Bäcklund Transformation for the BC-Type Toda Lattice - Kuznetsov, V.; Sklyanin, E. (Symmetry, Integrability and Geometry: Methods and Applications, 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.