Viscous Shocks in the Destabilized Kuramoto-Sivashinsky Equation

Abstract

We study stationary periodic solutions of the Kuramoto-Sivashinsky (KS) model for complex spatio-temporal dynamics in the presence of an additional linear destabilizing term. In particular, we show the phase space origins of the previously observed stationary “viscous shocks” and related solutions. These arise in a reversible four-dimensional dynamical system as perturbed heteroclinic connections whose tails are joined through a reinjection mechanism due to the linear term. We present numerical evidence that the transition to the KS limit contains a rich bifurcation structure even within the class of stationary reversible solutions.