Abstract
The effect of partial incoherence on the modulational instability (MI) of two optical waves that interact through cross-phase modulation caused by the Kerr nonlinearity is analyzed by using the Wigner approach. The problem is solved as an initial value problem providing a complete description of the time evolution of the wave perturbations. It is shown that the partial incoherence tends to suppress the MI of the two interacting waves by giving rise to a damping effect directly determined by the characteristic coherence length of the stochastic process.
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