Multidimensional Toda Lattices: Continuous and Discrete Time

TL;DR

This paper introduces multidimensional versions of continuous and discrete Toda lattices, extending integrable systems to multiple spatial dimensions using a generalized orthogonal polynomial approach.

Contribution

It develops a novel framework for multidimensional Toda lattices by generalizing the orthogonal polynomial method to multiple variables, advancing the theory of integrable systems.

Findings

Constructed multidimensional Toda lattice models.

Extended orthogonal polynomial techniques to multiple dimensions.

Provided new integrable systems with multiple spatial coordinates.

Abstract

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.