An extended method and its application to Whitham–Broer–Kaup equation and two-dimensional perturbed KdV equation

An extended method is proposed for constructing new forms of exact travelling wave solutions to nonlinear evolution equations by making a more general transformation. For illustration, we apply the extended method to Whitham–Broer–Kaup equation and two-dimensional perturbed KdV equation and successfully cover the previously known travelling wave solutions found by Chen’s method [Chaos, Solitons and Fractals 22 (2004) 675; Int. J. Mod. Phys. C 4 (2004) 595]. Moreover, some new forms of solutions are obtained.