论文标题
多组分Gelfand-Dickey Systems的Virasoro对称性
Virasoro symmetries of Multi-Component Gelfand-Dickey systems
论文作者
论文摘要
在本文中，我们主要研究了多组分Gelfand-Dickey层次结构的其他对称性和$τ$函数，该层次结构包括许多经典的集成系统，例如多组分KDV层次结构和多组件BousSinesQ层次结构。通过其他类型的减少，我们可以得出A型多组分Gelfand-Dickey层次结构和A类型多组分Gelfand-Dickey层次结构。在我们的研究中，附加对称性的其他流都不能全部生存。通过计算，我们发现C类型多组分Gelfand-Dickey层次结构的附加对称性的发生器与B类型多组分Gelfand-Dickey层次结构的生成器不同，而其存活的其他流的形式则是相同的。
In this paper, we mainly study the additional symmetry and $τ$ 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.
