Hulya durur,
- Associate Professor,, Department of Computer Engineering, Faculty of Engineering, Ardahan, Ardahan, Turkey
Abstract
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Equations for nonlinear evolution are mathematical representations of physical phenomena.
The viewpoint of many natural processes is enhanced by the physical interpretation of the
solution functions of these equations. Numerous scientists who acknowledge this truth have
focused their research efforts in 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 nonlinear 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. For scientists that study shock wave structure and asymptotic
behavior, these solutions play a significant role. 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 3-
dimensional, 2-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
nonlinear evolution equations. It is a technique that is suggested for figuring out how to solve
nonlinear evolution equations (NLEEs).
Keywords: Nonlinear evolution equations, exact solution, traveling wave solution, the modified sub equation method, Kuramoto-Sivashinsky equation.
[This article belongs to Research & Reviews: Discrete Mathematical Structures (rrdms)]
Hulya durur. Exact solutions of Kuramoto-Sivashinsky equation using modified sub equation method. Research & Reviews: Discrete Mathematical Structures. 2024; 11(02):25-32.
Hulya durur. Exact solutions of Kuramoto-Sivashinsky equation using modified sub equation method. Research & Reviews: Discrete Mathematical Structures. 2024; 11(02):25-32. Available from: https://journals.stmjournals.com/rrdms/article=2024/view=0
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Research & Reviews: Discrete Mathematical Structures
| Volume | 11 |
| Issue | 02 |
| Received | 30/08/2024 |
| Accepted | 31/08/2024 |
| Published | 31/08/2024 |