Solitary water wave interactions

Our concern in this talk is the problem of free surface water waves, the form of solitary wave solutions, and their behavior under collisions. Solitary waves for the Euler equations have been described since the time of Stokes. In a long wave perturbation regime they are well described by single soliton solutions of the Korteweg deVries equation (KdV). It is a famous result that multiple soliton solutions of the KdV exhibit elastic collisions. The question is as to what extent interactions between Stokes solitary waves deviate from being elastic. In this talk I will present numerical, experimental and analytical results on this question, concerning both co-propagating and counter-propagating cases of large amplitude solitary waves. In all cases we find evidence of inelastic interactions, but it is remarkable to me how collisions of even large solitary waves are very close to being elastic, and how small is the residual. This work is the result of a collaboration with P. Guyenne (Delaware), J. Hammack and D. Henderson (PSU), and C. Sulem (Toronto), which appears in the paper [4].