Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 113, 50 pages      arXiv:1804.10369      https://doi.org/10.3842/SIGMA.2018.113
Contribution to the Special Issue on Painlevé Equations and Applications in Memory of Andrei Kapaev

Three-Parameter Solutions of the PV Schlesinger-Type Equation near the Point at Infinity and the Monodromy Data

Shun Shimomura
Department of Mathematics, Keio University, 3-14-1, Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan

Received May 01, 2018, in final form October 03, 2018; Published online October 22, 2018

Abstract
For the Schlesinger-type equation related to the fifth Painlevé equation (V) via isomonodromy deformation, we present a three-parameter family of matrix solutions along the imaginary axis near the point at infinity, and also the corresponding monodromy data. Two-parameter solutions of (V) with their monodromy data immediately follow from our results. Under certain conditions, these solutions of (V) admit sequences of zeros and of poles along the imaginary axis. The monodromy data are obtained by matching techniques for a perturbed linear system.

Key words: Schlesinger-type equation; fifth Painlevé equation; isomonodromy deformation; monodromy data.

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