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

被引：1

作者：

Garifullin, R. N. ^{[1
]}

机构：

[1] Russian Acad Sci, Ufa Fed Res Ctr, Inst Math, Comp Ctr, Ufa, Russia

来源：

THEORETICAL AND MATHEMATICAL PHYSICS | 2023年 / 217卷 / 02期

基金：

俄罗斯科学基金会;

关键词：

integrability; generalized symmetry; classification; semidiscrete equation; hyperbolic type; EVOLUTION-EQUATIONS;

D O I：

10.1134/S0040577923110119

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We classify semidiscrete equations of hyperbolic type. We study the class of equations of the form du(n+1)/dx = f(du(n)/dx , u(n+1,) u(n)) 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.

引用

页码：1767 / 1776

页数：10

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