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

Abstract

In this paper, the new auxiliary equation method [Sirendaoreji, A new auxiliary equation and exact travelling wave solutions of non-linear equations, Phys. Lett. A 356 (2006) 124–130] is improved and a generalized new auxiliary equation method is proposed to construct more general exact solutions of non-linear partial differential equations. With the aid of symbolic computation, we choose the (2 + 1)-dimensional breaking soliton equations to illustrate the validity and advantages of the method. 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.