Asymptotic stability of solitons for mKdV

Pierre Germain, Fabio Pusateri, Frédéric Rousset

Research output: Contribution to journalArticle

Abstract

We prove a full asymptotic stability result for solitary wave solutions of the mKdV equation. We consider small perturbations of solitary waves with polynomial decay at infinity and prove that solutions of the Cauchy problem evolving from such data tend uniformly, on the real line, to another solitary wave as time goes to infinity. We describe precisely the asymptotics of the perturbation behind the solitary wave showing that it satisfies a nonlinearly modified scattering behavior. This latter part of our result relies on a precise study of the asymptotic behavior of small solutions of the mKdV equation.

Original languageEnglish (US)
Pages (from-to)272-330
Number of pages59
JournalAdvances in Mathematics
Volume299
DOIs
StatePublished - Aug 20 2016

Fingerprint

Solitary Waves
Asymptotic Stability
Solitons
Infinity
Polynomial Decay
Small Solutions
Solitary Wave Solution
Small Perturbations
Real Line
Cauchy Problem
Asymptotic Behavior
Scattering
Tend
Perturbation

Keywords

  • Asymptotic stability
  • MKdV
  • Modified scattering
  • Solitons

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Asymptotic stability of solitons for mKdV. / Germain, Pierre; Pusateri, Fabio; Rousset, Frédéric.

In: Advances in Mathematics, Vol. 299, 20.08.2016, p. 272-330.

Research output: Contribution to journalArticle

Germain, Pierre ; Pusateri, Fabio ; Rousset, Frédéric. / Asymptotic stability of solitons for mKdV. In: Advances in Mathematics. 2016 ; Vol. 299. pp. 272-330.
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