Bi-Hamiltonian Structure of the Supersymmetric Nonlinear Schrodinger Equation

TL;DR

This paper demonstrates that the supersymmetric nonlinear Schrödinger equation is a bi-Hamiltonian integrable system, deriving its Hamiltonian structures from the supersymmetric two boson hierarchy and linking it to the supersymmetric KdV equation.

Contribution

It introduces the bi-Hamiltonian structure of the supersymmetric nonlinear Schrödinger equation and connects it to the supersymmetric two boson hierarchy and supersymmetric KdV equation.

Findings

The supersymmetric nonlinear Schrödinger equation is bi-Hamiltonian.

Hamiltonian structures are derived from the supersymmetric two boson hierarchy.

Connections between supersymmetric NLS, two boson hierarchy, and supersymmetric KdV are established.

Abstract

We show that the supersymmetric nonlinear Schr\"odinger equation is a bi-Hamiltonian integrable system. We obtain the two Hamiltonian structures of the theory from the ones of the supersymmetric two boson hierarchy through a field redefinition. We also show how the two Hamiltonian structures of the supersymmetric KdV equation can be derived from a Hamiltonian reduction of the supersymmetric two boson hierarchy as well.