On the numerical study of the rational solutions of the nonlinear Schrödinger equation
In: AIP Conference Proceedings, 2016
Online
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Zugriff:
The stability of the rational solutions of the nonlinear Schrodinger (NLS) equation has only recently began to be addressed. In this paper we develop a Chebyshev pseudo-spectral method for the NLS equation to study the stability of the rational solutions. Using the map x = cot θ and the Fast Fourier Transform (FFT) to approximate uxx, the Chebyshev scheme effectively handles the infinite line boundary conditions. An extensive numerical study, involving large ensembles of perturbed initial data for the Peregrine solution (the lowest order rational solution), indicates it is linearly unstable.Working with unstable solutions is numerically challenging. In the current literature, numerical experiments related to the Peregrine solution frequently employ standard Fourier methods without a discussion of the related numerical issues. We examine the performance of a Fourier pseudo-spectral method (FPS4) using Peregrine initial data. Applying FPS4, tiny Gibbs oscillations occur in the first few steps of the numeric...
Titel: |
On the numerical study of the rational solutions of the nonlinear Schrödinger equation
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Autor/in / Beteiligte Person: | Islas, A. ; Schober, C. M. |
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Zeitschrift: | AIP Conference Proceedings, 2016 |
Veröffentlichung: | Author(s), 2016 |
Medientyp: | unknown |
ISSN: | 0094-243X (print) |
DOI: | 10.1063/1.4964993 |
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