Multidimensional Toda Lattices: Continuous and Discrete Time

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.

References in corpus (1)

• Computing recurrence coefficients of multiple orthogonal polynomials

Cited by in corpus (5)

• Solitons of the (2+2)-dimensional Toda lattice
• Nonautonomous ultradiscrete hungry Toda lattice and a generalized box-ball system
• Non-autonomous multidimensional Toda system and multiple interpolation problem
• Christoffel Transform and Multiple Orthogonal Polynomials
• Determinantal approach to multiple orthogonal polynomials, and the corresponding integrable equations