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

P. Lazaridis, G. Debarge, P. Gallion

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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 languageEnglish
Pages (from-to)325-329
Number of pages5
JournalInternational Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Issue number4
Early online date16 Mar 2001
Publication statusPublished - Jul 2001
Externally publishedYes


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