TY - JOUR

T1 - Exponential fourth order schemes for direct Zakharov-Shabat problem

AU - Medvedev, Sergey

AU - Vaseva, Irina

AU - Chekhovskoy, Igor

AU - Fedoruk, Mikhail

PY - 2020/1/1

Y1 - 2020/1/1

N2 - Nowadays, improving the accuracy of computational methods to solve the initial value problem of the Zakharov-Shabat system remains an urgent problem in optics. In particular, increasing the approximation order of the methods is important, especially in problems where it is necessary to analyze the structure of complex waveforms. In this work, we propose two finite-difference algorithms of fourth order of approximation in the time variable. Both schemes have the exponential form and conserve the quadratic invariant of Zakharov-Shabat system. The second scheme allows applying fast algorithms with low computational complexity (fast nonlinear Fourier transform).

AB - Nowadays, improving the accuracy of computational methods to solve the initial value problem of the Zakharov-Shabat system remains an urgent problem in optics. In particular, increasing the approximation order of the methods is important, especially in problems where it is necessary to analyze the structure of complex waveforms. In this work, we propose two finite-difference algorithms of fourth order of approximation in the time variable. Both schemes have the exponential form and conserve the quadratic invariant of Zakharov-Shabat system. The second scheme allows applying fast algorithms with low computational complexity (fast nonlinear Fourier transform).

KW - NONLINEAR FOURIER-TRANSFORM

KW - DIRECT SCATTERING TRANSFORM

KW - INVERSE SYNTHESIS

KW - TRANSMISSION

KW - MODULATION

KW - ALGORITHMS

KW - COMPUTATION

KW - ACCURACY

KW - STANDARD

UR - http://www.scopus.com/inward/record.url?scp=85078065570&partnerID=8YFLogxK

U2 - 10.1364/OE.377140

DO - 10.1364/OE.377140

M3 - Article

C2 - 32118938

AN - SCOPUS:85078065570

VL - 28

SP - 20

EP - 39

JO - Optics Express

JF - Optics Express

SN - 1094-4087

IS - 1

ER -