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We have developed a new family of limited-diffraction electromagnetic X-shaped waves based on the scalar "X waves" discovered previously. These waves are diffraction-free in theory and particle-like (wave packets), in that they maintain…
Recent measurements at RHIC suggest that a nearly perfect fluid of quarks and gluons is produced in AA collisions. Moreover the passage of supersonic partons through this medium seems to produce waves. These waves might pile up and form…
We present a robust iterative technique for solving complex transcendental dispersion equations routinely encountered in integrated optics. Our method especially befits the multilayer dielectric and plasmonic waveguides forming the basis…
In this paper, we develop a comprehensive mathematical toolbox for the construction and spectral stability analysis of stationary multiple front and pulse solutions to general semilinear evolution problems on the real line with spatially…
A multifield asymptotic homogenization technique for periodic thermo-diffusive elastic materials is provided in the present study. Field equations for the first-order equivalent medium are derived and overall constitutive tensors are…
Large-scale simulations of the wave equation in electromagnetism, seismology, and acoustics, can be solved efficiently by finite difference methods. The accuracy of these numerical solutions usually depends on the minimization of…
The three dimensional cubic defocusing nonlinear wave equation is known to be ill-posed for general low regularity initial data. However, well-posedness can be recovered globally in time on a probabilistic level when considering random…
A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. They depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the…
A wave packet undergoes a strong spatial and temporal dispersion while propagating through a complex medium. This wave scattering is often seen as a nightmare in wave physics whether it be for focusing, imaging or communication purposes.…
This paper uses an alternative approach to study the monochromatic plane wave propagation within dielectric and conductor linear media of plane-parallel-faces. This approach introduces the time-averaged Poynting vector modulus as field…
Motivated by the example of a curved waveguide embedded in a photonic crystal, we examine the effects of geometry in a ``quantum channel'' of parabolic form. We study the linear case and derive exact as well as approximate expressions for…
It is shown that the Maxwell's equations for surface electromagnetic TM-waves, propagating along the plane boundary between two nonlinear dielectrics with arbitrary diagonal tensor of dielectric permittivity, depending of |{\bf E}|, can be…
We report on the theoretical investigation of the plasmonic wave propagation in the coaxial cylindrical cables fabricated of both right-handed medium (RHM) [with $\epsilon >0$, $\mu >0$] and left-handed medium (LHM) [with $\epsilon(\omega)…
This paper is devoted to the study of periodic (in time) solutions to an one-dimensional semilinear wave equation with $x$-dependent coefficients under various homogeneous boundary conditions. Such a model arises from the forced vibrations…
The propagation of small-amplitude inhomogeneous plane waves in an isotropic homogeneous incompressible Mooney--Rivlin material is considered when the material is maintained in a state of finite static homogeneous deformation. Disturbances…
Nonlinear self-modulation of the dust acoustic waves is studied, in the presence of non-thermal (non-Maxwellian) ion and electron populations. By employing a multiple scale technique, a nonlinear Schrodinger-type equation (NLSE) is derived…
We derive the invariant imbedding equations for plane electromagnetic waves propagating in stratified magnetic media, where both dielectric and magnetic permeabilities vary in one spatial direction in an arbitrary manner. These equations…
We study the propagation of ultra-short short solitons in a cubic nonlinear medium modeled by nonlinear Maxwell's equations with stochastic variations of media. We consider three cases: variations of (a) the dispersion, (b) the phase…
A time-domain approach is proposed for the propagation of ultrashort electro- magnetic wave packets beyond the paraxial and the slowly-varying-envelope approximations. An analytical method based on perturbation theory is used to solve the…
In order to choose a numerical method for solving the time dependent equations of radiative transport, we obtain an exact solution for the time dependent radiation field in a one dimensional infinite medium with monochromatic, isotropic…