N=3 Supersymmetric Extension of KdV Equation

Details N=3 Supersymmetric Extension of KdV Equation N=3 Supersymmetric Extension of KdV Equation

1992-10-10

arxiv.org/abs/hep-th/9210059v1

Physics

High Energy Physics

High Energy Physics - Theory

13 pages, LaTeX

Scientific paper

We construct a one-parameter family of N=3 supersymmetric extensions of the KdV equation as a Hamiltonian flow on N=3 superconformal algebra and argue that it is non-integrable for any choice of the parameter. Then we propose a modified N=3 super KdV equation which possesses the higher order conserved quantities and so is a candidate for an integrable system. Upon reduction to N=2, it yields the recently discussed ``would-be integrable'' version of the N=2 super KdV equation. In the bosonic core it contains a coupled system of the KdV type equation and a three-component generalization of the mKdV equation. We give a Hamiltonian formulation of the new N=3 super KdV equation as a flow on some contraction of the direct sum of two N=3 superconformal algebras.

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