Weak oblique collisions of interfacial solitary waves

A third order perturbation solution is developed to describe the interaction between two solitary waves approaching each other at an angle close to 180 ° on the interface between two immiscible inviscid homogeneous fluids. The solution is steady in the frame of reference moving with the point of intersection of the waves. To lowest order, the solution consists simply of the superposition of the undisturbed solitary waves. Second-order collision effects include interaction terms localized near the point of intersection and a phase shift in the solitary waves. In addition to corrections to the phase shift and localized interaction terms, third order effects are found to include a wave train that is stationary in the frame of reference moving with the point of intersection of the solitary waves. The amplitudes of the wave train and localized interaction terms diminish with distance from the point of intersection, and the solitary waves recover their initial shape asymptotically long after the collision. Thus, the only long-term effect of the collision is a phase shift.