Factorization of the (2+1)-dimensional BLP integrable system by the periodic fixed points of its Bäcklund transformations

Abstract

Previously, we have found a factorization of the (1+1)-dimensional Toda lattice by the periodic fixed points of its Bäcklund transformations. The Toda flow is realized by two commuting, one-dimensional Hamiltonian flows. By a result of Konopelchenko, the Laplace-Darboux transformation is a Bäcklund transformation for the (2+1)-dimensional Boiti-Leon-Pempinelli (BLP) equation. A periodic fixed point of the Laplace transformation is an invariant manifold of the BLP flow. This manifold is determined by solutions of the (1+1)-dimensional Toda lattice equations. From these results we find that the 2+1 BLP flow is factored by three commuting, one-dimensional Hamiltonian flows that are the periodic fixed points of its Bäcklund transformations.