New equation for the description of inelastic interaction of nonlinear localized waves in dispersive media

A wave equation for the simulation of nonlinear plane solitary perturbations of the free surface of a shallow fluid has been derived. In contrast to the modified Boussinesq equation, the new one correctly describes the interaction of counter-propagating small-amplitude waves. It has been shown analytically that collisions of solitons are inelastic even in the first-order perturbation theory and the nonlinear dynamics of such collisions is qualitatively different from that described by the modified Boussinesq equation.