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This article is cited in 1 scientific paper (total in 1 paper)
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
Abstract:
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.
Keywords:
Lax integrable differential-difference systems; Bäcklund transformation; squared eigenfunction symmetries.
Received: November 16, 2009; in final form February 24, 2010; Published online April 17, 2010
Citation:
Oksana Ye. Hentosh, “The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces”, SIGMA, 6 (2010), 034, 14 pp.
Linking options:
https://www.mathnet.ru/eng/sigma491 https://www.mathnet.ru/eng/sigma/v6/p34
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