  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.
