Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear Optical Vector Ampliude Equations. Polarization and Vortex
  Solutions   We investigate two kind of polarization of localized optical waves in
nonlinear Kerr type media, linear and combination of linear and circular. In
the first case of linear polarized components we obtained the vector version of
3D+1 Nonlinear Schr\"{o}dinger Equation (VNSE). It is shown that these
equations admit exact vortex solutions with spin l=1. We have determined the
dispersion region and the medium parameters necessary for experimental
observation of these vortices. In the second case we represent the electric and
magnetic fields as sum of circular and linear components. We supouse also that
our nonlinear media admit linear magnetic polarization. This allows us to
reduce the Maxwell's equations to a set of amplitude Nonlinear Dirac Equations
(NDE). WE find two representation of the NDE- spherical and spinor. In the
spherical representation we obtain exact vortex solutions with spin l-1 and in
the spinor representation, exact vortex solutions with spin j=1/2.

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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
3
The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga