Invariant solutions of supersymmetric nonlinear wave equations

Systematic group-theoretical analyses of two supersymmetric nonlinear wave equations, namely the supersymmetric sinh-Gordon and polynomial Klein-Gordon equations, are performed. In each case, a generalization of the method of prolongations is used to determine the Lie superalgebra of symmetries, and...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2011-02, Vol.44 (8), p.085204-22
Main Authors: Grundland, A M, Hariton, A J, Šnobl, L
Format: Article
Language:English
Subjects:
Exact sciences and technology
Invariants
Klein-Gordon equation
Mathematical analysis
Nonlinearity
Physics
Polynomials
Prolongation
Supersymmetry
Symmetry
Wave equations
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Summary:Systematic group-theoretical analyses of two supersymmetric nonlinear wave equations, namely the supersymmetric sinh-Gordon and polynomial Klein-Gordon equations, are performed. In each case, a generalization of the method of prolongations is used to determine the Lie superalgebra of symmetries, and the method of symmetry reduction is applied in order to obtain invariant solutions of the supersymmetric equations under consideration. In the case of the supersymmetric sinh-Gordon equation, the results are compared with those previously found for the supersymmetric sine-Gordon equation. The presence of non-standard invariants is discussed for the supersymmetric sinh-Gordon and polynomial Klein-Gordon equations.
ISSN:1751-8121
1751-8113
1751-8121
DOI:10.1088/1751-8113/44/8/085204