Extreme events in discrete nonlinear lattices

Rogue waves in disordered 1D photonic lattices

In this work, we study the phenomena of Rogue waves (RW) on one-dimensional (1D) photonic lattices presenting diagonal and non-diagonal disorder. Our results show the appearance of extreme events coming from the superposition of different, extended and localized, linear waves for weak disorder. We perform experiments on femtosecond laser written waveguide arrays having disorder in coupling constants, which is originated from a random waveguide distribution. Both, numerics and experiments, are in good agreement and show that RW are generically present in 1D lattices for weak disorder only, after a mandatory data filtering process.

Statistics of vector Manakov rogue waves

We present a statistical analysis based on the height and return-time probabilities of high-amplitude wave events in both focusing and defocusing Manakov systems. We find that analytical rational or semirational solutions, associated with extreme, rogue wave (RW) structures, are the leading high-amplitude events in this system. We define the thresholds for classifying an extreme wave event as a RW. Our results indicate that there is a strong relationship between the type of RW and the mechanism which is responsible for its creation. Initially, high-amplitude events originate from modulation instability. Upon subsequent evolution, the interaction among these events prevails as the mechanism for RW creation. We suggest a strategy for confirming the basic properties of different extreme events. This involves the definition of proper statistical measures at each stage of the RW dynamics. Our results point to the need for redefining criteria for identifying RW events.

Extreme events in the forced Liénard system

We observe extremely large amplitude intermittent spikings in a dynamical variable of a periodically forced Liénard-type oscillator and characterize them as extreme events, which are rare, but recurrent and larger in amplitude than a threshold. The extreme events occur via two processes, an interior crisis and intermittency. The probability of occurrence of the events shows a long-tail distribution in both the cases. We provide evidence of the extreme events in an experiment using an electronic analog circuit of the Liénard oscillator that shows good agreement with our numerical results.

Influence of disorder on generation and probability of extreme events in Salerno lattices

Extreme events (EEs) in nonlinear and/or disordered one-dimensional photonic lattice systems described by the Salerno model with on-site disorder are studied. The goal is to explain particular properties of these phenomena, essentially related to localization of light in the presence of nonlinear and/or nonlocal couplings in the considered systems. Combining statistical and nonlinear dynamical methods and measures developed in the framework of the theory of localization phenomena in disordered and nonlinear systems, particularities of EEs are qualitatively clarified. Findings presented here indicate that the best environment for EEs' creation are disordered near-integrable Salerno lattices. In addition, it is been shown that the leading role in the generation and dynamical properties of EEs in the considered model is played by modulation instability, i.e., by nonlinearities in the system, although EEs can be induced in linear lattices with on-site disorder too.

Extreme events due to localization of energy

We study a one-dimensional chain of harmonically coupled units in an asymmetric anharmonic soft potential. Due to nonlinear localization of energy, this system exhibits extreme events in the sense that individual elements of the chain show very large excitations. A detailed statistical analysis of extremes in this system reveals some unexpected properties, e.g., a pronounced pattern in the interevent interval statistics. We relate these statistical properties to underlying system dynamics and notice that often when extreme events occur the system dynamics adopts (at least locally) an oscillatory behavior, resulting in, for example, a quick succession of such events. The model therefore might serve as a paradigmatic model for the study of the interplay of nonlinearity, energy transport, and extreme events.

Extreme-value statistics in supercontinuum generation by cascaded stimulated Raman scattering

We study experimentally the statistical fluctuations observed in a supercontinuum generated in the normal dispersion regime through cascaded stimulated Raman scattering. Specifically, we show that the statistical distribution of shot-to-shot spectral variations evolves from a quasi-Gaussian in the saturated regime for Stokes orders near the pump to a long-tailed extreme-value distribution for Stokes orders at a large separation from the pump in the unsaturated regime.

Wave-packet dynamics in chains with delayed electronic nonlinear response

We study the dynamics of one electron wave packet in a chain with a nonadiabatic electron-phonon interaction. The electron-phonon coupling is taken into account in the time-dependent Schrödinger equation by a delayed cubic nonlinearity. In the limit of an adiabatic coupling, the self-trapping phenomenon occurs when the nonlinearity parameter exceeds a critical value of the order of the bandwidth. We show that a weaker nonlinearity is required to produce self-trapping in the regime of short delay times. However, this trend is reversed for slow nonlinear responses, resulting in a reentrant phase diagram. In slowly responding media, self-trapping only takes place for very strong nonlinearities.