2024/04/25 by Yang, Di, Zhang, Cheng, Zhou, Zejun
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2404.16458
Inspired by a recent work of Dubrovin [7], for each simple Lie algebra \mathfrakg, we introduce an infinite family of pairwise commuting ODEs and define their τ-functions. We show that these τ-functions can be identified with the τ-functions for the Drinfeld--Sokolov hierarchy of \mathfrakg-type. Explicit examples for \mathfrakg=A1 and A2 are provided, which are connected to the KdV hierarchy and the Boussinesq hierarchy respectively.