Algebro-Geometric Solutions to a New Hierarchy of Soliton Equations
Algebro-Geometric Solutions to a New Hierarchy of Soliton Equations
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DOI：
10.15407/mag11.04.359
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发表时间：
2015-12
期刊：
影响因子：
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通讯作者：
Hui Wang;X. Geng
中科院分区：
文献类型：
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作者：
Hui Wang;X. Geng
借助于Lenard递推方程，我们导出了一个新的与3×3矩阵谱问题相关的孤子方程族，并利用引入的m−-1算术亏格的三角曲线Km−1建立了Dubroven型方程.基于代数曲线理论，我们在Km−1上构造了相应的Baker-Akhiezer函数和亚纯函数.已知的Baker-Akhiezer函数和亚纯函数的零极点允许我们找到它们的theta函数表示，由此得到整个孤子方程族的代数几何结构和theta函数表示.
With the help of the Lenard recursion equations, we derive a new hierarchy of soliton equations associated with a 3×3 matrix spectral problem and establish Dubrovin type equations in terms of the introduced trigonal curve Km−1 of arithmetic genus m − 1. Basing on the theory of algebraic curve, we construct the corresponding Baker–Akhiezer functions and meromorphic functions on Km−1. The known zeros and poles for the Baker–Akhiezer function and meromorphic functions allow us to find their theta function representations, from which algebro-geometric constructions and theta function representations of the entire hierarchy of soliton equations are obtained.