By employing an invariant embedding method a partial differential equation is derived for the complex reflection amplitude R(L) of a one-dimensional nonlinear random medium of length L. The method of characteristics reduces this equation to a dynamical system. Averaging of the perturbation of orbits by weak disorder is used to investigate the probability distribution of R(L). For a large class of nonlinearities, a power law decay of 1 - |R|2 is shown to take place at large L, and the associated fluctuations are obtained.
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Douçot et al. (1987) studied this question.
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