Coupled discrete Sawada–Kotera equations and their explicit quasi-periodic solutions
Coupled discrete Sawada–Kotera equations and their explicit quasi-periodic solutions
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DOI：
10.1007/s13324-021-00577-2
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发表时间：
2021-07
影响因子：
1.7
通讯作者：
Mi Jia;X. Geng;Jiao Wei;Yunyun Zhai;Huan Liu
中科院分区：
文献类型：
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作者：
Mi Jia;X. Geng;Jiao Wei;Yunyun Zhai;Huan Liu
本文提出了一类与矩阵谱问题相关的耦合离散Sawada-Kotera方程。利用离散耦合Sawada-Kotera方程的Lax矩阵的特征多项式，引入了一个三角曲线、一个Baker-Akhiezer函数和一个亚纯函数。研究了三角形曲线上两个无穷点和两个零点附近的Baker-Akhiezer函数和亚纯函数的渐近性质。利用阿贝尔映射和亚纯微分精确地给出了各种流的拉直。在这些结果的基础上，利用代数曲线的理论，我们得到了整个耦合离散Sawada-Kotera层次的显式拟周期解。
In this paper, we propose a hierarchy of coupled discrete Sawada–Kotera equations associated with amatrix 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.