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SIGMA 3 (2007), 080, 17 pages arXiv:0707.1950
https://doi.org/10.3842/SIGMA.2007.080
Contribution to the Vadim Kuznetsov Memorial Issue
Bäcklund Transformation for the BC-Type Toda Lattice
Vadim Kuznetsov a and Evgeny Sklyanin b
a) Deceased
b) Department of Mathematics, University of York, York YO10 5DD, UK
Received July 13, 2007; Published online July 25, 2007
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 Bäcklund transformation and prove its basic properties:
canonicity, commutativity and spectrality.
The Bäcklund 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.
Key words:
Bäcklund transformation; Toda lattice; integrability; boundary conditions; classical Lie algebras.
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