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

Symmetry Integrability and Geometry-Methods and Applications

article

Oksana Ye. Hentosh¹ 

[1] Institute for Applied Problems of Mechanics and Mathematics, National Academy of Sciences of Ukraine

关键词: Lax integrable dif ferential-dif ference systems;    B¨acklund transformation;    squared eigenfunction symmetries;   

DOI  :  10.3842/SIGMA.2010.034

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown