Oliinyk A. Topological structures in nonlinear media

Thesis for a scientific degree of Doctor of Philosophy in speciality 104 ¬ «Physics and astronomy» (10 – Natural science). – Taras Shevchenko National University of Kyiv. – Taras Shevchenko National University of Kyiv, Kyiv, 2021. The thesis is devoted to the study of the dynamics of vortex structures in nonlinear media. The investigation of the effects related to the evolution of such topological defects in nonlinear media is an important area of modern research in condensed matter physics and nonlinear optics. The rapid development of these areas offers significant prospects in the field of quantum computing, energy and angular momentum transport, fundamental research, accurate acceleration measurements, creation of rotation sensors, etc. The dynamics of vortexes in many nonlinear media may be depicted by similar models, which allows for theoretical research in various fields of nonlinear physics using analogous approaches. In the thesis, the formation and features of the evolution of quantum vortex structures around an optical soliton propagating through a nonlinear nonlocal medium and in systems of two Bose-Einstein condensates connected through a barrier and trapped by electromagnetic potentials of different geometries are studied with numerical simulations. In the thesis, сonsiderable attention is concentrated on the study of the dynamics of vortices systems with weak and strong coupling between annular axial vertically connected superfluid flows.