Note on the Singularity Reduction of Isomonodromy Systems Associated with Garnier Systems

2025/03/28 by Iwaki, Kohei, Kato, Seiya, Sakurai, Shotaro
#34M55 (Primary) 34M56 #34M60 (Secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.22198

Abstract

In this paper, we study the isomonodromy systems associated with the Garnier systems of type 9/2 and type 5/2+3/2. We show that the both of isomonodromy systems admit the singularity reduction (restriction to a movable pole), and the resulting linear differential equations are isomonodromic with respect to the second variable of the Garnier systems. Furthermore, we find two fourth-order nonlinear ordinary differential equations that describe the isomonodromy deformation but lack the Painlevé property. One of these equations has been already found by Dubrovin--Kapaev in 2014, while the other provides a new example.

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