Article

Journal of Nonlinear Science

, Volume 12, Issue 4, pp 415-422

First online:

Stability of the Camassa-Holm solitons

  • ConstantinAffiliated withDepartment of Mathematics, Lund University, P.O. Box 118, S-22100, Lund, Sweden e-mail: adrian.constantin@math.lu.se
  • , StraussAffiliated withDepartment of Mathematics and Lefschetz Center for Dynamical Systems, Brown University, Providence, RI 02912, U.S.A. e-mail: wstrauss@math.brown.edu

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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.

AMS Classification. 35Q35, 35Q51