Exact Solutions for (4+1)-Dimensional Nonlinear Fokas Equation Using Extended F-Expansion Method and Its Variant

Table 2

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

Case	ℎ2,Δ	𝐹(𝜉)	Case	ℎ2,Δ	𝐹(𝜉)
1	ℎ2>0	−ℎ2ℎ3sech^2((ℎ2/2)𝜉)ℎ^23−ℎ2ℎ4(1+𝜀tanh((ℎ2/2)𝜉)^2	2	ℎ2>0	−ℎ2ℎ3csch^2((ℎ2/2)𝜉)ℎ^23−ℎ2ℎ4(1+𝜀coth((ℎ2/2)𝜉)^2
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^2((ℎ2/2)𝜉)ℎ3+2𝜀ℎ2ℎ4tanh((ℎ2/2)𝜉)	8	ℎ2<0, ℎ4>0	−ℎ2sec^2((−ℎ2/2)𝜉)ℎ3+2𝜀−ℎ2ℎ4tan((−ℎ2/2)𝜉)
9	ℎ2>0, ℎ4>0	ℎ2csch^2((ℎ2/2)𝜉)ℎ3+2𝜀ℎ2ℎ4coth((ℎ2/2)𝜉)	10	ℎ2<0, ℎ4>0	−ℎ2csc^2((−ℎ2/2)𝜉)ℎ3+2𝜀−ℎ2ℎ4cot((−ℎ2/2)𝜉)
11	ℎ2>0, Δ=0	−ℎ2ℎ31+𝜀tanhℎ22𝜉	12	ℎ2>0, Δ=0	−ℎ2ℎ31+𝜀cothℎ22𝜉
13	ℎ2>0	4ℎ2exp𝜀ℎ2𝜉exp𝜀ℎ2𝜉−ℎ3^2−4ℎ2ℎ4	14	ℎ2>0, ℎ3=0	4ℎ2exp𝜀ℎ2𝜉1−4ℎ2ℎ4exp2𝜀ℎ2𝜉