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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| Дата: | 2006 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2006
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146106 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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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irk-123456789-1461062019-02-08T01:23:34Z Prolongation Loop Algebras for a Solitonic System of Equations Agrotis, M.A. 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. 2006 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146106 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 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. |
| format |
Article |
| author |
Agrotis, M.A. |
| spellingShingle |
Agrotis, M.A. Prolongation Loop Algebras for a Solitonic System of Equations Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Agrotis, M.A. |
| author_sort |
Agrotis, M.A. |
| title |
Prolongation Loop Algebras for a Solitonic System of Equations |
| title_short |
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_sort |
prolongation loop algebras for a solitonic system of equations |
| publisher |
Інститут математики НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146106 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT agrotisma prolongationloopalgebrasforasolitonicsystemofequations |
| first_indexed |
2023-05-20T17:23:50Z |
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2023-05-20T17:23:50Z |
| _version_ |
1796153201490132992 |