Related papers: Local gaps in three-dimensional periodic media
In a prior work, the authors proved a global bifurcation theorem for spatially periodic interfacial hydroelastic traveling waves on infinite depth, and computed such traveling waves. The formulation of the traveling wave problem used both…
A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. They depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the…
In this paper we study a broad class of non-local advection-diffusion models describing the behaviour of an arbitrary number of interacting species, each moving in response to the non-local presence of others. Our model allows for different…
It has recently been shown that periodic layered media can reflect strongly for all incident angles and polarizations in a given frequency range. The standard treatment gets these band gaps from an eigenvalue equation for the Bloch factor…
We consider the linear water-wave problem in a periodic channel $\Pi^h \subset \mathbb{R}^3$, which is shallow except for a periodic array of deep potholes in it. Motivated by applications to surface wave propagation phenomena, we study the…
We analyze the existence and stability of nonlinear localized waves in a periodic medium described by the Kronig-Penney model with a nonlinear defect. We demonstrate the existence of a novel type of stable nonlinear band-gap localized…
The propagation of waves through microstructured media with periodically arranged inclusions has applications in many areas of physics and engineering, stretching from photonic crystals through to seismic metamaterials. In the…
Although local existence of multidimensional shock waves has been established in some fundamental references, there are few results on the global existence of those waves except the ones for the unsteady potential flow equations in…
We show the existence of periodic traveling waves at the free surface of a two dimensional, infinitely deep, and constant vorticity flow, under gravity, whose profiles are overhanging, including one which intersects itself to enclose a…
It is demonstrated that a standard coupled-mode theory can successfully describe weakly-nonlinear gravity water waves in Bragg resonance with a periodic one-dimensional topography. Analytical solutions for gap solitons provided by this…
The paper gives a description of wave propagation in discrete-periodic one-dimensional media with block structure. For one-dimensional problems mathematical models are proposed that describe block structures in the form of a mass chain or…
The paper presents an investigation of local-time effect - one of the manifestations of macroscopic fluctuations phenomena. Was shown the existence of the named effect for longitudinal distance between locations of measurements up to 500…
Formulas are derived for solutions of many-body wave scattering problems by small particles in the case of acoustically soft, hard, and impedance particles embedded in an inhomogeneous medium. The limiting case is considered, when the size…
The main subject of the work is experimental investigation of local-time effect existence on laboratory scale, which means longitudinal distances between locations of measurements from tens to one meter. Also short revue of our…
The goal of this monograph is to prove that any solution of the Cauchy problem for the capillarity-gravity water waves equations, in one space dimension, with periodic, even in space, initial data of small size $\epsilon$, is almost…
Dimension is a fundamental property of objects and the space in which they are embedded. Yet ideal notions of dimension, as in Euclidean spaces, do not always translate to physical spaces, which can be constrained by boundaries and…
This work extends the theory of topological protection to dispersive systems. This theory has emerged from the field of topological insulators and has been established for continuum models in both classical and quantum settings. It predicts…
Consider the mixed problem with Dirichelet condition associated to the wave equation $\partial_t^2u-\Div_{x}(a(t,x)\nabla_{x}u)=0$, where the scalar metric $a(t,x)$ is $T$-periodic in $t$ and uniformly equal to 1 outside a compact set in…
The purpose of this paper is to show how local energy decay estimates for certain linear wave equations involving compact perturbations of the standard Laplacian lead to optimal global existence theorems for the corresponding small…
Propagation of acoustic waves in an one-dimensional water duct containing many air filled blocks is studied by the transfer matrix formalism. Energy distribution and interface vibration of the air blocks are computed. For periodic…