  We show that an interacting double soliton solution to the perturbed mKdV
equation is close in $H^2$ to a double soliton following an effective dynamics
obtained as Hamilton's equations for the restriction of the mKdV Hamiltonian to
the submanifold of solitons. The interplay between algebraic aspects of
complete integrability of the unperturbed equation and the analytic ideas
related to soliton stability is central in the proof.
