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

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

2010-04-17

arxiv.org/abs/1004.2945v1

SIGMA 6 (2010), 034, 14 pages

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

10.3842/SIGMA.2010.034

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 Backlund 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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