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

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Abstract

The linear Bäcklund 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. © 1987.

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Saito, S., & Saitoh, N. (1987). Laplace, Bäcklund and gauge transformations in the two-dimensional Toda lattice. Physics Letters A, 123(6), 283–286. https://doi.org/10.1016/0375-9601(87)90228-3

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