Exp-function method for a nonlinear ordinary differential equation and new exact solutions of the dispersive long wave equations

Abstract

In this paper, the Exp-function method is used to obtain general solutions of a first-order nonlinear ordinary differential equation with a fourth-degree nonlinear term. Based on the first-order nonlinear ordinary equation and its general solutions, new and more general exact solutions with free parameters and arbitrary functions of the ( 2 + 1 )-dimensional dispersive long wave equations are obtained, from which some hyperbolic function solutions are also derived when setting the free parameters as special values. It is shown that the Exp-function method with the help of symbolic computation provides a straightforward and very effective mathematical tool for solving nonlinear evolution equations in mathematical physics.