Related papers: Saturation of Rogue Wave Amplification over Steep …
We present a brief discussion on the nonlinear Schr{\"o}dinger equation for modeling the propagation of the deep-water wavetrains and a discussion on its doubly-localized breather solutions that can be connected to the sudden formation of…
An overdense plasma layer irradiated by an intense light can exhibit dramatic nonlinear-optical effects due to a relativistic mass-effect of free electrons: highly-multiple hysteresises of reflection and transition, and emergence of…
Internal waves propagate on the ocean's stratification, carrying energy and redistributing momentum through the ocean. When internal waves break, they contribute to diapycnal mixing in the ocean interior, but this breaking behaviour depends…
A wave equation for a time-dependent perturbation about the steady shallow-water solution emulates the metric an acoustic white hole, even upon the incorporation of nonlinearity in the lowest order. A standing wave in the sub-critical…
Spatially-bounded rogue waves, i.e., rogue waves that arise in a limited region of a multi-dimensional space, are interesting and important from both theoretical and applied points of view. In this paper, we determine spatially-bounded…
The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable…
As an example for complex systems with extreme events we investigate ocean wave states exhibiting rogue waves. We present a statistical method of data analysis based on multi-point statistics which for the first time allows grasping extreme…
The amplitude equation for an unstable electrostatic wave in a multi-species Vlasov plasma has been derived. The dynamics of the mode amplitude $\rho(t)$ is studied using an expansion in $\rho$; in particular, in the limit…
We argue that symmetries and conservation laws greatly restrict the form of the terms entering the long wavelength description of growth models exhibiting anomalous roughening. This is exploited to show by dynamic renormalization group…
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…
Random excitation of intense periodic highly-localized single-cycle light pulses in a stochastic background by continuous-wave stimulated Brillouin scattering in long optical fibers with weak feedback is found experimentally. Events with…
Prediction is a central goal and a yet-unresolved challenge in the investigation of oceanic rogue waves. Here we define a horizon of predictability for oceanic rogue waves and derive, via extensive computational experiments, the first…
The mild-slope equation and its various modifications aim to model, with varying degrees of success, linear water wave propagation over sloping or undulating seabed topography. However, despite multiple modifications and attempted…
We experimentally investigate the dynamics of a sphere rolling up a granular slope. During the rolling-up motion, the sphere experiences slipping and penetration (groove formation) on the surface of the granular layer. The former relates to…
We consider the effect of the wind and the dissipation on the nonlinear stages of the modulational instability. By applying a suitable transformation, we map the forced/damped Nonlinear Schr\"odinger (NLS) equation into the standard NLS…
We present a numerical study of the evolution dynamics of ``optical rogue waves'', statistically-rare extreme red-shifted soliton pulses arising from supercontinuum generation in photonic crystal fiber [D. R. Solli et al. Nature Vol. 450,…
The stability and transition in the bottom boundary layer under a solitary wave are analysed in the presence of finite amplitude disturbances. First, the receptivity of the boundary layer is investigated using a linear input-output…
We predict the existence of linear discrete rogue waves governed by the discrete nonlinear Schrodinger equation. We discuss that Josephson effect is the underlying reason for the formation of such waves.
Effects of spatially varying interfacial parameters on the propagation of surface waves are studied. These variations can arise from inhomogeneities in coverage of surface active substances such as amphiphillic molecules at the fluid/gas…
We study coherent wave scattering through waveguides with a step-like surface disorder and find distinct enhancements in the reflection coefficients at well-defined resonance values. Based on detailed numerical and analytical calculations,…