Dark solitons in atomic Bose-Einstein condensates: from theory to experiments

This review paper presents an overview of the theoretical and experimental progress on the study of matter-wave dark solitons in atomic Bose-Einstein condensates. Upon introducing the general framework, we discuss the statics and dynamics of single and multiple matter-wave dark solitons in the quasi one-dimensional setting, in higher dimensional settings, as well as in the dimensionality crossover regime. Special attention is paid to the connection between theoretical results, obtained by various analytical approaches, and relevant experimental observations.