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Symmetry 2013, 5(3), 253-270; doi:10.3390/sym5030253

Supersymmetric Version of the Euler System and Its Invariant Solutions

1,2,*  and 1
1 Centre de Recherches Mathématiques, Université de Montréal, C. P. 6128, Succ. Centre–ville, Montréal, QC H3C 3J7, Canada 2 Department of Mathematics and Computer Science, Université du Québec, C.P. 500, Trois–Rivières, QC G9A 5H7, Canada
* Author to whom correspondence should be addressed.
Received: 8 April 2013 / Revised: 14 June 2013 / Accepted: 3 July 2013 / Published: 12 July 2013
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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.
Keywords: supersymmetric models; lie superalgebras; symmetry reduction supersymmetric models; lie superalgebras; symmetry reduction
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Grundland, A.M.; Hariton, A.J. Supersymmetric Version of the Euler System and Its Invariant Solutions. Symmetry 2013, 5, 253-270.

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