The Discovery of Truncated M-Fractional Exact Solitons and a Qualitative Analysis of the Generalized Bretherton Model
Abstract
:1. Introduction
Truncated M-Fractional Derivative (TMFD)
2. Model Presentation and Its Mathematical Treatment
3. Explanation and Application of the EShGEE Method
3.1. Description
- Stage 1:
- Stage 2:
- Stage 3:
- Stage 4:
3.2. Application to the EShGEE Scheme
- Set 1:
- Set 2:
- Set 3:
- Set 4:
- Set 5:
- Set 6:
4. Explanation of the Modified -Expansion Scheme
- Step 1:
- Step 2:
- Case 1: If , then
- Case 2: If , then
- Case 3: If and , then
- Step 3:
- Step 4:
Application
- Set 1:
- Set 2:
- Set 3:
- Set 4:
- Set 5:
- Set 6:
5. Graphical Explanation
6. Physical Interpretation
7. Stability Analysis
8. Modulation Instability (MI)
9. Results and Discussion
10. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Qawaqneh, H.; Hakami, K.H.; Altalbe, A.; Bayram, M. The Discovery of Truncated M-Fractional Exact Solitons and a Qualitative Analysis of the Generalized Bretherton Model. Mathematics 2024, 12, 2772. https://doi.org/10.3390/math12172772
Qawaqneh H, Hakami KH, Altalbe A, Bayram M. The Discovery of Truncated M-Fractional Exact Solitons and a Qualitative Analysis of the Generalized Bretherton Model. Mathematics. 2024; 12(17):2772. https://doi.org/10.3390/math12172772
Chicago/Turabian StyleQawaqneh, Haitham, Khalil Hadi Hakami, Ali Altalbe, and Mustafa Bayram. 2024. "The Discovery of Truncated M-Fractional Exact Solitons and a Qualitative Analysis of the Generalized Bretherton Model" Mathematics 12, no. 17: 2772. https://doi.org/10.3390/math12172772