Generation of Rogue Waves in Gyrotrons Operating in the Regime of Developed Turbulence

Super rogue waves: Collision of rogue waves in Bose-Einstein condensate

An important and incompletely answered question is whether a high-order rogue wave (RW) can be excited by the collision of first-order RWs, especially for its generation and propagation mechanisms. In this paper, the evolution properties of collisions between RWs are studied numerically for two-component coupled Bose-Einstein condensates. We find that whether a second-order RW can be successfully excited strongly depends on the location and time of the first-order RWs encountered. Only when the highest peaks of two RWs meet at the same position at the same time, can the standard second-order RW be triggered and its structure is in good agreement with the exact solution. Further, we demonstrate that such results are also applicable to the collision of subordinate RWs. This paper not only reveals the collision properties of RWs, but also provides a feasible scheme to generate higher-order RWs for experimental realization.

Fundamental Peregrine Solitons of Ultrastrong Amplitude Enhancement through Self-Steepening in Vector Nonlinear Systems

We report the universal emergence of anomalous fundamental Peregrine solitons, which can exhibit an unprecedentedly ultrahigh peak amplitude comparable to any higher-order rogue wave events, in the vector derivative nonlinear Schrödinger system involving the self-steepening effect. We present the exact explicit rational solutions on either a continuous-wave or a periodical-wave background, for a broad range of parameters. We numerically confirm the buildup of anomalous Peregrine solitons from strong initial harmonic perturbations, despite the onset of competing modulation instability. Our results may stimulate the experimental study of such Peregrine soliton anomaly in birefringent crystals or other similar vector systems.

General rogue wave solutions of the coupled Fokas-Lenells equations and non-recursive Darboux transformation

We formulate a non-recursive Darboux transformation technique to obtain the general nth-order rational rogue wave solutions to the coupled Fokas-Lenells system, which is an integrable extension of the noted Manakov system, by considering both the double-root and triple-root situations of the spectral characteristic equation. Based on the explicit fundamental and second-order rogue wave solutions, we demonstrate several interesting rogue wave dynamics, among which are coexisting rogue waves and anomalous Peregrine solitons. Our solutions are generalized to include the complete background-field parameters and therefore helpful for future experimental study.

Correlations Preceding High-Intensity Events in the Chaotic Dynamics of a Raman Fiber Laser

We study the time series of the output intensity of a Raman fiber laser with an ordinal patterns analysis in the laminar-turbulent transition. We look for signatures among consecutive events that indicate when the system changes from triggering low-intensity to high-intensity events. We set two thresholds, a low one and a high one, to distinguish between low intensity versus high-intensity events. We find that when the time series is performing low-intensity events (below the low threshold), it shows some preferred temporal patterns before triggering high-intensity events (above a high threshold). The preferred temporal patterns remain the same all through the pump current range studied, even though two clearly different dynamical regimes are covered (laminar regime for low pump currents and turbulent regime for high pump currents). We also find that the turbulent regime shows clearer signatures of determinism than the laminar regime.

Peregrine Solitons Beyond the Threefold Limit and Their Two-Soliton Interactions

Within the coupled Fokas-Lenells equations framework, we show explicitly that, in contrast to the expected threefold-amplitude magnification, Peregrine solitons can reach a peak amplitude as high as 5 times the background level. Besides, the interaction of two such anomalous Peregrine solitons can generate a spikelike rogue wave of extremely high peak amplitude, depending on the parameters used. We numerically confirm that the Peregrine soliton beyond the threefold limit can be reproduced from either a deterministic initial profile or a chaotic background field, hence anticipating the feasibility of its experimental observation.

Forecasting Events in the Complex Dynamics of a Semiconductor Laser with Optical Feedback

Complex systems performing spiking dynamics are widespread in Nature. They cover from earthquakes, to neurons, variable stars, social networks, or stock markets. Understanding and characterizing their dynamics is relevant in order to detect transitions, or to predict unwanted extreme events. Here we study, under an ordinal patterns analysis, the output intensity of a semiconductor laser with feedback in a regime where it develops a complex spiking behavior. We unveil that, in the transitions towards and from the spiking regime, the complex dynamics presents two competing behaviors that can be distinguished with a thresholding method. Then we use time and intensity correlations to forecast different types of events, and transitions in the dynamics of the system.