N=2 Super Boussinesq Hierarchy: Lax Pairs and Conservation Laws

Abstract

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-$W_3$ 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, $\alpha =-2,-1/2,5/2$. We find 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.

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References in corpus (1)

• Superfield Realizations of $N=2$ Super-$W_3$

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