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We use the mathematical toolbox of the inverse scattering transform to studyquantitatively the number of solitons in a far from equilibrium one-dimensionalsystem described by the defocusing nonlinear Schr{\"o}dinger equation. We showthat combining two simple criteria we are able to identify the localizedeigenvalues of the Lax operator, corresponding to grey solitons and distinguishthem from the continuous part of the spectrum, corresponding to plane-waveexcitations. We apply this to the study of spatially periodic states andevidence the opening of multiple gaps in the spectrum. Our method can beapplied in principle to all physical systems described by the defocusingnonlinear Schr{\"o}dinger equation and allows to identify the solitons innumerical simulations.

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