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<p>This research focuses on investigating soliton solutions for the space-time fractional modified third-order Korteweg-de Vries equation using the auxiliary equation method. The Korteweg-de Vries equation is renowned for its application in modeling shallow-water waves, oceanographic dynamics, and ion-acoustic waves in plasma. By employing a traveling wave transformation, the fractional-order partial differential equation is converted into a nonlinear ordinary differential equation. This study used conformable derivatives to solve the fractional differential equation. Soliton solutions, including bright, dark, singular, periodic singular, combined bright-dark, and combined dark-singular forms, are derived through the application of auxiliary equation method to the reduced equation.</p>

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Abundant different types of soliton solutions for fractional modified KdV equation using auxiliary equation method

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月10日

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  • Akhtar Hussain,
  • Tarek F. Ibrahim,
  • Fathea M. Osman Birkea,
  • M. Sh. Yahya,
  • Abaker A. Hassaballa,
  • Herbert Mukalazi

摘要

This research focuses on investigating soliton solutions for the space-time fractional modified third-order Korteweg-de Vries equation using the auxiliary equation method. The Korteweg-de Vries equation is renowned for its application in modeling shallow-water waves, oceanographic dynamics, and ion-acoustic waves in plasma. By employing a traveling wave transformation, the fractional-order partial differential equation is converted into a nonlinear ordinary differential equation. This study used conformable derivatives to solve the fractional differential equation. Soliton solutions, including bright, dark, singular, periodic singular, combined bright-dark, and combined dark-singular forms, are derived through the application of auxiliary equation method to the reduced equation.