Characterizing far from equilibrium states of the one-dimensional nonlinear Schr{\"o}dinger equation

We use the mathematical toolbox of the inverse scattering transform to study quantitatively the number of solitons in far from equilibrium one-dimensional systems described by the defocusing nonlinear Schr{\"o}dinger equation. We present a simple method to identify the discrete eigenvalues in the Lax spectrum and provide a extensive benchmark of its efficiency. Our method can be applied in principle to all physical systems described by the defocusing nonlinear Schr{\"o}dinger equation and allows to identify the solitons velocity distribution in numerical simulations and possibly experiments.