  Multi-kink solutions of the defocusing, modified Korteweg-de Vries equation
(mKdV) found by Grosse are shown to be globally $H^1$-stable. Stability in the
one-kink case was previously established by Zhidkov, and Merle-Vega. The proof
uses transformations linking the mKdV equation with focusing, Gardner-like
equations, where stability and asymptotic stability in the energy space are
known. We generalize our results by considering the existence, uniqueness and
the dynamics of generalized multi-kinks of defocusing, non-integrable gKdV
equations, showing the inelastic character of the 4-kink collision in some
regimes.
