  We consider solutions of the generalized Korteweg-de Vries equations (gKdV)
which are non dispersive in some sense (in the spirit of [18]) and which remain
close to multi-solitons. We show that these solutions are necessarily pure
multi-solitons. For the Korteweg-de Vries equation (KdV) and the modified
Korteweg-de Vries equation (mKdV) in particular, we obtain a characterization
of multi-solitons and multi-breathers in terms of non-dispersion.
