Integrable Extensions of N=2 Supersymmetric KdV Hierarchy Associated with the Nonuniqueness of the Roots of the Lax operator

Abstract

We preesent a new supersymmetric integrable extensions of the a=4,N=2 KdV hierarchy. The root of the supersymmetric Lax operator of the KdV equation is generalized, by including additional fields. This generalized root generate new hierarchy of integrable equations, for which we investigate the hamiltonian structure. In special case our system describes the interaction of the KdV equation with the two MKdV equations.