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Abstract <p> We consider a class of systems of difference equations defined on an elementary quadrilateral of the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11232_2025_2670_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb{Z}^2\)</EquationSource> </InlineEquation> 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. </p>

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Systems of difference equations, symmetries, and integrability conditions

  • 期刊论文

  • 发表日期：

    2025年8月23日

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  • L. Brady,
  • P. Xenitidis

摘要

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.