Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation
| Parent link: | Arxiv.org.— 2013.— Mathematical Physics |
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| Main Author: | |
| Other Authors: | , |
| Summary: | Title screen We consider the symmetry properties of an integro-differential multidimensional Gross-Pitaevskii equation with a nonlocal nonlinear (cubic) term in the context of symmetry analysis using the formalism of semiclassical asymptotics. This yields a semiclassically reduced nonlocal Gross-Pitaevskii equation, which can be treated as a nearly linear equation, to determine the principal term of the semiclassical asymptotic solution. Our main result is an approach which allows one to construct a class of symmetry operators for the reduced Gross-Pitaevskii equation. These symmetry operators are determined by linear relations including intertwining operators and additional algebraic conditions. The basic ideas are illustrated with a 1D reduced Gross-Pitaevskii equation. The symmetry operators are found explicitly, and the corresponding families of exact solutions are obtained |
| Language: | English |
| Published: |
2013
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| Subjects: | |
| Online Access: | http://arxiv.org/abs/1302.3326 |
| Format: | Electronic Book Chapter |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=636446 |