Polynomial algebras and exact solutions of general quantum non-linear optical models II: Multi-mode boson systems

We present higher order polynomial algebras which are the dynamical symmetry algebras of a wide class of multi-mode boson systems in non-linear optics. We construct their unitary representations and the corresponding single-variable differential operator realizations. We then use the results to obtain exact (Bethe ansatz) solutions to the multi-mode boson systems, including the BEC models as special cases.