On Conservation Forms and Invariant Solutions for Classical Mechanics Problems of Liénard Type
In this study we apply partial Noether and λ-symmetry approaches to a second-order nonlinear autonomous equation of the form y′′+fyy′+g(y)=0, called Liénard equation corresponding to some important problems in classical mechanics field with respect to f(y) and g(y) functions. As a first approach we...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2014/107895 |
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| _version_ | 1849308500769898496 |
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| author | Gülden Gün Polat Teoman Özer |
| author_facet | Gülden Gün Polat Teoman Özer |
| author_sort | Gülden Gün Polat |
| collection | DOAJ |
| description | In this study we apply partial Noether and λ-symmetry approaches to a second-order nonlinear autonomous equation of the form y′′+fyy′+g(y)=0, called Liénard equation corresponding to some important problems in classical mechanics field with respect to f(y) and g(y) functions. As a first approach we utilize partial Lagrangians and partial Noether operators to obtain conserved forms of Liénard equation. Then, as a second approach, based on the λ-symmetry method, we analyze λ-symmetries for the case that λ-function is in the form of λ(x,y,y′)=λ1(x,y)y′+λ2(x,y). Finally, a classification problem for the conservation forms and invariant solutions are considered. |
| format | Article |
| id | doaj-art-059e4441fb7a4180a67412403c5cbd9b |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-059e4441fb7a4180a67412403c5cbd9b2025-08-20T03:54:25ZengWileyAdvances in Mathematical Physics1687-91201687-91392014-01-01201410.1155/2014/107895107895On Conservation Forms and Invariant Solutions for Classical Mechanics Problems of Liénard TypeGülden Gün Polat0Teoman Özer1Department of Mathematics, Faculty of Science and Letters, Istanbul Technical University, Maslak, 34469 Istanbul, TurkeyDivision of Mechanics, Faculty of Civil Engineering, Istanbul Technical University, Maslak, 34469 Istanbul, TurkeyIn this study we apply partial Noether and λ-symmetry approaches to a second-order nonlinear autonomous equation of the form y′′+fyy′+g(y)=0, called Liénard equation corresponding to some important problems in classical mechanics field with respect to f(y) and g(y) functions. As a first approach we utilize partial Lagrangians and partial Noether operators to obtain conserved forms of Liénard equation. Then, as a second approach, based on the λ-symmetry method, we analyze λ-symmetries for the case that λ-function is in the form of λ(x,y,y′)=λ1(x,y)y′+λ2(x,y). Finally, a classification problem for the conservation forms and invariant solutions are considered.http://dx.doi.org/10.1155/2014/107895 |
| spellingShingle | Gülden Gün Polat Teoman Özer On Conservation Forms and Invariant Solutions for Classical Mechanics Problems of Liénard Type Advances in Mathematical Physics |
| title | On Conservation Forms and Invariant Solutions for Classical Mechanics Problems of Liénard Type |
| title_full | On Conservation Forms and Invariant Solutions for Classical Mechanics Problems of Liénard Type |
| title_fullStr | On Conservation Forms and Invariant Solutions for Classical Mechanics Problems of Liénard Type |
| title_full_unstemmed | On Conservation Forms and Invariant Solutions for Classical Mechanics Problems of Liénard Type |
| title_short | On Conservation Forms and Invariant Solutions for Classical Mechanics Problems of Liénard Type |
| title_sort | on conservation forms and invariant solutions for classical mechanics problems of lienard type |
| url | http://dx.doi.org/10.1155/2014/107895 |
| work_keys_str_mv | AT guldengunpolat onconservationformsandinvariantsolutionsforclassicalmechanicsproblemsoflienardtype AT teomanozer onconservationformsandinvariantsolutionsforclassicalmechanicsproblemsoflienardtype |