Numerical investigation of the stability of the rational solutions of the nonlinear Schrödinger equation

A. Islas and C.M. Schober

Applied Mathematics and Computation, 2017, vol. 305, issue C, 17-26

Abstract: The rational solutions of the nonlinear Schrödinger (NLS) equation have been proposed as models for rogue waves. In this article, we develop a highly accurate Chebyshev pseudo-spectral method (CPS4) to numerically study the stability of the rational solutions of the NLS equation. The scheme CPS4, using the map x=cotθ and the FFT to approximate uxx, correctly handles the infinite line problem. A broad numerical investigation using CPS4 and involving large ensembles of perturbed initial data, indicates the Peregrine and second order rational solutions are linearly unstable.

Keywords: Rogue waves; Peregrine solution; Stability; Spectral splitting; Chebyshev spectral methods; Spectral methods (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:305:y:2017:i:c:p:17-26

DOI: 10.1016/j.amc.2017.01.060

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