Directional soliton and breather beams

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.

Directional Coherent Wave Group From an Assimilated Non-linear Wavefield

“…The estimated wave period roughly corresponds to the dominant wave in the observed spectrum (Figure 1). Unlike the directional soliton studied in Chabchoub et al [8], the observed wave group is confined in the propagation direction as well. Longcrested envelope solitons are known to be unstable to transverse perturbation (e.g., [28]).…”

“…The theoretical framework of the directional wave group follows Chabchoub et al [8]. By applying a coordinate transformation, T = t cos θ − y c g sin θ , the 2D+T NLSE reduces to a 1D+T NLSE in which stable planar wave solutions exist.…”

“…As such, the key to understand the ocean waves, especially in the context of extremes, is to show the presence of coherent two-dimensional wave groups. A recent study by Chabchoub et al [8] employed an innovative scheme of transforming the 2D+T NLSE into a 1D+pseudo time NLSE and vice-versa thus, allowing the application of a known solution of the long-crested (1D+T) NLSE to model a short-crested two-dimensional wave group. As a result, an oblique wave group, oriented at an angle to the propagation direction, is formed, as suggested in the theoretical study [9].…”

“…This paper reports the first successful implementation of the SWEAD [12] to reconstruct a wave field, which analyzes the stereo reconstructed wave field and extends the estimated wave field to an area 900 times larger (30 by 30) than the observation. By a careful look at the reconstructed wave field, a coherent wave group whose envelope is oriented obliquely to the wave propagation direction was discovered and was shown to resemble the directional soliton [8]. The ocean tower observation by the stereo camera and the data assimilation scheme is introduced in section Observation and data assimilation.…”

Untitled

“…Preprocessing was done with a bandpass filter with a bandwidth from 20 min to 2.5 h. Visual analysis of the filtered time series of observations in the area of Cape Castricum revealed wave packets covering waves with a period of about 1.6 h. The wave packets occurred in groups of approximately 6 waves and appear to be synchronized with the beginning of the K1 (diurnal) tide. It is conjectured that the detected waves can be attributed to soliton-like oscillations or breathers [1][2][3][4][5][6], in which the oscillations are modulated within a soliton-like envelope. In work [6, p. 9759], the definition of soliton-like waves and breathers is given: "… these are nonlinear modes existing in a wide range of physical systems.…”