الفهرس 
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Abstract
In this thesis, we study some nonlinear partial differential equation in magneto hydrodynamic and its applications.
We obtained exact solutions for some important equations
which describe physical models. This thesis consists of an introduction, four chapters, 40 figures and a list of references at the end of this thesis, together with English and Arabic summary. This thesis is organized as follow:
Introduction.
In this introduction, we give brief for solitary wave, shock wave, solitary and shock waves in plasma
Chapter one.
We study the head- on collision of two quantum ion acoustic solitary waves (QIASWs) in homogeneous three component dense quantum plasma composed of electrons, positrons and singly charged positive ions in presence of an uniform external magnetic field and we application of extended PLK method to obtain the two sided KdV equation as well as the two sided mKdV equations and the derivation of trajectories as well as phase shifts for the two solitons. In this chapter, we used the conservation laws, the direct algebraic function method and the extended (G^’/G) expansion method to obtain a series of exact solutions of the two sided KdV equation and the two sided mKdV equations. Published in International Journal of Applied Mathematical Research.
Chapter two.
We examine the nonlinear properties of IA solitary and rogue waves in a non-planar (cylindrical) geometry in
a degenerate dense plasma. The effects of plasma number density and temperature ratio are examined on the profiles of IA solitary and rogue waves. basic equations for degenerate dense plasma are used to derive a cylindrical KP equation, by using some transformation, cylindrical KP equation is transformed to KdV equation and it has been transformed to get the NLS equation, which is solved analytically for rogue wave solution.
We use The Exp (−ϕ(ξ))-Expansion Method to obtain series of exact solutions of the NLS equation. Submitted
Chapter three.
We have applied auto-Ba ̈cklund (BT) transformation method to the three nonlinear evolution namely, Vakhnenko-parkes
equation, Regularized long wave (RLW) equation and Symmetric regularized long wave (SRLW) equation and new exact solution has been obtained also we have applied the
exp(−ϕ(ξ))-expansion method and exact solutions have been obtained, and the solutions of the nonlinear evolution equation have many potential applications in mathematical physics and engineering.
Chapter four.
In this chapter, the Ba ̈cklund transformations and a series of new exact explicit solutions of the (2+1) DZK equation have been established. An extension of the homogeneous balance method was successfully used to develop these solutions. The solutions include, the algebraic solitary wave solution of rational function, single-soliton solutions, double-soliton solutions from two wayes, N-soliton solutions, singular Traveling solutions, and the periodic wave solutions of trigonometric function type.