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 |
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| Date: | 2010 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2010
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| 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| _version_ | 1862739737688670208 |
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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.
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| first_indexed | 2025-12-07T20:11:12Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146352 |
| 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 |
| record_format | dspace |
| 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 published earlier |
| 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 |
| work_keys_str_mv | AT hentoshoye thelaxintegrabledifferentialdifferencedynamicalsystemsonextendedphasespaces AT hentoshoye laxintegrabledifferentialdifferencedynamicalsystemsonextendedphasespaces |