الفهرس 
Chapter 1 preliminary ideas and fundamental conceptsOnly 14 pages are availabe for public view
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Abstract
This thesis is dedicated to solving nonlinear partial differential equations (PDEs) and obtaining exact solutions for them. These equations represent a significant class of problems in applied physics and applied mathematics, playing a prominent role in understanding and analyzing various natural and technological phenomena. The research aims to explore exact wave solutions, contributing to the advancement of mathematics and applied sciences in general. These solutions will be reviewed and analyzed in the thesis. This thesis comprises five chapters organized as follows:
Chapter 1: Preliminary ideas and fundamental concepts
In this chapter, the introduction is divided into four sections. The first section explores the significance of nonlinear partial differential equations in modeling various physical phenomena. The second section introduces different types of traveling wave solutions. In the third section, we delve into the examination of wave phenomena properties. The fourth section provides a comprehensive review of essential techniques for solving nonlinear partial differential equations.
Chapter 2: Exploration of new solitons in optical medium with higher-order dispersive and nonlinear effects via improved modified extended tanh function method
In this chapter, the improved modified extended tanh function method is presented for deriving new travelling wave solutions in different forms of nonlinear Schrödinger equation (NLSE) with higher-order dispersive and nonlinear effects that describes the propagation of ultra-short optical solitons in an optical fiber medium.
Chapter 3: Extraction of solitons in magneto–optic waveguides for coupled NLSEs with Kudryashov’s law of nonlinearity via modified extended direct algebraic method.
In this chapter, we employ the modified extended direct algebraic method to uncover a range of novel traveling wave solutions for the coupled nonlinear Schrödinger equation (NLSE) characterized by Kudryashov’s nonlinearity law. This particular model serves as a framework for elucidating the behavior of optical solitons as they propagate
through magneto-optic waveguides.
Chapter 4: Extraction of solitons in multimode fiber for coupled higher-order nonlinear Schrödinger equations via improved modified extended tanh function method.
In this chapter, we delve into the examination of coupled higher-order nonlinear Schrödinger equations, which emulate the dynamics of solitons propagating through multimode fibers. To investigate this scenario, we employ the improved modified extended tanh function method.
Chapter 5: Extraction of solitons in optical fibers for the (2+1)-dimensional perturbed nonlinear Schrödinger equation via the improved modified extended tanh function technique.
In this chapter, we investigate the (2+1)-dimensional perturbed nonlinear Schrödinger model, which incorporates a range of phenomena, including fourth-order dispersion, group velocity dispersion, intermodal dispersion, nonlinear dispersion, Kerr nonlinearity, and self-steepening effects.