Long-wavelength properties of the Kuramoto-Sivashinsky equation

Abstract
We study the long-wavelength properties of the one-dimensional Kuramoto-Sivashinsky equation. We determine all the parameters in the effective long-wavelength equation, interpret the phenomenological coefficients in terms of microscopic quantities, and estimate the time and length scales where the behavior crosses over from linear diffusive to that of the full nonlinear equation. We corroborate our analysis by studying variants of the model with more general linear terms.