  Interrelation between Thom's catastrophes and differential equations
revisited. It is shown that versal deformations of critical points for
singularities of A,D,E type are described by the systems of Hamilton-Jacobi
type equations. For particular nonversal unfoldings the corresponding equations
are equivalent to the integrable two-component hydrodynamic type systems like
classical shallow water equation and dispersionless Toda system and others.
Pecularity of such integrable systems is that the generating functions for
corresponding hierarchies, which obey Euler-Poisson-Darboux equation, contain
information about normal forms of higher order and higher corank singularities.
