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.
|Number of pages||67|
|Journal||Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire|
|State||Published - Nov 1 2021|
Bibliographical noteFunding Information:
We want to thank Prof. Catherine Sulem for her many useful comments.
© 2021 L'Association Publications de l'Institut Henri Poincaré
- Breather stability
- Long time asymptotics
- Riemann-Hilbert problems
- Soliton resolution
ASJC Scopus subject areas
- Mathematical Physics
- Applied Mathematics