Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Long-Time Asymptotics for Solutions of the NLS Equation with a Delta
  Potential and Even Initial Data   We consider the one-dimensional focusing nonlinear Schr\"odinger equation
(NLS) with a delta potential and even initial data. The problem is equivalent
to the solution of the initial/boundary problem for NLS on a half-line with
Robin boundary conditions at the origin. We follow the method of Bikbaev and
Tarasov which utilizes a B\"acklund transformation to extend the solution on
the half-line to a solution of the NLS equation on the whole line. We study the
asymptotic stability of the stationary 1-soliton solution of the equation under
perturbation by applying the nonlinear steepest-descent method for
Riemann-Hilbert problems introduced by Deift and Zhou. Our work strengthens,
and extends, earlier work on the problem by Holmer and Zworski.

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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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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: nucl-th