On head-on collisions between two solitary waves of Nwogu's Boussinesq model

In this paper, we consider the head-on collision between two solitary waves of Nwogu's Boussinesq equation which contains one parameter c that is related to that the horizontal velocities at what level are chosen as the horizontal velocity variables. We apply the perturbation method to derive an approximate solution to this equation and investigate the mechanics of the head-on collision. The impacts of the parameter c on the phase shifts and the maximum run-up amplitude of two colliding waves are studied. Comparison between our results and that of the integrable classical Boussinesq equation is also given.