الفهرس 
Chapter 1: Lie group analysis of partial differential equationOnly 14 pages are availabe for public view
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Abstract
The description of certain phenomena such as optical fiber, fluid mechanics, solid state physics, plasma physics, geochemistry and chemical physics are carried out using nonlinear partial differential equations (NLPDEs) with the development of nonlinear science. Despite of the complexity and difficulty of solving variable coefficient NLPDEs, many researchers shifted their interest from constant coefficient NLPDEs to variable coefficient NLPDEs due to the importance of using variable coefficient NLPDEs. The real physical settings and crucial understanding of complex nonlinear phenomena can be described by the use of variable coefficient nonlinear evolution equations with comparison to the constant coefficient nonlinear evolution equations which only describe highly idealized systems. In the past several decades, many effective methods for obtaining exact solutions to NLPDEs have been presented. Lie symmetry analysis is considered as one of the most influential methods for seeking exact solutions of partial differential equations (PDEs). It is used on a large scale especially for solving and studying group classification of PDEs with variable coefficients which depends on finding a transformation that reduces the number of independent variables of the PDE. The objective of this thesis is to apply Lie symmetry method to transform some nonlinear PDE to ordinary differential equations which can be solved in easier ways. The thesis is organized in five chapters: Chapter one is an introduction to the concepts of symmetry and Lie Groups. Also, we illustrate how the infinitesimal generators are obtained. These generators are used to reduce the number of independent variables of the PDEs by one in each time. In chapters (2, 3), group classification of some (1+1)-dimensional PDEs with time dependent coefficients are studied. The problems solved in these chapters include Fisher equations with three forms as well as Benny equation and the fifth-order korteweg-de vries equation. In chapter 4, group classification of (2+1), and-(3+1) dimensional PDEs with variable coefficient are investigated. The problems considered in this chapter are (2+1) dimensional Boussinesq equation with time dependent coefficients, (3+1) dimensional quantum Zakharov-Kuznetsov equations with variable coefficients, (2+1) dimensional KP equation with variable coefficient, (2+1) dimensional Boiti- Leon Pempinelli system. In chapter 5, we present the conclusion of the work in this thesis and suggest some points for future work.