Singular asymptotics for the Clarkson-McLeod solutions of the fourth Painlevé equation

DOI10.1016/j.physd.2022.133254zbMath1491.34100arXiv2204.00733OpenAlexW4220816205MaRDI QIDQ2140101

Jun Xia, Shuai-Xia Xu, Yu-Qiu Zhao

Publication date: 20 May 2022

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.00733

zbMATH Keywords

fourth Painlevé equationRiemann-Hilbert problemsconnection formulassingular asymptoticsDeift-Zhou nonlinear steepest descent methodClarkson-McLeod solutions

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55)

Related Items (4)

Takasaki’s rational fourth Painlevé-Calogero system and geometric regularisability of algebro-Painlevé equations ⋮ Preface to the special issue: orthogonal polynomials and integrable systems, peakons, Toda lattices and Painlevé transcendents ⋮ Clarkson-McLeod solutions of the fourth Painlevé equation and the parabolic cylinder-kernel determinant ⋮ Asymptotics of the deformed higher order Airy-kernel determinants and applications

Uses Software

• DLMF

Cites Work

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• Uniform asymptotics of the Pollaczek polynomials via the Riemann–Hilbert approach
• ON THE CONNECTION FORMULAS OF THE FOURTH PAINLEVÉ TRANSCENDENT
• Integral equations and exact solutions for the fourth Painlevé equation
• Justification of Asymptotic Formulas for the Fourth Painlevé Equation
• Connection formulae for the fourth Painlevé transcendent; Clarkson-McLeod solution
• Painlevé IV with both Parameters Zero: A Numerical Study
• Singular asymptotics for solutions of the inhomogeneous Painlevé II equation
• Error Bounds for Asymptotic Approximations of Zeros of Transcendental Functions

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