	1	[	[	X
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ap-5513	422	3	]	]	X
ap-5513	422	4	s.	s.	PROPN
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ap-5513	422	6	,	,	PUNCT
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ap-5513	422	9	.	.	PUNCT
ap-5513	423	1	sym	sym	NOUN
ap-5513	423	2	:	:	PUNCT
ap-5513	423	3	a	a	DET
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ap-5513	423	5	symmetry	symmetry	NOUN
ap-5513	423	6	-	-	PUNCT
ap-5513	423	7	finding	find	VERB
ap-5513	423	8	package	package	NOUN
ap-5513	423	9	for	for	ADP
ap-5513	423	10	mathematica	mathematica	PROPN
ap-5513	423	11	.	.	PUNCT
ap-5513	424	1	group	group	NOUN
ap-5513	424	2	analysis	analysis	NOUN
ap-5513	424	3	of	of	ADP
ap-5513	424	4	differential	differential	ADJ
ap-5513	424	5	equations	equation	NOUN
ap-5513	424	6	pp	pp	PRON
ap-5513	424	7	.	.	PUNCT
ap-5513	425	1	64	64	NUM
ap-5513	425	2	–	–	SYM
ap-5513	425	3	70	70	NUM
ap-5513	425	4	,	,	PUNCT
ap-5513	425	5	2004	2004	NUM
ap-5513	425	6	.	.	PUNCT
ap-5513	426	1	[	[	X
ap-5513	426	2	23	23	NUM
ap-5513	426	3	]	]	X
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ap-5513	426	6	,	,	PUNCT
ap-5513	426	7	d.	d.	PROPN
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ap-5513	426	9	.	.	PUNCT
ap-5513	427	1	a	a	DET
ap-5513	427	2	new	new	ADJ
ap-5513	427	3	mathematica	mathematica	PROPN
ap-5513	427	4	-	-	PUNCT
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ap-5513	427	13	.	.	PUNCT
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ap-5513	428	5	mathematica	mathematica	PROPN
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ap-5513	428	7	.	.	PUNCT
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ap-5513	428	9	.	.	PUNCT
ap-5513	429	1	[	[	X
ap-5513	429	2	24	24	NUM
ap-5513	429	3	]	]	X
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ap-5513	429	5	t.	t.	PROPN
ap-5513	429	6	thomson	thomson	PROPN
ap-5513	429	7	,	,	PUNCT
ap-5513	429	8	m.	m.	PROPN
ap-5513	429	9	d.	d.	PROPN
ap-5513	429	10	dahleh	dahleh	PROPN
ap-5513	429	11	.	.	PUNCT
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ap-5513	430	2	of	of	ADP
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ap-5513	430	4	with	with	ADP
ap-5513	430	5	applications	application	NOUN
ap-5513	430	6	.	.	PUNCT
ap-5513	431	1	prentice	prentice	NOUN
ap-5513	431	2	-	-	PUNCT
ap-5513	431	3	hall	hall	NOUN
ap-5513	431	4	,	,	PUNCT
ap-5513	431	5	new	new	PROPN
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ap-5513	431	7	,	,	PUNCT
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ap-5513	431	9	.	.	PUNCT
ap-5513	432	1	[	[	X
ap-5513	432	2	25	25	NUM
ap-5513	432	3	]	]	PUNCT
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ap-5513	432	6	,	,	PUNCT
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ap-5513	432	9	,	,	PUNCT
ap-5513	432	10	h.	h.	PROPN
ap-5513	432	11	segur	segur	PROPN
ap-5513	432	12	.	.	PUNCT
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ap-5513	433	2	evolution	evolution	NOUN
ap-5513	433	3	equations	equation	NOUN
ap-5513	433	4	and	and	CCONJ
ap-5513	433	5	ordinary	ordinary	ADJ
ap-5513	433	6	differential	differential	ADJ
ap-5513	433	7	equations	equation	NOUN
