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Teoreticheskaya i Matematicheskaya Fizika, 2020, Volume 205, Number 1, Pages 102–123
DOI: https://doi.org/10.4213/tmf9826 (Mi tmf9826) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Virasoro symmetries of multicomponent Gelfand–Dickey systems

Ling  An, Chuanzhong Li

School of Mathematics and Statistics, Ningbo University, Ningbo, China
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DOI: https://doi.org/10.4213/tmf9826
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.
Funding agency Grant number
National Natural Science Foundation of China 12071237
K. C. Wong Magna Fund (Ningbo University)
The research of Chuanzhong Li is supported by the National Natural Science Foundation of China (Grant No. 12071237) and the K. C. Wong Magna Fund in Ningbo University.
Received: 22.09.2019
Revised: 17.03.2020
English version:
Theoretical and Mathematical Physics, 2020, Volume 205, Issue 1, Pages 1333–1352
DOI: https://doi.org/10.1134/S0040577920100074
Bibliographic databases:
Document Type: Article
PACS: 05.45.Yv, 02.30.Jr, 02.30.Ik
MSC: 37K05, 37K10
Language: Russian
Citation: Ling  An, Chuanzhong Li, “Virasoro symmetries of multicomponent Gelfand–Dickey systems”, TMF, 205:1 (2020), 102–123; Theoret. and Math. Phys., 205:1 (2020), 1333–1352
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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