Algebro-Geometric Solutions for a Discrete Integrable Equation
Algebro-Geometric Solutions for a Discrete Integrable Equation
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DOI：
10.1155/2017/5258375
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发表时间：
2017-11
影响因子：
1.4
通讯作者：
Mengshuang Tao;Huanhe Dong
中科院分区：
文献类型：
--
作者：
Mengshuang Tao;Huanhe Dong
利用元为矩阵的李代数，引入了一个离散谱问题。利用离散的零曲率方程，得到了一个离散的可积层次。通过对离散系统的分解，导出了具有两势函数的微分-差分可积系统。通过构造Abel-Jacobi坐标来拉直连续流和离散流，提出了Riemann函数。基于黎曼函数，得到了离散可积系统的代数-几何解。
With the assistance of a Lie algebra whose element is a matrix, we introduce a discrete spectral problem. By means of discrete zero curvature equation, we obtain a discrete integrable hierarchy. According to decomposition of the discrete systems, the new differential-difference integrable systems with two-potential functions are derived. By constructing the Abel-Jacobi coordinates to straighten the continuous and discrete flows, the Riemann theta functions are proposed. Based on the Riemann theta functions, the algebro-geometric solutions for the discrete integrable systems are obtained.