Modulational instability of dust-ion acoustic waves in generalized (r, q) distributed electron dissipative plasmas

The modulational instability of the dust-ion acoustic waves in a dissipative dusty plasma system containing warm ions, generalized (r,q) distributed electrons, and immobile dust grains has been studied. The Krylov-Bogoliubov-Mitropolsky (KBM) perturbation method is employed to analyze the amplitude modulation of a monochromatic plane wave through the derivation of a nonlinear Schr & ouml;dinger equation. This equation is solved analytically to determine the modulational instability region, and the corresponding dissipative rogue wave solution is obtained. The effects of various system parameters, such as the kinematic viscosity of the ions (upsilon), the wavenumber (k), the ion to electron temperature ratio (sigma(i)), the unperturbed ion to electron density ratio (gamma) as well as the electron distribution parameters: r and q, are investigated. The dependence of the amplitude of dissipated rogue waves on upsilon is discussed. It is found that various system parameters have significant effects on the features of dissipated rogue waves. The present investigation can be relevance to the electrostatic rogue structures in various cosmic dust-laden plasmas such as Saturn's F-ring.