Numerical solution of the direct scattering problem for the nonlinear Schrödinger equation

We illustrate a numerical method to compute the scattering data for the Zhakarov-Shabat system associated to the initial value problem for the nonlinear Schrödinger equation. This numerical method which, to our best knowledge, is the first method proposed to compute all scattering data under general assumptions, is based on the version of the Inverse Scattering Transform method proposed by one of the authors.