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The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schrodinger equation (NLS). Within the class of exact NLS breather solutions on finite background, which describe the modulational instability of monochromatic wave trains, the hierarchy of both in time and space localized rational solutions are considered to be appropriate prototypes to model rogue wave dynamics. Here, we use the time-reversal invariance of the NLS to propose and experimentally demonstrate a new approach to construct strongly nonlinear localized waves focused both in time and space. The potential areas of applications of this time-reversal approach range from remote sensing to motivated analogous experimental analysis in other nonlinear dispersive media, such as optics, Bose-Einstein condensates and plasma, where the wave motion dynamics is governed by the NLS.
Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrowband in frequency but not necessarily with narrow angular distributions the developed asymptotic weakly nonl
We review the study of rogue waves and related instabilities in optical and oceanic environments, with particular focus on recent experimental developments. In optics, we emphasize results arising from the use of real-time measurement techniques, whi
A statistical theory of rogue waves is proposed and tested against experimental data collected in a long water tank where random waves with different degrees of nonlinearity are mechanically generated and free to propagate along the flume. Strong evi
The Peregrine breather, today widely regarded as a prototype for spatio-temporally localized rogue waves on the ocean caused by nonlinear focusing, is analyzed by direct numerical simulations based on two-phase Navier-Stokes equations. A finite-volum
We show experimentally that a stable wave propagating into a region characterized by an opposite current may become modulationaly unstable. Experiments have been performed in two independent wave tank facilities; both of them are equipped with a wave