Exact rational solutions to a Boussinesq-like equation in (1+1)-dimensions

被引：45

作者：

Shi, Chang-Guang ^{[1
]}

Zhao, Bao-Zhu ^{[1
]}

Ma, Wen-Xiu ^{[1
,2
]}

机构：

[1] Shanghai Univ Elect Power, Coll Math & Phys, Shanghai 200090, Peoples R China

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

来源：

APPLIED MATHEMATICS LETTERS | 2015年 / 48卷

基金：

上海市自然科学基金;

关键词：

Rational solution; Boussinesq equation; Generalized bilinear form; TRAVELING-WAVE SOLUTIONS; PETVIASHVILI KP EQUATION; BILINEAR EQUATIONS; RESONANT SOLUTIONS; BELL POLYNOMIALS; FORM;

D O I：

10.1016/j.aml.2015.04.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A Boussinesq-like nonlinear differential equation in (1 + 1)-dimensions is introduced by using a generalized bilinear differential equation with the generalized bilinear derivatives D-3,D-x and D-3,D-t. A class of rational solutions, generated from polynomial solutions to the associated generalized bilinear equation, is constructed for the presented Boussinesq-like equation. It is conjectured that this class of rational solutions contain all such rational solutions to the new Boussinesq-like equation. More concretely, the conjecture says that if a polynomial f = f(x, t) in x and t solves f(ttf) f - f(t)(2) + 3f(xx)(2) = 0, then the degree of f with respect to t must be less than or equal to 1. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：170 / 176

页数：7

共 27 条

[1]

Ablowitz M.J., 1991, SOLITONS NONLINEAR E

[2] Recent progress in investigating optical rogue waves [J].

Akhmediev, N. ;

Dudley, J. M. ;

Solli, D. R. ;

Turitsyn, S. K. .

JOURNAL OF OPTICS, 2013, 15 (06)

[3] Generalized Bilinear Differential Operators, Binary Bell Polynomials, and Exact Periodic Wave Solution of Boiti-Leon-Manna-Pempinelli Equation [J].

Dong, Huanhe ;

Zhang, Yanfeng ;

Zhang, Yongfeng ;

Yin, Baoshu .

ABSTRACT AND APPLIED ANALYSIS, 2014,

[4] Nonlinear Schrodinger equation: Generalized Darboux transformation and rogue wave solutions [J].

Guo, Boling ;

Ling, Liming ;

Liu, Q. P. .

PHYSICAL REVIEW E, 2012, 85 (02)

[5]

Hirota R., 2004, The Direct Method in Soliton Theory, DOI 10.1017/CBO9780511543043

[6] New exact traveling wave solutions of the (3+1) dimensional Kadomtsev-Petviashvili (KP) equation [J].

Khalfallah, Mohammed .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2009, 14 (04) :1169-1175

[7]

Kharif C, 2009, ADV GEOPHYS ENV MECH, P1, DOI 10.1007/978-3-540-88419-4_1

[8] The Cauchy problem for the equation of the Burgers hierarchy [J].

Kudryashov, Nikolai A. ;

Sinelshchikov, Dmitry I. .

NONLINEAR DYNAMICS, 2014, 76 (01) :561-569

[9]

Ma W.X., 2011, Studies Nonl. Sci, V2, P140

[10]

Ma W.X., CHAOS SOLITONS FRACT

← 1 2 3 →