Abstract
A three-dimensional multi-component magneto-plasma system consisting of hybrid nonextensive-nonthermal-distributed electrons, positive ions, and immobile negatively charged dust grains is considered to examine the modulational instability (MI) of dust ion-acoustic waves (DIAWs). The reductive perturbation method, which is valid for small but finite amplitude DIAWs, is employed to derive the (3 + 1)-dimensional nonlinear Schrodinger equation (NLSE). The NLSE leads to the MI of DIAWs as well as the formation of dust ion-acoustic rogue waves (DIARWs), which are formed due to the effects of nonlinearity in the propagation of DIAWs. It is found that the basic features (viz. amplitude and width) of the DIAWs and DIARWs (which is formed in the unstable region) are significantly modified by the various plasma parameters such as non-extensive (non-thermal) parameter q(α), number densities of plasma species, threshold modulational obliqueness ($${{\theta }_{c}}$$), etc. The application of the results in space and laboratory magneto-plasma system is briefly discussed.
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