Modulation instability of incoherent waves

Summary form only given. Modulation instability (MI) is a common phenomenon in coherent non-linear wave systems; it can be typically observed on top of a broad pulse or an optical beam. In this case, small noise perturbations grow exponentially as the pulse propagates, transferring energy from large wavelengths into smaller wavelengths. In a sense, MI phenomena can be regarded as a precursor of bright optical solitons. The recent demonstration of existence of incoherent solitons led us to wander whether MI can be observed with incoherent waves as well. Here, we demonstrate analytically and numerically that MI can exist in nonlinear incoherent systems.