A J Hariton 2006 J. Phys. A: Math. Gen. 39 7105 doi:10.1088/0305-4470/39/22/021
A J Hariton1
Show affiliationsIn this paper, a supersymmetric extension of the scalar Born–Infeld equation is constructed through a superspace formalism which involves the addition of one independent fermionic Grassmann variable to the existing bosonic spacetime coordinates. The bosonic scalar field is replaced by a fermionic superfield which is composed of two component fields, one bosonic and one fermionic. The resulting equation is invariant under a space supersymmetric transformation and, in its most general form, involves four arbitrary parameters. For a certain specific case, the Lie superalgebra of symmetries was identified, and the one-dimensional subalgebras were systematically classified into splitting and non-splitting conjugate classes. A number of group-invariant solutions were obtained, including polynomial solutions, solutions by radicals and solitary waves (including bumps, kinks and doubly periodic solutions).
12.60.Jv Supersymmetric models
17Bxx Lie algebras and Lie superalgebras (For Lie groups, see 22Exx)
Issue 22 (2 June 2006)
Received 20 December 2005, in final form 26 December 2005
Published 16 May 2006
A J Hariton 2006 J. Phys. A: Math. Gen. 39 7105
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