Low-frequency modulated dust ion-acoustic structures in electronegative plasma with q-distributed electrons

The present work examines the amplitude modulation and nonlinear propagation of low-frequency dust ion-acoustic waves (DIAWs) in an electronegative complex plasma comprising inertial negative ions, inertialess q -nonextensive electrons, Maxwellian positive ions, and stationary negative dust grains. Using a standard fluid description together with the derivative expansion method (DEM), the governing set of fluid and Poisson equations is reduced to a planar nonlinear Schrödinger equation (NLSE) for the slowly varying DIAW envelope. The resulting dispersion and nonlinearity coefficients, expressed in terms of the nonextensive index, the electron temperature ratio, the negative ion concentration, and the electron concentration, yield precise conditions for modulational instability (MI). It is shown that the MI threshold, the width of the unstable band, and the associated gain are very sensitive to these parameters, which in turn dictate the existence domains of stable and unstable modulated structures. In the modulationally unstable regime, the plasma supports bright envelope solitons, breather-type excitations, and rogue waves, whereas in the modulationally stable regime, gray and black envelope solitons propagate. The influence of various related physical parameters on the carrier frequency and group velocity, on the MI domains, and on the profiles of bright and dark solitons, breathers, and rogue waves is numerically investigated. The results provide physically transparent insight into energy localization and extreme-amplitude events in space and laboratory electronegative dusty plasmas with superthermal electron populations.