Related papers: Extreme dynamics of wave groups on jet currents
The aim of this work is to study trapped waves and their collisions between two topographic obstacles for the forced Korteweg-de Vries equation. Numerical simulations show that solitary waves remain trapped bouncing back and forth between…
Interactions between solitary waves have been pivotal to understanding nonlinear phenomena across various disciplines. The dynamics of rarefaction solitary waves holds great potential, yet their fundamental characteristics and interactions…
Rogue waves are extreme and rare fluctuations of the wave field that have been discussed in many physical systems. Their presence substantially influences the statistical properties of an incoherent wave field. Their understanding is…
Solitons are universal nonlinear excitations that appear in settings as varied as optics, water waves, and quantum gases [1-5]. While reduced models of soliton dynamics are well established, their validity and dynamical behaviour in…
A numerical fluid simulation investigation of the temporal evolution of a special class of traveling wave solution of the one dimensional relativistic cold plasma model is reported.The solutions consist of coupled electromagnetic and plasma…
We study numerically the properties of (statistically) homogeneous soliton gas depending on soliton density (proportional to number of solitons per unit length) and soliton velocities, in the framework of the focusing one-dimensional…
Solitons are localised wave disturbances that propagate without changing shape, a result of a nonlinear interaction which compensates for wave packet dispersion. Individual solitons may collide, but a defining feature is that they pass…
Large amplitude water waves on deep water has long been known in the sea faring community, and the cause of great concern for, e.g., oil platform constructions. The concept of such freak waves is nowadays, thanks to satellite and radar…
Extreme or rogue waves are large and unexpected waves appearing with higher probability than predicted by Gaussian statistics. Although their formation is explained by both linear and nonlinear wave propagation, nonlinearity has been…
We investigate the weakly nonlinear dynamics of transient gravity waves at infinite depth under the influence of a shear current varying linearly with depth. An analytical solution is permitted via integration of the Euler equations.…
The model we deal with is the mathematical model for mutually penetrating continua one of which is the carrying medium obeying the wave equation whereas the other one is the oscillating inclusion described by the equation for oscillators.…
The study of the Euler equations in flows with constant vorticity has piqued the curiosity of a considerable number of researchers over the years. Much research has been conducted on this subject under the assumption of steady flow. In this…
Non-deterministic giant waves, denoted as rogue, killer, monster or freak waves, have been reported in many different branches of physics. Their origin is however still unknown: despite the massive numerical and experimental evidence, the…
The processes that generate rogue waves on the sea surface remain a mystery. Despite their different natures, the nonlinear bending waves generated in a thin elastic plate share some similarities with waves on the surface of the sea. For…
We study the nonlinear propagation of electrostatic wave packets in a collisional plasma composed of strongly coupled ions and relativistically degenerate electrons. The equilibrium of ions is maintained by an effective temperature…
Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…
We consider a coherently coupled nonlinear Schr\"odinger equation with modulated self-phase modulation, cross-phase modulation, and four-wave mixing nonlinearities and varying refractive index in anisotropic graded index nonlinear medium.…
We study the waves at the interface between two thin horizontal layers of immiscible fluids subject to high-frequency horizontal vibrations. Previously, the variational principle for energy functional, which can be adopted for treatment of…
Systems of solitary-waves in the 1D Gross-Pitaevskii equation, which models a trapped atomic Bose-Einstein condensate, are investigated theoretically. To analyse the soliton-like nature of these solitary-waves, a particle analogy for the…
We present a complete calculation of solitary waves propagating in a steady state with constant velocity v along a cigar-shaped Bose-Einstein trap approximated as infinitely-long cylindrical. For sufficiently weak couplings (densities) the…