Classification of semidiscrete hyperbolic type equations. The case of third order symmetries

2022/12/05 by R. N. Garifullin, Garifullin, R. N.
Mathematics · #37K10 #39A36 #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2212.02063

openalex publication_date 2022/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, a classification of semidiscrete equations of hyperbolic type is carried out. We study the class of equations of the form \fracdu_n+1dx=f(\fracdu_ndx,u_n+1,u_n), here is the unknown function u_n (x) depends on one discrete n and one continuous x variables. The classification is based on the requirement for the existence of higher symmetries in the discrete and continuous directions. The case is considered when the symmetries are of order 3 in both directions. As a result, a list of equations with the required conditions is obtained.

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