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Journals / Mathematical Modelling and Numerical Simulation with Applications / 2022 / Cilt: 2 Sayı: 3

The investigation of several soliton solutions to the complex Ginzburg-Landau model with Kerr law nonlinearity

Muhammad Abubakar ISAH
Asıf YOKUS
Pages
147–163
Publication Date
2022-09-30
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The obtained solutions' 2-dimensional, 3-dimensional, and contour plots are shown.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This work investigates the complex Ginzburg-Landau equation (CGLE) with Kerr law in nonlinear optics, which represents soliton propagation in the presence of a detuning factor.
📊
Key Findings & Data:The $\varphi^{6}$-model expansion approach is used to find optical solitons such as dark, bright, singular, and periodic as well as the combined soliton solutions to the model.
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Conclusion & Impact:The obtained solutions' 2-dimensional, 3-dimensional, and contour plots are shown.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:$\varphi^{6}$-model expansion method · complex Ginzburg-Landau equation · traveling wave solution

Abstract

This work investigates the complex Ginzburg-Landau equation (CGLE) with Kerr law in nonlinear optics, which represents soliton propagation in the presence of a detuning factor. The $\varphi^{6}$-model expansion approach is used to find optical solitons such as dark, bright, singular, and periodic as well as the combined soliton solutions to the model. The results presented in this study are intended to improve the CGLE's nonlinear dynamical characteristics, it might also assist in comprehending some of the physical implications of various nonlinear physics models. The hyperbolic sine, for example, appears in the calculation of the Roche limit and gravitational potential of a cylinder, while the hyperbolic cotangent appears in the Langevin function for magnetic polarization. The current research is frequently used to report a variety of fascinating physical phenomena, such as the Kerr law of non-linearity, which results from the fact that an external electric field causes non-harmonic motion of electrons bound in molecules, which causes nonlinear responses in a light wave in an optical fiber. The obtained solutions' 2-dimensional, 3-dimensional, and contour plots are shown.

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Cite This Article

ISAH, M. A., YOKUS, A. (2022). The investigation of several soliton solutions to the complex Ginzburg-Landau model with Kerr law nonlinearity. Mathematical Modelling and Numerical Simulation with Applications, Cilt: 2 Sayı: 3, 147–163. https://ajindex.com/articles/977623

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