Ma Wen-Xiu
Department of Mathematics, Zhejiang Normal University, Jinhua 321004, People's Republic of China.
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, People's Republic of China.
Proc Math Phys Eng Sci. 2017 Jul;473(2203):20170232. doi: 10.1098/rspa.2017.0232. Epub 2017 Jul 5.
This is the first part of a study, consisting of two parts, on Riemann theta function representations of algebro-geometric solutions to soliton hierarchies. In this part, using linear combinations of Lax matrices of soliton hierarchies, we introduce trigonal curves by their characteristic equations, explore general properties of meromorphic functions defined as ratios of the Baker-Akhiezer functions, and determine zeros and poles of the Baker-Akhiezer functions and their Dubrovin-type equations. We analyse the four-component AKNS soliton hierarchy in such a way that it leads to a general theory of trigonal curves applicable to construction of algebro-geometric solutions of an arbitrary soliton hierarchy.
这是一项研究的第一部分，该研究由两部分组成，内容是关于孤子层级的代数几何解的黎曼θ函数表示。在这一部分中，我们利用孤子层级的拉克斯矩阵的线性组合，通过其特征方程引入三角曲线，探讨定义为贝克 - 阿基耶泽函数之比的亚纯函数的一般性质，并确定贝克 - 阿基耶泽函数的零点和极点及其杜布罗温型方程。我们以这样一种方式分析四分量AKNS孤子层级，即它引出了一种适用于构建任意孤子层级的代数几何解的三角曲线通用理论。
