Fluctuations and pattern selection near an Eckhaus instability

We study the effect of fluctuations in the vicinity of an Eckhaus instability. Fluctuations smear out the stability limit into a region in which fluctuations and nonlinearities dominate the decay of unstable states. We also find an effective stability boundary that depends on the intensity of fluctuations. A numerical solution of the stochastic Swift-Hohenberg equation in one dimension is used to test these predictions and to study pattern selection when the initial unstable state lies within the fluctuation dominated region. The nonlinear relaxation is shown to exhibit a scaling form.