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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2010-06-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2010.046 |
| _version_ | 1831739879470399488 |
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| author | Bergfinnur Durhuus Victor Gayral |
| author_facet | Bergfinnur Durhuus Victor Gayral |
| author_sort | Bergfinnur Durhuus |
| collection | DOAJ |
| 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 | 2024-12-21T13:47:22Z |
| format | Article |
| id | doaj.art-6a8bc58e652b410da937f2793b51dbca |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-21T13:47:22Z |
| publishDate | 2010-06-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-6a8bc58e652b410da937f2793b51dbca2022-12-21T19:01:49ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592010-06-016046The Scattering Problem for a Noncommutative Nonlinear Schrödinger EquationBergfinnur DurhuusVictor GayralWe 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.http://dx.doi.org/10.3842/SIGMA.2010.046noncommutative geometrynonlinear wave equationsscattering theoryJacobi polynomials |
| spellingShingle | Bergfinnur Durhuus Victor Gayral The Scattering Problem for a Noncommutative Nonlinear Schrödinger Equation Symmetry, Integrability and Geometry: Methods and Applications noncommutative geometry nonlinear wave equations scattering theory Jacobi polynomials |
| 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 schrodinger equation |
| topic | noncommutative geometry nonlinear wave equations scattering theory Jacobi polynomials |
| url | http://dx.doi.org/10.3842/SIGMA.2010.046 |
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