Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence and stability of standing waves for coupled nonlinear Hartree
  type equations   We study existence and stability of standing waves for coupled nonlinear
Hartree type equations \[ -i\frac{\partial}{\partial t}\psi_j=\Delta
\psi_j+\sum_{k=1}^m \left(W\star |\psi_k|^p \right)|\psi_j|^{p-2}\psi_j, \]
where $\psi_j:\mathbb{R}^N\times \mathbb{R}\to \mathbb{C}$ for $j=1, \ldots, m$
and the potential $W:\mathbb{R}\to [0, \infty)$ satisfies certain assumptions.
Our method relies on a variational characterization of standing waves based on
minimization of the energy when $L^2$ norms of component waves are prescribed.
We obtain existence and stability results for two and three-component systems
and for a certain range of $p$. In particular, our argument works in the case
when $W(x)=|x|^{-\alpha}$ for some $\alpha>0.$

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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: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: cs
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph