Symmetries of Discrete Dynamical Systems Involving Two Species
  The Lie point symmetries of a coupled system of two nonlinear differential-difference equations are investigated. It is shown that in special cases the symmetry group can be infinite dimensional, in other cases up to 10 dimensional. The equations can describe the interaction of two long molecular chains, each involving one type of atoms. 
D. Gomez-Ullate, S. Lafortune and P. Winternitz