Soliton Behaviours for the Conformable Space–Time Fractional Complex Ginzburg–Landau Equation in Optical Fibers
In this work, we investigate the conformable space−time fractional complex Ginzburg−Landau (GL) equation dominated by three types of nonlinear effects. These types of nonlinearity include Kerr law, power law, and dual-power law. The symmetry case in the GL equation due to the thr...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-02-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/12/2/219 |
| _version_ | 1817993424466345984 |
|---|---|
| author | Khalil S. Al-Ghafri |
| author_facet | Khalil S. Al-Ghafri |
| author_sort | Khalil S. Al-Ghafri |
| collection | DOAJ |
| description | In this work, we investigate the conformable space−time fractional complex Ginzburg−Landau (GL) equation dominated by three types of nonlinear effects. These types of nonlinearity include Kerr law, power law, and dual-power law. The symmetry case in the GL equation due to the three types of nonlinearity is presented. The governing model is dealt with by a straightforward mathematical technique, where the fractional differential equation is reduced to a first-order nonlinear ordinary differential equation with solution expressed in the form of the Weierstrass elliptic function. The relation between the Weierstrass elliptic function and hyperbolic functions enables us to derive two types of optical soliton solutions, namely, bright and singular solitons. Restrictions for the validity of the optical soliton solutions are given. To shed light on the behaviour of solitons, the graphical illustrations of obtained solutions are represented for different values of various parameters. The symmetrical structure of some extracted solitons is deduced when the fractional derivative parameters for space and time are symmetric. |
| first_indexed | 2024-04-14T01:39:37Z |
| format | Article |
| id | doaj.art-a2190a56ab6a4d018ea9a607792909f4 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-14T01:39:37Z |
| publishDate | 2020-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-a2190a56ab6a4d018ea9a607792909f42022-12-22T02:19:49ZengMDPI AGSymmetry2073-89942020-02-0112221910.3390/sym12020219sym12020219Soliton Behaviours for the Conformable Space–Time Fractional Complex Ginzburg–Landau Equation in Optical FibersKhalil S. Al-Ghafri0Ministry of Higher Education, Ibri College of Applied Sciences, P.O. Box 14, Ibri 516, OmanIn this work, we investigate the conformable space−time fractional complex Ginzburg−Landau (GL) equation dominated by three types of nonlinear effects. These types of nonlinearity include Kerr law, power law, and dual-power law. The symmetry case in the GL equation due to the three types of nonlinearity is presented. The governing model is dealt with by a straightforward mathematical technique, where the fractional differential equation is reduced to a first-order nonlinear ordinary differential equation with solution expressed in the form of the Weierstrass elliptic function. The relation between the Weierstrass elliptic function and hyperbolic functions enables us to derive two types of optical soliton solutions, namely, bright and singular solitons. Restrictions for the validity of the optical soliton solutions are given. To shed light on the behaviour of solitons, the graphical illustrations of obtained solutions are represented for different values of various parameters. The symmetrical structure of some extracted solitons is deduced when the fractional derivative parameters for space and time are symmetric.https://www.mdpi.com/2073-8994/12/2/219optical solitonsginzburg–landau equationweierstrass elliptic function |
| spellingShingle | Khalil S. Al-Ghafri Soliton Behaviours for the Conformable Space–Time Fractional Complex Ginzburg–Landau Equation in Optical Fibers Symmetry optical solitons ginzburg–landau equation weierstrass elliptic function |
| title | Soliton Behaviours for the Conformable Space–Time Fractional Complex Ginzburg–Landau Equation in Optical Fibers |
| title_full | Soliton Behaviours for the Conformable Space–Time Fractional Complex Ginzburg–Landau Equation in Optical Fibers |
| title_fullStr | Soliton Behaviours for the Conformable Space–Time Fractional Complex Ginzburg–Landau Equation in Optical Fibers |
| title_full_unstemmed | Soliton Behaviours for the Conformable Space–Time Fractional Complex Ginzburg–Landau Equation in Optical Fibers |
| title_short | Soliton Behaviours for the Conformable Space–Time Fractional Complex Ginzburg–Landau Equation in Optical Fibers |
| title_sort | soliton behaviours for the conformable space time fractional complex ginzburg landau equation in optical fibers |
| topic | optical solitons ginzburg–landau equation weierstrass elliptic function |
| url | https://www.mdpi.com/2073-8994/12/2/219 |
| work_keys_str_mv | AT khalilsalghafri solitonbehavioursfortheconformablespacetimefractionalcomplexginzburglandauequationinopticalfibers |