الفهرس 
Preliminary ideas and fundamental concepts
Cubic–Quartic solitons and other solutionsOnly 14 pages are availabe for public view
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Abstract
Exact solutions for partial differential equations (PDEs) are crucial in describing, sim- ulating, and predicting nonlinear phenomena in various fields of the physical and engi- neering sciences. As a result, our focus has been on this area, leading us to use two primary methods for solving PDEs. These methods are the improved modified extended Tanh function and the generalized Kudryashov’s methods. These techniques have been applied to address solitary wave solutions for various physical and engineering problems. Examples of these problems are The Biswas-Milovic model with dual-power law nonlin- earity, the highly dispersive model introduced by Kudryashov with arbitrary refractive index, the Kaup-Newell equation, the nonlinear Schr¨odinger equation with diverse types of nonlinearities, the newly generalized nonlinear Schr¨odinger equation featuring triple refractive index and nonlocal nonlinearity, and other models. In our thesis, we utilized the proposed techniques for some of these problems and obtained novel solutions that will help in more understanding and illustration of these models.
The thesis is divided into four chapters as listed below:
Chapter 1: “Preliminary ideas and fundamental concepts”:.
In this chapter, we introduced and explained key concepts such as linear and nonlinear partial differential equations (PDEs), solitary traveling wave solutions, bright, dark soli- tons, peakons, cuspons, and periodic solutions of PDEs. Additionally, we outlined the two primary proposed integration schemes used to solve various engineering and physical problems in the subsequent chapters.
Chapter 2: ” Derivation of new optical solitons for Biswas-Milovic equation with dual-power law nonlinearity using improved modified extended
tanh-function method”:
In this chapter, we utilized the improved modified extended tanh-function method for the Biswas-Milovic model with dual-power law nonlinearity. We derived cubic-quartic optical solitons and other solutions to this model. The extracted solutions include bright solitons, dark solitons, singular solitons, singular periodic solutions, Jacobi elliptic, and hyperbolic solutions. Furthermore, and for more physical illustration, we provided vi- sual representations in the form of three and two-dimensional graphics for some of the obtained solutions.
Chapter 3: ”Optical solitons of higher order mathematical model with refractive index using Kudryashov method”:
Thesis Summary xiv
In this chapter, we addressed the highly dispersive model introduced by Kudryashov, which incorporates a general arbitrary refractive index. We obtained this model’s dark and singular soliton solution using the powerful generalized Kudryashov integration method. For a more comprehensive and visually appealing illustration of the solutions obtained, and for providing additional evidence and support for our findings, we pre- sented 3D and 2D graphs for some of the obtained solutions.
Chapter 4: ”New visions of optical soliton to a class of generalized nonlinear Schr¨odinger equation with triple refractive index and non-local nonlinearity”:
This chapter explores the generalized form of the nonlinear Schr¨odinger equation, which incorporates a triple power of nonlinearity. By utilizing the improved modified extended tanh function technique, we have successfully derived optical soliton solutions for this innovative model. The obtained results cover many solitons, including bright, dark, singular, periodic, singular periodic, and hyperbolic solutions. To enhance clarity and provide a visual representation, we have presented selected solutions graphically in both two-dimensional and three-dimensional formats.