On a Trivial Family of Noncommutative Integrable Systems
Andrey V. Tsiganov
TL;DR
This paper explores trivial deformations of canonical Poisson brackets in various integrable systems and introduces a new family of noncommutative integrable systems derived from these deformations.
Contribution
It presents a novel trivial family of noncommutative integrable systems obtained through deformations of well-known classical systems.
Findings
New trivial family of noncommutative integrable systems
Application of deformations to classical integrable models
Extension of the understanding of Poisson bracket deformations
Abstract
We discuss trivial deformations of the canonical Poisson brackets associated with the Toda lattices, relativistic Toda lattices, Henon-Heiles, rational Calogero-Moser and Ruijsenaars-Schneider systems and apply one of these deformations to construct a new trivial family of noncommutative integrable systems.
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