General Solution of Generalized (2+1)–Dimensional Kadomtsev-Petviashvili (KP) Equation by Using the –Expansion Method

Abdollah Borhanifar,Reza Abazari

doi:10.4236/ajcm.2011.14025

Abstract

In this work, the (G,/G)- --expansion method is proposed for constructing more general exact solutions of the (2 + 1)--dimensional Kadomtsev-Petviashvili (KP) equation and its generalized forms. Our work is motivated by the fact that the (G,/G)---expansion method provides not only more general forms of solutions but also periodic and solitary waves. If we set the parameters in the obtained wider set of solutions as special values, then some previously known solutions can be recovered. The method appears to be easier and faster by means of a symbolic computation system.

Highlights

Nonlinear evolution equations (NLEEs) have been the subject of study in various branches of mathematicalphysical sciences such as physics, biology, chemistry, etc
The analytical solutions of such equations are of fundamental importance since a lot of mathematical-physical models are described by NLEEs
There is a wide variety of approaches to nonlinear problems for constructing traveling wave solutions

Summary

Introduction

Nonlinear evolution equations (NLEEs) have been the subject of study in various branches of mathematicalphysical sciences such as physics, biology, chemistry, etc. There is a wide variety of approaches to nonlinear problems for constructing traveling wave solutions. Some of these approaches are the Jacobi elliptic function method [1], inverse scattering method [2], Hirotas bilinear method [3], homogeneous balance method [4], homotopy perturbation method [5], Weierstrass function method [6], symmetry method [7], Adomian decomposition method [8], sine/cosine method [9], tanh/coth method [10], the Exp-function method [11,12,13,14,15,16] and so on. Most of the methods may sometimes fail or can only lead to a kind of special solution and the solution procedures become very complex as the degree of nonlinearity increases

Objectives

Methods

Conclusion