Related papers: Evolution of Rogue Waves in Interacting Wave Syste…
Light manifests extreme localized waves with long-tail statistics that seem analogous to the still little understood rogue waves in oceans, and optical setups promise to become laboratory test-beds for their investigation. However, to date…
In this paper we examine the flow generated by coupled surface and internal small-amplitude water waves in a two-fluid layer model, where we take the upper layer to be rotational (constant vorticity) and the lower layer to be irrotational.…
The defocusing nonlinear Schr\"odinger (NLS) equation has no the modulational instability, and was not found to possess the rogue wave (RW) phenomenon up to now. In this paper, we firstly investigate some novel nonlinear wave structures in…
There has been a recent tendency to apply Schroedinger's wave equation to macroscopic domains, from Bose-Einstein condensates in neutron stars to planetary orbits. In these applications a hydrodynamical interpretation, involving vortices in…
In this letter,the designable integrability(DI) of the variable coefficient derivative nonlinear Schr\"odinger equation (VCDNLSE) is shown by construction of an explicit transformation which maps VCDNLSE to the usual derivative nonlinear…
A specific, genuinely three-dimensional mechanism of rogue wave formation, in a late stage of the modulational instability of a perturbed Stokes deep-water wave, is recognized through numerical experiments. The simulations are based on…
We report the first observation of extreme wave events (rogue waves) in parametrically driven capillary waves. Rogue waves are observed above a certain threshold in forcing. Above this threshold, frequency spectra broaden and develop…
It is shown that evolution of an open quantum system can be exactly described in terms of wave function which obeys Schrodinger equation with randomly varying parameters whose statistics is universally determined by separate dynamics of the…
The Riemann problem of one dimensional shallow water equations with discontinuous topography has been constructed recently. The elementary waves include shock waves, rarefaction waves, and the stationary wave. The stationary wave appears…
This paper is devoted to a comprehensive analysis of a family of solutions of the focusing nonlinear Schr\"odinger equation called general rogue waves of infinite order. These solutions have recently been shown to describe various limit…
In this paper, by considering the potential application in two mode nonlinear waves in nonlinear fibers under a certain case, we define a coupled nonlinear Schr\"odinger equation(called Frobenius NLS equation) including its Lax pair.…
We report direct observations of surface waves from a stereo camera system along with concurrent measurements of wind speed during an expedition across the Southern Ocean in the austral winter aboard South African icebreaker…
We describe and rigorously justify the nonlinear interaction of highly oscillatory waves in nonlinear Schrodinger equations, posed on Euclidean space or on the torus. Our scaling corresponds to a weakly nonlinear regime where the…
To better understand the inner workings of information spreading, network researchers often use simple models to capture the spreading dynamics. But most models only highlight the effect of local interactions on the global spreading of a…
This is a study of the Euler equations for free surface water waves in the case of varying bathymetry, considering the problem in the shallow water scaling regime. In the case of rapidly varying periodic bottom boundaries this is a problem…
We explore rogue wave formation in multimode silicon nitride (Si$_3$N$_4$) waveguides with multimode nonlinear Schr\"odinger equation-based simulations. Pure fundamental-mode excitation produces smooth propagation without extreme events,…
In addition to deep-water rogue waves which develop from the modulation instability of an optical CW, wave propagation in optical fibers may also produce shallow water rogue waves. These extreme wave events are generated in the…
A review of three-dimensional waves on deep-water is presented. Three forms of three dimensionality, namely oblique, forced and spontaneous type, are identified. An alternative formulation for these three-dimensional waves is given through…
We review the theory of wave interaction in finite and infinite depth. Both of these strands of water-wave research begin with the deterministic governing equations for water waves, from which simplified equations can be derived to model…
The investigation of dynamics of intense solitary wave groups of collinear surface waves is performed by means of numerical simulations of the Euler equations and laboratory experiments. The processes of solitary wave generation, reflection…