الفهرس 
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Abstract
The main concern of this thesis is to explore the existence and propagation of nonlinear dust ion acoustic waves (DIAWs) in bipolar dusty plasmas, i. e. dusty plasmas consist of positive and negative dust grains focusing attention principally on inhomogeneity and dust grain charge fluctuation. In the case of unmagnetized inhomogeneous dusty plasma (IDP), three problems that particularly significant have been addressed in multi-component dusty plasma composed of cold positive ions, cold massive charged dust grains, and isothermal electrons. First, the fluid system contains mobile positive and negative dust grains with constant charge. The DIAWs are investigated through the derivation of variable coefficient Kortewege–de Vries (KdV) equation by employing reductive perturbation theory. Remarkably, it is seen that when ion density reaches to the certain critical value, i.e. the coefficient of the nonlinear term in the KdV equation vanishes, new set of stretched coordinates is adapted to derive a new governing nonlinear equation named modified Kortewege–de Vries (mKdV) equation. It is found that, both compressive and rarefactive soliton solutions coexist. Below (above) this critical point the system supports rarefactive (compressive) solitons. Second, in this case the dust grains are assumed immobile with charge fluctuation. Noticeably, it is found that rather KdV nor mKdV equation is suitable for describing the DIAWs, so further modified KdV (fmKdV) equation has been obtained in the vicinity of the critical ion density. The soliton solutions of these equations are derived. It was mentioned that all classes of the resulting equations are obtained directly from the first and second order calculation. In order to examine the effect of higher order dispersion, we extended our analysis to obtain the KdV equation with fifth-order dispersion term. Finally, we study the propagation of DIAWs in adiabatic and nonadiabtic dust charge variation and with the presence of ionization source model. The dissipative effects of nonadiabtic dust charge variation has been taken into account which cause generation of dust ion acoustic shock waves (DIASWs) governed by what is called KdV Burger (KdVB) equation. For magnetized polar IDP, Zakharov and Kuznetsov (ZK) equation has been derived from the basic set of fluid equations by using the reductive perturbation technique. Either compressive or rarefactive solitons are shown to exist depending on the critical value of the ion density, which in turn, depends on the inhomogeneous distribution of the ion. The effects of inhomogeneity, the external magnetic field, and dust charge fluctuations on the profile (amplitude and width) and the velocity of the soliton are investigated in some details.