Browsing by Author "Tarla, Sibel"

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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.