Abstract. A higher-order strongly nonlinear model is derived to describe the evolution of large amplitude internal waves over arbitrary bathymetric variations in a two-layer system where the upper layer is shallow while the lower layer is comparable to the characteristic wavelength. The new system of nonlinear evolution equations with variable coefficients is a generalization of the deep config...

A model of surface waves generated on deep water by strong winds is proposed. A two-layer approximation is adopted, in which a shallow turbulent layer overlies the lower, infinitely deep layer. The dynamics of the upper layer, which is directly exposed to the wind, are nonlinear and coupled to the linear dynamics in the deep fluid. The authors demonstrate that in such a system there exist stead...

We analyze stability of the TM polarized optical solitons and nonlinear guided waves localized at a metal-dielectric interface. We demonstrate, both analytically and numerically, that the spatial solitons can experience vectorial transverse modulational instability that leads to the generation of arrays of two-dimensional TM polarized self-trapped localized beams. In a sharp contrast, we reveal...

We generalize the nonlinear one-dimensional equation for a fluid layer surface to any geometry and we introduce a new infinite order differential equation for its traveling solitary waves solutions. This equation can be written as a finite-difference expression, with a general solution that is a power series expansion with coefficients satisfying a nonlinear recursion relation. In the limit of ...

In 1968 V.E. Zakharov derived the Nonlinear Schrödinger equation for the 2D water wave problem in the absence of surface tension, i.e., for the evolution of gravity driven surface water waves, in order to describe slow temporal and spatial modulations of a spatially and temporarily oscillating wave packet. In this paper we give a rigorous proof that the wave packets in the two-dimensional water...

The ability to send a wave to fetch an object from a distance would find a broad range of applications. Quasi-standing Faraday waves on water create horizontal vortices1,2, yet it is not known whether propagating waves can generate large-scale flows—small-amplitude irrotational waves only push particles in the direction of propagation3–5. Here we show that when waves become three-dimensional as...

This is a study of two-dimensional steady periodic travelling waves on the surface of an infinitely deep irrotational ocean, when the top streamline is in contact with a membrane which has a nonlinear response to stretching and bending, and the pressure in the air above is constant. It is not supposed that the waves have small amplitude. The problem of existence of such waves is addressed using...

The propagation of intense electromagnetic waves in cold magnetized plasma is tackled through a relativistic hydrodynamic approach. The analysis of coupled transverse-longitudinal plasma oscillations is performed for traveling plane waves. When these waves propagate perpendicularly to a static magnetic field, the model is describable in terms of a nonlinear dynamical system with 2 degrees of fr...

We propose consistent scaling of solitary waves on inertia-dominated falling liquid films, which accurately accounts for the driving physical mechanisms and leads to a self-similar characterization of solitary waves. Direct numerical simulations of the entire two-phase system are conducted using a state-of-the-art finite volume framework for interfacial flows in an open domain that was previous...

The existence of traveling waves for the original Whitham equation is investigated. This equation combines a generic nonlinear quadratic term with the exact linear dispersion relation of surface water waves of finite depth. It is found that there exist small-amplitude periodic traveling waves with sub-critical speeds. As the period of these traveling waves tends to infinity, their velocities ap...