Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modulational and Parametric Instabilities of the Discrete Nonlinear
  Schr\"odinger Equation   We examine the modulational and parametric instabilities arising in a
non-autonomous, discrete nonlinear Schr{\"o}dinger equation setting. The
principal motivation for our study stems from the dynamics of Bose-Einstein
condensates trapped in a deep optical lattice. We find that under periodic
variations of the heights of the interwell barriers (or equivalently of the
scattering length), additionally to the modulational instability, a window of
parametric instability becomes available to the system. We explore this
instability through multiple-scale analysis and identify it numerically. Its
principal dynamical characteristic is that, typically, it develops over much
larger times than the modulational instability, a feature that is qualitatively
justified by comparison of the corresponding instability growth rates.

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The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs