Global existence for the derivative nonlinear Schrodinger equation with arbitrary spectral singularities

Robert Jenkins, Jiaqi Liu, Peter Perry, Catherine Sulem

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

We show that the derivative nonlinear Schrodinger (DNLS) equation is globally well-posed in the weighted Sobolev space H2,2(R). Our result exploits the complete integrability of the DNLS equation and removes certain spectral conditions on the initial data required by our previous work, thanks to Zhou's analysis (Comm. Pure Appl. Math. 42:7 (1989), 895-938) on spectral singularities in the context of inverse scattering.

Original languageEnglish
Pages (from-to)1539-1578
Number of pages40
JournalAnalysis and PDE
Volume13
Issue number5
DOIs
StatePublished - 2020

Bibliographical note

Publisher Copyright:
© 2020 Mathematical Sciences Publishers.

Funding

We thank Deniz Bilman and Peter Miller for helpful discussions on Zhou\u2019s ideas. This work was supported by a grant from the Simons Foundation/SFARI (359431, PAP). CS is supported in part by Discovery Grant 2018-04536 from the Natural Sciences and Engineering Research Council of Canada.

FundersFunder number
Simons Foundation/SFARI
Simons Foundation
Simons Foundation Autism Research Initiative2018-04536, 359431
Natural Sciences and Engineering Research Council of Canada

    Keywords

    • Derivative nonlinear schrödinger
    • Global well-posedness
    • Inverse scattering

    ASJC Scopus subject areas

    • Analysis
    • Numerical Analysis
    • Applied Mathematics

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