The formal derivatives of the Yang–Baxter equation with respect to its spectral parameters, evaluated at some fixed point of these parameters, provide us with two systems of differential equations. The derivatives of the R matrix elements, however, can be regarded as independent variables and eliminated from the systems, after which, two systems of polynomial equations are obtained in their place. In general, these polynomial systems have a non-zero Hilbert dimension, which means that not all elements of the R matrix can be fixed through them. Nevertheless, the remaining unknowns can be found by solving a few simple differential equations that arise as consistency conditions of the method. The branches of the solutions can also be easily analyzed by this method, which ensures the uniqueness and generality of the solutions. In this work, we consider the Yang–Baxter equation for (n + 1) (2n + 1)-vertex models with a generalization based on the A _n−1 symmetry. This differential approach allows us to solve the Yang–Baxter equation in a systematic way.

Yang-Baxter 方程相对于其光谱参数的形式导数，在这些参数的某个固定点处评估，为我们提供了两个微分方程组。然而，R矩阵元素的导数可以看作是自变量并从系统中消除，之后，在它们的位置上获得两个多项式方程组。通常，这些多项式系统具有非零的希尔伯特维数，这意味着并非R 的所有元素矩阵可以通过它们固定。然而，剩余的未知数可以通过求解作为该方法的一致性条件出现的一些简单微分方程来找到。这种方法也可以很容易地分析解的分支，保证了解的唯一性和通用性。在这项工作中，我们考虑 ( n + 1) (2 n + 1)-顶点模型的 Yang-Baxter 方程，其泛化基于A _{n -1}对称性。这种微分方法使我们能够以系统的方式求解 Yang-Baxter 方程。