Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Whitham Averaged Equations and Modulational Stability of Periodic
  Traveling Waves of a Hyperbolic-Parabolic Balance Law   In this note, we report on recent findings concerning the spectral and
nonlinear stability of periodic traveling wave solutions of
hyperbolic-parabolic systems of balance laws, as applied to the St. Venant
equations of shallow water flow down an incline. We begin by introducing a
natural set of spectral stability assumptions, motivated by considerations from
the Whitham averaged equations, and outline the recent proof yielding nonlinear
stability under these conditions. We then turn to an analytical and numerical
investigation of the verification of these spectral stability assumptions.
While spectral instability is shown analytically to hold in both the Hopf and
homoclinic limits, our numerical studies indicates spectrally stable periodic
solutions of intermediate period. A mechanism for this moderate-amplitude
stabilization is proposed in terms of numerically observed "metastability" of
the the limiting homoclinic orbits.

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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: funct-an