الفهرس 
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Abstract
The objective of this thesis is to study the exact solutions for some nonlinear partial differential equations, and some equations with variable coefficients in order to find new exact solutions by applying various techniques. These techniques are: symmetry, first integral, direct integral, modified extended tanh- function, modified Kudryashov, homotopy perturbation and variational iteration methods. In addition, we present a new method which is called new extended rational- function method.
This thesis consists of five chapters, together with an Arabic and English summaries. It is organized as follows:
Chapter (I): Comprise an introduction contained in a brief survey. Development of the available literature relevant to the work given in chapters II-V and includes the general notations and mathematical tools.
Chapter (II): Here in Calogero-Bogoyvlenskii-Schiff equation and the coupled Burgers-type equations which appear in a wide variety of physical applications have been analyzed via symmetry method. Also, using the infinitesimal symmetries, there are six basic fields determined for the first equation while in the second only two basic fields are obtained. These fields which help us to reduce the first equation into partial differential equations with two variables and the second system also reduced to nonlinear system of ordinary differential equations. For each case of the six cases arises in the first equation, the reduced partial differential equations are transformed to nonlinear ordinary differential equations. The search for the solutions of those reduced ordinary equations, corresponding to the equation under consideration, has yielded new certain classes of exact solutions for the Calogero-Bogoyvlenskii-Schiff equation and the coupled Burgers-type equations.
Chapter (III): The objective of this chapter is to study the exact solutions of the nonlinear partial differential equations with variable coefficients in order to find new exact solutions by applying the first integral and the direct integral methods.
This chapter contains eight sections. In the first and second sections, we have studied the Long-Short wave resonance equations. In the third and fourth sections, we study the nonlinear Schrödinger equation with variable coefficients. In the fifth and sixth sections, we study the two-dimensional Burger equation with variable coefficients. In the seventh and eighth sections, we study the (2+1)-dimensional Broer-Kaup system with variable coefficients. The application of the first integral and the direct integral methods yields many exact solutions in the form of trigonometric, hyperbolic and Jacobi elliptic functions.
In Chapter (IV), we make use of the modified extended tanh-function and new extended rational-function methods for finding an exact solution of Zabolotskay-Khoklov equation (Burger’s equation in two-space dimension). Also the modified Kudryashov method with the aid of symbolic computation has been applied to obtain exact solutions of the (2+1)-dimensional modified Korteweg-de Vries equation and nonlinear Drinfeld-Sokolov system.
The third and fourth sections have been published in American Journal of Computational and Applied Mathematics.
In Chapter (V), we study Zabolotskay-Khoklov equation (Burger’s equation in two-space dimension), and the (2 + 1)-dimensional Konopelchenko-Dubrovsky (KD) equations by using variational iteration (VIM) and homotopy perturbation methods (HPM). Comparison between the exact solutions obtained before and solutions obtained by HPM and VIM has been made to judge how accurate solutions are those methods.