Split-step-Gauss-Hermite algorithm for fast and accurate simulation of soliton propagation

P. Lazaridis, G. Debarge, P. Gallion

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

A simple and efficient algorithm is proposed for the numerical solution of the non-linear Schrödinger equation. Operator splitting is used, as with the split-step-Fourier method, in order to treat the linear part and the non-linear part of the equation separately. However, in our method, the FFT solution of the linear part is replaced by a very accurate Gauss-Hermite orthogonal expansion. Gaussian quadrature nodes and weights are used in order to calculate the expansion coefficients. Our methods is found to be very accurate and faster than the split-step-Fourier method for the model problem of single soliton propagation.

LanguageEnglish
Pages325-329
Number of pages5
JournalInternational Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Volume14
Issue number4
Early online date16 Mar 2001
DOIs
Publication statusPublished - Jul 2001
Externally publishedYes

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Fourier Method
Hermite
Solitons
Gauss
Hermite Expansion
Propagation
Orthogonal Expansion
Gaussian Quadrature
Operator Splitting
Nonlinear equations
Fast Fourier transforms
Nonlinear Schrödinger Equation
Mathematical operators
Simulation
Efficient Algorithms
Numerical Solution
Calculate
Coefficient
Vertex of a graph
Model

Cite this

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abstract = "A simple and efficient algorithm is proposed for the numerical solution of the non-linear Schr{\"o}dinger equation. Operator splitting is used, as with the split-step-Fourier method, in order to treat the linear part and the non-linear part of the equation separately. However, in our method, the FFT solution of the linear part is replaced by a very accurate Gauss-Hermite orthogonal expansion. Gaussian quadrature nodes and weights are used in order to calculate the expansion coefficients. Our methods is found to be very accurate and faster than the split-step-Fourier method for the model problem of single soliton propagation.",
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AU - Gallion, P.

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AB - A simple and efficient algorithm is proposed for the numerical solution of the non-linear Schrödinger equation. Operator splitting is used, as with the split-step-Fourier method, in order to treat the linear part and the non-linear part of the equation separately. However, in our method, the FFT solution of the linear part is replaced by a very accurate Gauss-Hermite orthogonal expansion. Gaussian quadrature nodes and weights are used in order to calculate the expansion coefficients. Our methods is found to be very accurate and faster than the split-step-Fourier method for the model problem of single soliton propagation.

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