Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of Periodic Kuramoto-Sivashinsky Waves   In this note, we announce a general result resolving the long-standing
question of nonlinear modulational stability, or stability with respect to
localized perturbations, of periodic traveling-wave solutions of the
generalized Kuramoto-Sivashinsky equation, establishing that spectral
modulational stability, defined in the standard way, implies nonlinear
modulational stability with sharp rates of decay. The approach extends readily
to other second- and higher-order parabolic equations, for example, the
Cahn-Hilliard equation or more general thin film models.

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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: quant-ph