N=2 Super Boussinesq Hierarchy: Lax Pairs and Conservation Laws
Bellucci, S. · Ivanov, E. · Krivonos, S. · Pichugin, A.
Original · EN
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 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.
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