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<p>Nonlinear stochastic conformable equations are crucial for understanding complex real-world phenomena across various scientific fields, including plasma physics, wave propagation and conceptual modelling. In this study, we introduce and analytically investigate the stochastic space–time conformable phi-four (STCPF) equation for the first time. This equation is particularly significant in particle and plasma physics, where nonlinear wave interactions and stochastic effects are prevalent. To solve the stochastic STCPF equation, we propose a novel conformable sinh-Gordon method (CSGM) and compare its effectiveness with the modified tanh-function method (MTFM). Through these approaches, we derive stochastic soliton solutions and analyse their dynamic behaviour. Additionally, we explore the influence of time-dependent stochastic parameters on soliton structures by illustrating the solutions through 3D and contour plots. The findings reveal that temporal variations in the stochastic parameter significantly impact soliton height and shape, leading to multiple solitons.</p>

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Understanding nonlinear phenomena by analysing the stochastic space–time conformable phi-four equation

  • 期刊论文

  • 发表日期：

    2026年1月6日

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  • A Nazari-Golshan,
  • V Fallahi

摘要

Nonlinear stochastic conformable equations are crucial for understanding complex real-world phenomena across various scientific fields, including plasma physics, wave propagation and conceptual modelling. In this study, we introduce and analytically investigate the stochastic space–time conformable phi-four (STCPF) equation for the first time. This equation is particularly significant in particle and plasma physics, where nonlinear wave interactions and stochastic effects are prevalent. To solve the stochastic STCPF equation, we propose a novel conformable sinh-Gordon method (CSGM) and compare its effectiveness with the modified tanh-function method (MTFM). Through these approaches, we derive stochastic soliton solutions and analyse their dynamic behaviour. Additionally, we explore the influence of time-dependent stochastic parameters on soliton structures by illustrating the solutions through 3D and contour plots. The findings reveal that temporal variations in the stochastic parameter significantly impact soliton height and shape, leading to multiple solitons.