Prykhodko O. Two-dimensional localized structures in nonlinear media

A systematic theoretical investigation of properties and dynamics of different two-dimensional localized structures in nonlinear media is performed in the dissertation. Several nonlinear models, based on a generalized nonlinear Schrodinger equation, are used to study different types of localized structures. Main attention is paid to nonlocal nonlinearity that can be found in a variety of different media. For a nonlocal model with regular integration kernel in a Gaussian form different stationary solutions, such as vortices, solitons with nodes were obtained. Using a model with thermal nonlinearity formation and stability of multi-soliton structures is analyzed. The propagation of two-dimensional soliton-soliton pairs in two-component media with attractive intra-component and repulsive inter-component interaction is also studied in the dissertation.