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

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.