Supersymmetry for integrable hierarchies on loop superalgebras

TL;DR

This paper develops an algebraic framework to implement N=2 supersymmetry in integrable systems based on loop superalgebras, deriving solutions for specific models and extending the understanding of supersymmetric integrable hierarchies.

Contribution

It introduces an algebraic formulation of N=2 supersymmetry for integrable hierarchies on loop superalgebras, including explicit solutions for the p=1 case.

Findings

Derived the one-soliton solution for p=1

Extended integrable hierarchies to include supersymmetric sectors

Formulated N=2 supersymmetry transformations algebraically

Abstract

The algebraic approach is employed to formulate N=2 supersymmetry transformations in the context of integrable systems based on loop superalgebras $\hat{\rm sl}(p+1,p), p \ge 1$ with homogeneous gradation. We work with extended integrable hierarchies, which contain supersymmetric AKNS and Lund-Regge sectors. We derive the one-soliton solution for $p=1$ which solves positive and negative evolution equations of the N=2 supersymmetric model.