PT-symmetric extensions of the supersymmetric Korteweg-de Vries equation

TL;DR

This paper introduces new PT-symmetric deformations of the supersymmetric Korteweg-de Vries equation, exploring both supersymmetry-breaking and preserving extensions, and establishing their non-Hermitian Hamiltonian structure with conserved charges.

Contribution

It proposes novel PT-symmetric deformations of the supersymmetric KdV equation, including both fermionic extensions and true supersymmetric models, with Hamiltonian formulations and conserved charges.

Findings

New PT-symmetric deformations of superderivatives and KdV equation

Existence of non-Hermitian Hamiltonian formulations with conserved charges

Identification of both supersymmetry-breaking and preserving extensions

Abstract

We discuss several PT-symmetric deformations of superderivatives. Based on these various possibilities, we propose new families of complex PT-symmetric deformations of the supersymmetric Korteweg-de Vries equation. Some of these new models are mere fermionic extensions of the former in the sense that they are formulated in terms of superspace valued superfields containing bosonic and fermionic fields, breaking however the supersymmetry invariance. Nonetheless, we also find extensions, which may be viewed as new supersymmetric Korteweg-de Vries equation. Moreover, we show that these deformations allow for a non-Hermitian Hamiltonian formulation and construct three charges associated to the corresponding flow.