B\"acklund Transformation for the BC-Type Toda Lattice
Exactly Solvable and Integrable Systems
2008-04-24 v2 Mathematical Physics
math.MP
Abstract
We study an integrable case of n-particle Toda lattice: open chain with boundary terms containing 4 parameters. For this model we construct a B\"acklund transformation and prove its basic properties: canonicity, commutativity and spectrality. The B\"acklund transformation can be also viewed as a discretized time dynamics. Two Lax matrices are used: of order 2 and of order 2n+2, which are mutually dual, sharing the same spectral curve.
Keywords
Cite
@article{arxiv.0707.1950,
title = {B\"acklund Transformation for the BC-Type Toda Lattice},
author = {Vadim Kuznetsov and Evgeny Sklyanin},
journal= {arXiv preprint arXiv:0707.1950},
year = {2008}
}
Comments
This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/