TY - JOUR
T1 - On universality of critical behaviour in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the \\\\it tritronquée solution to the Painlevé-I equation
JF - J. Nonlinear Sci. 19 (2009) 57-94
Y1 - 2009
A1 - Boris Dubrovin
A1 - Tamara Grava
A1 - Christian Klein
AB - 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.
UR - http://hdl.handle.net/1963/2525
U1 - 1593
U2 - Mathematics
U3 - Mathematical Physics
ER -