Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Instability of an integrable nonlocal NLS   In this note we discuss the global dynamics of an integrable nonlocal NLS on
$\mathbb{R}$, which has been the object of recent investigation by integrable
systems methods. We prove two results which are in striking contrast with the
case of the local cubic focusing NLS on $\mathbb{R}$. First, finite time
blow-up solutions exist with arbitrarily small initial data in
$H^s(\mathbb{R})$, for any $s\geqslant0$. On the other hand, the solitons of
the local NLS, which are also solutions of the nonlocal equation, are unstable
by blow-up for the latter.

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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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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: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol