O ct 1 99 2 N = 3 SUPERSYMMETRIC EXTENSION OF KdV EQUATION
نویسنده
چکیده
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.
منابع مشابه
ar X iv : h ep - t h / 92 11 01 4 v 1 3 N ov 1 99 2 UR – 1284 ER – 40685 – 734 SELF - DUALITY AND THE SUPERSYMMETRIC KdV HIERARCHY
We show how the supersymmetric KdV equation can be obtained from the self–duality condition on Yang–Mills fields in four dimension associated with the graded Lie algebra OSp(2/1). We also obtain the hierarchy of Susy KdV equations from such a condition. We formulate the Susy KdV hierarchy as a vanishing curvature condition associated with the U(1) group and show how an Abelian self–duality cond...
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