  We discuss the structure of shock singularities of the Burgers-Hopf
hierarchy. It is shown that the set of singular solutions defines a
stratification of the affine space of the flow parameters in the hierarchy. The
stratification is associated with the Birkhoff decomposition of the
Grassmannian given by the set of linear spaces spanned by the hierarchy. We
then construct integrable hierarchy on each stratum and demonstrate that it
describes a deformation of a hyperelliptic curve parametrizing the stratum. The
hierarchy is called the hidden Burgers-Hopf hierarchy, and we found the Riemann
invarint form and the hodograph solution.
