The sixth Painleve equation as similarity reduction of gl_3 hierarchy
- Resource Type
- Working Paper
- Authors
- Kakei, Saburo; Kikuchi, Tetsuya
- Source
- Subject
- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- Language
Scaling 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.
Comment: 16 pages