1998/10/08 by A. V. Kitaev, D. A. Korotkin
Physics and Astronomy · Mathematics · #math-ph #gr-qc #hep-th #math.MP #nlin.SI #solv-int
published as International Mathematics Research Notices No.17 (1998) 877-905
arxiv created 1998/10/08 · arxiv updated 2009/11/30
In this paper we construct explicit solutions and calculate the corresponding τ-function to the system of Schlesinger equations describing isomonodromy deformations of 2× 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.