Letters in Mathematical Physics

, Volume 76, Issue 2, pp 297–316

Finite-gap Solutions of the Fuchsian Equations


DOI: 10.1007/s11005-006-0070-x

Cite this article as:
Smirnov, A.O. Lett Math Phys (2006) 76: 297. doi:10.1007/s11005-006-0070-x


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)



Fuchsian equationsHeun equationSchrödinger operatorsfinite-gap solutionselliptic potentialselliptic solitonshyperelliptic curvesspectral curves

Copyright information

© Springer 2006

Authors and Affiliations

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