Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On stability of small solitons of the 1--D NLS with a trapping delta
  potential   We consider a Nonlinear Schr\"odinger Equation with a very general non linear
term and with a trapping $\delta $ potential on the line. We then discuss the
asymptotic behavior of all its small solutions, generalizing a recent result by
Masaki et al. We give also a result of dispersion in the case of defocusing
equations with a non--trapping delta potential.

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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: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc