On Hamiltonian perturbations of hyperbolic systems of conservation laws, II: universality of critical behaviour

Details On Hamiltonian perturbations of hyperbolic systems of conservation laws, II: universality of critical behaviour On Hamiltonian perturbations of hyperbolic systems of conservation laws, II: universality of critical behaviour

2005-10-10

arxiv.org/abs/math-ph/0510032v2

Physics

Mathematical Physics

24 pages; section 7 improved; references added; misprints corrected

Scientific paper

10.1007/s00220-006-0021-5

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.

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