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

Abstract 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.

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