On solutions of the Schlesinger Equations in Terms of $Θ$-Functions

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dc.creatorKitaev, A. V.
dc.creatorKorotkin, D. A.
dc.date1998-10-08
dc.date.accessioned2026-07-07T04:32:33Z
dc.date.available2026-07-07T04:32:33Z
dc.descriptionIn this paper we construct explicit solutions and calculate the corresponding $τ$-function to the system of Schlesinger equations describing isomonodromy deformations of $2\times 2$ matrix linear ordinary differential equation whose coefficients are rational functions with poles of the first order; in particular, in the case when the coefficients have four poles of the first order and the corresponding Schlesinger system reduces to the sixth Painlevé equation with the parameters $1/8, -1/8, 1/8, 3/8$, our construction leads to a new representation of the general solution to this Painlevé equation obtained earlier by K. Okamoto and N. Hitchin, in terms of elliptic theta-functions.
dc.identifierhttps://arxiv.org/abs/math-ph/9810007
dc.identifierhttp://arxiv.org/abs/math-ph/9810007
dc.identifierInternational Mathematics Research Notices No.17 (1998) 877-905
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58230
dc.subjectMathematical Physics
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.subjectExactly Solvable and Integrable Systems
dc.titleOn solutions of the Schlesinger Equations in Terms of $Θ$-Functions
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