A second look at the Gaussian semiclassical soliton ensemble for the focusing nonlinear Schrödinger equation

Abstract

We study the Gaussian semiclassical soliton ensemble, a collection of multisoliton solutions of the focusing nonlinear Schrödinger equation. The ensemble is generated by adding a particular asymptotically vanishing sequence of perturbations to Gaussian initial data. Recent results (Lee et al., 2012) [21] suggest that, remarkably, these perturbations — interlaced as they are with the integrable structure of the equation — do not excite the acute modulational instabilities known to be present in the semiclassical regime. Our results here highlight the exceptional nature of these perturbations and provide new insight into the sensitivity properties of the related semiclassical limit problem.