On UrKdV and UrKP

Abstract

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.

13 pages, plain TeX (no macros), no figures

Cited by in corpus (3)

• Conformal Properties and Baecklund Transform for the Associated Camassa-Holm Equation
• Bäcklund Transformations and Non-Abelian Nonlinear Evolution Equations: a Novel Bäcklund Chart
• KdV-type equations linked via Baecklund transformations: remarks and perspectives