Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data

Jiaqi Liu; Peter A. Perry; Catherine Sulem

doi:10.1016/j.anihpc.2017.04.002

Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data

Translated title of the contribution: Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data

Jiaqi Liu, Peter A. Perry, Catherine Sulem

Mathematics

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

40 Scopus citations

Abstract

The large-time behavior of solutions to the derivative nonlinear Schrödinger equation is established for initial conditions in some weighted Sobolev spaces under the assumption that the initial conditions do not support solitons. Our approach uses the inverse scattering setting and the nonlinear steepest descent method of Deift and Zhou as recast by Dieng and McLaughlin.

Translated title of the contribution	Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data
Original language	English
Pages (from-to)	217-265
Number of pages	49
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	35
Issue number	1
DOIs	https://doi.org/10.1016/j.anihpc.2017.04.002
State	Published - Jan 2018

Bibliographical note

Funding Information:
P. Perry supported in part by a Simons Research and Travel Grant 359431 . C. Sulem supported in part by NSERC Grant 46179-13 .

Publisher Copyright:
© 2017 Elsevier Masson SAS

Keywords

Inverse scattering method
Nonlinear steepest descent method
Riemann–Hilbert problem

ASJC Scopus subject areas

Analysis
Mathematical Physics
Applied Mathematics

Access to Document

10.1016/j.anihpc.2017.04.002

Cite this

@article{49538d7085a74b26905517fda1244ef6,

title = "Long-time behavior of solutions to the derivative nonlinear Schr{\"o}dinger equation for soliton-free initial data",

abstract = "The large-time behavior of solutions to the derivative nonlinear Schr{\"o}dinger equation is established for initial conditions in some weighted Sobolev spaces under the assumption that the initial conditions do not support solitons. Our approach uses the inverse scattering setting and the nonlinear steepest descent method of Deift and Zhou as recast by Dieng and McLaughlin.",

keywords = "Inverse scattering method, Nonlinear steepest descent method, Riemann–Hilbert problem",

author = "Jiaqi Liu and Perry, {Peter A.} and Catherine Sulem",

note = "Funding Information: P. Perry supported in part by a Simons Research and Travel Grant 359431 . C. Sulem supported in part by NSERC Grant 46179-13 . Publisher Copyright: {\textcopyright} 2017 Elsevier Masson SAS",

year = "2018",

month = jan,

doi = "10.1016/j.anihpc.2017.04.002",

language = "English",

volume = "35",

pages = "217--265",

number = "1",

}

TY - JOUR

T1 - Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data

AU - Liu, Jiaqi

AU - Perry, Peter A.

AU - Sulem, Catherine

PY - 2018/1

Y1 - 2018/1

N2 - The large-time behavior of solutions to the derivative nonlinear Schrödinger equation is established for initial conditions in some weighted Sobolev spaces under the assumption that the initial conditions do not support solitons. Our approach uses the inverse scattering setting and the nonlinear steepest descent method of Deift and Zhou as recast by Dieng and McLaughlin.

AB - The large-time behavior of solutions to the derivative nonlinear Schrödinger equation is established for initial conditions in some weighted Sobolev spaces under the assumption that the initial conditions do not support solitons. Our approach uses the inverse scattering setting and the nonlinear steepest descent method of Deift and Zhou as recast by Dieng and McLaughlin.

KW - Inverse scattering method

KW - Nonlinear steepest descent method

KW - Riemann–Hilbert problem

UR - http://www.scopus.com/inward/record.url?scp=85030469928&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85030469928&partnerID=8YFLogxK

U2 - 10.1016/j.anihpc.2017.04.002

DO - 10.1016/j.anihpc.2017.04.002

M3 - Article

AN - SCOPUS:85030469928

SN - 0294-1449

VL - 35

SP - 217

EP - 265

JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

IS - 1

ER -

Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this