On the Drinfeld-Sokolov Hierarchies of D type
Si-Qi Liu, Chao-Zhong Wu, Youjin Zhang

TL;DR
This paper extends pseudo-differential operator techniques to represent Drinfeld-Sokolov hierarchies of D type, introduces tau functions, and proves their equivalence to known integrable hierarchies from affine Kac-Moody algebra representations.
Contribution
It develops a pseudo-differential operator framework for D-type hierarchies and establishes their equivalence to existing integrable systems.
Findings
Representation of D-type hierarchies via pseudo-differential operators
Introduction of tau functions for these hierarchies
Proof of equivalence to hierarchies from Kac-Moody algebra representations
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 .
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Taxonomy
TopicsNonlinear Waves and Solitons · Algebraic structures and combinatorial models · Advanced Algebra and Geometry
