A generalized auxiliary equation method and its application to (2+1) -dimensional Korteweg–de Vries equations

A generalized auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equations. With the aid of symbolic computation, we choose the (2+1)-dimensional Korteweg–de Vries equations to illustrate the validity and advantages of this method. As a result, many new and more general exact non-travelling wave and coefficient function solutions are obtained, which include soliton-like solutions, triangular-like solutions, single and combined non-degenerate Jacobi elliptic wave function-like solutions and Weierstrass elliptic doubly-like periodic solutions.