A Family of Hyperbolic Spin Calogero-Moser Systems and the Spin Toda Lattices

TL;DR

This paper develops a general framework for integrable systems related to dynamical Lie algebroids, introducing new hyperbolic spin Calogero-Moser systems and spin Toda lattices, with explicit solutions provided.

Contribution

It introduces a unifying scheme for integrable systems, including new hyperbolic spin Calogero-Moser and spin Toda lattice models, with a factorization method for explicit solutions.

Findings

Developed a factorization method for Hamiltonian flows.

Presented new hyperbolic spin Calogero-Moser systems.

Constructed spin Toda lattice models and solved them explicitly.

Abstract

In this paper, we continue to develop a general scheme to study a broad class of integrable systems naturally associated with the coboundary dynamical Lie algebroids. In particular, we present a factorization method for solving the Hamiltonian flows. We also present two important class of new examples, a family of hyperbolic spin Calogero-Moser systems and the spin Toda lattices. To illustrate our factorization theory, we show how to solve these Hamiltonian systems explicitly.