الفهرس 
Introduction and PreliminariesOnly 14 pages are availabe for public view
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Abstract
Partial differential equations (PDEs) are clearly important in characterizing, simulating and predicting nonlinear phenomena across a wide range of physical and engineering science disciplines. As a result, we became interested in finding exact solutions to
these equations and used three main methods to find these solutions. These methods
are the modified extended tanh function method, the modified expanded direct algebraic method, and the modified expanded mapping method. These methods have been
applied to many models such as Kundu-Eckhaus, Davy-Stewartson equation, complex
Ginzburg-Landau equation, and nonlinear Kurteweg-de Vries-Kadomtsev-Petviashvili
equation. This thesis aims to find isolated wave solutions and other exact solutions of
some nonlinear partial differential equations (NLPDEs).
The thesis is divided into nine chapters, which are as follows:
Chapter (1):
It is an introductory chapter that includes seven sections. The first section explains
the importance of nonlinear partial differential equations in modeling many physical
phenomena. The second section provides the historical background of the soliton. The
third section explains the classifications of nonlinear effects that can be applied to partial
differential equations. In the fourth section, we discuss the various types of traveling
wave solutions. In the fifth section, we discuss the principle of homogeneous balance.
The importance and applications of solitons in life are discussed in the sixth section. We
discuss some main analytical methods for solving nonlinear partial differential equations
in the seventh section.
Chapter (2):
In this chapter, the improved modified extended tanh function method is applied for the
purpose of finding new analytical solitons and several other solutions of the Kundu–Eckhaus
equation describing the propagation of ultrashort light pulses in optical fibers taking into
account pentagonal nonlinearity and Raman effect in the study. Moreover, some of the
solutions obtained are presented graphically in 2D and 3D graphs and contour plots.
Chapter (3):
We discuss the generalized Kundu–Eckhaus equation with additive dispersion via the
improved modified extended tanh function technique which has led us to several new
and innovative exact and soliton solutions in optical fibers in this chapter. Furthermore,
some of the solutions obtained were illustrated graphically in the form of 2D, 3D and
contour plots.
Chapter (4):
This chapter is concerned with applying the modified extended mapping method to
obtain new optical solitons of magnetic waves using Kudryashov’s law of nonlinear refraction of a coupled system from the generalized nonlinear Schr¨odinger equation. In
addition, some of the derived solutions are graphically illustrated in the form of 2D, 3D,
and contour plots.
Chapter (5):
This chapter discusses the Davey-Stewartson equation (DSE), which explains how waves
move through water at a finite depth while being affected by gravity and surface tension,
and is analyzed using a modified extended mapping method to find many different soliton
solutions. In addition, some of the solutions obtained are graphically illustrated in the
form of 2D, 3D, and contour graphs.
Chapter (6):
In this chapter, the modified extended direct algebraic method is applied to search for
the derivation of new solitons and other exact wave solutions of a coupled system from
the highly dispersive complex Ginzburg-Landau equation in birefringent fibers with the
polynomial nonlinearity law. Moreover, some of the solutions obtained were represented
in 2D and 3D graphic form and contour plots.
Chapter (7):
In this chapter, the Nonlinear Schr¨odinger Equation (NLSE) with dimensions (2+1)
with nonlinearity and fourth-order dispersion was studied. Several photonic soliton
solutions are suitable for the present problem are analyzed using a modified extended
direct algebraic method. Moreover, some of the solutions obtained were represented
graphically in the form of 2D, 3D, and contour plots.
Chapter (8):
This chapter represents a study of solitary wave solutions of the nonlinear Kortewegde Vries-Kadomtsev-Petviashvili equation arising in water waves using the improved
modified extended tanh function technique. Moreover, some of the solutions obtained
were represented graphically.
Chapter (9):
In this chapter, we studied the generalized nonlinear Schr¨odinger equation (NLSE) using the improved modified extended tanh function method and obtained explicit exact
solutions by applying the improved modified extended tanh method. The results of the
study have important implications for how solitons propagate in nonlinear optics. Moreover, to better understand the behaviors of some of these found solutions, we showed
their outlines in 2D, 3D, and contour graphs.