External fluctuations in front dynamics with inertia: the overdamped limit

We study the dynamics of fronts when both inertial effects and external fluctuations are taken into account. Stochastic fluctuations are introduced as multiplicative white noise arising from a control parameter of the system. Contrary to the non-inertial (overdamped) case, we find that important features of the system, such as the velocity selection picture, are not modified by the noise. We then compute the overdamped limit of the underdamped dynamics in a more careful way, finding that it does not exhibit any effect of noise either. Our result poses the question as to whether or not external noise sources can be measured in physical systems of this kind. PACS. 05.40.-a Fluctuation phenomena, random processes, noise and Brownian motion – 05.45.-a Nonlinear dynamics and nonlinear dynamical systems – 47.54.+r Pattern selection; pattern formation – 47.20.Ky Nonlinearity (including bifurcation theory)