Stability of the Camassa-Holm solitons. (English) Zbl 1022.35053

Constantin, A.; Strauss, W. A.

J. Nonlinear Sci. 12, No. 4, 415-422 (2002).

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

Keywords:

stability; solitary wave solutions; shallow water waves