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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2010 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2010
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146317 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| _version_ | 1862599484841656320 |
|---|---|
| author | Durhuus, B. Gayral, V. |
| author_facet | Durhuus, B. Gayral, V. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
|
| first_indexed | 2025-11-27T21:27:18Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146317 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-27T21:27:18Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation Durhuus, B. Gayral, V. |
| title | 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_short | The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation |
| title_sort | scattering problem for a noncommutative nonlinear schrödinger equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146317 |
| work_keys_str_mv | AT durhuusb thescatteringproblemforanoncommutativenonlinearschrodingerequation AT gayralv thescatteringproblemforanoncommutativenonlinearschrodingerequation AT durhuusb scatteringproblemforanoncommutativenonlinearschrodingerequation AT gayralv scatteringproblemforanoncommutativenonlinearschrodingerequation |