On solutions of the Schlesinger Equations in Terms of Θ-Functions
نویسنده
چکیده
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 thetafunctions. Mathematics Subject Classification (1991): 34A20, 32G34. Short title: On Θ-Function Solutions of Schlesinger Equations ∗ E-mail: [email protected] . Supported by Alexander von Humboldt Foundation E-mail: [email protected]
منابع مشابه
Autoconvolution equations and generalized Mittag-Leffler functions
This article is devoted to study of the autoconvolution equations and generalized Mittag-Leffler functions. These types of equations are given in terms of the Laplace transform convolution of a function with itself. We state new classes of the autoconvolution equations of the first kind and show that the generalized Mittag-Leffler functions are solutions of these types of equations. In view of ...
متن کاملFundamental Steady state Solution for the Transversely Isotropic Half Space
Response of a transversely isotropic 3-D half-space subjected to a surface time-harmonic excitation is presented in analytical form. The derivation of the fundamental solutions expressed in terms of displacements is based on the prefect series of displacement potential functions that have been obtained in the companion paper by the authors. First the governing equations are uncoupled in the cyl...
متن کاملIsomonodromic deformations in genus zero and one: algebrogeometric solutions and Schlesinger transformations
Here we review some recent developments in the theory of isomonodromic deformations on Riemann sphere and elliptic curve. For both cases we show how to derive Schlesinger transformations together with their action on tau-function, and construct classes of solutions in terms of multi-dimensional theta-functions. The theory of isomonodromic deformations of ordinary matrix differential equations o...
متن کاملAdomian Polynomial and Elzaki Transform Method of Solving Fifth Order Korteweg-De Vries Equation
Elzaki transform and Adomian polynomial is used to obtain the exact solutions of nonlinear fifth order Korteweg-de Vries (KdV) equations. In order to investigate the effectiveness of the method, three fifth order KdV equations were considered. Adomian polynomial is introduced as an essential tool to linearize all the nonlinear terms in any given equation because Elzaki transform cannot handle n...
متن کاملClosed-Form Solutions for Broad-Band Equivalent Circuit of Vertical Rod Buried in Lossy Grounds Subjected to Lightning Strokes
Abstract— In this paper, input impedance of a vertical rod under lightning stroke is first computed by applying the method of moments (MoM) on the Maxwell’s equations. The circuit model is then achieved through applying modified vector fitting (MVF) on the computed input impedance. After then the equivalent circuit is again extracted for a few values of soil conductivity and rod radius. Finally...
متن کامل