Geodesic
Virasoro symmetries of multicomponent Gelfand--Dickey systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 1, pp. 102-123

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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. 
@article{TMF_2020_205_1_a6,
     author = {Ling An and Chuanzhong Li},
     title = {Virasoro symmetries of multicomponent {Gelfand--Dickey} systems},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {102--123},
     publisher = {mathdoc},
     volume = {205},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2020_205_1_a6/}
}
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Ling An; Chuanzhong Li. Virasoro symmetries of multicomponent Gelfand--Dickey systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 1, pp. 102-123. http://geodesic.mathdoc.fr/item/TMF_2020_205_1_a6/