On universality of critical behaviour in Hamiltonian PDEs

Details On universality of critical behaviour in Hamiltonian PDEs On universality of critical behaviour in Hamiltonian PDEs

2008-04-23

arxiv.org/abs/0804.3790v1

Mathematics

Analysis of PDEs

59 pages, 2 figures. Amer. Math. Soc. Transl., to appear

Scientific paper

Our main goal is the comparative study of singularities of solutions to the systems of first order quasilinear PDEs and their perturbations containing higher derivatives. The study is focused on the subclass of Hamiltonian PDEs with one spatial dimension. For the systems of order one or two we describe the local structure of singularities of a generic solution to the unperturbed system near the point of "gradient catastrophe" in terms of standard objects of the classical singularity theory; we argue that their perturbed companions must be given by certain special solutions of Painleve' equations and their generalizations.

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