Fast Algorithms for Solving the Inverse Scattering Problem for the Zakharov–Shabat System of Equations and Their Applications

The problem of numerical solution of a nonlinear Schrödinger equation is considered from the point of view of applications to the compensation of signal distortions in a fiber optic communication line. The problem of constructing fast algorithms for the direct and inverse scattering problems for the Zakharov–Shabat system of equations is studied. An overview of the main methods used currently is given. The time complexity of the algorithms is described together with their applicability to realistic signals.