Bäcklund Transformation for the BC-Type Toda Lattice

Details Bäcklund Transformation for the BC-Type Toda Lattice Bäcklund Transformation for the BC-Type Toda Lattice

2007-07-13

arxiv.org/abs/0707.1950v2

SIGMA 3 (2007), 080, 17 pages

Nonlinear Sciences

Exactly Solvable and Integrable Systems

This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Sym

Scientific paper

10.3842/SIGMA.2007.080

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.

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