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Register a new userFrom Painleve to Zakharov-Shabat and beyond: Fredholm determinants and integro-differential hierarchies
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Added by
Alexandre Krajenbrink
Publication date
2020
fields
Physics
and research's language is
English
Authors
Alexandre Krajenbrink
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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 Painleve 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.
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