ORBITAL STABILITY OF PEAKONS AND MULTI-PEAKONS FOR A GENERALIZED QUINTIC-SEPTIC CAMASSA-HOLM TYPE EQUATION

被引：0
|
作者：
He, Dandan [1 ]
Deng, Tongjie [2 ]
Zhang, Kelei [3 ]
机构：
[1] Guilin Univ Elect Technol, Sch Math & Comp Sci, Guilin 541004, Peoples R China
[2] Guangxi Minzu Univ, Ctr Appl Math Guangxi, Sch Math & Phys, Nanning 530006, Peoples R China
[3] Guilin Univ Elect Technol, Sch Math & Comp Sci, Guangxi Coll & Univ Key Lab Data Anal & Computat, Guilin 541004, Peoples R China
来源：
QUARTERLY OF APPLIED MATHEMATICS | 2024年
关键词：
Generalized quintic-septic CH equation; peakons; multi-peakons; orbital stability; SHALLOW-WATER EQUATION; BREAKING WAVES; CAUCHY-PROBLEM;
D O I：
10.1090/qam/1699
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the generalized quintic-septic Camassa-Holm (gqsCH) equation, which is actually an extension of the quintic CH equation and the septic CH equation. We first prove the existence of the single peakon. Then, by constructing certain Lyapunov functionals, we prove the stability of peakons in the energy space H1(R)-norm. 1 ( R)-norm. Finally, we also prove that the sum of N sufficiently decoupled peakons is orbitally stable in the energy space by using energy argument, combining the method of the orbital stability of single peakons with monotonicity of the local energy norm.
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页数：38
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