الفهرس 
Introduction Introduction IntroductionOnly 14 pages are availabe for public view
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Abstract
The nonlinear partial differential equations (NLPDEs) are widely used as models to describe many important dynamical systems in various fields of natural sciences, particularly in quantum mechanics, solid state physics, plasma physics and nonlinear optical fibers. The construction of exact solutions of NLPDEs has become recently one of the most essential task in nonlinear science for understanding the nonlinear physical phenomena. There are many methods that have been used to construct explicit traveling and solitary wave solutions of NLPDEs in the past decades such as the inverse scattering method, the tanh-function method, the truncated expansion method, the Jacobi elliptic functions method, the F-expansion method, the Kudryashov method, the extended F-expansion method and other methods.
This thesis consists of four chapters, organized as follows:
In chapter 1: We give a brief introduction to the subject and to cover some backgrounds to our thesis such as methods and some necessary functions in our study. In this thesis, we study some Schrödinger equations and find exact solutions of these equations through three methods:
The Nikiforov-Uvarov (NU) method, the F-expansion method and the extended F- expansion method. Using the first method, we study the linear Schrödinger equation to find the energy eigenvalues and the corresponding eigenfunctions for some potentials. Also, we study the higher order nonlinear Schrödinger (HONLS) equations and find the exact solutions of these equations by using the second and third methods.
In chapter 2: We apply the Nikiforov-Uvarov method to obtain the energy eigenvalues and the corresponding eigenfunctions of the linear Schrödinger equation with generalized Rosen-Morse plus modified Rosen-Morse potentials in compact form. Also, some special cases for the considered potential are studied.
In chapter 3: We use the F-expansion method with symbolic computations to solve a fourth-order dispersion nonlinear Schrödinger (NLS) equation with cubic-quintic nonlinearity, self-steeping and self-frequancy shift terms which describes the propagation of an optical pulse in optical fibers. According to this method, we investigated several types of exact solutions of this equation. As results, exact solutions including Jacobi elliptic functions (JEF) solutions, bright and dark solitary wave solutions are obtained. Solutions in the limiting cases are studied and the properties of the intensity of some solutions are also discussed. The results of this chapter are published in a research paper ( see [74] ).
In chapter 4: We employ the extended F-expansion method with the help of Maple to present several types of exact solutions of third order dispersion NLS equation with real parameters and quintic non-Kerr terms which describes the propagation of an optical pulse in optical fibers. As a results, abundant exact solutions have been obtained including not only JEF solutions but also solitary wave solutions in terms of hyperbolic functions. The present exact solutions may be describe various new features of waves and may be useful to explain some physical phenomena in nonlinear pulse propagation through optical fibers. When the modulus m → 1, some solitary wave solutions are also studied. The properties of the intensity of some solutions are shown by some figures.