Observation of a hierarchy of up to fifth-order rogue waves in a water tank

TLDR

Our results enhance understanding of rogue water wave dynamics and suggest similar experiments in other nonlinear dispersive media such as fiber optics and plasma physics. The study aims to experimentally observe the hierarchy of rational breather solutions of the nonlinear Schrödinger equation in a water wave tank. The authors generate these breathers in a water wave tank by exciting the NLS’s rational solutions. Five breather orders were successfully produced, confirming theory, while higher orders proved unstable due to wave breaking and low carrier steepness, limiting direct relevance to oceanic rogue waves.

Abstract

We present experimental observations of the hierarchy of rational breather solutions of the nonlinear Schr\"odinger equation (NLS) generated in a water wave tank. First, five breathers of the infinite hierarchy have been successfully generated, thus confirming the theoretical predictions of their existence. Breathers of orders higher than five appeared to be unstable relative to the wave-breaking effect of water waves. Due to the strong influence of the wave breaking and relatively small carrier steepness values of the experiment these results for the higher-order solutions do not directly explain the formation of giant oceanic rogue waves. However, our results are important in understanding the dynamics of rogue water waves and may initiate similar experiments in other nonlinear dispersive media such as fiber optics and plasma physics, where the wave propagation is governed by the NLS.