الفهرس 
Preliminaries, concepts, and surveyOnly 14 pages are availabe for public view
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Abstract
It is now obvious that partial differential equations (PDEs) and their exact solutions play a critical role in characterizing, simulating, and forecasting nonlinear processes in a variety of physical and engineering sciences’ disciplines. As a result, we’ve been interested in this subject and have implemented six main partial differential equation-solving methods. Those approaches were applied to various physical and engineering problems as: Dispersive Salerno equation for the nonlinear discrete electrical lattice, Longitudinal wave equation in magneto-elector-elastic circular rod, Highly dispersive nonlinear Schro¨dinger’s equation (NLSE) having Kudryashov’s arbitrary form, the Radhakrishnan-Kundu-Laksmannan (RKL) equation that describes the pulse propagation in optical fibers, The hierarchy of nonlinear evolution equations describing the propagation of a pulse in optical fibres, the nonlinear Schro¨dinger’s equation with Kudryashov’s genralized form of refractive index of the self-phase modulation, and the quartic cubic Bragg gratings accompanied with anti-cubic nonlinearity.
This thesis is divided into eight chapters, as follows:
Chapter 1 is an introductory chapter in which we revised and presented some important definitions as linear and nonlinear PDEs, solitary travelling wave solutions, bright and dark solitons, peakon, cuspon and periodic solutions of PDEs. Also, we presented the six main integration schemes that have been utilized in solving different engineering and physical problems in the remaining chapters. In chapter 2, the modified Jacobi elliptic function method is applied for Salerno equation which describes the nonlinear behaviour of the discrete electrical lattice in the forbidden band gaps. Dark and bright solitons are obtained. Also, periodic solutions and periodic Jacobi elliptic function solutions are reported. Moreover, for the physical illustration of the obtained solutions, 3D and 2D graphs are presented.
In chapter 3, the modified simple equation method and the extended auxiliary equation method are applied to obtain new optical soliton solutions for the nonlinear longitudinal wave equation in magneto-electro-elastic circular rod. Bright solitons, singular solitons and singular periodic solutions are extracted. Moreover, for the physical illustration of the obtained solutions, some graphs are presented.
In chapter 4, a simple integration scheme (Kudryashov’s method) is executed to secure new dark and singular soliton solutions for the highly dispersive non-linear Schro¨dinger’s equation having Kudryashov’s arbitrary form with generalized nonlocal laws and sextic-power law refractive index. 3D and 2D graphs are graphically displayed for some solutions.
In chapter 5, we studied the RKL equation which is used to describe the pulse propagation in optical fiber communications. By using improved modified extended tanh function method various types of solutions are extracted such as bright solitons, singular solitons, singular periodic wave solutions, Jacobi elliptic solutions, periodic wave solutions and Weierstrass elliptic doubly periodic solutions. Moreover, some of the obtained solutions are represented graphically. In chapter 6, the improved extended modified tanh function method is applied to the hierarchy of nonlinear partial evolution equations that model the propagation of a pulse in optical fibers with second order dispersion (M = 1). Bright, dark, and singular soliton solutions are obtained. Also, periodic singular solutions and elliptic Weierstrass doubly periodic type solutions are acquired. Graphs of some of the obtained results are presented.
Chapter 7 addresses the NLSE with Kudryashov’s generalized form of refractive index using two approaches to secure soliton solutions to this model. These approaches are modified Jacobi’s elliptic function and extended auxiliary equation. The existence restrictions of these solitary solutions are being labeled as constraint conditions and are also exhibited.
In chapter 8, we recover novel optical cubic–quartic solitons in fiber Bragg gratings with dispersive reflectivity and anti–cubic nonlinear form. The extended modified direct algebraic integration scheme is utilized to study these new optical solutions. New Optical bright, dark, singular periodic, singular solitons, Jacobi elliptic based functions and other solutions have been secured. Some of the acquired results are represented graphically.
At the end of each chapter, a conclusion to the whole chapter and discussions are presented.