Algebro-geometric solutions for the Hunter–Saxton hierarchy
Algebro-geometric solutions for the Hunter–Saxton hierarchy
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DOI：
10.1007/s00033-013-0339-8
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发表时间：
2013-05
期刊：
影响因子：
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通讯作者：
Yuanyuan Hou;E. Fan;Peng Zhao
中科院分区：
文献类型：
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作者：
Yuanyuan Hou;E. Fan;Peng Zhao
通过对一个代数几何初值问题的研究，给出了Hunter-Saxton（HS）方程族代数几何解的theta函数表示及相关的关键量.我们的主要工具包括多项式递归形式，超椭圆曲线与有限个亏格，Baker-Akhiezer函数，亚纯函数，Dubrovin型方程的辅助因子，以及相关的迹公式。借助这些工具，得到了整个HS族的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 Hunter–Saxton (HS) hierarchy through studying an algebro-geometric initial value problem. 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 algebro-geometric solutions are obtained for the entire HS hierarchy.