New explicit solitary wave solutions and periodic wave solutions for Whitham-Broer-Kaup equation in shallow water

Based upon the well-known Riccati equation, a new generalized transformatio n is presented and applied to solve Whitham-Broer-Kaup (WBK) equation in sh allow water As a result, many explicit exact solutions, which contain new s olitary wave solutions, periodic wave solutions and the combined formal sol itary wave solutions and periodic wave solutions, are obtained. And variant Boussinesq equation and the system of approximate equation for long water waves, as the special cases of WBK equation, can also obtain the correspond ing solitary wave solutions and periodic wave solutions. In addition, with the aid of Mathematica and Wu elimination method to solve a large system of algebraic equations, the course of solving equations can be carried out in computer. (C) 2001 Published by Elsevier Science B.V.