ap-5513	433	8	of	of	ADP
ap-5513	433	9	painleve’type	painleve’type	NOUN
ap-5513	433	10	.	.	PUNCT
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ap-5513	433	12	al	al	PROPN
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ap-5513	433	16	–	–	PUNCT
ap-5513	433	17	338	338	NUM
ap-5513	433	18	,	,	PUNCT
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ap-5513	433	20	.	.	PUNCT
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ap-5513	434	2	/	/	SYM
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ap-5513	434	4	.	.	PUNCT
ap-5513	435	1	[	[	X
ap-5513	435	2	26	26	NUM
ap-5513	435	3	]	]	PUNCT
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ap-5513	435	5	j.	j.	PROPN
ap-5513	435	6	ablowitz	ablowitz	PROPN
ap-5513	435	7	,	,	PUNCT
ap-5513	435	8	a.	a.	NOUN
ap-5513	435	9	ramani	ramani	PROPN
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ap-5513	435	11	h.	h.	PROPN
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ap-5513	435	13	.	.	PUNCT
ap-5513	436	1	a	a	DET
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ap-5513	436	4	nonlinear	nonlinear	ADJ
ap-5513	436	5	evolution	evolution	NOUN
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ap-5513	436	8	ordinary	ordinary	ADJ
ap-5513	436	9	differential	differential	ADJ
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ap-5513	436	11	of	of	ADP
ap-5513	436	12	p	p	NOUN
ap-5513	436	13	-	-	PUNCT
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ap-5513	436	15	.	.	PUNCT
ap-5513	437	1	i.	i.	PROPN
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ap-5513	437	3	of	of	ADP
ap-5513	437	4	mathematical	mathematical	ADJ
ap-5513	437	5	physics	physics	NOUN
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ap-5513	437	7	–	–	PUNCT
ap-5513	437	8	721	721	NUM
ap-5513	437	9	,	,	PUNCT
ap-5513	437	10	1980	1980	NUM
ap-5513	437	11	.	.	PUNCT
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ap-5513	438	2	.	.	PUNCT
ap-5513	439	1	[	[	X
ap-5513	439	2	27	27	NUM
ap-5513	439	3	]	]	PUNCT
ap-5513	439	4	m.	m.	NOUN
ap-5513	439	5	j.	j.	PROPN
ap-5513	439	6	ablowitz	ablowitz	PROPN
ap-5513	439	7	,	,	PUNCT
ap-5513	439	8	a.	a.	NOUN
ap-5513	439	9	ramani	ramani	PROPN
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ap-5513	440	4	nonlinear	nonlinear	ADJ
ap-5513	440	5	evolution	evolution	NOUN
ap-5513	440	6	equations	equation	NOUN
ap-5513	440	7	and	and	CCONJ
ap-5513	440	8	ordinary	ordinary	ADJ
ap-5513	440	9	differential	differential	ADJ
ap-5513	440	10	equations	equation	NOUN
ap-5513	440	11	of	of	ADP
ap-5513	440	12	p	p	NOUN
ap-5513	440	13	-	-	PUNCT
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ap-5513	440	15	.	.	PUNCT
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ap-5513	441	2	.	.	PROPN
ap-5513	441	3	journal	journal	PROPN
ap-5513	441	4	of	of	ADP
ap-5513	441	5	mathematical	mathematical	ADJ
ap-5513	441	6	physics	physics	NOUN
ap-5513	441	7	21(5):1006	21(5):1006	NUM
ap-5513	441	8	–	–	PUNCT
ap-5513	441	9	1015	1015	NUM
ap-5513	441	10	,	,	PUNCT
ap-5513	441	11	1980	1980	NUM
ap-5513	441	12	.	.	PUNCT
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ap-5513	442	2	.	.	PUNCT
ap-5513	443	1	[	[	X
