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Some novel optical pulses in hydrodynamical nonlinear complex equation using M-truncated fractional derivative
Esin Ilhan1, Shafqat Ur Rehman2, Muhammad Bilal3
1Faculty of Engineering and Architecture, Kirsehir Ahi Evran University, Kirsehir, Turkey.
Scientific Reports
|September 1, 2025
Summary
Researchers explored complex Ginzburg-Landau equation wave dynamics using analytical methods. Novel soliton solutions were derived, revealing diverse wave behaviors crucial for physical oceanography and nonlinear equation studies.
Area of Science:
- Nonlinear Dynamics
- Mathematical Physics
- Physical Oceanography
Background:
- The complex Ginzburg-Landau (CGL) equation models wave propagation in diverse physical systems.
- Understanding soliton solutions and dynamic wave structures is critical for these systems.
Purpose of the Study:
- To investigate soliton solutions and dynamic wave structures within the CGL equation.
- To derive novel closed-form solutions using advanced analytical techniques.
- To explore the behavior of these solutions under fractional derivative influence.
Main Methods:
- Employed the Kumar-Malik method, generalized Arnous method, and energy balance method.
- Derived exact solutions expressed via hyperbolic, trigonometric, and Jacobi elliptic functions.
- Utilized Mathematica for verification via back-substitution and generated plots for visualization.
Main Results:
- Discovered new families of exact solitary waves and diverse soliton solutions.
- Observed multi-wave solitons, complex solitons, singular solitons, and periodic waves.
- Visualized solution behaviors, including dark-wave and bright-wave profiles, with M-truncated fractional derivatives.
Conclusions:
- The study provides significant insights into wave dynamics in physical oceanography.
- The derived novel solutions offer a foundation for future research on nonlinear equations.
- This work enhances the understanding of solitonic phenomena in complex systems.
Keywords:
Complex Ginzburg–Landau equationEnergy balance methodFractional derivativeGeneralized Arnous methodKumar-Malik methodSoliton solutionsMore Related Videos
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