Rogue wave

About: Rogue wave is a research topic. Over the lifetime, 2977 publications have been published within this topic receiving 70933 citations. The topic is also known as: freak wave & monster wave.

Multi-breathers and high order rogue waves for the nonlinear Schr\"odinger equation on the elliptic function background

Abstract: We construct the multi-breather solutions of the focusing nonlinear Schrodinger equation (NLSE) on the background of elliptic functions by the Darboux transformation, and express them in terms of the determinant of theta functions. The dynamics of the breathers in the presence of various kinds of backgrounds such as dn, cn, and non-trivial phase-modulating elliptic solutions are presented, and their behaviors dependent on the effect of backgrounds are elucidated. We also determine the asymptotic behaviors for the multi-breather solutions with different velocities in the limit $t\to\pm\infty$, where the solution in the neighborhood of each breather tends to the simple one-breather solution. Furthermore, we exactly solve the linearized NLSE using the squared eigenfunction and determine the unstable spectra for elliptic function background. By using them, the Akhmediev breathers arising from these modulational instabilities are plotted and their dynamics are revealed. Finally, we provide the rogue-wave and higher-order rogue-wave solutions by taking the special limit of the breather solutions at branch points and the generalized Darboux transformation. The resulting dynamics of the rogue waves involves rich phenomena: depending on the choice of the background and possessing different velocities relative to the background. We also provide an example of the multi- and higher-order rogue wave solution.

Experimental study of spatiotemporally localized surface gravity water waves.

Abstract: We present experimental results on the study of spatiotemporally localized surface wave events on deep water that can be modeled using the Peregrine breather solution of the nonlinear Schr\"odinger equation. These are often considered as prototypes of oceanic rogue waves that can focus wave energy into a single wave packet. For small steepness values of the carrier gravity waves the Peregrine breathers are relatively wide, thus providing an excellent agreement between the theory and experimental results. For larger steepnesses the focusing leads to temporally and spatially shorter events. Nevertheless, agreement between measurements and the Peregrine breather theory remains reasonably good, with discrepancies of modulation gradients and spatiotemporal symmetries being tolerable. Lifetimes and travel distances of the spatiotemporally localized wave events determined from the experiment are in good agreement with the theory.

Optical Rogue Waves in Whispering-Gallery-Mode Resonators

Abstract: We report a theoretical study showing that rogue waves can emerge in whispering-gallery-mode resonators as the result of the chaotic interplay between Kerr nonlinearity and anomalous group-velocity dispersion. The nonlinear dynamics of the propagation of light in a whispering-gallery-mode resonator is investigated using the Lugiato-Lefever equation, and we give evidence of a range of parameters where rare and extreme events associated with non-Gaussian statistics of the field maxima are observed.

Controlled giant rogue waves in nonlinear fiber optics

Abstract: We show the existence of self-similar giant rogue waves in a tapered graded-index nonlinear fiber and analytically illustrate their amplification in a rather small spatiotemporal domain by controlled manipulation of the phase. Our exact analysis takes recourse to the large manifold of available tapering profiles in conjunction with appropriate gain functions, which are allowed by the dynamical equation governing the tapered graded-index nonlinear fiber. The fact that these profiles and gain functions provide a wide class of boundary conditions makes them particularly relevant for transient rogue waves, which manifest rather rarely.

Tracking Breather Dynamics in Irregular Sea State Conditions

Abstract: Breather solutions of the nonlinear Schrodinger equation (NLSE) are known to be considered as backbone models for extreme events in the ocean as well as in Kerr media. These exact deterministic rogue wave (RW) prototypes on a regular background describe a wide range of modulation instability configurations. Alternatively, oceanic or electromagnetic wave fields can be of chaotic nature and it is known that RWs may develop in such conditions as well. We report an experimental study confirming that extreme localizations in an irregular oceanic Joint North Sea Wave Project wave field can be tracked back to originate from exact NLSE breather solutions, such as the Peregrine breather. Numerical NLSE as well as modified NLSE simulations are both in good agreement with laboratory experiments and highlight the significance of universal weakly nonlinear evolution equations in the emergence as well as prediction of extreme events in nonlinear dispersive media.