Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiple-scale analysis for resonance reflection by a one-dimensional
  rectangular barrier in the Gross-Pitaevskii problem   We consider a quantum above-barrier reflection of a Bose-Einstein condensate
by a one-dimensional rectangular potential barrier, or by a potential well, for
nonlinear Schroedinger equation (Gross-Pitaevskii equation) with a small
nonlinearity. The most interesting case is realized in resonances when the
reflection coefficient is equal to zero for the linear Schroedinger equation.
Then the reflection is determined only by small nonlinear term in the
Gross-Pitaevskii equation. A simple analytic expression has been obtained for
the reflection coefficient produced only by the nonlinearity. An analytical
condition is found when common action of potential barrier and nonlinearity
produces a zero reflection coefficient. The reflection coefficient is derived
analytically in the vicinity of resonances which are shifted by nonlinearity.

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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph