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Deterministic effective equations for the propagation of expectation in noisy nonlinear optical fibers

We consider electromagnetic propagation in optical fibers as described by a nonlinear Schrödinger equation. The equation is endowed with input data representing a signal affected by a Gaussian white noise. Assuming both the nonlinearity and the noise to be small of the same order ε, we derive a hierarchy, at various orders in ε, of deterministic effective equations for the expectation of the propagated signal. Copyright © 2010 John Wiley & Sons, Ltd.