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

Table 2

Solutions of (33) with Δ=ℎ²₃−4ℎ₂ℎ₄, 𝜀=±1.

Case	ℎ4,Δ	𝐹(𝜉)
1	ℎ2>0	−ℎ2ℎ3secℎ^2ℎ2/2𝜉ℎ^23−ℎ2ℎ41+𝜀tanℎℎ2/2𝜉
2	ℎ2>0	−ℎ2ℎ3cscℎ^2ℎ2/2𝜉ℎ^23−ℎ2ℎ41+𝜀cotℎℎ2/2𝜉
3	ℎ2>0,Δ>0	2ℎ2secℎ(ℎ2𝜉)𝜀√Δ−ℎ3secℎ(ℎ2𝜉)
4	ℎ2<0,Δ>0	2ℎ2sec(−ℎ2𝜉)𝜀√Δ−ℎ3sec(−ℎ2𝜉)
5	ℎ2>0,Δ<0	2ℎ2cscℎ(ℎ2𝜉)𝜀√−Δ−ℎ3cscℎ(ℎ2𝜉)
6	ℎ2<0,Δ>0	2ℎ2csc(−ℎ2𝜉)𝜀√Δ−ℎ3csc(−ℎ2𝜉)
7	ℎ2>0,ℎ4>0	−ℎ2secℎ^2ℎ2/2𝜉ℎ3+2𝜀ℎ2ℎ4tanℎℎ2/2𝜉
8	ℎ2<0,ℎ4>0	−ℎ2sec^2−ℎ2/2𝜉ℎ3+2𝜀−ℎ2ℎ4tan−ℎ2/2𝜉
9	ℎ2>0,ℎ4>0	ℎ2cscℎ^2ℎ2/2𝜉ℎ3+2𝜀ℎ2ℎ4cotℎℎ2/2𝜉
10	ℎ2<0,ℎ4>0	−ℎ2csc^2−ℎ2/2𝜉ℎ3+2𝜀−ℎ2ℎ4cot−ℎ2/2𝜉
11	ℎ2>0,Δ=0	−ℎ2ℎ3(1+𝜀tanℎ(ℎ22)𝜉)
12	ℎ2>0,Δ=0	−ℎ2ℎ3(1+𝜀cotℎ(ℎ22)𝜉)
13	ℎ2>0	4ℎ2exp(𝜀ℎ2𝜉)(exp(𝜀ℎ2𝜉)−ℎ3)^2−4ℎ2ℎ4
14	ℎ2>0,ℎ3=0	4ℎ2exp(𝜀ℎ2𝜉)1−4ℎ2ℎ4exp(2𝜀ℎ2𝜉)