The nonlinear Schrödinger equation is widely used in telecommunication applications, because it allows one to describe the propagation of pulses in an optical fiber. Recently some new approaches based on the nonlinear Fourier transform (NFT) have been actively explored to compensate for fiber nonlinearity and to exceed the limitations of nonlinearity-imposed limits of linear transmission methods. The first step in the NFT method is the solution of the direct scattering problem for the Zakharov-Shabat (ZS) system. Improving the accuracy of computational methods to solve the direct ZS problem remains an urgent problem in optics. In particular, it is important to increase the approximation order of the methods, especially in problems where it is necessary to analyze the structure of complex waveforms. In addition multi-soliton pulses are potential candidates for fiber optical transmission, where the information is modulated and recovered in the so-called nonlinear Fourier domain. To correctly describe them and their spectral parameters, more accurate and fast numerical methods are needed.