الفهرس 
Chapter 1 Lie Point symmetry, First integrals and Lagrangians of Ordinary Differential EquationOnly 14 pages are availabe for public view
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Abstract
In this thesis we investigate some important methods to find first integrals of ODEs such as, lie symmetry method and the direct method . Also we obtained some standard and nonstandard Lagrangians for some ODEs. Finally ,we obtain some exact solutions for these ODEs . The thesis is organized in four chapters as follows: In Chapter 1, we present a brief introduction to the basic concepts needed in our study. First ,we introduce what is symmetry and what is the invariance of differential equations. And how to find Lie point symmetries of differential equations and canonical coordinates . Also, we show how to reduce the order of the ODEs . Finally ,we show how to find the first integral and Lagrangine of ODEs. In chapter 2, we study the complex Ginzburg–Landau equation (CGLE) which is widely used in modeling wave propagation in fiber optics and metamaterials .Using travelling wave transformation and lie point symmetry Also,we obtained some new bright and dark soliton solutions. we obtain some implicit solutions and some explicit solutions in the form of Jacobi and Weierstrass elliptic functions. In chapter 3,we study a class of generalized Liénard-type equations. We obtained standard and nonstandard Lagrangian using direct method . We obtained autonomous and non autonomous first integral which we used to obtain some exact solutions. For this class, We also studied Camassa- Holm equation and used travelling wave transformation to obtain a Liénard-type. Finally, we obtained some new bright and dark soliton solutions of the Camassa-Holm equation. In chapter 4, we give the conclusion and suggested future work.