A generalized method and general form solutions to the Whitham–Broer–Kaup equation

Based on a more general transformation presented in this paper, a generalized method for finding more types travelling wave solutions of nonlinear evolution equations (NLEEs) is presented and implemented in a computer algebraic system. As an application of the method, Whitham–Broer–Kaup (WBK) equation is studied to illustrate the method. As a result, We cannot only successfully recover the previously known travelling wave solutions found by Fanʹs method [J. Phys. A 35 (2002) 6853; Comput. Phys. Commun. 53 (2003) 17], but also obtain some new formal solutions. The solutions obtained in this paper include polynomial, exponential, solitary wave, rational, triangular periodic, Jacobi and Weierstrass doubly periodic solutions.