Related papers: Quaternionic equation for electromagnetic fields i…
Many papers have been published over the years that either conjecture or even (claim to) prove the universality of the form of Maxwell's equations. We present yet another derivation of Maxwell's equations and discuss the conclusions…
The Maxwell equations have a fairly simple form. However, finding solutions of Maxwell's equations is an extremely difficult task. Therefore, various simplifying approaches are often used in optics. One such simplifying approach is to use…
We provide sufficient conditions for systems of polynomial equations over general (real or complex) algebras to have a solution. This generalizes known results on quaternions, octonions and matrix algebras. We also generalize the…
We study one of the interesting properties of the electromagnetic wave propagation in the curved Schwarzschild background spacetime in the framework of general relativity (GR). The electromagnetic wave equation has been derived from vacuum…
The article is devoted to application of tensorial formalism for derivation of different types of Maxwell's equations. The Maxwell's equations are written in the covariant coordinate-free and the covariant coordinate forms. Also the…
It is shown that the Lorentz condition which is a conservation law on the electromagnetic four-vector-density A, plus the Lorentz transformation, taken together, are equivalent to the microscopic Maxwell's equations.
For explicitly time depending mass density, which satisfies a continuity equation, it is shown that Maxwell-like equations for gravitational field follow naturally without any need of General Relativity Theory approximation or related…
We present a systematic derivation of the wave kinetic equation describing the dynamics of a statistically inhomogeneous incoherent wave field in a medium with a weak quadratic nonlinearity. The medium can be nonstationary and…
In this paper, based on a proposed notion of generalized conjugate harmonic pairs in the framework of complex Clifford analysis, necessary and sufficient conditions for the solvability of inhomogeneous perturbed generalized…
At a boundary between two transparent, linear, isotropic, homogeneous materials, derivations of the electromagnetic boundary conditions and the Fresnel relations typically proceed from the Minkowski {E,B,D,H} representation of the…
Analytical solutions are presented for the electromagnetic radiation by an arbitrary pulsed source into a homogeneous time-varying background medium. In the constant-impedance case an explicit radiation formula is obtained for the…
Maxwell's equations with massive photons and magnetic monopoles are formulated using spacetime algebra. It is demonstrated that a single non-homogeneous multi-vectorial equation describes the theory. Two limiting cases are considered and…
This paper offers a conceptually straightforward method for the calculation of stresses in polarisable media based on the notion of a drive form and its property of being closed in spacetimes with symmetry. After an outline of the notation…
This paper considers one-dimensional equations of acoustics equations of inhomogeneous media and the system of gas dynamics equations with constant entropy. Using the Riemann approach, the gas dynamics equations are reduced to a…
Using the biquaternions algebra with involution and mutual quaternional gradients the equations of one model of electro-gravimagnetic (EGM) field are constructed on the base of Hamilton form of Maxwell equations. For this field the…
We solve time-harmonic Maxwell's equations in anisotropic, spatially homogeneous media in intersections of $L^p$-spaces. The material laws are time-independent. The analysis requires Fourier restriction-extension estimates for perturbations…
We prove Strichartz estimates for solutions to Maxwell equations in three dimensions with rough permittivities, which have less than three different eigenvalues. To this end, Maxwell equations are conjugated to half-wave equations in phase…
In this paper we consider an abstract Cauchy problem for a Maxwell system modelling electromagnetic fields in the presence of an interface between optical media. The electric polarization is in general time-delayed and nonlinear, turning…
It is shown that the set of equations known as Maxwell's equations perfectly describe two very different systems: (1) the usual electromagnetic phenomena in vacuum or in the matter and (2) the deformation of isotropic solid lattices,…
In the current paper we consider an inverse boundary value problem of electromagnetism in a nonlinear Kerr medium. We show the unique determination of the electromagnetic material parameters and the nonlinear susceptibility parameters of…