The sixth Painleve equation as similarity reduction of gl3 hierarchy
Saburo Kakei, Tetsuya Kikuchi
Abstract
Scaling symmetry of gln-type Drinfel'd-Sokolov hierarchy is investigated. Applying similarity reduction to the hierarchy, one can obtain the Schlesinger equation with (n+1) regular singularities. Especially in the case of n=3, the hierarchy contains the three-wave resonant system and the similarity reduction gives the generic case of the Painleve VI equation. We also discuss Weyl group symmetry of the hierarchy.
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