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Journal of Scientific Computing
Erschienen in: Journal of Scientific Computing 2/2023

01.05.2023

Numerical Methods for Some Nonlinear Schrödinger Equations in Soliton Management

verfasst von: Ying He, Xiaofei Zhao

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2023

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Abstract

In this work, we consider the numerical solutions of a dispersion-managed nonlinear Schrödinger equation (DM-NLS) and a nonlinearity-managed NLS equation (NM-NLS). The two equations arise from the soliton managements in optics and matter waves, and they involve temporal discontinuous coefficients with possible frequent jumps and stiffness which cause numerical difficulties. We analyze to see the order reduction problems of some popular traditional methods, and then we propose a class of exponential-type dispersion-map integrators for both DM-NLS and NM-NLS. The proposed methods are explicit, efficient under Fourier pseudospectral discretizations and second order accurate in time regardless the jumps/jump-period in the dispersion map. The extension to the fast & strong management regime of DM-NLS is made with uniform accuracy.
Vorheriger Artikel Analysis of a Fourier–Galerkin Method for the Transmission Eigenvalue Problem based on a Boundary Integral Formulation
Nächster Artikel Superconvergence Analysis of Curlcurl-Conforming Elements on Rectangular Meshes

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Metadaten
Titel
Numerical Methods for Some Nonlinear Schrödinger Equations in Soliton Management
verfasst von
Ying He
Xiaofei Zhao
Publikationsdatum
01.05.2023
Verlag
Springer US
Erschienen in
Journal of Scientific Computing / Ausgabe 2/2023
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-023-02181-x

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