Related papers: Deterministic aspects of nonlinear modulation inst…
Modulational, Benjamin-Feir, instability is studied for the down-stream evolution of surface gravity waves. An explicit solution, the soliton on finite background, of the NLS equation in physical space is used to study various phenomena in…
A nonlinear Schr\"odinger equation with repulsive (defocusing) nonlinearity is considered. As an example, a system with a spatially varying coefficient of the nonlinear term is studied. The nonlinearity is chosen to be repelling except on a…
Wave amplification in nonlinear dispersive wave equations may be caused by nonlinear focussing of waves from a certain background. In the model of nonlinear Schr\"odinger equation we will introduce a transformation to displaced…
The Nonlinear Schr\"odinger (NLS) equation is used to model surface waves in wave tanks of hydrodynamic laboratories. Analysis of the linearized NLS equation shows that its harmonic solutions with a small amplitude modulation have a…
The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…
The modulation instability is a focusing mechanism responsible for the formation of strong wave localizations not only on the water surface, but also in a variety of nonlinear dispersive media. Such dynamics is initiated from the injection…
This thesis deals with some theoretical aspects of deterministic freak wave generation in the wave basin of a hydrodynamic laboratory. We adopt the spatial nonlinear Schr\"odinger equation as a mathematical model to describe the deformation…
We study experimentally, in a large-scale basin, the propagation of unidirectional deep water gravity waves stochastically modulated in phase. We observe the emergence of nonlinear localized structures that evolve on a stochastic wave…
In this manuscript we investigate the Benjamin-Feir (or modulation) instability for the spatial evolution of water waves from the perspective of the discrete, spatial Zakharov equation, which captures cubically nonlinear and resonant wave…
This paper deals with a one-dimensional wave equation with a nonlinear dynamic boundary condition and a Neumann-type boundary control acting on the other extremity. We consider a class of nonlinear stabilizing feedbacks that only depend on…
This thesis deals with mathematical and physical aspects of deterministic freak wave generation in a hydrodynamic laboratory. We adopt the nonlinear Schr\"odinger (NLS) equation as a mathematical model for the evolution of the surface…
Irregular waves which experience the time-limited external forcing within the framework of the nonlinear Schrodinger (NLS) equation are studied numerically. It is shown that the adiabatically slow pumping (the time scale of forcing is much…
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…
A number of qualitative comparisons of experimental results on unidirectional freak wave generation in a hydrodynamic laboratory are presented in this paper. A nonlinear dispersive type of wave equation, the nonlinear Schr\"{o}dinger…
This paper sets out to explore the modulational (or Benjamin-Feir) instability of a monochromatic wave propagating in the presence of damping such as that induced by sea-ice on the ocean surface. The fundamental wave motion is modelled…
We perform statistical analysis on discrete nonlinear waves generated though modulational instability in the context of the Salerno model that interpolates between the intergable Ablowitz-Ladik (AL) equation and the nonintegrable discrete…
The nonlinear stage of the modulational (Benjamin - Feir) instability of unidirectional deep water surface gravity waves is simulated numerically by the firth-order nonlinear envelope equations. The conditions of steep and breaking waves…
The modulational instability of waves in a medium under the action of an external monochromatic force and dissipation is considered. The model which describes the nonlinear stage of the modulation instability was constructed with using…
The description of complex wave processes, in addition to the shoaling problem, is often cumbersome even for the evolution of regular waves. For reflection under the regime of wave breaking, the surf similarity is generally accepted as the…
We report water wave experiments performed in a long tank where we consider the evolution of nonlinear deep-water surface gravity waves with the envelope in the form of a large-scale rectangular barrier. Our experiments reveal that, for a…