Related papers: On Resonant Waves in Lattices
We study the standing periodic waves in the semi-discrete integrable system modelled by the Ablowitz-Ladik equation. We have related the stability spectrum to the Lax spectrum by separating the variables and by finding the characteristic…
We consider the linear water-wave problem in a periodic channel which consists of infinitely many identical containers connected with apertures of width $\epsilon$. Motivated by applications to surface wave propagation phenomena, we study…
The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. Bounds for stream functions as well as free-surface profiles and the total head are obtained under the…
The discrete multiscale analysis for boundary value problems in nonlinear discrete systems leads to a first order discrete modulational instability above a threshold amplitude for wave numbers beyond the zero of group velocity dispersion.…
We study the problem of resonant extraordinary transmission of electromagnetic and acoustic waves through subwavelength slits in an infinite plate, whose thickness is close to a half-multiple of the wavelength. We build on the…
Manifolds with infinite cylindrical ends have continuous spectrum of increasing multiplicity as energy grows, and in general embedded resonances (resonances on the real line, embedded in the continuous spectrum) and embedded eigenvalues can…
The impedance matrix method is applied to study the scattering of flexural waves propagating in an infinite thin plate containing an $N$-beam resonator. The resonator consists of a circular hole containing a smaller plate connected to the…
We study the solutions to the wave equation in a two-dimensional tube of unit width comprised of two straight regions connected by a region of constant curvature. We introduce a numerical method which permits high accuracy at high…
Certain lattice wave systems in translationally invariant settings have one or more spectral bands that are strictly flat or independent of momentum in the tight binding approximation, arising from either internal symmetries or fine-tuned…
Resonant scattering of fast particles off low frequency plasma waves is a major process determining transport characteristics of energetic particles in the heliosphere and contributing to their acceleration. Usually, only Alfv\'en waves are…
Recent studies have shown some unusual nonlinear dispersion behaviors that are disconnected from the linear regime. However, existing analytical techniques, such as perturbation methods, fail to correctly capture these behaviors. Here we…
To date, the influence of non-linear stratifications and two layer stratifications on internal wave propagation has been studied for two-dimensional wave fields in a cartesian geometry. Here, we use a novel wave generator configuration to…
We consider a Dice model with Dirac cones intersected by a topologically flat band at the charge neutrality point and analyze the inelastic scattering of massless pseudospin-1 particles on a circular, gate-defined, oscillating barrier.…
A class of truncated tight-binding Hermitian and non-Hermitian lattices with commensurate energy levels, showing periodic reconstruction of the wave packet, is presented. Examples include exact Bloch oscillations on a finite lattice,…
We show that resonant frequencies of a system of coupled resonators in a truncated periodic lattice converge to the essential spectrum of corresponding infinite lattice. We use the capacitance matrix as a model for fully coupled resonators…
In this paper, we consider the problem of the scattering of in-plane waves at an interface between a homogeneous medium and a metamaterial. The relevant eigenmodes in the two regions are calculated by solving a recently described non…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
This work is concerned with the propagation of electromagnetic waves in isotropic chiral media and with the effects produced by a plane boundary between two such media. In analogy with the phenomena of reflection and refraction of plane…
The dispersion characteristics of an circularly polarized electromagnetic wave of arbitrary amplitude, propagating in a highly (thermally and kinematically) relativistic plasma, are shown to approach those of a linear wave in an…
In this work we derive evolution equations for the nonlinear behavior of a coasting beam under the influence of a resonator impedance. Using a renormalization group approach we find a set of coupled nonlinear equations for the beam density…