id	sid	eid	entity	type
ma-140	1	1	2023	CARDINAL
ma-140	2	1	j. math	PERSON
ma-140	4	1	3 (	CARDINAL
ma-140	4	2	2023	CARDINAL
ma-140	4	3	13doi	CARDINAL
ma-140	4	4	10.28924	CARDINAL
ma-140	4	5	joseph owuor owino	PERSON
ma-140	4	6	kenya	GPE
ma-140	4	7	kenya	GPE
ma-140	6	1	third	ORDINAL
ma-140	6	2	one	CARDINAL
ma-140	7	1	first	ORDINAL
ma-140	10	1	1.	CARDINAL
ma-140	10	2	1	CARDINAL
ma-140	11	1	0	CARDINAL
ma-140	11	2	1.1	CARDINAL
ma-140	13	1	1.1	CARDINAL
ma-140	13	2	first	ORDINAL
ma-140	13	3	morrison	PERSON
ma-140	13	4	2	CARDINAL
ma-140	13	5	1.1	CARDINAL
ma-140	14	1	3	CARDINAL
ma-140	15	1	4	CARDINAL
ma-140	16	1	first	ORDINAL
ma-140	17	1	2	CARDINAL
ma-140	18	1	3 nov 2022	CARDINAL
ma-140	20	1	solutions;symmetry	ORG
ma-140	21	1	1	CARDINAL
ma-140	21	2	https://orcid.org/0000-0002-4178-736x	CARDINAL
ma-140	22	1	j. math	PERSON
ma-140	24	1	10.28924	CARDINAL
ma-140	24	2	2	CARDINAL
ma-140	25	1	5	CARDINAL
ma-140	27	1	2.1	CARDINAL
ma-140	29	1	⊂	GPE
ma-140	29	2	⊂	GPE
ma-140	29	3	2.1	CARDINAL
ma-140	30	1	2.1	CARDINAL
ma-140	32	1	∈ n ′ ⊂ n	ORG
ma-140	32	2	∈	ORG
ma-140	34	1	0	CARDINAL
ma-140	36	1	∈	PRODUCT
ma-140	36	2	ε ∈ n ′ ⊂ n	ORG
ma-140	36	3	ε−1 ∈ n	ORG
ma-140	37	1	2.2	CARDINAL
ma-140	39	1	u(1	ORG
ma-140	41	1	u(π	ORG
ma-140	42	1	0	CARDINAL
ma-140	42	2	2.2	CARDINAL
ma-140	42	3	u(1	ORG
ma-140	42	4	u(2	ORG
ma-140	43	1	u(π	ORG
ma-140	44	1	first	ORDINAL
ma-140	44	2	second	ORDINAL
ma-140	49	1	∂uα	GPE
ma-140	51	1	2.3	CARDINAL
ma-140	53	1	di(x j	PERSON
ma-140	54	1	2.4	CARDINAL
ma-140	54	2	2.4	CARDINAL
ma-140	54	3	6].(1	CARDINAL
ma-140	55	1	2.5	CARDINAL
ma-140	55	2	0	CARDINAL
ma-140	55	3	2.3	CARDINAL
ma-140	56	1	2.5	CARDINAL
ma-140	59	1	≈	CARDINAL
ma-140	59	2	2.6	CARDINAL
ma-140	60	1	j. math	PERSON
ma-140	62	1	10.28924	CARDINAL
ma-140	62	2	2.1	CARDINAL
ma-140	62	3	taylor	PERSON
ma-140	64	1	ξi(x	GPE
ma-140	67	1	2.7	CARDINAL
ma-140	67	2	2.4	CARDINAL
ma-140	68	1	2.6	CARDINAL
ma-140	70	1	≈	CARDINAL
ma-140	70	2	1 +x)x	DATE
ma-140	71	1	≈	CARDINAL
ma-140	71	2	1 +x)uα	CARDINAL
ma-140	71	3	2.8	CARDINAL
ma-140	73	1	∂uα	GPE
ma-140	73	2	2.9	CARDINAL
ma-140	73	3	2.5	CARDINAL
ma-140	74	1	2.5	CARDINAL
ma-140	75	1	di = di(ϕ j)d̄j	ORG
ma-140	75	2	2.10	CARDINAL
ma-140	75	3	2.1	CARDINAL
ma-140	81	1	2.11	CARDINAL
ma-140	81	2	2.10	CARDINAL
ma-140	81	3	2.5	CARDINAL
ma-140	82	1	2.12	CARDINAL
ma-140	82	2	2.12	CARDINAL
ma-140	83	1	∂ϕj ∂uβ	PERSON
ma-140	87	1	∂uβ	PERSON
ma-140	88	1	2.13	CARDINAL
ma-140	88	2	u(1	ORG
ma-140	88	3	u(1	ORG
ma-140	89	1	2.14	CARDINAL
ma-140	89	2	2.6	CARDINAL
ma-140	90	1	2.5	CARDINAL
ma-140	90	2	2.14	CARDINAL
ma-140	90	3	first	ORDINAL
