Solving the (3+1)-dimensional generalized KP and BKP equations by the multiple exp-function algorithm

被引：366

作者：

Ma, Wen-Xiu ^{[1
]}

Zhu, Zuonong ^{[2
]}

机构：

[1] Univ S Florida, Dept Math & Stat, Tampa, FL 33620 USA

[2] Shanghai Jiao Tong Univ, Dept Math, Shanghai 200240, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2012年 / 218卷 / 24期

基金：

中国国家自然科学基金; 上海市自然科学基金;

关键词：

Hirota bilinear form; Soliton equation; Multiple wave solution; NONLINEAR EVOLUTION-EQUATIONS; TRAVELING-WAVE SOLUTIONS; COMPLEXITON SOLUTIONS; SOLITON-SOLUTIONS; FORM; TRANSFORMATIONS;

D O I：

10.1016/j.amc.2012.05.049

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The multiple exp-function algorithm, as a generalization of Hirota's perturbation scheme, is used to construct multiple wave solutions to the (3 + 1)-dimensional generalized KP and BKP equations. The resulting solutions involve generic phase shifts and wave frequencies containing many existing choices. It is also pointed out that the presented phase shifts for the two considered equations are all not of Hirota type. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：11871 / 11879

页数：9

共 50 条

[1] A note on the elliptic equation method [J].

Chen, Huaitang ;

Yin, Huicheng .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2008, 13 (03) :547-553

[2]

Darvishi M. T., 2011, American Journal of Computational and Applied Mathematics, V1, P41, DOI [10.5923/j.ajcam.20110102.08, DOI 10.5923/J.AJCAM.20110102.08]

[3] Application of Exp-function method for nonlinear evolution equations with variable coefficients [J].

El-Wakil, S. A. ;

Madkour, M. A. ;

Abdou, M. A. .

PHYSICS LETTERS A, 2007, 369 (1-2) :62-69

[4] N-soliton solution and its Wronskian form of a (3+1)-dimensional nonlinear evolution equation [J].

Geng, Xianguo ;

Ma, Yunling .

PHYSICS LETTERS A, 2007, 369 (04) :285-289

[5] On the combinatorics of the Hirota D-operators [J].

Gilson, C ;

Lambert, F ;

Nimmo, J ;

Willox, R .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1996, 452 (1945) :223-234

[6] Exp-function method for nonlinear wave equations [J].

He, Ji-Huan ;

Wu, Xu-Hong .

CHAOS SOLITONS & FRACTALS, 2006, 30 (03) :700-708

[7] Symbolic methods to construct exact solutions of nonlinear partial differential equations [J].

Hereman, W ;

Nuseir, A .

MATHEMATICS AND COMPUTERS IN SIMULATION, 1997, 43 (01) :13-27

[8]

Hietarinta J., 2005, PHYS AUC, V15, P31

[9] RESONANCE OF SOLITONS IN ONE DIMENSION [J].

HIROTA, R ;

ITO, M .

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1983, 52 (03) :744-748

[10] SOLITON-SOLUTIONS TO THE BKP EQUATIONS .1. THE PFAFFIAN TECHNIQUE [J].

HIROTA, R .

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1989, 58 (07) :2285-2296

← 1 2 3 4 5 →