Research demonstrates various soliton solutions in fractional-order KdV equation, indicating applications in oceanographic dynamics and ion-acoustic waves.
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.
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Hussain et al. (2025) studied this question.
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