In this paper, we propose a hierarchy of coupled discrete Sawada–Kotera equations associated with a \(3\times 3\) matrix spectral problem. Using the characteristic polynomial of Lax matrix for the hierarchy of coupled discrete Sawada–Kotera equations, we introduce a trigonal curve, a Baker–Akhiezer function and a meromorphic function. We study the asymptotic properties of the Baker–Akhiezer function and the meromorphic function near two infinite points and two zero points on the trigonal curve. The straightening out of various flows is exactly given by means of the Abel map and the meromorphic differential. On the basis of these results and the theory of theory of algebraic curves, we obtain explicit quasi-periodic solutions of the entire coupled discrete Sawada–Kotera hierarchy.

在本文中，我们提出了与\(3\times 3\)矩阵谱问题相关的耦合离散 Sawada-Kotera 方程的层次结构。将 Lax 矩阵的特征多项式用于耦合离散 Sawada-Kotera 方程的层次结构，我们引入了三角曲线、Baker-Akhiezer 函数和亚纯函数。我们研究了三角曲线上两个无穷大点和两个零点附近的 Baker-Akhiezer 函数和亚纯函数的渐近性质。通过阿贝尔映射和亚纯微分精确地给出了各种流的理顺。在这些结果和代数曲线理论的基础上，我们获得了整个耦合离散 Sawada-Kotera 层次的显式拟周期解。