The Supersymmetric Two Boson Hierarchies

Abstract

We construct the most general supersymmetric two boson system that is integrable. We obtain the Lax operator and the nonstandard Lax representation for this system. We show that, under appropriate redefinition of variables, this reduces to the supersymmetric nonlinear Schrödinger equation without any arbitrary parameter which is known to be integrable. We show that this supersymmetric system has three local Hamiltonian structures just like the bosonic counterpart and we show how the supersymmetric KdV equation can be embedded into this system.

11 pages, plain TeX, University of Rochester UR-1362, ER-40685-812

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Cited by in corpus (25)

• On the Super-NLS Equation and its Relation with N=2 Super-KdV within Coset Approach
• Supersymmetric Extensions of the Harry Dym Hierarchy
• Supersymmetric KP Hierarchy: ``Ghost'' Symmetry Structure, Reductions and Darboux-Backlund Solutions
• Supersymmetric Two-Boson Equation: Bilinearization and Solutions
• Bilinear Approach to N=2 Supersymmetric KdV equations
• Properties of Nonlocal Charges in the Supersymmetric Two Boson Hierarchy
• Manifestly Supersymmetric Lax Integrable Hierarchies
• The sAKNS Hierarchy
• Hamiltonian Structures of Generalized Manin-Radul Super KdV and Constrained Super KP Hierarchies
• Zero Curvature Formalism for Supersymmetric Integrable Hierarchies in Superspace
• On the Integrable Hierarchies Associated With N=2 Super $W_n$ Algebra
• Deformations of N=2 super-conformal algebra and supersymmetric two-component Camassa-Holm equation
• The sTB-B Hierarchy
• Symmetries of Supersymmetric Integrable Hierarchies of KP Type
• Moyal Noncommutative Integrability and the Burgers-KdV Mapping
• Gardner's deformations of the N=2 supersymmetric a=4-KdV equation
• New Nonlocal Charges in SUSY Integrable Models
• Dispersionless sTB
• Super Extensions of the Short Pulse Equation
• Canonical gauge equivalences of the sAKNS and sTB hierarchies
• Invariant vector fields and the prolongation method for supersymmetric quantum systems
• Darboux transformation and multi-soliton solutions of Two-Boson hierarchy
• On the Miura and Backlund transformations associated with the supersymmetric Gelfand-Dickey bracket
• Fully Supersymmetric Hierarchies From A Energy Dependent Super Hill Operator
• Integrable Models and the Higher Dimensional Representations of Graded Lie Algebras