论文标题
差异方程式，对称性和集成性条件的系统
Systems of difference equations, symmetries and integrability conditions
论文作者
论文摘要
我们考虑在$ {\ mathbb {z}}}^2 $ lattice上定义的基本四边形定义的差分方程系统，定义了它们可消除和动态变量，并证明其使用。使用对称性的无限层次结构作为集成性标准，我们得出了必要的集成性条件，并将其用于构建给定系统的最低顺序对称性。在正在考虑的系统类别的三个系统的帮助下，证明了这些考虑因素。
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.
