Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data

  • Jiaqi Liu

    Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, United States
  • Peter A. Perry

    Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, United States
  • Catherine Sulem

    Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4, Canada

Abstract

The large-time behavior of solutions to the derivative nonlinear Schrödinger equation is established for initial conditions in some weighted Sobolev spaces under the assumption that the initial conditions do not support solitons. Our approach uses the inverse scattering setting and the nonlinear steepest descent method of Deift and Zhou as recast by Dieng and McLaughlin.

Résumé

On établit le comportement au temps long des solutions de l'équation de Schrödinger nonlinéraire avec dérivée dans des espaces de Sobolev à poids, sous l'hypothèse que les conditions initiales ne supportent pas de solitons. Notre approche utilise l'inverse scattering et la méthode de la plus grande pente (“steepest descent”) nonlinéaire de Deift et Zhou revisitée par Dieng et McLaughlin.

Cite this article

Jiaqi Liu, Peter A. Perry, Catherine Sulem, Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data. Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 1, pp. 217–265

DOI 10.1016/J.ANIHPC.2017.04.002