Hydrodynamic X Waves

James N. Steer, Alistair G.L. Borthwick, Miguel Onorato, Amin Chabchoub, Ton S. Van Den Bremer

Research output: Contribution to journalArticleScientificpeer-review

10 Citations (Scopus)


Stationary wave groups exist in a range of nonlinear dispersive media, including optics, Bose-Einstein condensates, plasma, and hydrodynamics. We report experimental observations of nonlinear surface gravity X waves, i.e., X-shaped wave envelopes that propagate over long distances with constant form. These can be described by the 2D+1 nonlinear Schrödinger equation, which predicts a balance between dispersion and diffraction when the envelope (the arms of the X) travel at ±arctan(1/2)≈±35.26° to the carrier wave. Our findings may help improve understanding the lifetime of extremes in directional seas and motivate further studies in other nonlinear dispersive media.

Original languageEnglish
Article number184501
JournalPhysical Review Letters
Issue number18
Publication statusPublished - 29 Oct 2019
Externally publishedYes


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