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The nonlinear propagation of the dust-acoustic bright and dark envelopesolitons in an opposite polarity dusty plasma system (composed of non-extensive$q$-distributed electrons, isothermal ions, and positively as well asnegatively charged warm dust) have been theoretically investigated. Thereductive perturbation method (which is valid for a small, but finite amplitudelimit) is employed to derive the nonlinear Schr\"{o}dinger equation. Two typesof modes (namely, fast and slow dust-acoustic (DA) modes) have been observed.The conditions for the modulational instability (MI) and its growth rate in theunstable regime of the DA waves are significantly modified by the effects ofnon-extensive electrons, dust mass, temperatures of different plasma species,etc. The implications of the obtained results from our current investigation inspace (viz. Jupiters magnetosphere, upper mesosphere, and comets tails) andlaboratory (e.g. direct current and radio-frequency discharges, plasmaprocessing reactors, fusion plasma devices, and solid-fuel combustion products,etc.) dusty plasmas are briefly discussed.

Modulated dust-acoustic wave packets in an opposite polarity dusty plasma system