Strong interaction of solitons governed by Korteweg-de Vries equation

Properties of the strong nonlinear interaction between solitons have been investigated in detail. In this case, the solitons behave exactly like particles colliding elastically in a potential field: they never pass through each other, but bounce back at a distance. Momentum transfer is considered to be the basic mechanism of interaction. Thus, the velocity of propagation of each soliton is a function of time during collision. Explicit expressions for the minimum distance between solitons, the time when this distance occurs, and the amplitudes of solitons at this time have all been derived. Reversibility and other important properties have also been proved.