Extensions of the N=2 Supersymmetric a=-2 Boussinesq Hierarchy

TL;DR

This paper introduces two new Lax operators for an N=2 supersymmetric extension of the a=-2 Boussinesq hierarchy, linking supersymmetric algebras and integrable systems.

Contribution

It provides novel Lax operators for the N=2 supersymmetric a=-2 Boussinesq hierarchy, connecting different supersymmetric conformal algebras through gauge transformations.

Findings

Two distinct Lax operators for the hierarchy

Establishment of a Miura transformation linking algebras

Extension of supersymmetric integrable systems

Abstract

We present two different Lax operators for a manifestly N=2 supersymmetric extension of "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 provide the Miura link between the "small" N=4 supersymmetric conformal algebra and the supersymmetric $W_{3}$ algebra .