On the phase-shifts due to the interaction of a large and a small solitary wave

The phase-shift of the large solitary wave (on the surface of water) is obtained to leading order as ? → 0, where ? is the non-dimensional amplitude of the small solitary wave. The other phase-shift is deduced from a conserved density of the full governing equations, assuming that such a two-wave interaction exists. The phase-shifts are matched (for two small waves) to both the KdV theory (overtaking collision) and the Boussinesq case (head-on collision).