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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Main Author: M. Iwasa
Format: Article
Language:English
Published: Wiley 2012-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2012/505281
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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.
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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