The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces
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 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.
Cite
@article{arxiv.1004.2945,
title = {The Lax Integrable Differential-Difference Dynamical Systems on Extended Phase Spaces},
author = {Oksana Ye. Hentosh},
journal= {arXiv preprint arXiv:1004.2945},
year = {2010}
}