English

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/