Exact Solutions of Kuramoto–Sivashinsky Equation Using Modified Sub-equation Method


Year : 2024 | Volume : 11 | Issue : 02 | Page : 25-33
    By

    Hulya durur,

  1. Associate Professor, Department of Computer Engineering, Faculty of Engineering , Ardahan University, Ardahan, TURKEY

Abstract

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Equations for non-linear evolution are mathematical representations of physical phenomena. The physical interpretation of the solution functions of these equations enhances the viewpoint of many natural processes. Numerous scientists who acknowledge this truth have focused on this area. These mathematical models are even more important since they provide light on a multitude of events when their solutions take on a physical significance. Through their research, numerous scientists create methods and solutions for non-linear evolution equations. In this work, wave solutions of mathematical equations utilized in physics, engineering, and many other applied sciences are generated using a different approach. The Kuramoto–Sivashinsky equation, which has a physically significant role in mathematics, will be covered in this study. The Kuramoto–Sivashinsky equation was successfully created with the modified sub-equation method, which is one of the exact solution production tools in mathematics. Trigonometric and hyperbolic solutions were obtained with this method. These solutions play a significant role for scientists who study shock wave structure and asymptotic behavior. To get at these solutions, numerous laborious and intricate procedures had to be completed. The modern computer technology makes it easy to solve these challenges. The state of the wave at any given time is displayed using three-dimensional, two-dimensional, and contour graphs by assigning unique values to the constants in the found solutions. The technique applied is a practical and trustworthy way to solve non-linear evolution equations. It is a technique that is suggested for figuring out how to solve non-linear evolution equations (NLEEs).

Keywords: Non-linear evolution equations, exact solution, traveling wave solution, the modified sub-equation method, Kuramoto–Sivashinsky equation

[This article belongs to Research & Reviews: Discrete Mathematical Structures ]

How to cite this article:
Hulya durur. Exact Solutions of Kuramoto–Sivashinsky Equation Using Modified Sub-equation Method. Research & Reviews: Discrete Mathematical Structures. 2024; 11(02):25-33.
How to cite this URL:
Hulya durur. Exact Solutions of Kuramoto–Sivashinsky Equation Using Modified Sub-equation Method. Research & Reviews: Discrete Mathematical Structures. 2024; 11(02):25-33. Available from: https://journals.stmjournals.com/rrdms/article=2024/view=0


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Regular Issue Subscription Original Research
Volume 11
Issue 02
Received 30/08/2024
Accepted 31/08/2024
Published 31/08/2024
Publication Time 1 Days
59

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