New extension of the tanh-function method and application to the Whitham–Broer–Kaup shallow water model with symbolic computation

In this Letter, the tanh-function method is further extended by introducing a more generalized expansion form. Compared with other existing tanh-function methods, our algorithm provides the possibility for constructing more types of travelling-wave solutions (especially the solitary-wave solutions) for a given system of nonlinear evolution equations (NLEEs). Applying such an algorithm to the Whitham–Broer–Kaup shallow water model with symbolic computation, abundant solitary-wave solutions are obtained and some novel solitary-wave structures are also revealed under certain parametric conditions. After suitable improvements, this algorithm can also be applicable to the construction of nontravelling solitary-wave solutions for variable-coefficient and higher-dimensional NLEEs.