ma-140	91	1	2.7	CARDINAL
ma-140	91	2	first	ORDINAL
ma-140	92	1	u(1	ORG
ma-140	93	1	2.15	CARDINAL
ma-140	93	2	2.8	CARDINAL
ma-140	94	1	2.6	CARDINAL
ma-140	94	2	2.15	CARDINAL
ma-140	95	1	2	CARDINAL
ma-140	96	1	j. math	PERSON
ma-140	98	1	10.28924	CARDINAL
ma-140	98	2	2.9	CARDINAL
ma-140	99	1	2.12	CARDINAL
ma-140	99	2	2.6	CARDINAL
ma-140	99	3	7	CARDINAL
ma-140	99	4	j + ξjε)(uαj +	FAC
ma-140	99	5	2.16	CARDINAL
ma-140	103	1	2.17	CARDINAL
ma-140	103	2	α)− uαj di(ξj	PERSON
ma-140	104	1	2.18	CARDINAL
ma-140	104	2	first	ORDINAL
ma-140	105	1	2.10	CARDINAL
ma-140	106	1	one	CARDINAL
ma-140	106	2	7	CARDINAL
ma-140	111	1	2.19	CARDINAL
ma-140	111	2	2.11	CARDINAL
ma-140	113	1	gare x[1	ORG
ma-140	117	1	∂ζαi1,	PERSON
ma-140	117	2	1	CARDINAL
ma-140	117	3	2.20	CARDINAL
ma-140	117	4	2.9	CARDINAL
ma-140	119	1	2.12	CARDINAL
ma-140	120	1	2.1	CARDINAL
ma-140	121	1	ūα	PERSON
ma-140	122	1	2.21	CARDINAL
ma-140	122	2	2.13	CARDINAL
ma-140	123	1	2.1	CARDINAL
ma-140	123	2	first	ORDINAL
ma-140	123	3	linear pde	ORG
ma-140	124	1	8	CARDINAL
ma-140	126	1	0	CARDINAL
ma-140	126	2	2.22	CARDINAL
ma-140	126	3	2.13	CARDINAL
ma-140	127	1	2.14	CARDINAL
ma-140	128	1	2.1	CARDINAL
ma-140	129	1	9	CARDINAL
ma-140	129	2	first	ORDINAL
ma-140	131	1	ψn−1(x	ORG
ma-140	131	2	2.23	CARDINAL
ma-140	131	3	2.22	CARDINAL
ma-140	131	4	dx	ORG
ma-140	133	1	2.24	CARDINAL
ma-140	134	1	j. math	PERSON
ma-140	136	1	10.28924	CARDINAL
ma-140	136	2	5	CARDINAL
ma-140	137	1	2.15	CARDINAL
ma-140	138	1	2.9	CARDINAL
ma-140	138	2	2.2	CARDINAL
ma-140	138	3	1	CARDINAL
ma-140	140	1	1	CARDINAL
ma-140	140	2	2.25	CARDINAL
ma-140	140	3	x[π	ORG
ma-140	141	1	2.16	CARDINAL
ma-140	142	1	2.2	CARDINAL
ma-140	142	2	2.2	CARDINAL
ma-140	142	3	ūα	PERSON
ma-140	145	1	0	CARDINAL
ma-140	146	1	2.26	CARDINAL
ma-140	146	2	2.17	CARDINAL
ma-140	147	1	2.1	CARDINAL
ma-140	147	2	2.5	CARDINAL
ma-140	147	3	ūα	PERSON
ma-140	148	1	2.27	CARDINAL
ma-140	148	2	algebras	ORG
ma-140	149	1	2.18	CARDINAL
ma-140	150	1	2.9	CARDINAL
ma-140	151	1	xixj −xjxi	PERSON
ma-140	151	2	2.28	CARDINAL
ma-140	151	3	1	CARDINAL
ma-140	153	1	2.19	CARDINAL
ma-140	154	1	jacobi	ORG
ma-140	154	2	5	CARDINAL
ma-140	155	1	2.20	CARDINAL
ma-140	156	1	2.25	CARDINAL
ma-140	156	2	10	CARDINAL
ma-140	158	1	jacobi	ORG
ma-140	158	2	9	CARDINAL
ma-140	158	3	11	CARDINAL
ma-140	160	1	11	CARDINAL
ma-140	161	1	2.21	CARDINAL
ma-140	162	1	euler	PERSON
ma-140	164	1	2.29	CARDINAL
ma-140	164	2	11	CARDINAL
ma-140	166	1	2.30	CARDINAL
ma-140	167	1	j. math	PERSON
ma-140	169	1	10.28924	CARDINAL
ma-140	169	2	2.22	CARDINAL
ma-140	170	1	2.30	CARDINAL
