Special solutions of the first and second Painlevé equations and singularities of the monodromy data manifold

DOI10.1134/S0081543813050106zbMath1301.34111OpenAlexW2006874982MaRDI QIDQ2447028

Victor Yu. Novokshenov

Publication date: 23 April 2014

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0081543813050106

zbMATH Keywords

Padé approximationsPainlevé equationsisomonodromic deformationspole distributionspecial solutions

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35)

Related Items (2)

Isomonodromic quantization of the second Painlevé equation by means of conservative Hamiltonian systems with two degrees of freedom ⋮ Painlevé I and exact WKB: Stokes phenomenon for two-parameter transseries

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
• Connection formulae for the first Painlevé transcendent in the complex domain
• On orthogonal and symplectic matrix ensembles
• On universality of critical behavior in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the Tritronquée solution to the Painlevé-I equation
• THE BOUTROUX ANSATZ FOR THE SECOND PAINLEVÉ EQUATION IN THE COMPLEX DOMAIN
• Asymptotic Solutions of the Korteweg-deVries Equation
• Quasi-linear Stokes phenomenon for the Painlevé first equation
• Unnamed Item

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