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ap-5513	443	3	]	]	PUNCT
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ap-5513	443	5	paliathanasis	paliathanasis	NOUN
ap-5513	443	6	,	,	PUNCT
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ap-5513	443	8	g.	g.	PROPN
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ap-5513	443	11	.	.	PUNCT
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ap-5513	444	3	differential	differential	ADJ
ap-5513	444	4	equations	equation	NOUN
ap-5513	444	5	:	:	PUNCT
ap-5513	444	6	a	a	DET
ap-5513	444	7	discussion	discussion	NOUN
ap-5513	444	8	on	on	ADP
ap-5513	444	9	symmetries	symmetry	NOUN
ap-5513	444	10	and	and	CCONJ
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ap-5513	444	12	.	.	PUNCT
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ap-5513	445	2	journal	journal	NOUN
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ap-5513	445	9	13(07):1630009	13(07):1630009	NUM
ap-5513	445	10	,	,	PUNCT
ap-5513	445	11	2016	2016	NUM
ap-5513	445	12	.	.	PUNCT
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ap-5513	446	2	/	/	SYM
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ap-5513	446	4	.	.	PROPN
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ap-5513	450	7	.	.	PUNCT
ap-5513	451	1	nonlinear	nonlinear	ADJ
ap-5513	451	2	self	self	NOUN
ap-5513	451	3	-	-	PUNCT
ap-5513	451	4	adjointness	adjointness	NOUN
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ap-5513	451	8	.	.	PUNCT
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ap-5513	452	5	:	:	PUNCT
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ap-5513	452	7	and	and	CCONJ
ap-5513	452	8	theoretical	theoretical	ADJ
ap-5513	452	9	44(43):432002	44(43):432002	NUM
ap-5513	452	10	,	,	PUNCT
ap-5513	452	11	2011	2011	NUM
ap-5513	452	12	.	.	PUNCT
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ap-5513	453	2	-	-	PUNCT
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ap-5513	453	4	.	.	PUNCT
ap-5513	454	1	[	[	X
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ap-5513	454	3	]	]	X
ap-5513	454	4	n.	n.	PROPN
ap-5513	454	5	h.	h.	PROPN
ap-5513	454	6	ibragimov	ibragimov	PROPN
ap-5513	454	7	.	.	PUNCT
ap-5513	455	1	a	a	DET
ap-5513	455	2	new	new	ADJ
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ap-5513	455	4	theorem	theorem	NOUN
ap-5513	455	5	.	.	PROPN
ap-5513	455	6	journal	journal	PROPN
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ap-5513	455	13	–	–	PUNCT
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ap-5513	455	17	.	.	PUNCT
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ap-5513	456	4	.	.	PUNCT
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ap-5513	457	3	]	]	PUNCT
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ap-5513	457	10	m.	m.	PROPN
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ap-5513	457	16	.	.	PUNCT
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ap-5513	458	2	self	self	NOUN
ap-5513	458	3	-	-	PUNCT
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ap-5513	458	5	,	,	PUNCT
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ap-5513	458	16	evolution	evolution	NOUN
ap-5513	458	17	equations	equation	NOUN
