Global meromorphy of solutions of the Painlevé equations and their hierarchies

DOI10.1134/S0081543820060061zbMath1461.30074OpenAlexW3129038372MaRDI QIDQ2227086

B. I. Suleimanov, M. A. Shumkin, Andrei Domrin

Publication date: 9 February 2021

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543820060061

zbMATH Keywords

Painlevé equationsmeromorphic extension of local holomorphic solutions

Mathematics Subject Classification ID

Entire and meromorphic solutions to ordinary differential equations in the complex domain (34M05) Meromorphic functions of one complex variable (general theory) (30D30) Nonlinear ordinary differential equations and systems in the complex domain (34M04)

Related Items (2)

Meromorphy of solutions for a wide class of ordinary differential equations of Painlevé type ⋮ On solutions of matrix soliton equations

Cites Work

• The first, second and fourth Painlevé equations on weighted projective spaces
• Painlevé property of monodromy preserving deformation equations and the analyticity of \(\tau\) functions
• Turning points of linear systems and the double asymptotics of the Painlevé transcendents
• Basic theory of ordinary differential equations
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• Remarks on the local version of the inverse scattering method
• Nevanlinna theory, normal families, and algebraic differential equations
• Andrew Lenard: a mystery unraveled
• Meromorphic Painlevé transcendents at a fixed singularity
• Higher-order analogues of the Tracy-Widom distribution and the Painlevé II hierarchy
• Meromorphic extension of solutions of soliton equations
• Almost Periodic Solutions of the KdV Equation
• A Direct Proof that Solutions of the Six Painlevé Equations Have No Movable Singularities Except Poles
• On the Riemann--Hilbert--Birkhoff inverse monodromy problem and the Painlevé equations
• Higher‐order Painlevé Equations in the Polynomial Class I. Bureau Symbol P2
• Rational Solutions of Painlevé Equations
• Solutions of the first and second Painlevé equations are meromorphic
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