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

摘要

It is well-known that peakons in the Camassa-Holm equation are H-1-orbitally stable thanks to 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. We also show that the linearized stability analysis near peakons contradicts the H-1-orbital stability result, hence passage from linear to nonlinear theory is false in H-1. (C) 2019 Elsevier Inc. All rights reserved.