Turning points of linear systems and the double asymptotics of the Painlevé transcendents

DOI10.1007/BF02364567zbMath0834.34005OpenAlexW4234183837MaRDI QIDQ1189601

Alexander V. Kitaev

Publication date: 27 September 1992

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02364567

zbMATH Keywords

turning pointsspecial functionsPainlevé equationsdouble asymptoticslinear systems of ordinary differential equations

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20)

Related Items (8)

Isomonodromic quantization of the second Painlevé equation by means of conservative Hamiltonian systems with two degrees of freedom ⋮ Meromorphy of solutions for a wide class of ordinary differential equations of Painlevé type ⋮ Lectures on Random Matrix Models ⋮ Nonautonomous symmetries of the KdV equation and step-like solutions ⋮ Asymptotics of the Gurevich-Pitaevskii universal special solution of the Korteweg-de Vries equation as \(|x|\to\infty\) ⋮ Global meromorphy of solutions of the Painlevé equations and their hierarchies ⋮ Continual limit in the Hermitian matrix model \(\Phi^ 6\) ⋮ Integrable Abel equation and asymptotics of symmetry solutions of Korteweg-de Vries equation

Cites Work

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• Monodromy problem and the boundary condition for some Painlevé equations
• Geometry of the string equations
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. II
• Connection formulae for Painlevé V functions
• Effective sufficient conditions for the solvability of the inverse problem of monodromy theory for systems of linear ordinary differential equations
• On a unified approach to transformations and elementary solutions of Painlevé equations

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