Linear instability of the Peregrine breather: numerical and analytical investigations
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Publication:2000083
DOI10.1016/J.APNUM.2018.11.005zbMATH Open1420.35345arXiv1803.06584OpenAlexW2963522025WikidataQ128901776 ScholiaQ128901776MaRDI QIDQ2000083
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Publication date: 27 June 2019
Published in: (Search for Journal in Brave)
Abstract: We study the linear stability of the Peregrine breather both numerically and with analytical arguments based on its derivation as the singular limit of a single-mode spatially periodic breather as the spatial period becomes infinite. By constructing solutions of the linearization of the nonlinear Schr"odinger equation in terms of quadratic products of components of the eigenfunctions of the Zakharov-Shabat system, we show that the Peregrine breather is linearly unstable. A numerical study employing a highly accurate Chebychev pseudo-spectral integrator confirms exponential growth of random initial perturbations of the Peregrine breather.
Full work available at URL: https://arxiv.org/abs/1803.06584
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