THE TWO-COMPONENT μ-CAMASSA-HOLM SYSTEM WITH PEAKED SOLUTIONS

被引：0
|
作者：
Li, Yingying [1 ,2 ]
Fu, Ying [3 ,4 ]
Qu, Changzheng [1 ,2 ]
机构：
[1] Ningbo Univ, Sch Math & Stat, Ningbo 315211, Peoples R China
[2] Ningbo Univ, Ctr Nonlinear Studies, Ningbo 315211, Peoples R China
[3] Northwest Univ, Sch Math, Xian 710127, Peoples R China
[4] Northwest Univ, Ctr Nonlinear Studies, Xian 710127, Peoples R China
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2020年 / 40卷 / 10期
关键词：
The Camassa-Holm equation; the mu-Camassa-Holm equation; two-component; mu-Camassa-Holm system; peaked solution; conservation law; blow-up; SHALLOW-WATER EQUATION; GLOBAL WEAK SOLUTIONS; CONSERVATIVE SOLUTIONS; WAVE-BREAKING; GEODESIC-FLOW; STABILITY; TRANSFORM; SOLITONS; GEOMETRY;
D O I：
10.3934/dcds.2020253
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is mainly concerned with the classification of the general two-component mu-Camassa-Holm systems with quadratic nonlinearities. As a conclusion of such classification, a two-component mu-Camassa-Holm system admitting multi-peaked solutions and H-1-norm conservation law is found, which is a mu-version of the two-component modified Camassa-Holm system and can be derived from the semidirect-product Euler-Poincare equations corresponding to a Lagrangian. The local well-posedness for solutions to the initial value problem associated with the two-component mu-Camassa-Holm system is established. And the precise blow-up scenario, wave breaking phenomena and blow-up rate for solutions of this problem are also investigated.
引用
收藏
页码：5929 / 5954
页数：26
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