ma-140	171	1	∂uαi1i2	ORG
ma-140	171	2	2.31	CARDINAL
ma-140	174	1	ζαi1	PERSON
ma-140	175	1	j = 1	PERSON
ma-140	176	1	n.	PERSON
ma-140	176	2	2.32	CARDINAL
ma-140	176	3	− ξjuαj	PERSON
ma-140	177	1	2.33	CARDINAL
ma-140	177	2	2.23	CARDINAL
ma-140	178	1	2.31	CARDINAL
ma-140	178	2	∂uα	GPE
ma-140	179	1	∂uαi1i2	ORG
ma-140	180	1	2.34	CARDINAL
ma-140	181	1	2.24	CARDINAL
ma-140	183	1	u(1	ORG
ma-140	184	1	2.2	CARDINAL
ma-140	184	2	7	CARDINAL
ma-140	185	1	2.35	CARDINAL
ma-140	186	1	2.25	CARDINAL
ma-140	187	1	one	CARDINAL
ma-140	187	2	2.36	CARDINAL
ma-140	188	1	10	CARDINAL
ma-140	188	2	0	CARDINAL
ma-140	188	3	2.36	CARDINAL
ma-140	189	1	5	CARDINAL
ma-140	189	2	2.2	CARDINAL
ma-140	190	1	2.26	CARDINAL
ma-140	191	1	adjoint	ORG
ma-140	191	2	2.2	CARDINAL
ma-140	193	1	u(π	ORG
ma-140	194	1	0	CARDINAL
ma-140	194	2	2.37	CARDINAL
ma-140	194	3	2.27	CARDINAL
ma-140	195	1	2.2	CARDINAL
ma-140	195	2	2.37	CARDINAL
ma-140	195	3	8	CARDINAL
ma-140	197	1	u(1	ORG
ma-140	198	1	u(π	ORG
ma-140	199	1	2.38	CARDINAL
ma-140	199	2	2.28	CARDINAL
ma-140	200	1	infinitesimal	NORP
ma-140	200	2	2.2	CARDINAL
ma-140	200	3	6	CARDINAL
ma-140	200	4	0	CARDINAL
ma-140	200	5	2.39	CARDINAL
ma-140	205	1	−dk	GPE
ma-140	208	1	∂uαijk −	PERSON
ma-140	209	1	2.40	CARDINAL
ma-140	210	1	j. math	PERSON
ma-140	212	1	10.28924	CARDINAL
ma-140	213	1	3.1	CARDINAL
ma-140	214	1	first	ORDINAL
ma-140	214	2	1.1	CARDINAL
ma-140	214	3	one	CARDINAL
ma-140	215	1	3.1	CARDINAL
ma-140	215	2	0	CARDINAL
ma-140	215	3	3.2	CARDINAL
ma-140	215	4	∂ux	ORG
ma-140	215	5	∂utxx	GPE
ma-140	215	6	3.3	CARDINAL
ma-140	215	7	third	ORDINAL
ma-140	215	8	2.20	CARDINAL
ma-140	215	9	3.4	CARDINAL
ma-140	215	10	3.5	CARDINAL
ma-140	215	11	3.6	CARDINAL
ma-140	216	1	3.7	CARDINAL
ma-140	216	2	2.19	CARDINAL
ma-140	218	1	∂ux + utt	ORG
ma-140	218	2	3.8	CARDINAL
ma-140	220	1	∂ux + utx	ORG
ma-140	221	1	3.9	CARDINAL
ma-140	221	2	dx	ORG
ma-140	221	3	3.8	CARDINAL
ma-140	221	4	3.9	CARDINAL
ma-140	224	1	−τu	ORG
ma-140	231	1	+ uxx(−ξt	GPE
ma-140	233	1	+ ux(ηu	PERSON
ma-140	236	1	j. math	PERSON
ma-140	238	1	10.28924	CARDINAL
ma-140	239	1	2ξtx	CARDINAL
ma-140	240	1	2ξx	ORDINAL
ma-140	241	1	2τtxu	CARDINAL
ma-140	244	1	2τtx	CARDINAL
ma-140	244	2	ξxx	CARDINAL
ma-140	246	1	2ξxuu	CARDINAL
ma-140	248	1	2	CARDINAL
ma-140	248	2	u2 xu 2	PERSON
ma-140	248	3	t (−τuuu	ORG
ma-140	249	1	uxutxx(−2ξu	ORG
ma-140	250	1	3 x	QUANTITY
ma-140	250	2	+ uttx(−2τx	PERSON
ma-140	252	1	3.10	CARDINAL
ma-140	252	2	3.2	CARDINAL
ma-140	253	1	0	CARDINAL
ma-140	253	2	3.11	CARDINAL
ma-140	253	3	ζ1	GPE
ma-140	253	4	3.11	CARDINAL
ma-140	256	1	−τu	ORG
