Prolongation Loop Algebras for a Solitonic System of Equations
We consider an integrable system of reduced Maxwell-Bloch equations that describes the evolution of an electromagnetic field in a two-level medium that is inhomogeneously broadened. We prove that the relevant Bäcklund transformation preserves the reality of the n-soliton potentials and establish the...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2006 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2006
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146106 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Prolongation Loop Algebras for a Solitonic System of Equations / M.A. Agrotis // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 24 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862714014823350272 |
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| author | Agrotis, M.A. |
| author_facet | Agrotis, M.A. |
| citation_txt | Prolongation Loop Algebras for a Solitonic System of Equations / M.A. Agrotis // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 24 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We consider an integrable system of reduced Maxwell-Bloch equations that describes the evolution of an electromagnetic field in a two-level medium that is inhomogeneously broadened. We prove that the relevant Bäcklund transformation preserves the reality of the n-soliton potentials and establish their pole structure with respect to the broadening parameter. The natural phase space of the model is embedded in an infinite dimensional loop algebra. The dynamical equations of the model are associated to an infinite family of higher order Hamiltonian systems that are in involution. We present the Hamiltonian functions and the Poisson brackets between the extended potentials.
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| first_indexed | 2025-12-07T17:48:24Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146106 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:48:24Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Agrotis, M.A. 2019-02-07T13:27:51Z 2019-02-07T13:27:51Z 2006 Prolongation Loop Algebras for a Solitonic System of Equations / M.A. Agrotis // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 24 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 37K10; 37N20; 35A30; 35Q60; 78A60 https://nasplib.isofts.kiev.ua/handle/123456789/146106 We consider an integrable system of reduced Maxwell-Bloch equations that describes the evolution of an electromagnetic field in a two-level medium that is inhomogeneously broadened. We prove that the relevant Bäcklund transformation preserves the reality of the n-soliton potentials and establish their pole structure with respect to the broadening parameter. The natural phase space of the model is embedded in an infinite dimensional loop algebra. The dynamical equations of the model are associated to an infinite family of higher order Hamiltonian systems that are in involution. We present the Hamiltonian functions and the Poisson brackets between the extended potentials. The author would like to thank P. Shipman for useful discussions and the Cyprus Research Promotion Foundation for support through the grant CRPF0504/03. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Prolongation Loop Algebras for a Solitonic System of Equations Article published earlier |
| spellingShingle | Prolongation Loop Algebras for a Solitonic System of Equations Agrotis, M.A. |
| title | Prolongation Loop Algebras for a Solitonic System of Equations |
| title_full | Prolongation Loop Algebras for a Solitonic System of Equations |
| title_fullStr | Prolongation Loop Algebras for a Solitonic System of Equations |
| title_full_unstemmed | Prolongation Loop Algebras for a Solitonic System of Equations |
| title_short | Prolongation Loop Algebras for a Solitonic System of Equations |
| title_sort | prolongation loop algebras for a solitonic system of equations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146106 |
| work_keys_str_mv | AT agrotisma prolongationloopalgebrasforasolitonicsystemofequations |