The dynamical study of fractional complex coupled maccari system in nonlinear optics via two analytical approaches
In this work, the modified auxiliary equation method (MAEM) and the Riccati–Bernoulli sub-ODE method (RBM) are used to investigate the soliton solutions of the fractional complex coupled maccari system (FCCMS). Nonlinear partial differential equations (NLPDEs) can be transformed into a collection of...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-09-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379723005685 |
| _version_ | 1797682891177590784 |
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| author | Haiqa Ehsan Muhammad Abbas Magda Abd El-Rahman Mohamed R. Ali A.S. Hendy |
| author_facet | Haiqa Ehsan Muhammad Abbas Magda Abd El-Rahman Mohamed R. Ali A.S. Hendy |
| author_sort | Haiqa Ehsan |
| collection | DOAJ |
| description | In this work, the modified auxiliary equation method (MAEM) and the Riccati–Bernoulli sub-ODE method (RBM) are used to investigate the soliton solutions of the fractional complex coupled maccari system (FCCMS). Nonlinear partial differential equations (NLPDEs) can be transformed into a collection of algebraic equations by utilizing a travelling wave transformation, the MAEM, and the RBM. As a result, solutions to hyperbolic, trigonometric and rational functions with unconstrained parameters are obtained. The travelling wave solutions can also be used to generate the solitary wave solutions when the parameters are given particular values. There are several solutions that are modelled for different parameter combinations. We have developed a number of novel solutions, such as the kink, periodic, M-waved, W-shaped, bright soliton, dark soliton, and singular soliton solution. We simulate our figures in Mathematica and provide many 2D and 3D graphs to show how the beta derivative, M-truncated derivative and conformable derivative impacts the analytical solutions of the FCCMS.The results show how effectively the MAEM and RBM work together to extract solitons for fractional-order nonlinear evolution equations in science, technology, and engineering. |
| first_indexed | 2024-03-12T00:06:29Z |
| format | Article |
| id | doaj.art-bf2aaa8f0b7e49b1b04877f30ff63f12 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-03-12T00:06:29Z |
| publishDate | 2023-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-bf2aaa8f0b7e49b1b04877f30ff63f122023-09-17T04:56:11ZengElsevierResults in Physics2211-37972023-09-0152106775The dynamical study of fractional complex coupled maccari system in nonlinear optics via two analytical approachesHaiqa Ehsan0Muhammad Abbas1Magda Abd El-Rahman2Mohamed R. Ali3A.S. Hendy4Department of Mathematics, University of Sargodha, 40100 Sargodha, PakistanDepartment of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan; Corresponding authors.Department of Physics, College of Science, King Khalid University, Abha, 61413, Saudi ArabiaBasic Engineering Science Department, Benha Faculty of Engineering, Benha University, Benha, Egypt; Faculty of Engineering and Technology, Future University in Egypt, New Cairo, 11835, Egypt; Corresponding authors.Department of Computational Mathematics and Computer Science, Institute of Natural Sciences and Mathematics, Ural Federal University, 19 Mira St., 620002 Yekaterinburg, RussiaIn this work, the modified auxiliary equation method (MAEM) and the Riccati–Bernoulli sub-ODE method (RBM) are used to investigate the soliton solutions of the fractional complex coupled maccari system (FCCMS). Nonlinear partial differential equations (NLPDEs) can be transformed into a collection of algebraic equations by utilizing a travelling wave transformation, the MAEM, and the RBM. As a result, solutions to hyperbolic, trigonometric and rational functions with unconstrained parameters are obtained. The travelling wave solutions can also be used to generate the solitary wave solutions when the parameters are given particular values. There are several solutions that are modelled for different parameter combinations. We have developed a number of novel solutions, such as the kink, periodic, M-waved, W-shaped, bright soliton, dark soliton, and singular soliton solution. We simulate our figures in Mathematica and provide many 2D and 3D graphs to show how the beta derivative, M-truncated derivative and conformable derivative impacts the analytical solutions of the FCCMS.The results show how effectively the MAEM and RBM work together to extract solitons for fractional-order nonlinear evolution equations in science, technology, and engineering.http://www.sciencedirect.com/science/article/pii/S2211379723005685Fractional complex coupled maccari systemModified auxiliary equation methodRiccati–Bernoulli sub-ODE methodBeta-derivativeM-truncated derivativeConformable derivative |
| spellingShingle | Haiqa Ehsan Muhammad Abbas Magda Abd El-Rahman Mohamed R. Ali A.S. Hendy The dynamical study of fractional complex coupled maccari system in nonlinear optics via two analytical approaches Results in Physics Fractional complex coupled maccari system Modified auxiliary equation method Riccati–Bernoulli sub-ODE method Beta-derivative M-truncated derivative Conformable derivative |
| title | The dynamical study of fractional complex coupled maccari system in nonlinear optics via two analytical approaches |
| title_full | The dynamical study of fractional complex coupled maccari system in nonlinear optics via two analytical approaches |
| title_fullStr | The dynamical study of fractional complex coupled maccari system in nonlinear optics via two analytical approaches |
| title_full_unstemmed | The dynamical study of fractional complex coupled maccari system in nonlinear optics via two analytical approaches |
| title_short | The dynamical study of fractional complex coupled maccari system in nonlinear optics via two analytical approaches |
| title_sort | dynamical study of fractional complex coupled maccari system in nonlinear optics via two analytical approaches |
| topic | Fractional complex coupled maccari system Modified auxiliary equation method Riccati–Bernoulli sub-ODE method Beta-derivative M-truncated derivative Conformable derivative |
| url | http://www.sciencedirect.com/science/article/pii/S2211379723005685 |
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