ap-5513	458	18	.	.	PUNCT
ap-5513	459	1	communications	communication	NOUN
ap-5513	459	2	in	in	ADP
ap-5513	459	3	nonlinear	nonlinear	ADJ
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ap-5513	459	5	and	and	CCONJ
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ap-5513	459	9	–	–	PUNCT
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ap-5513	459	11	,	,	PUNCT
ap-5513	459	12	2014	2014	NUM
ap-5513	459	13	.	.	PUNCT
ap-5513	460	1	doi:10.1016	doi:10.1016	PROPN
ap-5513	460	2	/	/	SYM
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ap-5513	460	4	.	.	PUNCT
ap-5513	461	1	[	[	X
ap-5513	461	2	32	32	NUM
ap-5513	461	3	]	]	PUNCT
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ap-5513	461	7	r.	r.	PROPN
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ap-5513	461	9	.	.	PUNCT
ap-5513	462	1	nonlinear	nonlinear	ADJ
ap-5513	462	2	self	self	NOUN
ap-5513	462	3	-	-	PUNCT
ap-5513	462	4	adjointness	adjointness	NOUN
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ap-5513	462	7	solutions	solution	NOUN
ap-5513	462	8	of	of	ADP
ap-5513	462	9	a	a	DET
ap-5513	462	10	2d	2d	NUM
ap-5513	462	11	rossby	rossby	ADJ
ap-5513	462	12	wave	wave	NOUN
ap-5513	462	13	equation	equation	NOUN
ap-5513	462	14	.	.	PUNCT
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ap-5513	463	4	of	of	ADP
ap-5513	463	5	physics	physics	PROPN
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ap-5513	463	7	–	–	PUNCT
ap-5513	463	8	89	89	NUM
ap-5513	463	9	,	,	PUNCT
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ap-5513	463	11	.	.	PUNCT
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ap-5513	464	2	/	/	SYM
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ap-5513	464	4	-	-	PUNCT
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ap-5513	464	6	-	-	PUNCT
ap-5513	464	7	0430	0430	NUM
ap-5513	464	8	-	-	PUNCT
ap-5513	464	9	6	6	NUM
ap-5513	464	10	.	.	NOUN
ap-5513	465	1	110	110	NUM
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ap-5513	465	3	http://dx.doi.org/10.1016/j.jmaa.2006.10.078	http://dx.doi.org/10.1016/j.jmaa.2006.10.078	PROPN
ap-5513	465	4	http://dx.doi.org/10.1016/j.cnsns.2013.12.005	http://dx.doi.org/10.1016/j.cnsns.2013.12.005	PROPN
ap-5513	465	5	http://dx.doi.org/10.2478/s11534-014-0430-6	http://dx.doi.org/10.2478/s11534-014-0430-6	PROPN
ap-5513	465	6	acta	acta	PROPN
ap-5513	465	7	polytechnica	polytechnica	PROPN
ap-5513	465	8	60(2):1–13	60(2):1–13	NUM
ap-5513	465	9	,	,	PUNCT
ap-5513	465	10	2020	2020	NUM
ap-5513	465	11	1	1	NUM
ap-5513	465	12	introduction	introduction	NOUN
ap-5513	465	13	2	2	NUM
ap-5513	465	14	lie	lie	NOUN
ap-5513	465	15	symmetry	symmetry	NOUN
ap-5513	465	16	analysis	analysis	NOUN
ap-5513	465	17	2.1	2.1	NUM
ap-5513	465	18	the	the	DET
ap-5513	465	19	euler	euler	NOUN
ap-5513	465	20	-	-	PUNCT
ap-5513	465	21	bernoulli	bernoulli	NOUN
ap-5513	465	22	equation	equation	NOUN
ap-5513	465	23	.	.	PUNCT
ap-5513	466	1	2.2	2.2	NUM
ap-5513	466	2	the	the	DET
ap-5513	466	3	rayleigh	rayleigh	PROPN
ap-5513	466	4	equation	equation	NOUN
ap-5513	466	5	.	.	PUNCT
ap-5513	467	1	2.3	2.3	NUM
ap-5513	467	2	the	the	DET
ap-5513	467	3	timoshenko	timoshenko	ADJ
