Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Motions in a Bose condensate: X. New results on stability of
  axisymmetric solitary waves of the Gross-Pitaevskii equation   The stability of the axisymmetric solitary waves of the Gross-Pitaevskii (GP)
equation is investigated. The Implicitly Restarted Arnoldi Method for banded
matrices with shift-invert was used to solve the linearised spectral stability
problem. The rarefaction solitary waves on the upper branch of the
Jones-Roberts dispersion curve are shown to be unstable to axisymmetric
infinitesimal perturbations, whereas the solitary waves on the lower branch and
all two-dimensional solitary waves are linearly stable. The growth rates of the
instabilities on the upper branch are so small that an arbitrarily specified
initial perturbation of a rarefaction wave at first usually evolves towards the
upper branch as it acoustically radiates away its excess energy. This is
demonstrated through numerical integrations of the GP equation starting from an
initial state consisting of an unstable rarefaction wave and random
non-axisymmetric noise. The resulting solution evolves towards, and remains for
a significant time in the vicinity of, an unperturbed unstable rarefaction
wave. It is shown however that, ultimately (or for an initial state extremely
close to the upper branch), the solution evolves onto the lower branch or is
completely dissipated as sound.

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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph