Theory of integrable three-dimensional nonlinear lattice equations

Abstract

A linear inhomogeneous system of equations, which is invariant under a general type of nonlocal integral transformations, is investigated. The compatibility conditions of this system lead to a general class of nonlinear integrable partial difference equations on a three-dimensional lattice in terms of its coefficients. This class includes, e.g., specific lattice versions of the Kadomtsev-Petviashvili equation, the nonlinear Schrodinger equation, and the isotropic Heisenberg spin chain in 2+1 dimensions.