New Abundant Optical Solutions for The Stochastic Heisenberg Ferromagnetic Equation Used in a Ferromagnet via Two Different Methods (European Journal of Pure and Applied Mathematics, 2025)
In this study, we look at the stochastic Heisenberg Ferromagnetic equation (SHFE) perturbed in the Itô sense by multiplicative Brownian motion. The SHFE is transformed into a different Heisenberg Ferromagnetic equation with random variable coefficients (HFE-RVCs) utilizing the proper transformation. To provide novel solutions for trigonometric functions, hyperbolic functions, and rational functions for HFE-RVCs, we employ the generalizing Riccati equation mapping technique (GREM-method) and Jacobi elliptic functions (JEF-method). The solutions of SHFE can then be obtained. For the first time, we postulate that the solution to the Heisenberg Ferromagnetic equation is stochastic, in contrast to earlier research that suggested it was deterministic. Additionally, we investigate the impact of multiplicative Brownian motion on the exact solutions of the SHFE by offering several graphical representations.
Keywords: White noise; stochastic solutions; Jacobi elliptic functions method; random variable coefficients