The supersymmetric two boson hierarchies

We study, systematically, the properties of the supersymmetric AKNS (sAKNS) hierarchy. In particular, we discuss the Lax representation in terms of a bosonic Lax operator and some special features of the equations and construct the bosonic local charges as well as the fermionic nonlocal charges associated with the system starting from the Lax operator. We obtain the Hamiltonian structures of the system and check the Jacobi identity through the method of prolongation. We also show that this hierarchy of equations can equivalently be described in terms of a fermionic Lax operator. We obtain the zero curvature formulation as well as the conserved charges of the system starting from this fermionic Lax operator which suggests a connection between the two. Finally, starting from the fermionic description of the system, we construct the soliton solutions for this system of equations through Darboux-Bäcklund transformations and describe some open problems.

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“…Finding the higher ones, though, can be tricky as was already noticed in [9,16]. Let us point out how one can run into problems here also.…”

Section: Hamiltonian Structuresmentioning

confidence: 86%

“…Several such models have already been constructed [7][8][9] and more recently, a supersymmetric formulation of the AKNS (sAKNS) hierarchy has also been given [10][11]. It is expected to be at least as important in the study of supersymmetric integrable models as the AKNS hierarchy is within the context of the bosonic integrable systems.…”

Section: Introductionmentioning

confidence: 99%

THE sAKNS HIERARCHY

Aratyn

Das

1998

Mod. Phys. Lett. A

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“…(We follow the notation in ref. [16].) This system can also be obtained from the following nonstandard Lax equation…”

mentioning

confidence: 99%

“…The crucial observation [16], for our analysis, is the fact that the sNLS equation and the sTB equation are related to each other through the field redefinition (Miura transformation)…”

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confidence: 99%

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Bi-Hamiltonian Structure of the Supersymmetric Nonlinear Schrödinger Equation

Brunelli

Das

1995

Mod. Phys. Lett. A

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We show that the supersymmetric nonlinear Schrödinger equation is a bi-Hamiltonian integrable system. We obtain the two Hamiltonian structures of the theory from the ones of the supersymmetric two boson hierarchy through a field redefinition. We also show how the two Hamiltonian structures of the supersymmetric KdV equation can be derived from a Hamiltonian reduction of the supersymmetric two boson hierarchy as well.

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Zero curvature formalism in superspace

Aratyn

Das

Rasinariu

et al.

Supersymmetry and Integrable Models

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We discuss the generalization of the Drinfeld-Sokolov formalism to superspace in the case of supersymmetric integrable systems. We bring out the connection between this and the zero curvature formulations, for these systems, in components. Various examples are worked out in detail. We show how the symmetric space techniques can be profitably used to solve the zero curvature conditions and to obtain the hierarchy of equations in the case of sAKNS hierarchy. The dynamical equations are formulated also as the Cartan-Maurer equations in superspace and we show how the zero curvature condition can be solved, alternately, by expanding potentials according to the grading charge. We also discuss the sTB-B hierarchy to bring out some open questions.

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The supersymmetric two boson hierarchies

Cited by 53 publications

References 25 publications

THE sAKNS HIERARCHY

THE sAKNS HIERARCHY

Bi-Hamiltonian Structure of the Supersymmetric Nonlinear Schrödinger Equation

Zero curvature formalism in superspace

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