Related papers: Statistics of Vector Manakov Rogue Waves
Rogue waves (RWs) can form on the ocean surface due to quasi-four wave resonant interaction or superposition principle. Both mechanisms have been acutely studied. The first of the two is known as the nonlinear focusing mechanism and leads…
Extreme events gain the attention of researchers due to their utmost importance in various contexts ranging from finance to climatology. This brings such recurrent events to the limelight of attention in interdisciplinary research. A…
We explore extreme event occurrence in the integrable turbulence with self-similar asymptotics. We posit that rogue waves in such systems manifest themselves as giant fluctuations away from average self-similar dynamics of the system. We…
An unexpected wave is defined by Gemmrich & Garrett (2008) as a wave that is much taller than a set of neighboring waves. Their definition of "unexpected" refers to a wave that is not anticipated by a casual observer. Clearly, unexpected…
A statistical theory of rogue waves is proposed and tested against experimental data collected in a long water tank where random waves with different degrees of nonlinearity are mechanically generated and free to propagate along the flume.…
The numerical simulation of the nonlinear dynamics of the sea surface has shown that the collision of two groups of relatively low waves with close but noncollinear wave vectors (two or three waves in each group with a steepness of about…
It is known that rogue waves (RWs) are generated by the modulational instability (MI) of the baseband type. Starting with the Bers-Kaup-Reiman system for three-wave resonant interactions, we identify a specific RW-building mechanism based…
General higher order rogue waves of a vector nonlinear Schrodinger equation (Manakov system) are derived using a Darboux-dressing transformation with an asymptotic expansion method. The Nth order semi-rational solutions containing 3N free…
We advance a statistical theory of extreme event emergence in random nonlinear wave systems with self-similar intermediate asymptotics. We show, within the framework of a generic (1 + 1)D nonlinear Schrodinger equation with linear gain,…
We construct and discuss a semi-rational, multi-parametric vector solution of coupled nonlinear Schr\"odinger equations (Manakov system). This family of solutions includes known vector Peregrine solutions, bright-dark-rogue solutions, and…
Powerful rogue ocean waves have been objects of fascination for centuries. Elusive and awe-inspiring, with the ability to inflict catastrophic damage, rogue waves remain unpredictable and imperfectly understood. To gain further insight into…
Numerical simulations of fully nonlinear equations of motion for long-crested waves at deep water demonstrate that in elongate wave groups the formation of extreme waves occurs most intensively if in an initial state the wave fronts are…
The issue of accounting of the wave breaking phenomenon in direct numerical simulations of oceanic waves is discussed. It is emphasized that this problem is crucial for the deterministic description of waves, and also for the dynamical…
Weak Gaussian perturbations on a plane wave background could trigger lots of rogue waves, due to modulational instability. Numerical simulations showed that these rogue waves seemed to have similar unit structure. However, to the best of…
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…
The appearance of rogue waves in deep sea is investigated using the modified nonlinear Schr\"odinger (MNLS) equation in one spatial-dimension with random initial conditions that are assumed to be normally distributed, with a spectrum…
An integrable system of two-component nonlinear Ablowitz-Ladik (AL) equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability of continuous waves is studied in the system.…
We investigate the statistics of rogue waves occurring in the inverse cascade of surface gravity wave turbulence. In such statistically homogeneous, stationary and isotropic wave fields, low-frequency waves are generated by nonlinear…
Wave impact and run-up onto vertical obstacles are among the most important phenomena which must be taken into account in the design of coastal structures. From linear wave theory, we know that the wave amplitude on a vertical wall is twice…
In this paper, we study the general rogue wave solutions and their patterns in the vector (or $M$-component) nonlinear Schr\"{o}dinger (NLS) equation. By applying the Kadomtsev-Petviashvili hierarchy reduction method, we derived an explicit…