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Letters in Mathematical Physics

, Volume 76, Issue 2–3, pp 297–316 | Cite as

Finite-gap Solutions of the Fuchsian Equations

  • Alexander O. SmirnovEmail author
Article

Abstract

We find a new class of Fuchsian equations, with algebro-geometric solutions associated to a hyperelliptic curve. A method for calculating its arithmetic genus and branching points is suggested. Numerous examples are given.

Mathematics Subject Classification (2000)

33E30 34L40 14H70 

Keywords

Fuchsian equations Heun equation Schrödinger operators finite-gap solutions elliptic potentials elliptic solitons hyperelliptic curves spectral curves 

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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Department of MathematicsSt.-Petersburg State University of Aerospace InstrumentationSt.-PetersburgRussia

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