Related papers: Trajectory Characters of Rogue Waves
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 introduce a novel family of analytic solutions of the three-wave resonant interaction equations to the purpose of modeling unique events, i.e. "amplitude peaks" which are isolated in space and time. The description of these solutions is…
General high-order rogue waves in the nonlinear Schroedinger equation are derived by the bilinear method. These rogue waves are given in terms of determinants whose matrix elements have simple algebraic expressions. It is shown that 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…
In this paper, general higher-order rogue wave solutions of the parity-time ($\mathcal {P}\mathcal {T}$) symmetric scalar and coupled nonlocal nonlinear Schr\"{o}dinger equations (NLSEs) are calculated theoretically via a Darboux…
Freak waves, or rogue waves, are one of the fascinating manifestations of the strength of nature. These devastating walls of water appear from nowhere, are short-lived and extremely rare. Despite the large amount of research activities on…
We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small…
We review the study of rogue waves and related instabilities in optical and oceanic environments, with particular focus on recent experimental developments. In optics, we emphasize results arising from the use of real-time measurement…
We introduce a representation learning framework for spatial trajectories. We represent partial observations of trajectories as probability distributions in a learned latent space, which characterize the uncertainty about unobserved parts…
In this paper we propose an efficient tomographic approach for the early detection of 2D rogue waves. The method relies on the principle of detecting conical spectral features before rogue wave becomes evident in time. More specifically,…
Rogue waves in (2+1)-dimensional three-wave resonant interactions are studied. General rogue waves arising from a constant background, from a lump-soliton background and from a dark-soliton background have been derived, and their dynamics…
Recent results of numerical simulations of fully nonlinear evolutionary equations for long-crested deep-water waves are discussed, where formation of extreme waves was observed. Several examples demonstrate that three-dimensionality of the…
Rogue wave formation and enhancement over coastal areas have been documented over the last decade. However, this recent knowledge is in apparent contradiction with the established observation of sub-Gaussian wave statistics near shallow…
This article addresses the question of general rogue-wave solutions in the nonlocal parity-time-symmetric nonlinear Schrodinger equation. By generalizing the previous bilinear Kadomtsev-Petviashvili reduction method, large classes of rogue…
We demonstrate a simple cascade mechanism that drives the formation and emergence of rogue waves in the generalized non-linear Schr\"{o}dinger equation with third-order dispersion. This conceptually novel generation mechanism is based on…
We consider solutions of a scalar reaction-diffusion equation of the ignition type with a random, stationary and ergodic reaction rate. We show that solutions of the Cauchy problem spread with a deterministic rate in the long time limit. We…
We report new rogue wave patterns whose wave crests form closed or open curves in the spatial plane, which we call rogue curves, in the Davey-Stewartson I equation. These rogue curves come in various striking shapes, such as rings, double…
We calculate certain estimates for the solution of the characteristic problem of the wave equation reduced to first order, in terms of the free data prescribed on two transverse surfaces, one of which is characteristic. Estimates of such…
We show that new types of rogue wave patterns exist in integrable systems, and these rogue patterns are described by root structures of Okamoto polynomial hierarchies. These rogue patterns arise when the $\tau$ functions of rogue wave…
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…