Conservation laws, solitary wave solutions, and lie analysis for the nonlinear chains of atoms
Abstract Nonlinear chains of atoms (NCA) are complex systems with rich dynamics, that influence various scientific disciplines. The lie symmetry approach is considered to analyze the NCA. The Lie symmetry method is a powerful mathematical tool for analyzing and solving differential equations with sy...
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2023-07-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-023-38658-w |
| _version_ | 1797774196432961536 |
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| author | Muhammad Junaid-U-Rehman Grzegorz Kudra Jan Awrejcewicz |
| author_facet | Muhammad Junaid-U-Rehman Grzegorz Kudra Jan Awrejcewicz |
| author_sort | Muhammad Junaid-U-Rehman |
| collection | DOAJ |
| description | Abstract Nonlinear chains of atoms (NCA) are complex systems with rich dynamics, that influence various scientific disciplines. The lie symmetry approach is considered to analyze the NCA. The Lie symmetry method is a powerful mathematical tool for analyzing and solving differential equations with symmetries, facilitating the reduction of complexity and obtaining solutions. After getting the entire vector field by using the Lie scheme, we find the optimal system of symmetries. We have converted assumed PDE into nonlinear ODE by using the optimal system. The new auxiliary scheme is used to find the Travelling wave solutions, while graphical behaviour visually represents relationships and patterns in data or mathematical models. The multiplier method enables the identification of conservation laws, and fundamental principles in physics that assert certain quantities remain constant over time. |
| first_indexed | 2024-03-12T22:17:29Z |
| format | Article |
| id | doaj.art-0d558e89d07f4a51b777250a0a887ddc |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-03-12T22:17:29Z |
| publishDate | 2023-07-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-0d558e89d07f4a51b777250a0a887ddc2023-07-23T11:12:32ZengNature PortfolioScientific Reports2045-23222023-07-0113111310.1038/s41598-023-38658-wConservation laws, solitary wave solutions, and lie analysis for the nonlinear chains of atomsMuhammad Junaid-U-Rehman0Grzegorz Kudra1Jan Awrejcewicz2Department of Automation, Biomechanics, and Mechatronics, Lodz University of TechnologyDepartment of Automation, Biomechanics, and Mechatronics, Lodz University of TechnologyDepartment of Automation, Biomechanics, and Mechatronics, Lodz University of TechnologyAbstract Nonlinear chains of atoms (NCA) are complex systems with rich dynamics, that influence various scientific disciplines. The lie symmetry approach is considered to analyze the NCA. The Lie symmetry method is a powerful mathematical tool for analyzing and solving differential equations with symmetries, facilitating the reduction of complexity and obtaining solutions. After getting the entire vector field by using the Lie scheme, we find the optimal system of symmetries. We have converted assumed PDE into nonlinear ODE by using the optimal system. The new auxiliary scheme is used to find the Travelling wave solutions, while graphical behaviour visually represents relationships and patterns in data or mathematical models. The multiplier method enables the identification of conservation laws, and fundamental principles in physics that assert certain quantities remain constant over time.https://doi.org/10.1038/s41598-023-38658-w |
| spellingShingle | Muhammad Junaid-U-Rehman Grzegorz Kudra Jan Awrejcewicz Conservation laws, solitary wave solutions, and lie analysis for the nonlinear chains of atoms Scientific Reports |
| title | Conservation laws, solitary wave solutions, and lie analysis for the nonlinear chains of atoms |
| title_full | Conservation laws, solitary wave solutions, and lie analysis for the nonlinear chains of atoms |
| title_fullStr | Conservation laws, solitary wave solutions, and lie analysis for the nonlinear chains of atoms |
| title_full_unstemmed | Conservation laws, solitary wave solutions, and lie analysis for the nonlinear chains of atoms |
| title_short | Conservation laws, solitary wave solutions, and lie analysis for the nonlinear chains of atoms |
| title_sort | conservation laws solitary wave solutions and lie analysis for the nonlinear chains of atoms |
| url | https://doi.org/10.1038/s41598-023-38658-w |
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