Canonical and Backlund transformations for discrete integrable systems and classical r-matrix

摘要

Certain new ideas, relevant to the recently proposed study of Backlund transformations from the canonical view point. are presented on the basis of two classes of r-matrices. A general method is proposed for constructing the similarity transformation leading to the required Backlund transformation. In one such case we reproduce the results of Kuznetsov and Sklyanin (J. Phys. A: Math. Cen. 31 (1998) 2241). Furthermore we analyse the effect of deforming the Lax operator and study its connection to these ideas. Lastly we show that the proof of the spectrality property can be carried out explicitly (C) 2001 Published by Elsevier Science B.V. [References: 18]