## 5 Scientific Novelty and Scientific and Practical Significance of the Research Results  
### Scientific Novelty--Justification of the Scientific Novelty of the Research  
The scientific novelty of this article consists in the development and study of a universal, fairly simple, from the point of view of symmetry and the level of complexity of equations, physical and mathematical model describing the mechanisms of nonlinear relaxation polarization and conductivity for a wide class of dielectric structures of the class of ion-molecular chemical bonded crystals (IMCBC) in a wide range of field parameters (0.1-1000 MV/m, 1 kHz-300 GHz) and temperatures (1-1550 K). Previously, applied theoretical problems of this kind, at the junction of theory and experiment, universal in the structure of the methodological apparatus, applicable to a wide class of materials in a wide range of field parameters and temperatures (especially by quite strictly taking into account the influence of quantum effects on relaxation polarization processes in dielectrics) were not being solved. The novelty of the results obtained is based on the following provisions. 1. A generalized (for a wide class of ionic dielectrics and a wide range of field parameters and temperatures) quasi-classical (according to the scheme of construction and properties of the equation) nonlinear kinetic equation describing the transfer (both drift and relaxation) of an electric charge in a spatially inhomogeneous crystalline potential perturbed by a polarizing field has been constructed and investigated (both analytically and numerically). The peculiarity of this model is its simplicity (in comparison with existing models of kinetic processes in optical and electro-physical systems), due to the use of a physically substantiated (based on the geometry of the crystal lattices of materials of the class of ion-molecular chemical bonded crystals) model of one-dimensional crystalline potential pattern. The universality of this model lies in the possibility of using a single nonlinear system of equations (electrodynamic, kinetic, and quantum-mechanical) to describe a wide range of electrophysical processes (polarization and conductivity) in ion-molecular chemical bonded crystals (silicates, crystal hydrates, ceramics, and perovskites). 2. As a special case, a phenomenological nonlinear kinetic equation of the Fokker-Planck type, solved in complex with the Poisson equation, is comprehensively analyzed and investigated as a result of the zero approximation in the dimensionless small parameter of perturbation theory. The novelty of the methods proposed for solving this system of equations consists in the development of a universal apparatus based on the derivation of a recurrent formula for calculating the complex amplitude of the relaxation mode of the volume charge density, calculated in a given approximation of perturbation theory k by a dimensionless small parameter, through the results of calculations in all previous approximations of perturbation theory by the parameter m = 0, \(\ldots\), k \(-\) 1. In the stationary polarization mode (with the observation time of the process much longer than the relaxation time), this recurrent formula acquires an additional indicator of universality associated with the possibility of calculating the complex amplitude of multiplicity \(r\), using complex amplitudes of multiplicities from 1 to \(r-1\) by the frequency of the alternating field. This formula for the volume charge density, recurrent in two perturbation theory indicators (k; \(r\)), is new and makes it possible to calculate the polarization of the crystal in the form of expansionsin infinite power series in frequency harmonics, with the ability to limit ourselves to a certain approximation in the degree of the external field, depending on the degree of nonlinearity of the process. This methodology is relevant from the point of view of applications of theory to experiment.