Lie Algebra Classification, Conservation Laws, and Invariant Solutions for a Generalization of the Levinson–Smith Equation
We obtain the optimal system’s generating operators associated with a generalized Levinson–Smith equation; this one is related to the Liénard equation which is important for physical, mathematical, and engineering points of view. The underlying equation has applications in mechanics and nonlinear dy...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2021/6628243 |
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| _version_ | 1832565959019200512 |
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| author | G. Loaiza Y. Acevedo O.M.L. Duque Danilo A. García Hernández |
| author_facet | G. Loaiza Y. Acevedo O.M.L. Duque Danilo A. García Hernández |
| author_sort | G. Loaiza |
| collection | DOAJ |
| description | We obtain the optimal system’s generating operators associated with a generalized Levinson–Smith equation; this one is related to the Liénard equation which is important for physical, mathematical, and engineering points of view. The underlying equation has applications in mechanics and nonlinear dynamics as well. This equation has been widely studied in the qualitative scheme. Here, we treat the equation by using the Lie group method, and we obtain certain operators; using those operators, we characterized all invariants solutions associated with the generalized equation of Levinson Smith considered in this paper. Finally, we classify the Lie algebra associated with the given equation. |
| format | Article |
| id | doaj-art-d7d4e7a30f124c3791d871aad56d8d34 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-d7d4e7a30f124c3791d871aad56d8d342025-02-03T01:05:30ZengWileyInternational Journal of Differential Equations1687-96431687-96512021-01-01202110.1155/2021/66282436628243Lie Algebra Classification, Conservation Laws, and Invariant Solutions for a Generalization of the Levinson–Smith EquationG. Loaiza0Y. Acevedo1O.M.L. Duque2Danilo A. García Hernández3Universidad EAFIT, Medellín, ColombiaUniversidad EAFIT, Medellín, ColombiaUniversidad EAFIT, Medellín, ColombiaIMECC-UNICAMP, Campinas, BrazilWe obtain the optimal system’s generating operators associated with a generalized Levinson–Smith equation; this one is related to the Liénard equation which is important for physical, mathematical, and engineering points of view. The underlying equation has applications in mechanics and nonlinear dynamics as well. This equation has been widely studied in the qualitative scheme. Here, we treat the equation by using the Lie group method, and we obtain certain operators; using those operators, we characterized all invariants solutions associated with the generalized equation of Levinson Smith considered in this paper. Finally, we classify the Lie algebra associated with the given equation.http://dx.doi.org/10.1155/2021/6628243 |
| spellingShingle | G. Loaiza Y. Acevedo O.M.L. Duque Danilo A. García Hernández Lie Algebra Classification, Conservation Laws, and Invariant Solutions for a Generalization of the Levinson–Smith Equation International Journal of Differential Equations |
| title | Lie Algebra Classification, Conservation Laws, and Invariant Solutions for a Generalization of the Levinson–Smith Equation |
| title_full | Lie Algebra Classification, Conservation Laws, and Invariant Solutions for a Generalization of the Levinson–Smith Equation |
| title_fullStr | Lie Algebra Classification, Conservation Laws, and Invariant Solutions for a Generalization of the Levinson–Smith Equation |
| title_full_unstemmed | Lie Algebra Classification, Conservation Laws, and Invariant Solutions for a Generalization of the Levinson–Smith Equation |
| title_short | Lie Algebra Classification, Conservation Laws, and Invariant Solutions for a Generalization of the Levinson–Smith Equation |
| title_sort | lie algebra classification conservation laws and invariant solutions for a generalization of the levinson smith equation |
| url | http://dx.doi.org/10.1155/2021/6628243 |
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