On Hamiltonian perturbations of hyperbolic systems of conservation laws, II: universality of critical behaviour
Dubrovin, Boris
arXiv, 0510032 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-10-10
Classification:  Mathematical Physics,  Nonlinear Sciences - Exactly Solvable and Integrable Systems 
@article{0510032,
     author = {Dubrovin, Boris},
     title = {On Hamiltonian perturbations of hyperbolic systems of conservation laws,
  II: universality of critical behaviour},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0510032}
}

Dubrovin, Boris. On Hamiltonian perturbations of hyperbolic systems of conservation laws,
  II: universality of critical behaviour. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0510032/