A study of variation in dynamical behavior of fractional complex Ginzburg-Landau model for different fractional operators
The fractional complex Ginzburg–Landau model is widely used in the description of wave propagation through optical transmission lines. It has many useful applications in the fields of telecommunications and nonlinear optics. This paper investigates the fractional effects of the complex Ginzburg–Land...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-09-01
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| Series: | Ain Shams Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090447923000096 |
| _version_ | 1797676275015352320 |
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| author | Ghazala Akram Saima Arshed Maasoomah Sadaf Kainat Farooq |
| author_facet | Ghazala Akram Saima Arshed Maasoomah Sadaf Kainat Farooq |
| author_sort | Ghazala Akram |
| collection | DOAJ |
| description | The fractional complex Ginzburg–Landau model is widely used in the description of wave propagation through optical transmission lines. It has many useful applications in the fields of telecommunications and nonlinear optics. This paper investigates the fractional effects of the complex Ginzburg–Landau model with quadratic–cubic, anti–cubic and generalized anti–cubic laws of nonlinearity by using generalized projective Riccati equation method. The variation in the traveling wave behavior of the governing model is examined for beta, conformable and M-truncated derivatives. Some constraint conditions are carried out during mathematical analysis, which are further used for evaluating the traveling wave solutions. The analytic solutions of the considered model are determined in terms of hyperbolic and trigonometric function solutions. Consequently, dark, bright, kink, bell-shaped and singular solitons are extracted. The reported solutions are presented using 2D and 3D graphs. These graphs are showing the fractional effects for different values of fractional parameter. The evolution of the wave profiles shows that the retrieved solitons become similar for all three definitions of fractional derivatives as the fractional parameter approaches unity. |
| first_indexed | 2024-03-11T22:26:37Z |
| format | Article |
| id | doaj.art-2ad3b79cc22d49a29e045144d08340cb |
| institution | Directory Open Access Journal |
| issn | 2090-4479 |
| language | English |
| last_indexed | 2024-03-11T22:26:37Z |
| publishDate | 2023-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Ain Shams Engineering Journal |
| spelling | doaj.art-2ad3b79cc22d49a29e045144d08340cb2023-09-24T05:14:50ZengElsevierAin Shams Engineering Journal2090-44792023-09-01149102120A study of variation in dynamical behavior of fractional complex Ginzburg-Landau model for different fractional operatorsGhazala Akram0Saima Arshed1Maasoomah Sadaf2Kainat Farooq3Department of Mathematics, University of the Punjab, Lahore 54590, PakistanDepartment of Mathematics, University of the Punjab, Lahore 54590, PakistanDepartment of Mathematics, University of the Punjab, Lahore 54590, PakistanDepartment of Mathematics, University of the Punjab, Lahore 54590, PakistanThe fractional complex Ginzburg–Landau model is widely used in the description of wave propagation through optical transmission lines. It has many useful applications in the fields of telecommunications and nonlinear optics. This paper investigates the fractional effects of the complex Ginzburg–Landau model with quadratic–cubic, anti–cubic and generalized anti–cubic laws of nonlinearity by using generalized projective Riccati equation method. The variation in the traveling wave behavior of the governing model is examined for beta, conformable and M-truncated derivatives. Some constraint conditions are carried out during mathematical analysis, which are further used for evaluating the traveling wave solutions. The analytic solutions of the considered model are determined in terms of hyperbolic and trigonometric function solutions. Consequently, dark, bright, kink, bell-shaped and singular solitons are extracted. The reported solutions are presented using 2D and 3D graphs. These graphs are showing the fractional effects for different values of fractional parameter. The evolution of the wave profiles shows that the retrieved solitons become similar for all three definitions of fractional derivatives as the fractional parameter approaches unity.http://www.sciencedirect.com/science/article/pii/S2090447923000096Complex Ginzburg-Landau equationGeneralize projective Riccati equation methodQuadratic–cubic lawNonlinear wavesAnti-cubic lawGeneralized anti-cubic law |
| spellingShingle | Ghazala Akram Saima Arshed Maasoomah Sadaf Kainat Farooq A study of variation in dynamical behavior of fractional complex Ginzburg-Landau model for different fractional operators Ain Shams Engineering Journal Complex Ginzburg-Landau equation Generalize projective Riccati equation method Quadratic–cubic law Nonlinear waves Anti-cubic law Generalized anti-cubic law |
| title | A study of variation in dynamical behavior of fractional complex Ginzburg-Landau model for different fractional operators |
| title_full | A study of variation in dynamical behavior of fractional complex Ginzburg-Landau model for different fractional operators |
| title_fullStr | A study of variation in dynamical behavior of fractional complex Ginzburg-Landau model for different fractional operators |
| title_full_unstemmed | A study of variation in dynamical behavior of fractional complex Ginzburg-Landau model for different fractional operators |
| title_short | A study of variation in dynamical behavior of fractional complex Ginzburg-Landau model for different fractional operators |
| title_sort | study of variation in dynamical behavior of fractional complex ginzburg landau model for different fractional operators |
| topic | Complex Ginzburg-Landau equation Generalize projective Riccati equation method Quadratic–cubic law Nonlinear waves Anti-cubic law Generalized anti-cubic law |
| url | http://www.sciencedirect.com/science/article/pii/S2090447923000096 |
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