Modulated wave trains in generalized Kuramoto-Sivashinksi equations
Analysis of PDEs
2010-12-09 v1
Abstract
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.
Cite
@article{arxiv.1012.1733,
title = {Modulated wave trains in generalized Kuramoto-Sivashinksi equations},
author = {Pascal Noble and Luis Miguel Rodrigues},
journal= {arXiv preprint arXiv:1012.1733},
year = {2010}
}