Author(s)

F. P. Barrera1, T. Brugarino2 & F. Montano1

Abstract

In this paper two-dimensional Boussinesq and dispersive water waves equations are investigated in exact solutions. The Exp-function method is used for seeking exact solutions of the equations through symbolic computation. Keywords: analytical solutions, nonlinear waves equations, Exp-function method. 1 Introduction Recently new methods have been presented to solve the analytical solutions of the nonlinear wave equations, tanh-function method [1, 2], homotopy method [3] and Adomian decomposition method [4]. The Exp-function method was proposed by He andWu to obtain solutions of nonlinear evolution equations arising in many physic problems [5]. It is simple to find numerical solutions of linear systems using computers, but this is not true for nonlinear problems. Indeed, numerical methods are connected to initial solutions and it is not easy to have convergent results for strong nonlinearity. The procedure of the Exp-functionmethod for the solution of PDE is straightforward. The symbol computation is an essential tool to apply the presented method. The examination of two-dimensional Boussinesq equation arises when we consider the propagation of gravity waves on the surface of water. The structure of this equation leads to consider the propagation of waves in opposite directions.

Keywords

analytical solutions, nonlinear waves equations, Exp-function method