Soliton resolution for the focusing modified KdV equation

Gong Chen, Jiaqi Liu

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


The soliton resolution for the focusing modified Korteweg-de Vries (mKdV) equation is established for initial conditions in some weighted Sobolev spaces. Our approach is based on the nonlinear steepest descent method and its reformulation through ∂‾-derivatives. From the view of stationary points, we give precise asymptotic formulas along trajectory x=vt for any fixed v. To extend the asymptotics to solutions with initial data in low regularity spaces, we apply a global approximation via PDE techniques. As by-products of our long-time asymptotics, we also obtain the asymptotic stability of nonlinear structures involving solitons and breathers.

Original languageEnglish
Pages (from-to)2005-2071
Number of pages67
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Issue number6
StatePublished - Nov 1 2021

Bibliographical note

Funding Information:
We want to thank Prof. Catherine Sulem for her many useful comments.

Publisher Copyright:
© 2021 L'Association Publications de l'Institut Henri Poincaré


  • Breather stability
  • Long time asymptotics
  • Riemann-Hilbert problems
  • Soliton resolution

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics


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