Random Traveling Wave Equations for the Heisenberg Ferromagnetic Spin Chain Model and Their Optical Stochastic Solutions in a Ferromagnetic Materials

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 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.

Keywords

• stochastic solutions
• multiplicative noise
• random variable coefficients
• mapping method