Modulational instability of dust-ion acoustic waves in the presence of generalized (r, q) distributed electrons

Abstract

We have investigated the modulational instability (MI) of dust-ion acoustic waves in a dusty plasma model containing warm ions fluid, generalized (r, q) distributed electrons, and immobile dust grains. Using the Krylov-Bogoliubov-Mitropolsky method, the amplitude modulation of a monochromatic plane wave is analyzed through derivation of a nonlinear Schrödinger equation. The MI condition is calculated. Moreover, the effects of the plasma parameters such as the ion-to-electron temperature ratio, the wavenumber, and the unperturbed dust-to-electron number density ratio as well as the electron distribution dual parameters (r, q) are discussed. Our investigations have shown that the unstable region is bounded by two stable regions, i.e., two critical wavenumbers [kcl(lower) and kch(higher)] are found. The applications of the present theoretical study are briefly discussed in space physics whether positive or negative dust grains are enclosed.