Finite-gap Solutions of the Fuchsian Equations
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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
KeywordsFuchsian equations Heun equation Schrödinger operators finite-gap solutions elliptic potentials elliptic solitons hyperelliptic curves spectral curves
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