Abstract
The dynamics of gap solitons in random gratings is studied. We show that the influence of disorder is averaged over the soliton width, so that the soliton acts as a low-pass filter. The averaging results in an effective potential, which can trap solitons. The statistical properties of the potential are found. We show that soliton trapping is related to level crossing by a random function, which allows us to find the mean number of soliton reflections and the mean distance between consecutive reflections.
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