@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}
}