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

Abstract 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.

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