Towards an integrable N=3 super KdV equation

Abstract 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