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In this work, we examine the collision of an atomic dark-bright soliton, in a two-component Bose-Einstein condensate, with a Gaussian barrier or well. Our study has both an experimental component and a theoretical/computational one. First, we present the results of an experiment, illustrating the classical particle phenomenology (transmission or reflection) in the case of an equal barrier in both components. Then, motivated by the experimental observations, we perform systematic simulations considering not only the case of equal heights of a barrier (or a well), but also the considerably more complex setting, where the potential affects only one of the two components. We systematically classify the ensuing cases within a two-parameter diagram of potential amplitudes in the two components, and provide intuitive explanations for the resulting observations, as well as of their variations as the strength of the potential changes. [ABSTRACT FROM AUTHOR]

Motivated by recent experimental results, we study beating dark-dark (DD) solitons as a prototypical coherent structure that emerges in two-component Bose-Einstein condensates. We showcase their connection to dark-bright solitons via SO(2) rotation, and infer from it both their intrinsic beating frequency and their frequency of oscillation inside a parabolic trap. We identify them as exact periodic orbits in the Manakov limit of equal inter- and intra-species nonlinearity strengths with and without the trap and showcase the persistence of such states upon weak deviations from this limit. We also consider large deviations from the Manakov limit illustrating that this breathing state may be broken apart into dark-anti-dark soliton states. Finally, we consider the dynamics and interactions of two beating DD solitons in the absence and in the presence of the trap, inferring their typically repulsive interaction. [ABSTRACT FROM AUTHOR]