Effects of external noise on the Swift-Hohenberg equation.
The Swift-Hohenberg equation is studied in the presence of a multiplicative noise. This stochastic equation could describe a situation in which a noise has been superimposed on the temperature gradient between the two plates of a Rayleigh-Benard cell. A linear stability analysis and numerical simulations show that, in constrast to the additive-noise case, convective structures appear in a regime in which a deterministic analysis predicts a homogeneous solution