Exact Solutions Of The Two-dimensional
Boussinesq And Dispersive
Water Waves Equations
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
Related Book
Other papers in this volume
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