Multidomain spectral method for Schrödinger equations

Abstract : A multidomain spectral method with compactified exterior domains combined with stable second and fourth order time integrators is presented for Schrodinger equations. The numerical approach allows high precision numerical studies of solutions on the whole real line. At examples for the linear and cubic nonlinear Schrodinger 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.
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Advances in Computational Mathematics, Springer Verlag, 2016, 42 (2), pp.395 - 423. <http://link.springer.com/article/10.1007%2Fs10444-015-9429-9>. <10.1007/s10444-015-9429-9>
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https://hal-univ-bourgogne.archives-ouvertes.fr/hal-01413426
Contributeur : Imb - Université de Bourgogne <>
Soumis le : vendredi 9 décembre 2016 - 17:24:35
Dernière modification le : mardi 13 décembre 2016 - 09:30:19

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Mira Birem, Christian Klein. Multidomain spectral method for Schrödinger equations. Advances in Computational Mathematics, Springer Verlag, 2016, 42 (2), pp.395 - 423. <http://link.springer.com/article/10.1007%2Fs10444-015-9429-9>. <10.1007/s10444-015-9429-9>. <hal-01413426>

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