The Formation and Propagation of Soliton Wave Profiles for the Shynaray-IIa Equation

Figures & Tables

		m → 1	m → 0			m → 1	m → 0
1	snu	tanhu	sinu	7	dcu	1	secu
2	cnu	sechu	cosu	8	ncu	coshu	secu
3	dnu	sechu	1	9	scu	sinhu	tanu
4	cdu	1	cosu	10	nsu	cothu	cscu
5	sdu	sinhu	sinu	11	dsu	cschu	cscu
6	ndu	coshu	1	12	csu	cschu	cotu

	P	Q	R	F
1	m²	−(1 + m²)	1	sn, cd
2	−m²	2m² − 1	1 − m²	cn
3	−1	2 − m²	m² − 1	dn
4	1	−(1 + m²)	m²	ns, dc
5	1 − m²	2m² − 1	−m²	nc
6	m² − 1	2 − m²	−1	nd
7	1 − m²	2 − m²	1	sc
8	−m²(1 − m²)	2m² − 1	1	sd
9	1	2 − m²	1 − m²	cs
10	1	2m² − 1	-m²(1 − m²)	ds
11	−14 {{ - 1} \over 4}	m2+12 {{{m^2} + 1} \over 2}	−(1−m2)24 {{ - {{(1 - {m^2})}^2}} \over 4}	mcn ∓ dn
12	14 {1 \over 4}	−2m2+12 {{ - 2{m^2} + 1} \over 2}	14 {1 \over 4}	ns ∓ cs
13	1−m24 {{1 - {m^2}} \over 4}	m2+12 {{{m^2} + 1} \over 2}	1−m24 {{1 - {m^2}} \over 4}	nc ∓ sc
14	14 {1 \over 4}	m2−22 {{{m^2} - 2} \over 2}	m44 {{{m^4}} \over 4}	ns ∓ ns
15	m24 {{{m^2}} \over 4}	m2−22 {{{m^2} - 2} \over 2}	m24 {{{m^2}} \over 4}	sn∓icn,sn1−m2sn sn \mp icn,{{sn} \over {\sqrt {1 - {m^2}sn} }}
16	14 {1 \over 4}	1−2m22 {{1 - 2{m^2}} \over 2}	14 {1 \over 4}	mcn∓idn,sn1∓cn mcn \mp idn,{{sn} \over {1 \mp cn}}
17	m24 {{{m^2}} \over 4}	m2−22 {{{m^2} - 2} \over 2}	14 {1 \over 4}	sn1∓dn {{sn} \over {1 \mp dn}}
18	m2−14 {{{m^2} - 1} \over 4}	m2+12 {{{m^2} + 1} \over 2}	m2−14 {{{m^2} - 1} \over 4}	dn1∓msn {{dn} \over {1 \mp msn}}
19	1−m24 {{1 - {m^2}} \over 4}	m2+12 {{{m^2} + 1} \over 2}	−m2+14 {{ - {m^2} + 1} \over 4}	cn1∓sn {{cn} \over {1 \mp sn}}
20	(1−m2)24 {{{{(1 - {m^2})}^2}} \over 4}	m2+12 {{{m^2} + 1} \over 2}	14 {1 \over 4}	sndn∓cn {{sn} \over {dn \mp cn}}
21	m44 {{{m^4}} \over 4}	m2−22 {{{m^2} - 2} \over 2}	14 {1 \over 4}	cn1−m2∓dn {{cn} \over {\sqrt {1 - {m^2} \mp dn} }}