Geodesic
Recursion operators, conservation laws, and integrability conditions for difference equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 1, pp. 23-49

Voir la notice de l'article provenant de la source Math-Net.Ru

We attempt to propose an algebraic approach to the theory of integrable difference equations. We define the concept of a recursion operator for difference equations and show that it generates an infinite sequence of symmetries and canonical conservation laws for a difference equation. As in the case of partial differential equations, these canonical densities can serve as integrability conditions for difference equations. We obtain the recursion operators for the Viallet equation and all the Adler–Bobenko–Suris equations.
Keywords: difference equation, integrability, integrability condition, symmetry, conservation law, recursion operator. 
@article{TMF_2011_167_1_a1,
     author = {A. V. Mikhailov and J. P. Wang and P. Xenitidis},
     title = {Recursion operators, conservation laws, and integrability conditions for difference equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {23--49},
     publisher = {mathdoc},
     volume = {167},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_167_1_a1/}
}
TY  - JOUR
AU  - A. V. Mikhailov
AU  - J. P. Wang
AU  - P. Xenitidis
TI  - Recursion operators, conservation laws, and integrability conditions for difference equations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2011
SP  - 23
EP  - 49
VL  - 167
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2011_167_1_a1/
LA  - ru
ID  - TMF_2011_167_1_a1
ER  - 
%0 Journal Article
%A A. V. Mikhailov
%A J. P. Wang
%A P. Xenitidis
%T Recursion operators, conservation laws, and integrability conditions for difference equations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2011
%P 23-49
%V 167
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2011_167_1_a1/
%G ru
%F TMF_2011_167_1_a1
A. V. Mikhailov; J. P. Wang; P. Xenitidis. Recursion operators, conservation laws, and integrability conditions for difference equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 167 (2011) no. 1, pp. 23-49. http://geodesic.mathdoc.fr/item/TMF_2011_167_1_a1/