On UrKdV and UrKP

Didier A. Depireux; Jeremy Schiff

doi:10.1007/BF00739799

On UrKdV and UrKP

Didier A. Depireux, Jeremy Schiff

Department of Mathematics

University of Montreal

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

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 Bäcklund transformations for the modified KP and KP equations.

Original language	English
Pages (from-to)	99-111
Number of pages	13
Journal	Letters in Mathematical Physics
Volume	33
Issue number	2
DOIs	https://doi.org/10.1007/BF00739799
State	Published - Feb 1995

Keywords

Mathematics Subject Classification (1991): 35Q53

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10.1007/BF00739799

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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 B{\"a}cklund transformations for the modified KP and KP equations.",

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AB - 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 Bäcklund transformations for the modified KP and KP equations.

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On UrKdV and UrKP

Abstract

Keywords

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