  It is shown that the hodograph solutions of the dispersionless coupled KdV
(dcKdV) hierarchies describe critical and degenerate critical points of a
scalar function which obeys the Euler-Poisson-Darboux equation. Singular
sectors of each dcKdV hierarchy are found to be described by solutions of
higher genus dcKdV hierarchies. Concrete solutions exhibiting shock type
singularities are presented.
