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

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.