Geodesic
Classification of semidiscrete equations of hyperbolic type. The~case of third-order symmetries
Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 2, pp. 404-415

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

We classify semidiscrete equations of hyperbolic type. We study the class of equations of the form $$ \frac{du_{n+1}}{dx}=f\biggl(\frac{du_{n}}{dx},u_{n+1},u_{n}\biggr), $$ where the unknown function $u_n(x)$ depends on one discrete ($n$) and one continuous ($x$) variables. The classification is based on the requirement that generalized symmetries exist in the discrete and continuous directions. We consider the case where the symmetries are of order $3$ in both directions. As a result, a list of equations with the required conditions is obtained.
Keywords: integrability, generalized symmetry, semidiscrete equation, hyperbolic type.
Mots-clés : classification 
@article{TMF_2023_217_2_a10,
     author = {R. N. Garifullin},
     title = {Classification of semidiscrete equations of hyperbolic type. {The~case} of third-order symmetries},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {404--415},
     publisher = {mathdoc},
     volume = {217},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_217_2_a10/}
}
TY  - JOUR
AU  - R. N. Garifullin
TI  - Classification of semidiscrete equations of hyperbolic type. The~case of third-order symmetries
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2023
SP  - 404
EP  - 415
VL  - 217
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2023_217_2_a10/
LA  - ru
ID  - TMF_2023_217_2_a10
ER  - 
%0 Journal Article
%A R. N. Garifullin
%T Classification of semidiscrete equations of hyperbolic type. The~case of third-order symmetries
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2023
%P 404-415
%V 217
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2023_217_2_a10/
%G ru
%F TMF_2023_217_2_a10
R. N. Garifullin. Classification of semidiscrete equations of hyperbolic type. The~case of third-order symmetries. Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 2, pp. 404-415. http://geodesic.mathdoc.fr/item/TMF_2023_217_2_a10/