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By numerical simulations, we show that properly arranged two dimensional periodic arrays, formed by dielectric cylinders embedded in parallel in a uniform medium, can indeed act as an optical lens to focus electromagnetic waves, in…
The new type of multilevel Fresnel zone plate, consisting of stacked layers with bi-level zone profile has been investigated. The conditions of layers acting as single multilevel Fresnel zone plate have been discussed by numerical…
We outline a general theory for the analysis of flow-distributed standing and travelling wave patterns in one-dimensional, open plug-flows of oscillatory chemical media. We treat both the amplitude and phase dynamics of small and…
Here the multipole approach [13], in combination with the density matrix formalism is used for establishing of the model for MMs with gain. This approach allows us to investigate analytically or semi-analytically the interplay between gain…
We present the study of bound surface modes sustained at the termination of truncated bulk dielectric photonic crystals and isolated metasurfaces of dielectric meta-atoms. We discuss the origins of bound modes in the two systems and their…
Oscillons are localised long-lived pulsating states in the three-dimensional $\phi^4$ theory. We gain insight into the spatio-temporal structure and bifurcation of the oscillons by studying time-periodic solutions in a ball of a finite…
Excitable waves arise in many spatially-extended systems of either biological, chemical, or physical nature due to the interplay between local reaction and diffusion processes. Here we demonstrate that similar phenomena are encoded in the…
We examine numerically the time-dependent properties of nonlinear bistable multilayer structures for constant wave illumination. We find that our system exhibits both steady-state and self-pulsing solutions. In the steady state regime, we…
We show how multiplexing influences propagating fronts in multilayer networks of coupled bistable oscillators. Using numerical simulation, we investigate both deterministic and noise-sustained propagation. In particular, we demonstrate that…
A model of laminated wave turbulence is presented. This model consists of two co-existing layers - one with continuous waves' spectra, covered by KAM theory and Kolmogorov-like power spectra, and one with discrete waves' spectra, covered by…
The problem of standing wave formation by superposing two counter-propagating whistler waves in an overdense plasma, studied recently by Sano et al. (Phys. Rev. E 100, 053205 (2019) and Phys. Rev. E 101, 013206 (2020)), has been revisited…
The widespread development and use of neural networks have significantly enriched a wide range of computer algorithms and promise higher speed at lower cost. However, the imitation of neural networks by means of modern computing substrates…
Oscillatory systems with time-delayed pulsatile feedback appear in various applied and theoretical research areas, and received a growing interest in the last years. For such systems, we report a remarkable scenario of destabilization of a…
With the wave interferometric approach, we study how extrinsically multiple coherent waves excitation can dramatically alter the overall scattering states, resulting in tailoring the energy assignment among radiation and dissipation. To…
The time-frequency integrals and the two-dimensional stationary phase method are applied to study the electromagnetic waves radiated by moving modulated sources in dispersive media. We show that such unified approach leads to explicit…
A method for creating metasurfaces using a standing wave, formed in a dielectric, is proposed. Such metasurfaces are formed from metal suspensions, deposited on a dielectric plate, placed in a metal frame-screen. A series of parameters for…
We rigorously show that a class of systems of partial differential equations modeling wave bifurcations supports stationary equivariant bifurcation dynamics through deriving its full dynamics on the center manifold(s). A direct consequence…
We study stationary solutions in the differential kinetic equation, which was introduced in for description of a local dual cascade wave turbulence. We give a full classification of single-cascade states in which there is a finite flux of…
Time-decaying perturbations of nonlinear oscillatory systems in the plane are considered. It is assumed that the unperturbed systems are non-isochronous and the perturbations oscillate with an asymptotically constant frequency. Resonance…
We consider principal properties of various wave regimes in two selected excitable systems with linear cross-diffusion in one spatial dimension observed at different parameter values. This includes fixed-shape propagating waves, envelope…