Related papers: Rogue Waves and Large Deviations in Deep Sea
In this work, we study the dynamics of rogue waves in the partially $\cal{PT}$-symmetric nonlocal Davey-Stewartson(DS) systems. Using the Darboux transformation method, general rogue waves in the partially $\cal{PT}$-symmetric nonlocal DS…
We study a deformation of the nonlinear Schr\"odinger equation recently derived in the context of deformation of hierarchies of integrable systems. This systematic method also led to known integrable equations such as the Camassa-Holm…
A computational strategy based on large deviation theory (LDT) is used to study the anomalous statistical features of turbulent surface waves propagating past an abrupt depth change created via a step in the bottom topography. The dynamics…
General rogue waves in the Davey-Stewartson-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…
Optical rogue waves are demonstrated in the far-field scattered radiation from photonic arrays designed according to the aperiodic distributions of prime elements in complex quadratic fields. Specifically, by studying light diffraction from…
We presented numerical simulation of long waves, interacting with arrays of emergent cylinders inside regularly spaced patches, representing discontinues patchy coastal vegetation. We employed the fully nonlinear and weakly dispersive…
We study the cubic weakly nonlinear Schr\"odinger equation with randomized spatially quasi-periodic initial data in higher dimensions. Under a polynomial decay assumption in Fourier space, we establish a {\em Large Deviations Principle} for…
The nonlinear dynamics of an obliquely oriented wave packet at sea surface is studied both analytically and numerically for various initial parameters of the packet, in connection with the problem of oceanic rogue waves. In the framework of…
A prototypical example of a rogue wave structure in a two-dimensional model is presented in the context of the Davey-Stewartson~II (DS~II) equation arising in water waves. The analytical methodology involves a Taylor expansion of an…
We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation.…
We present a spatio-temporal mechanism for producing 2D optical rogue waves in the presence of a turbulent state with creation, interaction and annihilation of optical vortices. Spatially periodic structures with bound phase lose stability…
Rogue waves are known to be much more common on jet currents. A possible explanation was put forward in [ [V. Shrira and A. Slunyaev, Nonlinear dynamics of trapped waves on jet currents and rogue waves, Phys. Rev. E 89, 041002, 2014]]: for…
We study nonlinear internal gravity waves (IGWs) in the atmosphere. The reductive perturbation method is used to derive a system of two-dimensional nonlinear equations for the envelope of velocity stream function and the mean flow. In the…
This paper numerically investigates the statistical properties of rogue waves and their generation mechanisms in integrable turbulence, taking the Gerdjikov-Ivanov (GI) equation as the research object. The eigenvalue spectra of the…
Peregrine soliton (PS) is widely regarded as a prototype nonlinear structure capturing properties of rogue waves that emerge in the nonlinear propagation of unidirectional wave trains. As an exact breather solution of the one-dimensional…
We investigate experimentally the statistical properties of a wind-generated wave field and the spontaneous formation of rogue waves in an annular flume. Unlike many experiments on rogue waves, where waves are mechanically generated, here…
In this paper, we calculate the region of emergence of rogue waves in the Sasa-Satsuma equation by performing Penrose stability analysis. We consider Wigner-transformed Sasa-Satsuma equation and separate out unstable solutions, namely…
We study the formation of extreme events in incoherent systems described by envelope equations, such as the Nonliner Schr\"odinger equation. We derive an identity that relates the evolution of the kurtosis (a measure of the relevance of the…
Modulational instability (MI) of dust acoustic waves (DAWs), which propagates in an opposite polarity dusty plasma system, containing inertial warm negatively and positively charged dust particles as well as non-extensive q-distributed…
We present exact rational solution for a modified nonlinear Schr$\ddot{o}$dinger equation that takes into account quintic nonlinearity and nonlinear dispersion corrections to the cubic nonlinearity, which could be used to describe rogue…