Elliptic solitons and Heun's equation

2001/09/30 by A. O. Smirnov
Mathematics · #math.CA #math.SP

paper · pdf

published as CRM Proceedings and Lecture Notes, 2002, v.32, p.287-305. · 19 pages, LaTeX2e (AMSLaTeX);Proposition 1 was corrected, two footnotes were added

arxiv created 2001/10/19 · arxiv updated 2009/11/30

Abstract

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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