Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Paraxial light in a Cole-Cole nonlocal medium: integrable regimes and
  singularities   Nonlocal nonlinear Schroedinger-type equation is derived as a model to
describe paraxial light propagation in nonlinear media with different `degrees'
of nonlocality. High frequency limit of this equation is studied under specific
assumptions of Cole-Cole dispersion law and a slow dependence along propagating
direction. Phase equations are integrable and they correspond to dispersionless
limit of Veselov-Novikov hierarchy. Analysis of compatibility among intensity
law (dependence of intensity on the refractive index) and high frequency limit
of Poynting vector conservation law reveals the existence of singular
wavefronts. It is shown that beams features depend critically on the
orientation properties of quasiconformal mappings of the plane. Another class
of wavefronts, whatever is intensity law, is provided by harmonic minimal
surfaces. Illustrative example is given by helicoid surface. Compatibility with
first and third degree nonlocal perturbations and explicit solutions are also
discussed.

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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: eess
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom