Analytical and numerical treatments for the Kaup–Newell dynamical equation
The present paper examines both analytically and numerically the Kaup–Newell equation being an important class of nonlinear Schrödinger equations with lots of applications in optical fibers. The Riccati equation method is employed for the analytical study and revealed quite a number of interesting s...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2020-12-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379720319203 |
| _version_ | 1818599401264775168 |
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| author | A.A. Al Qarni A.A. Alshaery H.O. Bakodah M.A. Banaja A.S.H.F. Mohammed |
| author_facet | A.A. Al Qarni A.A. Alshaery H.O. Bakodah M.A. Banaja A.S.H.F. Mohammed |
| author_sort | A.A. Al Qarni |
| collection | DOAJ |
| description | The present paper examines both analytically and numerically the Kaup–Newell equation being an important class of nonlinear Schrödinger equations with lots of applications in optical fibers. The Riccati equation method is employed for the analytical study and revealed quite a number of interesting soliton solutions including bright-singular, dark-singular, and singular soliton solutions to mention a few; while the Adomian’s improved decomposition method is adopted on the hand for the numerical investigation. More, since bright, dark and singular solitons are very important types of solitons that arising in laminar jet and nonlinear dispersive media; we considered certain hyperbolic ansatz to construct exact soliton solutions for the numerical comparative study. The presented numerical scheme thus validated the exact analytical solutions and turned out to possess a high-level of accuracy. We finally provided some comparison tables and depictions to support the reported results after inviting the classical Adomian’s method to assess the devised numerical technique. |
| first_indexed | 2024-12-16T12:19:00Z |
| format | Article |
| id | doaj.art-118e31f9ea024066b38fd20a7243034d |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-12-16T12:19:00Z |
| publishDate | 2020-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-118e31f9ea024066b38fd20a7243034d2022-12-21T22:32:01ZengElsevierResults in Physics2211-37972020-12-0119103461Analytical and numerical treatments for the Kaup–Newell dynamical equationA.A. Al Qarni0A.A. Alshaery1H.O. Bakodah2M.A. Banaja3A.S.H.F. Mohammed4Department of Mathematics, College of Science, University of Bisha, P.O. Box 551, Bisha 61922, Saudi Arabia; Department of Mathematics, College of Science, King Abdulaziz University, Jeddah, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah, Saudi Arabia; Corresponding author.Department of Mathematics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah, Saudi ArabiaDepartment of Mathematics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah, Saudi ArabiaThe present paper examines both analytically and numerically the Kaup–Newell equation being an important class of nonlinear Schrödinger equations with lots of applications in optical fibers. The Riccati equation method is employed for the analytical study and revealed quite a number of interesting soliton solutions including bright-singular, dark-singular, and singular soliton solutions to mention a few; while the Adomian’s improved decomposition method is adopted on the hand for the numerical investigation. More, since bright, dark and singular solitons are very important types of solitons that arising in laminar jet and nonlinear dispersive media; we considered certain hyperbolic ansatz to construct exact soliton solutions for the numerical comparative study. The presented numerical scheme thus validated the exact analytical solutions and turned out to possess a high-level of accuracy. We finally provided some comparison tables and depictions to support the reported results after inviting the classical Adomian’s method to assess the devised numerical technique.http://www.sciencedirect.com/science/article/pii/S2211379720319203Riccati equation methodImproved Adomian decomposition methodKaup–Newell equationNonlinear Schrödinger equation |
| spellingShingle | A.A. Al Qarni A.A. Alshaery H.O. Bakodah M.A. Banaja A.S.H.F. Mohammed Analytical and numerical treatments for the Kaup–Newell dynamical equation Results in Physics Riccati equation method Improved Adomian decomposition method Kaup–Newell equation Nonlinear Schrödinger equation |
| title | Analytical and numerical treatments for the Kaup–Newell dynamical equation |
| title_full | Analytical and numerical treatments for the Kaup–Newell dynamical equation |
| title_fullStr | Analytical and numerical treatments for the Kaup–Newell dynamical equation |
| title_full_unstemmed | Analytical and numerical treatments for the Kaup–Newell dynamical equation |
| title_short | Analytical and numerical treatments for the Kaup–Newell dynamical equation |
| title_sort | analytical and numerical treatments for the kaup newell dynamical equation |
| topic | Riccati equation method Improved Adomian decomposition method Kaup–Newell equation Nonlinear Schrödinger equation |
| url | http://www.sciencedirect.com/science/article/pii/S2211379720319203 |
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