New soliton solutions for Kaup-Boussinesq system

Houshang Najafi,Malihe Najafi,Somayeh Arbabi Mohammad-Abadi

doi:10.14419/ijamr.v1i4.310

Abstract

In this Letter, we study Kaup-Boussinesq system by using the well-known He's variational approach. In fact, the He's variational method is a promising method to various systems of linear and nonlinear equations.

Highlights

We can present many important phenomena and dynamic processes in physics, mechanics, chemistry, biology, nonlinear optics, the theory of shallow water waves, plasma physics and others by nonlinear partial differential equations
Most scientific problems and physical phenomena occur nonlinearly
The study of exact solutions of nonlinear evolution equations plays an important role in soliton theory and explicit formulas of nonlinear partial differential equations play an essential role in the nonlinear science

Summary

Introduction

We can present many important phenomena and dynamic processes in physics, mechanics, chemistry, biology, nonlinear optics, the theory of shallow water waves, plasma physics and others by nonlinear partial differential equations. The study of exact solutions of nonlinear evolution equations plays an important role in soliton theory and explicit formulas of nonlinear partial differential equations play an essential role in the nonlinear science. There have been a multitude of methods presented for solving Nonlinear partial differential equations (NPDEs), for instance, the Adomian decomposition method [1],the homotopy perturbation method [2],the variational iteration method [3, 4] , the He’s variational approach [5], the F −expansion method [6], three-wave method [7], extended homoclinic test approach [8, 9], the ( GG )−expansion method [6] and the exp-function method [10]. By means of the He’s variational approach, we will obtain some

Results

Conclusion