د.خالد علي الريفي2024-11-262024-11-26https://dspace.academy.edu.ly/handle/123456789/361The nonlinear PDE is an important model for describing the problems of Nonlinear phenomenon, such as hydrodynamics, plasma physics, chemical dynamics, photobiology, solid physics, Marine and atmospheric phenomena, and so on. It can be seen from these fields that the travelling wave solutions of nonlinear evolution equations play an important role in the study.bstract In this thesis, we apply the original ( G ′ G , 1 G ) –expansion method to find the exact solutions of two higher order nonlinear Schrödinger equations describing the propagation of ultrashort of femtosecond pulses in nonlinear optical fibers and the propagation of femtosecond pulses in nonlinear optical fibers. The ( G ′ G , 1 G ) –expansion method is a combination between two different methods namely ( G ′ G ) expansion method and ( 1 G ) –expansion method. Also, based on the Jacobi elliptic equation and the Lienard equation, we find many other exact solutions of the nonlinear Schrödinger equations. The obtained exact traveling wave solutions include, solitary wave solutions, periodic solutions, Jacobi elliptic functions solutions and the rational function solutions. In addition, we drew some graphs of the exact solutions using Maple software. The given methods in this thesis are straightforward and concise, and it can also be applied to other nonlinear PDEs in mathematical physicThe ( 𝐆 ′ 𝐆 , 𝟏 𝐆 ) Expansion Method and its Applications to Some Nonlinear Schrödinger Equations