Lie point symmetry infinitesimals, optimal system, power series solution, and modulational gain spectrum to the mathematical Noyes–Field model of nonlinear homogeneous oscillatory Belousov–Zhabotinsky reaction
Introduction:: The chemical oscillators are identified as open system that demonstrate periodic changes in the concentration of some reaction species as a result of intricate physico-chemical mechanisms which can lead to bi-stability, the occurrence of limit cycle attractors, the emergence of spiral...
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Elsevier
2023-01-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379722007379 |
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| author | Ebrahem A. Algehyne Magda Abd El-Rahman Waqas Ali Faridi Muhammad Imran Asjad Sayed M. Eldin |
| author_facet | Ebrahem A. Algehyne Magda Abd El-Rahman Waqas Ali Faridi Muhammad Imran Asjad Sayed M. Eldin |
| author_sort | Ebrahem A. Algehyne |
| collection | DOAJ |
| description | Introduction:: The chemical oscillators are identified as open system that demonstrate periodic changes in the concentration of some reaction species as a result of intricate physico-chemical mechanisms which can lead to bi-stability, the occurrence of limit cycle attractors, the emergence of spiral waves and turing patterns, and finally, deterministic chaos. Objectives:: The main objective of this paper is to analyze the simple Noyes–Field governing system of differential equations for the nonlinear Belousov–Zhabotinsky reaction which delineates the non-linear oscillatory behavior of chemical systems that occurs in the homogeneous media. Methodology:: The Lie symmetry invariance analysis performed to extract the symmetries infinitesimal generators and the adjoint representation carried out to develop optimal system for the obtained Lie vectors. The significant power series approach applied to obtain the analytical solution. The modulation instability criteria ensured the stability of nonlinear oscillatory Belousov–Zhabotinsky reaction process. Results:: The one-dimensional Lie symmetry generators algebra of the mathematical Noyes–Field governing system for oscillatory reaction is established. Furthermore, similarity reductions are carried out as well as the development of an optimal system of the sub-algebras. The similarity transformation technique converted the controlling system to ordinary differential equations and generates the large quantity of analytical traveling wave solutions. Moreover, the closed-form analytical solution for the proposed homogeneous nonlinear oscillatory chemical process is secured. The (MI) gain spectrum graphically visualized with the suitable choice of arbitrary parameters. Conclusion:: The graphical performance of the Noyes–Field model solution at various settings reveals new perspectives and fascinating model phenomena. The attained outcomes have significant applications and have opened up innovative development areas for research across numerous scientific fields. |
| first_indexed | 2024-04-10T22:21:30Z |
| format | Article |
| id | doaj.art-f39ea1faeb4b49278d1b214ab001dd69 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-04-10T22:21:30Z |
| publishDate | 2023-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-f39ea1faeb4b49278d1b214ab001dd692023-01-18T04:30:28ZengElsevierResults in Physics2211-37972023-01-0144106123Lie point symmetry infinitesimals, optimal system, power series solution, and modulational gain spectrum to the mathematical Noyes–Field model of nonlinear homogeneous oscillatory Belousov–Zhabotinsky reactionEbrahem A. Algehyne0Magda Abd El-Rahman1Waqas Ali Faridi2Muhammad Imran Asjad3Sayed M. Eldin4Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia; Nanotechnology Research Unit (NRU), University of Tabuk, Tabuk 71491, Saudi ArabiaDepartment of Physics, College of Science, King Khalid University, Abha, 61413, Saudi Arabia; Department of Radiation Physics, National Center of Radiation Research and Technology (NCRRT), Atomic Energy Authority, 11787 Cairo, EgyptDepartment of Mathematics, University of Management and Technology, Lahore, Pakistan; Corresponding author.Department of Mathematics, University of Management and Technology, Lahore, PakistanCenter of research, Faculty of Engineering and Technology, Future University