Related papers: Nonlinear wave dynamics in honeycomb lattices
The propagation of localized edge modes in photonic honeycomb lattices, formed from an array of adiabatically varying periodic helical waveguides, is considered. Asymptotic analysis leads to an explicit description of the underlying…
Wave dynamics in topological materials has been widely studied recently. A striking feature is the existence of robust and chiral wave propagations that have potential applications in many fields. A common way to realize such wave patterns…
We study the dynamics of an Airy wavepacket moving in a one-dimensional lattice potential. In contrast to the usual case of propagation in a continuum, for which such a wavepacket experiences a uniform acceleration, the lattice bounds its…
Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional…
We analyze mechanisms and regimes of wave packet spreading in nonlinear disordered media. We predict that wave packets can spread in two regimes of strong and weak chaos. We discuss resonance probabilities, nonlinear diffusion equations,…
The nonlinear amplitude modulation of longitudinal dust lattice waves (LDLWs) propagating in a dusty plasma crystal is investigated in a continuum approximation. It is shown that long wavelength LDLWs are modulationally stable, while…
We investigate experimentally and theoretically the nonlinear propagation of 87Rb Bose Einstein condensates in a trap with cylindrical symmetry. An additional weak periodic potential which encloses an angle with the symmetry axis of the…
The propagation of linear and nonlinear edge modes in bounded photonic honeycomb lattices formed by an array of rapidly varying helical waveguides is studied. These edge modes are found to exhibit strong transmission (reflection) around…
Nonreciprocal wave propagation allows for directional energy transport. In this work, we systematically investigate wave dynamics in an elastic lattice that combines nonreciprocal stiffness with viscous damping. After establishing how…
Linear and nonlinear mechanisms for conical wave propagation in two-dimensional lattices are explored in the realm of phononic crystals. As a prototypical example, a statically compressed granular lattice of spherical particles arranged in…
Solitary electromagnetic waves propagating along the waveguides forming a rhombic one-dimensional lattice are considered. Two waveguides that are part of the unit cell are assumed to be made of an optical linear material, while the third…
We consider general reaction diffusion systems posed on rectangular lattices in two or more spatial dimensions. We show that travelling wave solutions to such systems that propagate in rational directions are nonlinearly stable under small…
The nonlinear propagation of 3D wave-packets in a 1D Bragg-induced band-gap system, shows that tranverse effects (free space diffraction) affect the interplay of periodicity and nonlinearity, leading to the spontaneous formation of fast and…
We study travelling waves on a two--dimensional lattice with linear and nonlinear coupling between nearest particles and a periodic nonlinear substrate potential. Such a discrete system can model molecules adsorbed on a substrate crystal…
In a recent article [10], the authors proved that the non-relativistic Schr\"odinger operator with a generic honeycomb lattice potential has conical (Dirac) points in its dispersion surfaces. These conical points occur for quasi-momenta,…
Probably yes, since we find a striking similarity in the spatio-temporal evolution of nonlinear diffusion equations and wave packet spreading in generic nonlinear disordered lattices, including self-similarity and scaling.
A quantum particle transport induced in a spatially-periodic potential by a propagating plane wave has a number important implications in a range of topical physical systems. Examples include acoustically driven semiconductor superlattices…
We present a theoretical investigation of wave dynamics in two-dimensional non-Hermitian $\mathcal{PT}$-symmetric lattices, where onsite, as well as inter-site control couplings are employed. Our analysis shows that these couplings can be…
The generation and evolution of nonlinear waves in microwave amplifiers such as travelling wave tubes, free electron lasers and klystrons have been studied. The analysis is based on the hydrodynamic and field equations for the…
In the work of Colliander et al. (2010), a minimal lattice model was constructed describing the transfer of energy to high frequencies in the defocusing nonlinear Schr\"odinger equation. In the present work, we present a systematic study of…