  In this paper we describe the inelastic character of solitons of some slowly
varying gKdV equations. We give precise lower bounds, in the energy space, of
the defect induced by the potential on the solution as time goes to infinite.
For the proof, we consider suitable Lyapunov functionals that propagate the
defect along the dynamics in a non trivial fashion, in the spirit of the recent
breakthroughs made by Martel and Merle in the case of the two soliton collision
for non integrable gKdV equations. In addition, we also consider a special,
degenerate case, where the defect is formally of second order.
