الفهرس 
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Abstract
This thesis is mainly concerned with the study some nonlinear models in plasma physics and its applications. We obtained exact solutions for some important equations which describe physical quantities. This thesis consists of an introduction, four chapters, and a list of references, together with English and Arabic summary. This thesis is organized as follows:
Introduction
In this introduction, we give a quick hint for what is plasma, waves in plasmas, dusty plasmas.
Chapter 1.
Properties of small but finite amplitude nonlinear ion-acoustic monotonic double layers (DLs) in a plasma consisting of positive-negative ions with trapped electron are investigated. The reductive perturbation method is employed to reduce the basic set of fluid equations to the Schamel-Korteweg–de Vries (SKdV) equation. The effects of negative ions and the density on the properties of the monotonic double layer are discussed. New exact solutions for SKdV are obtain by using Bäcklund transformations and extended (G^’/G) method. Conditions are obtained under which large amplitude stationary ion-acoustic double layers can exist. For the physical parameters of interest, double layers profiles and the relationship between the maximum double layers amplitude and the mach number are found.
Chapter 2.
Many transport phenomena arising in natural science have been successfully described by the nonlinear reaction-diffusion (NRD) model. The applications NRD model have had wide variety including population dynamics, transport in porous medium, combustion theory and plasma physics. In this chapter, we have developed a variation of (G^’/G)-expansion method, in which we have used the full advantage of the well known solution of the coupled Riccati equation. The presented method is used to find new exact travelling wave solutions of the Fisher equation, Burgers-Fisher equation and FitzHugh-Nagumo equation as examples of NRD model, and we have applied an auto-Bäcklund transformation (BT) to obtained new exact solitons solutions of the Fisher equation, Burgers-Fisher equation and FitzHugh-Nagumo equation as examples of NRD model.
Published in International Journal of Pure and Applied Mathematics
Chapter 3.
We consider an unmagnetized dusty plasma, whose constituents are charge fluctuating stationary dust, inertial warm ions, and non-isothermal electrons following the vortex-like distribution. The nonlinear dynamics of the DIA waves, whose phase speed is much smaller than the electron thermal speed. To derive a dynamical equation for the nonlinear propagation of the DIA waves (modified Burgers equation). We consider a strongly coupled dusty plasma containing strongly correlated arbitrarily (positively or negatively) charged dust, and weakly coupled electrons and ions obeying the Boltzmann distribution. To derive a dynamical equation for the DA shock waves (standard Burgers equation). In this chapter we would like to use the new generalized extended (G^’/G)-expansion method to obtained travelling wave solutions of modified Burgers equation and standard Burgers equation.
Chapter 4.
There has been considerable interest in the KdV and BBM equations, which arises in many physical applications including shallow water waves and plasma physics. The KdV equation describes the theory of water waves in shallow channels. It is a non-linear equation which exhibits special solutions, known as solitons, which are stable and do not disperse with time. In this chapter we would like to use the homogeneous balance method to constructed an auto-Bäcklund transformation (BT), new exact solitons solutions of KdV equation and BBM equation are obtained, and we have applied the extended (G^’/G)method to obtained a new travelling wave solutions of KdV equation and BBM equation.