Multidimensional Toda Lattices: Continuous and Discrete Time

[摘要] In this paper we present multidimensional analogues of both the continuous- and discrete-time Toda lattices. The integrable systems that we consider here have two or more space coordinates. To construct the systems, we generalize the orthogonal polynomial approach for the continuous and discrete Toda lattices to the case of multiple orthogonal polynomials.

[关键词] multiple orthogonal polynomials;orthogonal polynomials;recurrence relations;Toda equation;discrete integrable system;Toda lattice