Travelling wave solutions of the Fornberg-Whitham equation

被引：30

作者：

Chen, Aiyong ^{[1
,2
]}

Li, Jibin ^{[1
]}

Deng, Xijun ^{[3
]}

Huang, Wentao ^{[2
]}

机构：

[1] Kunming Univ Sci & Technol, Ctr Nonlinear Sci Studies, Kunming 650093, Yunnan, Peoples R China

[2] Guilin Univ Elect Technol, Sch Math & Comp Sci, Guilin 541004, Guangxi, Peoples R China

[3] Yangtze Univ, Sch Informat & Math, Jinzhou 434023, Hubei, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2009年 / 215卷 / 08期

基金：

中国国家自然科学基金;

关键词：

Fornberg-Whitham equation; Periodic wave solution; Solitary wave solution; Loop-soliton solutions; CAMASSA-HOLM EQUATION; CH-GAMMA EQUATION;

D O I：

10.1016/j.amc.2009.09.057

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Zhou and Tian [J.B. Zhou, L. X. Tian, A type of bounded travelling wave solutions for the Fornberg-Whitham equation, J. Math. Anal. Appl. 346 (2008) 255-261] successfully found a type of bounded travelling wave solutions of the Fornberg-Whitham equation. In this paper, we improve the previous result by using the phase portrait analytical technology. Moreover, some smooth periodic wave, smooth solitary wave, periodic cusp wave and loop-soliton solutions are given, and the numerical simulation is made. The results show that our theoretical analysis agrees with the numerical simulation. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：3068 / 3075

页数：8

共 16 条

[1] AN INTEGRABLE SHALLOW-WATER EQUATION WITH PEAKED SOLITONS [J].

CAMASSA, R ;

HOLM, DD .

PHYSICAL REVIEW LETTERS, 1993, 71 (11) :1661-1664

[2]

Feng CX, 2009, Int J Nonlinear Sci, V7, P353

[3] NUMERICAL AND THEORETICAL-STUDY OF CERTAIN NON-LINEAR WAVE PHENOMENA [J].

FORNBERG, B ;

WHITHAM, GB .

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1978, 289 (1361) :373-404

[4] Two new types of hounded waves of CH-γ equation [J].

Guo, BL ;

Liu, ZR .

SCIENCE IN CHINA SERIES A-MATHEMATICS, 2005, 48 (12) :1618-1630

[5] Traveling wave solutions of the Camassa-Holm equation [J].

Lenells, J .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2005, 217 (02) :393-430

[6] Traveling wave solutions of the Camassa-Holm and Korteweg-de Vries equations [J].

Lenells, J .

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2004, 11 (04) :508-520

[7] Smooth and non-smooth traveling waves in a nonlinearly dispersive equation [J].

Li, JB ;

Liu, ZR .

APPLIED MATHEMATICAL MODELLING, 2000, 25 (01) :41-56

[8] On a class of singular nonlinear traveling wave equations [J].

Li, Jibin ;

Chen, Guanrong .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2007, 17 (11) :4049-4065

[9] Exact loop solutions, cusp solutions, solitary wave solutions and periodic wave solutions for the special CH-DP equation [J].

Li, Jibin ;

Zhang, Yi .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2009, 10 (04) :2502-2507

[10] New bounded traveling waves of Camassa-Holm equation [J].

Liu, ZG ;

Li, QX ;

Lin, QM .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2004, 14 (10) :3541-3556

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