Supersymmetric Extensions of the Harry Dym Hierarchy

Details Supersymmetric Extensions of the Harry Dym Hierarchy Supersymmetric Extensions of the Harry Dym Hierarchy

2003-04-24

arxiv.org/abs/nlin/0304047v1

J.Math.Phys. 44 (2003) 4756-4767

Nonlinear Sciences

Exactly Solvable and Integrable Systems

15 pages, Latex file

Scientific paper

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.

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