The influence of a fluctuating nonlinearity on the propagation of spatial solitons in quadratic media is studied. We derive mean field evolution equations for both frequency components and show that fluctuations of the nonlinearity induce effective nonlinear losses. The predictions of the mean field theory are in good agreement with numerical simulations of the full stochastic system. We find an approximate analytical expression for the damping rate of spatial solitons and show that the amplitude of the fundamental wave decreases more rapidly than the amplitude of the second harmonic.
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