  We investigate the response of harmonically confined bosons with contact
interactions (trapped Lieb-Liniger gas) to modulations of the trapping
strength. We explain the structure of resonances at a series of driving
frequencies, where size oscillations and energy grow exponentially. For strong
interactions (Tonks-Girardeau gas), we show the effect of resonant driving on
the bosonic momentum distribution. The treatment is `exact' for zero and
infinite interactions, where the dynamics is captured by a single-variable
ordinary differential equation. For finite interactions the system is no longer
exactly solvable. For weak interactions, we show how interactions modify the
resonant behavior for weak and strong driving, using a variational
approximation which adds interactions to the single-variable description in a
controlled way.
