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arXiv · 2503.22198

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

Kohei Iwaki·Seiya Kato·Shotaro Sakurai
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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 Painlev\'e 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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Kohei Iwaki, Seiya Kato, Shotaro Sakurai. 2025-03-28. Note on the Singularity Reduction of Isomonodromy Systems Associated with Garnier Systems. https://arxiv.org/abs/2503.22198

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