Gerasimchuk I. Nonlinear localized states in structured media

The theoretical models of nonlinear localized states in structured media of different physical nature and various types, in inhomogeneous defect media and periodic structures are created in the thesis. All possible nonlinear states localized near a single defect (defect layer) in an anharmonic medium in the cases of nonlinear defect and "combined" defect with linear and nonlinear components are analytically described. The stability conditions of the investigated localized states are determined. The conditions of nonlinear spin waves localization in layered magnetic structures with plane magnetic defect are found. The peculiarities of the localized states in systems with one and two traps that are modeled by rectangular potential wells, depending on the linearity/nonlinearity of media in potential wells and in environment are determined. The peculiarities of nonlinear excitations localization in incommensurate structures are found. The character of polymer chains adsorption in the system of two penetrable interfaces within the mean-field approximation taking into account the excluded volume interaction in the cases of zero and fixed polymer concentrations at infinity, and in the system of two hard surfaces that are nonpenetrable to polymer is determined.