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. B291 (1992) 63) as a hamiltonian flow on the N = 2 super-W_3 algebra. We show that it admits nontrivial higher order conserved quantities and hence gives rise to integrable hierarchies only for three values of the involved parameter, \α = -2, -1/2, 5/2. We find that for the case \α = -1/2 there exists a Lax pair formulation in terms of local N = 2 pseudo-differential operators, while for \α = -2 the associated equation turns out to be bi-hamiltonian.