Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation
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 equat...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2013 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2013
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/149358 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation / A.L. Lisok, A.V. Shapovalov, A.Y. Trifonov // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 34 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-149358 |
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Lisok, A.L. Shapovalov, A.V. Trifonov, A.Y. 2019-02-21T07:12:56Z 2019-02-21T07:12:56Z 2013 Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation / A.L. Lisok, A.V. Shapovalov, A.Y. Trifonov // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 34 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 35Q55; 45K05; 76M60; 81Q20 DOI: http://dx.doi.org/10.3842/SIGMA.2013.066 https://nasplib.isofts.kiev.ua/handle/123456789/149358 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. We would like to thank the anonymous referees who gave a relevant contribution to improve the paper. The work was supported in part by the Russian Federation programs “Kadry” (contract No. 16.740.11.0469) and “Nauka” (contract No. 1.604.2011) and by Tomsk State University project No. 2.3684.2011. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation |
| spellingShingle |
Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation Lisok, A.L. Shapovalov, A.V. Trifonov, A.Y. |
| title_short |
Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation |
| title_full |
Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation |
| title_fullStr |
Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation |
| title_full_unstemmed |
Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation |
| title_sort |
symmetry and intertwining operators for the nonlocal gross-pitaevskii equation |
| author |
Lisok, A.L. Shapovalov, A.V. Trifonov, A.Y. |
| author_facet |
Lisok, A.L. Shapovalov, A.V. Trifonov, A.Y. |
| publishDate |
2013 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149358 |
| citation_txt |
Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation / A.L. Lisok, A.V. Shapovalov, A.Y. Trifonov // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 34 назв. — англ. |
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2025-12-07T20:07:09Z |
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2025-12-07T20:07:09Z |
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