This article is cited in 2 papers

Systems of difference equations, symmetries, and integrability conditions

L. Brady, P. Xenitidis

School of Computer Science and the Environment, Liverpool Hope University, Liverpool, UK

Abstract: 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.

Keywords: difference equations, integrable discrete systems, symmetries, conservation laws, integrability conditions, difference operators, functional equations.

MSC: 39A36, 39A70, 39B22, 37C79, 37K60

Received: 19.02.2025
Revised: 19.03.2025

DOI: 10.4213/tmf10943

 English version: Theoretical and Mathematical Physics, 2025, 224:2, 1324–1339

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