الفهرس 
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Abstract
In this thesis, we study some nonlinear partial differential equations (NLPDEs) in plasma physics. Some physical models described by some NLPDEs are studied. The exact solutions for these models and related physical quantities by using several methods are obtained. This thesis consists of an introduction, five chapters, 42 figures and a list of references at the end of each chapter, together with English and Arabic summary. This thesis is organized as follows:
Introduction.
In this introduction, we give quick hint for the importance of Magnetohydrodynamics (MHD) and plasma physics with its applications.
Chapter 1.
We considered a background for the material used in this thesis in this chapter. It cover the fundamental concepts of known results concerning our objects to make this thesis somewhat self contained.
Chapter 2.
In this chapter, we study a family of nonlinear force-free magnetic fields (FFMFs) by using F-expansion Method. In Cartesian geometry under assumption of translational symmetry, as simple models of magnetic fields in the solar corona, are obtained. The FFMFs are governed by an elliptic second order nonlinear PDE for the poloidal magnetic flux function coupled with an algebraic Bernoulli equation. We have specified several nonlinear forms of the arbitrary flux functions. Consequently, We construct explicit exact solutions by JEFs of FFMFs for constant and non-constant Mach number flows. Several exact solution classes to the result equations are obtained. These solutions include double periodic wave solutions, solitary wave solutions and singular solutions.
Chapter 3.
In this chapter, nonlinear waves in warm dusty plasmas with variable dust charge, two-temperature ions, and nonthermal electrons are studied. The reductive perturbation method has been employed to drive Kadomtsev–Petviashivili (KP) and modified (KP) equations. We find several exact solutions for this equations by using Elliptic expansion function method. It is interesting that exact solutions for this models may be expressed by hyperbolic functions and jacobi elliptic functions.
Chapter 4.
In this chapter, Exact solutions for two-dimensional ideal magnetohydrodynamic plasma with steady incompressible flow described by Liouvelle, double sinh, combined sinh-cosh, and combined double sinh-cosh Poisson equations are derived. The domain is then of cylindrical shape with arbitrary cross section. Several classes of exact solutions for nonlinear
cases are obtained by using generalized tanh method.
Chapter 5.
In this chapter, We discussed the derivation of Sagdeev potential, as a results of which, could be analyzed to predict the existence of various features of localized solitons in various configurations of plasmas. The advantages of the method in finding the solitary waves or double layers stemming from the nonlinear waves was found useful in investigating the large and small amplitude wave propagation. The study advances to describe the spiky and explosive solitary waves along with the possible existence of double layers causeway from the interaction of trapped electrons which are to be expected as common features in space plasmas. Moreover we find exact wave solution of the Korteweg-de Vries (KdV) equation, the KdV equation derived with mixed nonlinearity, the equation in general form, Schamel equation and generalized Schamel equation by using Jacobi elliptic function expansion method.