Browsing by Author "Ibrahim, Salisu"

Now showing 1 - 5 of 5

Citation - WoS: 12
Citation - Scopus: 16
Classes of solitary solution for nonlinear Schrödinger equation arising in optical fibers and their stability analysis
(Springer, 2023) Ibrahim, Salisu; Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
In this work, we realised the soliton solutions of nonlinear Schrodinger equation (NLSE) that arise from optical fibers, we considered the modified Sardar sub-equation method (MSSEM) to find solitary solutions analytically. The stability of the retrieved soliton solutions realised from the NLSE are investigated. We demonstrate the soliton solutions that are stable and can last for a very long time without losing its form or energy under specific circumstances and those soliton solutions that are unstable. The MSSEM is a frequently employed technique in research for addressing specific mathematical modeling or physical phenomena problems. Its selection in this specific study might stem from its proven efficacy in handling the particular problem under investigation. The decision to utilize MSSEM could be driven by several considerations, including its precision, computationally efficient, effectiveness, greater accuracy and capability to manage intricate systems. Finally, our method offers greater flexibility in modeling various physical phenomena, which makes it particularly useful in applications in diverse fields such as quantum mechanics and nonlinear optics. The findings have ramifications for the architecture of optical fiber communications and offer significant new insights into the behavior of solitons in optical systems. The NLSE has proven to be an effective tool for understanding wave behavior in fiber optics. Its applications have helped engineers and scientists optimize the design of optical fibers and predict the behavior of various conditions. Moreover, our study provides insights into the fundamental properties of solitary solutions in the NLSEs and their practical implications in physical systems.
Citation - WoS: 0
Citation - Scopus: 0
Commutativity of Cascaded Connected Fractional Order Linear Time-Varying Systems
(World Scientific Publ Co Pte Ltd, 2025) Baleanu, Dumitru; Isah, Abdulnasir; Iqbal, Mujahid; Chang, Phang; Baleanu, Dumitru; Matematik
In this work, we present a comprehensive study of the commutativity of fractional-order linear time-varying systems (LTVSs). Commutativity is a fundamental property in the analysis and control of dynamic systems and is often used to simplify the design of controllers. Fractional-order systems, which are characterized by a noninteger-order derivative, have been widely studied in recent years due to their ability to model a wide range of phenomena. However, the commutativity of fractional-order LTVSs has not been widely explored. In this work, we present a comprehensive study of the commutativity of fractional-order LTVSs. We first provide a mathematical definition of commutativity for these systems and demonstrate that it is equivalent to the commutativity of their transfer functions. We then propose a method for verifying the general condition for commutativity of fractional-order LTVSs under zero initial conditions (ICs) and prove it mathematically. Based on our findings, we realized that the commutative requirements, properties, theories, and conditions are general for fractional-order LTVSs, please observed that some fractional-order LTVSs are commutative, some are not commutative, while some are commutative under certain conditions. Based on this fact, we can say that not all fractional-order LTVSs are commutative.We apply explicit commutative results to several examples of fractional-order LTVSs. Our theoretical and simulation results show a good agreement and prove that our fractional-order LTVSs are commutative under certain conditions, moreover, the commutativity property holds for certain conditions and classes of fractional-order LTVSs, but not for others. Because of the application of fraction commutativity in various fields of science and engineering, we find it necessary to come up with explicit results for the first time.
Citation - WoS: 18
Citation - Scopus: 14
Families of optical soliton solutions for the nonlinear Hirota-Schrodinger equation
(Springer, 2022) Ibrahim, Salisu; Baleanu, Dumitru; Sulaiman, Tukur Abdulkadir; Yusuf, Abdullahi; Alshomrani, Ali S.; Baleanu, Dumitru; 56389; Matematik
This work employs a novel variation of the Sardar sub-equation approach to investigate the optical solitons for the nonlinear Hirota-Schrodinger equation. Different soliton solutions, including bright solitons, dark solitons, singular solitons, combined bright-singular solitons, periodic, exponential, and rational solutions are derived along with nonlinear models. The obtained solitons solutions are crucial to mathematics, physics, science, and engineering.
Citation - WoS: 31
Citation - Scopus: 34
Realization of optical solitons from nonlinear Schrödinger equation using modified Sardar sub-equation technique
(Springer, 2023) Ibrahim, Salisu; Baleanu, Dumitru; Ashir, Abubakar M.; Sabawi, Younis A.; Baleanu, Dumitru; 56389; Matematik
This study presents a novel modification of the Sardar sub-equation method for solving the nonlinear Schrodinger equation (NLSE) with second order spatiotemporal dispersion and group velocity dispersion, which is used to describe and model the propagation of optical solitons in nonlinear media. The modification is based on introducing a new function that is used to approximate the solution of the equation. By applying this modified method, we are able to obtain exact analytical solutions for the NLSE with several classes of optical soliton solutions. The method is tested on a variety of nonlinear optical systems and is shown to be highly effective in producing accurate solutions. The results of this study demonstrate the potential of this novel approach for solving the NLSE in the context of optical solitons. These soliton solutions are of great importance in the field of science, physics, mathematics, and engineering.
Citation - WoS: 12
Citation - Scopus: 15
Wave Propagation To the Doubly Dispersive Equation and the Improved Boussinesq Equation
(Springer, 2024) Baleanu, Dumitru; Sulaiman, Tukur A.; Yusuf, Abdullahi; Ozsahin, Dilber Uzun; Baleanu, Dumitru; Matematik
In this paper, we examine the optical solitons for the nonlinear doubly dispersive equation and the modified Boussinesq equation, which explain the flow of shallow water in a small-amplitude surface system. We realize a variety of solitons using the Sardar sub-equation approach, including bright solitons, dark solitons, singular solitons, mixed bright-singular solitons, periodic, exponential, and rational solutions. The generated optical solutions can be used to simulate water waves and the free movement of a fluid surface, both of which are important in computing models of nonlinear partial differential equations in science, engineering, and mathematical physics. For the physical interpretation of the data, the well-known symbolic software Mathematica 12 was employed.