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...
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| Datum: | 2010 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2010
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/146317 |
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| 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. |
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irk-123456789-1463172019-02-09T01:24:20Z The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation Durhuus, B. Gayral, V. 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. 2010 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146317 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Durhuus, B. Gayral, V. |
| spellingShingle |
Durhuus, B. Gayral, V. The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Durhuus, B. Gayral, V. |
| author_sort |
Durhuus, B. |
| title |
The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2025-07-10T23:28:38Z |
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2025-07-10T23:28:38Z |
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