Blow-up and peakons for a higher-order μ-Camassa-Holm equation

被引：0
|
作者：
Wang, Hao [1 ]
Luo, Ting [2 ]
Fu, Ying [3 ,4 ]
Qu, Changzheng [5 ]
机构：
[1] Najing Univ Sci & Technol, Sch Sci, Nanjing 210014, Peoples R China
[2] Zhejiang Normal Univ, Coll Math & Comp Sci, Jinhua 321004, Zhejiang, Peoples R China
[3] Northwest Univ, Sch Math, Xian 710127, Peoples R China
[4] Northwest Univ, Ctr Nonlinear Studies, Xian 710127, Peoples R China
[5] Ningbo Univ, Sch Math & Stat, Ningbo 315211, Peoples R China
来源：
JOURNAL OF EVOLUTION EQUATIONS | 2022年 / 22卷 / 01期
关键词：
Camassa-Holm equation; mu-Camassa-Holm equation; Higher-order equation; Peaked soliton; Conservation law; Local well-posedness; Wave breaking; WELL-POSEDNESS; STABILITY; DYNAMICS; FAMILY;
D O I：
10.1007/s00028-022-00774-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper proposes a higher-order mu-Camassa-Holm equation, which is regarded as a higherorder extension of the mu-Camassa-Holm equation, and preserves some properties of the mu-Camassa-Holm equation. We first show that the equation admits the peaked traveling wave solution, which is given by a Green function of the momentum operator. Local well-posedness of the Cauchy problem in the suitable Sobolev space is established. Finally, the blow-up criterion and wave breaking mechanism for solutions with certain initial profiles are studied. It turns out that all the nonlinearities even the first-order nonlinearity may have the effect on the blow up.
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收藏
页数：33
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