arXiv math/01091492001-09math.CAmath.SP

Elliptic solitons and Heun's equation

A. O. Smirnov

备注：: 19 pages, LaTeX2e (AMSLaTeX);Proposition 1 was corrected, two footnotes were added
发表信息：: CRM Proceedings and Lecture Notes, 2002, v.32, p.287-305.

英文摘要：

We find a new class of algebraic geometric solutions of Heun's equation with the accessory parameter belonging to a hyperelliptic curve. Dependence of these solutions from the accessory parameter as well as their relation to Heun's polynomials is studied. Methods of calculating the algebraic genus of the curve, and its branching points, are suggested. Monodromy group is considered. Numerous examples are given.

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