Description of the inelastic collision of two solitary waves for the BBM   equation
  We prove that the collision of two solitary waves of the BBM equation is inelastic but almost elastic in the case where one solitary wave is small in the energy space. We show precise estimates of the nonzero residue due to the collision. Moreover, we give a precise description of the collision phenomenon (change of size of the solitary waves). 
Y. Martel, F. Merle, T. Mizumachi