Solving solitary wave solutions of nonlinear evolution equations with the homotopy analysis method

Abstract

We solved the Burgers equation by using the homotopy analysis method (HAM) and obtained its approximate kink solitary wave solutions. The solutions agree very well with the exact solutions. The results indicate that the HAM is valid for finding the solitary wave solutions of a class of nonlinear evolution equations. We also made some efforts to extend the HAM. As an example, we got the bell-like solitary wave solutions of KP equation by this approach. Our extended method can be used to find the approximate solitary wave solutions for more nonlinear evolution equations in an easy way.