Alexander I. Aptekarev, Maxim Derevyagin, Hiroshi Miki, Walter Van Assche, “Multidimensional Toda Lattices: Continuous and Discrete Time”, SIGMA, 2016, Volume 12,054, 30 pp.

This article is cited in 13 papers

Multidimensional Toda Lattices: Continuous and Discrete Time

Alexander I. Aptekarev^a, Maxim Derevyagin^b, Hiroshi Miki^c, Walter Van Assche^d

^a Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, 125047 Moscow, Russia
^b University of Mississippi, Department of Mathematics, Hume Hall 305, P. O. Box 1848, University, MS 38677-1848, USA
^c Doshisha University, Department of Electronics, Faculty of Science and Engineering, Kyotanabe city, Kyoto 610 0394, Japan
^d KU Leuven, Department of Mathematics, Celestijnenlaan 200B box 2400, BE-3001 Leuven, Belgium

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.

Keywords: multiple orthogonal polynomials; orthogonal polynomials; recurrence relations; Toda equation; discrete integrable system; Toda lattice.

MSC: 42C05; 37K10; 39A14; 65Q10

Received: January 5, 2016; in final form June 1, 2016; Published online June 13, 2016

Language: English

DOI: 10.3842/SIGMA.2016.054