Algebro-geometric solutions for the Gerdjikov-Ivanov hierarchy
Algebro-geometric solutions for the Gerdjikov-Ivanov hierarchy
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DOI：
10.1063/1.4812559
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发表时间：
2013-07
影响因子：
1.3
通讯作者：
Yuanyuan Hou;E. Fan;Peng Zhao
中科院分区：
文献类型：
--
作者：
Yuanyuan Hou;E. Fan;Peng Zhao
本文致力于为 Gerdjikov-Ivanov (GI) 层次结构提供代数几何解和相关关键量的 theta 函数表示。我们的主要工具包括多项式递归形式、有限格数超椭圆曲线、Baker-Akhiezer 函数、亚纯函数、辅助除数的 Dubrovin 型方程以及相关的迹公式。在这些工具的帮助下，可以获得整个 GI 层次结构的 Baker-Akhiezer 函数、亚纯函数和代数几何解的显式表示。
This paper is dedicated to provide theta function representations of algebro-geometric solutions and related crucial quantities for the Gerdjikov-Ivanov (GI) hierarchy. Our main tools include the polynomial recursive formalism, the hyperelliptic curve with finite number of genus, the Baker-Akhiezer functions, the meromorphic function, the Dubrovin-type equations for auxiliary divisors, and the associated trace formulas. With the help of these tools, the explicit representations of the Baker-Akhiezer functions, the meromorphic function, and the algebro-geometric solutions are obtained for the entire GI hierarchy.