Advances in Computational Mathematics

, Volume 42, Issue 2, pp 395–423 | Cite as

Multidomain spectral method for Schrödinger equations

  • Mira Birem
  • Christian KleinEmail author


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. 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.


Schrödinger equation Nonlinear Schrödinger equation Spectral methods Transparent boundary conditions Perfectly matched layers Rogue waves 

Mathematics Subject Classifications (2010)

65M70 35Q41 35Q55 


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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institut de Mathématiques de BourgogneUniversité de BourgogneDijon CedexFrance

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