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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 
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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/

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