00978nas a2200121   4500008004300000245018700043210006900230520046200299100002000761700001800781700002100799856003600820       2009                        en_Ud  00aOn universality of critical behaviour in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the {\\\\it tritronquée} solution to the Painlevé-I equation0 auniversality of critical behaviour in the focusing nonlinear Sch3 aWe 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.1 aDubrovin, Boris1 aGrava, Tamara1 aKlein, Christian  uhttp://hdl.handle.net/1963/2525