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arXiv · 1110.2023

A non-standard Lax formulation of the Harry Dym hierarchy and its supersymmetric extension

Kai Tian·Ziemowit Popowicz·Q. P. Liu
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Abstract

For the Harry Dym hierarchy, a non-standard Lax formulation is deduced from that of Korteweg-de Vries (KdV) equation through a reciprocal transformation. By supersymmetrizing this Lax operator, a new N=2 supersymmetric extension of the Harry Dym hierarchy is constructed, and is further shown to be linked to one of the N=2 supersymmetric KdV equations through superconformal transformation. The bosonic limit of this new N=2 supersymmetric Harry Dym equation is related to a coupled system of KdV-MKdV equations.

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Kai Tian, Ziemowit Popowicz, Q. P. Liu. 2011-10-10. A non-standard Lax formulation of the Harry Dym hierarchy and its supersymmetric extension. https://doi.org/10.1088/1751-8113%2F45%2F12%2F122001

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