Exploration of Soliton Solutions to the Special Korteweg–De Vries Equation with a Stability Analysis and Modulation Instability
Abstract
:1. Introduction
2. Presentation of Methods
2.1. Hirota Bilinear Method
2.2. Summary of Function Method
2.3. Description of the Sardar Sub-Equation Method
3. Breather Wave Soliton
4. Soliton Solutions
4.1. 1-Soliton Solutions
4.2. 2-Soliton Solutions
4.3. New Three-Wave Soliton
4.4. New Periodic-Wave
5. Exact Wave Solutions
5.1. Exact Siliton Solutions by Function Method
5.2. Exact Soliton Results via the Sardar Sub-Equation Method
6. Graphical Explanation
7. Stability Analysis
8. Modulation Instability (MI)
9. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Alomair, A.; Al Naim, A.S.; Bekir, A. Exploration of Soliton Solutions to the Special Korteweg–De Vries Equation with a Stability Analysis and Modulation Instability. Mathematics 2025, 13, 54. https://doi.org/10.3390/math13010054
Alomair A, Al Naim AS, Bekir A. Exploration of Soliton Solutions to the Special Korteweg–De Vries Equation with a Stability Analysis and Modulation Instability. Mathematics. 2025; 13(1):54. https://doi.org/10.3390/math13010054
Chicago/Turabian StyleAlomair, Abdulrahman, Abdulaziz S. Al Naim, and Ahmet Bekir. 2025. "Exploration of Soliton Solutions to the Special Korteweg–De Vries Equation with a Stability Analysis and Modulation Instability" Mathematics 13, no. 1: 54. https://doi.org/10.3390/math13010054
APA StyleAlomair, A., Al Naim, A. S., & Bekir, A. (2025). Exploration of Soliton Solutions to the Special Korteweg–De Vries Equation with a Stability Analysis and Modulation Instability. Mathematics, 13(1), 54. https://doi.org/10.3390/math13010054