Stability of Solitary Waves and Global Existence of a Generalized Two-Component Camassa-Holm System

被引：29

作者：

Chen, Robin Ming ^{[1
]}

Liu, Yue ^{[2
]}

Qiao, Zhijun ^{[3
]}

机构：

[1] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

[2] Univ Texas Arlington, Dept Math, Arlington, TX 76019 USA

[3] Univ Texas Pan Amer, Dept Math, Edinburg, TX 78541 USA

来源：

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2011年 / 36卷 / 12期

基金：

美国国家科学基金会;

关键词：

Generalized two-component Camassa-Holm system; Global solutions; Solitary waves; Stability; SHALLOW-WATER EQUATION; COMPRESSIBLE ELASTIC RODS; WELL-POSEDNESS; PERIODIC PEAKONS; MODEL-EQUATIONS; BLOW-UP; BREAKING; SOLITONS;

D O I：

10.1080/03605302.2011.556695

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study here the existence of solitary wave solutions of a generalized two-component Camassa-Holm system. In addition to those smooth solitary-wave solutions, we show that there are solitary waves with singularities: peaked and cusped solitary waves. We also demonstrate that all smooth solitary waves are orbitally stable in the energy space. We finally give a sufficient condition for global strong solutions to the equation in some special case.

引用

页码：2162 / 2188

页数：27

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