Elliptic solitons and Heun's equation

Details Elliptic solitons and Heun's equation Elliptic solitons and Heun's equation

2001-09-20

arxiv.org/abs/math/0109149v2

CRM Proceedings and Lecture Notes, 2002, v.32, p.287-305.

Mathematics

Classical Analysis and ODEs

19 pages, LaTeX2e (AMSLaTeX);Proposition 1 was corrected, two footnotes were added

Scientific paper

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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