Soliton interactions with an external forcing: The modified Korteweg–de Vries framework

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