Transverse Evolution Operator for the Gross-Pitaevskii Equation in Semiclassical Approximation
The Gross-Pitaevskii equation with a local cubic nonlinearity that describes a many-dimensional system in an external field is considered in the framework of the complex WKB-Maslov method. Analytic asymptotic solutions are constructed in semiclassical approximation in a small parameter h, h → 0, in...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2005 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2005
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209341 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Transverse Evolution Operator for the Gross-Pitaevskii Equation in Semiclassical Approximation / A. Borisov, A. Shapovalov, A. Trifonov // Symmetry, Integrability and Geometry: Methods and Applications. — 2005. — Т. 1. — Бібліогр.: 33 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862736163475816448 |
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| author | Borisov, A. Shapovalov, A. Trifonov, A. |
| author_facet | Borisov, A. Shapovalov, A. Trifonov, A. |
| citation_txt | Transverse Evolution Operator for the Gross-Pitaevskii Equation in Semiclassical Approximation / A. Borisov, A. Shapovalov, A. Trifonov // Symmetry, Integrability and Geometry: Methods and Applications. — 2005. — Т. 1. — Бібліогр.: 33 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The Gross-Pitaevskii equation with a local cubic nonlinearity that describes a many-dimensional system in an external field is considered in the framework of the complex WKB-Maslov method. Analytic asymptotic solutions are constructed in semiclassical approximation in a small parameter h, h → 0, in the class of functions concentrated in the neighborhood of an unclosed surface associated with the phase curve that describes the evolution of the surface vertex. The functions of this class are of the one-soliton form along the direction of the surface normal. The general constructions are illustrated by examples.
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| first_indexed | 2025-12-07T19:52:24Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209341 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:52:24Z |
| publishDate | 2005 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Borisov, A. Shapovalov, A. Trifonov, A. 2025-11-19T12:23:21Z 2005 Transverse Evolution Operator for the Gross-Pitaevskii Equation in Semiclassical Approximation / A. Borisov, A. Shapovalov, A. Trifonov // Symmetry, Integrability and Geometry: Methods and Applications. — 2005. — Т. 1. — Бібліогр.: 33 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81Q20; 81R30; 35Q55 https://nasplib.isofts.kiev.ua/handle/123456789/209341 https://doi.org/10.3842/SIGMA.2005.019 The Gross-Pitaevskii equation with a local cubic nonlinearity that describes a many-dimensional system in an external field is considered in the framework of the complex WKB-Maslov method. Analytic asymptotic solutions are constructed in semiclassical approximation in a small parameter h, h → 0, in the class of functions concentrated in the neighborhood of an unclosed surface associated with the phase curve that describes the evolution of the surface vertex. The functions of this class are of the one-soliton form along the direction of the surface normal. The general constructions are illustrated by examples. The work was supported in part by a Grant of the President of the Russian Federation (No.NSh1743.2003.2). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Transverse Evolution Operator for the Gross-Pitaevskii Equation in Semiclassical Approximation Article published earlier |
| spellingShingle | Transverse Evolution Operator for the Gross-Pitaevskii Equation in Semiclassical Approximation Borisov, A. Shapovalov, A. Trifonov, A. |
| title | Transverse Evolution Operator for the Gross-Pitaevskii Equation in Semiclassical Approximation |
| title_full | Transverse Evolution Operator for the Gross-Pitaevskii Equation in Semiclassical Approximation |
| title_fullStr | Transverse Evolution Operator for the Gross-Pitaevskii Equation in Semiclassical Approximation |
| title_full_unstemmed | Transverse Evolution Operator for the Gross-Pitaevskii Equation in Semiclassical Approximation |
| title_short | Transverse Evolution Operator for the Gross-Pitaevskii Equation in Semiclassical Approximation |
| title_sort | transverse evolution operator for the gross-pitaevskii equation in semiclassical approximation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209341 |
| work_keys_str_mv | AT borisova transverseevolutionoperatorforthegrosspitaevskiiequationinsemiclassicalapproximation AT shapovalova transverseevolutionoperatorforthegrosspitaevskiiequationinsemiclassicalapproximation AT trifonova transverseevolutionoperatorforthegrosspitaevskiiequationinsemiclassicalapproximation |