The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces

The Hamiltonian representation for the hierarchy of Lax-type flows on a dual space to the Lie algebra of shift operators coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems is found by means of a specially constructed Bäcklund transformation. Th...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2010
Main Author: Hentosh, O.Ye.
Format: Article
Language:English
Published: Інститут математики НАН України 2010
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/146352
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces / O.Ye. Hentosh // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 45 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Hentosh, O.Ye.
author_facet Hentosh, O.Ye.
citation_txt The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces / O.Ye. Hentosh // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 45 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description The Hamiltonian representation for the hierarchy of Lax-type flows on a dual space to the Lie algebra of shift operators coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems is found by means of a specially constructed Bäcklund transformation. The Hamiltonian description for the corresponding set of squared eigenfunction symmetry hierarchies is represented. The relation of these hierarchies with Lax integrable (2+1)-dimensional differential-difference systems and their triple Lax-type linearizations is analysed. The existence problem of a Hamiltonian representation for the coupled Lax-type hierarchy on a dual space to the central extension of the shift operator Lie algebra is solved also.
first_indexed 2025-12-07T20:11:12Z
format Article
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T20:11:12Z
publishDate 2010
publisher Інститут математики НАН України
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spelling Hentosh, O.Ye.
2019-02-09T09:23:32Z
2019-02-09T09:23:32Z
2010
The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces / O.Ye. Hentosh // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 45 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 37J05; 37K10; 37K30; 37K35; 37K60
DOI:10.3842/SIGMA.2010.034
https://nasplib.isofts.kiev.ua/handle/123456789/146352
The Hamiltonian representation for the hierarchy of Lax-type flows on a dual space to the Lie algebra of shift operators coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems is found by means of a specially constructed Bäcklund transformation. The Hamiltonian description for the corresponding set of squared eigenfunction symmetry hierarchies is represented. The relation of these hierarchies with Lax integrable (2+1)-dimensional differential-difference systems and their triple Lax-type linearizations is analysed. The existence problem of a Hamiltonian representation for the coupled Lax-type hierarchy on a dual space to the central extension of the shift operator Lie algebra is solved also.
This paper is a contribution to the Proceedings of the Eighth International Conference “Symmetry in Nonlinear Mathematical Physics” (June 21–27, 2009, Kyiv, Ukraine). The full collection is available at http://www.emis.de/journals/SIGMA/symmetry2009.html.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces
Article
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spellingShingle The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces
Hentosh, O.Ye.
title The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces
title_full The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces
title_fullStr The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces
title_full_unstemmed The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces
title_short The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces
title_sort lax integrable differential-difference dynamical systems on extended phase spaces
url https://nasplib.isofts.kiev.ua/handle/123456789/146352
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AT hentoshoye laxintegrabledifferentialdifferencedynamicalsystemsonextendedphasespaces