Lie group analysis, solitons, self-adjointness and conservation laws of the nonlinear elastic structural element equation
This study is based on the Lie group method for the nonlinear elastic structural element equation (ESE Equation). We obtain a three-dimensional Lie algebra. By utilizing this Lie algebra a four-dimensional optimal system is constructed. The governing ESE Equation is converted to nonlinear ordinary d...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2024-12-01
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| Series: | Journal of Taibah University for Science |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/16583655.2023.2294554 |
| _version_ | 1797386827722653696 |
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| author | Akhtar Hussain Muhammad Usman Fiazuddin Zaman |
| author_facet | Akhtar Hussain Muhammad Usman Fiazuddin Zaman |
| author_sort | Akhtar Hussain |
| collection | DOAJ |
| description | This study is based on the Lie group method for the nonlinear elastic structural element equation (ESE Equation). We obtain a three-dimensional Lie algebra. By utilizing this Lie algebra a four-dimensional optimal system is constructed. The governing ESE Equation is converted to nonlinear ordinary differential equations (ODEs) via symmetry reduction. We use a modified auxiliary equation (MAE) procedure to deal with nonlinear ODEs. These ODEs reveal the dynamics of the periodic and soliton solutions. We obtain soliton solutions through rational, trigonometric, and hyperbolic functions. Wolfram Mathematica simulations vividly illustrate the wave characteristics of the derived solutions, affirming their properties as singular periodic solutions, a singular solution, an optical dark soliton solution, and a singular soliton solution. We also obtain the local conservation laws by a new conservation theorem introduced by Ibragimov. |
| first_indexed | 2024-03-08T22:15:01Z |
| format | Article |
| id | doaj.art-29549e90821f4f5eb9632eb762989231 |
| institution | Directory Open Access Journal |
| issn | 1658-3655 |
| language | English |
| last_indexed | 2024-03-08T22:15:01Z |
| publishDate | 2024-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Taibah University for Science |
| spelling | doaj.art-29549e90821f4f5eb9632eb7629892312023-12-19T01:32:19ZengTaylor & Francis GroupJournal of Taibah University for Science1658-36552024-12-0118110.1080/16583655.2023.2294554Lie group analysis, solitons, self-adjointness and conservation laws of the nonlinear elastic structural element equationAkhtar Hussain0Muhammad Usman1Fiazuddin Zaman2Abdus Salam School of Mathematical Sciences, Government College University, Lahore, PakistanCollege of Electrical and Mechanical Engineering (CEME), National University of Sciences and Technology (NUST), Islamabad, PakistanAbdus Salam School of Mathematical Sciences, Government College University, Lahore, PakistanThis study is based on the Lie group method for the nonlinear elastic structural element equation (ESE Equation). We obtain a three-dimensional Lie algebra. By utilizing this Lie algebra a four-dimensional optimal system is constructed. The governing ESE Equation is converted to nonlinear ordinary differential equations (ODEs) via symmetry reduction. We use a modified auxiliary equation (MAE) procedure to deal with nonlinear ODEs. These ODEs reveal the dynamics of the periodic and soliton solutions. We obtain soliton solutions through rational, trigonometric, and hyperbolic functions. Wolfram Mathematica simulations vividly illustrate the wave characteristics of the derived solutions, affirming their properties as singular periodic solutions, a singular solution, an optical dark soliton solution, and a singular soliton solution. We also obtain the local conservation laws by a new conservation theorem introduced by Ibragimov.https://www.tandfonline.com/doi/10.1080/16583655.2023.2294554Lie group methodoptimal systemnonlinear elastic structural element equationLie algebramodified auxiliary equation procedure |
| spellingShingle | Akhtar Hussain Muhammad Usman Fiazuddin Zaman Lie group analysis, solitons, self-adjointness and conservation laws of the nonlinear elastic structural element equation Journal of Taibah University for Science Lie group method optimal system nonlinear elastic structural element equation Lie algebra modified auxiliary equation procedure |
| title | Lie group analysis, solitons, self-adjointness and conservation laws of the nonlinear elastic structural element equation |
| title_full | Lie group analysis, solitons, self-adjointness and conservation laws of the nonlinear elastic structural element equation |
| title_fullStr | Lie group analysis, solitons, self-adjointness and conservation laws of the nonlinear elastic structural element equation |
| title_full_unstemmed | Lie group analysis, solitons, self-adjointness and conservation laws of the nonlinear elastic structural element equation |
| title_short | Lie group analysis, solitons, self-adjointness and conservation laws of the nonlinear elastic structural element equation |
| title_sort | lie group analysis solitons self adjointness and conservation laws of the nonlinear elastic structural element equation |
| topic | Lie group method optimal system nonlinear elastic structural element equation Lie algebra modified auxiliary equation procedure |
| url | https://www.tandfonline.com/doi/10.1080/16583655.2023.2294554 |
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