The nonlinear frequency shift of a low-frequency, coherent dust ion-acoustic wave in the presence of higher-frequency dust ion-acoustic turbulence is investigated in the framework of weak turbulence theory. It is found that the frequency shift of the dust ion-acoustic wave in an unmagnetized dusty plasma is always positive irrespective of the propagation direction of the coherent wave, as in the case of the customary ion-acoustic wave in the absence of dust particles. It is also found that the magnitude of the frequency shift decreases with increasing dust density.

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