AccScience Publishing / IJOCTA / Volume 15 / Issue 2 / DOI: 10.36922/ijocta.1715
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RESEARCH ARTICLE

Effect of diffusion parameters on traveling wave solutions of singular perturbed Boussinesq equation

Asıf Yokuş1 ,  Hülya Durur2* ,  Mehmet Hakan Ekici3
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1 Department of Mathematics, Faculty of Science, Firat University, Elazig, Türkiye
2 Department of Computer Engineering, Faculty of Engineering, Ardahan University, Ardahan, Türkiye
3 Institute of Graduate Education, Department of Advanced Technologies, Ardahan University, Ardahan, Türkiye
IJOCTA 2025, 15(2), 142–152; https://doi.org/10.36922/ijocta.1715
Received: 29 October 2024 | Accepted: 19 February 2025 | Published online: 15 April 2025
© 2025 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )
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Abstract

This paper focuses on the nature of the traveling wave solutions of the singular perturbed (sixth-order) Boussinesq equation, which is important for the physical relationships of water waves and shows strong interactions. Most studies of this equation have been analyzed by numerical methods and it has been observed that analytical solutions are limited. This has formed the main motivation for an analytical method, the Kudryashov method, for the generation of traveling wave solutions. One of the important goals of this work is to analyze the wave propagation phenomena in detail. For this purpose, the model has been extended by adding parameters to the diffusion term, which can illuminate shallow fluid layers and nonlinear atomic phenomena. This model aims to provide a deeper understanding of the motion of waves and the behavior of fluids, as well as its solution by the analytical method. To deepen the physical discussion, the responses of the solution are simulated for different values of the diffusion coefficient and the parameter associated with the wave velocity.

Keywords
The Singular Perturbed (sixth-order)
Boussinesq Equation
The Kudryashov method
Traveling wave solution
Nonlinear wave propagation
Funding
None.
Conflict of interest
The authors declare that they have no conflict of interest regarding the publication of this article.
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An International Journal of Optimization and Control: Theories & Applications, Electronic ISSN: 2146-5703 Print ISSN: 2146-0957, Published by AccScience Publishing
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