Necessary and sufficient conditions for the existence of symmetry groups for systems of differential-difference equations with partial derivatives

In the present paper, we obtain necessary and sufficient conditions for the existence of symmetry groups for systems of differential-difference equations with partial derivatives. Constructions of symmetry groups and recursion operators for various differential-difference equations are described. The corresponding symmetry generators that transform solutions of given equations into other solutions are obtained. © 2012 Springer Science+Business Media, Inc.