Symmetry Classification of Diatomic Molecular Chains
  A symmetry classification of possible interactions in a diatomic molecular chain is provided. For nonlinear interactions the group of Lie point transformations, leaving the lattice invariant and taking solutions into solutions, is at most five-dimensional. An example is considered in which subgroups of the symmetry group are used to reduce the dynamical differential-difference equations to purely difference ones. 
S. Lafortune, S. Tremblay and P. Winternitz