الفهرس 
الغلافيوجد فقط 14 صفحة متاحة للعرض العام
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المستخلص
In this thesis, we present some aspects of a few methods that have been introduced recently in order to solve nonlinear partial differential equations (PDEs) which represent some physically relevant systems in applied mathematics, applied physics, especially in optics, fluids and few works in electronics. The thesis comprises four chapters organized as follows: Chapter one is introductory and consists of three sections. One is a general introduction. The second is the concepts of solitons and its history. The second is an outline of the main steps of the methods used in this work. Chapter-2, consists of two sections. In section one, the fiber Bragg Gratings (FBGs) model with five types of nonlinearity studied using the modified simple eqution method. FBGs are considered excellent sensor elements, suitable for measuring various engineering parameters such as temperature, strain, pressure, tilt, displacement, acceleration, load, as well as the presence of various industrial, biomedical and chemical substances in both static and dynamic modes of operation. The FBG is also an excellent signal shaping and filtering element for a growing field of applications. The obtained solution are dark and soliton solutions. In section two, the perturbed nonlinear shro¨dinger equation is studied with four different nonlinearity structures. The obtained solution is also dark and singular solitons. In Chapter three , we obtain optical soliton solutions to the governing perturbed nonlinear Schro¨dinger’s equation. The integration algorithm that is employed in this chapter is the extended simplest equation method. This leads to bright, dark and singular soliton solutions that are valuable in the field of optoelectronics. The soliton solutions appear with all necessary constraints that are deemed necessary for them to exist. There are four types of nonlinear studied in this chapter. They are Kerr law, power law, parabolic law and the dual-power law. In Chapter four, we apply the new jacobi elliptic function method to the longitudinal wave equation of the magneto-electro-elastic circular rod and the (3+1)-dimensional potential-Yu-TodaSasa-Fukuyama equation. Multi solitons of different forms are obtained by using the proposed method.