相关论文: From modulational instability to focusing dam brea…
This work explores the interplay between dispersive parity breaking and non-linearity in two contrasting continuous dynamical systems that exhibit Modulation Instability (MI). We begin by examining deep water odd surface gravity waves and…
We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation.…
We study the evolution of nonlinear surface gravity water-wave packets developing from modulational instability over an uneven bottom. A nonlinear Schr\"odinger equation (NLSE) with coefficients varying in space along propagation is used as…
The propagation of internal waves in a hydrodynamic system comprising a solid bottom and an upper half-space is investigated. The study is conducted within the framework of a nonlinear low-dimensional model incorporating surface tension on…
The dynamics of wave groups is studied for long waves, using the framework of the Benjamin-Bona-Mahony (BBM) equation and its generalizations. It is shown that the dynamics are richer than the corresponding results obtained just from the…
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…
In the present work we study the nucleation of Dispersive shock waves (DSW) in the {defocusing}, discrete nonlinear Schr{\"o}dinger equation (DNLS), a model of wide relevance to nonlinear optics and atomic condensates. Here, we study the…
By numerical simulation of exact equations of motion (in terms of conformal variables) for planar non-stationary potential flows of an ideal fluid with a free surface over a strongly non-uniform bottom profile, the effect of nonlinear…
Dispersive shock waves (DSWs) are expanding nonlinear wave trains that arise when dispersion regularizes a steepening front, a phenomenon observed in fluids, plasmas, optics, and superfluids. Here we report the first experimental…
Nonlinear wave focusing originating from the universal modulation instability (MI) is responsible for the formation of strong wave localizations on the water surface and in nonlinear wave guides, such as optical Kerr media and plasma. Such…
Strongly nonlinear models of internal wave propagation for incompressible stratified Euler fluids are investigated numerically and analytically to determine the evolution of a class of initial conditions of interest in laboratory…
Dissipationless shock waves in modulational unstable one-dimensional medium are investigated on the simplest example of integrable focusing nonlinear Schr\''odinger (NS) equation. Our approach is based on the construction of special exact…
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…
We introduce a dynamic stabilization scheme universally applicable to unidirectional nonlinear coherent waves. By abruptly changing the waveguiding properties, the breathing of wave packets subject to modulation instability can be…
A nonlinear Schr\"odinger equation for the envelope of two dimensional surface water waves on finite depth with non zero constant vorticity is derived, and the influence of this constant vorticity on the well known stability properties of…
We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we…
In graphene, where the electron-electron scattering is dominant, electrons collectively act as a fluid. This hydrodynamic behaviour of charge carriers leads to exciting nonlinear phenomena such as solitary waves and shocks, among others. In…
We report on the formation of a dispersive shock wave in a nonlinear optical medium. We monitor the evolution of the shock by tuning the incoming beam power. The experimental observations for the position and intensity of the solitonic edge…
Nonlinear initial-boundary value problem on deep-water gravity waves of finite amplitude is solved approximately (up to small terms of higher order) assuming that the waves are generated by an initial disturbance to the water and the…
Surface and interfacial weakly-nonlinear ring waves in a two-layer fluid are modelled numerically, within the framework of the recently derived 2+1-dimensional cKdV-type equation. In a case study, we consider concentric waves from a…