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 language | English (US) |
|---|---|
| Pages (from-to) | 2297-2319 |
| Number of pages | 23 |
| Journal | Nonlinearity |
| Volume | 27 |
| Issue number | 9 |
| DOIs | |
| State | Published - Sep 1 2014 |
Keywords
- Camassa-Holm equation
- integrable system
- modified Camassa-Holm equation
- orbital stability
- peakon