  Hamiltonian perturbations of the simplest hyperbolic equation $u_t + a(u)
u_x=0$ are studied. We argue that the behaviour of solutions to the perturbed
equation near the point of gradient catastrophe of the unperturbed one should
be essentially independent on the choice of generic perturbation neither on the
choice of generic solution. Moreover, this behaviour is described by a special
solution to an integrable fourth order ODE.
