2017/12/08 by C. B. Ward, P. G. Kevrekidis, Ward, C. B. +3 · 1 citation
Earth and Planetary Sciences · Physics and Astronomy · #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Ocean Waves and Remote Sensing #Pattern Formation and Solitons (nlin.PS)
paper · pdf · doi:10.48550/arxiv.1712.03292
openalex publication_date 2017/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.