Analysis of lump solutions and modulation instability to fractional complex Ginzburg–Landau equation arise in optical fibers
In this paper, the fractional complex Ginzburg–Landau equation (CGLE) with Kerr law in nonlinear optics, which simulates soliton propagation in various waveguides in the presence of a detuning component which comes from the nonlinear Schrödinger equation (NLSE) with the inclusion of the growth and d...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-10-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379723007842 |
| _version_ | 1797660512052314112 |
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| author | Sonia Akram Jamshad Ahmad Shafqat-Ur-Rehman Shalan Alkarni Nehad Ali Shah |
| author_facet | Sonia Akram Jamshad Ahmad Shafqat-Ur-Rehman Shalan Alkarni Nehad Ali Shah |
| author_sort | Sonia Akram |
| collection | DOAJ |
| description | In this paper, the fractional complex Ginzburg–Landau equation (CGLE) with Kerr law in nonlinear optics, which simulates soliton propagation in various waveguides in the presence of a detuning component which comes from the nonlinear Schrödinger equation (NLSE) with the inclusion of the growth and damping terms, is examined. The Hirota bilinear method is exercised to retrieve lump solitons such as the 1-kink wave solution, 2-kink wave solution, double exponential wave solution, and homoclinic breather wave solution to the model. We also scrutinize some M-shaped solutions in the forms of M-shaped rational solutions and the M-shaped interaction with rogue and kink waves. In addition, the instability modulation and gain spectra of the CGLE are examined. The originality of the study lies in the secured outcomes, which were never before produced and effectively balance the nonlinear physical aspects. To illustrate the dynamic of these waves, some of the solutions are sketched in three-dimensional, two-dimensional, contour, and density plots. The produced results are encouraging which can be used to describe the phenomena occurring in nonlinear optical or plasma physics. The computed solutions demonstrate that the suggested approaches are skillful, categorical, consistent, and effective in identifying exact solutions to a variety of complicated nonlinear problems that have recently arisen in nonlinear optics, applied sciences, and engineering. |
| first_indexed | 2024-03-11T18:30:58Z |
| format | Article |
| id | doaj.art-6d5c0a90b9db488695048bc96f7fbb14 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-03-11T18:30:58Z |
| publishDate | 2023-10-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-6d5c0a90b9db488695048bc96f7fbb142023-10-13T11:04:21ZengElsevierResults in Physics2211-37972023-10-0153106991Analysis of lump solutions and modulation instability to fractional complex Ginzburg–Landau equation arise in optical fibersSonia Akram0Jamshad Ahmad1 Shafqat-Ur-Rehman2Shalan Alkarni3Nehad Ali Shah4Department of Mathematics, Faculty of Science, University of Gujrat, 50700, PakistanDepartment of Mathematics, Faculty of Science, University of Gujrat, 50700, Pakistan; Corresponding author.Department of Mathematics and Statistics, Grand Asian University, Sialkot, 51310, PakistanDepartment of Mathematics, College of Science, King Saud University, P.O. Box-2455 Riyadh 11451, Saudi ArabiaDepartment of Mechanical Engineering, Sejong University, Seoul 05006, South KoreaIn this paper, the fractional complex Ginzburg–Landau equation (CGLE) with Kerr law in nonlinear optics, which simulates soliton propagation in various waveguides in the presence of a detuning component which comes from the nonlinear Schrödinger equation (NLSE) with the inclusion of the growth and damping terms, is examined. The Hirota bilinear method is exercised to retrieve lump solitons such as the 1-kink wave solution, 2-kink wave solution, double exponential wave solution, and homoclinic breather wave solution to the model. We also scrutinize some M-shaped solutions in the forms of M-shaped rational solutions and the M-shaped interaction with rogue and kink waves. In addition, the instability modulation and gain spectra of the CGLE are examined. The originality of the study lies in the secured outcomes, which were never before produced and effectively balance the nonlinear physical aspects. To illustrate the dynamic of these waves, some of the solutions are sketched in three-dimensional, two-dimensional, contour, and density plots. The produced results are encouraging which can be used to describe the phenomena occurring in nonlinear optical or plasma physics. The computed solutions demonstrate that the suggested approaches are skillful, categorical, consistent, and effective in identifying exact solutions to a variety of complicated nonlinear problems that have recently arisen in nonlinear optics, applied sciences, and engineering.http://www.sciencedirect.com/science/article/pii/S2211379723007842Complex Ginzburg–Landau modelHirota bilinear methodTruncated M-fractional derivativeRational solitonsStability analysis |
| spellingShingle | Sonia Akram Jamshad Ahmad Shafqat-Ur-Rehman Shalan Alkarni Nehad Ali Shah Analysis of lump solutions and modulation instability to fractional complex Ginzburg–Landau equation arise in optical fibers Results in Physics Complex Ginzburg–Landau model Hirota bilinear method Truncated M-fractional derivative Rational solitons Stability analysis |
| title | Analysis of lump solutions and modulation instability to fractional complex Ginzburg–Landau equation arise in optical fibers |
| title_full | Analysis of lump solutions and modulation instability to fractional complex Ginzburg–Landau equation arise in optical fibers |
| title_fullStr | Analysis of lump solutions and modulation instability to fractional complex Ginzburg–Landau equation arise in optical fibers |
| title_full_unstemmed | Analysis of lump solutions and modulation instability to fractional complex Ginzburg–Landau equation arise in optical fibers |
| title_short | Analysis of lump solutions and modulation instability to fractional complex Ginzburg–Landau equation arise in optical fibers |
| title_sort | analysis of lump solutions and modulation instability to fractional complex ginzburg landau equation arise in optical fibers |
| topic | Complex Ginzburg–Landau model Hirota bilinear method Truncated M-fractional derivative Rational solitons Stability analysis |
| url | http://www.sciencedirect.com/science/article/pii/S2211379723007842 |
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