On a Discrete Analogue of the Two-Dimensional Toda Lattice Hierarchy

Abstract

A discrete analogue of the two-dimensional Toda lattice hierarchy, which includes the discrete analogue of the two-dimensional Toda lattice equation, is obtained by extending the theory of the Toda lattice hierarchy. Special solutions and bilinear equations for the discrete analogue of the two-dimensional Toda lattice hierarchy are presented. It is shown that the subjects originated from the Sato theory are useful for the discrete-time integrable systems.