When a planar front (for example, in a reaction--diffusion system) deforms, the dynamics of large-scale disturbances are generally governed by the Kuramoto-Sivashinsky equation. The linear terms in the this equation need modification, however, when the band of unstable modes does not extend down to zero wavenumber. In this event, Nikolaevsky's equation instead provides the relevant description of the dynammics.
Nikolaevsky's equation predicts a supercritical bifurcation to a steady, spatially periodic disturbance to the front. However, this regular perturbation is itself unstable to an explosive secondary instability, resulting in persistent complicated dynamics. This talk will discuss aspects of the transition to complicated dynamics.