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)|
|Number of pages||23|
|State||Published - Sep 1 2014|
- Camassa-Holm equation
- integrable system
- modified Camassa-Holm equation
- orbital stability