Solitons in Magnetic Systems

This doctoral thesis reports the results of theoretical research in the field of Bose-Einstein condensate (BEC) mixtures, with its main focus on the dynamics of solitary waves in such systems in conditions of broken integrability and with reference to the formal and physical analogies between BEC mixtures and the classical magnetization dynamics of solid-state ferromagnets. Chapter 2 introduces the physical systems under consideration and the relevant theoretical tools. Chapter 3 reports results on oscillations of magnetic solitons under a uniform external force field in immiscible BEC mixtures/easy-axis ferromagnets, interpreting the phenomenon as an example of Josephson physics. Chapter 4 explores the collisional dynamics of solitary waves increasingly far from the integrable limit. Chapter 5 reports preliminary results on the formation of finite-lifetime soliton bound states and on soliton dynamics induced by the presence of coherent coupling.