Bäcklund transformations of MKdV and Painlevé equations

Jeremy Schiff

doi:10.1088/0951-7715/7/1/015

Bäcklund transformations of MKdV and Painlevé equations

Jeremy Schiff

Department of Mathematics

Institute for Advanced Studies

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

13 Scopus citations

Abstract

For N ≥ 3 there are S_N and D_N actions on the space of solutions of the first nontrivial equation in the SL(N) MKdV hierarchy, generalizing the two Z₂ actions on the space of solutions of the standard MKdV equation. These actions survive scaling reduction, and give rise to transformation groups for certain (systems of) ODEs, including the second, fourth and fifth Painleve equations.

Original language	English
Pages (from-to)	305-312
Number of pages	8
Journal	Nonlinearity
Volume	7
Issue number	1
DOIs	https://doi.org/10.1088/0951-7715/7/1/015
State	Published - Jan 1994

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title = "B{\"a}cklund transformations of MKdV and Painlev{\'e} equations",

abstract = "For N ≥ 3 there are SN and DN actions on the space of solutions of the first nontrivial equation in the SL(N) MKdV hierarchy, generalizing the two Z2 actions on the space of solutions of the standard MKdV equation. These actions survive scaling reduction, and give rise to transformation groups for certain (systems of) ODEs, including the second, fourth and fifth Painleve equations.",

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AB - For N ≥ 3 there are SN and DN actions on the space of solutions of the first nontrivial equation in the SL(N) MKdV hierarchy, generalizing the two Z2 actions on the space of solutions of the standard MKdV equation. These actions survive scaling reduction, and give rise to transformation groups for certain (systems of) ODEs, including the second, fourth and fifth Painleve equations.

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Bäcklund transformations of MKdV and Painlevé equations

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