ma-140	257	1	− ξx	PERSON
ma-140	259	1	2ξtx	CARDINAL
ma-140	261	1	2ξx	ORDINAL
ma-140	262	1	2τtxu	CARDINAL
ma-140	265	1	2τtx	CARDINAL
ma-140	265	2	ξxx	CARDINAL
ma-140	267	1	2ξxuu	CARDINAL
ma-140	269	1	2	CARDINAL
ma-140	269	2	u2 xu 2	PERSON
ma-140	269	3	t (−τuuu	ORG
ma-140	270	1	uxutxx(−2ξu	ORG
ma-140	271	1	3 x	QUANTITY
ma-140	271	2	+ uttx(−2τx	PERSON
ma-140	273	1	u txx=− ut β −α	ORG
ma-140	273	2	3.12	CARDINAL
ma-140	274	1	uux	ORG
ma-140	274	2	3.12	CARDINAL
ma-140	275	1	j. math	PERSON
ma-140	277	1	10.28924	CARDINAL
ma-140	280	1	−τu	ORG
ma-140	281	1	− ξx	PERSON
ma-140	283	1	2ξtx	CARDINAL
ma-140	284	1	2ξx	ORDINAL
ma-140	285	1	2τtxu	CARDINAL
ma-140	288	1	2τtx	CARDINAL
ma-140	288	2	ξxx	CARDINAL
ma-140	290	1	2ξxuu	CARDINAL
ma-140	292	1	2	CARDINAL
ma-140	292	2	u2 xu 2	PERSON
ma-140	292	3	t (−τuuu	ORG
ma-140	292	4	3 x	QUANTITY
ma-140	292	5	+ uttx(−2τx	PERSON
ma-140	295	1	3.13	CARDINAL
ma-140	296	1	+ 2ξx	CARDINAL
ma-140	297	1	2βηtxu	CARDINAL
ma-140	299	1	− 2βξtxu	PERSON
ma-140	300	1	2ξtx	CARDINAL
ma-140	303	1	2τtx	CARDINAL
ma-140	304	1	2ξxuu	CARDINAL
ma-140	305	1	2	CARDINAL
ma-140	305	2	u2 xu 2	PERSON
ma-140	305	3	t (−τuuu	ORG
ma-140	307	1	3 x	QUANTITY
ma-140	307	2	+ uttx(−2τx	PERSON
ma-140	310	1	3.14	CARDINAL
ma-140	311	1	j. math	PERSON
ma-140	313	1	10.28924	CARDINAL
ma-140	314	1	η	ORG
ma-140	315	1	0	CARDINAL
ma-140	315	2	3.15	CARDINAL
ma-140	315	3	0	CARDINAL
ma-140	315	4	3.16	CARDINAL
ma-140	315	5	0	CARDINAL
ma-140	315	6	3.17	CARDINAL
ma-140	315	7	3.15	CARDINAL
ma-140	315	8	3.18	CARDINAL
ma-140	315	9	3.19	CARDINAL
ma-140	315	10	+ b(t	PERSON
ma-140	316	1	3.20	CARDINAL
ma-140	316	2	3.17	CARDINAL
ma-140	316	3	+ bx(t	PERSON
ma-140	317	1	0	CARDINAL
ma-140	318	1	3.21	CARDINAL
ma-140	318	2	3.21	CARDINAL
ma-140	318	3	3.22	CARDINAL
ma-140	318	4	bx(t	PERSON
ma-140	318	5	0	CARDINAL
ma-140	318	6	3.23	CARDINAL
ma-140	318	7	0	CARDINAL
ma-140	319	1	3.24	CARDINAL
ma-140	319	2	3.22	CARDINAL
ma-140	319	3	3.23	CARDINAL
ma-140	319	4	3.25	CARDINAL
ma-140	320	1	3.26	CARDINAL
ma-140	320	2	3.26	CARDINAL
ma-140	320	3	3.24	CARDINAL
ma-140	320	4	0	CARDINAL
ma-140	321	1	3.27	CARDINAL
ma-140	321	2	3.27	CARDINAL
ma-140	321	3	b(t	PERSON
ma-140	322	1	3.28	CARDINAL
ma-140	322	2	3.16	CARDINAL
ma-140	322	3	c2u + c3	PERSON
ma-140	323	1	0	CARDINAL
ma-140	324	1	3.29	CARDINAL
ma-140	324	2	3.29	CARDINAL
ma-140	327	1	3.30	CARDINAL
ma-140	328	1	j. math	PERSON
ma-140	330	1	10.28924	CARDINAL
ma-140	332	1	3.31	CARDINAL
ma-140	333	1	3.32	CARDINAL
ma-140	333	2	η =c2u + c3	PERSON
ma-140	334	1	3.33	CARDINAL
ma-140	334	2	four	CARDINAL
ma-140	334	3	3.34	CARDINAL
