论文标题
兼容地图，相关的可集成差异系统和杨 - 巴克斯特地图的非亚伯层层次结构
Non-Abelian hierarchies of compatible maps, associated integrable difference systems and Yang-Baxter maps
论文作者
论文摘要
我们介绍了非兼容地图的两个非等效层次的非等效家族，并提供了他们的宽松对配方。这些地图与非亚洲阳式地图的层次结构家族有关，我们明确地提供了这些图。此外，这些层次结构对应于可集成的差异系统，其变量在$ \ mathbb {z}^2 $ graph的基本单元格的边缘上定义，这又导致差异系统的层次结构，其在同一单元格的顶点上定义的变量。在这方面，我们获得了非亚伯晶格修饰的凝胶式 - 二基层次结构，以及我们称为lattice-nqc（或lattice-lattice-$（q3）_0 $ _0 $）gel'fand-dikii Hierierarchy的明确形式。
We present two non-equivalent families of hierarchies of non-Abelian compatible maps and we provide their Lax pair formulation. These maps are associated with families of hierarchies of non-Abelian Yang-Baxter maps, which we provide explicitly. In addition, these hierarchies correspond to integrable difference systems with variables defined on edges of an elementary cell of the $\mathbb{Z}^2$ graph, that in turn lead to hierarchies of difference systems with variables defined on vertices of the same cell. In that respect we obtain the non-Abelian lattice-modified Gel'fand-Dikii hierarchy, together with the explicit form of a non-Abelian hierarchy that we refer to as the lattice-NQC (or lattice-$(Q3)_0$) Gel'fand-Dikii hierarchy.
