Connection formulas for the Ablowitz–Segur solutions of the inhomogeneous Painlevé II equation

DOI10.1088/1361-6544/aa72c1zbMath1380.34132arXiv1611.05285OpenAlexW3100321101MaRDI QIDQ4978492

Weiying Hu, Dan Dai

Publication date: 11 August 2017

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.05285

zbMATH Keywords

Riemann-Hilbert problemPainlevé II equationasymptotic behaviorsconnection formulas

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain (34M40) Oscillation, growth of solutions to ordinary differential equations in the complex domain (34M10)

Related Items (8)

Open problems for Painlevé equations ⋮ On integrals of the tronquée solutions and the associated Hamiltonians for the Painlevé II equation ⋮ Connection Problem of the First Painlevé Transcendent Between Poles and Negative Infinity ⋮ Asymptotics of the deformed Fredholm determinant of the confluent hypergeometric kernel ⋮ Double Spiral Singularities for a Flow of Regular Planar Curves ⋮ On the quasi-Ablowitz–Segur and quasi-Hastings–McLeod solutions of the inhomogeneous Painlevé II equation ⋮ Singular asymptotics for solutions of the inhomogeneous Painlevé II equation ⋮ On global solutions of defocusing mKdV equation with specific initial data of critical regularity

Uses Software

• DLMF

Cites Work

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• Hankel determinant and orthogonal polynomials for a Gaussian weight with a discontinuity at the edge
• Critical edge behavior and the Bessel to Airy transition in the singularly perturbed Laguerre unitary ensemble
• A computational exploration of the second Painlevé equation
• Transition asymptotics for the Painlevé II transcendent
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I: General theory and \(\tau \)-function
• Asymptotic solutions of nonlinear evolution equations and a Painlevé transcedent
• A connection formula for the second Painlevé transcendent
• A boundary value problem associated with the second Painleve transcendent and the Korteweg-de Vries equation
• Monodromy- and spectrum-preserving deformations. I
• On the solvability of Painlevé II and IV
• Application of uniform asymptotics to the second Painlevé transcendent
• Connection formulae for Painlevé functions
• Painlevé differential equations in the complex plane
• The nonlinear steepest descent approach to the singular asymptotics of the second Painlevé transcendent
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Multi-critical unitary random matrix ensembles and the general Painlevé II equation
• A computational overview of the solution space of the imaginary Painlevé II equation
• Special functions, integral equations and a Riemann-Hilbert problem
• Solitonic Asymptotics for the Korteweg–de Vries Equation in the Small Dispersion Limit
• Asymptotic Solutions of the Korteweg-deVries Equation
• Existence and uniqueness of tri-tronqu e solutions of the second Painlev  hierarchy
• Quasi-linear Stokes phenomenon for the Painlevé first equation
• Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory
• THE METHOD OF ISOMONODROMY DEFORMATIONS AND CONNECTION FORMULAS FOR THE SECOND PAINLEVÉ TRANSCENDENT
• Quasi-linear Stokes phenomenon for the second Painlev  transcendent
• Asymptotics for the painlevé II equation
• Large-degree asymptotics of rational Painlevé-II functions: critical behaviour

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