✦ LIBER ✦

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

✍ Scribed by P. Lazaridis; G. Debarge; P. Gallion

Publisher: John Wiley and Sons
Year: 2001
Tongue: English
Weight: 59 KB
Volume: 14
Category: Article
ISSN: 0894-3370
DOI: 10.1002/jnm.415

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✦ Synopsis

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. Copyright © 2001 John Wiley & Sons, Ltd.

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