2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/81051Scaling symmetry of gl_n-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.16 pagesExactly Solvable and Integrable Systemstext