On an isomonodromy deformation equation without the Painlevé property

DOI10.1134/S1061920814010026zbMath1322.34102arXiv1301.7211OpenAlexW1976920057MaRDI QIDQ2344136

Andrei A. Kapaev, B. A. Dubrovin

Publication date: 12 May 2015

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.7211

zbMATH Keywords

Painlevé propertyRiemann-Hilbert problemsdynamical poles theoryisomonodromy deformatuinsteepest-descent asymptotic analysis

Mathematics Subject Classification ID

Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50) Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain (34M40) Isomonodromic deformations for ordinary differential equations in the complex domain (34M56)

Related Items (6)

Meromorphy of solutions for a wide class of ordinary differential equations of Painlevé type ⋮ Systematic construction of nonautonomous Hamiltonian equations of Painlevé type. I. Frobenius integrability ⋮ Non-autonomous Hénon-Heiles system from Painlevé class ⋮ Tronquée solutions of the third and fourth Painlevé equations ⋮ On the tritronquée solutions of \(\mathrm{P}_{\mathrm{I}}^2\) ⋮ Painlevé representation of Tracy-Widom\(_\beta\) distribution for \(\beta=6\)

Cites Work

• Geometry of the string equations
• Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach
• On Hamiltonian perturbations of hyperbolic systems of conservation laws. II: Universality of critical behaviour
• Monodromy preserving deformation of linear ordinary differential equations with rational coefficients. I: General theory and \(\tau \)-function
• Painlevé property of monodromy preserving deformation equations and the analyticity of \(\tau\) functions
• Weakly nonlinear solutions of equation \(P^ 2_ 1\)
• Rational surfaces associated with affine root systems and geometry of the Painlevé equations
• Painlevé differential equations in the complex plane
• On the tritronquée solutions of \(\mathrm{P}_{\mathrm{I}}^2\)
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Moduli of unramified irregular singular parabolic connections on a smooth projective curve
• Differential equations with fixed critical points
• Pole loci of solutions of a degenerate Garnier system
• Asymptotics for a special solution to the second member of the Painlevé I hierarchy
• Fuchs and the theory of differential equations
• On universality of critical behaviour in Hamiltonian PDEs
• Algebro-geometric construction of self-similar solutions of the Whitham equations
• The Riemann–Hilbert Problem and Inverse Scattering
• Higher‐order Painlevé Equations in the Polynomial Class I. Bureau Symbol P2
• Asymptotics for the painlevé II equation
• The existence of a real pole-free solution of the fourth order analogue of the Painlevé I equation
• Painlevé II asymptotics near the leading edge of the oscillatory zone for the Korteweg—de Vries equation in the small‐dispersion limit
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On an isomonodromy deformation equation without the Painlevé property