A novel fourth-order difference scheme for the direct Zakharov-Shabat problem

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Abstract

The numerical implementation of the nonlinear Fourier transformation (NFT) for the nonlinear Shrodinger equation (NLSE) requires effective numerical algorithms for each stage of the method. The very first step in this scheme is the solution of the direct scattering problem for the Zakharov-Shabat system. One of the most efficient methods for the solution of this problem is the second-order Boffetta-Osborne algorithm [1]. A review of numerical methods for direct NFT associated with the focusing NLSE is presented in [2]. Among the methods considered in this paper only the Runge-Kutta method is of fourth order of approximation. However, the application of the Runge-Kutta method is limited by the potentials specified analytically. The NFT algorithms of higher order presented recently in [3] require special nonuniform distribution of the signal.

Original languageEnglish
Title of host publicationThe European Conference on Lasers and Electro-Optics, CLEO_Europe_2019
PublisherOSA - The Optical Society
ISBN (Electronic)9781557528209
Publication statusPublished - 1 Jan 2019
EventThe European Conference on Lasers and Electro-Optics, CLEO_Europe_2019 - Munich, Germany
Duration: 23 Jun 201927 Jun 2019

Publication series

NameOptics InfoBase Conference Papers
VolumePart F140-CLEO_Europe 2019

Conference

ConferenceThe European Conference on Lasers and Electro-Optics, CLEO_Europe_2019
CountryGermany
CityMunich
Period23.06.201927.06.2019

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