ma-140	335	1	3.35	CARDINAL
ma-140	335	2	3.36	CARDINAL
ma-140	336	1	3.37	CARDINAL
ma-140	336	2	3.2	CARDINAL
ma-140	339	1	9	CARDINAL
ma-140	340	1	x4	PERSON
ma-140	341	1	0	CARDINAL
ma-140	342	1	3.38	CARDINAL
ma-140	342	2	3.1	CARDINAL
ma-140	344	1	1	CARDINAL
ma-140	350	1	x4 x3 0	PERSON
ma-140	351	1	0 1 ux4 x4 0 -x4 1 ux4	QUANTITY
ma-140	351	2	0	CARDINAL
ma-140	351	3	1	CARDINAL
ma-140	353	1	3.3	CARDINAL
ma-140	355	1	one	CARDINAL
ma-140	355	2	6	CARDINAL
ma-140	356	1	1	CARDINAL
ma-140	356	2	2	DATE
ma-140	356	3	3	DATE
ma-140	356	4	4	DATE
ma-140	357	1	one	CARDINAL
ma-140	358	1	3.39	CARDINAL
ma-140	359	1	j. math	PERSON
ma-140	361	1	10.28924	CARDINAL
ma-140	361	2	0	CARDINAL
ma-140	361	3	1	CARDINAL
ma-140	361	4	0	CARDINAL
ma-140	361	5	3.40	CARDINAL
ma-140	361	6	3.40	CARDINAL
ma-140	361	7	one	CARDINAL
ma-140	362	1	3.41	CARDINAL
ma-140	362	2	one	CARDINAL
ma-140	362	3	t̄	GPE
ma-140	363	1	3.42	CARDINAL
ma-140	363	2	five	CARDINAL
ma-140	363	3	one	CARDINAL
ma-140	363	4	t̄	GPE
ma-140	363	5	t̄	GPE
ma-140	364	1	ueε2	PERSON
ma-140	364	2	t̄	GPE
ma-140	364	3	t̄	GPE
ma-140	364	4	t + ε4	DATE
ma-140	365	1	3.43	CARDINAL
ma-140	365	2	3.4	CARDINAL
ma-140	369	1	illustratethese	NORP
ma-140	370	1	1.1	CARDINAL
ma-140	370	2	3.44	CARDINAL
ma-140	371	1	one	CARDINAL
ma-140	371	2	x)e−ε2	ORG
ma-140	372	1	3.45	CARDINAL
ma-140	372	2	3.5	CARDINAL
ma-140	376	1	lagrangian	ORG
ma-140	377	1	j. math	PERSON
ma-140	379	1	10.28924	CARDINAL
ma-140	379	2	0	CARDINAL
ma-140	380	1	1	CARDINAL
ma-140	380	2	3.46	CARDINAL
ma-140	380	3	two	CARDINAL
ma-140	380	4	j2 = u. thus	ORG
ma-140	380	5	j2 = φ(j1	ORG
ma-140	380	6	u(t	ORG
ma-140	381	1	3.47	CARDINAL
ma-140	382	1	0	CARDINAL
ma-140	383	1	1.1	CARDINAL
ma-140	383	2	first	ORDINAL
ma-140	383	3	0	CARDINAL
ma-140	383	4	φ(t	ORG
ma-140	383	5	3.48	CARDINAL
ma-140	386	1	lagrangian	ORG
ma-140	388	1	3.49	CARDINAL
ma-140	388	2	j2 = tu	PERSON
ma-140	389	1	3.50	CARDINAL
ma-140	389	2	3.51	CARDINAL
ma-140	390	1	3.52	CARDINAL
ma-140	390	2	3.53	CARDINAL
ma-140	390	3	1.1	CARDINAL
ma-140	390	4	second	ORDINAL
ma-140	392	1	0	CARDINAL
ma-140	393	1	3.54	CARDINAL
ma-140	394	1	j. math	PERSON
ma-140	396	1	10.28924	CARDINAL
ma-140	396	2	14hence	CARDINAL
ma-140	397	1	1.1	CARDINAL
ma-140	397	2	u(t	ORG
ma-140	397	3	3.55	CARDINAL
ma-140	397	4	3.54).(iii	CARDINAL
ma-140	398	1	x3	PERSON
ma-140	398	2	− tu = dx 0	PERSON
ma-140	399	1	1	CARDINAL
ma-140	399	2	3.56	CARDINAL
ma-140	399	3	j2 = tu	PERSON
ma-140	401	1	x4	PERSON
ma-140	404	1	∂tcharacteristic	ORG
ma-140	404	2	x4	PERSON
ma-140	404	3	1	CARDINAL
ma-140	405	1	3.57	CARDINAL
