On solutions of the Schlesinger Equations in Terms of $\Theta$-Functions
Kitaev, A. V. ; Korotkin, D. A.
arXiv, 9810007 / Harvested from arXiv
Text on arXiv
In this paper we construct explicit solutions and calculate the corresponding $\tau$-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 Painlev\'e 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 Painlev\'e equation obtained earlier by K. Okamoto and N. Hitchin, in terms of elliptic theta-functions.
Publié le : 1998-10-08
Classification:  Mathematical Physics,  General Relativity and Quantum Cosmology,  High Energy Physics - Theory,  Nonlinear Sciences - Exactly Solvable and Integrable Systems 
@article{9810007,
     author = {Kitaev, A. V. and Korotkin, D. A.},
     title = {On solutions of the Schlesinger Equations in Terms of $\Theta$-Functions},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9810007}
}

Kitaev, A. V.; Korotkin, D. A. On solutions of the Schlesinger Equations in Terms of $\Theta$-Functions. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9810007/