Orbital stability of the sum of N peakons for the mCH-Novikov equation

This paper investigates a generalized Camassa-Holm equation with cubic nonlinearities (alias the mCH-Novikov equation), which is a generalization of some special equations. The mCH-Novikov equation possesses well-known peaked solitary waves that are called peakons. The peakons were proved orbital st...

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Bibliographic Details
Published in:Applicable analysis 2024-03, Vol.103 (5), p.874-897
Main Authors: Wang, Jiajing, Deng, Tongjie, Zhang, Kelei
Format: Article
Language:English
Subjects:
Camassa-Holm equation
Mathematical analysis
mCH-Novikov equation
multi-peakons
Orbital stability
peakons
Shallow water equations
Solitary waves
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Summary:This paper investigates a generalized Camassa-Holm equation with cubic nonlinearities (alias the mCH-Novikov equation), which is a generalization of some special equations. The mCH-Novikov equation possesses well-known peaked solitary waves that are called peakons. The peakons were proved orbital stable by Chen et al. in [Stability of peaked solitary waves for a class of cubic quasilinear shallow-water equations. Int Math Res Not. 2022;1-33]. We mainly prove the orbital stability of the multi-peakons in the mCH-Novikov equation. In this paper, it is proved that the sum of N fully decoupled peaks is orbitally stable in the energy space by using energy argument, combining the orbital stability of single peakons and local monotonicity of the method.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2023.2210600