Related papers: Unidirectional decomposition method for obtaining …
We propose a generalized finite element method for the strongly damped wave equation with highly varying coefficients. The proposed method is based on the localized orthogonal decomposition introduced and is designed to handle independent…
We construct a novel family of exact cnoidal wave and soliton solutions of the focusing and defocusing Ablowitz-Ladik equations. Unlike cnoidal waves that were obtained by earlier authors, the phase variable of the new solutions exhibits a…
We propose a novel variant of the Localized Orthogonal Decomposition (LOD) method for time-harmonic scattering problems of Helmholtz type with high wavenumber $\kappa$. On a coarse mesh of width $H$, the proposed method identifies local…
The availability of electromagnetic pulses with controllable field waveform and extremely short duration, even below a single optical cycle, is imperative to fully harness strong-field processes and to gain insight into ultrafast…
This paper is devoted to numerical approximations for the wave equation with a multiscale character. Our approach is formulated in the framework of the Localized Orthogonal Decomposition (LOD) interpreted as a numerical homogenization with…
The problem of resolving the fine details of a signal from its coarse scale measurements or, as it is commonly referred to in the literature, the super-resolution problem arises naturally in engineering and physics in a variety of settings.…
In this paper, we focus on the two-component (2+1)-dimensional Fokas-Lenells equation, which models the propagation of ultrashort optical pulses in nonlinear media with multi-mode interactions and multi-dimensional effects. Firstly, we…
We explore the problem of scattering in a medium modulated by a superluminal rectangular pulse, with the pulse modulation realized through transverse excitations. We solve this problem in the moving frame where the modulation appears purely…
I derive unidirectional wave equations for fields propagating in materials with both electric and magnetic dispersion and nonlinearity. The derivation imposes no conditions on the pulse profile except that the material modulates the…
Wave-speed management of soliton pulses in a nonlinear metamaterial exhibiting a rich variety of physical effects that are important in a wide range of practical applications, is studied both theoretically and numerically. Ultrashort…
In this paper we set forth new exact analytical Superluminal localized solutions to the wave equation for arbitrary frequencies and adjustable bandwidth. The formulation presented here is rather simple, and its results can be expressed in…
The fundamental solution of a variant of the three-dimensional wave equation known as "unidirectional pulse propagation equation" (UPPE) and its paraxial approximation is obtained. It is shown that the fundamental solution can be presented…
We propose a decomposition method for the spectral peaks in an observed frequency spectrum, which is efficiently acquired by utilizing the Fast Fourier Transform. In contrast to the traditional methods of waveform fitting on the spectrum,…
The equation is considered for a composite scalar particle with polarizabilities in an external quantized electromagnetic plane wave. This equation is reduced to a system of equations for infinite number of interacting oscillators. After…
Defect detection by ultrasonic method is limited by the pulse width. Resolution can be improved through a deconvolution process with a priori information of the pulse or by its estimation. In this paper a regularization of the Wiener filter…
A nonlocal perfectly matched layer (PML) is formulated for the nonlocal wave equation in the whole real axis and numerical discretization is designed for solving the reduced PML problem on a bounded domain. The nonlocal PML poses challenges…
A vital requirement for a quantum computer is the ability to locally address, with high fidelity, any of its qubits without affecting their neighbors. We propose an addressing method using composite sequences of laser pulses, which reduces…
The general form of the cubic Boussinesq-type equation is considered. In special cases, this equation is reduced to the three different versions of the cubic Boussinesq equations and also the generalized modified cubic Boussinesq equation.…
Overcoming the diffraction limit, meaning focusing waves on a sub-wavelength scale, has received considerable attention for applications involving light and acoustics. Indeed, the intense focusing achieved enhances the interactions between…
We introduce a novel control method for robust quantum information processing suited for quantum integrated photonics. We utilize off-resonant detunings as control parameters to derive a new family of composite pulses for high-fidelity…