Geodesic
Necessary and sufficient conditions for the existence of symmetry groups for systems of differential-difference equations with partial derivatives
Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 37 (2010), pp. 5-15

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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. 
@article{CMFD_2010_37_a0,
     author = {I. A. Kolesnikova},
     title = {Necessary and sufficient conditions for the existence of symmetry groups for systems of differential-difference equations with partial derivatives},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {5--15},
     publisher = {mathdoc},
     volume = {37},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2010_37_a0/}
}
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I. A. Kolesnikova. Necessary and sufficient conditions for the existence of symmetry groups for systems of differential-difference equations with partial derivatives. Contemporary Mathematics. Fundamental Directions, Proceedings of the Crimean autumn mathematical school-symposium, Tome 37 (2010), pp. 5-15. http://geodesic.mathdoc.fr/item/CMFD_2010_37_a0/