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The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces
Інший ID:
2010 Mathematics Subject Classification: 37J05; 37K10; 37K30; 37K35; 37K60
DOI:10.3842/SIGMA.2010.034
DOI:10.3842/SIGMA.2010.034
Посилання:
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.
Підтримка:
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.
Дата:
2010
Переглядів:
443
Завантажень:
236
Анотація:
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.
