Stability of multi antipeakon-peakons profile
Khaled El Dika (LAGA), Luc Molinet (LMPT)
TL;DR
This paper extends the stability analysis of the Camassa-Holm equation to include ordered trains of anti-peakons and peakons, broadening understanding of their dynamic stability.
Contribution
It provides the first stability results for ordered trains of anti-peakons and peakons, building on previous work on individual peakons.
Findings
Stability of trains of anti-peakons and peakons established
Extension of previous stability results to new configurations
Supports the robustness of multi-peakon solutions
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 \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.
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