From: Assessment of the further improved (G'/G)-expansion method and the extended tanh-method in probing exact solutions of nonlinear PDEs
No
G ( ξ )
1
− p q sec h 2 p ξ q 2 − p r 1 ± tanh p ξ 1 2 or − p q csc h 2 p ξ q 2 − p r 1 ± coth p ξ 1 2
6
− p sec 2 − p ξ q ± 2 − p r tan − p ξ 1 2 or − p csc 2 − p ξ q ± 2 − p r cot − p ξ 1 2 , p < 0 , r > 0
2
2 p ± Δ cosh 2 p ξ − q 1 2 , p > 0 , Δ > 0
7
p e ± 2 p ξ e ± 2 p ξ − 4 q 2 − 64 p r 1 2 , p > 0
3
2 p ± Δ cos 2 − p ξ − q 1 2 or 2 p ± Δ sin 2 − p ξ − q 1 2 , p < 0 , Δ > 0
8
− p q 1 ± tanh 1 2 p ξ 1 2 or − p q 1 ± coth 1 2 p ξ 1 2 , p > 0 , Δ = 0
4
2 p ± − Δ sinh 2 p ξ − q 1 2 , p > 0 , Δ < 0
9
± p e ± 2 p ξ 1 − 64 p r e ± 4 p ξ 1 2 , p > 0 , q = 0
5
− p sec h 2 p ξ q ± 2 p r tanh p ξ 1 2 or p csc h 2 p ξ q ± 2 p r coth p ξ 1 2 , p > 0 , r > 0
10
± 1 q ξ , p = 0 , r = 0