Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii Equation
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| Creator |
Lisok, A.L.
Shapovalov, A.V. Trifonov, A.Y. |
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| 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.
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| Date |
2019-02-21T07:12:56Z
2019-02-21T07:12:56Z 2013 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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