A Hirota bilinear equation for Painlevé transcendents PIV, PII and PI

DOI10.1142/S2010326318400014zbMath1422.34253arXiv1706.02341OpenAlexW3104782522MaRDI QIDQ5226433

Andrew N. W. Hone, Federico Zullo

Publication date: 31 July 2019

Published in: Random Matrices: Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.02341

zbMATH Keywords

Painlevé equationseries expansionsHirota bilinear formtau-function

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Formal solutions and transform techniques for ordinary differential equations in the complex domain (34M25)

Related Items (3)

2-parameter \(\tau\)-function for the first Painlevé equation: topological recursion and direct monodromy problem via exact WKB analysis ⋮ On Bäcklund transformations for some second-order nonlinear differential equations ⋮ Properties of solutions of two second-order differential equations with the Painlevé property

Cites Work

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• Application of the \(\tau\)-function theory of Painlevé equations to random matrices: PIV, PII and the GUE.
• Solutions of the first and second Painlevé equations are meromorphic

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