State selection in the noisy stabilized Kuramoto-Sivashinsky equation

Dina Obeid, J M Kosterlitz, Bjorn Sandstede

Abstract: In this work, we study the one-dimensional stabilized Kuramoto Sivashinsky equation with additive uncorrelated stochastic noise. The Eckhaus stable band of the deterministic equation collapses to a narrow region near the center of the band. This is consistent with the behavior of the phase diffusion constants of these states. Some connections to the phenomenon of state selection in driven out of equilibrium systems are made.