Wave-Breaking and Peakons for a Modified Camassa-Holm Equation

被引：192
|
作者：
Gui, Guilong [1 ,2 ]
Liu, Yue [3 ]
Olver, Peter J. [4 ]
Qu, Changzheng [5 ]
机构：
[1] Jiangsu Univ, Dept Math, Zhenjiang 212013, Peoples R China
[2] Chinese Univ Hong Kong, Inst Math Sci, Shatin, Hong Kong, Peoples R China
[3] Univ Texas Arlington, Dept Math, Arlington, TX 76019 USA
[4] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA
[5] Ningbo Univ, Dept Math, Ningbo 315211, Zhejiang, Peoples R China
来源：
COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2013年 / 319卷 / 03期
基金：
美国国家科学基金会;
关键词：
SHALLOW-WATER EQUATION; KORTEWEG-DE-VRIES; GEODESIC-FLOW; SCATTERING; HIERARCHY; EXISTENCE; SOLITONS; PULSES;
D O I：
10.1007/s00220-012-1566-0
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper, we investigate the formation of singularities and the existence of peaked traveling-wave solutions for a modified Camassa-Holm equation with cubic nonlinearity. The equation is known to be integrable, and is shown to admit a single peaked soliton and multi-peakon solutions, of a different character than those of the Camassa-Holm equation. Singularities of the solutions can occur only in the form of wave-breaking, and a new wave-breaking mechanism for solutions with certain initial profiles is described in detail.
引用
收藏
页码：731 / 759
页数：29
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