Joint Application of Bilinear Operator and F-Expansion Method for (2+1)-Dimensional Kadomtsev-Petviashvili Equation

Shaolin Li,Yinghui He,Yao Long

doi:10.1155/2014/156483

Abstract

The bilinear operator and F-expansion method are applied jointly to study (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation. An exact cusped solitary wave solution is obtained by using the extended single-soliton test function and its mechanical feature which blows up periodically in finite time for cusped solitary wave is investigated. By constructing the extended double-soliton test function, a new type of exact traveling wave solution describing the assimilation of solitary wave and periodic traveling wave is also presented. Our results validate the effectiveness for joint application of the bilinear operator and F-expansion method.

Highlights

In the past few decades, much effort has been devoted to the investigation of dynamical behaviours of nonlinear evolution equation
Much efforts have been spent on this task and many significant methods have been established such as variational iteration method [8], homotopy perturbation method [9, 10], Fan subequation method [11, 12], exp-function method [13], Hirota’s bilinear method [14, 15], G󸀠/G-expansion method [16, 17], and F-expansion method [18,19,20,21]
We consider the joint application of bilinear operator and F-expansion method

Summary

Introduction

In the past few decades, much effort has been devoted to the investigation of dynamical behaviours of nonlinear evolution equation. There has been much literature on traveling wave of nonlinear evolution equation due to the abundant type of nonlinear traveling wave and some well-known concepts (e.g., solitary wave [1,2,3], periodic wave [4, 5], kink wave [6], cusped wave [7], etc.) have been used and generalized extensively. Kinds of research fields and solution types of KP equation have been studied extensively in various aspects [22,23,24]; exact multiple solitary wave solution, periodic solitary wave solution, quasiperiodic solutions, and so forth have been obtained. By single-soliton test approach, a new type of solitary wave solution which possesses cusped structure is obtained.

Cusped Solitary Wave Solution

Interaction of Solitary Wave and Periodic Wave

Conclusions