Evaluating the Robustness of Rogue Waves Under Perturbations

TL;DR

This paper introduces a numerical method to identify and analyze rogue wave solutions in non-integrable models, demonstrating their robustness under perturbations and extending understanding beyond idealized integrable systems.

Contribution

A novel numerical approach for detecting rogue wave solutions in non-integrable models and assessing their parametric robustness.

Findings

Rogue waves can be continued over parameter variations in non-integrable models.

The methodology confirms the numerical propagation of known solutions with controllable error.

Peregrine-like waveforms are robust under perturbations and exist beyond integrable systems.

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.