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arXiv · hep-th/9305078

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

S. Bellucci·E. Ivanov·S. Krivonos·A. Pichugin
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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, $α=-2,\;-1/2,\;5/2$. 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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S. Bellucci, E. Ivanov, S. Krivonos, A. Pichugin. 1993-05-21. N=2 Super Boussinesq Hierarchy: Lax Pairs and Conservation Laws. https://doi.org/10.1016/0370-2693(93)90983-o

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