The Painlevé transcendents with solvable monodromy

2007/01/09 by Kazuo Kaneko, Kaneko, Kazuo
Mathematics · Physics and Astronomy · #33C15 #34M55 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.math/0701241

openalex publication_date 2007/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We will study special solutions of the fourth, fifth and sixth Painlevé equations with generic values of parameters whose linear monodromy can be calculated explicitly. We will show the relation between Umemura's classical solutions and our solutions.

Citations

• Sur les équations différentielles du second ordre et du premier degré dont l'intégrale générale est a points critiques fixes

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