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- W4382989437 abstract "Представлен обзор актуальных численных алгоритмов, применяющихся для решения нелинейного уравнения Шрёдингера с помощью метода обратной задачи рассеяния. Рассмотрены как методы для прямой задачи, позволяющие вычислить так называемый нелинейный спектр Фурье, так и методы, с помощью которых можно по нелинейному спектру восстановить решение при любом значении эволюционной переменной (обратная задача). The paper presents an overview of the current numerical algorithms for implementing the inverse scattering transform (IST). The IST attracted special attention since it was proposed to use solitons as a bit of information for data transmission. Solitons are capable to compensate for nonlinear signal distortions and go beyond the limitations of linear data transmission methods. Accurate and fast numerical methods are needed to correctly describe and analyze the structure of complex multisoliton signals. Solitons are special solutions to the nonlinear Schr¨odinger equation (NLSE), which describes the propagation of pulses in an optical fiber. The IST allows one to integrate the NLSE. The paper considers methods for the direct Zakharov – Shabat (ZS) problem, which is a part of the IST. It allows calculating the nonlinear Fourier spectrum for a given potential. In particular, the paper presents the fast methods, needed for solving the problem for a large number of values of the spectral parameter. Special attention is given to the conservation property of the quadratic invariant of the ZS system. Since the integration takes place over a large area, the conservation of the quadratic invariant in computational algorithms must be exact. The paper also considers methods to restore the NLSE solution from a known nonlinear spectrum (inverse problem). Computational problems arising for a soliton spectrum are described. The methods described in the paper will be useful for more accurate and realistic calculations for the construction of telecommunication data transmission systems based on NLSE soliton solutions." @default.
- W4382989437 created "2023-07-04" @default.
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- W4382989437 date "2023-06-21" @default.
- W4382989437 modified "2023-10-18" @default.
- W4382989437 title "On numerical algorithms for solving the direct and inverse scattering problems of the Zakharov – Shabat system" @default.
- W4382989437 doi "https://doi.org/10.25743/ict.2023.28.3.005" @default.
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