الفهرس 
INTRODUCTION
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Abstract
Propagation of both linear and nonlinear dust acoustic waves (DAWs) in an inhomogeneous, magnetized, collisional, and warm dusty plasma (DP) consisting of Boltzmann ions, nonextensive electrons and inertial dust particles is investigated. The number density gradients of all DP components besides the inhomogeneities of electrostatic potential and the initial dust fluid velocity are taken into account. The linear dispersion relation and the nonlinear modified Zakharov-Kusnetsov (MZK) equation, governing the propagation of the three-dimensional DAWs, are derived using a reductive perturbation theory (RPT). The analytical solution of the MZK reveals the creation of both compressive and rarefactive DAWs solitons in the proposed model. It is found that the inhomogeneity dimension parameter and the electron nonextensive parameter affect significantly the nonlinear DAWs’ amplitude, width, and Mach number.
Moreover, the effect of an adiabatic dust grain charge fluctuation on nonlinear properties of three-dimensional DAWs is considered. The considered plasma model is a warm and strongly magnetized DP which is consisting of negatively charged dust particles, Boltzmann ions and nonextensive electrons. The perturbation theory leads to a nonlinear MZK equation. Solving this equation reveals that the solution has two parts, one is the amplitude factor and the other is a solitary soliton solution of the form Sech2. It is found that increasing either the magnetic field or the nonextensive electron parameters reduces both of the wave velocity and width. Including the charge variation of dust grain surface yields significant modifications of the main characteristics of the nonlinear DAWs. The present results will be useful to understand recorded phenomena in astrophysical inhomogeneous DP situations or experiments on DAWs where nonextensive electrons and dust charging process are present.