The rouge waves in an optically injected semiconductor lasers are receiving a lot of interest. In this work, the generating and controlling of the rogue waves in semiconductor lasers have been investigated. For this purpose, the laser’s rate equations are solved numerically in a specified time interval, then the field amplitude and the intensity versus time are calculated and analyzed. To solve...

General rogue waves in the Davey–Stewartson (DS)II equation are derived by the bilinear method, and the solutions are given through determinants. It is shown that the simplest (fundamental) rogue waves are line rogue waves which arise from the constant background in a line profile and then retreat back to the constant background again. It is also shown that multi-rogue waves describe the intera...

We report and discuss analytical solutions of the vector nonlinear Schrödinger equation that describe rogue waves in the defocusing regime. This family of solutions includes bright-dark and dark-dark rogue waves. The link between modulational instability (MI) and rogue waves is displayed by showing that only a peculiar kind of MI, namely baseband MI, can sustain rogue-wave formation. The existe...

General rogue waves in the focusing and defocusing Ablowitz–Ladik equations are derived by the bilinear method. In the focusing case, it is shown that rogue waves are always bounded. In addition, fundamental rogue waves reach peak amplitudes which are at least three times that of the constant background, and higher-order rogue waves can exhibit patterns such as triads and circular arrays with d...

Rogue waves are unexpectedly large and localized displacements from an equilibrium position or an otherwise calm background. For the nonlinear Schrödinger (NLS) model widely used in fluid mechanics and optics, these waves can occur only when dispersion and nonlinearity are of the same sign, a regime of modulation instability. For coupled NLS equations, rogue waves will arise even if dispersion ...

We report the first observation of extreme wave events (rogue waves) in parametrically driven capillary waves. Rogue waves are observed above a certain threshold in forcing. Above this threshold, frequency spectra broaden and develop exponential tails. For the first time we present evidence of strong four-wave coupling in nonlinear waves (high tricoherence), which points to modulation instabili...

We reanalyse the probability for formation of extreme waves using the simple model of linear interference of a finite number of elementary waves with fixed amplitude and random phase fluctuations. Under these model assumptions no rogue waves appear when less than 10 elementary waves interfere with each other. Above this threshold rogue wave formation becomes increasingly likely, with appearance...

General rogue waves in the Davey-Stewartson-I equation are derived by the bilinear method. It is shown that the simplest (fundamental) rogue waves are line rogue waves which arise from the constant background with a line profile and then disappear into the constant background again. It is also shown that multirogue waves describe the interaction of several fundamental rogue waves. These multiro...

Rogue waves are one of those fascinating destructive phenomena in nature that have not been fully explained so far 1–3 . There is a variety of approaches to deal with rogue waves 4,5 . Oceanographers commonly agree that linear theories cannot provide explanations for their existence 6,7 . Only nonlinear theories can explain the dramatic concentration of energy into a single “wall of water” well...

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 twofold Darboux transformations, we construct explicitly the rogue periodic waves of the mKdV equation. Since the dn-periodic wave i...