On the orbital stability of the Degasperis-Procesi antipeakon-peakon profile
Bashar Khorbatly (IDP), Luc Molinet (IDP)
TL;DR
This paper proves the orbital stability of the antipeakon-peakon profile in the Degasperis-Procesi equation under specific momentum perturbations, advancing understanding of its dynamic stability properties.
Contribution
It establishes the orbital stability of the antipeakon-peakon profile for the first time under certain momentum conditions, extending previous stability results.
Findings
Orbital stability of the antipeakon-peakon profile is proven.
Stability holds for perturbations with initial negative then positive momentum density.
Results contribute to the understanding of the Degasperis-Procesi equation dynamics.
Abstract
In this paper, we prove an orbital stability result for the Degasperis-Procesi peakon with respect to perturbations having a momentum density that is first negative and then positive. This leads to the orbital stability of the antipeakon-peakon profile with respect to such perturbations.
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