Mathematical Society of Japan Memoirs

Part 2. Degeneration scheme of 4-dimensional Painlevé-type equations

Hiroshi Kawakami, Akane Nakamura, and Hidetaka Sakai

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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.

Chapter information

Kazuki Hiroe, Hiroshi Kawakami, Akane Nakamura, Hidetaka Sakai, 4-dimensional Painlevé-type equations (Tokyo: The Mathematical Society of Japan, 2018), 25-111

First available in Project Euclid: 12 December 2018

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Copyright © 2018, The Mathematical Society of Japan


Kawakami, Hiroshi; Nakamura, Akane; Sakai, Hidetaka. Part 2. Degeneration scheme of 4-dimensional Painlevé-type equations. 4-dimensional Painlevé-type equations, 25--111, The Mathematical Society of Japan, Tokyo, Japan, 2018. doi:10.2969/msjmemoirs/03701C020.

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