  This work deals with the effects of an anharmonic trap on an interacting
two-boson system in one dimension. Our primary focus is on the role of the
induced coupling between the center of mass and the relative motion as both
anharmonicity and the (repulsive) interaction strength are varied. The ground
state reveals a strong localization in the relative coordinate, counteracting
the tendency to fragment for stronger repulsion. To explore the quantum
dynamics, we study the system's response upon (i) exciting the harmonic ground
state by continuously switching on an additional anharmonicity, and (ii)
displacing the center of mass, this way triggering collective oscillations. The
interplay between collective and internal dynamics materializes in the collapse
of oscillations, which are explained in terms of few-mode models.
