New Jacobi Elliptic Function Solutions for the Kudryashov-Sinelshchikov Equation Using Improved F-Expansion Method

Table 1

Relations between values of 𝑟, 𝑝, 𝑞, and corresponding 𝐹(𝜉) in 𝐹^′2=𝑞𝐹³+𝑝𝐹²+𝑟𝐹.

Case	𝑟	𝑝	𝑞	𝐹(𝜉)
1	4	−4(𝑚^2+1)	4𝑚^2	sn^2(𝜉)
2	4(1−𝑚^2)	4(2𝑚^2−1)	−4𝑚^2	cn^2(𝜉)
3	−4(1−𝑚^2)	4(2−𝑚^2)	−4	dn^2(𝜉)
4	𝑚^2	2(1+𝑚^2)	𝑚^2	(sn(𝜉)±𝑖cn(𝜉))^2
5	−(1−𝑚^2)^2	2(𝑚^2−2)	−1	(𝑚cn(𝜉)±dn(𝜉))^2
6	1−𝑚^2	2(1+𝑚^2)	1−𝑚^2	cn(𝜉)1+sn(𝜉)^2
7	𝑚^2−1	2(1+𝑚^2)	𝑚^2−1	dn(𝜉)1+𝑚sn(𝜉)^2
8	𝑚^2	2(𝑚^2−1)	𝑚^2	𝑚sn(𝜉)1+dn(𝜉)^2
9	1	2(1−2𝑚^2)	1	sn(𝜉)1+cn(𝜉)^2