Browsing by Author "Ali, Karmina K."

Now showing 1 - 4 of 4

Citation Count: 1
Bifurcation analysis, chaotic structures and wave propagation for nonlinear system arising in oceanography
(Elsevier, 2024) Ali, Karmina K.; Faridi, Waqas Ali; Yusuf, Abdullahi; Abd El-Rahman, Magda; Ali, Mohamed R.
This study focuses on the variant Boussinesq equation, which is used to model waves in shallow water and electrical signals in telegraph lines based on tunnel diodes. The aim of this study is to find closed-form wave solutions using the extended direct algebraic method. By employing this method, a range of wave solutions with distinct shapes, including shock, mixed-complex solitary-shock, singular,mixed-singular, mixed trigonometric, periodic, mixed-shock singular, mixed-periodic, and mixed-hyperbolic solutions, are attained. To illustrate the propagation of selected exact solutions, graphical representations in 2D, contour, and 3D are provided with various parametric values. The equation is transformed into a planar dynamical structure through the Galilean transformation. By utilizing bifurcation theory, the potential phase portraits of nonlinear and super-nonlinear traveling wave solutions are investigated. The Hamiltonian function of the dynamical system of differential equations is established, revealing the system's conservative nature over time. The graphical representation of energy levels offers valuable insights and demonstrates that the model has closed-form solutions.
Citation Count: 0
Dynamics of pulse propagation with solitary waves in monomode optical fibers with nonlinear Fokas system
(World Scientific Publ Co Pte Ltd, 2024) Ali, Karmina K.; Tarla, Sibel; Yusuf, Abdullahi; Umar, Huzaifa; Yilmazer, Resat
In this study, a unified auxiliary equation method, which is one of the powerful methods for exploring nonlinear model solutions, is used in the Fokas system, with complex functions representing nonlinear pulse propagation in monomode optical fibers. As a result, we get some solutions, including dark-bright, singular, periodic, bright-dark, Jacobi elliptic functions, trigonometric, hyperbolic and exponential ones. In addition, we use a computer program to generate 3D, 2D and counterplot graphics from the obtained solutions by assigning specific values to the involved parameters. While discussing, the graphs for various values of an arbitrary constant are examined. These findings constitute an important step in understanding how solitary waves are generated in nonlinear media. Since the studied model is used in many domains, including Bose-Einstein condensates and plasma physics, these results improve our theoretical knowledge and open up new avenues for potential real-world applications and the development of cutting-edge technologies.
Citation Count: 0
Exact solutions of the (2+1)-dimensional Konopelchenko-Dubrovsky system using Sardar sub-equation method
(World Scientific Publ Co Pte Ltd, 2024) Tarla, Sibel; Salahshour, Soheıl; Yusuf, Abdullahi; Uzun, Berna; Salahshour, Soheil
In this paper, the new modification of the Sardar sub-equation method is used to generate a wide variety of exact solutions for the (2+1)-dimensional Konopelchenko-Dubrovsky system. We focus on investigating the Konopelchenko-Dubrovsky equation, which serves as a mathematical model for studying nonlinear waves in the field of mathematical physics. This equation specifically captures the behavior of waves with weak dispersion, allowing us to explore the intricate dynamics and characteristics associated with such wave phenomena. By delving into the properties and solutions of this system, we aim to deepen our understanding of nonlinear wave propagation and its implications in the broader field of mathematical physics. The exact solutions generated through this modified method provide valuable insights into the propagation and interaction of waves with weak dispersion in the system. The obtained novel solutions are expressed as hyperbolic, and trigonometric functions. The proposed model successfully constructs various types of solutions, including singular, dark, bright, trigonometric, periodic, dark-bright, exponential, and hyperbolic. These solutions are presented with appropriate parameter values in both 3D and 2D graphics.
Citation Count: 0
Soliton waves with optical solutions to the three-component coupled nonlinear Schrödinger equation
(World Scientific Publ Co Pte Ltd, 2024) Ali, Karmina K.; Yusuf, Abdullahi
This study uses the modified Sardar sub-equation method to find novel soliton solutions to the nonlinear three-component coupled nonlinear Schr & ouml;dinger equation (NLSE), which is used for pulse propagation in nonlinear optical fibers. Multi-component NLSE equations are widely used because they can represent a wide range of complex observable systems and more dynamic patterns of localized wave solutions. The optical solutions proposed in this study are novel and can be described using hyperbolic, trigonometric, and exponential functions. These solutions are categorized as bright, dark, singular, combo bright-singular, and periodic solutions. Some solutions' dynamic behaviors are demonstrated by selecting appropriate physical parameter values. The results and computational analysis indicate that the techniques provided are simple, effective, and adaptable. They can be applied to a variety of nonlinear evolution equations, whether stable or unstable, and can be used in fields such as mathematics, mathematical physics, and applied sciences.