Properties of the series solution for Painlevé I

DOI10.1080/14029251.2013.862436zbMath1420.33005arXiv1210.6822OpenAlexW2963195989MaRDI QIDQ5230926

Andrew N. W. Hone, Orlando Ragnisco, Federico Zullo

Publication date: 29 August 2019

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.6822

zbMATH Keywords

Painlevé equationsigma functiontau-function

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Elliptic functions and integrals (33E05) Painlevé-type functions (33E17)

Related Items (3)

On the connection problem for Painlevé I ⋮ On the dynamics of the zeros of solutions of the Airy equation ⋮ A Hirota bilinear equation for Painlevé transcendents PIV, PII and PI

Cites Work

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• Okamoto's space for the first Painlevé equation in Boutroux coordinates
• On the \(\tau \)-function of the Painlevé equations
• Conformal field theory of Painlevé VI
• Generalized Bernoulli-Hurwitz numbers and the universal Bernoulli numbers
• The Coefficients of the Lemniscate Function
• Painlevé Tests, Singularity Structure and Integrability
• On the solvability of Painleve I, III and V
• A Direct Proof that Solutions of the Six Painlevé Equations Have No Movable Singularities Except Poles
• Bilinear operators and the power series for the Weierstrass sigma function
• On Painlevé's equations I, II and IV
• Solutions of the first and second Painlevé equations are meromorphic

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