Supersymmetric Two Boson Equation, Its Reductions and the Nonstandard Supersymmetric KP Hierarchy

TL;DR

This paper explores the supersymmetric Two Boson system, its properties, reductions, and its role in unifying supersymmetric KP hierarchies, revealing new integrable models and algebraic structures.

Contribution

It introduces a nonstandard supersymmetric KP hierarchy that unifies various flows and reveals hidden supersymmetry in the Two Boson system.

Findings

Constructed local and nonlocal conserved charges.

Showed the system's relation to known supersymmetric models.

Identified a hidden N=2 supersymmetry.

Abstract

In this paper, we review various properties of the supersymmetric Two Boson (sTB) system. We discuss the equation and its nonstandard Lax representation. We construct the local conserved charges as well as the Hamiltoniam structures of the system. We show how this system leads to various other known supersymmetric integrable models under appropriate field redefinition. We discuss the sTB and the supersymmetric nonlinear Schr\"odinger (sNLS) equations as constrained, nonstandard supersymmetric Kadomtsev-Petviashvili (sKP) systems and point out that the nonstandard sKP systems naturally unify all the KP and mKP flows while leading to a new integrable supersymmetrization of the KP equation. We construct the nonlocal conserved charges associated with the sTB system and show that the algebra of charges corresponds to a graded, cubic algebra. We also point out that the sTB system has a hidden supersymmetry making it an $N=2$ extended supersymmetric system.