Noise effect on soliton phenomena in fractional stochastic Kraenkel-Manna-Merle system using rational exponential method

Abstract

This study investigates the conformable stochastic Kraenkel-Manna-Merle (KMM) system, a fundamental nonlinear model for describing magnetic phenomena in ferromagnetic materials. Employing the modified generalized exponential rational function (mGERF) method, a diverse family of exact stochastic soliton solutions-including hyperbolic, trigonometric, rational, and polynomial types—is constructed. These analytical solutions provide valuable insights into the magnetic field behavior of zero-conductivity ferromagnets. The dynamical characteristics of the derived soliton structures are further examined through comprehensive two- and three-dimensional visualizations using Mathematica, emphasizing the influence of stochastic perturbations and noise on their evolution. The results demonstrate that stochasticity significantly modifies soliton amplitude, shape, and stability, thereby enhancing the understanding of magnetic field dynamics in ferromagnetic media governed by conformable stochastic KMM systems.