ma-140	406	1	j2 = u.	ORG
ma-140	406	2	1.1	CARDINAL
ma-140	406	3	j2 = φ(j1	ORG
ma-140	407	1	u(t	ORG
ma-140	408	1	3.58	CARDINAL
ma-140	408	2	0	CARDINAL
ma-140	408	3	3.59	CARDINAL
ma-140	408	4	3.60	CARDINAL
ma-140	408	5	0	CARDINAL
ma-140	409	1	3.61	CARDINAL
ma-140	409	2	1.1	CARDINAL
ma-140	409	3	first	ORDINAL
ma-140	410	1	0	CARDINAL
ma-140	411	1	3.62	CARDINAL
ma-140	411	2	3.62	CARDINAL
ma-140	411	3	0 or φ′(x	DATE
ma-140	412	1	0	CARDINAL
ma-140	416	1	0	CARDINAL
ma-140	416	2	u(t	ORG
ma-140	417	1	3.63	CARDINAL
ma-140	417	2	3.6	CARDINAL
ma-140	419	1	consideringa linear	ORG
ma-140	419	2	x4	PERSON
ma-140	419	3	cx1 +x4	PERSON
ma-140	420	1	3.64	CARDINAL
ma-140	420	2	1	CARDINAL
ma-140	420	3	3.65	CARDINAL
ma-140	421	1	j. math	PERSON
ma-140	423	1	10.28924	CARDINAL
ma-140	423	2	two	CARDINAL
ma-140	424	1	j2 = u.	ORG
ma-140	425	1	u(t	ORG
ma-140	425	2	3.66	CARDINAL
ma-140	425	3	1.1	CARDINAL
ma-140	425	4	second	ORDINAL
ma-140	425	5	αqq′ +	DATE
ma-140	425	6	0	CARDINAL
ma-140	425	7	3.67	CARDINAL
ma-140	426	1	0	CARDINAL
ma-140	426	2	3.68	CARDINAL
ma-140	427	1	3.68	CARDINAL
ma-140	427	2	2βc	ORDINAL
ma-140	428	1	2cq	ORDINAL
ma-140	430	1	3.69	CARDINAL
ma-140	430	2	2βc	ORDINAL
ma-140	430	3	1 2c	CARDINAL
ma-140	430	4	2c	CARDINAL
ma-140	430	5	1	CARDINAL
ma-140	430	6	1 2c	CARDINAL
ma-140	430	7	3.70	CARDINAL
ma-140	430	8	c3	PERSON
ma-140	431	1	q(x − ct	PERSON
ma-140	433	1	3.71	CARDINAL
ma-140	433	2	u(t	ORG
ma-140	434	1	3.72	CARDINAL
ma-140	434	2	4	CARDINAL
ma-140	434	3	1.1	CARDINAL
ma-140	435	1	4.1	CARDINAL
ma-140	437	1	euler	PERSON
ma-140	437	2	6	CARDINAL
ma-140	439	1	0	CARDINAL
ma-140	440	1	4.1	CARDINAL
ma-140	440	2	∂ux	ORG
ma-140	440	3	∂utxx +	GPE
ma-140	442	1	4.2	CARDINAL
ma-140	442	2	4.1	CARDINAL
ma-140	444	1	0	CARDINAL
ma-140	445	1	4.3	CARDINAL
ma-140	446	1	j. math	PERSON
ma-140	448	1	10.28924	CARDINAL
ma-140	450	1	∂ux + utt	ORG
ma-140	450	2	4.4	CARDINAL
ma-140	452	1	∂ux + utx	ORG
ma-140	453	1	4.5	CARDINAL
ma-140	453	2	4.3	CARDINAL
ma-140	454	1	2	CARDINAL
ma-140	454	2	4.6	CARDINAL
ma-140	454	3	4.6	CARDINAL
ma-140	454	4	four	CARDINAL
ma-140	454	5	0	CARDINAL
ma-140	454	6	4.7	CARDINAL
ma-140	454	7	0	CARDINAL
ma-140	454	8	4.8	CARDINAL
ma-140	454	9	4.9	CARDINAL
ma-140	454	10	0	CARDINAL
ma-140	454	11	4.10	CARDINAL
ma-140	454	12	4.7	CARDINAL
ma-140	454	13	+ b(t	PERSON
ma-140	454	14	4.11	CARDINAL
ma-140	454	15	4.8-4.9	CARDINAL
ma-140	454	16	+ b(t	PERSON
ma-140	455	1	4.12	CARDINAL
ma-140	455	2	4.12	CARDINAL
ma-140	455	3	4.10	CARDINAL
ma-140	456	1	0	CARDINAL
ma-140	457	1	4.13	CARDINAL
ma-140	457	2	4.13	CARDINAL
ma-140	457	3	bx(t	PERSON
