The nonlinear steepest descent approach to the singular asymptotics of the second Painlevé transcendent

DOI10.1016/j.physd.2012.02.014zbMath1266.34142arXiv1209.5415OpenAlexW2009588942MaRDI QIDQ1935159

Thomas Bothner, Alexander R. Its

Publication date: 30 January 2013

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

Full work available at URL: https://arxiv.org/abs/1209.5415

zbMATH Keywords

Riemann-Hilbert problemisomonodromic deformationsPainlevé IIsingular asymptoticsDeift-Zhou steepest descent method

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Isomonodromic deformations for ordinary differential equations in the complex domain (34M56) Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) (34M60)

Related Items (13)

Singular asymptotics for the Clarkson-McLeod solutions of the fourth Painlevé equation ⋮ Open problems for Painlevé equations ⋮ Hankel determinant and orthogonal polynomials for a Gaussian weight with a discontinuity at the edge ⋮ On the connection problem for the second Painlevé equation with large initial data ⋮ 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 ⋮ Asymptotics of the deformed higher order Airy-kernel determinants and applications ⋮ The matching condition for larger size Riemann-Hilbert problems ⋮ Connection formulas for the Ablowitz–Segur solutions of the inhomogeneous Painlevé II equation ⋮ On the origins of Riemann–Hilbert problems in mathematics* ⋮ Singular asymptotics for solutions of the inhomogeneous Painlevé II equation ⋮ Fredholm determinant representation of the homogeneous Painlevé II τ-function ⋮ Asymptotics of a cubic sine kernel determinant

Cites Work

• Monodromy- and spectrum-preserving deformations. I
• Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• On the Riemann--Hilbert--Birkhoff inverse monodromy problem and the Painlevé equations
• Asymptotics for the painlevé II equation
• The spectral theory of a functional-difference operator in conformal field theory
• The nonlinear Schrödinger equation on the half-line
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