Complete coalescent diagram of the Painleve equations

2006/01/25 by Yousuke Ohyama, Ohyama, Yousuke, Shoji Okumura +1
Mathematics · Physics and Astronomy · #33E17 #34M55 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.math/0601614

openalex publication_date 2006/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We will revise Garnier-Okamoto's coalescent diagram of isomonodromic deformations and give a complete coalescent diagram. In our viewpoint, we have ten types of isomonodromic deformations and two of them give the same type of the Painlevé equation. We can naturally put the thirty-fourth Painleve equation in our diagram, which corresponds to the Flaschka-Newell form of the second Painlevé equation.

Citations

• Sur les équations différentielles du second ordre et du premier degré dont l'intégrale générale est a points critiques fixes
• Monodromy perserving deformation of linear ordinary differential equations with rational coefficients. II

Related

• New Coalescences for the Painlevé Equations
• Six results on Painleve VI
• On some examples of identifying Painlevé equations using the geometry of the Okamoto space of initial conditions
• Degeneration scheme of 4-dimensional Painlevé-type equations
• A new interpretation of Jimbo's formula for Painlevé VI