  We study the long-time dynamics of complex-valued modified Korteweg-de Vries
(mKdV) solitons, which are recognized because they blow-up in finite time. We
establish stability properties at the H^1 level of regularity, uniformly away
from each blow-up point. These new properties are used to prove that mKdV
breathers are H^1 stable, improving our previous result, where we only proved
H^2 stability. The main new ingredient of the proof is the use of a B\"acklund
transformation which links the behavior of breathers, complex-valued solitons
and small real-valued solutions of the mKdV equation. We also prove that
negative energy breathers are asymptotically stable. Since we do not use any
method relying on the Inverse Scattering Transformation, our proof works even
under rough perturbations, provided a corresponding local well-posedness theory
is available.
