Bäcklund Transformations of MKdV and Painlevé Equations

Details Bäcklund Transformations of MKdV and Painlevé Equations Bäcklund Transformations of MKdV and Painlevé Equations

1993-05-19

arxiv.org/abs/solv-int/9305002v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

8 pages, plain tex

Scientific paper

10.1088/0951-7715/7/1/015

For $N\ge 3$ 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 $Z_2$ 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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