Integrable Discrete Equations Derived by Similarity Reduction of the Extended Discrete KP Hierarchy

We consider the extended discrete KP hierarchy and show that similarity reduction of its subhierarchies lead to purely discrete equations with dependence on some number of parameters together with equations governing deformations with respect to these parameters. It is written down discrete equation...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2006
Main Author: Svinin, A.K.
Format: Article
Language:English
Published: Інститут математики НАН України 2006
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/146423
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Integrable Discrete Equations Derived by Similarity Reduction of the Extended Discrete KP Hierarchy / A.K. Svinin // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 22 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Svinin, A.K.
author_facet Svinin, A.K.
citation_txt Integrable Discrete Equations Derived by Similarity Reduction of the Extended Discrete KP Hierarchy / A.K. Svinin // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 22 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We consider the extended discrete KP hierarchy and show that similarity reduction of its subhierarchies lead to purely discrete equations with dependence on some number of parameters together with equations governing deformations with respect to these parameters. It is written down discrete equations which naturally generalize the first discrete Painlevé equation dPI in a sense that autonomous version of these equations admit the limit to the first Painlevé equation. It is shown that each of these equations describes Bäcklund transformations of Veselov-Shabat periodic dressing lattices with odd period known also as Noumi-Yamada systems of type A2(n-1)⁽¹⁾.
first_indexed 2025-11-30T23:10:39Z
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 2025-11-30T23:10:39Z
publishDate 2006
publisher Інститут математики НАН України
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spelling Svinin, A.K.
2019-02-09T16:48:15Z
2019-02-09T16:48:15Z
2006
Integrable Discrete Equations Derived by Similarity Reduction of the Extended Discrete KP Hierarchy / A.K. Svinin // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 22 назв. — англ.
1815-0659
2000 Mathematics Subject Classification: 37K10
https://nasplib.isofts.kiev.ua/handle/123456789/146423
We consider the extended discrete KP hierarchy and show that similarity reduction of its subhierarchies lead to purely discrete equations with dependence on some number of parameters together with equations governing deformations with respect to these parameters. It is written down discrete equations which naturally generalize the first discrete Painlevé equation dPI in a sense that autonomous version of these equations admit the limit to the first Painlevé equation. It is shown that each of these equations describes Bäcklund transformations of Veselov-Shabat periodic dressing lattices with odd period known also as Noumi-Yamada systems of type A2(n-1)⁽¹⁾.
The author thanks the organizers of Sixth International Conference “Symmetry in Nonlinear Mathematical Physics” (June 20–26, 2005, Kyiv) for hospitality and their work which allows to create friendly atmosphere during this Conference. The present paper is the written version of the talk delivered by the author at this conference.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Integrable Discrete Equations Derived by Similarity Reduction of the Extended Discrete KP Hierarchy
Article
published earlier
spellingShingle Integrable Discrete Equations Derived by Similarity Reduction of the Extended Discrete KP Hierarchy
Svinin, A.K.
title Integrable Discrete Equations Derived by Similarity Reduction of the Extended Discrete KP Hierarchy
title_full Integrable Discrete Equations Derived by Similarity Reduction of the Extended Discrete KP Hierarchy
title_fullStr Integrable Discrete Equations Derived by Similarity Reduction of the Extended Discrete KP Hierarchy
title_full_unstemmed Integrable Discrete Equations Derived by Similarity Reduction of the Extended Discrete KP Hierarchy
title_short Integrable Discrete Equations Derived by Similarity Reduction of the Extended Discrete KP Hierarchy
title_sort integrable discrete equations derived by similarity reduction of the extended discrete kp hierarchy
url https://nasplib.isofts.kiev.ua/handle/123456789/146423
work_keys_str_mv AT svininak integrablediscreteequationsderivedbysimilarityreductionoftheextendeddiscretekphierarchy