Exact structures for the KdV–mKdV equation with variable coefficients via the functional variable method

Abstract

In this study we introduce the functional variable method (fvm for short) for obtaining new exact travelling solutions of the combined KdV–mKdV equation. The technique of the homogeneous balance method is used in second stage to handle the appropriated solutions. We show that, the method is straightforward and concise for several kind of nonlinear problems. Many new exact traveling wave solutions are successfully obtained.