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We present a phenomenological approach to dispersion in nonlinear elasticity. A simple, thermomechanically sound, constitutive model is proposed to describe the (non-dissipative) properties of a hyperelastic dispersive solid, without…
Overcoming the diffraction limit to achieve high optical resolution is one of the main challenges in the fields of plasmonics, nanooptics and nanophotonics. In this work, we introduce novel plasmonic structures consisting of nanoantennas…
A comprehensive analytical theory for nonlinear excitations related to horizontal (longitudinal, acoustic mode) as well as vertical (transverse, optical mode) motion of charged dust grains in a dust crystal is presented. Different types of…
One-dimensional defect photonic crystal (Bragg waveguide) is studied from the viewpoint of the slow light problem. The calculations are presented showing that in the TiO$_2$/SiO$_2$-based Bragg waveguide one can obtain the group index of…
We study the short pulse dynamics in the deterministic and stochastic environment in this thesis. The integrable short pulse equation is a modelling equation for ultra-short pulse propagation in the infrared range in the optical fibers. We…
We propose lattice soleakons: self-trapped waves that self-consistently populate leaky modes of their self-induced defects in periodic potentials. Two types, discrete and Bragg, lattice soleakons are predicted. Discrete soleakons that are…
The response of optical fibre modes to plane gravitational waves of low frequency is computed. By solving perturbatively the Maxwell equations for step-index optical fibres in a gravitational wave background and implementing appropriate…
We study the propagation of ultra-short pulses in a cubic nonlinear medium. Using multiple-scale technique, we derive a new wave equation that preserves the nonlocal dispersion present in Maxwell's equations. As a result, we are able to…
A theoretical investigation has been made of electron acoustic wave propagating in unmagnetized collisionless plasma consisting of a cold electron fluid and isothermal ions with two different temperatures obeying Boltzmann type…
We construct examples of oscillating solutions with persistent oscillations for various hyperbolic-parabolic systems with singular diffusion matrices that appear in mechanics. These include, an example for the equations of nonlinear…
By means of magnetohydrodynamic equations in a non relativistic multi fluid framework, we study the behavior of small amplitude perturbations in cold Quark Gluon Plasmas (QGP). Magnetohydrodynamic equations, along with the QGP equation of…
In the present work we explore features of single and pairs of solitary waves in a fractional variant of the nonlinear Schr{\"o}dinger equation. Motivated by the recent experimental realization of arbitrary fractional exponents, upon…
We study Bragg spectroscopy of strongly interacting one dimensional bosons loaded in an optical lattice plus an additional parabolic potential. We calculate the dynamic structure factor by using Monte Carlo simulations for the Bose-Hubbard…
Review of a matrix method used in optics of thin films for the calculation of reflectance, transmittance, absorptance, the electric field distribution inside the stack and the photonic dispersion considering the stack as perfect…
The motion of three-dimensional (3D) solitary waves and solitons in nonlinear crystal-like structures, such as photonic materials, is studied. It is demonstrated that collective excitations in these systems can be tailored to move in…
We demonstrate how to control independently both spatial and temporal dynamics of slow light. We reveal that specially designed nonlinear waveguide arrays with phase-shifted Bragg gratings demonstrate the frequency-independent spatial…
Propagation of extremely short electromagnetic pulses in a homogeneous doubly-resonant medium is considered in the framework of the total Maxwell-Duffing-Lorentz model, where the Duffing oscillators (anharmonic oscillators with cubic…
A theory of light propagation through one-dimensional photonic crystals and deterministic aperiodic structures, including quasicrystals, based on doped quantum-well structures has been developed. The resonant Bragg condition, leading to the…
An electron beam traversing a structured plasmonic field is shown to undergo diffraction with characteristic angular patterns of both elastic and inelastic outgoing electron components. In particular, a plasmonic {\it grating} (e.g., a…
A simple empirical model and approach are introduced for calculation of the vibrational spectra of arbitrary single wall carbon nanotubes. Differently from the frequently used force constants description, the model employs only invariant…