2021/12/01 by Gong Chen, Jiaqi Liu · 35 citations
paper · doi:10.1016/j.anihpc.2021.02.008
published in Annales de l'Institut Henri Poincaré C, Analyse non linéaire 38(6), 2005-2071 (European Mathematical Society - EMS - Publishing House GmbH)
crossref created 2021/02/21 · crossref issued 2021/12/01 · crossref published 2021/12/01 · crossref published-print 2021/12/01 · crossref deposited 2025/07/31 · crossref indexed 2026/08/06
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.