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ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2010, том 6, 034, 14 стр. (Mi sigma491)

Эта публикация цитируется в 1 статье

The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces

Oksana Ye. Hentosh

Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine, 3B Naukova Str., Lviv, 79060, Ukraine

Аннотация: 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.

Ключевые слова: Lax integrable differential-difference systems; Bäcklund transformation; squared eigenfunction symmetries.

MSC: 37J05; 37K10; 37K30; 37K35; 37K60

Поступила: 16 ноября 2009 г.; в окончательном варианте 24 февраля 2010 г.; опубликована 17 апреля 2010 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2010.034



Реферативные базы данных:
ArXiv: 1004.2945


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