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2020 Global existence for the derivative nonlinear Schrödinger equation with arbitrary spectral singularities
Robert Jenkins, Jiaqi Liu, Peter Perry, Catherine Sulem
Anal. PDE 13(5): 1539-1578 (2020). DOI: 10.2140/apde.2020.13.1539

Abstract

We show that the derivative nonlinear Schrödinger (DNLS) equation is globally well-posed in the weighted Sobolev space H2,2(). 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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Robert Jenkins. Jiaqi Liu. Peter Perry. Catherine Sulem. "Global existence for the derivative nonlinear Schrödinger equation with arbitrary spectral singularities." Anal. PDE 13 (5) 1539 - 1578, 2020. https://doi.org/10.2140/apde.2020.13.1539

Information

Received: 5 September 2018; Revised: 16 April 2019; Accepted: 31 May 2019; Published: 2020
First available in Project Euclid: 17 September 2020

zbMATH: 07271838
MathSciNet: MR4149070
Digital Object Identifier: 10.2140/apde.2020.13.1539

Subjects:
Primary: 35Q55 , 37K15
Secondary: 35P25 , 35R30

Keywords: derivative nonlinear Schrödinger , global well-posedness , inverse scattering

Rights: Copyright © 2020 Mathematical Sciences Publishers

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