Coboundary dynamical Poisson groupoids and integrable systems

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.