Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups
Lie group analysis has been applied to singular perturbation problems in both ordinary differential and difference equations and has allowed us to find the reduced dynamics describing the asymptotic behavior of the dynamical system. The present study provides an extended method that is also applicab...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/601657 |
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| _version_ | 1832568118887579648 |
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| author | Masatomo Iwasa |
| author_facet | Masatomo Iwasa |
| author_sort | Masatomo Iwasa |
| collection | DOAJ |
| description | Lie group analysis has been applied to singular perturbation problems in both ordinary differential and difference equations and has allowed us to find the reduced dynamics describing the asymptotic behavior of the dynamical system. The present study provides an extended method that is also applicable to partial differential equations. The main characteristic of the extended method is the restriction of the manifold by some constraint equations on which we search for a Lie symmetry group. This extension makes it possible to find a partial Lie symmetry group, which leads to a reduced dynamics describing the asymptotic behavior. |
| format | Article |
| id | doaj-art-fb0470ab81394a1598ad41b10fc0d2ad |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-fb0470ab81394a1598ad41b10fc0d2ad2025-02-03T00:59:51ZengWileyJournal of Applied Mathematics1110-757X1687-00422015-01-01201510.1155/2015/601657601657Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry GroupsMasatomo Iwasa0General Education Department, Aichi Institute of Technology, 1247 Yachigusa Yakusacho, Toyota 470-0392, JapanLie group analysis has been applied to singular perturbation problems in both ordinary differential and difference equations and has allowed us to find the reduced dynamics describing the asymptotic behavior of the dynamical system. The present study provides an extended method that is also applicable to partial differential equations. The main characteristic of the extended method is the restriction of the manifold by some constraint equations on which we search for a Lie symmetry group. This extension makes it possible to find a partial Lie symmetry group, which leads to a reduced dynamics describing the asymptotic behavior.http://dx.doi.org/10.1155/2015/601657 |
| spellingShingle | Masatomo Iwasa Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups Journal of Applied Mathematics |
| title | Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups |
| title_full | Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups |
| title_fullStr | Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups |
| title_full_unstemmed | Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups |
| title_short | Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups |
| title_sort | derivation of asymptotic dynamical systems with partial lie symmetry groups |
| url | http://dx.doi.org/10.1155/2015/601657 |
| work_keys_str_mv | AT masatomoiwasa derivationofasymptoticdynamicalsystemswithpartialliesymmetrygroups |