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

Muhammad Abubakar Isah; Asıf Yokus

doi:10.53391/mmnsa.2022.012

EN

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

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.

Keywords

$\varphi^{6}$-model expansion method, complex Ginzburg-Landau equation, traveling wave solution, Kerr law nonlinearity

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Details

Primary Language

English

Subjects

Applied Mathematics

Journal Section

Research Article

Authors

Muhammad Abubakar Isah ^*
0000-0001-9129-5657
Türkiye

Asıf Yokus This is me
0000-0002-1460-8573
Türkiye

Publication Date

September 30, 2022

Submission Date

July 6, 2022

Acceptance Date

September 14, 2022

Published in Issue

Year 2022 Volume: 2 Number: 3

DOI

https://doi.org/10.53391/mmnsa.2022.012

IZ

https://izlik.org/JA62DC26ZY

APA

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, 2(3), 147-163. https://doi.org/10.53391/mmnsa.2022.012

AMA

1.Isah MA, Yokus A. The investigation of several soliton solutions to the complex Ginzburg-Landau model with Kerr law nonlinearity. MMNSA. 2022;2(3):147-163. doi:10.53391/mmnsa.2022.012

Chicago

Isah, Muhammad Abubakar, and Asıf Yokus. 2022. “The Investigation of Several Soliton Solutions to the Complex Ginzburg-Landau Model With Kerr Law Nonlinearity”. Mathematical Modelling and Numerical Simulation With Applications 2 (3): 147-63. https://doi.org/10.53391/mmnsa.2022.012.

EndNote

Isah MA, Yokus A (September 1, 2022) The investigation of several soliton solutions to the complex Ginzburg-Landau model with Kerr law nonlinearity. Mathematical Modelling and Numerical Simulation with Applications 2 3 147–163.

IEEE

[1]M. A. Isah and A. Yokus, “The investigation of several soliton solutions to the complex Ginzburg-Landau model with Kerr law nonlinearity”, MMNSA, vol. 2, no. 3, pp. 147–163, Sept. 2022, doi: 10.53391/mmnsa.2022.012.

ISNAD

Isah, Muhammad Abubakar - Yokus, Asıf. “The Investigation of Several Soliton Solutions to the Complex Ginzburg-Landau Model With Kerr Law Nonlinearity”. Mathematical Modelling and Numerical Simulation with Applications 2/3 (September 1, 2022): 147-163. https://doi.org/10.53391/mmnsa.2022.012.

JAMA

1.Isah MA, Yokus A. The investigation of several soliton solutions to the complex Ginzburg-Landau model with Kerr law nonlinearity. MMNSA. 2022;2:147–163.

MLA

Isah, Muhammad Abubakar, and Asıf Yokus. “The Investigation of Several Soliton Solutions to the Complex Ginzburg-Landau Model With Kerr Law Nonlinearity”. Mathematical Modelling and Numerical Simulation With Applications, vol. 2, no. 3, Sept. 2022, pp. 147-63, doi:10.53391/mmnsa.2022.012.

Vancouver

1.Muhammad Abubakar Isah, Asıf Yokus. The investigation of several soliton solutions to the complex Ginzburg-Landau model with Kerr law nonlinearity. MMNSA. 2022 Sep. 1;2(3):147-63. doi:10.53391/mmnsa.2022.012