Numerical Solution of the Direct Zakharov–Shabat ScatteringProblem

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