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Abundant different types of soliton solutions for fractional modified KdV equation using auxiliary equation method
Akhtar Hussain1, Tarek F Ibrahim2, Fathea M Osman Birkea3
1Department of Mathematics, University of Management and Technology, Lahore, 54770, Pakistan.
Abstract:
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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