ma-140	457	4	0	CARDINAL
ma-140	457	5	4.14	CARDINAL
ma-140	457	6	0	CARDINAL
ma-140	458	1	4.15	CARDINAL
ma-140	458	2	4.14	CARDINAL
ma-140	459	1	bx(t	ORG
ma-140	459	2	4.16	CARDINAL
ma-140	459	3	b(t	PERSON
ma-140	460	1	4.17	CARDINAL
ma-140	461	1	4.18	CARDINAL
ma-140	462	1	j. math	PERSON
ma-140	464	1	10.28924	CARDINAL
ma-140	464	2	two	CARDINAL
ma-140	464	3	1	CARDINAL
ma-140	464	4	4.19	CARDINAL
ma-140	465	1	4.20	CARDINAL
ma-140	465	2	4.1	CARDINAL
ma-140	467	1	x(t	PERSON
ma-140	468	1	4.21	CARDINAL
ma-140	469	1	1expansion	CARDINAL
ma-140	469	2	4.21	CARDINAL
ma-140	469	3	1{ut	CARDINAL
ma-140	471	1	uxt x	PERSON
ma-140	472	1	4.22	CARDINAL
ma-140	472	2	4.22	CARDINAL
ma-140	472	3	third	ORDINAL
ma-140	475	1	uxt x	PERSON
ma-140	476	1	4.24	CARDINAL
ma-140	476	2	4.23	CARDINAL
ma-140	476	3	βutx	PERSON
ma-140	477	1	4.25	CARDINAL
ma-140	477	2	4.25	CARDINAL
ma-140	477	3	4.22	CARDINAL
ma-140	478	1	4.26	CARDINAL
ma-140	478	2	second	ORDINAL
ma-140	478	3	4.27	CARDINAL
ma-140	478	4	0	CARDINAL
ma-140	479	1	4.29	CARDINAL
ma-140	479	2	4.27	CARDINAL
ma-140	479	3	4.28	CARDINAL
ma-140	480	1	4.29	CARDINAL
ma-140	480	2	4.30	CARDINAL
ma-140	480	3	first	ORDINAL
ma-140	482	1	1	CARDINAL
ma-140	482	2	4.31	CARDINAL
ma-140	484	1	0	CARDINAL
ma-140	485	1	4.33	CARDINAL
ma-140	486	1	j. math	PERSON
ma-140	488	1	10.28924	CARDINAL
ma-140	489	1	4.31-4.32	CARDINAL
ma-140	489	2	+ b(t	PERSON
ma-140	489	3	4.34	CARDINAL
ma-140	489	4	u2 2 + c(t	PERSON
ma-140	489	5	4.35	CARDINAL
ma-140	489	6	4.33	CARDINAL
ma-140	490	1	0	CARDINAL
ma-140	491	1	4.36	CARDINAL
ma-140	491	2	c(t	ORG
ma-140	491	3	4.37	CARDINAL
ma-140	492	1	u2 2 +	PERSON
ma-140	492	2	4.38	CARDINAL
ma-140	492	3	1	CARDINAL
ma-140	493	1	+dx	GPE
ma-140	494	1	0	CARDINAL
ma-140	495	1	4.39	CARDINAL
ma-140	498	1	uxt x	PERSON
ma-140	499	1	4.40	CARDINAL
ma-140	499	2	4.40	CARDINAL
ma-140	499	3	third	ORDINAL
ma-140	502	1	uxt x	PERSON
ma-140	503	1	4.42	CARDINAL
ma-140	503	2	4.41	CARDINAL
ma-140	504	1	4.43	CARDINAL
ma-140	504	2	4.43	CARDINAL
ma-140	504	3	4.40	CARDINAL
ma-140	506	1	4.44	CARDINAL
ma-140	506	2	second	ORDINAL
ma-140	506	3	4.45	CARDINAL
ma-140	508	1	4.47	CARDINAL
ma-140	509	1	j. math	PERSON
ma-140	511	1	10.28924	CARDINAL
ma-140	511	2	4.45	CARDINAL
ma-140	511	3	4.46	CARDINAL
ma-140	511	4	2 x	QUANTITY
ma-140	512	1	equation(4.47	ORG
ma-140	512	2	4.48	CARDINAL
ma-140	512	3	first	ORDINAL
ma-140	512	4	4.49	CARDINAL
ma-140	512	5	0	CARDINAL
ma-140	513	1	4.51	CARDINAL
ma-140	513	2	4.49-4.50	CARDINAL
ma-140	513	3	4.52	CARDINAL
ma-140	513	4	3 +d(t	QUANTITY
ma-140	513	5	4.53	CARDINAL
ma-140	513	6	4.51	CARDINAL