ap-5513	467	4	-	-	PUNCT
ap-5513	467	5	prescott	prescott	NOUN
ap-5513	467	6	equation	equation	NOUN
ap-5513	467	7	.	.	PUNCT
ap-5513	468	1	3	3	NUM
ap-5513	468	2	the	the	DET
ap-5513	468	3	travelling	travel	VERB
ap-5513	468	4	-	-	PUNCT
ap-5513	468	5	wave	wave	NOUN
ap-5513	468	6	solution	solution	NOUN
ap-5513	468	7	3.1	3.1	NUM
ap-5513	468	8	further	further	ADJ
ap-5513	468	9	reduction	reduction	NOUN
ap-5513	468	10	of	of	ADP
ap-5513	468	11	the	the	DET
ap-5513	468	12	euler	euler	NOUN
ap-5513	468	13	-	-	PUNCT
ap-5513	468	14	bernoulli	bernoulli	PROPN
ap-5513	468	15	equation	equation	NOUN
ap-5513	468	16	.	.	PUNCT
ap-5513	469	1	3.2	3.2	NUM
ap-5513	469	2	the	the	DET
ap-5513	469	3	travelling	travel	VERB
ap-5513	469	4	wave	wave	NOUN
ap-5513	469	5	solution	solution	NOUN
ap-5513	469	6	for	for	ADP
ap-5513	469	7	the	the	DET
ap-5513	469	8	rayleigh	rayleigh	PROPN
ap-5513	469	9	equation	equation	NOUN
ap-5513	469	10	.	.	PUNCT
ap-5513	470	1	3.3	3.3	NUM
ap-5513	470	2	the	the	DET
ap-5513	470	3	travelling	travel	VERB
ap-5513	470	4	-	-	PUNCT
ap-5513	470	5	wave	wave	NOUN
ap-5513	470	6	solution	solution	NOUN
ap-5513	470	7	for	for	ADP
ap-5513	470	8	the	the	DET
ap-5513	470	9	timoshenko	timoshenko	ADJ
ap-5513	470	10	-	-	PUNCT
ap-5513	470	11	prescott	prescott	NOUN
ap-5513	470	12	equation	equation	NOUN
ap-5513	470	13	.	.	PUNCT
ap-5513	471	1	4	4	NUM
ap-5513	471	2	symmetry	symmetry	NOUN
ap-5513	471	3	analysis	analysis	NOUN
ap-5513	471	4	with	with	ADP
ap-5513	471	5	a	a	DET
ap-5513	471	6	source	source	NOUN
ap-5513	471	7	term	term	NOUN
ap-5513	471	8	4.1	4.1	NUM
ap-5513	471	9	euler	euler	NOUN
ap-5513	471	10	-	-	PUNCT
ap-5513	471	11	bernoulli	bernoulli	NOUN
ap-5513	471	12	.	.	PUNCT
ap-5513	472	1	4.2	4.2	NUM
ap-5513	472	2	rayleigh	rayleigh	ADJ
ap-5513	472	3	and	and	CCONJ
ap-5513	472	4	timoshenko	timoshenko	NOUN
ap-5513	472	5	-	-	PUNCT
ap-5513	472	6	prescott	prescott	NOUN
ap-5513	472	7	equations	equation	NOUN
ap-5513	472	8	.	.	PUNCT
ap-5513	473	1	4.3	4.3	NUM
ap-5513	473	2	symmetry	symmetry	NOUN
ap-5513	473	3	classification	classification	NOUN
ap-5513	473	4	of	of	ADP
ap-5513	473	5	ode	ode	PROPN
ap-5513	473	6	.	.	PUNCT
ap-5513	473	7	4.4	4.4	NUM
ap-5513	473	8	scaling	scale	VERB
ap-5513	473	9	solutions	solution	NOUN
ap-5513	473	10	for	for	ADP
ap-5513	473	11	the	the	DET
ap-5513	473	12	forced	force	VERB
ap-5513	473	13	euler	euler	PROPN
ap-5513	473	14	-	-	PUNCT
ap-5513	473	15	bernoulli	bernoulli	NOUN
ap-5513	473	16	equation	equation	NOUN
ap-5513	473	17	.	.	PUNCT
ap-5513	474	1	5	5	NUM
ap-5513	474	2	singularity	singularity	NOUN
ap-5513	474	3	analysis	analysis	NOUN
ap-5513	474	4	6	6	NUM
ap-5513	474	5	conservation	conservation	NOUN
ap-5513	474	6	laws	law	NOUN
ap-5513	474	7	6.1	6.1	NUM
ap-5513	474	8	conservation	conservation	NOUN
ap-5513	474	9	laws	law	NOUN
ap-5513	474	10	for	for	ADP
ap-5513	474	11	the	the	DET
ap-5513	474	12	various	various	ADJ
ap-5513	474	13	form	form	NOUN
ap-5513	474	14	of	of	ADP
ap-5513	474	15	beam	beam	NOUN
ap-5513	474	16	.	.	PUNCT
ap-5513	475	1	7	7	NUM
ap-5513	475	2	conclusion	conclusion	NOUN
ap-5513	475	3	acknowledgements	acknowledgement	NOUN
ap-5513	475	4	references	reference	NOUN