Orbital stability of peakons for a generalization of the modified Camassa-Holm equation (Q2924847)
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scientific article; zbMATH DE number 6358221
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Orbital stability of peakons for a generalization of the modified Camassa-Holm equation |
scientific article; zbMATH DE number 6358221 |
Statements
17 October 2014
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integrable system
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peaked solitary wave
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cubic and quadratic nonlinearities
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shallow-water wave approximations
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Orbital stability of peakons for a generalization of the modified Camassa-Holm equation (English)
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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. The authors prove 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.
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