Exploring Wave Interactions and Conserved Quantities of KdV–Caudrey–Dodd–Gibbon Equation Using Lie Theory
Abstract
:1. Introduction
2. Preliminaries
The Idea of the Proposed Method
- Type 1: When ,
- Type 2: When , ,
- Type 3: When , ,
- Type 4: When , ,
- Type 5: When , ,
- Type 6: When , ,
- Type 7: When ,
- Type 8: When , ,
- Type 9: When ,
3. Symmetry Analysis of Equation (1)
4. Traveling Waves of Equation (1) by Abelian Algebra
- For Family 1: When ,
- For Family 2: When , ,
- For Family 3: When , ,
- For Family 4: When , ,
- For Family 5: When , ,
- For Family 6: When , ,
- For Family 7: When ,
- For Family 8: When and
- For Family 9: When ,
- For Family 10: When , ,
5. Graphical Representations
- Figure 1 demonstrates the 3D and 2D versions of for , , , , , and .
- The plotted curves of can be seen for , , , , , and . Their corresponding values are shown in Figure 2.
- The graphics of for , , , , and are shown in Figure 3. It shows the effect of the velocity of the soliton.
- Furthermore, Figure 4 shows the 3D and 2D graph of for , , , , , and .
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Almusawa, H.; Jhangeer, A. Exploring Wave Interactions and Conserved Quantities of KdV–Caudrey–Dodd–Gibbon Equation Using Lie Theory. Mathematics 2024, 12, 2242. https://doi.org/10.3390/math12142242
Almusawa H, Jhangeer A. Exploring Wave Interactions and Conserved Quantities of KdV–Caudrey–Dodd–Gibbon Equation Using Lie Theory. Mathematics. 2024; 12(14):2242. https://doi.org/10.3390/math12142242
Chicago/Turabian StyleAlmusawa, Hassan, and Adil Jhangeer. 2024. "Exploring Wave Interactions and Conserved Quantities of KdV–Caudrey–Dodd–Gibbon Equation Using Lie Theory" Mathematics 12, no. 14: 2242. https://doi.org/10.3390/math12142242
APA StyleAlmusawa, H., & Jhangeer, A. (2024). Exploring Wave Interactions and Conserved Quantities of KdV–Caudrey–Dodd–Gibbon Equation Using Lie Theory. Mathematics, 12(14), 2242. https://doi.org/10.3390/math12142242