New Exact Solutions for a Higher Order Wave Equation of KdV Type Using Multiple 𝐺^′/𝐺-Expansion Methods

Table 1

Solutions of 𝐺(𝜉) in 𝐺^′2=ℎ₀+ℎ₂𝐺²+ℎ₄𝐺⁴.

Case	ℎ0	ℎ2	ℎ4	𝐺(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	1/4	(1−2𝑚^2)/2	1/4	ns(𝜉)±cs(𝜉)
12	(1−𝑚^2)/4	(1+𝑚^2)/2	(1−𝑚^2)/4	nc(𝜉)±sc(𝜉)
13	𝑚^2/4	(𝑚^2−2)/2	1/4	ns(𝜉)±ds(𝜉)
14	𝑚^2/4	(𝑚^2−2)/2	𝑚^2/4	sn(𝜉)±𝑖cn(𝜉)