# 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.

Original language English 325-329 5 International Journal of Numerical Modelling: Electronic Networks, Devices and Fields 14 4 16 Mar 2001 https://doi.org/10.1002/jnm.415 Published - Jul 2001 Yes

### Fingerprint

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

### Cite this

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title = "Split-step-Gauss-Hermite algorithm for fast and accurate simulation of soliton propagation",
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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T1 - Split-step-Gauss-Hermite algorithm for fast and accurate simulation of soliton propagation

AU - Lazaridis, P.

AU - Debarge, G.

AU - Gallion, P.

PY - 2001/7

Y1 - 2001/7

N2 - 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.

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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U2 - 10.1002/jnm.415

DO - 10.1002/jnm.415

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VL - 14

SP - 325

EP - 329

JO - International Journal of Numerical Modelling: Electronic Networks, Devices and Fields

JF - International Journal of Numerical Modelling: Electronic Networks, Devices and Fields

SN - 0894-3370

IS - 4

ER -