A new solution of the fourth Painlevé equation with a solvable monodromy

DOI10.3792/pjaa.81.75zbMath1097.34555OpenAlexW1992581390MaRDI QIDQ815153

Kazuo Kaneko

Publication date: 21 February 2006

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.81.75

zbMATH Keywords

Painlevé equationmonodromy data

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15) Painlevé-type functions (33E17) Applications of quantum theory to specific physical systems (81Vxx)

Related Items

On symmetric solutions of the fourth q-Painlevé equation ⋮ Painlevé VI transcendents which are meromorphic at a fixed singularity. ⋮ Symmetric solutions for the two dimensional degenerate Garnier system G(5) ⋮ Symmetric solutions to the four dimensional degenerate Painlevé type equation NY ^{A ₄} ⋮ Local expansion of Painlevé VI transcendents around a fixed singularity

Cites Work

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• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
• On the solvability of Painlevé II and IV
• Solutions of the second and fourth Painlevé equations, I
• The Stokes Phenomenon and the Whittaker Function
• Picard and Chazy solutions to the Painlevé VI equation

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