Numerical Solution of the Direct Zakharov–Shabat Scattering Problem


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.

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This work was supported by the Russian Foundation for Basic Research (project no. 16-29-15122 ofi-m), by the Russian Science Foundation (project no. 17-72-30006), and by the Ministry of Science and Education of the Russian Federation (project no. 1201364502 (LLF)).

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Correspondence to N. I. Gorbenko or V. P. Il’in or A. M. Krylov or L. L. Frumin.

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Gorbenko, N.I., Il’in, V.P., Krylov, A.M. et al. Numerical Solution of the Direct Zakharov–Shabat Scattering Problem. Numer. Analys. Appl. 13, 95–102 (2020).

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  • direct scattering problem
  • fourth order difference scheme
  • Marchuk identity