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Table 1 The general solutions of Eq. (5) are as follows (Yomba2008; Zhang & Xia2007)

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 )

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

  1. where Δ = q2pr.