Alam Badar E, Morales-Luna Gesuri, Fernandez-Anaya Guillermo
Department of Physics and Mathematics, Universidad Iberoamericana Ciudad de México, Prolongación Paseo de Reforma 880, Lomas de Santa Fe, Mexico City, 01219, Mexico.
Sci Rep. 2025 Jul 20;15(1):26325. doi: 10.1038/s41598-025-11975-y.
This study employs advanced mathematical techniques to investigate exact solutions for the fractional (2+1)-dimensional Heisenberg ferromagnetic spin chain (HFSC) equation. Novel complex transformations-based on the generalized conformable derivative, exponential functions, arctanh, and arctan-are used to reduce the partial differential equation to an ordinary one. Three analytical methods are applied to obtain solutions: the modified Kudryashov method, the improved Bernoulli subequation function method (IBSEFM), and the modified extended direct algebraic method (mEDAM). These methods yield kink-wave, hyperbolic, trigonometric, and periodic wave solutions, which are validated through 2D, 3D, and contour plots for specific parameter choices. The main objective of this study is to derive exact soliton solutions of the Heisenberg spin chain equation using generalized conformable derivatives through multiple analytical methods. A sensitivity analysis is also performed to study how small changes in initial conditions affect the system's behavior. These findings may contribute to future data storage technologies and magnetic memory developments. The proposed approaches demonstrate efficiency in solving nonlinear fractional equations and have potential applications in shallow water waves, fluid dynamics, quantum mechanics, lattice vibrations in condensed matter, shock wave propagation in plasma, and phase transitions in ferromagnetic materials. The study highlights the effectiveness and reliability of the employed techniques.
本研究采用先进的数学技术来研究分数阶(2 + 1)维海森堡铁磁自旋链(HFSC)方程的精确解。基于广义一致导数、指数函数、反双曲正切和反正切的新型复变换被用于将偏微分方程简化为常微分方程。应用三种解析方法来获得解：改进的 Kudryashov 方法、改进的 Bernoulli 子方程函数方法(IBSEFM)和改进的扩展直接代数方法(mEDAM)。这些方法产生扭结波、双曲、三角和周期波解，并通过针对特定参数选择的二维、三维和等高线图进行验证。本研究的主要目标是通过多种解析方法使用广义一致导数推导海森堡自旋链方程的精确孤子解。还进行了敏感性分析，以研究初始条件的微小变化如何影响系统行为。这些发现可能有助于未来的数据存储技术和磁存储器发展。所提出的方法在求解非线性分数阶方程方面显示出效率，并且在浅水波、流体动力学、量子力学、凝聚态物质中的晶格振动、等离子体中的冲击波传播以及铁磁材料中的相变等方面具有潜在应用。该研究突出了所采用技术的有效性和可靠性。
