Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 3 (2007), 080, 17 pages      arXiv:0707.1950
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

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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