Emergence of coherent wave groups in deep-water random sea

The nonlinear Schrödinger equation and the propagation of weakly nonlinear waves in optical fibers and on the water surface

“…The NLSE can be considered as a universal equation in the sense that it describes the propagation of waves in a number of physical systems such as fiber optics [4,5], water waves [6,7], plasma waves [8] and Bose-Einstein condensation [9]; indeed, it can be a very useful tool not only for understanding physical analogies but also differences in the nonlinear behavior of the dispersive waves. An example that has attracted the scientific community recently is the dynamics of rogue waves in nonlinear dispersive media [10][11][12][13]. Those waves have been firstly discussed in the context of water waves and, more recently, have been the subject of intensive studies in nonlinear optics.…”

Anomalous wave statistics induced by abrupt depth change

“…From this perspective of anomalous behavior, rogue waves can be considered under the more general framework of turbulent dynamical systems [17,23,25,24,7,16]. Several physical mechanisms have been shown to produce rogue waves, most notably the Benjamin-Feir (BF) instability that occurs in deep water 1 [2,20,6,32,1,8,5,10], as well as wind excitation [3,28], opposing currents [21,29], and geometric ray focusing from 2D bathymetry [13,33].…”

Turbulent dynamics of an incoherently pumped passive optical fiber cavity: Quasisolitons, dispersive waves, and extreme events

“…An important question is to understand the formation of rogue waves from a turbulent state of the wave system [3,11,[17][18][19][20]. In the particular context of optics, this problem has been addressed in nonintegrable Hamiltonian systems by considering the NLS equation in the presence of third-order dispersion (TOD) [21,22].…”