On the Drinfeld-Sokolov Hierarchies of D type
Exactly Solvable and Integrable Systems
2009-12-31 v1
Abstract
We extend the notion of pseudo-differential operators that are used to represent the Gelfand-Dickey hierarchies, and obtain a similar representation for the full Drinfeld-Sokolov hierarchies of type. By using such pseudo-differential operators we introduce the tau functions of these bi-Hamiltonian hierarchies, and prove that these hierarchies are equivalent to the integrable hierarchies defined by Date-Jimbo-Kashiware-Miwa and Kac-Wakimoto from the basic representation of the Kac-Moody algebra .
Keywords
Cite
@article{arxiv.0912.5273,
title = {On the Drinfeld-Sokolov Hierarchies of D type},
author = {Si-Qi Liu and Chao-Zhong Wu and Youjin Zhang},
journal= {arXiv preprint arXiv:0912.5273},
year = {2009}
}
Comments
With 3 Figures