A note on the gauge equivalence between the Manin-Radul and Laberge-Mathieu super KdV hierarchies

Abstract

The gauge equivalence between the Manin-Kadul and Labarge-Mathieu super KdV hierarchies is revisited. Apart from the Inami-Kanno transformation, we show that there is another gauge transformation which also possesses the cancnical property. We explore the relationship of these two gauge transformations from the Kupershmidt-Wilson theorem viewpoint and, as a by-product, obtain the Darboux-Backlund transformation for the Manin-Radul super KdV hierarchy. The geometrical intepretation of these transformations is also briefly discussed.