Fredholm determinants and pole-free solutions to the noncommutative Painlevé II equation

DOI10.1007/s00220-011-1383-xzbMath1234.35171arXiv1101.3997OpenAlexW3104693113MaRDI QIDQ663289

Mattia Cafasso, Marco Bertola

Publication date: 14 February 2012

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.3997

zbMATH Keywords

Fredholm determinantsPainlevé equationsRiemann-Hilbert problemsintegrable operatorsmatrix convolution operators

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Applications of operator theory to differential and integral equations (47N20) Riemann-Hilbert problems in context of PDEs (35Q15)

Related Items (10)

The Toda and Painlevé systems associated with semiclassical matrix-valued orthogonal polynomials of Laguerre type ⋮ Correction to: ``The dependence on the monodromy data of the isomonodromic tau function ⋮ Riemann-Hilbert approach to multi-time processes: the Airy and the Pearcey cases ⋮ Soliton versus the gas: Fredholm determinants, analysis, and the rapid oscillations behind the kinetic equation ⋮ Lax pair representation and Darboux transformation of noncommutative Painlevé's second equation ⋮ Non-commutative Painlevé equations and Hermite-type matrix orthogonal polynomials ⋮ Noncommutative Painlevé equations and systems of Calogero type ⋮ A fully noncommutative Painlevé II hierarchy: Lax pair and solutions related to Fredholm determinants ⋮ Painlevé IV critical asymptotics for orthogonal polynomials in the complex plane ⋮ Noncommutative extensions of elliptic integrable Euler–Arnold tops and Painlevé VI equation

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