Optical solutions to time-fractional improved (2+1)-dimensional nonlinear Schrödinger equation in optical fibers
Abstract In this paper, we investigate the time-fractional improved (2+1)-dimensional nonlinear Schrödinger equation with power-law nonlinearity, group-velocity dispersion, and spatio-temporal dispersion in nonlinear optics. This equation models the propagation of optical pulses in nonlinear optical...
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| Language: | English |
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Nature Portfolio
2025-08-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-025-14818-y |
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| author | Muhammad Amin S. Murad Ali. H. Tedjani Zhao Li Ejaz Hussain |
| author_facet | Muhammad Amin S. Murad Ali. H. Tedjani Zhao Li Ejaz Hussain |
| author_sort | Muhammad Amin S. Murad |
| collection | DOAJ |
| description | Abstract In this paper, we investigate the time-fractional improved (2+1)-dimensional nonlinear Schrödinger equation with power-law nonlinearity, group-velocity dispersion, and spatio-temporal dispersion in nonlinear optics. This equation models the propagation of optical pulses in nonlinear optical fibers. We derive novel optical soliton solutions expressed through exponential and hyperbolic functions, which include bright, bell-shaped, wave, and singular solitons. To illustrate the characteristics of these solutions, we provide two-dimensional, three-dimensional, and contour plots that visualize the magnitude of the conformable improved (2+1)-dimensional nonlinear Schrödinger equation. By selecting suitable values for physical parameters, we demonstrate the diversity of soliton structures and their behaviors. Furthermore, we investigated the influence of the temporal parameter and the conformable fractional-order derivative on the behavior of soliton solutions. The results highlighted the effectiveness and versatility of the modified Kudryashov method in addressing both integer- and fractional-order differential equations, providing analytical solutions that deepen our insight into the dynamics of complex optical systems. These results contribute to the advancement of soliton theory in nonlinear optics and mathematical physics. |
| format | Article |
| id | doaj-art-35aa6e3c2d774928997dde88ec008b09 |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-35aa6e3c2d774928997dde88ec008b092025-08-20T03:42:57ZengNature PortfolioScientific Reports2045-23222025-08-0115111310.1038/s41598-025-14818-yOptical solutions to time-fractional improved (2+1)-dimensional nonlinear Schrödinger equation in optical fibersMuhammad Amin S. Murad0Ali. H. Tedjani1Zhao Li2Ejaz Hussain3Department of Mathematics, College of Science, University of DuhokDepartment of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU)College of Computer Science, Chengdu UniversityDepartment of Mathematics, University of the Punjab, Quaid-e-Azam CampusAbstract In this paper, we investigate the time-fractional improved (2+1)-dimensional nonlinear Schrödinger equation with power-law nonlinearity, group-velocity dispersion, and spatio-temporal dispersion in nonlinear optics. This equation models the propagation of optical pulses in nonlinear optical fibers. We derive novel optical soliton solutions expressed through exponential and hyperbolic functions, which include bright, bell-shaped, wave, and singular solitons. To illustrate the characteristics of these solutions, we provide two-dimensional, three-dimensional, and contour plots that visualize the magnitude of the conformable improved (2+1)-dimensional nonlinear Schrödinger equation. By selecting suitable values for physical parameters, we demonstrate the diversity of soliton structures and their behaviors. Furthermore, we investigated the influence of the temporal parameter and the conformable fractional-order derivative on the behavior of soliton solutions. The results highlighted the effectiveness and versatility of the modified Kudryashov method in addressing both integer- and fractional-order differential equations, providing analytical solutions that deepen our insight into the dynamics of complex optical systems. These results contribute to the advancement of soliton theory in nonlinear optics and mathematical physics.https://doi.org/10.1038/s41598-025-14818-yNew Kudryashov approachTime-fractional improved (2+1)-dimensional nonlinear Schrödinger equationNonlinear optical |
| spellingShingle | Muhammad Amin S. Murad Ali. H. Tedjani Zhao Li Ejaz Hussain Optical solutions to time-fractional improved (2+1)-dimensional nonlinear Schrödinger equation in optical fibers Scientific Reports New Kudryashov approach Time-fractional improved (2+1)-dimensional nonlinear Schrödinger equation Nonlinear optical |
| title | Optical solutions to time-fractional improved (2+1)-dimensional nonlinear Schrödinger equation in optical fibers |
| title_full | Optical solutions to time-fractional improved (2+1)-dimensional nonlinear Schrödinger equation in optical fibers |
| title_fullStr | Optical solutions to time-fractional improved (2+1)-dimensional nonlinear Schrödinger equation in optical fibers |
| title_full_unstemmed | Optical solutions to time-fractional improved (2+1)-dimensional nonlinear Schrödinger equation in optical fibers |
| title_short | Optical solutions to time-fractional improved (2+1)-dimensional nonlinear Schrödinger equation in optical fibers |
| title_sort | optical solutions to time fractional improved 2 1 dimensional nonlinear schrodinger equation in optical fibers |
| topic | New Kudryashov approach Time-fractional improved (2+1)-dimensional nonlinear Schrödinger equation Nonlinear optical |
| url | https://doi.org/10.1038/s41598-025-14818-y |
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