A note on Miura’s transformation
- 1 June 1979
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 20 (6) , 999-1003
- https://doi.org/10.1063/1.524197
Abstract
It has been observed by Miura that the solutions of the modified Korteweg–deVries equation can be mapped into those of the Korteweg–deVries equation. In this note we show that all of the solutions of the former, decaying sufficiently rapidly as ‖x‖→∞, map into a sparse solution set of the KdV equation. We use certain results regarding the second Painlevé transcendent to exhibit this fact.Keywords
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