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

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 Schrödinger (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.

44 pages, plain TeX

References in corpus (2)

• THE MINIMAL N=2 SUPEREXTENSION OF THE NLS EQUATION
• Non-Perturbative Approach to 2D-Supergravity and Super-Virasoro Constraints

Cited by in corpus (18)

• The Supersymmetric Two Boson Hierarchies
• New Integrable Extensions of N=2 KdV and Boussinesq Hierarchies
• Supersymmetric Two-Boson Equation: Bilinearization and Solutions
• Bilinear Approach to N=2 Supersymmetric KdV equations
• Manifestly Supersymmetric Lax Integrable Hierarchies
• Hamiltonian Structures of Generalized Manin-Radul Super KdV and Constrained Super KP Hierarchies
• Dispersionless Fermionic KdV
• Supersymmetric Moyal-Lax Representations
• Properties of Moyal-Lax Representation
• The sTB-B Hierarchy
• Moyal Noncommutative Integrability and the Burgers-KdV Mapping
• Dispersionless sTB
• New Nonlocal Charges in SUSY Integrable Models
• Canonical gauge equivalences of the sAKNS and sTB hierarchies
• Lagrangian Approach to Dispersionless KdV Hierarchy
• Alternative dispersionless limit of N=2 supersymmetric KdV-type hierarchies
• Darboux transformation and multi-soliton solutions of Two-Boson hierarchy
• Lightfront Hamiltonian Structures for the Nonlinear Sigma Model