Related papers: Nearly linear dynamics of nonlinear dispersive wav…
We report on a systematic study of the dynamics of gravitational waves in full 3D numerical relativity. We find that there exists an interesting regime in the parameter space of the wave configurations: a near-linear regime in which the…
We study here the water-waves problem for uneven bottoms in a highly nonlinear regime where the small amplitude assumption of the Korteweg-de Vries (KdV) equation is enforced. It is known, that for such regimes, a generalization of the KdV…
Three dimensional nonlinear wave interactions have been analytically described. The procedure under interest can be applied to three dimensional quasilinear systems of first order, whose hydrodynamic reductions are homogeneous…
We study the asymptotic behavior of solutions for the semilinear damped wave equation with variable coefficients. We prove that if the damping is effective, and the nonlinearity and other lower order terms can be regarded as perturbations,…
The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom…
A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for…
This work is concerned with a singularly perturbed stochastic nonlinear wave equation with a random dynamical boundary condition. A splitting skill is used to derive the approximating equation of the system in the sense of probability…
We investigate the fractional diffusion approximation of a kinetic equation in the upper-half plane with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…
Two-dimensional nonlinear gravity waves travelling in shallow water on a vertically sheared current of constant vorticity are considered. Using Euler equations, in the shallow water approximation, hyperbolic equations for the surface…
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and…
We present a phenomenological approach to dispersion in nonlinear elasticity. A simple, thermomechanically sound, constitutive model is proposed to describe the (non-dissipative) properties of a hyperelastic dispersive solid, without…
We consider a layer of an inviscid fluid with free surface which is subject to vertical high-frequency vibrations. We derive three asymptotic systems of equations that describe slowly evolving (in comparison with the vibration frequency)…
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
We derive the hydrodynamic limit of a kinetic equation with a stochastic, short range perturbation of the velocity operator. Under some mixing hypotheses on the stochastic perturbation, we establish a diffusion-approximation result: the…
In this paper we study the dispersive properties related to a model of peridynamic evolution, governed by a non local initial value problem, in the cases of two and three spatial dimensions. The features of the wave propagation…
A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the…
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause…
The work presented here emanates from questions arising from experimental observations of the propagation of surface water waves. The experiments in question featured a periodically moving wavemaker located at one end of a flume that…
Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for sufficiently regular initial configurations. Our findings give…
Dynamics of interacting cold atomic gases have recently become a focus of both experimental and theoretical studies. Often cold atom systems show hydrodynamic behavior and support the propagation of nonlinear dispersive waves. Although this…