Soliton solutions, bifurcations, and sensitivity analysis to the higher-order nonlinear fractional Schrödinger equation in optical fibers
In this article, we present new exact soliton solutions for the space-time fractional higher-order nonlinear Schrödinger equation, which describes the propagation of ultra-short pulses in nonlinear optical fibers. We apply a traveling wave transformation with the Beta derivative to convert the nonli...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-03-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124004431 |
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| author | Md. Al Amin M. Ali Akbar M. Ashrafuzzaman Khan Md. Sagib |
| author_facet | Md. Al Amin M. Ali Akbar M. Ashrafuzzaman Khan Md. Sagib |
| author_sort | Md. Al Amin |
| collection | DOAJ |
| description | In this article, we present new exact soliton solutions for the space-time fractional higher-order nonlinear Schrödinger equation, which describes the propagation of ultra-short pulses in nonlinear optical fibers. We apply a traveling wave transformation with the Beta derivative to convert the nonlinear fractional differential equation into a standard nonlinear differential equation. To find the exact analytical solutions, we implement the extended Riccati equation method, which led to a variety of soliton and soliton-like solutions, including trigonometric, hyperbolic, and rational functions. The graphical representations of these solutions show different physical forms, such as kink, periodic, bright bell, and dark bell structures. Additionally, we used planar dynamical systems theory to investigate the bifurcation phenomena in the derived system. A detailed sensitivity analysis was also performed on the dynamical system utilizing the Runge-Kutta method. These exact solitons play a vital role in understanding wave propagation and are essential for validating both numerical simulations and experimental findings in areas such as quantum mechanics, nonlinear optics and engineering. |
| format | Article |
| id | doaj-art-3ff03b09b89f441b9e8cc8f38da4c97c |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-3ff03b09b89f441b9e8cc8f38da4c97c2025-01-08T04:53:45ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-03-0113101057Soliton solutions, bifurcations, and sensitivity analysis to the higher-order nonlinear fractional Schrödinger equation in optical fibersMd. Al Amin0M. Ali Akbar1M. Ashrafuzzaman Khan2Md. Sagib3Department of Mathematics, Hajee Mohammad Danesh Science and Technology University, Dinajpur, BangladeshDepartment of Applied Mathematics, University of Rajshahi, Bangladesh; Corresponding author.Department of Applied Mathematics, University of Rajshahi, BangladeshDepartment of Mathematics, Hajee Mohammad Danesh Science and Technology University, Dinajpur, BangladeshIn this article, we present new exact soliton solutions for the space-time fractional higher-order nonlinear Schrödinger equation, which describes the propagation of ultra-short pulses in nonlinear optical fibers. We apply a traveling wave transformation with the Beta derivative to convert the nonlinear fractional differential equation into a standard nonlinear differential equation. To find the exact analytical solutions, we implement the extended Riccati equation method, which led to a variety of soliton and soliton-like solutions, including trigonometric, hyperbolic, and rational functions. The graphical representations of these solutions show different physical forms, such as kink, periodic, bright bell, and dark bell structures. Additionally, we used planar dynamical systems theory to investigate the bifurcation phenomena in the derived system. A detailed sensitivity analysis was also performed on the dynamical system utilizing the Runge-Kutta method. These exact solitons play a vital role in understanding wave propagation and are essential for validating both numerical simulations and experimental findings in areas such as quantum mechanics, nonlinear optics and engineering.http://www.sciencedirect.com/science/article/pii/S2666818124004431Space time-fractional higher order nonlinear schrödinger equationBeta derivativeExtended Riccati equation methodOptical solitonsBifurcation analysis and sensitivity analysis |
| spellingShingle | Md. Al Amin M. Ali Akbar M. Ashrafuzzaman Khan Md. Sagib Soliton solutions, bifurcations, and sensitivity analysis to the higher-order nonlinear fractional Schrödinger equation in optical fibers Partial Differential Equations in Applied Mathematics Space time-fractional higher order nonlinear schrödinger equation Beta derivative Extended Riccati equation method Optical solitons Bifurcation analysis and sensitivity analysis |
| title | Soliton solutions, bifurcations, and sensitivity analysis to the higher-order nonlinear fractional Schrödinger equation in optical fibers |
| title_full | Soliton solutions, bifurcations, and sensitivity analysis to the higher-order nonlinear fractional Schrödinger equation in optical fibers |
| title_fullStr | Soliton solutions, bifurcations, and sensitivity analysis to the higher-order nonlinear fractional Schrödinger equation in optical fibers |
| title_full_unstemmed | Soliton solutions, bifurcations, and sensitivity analysis to the higher-order nonlinear fractional Schrödinger equation in optical fibers |
| title_short | Soliton solutions, bifurcations, and sensitivity analysis to the higher-order nonlinear fractional Schrödinger equation in optical fibers |
| title_sort | soliton solutions bifurcations and sensitivity analysis to the higher order nonlinear fractional schrodinger equation in optical fibers |
| topic | Space time-fractional higher order nonlinear schrödinger equation Beta derivative Extended Riccati equation method Optical solitons Bifurcation analysis and sensitivity analysis |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124004431 |
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