The Study of the Solution to a Generalized KdV-mKdV Equation

Table 1

No.	𝑧(𝜉)	𝑐3	𝑐2	𝑐1
1	sn(𝜉),cd(𝜉)=cn(𝜉)dn(𝜉)	2𝑟^2	−𝑟^2+1	1
2	cn(𝜉)	−2𝑟^2	2𝑟^2−1	1−𝑟^2
3	dn(𝜉)	−2	2−𝑟^2	𝑟^2−1
4	1nc(𝜉)=cn(𝜉)	2(1−𝑟^2)	2𝑟^2−1	−𝑟^2
5	1ns(𝜉)=sn(𝜉),dc(𝜉)=dn(𝜉)cn(𝜉)	2	−(𝑟^2+1)	𝑟^2
6	1nd(𝜉)=dn(𝜉)	2(𝑟^2−1)	2−𝑟^2	−1
7	cs(𝜉)=cn(𝜉)sn(𝜉)	2	2−𝑟^2	1−𝑟^2
8	sc(𝜉)=sn(𝜉)cn(𝜉)	21−𝑟^2	2−𝑟^2	1
9	sd(𝜉)=sn(𝜉)dn(𝜉)	2𝑟^2𝑟^2−1	2𝑟^2−1	1
10	ds(𝜉)=dn(𝜉)sn(𝜉)	2	2𝑟^2−1	𝑟^4−𝑟^2
11	𝑟cn(𝜉)±dn(𝜉)	−12	𝑟^2+12	−(1−𝑟^2)^24
12	1±sn(𝜉)cn(𝜉)sn(𝜉)	12	−2𝑟^2+12	14
13	1±cn(𝜉)sn(𝜉)cn(𝜉)	1−𝑟^22	𝑟^2+12	1−𝑟^24
14	1±sn(𝜉)dn(𝜉)sn(𝜉)	12	𝑟^2−22	𝑟^44
15	sn(𝜉)±𝑖cn(𝜉),dn(𝜉)√1−𝑟^2sn(𝜉)±cn(𝜉)	𝑟^22	𝑟^2−22	𝑟^24
16	𝑟sn(𝜉)±𝑖dn(𝜉),sn(𝜉)1±cn(𝜉)	12	1−2𝑟^22	14
17	sn(𝜉)1±dn(𝜉)	𝑟^22	𝑟^2−22	14
18	dn(𝜉)1±rsn(𝜉)	𝑟^2−12	𝑟^2+12	𝑟^2−14
19	cn(𝜉)1±sn(𝜉)	1−𝑟^22	𝑟^2+12	−𝑟^2+14
20	sn(𝜉)dn(𝜉)±cn(𝜉)	(1−𝑟^2)^22	𝑟^2+12	14
21	cn(𝜉)√1−𝑟^2±dn(𝜉)	𝑟^42	𝑟^2−22	14