Two-dimensional and three-dimensional topological defects, solitons, and textures in magnetics

The monograph contains a presentation of the theory of two- and three-dimensional solitons and localized structures in magnetic media. Direct methods of integration, namely: special substitutions, the method of hirota, backlund transformation, the “dressing "procedure” are used to build and analyze spatially repulsive solutions of typical models of ferro- and antifermeemagnetics. With their help, vortex solitons and gratings made of solitone vortices are analytically described not only against the background of a homogeneous main state of the magnetic environment, but also against the background of a strip domain structure or nonlinear spin wave. Ring waves in magnetics, spiral mesostructures of exchange origin, solitonic states near magnetic disclamps that show macroscopic quantification of energy were studied.
To solve nonlinear marginal problems associated with the calculation of the fields of topological defects, special options for the method of scattering are proposed, new methods of integrating non -linear equations based on differential geometry methods are developed. Within the framework of the models under consideration, this made it possible to find solutions describing "targets" from the ring domains, spiral wilds, consisting of segments of domain boundaries with spiral twisting, string configurations from the segments of domain walls, including against the background of a domain structure, three -dimensional defects of the type filamentary gelicoid-vicheal structures, etc.
The results of the numerical modeling of three -dimensional solitons in light -axial ferromagnetics with non -equal Hopf invariant and ultimate energy, the internal structure of which are engraving of vortex rings, are set out. The basic theoretical and experimental work on the study of rockets in ciral magnets are considered. The mechanisms of the formation of skin, scenarios of their evolution in the crystals of limited geometry (in nano -wires and nanopolosics), and the interaction of the stagmines with each other and with the edges of the samples are discussed. In the films of the chill Magnetics, the new types of skin, kiral vortices and their gratings are theoretically described and theoretically described.
The monograph is addressed to researchers, graduate students and university students of the corresponding specialties