Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetry and Intertwining Operators for the Nonlocal Gross-Pitaevskii
  Equation   We consider the symmetry properties of an integro-differential
multidimensional Gross-Pitaevskii equation with a nonlocal nonlinear (cubic)
term in the context of symmetry analysis using the formalism of semiclassical
asymptotics. This yields a semiclassically reduced nonlocal Gross-Pitaevskii
equation, which can be treated as a nearly linear equation, to determine the
principal term of the semiclassical asymptotic solution. Our main result is an
approach which allows one to construct a class of symmetry operators for the
reduced Gross-Pitaevskii equation. These symmetry operators are determined by
linear relations including intertwining operators and additional algebraic
conditions. The basic ideas are illustrated with a 1D reduced Gross-Pitaevskii
equation. The symmetry operators are found explicitly, and the corresponding
families of exact solutions are obtained.

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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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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: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph