Analysis of the propagation of nonlinear waves arise in the Heisenberg ferromagnetic spin chain

• Published in: Optical and quantum electronics Vol. 56; no. 8
• Main Authors: Haque, Abdullah, Islam, Md. Tarikul, Akbar, Md. Ali, Osman, M. S.
• Format: Journal Article
• Language: English
• Published: New York Springer US 18.07.2024; Springer Nature B.V
• Subjects: Characterization and Evaluation of Materials; Computer Communication Networks; Dimensional analysis; Dynamical systems; Electrical Engineering; Electromagnetic radiation; Exact solutions; Ferromagnetic materials; Hyperbolic functions; Lasers; Magnets; Nonlinear dynamics; Nonlinear systems; Optical Devices; Optics; Photonics; Physics; Physics and Astronomy; Schrodinger equation; Spin dynamics; Traveling waves; Wave propagation; Improved auxiliary equation approach; Solitons; 35R11; Heisenberg ferromagnetic spin chain equation; Improved tanh technique; 35C08; Exact solution
• ISSN: 1572-817X; 0306-8919; 1572-817X
• DOI: 10.1007/s11082-024-07181-1

The (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation which is used to characterize the nonlinear behavior of magnets and describe how ferromagnetic materials are ordered is the main subject of this investigation. The system’s dynamics are governed by the Schrödinger equation, which explains the variations in its quantum state over time. We implement two modern and efficient techniques, the improved auxiliary equation scheme, and the improved tanh method to find the exact solutions of HSFC model and develop travelling wave solutions in terms of rational, trigonometric, and hyperbolic functions with arbitrary parameters. Numerical findings are shown in 3-D plots, 2-D curves, and contours with carefully selected parametric values used to illustrate the dynamic wave shape using MATLAB software. The acquired results provide important insights into the physical implications of nonlinear dynamics in magnetic systems and significantly contribute to the understanding of electromagnetic wave models. The article finishes with a thorough appraisal of the physical interpretations generated from the obtained results.