In this paper we have investigated the fundamental properties of the solutions of Maxwell’s equations describing free electromagnetic waves in stationary anisotropic media, with tensor characteristics along the Z axis. A matrix of coefficients, the structure of the matrix of Maxwell’s equations, dispersion equations and indicatrix curves for a transparent anisotropic one-dimensional inhomogeneous conductive medium have been obtained. Exact analytical solutions in case of homogeneous anisotropic media are constructed on the basis of the matrix structure.

The thermoelastic wave propagation in a tetragonal syngony anisotropic medium of classes 4, 4/m having heterogeneity along z axis has been investigated by employing matrizant method. This medium has an axis of second-order symmetry parallel to z axis. In the case of the fourth-order matrix coefficients, the problems of wave refraction and reflection on the interface of homogeneous anisotropic thermoelastic mediums are solved analytically.

The investigation of wave propagation in elastic medium with thermomechanical effects is bound to have important economic implications in the field of composite materials, seismology, geophysics, and so on. In this article, thermoelastic wave propagation in anisotropic mediums of orthorhombic and hexagonal syngony having heterogeneity along -axis is studied. Such medium has second-order axis symmetry. By using analytical matriciant method, a set of equations of motions in thermoelastic medium are reduced to an equivalent set of the first-order differential equations. In the general case, for the given set of equations, structures of fundamental solutions are made and dispersion relations are obtained.

The investigation of thermoelastic wave propagation in elastic media is bound to have much influence in the fields of material science, geophysics, seismology, and so on. The heat conduction equations and bound equations of motions differ by the difficulty level and presence of many physical and mechanical parameters in them. Therefore thermoelasticity is being extensively studied and developed. In this paper by using analytical matrizant method set of equation of motions in elastic media are reduced to equivalent set of first-order differential equations. Moreover, for given set of equations, the structure of fundamental solutions for the general case has been derived and also dispersion relations are obtained.

In the article we consider porpagation and interaction of electromagnetic waves of different polarization, in anisotropic medium that is inhomogeneous along the Z axis with magnetoelectric effect of tetragonal, trigonal, and hexagonal symmetries are described by the structure of the matrix coefficients. The matricant structure of the original system of equations follows from the structure of coefficient matrix. In unlimited periodic structures, dispersion relations of electromagnetic waves are determined from the new modified conditions for the existence of non-trivial solutions which are the consequence of the matricant structure. Obvious analitical form of the matricants for the homogeneous anisotropic dielectric medium with magnetoelectric effects follows from the matricant structure. Analytical equations for homogeneous anisotropic medium with magnetoelectric effects allow one, in matrix setting, to obtain analytical solutions for the problem of reflection and refraction on the border of isotropic and anisotropic medium with magnetoelectric effect based on the matricant method. Initial relationships that describe electromagnetic wave propagation in anisotropic magnetoelectric medium are reduced to the system of linear homogeneous first order differential equations. The structure of the matricant is obtained. Dispersion equations of electromagnetic waves in periodic inhomogeneous medium with magnetoelectric effects are constructed. Averaged matricant describing the propagation of electromagnetic waves in homogeneous anisotropic medium with magnetoelectric medium are also constructed. Besides, the graphs of energy reflection coefficient of TE and TM electromagnetic waves and incident angle are plotted.