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

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

Jiaqi Liu, Peter A. Perry, Catherine Sulem

Research output: Contribution to journalArticlepeer-review

46 Scopus citations

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.

Translated title of the contributionLong-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data
Original languageEnglish
Pages (from-to)217-265
Number of pages49
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume35
Issue number1
DOIs
StatePublished - Jan 2018

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Masson SAS

Keywords

  • Inverse scattering method
  • Nonlinear steepest descent method
  • Riemann–Hilbert problem

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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