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Dynamical Structure of the Soliton Solution of M‐Fractional (2 + 1)‐Dimensional Heisenberg Ferromagnetic Spin Chain Model Through Advanced exp(−ϕ(ξ))‐Expansion Schemes in Mathematical Physics

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  • Sakhawat Hossain
  • M. M. Rahman
  • Md. Habibul Bashar
  • Shimul Biswas
  • Md Mamunur Roshid

Abstract

In this piece of work, we give the particular traveling wave answers for the truncated time M‐fractional (2 + 1)‐Heisenberg ferromagnetic spin chain model that is researched by executing the advanced exp (−φ(ξ)) expansion technique. In order to reconnoiter such dynamics, the advanced exp(−φ(ξ)) expansion method integrates the truncated time M‐fractional (2 + 1)‐Heisenberg ferromagnetic spin chain to achieve creative solitonic and traveling envelopes. Consequently, the suggested method has been used to find trigonometric and hyperbolic solutions. 3D and density charts show the dynamical properties of the derived solutions for any selected set of the permitted parameters. By defining the particular advantages of the summarized parameters through the representation of figures and by interpreting the physical events, we have constructed appropriate soliton arrangements and addressed the physical significance of the obtained arrangements. All solitons are checked through the relating conditions with the assistance of Maple bundle program. The advanced exp (−φ(ξ)) expansion technique is strong treatment for looking for central nonlinear waves that further develop assortment of dynamical frameworks which emerges in arranging fields.

Suggested Citation

  • Sakhawat Hossain & M. M. Rahman & Md. Habibul Bashar & Shimul Biswas & Md Mamunur Roshid, 2025. "Dynamical Structure of the Soliton Solution of M‐Fractional (2 + 1)‐Dimensional Heisenberg Ferromagnetic Spin Chain Model Through Advanced exp(−ϕ(ξ))‐Expansion Schemes in Mathematical Physics," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnljam:v:2025:y:2025:i:1:n:5535543
    DOI: 10.1155/jama/5535543
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    References listed on IDEAS

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    1. Yun-Mei Zhao, 2014. "New Exact Solutions for a Higher-Order Wave Equation of KdV Type Using the Multiple Simplest Equation Method," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-13, June.
    2. Yun-Mei Zhao, 2014. "New Exact Solutions for a Higher‐Order Wave Equation of KdV Type Using the Multiple Simplest Equation Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
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    4. Peng Xu & Fu-Tang Long & Chun Shan & Geng Li & Feng Shi & Kang-Jia Wang, 2024. "The Fractal Modification Of The Rosenau–Burgers Equation And Its Fractal Variational Principle," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(06), pages 1-6.
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