Abstract
Using the reductive perturbation method, a cylindrically and spherically modified nonlinear Schrödinger equation describing the slow modulation of the dust ion-acoustic wave amplitude in an unmagnetized dusty plasma is obtained for the first time. The modulational instability of the dust ion-acoustic waves due to the cylindrical and spherical geometry effect is investigated. It is shown that the properties of the modulational instability of dust ion-acoustic wave in a cylindrical and spherical geometry differ from those in a planar one-dimensional geometry.
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