Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new class of Traveling Solitons for cubic Fractional Nonlinear
  Schrodinger equations   We consider the one-dimensional cubic fractional nonlinear Schr\"odinger
equation $$i\partial_tu-(-\Delta)^\sigma u+|u|^{2}u=0,$$ where $\sigma \in
(\frac12,1)$ and the operator $(-\Delta)^\sigma$ is the fractional Laplacian of
symbol $|\xi|^{2\sigma}$. Despite of lack of any Galilean-type invariance, we
construct a new class of traveling soliton solutions of the form
$$u(t,x)=e^{-it(|k|^{2\sigma}-\omega^{2\sigma})}Q_{\omega,k}(x-2t\sigma|k|^{2\sigma-2}k),\quad
k\in\mathbb{R},\ \omega>0$$ by a rather involved variational argument.

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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat