الفهرس Only 14 pages are availabe for public view
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Abstract
The thesis in all comprises six chapters together with an Arabic and English summaries in addition to a list of references. In the following we outline briefly the details of each of
the chapters.
Chapter (I): This chapter is devoted to a brief survey and development of the works related the techniques used in the chapters II-VI. Also included in this chapter necessary mathematical tools for establishing similarity and travelling wave solutions to nonlinear
partial differential equations.
Chapter (II): In this chapter the generalized Kortweg de-Vries-Burger equation have been analyzed via symmetry method. For different choices to the function of the dependent variable contained in the equation under consideration,the infinitesimals,
similarity variables,dependent variables and reduction to quadrature or exact solutions are given and tabulated.
Chapter (III): In this chapter we have taken up the application of the Lie group method by using the extension of the infinitesimal operato (Prolongation) to investigate invariant
solutions of quasilinear wave equation. The solution of the over determined partial differential equations generated from the invariant condition, has led us to five cases for
determination of the infinitesimals and the similarity variables. Also is indicated the group theoretic property of the given equation. The search for solutions to the surface condition in each case has yielded a reduction to ordinary differential equations then to
exact solutions.
Chapter (IV): In this chapter we have made use of Lie group method(prolongation) for a model represent the problem ”2+1 dimensional viscous flow between slowly expanding or contracting walls with weak permeability”. The equations of motion and the continuity equation are reduced to partial differential equations in terms of stream function. Unlike
chapter III, wherein we have applied the invariant condition to a single equation, herein, we have applied the invariant condition to a coupled system.
Chapter (V): Herein, we have analyzed single nonlinear partial differential equations represented by Calogero- Degasperis- Fokas modified KdV, fifth- order KdV and Rosenau-Burgers equations via the tanh-method. Some interesting outcomes of this study are the deductions of the new exact classes of travelling wave solutions.
Chapter (VI): Unlike chapter (V), wherein we have analyzed single equations via the tanh- method, herein, we have taken up the mentioned method to the determination of coupled systems represented by The Whitham-Broer-Kaup equation abbreviated by (WBK) equation, (2+1)-dimensional Broer- Kaup- Kupershmidt (BKK) equation and the variable coefficient nonlinear Schrödinger equation abbreviated by (VCNLS)
equation. Some interesting outcomes of this study are the deductions of the new exact of travelling wave solutions.