Global well-posedness for the derivative non-linear Schrödinger equation

Robert Jenkins, Jiaqi Liu, Peter A. Perry, Catherine Sulem

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We study the derivative nonlinear Schrödinger (DNLS) equation for general initial conditions in weighted Sobolev spaces that can support bright solitons (but exclude spectral singularities). We show that the set of such initial data is open and dense in a weighted Sobolev space, and includes data of arbitrarily large L 2 -norm. We prove global well-posedness on this open and dense set. In a subsequent paper, we will use these results and a steepest descent analysis to prove the soliton resolution conjecture for the DNLS equation with the initial data considered here and asymptotic stability of N-soliton solutions.

Original languageEnglish
Pages (from-to)1151-1195
Number of pages45
JournalCommunications in Partial Differential Equations
Issue number8
StatePublished - Aug 3 2018

Bibliographical note

Funding Information:
PAP was supported in part by NSF Grant DMS-1208778 and by Simons Foundation Research and Travel Grant 359431, and CS was supported in part by Grant 46179-13 from the Natural Sciences and Engineering Research Council of Canada.

Publisher Copyright:
© 2018, © 2018 Taylor & Francis.


  • Derivative nonlinear Schrödinger equation
  • global well-posedness
  • inverse scattering method
  • soliton solutions

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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