2019/08/19 by Siqi Liu, Chaozhong Wu, Liu, Si-Qi +3
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1908.06707
openalex publication_date 2019/08/19 · openalex created_date 2022/08/27 · openalex updated_date 2026/07/28
We construct a tau cover of the generalized Drinfeld-Sokolov hierarchy associated to an arbitrary affine Kac-Moody algebra with gradations s≤\mathds1 and derive its Virasoro symmetries. By imposing the Virasoro constraints we obtain solutions of the Drinfeld-Sokolov hierarchy of Witten-Kontsevich and of Brezin-Gross-Witten types, and of those characterized by certain ordinary differential equations of Painlevé type. We also show the existence of affine Weyl group actions on solutions of such Painlevé type equations, which generalizes the theory of Noumi and Yamada on affine Weyl group symmetries of the Painlevé type equations.