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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月21日

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  • A. Hussain,
  • A. Q. Alameri,
  • B. Oğul,
  • B. R. Al-Sinan,
  • A. A. Thaqfan,
  • Elkhateeb S. Aly,
  • T. F. Ibrahim

摘要

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.