%0 Journal Article %J J. Nonlinear Sci. 19 (2009) 57-94 %D 2009 %T On universality of critical behaviour in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the \\\\it tritronquée solution to the Painlevé-I equation %A Boris Dubrovin %A Tamara Grava %A Christian Klein %X We argue that the critical behaviour near the point of ``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. %B J. Nonlinear Sci. 19 (2009) 57-94 %G en_US %U http://hdl.handle.net/1963/2525 %1 1593 %2 Mathematics %3 Mathematical Physics %$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-11T13:11:26Z\\nNo. of bitstreams: 1\\n0704.0501v3.pdf: 568190 bytes, checksum: cf8471fc01eea53ce252339eda81b3cd (MD5) %R 10.1007/s00332-008-9025-y