The Exact Solutions of Variable Coefficient Auxiliary High Order Generalized KdV Equation

Abstract

Selecting appropriate trial functions, the nonlinear variable coefficient PDE can be convert transformed to algebraic equations. The exact solutions to a class of nonlinear variable coefficient partial differential equations are successfully derived. In this paper the second type KdV equation with variable coefficients is studied, and their exact solutions are obtain. The method is obviously suitable to solving other nonlinear partial differential equations with variable coefficients of the solution.