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From Painlevé to Zakharov-Shabat and beyond: Fredholm determinants and integro-differential hierarchies

Krajenbrink, Alexandre

Journal of physics. A, Mathematical and theoretical, 2021-01, Vol.54 (3), p.35001 [Periódico revisado por pares]

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Título:
From Painlevé to Zakharov-Shabat and beyond: Fredholm determinants and integro-differential hierarchies
Autor: Krajenbrink, Alexandre
Assuntos: Fredholm determinant ; Kardar-Parisi-Zhang equation ; Painlevé transcendent ; Riemann-Hilbert problem ; Zakharov-Shabat system
É parte de: Journal of physics. A, Mathematical and theoretical, 2021-01, Vol.54 (3), p.35001
Notas: JPhysA-114629.R1
Descrição: As Fredholm determinants are more and more frequent in the context of stochastic integrability, we unveil the existence of a common framework in many integrable systems where they appear. This consists in a quasi-universal hierarchy of equations, partly unifying an integro-differential generalization of the Painlevé II hierarchy, the finite-time solutions of the Kardar-Parisi-Zhang equation, multi-critical fermions at finite temperature and a notable solution to the Zakharov-Shabat system associated to the largest real eigenvalue in the real Ginibre ensemble. As a byproduct, we obtain the explicit unique solution to the inverse scattering transform of the Zakharov-Shabat system in terms of a Fredholm determinant.
Editor: IOP Publishing
Idioma: Inglês

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