  We analyze the case of a dense mKdV soliton gas and its large time behaviour
in the presence of a single trial soliton. We show that the solution can be
expressed in terms of Fredholm determinants as well as in terms of a
Riemann-Hilbert problem. We then show that the solution can be decomposed as
the sum of the background gas solution (a modulated elliptic wave), plus a
soliton solution: the individual expressions are however quite convoluted due
to the interaction dynamics. Additionally, we are able to derive the local
phase shift of the gas after the passage of the soliton, and we can trace the
location of the soliton peak as the dynamics evolves. Finally we show that the
soliton peak, while interacting with the soliton gas, has an oscillatory
velocity whose leading order average value satisfies the kinetic velocity
equation analogous to the one posited by V. Zakharov and G. El.
