English

Discrete time Toda systems

Mathematical Physics 2019-11-11 v1 math.MP Exactly Solvable and Integrable 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.

Keywords

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"

R2 v1 2026-06-23T00:41:07.688Z