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

P. Lazaridis; G. Debarge; P. Gallion

doi:10.1002/jnm.415

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

P. Lazaridis, G. Debarge, P. Gallion

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	325-329
Number of pages	5
Journal	International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Volume	14
Issue number	4
Early online date	16 Mar 2001
DOIs	https://doi.org/10.1002/jnm.415
Publication status	Published - Jul 2001
Externally published	Yes

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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.",

author = "P. Lazaridis and G. Debarge and P. Gallion",

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AU - Debarge, G.

AU - Gallion, P.

PY - 2001/7

Y1 - 2001/7

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

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