Centrally Extended Conformal Galilei Algebras and Invariant Nonlinear PDEs
We construct, for any given \( \ell = \frac{1}{2} + {\mathbb N}_0, \) second-order \textit{nonlinear} partial differential equations (PDEs) which are invariant under the transformations generated by the centrally extended conformal Galilei algebras. This is done for a particular realization of the a...
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| Format: | Article |
| Language: | English |
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MDPI AG
2015-11-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/7/4/1989 |
| _version_ | 1798038496088162304 |
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| author | Naruhiko Aizawa Tadanori Kato |
| author_facet | Naruhiko Aizawa Tadanori Kato |
| author_sort | Naruhiko Aizawa |
| collection | DOAJ |
| description | We construct, for any given \( \ell = \frac{1}{2} + {\mathbb N}_0, \) second-order \textit{nonlinear} partial differential equations (PDEs) which are invariant under the transformations generated by the centrally extended conformal Galilei algebras. This is done for a particular realization of the algebras obtained by coset construction and we employ the standard Lie point symmetry technique for the construction of PDEs. It is observed that the invariant PDEs have significant difference for \( \ell > \frac{1}{3}. \) |
| first_indexed | 2024-04-11T21:41:00Z |
| format | Article |
| id | doaj.art-30591f32ba4949199fc419cc9e4a33f4 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T21:41:00Z |
| publishDate | 2015-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-30591f32ba4949199fc419cc9e4a33f42022-12-22T04:01:35ZengMDPI AGSymmetry2073-89942015-11-01741989200810.3390/sym7041989sym7041989Centrally Extended Conformal Galilei Algebras and Invariant Nonlinear PDEsNaruhiko Aizawa0Tadanori Kato1Department of Mathematics and Information Sciences, Graduate School of Science, Osaka Prefecture University, Nakamozu Campus, Sakai, Osaka 599-8531, JapanDepartment of Mathematics and Information Sciences, Graduate School of Science, Osaka Prefecture University, Nakamozu Campus, Sakai, Osaka 599-8531, JapanWe construct, for any given \( \ell = \frac{1}{2} + {\mathbb N}_0, \) second-order \textit{nonlinear} partial differential equations (PDEs) which are invariant under the transformations generated by the centrally extended conformal Galilei algebras. This is done for a particular realization of the algebras obtained by coset construction and we employ the standard Lie point symmetry technique for the construction of PDEs. It is observed that the invariant PDEs have significant difference for \( \ell > \frac{1}{3}. \)http://www.mdpi.com/2073-8994/7/4/1989nonlinear PDEslie symmetryconformal Galilei algebras |
| spellingShingle | Naruhiko Aizawa Tadanori Kato Centrally Extended Conformal Galilei Algebras and Invariant Nonlinear PDEs Symmetry nonlinear PDEs lie symmetry conformal Galilei algebras |
| title | Centrally Extended Conformal Galilei Algebras and Invariant Nonlinear PDEs |
| title_full | Centrally Extended Conformal Galilei Algebras and Invariant Nonlinear PDEs |
| title_fullStr | Centrally Extended Conformal Galilei Algebras and Invariant Nonlinear PDEs |
| title_full_unstemmed | Centrally Extended Conformal Galilei Algebras and Invariant Nonlinear PDEs |
| title_short | Centrally Extended Conformal Galilei Algebras and Invariant Nonlinear PDEs |
| title_sort | centrally extended conformal galilei algebras and invariant nonlinear pdes |
| topic | nonlinear PDEs lie symmetry conformal Galilei algebras |
| url | http://www.mdpi.com/2073-8994/7/4/1989 |
| work_keys_str_mv | AT naruhikoaizawa centrallyextendedconformalgalileialgebrasandinvariantnonlinearpdes AT tadanorikato centrallyextendedconformalgalileialgebrasandinvariantnonlinearpdes |