Some Results on Equivalence Groups
The comparison of two common types of equivalence groups of differential equations is discussed, and it is shown that one type can be identified with a subgroup of the other type, and a case where the two groups are isomorphic is exhibited. A result on the determination of the finite transformations...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/484805 |
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| _version_ | 1832549302006710272 |
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| author | J. C. Ndogmo |
| author_facet | J. C. Ndogmo |
| author_sort | J. C. Ndogmo |
| collection | DOAJ |
| description | The comparison of two common types of equivalence groups of differential equations is discussed, and it is shown that one type can be identified with a subgroup of the other type, and a case where the two groups are isomorphic is exhibited. A result on the determination of the finite transformations of the infinitesimal generator of the larger group, which is useful for the determination of the invariant functions of the differential equation, is also given. In addition, the Levidecomposition of the Lie algebra associated with the larger group is found; the Levi factor of which is shown to be equal, up to a constant factor, to the Lie algebra associated with the smaller group. |
| format | Article |
| id | doaj-art-4be726088d244a9a85a31e2aa9641104 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-4be726088d244a9a85a31e2aa96411042025-02-03T06:11:36ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/484805484805Some Results on Equivalence GroupsJ. C. Ndogmo0School of Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South AfricaThe comparison of two common types of equivalence groups of differential equations is discussed, and it is shown that one type can be identified with a subgroup of the other type, and a case where the two groups are isomorphic is exhibited. A result on the determination of the finite transformations of the infinitesimal generator of the larger group, which is useful for the determination of the invariant functions of the differential equation, is also given. In addition, the Levidecomposition of the Lie algebra associated with the larger group is found; the Levi factor of which is shown to be equal, up to a constant factor, to the Lie algebra associated with the smaller group.http://dx.doi.org/10.1155/2012/484805 |
| spellingShingle | J. C. Ndogmo Some Results on Equivalence Groups Journal of Applied Mathematics |
| title | Some Results on Equivalence Groups |
| title_full | Some Results on Equivalence Groups |
| title_fullStr | Some Results on Equivalence Groups |
| title_full_unstemmed | Some Results on Equivalence Groups |
| title_short | Some Results on Equivalence Groups |
| title_sort | some results on equivalence groups |
| url | http://dx.doi.org/10.1155/2012/484805 |
| work_keys_str_mv | AT jcndogmo someresultsonequivalencegroups |