Structure of the Matriciant for Systems of Ordinary Differential Equations of First Order and Its Applications

The theory and methods of systems of ordinary differential equations of first order with variable coefficients have a wide range of applications in physics, mechanics, engineering, mathematical methods of economy, etc. This paper presents results on the construction of the structure of the normalized matrix of the fundamental solutions for a class of matrices of B coefficients. Researches have shown that this class contains equations of motion of elastic anisotropic media, the Maxwell equations describing wave processes in anisotropic dielectric media, propagation of thermoelastic, piezoelectric, piezomagnetic waves, waves in media with magnetoelectric effect, etc.