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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| Дата: | 2013 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2013
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1493582019-02-22T01:23:11Z Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation Lisok, A.L. Shapovalov, A.V. Trifonov, A.Y. 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. 2013 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/149358 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 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. |
| format |
Article |
| author |
Lisok, A.L. Shapovalov, A.V. Trifonov, A.Y. |
| spellingShingle |
Lisok, A.L. Shapovalov, A.V. Trifonov, A.Y. Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Lisok, A.L. Shapovalov, A.V. Trifonov, A.Y. |
| author_sort |
Lisok, A.L. |
| title |
Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation |
| 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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:32:48Z |
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