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

TitleOn Hamiltonian perturbations of hyperbolic systems of conservation laws, II: universality of critical behaviour
Publication TypePreprint
2006
AuthorsDubrovin, B
Series TitleComm. Math. Phys. 267 (2006) 117-139
Document NumberSISSA;89/2005/FM

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.

http://hdl.handle.net/1963/1786
10.1007/s00220-006-0021-5

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