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In this work, we present a conditionally stable finite-difference scheme that consistently approximates the solution of a general class of (3+1)-dimensional nonlinear equations that generalizes in various ways the quantitative model…

A basis of Bloch waves, distorted locally by the random potential, is introduced for electrons in the Anderson model. Matrix elements of the Hamiltonian between these distorted waves are averages over infinite numbers of independent…

We investigate the modulational instability of uniform wave packets governed by a discrete third-order nonlinear Schr\"odinger equation in finite square lattices, modeling light propagation in two-dimensional nonlinear waveguide arrays. We…

We have observed proximity resonances in a two dimensional system consisting of dielectric scatterers in a parallel plate waveguide. A numerical solution to the scattering problem supports the analysis of the experimental data.

In this paper, we use a straightforward numerical method to solve scattering models in one-dimensional lattices based on a tight-binding band structure. We do this by using the wave packet approach to scattering, which presents a more…

We introduce a model which gives rise to self-trapping of fundamental and higher-order localized states in a one-dimensional nonlinear Schr\"odinger equation with fractional diffraction and the strength of the self-defocusing nonlinearity…

Waveguide arrays offer enormous potential to design circuit elements essential to fabricate optical devices capable to processing information codified by light. In this work we study the existence and stability of localized beams in one…

Squeezed states of light are used for precision metrology and quantum-enhanced measurements, with applications spanning communication and sensing. State-of-the-art squeezed-light sources typically rely on optical cavities to achieve high,…

The focus of our work is dispersive, second-order effective model describing the low-frequency wave motion in heterogeneous (e.g.~functionally-graded) media endowed with periodic microstructure. For this class of quasi-periodic medium…

We consider a model problem of the scattering of linear acoustic waves in free homogeneous space by an elastic solid. The stress tensor in the solid combines the effect of a linear dependence of strains with the influence of an existing…

A stationary inflection point (SIP) in the Bloch dispersion relation of a periodic waveguide is an exceptional point degeneracy where three Bloch eigenmodes coalesce forming the so-called frozen mode with a divergent amplitude and vanishing…

We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong…

A new approach for analyzing waveguide junctions containing conductive cylindrical objects is proposed. The algorithm is based on mode matching technique using local projection functions, which improves the numerical conditioning of the…

We study the influences to the discrete soliton (DS) by introducing linearly long-range nonlocal interactions, which give rise to the off-diagonal elements of the linearly coupled matrix in the discrete nonlinear schrodinger equation to be…

We examine the dynamics of strongly localized periodic solutions (discrete breathers) in two-dimensional array of coupled finite one-dimensional chains of oscillators. Localization patterns with both single and multiple localization sites…

The effect of the presence of a finite impedance surface on the wave propagation properties of a two-dimensional periodic array of rigid cylinders with their axes perpendicular to the surface is both numerically and experimentally analyzed…

Wave interaction with graded metamaterials exhibits the phenomenon of rainbow reflection, in which broadband wave signals slow down and separate into their frequency components before being reflected. This phenomenon has been qualitatively…

In the present article the classical problem of electromagnetic scattering by a single homogeneous sphere is revisited. Main focus is the study of the scattering behavior as a function of the material contrast and the size parameters for…

We model pacemaker effects of an algebraically localized heterogeneity in a 1 dimensional array of oscillators with nonlocal coupling. We assume the oscillators obey simple phase dynamics and that the array is large enough so that it can be…

We study the propagation and scattering of electromagnetic waves by random arrays of dipolar cylinders in a uniform medium. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is…