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 |
| Summary: | 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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| ISSN: | 1815-0659 |