Exact Solutions for Nonlinear PDEs with the Variable Coefficients in Mathematical Physics

Abstract

In this article, we construct the exact solutions for nonlinear partial differential equations with the variable coefficients in the mathematical physics via the generalized time- dependent variable coefficients KdV-mKdV equation and the coupled modified KdV equations with non-uniformity terms by ) - expansion method with the variable coefficients, where G satisfies the using a generalized ( Jacobi elliptic equation. Many of the exact solutions in terms of Jacobi elliptic functions are obtained. The proposed method is reliable and effective and gives more new exact solutions.