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

ABSTRACT

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.

KEYWORDS:

• Camassa–Holm equation
• mCH-Novikov equation
• peakons
• multi-peakons
• orbital stability

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35B35
• 37K05
• 37K45

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Guangxi Key Laboratory of Cryptography and Information Security (No. GCIS202134). The authors would like to thank the referees for their fruitful comments and suggestions.