A generalized auxiliary equation method and its application to the (2Â +Â 1)-dimensional KdV equations

In this paper, a generalized auxiliary equation method is proposed to construct more general exact solutions of nonlinear partial differential equations. As an application of the method, the (2 + 1)-dimensional Korteweg-de Vries equations are considered. As a result, many new and more general non-travelling wave and coefficient function solutions are obtained including soliton-like solutions, trigonometric function solutions, exponential solutions and rational solutions.