Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variational Approach to the Modulational Instability   We study the modulational stability of the nonlinear Schr\"odinger equation
(NLS) using a time-dependent variational approach. Within this framework, we
derive ordinary differential equations (ODEs) for the time evolution of the
amplitude and phase of modulational perturbations. Analyzing the ensuing ODEs,
we re-derive the classical modulational instability criterion. The case
(relevant to applications in optics and Bose-Einstein condensation) where the
coefficients of the equation are time-dependent, is also examined.

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The categories of this paper are: nlin
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The categories of this paper are: funct-an
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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: chao-dyn
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The categories of this paper are: cmp-lg
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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: patt-sol
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The categories of this paper are: q-alg
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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: adap-org
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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: nucl-th