Tronquée solutions of the Painlevé II equation

DOI10.1007/s11232-012-0102-xzbMath1280.81045OpenAlexW1996913963MaRDI QIDQ394869

Victor Yu. Novokshenov

Publication date: 28 January 2014

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11232-012-0102-x

zbMATH Keywords

Painlevé equationRiemann-Hilbert problemanharmonic oscillatorcomplex WKB methoddistribution of polesBohr-Sommerfeld quantizationtruncated solution

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50)

Related Items (5)

Isomonodromic quantization of the second Painlevé equation by means of conservative Hamiltonian systems with two degrees of freedom ⋮ Open problems for Painlevé equations ⋮ A computational overview of the solution space of the imaginary Painlevé II equation ⋮ On the increasing tritronquée solutions of the Painlevé-II equation ⋮ Painlevé representation of Tracy-Widom\(_\beta\) distribution for \(\beta=6\)

Uses Software

• RHPackage

Cites Work

• Padé approximations for Painlevé I and II transcendents
• The isomonodromic deformation method in the theory of Painlevé equations
• A boundary value problem associated with the second Painleve transcendent and the Korteweg-de Vries equation
• Monodromy- and spectrum-preserving deformations. I
• On universality of critical behavior in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the Tritronquée solution to the Painlevé-I equation
• On the location of poles for the Ablowitz–Segur family of solutions to the second Painlevé equation
• THE BOUTROUX ANSATZ FOR THE SECOND PAINLEVÉ EQUATION IN THE COMPLEX DOMAIN
• Quasi-linear Stokes phenomenon for the Painlevé first equation

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