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On universality of critical behaviour in Hamiltonian PDEs

TitleOn universality of critical behaviour in Hamiltonian PDEs
Publication TypeBook Chapter
Year of Publication2006
AuthorsDubrovin, B
Book TitleGeometry, topology, and mathematical physics : S.P. Novikov\\\'s seminar : 2006-2007 / V.M. Buchstaber, I.M. Krichever, editors. - Providence, R.I. : American Mathematical Society, 2008. - pages : 59-109
Series VolumeAmerican Mathematical Society translations, ISSN 0065-9290;ser. 2;v. 224
PublisherAmerican Mathematical Society
ISBN Number978-0-8218-4674-2

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


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