Analytical approaches to the (2+1)-dimensional Heisenberg Ferromagnetic Spin Chain equation and their applications for optical devices

Document Type : Article


1 Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt

2 - Department of Physics, College of Sciences, University of Bisha, PO Box 344, Bisha 61922, Saudi Arabia - Physics Department, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt

3 Faculty of Engineering, MTI University, Cairo, Egypt


\textcolor{Red}{The Heisenberg ferromagnetic spin chain (HFSC) equation has substantial relevance in the fields of optics and electronics, particularly in the advancement of high-density electronic components and faster storage devices}. This integrable nonlinear Schrödinger equation characterizes the propagation of nonlinear waves in ferromagnetic spin chain systems. In a recent research paper, two powerful analytical methods, the $(\frac{\mathfrak{G}^{\prime}}{\mathfrak{K} \mathfrak{G}^{\prime}+\mathfrak{G}+\mathfrak{r}})$-expansion method and the extended hyperbolic function method (EHFM), were implemented to solve the (2+1)-dimensional HFSC equation. Most of the results obtained from the study are presented graphically, which can aid in the visualization and interpretation of the gained results. These findings will be useful in the development and optimization of spintronic devices and other electronic components that rely on the behavior of spin systems. \textcolor{Red}{The analytical solutions of the HFSC equation yield important insights that enhance our understanding and facilitate the application of magnetism, thermal properties, and topological phenomena across diverse fields such as materials science, condensed matter physics, and quantum technologies. These findings play a crucial role in advancing our knowledge and practical utilization of these phenomena in real-world applications.}\\


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