Soliton on a disordered lattice

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Abstract
A stochastic version of the lattice nonlinear Schrödinger equation, allowing treatment by means of the inverse-scattering technique and having an exact one-soliton solution, is introduced. It is shown that such a model is a useful tool for investigation of a wide class of nonlinear lattices affected by spatiotemporally random forces. A number of the most important statistical characteristics of soliton dynamics governed by such models can be evaluated without any assumption about the smallness of random perturbations. The problem is studied in detail in two limiting cases: small and large intensities of fluctuations of a stochastic term in the integrable equation.

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