Hydrodynamic X Waves

Abstract

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 þ 1 nonlinear Schrödinger equation, which predicts a balance between dispersion and diffraction when the envelope (the arms of the X) travel at AE arctanð1= ffiffi ffi 2 p Þ ≈ AE35.26°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.

Rapid spectral evolution of steep surface wave groups with directional spreading

“…The spreading parameter initially declines during focusing, indicating a more unidirectional wave group resembling the ‘wall of water’ effect described by Gibbs & Taylor (2005) and observed experimentally by Steer et al. (2019), followed by a rapid increase in directional spreading due to the oblique non-degenerate energy transfers shown in figure 3( c ). The increase in directional spreading occurs earlier for the steeper wave groups indicating an earlier onset of the non-degenerate interactions.…”

“…We note that suppressed linear dispersion has been observed by Steer et al. (2019) for modulations which propagate at to the wave group, which can increase the lifetime of a focused wave event. Thus, the energy transfers apparent in figure 3( b ) may contribute to the lifetime extension depicted in figure 2( a ).…”

“…Notably, there are spectral changes which arise during focus that do not reverse after focus indicating permanent changes to the spectrum. We note that suppressed linear dispersion has been observed by Steer et al (2019) for modulations which propagate at ±35.26 • to the wave group, which can increase the lifetime of a focused wave event. Thus, the ±35.26 • energy transfers apparent in figure 3(b) may contribute to the lifetime extension depicted in figure 2(a).…”

X-type Soliton, Resonance Y-type Soliton and Hybrid Solutions of a (2+1)-dimensional Hirota-Satsuma-Ito System for the Shallow Water Waves

“…Waves, one of the most common natural phenomena, have attracted people's attention [1][2][3][4][5][6]. It has been known that mechanical waves consist of the water waves, seismic waves, sound waves in air, electromagnetic waves, quantum waves, etc [7][8][9][10][11][12].…”

Kuznetsov–Ma breather-like solutions in the Salerno model

“…Whether they may arise "spontaneously out of nowhere a e-mail: jksullivan@umass.edu b e-mail: echarala@calpoly.edu (corresponding author) c e-mail: jcuevas@us.es d e-mail: kevrekid@math.umass.edu e e-mail: karan@aegean.gr and disappear without a trace" [8], or generated gradually through energy transfer in multiple soliton collision, they are studied intensely in a diverse range of settings [9][10][11][12]. Relevant studies have appeared from superfluid helium [13], to plasmas [14] and from nonlinear optics [15][16][17][18][19][20][21] to the, arguably, most natural venue of water waves [22][23][24][25].…”