A note on the Lax pairs for Painlevéequations

DOI10.1088/0305-4470/32/46/311zbMath0962.34068OpenAlexW2074921214MaRDI QIDQ4947877

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Publication date: 25 April 2000

Published in: Journal of Physics A: Mathematical and General (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0305-4470/32/46/311

zbMATH Keywords

solutionssine-Gordonmovable singularitiesPainlevé equationsnonlinear second-order differential equationsKdVpolesinverse spectral transformsolitonic partial differential equations

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50)

Related Items (12)

Generalized Hermite polynomials and monodromy-free Schrödinger operators ⋮ Critical edge behavior in the perturbed Laguerre unitary ensemble and the Painlevé V transcendent ⋮ Different linearizations of non-abelian second Painlevé systems and related monodromy surfaces ⋮ Four-dimensional Painlevé-type equations associated with ramified linear equations. III: Garnier systems and Fuji-Suzuki systems ⋮ On the Riemann–Hilbert approach to asymptotics of tronquée solutions of Painlevé I ⋮ Integrable equations associated with the finite‐temperature deformation of the discrete Bessel point process ⋮ Discrete gap probabilities and discrete Painlevé equations. ⋮ Singular Values of Products of Ginibre Random Matrices ⋮ Quantum aspects of the integrability of the third Painlevé equation and a non-stationary time Schrödinger equation with the Morse potential ⋮ On the linearization of the Painlevé III–VI equations and reductions of the three-wave resonant system ⋮ ``Quantizations of the second Painlevé equation and the problem of the equivalence of its \(L-A\) pairs ⋮ Applications in random matrix theory of a PIII′ τ-function sequence from Okamoto’s Hamiltonian formulation

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