TY - GEN

T1 - A novel fourth-order difference scheme for the direct zakharov-shabat problem

AU - Medvedev, Sergey B.

AU - Vaseva, Irina A.

AU - Chekhovskoy, Igor S.

AU - Fedoruk, Mikhail P.

N1 - Publisher Copyright: © 2019 IEEE.

PY - 2019/6/1

Y1 - 2019/6/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85074661769&partnerID=8YFLogxK

U2 - 10.1109/CLEOE-EQEC.2019.8872769

DO - 10.1109/CLEOE-EQEC.2019.8872769

M3 - Conference contribution

T3 - 2019 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2019

BT - 2019 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2019

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2019 Conference on Lasers and Electro-Optics Europe and European Quantum Electronics Conference, CLEO/Europe-EQEC 2019

Y2 - 23 June 2019 through 27 June 2019

ER -