Related papers: Are waves all localized in two dimensional random …

We solve here the so called division problem for wave equations with generic quadratic non-linearities in high dimensions. Specifically, we show that semilinear wave equations which can be written as systems involving quadratic derivative…

Plane waves are regarded as the general solution of the wave equation. However the plane wave expansion of standing waves by means of complex phasors leads to a theory in which the time coordinate does not receive the same treatment as the…

In this paper, a multi-dimensional fractional wave equation that describes propagation of the damped waves is introduced and analyzed. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional…

Structures with heavy-tailed distributions of disorder occur widely in nature. The evolution of such systems, as in foraging for food or the occurrence of earthquakes is generally analyzed in terms of an incoherent series of events. But the…

We consider the stability of spatially homogeneous plane-wave spacetimes. We carry out a full analysis for plane-wave spacetimes in (4+1) dimensions, and find there are two cases to consider; what we call non-exceptional and exceptional. In…

For semi-linear wave equations with null form non-linearities on $\mathbb{R}^{3+1}$, we exhibit an open set of initial data which are allowed to be large in energy spaces, yet we can still obtain global solutions in the future. We also…

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.…

It is well-known that in dimensions at least three semilinear wave equations with null conditions admit global solutions for small initial data. It is also known that in dimension two such result still holds for a certain class of…

The phenomenon of Anderson localization of waves in elastic systems is studied. We analyze this phenomenon in two different set of systems: disordered linear chains of harmonic oscillators and disordered rods which oscillate with torsional…

Wave resonance is the fundamental mechanism of non-linear instabilities of fluid flows, and affects the long-time evolution of fluid motions and other physical problems described by non-linear differential equations. Some significant…

This paper considers two-dimensional stably stratified steady periodic gravity water waves with surface profiles monotonic between crests and troughs. We provide sufficient conditions under which such waves are necessarily symmetric. This…

Distributions of wave characteristics of ocean waves, such as wave slope, waveheight or wavelength, are an important tool in a variety of oceanographic applications such as safety of ocean structures or in the study of ship stability, as…

We prove the exact controllability of two-dimensional hydroelastic waves in the periodic setting. We show that if the initial data and the final data are small, for exterior pressure whose support is any non-empty open set $\omega$, the…

Diffusion of electrons in a two-dimensional system with time-dependent random potentials is investigated numerically. In the absence of spin-orbit scattering, the conductivity shows universal weak localization correction. In the presence of…

In the absence of nonlinearity all eigenmodes of a chain with disorder are spatially localized (Anderson localization). The width of the eigenvalue spectrum, and the average eigenvalue spacing inside the localization volume, set two…

In this article, we mainly investigate the properties of vertical velocity v for two dimensional steady water waves over a flat bed. Firstly we prove the existence of the inflection point for each streamline, then we find the behavior of v…

The dispersion relation of surface waves of a magnetic fluid in a magnetic field is studied experimentally. We verify the theoretically predicted existence of a non-monotonic dispersion relation. In particular, we demonstrate the existence…

One of the open questions in the field of optical rogue waves is the relevance of the number of spatial dimensions in which waves propagate. Here we review recent results on extreme events obtained in 0, 1 and 2 spatial dimensions in the…

The scale invariant properties of wave functions in finite samples of one dimensional random systems with correlated disorder are analyzed. The random dimer model and its generalizations are considered and the wave functions are compared.…

The paper presents new results on localisation and transmission of flexural waves in a structured plate containing a semi-infinite two-dimensional array of rigid pins. In particular, surface waves are identified and studied at the interface…