``Quantizations of higher Hamiltonian analogues of the Painlevé I and Painlevé II equations with two degrees of freedom

DOI10.1007/s10688-014-0061-0zbMath1315.34099arXiv1204.4006OpenAlexW2964182694MaRDI QIDQ2258219

B. I. Suleimanov

Publication date: 3 March 2015

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.4006

zbMATH Keywords

HamiltonianintegrabilitySchrödinger equationquantizationPainlevé equationsisomonodromic deformations

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) 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)

Related Items (12)

Isomonodromic quantization of the second Painlevé equation by means of conservative Hamiltonian systems with two degrees of freedom ⋮ ``Quantization of an isomonodromic Hamiltonian garnier system with two degrees of freedom ⋮ On the method of a small parameter in nonlinear mathematical physics ⋮ Meromorphy of solutions for a wide class of ordinary differential equations of Painlevé type ⋮ Nonautonomous symmetries of the KdV equation and step-like solutions ⋮ Quantum aspects of the integrability of the third Painlevé equation and a non-stationary time Schrödinger equation with the Morse potential ⋮ “Quantizations” of isomonodromic Hamilton system $H^{\frac{7}{2}+1}$ ⋮ Solutions to analogues of non-stationary Schrödinger equations defined by isomonodromic Hamilton system $H^{2+1+1+1}$ ⋮ Integrable Abel equation and asymptotics of symmetry solutions of Korteweg-de Vries equation ⋮ Properties of solutions of two second-order differential equations with the Painlevé property ⋮ Classical-quantum correspondence and functional relations for Painlevé equations ⋮ On the tritronquée solutions of \(\mathrm{P}_{\mathrm{I}}^2\)

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