Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From Painlev\'e to Zakharov-Shabat and beyond: Fredholm determinants and
  integro-differential hierarchies   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 Painlev\'e 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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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas