The numerical solution of the direct Zakharov–Shabat scattering problem

The numerical solution of the direct scattering problem for a system of the Zakharov–Shabat equations is considered. Based on the Marchuk identity, a fourth order method of approximation accuracy is proposed. The numerical simulation of the scattering problem is carried out using an example of two characteristic boundary value problems with known solutions. The calculations have confirmed high accuracy of the algorithm proposed, which is necessary in a number of practical applications for optical and acoustic sensing of media in optics and geophysics applied.