00819nas a2200097 4500008004300000245011600043210006900159520043700228100002000665856003600685 2006 en_Ud 00aOn Hamiltonian perturbations of hyperbolic systems of conservation laws, II: universality of critical behaviour0 aHamiltonian perturbations of hyperbolic systems of conservation 3 aHamiltonian 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.1 aDubrovin, Boris uhttp://hdl.handle.net/1963/1786