ma-140	514	1	0	CARDINAL
ma-140	515	1	4.54	CARDINAL
ma-140	515	2	c(t	ORG
ma-140	515	3	c(t	ORG
ma-140	516	1	2 + u2 2	MONEY
ma-140	516	2	4.55	CARDINAL
ma-140	517	1	4.56	CARDINAL
ma-140	518	1	2 + u2 2	MONEY
ma-140	520	1	0	CARDINAL
ma-140	521	1	4.57	CARDINAL
ma-140	521	2	4.2	CARDINAL
ma-140	522	1	two	CARDINAL
ma-140	523	1	1	CARDINAL
ma-140	524	1	5	CARDINAL
ma-140	524	2	third	ORDINAL
ma-140	529	1	j. math	PERSON
ma-140	531	1	10.28924	CARDINAL
ma-140	534	1	1	CARDINAL
ma-140	534	2	one	CARDINAL
ma-140	534	3	cambridge university press	ORG
ma-140	534	4	cambridge	GPE
ma-140	534	5	1984.[2	CARDINAL
ma-140	534	6	morrison	GPE
ma-140	534	7	j.r. cary	PERSON
ma-140	535	1	11	CARDINAL
ma-140	535	2	1984	DATE
ma-140	536	1	324–336	CARDINAL
ma-140	537	1	l.r.t	NORP
ma-140	537	2	gardner	PERSON
ma-140	537	3	g.a. gardner	PERSON
ma-140	537	4	f.a. ayoub	ORG
ma-140	537	5	n.k. amein	PERSON
ma-140	537	6	commun	PERSON
ma-140	539	1	meth.engng	PERSON
ma-140	539	2	13 (1997	DATE
ma-140	540	1	583–592	CARDINAL
ma-140	542	1	l.r.t	NORP
ma-140	542	2	gardner	PERSON
ma-140	542	3	g.a. gardner	PERSON
ma-140	542	4	j. comput	PERSON
ma-140	544	1	101	CARDINAL
ma-140	544	2	1992	DATE
ma-140	544	3	218–223	CARDINAL
ma-140	545	1	owino	WORK_OF_ART
ma-140	545	2	one	CARDINAL
ma-140	546	1	j. adv.	PERSON
ma-140	547	1	multidisc	PERSON
ma-140	549	1	2 (	CARDINAL
ma-140	549	2	2022	CARDINAL
ma-140	549	3	525	CARDINAL
ma-140	549	4	korteweg-de vries	ORG
ma-140	551	1	multidisc	PERSON
ma-140	553	1	2 (	CARDINAL
ma-140	553	2	2022	CARDINAL
ma-140	553	3	76	CARDINAL
ma-140	553	4	j. owuor owino	PERSON
ma-140	553	5	korteweg-de vries	ORG
ma-140	555	1	1 (	CARDINAL
ma-140	555	2	2021	CARDINAL
ma-140	555	3	133–150	CARDINAL
ma-140	556	1	owino	WORK_OF_ART
ma-140	557	1	j. math	PERSON
ma-140	559	1	10 (2022	CARDINAL
ma-140	559	2	2894-2909	DATE
ma-140	560	1	j. owuor	PERSON
ma-140	560	2	korteweg-de vries	ORG
ma-140	561	1	j. math	PERSON
ma-140	563	1	10 (2022	CARDINAL
ma-140	564	1	j. o. owino	PERSON
ma-140	565	1	j. adv	PERSON
ma-140	568	1	2 (	CARDINAL
ma-140	568	2	2022	CARDINAL
ma-140	568	3	191-207.[11	CARDINAL
ma-140	568	4	j. o. owino	PERSON
ma-140	569	1	j. adv	PERSON
ma-140	572	1	2 (	CARDINAL
ma-140	572	2	2022	CARDINAL
ma-140	572	3	9	CARDINAL
ma-140	576	1	2	CARDINAL
ma-140	576	2	algebras conservation	ORG
ma-140	576	3	3	CARDINAL
ma-140	576	4	3.1	CARDINAL
ma-140	577	1	3.2	CARDINAL
ma-140	578	1	3.3	CARDINAL
ma-140	579	1	3.4	CARDINAL
ma-140	580	1	3.5	CARDINAL
ma-140	581	1	3.6	CARDINAL
ma-140	582	1	4	CARDINAL
ma-140	582	2	1.1	CARDINAL
ma-140	582	3	4.1	CARDINAL
ma-140	583	1	5	CARDINAL