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Multidomain spectral method for Schrödinger equations

Banff International Research Station for Mathematical Innovation and Discovery

A multidomain spectral method with compactified exterior domains combined with stable second and fourth order time integrators is presented for Schrödinger equations. The numerical approach allows high precision numerical studies of solutions on the whole real line or in higher dimensions. At examples for the linear and cubic nonlinear Schrödinger equation, this code is compared to transparent boundary conditions and perfectly matched layers approaches. The code can deal with asymptotically non vanishing solutions as the Peregrine breather being discussed as a model for rogue waves. It is shown that the Peregrine breather can be numerically propagated with essentially machine precision, and that localized perturbations of this solution can be studied

Mathematics; Fluid mechanics; Partial differential equations; Fluid dynamics

video/mp4

Author affiliation: Institut de Mathématiques de Bourgogne

2017-05-02

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/61425

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/