English

Virasoro symmetries of Multi-Component Gelfand-Dickey systems

Exactly Solvable and Integrable Systems 2020-12-02 v1 Mathematical Physics math.MP

Abstract

In this paper, we mainly study the additional symmetry and τ\tau functions of a multi-component Gelfand-Dickey hierarchy which includes many classical integrable systems, such as the multi-component KdV hierarchy and the multi-component Boussinesq hierarchy. With other kinds of reductions, we can derive a B type multi-component Gelfand-Dickey hierarchy and a C type multi-component Gelfand-Dickey hierarchy. In our research, the additional flows of the additional symmetries can not all survive. By calculating, we find that the generator of the additional symmetry of the C type multi-component Gelfand-Dickey hierarchy is different from that of the B type multi-component Gelfand-Dickey hierarchy, while the forms of their surviving additional flows are the same.

Keywords

Cite

@article{arxiv.2006.03295,
  title  = {Virasoro symmetries of Multi-Component Gelfand-Dickey systems},
  author = {Ling An and Chuanzhong Li},
  journal= {arXiv preprint arXiv:2006.03295},
  year   = {2020}
}

Comments

23 Pages, to appear in Theoretical and Mathematical Physics