In this paper we construct the autonomous quad-equations which admit as symmetries the five-point differential-difference equations belonging to known lists found by Garifullin, Yamilov and Levi. The obtained equations are classified up to autonomous point transformations and some simple non-autonomous transformations. We discuss our results in the framework of the known literature. There are among them a few new examples of both sine-Gordon and Liouville type equations.

中文翻译：

---

可积离散自治四元方程承认，作为广义对称性，已知的五点微分差分方程

在本文中，我们构造了自治四方程，它承认属于 Garifullin、Yamilov 和 Levi 发现的已知列表的五点微分差分方程是对称的。得到的方程分为自主点变换和一些简单的非自主变换。我们在已知文献的框架内讨论我们的结果。其中有一些正弦-戈登和刘维尔型方程的新例子。