B\"acklund 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 Painlev\'e equations.
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