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Proc Natl Acad Sci U S A. 2019 May 14;116(20):9759-9763. doi: 10.1073/pnas.1821970116. Epub 2019 Apr 26.

Directional soliton and breather beams.

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Centre for Wind, Waves and Water, School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia;
Department of Ocean Technology Policy and Environment, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba 277-8563, Japan.
Dynamics Group, Hamburg University of Technology, 21073 Hamburg, Germany.
Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, United Kingdom.
Department of Infrastructure Engineering, The University of Melbourne, Parkville, VIC 3010, Australia.
School of Engineering, University of Edinburgh, Edinburgh EH9 3FB, United Kingdom.
Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, United Kingdom.
Research School of Physics and Engineering, The Australian National University, Canberra, ACT 2600, Australia.
Dipartimento di Fisica, Università degli Studi di Torino, 10125 Torino, Italy.
Istituto Nazionale di Fisica Nucleare, Sezione di Torino, 10125 Torino, Italy.


Solitons and breathers are nonlinear modes that exist in a wide range of physical systems. They are fundamental solutions of a number of nonlinear wave evolution equations, including the unidirectional nonlinear Schrödinger equation (NLSE). We report the observation of slanted solitons and breathers propagating at an angle with respect to the direction of propagation of the wave field. As the coherence is diagonal, the scale in the crest direction becomes finite; consequently, beam dynamics form. Spatiotemporal measurements of the water surface elevation are obtained by stereo-reconstructing the positions of the floating markers placed on a regular lattice and recorded with two synchronized high-speed cameras. Experimental results, based on the predictions obtained from the (2D + 1) hyperbolic NLSE equation, are in excellent agreement with the theory. Our study proves the existence of such unique and coherent wave packets and has serious implications for practical applications in optical sciences and physical oceanography. Moreover, unstable wave fields in this geometry may explain the formation of directional large-amplitude rogue waves with a finite crest length within a wide range of nonlinear dispersive media, such as Bose-Einstein condensates, solids, plasma, hydrodynamics, and optics.


directional localizations; extreme events; nonlinear waves; solitons

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