  The passage of a magnetosonic (MS) soliton in a cold plasma leads to the
displacement of charged particles in the direction of a compressive pulse and
in the opposite direction of a rarefaction pulse. In the overdense plasma
limit, the displacement induced by a weakly nonlinear MS soliton is derived
analytically. This result is then used to derive an asymptotic expansion for
the displacement resulting from the bouncing motion of a MS soliton reflected
back and forth in a vacuum-bounded cold plasma slab. Particles' displacement
after the pulse energy has been lost to the vacuum region is shown to scale as
the ratio of light speed to Alfv\'en velocity. Results for the displacement
after a few MS soliton reflections are corroborated by particle-in-cell
simulations.
