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 
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/
@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},
     year = {2010},
     volume = {37},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2010_37_a0/}
}
TY  - JOUR
AU  - I. A. Kolesnikova
TI  - Necessary and sufficient conditions for the existence of symmetry groups for systems of differential-difference equations with partial derivatives
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2010
SP  - 5
EP  - 15
VL  - 37
UR  - http://geodesic.mathdoc.fr/item/CMFD_2010_37_a0/
LA  - ru
ID  - CMFD_2010_37_a0
ER  - 
%0 Journal Article
%A I. A. Kolesnikova
%T Necessary and sufficient conditions for the existence of symmetry groups for systems of differential-difference equations with partial derivatives
%J Contemporary Mathematics. Fundamental Directions
%D 2010
%P 5-15
%V 37
%U http://geodesic.mathdoc.fr/item/CMFD_2010_37_a0/
%G ru
%F CMFD_2010_37_a0

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

[1] Bellman R., Kuk K., Differentsialno-raznostnye uravneniya, Mir, M., 1967 | MR | Zbl

[2] Olver P., Prilozhenie grupp Li k differentsialnym uravneniyam, Mir, M., 1980 | MR

[3] Savchin V. M., Matematicheskie metody mekhaniki beskonechnomernykh nepotentsialnykh sistem, UDN, M., 1991 | MR

[4] Filippov V. M., Savchin V. M., Shorokhov S. G., Variatsionnye printsipy dlya nepotentsialnykh operatorov, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Noveishie dostizheniya, 40, VINITI, M., 1992 | MR | Zbl