The homogeneneous balance method and its application to the Swift-Hohenberg equation

Abstract

In this paper, homogeneous balance method (HBM) is proposed for seeking the traveling wave solutions for the Swift-Hohenberg equation. In this approach HBM is applied to solve the Riccati equation and the reduced nonlinear evolution equations, respectively. Many new exact travelling wave solutions are successfully obtained. The method is straightforward and concise, and can be also applied to other nonlinear evolution equations.