Stability of multi antipeakon-peakons profile

Khaled El Dika; Luc Molinet

doi:10.3934/dcdsb.2009.12.561

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2009, Volume 12, Issue 3: 561-577. Doi: 10.3934/dcdsb.2009.12.561

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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
2.
L.M.P.T., UFR Sciences et Techniques, Université de Tours, Parc Grandmont, 37200 Tours

Received: April 2009

Revised: May 2009

Published: May 2009

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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.

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Mathematics Subject Classification: 35Q58, 37K40.

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