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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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2006
Автор: Agrotis, M.A.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2006
Онлайн доступ:https://nasplib.isofts.kiev.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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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-146106
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
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Prolongation Loop Algebras for a Solitonic System of Equations
spellingShingle Prolongation Loop Algebras for a Solitonic System of Equations
Agrotis, M.A.
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
author Agrotis, M.A.
author_facet Agrotis, M.A.
publishDate 2006
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
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.
issn 1815-0659
url https://nasplib.isofts.kiev.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.
work_keys_str_mv AT agrotisma prolongationloopalgebrasforasolitonicsystemofequations
first_indexed 2025-12-07T17:48:24Z
last_indexed 2025-12-07T17:48:24Z
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