Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High-Frequency Instabilities of the Kawahara Equation: A Perturbative
  Approach   We analyze the spectral stability of small-amplitude, periodic,
traveling-wave solutions of the Kawahara equation. These solutions exhibit
high-frequency instabilities when subject to bounded perturbations on the whole
real line. We introduce a formal perturbation method to determine the
asymptotic growth rates of these instabilities, among other properties.
Explicit numerical computations are used to verify our asymptotic results.

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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc