Multidimensional Toda Lattices: Continuous and Discrete Time

Symmetry Integrability and Geometry-Methods and Applications

article

Alexander I. Aptekarev¹  Maxim Derevyagin²  Hiroshi Miki³  Walter Van Assche² 

[1] Keldysh Institute for Applied Mathematics, Russian Academy of Sciences;University of Mississippi, Department of Mathematics, University;Doshisha University, Department of Electronics, Faculty of Science and Engineering

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

DOI  :  10.3842/SIGMA.2016.054

来源: National Academy of Science of Ukraine

【 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.

【 授权许可】

Unknown