Orbital stability of peakons for a generalization of the modified Camassa-Holm equation

Xiaochuan Liu, Yue Liu, Peter J. Olver, Changzheng Qu

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

The orbital stability of the peaked solitary-wave solutions for a generalization of the modified Camassa-Holm equation with both cubic and quadratic nonlinearities is investigated. The equation is a model of asymptotic shallow-water wave approximations to the incompressible Euler equations. It is also formally integrable in the sense of the existence of a Lax formulation and bi-Hamiltonian structure. It is demonstrated that, when the Camassa-Holm energy counteracts the effect of the modified Camassa-Holm energy, the peakon and periodic peakon solutions are orbitally stable under small perturbations in the energy space.

Original languageEnglish (US)
Pages (from-to)2297-2319
Number of pages23
JournalNonlinearity
Volume27
Issue number9
DOIs
StatePublished - Sep 1 2014

Keywords

  • Camassa-Holm equation
  • integrable system
  • modified Camassa-Holm equation
  • orbital stability
  • peakon

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