A new Riccati equation expansion method with symbolic computation to construct new travelling wave solution of nonlinear differential equations

摘要

In this paper, based on a new system of Riccati equations, we present a triple Riccati equation expansion method. The nonlinear Klein-Gordon equation and the combined KdV-mKdV equation are chosen to illustrate the method. As a result, many new travelling solutions, which include bell-profile solitary wave solution, singular solitary solutions, periodic solutions are obtained. This method can be used to the other nonlinear evolution equations in mathematics physics. (c) 2005 Elsevier Inc. All rights reserved.