Internal solitary waves and their head-on collision. II

Abstract

The head-on collision between two modified Korteweg–de Vries (MKdV) solitary waves is investigated where cubic and quadratic nonlinearities balance dispersion. These waves propagate at the interface of an inviscid two-fluid system where the ratio of the fluids densities is comparable to the square of the ratio of depths. The third-order perturbation solution is obtained and it is found that the collision is inelastic because of a dispersive wave train generated behind each emergent solitary wave.