TOWARDS THE CONSTRUCTION OF N=2 SUPERSYMMETRIC INTEGRABLE HIERARCHIES

We formulate a conjecture for the three different Lax operators that d escribe the bosonic sectors of the three possible N = 2 supersymmetric integrable hierarchies with N = 2 super-W-n second Hamiltonian struct ure. We check this conjecture in the simplest cases, then we verify it in general in one of the three possible supersymmetric extensions, To this end we construct the N = 2 supersymmetric extensions of the Gene ralized Non-Linear Schrodinger hierarchy by exhibiting the correspondi ng super Lax operator. To find the correct Hamiltonians we are led to a new definition of super-residues for degenerate N = 2 supersymmetric pseudo-differential operators. We have found a new non-polynomials Mi ura-like realization for N = 2 superconformal algebra in terms of two bosonic chiral-anti-chiral free superfields.