Canonicity of Baecklund transformation: r-matrix approach. II
solv-int
2015-11-11 v1 Exactly Solvable and Integrable Systems
Abstract
This is the second part of the paper devoted to the general proof of canonicity of Baecklund transformation (BT) for a Hamiltonian integrable system governed by SL(2)-invariant r-matrix. Introducing an extended phase space from which the original one is obtained by imposing a 1st kind constraint, we are able to prove the canonicity of BT in a new way. The new proof allows to explain naturally the fact why the gauge transformation matrix M associated to the BT has the same structure as the Lax operator L. The technique is illustrated on the example of the DST chain.
Cite
@article{arxiv.solv-int/9903017,
title = {Canonicity of Baecklund transformation: r-matrix approach. II},
author = {E. K. Sklyanin},
journal= {arXiv preprint arXiv:solv-int/9903017},
year = {2015}
}
Comments
7 pages, LATEX 2e, macros included