论文标题
设置理论4-Simplex方程的杂种解决方案
Birational solutions to the set-theoretical 4-simplex equation
论文作者
论文摘要
4-Simplex方程是Zamolodchikov的四面体方程和Yang-Baxter方程的更高维度类似物，这是数学物理学中最基本的两个方程之一。在本文中，我们介绍了一种使用LAX矩阵重构问题来构建4个简洁图的方法，即对设置理论4-Simplex方程的解决方案。使用这种方法，我们构建了4个简洁图，该图在一定极限下给出了由Kashaev，Korepanov和Sergeev分类的四面体图。此外，我们构建了4-Simplex地图的Kadomtsev- petviashvili类型。最后，我们引入了一种构建4个简洁图的方法，该方法可以使用可集成PDE的Darboux转换限制在级别集合到参数4-Simplex图。我们构建了一个非线性schrödinger型参数4-Simplex图，这是文献中的第一个参数4-Simplex图。
The 4-simplex equation is a higher-dimensional analogue of Zamolodchikov's tetrahedron equation and the Yang--Baxter equation which are two of the most fundamental equations of mathematical physics. In this paper, we introduce a method for constructing 4-simplex maps, namely solutions to the set-theoretical 4-simplex equation, using Lax matrix refactorisation problems. Employing this method, we construct 4-simplex maps which at a certain limit give tetrahedron maps classified by Kashaev, Korepanov and Sergeev. Moreover, we construct a Kadomtsev--Petviashvili type of 4-simplex map. Finally, we introduce a method for constructing 4-simplex maps which can be restricted on level sets to parametric 4-simplex maps using Darboux transformations of integrable PDEs. We construct a nonlinear Schrödinger type parametric 4-simplex map which is the first parametric 4-simplex map in the literature.
