Can the bending waves be understood as purely kinematic structure, as has been suggested by @delavega2015, or is self-gravity essential to their evolution? Finally, is there a connection between the corrugations of @xu2015 and the bulk motions in the Solar neighbourhood on the one hand, and the warp at the edge of the Galactic disc on the other?

In this paper, we address these and other questions through a series of idealized isolated galaxy simulations of Milky Way-like models, as well as theoretical arguments based on both the eigenmode and WKB analysis of bending waves by @hunter1969, @sparke1984, @sparke1988, and @nelson1995. The bending waves in our simulations arise without any provocation apart from the random noise of the particle distributions used to characterize the (smooth) halo, bulge, and disc. We emphasize that our results are specific to Milky Way-like galaxies and may not generalize to other stellar discs. Indeed, there are very thin disc galaxies that show no sign of bending. These galaxies, which may well be low surface brightness galaxies viewed edge-on [@bizyaev2017], may not be as susceptible to the dynamical mechanisms described in this work as the galaxies considered here.

Attempts to understand the evolution of galactic bending 