N = 2 SUPER BOUSSINESQ HIERARCHY - LAX PAIRS AND CONSERVATION-LAWS

We study the integrability properties of the one-parameter family of N = 2 super Boussinesq equations obtained earlier by two of us (E.I. & S.K., Phys. Lett. B 291 (1992) 63) as a Hamiltonian flow on the N = 2 super-W3 algebra. We show that it admits nontrivial higher order conse rved quantities and hence gives rise to integrable hierarchies only fo r three values of the involved parameter, alpha = -2, -1/2, 5/2. We fi nd that for the case alpha = -1/2 there exists a Lax pair formulation in terms of local N = 2 pseudo-differential operators, while for alpha = -2 the associated equation turns out to be bi-Hamiltonian.