标题： 黑白格子上定义的离散方程的对称性和可积性 显示英文标题

标题： Symmetries and integrability of discrete equations defined on a black-white lattice

摘要： 我们研究了Adler、Bobenko和Suris最近提出的H方程的变形，这些方程自然定义在一个黑白格点上。对于每一个这样的方程，构造了两种不同的三腿形式，从而得到两种不同的离散Toda型方程。它们的多维一致性导致了连接该类不同成员的Bäcklund变换以及Lax对。它们的对称性分析给出了广义对称性的无限层次。 显示英文摘要

摘要： We study the deformations of the H equations, presented recently by Adler, Bobenko and Suris, which are naturally defined on a black-white lattice. For each one of these equations, two different three-leg forms are constructed, leading to two different discrete Toda type equations. Their multidimensional consistency leads to B{\"a}cklund transformations relating different members of this class, as well as to Lax pairs. Their symmetry analysis is presented yielding infinite hierarchies of generalized symmetries.