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 |
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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/123456789/146423 |
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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| _version_ | 1862637607285948416 |
|---|---|
| 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⁾.
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| first_indexed | 2025-11-30T23:10:39Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146423 |
| 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 |
| record_format | dspace |
| 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 |