Numerical Solution of the Direct Zakharov–Shabat Scattering Problem

A numerical solution of the direct scattering problem for the systemof Zakharov–Shabat equations is considered. Based on the Marchukidentity, a method of fourth-order approximation accuracy is proposed. Anumerical simulation of the scattering problem is made using twocharacteristic boundary value problems with known solutions as anexample. The calculations have shown that the algorithm has highaccuracy, which is necessary in many practical applications of opticaland acoustic sensing in applied optics and geophysics.