Evaluating the Robustness of Rogue Waves Under Perturbations

C. B. Ward; P. G. Kevrekidis; N. Whitaker

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arXiv · 1712.03292

Evaluating the Robustness of Rogue Waves Under Perturbations

C. B. Ward·P. G. Kevrekidis·N. Whitaker

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Abstract

Rogue waves, and their periodic counterparts, have been shown to exist in a number of integrable models. However, relatively little is known about the existence of these objects in models where an exact formula is unattainable. In this work, we develop a novel numerical perspective towards identifying such states as localized solutions in space-time. Importantly, we illustrate that this methodology in addition to benchmarking known solutions (and confirming their numerical propagation under controllable error) enables the continuation of such solutions over parametric variations to non-integrable models. As a result, we can answer in the positive the question about the parametric robustness of Peregrine-like waveforms and even of generalizations thereof on a cnoidal wave background.

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BibTeX RIS

C. B. Ward, P. G. Kevrekidis, N. Whitaker. 2017-12-08. Evaluating the Robustness of Rogue Waves Under Perturbations. https://arxiv.org/abs/1712.03292

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