The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation

We investigate scattering properties of a Moyal deformed version of the nonlinear Schrödinger equation in an even number of space dimensions. With rather weak conditions on the degree of nonlinearity, the Cauchy problem for general initial data has a unique globally defined solution, and also has so...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2010
Hauptverfasser: Durhuus, B., Gayral, V.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2010
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/146317
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation / B. Durhuus, V. Gayral // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 18 назв. — англ.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-146317
record_format dspace
spelling Durhuus, B.
Gayral, V.
2019-02-08T20:38:30Z
2019-02-08T20:38:30Z
2010
The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation / B. Durhuus, V. Gayral // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 18 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 35K99; 58B34; 53D55
DOI:10.3842/SIGMA.2010.046
https://nasplib.isofts.kiev.ua/handle/123456789/146317
We investigate scattering properties of a Moyal deformed version of the nonlinear Schrödinger equation in an even number of space dimensions. With rather weak conditions on the degree of nonlinearity, the Cauchy problem for general initial data has a unique globally defined solution, and also has solitary wave solutions if the interaction potential is suitably chosen. We demonstrate how to set up a scattering framework for equations of this type, including appropriate decay estimates of the free time evolution and the construction of wave operators defined for small scattering data in the general case and for arbitrary scattering data in the rotationally symmetric case.
This paper is a contribution to the Special Issue “Noncommutative Spaces and Fields”. The full collection is available at http://www.emis.de/journals/SIGMA/noncommutative.html.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation
spellingShingle The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation
Durhuus, B.
Gayral, V.
title_short The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation
title_full The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation
title_fullStr The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation
title_full_unstemmed The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation
title_sort scattering problem for a noncommutative nonlinear schrödinger equation
author Durhuus, B.
Gayral, V.
author_facet Durhuus, B.
Gayral, V.
publishDate 2010
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description We investigate scattering properties of a Moyal deformed version of the nonlinear Schrödinger equation in an even number of space dimensions. With rather weak conditions on the degree of nonlinearity, the Cauchy problem for general initial data has a unique globally defined solution, and also has solitary wave solutions if the interaction potential is suitably chosen. We demonstrate how to set up a scattering framework for equations of this type, including appropriate decay estimates of the free time evolution and the construction of wave operators defined for small scattering data in the general case and for arbitrary scattering data in the rotationally symmetric case.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/146317
citation_txt The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation / B. Durhuus, V. Gayral // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 18 назв. — англ.
work_keys_str_mv AT durhuusb thescatteringproblemforanoncommutativenonlinearschrodingerequation
AT gayralv thescatteringproblemforanoncommutativenonlinearschrodingerequation
AT durhuusb scatteringproblemforanoncommutativenonlinearschrodingerequation
AT gayralv scatteringproblemforanoncommutativenonlinearschrodingerequation
first_indexed 2025-11-27T21:27:18Z
last_indexed 2025-11-27T21:27:18Z
_version_ 1850852855547691008