Byelkin Y. The mathematical models of the modulation instability processes of waves in media with cubic nonlinearity.

Dissertation is devoted to the building of new mathematical models of the modulation instability of the intense quasimonochromatic waves in nonlinear media. Such processes occur during the propagation of magnetization waves in antiferromagnetics, of electromagnetic waves in plasma waveguides, of gravity waves on deep water. During the research the multi-mode mathematical model of the monochromatic wave, which propagates in medium with strong nonlinearity, is built. The multi-mode mathematical model of the propagation of the intense waves in media with strong disperse is built and researched. This model is able to describe the appearance of the anomalous wave on the ocean surface and can be used in satellite monitoring system’s software. The theory of the magnetization waves’ modulation instability in antiferromagnetics is evolved. The methods of model’s optimization and computation speedup are suggested. The algorithms of the automatic data processing and results interpretation are designed. The recommendations for practical usage of built models and obtained results in researching or developing of technical objects are proposed.