Related papers: Quantitative Relation between Modulational Instabi…
Modulational instability is a phenomenon that reveals itself as the exponential growth of weak perturbations in the presence of an intense pump beam propagating in a nonlinear medium. It plays a key role in such nonlinear optical processes…
We study nonlinear waves on a plane-wave background in an erbium-doped fiber system, which is governed by the coupled nonlinear Schr\"odinger and the Maxwell-Bloch equations. We find that prolific different types of nonlinear localized and…
We investigate theoretically the fundamental phenomenon of the spontaneous, noise-induced modulational instability (MI) of a plane wave. The long-term statistical properties of the noise-induced MI have been previously observed in…
We report numerical and experimental investigations into modulation instability in a nonlinear magnetoinductive waveguide. By numerical simulation we find that modulation instability occurs in an electrical circuit model of a…
In this paper we study the properties of the chaotic wave fields generated in the frame of the Kundu-Eckhaus equation (KEE). Modulation instability results in a chaotic wave field which exhibits small-scale filaments with a free propagation…
Numerical simulations of the onset phase of continuous wave supercontinuum generation from modulation instability show that the structure of the field as it develops can be interpreted in terms of the properties of Akhmediev Breathers.…
The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…
In multi-component systems, several rogue waves can be simultaneously excited using simple initial conditions in the form of a plane wave with a small amplitude single-peak perturbation. This is in drastic contrast with the case of…
Modulational instability (MI) is a fundamental phenomenon in the study of nonlinear dynamics, spanning diverse areas such as shallow water waves, optics, and ultracold atomic gases. In particular, the nonlinear stage of MI has recently been…
There are many examples in physics of systems showing rogue wave behaviour, the generation of high amplitude events at low probability. Although initially studied in oceanography, rogue waves have now been seen in many other domains, with…
Rogue wave patterns in the nonlinear Schr\"{o}dinger equation are analytically studied. It is shown that when an internal parameter in the rogue waves (which controls the shape of initial weak perturbations to the uniform background) is…
We present an overview of recent advances in the understanding of optical beams in nonlinear media with a spatially nonlocal nonlinear response. We discuss the impact of nonlocality on the modulational instability of plane waves, the…
Using experimental data from three different rogue wave supporting systems, determinism and predictability of the underlying dynamics are evaluated with methods of nonlinear time series analysis. We included original records from the…
A new exactly solvable (1+1)-dimensional complex nonlinear wave equation exhibiting rich ana- lytic properties has been introduced. A rogue wave (RW), localized in space-time like Peregrine RW solution, though richer due to the presence of…
The effect of the modulation instability on the propagation of solitary waves along one-dimensional discrete nonlinear Schr\"odinger equation with cubic nonlinearity is revisited. A self-contained quasicontinuum approximation is developed…
We study experimentally the Bloch-wave instabilities in optically-induced lattices. We reveal two different instability scenarios associated with either the transverse modulational instability of a single Bloch wave, or the nonlinear…
In the present work, we explore soliton and rogue-like wave solutions in the transmission line analogue of a nonlinear left-handed metamaterial. The nonlinearity is expressed through a voltagedependent and symmetric capacitance motivated by…
Extensive numerical simulations were performed to investigate all stages of modulation instability development from the initial pulse of pico-second duration in photonic crystal fiber: quasi-solitons and dispersive waves formation, their…
Nonlinear wave focusing originating from the universal modulation instability (MI) is responsible for the formation of strong wave localizations on the water surface and in nonlinear wave guides, such as optical Kerr media and plasma. Such…
Weak phase noise present on an optical field can be amplified by a self-focusing nonlinearity and form intense "rogue wave" features. Here, we study the effect of the coherence length (or grain size) of this phase noise on the likelihood of…