An analytical investigation of nonlinear time-fractional Schrödinger and coupled Schrödinger–KdV equations
This study applies the Fractional Reduced Differential Transform Method (FRDTM) to solve two nonlinear fractional equations: the time-fractional Schrödinger equation (TFSE) and the coupled Schrödinger–KdV (Sch–KdV) equation, which are prominent in quantum mechanics, plasma physics, and wave propagat...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-03-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379725000312 |
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| author | Yogeshwari F. Patel Mohammad Izadi |
| author_facet | Yogeshwari F. Patel Mohammad Izadi |
| author_sort | Yogeshwari F. Patel |
| collection | DOAJ |
| description | This study applies the Fractional Reduced Differential Transform Method (FRDTM) to solve two nonlinear fractional equations: the time-fractional Schrödinger equation (TFSE) and the coupled Schrödinger–KdV (Sch–KdV) equation, which are prominent in quantum mechanics, plasma physics, and wave propagation studies. These equations model various wave phenomena, including dust-acoustic waves, electromagnetic waves, and Langmuir waves, in plasma physics. Using the Liouville–Caputo fractional derivative, FRDTM effectively incorporates nonlocality and memory effects. The solutions are derived as rapidly convergent infinite series with terms that are straightforward to compute, ensuring both accuracy and efficiency. Numerical examples highlight the method’s ability to closely approximate exact solutions, with graphical and tabular comparisons illustrating the effect of the fractional order on solution behavior and validating the approach through computed absolute errors. Additionally, discussions on the modulation instability of the models reinforce the robustness of FRDTM as a powerful tool for solving complex nonlinear fractional systems. |
| format | Article |
| id | doaj-art-4c83660a789e474192a6ad18162b3990 |
| institution | Kabale University |
| issn | 2211-3797 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj-art-4c83660a789e474192a6ad18162b39902025-02-09T05:00:04ZengElsevierResults in Physics2211-37972025-03-0170108137An analytical investigation of nonlinear time-fractional Schrödinger and coupled Schrödinger–KdV equationsYogeshwari F. Patel0Mohammad Izadi1Department of Mathematical Sciences, P D Patel Institute of Applied Sciences, Charotar University of Science and Technology, Changa, Anand, Gujarat 388421, IndiaDepartment of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran; Corresponding author.This study applies the Fractional Reduced Differential Transform Method (FRDTM) to solve two nonlinear fractional equations: the time-fractional Schrödinger equation (TFSE) and the coupled Schrödinger–KdV (Sch–KdV) equation, which are prominent in quantum mechanics, plasma physics, and wave propagation studies. These equations model various wave phenomena, including dust-acoustic waves, electromagnetic waves, and Langmuir waves, in plasma physics. Using the Liouville–Caputo fractional derivative, FRDTM effectively incorporates nonlocality and memory effects. The solutions are derived as rapidly convergent infinite series with terms that are straightforward to compute, ensuring both accuracy and efficiency. Numerical examples highlight the method’s ability to closely approximate exact solutions, with graphical and tabular comparisons illustrating the effect of the fractional order on solution behavior and validating the approach through computed absolute errors. Additionally, discussions on the modulation instability of the models reinforce the robustness of FRDTM as a powerful tool for solving complex nonlinear fractional systems.http://www.sciencedirect.com/science/article/pii/S2211379725000312Analytical solutionsFractional PDEsLiouville–Caputo fractional derivativeSchrödinger–KdV equationNonlinear Schrödinger equationModulational instability |
| spellingShingle | Yogeshwari F. Patel Mohammad Izadi An analytical investigation of nonlinear time-fractional Schrödinger and coupled Schrödinger–KdV equations Results in Physics Analytical solutions Fractional PDEs Liouville–Caputo fractional derivative Schrödinger–KdV equation Nonlinear Schrödinger equation Modulational instability |
| title | An analytical investigation of nonlinear time-fractional Schrödinger and coupled Schrödinger–KdV equations |
| title_full | An analytical investigation of nonlinear time-fractional Schrödinger and coupled Schrödinger–KdV equations |
| title_fullStr | An analytical investigation of nonlinear time-fractional Schrödinger and coupled Schrödinger–KdV equations |
| title_full_unstemmed | An analytical investigation of nonlinear time-fractional Schrödinger and coupled Schrödinger–KdV equations |
| title_short | An analytical investigation of nonlinear time-fractional Schrödinger and coupled Schrödinger–KdV equations |
| title_sort | analytical investigation of nonlinear time fractional schrodinger and coupled schrodinger kdv equations |
| topic | Analytical solutions Fractional PDEs Liouville–Caputo fractional derivative Schrödinger–KdV equation Nonlinear Schrödinger equation Modulational instability |
| url | http://www.sciencedirect.com/science/article/pii/S2211379725000312 |
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