Bamadev Sahoo
Centre for Data Science, Siksha `O' Anusandhan (Deemed to be University), Bhubaneswar, Odisha, India.

Shruti Tomar
School of Physical Science, DIT University, Dehradun, Uttarakhand, India.

Sunita Chand
Department of Mathematics, Siksha `O' Anusandhan (Deemed to be University), Bhubaneswar, Odisha, India.

Ambit K. Pany
Institute of Mathematics and Applications, Bhubaneswar, Odisha, India.

Sanjaya K. Mohanty
Department of Mathematics, Siksha `O' Anusandhan (Deemed to be University), Bhubaneswar, Odisha, India.

DOI https://doi.org/10.33889/IJMEMS.2026.11.5.095

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Abstract

In this paper, we solve the Schamel Korteweg-de Vries (Schamel KdV) equation with the help of the Kudryashov expansion technique. The Schamel KdV equation is important in various physical contexts, particularly in wave phenomena across different media. It is relevant in non-linear optics, plasma physics, solid-state physics, and fluid dynamics. For example, it models long waves on water surfaces, including solitary waves and solitons, and describes wave propagation in shallow water. The Kudryashov expansion technique is a simple and efficient technique. The obtained solutions are of the form of exponential functions, and two-dimensional, contour, and three-dimensional plots are also shown. The bifurcation analysis for the Schamel KdV equation is derived, and the stability of the model is also discussed.

Keywords- The Kudryashov expansion method, The Schamel KdV equation, Lyapunov exponent, Stability analysis.

Citation

Sahoo, B., Tomar, S., Chand, S., K. Pany, A., & K. Mohanty, S. (2026). Kink and Anti-Kink Wave Solutions of the Forced Schamel KdV Equation and its Stability Analysis. International Journal of Mathematical, Engineering and Management Sciences, 11(5), 2362-2380. https://doi.org/10.33889/IJMEMS.2026.11.5.095.