الفهرس 
Introduction and mathematical toolsOnly 14 pages are availabe for public view
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Abstract
The aim of this thesis is to investigate some selected nonlinear partial differential equations in mathematical physical. New analytical exact solutions are obtained including real solutions, complex solutions, soliton solutions, periodic solutions, single soliton solution, kink soliton solutions, singular soliton solutions, hyperbolic function solutions, trigonometric function solutions, bright soliton solutions, Jacobi elliptic function solutions, rational function solutions, Bell-type solitary wave solutions, and other solutions by stratifying several methods. These methods are the extended simplest equation method, the extended auxiliary equation method, the fractional Riccati method, the rational fractional -expansion method, the modified simple equation method, the -expansion method, the two variables -expansion method, the -expansion method, the new Sub-ODE method and the simplified Hirota’s method.
The importance of researching this topic is to investigate the validity of extending and applying some analytical methods for solving some famous partial differential equations in a trial to present new exact analytical solutions which is considered important for mathematicians, physists, and engineers.
The objective of this thesis is to be considered as a guidline for researches in this field to further improve such methods to suit more nonlinear partial diffrential equations.
We conclude here that our researh work presents new analytical solutions using some powerful methods. These new solutions are in complete agreement and comparable well with other existing results in literature.
The thesis contains six chapters in addition to english and arabic summaries classified follows:
Chapter I: This chapter deals with the introduction and a brief description of the considered methods. Bird’s eye view of the mathematical methods used to obtain the exact solutions for the selected nonlinear partial differential equations are given in chapters II up to VI.
Chapter II: In this chapter two different methods namely, the extended simplest equation method and the extended auxiliary equation method are considered to obtain optical soliton solutions to the improved Gerdjikov-Ivanov equation in dense wavelength division multiplexed (DWDM) system for both kerr law and parabolic law nonlinearities. The procedure reveals new singular soliton solutions, bright soliton solutions, Bell-type solitary wave solutions, trigonometric function solution, solutions in terms of Jacobi’s elliptic function and, in the limiting case of the modulus of ellipticity, new singular and singular-periodic soliton solutions are obtained.
Chapter III: In this chapter two different methods namely, the fractional Riccati method and the rational fractional -expansion method are considered to obtain traveling wave solutions, periodic wave solutions, dark soliton solutions trigonometric function solutions, rational function solutions and hyperbolic function solution for generalized anti-cubic (AC) nonlinearity relevant to fiber Bragg gratings (BGs) including fractional temporal evolution. The concepts of modified Riemann - Liouvill derivative of Jumarie of order and Khalil’s conformable fractional derivative of order are also used.
Chapter IV: In this chapter four different methods have been used to obtain new solutions of the -dimensional coupled Burgers equations. First, we have applied the modified simple equation method to obtain new exact solutions. In a special case we obtained kink and singular soliton solutions. Second, we applied the -expansion method to obtain hyperbolic and trigonometric function solutions. Third, we applied the two variables -expansion method to find hyperbolic and trigonometric function solution. Fourth, we applied the -expansion method to obtain rational function solutions.
Chapter V: In this chapter, the new Sub-ODE method is applied to obtain dark and bright soliton solutions, periodic, rational, Weierstrass and Jacobian elliptic function solutions for the Lakshmanan-Porsezian Daniel model in birefringent fibers.
Chapter VI: In this chapter, the simplified Hirota’s method is applied to obtain real and complex solutions for three different variants of Boussinesq equation. These solutions came to be soliton, periodic, single soliton, and interaction of two soliton solutions.