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Pré-Publication, Document De Travail Année : 2010

Modulated wave trains in generalized Kuramoto-Sivashinksi equations

Pascal Noble
Luis Miguel Miguel Rodrigues
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Résumé

This paper is concerned with the stability of periodic wave trains in a generalized Kuramoto-Sivashinski (gKS) equation. This equation is useful to describe the weak instability of low frequency perturbations for thin film flows down an inclined ramp. We provide a set of equations, namely Whitham's modulation equations, that determines the behaviour of low frequency perturbations of periodic wave trains. As a byproduct, we relate the spectral stability in the small wavenumber regime to properties of the modulation equations. This stability is always critical since $0$ is a $0$-Floquet number eigenvalue associated to translational invariance.
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Dates et versions

hal-00544443 , version 1 (08-12-2010)

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Pascal Noble, Luis Miguel Miguel Rodrigues. Modulated wave trains in generalized Kuramoto-Sivashinksi equations. 2010. ⟨hal-00544443⟩
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