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By Khaled El Dika and Luc Molinet


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. 1. Introduction. The Camassa-Holm equation (C-H), ut − utxx = −3uux + 2uxuxx + uuxxx, (t, x) ∈ IR 2, (1) can be derived as a model for the propagation of unidirectional shalow water waves over a flat bottom by writing the Green-Naghdi equations in Lie-Poisson Hamiltonian form and then making an asymptotic expansion which keeps the Hamiltonia

Year: 2011
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