New Exact Solutions for a Higher-Order Wave Equation of KdV Type Using Extended F-Expansion Method

Table 1

Solutions of 𝐹(𝜉) in 𝐹^′2=ℎ₀+ℎ₂𝐹²+ℎ₄𝐹⁴.

Case	ℎ0	ℎ2	ℎ4	𝐹(𝜉)
1	1	−(𝑚^2+1)	𝑚^2	sn(𝜉),cd(𝜉)
2	1−𝑚^2	𝑚^2−1	−𝑚^2	cn(𝜉)
3	𝑚^2−1	2−𝑚^2	−1	dn(𝜉)
4	𝑚^2	−(𝑚^2+1)	1	ns(𝜉),dc(𝜉)
5	−𝑚^2	2𝑚^2−1	1−𝑚^2	nc(𝜉)
6	−1	2−𝑚^2	𝑚^2−1	nd(𝜉)
7	1	2−𝑚^2	1−𝑚^2	sc(𝜉)
8	1	2𝑚^2−1	−𝑚^2(1−𝑚^2)	sd(𝜉)
9	1−𝑚^2	2−𝑚^2	1	cs(𝜉)
10	−𝑚^2(1−𝑚^2)	2𝑚^2−1	1	sd(𝜉)
11	14	1−2𝑚^22	14	ns(𝜉)±cs(𝜉)
12	1−𝑚^24	1+𝑚^22	1−𝑚^24	nc(𝜉)±sc(𝜉)
13	𝑚^24	𝑚^2−22	14	ns(𝜉)±ds(𝜉)
14	𝑚^24	𝑚^2−22	𝑚^24	sn(𝜉)±𝑖cn(𝜉)