Coboundary dynamical Poisson groupoids and integrable systems

TL;DR

This paper introduces a new scheme for constructing integrable systems using coboundary dynamical Poisson groupoids, providing a factorization method for solving Hamiltonian flows and illustrating it with hyperbolic spin models.

Contribution

It presents a novel framework for integrable systems based on coboundary dynamical Poisson groupoids and introduces a factorization technique for solving Hamiltonian flows.

Findings

Developed a general scheme for integrable systems construction.

Applied the scheme to hyperbolic spin Ruijsenaars-Schneider models.

Solved equations of motion in a specific case.

Abstract

In this paper, we present a general scheme to construct integrable systems based on realization in the coboundary dynamical Poisson groupoids of Etingof and Varchenko. We also present a factorization method for solving the Hamiltonian flows. To illustrate our scheme and factorization theory, we consider a family of hyperbolic spin Ruijsenaars-Schneider models related to affine Toda field theories and solve the equations of motion in a simple case.