Discrete time Toda systems
Abstract
In this paper, we discuss several concepts of the modern theory of discrete integrable systems, including: - Time discretization based on the notion of B\"acklund transformation; - Symplectic realizations of multi-Hamiltonian structures; - Interrelations between discrete 1D systems and lattice 2D systems; - Multi-dimensional consistency as integrability of discrete systems; - Interrelations between integrable systems of quad-equations and integrable systems of Laplace type; - Pluri-Lagrangian structure as integrability of discrete variational systems. All these concepts are illustrated by the discrete time Toda lattices and their relativistic analogs.
Cite
@article{arxiv.1803.01263,
title = {Discrete time Toda systems},
author = {Yuri B. Suris},
journal= {arXiv preprint arXiv:1803.01263},
year = {2019}
}
Comments
60 pp. This is a contribution to the special issue of J. Phys. A "Fifty years of the Toda lattice"