TOWARDS AN INTEGRABLE N=3 SUPER KDV EQUATION

Starting with a most general SO(3) symmetric N = 3 superfield extension of the KdV equation and requiring the existence of both a higher-order conservation law for it and a proper reduction to the N = 2 super KdV equation we deduce a new N = 3 super KdV equation which under these assumptions is a unique candidate for being integrable. Upon reduction to the N = 2 case it yields the recently discussed ''would-be'' integrable version of the N = 2 super KdV equation. It can be interpreted as a Hamiltonian flow on some contraction of the direct sum of two N = 3 superconformal algebras.