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.
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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.
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An, L., Li, C. Virasoro symmetries of multicomponent Gelfand–Dickey systems. Theor Math Phys 205, 1333–1352 (2020). https://doi.org/10.1134/S0040577920100074
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DOI: https://doi.org/10.1134/S0040577920100074