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Zbl 1072.34102
Smirnov, Alexander O.
Elliptic solitons and Heun's equation. (English)
[A] Kuznetsov, V. B. (ed.), The Kowalevski property. Providence, RI: American Mathematical Society (AMS). CRM Proc. Lect. Notes 32, 287-305 (2002). ISBN 0-8218-2885-1/pbk

Summary: 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 are studied. Methods for calculating the algebraic genus of the curve, and its branching points, are suggested. Monodromy group is considered. Numerous examples are given.

MSC 2000:: *34M35 Singularities, monodromy, local behavior of solutions, normal forms
33E30 Functions coming from diff., difference and integral equations
33E10 Spheroidal wave functions, etc.
34L40 Particular ordinary differential operators

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