  The totality of all Zakharov-Shabat equations (ZS), i.e., zero-curvature
equations with rational dependence on a spectral parameter, if properly
defined, can be considered as a hierarchy. The latter means a collection of
commuting vector fields in the same phase space. Further properties of the
hierarchy are discussed, such as additional symmetries, an analogue to the
string equation, a Grassmannian related to the ZS hierarchy, and a Grassmannian
definition of soliton solutions.
