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October  2009, 12(3): 561-577. doi: 10.3934/dcdsb.2009.12.561

Stability of multi antipeakon-peakons profile

Khaled El Dika 1, and  Luc Molinet 2,

1. 

L.A.G.A., Institut Galilée, Université Paris 13, 93430 Villetaneuse, France
2. 

L.M.P.T., UFR Sciences et Techniques, Université de Tours, Parc Grandmont, 37200 Tours, France

Received  April 2009 Revised  May 2009 Published  July 2009

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, anti-peakons., peakons, orbital stability.
Mathematics Subject Classification: 35Q58, 37K4.
Citation: Khaled El Dika, Luc Molinet. Stability of multi antipeakon-peakons profile. Discrete and Continuous Dynamical Systems - B, 2009, 12 (3) : 561-577. doi: 10.3934/dcdsb.2009.12.561
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