New exact Jacobi elliptic solutions for the generalized time-dependent variable coefficients KdV- mKdV equation

Abstract

In this article, we use the improved general mapping deformation method based on the generalized Jacobi elliptic functions expansion method with computerized symbolic computation to construct more new exact solutions of a generalized time-dependent variable coefficients KdV- mKdV equation. As a result, new generalized Jacobi elliptic function-like solutions, soliton-like solutions and trigonometric function solutions are obtained by using this method. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics. Key words: Exact solutions, generalized time-dependent variable coefficients KdV- mKdV equation, improved general mapping deformation method, Jacobi elliptic functions.