  The aim of this work is to study asymptotically and numerically the
interaction of solitons with an external forcing with variable speed using the
forced modified Korteweg-de Vries equation (mKdV). We show that the asymptotic
predictions agree well with numerical solutions for forcing with constant speed
and linear variable speed. Regarding forcing with linear variable speed, we
find regimes in which the solitons are trapped at the external forcing and its
amplitude increases or decreases in time depending on whether the forcing
accelerates or decelerates.
