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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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2010-04-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Online Access: | http://dx.doi.org/10.3842/SIGMA.2010.034 |
| _version_ | 1818200276923842560 |
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| author | Oksana Ye. Hentosh |
| author_facet | Oksana Ye. Hentosh |
| author_sort | Oksana Ye. Hentosh |
| collection | DOAJ |
| 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 | 2024-12-12T02:35:06Z |
| format | Article |
| id | doaj.art-aa79cf5877a3428eb33b3a343a1f4071 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-12T02:35:06Z |
| publishDate | 2010-04-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-aa79cf5877a3428eb33b3a343a1f40712022-12-22T00:41:18ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592010-04-016034The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase SpacesOksana Ye. HentoshThe 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.http://dx.doi.org/10.3842/SIGMA.2010.034Lax integrable differential-difference systemsBäcklund transformationsquared eigenfunction symmetries |
| spellingShingle | Oksana Ye. Hentosh The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces Symmetry, Integrability and Geometry: Methods and Applications Lax integrable differential-difference systems Bäcklund transformation squared eigenfunction symmetries |
| 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 |
| topic | Lax integrable differential-difference systems Bäcklund transformation squared eigenfunction symmetries |
| url | http://dx.doi.org/10.3842/SIGMA.2010.034 |
| work_keys_str_mv | AT oksanayehentosh thelaxintegrabledifferentialdifferencedynamicalsystemsonextendedphasespaces AT oksanayehentosh laxintegrabledifferentialdifferencedynamicalsystemsonextendedphasespaces |