N=3 Supersymmetric Extension of KdV Equation
Abstract
We construct a oneparameter family of N=3 supersymmetric extensions of the KdV equation as a Hamiltonian flow on N=3 superconformal algebra and argue that it is nonintegrable 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 ``wouldbe 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 threecomponent 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.
 Publication:

arXiv eprints
 Pub Date:
 October 1992
 arXiv:
 arXiv:hepth/9210059
 Bibcode:
 1992hep.th...10059B
 Keywords:

 High Energy Physics  Theory
 EPrint:
 13 pages, LaTeX