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<p>The primary objective of this study is to develop a fractional Korteweg–de Vries (KdV) model that characterises nonlinear space–time dynamics in a dusty plasma environment with variable temperature. A key focus is placed on examining how the fractional order influences critical wave properties such as phase velocity, amplitude and width. The fractional KdV equation is addressed using analytical techniques, including the Adomian decomposition method (ADM), direct integration and the F-expansion method. Results reveal that soliton behaviour varies significantly with different ion and electron streaming rates, depending on the fractional order. Notably, the evolution of fractional space–time KdV solitons exhibits both enhancement and suppression patterns, depending on the initial streaming velocities of the charged species. Numerical simulations further indicate that the soliton amplitude is sensitive to initial physical parameters, such as ion and electron velocities and charge densities. For specific ion velocities, the fractional order initially does not affect amplitude, but beyond a threshold, it begins to influence it. Additionally, amplitude variations to electron velocity display nearly uniform differences across fractional orders. It is also observed that decreasing the fractional order consistently leads to an increase in soliton width under fixed physical conditions, highlighting the significant role of fractional dynamics in wave propagation.</p>

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Analysing ion-acoustic fractional space–time Korteweg–de Vries solitons with variable temperatures in dusty plasmas

  • 期刊论文

  • 发表日期：

    2026年3月4日

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  • E A-B Abdel-Salam,
  • Mohamed I Nouh,
  • M S Jazmati,
  • Abaker A Hassaballa,
  • Hala H Taha,
  • A M Awad

摘要

The primary objective of this study is to develop a fractional Korteweg–de Vries (KdV) model that characterises nonlinear space–time dynamics in a dusty plasma environment with variable temperature. A key focus is placed on examining how the fractional order influences critical wave properties such as phase velocity, amplitude and width. The fractional KdV equation is addressed using analytical techniques, including the Adomian decomposition method (ADM), direct integration and the F-expansion method. Results reveal that soliton behaviour varies significantly with different ion and electron streaming rates, depending on the fractional order. Notably, the evolution of fractional space–time KdV solitons exhibits both enhancement and suppression patterns, depending on the initial streaming velocities of the charged species. Numerical simulations further indicate that the soliton amplitude is sensitive to initial physical parameters, such as ion and electron velocities and charge densities. For specific ion velocities, the fractional order initially does not affect amplitude, but beyond a threshold, it begins to influence it. Additionally, amplitude variations to electron velocity display nearly uniform differences across fractional orders. It is also observed that decreasing the fractional order consistently leads to an increase in soliton width under fixed physical conditions, highlighting the significant role of fractional dynamics in wave propagation.