Universality for the Focusing Nonlinear Schrödinger Equation at the Gradient Catastrophe Point: Rational Breathers and Poles of the Tritronquée Solution to Painlevé I

• Published in: Communications on pure and applied mathematics Vol. 66; no. 5; pp. 678 - 752
• Main Authors: Bertola, Marco, Tovbis, Alexander
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.05.2013; John Wiley and Sons, Limited
• Subjects: Approximation; Hilbert space; Matrix; Nonlinear equations; Schrodinger equation; Solutions

The semiclassical (zero‐dispersion) limit of solutions $q=q(x,t,\epsilon)$ to the one‐dimensional focusing nonlinear Schrödinger equation (NLS) is studied in a scaling neighborhood D of a point of gradient catastrophe ($x_0,t_0$). We consider a class of solutions, specified in the text, that decay a...