The non-Abelian (1 + 1)-dimensional Toda lattice as the periodic fixed point of the Laplace transform for (2 + 1)-dimensional integrable systems

Abstract

The non-Abelian Laplace transform is considered. It is shown that the periodic fixed point of this transform is described by the non-Abelian (1 + 1)-dimensional Toda lattice equation. The (2 + 1)-dimensional integrable system is presented for which the Laplace transformation is the Bäcklund transformation and the periodic (1 + 1)-dimensional Toda lattice defines the submanifold of solutions invariant under this transformation.