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Stability of the Camassa-Holm solitons. (English) Zbl 1022.35053
Summary: We consider the stability problem of the solitary wave solutions of a completely integrable equation that arises as a model for the unidirectional propagation of shallow water waves. We prove that the solitary waves possess the spectral properties of solitons and that their shapes are stable under small disturbances.

MSC:
35Q51 Soliton equations
37K45 Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems
35Q35 PDEs in connection with fluid mechanics
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