Canonicity of Baecklund transformation: r-matrix approach. I
solv-int
2015-11-12 v1 Exactly Solvable and Integrable Systems
Abstract
For the Hamiltonian integrable systems governed by SL(2)-invariant r-matrix (such as Heisenberg magnet, Toda lattice, nonlinear Schroedinger equation) a general procedure for constructing Baecklund transformation is proposed. The corresponding BT is shown to preserve the Poisson bracket. The proof is given by a direct calculation using the r-matrix expression for the Poisson bracket.
Keywords
Cite
@article{arxiv.solv-int/9903016,
title = {Canonicity of Baecklund transformation: r-matrix approach. I},
author = {E. K. Sklyanin},
journal= {arXiv preprint arXiv:solv-int/9903016},
year = {2015}
}
Comments
7 pages, LATEX-2e, macros included