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• W2111127002 abstract "In this note, we report on recent ndings 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 ow 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 verication 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." @default.
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• W2111127002 date "2010-12-14" @default.
• W2111127002 modified "2023-09-25" @default.
• W2111127002 title "Whitham averaged equations and modulational stability of periodic traveling waves of a hyperbolic-parabolic balance law" @default.
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• W2111127002 doi "https://doi.org/10.5802/jedp.60" @default.
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