Related papers: Unified matrix-vector wave equation, reciprocity a…
Inhomogeneous media commonly support a discrete number of wave modes that are trapped along interfaces defined by spatially varying parameters. When they are robust against continuous deformations of parameters, such waves are said to be of…
We choose a complete set of square integrable functions as basis for the expansion of the wavefunction in configuration space such that the matrix representation of the nonrelativistic time-independent wave operator is tridiagonal and…
The geometric representation at a fixed frequency of the wavevector (or dispersion) surface $\omega(\vec k)$ for lossless, homogeneous dielectric--magnetic uniaxial materials is explored, when the elements of the relative permittivity and…
We consider the wave scattering and inverse scattering in an inhomogeneous medium embedded a homogeneous droplet with a small size, which is modeled by a constant mass density and a small bulk modulus. Based on the Lippmann-Schwinger…
We develop the method of vector-fields to further study Dispersive Wave Equations. Radial vector fields are used to get a-priori estimates such as the Morawetz estimate on solutions of Dispersive Wave Equations. A key to such estimates is…
Triad resonances for gravity waves propagating in opposite direction with respect to uniform current are introduced. They are produced by multivalued and anisotropic dispersion and occur even in deep water. In contrast, existing literature…
We develop a transfer-matrix formulation of the scattering of electromagnetic waves by a general isotropic medium which makes use of a notion of electromagnetic transfer matrix $\mathbf{M}$ that does not involve slicing of the scattering…
This work presents results on solutions of the one-dimensional damped wave equation, also called telegrapher's equation, when the initial conditions are general distributions, not only functions. We make a complete deduction of its…
Coherent control of wave transmission and reflection is crucial for applications in communication, imaging, and sensing. However, many practical scenarios involve partially coherent waves rather than fully coherent ones. We present a…
The article explores the acoustic equations in inhomogeneous media and the linearized shallow water equations. Two methods for integrating these equations are proposed. The first method is based on the of the Laplace cascade method, while…
The representation of solutions of Maxwell's equations as superpositions of scalar wavelets with vector coefficients developed earlier is generalized to wavelets with polarization, which are matrix-valued. The construction proceeds in four…
The complex form of Maxwell equations has been constructed as one equation for 3-dimensional complex A-vector. The real and imaginary parts of this vector are described with use of electric and magnetic tensions accordingly. With using a…
The purpose of this paper is to study the equivalence relation on unitary bases defined by R. F. Werner [{\it J. Phys. A: Math. Gen.} {\bf 34} (2001) 7081], relate it to local operations on maximally entangled vectors bases, find an…
Vector spherical wavefunctions were derived in closed-form to represent time-harmonic electromagnetic fields in an orthorhombic dielectric-magnetic material with gyrotropic-like magnetoelectric properties. These wavefunctions were used to…
This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using…
An inverse problem of wave propagation into a weakly laterally inhomogeneous medium occupying a half-space is considered in the acoustic approximation. The half-space consists of an upper layer and a semi-infinite bottom separated with an…
Vector solitary waves are nonlinear waves of coupled polarizations that propagate with constant velocity and shape. In mechanics, they hold the potential to control locomotion, mitigate shocks and transfer information, among other…
A general algorithm for calculating the reflection and refraction of nonuniform plane waves from an arbitrarily oriented and charged planar interface between two lossy isotropic media is proposed based on the decomposition of the complex…
A method is presented for solving the characteristic initial value problem for the collision and subsequent nonlinear interaction of plane gravitational or gravitational and electromagnetic waves in a Minkowski background. This method…
The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these…