Asymptotic uniqueness of the sliding state for charge-density waves

Analytic results are presented for the dynamic behavior of sliding charge-density waves (CDW's) and related extended nonlinear systems with randomness. It is shown that, in the limit of long times, a sliding configuration approaches a unique solution. In CDW models, the velocity of this asymptotic solution is periodic in time. These results explain previous numerical observations, simplify further analysis and simulation, and have direct experimental implications.