  Energy exchange mechanisms have important applications in particle physics,
gravity, fluid mechanics, and practically every field in physics. In this
letter we show, both in frequency and time domain, that energy enhancement is
possible for waves scattering off fundamental solitons (time-periodic localized
structures of bosonic fields), without the need for rotation nor translational
motion. We use two-dimensional Q-balls as a testbed, providing the correct
criteria for energy amplification, as well as the respective amplification
factors, and we discuss possible instability mechanisms. Our results lend
support to the qualitative picture drawn in ( arXiv:2212.03269 [gr-qc] );
however we show that this enhancement mechanism is not of superradiant-type,
but instead a "blueshift-like" energy exchange between scattering states
induced by the background Q-ball, which should occur generically for any
time-periodic fundamental soliton. This mechanism does not seem to lead to
instabilities.
