BIFURCATIONS OF TRAVELING WAVE SOLUTIONS FOR A GENERALIZED CAMASSA-HOLM EQUATION

被引：1

作者：

Wei, Minzhi ^{[1
]}

Sun, Xianbo ^{[1
]}

Zhu, Hongying ^{[1
]}

机构：

[1] Guangxi Univ Finance & Econ, Dept Appl Math, Nanning 530003, Guangxi, Peoples R China

来源：

JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2018年 / 8卷 / 06期

基金：

中国国家自然科学基金;

关键词：

Generalized Camassa-Holm equation; bifurcation theory; peakon; solitary wave solution; kink and anti-kink wave solutions; SHALLOW-WATER EQUATION; SMOOTH SOLITONS; INTEGRABLE EQUATION; K(2,2) EQUATION; PEAKON; CUSPONS;

D O I：

10.11948/2018.1851

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the traveling wave solutions for a generalized CamassaHolm equation u(t)-u(xxt) = 1/2 (p+1)(p+2)u(p)u(x) -1/2p(p-1)u(p-2)u(x)(3)-2pu(p-1)u(x)u(xx)-u(p)u(xxx) are investigated. By using the bifurcation method of dynamical systems, three major results for this equation are highlighted. First, there are one or two singular straight lines in the two-dimensional system under some different conditions. Second, all the bifurcations of the generalized CamassaHolm equation are given for p either positive or negative integer. Third, we prove that the corresponding traveling wave system of this equation possesses peakon, smooth solitary wave solution, kink and anti-kink wave solution, and periodic wave solutions.

引用

页码：1851 / 1862

页数：12

共 25 条

[1]

Anco S. C., 2015, DISCRETE CONT DYN-A, P29, DOI DOI 10.3934/PROC.2015.0029

[2]

Byrd PF, 1971, Handbook of elliptic integrals for engineers and scientists, V2

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

CAMASSA, R ;

HOLM, DD .

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

[4]

Camassa R., 1994, ADV APPL MECH, V31, P1, DOI [10.1016/S0065-2156(08)70254-0, DOI 10.1016/S0065-2156(08)70254-0]

[5] Single peak solitary wave solutions for the osmosis K(2,2) equation under inhomogeneous boundary condition [J].

Chen, Aiyong ;

Li, Jibin .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 369 (02) :758-766

[6] Travelling wave solutions of the Fornberg-Whitham equation [J].

Chen, Aiyong ;

Li, Jibin ;

Deng, Xijun ;

Huang, Wentao .

APPLIED MATHEMATICS AND COMPUTATION, 2009, 215 (08) :3068-3075

[7] On the blow-up rate and the blow-up set of breaking waves for a shallow water equation [J].

Constantin, A ;

Escher, J .

MATHEMATISCHE ZEITSCHRIFT, 2000, 233 (01) :75-91

[8] Existence of permanent and breaking waves for a shallow water equation: A geometric approach [J].

Constantin, A .

ANNALES DE L INSTITUT FOURIER, 2000, 50 (02) :321-+

[9] A new integrable equation with peakon solutions [J].

Degasperis, A ;

Holm, DD ;

Hone, ANW .

THEORETICAL AND MATHEMATICAL PHYSICS, 2002, 133 (02) :1463-1474

[10]

Han M., 2006, Handbook of Differential Equations, Ordinary Differential Equations, V3

← 1 2 3 →