Exact Dynamics Of Interacting Bose Gases In One Spatial Dimension

Ultracold atomic gases in one dimension are often described using the Lieb-Liniger model of interacting bosons. The model is exactly solvable using techniques of integrability and the Bethe Ansatz. In the repulsive regime, it describes a strongly correlated quantum gas with finite compressibility. In the attractive regime, the model exhibits additional richness in the form of bound states of constituent particles. The unique combination of experimental feasibility and exact theoretical solvability, as well as the possibility to compare the exact theory with various effective approaches, make the Lieb-Liniger model an extraordinary platform to study the many-body physics of strongly correlated systems. The thesis investigates the dynamical properties of the model in both the attractive and repulsive regimes, by constructing particular solutions of the quantum theory that are the analogue classical solitons. Therefore extensive comparisons are made between the exact results of the quantum theory and those of the related mean field theory. A detailed discussion of the ground state and the excitation spectrum of the system, using a combination of exact and effective approaches, contributes to this main objective.