Supersymmetric Version of the Euler System and Its Invariant Solutions
In this paper, we formulate a supersymmetric extension of the Euler system of equations. We compute a superalgebra of Lie symmetries of the supersymmetric system. Next, we classify the one-dimensional subalgebras of this superalgebra into 49 equivalence conjugation classes. For some of the subalgebr...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2013-07-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/5/3/253 |
| _version_ | 1798034233786105856 |
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| author | A. Michel Grundland Alexander J. Hariton |
| author_facet | A. Michel Grundland Alexander J. Hariton |
| author_sort | A. Michel Grundland |
| collection | DOAJ |
| description | In this paper, we formulate a supersymmetric extension of the Euler system of equations. We compute a superalgebra of Lie symmetries of the supersymmetric system. Next, we classify the one-dimensional subalgebras of this superalgebra into 49 equivalence conjugation classes. For some of the subalgebras, the invariants have a non-standard structure. For nine selected subalgebras, we use the symmetry reduction method to find invariants, orbits and reduced systems. Through the solutions of these reduced systems, we obtain solutions of the supersymmetric Euler system. The obtained solutions include bumps, kinks, multiple wave solutions and solutions expressed in terms of arbitrary functions. |
| first_indexed | 2024-04-11T20:41:32Z |
| format | Article |
| id | doaj.art-4408ba0ddac74f8eb9fe955a7c5f9d83 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T20:41:32Z |
| publishDate | 2013-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-4408ba0ddac74f8eb9fe955a7c5f9d832022-12-22T04:04:11ZengMDPI AGSymmetry2073-89942013-07-015325327010.3390/sym5030253Supersymmetric Version of the Euler System and Its Invariant SolutionsA. Michel GrundlandAlexander J. HaritonIn this paper, we formulate a supersymmetric extension of the Euler system of equations. We compute a superalgebra of Lie symmetries of the supersymmetric system. Next, we classify the one-dimensional subalgebras of this superalgebra into 49 equivalence conjugation classes. For some of the subalgebras, the invariants have a non-standard structure. For nine selected subalgebras, we use the symmetry reduction method to find invariants, orbits and reduced systems. Through the solutions of these reduced systems, we obtain solutions of the supersymmetric Euler system. The obtained solutions include bumps, kinks, multiple wave solutions and solutions expressed in terms of arbitrary functions.http://www.mdpi.com/2073-8994/5/3/253supersymmetric modelslie superalgebrassymmetry reduction |
| spellingShingle | A. Michel Grundland Alexander J. Hariton Supersymmetric Version of the Euler System and Its Invariant Solutions Symmetry supersymmetric models lie superalgebras symmetry reduction |
| title | Supersymmetric Version of the Euler System and Its Invariant Solutions |
| title_full | Supersymmetric Version of the Euler System and Its Invariant Solutions |
| title_fullStr | Supersymmetric Version of the Euler System and Its Invariant Solutions |
| title_full_unstemmed | Supersymmetric Version of the Euler System and Its Invariant Solutions |
| title_short | Supersymmetric Version of the Euler System and Its Invariant Solutions |
| title_sort | supersymmetric version of the euler system and its invariant solutions |
| topic | supersymmetric models lie superalgebras symmetry reduction |
| url | http://www.mdpi.com/2073-8994/5/3/253 |
| work_keys_str_mv | AT amichelgrundland supersymmetricversionoftheeulersystemanditsinvariantsolutions AT alexanderjhariton supersymmetricversionoftheeulersystemanditsinvariantsolutions |