Fast Eigenvalue Evaluation of the Direct Zakharov-Shabat Problem in Telecommunication Signals Using Adaptive Phase Jump Tracking

The inverse scattering transform (IST) allows to integrate the nonlinear Schrödinger equation (NLSE) equation analytically [1] and consists of three main steps: the first step is solving the direct Zakharov-Shabat problem (ZSP) to determine scattering data, the second is an evolution of the scattering data, and the third step is solving the inverse scattering problem to restore a solution from the scattering data. This method, also known as the nonlinear Fourier transform (NFT), has recently attracted much attention in areas where NLSE is used to describe various types of optical signals such as lasers and telecommunications.