Invariant solutions of the supersymmetric sine-Gordon equation

Details Invariant solutions of the supersymmetric sine-Gordon equation Invariant solutions of the supersymmetric sine-Gordon equation

2008-12-19

arxiv.org/abs/0812.3862v2

J.Phys.A42:335203,2009

Physics

Mathematical Physics

27 pages, major revision, the published version

Scientific paper

10.1088/1751-8113/42/33/335203

A comprehensive symmetry analysis of the N=1 supersymmetric sine-Gordon equation is performed. Two different forms of the supersymmetric system are considered. We begin by studying a system of partial differential equations corresponding to the coefficients of the various powers of the anticommuting independent variables. Next, we consider the super-sine-Gordon equation expressed in terms of a bosonic superfield involving anticommuting independent variables. In each case, a Lie (super)algebra of symmetries is determined and a classification of all subgroups having generic orbits of codimension 1 in the space of independent variables is performed. The method of symmetry reduction is systematically applied in order to derive invariant solutions of the supersymmetric model. Several types of algebraic, hyperbolic and doubly periodic solutions are obtained in explicit form.

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