Supersymmetric extensions of the Harry Dym hierarchy

We study the supersymmetric extensions of the Harry Dym hierarchy of equations. We obtain the susy-B extension, the doubly susy-B extension as well as the N=1 and the N=2 supersymmetric extensions for this system. The N=2 supersymmetric extension is particularly interesting, since it leads to new cl...

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Bibliographic Details
Published in:Journal of mathematical physics 2003-10, Vol.44 (10), p.4756-4767
Main Authors: Brunelli, J. C., Das, Ashok, Popowicz, Ziemowit
Format: Article
Language:English
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Summary:We study the supersymmetric extensions of the Harry Dym hierarchy of equations. We obtain the susy-B extension, the doubly susy-B extension as well as the N=1 and the N=2 supersymmetric extensions for this system. The N=2 supersymmetric extension is particularly interesting, since it leads to new classical integrable systems in the bosonic limit. We prove the integrability of these systems through the bi-Hamiltonian formulation of integrable models and through the Lax description. We also discuss the supersymmetric extension of the Hunter–Zheng equation which belongs to the Harry Dym hierarchy of equations.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.1606527