ABSTRACT We numerically follow the response of density-enhanced slabs to impulsive, localized, transverse velocity perturbations by working in the framework of ideal magnetohydrodynamics (MHD). Both linear and non-linear regimes are addressed. Kink wave trains are seen to develop along the examined slabs, sharing the characteristics that more oscillatory patterns emerge with time and that the apparent wavelength increases with distance at a given instant. Two features none the less arise due to non-linearity, one being a density cavity close to the exciter and the other being the appearance of shocks both outside and inside the nominal slab. These features may be relevant for understanding the interaction between magnetic structures and such explosive events as coronal mass ejections. Our numerical findings on kink wave trains in solar coronal slabs are discussed in connection with typical measurements of streamer waves.