Laplace, Bäcklund and gauge transformations in the two-dimensional Toda lattice

Abstract The linear Backlund transformation (LBT) associated with the two-dimensional Toda lattice is shown to be equivalent to a sequence of Laplace transformations of a hyperbolic linear differential equation. When the Toda lattice is cut at a point, the corresponding Laplace invariant vanishes and the LBT can be integrated.