in Egypt, New Cairo 11835, EgyptIntroduction:: The chemical oscillators are identified as open system that demonstrate periodic changes in the concentration of some reaction species as a result of intricate physico-chemical mechanisms which can lead to bi-stability, the occurrence of limit cycle attractors, the emergence of spiral waves and turing patterns, and finally, deterministic chaos. Objectives:: The main objective of this paper is to analyze the simple Noyes–Field governing system of differential equations for the nonlinear Belousov–Zhabotinsky reaction which delineates the non-linear oscillatory behavior of chemical systems that occurs in the homogeneous media. Methodology:: The Lie symmetry invariance analysis performed to extract the symmetries infinitesimal generators and the adjoint representation carried out to develop optimal system for the obtained Lie vectors. The significant power series approach applied to obtain the analytical solution. The modulation instability criteria ensured the stability of nonlinear oscillatory Belousov–Zhabotinsky reaction process. Results:: The one-dimensional Lie symmetry generators algebra of the mathematical Noyes–Field governing system for oscillatory reaction is established. Furthermore, similarity reductions are carried out as well as the development of an optimal system of the sub-algebras. The similarity transformation technique converted the controlling system to ordinary differential equations and generates the large quantity of analytical traveling wave solutions. Moreover, the closed-form analytical solution for the proposed homogeneous nonlinear oscillatory chemical process is secured. The (MI) gain spectrum graphically visualized with the suitable choice of arbitrary parameters. Conclusion:: The graphical performance of the Noyes–Field model solution at various settings reveals new perspectives and fascinating model phenomena. The attained outcomes have significant applications and have opened up innovative development areas for research across numerous scientific fields.http://www.sciencedirect.com/science/article/pii/S2211379722007379Lie analysisOptimal systemSeries solutionMI gain spectrumNoyes–Field modelNonlinear Belousov–Zhabotinsky reaction |
| spellingShingle | Ebrahem A. Algehyne Magda Abd El-Rahman Waqas Ali Faridi Muhammad Imran Asjad Sayed M. Eldin Lie point symmetry infinitesimals, optimal system, power series solution, and modulational gain spectrum to the mathematical Noyes–Field model of nonlinear homogeneous oscillatory Belousov–Zhabotinsky reaction Results in Physics Lie analysis Optimal system Series solution MI gain spectrum Noyes–Field model Nonlinear Belousov–Zhabotinsky reaction |
| title | Lie point symmetry infinitesimals, optimal system, power series solution, and modulational gain spectrum to the mathematical Noyes–Field model of nonlinear homogeneous oscillatory Belousov–Zhabotinsky reaction |
| title_full | Lie point symmetry infinitesimals, optimal system, power series solution, and modulational gain spectrum to the mathematical Noyes–Field model of nonlinear homogeneous oscillatory Belousov–Zhabotinsky reaction |
| title_fullStr | Lie point symmetry infinitesimals, optimal system, power series solution, and modulational gain spectrum to the mathematical Noyes–Field model of nonlinear homogeneous oscillatory Belousov–Zhabotinsky reaction |
| title_full_unstemmed | Lie point symmetry infinitesimals, optimal system, power series solution, and modulational gain spectrum to the mathematical Noyes–Field model of nonlinear homogeneous oscillatory Belousov–Zhabotinsky reaction |
| title_short | Lie point symmetry infinitesimals, optimal system, power series solution, and modulational gain spectrum to the mathematical Noyes–Field model of nonlinear homogeneous oscillatory Belousov–Zhabotinsky reaction |
| title_sort | lie point symmetry infinitesimals optimal system power series solution and modulational gain spectrum to the mathematical noyes field model of nonlinear homogeneous oscillatory belousov zhabotinsky reaction |
| topic | Lie analysis Optimal system Series solution MI gain spectrum Noyes–Field model Nonlinear Belousov–Zhabotinsky reaction |
| url | http://www.sciencedirect.com/science/article/pii/S2211379722007379 |
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