This article is cited in 1 paper

Virasoro symmetries of multicomponent Gelfand–Dickey systems

Ling  An, Chuanzhong Li

School of Mathematics and Statistics, Ningbo University, Ningbo, China

Abstract: We study the additional symmetries and $\tau$-functions of multicomponent Gelfand–Dickey hierarchies, which include classical integrable systems such as the multicomponent Korteweg–de Vries and Boussinesq hierarchies. Using various reductions, we derive B- and C-type multicomponent Gelfand–Dickey hierarchies. We show that not all flows of their additional symmetries survive. We find that the generators of the additional symmetries of the B- and C-type multicomponent Gelfand–Dickey hierarchies differ but the forms of their additional flows are the same.

Keywords: multicomponent Gelfand–Dickey hierarchy, additional symmetry, string equation, $\tau$-function, Virasoro constraint.

PACS: 05.45.Yv, 02.30.Jr, 02.30.Ik

MSC: 37K05, 37K10

Received: 22.09.2019
Revised: 17.03.2020

DOI: 10.4213/tmf9826

 English version: Theoretical and Mathematical Physics, 2020, 205:1, 1333–1352

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