Properties of Nonlocal Charges in the Supersymmetric Two Boson Hierarchy

TL;DR

This paper derives and analyzes nonlocal conserved charges in the supersymmetric two boson hierarchy, showing their relation to the supersymmetric KdV system and exploring their algebraic structure.

Contribution

It introduces a method to obtain nonlocal charges from fractional powers of the Lax operator and studies their algebraic properties within the hierarchy.

Findings

Nonlocal charges reduce to supersymmetric KdV charges under reduction.

Charges form a graded nonlinear cubic algebra.

Algebraic structure relates to Hamiltonian structures of the system.

Abstract

We obtain the conserved, nonlocal charges for the supersymmetric two boson hierarchy from fractional powers of its Lax operator. We show that these charges reduce to the ones of the supersymmetric KdV system under appropriate reduction. We study the algebra of the nonlocal, local and supersymmetry charges with respect to the first and the second Hamiltonian structures of the system and discuss how they close as a graded nonlinear cubic algebra.