%0 Journal Article
%T The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces
%A Oksana Ye. Hentosh
%J Symmetry, Integrability and Geometry : Methods and Applications
%D 2010
%I National Academy of Science of Ukraine
%X 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 B cklund 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.
%K Lax integrable differential-difference systems
%K B cklund transformation
%K squared eigenfunction symmetries
%U http://dx.doi.org/10.3842/SIGMA.2010.034