  We study the problem of 2-soliton collision for the generalized Korteweg-de
Vries equations, completing some recent works of Y. Martel and F. Merle. We
classify the nonlinearities for which collisions are elastic or inelastic. Our
main result states that in the case of small solitons, with one soliton smaller
than the other one, the unique nonlinearities allowing a perfectly elastic
collision are precisely the integrable cases, namely the quadratic (KdV), cubic
(mKdV) and Gardner nonlinearities.
