The orbital stability of the solitary wave solutions of the generalized Camassa-Holm equation

被引：7

作者：

Liu, Xiaohua ^{[2
]}

Zhang, Weiguo ^{[1
]}

Li, Zhengming ^{[1
]}

机构：

[1] Shanghai Univ Sci & Technol, Shanghai 200093, Peoples R China

[2] Guizhou Minzu Univ, Guiyang 550025, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2013年 / 398卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Generalized Camassa-Holm equation; Stability; Solitary wave solution; PEAKONS; COMPACT;

D O I：

10.1016/j.jmaa.2012.09.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the orbital stability of smooth solitary wave solutions of the generalized Camassa-Holm equation. By constructing the functional extremum problem and using the orbital stability theory presented by Grillakis, Shatah, Strauss and Bona, and Souganidis, we show that the solitary wave solutions of the generalized Camassa-Holm equation are orbitally stable or unstable as determined by the sign of a discriminant. The conclusions presented by the previous authors, such as Hakkaev and Kirchev, Constantin and Strauss, can be considered as a special case of our results. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：776 / 784

页数：9

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