ON THE CONNECTION FORMULAS OF THE FOURTH PAINLEVÉ TRANSCENDENT

DOI10.1142/S021953050900144XzbMath1182.33034MaRDI QIDQ3646147

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Publication date: 19 November 2009

Published in: Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

uniform asymptoticsparabolic cylinder functionsWhittaker's functions

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Asymptotic expansions of solutions to ordinary differential equations (34E05) Painlevé-type functions (33E17)

Related Items (12)

Singular asymptotics for the Clarkson-McLeod solutions of the fourth Painlevé equation ⋮ On the connection problem for the second Painlevé equation with large initial data ⋮ Takasaki’s rational fourth Painlevé-Calogero system and geometric regularisability of algebro-Painlevé equations ⋮ Connection Problem of the First Painlevé Transcendent Between Poles and Negative Infinity ⋮ Clarkson-McLeod solutions of the fourth Painlevé equation and the parabolic cylinder-kernel determinant ⋮ On the numerical solution to a nonlinear wave equation associated with the first Painlevé equation: an operator-splitting approach ⋮ A note on the connection problem of some special Painlevé V functions ⋮ On integrable Ermakov-Painlevé IV systems ⋮ In memoriam Frank W. J. Olver (1924–2013) ⋮ Application of uniform asymptotics to the connection formulas of the fifth Painlevé equation ⋮ Painlevé IV: A numerical study of the fundamental domain and beyond ⋮ On the connection problem for nonlinear differential equation

Cites Work

• Unnamed Item
• Application of uniform asymptotics to the second Painlevé transcendent
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Uniform Asymptotic Solutions of Second-Order Linear Differential Equations Having a Double Pole with Complex Exponent and a Coalescing Turning Point
• Uniform Asymptotic Solutions of a Class of Second-Order Linear Differential Equations Having a Turning Point and a Regular Singularity, with an Application to Legendre Functions
• Integral equations and exact solutions for the fourth Painlevé equation
• Second-order linear differential equations with two turning points
• Uniform Asymptotic Solutions of Second-Order Linear Differential Equations Having a Simple Pole and a Coalescing Turning Point in the Complex Plane
• Connection formulae for the fourth Painlevé transcendent; Clarkson-McLeod solution

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