Related papers: Traveling surface wave propagation on shallow wate…
Long-distance transmission of energy by waves is a key mechanism for many natural processes. It becomes possible when the inhomogeneous medium is arranged in such a manner that it enables a specific type of waves to propagate with virtually…
In the linear approximation, we study a one-dimensional problem of the reflectionless wave propagation on a surface of a shallow duct with the spatially varying water depth, duct width, and current. We show that both global and bounded…
In this paper, we present a new multiscale method which is capable of coupling atomistic and continuum domains for high frequency wave propagation analysis. The problem of non-physical wave reflection, which occurs due to the change in…
The article explores the acoustic equations in inhomogeneous media and the linearized shallow water equations. Two methods for integrating these equations are proposed. The first method is based on the of the Laplace cascade method, while…
The aim of this article is to study the attenuation of transient low-frequency waves in 2D lattices in both plane and antiplane problems. The main idea of this article is that analytical solutions to problems of mechanics of discrete…
We show that in the linear approximation there are three classes of reflectionless wave propagation on a surface of shallow water in the channel with spatially varying depth, width, and current speed. Two of these classes have been…
Long waves in shallow water propagating over a background shear flow towards a sloping beach are being investigated. The classical shallow-water equations are extended to incorporate both a background shear flow and a linear beach profile,…
Effects of spatially varying interfacial parameters on the propagation of surface waves are studied. These variations can arise from inhomogeneities in coverage of surface active substances such as amphiphillic molecules at the fluid/gas…
We study the behavior of shallow water waves propagating over bathymetry that varies periodically in one direction and is constant in the other. Plane waves traveling along the constant direction are known to evolve into solitary waves, due…
We generalize the invariant imbedding theory of the wave propagation and derive new invariant imbedding equations for the propagation of arbitrary number of coupled waves of any kind in arbitrarily-inhomogeneous stratified media, where the…
We consider the propagation of surface water waves in a straight planar channel perturbed at the bottom by several thin curved tunnels and wells. We propose a method to construct non reflecting underwater topographies of this type at an…
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.…
In current scientific and technological scenario, studies of transmittance of surface waves across structured interfaces have gained some wind amidst applications to metasurfaces, electronic edge-waves, crystal grain boundaries, etc. The…
We present an exact treatment of wave propagation in some inhomogeneous thin films with highly space-dependent dielectric constant. It is based on a space transformation which replaces the physical space by the optical path. In the new…
We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with…
We discuss the propagation of harmonic and transient waves for systems governed by a wave equation with memory whose integral kernel involves ratios of modified Bessel functions of the first kind in the Laplace domain. In particular, the…
We use Maxwell's equations in a sourceless, inhomogeneous medium with continuous permeability $\mu (\mathbf{r}) $ and permittivity $% \epsilon (\mathbf{r}) $ to study the wave propagation. The general form of the wave equation is derived…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
The analytical study of long wave scattering in a canal with a rapidly varying cross-section is presented. It is assumed that waves propagate on a stationary current with a given flow rate. Due to the fixed flow rate, the current speed is…
Wave propagation in one-dimensional heterogeneous bistable media is studied using the Schl\"ogl model as a representative example. Starting from the analytically known traveling wave solution for the homogeneous medium, infinitely extended,…