Related papers: Higher-order effects and ultra-short solitons in l…
Temporal metamaterials are artificially manufactured materials with time-dependent material properties that exhibit interesting phenomena when waves propagate through them. The propagation of electromagnetic waves in such time-varying…
We present a method to compute the magnetic moment of a bulk, finite-size, three-dimensional, anisotropic superconductor. Our numerically implemented perturbative procedure is based on a solution of the nonlinear Maxwell- London equations,…
General nonlinear and nonparaxial dissipative complex Helmholtz equations for magnetic and electric fields propagating in negative refractive index materials (NIMs) are derived ab initio from Maxwell equations. In order to describe…
The Maxwell-Bloch system describes a quantum two-level medium interacting with a classical electromagnetic field by mediation of the the population density. This population density variation is a purely quantum effect which is actually at…
The higher order multipoles above the electric quadrupole are commonly neglected in metamaterial homogenization. We show that they nevertheless can be significant when second order spatial dispersive effects, such as the magnetic response,…
We analyze one-dimensional photonic superlattices which alternate layers of air and a left-handed material. We assume Drude-type dispersive responses for the dielectric permittivity and magnetic permeability of the left-handed material.…
For the system of Maxwell equations of electromagnetism in an $l$-periodic composite medium of overall size $L$ ($0<l<L<\infty$), in the low-frequency quasistatic approximation, we develop an electromagnetic version of strain-gradient…
Structuring optical materials on a nanometer scale can lead to artificial effective media, or metamaterials, with strongly altered optical behavior. Metamaterials can provide a wide range of linear optical properties such as negative…
The integrable focusing nonlinear Schrodinger equation admits soliton solutions whose associated spectral data consist of a single pair of conjugate poles of arbitrary order. We study families of such multiple-pole solitons generated by…
We demonstrate that families of vortex solitons are possible in a bi-dispersive three-dimensional nonlinear Schrodinger equation. These solutions can be considered as extensions of two-dimensional dark vortex solitons which, along the third…
We find non-commutative inspired electrically and magnetically charged black hole solutions in Euler-Heisenberg non-linear electrodynamics. For these solutions, we determine the non-commutative corrections to the horizon radius for the…
We develop a robust and efficient method for soliton calculations for nonlinear Schr\"odinger equations. The method is based on the recently developed sparsifying preconditioner combined with Newton's iterative method. The performance of…
Third-order nonlinear dispersion equations (NDEs) are shown to admit both shock and rarefaction waves (as weak solutions), which are distinguished by a smooth deformation approach. Compacton-type travelling wave solutions are proved to be…
The system of equations describing an ultrashort optical pulses propagation in semiconductor superlattice with applied magnetic field was obtained based on Boltzmann equation in the relaxation-time approximation for the single electron…
The response of bright and dark solitons to rapid variations in an expulsive longitudinal trap is investigated. We concentrate on the effect of transient changes in the trap frequency in the form of temporal delta kicks and the hyperbolic…
We study the Schr\"odinger equation on $\R$ with a potential behaving as $x^{2l}$ at infinity, $l\in[1,+\infty)$ and with a small time quasiperiodic perturbation. We prove that, if the perturbation belongs to a class of unbounded symbols…
Nonlinear processes are at the core of many optical technologies including lasers, information processing, sensing, and security, and require optimised materials suitable for nanoscale integration. Here we demonstrate the emergence of a…
We study a two-component nonlinear Schr{\"{o}}dinger system with equal, repulsive cubic interactions and different dispersion coefficients in the two components. We consider states that have a dark solitary wave in one component. Treating…
This paper studies highly oscillatory solutions to a class of systems of semilinear hyperbolic equations with a small parameter, in a setting that includes Klein--Gordon equations and the Maxwell--Lorentz system. The interest here is in…
The inverse scattering transform is developed to solve the Maxwell-Bloch system of equations that describes two-level systems with inhomogeneous broadening, in the case of optical pulses that do not vanish at infinity in the future. The…