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Search Results (3)

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Keywords = stochastic Heisenberg ferromagnetic equation

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12 pages, 1132 KB  
Article
Random Traveling Wave Equations for the Heisenberg Ferromagnetic Spin Chain Model and Their Optical Stochastic Solutions in a Ferromagnetic Materials
by Wael W. Mohammed, Fakhr Gassem and Rabeb Sidaoui
Axioms 2024, 13(12), 864; https://doi.org/10.3390/axioms13120864 - 10 Dec 2024
Cited by 1 | Viewed by 1277
Abstract
In this paper, we investigate the stochastic Heisenberg ferromagnetic equation (SHFE) derived by a multiplicative Wiener process. We use a suitable transformation to change the SHF equation into another Heisenberg ferromagnetic equation with random variable coefficients (HFE-RVCs). We employ the mapping approach to [...] Read more.
In this paper, we investigate the stochastic Heisenberg ferromagnetic equation (SHFE) derived by a multiplicative Wiener process. We use a suitable transformation to change the SHF equation into another Heisenberg ferromagnetic equation with random variable coefficients (HFE-RVCs). We employ the mapping approach to obtain novel rational, trigonometric, elliptic and hyperbolic function solutions for HFE-RVCs. Following that, we can attain the solutions of the SHFE. For the first time in the Heisenberg ferromagnetic equation, we postulate that the solution to the wave equation is stochastic, whereas all previous investigations supposed that it was deterministic. Moreover, we give various visual representations to demonstrate the impact of the multiplicative Wiener process on the exact solutions to the stochastic Heisenberg ferromagnetic equation. Full article
(This article belongs to the Special Issue Applied Nonlinear Dynamical Systems in Mathematical Physics)
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13 pages, 565 KB  
Article
Characteristics of Solitary Stochastic Structures for Heisenberg Ferromagnetic Spin Chain Equation
by Munerah Almulhem, Samia Z. Hassan, Alanwood Al-buainain, Mohammed A. Sohaly and Mahmoud A. E. Abdelrahman
Symmetry 2023, 15(4), 927; https://doi.org/10.3390/sym15040927 - 17 Apr 2023
Cited by 1 | Viewed by 1833
Abstract
The impact of Stratonovich integrals on the solutions of the Heisenberg ferromagnetic spin chain equation using the unified solver approach is examined in this study. In particular, using arbitrary parameters, the traveling wave arrangements of rational, trigonometric, and hyperbolic functions are developed. The [...] Read more.
The impact of Stratonovich integrals on the solutions of the Heisenberg ferromagnetic spin chain equation using the unified solver approach is examined in this study. In particular, using arbitrary parameters, the traveling wave arrangements of rational, trigonometric, and hyperbolic functions are developed. The detailed arrangements are exceptionally critical for clarifying diverse complex wonders in plasma material science, optical fiber, quantum mechanics, super liquids and so on. Here, the Itô stochastic calculus and the Stratonovich stochastic calculus are considered. To describe the dynamic behaviour of random solutions, some graphical representations for these solutions are described with appropriate parameters. Full article
(This article belongs to the Section B: Mathematics)
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9 pages, 1417 KB  
Article
Wiener Process Effects on the Solutions of the Fractional (2 + 1)-Dimensional Heisenberg Ferromagnetic Spin Chain Equation
by Wael W. Mohammed, Farah M. Al-Askar, Clemente Cesarano, Thongchai Botmart and M. El-Morshedy
Mathematics 2022, 10(12), 2043; https://doi.org/10.3390/math10122043 - 13 Jun 2022
Cited by 9 | Viewed by 2267
Abstract
The stochastic fractional (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation (SFHFSCE), which is driven in the Stratonovich sense by a multiplicative Wiener process, is considered here. The analytical solutions of the SFHFSCE are attained by utilizing the Jacobi elliptic function method. Various [...] Read more.
The stochastic fractional (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation (SFHFSCE), which is driven in the Stratonovich sense by a multiplicative Wiener process, is considered here. The analytical solutions of the SFHFSCE are attained by utilizing the Jacobi elliptic function method. Various kinds of analytical fractional stochastic solutions, for instance, the elliptic functions, are obtained. Physicists can utilize these solutions to understand a variety of important physical phenomena because magnetic solitons have been categorized as one of the interesting groups of non-linear excitations representing spin dynamics in semi-classical continuum Heisenberg systems. To study the impact of the Wiener process on these solutions, the 3D and 2D surfaces of some achieved exact fractional stochastic solutions are plotted. Full article
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