Generalized Teplitzev inner fringing method for solving the Gelfand-Levitan-Marchenko equations

The paper discusses a new numerical method for solving the inverse Zakharov-Shabat problem, which is an integral part of the inverse scattering problem method for solving nonlinear Schrodinger equations. The inverse problem is to reconstruct the signal from the given spectral data and can be described using a system of Gelfand-Levitan-Marchenko equations. The method works for signals containing a continuous and discrete spectrum. For a discrete spectrum, a procedure is proposed for cutting off exponentially growing matrix elements that violate the stability of the computational process.