Within the zero curvature formulation, a hierarchy of integrable lattice equations is constructed from an arbitrary-order matrix discrete spectral problem of Ablowitz-Ladik type. The existence of infinitely many symmetries and conserved functionals is a consequence of the Lax operator algebra and the trace identity. When the involved two potential vectors are scalar, all the resulting integrable lattice equations are reduced to the standard Ablowitz-Ladik hierarchy.

中文翻译：

---

具有多个势能的 Ablowitz-Ladik 可积格子层次结构

在零曲率公式中，可积分晶格方程的层次结构由 Ablowitz-Ladik 类型的任意阶矩阵离散谱问题构成。无限多个对称性和守恒泛函的存在是 Lax 算子代数和迹恒等式的结果。当涉及的两个势向量是标量时，所有得到的可积点阵方程都简化为标准的 Ablowitz-Ladik 层次结构。