Abstract
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.
Highlights
Nonlinear waves | solitons | directional localizations | extreme events tion must be answered before considering more complicated cases
In a simplified way, such a wave field consists of many waves crossing each other at various angles, implying at a linear level that the water surface is a mere interference of short- and long-crested waves coming from different directions [4,5,6]
We report a theoretical framework, based on the universal (2D + 1) nonlinear Schrodinger equation, that allows the construction of slanted solitons and breathers on the water surface
Summary
Amin Chabchouba,b,1, Kento Mozumib, Norbert Hoffmannc,d, Alexander V. Being an integrable evolution equation, it allows for the study of particular and localized coherent wave patterns, such as solitons and breathers [8,9,10] The latter are of major relevance to study the fundamental wave dynamics in nonlinear dispersive media with a wide range of applications [11,12,13]. We report a theoretical framework, based on the universal (2D + 1) nonlinear Schrodinger equation, that allows the construction of slanted solitons and breathers on the water surface. Our corresponding wave flume observations emphasize and uniquely reveal that short-crested localizations can be described as a result of nonlinear wave dynamics, complementing the linear superposition and interference arguments as has been generally suggested for directional ocean waves. Our results confirm and prove the existence of such unique and coherent beams of a quasi-1D and short-crested wave group in a nonlinear dispersive medium
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