Asymptotic stability of the Degasperis–Procesi antipeakon–peakon profile. (April 2022)

• Record Type: Journal Article
• Authors: Khorbatly, Bashar
• Is Part Of: Nonlinear analysis. Volume 64(2022)
• Publication Date: 2022-04
• Subjects: 35Q35 -- 35Q51 -- 35B40; Degasperi–Procesi equation -- Asymptotic stability -- Antipeakon–peakon profile; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103428
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: The aim of this paper is to prove that the Degasperis–Procesi antipeakon–peakon profile is asymptotically stable for all time. We start by proving the asymptotic stability of a single Degasperis–Procesi peakon and antipeakon with respect to perturbations having a momentum density that is first negative and then positive. Then this result is extended towards a well-ordered trains of antipeakons–peakons under such perturbations. In particular, the asymptotic stability of the antipeakon–peakon profile holds.