Related papers: Trajectory Characters of Rogue Waves
A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…
Steady linear gravity waves of small amplitude travelling on a current of constant vorticity are found. For negative vorticity we show the appearance of internal waves and vortices, wherein the particle trajectories are not any more closed…
Based on modulation instability analysis and generalized Darboux transformation, we derive a hierarchy of rogue wave solutions for a variable-coefficients coupled Hirota equations. The explicit first-order rogue wave solution is presented,…
Exact explicit rational solutions of two- and one- dimensional multicomponent Yajima-Oikawa (YO) systems, which contain multi-short-wave components and single long-wave one, are presented by using the bilinear method. For two-dimensional…
We analyze data from direct numerical simulations of homogeneous and isotropic turbulence (at Re_\lambda \approx 280) and study the statistics of curvature and torsion of Lagrangian trajectories in order to extract informations on 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…
Rotating spiral waves are a form of self-organization observed in spatially extended systems of physical, chemical, and biological nature. In the presence of a small perturbation, the spiral wave's centre of rotation and fiducial phase may…
In this paper, persistence of solitary wave solutions of the regularized long wave equation with small perturbations are investigated by the geometric singular perturbation theory. Two different kinds of the perturbations are considered in…
Here we find the spectral curves, corresponding to the known rational or quasi-rational solutions of AKNS hierarchy equations, ultimately connected with the modeling of the rogue waves events in the optical waveguides and in hydrodynamics.…
General rogue waves in (1+1)-dimensional three-wave resonant interaction systems are derived by the bilinear method. These solutions are divided into three families, which correspond to a simple root, two simple roots and a double root of a…
Microwave transport experiments have been performed in a quasi-two-dimensional resonator with randomly distributed scatterers, each mimicking an $r^{-2}$ repulsive potential. Analysis of both stationary wave fields and transient transport…
We present the Fourier Transform of a continuous gravitational wave. We have analysed the data set for one day observation time and our analysis is applicable for arbitrary location of detector and source. We have taken into account the…
Based on data from the Japan Sea and the North Sea the occurrence of rogue waves is analyzed by a scale dependent stochastic approach, which interlinks fluctuations of waves for different spacings. With this approach we are able to…
Binary systems containing exotic compact objects may emit repeated bursts of gravitational waves (GWs) following coalescence. Such GW echoes would provide a clear signature of new physics, but searches for them have not yielded a convincing…
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.…
The higher-order dispersive and nonlinear effects (alias {\it the perturbation terms}) like the third-order dispersion, the self-steepening, and the self-frequency shift play important roles in the study of the ultra-short optical pulse…
In the linear approximation, we study a one-dimensional problem of the reflectionless wave propagation on a surface of a shallow duct with the spatially varying water depth, duct width, and current. We show that both global and bounded…
The numerical simulation of the nonlinear dynamics of random sea waves at moderately small Benjamin-Feir indices and its comparison with the linear dynamics (at the coincidence of spatial Fourier harmonics near a spectral peak at a certain…
Unstable periodic orbits scar wave functions in chaotic systems. This also influences the associated spectra, that follow the otherwise universal Porter--Thomas intensity distribution. We show here how this deviation extend to other longer…
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…