On UrKdV and UrKP

Didier A. Depireux and Jeremy Schiff

Letters in Mathematical Physics 33 99-111 (1995).

We present two extensions of Wilson's explanation of the Miura map from MKdV to KdV. In the first we explain the map of Svinolupov et.al. from a certain UrKdV-like equation to KdV, and in the second we explain Konopelchenko's map from the modified KP equation to KP. In the course of the latter we introduce an `UrKP' system, with an infinite dimensional symmetry, providing us with a systematic method to construct Backlund transformations for the modified KP and KP equations.