An auxiliary ordinary differential equation and the exp-function method

Abstract

In this paper, the new idea of finding the exact solutions of the nonlinear evolution equations is introduced. The idea is that the exact solutions of the auxiliary ordinary differential equation are derived by using exp-function method, and then the exact solutions of the nonlinear evolution equations are derived with aid of the auxiliary ordinary differential equation. As examples, the classical KdV equation, Boussinesq equation, (3+1)-dimensional Jimbo–Miwa equation and Benjamin–Bona–Mahony equation are discussed and the exact solutions are derived.