Modulational instability (MI) of dust acoustic waves (DAWs), which propagatesin an opposite polarity dusty plasma system, containing inertial warmnegatively and positively charged dust particles as well as non-extensiveq-distributed elec- trons and ions, has been theoretically investigated. Thenonlinear Schrodinger (NLS) equation is derived by employing the reductiveperturbation method. The NLS equation leads to the MI of DAWs as well as to theformation of DAW rogue waves (DARWs), which are formed due to the effects ofnonlinearity in the propagation of DAWs. Both stable and unstable regions arerevealed from the analysis of the NLS equation. It is observed that the basicfeatures of the DAWs (viz. stability of the wave profile, MI growth rate,amplitude, and width of DARWs) are significantly modified by the various plasmaparameters such as non-extensive parameter, electron number density, andelectron temperature. The existence of the non-extensive electron/iondistribution creates an influence on the MI of the waves. It is observed thatnon-extensive distributed ions have more effect on the MI of the DAWs thanelectrons.
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