Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Stability of multi antipeakon-peakons profile

Pages: 561 - 577, Volume 12, Issue 3, October 2009      doi:10.3934/dcdsb.2009.12.561

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Khaled El Dika - L.A.G.A., Institut Galilée, Université Paris 13, 93430 Villetaneuse, France (email)
Luc Molinet - L.M.P.T., UFR Sciences et Techniques, Université de Tours, Parc Grandmont, 37200 Tours, France (email)

Abstract: The Camassa-Holm equation possesses well-known peaked solitary waves that can travel to both directions. The positive ones travel to the right and are called peakon whereas the negative ones travel to the left and are called antipeakons. Their orbital stability has been established by Constantin and Strauss in [20]. In [28] we have proven the stability of trains of peakons. Here, we continue this study by extending the stability result to the case of ordered trains of anti-peakons and peakons.

Keywords:  Camassa-Holm equation, orbital stability, peakons, anti-peakons.
Mathematics Subject Classification:  35Q58, 37K40.

Received: April 2009;      Revised: May 2009;      Available Online: July 2009.