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Exploring soliton solutions of stochastic Phi-4 equation through extended Sinh-Gordon expansion method

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Abstract

Numerous systems and phenomena that appear to fluctuate randomly are mathematically modeled using stochastic processes. In this paper stochastic Phi-4 equation is considered with the multiplicative Wiener process that represents the temporal change of fluctuations. In particle and nuclear physics, the stochastic Phi-4 equation appears to be crucial. Stochastic phenomena represent the microscopic randomness of the nuclear particle. The extended sinh-Gordon expansion approach is used to study the stochastic model in terms of Itô formulation. With the use of this method, variety of solutions from important physical prospectives, such as dark, bright, singular, and periodic solitons has been examined, Furthermore, based on the Itô, the impact of the noise term on Brownian motion is examined. Both 2D and 3D graphs are used to show the impact of the noise term on the obtained soliton solutions. The computations and outcomes demonstrate the method’s importance, precision, and effectiveness. Numerous robust nonlinear stochastic differential equations from mathematics, physics, and other relevant domains can be resolved using this method.

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Authors and Affiliations

  1. School of Mathematics, Minhaj University, Lahore, 54590, Pakistan

    Fiza Batool & Zeshan Ali

  2. Faculty of Engineering Technology, Amol University of Special Modern Technologies, Amol, Iran

    Hadi Rezazadeh

  3. Department of Mathematics, Faculty of Arts and Sciences, Mersin, Turkey

    Ulviye Demirbilek

Authors
  1. Fiza Batool
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  2. Hadi Rezazadeh
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  3. Zeshan Ali
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  4. Ulviye Demirbilek
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Contributions

Methodology, writing review and conceptualization: Fiza Batool. Data curation: Hadi Rezazadeh. Formal analysis: Zeshan Ali. Writing review & editing: Ulviye Demirbilek.

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Correspondence to Hadi Rezazadeh.

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Batool, F., Rezazadeh, H., Ali, Z. et al. Exploring soliton solutions of stochastic Phi-4 equation through extended Sinh-Gordon expansion method. Opt Quant Electron 56, 785 (2024). https://doi.org/10.1007/s11082-024-06385-9

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