Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Blow-up solutions of Helmholtz equation for a Kerr slab with a complex
  linear and nonlinear permittivity   We show that the Helmholtz equation describing the propagation of transverse
electric waves in a Kerr slab with a complex linear permittivity and a complex
Kerr coefficient admits blow-up solutions provided that the real part of the
Kerr coefficient is negative, i.e., the slab is defocusing. This result applies
to homogeneous as well as inhomogeneous Kerr slabs whose linear permittivity
and Kerr coefficient are continuous functions of the transverse coordinate. For
an inhomogeneous Kerr slab, blow-up solutions exist if the real part of Kerr
coefficient is bounded above by a negative number.

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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: hep-lat