Connection formulae for asymptotics of the fifth Painlevé transcendent on the real axis

DOI10.1088/0951-7715/13/5/319zbMath0970.34076OpenAlexW2016136327MaRDI QIDQ4515412

F. V. Andreev, Alexander V. Kitaev

Publication date: 13 October 2001

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/13/5/319

zbMATH Keywords

monodromyWKB methodisomonodromy deformationPainlevé equations\(\tau\)-functionconnection problemStokes multiplierStokes curve

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Painlevé-type functions (33E17) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50) Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain (34M40) Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) (34M60)

Related Items (15)

Three-parameter solutions of the PV Schlesinger-type equation near the point at infinity and the monodromy data ⋮ On a general singular solution of the fifth Painlevé equation along the positive real axis ⋮ Kerr scattering coefficients via isomonodromy ⋮ ELLIPTIC ASYMPTOTIC REPRESENTATION OF THE FIFTH PAINLEVÉ TRANSCENDENTS ⋮ CORRIGENDUM: ELLIPTIC ASYMPTOTIC REPRESENTATION OF THE FIFTH PAINLEVÉ TRANSCENDENTS ⋮ Frequency of \(a\)-points for the fifth and the third Painlevé transcendents in a sector ⋮ A note on the connection problem of some special Painlevé V functions ⋮ Unnamed Item ⋮ Emergence of a singularity for Toeplitz determinants and Painlevé V ⋮ On the analysis of incomplete spectra in random matrix theory through an extension of the Jimbo-Miwa-Ueno differential ⋮ Asymptotics of Discrete Painlevé V transcendents via the Riemann–Hilbert Approach ⋮ Irregular conformal blocks and connection formulae for Painlevé V functions ⋮ Application of uniform asymptotics to the connection formulas of the fifth Painlevé equation ⋮ Local expansion of Painlevé VI transcendents around a fixed singularity ⋮ A review of the sixth Painlevé equation

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