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

Symmetry Integrability and Geometry-Methods and Applications

article

Shun Shimomura¹ 

[1] Department of Mathematics, Keio University

关键词: Schlesinger-type equation;    fifth Painlev´e equation;    isomonodromy deformation;    monodromy data;   

DOI  :  10.3842/SIGMA.2018.113

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown