Systems of difference equations, symmetries and integrability conditions

Brady, Louis and Xenitidis, Pavlos (2025) Systems of difference equations, symmetries and integrability conditions. Theoretical and Mathematical Physics. ISSN 0040-5779 (Accepted for Publication)

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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.

Item Type:	Article
Keywords:	Difference equations; integrable discrete systems; symmetries; conservation laws; integrability conditions; difference operators; functional equations
Faculty / Department:	Faculty of Human and Digital Sciences > School of Computer Science and the Environment
Depositing User:	Pavlos Xenitidis
Date Deposited:	24 Mar 2025 16:31
Last Modified:	24 Mar 2025 16:31
URI:	https://hira.hope.ac.uk/id/eprint/4633

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