Stability of multi antipeakon-peakons profile

Khaled El Dika (1) , Luc Molinet (2)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 LMPT - Laboratoire de Mathématiques et Physique Théorique

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 \cite{CS1}. In \cite{EL2} 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.

Domaines: Equations aux dérivées partielles [math.AP]

Khaled El Dika, Luc Molinet. Stability of multi antipeakon-peakons profile. Discrete and Continuous Dynamical Systems - Series B, 2009, 12 (3), pp.561-577. ⟨hal-00424454⟩