“It came from nowhere, snapping giant ships in two. No one believed the survivors ... until now” screamed the cover of New Scientist magazine on 30 June 2001, introducing an article entitled “Monsters of the Deep”. The power and danger suggested by the term “rogue” add to the public fascination with extreme ocean waves, but they also present important and challenging scientific problems and pro...

We investigate the occurrence and dynamics of rogue waves using largescale, three-dimensional, phase-resolved simulations. The direct simulations are based on a high-order spectral method. The method resolves the phases of a large number (up to O(10)) of wave modes, and accounts for nonlinear interactions among them up to an arbitrary high order. Significantly, the simulations obtain exponentia...

In this paper, the generalized Darboux transformation is established to the AB system, which mainly describes marginally unstable baroclinic wave packets in geophysical fluids and ultra-short pulses in nonlinear optics. We find a unified formula of Nth-order rogue wave solution for the AB system by the direct iterative rule. In particular, rogue waves possessing several free parameters from fir...

Here we pose and answer the question of predictability of oceanic rogue waves: “How soon can we predict a rogue wave?”. We answer this question by considering, in its most general form, the governing Laplace’s equation with fully nonlinear boundary conditions. We look into a large number of rogue wave events, and discovered a statistically converged predictability time-scales which is a functio...

Exact explicit rogue-wave solutions of intricate structures are presented for the long-wave-short-wave resonance equation. These vector parametric solutions feature coupled dark- and bright-field counterparts of the Peregrine soliton. Numerical simulations show the robustness of dark and bright rogue waves in spite of the onset of modulational instability. Dark fields originate from the complex...

Rogue periodic waves stand for rogue waves on the periodic background. Two families of traveling periodic waves of the modified Korteweg–de Vries (mKdV) equation in the focusing case are expressed by the Jacobian elliptic functions dn and cn. By using one-fold and two-fold Darboux transformations of the travelling periodic waves, we construct new explicit solutions to the mKdV equation. Since t...

The appearance of rogue waves is well known in oceanographics, optics, and coldmatter systems. Here we show a possibility for the existence of atmospheric rogue waves. Solitary waves in plasmas, and similarly in the atmosphere, have been thoroughly investigated during more than four decades [1]. Observations [2, 3] of atmospheric disturbances propagating with no appreciable change in structure ...

We demonstrate that rogue waves provide a powerful tool to actively control a nonlinear system with minimal effort. Specifically, optical rogue waves--rare, bright flashes of broadband light arising in subthreshold supercontinuum generation--are initiated by an exceedingly weak stimulus. Using this effect, we produce an optically switchable, ultrastable, and bright supercontinuum with greatly e...

The concept of rogue waves arises from a mysterious and potentially calamitous phenomenon of oceanic surfaces. There is mounting evidence that they are actually commonplace in a variety of different physical settings. A set of defining criteria has been advanced; this set is of great generality and therefore applicable to a wide class of systems. The question arises naturally whether there are ...

Dispersion varying fibres have applications in optical pulse compression techniques. We investigate Akhmediev breathers, Kuznetsov–Ma (KM) solitons and optical rogue waves in a dispersion varying optical fibre based on a variable-coefficient nonlinear Schrödinger equation. Analytical solutions in the forms of Akhmediev breathers, KM solitons and rogue waves up to the second order of that equati...