A generalized new auxiliary equation method and its applications to nonlinear partial differential equations

In this Letter, a generalized new 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 combined KdV–mKdV equation and the (2+1)(2+1)-dimensional asymmetric Nizhnik–Novikov–Vesselov equations to illustrate the validity and advantages of the method. As a result, many new and more general exact solutions are obtained.