Multidimensional Quadrilateral Lattices are Integrable

Abstract

The notion of multidimensional quadrilateral lattice is introduced. It is shown that such a lattice is characterized by a system of integrable discrete nonlinear equations. Different useful formulations of the system are given. The geometric construction of the lattice is also discussed and, in particular, it is clarified the number of initial--boundary data which define the lattice uniquely.

Comments: 18 pages, LaTeX, 6 Postscript figures