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

Robert Jenkins; Jiaqi Liu; Peter Perry; Catherine Sulem

doi:10.2140/apde.2020.13.1539

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

Robert Jenkins, Jiaqi Liu, Peter Perry, Catherine Sulem

Mathematics

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

We show that the derivative nonlinear Schrodinger (DNLS) equation is globally well-posed in the weighted Sobolev space H^2,2(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 language	English
Pages (from-to)	1539-1578
Number of pages	40
Journal	Analysis and PDE
Volume	13
Issue number	5
DOIs	https://doi.org/10.2140/apde.2020.13.1539
State	Published - 2020

Bibliographical note

Publisher Copyright:
© 2020 Mathematical Sciences Publishers.

Keywords

Derivative nonlinear schrödinger
Global well-posedness
Inverse scattering

ASJC Scopus subject areas

Analysis
Numerical Analysis
Applied Mathematics

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10.2140/apde.2020.13.1539

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title = "Global existence for the derivative nonlinear Schrodinger equation with arbitrary spectral singularities",

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.",

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author = "Robert Jenkins and Jiaqi Liu and Peter Perry and Catherine Sulem",

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language = "English",

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AU - Jenkins, Robert

AU - Liu, Jiaqi

AU - Perry, Peter

AU - Sulem, Catherine

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Derivative nonlinear schrödinger

KW - Global well-posedness

KW - Inverse scattering

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JO - Analysis and PDE

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IS - 5

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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