Darboux transformations for the two-dimensional Toda system

Abstract

Binary Darboux transformations are constructed for the two‐dimensional (A∞) Toda lattice and for a generalized non‐Abelian Toda lattice. Invariance of these transformations under certain reductions produces the B∞ and C∞ Toda lattices as well as various periodic reductions corresponding to Kač–Moody algebras. The reduction to the D∞ lattice from the non‐Abelian lattice is studied in some detail.