差分方程组，对称性和可积性条件

IF 1.1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2025-08-23 DOI:10.1134/S0040577925080021

L. Brady, P. Xenitidis

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引用次数: 0

摘要

我们考虑了一类定义在\(\mathbb{Z}^2\)格的初等四边形上的差分方程组，定义了它们的可消变量和动态变量，并说明了它们的用途。利用对称无穷层次的存在性作为可积性判据，导出了系统的必要可积性条件，并将其用于构造系统的最低阶对称性。这些考虑是在所考虑的系统类别中的三个系统的帮助下证明的。

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Systems of difference equations, symmetries, and integrability conditions

We consider a class of systems of difference equations defined on an elementary quadrilateral of the \(\mathbb{Z}^2\) lattice, define their eliminable and dynamical variables, and demonstrate their use. Using the existence of infinite hierarchies of symmetries as integrability criterion, we derive necessary integrability conditions and employ them in the construction of the lowest-order symmetries of a given system. These considerations are demonstrated with the help of three systems from the class of systems under consideration.

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来源期刊

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.