Instability of $H^1$-stable peakons in the Camassa-Holm equation

22 Mar 2019 Natali Fabio Pelinovsky Dmitry E.

It is well-known that peakons in the Camassa-Holm equation are $H^1$-orbitally stable thanks to the presence of conserved quantities and properties of peakons as constrained energy minimizers. By using the method of characteristics, we prove that piecewise $C^1$ perturbations to peakons grow in time in spite of their stability in the $H^1$-norm... (read more)

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