  A model describing the dynamics of crystal exciton states on a hexagonal
lattice has been studied. The hamiltonian includes terms describing the
movement of the exciton throughout the crystal. Here we generalize the
hamiltonian by including first order couplings of such terms to the lattice
phonon fields. A discussion of the ground state configuration of the exciton
field as a function of the system couplings is given. Finally we analyse the
stability of certain excited states under perturbations.
