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

On the inelastic 2-soliton collision for gKdV equations with general nonlinearity