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<p>The Korteweg-De Vries equation is the most significant computational model that describes the behaviour of optical solitons and has an important impact on the study of shallow waves. In a recent paper, we investigated the sixth-order dessipative equation with the assistance of a powerful analytical technique, the Khater method. The aforementioned technique has considerable benefits, such as being easy to learn, logical, and capable of reducing the volume of essential calculations, which demonstrates its versatility. It is a robust, efficient, and productive way of obtaining precise solitary wave solutions to nonlinear conformable fractional partial differential equations. We investigate the KdV equation of sixth order for the first time using such an innovative approach and develop some unique analytical results. Higher order KdV model is essential for accurately describing nonlinear wave propagation in media where strong dispersion and higher order effects cannot be captured by classical third-order formulations.The inclusion of conformable fractional derivatives allows the model to account for memory and nonlocal effects, which arise naturally in complex physical systems such as shallow water dynamics and optical wave propagation. All the solutions acquired are stable and precise, having been incorporated into the equation to verify their existence. These solutions are visually represented in the form of 3D, 2D and contour graphs. To the best of our knowledge, these solutions have not been reported in the existing literature. This study highlights the Khater method’s effectiveness as a useful tool for solving higher-order nonlinear equations, providing opportunities for more investigation and application in the field of nonlinear science and engineering.</p>

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Investigating the Dynamic Patterns of Wave Structures in the Context of the 6th Order Korteweg–de Vries Equation Employing the Khater Technique

  • 期刊论文

  • 发表日期：

    2026年3月24日

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  • Javeria Murtaza,
  • Afraz Hussain Majeed,
  • Imran Siddique

摘要

The Korteweg-De Vries equation is the most significant computational model that describes the behaviour of optical solitons and has an important impact on the study of shallow waves. In a recent paper, we investigated the sixth-order dessipative equation with the assistance of a powerful analytical technique, the Khater method. The aforementioned technique has considerable benefits, such as being easy to learn, logical, and capable of reducing the volume of essential calculations, which demonstrates its versatility. It is a robust, efficient, and productive way of obtaining precise solitary wave solutions to nonlinear conformable fractional partial differential equations. We investigate the KdV equation of sixth order for the first time using such an innovative approach and develop some unique analytical results. Higher order KdV model is essential for accurately describing nonlinear wave propagation in media where strong dispersion and higher order effects cannot be captured by classical third-order formulations.The inclusion of conformable fractional derivatives allows the model to account for memory and nonlocal effects, which arise naturally in complex physical systems such as shallow water dynamics and optical wave propagation. All the solutions acquired are stable and precise, having been incorporated into the equation to verify their existence. These solutions are visually represented in the form of 3D, 2D and contour graphs. To the best of our knowledge, these solutions have not been reported in the existing literature. This study highlights the Khater method’s effectiveness as a useful tool for solving higher-order nonlinear equations, providing opportunities for more investigation and application in the field of nonlinear science and engineering.