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Abstract
The influence of white noise on a propagating stable front (SF) in an essentially dissipative system that is characterized by nonlinearities of N-type is analysed. The governing evolution equation of the considered SFs is a nonlinear partial differential equation of parabolic type, and the influence of the noise on SFs is described by the additive torque which fluctuates randomly in space and time. The randomly perturbed front solutions of the evolution equation are derived with the help of a perturbative technique that is useful in the quite general case of N-systems discussed here. A particular case of the stochastic PDE which describes Gunn waves, i.e. the propagating fronts of the electric field in a semiconductor specimen, is examined explicitly. Two different ensembles of the ‘randomly walking’ SFs are studied in detail. The averaged characteristics as well as the probability distributions, describing the randomly perturbed front solutions, are presented for each of the considered ensembles.