论文标题
六角形晶格的集成系统以及具有四边形和六角形脸部多塔的一致性
Integrable systems on hexagonal lattices and consistency on polytopes with quadrilateral and hexagonal faces
论文作者
论文摘要
将六角方程系统的新概念引入了一个过度确定的系统，该系统由六个以六角形的六个顶点定义的六个五点面式四分之一方程式。对于一个一致的六角方程系统，可以根据其他四个方面的唯一解决六角形的两个变量。在单个连接的点楼梯上定义的合适初始值问题下，一致的十六进制方程系统在六角形晶格中具有明确定义的独特演化。提出了十六进制方程系统的多维一致性，它是根据其在具有六角形和四边形面孔的某些多面体的一致性方面提出的，并为六角形的棱镜（伸长的十二面体），截断的八面体和6-6-二抗症提出了具体示例。可以通过以面部为中心的四方方程来构建此类多型的十六进制方程的一致系统，这些方程满足了一致性，以face为中心的立方体，结合了满足一致性acoundy-acound-a-a-cuber的常规四方程。
The new concept of a system of hex equations is introduced as an overdetermined system of six five-point face-centered quad equations defined on six vertices of a hexagon. For a consistent system of hex equations, two variables on neighbouring vertices of the hexagon can be solved for uniquely in terms of the other four. A consistent system of hex equations has a well-defined unique evolution in the hexagonal lattice under suitable initial value problems defined on a single connected staircase of points. Multidimensional consistency for systems of hex equations is proposed in terms of their consistency on certain polytopes which have both hexagonal and quadrilateral faces, and specific examples are presented for the hexagonal prism, the elongated dodecahedron, the truncated octahedron, and the 6-6-duoprism. Consistent systems of hex equations on such polytopes may be constructed from face-centered quad equations which satisfy consistency-around-a-face-centered-cube, in combination with regular quad equations that satisfy consistency-around-a-cube.
