Global existence for the derivative nonlinear Schrödinger equation by the method of inverse scattering

Jiaqi Liu, Peter A. Perry, Catherine Sulem

Research output: Contribution to journalArticlepeer-review

38 Scopus citations

Abstract

We develop inverse scattering for the derivative nonlinear Schrödinger equation (DNLS) on the line using its gauge equivalence with a related nonlinear dispersive equation. We prove Lipschitz continuity of the direct and inverse scattering maps from the weighted Sobolev spaces H2,2(ℝ) to itself. These results immediately imply global existence of solutions to the DNLS for initial data in a spectrally determined (open) subset of H2,2(ℝ) containing a neighborhood of 0. Our work draws ideas from the pioneering work of Lee and from more recent work of Deift and Zhou on the nonlinear Schrödinger equation.

Original languageEnglish
Pages (from-to)1692-1760
Number of pages69
JournalCommunications in Partial Differential Equations
Volume41
Issue number11
DOIs
StatePublished - Nov 1 2016

Bibliographical note

Publisher Copyright:
© 2016, Copyright © Taylor & Francis Group, LLC.

Keywords

  • Derivative nonlinear Schrodinger equation
  • global well-posedness
  • inverse scattering method
  • solitonless solutions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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