Using a collective-coordinate approach, we study kink propagation along nonlinear systems with local, randomly distributed inhomogeneities. We develop a general method to compute dynamical variable statistics which can be generalized to a number of soli ton-bearing systems, and we apply it to the sine-Gordon equation as an example. PACS number(s): 03.40. Kf, 42.25.Bs, 71.55.Jv
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