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VOL. 37 | 2018 Part 2. Degeneration scheme of 4-dimensional Painlevé-type equations


This is a continuation of Part 1 by one of the authors. We have shown that there are four 4-dimensional Painlevé-type equations derived from isomonodromic deformation of the Fuchsian equations: they are the Garnier system in two variables, the Fuji-Suzuki system, the Sasano system, and the sixth matrix Painlevé system. In Part 2, we degenerate these four source equations, and systematically obtain other 4-dimensional Painlevé-type equations, whose associated linear equations are of unramified type. There are 22 types of 4-dimensional Painlevé-type equations: 9 of them are partial differential equations, 13 of them are ordinary differential equations. Some well-known equations such as the Noumi-Yamada systems are included in this list. They are expressed as Hamiltonian systems, and their Hamiltonians are simply written by using the Hamiltonians of the classical Painlevé equations.


Published: 1 January 2018
First available in Project Euclid: 12 December 2018

Digital Object Identifier: 10.2969/msjmemoirs/03701C020

Rights: Copyright © 2018, The Mathematical Society of Japan


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