The $N=2$ super $W_4$ algebra and its associated generalized KdV hierarchies

Abstract

We construct the $N=2$ super $W_4$ algebra as a certain reduction of the second Gel'fand-Dikii bracket on the dual of the Lie superalgebra of $N=1$ super pseudo-differential operators. The algebra is put in manifestly $N=2$ supersymmetric form in terms of three $N=2$ superfields ${\Phi }_i(X)$, with ${\Phi }_1$ being the $N=2$ energy momentum tensor and ${\Phi }_2$ and ${\Phi }_3$ being conformal spin $2$ and $3$ superfields respectively. A search for integrable hierarchies of the generalized KdV variety with this algebra as Hamiltonian structure gives three solutions, exactly the same number as for the $W_2$ (super KdV) and $W_3$ (super Boussinesq) cases.

16 pages, LaTeX, UTAS-PHYS-92-32

References in corpus (1)

• Supersymmetric Gelfand-Dickey Algebra

Cited by in corpus (6)

• Toward the construction of N=2 supersymmetric integrable hierarchies
• On the Integrable Hierarchies Associated With N=2 Super $W_n$ Algebra
• Extended N=2 supersymmetric matrix (1,s)-KdV hierarchies
• Coset approach to the N=2 supersymmetric matrix GNLS hierarchies
• A note on the third family of N=2 supersymmetric KdV hierarchies
• Classical N=2 W-superalgebras From Superpseudodifferential Operators