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 Bäcklund 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.

60 pp. This is a contribution to the special issue of J. Phys. A "Fifty years of the Toda lattice"

References in corpus (2)

• Multi-time Lagrangian 1-forms for families of Bäcklund transformations. Relativistic Toda-type systems
• Discrete pluriharmonic functions as solutions of linear pluri-Lagrangian systems

Cited by in corpus (6)

• Lax matrices for lattice equations which satisfy consistency-around-a-face-centered-cube
• Superintegrable cellular automata and dual unitary gates from Yang-Baxter maps
• Discrete integrable equations on face-centered cubics: consistency and Lax pairs of corner equations
• Elliptic Ruijsenaars-Toda and elliptic Toda chains: classical r-matrix structure and relation to XYZ chain
• Integrable fishnet circuits and Brownian solitons
• Lax matrices for a 1-parameter subfamily of van Diejen--Toda chains