@article {2009,
title = {On universality of critical behaviour in the focusing nonlinear Schr{\"o}dinger equation, elliptic umbilic catastrophe and the {\\\\it tritronqu{\'e}e} solution to the Painlev{\'e}-I equation},
journal = {J. Nonlinear Sci. 19 (2009) 57-94},
number = {arXiv.org;0704.0501},
year = {2009},
abstract = {We argue that the critical behaviour near the point of {\textquoteleft}{\textquoteleft}gradient catastrophe\\\" of the solution to the Cauchy problem for the focusing nonlinear Schr\\\\\\\"odinger equation $ i\\\\epsilon \\\\psi_t +\\\\frac{\\\\epsilon^2}2\\\\psi_{xx}+ |\\\\psi|^2 \\\\psi =0$ with analytic initial data of the form $\\\\psi(x,0;\\\\epsilon) =A(x) e^{\\\\frac{i}{\\\\epsilon} S(x)}$ is approximately described by a particular solution to the Painlev\\\\\\\'e-I equation.},
doi = {10.1007/s00332-008-9025-y},
url = {http://hdl.handle.net/1963/2525},
author = {Boris Dubrovin and Tamara Grava and Christian Klein}
}
@inbook {2006,
title = {On universality of critical behaviour in Hamiltonian PDEs},
booktitle = {Geometry, 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},
number = {American Mathematical Society translations, ISSN 0065-9290;ser. 2;v. 224},
year = {2006},
publisher = {American Mathematical Society},
organization = {American Mathematical Society},
abstract = {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.},
isbn = {978-0-8218-4674-2},
url = {http://hdl.handle.net/1963/6491},
author = {Boris Dubrovin}
}