The sTB-B Hierarchy

TL;DR

This paper introduces a new supersymmetric two boson hierarchy, explores its mathematical properties, conserved quantities, Hamiltonian structures, and connections to other integrable systems, providing a comprehensive theoretical framework.

Contribution

The paper constructs the sTB-B hierarchy, derives its conserved quantities and Hamiltonian structures, and links it to the sKdV-B equation through reduction, with detailed zero curvature formulations.

Findings

Established the sTB-B hierarchy and its properties.

Derived conserved quantities and Hamiltonian structures.

Connected the hierarchy to the sKdV-B equation via reduction.

Abstract

We construct a new supersymmetric two boson (sTB-B) hierarchy and study its properties. We derive the conserved quantities and the Hamiltonian structures (proving the Jacobi identity) for the system. We show how this system gives the sKdV-B equation and its Hamiltonian structures upon appropriate reduction. We also describe the zero curvature formulation of this hierarchy both in the superspace as well as in components.