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Stability of peakons. (English) Zbl 1049.35149
The authors prove the orbital stability of peakon solutions of the Camassa-Holm equation in the \(H^1\) norm under the assumption of their existence. The proof is based on estimates for two conservation laws of the equation. Some comments on known results concerning the well-posedness of the initial value problem and the existence of solutions conclude the article.

MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
37K45 Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems
35B35 Stability in context of PDEs
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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