Bäcklund Transformation for the BC-Type Toda Lattice

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