Related papers: Linear and Nonlinear Surface Waves in Electrohydro…

In this paper we study existence and stability of shock profiles for a 1-D compressible Euler system in the context of Quantum Hydrodynamic models. The dispersive term is originated by the quantum effects described through the Bohm…

A new method is proposed to recover the water-wave surface elevation from pressure data obtained at the bottom of the fluid. The new method requires the numerical solution of a nonlocal nonlinear equation relating the pressure and the…

Recently, we have revealed an intrinsic instability of metals due to surface plasma waves (SPWs) and raised the prospect of using it to create lossless SPWs. The counter-intuitive nature of this finding prompts one to ask, why had not this…

We investigate the diffraction of singularities of solutions to the linear elastic equation on manifolds with edge singularities. Such manifolds are modeled on the product of a smooth manifold and a cone over a compact fiber. For the…

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 Hyperbolic Nonlinear Schrodinger equation (HypNLS) arises as a model for the dynamics of three-dimensional narrowband deep water gravity waves. In this study, the Petviashvili method is exploited to numerically compute bi-periodic…

The description of gravity waves propagating on the water surface is considered from a historical point of view, with specific emphasis on the development of a theoretical framework and equations of motion for long waves in shallow water.…

We consider three-dimensional inviscid irrotational flow in a two layer fluid under the effects of gravity and surface tension, where the upper fluid is bounded above by a rigid lid and the lower fluid is bounded below by a flat bottom. We…

We derived here in a systematic way, and for a large class of scaling regimes, asymptotic models for the propagation of internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid…

We derive a hyperbolic system of equations approximating the two-layer dispersive shallow water model for shear flows recently proposed by Gavrilyuk, Liapidevskii \& Chesnokov (J. Fluid Mech., vol. 808, 2016, pp. 441--468). The use of this…

Perturbation theory is an indispensable tool in quantum mechanics and electrodynamics that handles weak effects on particle motion or fields. However, its extension to plasmons involving complex motion of {\it both} particles and fields…

The Green-Naghdi equations are a nonlinear dispersive perturbation of the nonlinear shallow water equations, more precise by one order of approximation. These equations are commonly used for the simulation of coastal flows, and in…

The nonlinear disturbance caused by a localised forcing moving at constant speed on the free surface of a liquid of finite depth is investigated using the forced Kadometsev-Petviashvili equation. The presence of a steady v-shaped Kelvin…

Linear stability of stratified two-phase flows in horizontal channels to arbitrary wavenumber disturbances is studied. The problem is reduced to Orr-Sommerfeld equations for the stream function disturbances, defined in each sublayer and…

Nonlinear waves are studied in a mixture of liquid and gas bubbles. Influence of viscosity and heat transfer is taken into consideration on propagation of the pressure waves. Nonlinear evolution equations of the second and the third order…

We prove wave breaking --- bounded solutions with unbounded derivatives --- in the nonlinear nonlocal equations which combine the dispersion relation of water waves and the nonlinear shallow water equations, and which generalize the Whitham…

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…

Should it be a pebble hitting water surface or an explosion taking place underwater, concentric surface waves inevitably propagate. Except for possibly early times of the impact, finite amplitude concentric water waves emerge from a balance…

We consider the two-dimensional water-wave problem with a general non-zero vorticity field in a fluid volume with a flat bed and a free surface. The nonlinear equations of motion for the chosen surface and volume variables are expressed…

We investigate semilinear wave-type equations that can be recast as wave equations with derivatives perturbed by zero-order terms. This framework covers several well-studied cases, including the scale-invariant wave equation. In this…