Analysis Modulation Instability and Parametric Effect on Soliton Solutions for M-Fractional Landau–Ginzburg–Higgs (LGH) Equation Through Two Analytic Methods
Abstract
1. Introduction
2. Fractional Derivative
- i.
- .
- ii.
- .
- iii.
- .
- iv.
- ; here, is an arbitrary constant.
- v.
- .
3. Analytical Method
3.1. Modified F-Expansion Method
- If .
- If .
- If .
- If .
- If .
- If .
- If .
- If .
- If .
- If .
- If .
- If .
3.2. Newly Improved Kudryashov’s Method
4. Soliton Solutions of M-Fractional Landau–Ginzburg–Higgs Equation
4.1. Application of the Modified F-Expansion Method
4.2. Application of the Newly Improved Kudryashov’s Method
5. Figure Analysis
5.1. Figure Analysis of the Modified F-Expansion Method
5.2. Figure Analysis of the Newly Improved Kudryashov’s Method
6. Modulation Instability
7. Comparison and Novelty of This Work
7.1. Comparison with the Existing Works
7.2. Novelty of This Work
8. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Figure Type | Corresponding Equation | Parameter Values |
---|---|---|
Anti-kink soliton | Equation (11) | . |
Kink soliton | Equation (11) | . |
Interaction between anti-kink and periodic lump soliton | Equation (14) | . |
Periodic linked-lump soliton | Equation (14) | . |
Interaction between anti-kink and periodic lump soliton | Equation (14) | . |
Interaction between anti-kink and periodic lump soliton. | Equation (14) | . |
Singular soliton | Equation (24) | . |
Bright periodic soliton | Equation (30) | . |
Periodic multi-lump soliton | Equation (30) | . |
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Abdalla, M.; Roshid, M.M.; Uddin, M.; Ullah, M.S. Analysis Modulation Instability and Parametric Effect on Soliton Solutions for M-Fractional Landau–Ginzburg–Higgs (LGH) Equation Through Two Analytic Methods. Fractal Fract. 2025, 9, 154. https://doi.org/10.3390/fractalfract9030154
Abdalla M, Roshid MM, Uddin M, Ullah MS. Analysis Modulation Instability and Parametric Effect on Soliton Solutions for M-Fractional Landau–Ginzburg–Higgs (LGH) Equation Through Two Analytic Methods. Fractal and Fractional. 2025; 9(3):154. https://doi.org/10.3390/fractalfract9030154
Chicago/Turabian StyleAbdalla, Mohamed, Md. Mamunur Roshid, Mahtab Uddin, and Mohammad Safi Ullah. 2025. "Analysis Modulation Instability and Parametric Effect on Soliton Solutions for M-Fractional Landau–Ginzburg–Higgs (LGH) Equation Through Two Analytic Methods" Fractal and Fractional 9, no. 3: 154. https://doi.org/10.3390/fractalfract9030154
APA StyleAbdalla, M., Roshid, M. M., Uddin, M., & Ullah, M. S. (2025). Analysis Modulation Instability and Parametric Effect on Soliton Solutions for M-Fractional Landau–Ginzburg–Higgs (LGH) Equation Through Two Analytic Methods. Fractal and Fractional, 9(3), 154. https://doi.org/10.3390/fractalfract9030154