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We examine the modulational instability (MI) of ion-acoustic waves (IAWs) inan electronegative plasma containing positive and negative ions as well aselectrons that follow the nonextensive statistics proposed by Tsallis [J. Stat.Phys. 52, 479 (1988)]. Using the reductive perturbation method (RPM), thenonlinear Schr\"{o}dinger equation (NLSE) that governs the modulationalinstability of the IAWs is obtained. Inspired by the experimental work ofIchiki \emph{et al.} [Phys. Plasmas 8, 4275 (2001)], three types ofelectronegative plasmas are investigated. The effects of various parameters onthe propagation of IAWs are discussed in detail numerically. We find that theplasma supports both bright and dark solutions. The presence of thenon-extensively distributed electrons is found to play a crucial role in theformation of envelope excitations. The region in the parameter space where theMI exists depends sensitively on the positive to negative ion mass ratio (M)and negative to positive ion density ratio ($\nu$). An extensive range of thenonextensive $q$-parameters {$(-1<q<3)$} is considered and in each case the MIsets in under different conditions. The finding of this investigation is usefulfor understanding stable wave propagation of envelope ion-acoustic solitarywaves in space and laboratory plasmas comprising ions with both positive andnegative charges as well as non-Maxwellian electrons.

Envelope excitations in electronegative plasmas with electrons featuring the Tsallis distribution