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arXiv · 1803.01263

Discrete time Toda systems

Yuri B. Suris
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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.

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Yuri B. Suris. 2018-03-03. Discrete time Toda systems. https://doi.org/10.1088/1751-8121/aacbdc

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