2012/09/18 by Hiroshi Kawakami, Kawakami, Hiroshi, Akane Nakamura +3 · 4 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1209.3836
openalex publication_date 2012/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Four 4-dimensional Painlevé-type equations are obtained by isomonodromic deformation of Fuchsian equations: they are the Garnier system in two variables, the Fuji-Suzuki system, the Sasano system, and the sixth matrix Painlevé system. Degenerating these four source equations, we systematically obtained other 4-dimensional Painlevé-type equations. If we only consider 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 Noumi-Yamada systems are included in this list. They are written as Hamiltonian systems, and their Hamiltonians are neatly written using Hamiltonians of the classical Painlevé equations.