Reduction of Dynamics with Lie Group Analysis
This paper is mainly a review concerning singular perturbation methods by means of Lie group analysis which has been presented by the author. We make use of a particular type of approximate Lie symmetries in those methods in order to construct reduced systems which describe the long-time behavior of...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2012/505281 |
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| _version_ | 1849467477979824128 |
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| author | M. Iwasa |
| author_facet | M. Iwasa |
| author_sort | M. Iwasa |
| collection | DOAJ |
| description | This paper is mainly a review concerning singular perturbation methods
by means of Lie group analysis which has been presented by the author. We make use of
a particular type of approximate Lie symmetries in those methods in order to construct
reduced systems which describe the long-time behavior of the original dynamical
system. Those methods can be used in analyzing not only ordinary differential
equations but also difference equations. Although this method has been mainly used
in order to derive asymptotic behavior, when we can find exact Lie symmetries, we
succeed in construction of exact solutions. |
| format | Article |
| id | doaj-art-e72cf5bca4884d8ebb68c8c416159b95 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-e72cf5bca4884d8ebb68c8c416159b952025-08-20T03:26:11ZengWileyAdvances in Mathematical Physics1687-91201687-91392012-01-01201210.1155/2012/505281505281Reduction of Dynamics with Lie Group AnalysisM. Iwasa0Department of Complex Systems Science, Graduate School of Information Science, Nagoya University, Nagoya 464-8601, JapanThis paper is mainly a review concerning singular perturbation methods by means of Lie group analysis which has been presented by the author. We make use of a particular type of approximate Lie symmetries in those methods in order to construct reduced systems which describe the long-time behavior of the original dynamical system. Those methods can be used in analyzing not only ordinary differential equations but also difference equations. Although this method has been mainly used in order to derive asymptotic behavior, when we can find exact Lie symmetries, we succeed in construction of exact solutions.http://dx.doi.org/10.1155/2012/505281 |
| spellingShingle | M. Iwasa Reduction of Dynamics with Lie Group Analysis Advances in Mathematical Physics |
| title | Reduction of Dynamics with Lie Group Analysis |
| title_full | Reduction of Dynamics with Lie Group Analysis |
| title_fullStr | Reduction of Dynamics with Lie Group Analysis |
| title_full_unstemmed | Reduction of Dynamics with Lie Group Analysis |
| title_short | Reduction of Dynamics with Lie Group Analysis |
| title_sort | reduction of dynamics with lie group analysis |
| url | http://dx.doi.org/10.1155/2012/505281 |
| work_keys_str_mv | AT miwasa reductionofdynamicswithliegroupanalysis |