Turbal Y. Mathematical modelling of the solitary waves propagation processes in continuous media.

The thesis is devoted to the development of new methods for researching and modeling the solitary waves propagation in continuous mediathat are the theoretical basis of forecasting subsystems in the system of seismic and wave monitoring.The theoretical approaches allow to simulate solitary waves as well as their interaction.It was proposed the numerical modeling method for localized perturbations interaction that characterized, in particular, by the amplitude and profile calculation in a given control points and allow to study the effects of interactions and dynamics of changes in time localized initial perturbations. It was proposed method of circular solitary waves modeling in media where wave processes are determined by the shallow water equations, studied the existence of approximate solutions of the motion equations of gas dynamics having the character of a single wave. We investigated the constructive approach, which allows to explore the trajectory of solitary waves in areas of varying density. Method of Poincare sections is modified for describing the interaction of solitons with areas of increased density on the basis of special type operator transformations. Necessary and sufficient conditions for the existence of a solitary wave obtained in the classical theory of anisotropic solids. We propose the method of seismic shocks predicting, based on the soliton «triggers» .