Extensions of the N = 2 supersymmetric a = − 2 Boussinesq hierarchy

Abstract

We present two different Lax operators for a manifestly N = 2 supersymmetric extension of the “ a = −2” Boussinesq hierarchy. The first is the supersymmetric generalization of the Lax operator of the modified KdV equation. The second is the generalization of the supersymmetric Lax operator of the N = 2 supersymmetric a = − 2 KdV system. The gauge transformation of the first Lax operator provides the Miura link between the “small” N = 4 supersymmetric conformai algebra and the supersymmetric W 3 algebra.