Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Interaction of Nonlinear Schr\"odinger Solitons with an External
  Potential   Employing a particularly suitable higher order symplectic integration
algorithm, we integrate the 1-$d$ nonlinear Schr\"odinger equation numerically
for solitons moving in external potentials. In particular, we study the
scattering off an interface separating two regions of constant potential. We
find that the soliton can break up into two solitons, eventually accompanied by
radiation of non-solitary waves. Reflection coefficients and inelasticities are
computed as functions of the height of the potential step and of its steepness.

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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: physics